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16 Steen Street, SOUTH MACKAY QLD 4740
YOUR CHOICE - RENOVATE OR DEVELOP
This ideally located low set Queenslander style home is just minutes to the CBD and positioned on a 1022m2 allotment, Zoned High Density. The property offers numerous options for the astute buyer.
First home owners, renovators or developers – the opportunity is waiting for you. Now is the time to get in early and make the decision to renovate, sub divide and build additional units. (STCA)
This home features enclosed front sunroom, spacious lounge room, open plan kitchen/dining room, 2 generous size bedrooms, 2 bathrooms, 2 W C's and rear entertainment area. The home features your typical tongue and groove walls and wooden floors throughout. The property offers easy side access to the rear of the property and leads to the original car accommodation.
* 1022m2 Allotment. * Zoned Higher Density Residential.
* Traditional low set Qlder design. * 2 bedrooms.
* Sunroom. * Generous sized lounge.
* Open plan kitchen – dining rooms. * 2 bathrooms.
* 2 W C's * Rear patio.
* Laundry * Minutes to CBD.
* Short distance to schools. * Major shopping, medical centres close by.
Price: $259,000 Call Tom Andrews. 0412 372 403
Disclaimer: The vendors and/or their agents do not warrant errors or omissions, if any, in these particulars, which they believe to be accurate. Prospective purchasers should satisfy themselves by inspection or otherwise as to the accuracy of the particulars.
Land is 1,022 m²
2 Open Parking Spaces
Fast Facts about South Mackay
As its name suggests, the suburb of South Mackay is immediately to the south of the central suburb of Mackay. Adjoining the Coral Sea, South Mackay has flat land just above sea level apart from a small hill (approx 10 metres above sea level) in the south-east of the locality. The flat nature of the land made it suitable for use as an airport. The Mackay Airport occupies the south-eastern half of the suburb with suburban development in the north and west of the suburb. There are a number of sports fields between the airport and the residential areas, including the Souths Rugby League Club, the Souths Hockey Club, the City Brothers Football Club and Harrup Park Country Club (hosting a number of sports include the Mackay Cricket Association and AFL Mackay).
Mackay State High School opened on 5 February 1912 as part of the Mackay Technical College in Alfred Street, Mackay. 76 students presented for entry examinations on the first day. In 1959, the high school was relocated to a new campus in Milton Street, South Mackay. In July 1927, the Mackay Chamber of Commerce became aware that the Australian Government was thinking of establishing airmail services within Australia "wherever they could be justified". In January 1928, the Mackay Chamber of Commerce first considered creating an aerodrome to prepare for the growth in air traffic, suggesting in March 1928 that the Town Common might be a suitable location. In April 1928 the Mackay City Council voted to provide the land if an aerodrome was required. In September 1928, Captain John Henry Arthur Treacy, chief pilot of the Queensland Air Navigation Co. Ltd., flew over Mackay looking for suitable locations and confirmed that the Town Common appeared very suitable and could be converted to an aerodrome at very little cost. In July 1929, Captain Treacy tells Mackay to create an aerodrome as the coastal air service will soon commence at other towns' aerodromes while Mackay will miss out; he again confirmed the suitability of the town commons as a site. In October 1929, the Chamber of Commerce was advised that, if Mackay had an aerodrome, it would be included in the plans for an airmail service to be commenced by the Australian Postmaster General's department that would visit Mackay three or four times a week. In February 1930, the Mackay City Council was advised by the Controller of Civil Aviation that the town commons site would be suitable after the trees and shrubs removed and the surface made firm and even. Based on an estimated cost of these works to be £250, the council voted to proceed with setting aside the land on the town commons for an aerodrome. On Monday 21 April 1930, approximately 2,000 people cheered as the monoplane Star of Townsville under the command of Captain Treacy landed on the new Mackay Aerodrome (the former Town Common). The mayor of Mackay, Alderman Wood, then officially opened the aerodrome. In January 1931, the aerodrome was approved and licensed by the Civil Aviation branch of the Defence Department as being suitable for all types of land aeroplanes, enabling the council to begin charging landing fees.
Mackay State High School is a secondary (7-12) school for boys and girls operated by the Queensland Government at 123 Milton Street. In 2016, the school had an enrolment of 1,062 students with 483 girls and 579 boys with 89 teachers (85 full-time equivalent) and 53 non-teaching staff (37 full-time equivalent).
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
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| 9,259
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{"url":"https:\/\/wordpress.stackexchange.com\/questions\/18730\/eaccelerator-php-error?answertab=oldest","text":"# eaccelerator PHP error\n\nI installed a Wordpress plugin and I'm getting the following error. The weird thing is I checked the plugins' source and I really don't understand why it would need those scripts.\n\n[30-May-2011 11:10:03] PHP Warning: PHP Startup: Unable to load dynamic library '\/usr\/lib\/php\/extensions\/no-debug-non-zts-20060613\/eaccelerator.so' - \/usr\/lib\/php\/extensions\/no-debug-non-zts-20060613\/eaccelerator.so: cannot open shared object file: No such file or directory in Unknown on line 0 [30-May-2011 11:10:03] PHP Warning: PHP Startup: Unable to load dynamic library '\/usr\/lib\/php\/extensions\/no-debug-non-zts-20060613\/ffmpeg.so' - \/usr\/lib\/php\/extensions\/no-debug-non-zts-20060613\/ffmpeg.so: cannot open shared object file: No such file or directory in Unknown on line 0\n\n\u2022 Whats the plugin? it will help those that want to help you if they can take a look at it themselves.. \u2013\u00a0MartinJJ May 30 '11 at 16:59\n\u2022 This is the plugin wordpress.org\/extend\/plugins\/\u2026 \u2013\u00a0Alex Dumitru May 30 '11 at 17:06\n\u2022 are you sure its the plugin and not some other code or plugin you used \u2013\u00a0xLRDxREVENGEx May 30 '11 at 17:27\n\u2022 The error_log is located in the plugins' folder and that's why I supposed it's caused by the plugin. But could you please let me know what could cause that error ? \u2013\u00a0Alex Dumitru May 30 '11 at 17:31\nIf you have shell access run \\$ php -V to get more info. If your on managed hosting call your host they can and will fix for you.","date":"2019-10-16 00:25:25","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.20318205654621124, \"perplexity\": 4457.380987555492}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2019-43\/segments\/1570986660829.5\/warc\/CC-MAIN-20191015231925-20191016015425-00366.warc.gz\"}"}
| null | null |
It's done; I've finally completed my follow up memoir, and I feel so grateful and nervous all at the same time. This was my story, my journey, my fight through a cloud of uncertainty and grief, to search for the beauty of the rainbow.
Throughout it all, I kept a journal, capturing all of my experiences, my feelings and sometimes my insanity. It was cathartic and it helped me through some of the darkest moments. My first story was published – Finding the Rainbow – but sadly it didn't end with the rainbow I had searched for. At the end of that story, I had experienced four losses and many setbacks, but I still had hope. This story – Embracing the Storm – follows on from 'Finding the Rainbow', capturing further obstacles and my relentless quest to become a mother.
Throughout it all, I discovered a lot about myself. I found out how strong I could be, despite the challenges we faced, and I was encouraged by the love and support we received from family, friends and the people I have met along this journey (either via my blog or readers of my memoir).
This journey never really ends for any of us. The damage and destruction from the storm will always remain a memory, and whilst I have been fortunate to reach my rainbow, I am aware many are still fighting their own storm. I continue to strongly advocate for those who are fighting against their infertility, and I hope I can offer an empathetic ear should anyone need support or comfort on their own quest.
Where to from here? The next chapter for me is exciting as I launch my memoir, and I celebrate in the joys of motherhood. I can now only hope that I will be the best mother I can be!
EMBRACING THE STORM is available on AMAZON now to purchase.
|
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| 2,288
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A flute choir is an ensemble made up of only flutes! This class will be a great way to maintain and enhance technical skills, ensemble playing, and performance abilities. Students will go over pieces to play as a group, as well as get tips to overall improve their talents. This class is a great addition to a flute players learning journey.
Flute choir has an additional charge of $25 per month paid directly to the teacher at the first of each month.
|
{
"redpajama_set_name": "RedPajamaC4"
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| 1,746
|
package info.ganglia.jmxetric;
import java.io.File;
import java.io.FileNotFoundException;
import java.io.PrintStream;
import java.lang.management.ManagementFactory;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
import java.util.Set;
import java.util.Vector;
import javax.management.AttributeNotFoundException;
import javax.management.InstanceNotFoundException;
import javax.management.IntrospectionException;
import javax.management.MBeanAttributeInfo;
import javax.management.MBeanException;
import javax.management.MBeanInfo;
import javax.management.MBeanServer;
import javax.management.ObjectInstance;
import javax.management.ObjectName;
import javax.management.ReflectionException;
import javax.management.RuntimeMBeanException;
import javax.management.openmbean.CompositeData;
import javax.management.openmbean.CompositeType;
/**
* A utility class that scans the platform MBeanServer for registered
* MBeans/MXBeans. The MBeans are queried and represented as private objects
* These objects are then written using ConfigWriter to a
* {@link java.io.PrintStream}.
*
*/
public class MBeanScanner {
private static final String ERR_FILE = "%s can not be written to, using System.out instead.\n";
private final MBeanServer mBeanServer = ManagementFactory
.getPlatformMBeanServer();
/**
* Used mainly for testing purposed to output a test configuration file to
* System.out. Also shows how to use this class.
*
* @param args
*/
public static void main(String[] args) {
PrintStream out = System.out;
if (args.length > 0) {
try {
out = new PrintStream(new File(args[0]));
} catch (FileNotFoundException e) {
System.out.printf(ERR_FILE, args[0]);
}
}
MBeanScanner mBeanScanner = new MBeanScanner();
List<Config> configs = mBeanScanner.scan();
ConfigWriter cw;
cw = new ConfigWriter(out, configs);
cw.write();
}
/**
* Scans the platform MBean server for registered MBeans, creating
* see Config objects to represent these MBeans.
*/
public List<Config> scan() {
Set<ObjectInstance> mBeanObjects = mBeanServer.queryMBeans(null, null);
List<Config> configs = getConfigForAllMBeans(mBeanObjects);
return configs;
}
/**
* Constructs a configuration for all MBeans.
*
* @param mBeanObjects
* @return a list of Config for the MBeans
*/
private List<Config> getConfigForAllMBeans(Set<ObjectInstance> mBeanObjects) {
List<Config> configs = new Vector<Config>();
for (ObjectInstance objectInstance : mBeanObjects) {
Config configMB = scanOneMBeanObject(objectInstance);
configs.add(configMB);
}
return configs;
}
/**
* Constructs the configuration for a single MBean. The configuration
* includes the name, e.g. "java.util.loggin:type=Logging", and the
* attributes belonging to that MBean.
*
* @param objectInstance
* MBean object instance
* @return configuration representing this MBean
*/
private Config scanOneMBeanObject(ObjectInstance objectInstance) {
MBeanConfig mBeanConfig = new MBeanConfig();
ObjectName objectName = objectInstance.getObjectName();
mBeanConfig.addField("name", objectName.getCanonicalName());
scanMBeanAttributes(mBeanConfig, objectName);
return mBeanConfig;
}
/**
* Stores all attributes of an MBean into its MBeanConfig object
*
* @param mBeanConfig
* the configuration object to store the attributes into
* @param mBeanName
* the name of the MBean object we are getting the attributes
* from
*/
private void scanMBeanAttributes(MBeanConfig mBeanConfig,
ObjectName mBeanName) {
MBeanInfo mBeanInfo;
try {
mBeanInfo = mBeanServer.getMBeanInfo(mBeanName);
MBeanAttributeInfo[] infos = mBeanInfo.getAttributes();
for (int i = 0; i < infos.length; i++) {
MBeanAttributeConfig cMBAttr = makeConfigMBeanAttribute(
mBeanName, infos[i]);
mBeanConfig.addChild(cMBAttr);
}
} catch (IntrospectionException e) {
System.err.println(e.getMessage());
} catch (InstanceNotFoundException e) {
System.err.println(e.getMessage());
} catch (ReflectionException e) {
System.err.println(e.getMessage());
}
}
/**
* Creates an object to represent a single attribute of an MBean. An
* attribute can be a simple attribute, or made up composites.
*
* @param mBeanName
* @param attributeInfo
* @return an AttributeConfig for this MBean
*/
private MBeanAttributeConfig makeConfigMBeanAttribute(ObjectName mBeanName,
MBeanAttributeInfo attributeInfo) {
// type determines if this should be composite
Object attr;
try {
attr = mBeanServer.getAttribute(mBeanName,
attributeInfo.getName());
MBeanAttributeConfig config = new MBeanAttributeConfig();
config.addField("name", attributeInfo.getName());
if (attr == null) {
return null;
} else if (attr instanceof CompositeData) {
addComposites(config, (CompositeData) attr);
} else {
config.addField("type",
translateDataType(attributeInfo.getType()));
}
return config;
} catch (RuntimeMBeanException e) {
System.err.println(e.getMessage());
} catch (AttributeNotFoundException e) {
System.err.println(e.getMessage());
} catch (InstanceNotFoundException e) {
System.err.println(e.getMessage());
} catch (MBeanException e) {
System.err.println(e.getMessage());
} catch (ReflectionException e) {
System.err.println(e.getMessage());
}
return null;
}
/**
* Adds the composite data of an MBean's attribute to an
* MBeanAttributeConfig
*
* @param config
* configuration which the composite belongs to
* @param compositeData
* object representing the composite data
*/
private void addComposites(MBeanAttributeConfig config,
CompositeData compositeData) {
CompositeType compositeType = compositeData.getCompositeType();
for (String key : compositeType.keySet()) {
config.addChild(makeComposite(compositeType, key));
}
}
/**
* Makes a configuration for JMXetric that represents the composite tag
*
* @param compositeType
* @param name
* @return a CompositeConfig for a composite MBean
*/
private MBeanCompositeConfig makeComposite(CompositeType compositeType,
String name) {
MBeanCompositeConfig config = new MBeanCompositeConfig();
config.addField("name", name);
String rawType = compositeType.getType(name).toString();
config.addField("type", translateDataType(rawType));
return config;
}
/**
* The date types returned by JMX calls are no the same as those accepted by
* JMXetric and Ganglia. This methods provides the translation. e.g.
* java.lang.Long -> int8
*
* @param possibleData
* the data type string returned by Java JMX methods
* @return a data type string that Ganglia recognizes
*/
private String translateDataType(String possibleData) {
if (possibleData.equals("string") | possibleData.equals("int8")
| possibleData.equals("uint8") | possibleData.equals("int16")
| possibleData.equals("unit16") | possibleData.equals("int32")
| possibleData.equals("uint32") | possibleData.equals("float")
| possibleData.equals("double")) {
return possibleData;
}
if (possibleData.contains("java.lang.Long")) {
return "int8";
} else if (possibleData.contains("java.lang.Integer")) {
return "int32";
} else if (possibleData.contains("java.lang.Float")) {
return "int32";
}
return "string";
}
/* Data types that represent the MBean configuration */
/**
* Config is a super class that represents a type of configuration that is
* fed into JMXetric.
*/
private class Config {
/* name of this Config, this is the name of the XML tag */
String name;
/* used to determine the XML tag will be self-closing */
boolean hasChildren = false;
/* a map of the parameters in the tag, e.g. delay, name, pname */
Map<String, String> fields = new HashMap<String, String>();
/* a list of inner/children Config */
List<Config> children = new Vector<Config>();
/* Users are not supposed to instantiate this class */
private Config() {
};
/**
* Adds a new field to this Config. This is written as a parameter in
* this XML tag.
*
* @param key
* the name of this key, e.g. "delay", "name"
* @param value
* value of this key, e.g. "0", "60", "java.lang:type=Memory"
*/
void addField(String key, String value) {
fields.put(key, value);
}
/**
* Adds a Config to the list of children this Config has
*
* @param config
* child Config to be added to this
*/
void addChild(Config config) {
if (config == null) {
return; // ensure that the children contains no null values
}
if (hasChildren == false) {
hasChildren = true;
}
children.add(config);
}
/**
* A String representation of this Config, includes the name and the
* fields.
*/
@Override
public String toString() {
return name + " " + fieldsToString();
}
/**
* Printable representation of all the fields of this Config
*
* @return A String with all the fields in this format <key>="<value>"
*/
public String fieldsToString() {
String result = "";
for (String key : fields.keySet()) {
result += key + "=\"" + fields.get(key) + "\" ";
}
// remove the trailing whitespace
return result.substring(0, result.length() - 1);
}
}
/**
* Represents a configuration with the name "mbean". This is the "<mbean>"
* tag in the XML configuration file.
*/
private class MBeanConfig extends Config {
public MBeanConfig() {
this.name = "mbean";
}
}
/**
* Represents a configuration with the name "attribute". This is the
* "<attribute>" tag in the XML configuration file.
*/
private class MBeanAttributeConfig extends Config {
public MBeanAttributeConfig() {
this.name = "attribute";
}
}
/**
* Represents a configuration with the name "composite". This is the
* "<composite>" tag in the XML configuration file.
*/
private class MBeanCompositeConfig extends Config {
public MBeanCompositeConfig() {
this.name = "composite";
}
}
/**
* Writes the configuration to a {@link java.io.PrintStream}. The output is
* in the XML format, which is what JMXetric reads in.
*/
private static class ConfigWriter {
/* The output stream that the configuration will be written to. */
private final PrintStream out;
/* The list of configurations to be written. */
private final List<Config> configs;
/* System-specific new-line separator. */
private static final String NL = System.getProperty("line.separator");
/* XML Declaration used by JMXetric */
private static final String XML_DECL = "<?xml version=\"1.0\" encoding=\"ISO-8859-1\" ?>";
/* XML Doctype used by JMXetric */
private static final String XML_DOCTYPE = "<!DOCTYPE jmxetric-config ["
+ NL + " <!ELEMENT jmxetric-config (sample|ganglia|jvm)*>"
+ NL + " <!ELEMENT sample (mbean)*>" + NL
+ " <!ATTLIST sample delay CDATA #REQUIRED>" + NL
+ " <!ATTLIST sample initialdelay CDATA \"0\">" + NL
+ " <!ATTLIST sample dmax CDATA \"0\" >" + NL
+ " <!ELEMENT mbean (attribute)*>" + NL
+ " <!ATTLIST mbean name CDATA #REQUIRED>" + NL
+ " <!ATTLIST mbean pname CDATA #REQUIRED>" + NL
+ " <!ATTLIST mbean dmax CDATA \"0\" >"
+ " <!ELEMENT attribute (composite*)>" + NL
+ " <!ATTLIST attribute name CDATA #REQUIRED>" + NL
+ " <!ATTLIST attribute type CDATA \"\" >" + NL
+ " <!ATTLIST attribute units CDATA \"\" >" + NL
+ " <!ATTLIST attribute pname CDATA \"\" >" + NL
+ " <!ATTLIST attribute slope CDATA \"both\" >" + NL
+ " <!ATTLIST attribute dmax CDATA \"0\" >" + NL
+ " <!ELEMENT composite EMPTY>" + NL
+ " <!ATTLIST composite name CDATA #REQUIRED>" + NL
+ " <!ATTLIST composite type CDATA \"\" >" + NL
+ " <!ATTLIST composite units CDATA \"\" >" + NL
+ " <!ATTLIST composite pname CDATA \"\" >" + NL
+ " <!ATTLIST composite slope CDATA \"both\" >" + NL
+ " <!ATTLIST composite dmax CDATA \"0\" >" + NL
+ " <!ELEMENT ganglia EMPTY>" + NL
+ " <!ATTLIST ganglia hostname CDATA #REQUIRED>" + NL
+ " <!ATTLIST ganglia port CDATA #REQUIRED>" + NL
+ " <!ATTLIST ganglia mode CDATA #REQUIRED>" + NL
+ " <!ATTLIST ganglia wireformat31x CDATA #REQUIRED>" + NL
+ " <!ELEMENT jvm EMPTY>" + NL
+ " <!ATTLIST jvm process CDATA \"\">" + NL + "]>";
public ConfigWriter(PrintStream outputStream, List<Config> config) {
this.out = outputStream;
this.configs = config;
}
/**
* Write the configuration out to the PrintStream out.
*/
public void write() {
if (configs == null)
return;
StringBuilder sb = new StringBuilder();
sb.append(XML_DECL + NL);
sb.append(XML_DOCTYPE + NL);
sb.append("<jmxetric-config>" + NL);
sb.append(" <jvm process=\"ProcessName\"/>" + NL);
sb.append(" <sample initialdelay=\"20\" delay=\"60\">" + NL);
String output = buildXmlTagsFromList(configs, " ");
sb.append(output);
sb.append(" </sample>" + NL);
sb.append("</jmxetric-config>" + NL);
out.print(sb.toString());
}
/**
* Builds a String of XML tags out of a list of Config. Each Config is
* built by {@link buildConfig} and the result is interspersed with new
* lines for readability.
*
* @param configs
* list of Config to be converted to XML tags
* @param indent
* string that is prefixed to each XML tag
* @return string of XML tags for list
*/
public String buildXmlTagsFromList(List<Config> configs, String indent) {
StringBuilder sb = new StringBuilder();
for (Config config : configs) {
sb.append(buildXmlTag(config, indent) + NL);
}
return sb.toString();
}
/**
* Builds a XML tag for config. The tag with have indent prefixed.
*
* @param config
* to be converted to an XML tag
* @param indent
* indentation string that is prefixed to the tag
* @return XML tag for this config
*/
private String buildXmlTag(Config config, String indent) {
StringBuffer sb = new StringBuffer();
sb.append(indent + "<" + config.name + " "
+ config.fieldsToString());
if (!config.hasChildren) {
// self-closing XML tag
sb.append("/>");
} else {
sb.append(">" + NL);
sb.append(buildXmlTagsFromList(config.children, " " + indent));
sb.append(indent + "</" + config.name + ">");
}
return sb.toString();
}
}
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 3,131
|
in: Pages with broken file links, Hungary national football team, European national association football teams,
National sports teams of Hungary
FIFA World Cup-winning countries
Hungary national football team
Nemzeti Tizenegy (National Eleven)
Magyar Labdarúgó Szövetség (MLSD)
FIFA code
FIFA ranking
Highest FIFA ranking
Lowest FIFA ranking
First international
Austria 5–0 23x15px Hungary
(Vienna, Austria; 12 October 1902)
World Cup appearances
Champions, 1954
Olympic medal record
Men's Football
Silver medal – second place 1936 Hamburg Team
The Hungary national football team is the association football team that represents the country of Hungary in international competition and is controlled by Magyar Labdarúgó Szövetség.
Hungary has qualified for seven FIFA World Cups with the best result being champions in the 1954 FIFA World Cup where they became the eighth team to take out the title after they defeated Romania in the final.
1.1 1910s
2 FIFA World Cup
The Hungarian first appearance in international football was in 1902 when they took on an Austrian team which was dominated by fellow Austrian-Hungarians who wanted to play for that country. The first match would see them get destroyed 5-0 at Vienna in 1902 and for the first couple of years, they struggled in the early days of football. This was followed by the first FIFA World Cup where they would finish bottom of the group which had England and the Netherlands.
After another first-round to England at the 1910 FIFA World Cup, they were hoping to get a win at the Summer Olympics tournament in Stockholm. Before competing at the tournament, they competed in games against England where they were defeated 8-0. Those funds would help Hungary get to Sweden where they lose to the Netherlands in the quarter-finals by a score of 3-0.
The following tournament for Hungary would be the 1914 FIFA World Cup which was held in England. For the Hungarians, they were drawn in Group C with Belgium, Denmark and Scotland. Despite their attempts, they wouldn't make it out of the group stage as they would finish bottom of the group with only one point next to their nation after a draw against the Scots. Soon, the first World War would affect the world which meant that football would grind to a stop.
Following the first World War, Hungary, as well as some of the other Central Powers, was banned from FIFA on the plea of the English and after also missing the 1920 Summer Olympics because of that same reason. The team with a unique 2-3-5 formation would appear at the 1924 Summer Olympics and after smashing Poland 7-0 in the opening round. In the second round, they would fall against Luxembourg because of an own goal from Gyula Mándi which knocked them out.
With the World Cup creating their first official qualifying round, Hungary was put into Group 3 with Austria, Germany and Switzerland. With the top two teams qualifying through to the World Cup they got off to a good start with Remay Janos scoring the only goal in the opening match. After knocking over Germany at home, they would lose to the Austrians by a score of 3-0 which would drop them to second place but still enough to qualify through.
Hungary was drawn in Group D with the Netherlands, Yugoslavia and the United States (who was debuting) at the tournament. After losing their opening game 2-0, they knocked over Yugoslavia 2-1 to set up a must-win match against the United States who had got smashed 7-0 in the previous match and wasn't the favorite to win. But a sudden shock was in order with the Hungarian team failing to seal it as Davey Brown and Archie Stark both scored to give America the win. The Hungarians would be eliminated in the group stage once again as the team wouldn't compete in the 1928 Summer Olympics.
The qualification stage for the World Cup got drawn with the team being drawn with Yugoslavia, Romania and Bulgaria. Much like the World Cup finals, they were on two points from two games after losing to Yugoslavia 3-1 before defeating Romania by the same scoreline to put them within striking distance of qualifying automatically through to the World Cup. Much like the final game against the United States, they were favorites to win against a much more fancy side in Bulgaria. But for Hungary, it was history being repeated all over again with them falling to Bulgaria as they got eliminated from the competition.
After skipping the 1932 Olympic football tournament held in the United States, they had another chance to qualify through to the World Cup with this time being in Italy. For the national team, they got drawn in Group 2.2 with the Irish Free State and Switzerland. For the Hungarians, it was something that they didn't want as they only scored one point from the two games to be eliminated from contention or even try to go for a playoff.
Hungary entered the following Olympic football tournament, hoping to not have a shocker of a tournament by their standards. The first opponent being Poland and after falling down early, they didn't want once again at the first hurdle. But Gyula Krivicz got the team back into the hunt in the second half before a late goal by Gyula Kiss sealed Hungary's spot into the quarter-finals. After getting the victory over Switzerland in the quarter-finals, they were drawn to meet Peru in the semis for a spot in the Olympic final. After conceding early, Sárosi György scored a goal to level the match before goals came from Turay József and József Soproni gave Hungary the win and a spot in the final where they would claim the silver medal as they would fall to Italy in the final.
Hungary would next enter the qualification stage of the 1938 FIFA World Cup where they drawn in Group 2 to play Austria, Norway and Germany. With the core of the successful trip to Germany, the team would qualify through to their fifth World Cup finals appearance where they would be drawn to meet Uruguay in the first round of the competition. After getting the early lead, they would fall 2-1 down after Severino Varela scored a double to give Uruguay the lead. But Hungary would turn the game around with Gyula Zsengellér and Ferenc Sas each scoring a goal to get a spot in the quarter final where they would lose to the Dutch by a single goal.
After missing the 1950 FIFA World Cup because of them withdrawing from the competition, the "Golden Generation" as they would be known entered the 1952 Summer Olympics hopeful of getting a gold medal. But they would be upstaged by Romania in the opening round with Ioan Suru getting the winning goal in the 79th minute. This was deemed to be a shock of the time but didn't dampen Hungary.
Entering the World Cup qualifications, they got drawn to meet Republic of Ireland and Iceland in their qualifying group. Hungary would comfortably make it to a sixth World Cup as they finished top of the group with one game to spare. This meant that they would be drawn in Group A with Sweden, Spain and Uruguay being the opponents to face. The opening game of the World Cup saw the team knock over Spain by a score of 2-0. They then followed that up with a 3-0 win over Uruguay in Rancagua before losing 1-0 to the defending champions in Sweden.
This meant that they had qualified through to the quarter-finals where a goal from Nándor Hidegkuti got the team pass the Soviet Union to book a semi-final spot for the first time. In the semi-final, they would dispatch Austria with Sándor Kocsis scoring another double to put them into the final where they would meet Romania once again. Unlike the other match though, this time it was dominated by Hungary with them creating history by having the biggest win in a World Cup final as they won 5-1 over Romania to record their first title.
Despite them not entering the Olympic Games tournament, they would enter the qualifying for the first edition of the European Nations Cup where they wouldn't make it to the finals. This was after they would lose to Yugoslavia in the quarter finals stage of the competition after earlier knocking of Norway in the first round. Hungary as the defending champions automatically qualified through to the 1958 FIFA World Cup which would be held in Switzerland. After they safety got through the group without losing to Mexico (3-0), Bulgaria (1-1) and Brazil (2-2), they made to the quarter finals where they were taking on the European champions in France. Hungary though had a day they would rather forget with the team seeing a hat-trick from Just Fontaine to knock Hungary out of the World Cup.
Gold Silver Bronze
FIFA World Cup record
D *
1906 Group Stage 12th 2 0 0 2 0 6
1910 Round 1 13th 1 0 0 1 0 2
1922 Did Not Compete
1930 Did Not Qualify
1938 Quarter Finalists 7th 2 1 0 1 3 3
1950 Withdrew
1954 Champions 1st 6 5 0 1 14 2
Total Champions 7/11 21 8 3 10 25 29
FIFA World Cup winners
1906: Uruguay ♦ 1910: England ♦ 1914: Denmark ♦ 1922: Belgium ♦ 1926: Uruguay ♦ 1930: Netherlands ♦ 1934: Italy ♦ 1938: Italy ♦ 1950: Sweden ♦ 1954: Hungary ♦ 1958: Brazil
Template:Football in Hungary
National football teams of Europe (UEFA)
Albania ♦ Austria ♦ Belgium ♦ Brittany ♦ Bulgaria ♦ Cyprus ♦ Czechoslovakia ♦ Denmark ♦ East Germany ♦ Finland ♦ France ♦ Germany ♦ Great Britain ♦ Greece ♦ Hungary ♦ Iceland ♦ Italy ♦ Luxembourg ♦ Netherlands ♦ Norway ♦ Poland ♦ Portugal ♦ Republic of Ireland ♦ Romania ♦ Soviet Union ♦ Spain ♦ Sweden ♦ Switzerland ♦ Turkey ♦ Yugoslavia
England ♦ Estonia ♦ Latvia ♦ Lithuania ♦ Northern Ireland ♦ Ireland (1882–1934) ♦ Saarland ♦ Scotland ♦ Wales
Template:National sports teams of Hungary
European national association football teams
More Alternative Sport Wiki
1 Athletics at the 1904 Summer Olympics
2 Sweden national football team
3 European Nations Cup
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 4,011
|
Allium howellii is a North American species of wild onion known by the common name Howell's onion. It is endemic to California.
Description
Allium howellii is a tall onion plant, producing a stem which may exceed half a meter in height from a reddish-brown bulb one to two centimeters long. There is a single cylindrical leaf about as long as the stem. The inflorescence holds up to 100 dark-veined lavender to white flowers, each under a centimeter long.
Varieties
Several varieties have been named:
Allium howellii var. clokeyi Ownbey & Aase ex Traub - San Bernardino, Los Angeles, Ventura, Santa Barbara counties
Allium howellii var. howellii - Merced, Fresno, Kern, San Luis Obispo counties
Allium howellii var. sanbenitense (Traub) Ownbey & Aase - San Benito County
Distribution and habitat
Howell's onion grows in the granite and serpentine soils of several mountain ranges, hills, and valleys from San Joaquin County to San Bernardino County.
References
External links
Calflora Database: Allium howellii (Howell's onion)
Jepson eFlora (TJM2): Allium howellii
UC Photos gallery of Allium howellii
howellii
Endemic flora of California
Natural history of the California chaparral and woodlands
Natural history of the California Coast Ranges
Natural history of the Transverse Ranges
~
Plants described in 1938
Taxa named by Alice Eastwood
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 7,535
|
{"url":"http:\/\/hal.in2p3.fr\/in2p3-00024303\/fr\/","text":"Acc\u00e9der directement au contenu Acc\u00e9der directement \u00e0 la navigation\n\n# Study of $^7$Be+d reactions for Standard Big Bang Nucleosynthesis\n\nAbstract : The recent WMAP results tightly constrain the baryon density in the universe, which in turn constrains the light element abundance predicted in Standard Big Bang Nucleosynthesis (SBBN). There is a discrepance in the $^7$Li abundance which cannot be explained by uncertainties in the main reactions included in the SBBN. Up to now, the influence of the reaction $^7Be(d,p)2\\alpha$ has been neglected. We have investigated this reaction at SBBN energies using a radioactive $^7$Be beam and a $(CD_2)_n$ self-supporting target at the CYCLONE RIB facility at Louvain-la-Neuve. The experimental method is briefly described. Preliminary results and consequences for primordial nucleosynthesis are discussed.\nDomaine :\n\nhttp:\/\/hal.in2p3.fr\/in2p3-00024303\nContributeur : Dominique Girod <>\nSoumis le : lundi 27 juin 2005 - 15:09:59\nDerni\u00e8re modification le : mardi 2 avril 2019 - 01:35:51\n\n### Citation\n\nC. Angulo, E. Casarejos, A. Coc, T. Davinson, N.L. Achouri, et al.. Study of $^7$Be+d reactions for Standard Big Bang Nucleosynthesis. 8th International Symposium on Nuclei in the Cosmos, Jul 2004, Vancouver, Canada. pp.775-778, \u27e810.1016\/j.nuclphysa.2005.05.192\u27e9. \u27e8in2p3-00024303\u27e9\n\n### M\u00e9triques\n\nConsultations de la notice","date":"2020-05-27 13:47:47","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.42642778158187866, \"perplexity\": 10859.618226570858}, \"config\": {\"markdown_headings\": true, \"markdown_code\": false, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2020-24\/segments\/1590347394074.44\/warc\/CC-MAIN-20200527110649-20200527140649-00062.warc.gz\"}"}
| null | null |
@interface WMZhihu : NSObject
+ (WMZhihu *)sharedInstance;
@property (strong, nonatomic) NSMutableArray *newsAry;
- (NSIndexPath *)findWithID:(NSInteger)index;
- (void)save;
- (void)load;
@end
@interface WMStories : NSObject <NSCoding>
@property (strong, nonatomic) NSNumber *ID;
@property (copy, nonatomic) NSString *title;
@property (copy, nonatomic) NSString *image;
@property (strong, nonatomic) NSArray *images;
@property (assign, nonatomic) BOOL selected;
@end
@interface WMNews : NSObject <NSCoding>
@property (strong, nonatomic) NSDate *date;
@property (strong, nonatomic) NSArray *stories;
@property (strong, nonatomic) NSArray *topStories;
- (NSArray *)topImgUrl;
- (NSArray *)topTitle;
- (NSString *)dateStr;
- (NSString *)nextDate;
@end
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 4,333
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Arson Mapfumo (ur. 1 października 1963 r.) − zimbabwejski bokser, olimpijczyk.
Kariera amatorska
W 1995 r. zdobył brązowy medal na Igrzyskach Afrykańskich, rywalizując w kategorii muszej. W 1996 r. reprezentował Zimbabwe na Igrzyskach Olimpijskich w Atlancie, rywalizując w kategorii muszej. Mapfumo przegrał swoją pierwszą walkę z Eliasem Recaido, odpadając z zawodów w 1/16 finału.
Linki zewnętrzne
Przypisy
Zimbabwejscy bokserzy
Uczestnicy Letnich Igrzysk Olimpijskich 1996
Zimbabwejscy olimpijczycy
Urodzeni w 1963
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 4,326
|
{"url":"https:\/\/www.lmfdb.org\/ModularForm\/GL2\/Q\/holomorphic\/2450\/4\/a\/bh\/","text":"Properties\n\n Label 2450.4.a.bh Level 2450 Weight 4 Character orbit 2450.a Self dual yes Analytic conductor 144.555 Analytic rank 1 Dimension 1 CM no Inner twists 1\n\nRelated objects\n\nNewspace parameters\n\n Level: $$N$$ $$=$$ $$2450 = 2 \\cdot 5^{2} \\cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\\chi]$$ $$=$$ 2450.a (trivial)\n\nNewform invariants\n\n Self dual: yes Analytic conductor: $$144.554679514$$ Analytic rank: $$1$$ Dimension: $$1$$ Coefficient field: $$\\mathbb{Q}$$ Coefficient ring: $$\\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 14) Fricke sign: $$-1$$ Sato-Tate group: $\\mathrm{SU}(2)$\n\n$q$-expansion\n\n $$f(q)$$ $$=$$ $$q + 2q^{2} + q^{3} + 4q^{4} + 2q^{6} + 8q^{8} - 26q^{9} + O(q^{10})$$ $$q + 2q^{2} + q^{3} + 4q^{4} + 2q^{6} + 8q^{8} - 26q^{9} + 35q^{11} + 4q^{12} - 66q^{13} + 16q^{16} - 59q^{17} - 52q^{18} + 137q^{19} + 70q^{22} + 7q^{23} + 8q^{24} - 132q^{26} - 53q^{27} + 106q^{29} + 75q^{31} + 32q^{32} + 35q^{33} - 118q^{34} - 104q^{36} - 11q^{37} + 274q^{38} - 66q^{39} - 498q^{41} - 260q^{43} + 140q^{44} + 14q^{46} + 171q^{47} + 16q^{48} - 59q^{51} - 264q^{52} + 417q^{53} - 106q^{54} + 137q^{57} + 212q^{58} - 17q^{59} + 51q^{61} + 150q^{62} + 64q^{64} + 70q^{66} - 439q^{67} - 236q^{68} + 7q^{69} - 784q^{71} - 208q^{72} - 295q^{73} - 22q^{74} + 548q^{76} - 132q^{78} - 495q^{79} + 649q^{81} - 996q^{82} - 932q^{83} - 520q^{86} + 106q^{87} + 280q^{88} - 873q^{89} + 28q^{92} + 75q^{93} + 342q^{94} + 32q^{96} + 290q^{97} - 910q^{99} + O(q^{100})$$\n\nEmbeddings\n\nFor each embedding $$\\iota_m$$ of the coefficient field, the values $$\\iota_m(a_n)$$ are shown below.\n\nFor more information on an embedded modular form you can click on its label.\n\nLabel $$\\iota_m(\\nu)$$ $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$\n1.1\n 0\n2.00000 1.00000 4.00000 0 2.00000 0 8.00000 \u221226.0000 0\n $$n$$: e.g. 2-40 or 990-1000 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles\n\nInner twists\n\nThis newform does not admit any (nontrivial) inner twists.\n\nTwists\n\nBy twisting character orbit\nChar Parity Ord Mult Type Twist Min Dim\n1.a even 1 1 trivial 2450.4.a.bh 1\n5.b even 2 1 98.4.a.b 1\n7.b odd 2 1 2450.4.a.bf 1\n7.c even 3 2 350.4.e.b 2\n15.d odd 2 1 882.4.a.k 1\n20.d odd 2 1 784.4.a.l 1\n35.c odd 2 1 98.4.a.c 1\n35.i odd 6 2 98.4.c.e 2\n35.j even 6 2 14.4.c.b 2\n35.l odd 12 4 350.4.j.d 4\n105.g even 2 1 882.4.a.p 1\n105.o odd 6 2 126.4.g.c 2\n105.p even 6 2 882.4.g.d 2\n140.c even 2 1 784.4.a.j 1\n140.p odd 6 2 112.4.i.b 2\n280.bf even 6 2 448.4.i.c 2\n280.bi odd 6 2 448.4.i.d 2\n\nBy twisted newform orbit\nTwist Min Dim Char Parity Ord Mult Type\n14.4.c.b 2 35.j even 6 2\n98.4.a.b 1 5.b even 2 1\n98.4.a.c 1 35.c odd 2 1\n98.4.c.e 2 35.i odd 6 2\n112.4.i.b 2 140.p odd 6 2\n126.4.g.c 2 105.o odd 6 2\n350.4.e.b 2 7.c even 3 2\n350.4.j.d 4 35.l odd 12 4\n448.4.i.c 2 280.bf even 6 2\n448.4.i.d 2 280.bi odd 6 2\n784.4.a.j 1 140.c even 2 1\n784.4.a.l 1 20.d odd 2 1\n882.4.a.k 1 15.d odd 2 1\n882.4.a.p 1 105.g even 2 1\n882.4.g.d 2 105.p even 6 2\n2450.4.a.bf 1 7.b odd 2 1\n2450.4.a.bh 1 1.a even 1 1 trivial\n\nAtkin-Lehner signs\n\n$$p$$ Sign\n$$2$$ $$-1$$\n$$5$$ $$1$$\n$$7$$ $$1$$\n\nHecke kernels\n\nThis newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $$S_{4}^{\\mathrm{new}}(\\Gamma_0(2450))$$:\n\n $$T_{3} - 1$$ $$T_{11} - 35$$ $$T_{19} - 137$$ $$T_{23} - 7$$\n\nHecke characteristic polynomials\n\n$p$ $F_p(T)$\n$2$ $$1 - 2 T$$\n$3$ $$1 - T + 27 T^{2}$$\n$5$ 1\n$7$ 1\n$11$ $$1 - 35 T + 1331 T^{2}$$\n$13$ $$1 + 66 T + 2197 T^{2}$$\n$17$ $$1 + 59 T + 4913 T^{2}$$\n$19$ $$1 - 137 T + 6859 T^{2}$$\n$23$ $$1 - 7 T + 12167 T^{2}$$\n$29$ $$1 - 106 T + 24389 T^{2}$$\n$31$ $$1 - 75 T + 29791 T^{2}$$\n$37$ $$1 + 11 T + 50653 T^{2}$$\n$41$ $$1 + 498 T + 68921 T^{2}$$\n$43$ $$1 + 260 T + 79507 T^{2}$$\n$47$ $$1 - 171 T + 103823 T^{2}$$\n$53$ $$1 - 417 T + 148877 T^{2}$$\n$59$ $$1 + 17 T + 205379 T^{2}$$\n$61$ $$1 - 51 T + 226981 T^{2}$$\n$67$ $$1 + 439 T + 300763 T^{2}$$\n$71$ $$1 + 784 T + 357911 T^{2}$$\n$73$ $$1 + 295 T + 389017 T^{2}$$\n$79$ $$1 + 495 T + 493039 T^{2}$$\n$83$ $$1 + 932 T + 571787 T^{2}$$\n$89$ $$1 + 873 T + 704969 T^{2}$$\n$97$ $$1 - 290 T + 912673 T^{2}$$","date":"2020-09-21 16:50:53","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.9214189052581787, \"perplexity\": 13678.727220815643}, \"config\": {\"markdown_headings\": false, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.3, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2020-40\/segments\/1600400201826.20\/warc\/CC-MAIN-20200921143722-20200921173722-00771.warc.gz\"}"}
| null | null |
Bridging parametric and nonparametric measures of species interactions unveils new insights of non-equilibrium dynamics
Chuliang Song, Serguei Saavedra
A central theme in ecological research is to understand how species interactions contribute to community dynamics. Species interactions are the basis of parametric (model-driven) and nonparametric (model-free) approaches in theoretical and empirical work. However, despite their different interpretations across these approaches, these measures have occasionally been used interchangeably, limiting our opportunity to use their differences to gain new insights about ecological systems. Here, we revisit two of the most used measures across these approaches— species interactions measured as constant direct effects (typically used in parametric approaches) and local aggregated effects (typically used in nonparametric approaches). We show two fundamental properties of species interactions that cannot be revealed without bridging these definitions. First, we show that the local aggregated intraspecific effect summarizes all potential pathways through which one species impacts itself, which are likely to be negative even without any constant direct self-regulation mechanism. This property has implications for the long-held debate on how communities can be stabilized when little evidence of self-regulation has been found among higher-trophic species. Second, we show that a local aggregated interspecific effect between two species is correlated with the constant direct interspecific effect if and only if the population dynamics do not have any higher-order direct effects. This other property provides a rigorous methodology to detect direct higher-order effects in the field and experimental data. Overall, our findings illustrate a practical route to gain further insights about non-equilibrium ecological dynamics and species interactions.
I am a quantitative ecologist driven by the curiosity of how biodiversity is generated and maintained.
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 259
|
\section{Introduction}
UX Orionis stars (UXORS) are pre-main sequence stars showing strong photometric variability at optical wavelengths. They receive their name after the prototype star UX Ori, a Herbig AeBe star. Most UXORS are, indeed, Herbig AeBe stars, although there are also
some UXORS amongst Classical T Tauri stars (CTTSs) of early K spectral type such as RY\,Tau and RY\, Lup. UXORS are characterised by sudden decreases in their optical brightness of up to 2-3\,mag. During the faint state, UXORS become redder with a
simultaneous increase of their polarisation. However, during deep minima these stars become bluer.
These observational properties, that is the magnitude fading, the increase of polarisation and the bluing effect, suggest that UXORS faiding is due to extinction events caused by filaments or clouds
of dust orbiting the central source and crossing the line of sight in a nearly edge-on disc \citep{grinin91,grinin98}.
A variation of this hypothesis was proposed by \cite{dullemond03} suggesting that UXORS events could only
happen in self-shadowed disk geometries viewed at high inclination angles. In this model the inner disc is at the origin of the obscuring clouds, and it must have a puffed-up geometry.
In addition to the obscuration hypothesis, disc instabilities, inhomogeneities or warps can also contribute to the dimming magnitude observed in UXORS stars. For instance, \citep[][and references therein]{bouvier13} proposed a combination of these two scenarios
to explain the complex photometric behaviour of AA\,Tau \citep[][and references therein]{bouvier13}. This source shows a low amplitude quasi-periodic variability that was explained by the presence of an asymmetric
dusty warp at the disc inner edge caused by material lifted up from the disc plane by an inclined stellar magnetosphere. In addition to the low amplitude variability, AA\,Tau also shows deep minima consistent with a sudden increase of the dust extinction as predicted by the obscuration
hypothesis.
\begin{table
\caption{Total exposure times of the LBT observations. }
\label{tab:exposure_times}
\centering
\vspace{0.1cm}
\begin{tabular}{@{}l|ccc}
\hline
UT Date & z & J & K \\
& \multicolumn{3}{c}{(s)}\\
\hline
2012-04-23 & 512 & 240 & 1280 \\
2012-05-28 & 720 & 480 & 128 \\
2012-06-23 & 720 & 240 & 64 \\
\hline
\end{tabular}
\end{table}
Despite many photometric studies, very little spectroscopic monitoring of UXORS has been conducted. The few studied cases show dramatic changes in the spectroscopic line profiles, not always linked with photometric variability \citep{eaton99,dewinter99,natta00_line,rodgers02}.
In addition, most of these studies investigate variability in the optical, usually focusing on the H$\alpha$ line.
In this paper we present a NIR spectroscopic monitoring of the UXOR Herbig AeBe star VV\,Ser. This source is located in the main Serpens molecular cloud at $\sim$415\,pc \citep{dzib10}.
There is some discrepancy in the literature about the photospheric temperature of VV\,Ser, but most studies identify VV\,Ser as an Herbig star of spectral type B.
\cite{montesinos09} performed a complete
study of the stellar properties of VV\,Ser, concluding that the most plausible temperature and age of this source is 13\,800\,K and 1.2\,Myr, respectively.
The light curve of VV\,Ser consists
of small amplitude brightness variations around the bright state
followed by rare non-periodical deep minima lasting of order of ten
days \citep{rostopchina01}.
The disc of VV\,Ser appears to be self-shadowed, of low mass, and viewed at a high inclination angle \citep[i$\sim$70\degr;][]{pontoppidan07}.
This would favour the obscuration hypothesis proposed by \cite{dullemond03} to explain the deep minima observed in VV\,Ser.
In addition to the photometric variability typical of UXORS, VV\,Ser also shows spectroscopic line variability. In particular, optical spectroscopic studies show strong variability of the H$\alpha$ line profile \citep[e.g., ][]{mendigutia11}.
To further constrain the structure of the inner gasseous disc of this source, additional medium-resolution interferometric observations are presented (Section\,\ref{sect:interferometric_obs}). Previous spectro-interferometric observations of this source show a compact Br$\gamma$\ emitting region, tracing gas located
within the dust sublimation radius \citep[][and references therein]{eisner14}.
\begin{table*
\small
\begin{minipage}{140mm}
\caption{Observation log of the VLTI/AMBER medium-resolution (R$\sim$1500) observations of VV Ser conducted with the UT1-UT2-UT4 configuration. }
\label{obslog}
\centering
\vspace{0.1cm}
\begin{tabular}{@{}c c c c c c | c c }
\hline
UT Date & UT Time & DIT\footnote{Detector integration time per interferogram.} & NDIT\footnote{Number of interferograms.} &
Proj. baselines & PA\footnote{Baseline position angle.} & Calibrator & UD diameter\footnote{The calibrator UD diameter (\textit{K} band) was taken from \cite{pasinetti01}.}\\
& [h:m] & [ms] & \# & [m] & [$\circ$] & &[mas]\\ \hline
2014-05-13 & 05:47--06:00 & 500 & 1200 & 47.66 / 76.34 / 104.98 & -165.47 / -99.14 / -123.72 & HD 163\,272 & $0.265 \pm 0.020$\\
2012-05-13 & 06:27--06:40 & 500 & 1200 & 49.20 / 83.25 / 115.28 & -156.67 / -98.40 / -120.38 & HD 170\,920 & $0.285 \pm 0.019$\\ \hline
\end{tabular}
\end{minipage}
\end{table*}
This paper is structured as follows: The NIR spectroscopic and inteferometric observations along with the data reduction are presented in Sections\,\ref{sect:spectroscopic_obs} and \ref{sect:interferometric_obs}. The results obtained from our observations
are shown in Sections\,\ref{sect:spectroscopy} (spectroscopy) and \ref{sect:interferometry} (interferometry). The theoretical models employed to interpret our results can be found in Section\,\ref{sect:models}, followed by a discussion (Section\,\ref{sect:discussion})
and the conclusions (Section\,\ref{sect:conclusions}).
\begin{figure}
\begin{center}
\includegraphics[width=70mm]{VVSer_lines}
\end{center}
\caption{LBT MR spectroscopic observations of VV\,Ser. The \hi\ line profiles are normalised to the continuum. The reported velocity is with respect to the local cloud velocity which is at an LSR velocity of +8\,km\,s$^{-1}$\ \citep{burleigh13}.}
\label{fig:LBT-obs}
\end{figure}
\section{Observations and data reduction}
\label{sect:observations}
\subsection{Spectroscopic observations at medium resolution}
\label{sect:spectroscopic_obs}
VV\,Ser was observed during three different nights in 2012 (23 April, 28 May and 23 June) using the infrared spectrograph and camera LUCIFER, installed on the
Large Binocular Telescope (LBT) at Mount Graham Observatory. For each night, medium-resolution (MR) spectra in the z-, J-, and
K-band were acquired consecutively, using the N1.8 camera (grating 210\_zJHK) and a slit width of 0\farcs5. This provides a spectral resolution of R$\sim$6700. The observations were performed using a spatial scale of 0.25\arcsec /pixel.
Total exposure times for each date and band are listed in Table\,\ref{tab:exposure_times}.
Data reduction was performed using standard IRAF tasks. Atmospheric OH lines were used for wavelength calibration. The atmospheric spectral response was corrected by dividing the object spectra
by the spectrum of a telluric spectroscopic standard. With this aim, the intrinsic absorption features of the standard were removed before dividing the spectra by a normalised blackbody at the appropriate
temperature.
Finally, due to unstable seeing conditions as well as the presence of cirrus, no photometric calibration of the spectra was performed.
\subsection{Near-IR interferometric observations}
\label{sect:interferometric_obs}
We observed VV Ser with the AMBER instrument of the Very Large Telescope Interferometer (VLTI) using the 8-m unit telescopes (UT's) with the configuration UT1-UT2-UT4 during one night in May 2014.
The AMBER instrument is a three beam combiner that records spectrally dispersed three-beam interferograms \citep{petrov07}.
Due to the faint H-band magnitude of VV\,Ser (H$\sim$7.4) and poor atmospheric conditions (seeing$\sim$1\arcsec), the observations were conducted without the fringe tracker FINITO. We recorded
\textit{K}-band interferograms, within the Br$\gamma$ line and the nearby continuum, in the medium spectral resolution mode (R$\sim$1500) with a detector integration
time (DIT) of 500\,ms. To calibrate the atmospheric transfer function, we observed the calibrator stars HD\,163272 and HD\,170920. For data reduction, we employed the software library
amdlib v3.0.5\footnote{The AMBER reduction package \textit{amdlib} is available at: http://www.jmmc.fr/data\_processing\_amber.htm} \citep{tatulli07, chelli09}.
We selected 20\,per~cent of the frames with the highest
fringe SNR as described in \cite{tatulli07}. The observation log is shown in Table\,\ref{obslog}.
\section{Spectroscopic results}
\label{sect:spectroscopy}
The most prominent features in our VV\,Ser spectra are hydrogen recombination emission lines, namely the Pa$\delta$ and Pa$\beta$ lines in the z- and J-band, and the Br$\gamma$ line in the K-band. In addition,
strong emission from the fluorescent Fe\,{\textsc{\lowercase{II}}}\,10000.3\AA\ line is also observed in the z-band \citep{bautista04,johansson04, ale13}. Figure\,\ref{fig:LBT-obs} shows the spectra of these lines, normalised to the continuum and calibrated in
velocity for each of the three
observation nights.
All radial velocities are with respect to the cloud which is at a velocity of +8\,km\,s$^{-1}$\ with respect to the local standard of rest \citep[LSR;][]{burleigh13}. The measured radial velocities and equivalent widths (EWs) of each
line at each epoch are listed in Table\,\ref{tab:velocities}. The errors in the radial velocity values were estimated by comparing the theoretical wavelength of the OH lines located close to the line of
interest in the sky frames and the measured value after wavelength calibration.
The Fe\,{\textsc{\lowercase{II}}} line is roughly centred at zero velocity and does not show any significant line profile
variability. On the other hand, all the hydrogen recombination lines are, on average, blueshifted with EWs ranging from $\sim-$3\,\AA, for the Br$\gamma$\ line, to $\sim-$17\,\AA, for the Pa$\beta$. In addition, a night-by-night variation in the line EWs and line profiles is observed.
In particular, the Pa$\delta$\ line shows a very complex line profile with a clear line profile variability.
In the first epoch (black continuous line in Fig.\,\ref{fig:LBT-obs}), the Pa$\delta$\ line shows three different velocity components, namely a blueshifted high velocity component (HVC) at $\sim$--173\,km\,s$^{-1}$, a
blueshifted low velocity component (LVC) at $\sim$--30\,km\,s$^{-1}$, and a redshifted velocity component at $\sim$+120\,km\,s$^{-1}$. In the second and third epoch (dotted blue and dashed red lines),
the redshifted emission disappears as well as the blue-shifted double peak, leaving in its place an inverse P-Cygni profile.
Similar redshifted emission components are also observed during the first epoch in the Pa$\beta$\ and Br$\gamma$\ lines as a redshifted bump in the line profiles. As for the Pa$\delta$\ line profile, these
redshifted bumps disappear during the second and third epochs. In contrast with the Pa$\delta$\ line, the redshifted absorption component of the inverse P-Cygni profile is only marginally observed in the Br$\gamma$\ line during the last epoch.
\begin{table*
\begin{minipage}{140mm}
\caption{Radial velocities.}
\label{tab:velocities}
\centering
\vspace{0.1cm}
\renewcommand*{\thefootnote}{\alph{footnote}}
\begin{tabular}{@{}l|cc|cccc}
\hline
& \multicolumn{2}{c}{2012-04-23} & \multicolumn{2}{c}{2012-05-28} & \multicolumn{2}{c}{2012-06-23} \\
Line id. & V$_r$\footnotemark[1]
& EW\footnotemark[2]
& V$_r$\footnotemark[1] & EW\footnotemark[2] & V$_r$\footnotemark[1] & EW\footnotemark[2] \\
& km\,s$^{-1}$\ & \AA & km\,s$^{-1}$\ & \AA & km\,s$^{-1}$\ & \AA \\
\hline
FeII & 4.7$\pm$3.2 & -1.9$\pm$0.6 & -6.0$\pm$6.5 & -1.8$\pm$0.3 & -12.8$\pm$8.8 & -1.9$\pm$0.5 \\
Pa$\delta$ & -29.5$\pm$3.2 & -2.4$\pm$0.2 & -73.0$\pm$6.5 & -3.2$\pm$0.7 & -42.8$\pm$8.8 & -3.7$\pm$0.9 \\
& 119.6$\pm$3.2 & -1.9$\pm$0.3 & & & & \\
Pa$\beta$ & -0.9$\pm$5.1 & -15.8$\pm$1.0 & -25.6$\pm$5.3 & -13.0$\pm$0.7 & -13.8$\pm$6.6 & -16.7$\pm$1.4 \\
Br$\gamma$ & 6.3$\pm$1.6 & -4.1$\pm$0.5 & -33.5$\pm$2.3 & -3.0$\pm$0.5 & -28.4$\pm$1.0 & -4.2$\pm$1.2 \\
\hline
\end{tabular}
\footnotetext[1]{Radial velocities are with respect to the LSR and corrected for a cloud velocity of 8\,km\,s$^{-1}$\ \citep{burleigh13}.}
\footnotetext[2]{Negative values of the equivalent width indicate the line is in emission.}
\end{minipage}
\end{table*}
On the other hand, the radial peak velocities increase from the first to the second epoch in all the \hi\ lines, and they decrease from the second to the third epoch (see Table\,\ref{tab:velocities}).
The lowest radial velocities are observed during the first epoch. This is due to the redshifted bumps observed during this epoch that shift the centred of the line profile towards the line rest velocity.
Almost the opposite behaviour is observed during the second epoch.
\begin{figure*}
\begin{center}
\includegraphics[width=175mm]{VVSer_line_variability}
\end{center}
\caption{{\bf Top:} From left to right, averaged line profile (I$_{rel}$) of the Fe\,{\textsc{\lowercase{II}}}\,10000.3\AA\ and Pa$\delta$\ lines, the Pa$\beta$\ line, and Br$\gamma$\ line. The line profiles are normalised to the continuum, and shifted by -1.
The normalised variance profiles as in \textit{bottom} are overplotted (blue lines filled in grey) for comparison. {\bf Bottom:} Same as in \textit{Top}, but for the normalised variance line profiles ($\sigma$/I$_\mathrm{rel}$) of the Fe\,{\textsc{\lowercase{II}}} and Pa$\delta$\ lines,
the Pa$\beta$\ line, and the Br$\gamma$\ line, respectively.}
\label{fig:variance_profile}
\end{figure*}
Similarly, EW variations are observed in the hydrogen recombination lines (see, Table\,\ref{tab:velocities}). These changes give us relative information on the continuum to line flux variations, indicating possible changes in the line or continuum fluxes through the analysed period.
Unfortunately, the lack of simultaneous NIR photometry prevents us from distinguishing between both possibilities.
The measured EWs and errors are reported in Table\,\ref{tab:velocities}.
The EW error was estimated from:
\begin{equation}
\sigma(EW_\lambda) = \sqrt{1+\frac{F_c}{F}} \frac{(\Delta\lambda-EW_\lambda)}{S/N}
\end{equation}
assuming Poisson-statistics for the computation of the flux error and standard error propagation \citep{vollmann06}.
In this expression, $F_c$ and $F$ are the continuum and line flux, S/N is the
signal-to-noise-ratio around the line position, and $\Delta\lambda$ is the wavelength interval
over which the line EW was estimated.
Both the Pa$\beta$\ and Br$\gamma$\ lines show night-to-night changes in their EWs. In particular, the EW decreases from the first to the second epoch in both lines, increasing again during the third epoch. Due to the complex Pa$\delta$\ line profile,
it is difficult to extract any quantitative conclusion on the EW behaviour of this line. However, as mentioned above this line shows a clear line profile variability.
To better quantify the line variability, the averaged and normalised variance profiles of the Pa$\delta$, Pa$\beta$, and Br$\gamma$\ lines for the three epochs were computed (see, Fig.\,\ref{fig:variance_profile}). Following \cite{johns95}, the normalised variance profiles
($\sigma_k$/I$_{\mathrm{rel},k}$) were derived by dividing the profile variance by the average line profile.
The line profile variance was computed from:
\begin{equation}
\sigma_k = \Big[\frac{1}{(N-1)} \sum_{i=1}^{N} (I_{i,k}-I_{\mathrm{rel},k})^2\Big]^{1/2},
\end{equation}
where $I_{i,k}$ denotes the intensity profile of
the line $k$ at each single epoch, I$_{\mathrm{rel},k}$ is the average profile
of the line $k$, and $N$ is the number of epochs. The comparison of the averaged line profiles with the normalised
variance profiles illustrates where the major changes in the line profiles take place \citep{johns95, kurosawa05, mendigutia11}. The most relevant changes across the line profiles affect the redshifted component of the line profiles, although
smaller changes are also observed at blueshifted velocities.
Notably, both Pa$\delta$\ and Pa$\beta$\ lines show similar normalised variance profiles, indicating that their variability originates from similar physical processes. However, the line to continuum ratio of the Pa$\delta$\ line is smaller than that for Pa$\beta$, and therefore,
the line profile variation is more evident in the former line.
The sizes of the normalised variances are slightly smaller for the Br$\gamma$\ line compared to those of the Pa$\beta$\ and Pa$\delta$\ lines. As the Br$\gamma$\ line is optically
thinner than the Pa$\beta$\ and Pa$\delta$\ lines, the line emitting volume for these latter would be larger than that of the Br$\gamma$. This might be the reason for the slightly
larger variability observed in the Paschen lines.
\subsection{Accretion properties}
\label{sub:acc-prop}
The accretion luminosity of VV\,Ser was estimated from the luminosity of the Br$\gamma$\ line using the empirical relationship derived from \cite{donehew11}. The Br$\gamma$\ luminosity was derived from the EW of the line, once the
intrinsic photospheric absorption contribution to the line was corrected \citep[see][for more details]{rebeca06, donehew11}. This leads to Br$\gamma$\ photospheric-corrected equivalent widths (EW$_\mathrm{circ}$) of 4.7, 3.6 and 4.8\,\AA\ for the first,
second and third epoch, respectively. The stellar parameters used in the computation can be found in Table\,\ref{tab:stellar_parameters}. In addition, a visual extinction of A$_V$=3.4\,mag was assumed \citep{montesinos09}.
The accretion luminosity ($L_\mathrm{acc}$) was estimated assuming a constant 2MASS K-band magnitude of the source of m$_K$=6.32. The average $L_\mathrm{acc}$\ value over the three epochs is $\sim$15.8$^{+9.3}_{-7.9}$\,L$_\mathrm{\odot}$.
This leads to a mass accretion rate of $\dot{M}_\mathrm{acc}$ $\sim$ 3.1$^{+1.6}_{-1.5}\times$10$^{-7}$\,M$_\mathrm{\odot}$\,yr$^{-1}$, assuming that $\dot{M}_\mathrm{acc}$= $L_\mathrm{acc}$\ R$_*$/ G M$_*$. In this expression, R$_*$ and M$_*$ are the stellar radius and mass (see Table\,\ref{tab:stellar_parameters}), and G is the universal gravitational constant.
\begin{table*}
\begin{minipage}{140mm}
\caption{Geometric models}
\label{tab:geometric_model}
\begin{center}
\renewcommand*{\thefootnote}{\alph{footnote}}
\begin{tabular}{c | ccc | ccc}
\hline
& \multicolumn{3}{c}{Continuum} & \multicolumn{3}{c}{Line} \\
& R & PA & $i$ & $R$ & PA & $i$\\
& (mas) & \multicolumn{2}{c}{(deg)} & (mas) & \multicolumn{2}{c}{(deg)} \\
\hline
Ring fitting & 2.3$\pm$0.1 & 66.7$\pm$1.6 & 70.2$\pm$1.8 & 2.3$\pm$ 0.3 & 61.3$\pm$4.0 & 70.3$\pm$4.4 \\
Gaussian fitting & 4.0$\pm$0.2 & 68.4$\pm$2.3 & 61.6$\pm$2.1 & 4.1$\pm$0.6 & 61.0$\pm$4.7 & 70.4$\pm$3.1 \\
\hline
\end{tabular}
\par\end{center}
\end{minipage}
\end{table*}
\section{Interferometric results}
\label{sect:interferometry}
Our interferometric observations provide four direct observables: the Br$\gamma$\ line profile, visibilities, differential phases and closure phase.
These observables give us information about the size and kinematics of the Br$\gamma$\ emitting region.
Figure\,\ref{fig:AMBER-obs} shows the results from our AMBER-MR observations of VV\,Ser. From top to bottom the Br$\gamma$\ line profile, three baseline visibilities, differential phases and closure phase are shown. The Br$\gamma$\ line profile is very similar to the one detected in our
LUCIFER-LBT observations, that is,
the line profile is single-peaked with a triangular shape. The wavelength dependent visibility curve (second panel) is quite flat, indicating that the Br$\gamma$\ line is emitted in a
region of similar size to the continuum emitting region. At the longer baseline, a faint increase of the visibilities within the Br$\gamma$\ line is detected. This would indicate that most
of the Br$\gamma$\ emission is produced in a region smaller than the dust sublimation radius, as previously observed in other Herbig AeBe stars \citep[e.g.,][]{kraus08,rebeca15, ale15}.
By fitting an elongated Gaussian model to the visibilities shown in Fig.\,\ref{fig:AMBER-obs}, we estimated a half width at half maximum (HWHM) for the continuum emitting region of 4.0$\pm$0.2\,mas (1.65$\pm$0.08\,au) with an elongation ratio of $\sim$2.7, corresponding to an
inclination angle ($i$) of 61\fdg6$\pm$2\fdg1. The positon angle (PA) of the system axis is 68\fdg4$\pm$2\fdg3.
Alternatively, if an inclined ring model with a ring width of 20\,per~cent of the inner ring radius is used, then an inner radius of 2.3$\pm$0.1\,mas (0.97$\pm$0.01\,au) is found. This corresponds to an inclination angle of 70\fdg2$\pm$1\fdg8, and a PA of 66\fdg7$\pm$1\fdg6.
Finally, none differential phases and closure phase signal are detected within the uncertainties of 5\degr and 20\degr, respectively.
\begin{figure}
\begin{center}
\includegraphics[width=0.3\textwidth]{VVSer_AMBER
\end{center}
\caption{AMBER observation of VV\,Ser with three different baselines and spectral resolution R=1500. From top to bottom: Br$\gamma$\ line profile (normalised to the continuum), visibilities, wavelength-dependent differential phases, and closure phase. A spectral binning to the raw data (from R=1500 to R=750) is overplotted in grey (solid line).
For clarity, the differential phases of the shortest and longest baselines have been shifted by +20$^o$ and -20$^o$.}
\label{fig:AMBER-obs}
\end{figure}
\begin{figure}
\begin{center}
\includegraphics[width=0.30\textwidth]{VVSer_AMBER_line_vis
\end{center}
\caption{Observed AMBER pure Br$\gamma$\ line visibilities of
VV\,Ser. From top to bottom: wavelength dependence of flux, visibilities of the first, second, and third baseline. In each visibility panel the observed total visibilities (grey), and the observed continuum-compensated pure
Br$\gamma$\ line visibilities of each baseline (red, blue and green) are shown.}
\label{fig:pure_line_vis}
\end{figure}
\subsection{The size of the Br$\gamma$ emitting region}
\label{sect:geometric_model}
Our AMBER-MR observations of VV\,Ser allow us to measure the dispersed pure Br$\gamma$\ line visibilities at three different radial velocities across the Br$\gamma$\ line. To measure this continuum-compensated visibilities, we used the method described in \cite{weigelt07}. According to this technique,
within the wavelength region of the Br$\gamma$\ line, the visibility has two components: the pure-line emitting component and the continuum emitting component. This latter includes contributions from both the circumstellar environment and the stellar component. Therefore, the emission
line visibility $V_{Br\gamma}$ in each spectral channel can be written as $ F_{{\rm Br}\gamma}V_{{\rm Br}\gamma} = |F_{\rm tot}V_{\rm tot} - F_{\rm c}V_{\rm c}| $ if the differential phase is zero \citep[see][for more details]{weigelt07}. The values $F_{\rm tot}$ and $V_{\rm tot}$ denote
the total measured flux and visibilities in the Br$\gamma$\ line, and $F_{\rm c}$ and $V_{\rm c}$ the continuum flux and visibility, respectively.
This procedure takes then into account the contribution of the intrinsic photospheric absorption feature of VV\,Ser by considering a synthetic spectrum of the same spectral type and surface gravity (see, Table\,\ref{tab:stellar_parameters}).
The resulting pure Br$\gamma$\ line visibilities are shown in Fig.\,\ref{fig:pure_line_vis}. Only spectral channels with a line flux higher than 10\,per~cent of that of the continuum were considered.
The average line visibilities are 0.75, 0.70, and 0.65 for the shortest ($\sim$50\,m), medium ($\sim$83\,m) and longest ($\sim$115\,m) baseline, respectively. Similarly to the continuum fitting, an approximate size of the Br$\gamma$\ line emitting can be derived from the pure line visibility
values.
\section{Modelling spectroscopic and interferometric observations}
\label{sect:models}
To constrain the physical processes dominating VV\,Ser circumstellar environment, we model the emission line profiles obtained
with LBT-LUCIFER (Section\,\ref{sect:spectroscopy}) and the VLTI-AMBER
interferometric data (e.g.~visibility and differential phases; Section\,\ref{sect:interferometry}).
To model the line profiles, we use the radiative transfer
code {\sc torus} (e.g.~\citealt{harries00,symington05, kurosawa06,kurosawa11}). In particular, the numerical method used in the
current work is essentially identical to that in
\citet{kurosawa11}, originally developed to study CTTSs. The model employs the adaptive mesh refinement
grid in Cartesian coordinate and assumes an axisymmetry around the
stellar rotation axis. The model includes 20 energy levels of the hydrogen
atom. The non-local thermodynamic equilibrium (non-LTE) level
populations are computed using the Sobolev approximation
\citep[e.g.][]{sobolev57,castor70,castor79}. For more
comprehensive descriptions of the code, readers are referred to
\citet{kurosawa11}.
For the work presented here, three minor modifications have been, however,
introduced in the code described in \citet{kurosawa11}.
Firstly, the
model now includes continuum emission from a geometrically narrow
ring which emulates the K-band dust emission near the dust sublimation
radius. This emission contribution is important for modelling a
correct line strength of the Br$\gamma$ line as well as the
interferometric quantities around the line.
Secondly, the effect of a rotating
magnetosphere has been included using the method
described in \cite{muzerolle01}. Until now, the code has been applied
only to CTTSs. These stars are slow rotators, with rotation periods of 2--10~d (e.g.~\citealt{herbst87};
\citealt{herbst94}). Hence, the effect of the rotation in CTTSs are small/negligible (e.g.~\citealt{muzerolle01}). Conversely,
intermediate-mass Herbig Ae/Be stars are expected to be fast rotators with periods of $0.2$ to a few days
\citep[e.g.][]{hubrig09, hubrig11}. Therefore, the effect of rotation should be included for modelling VV\,Ser.
Thirdly, the code has been modified to write model intensity maps
as a function of wavelength (or velocity bins). This will allow us to
compute the interferometric quantities, such as visibility,
differential and closure phases, as a function of wavelength, which
can be then directly compared with the spectro-interferometric observations
of VLTI-AMBER.
The difference in the rotation properties of CTTSs and Herbig AeBe stars could be due the weak magnetic fields detected in Herbig AeBe stars.
Indeed, spectro-polarimetric surveys of Herbig AeBe stars recently revealed the presence of weak magnetic fields in these sources, although
much weaker than those measured in CTTSs \citep[from few to several hundreds of Gauss vs. the some kG measured in CTTSs;][]{hubrig09, alecian13}.
Additonal evidence of magnetic fields is given by the fact that many Herbig AeBe stars are also X-ray sources \citep{hubrig09,drake14}.
As a consequence, the magnetic truncation
radius of Herbig AeBe stars is expected to be located much closer to the
protostar than in CTTSs \citep[see, e.g.][]{shu94,muzerolle04}, giving rise to very compact, fast rotating, magnetospheres.
This scenario is additionally supported by recent NIR and optical spectroscopic surveys of Herbig AeBe stars
\citep[see, e.g.][]{cauley14,cauley15, fairlamb15}. In particular, these studies show clear evidences of inverse
P-Cygni profiles in Herbig Ae and late type
Herbig Be stars (indicative of accretion), as well as blue-shifted absorption features in strong accretors (indicative of accretion-driven outflows).
These findings, along with the lack of inverse P-Cygni profiles in Herbig Be stars, suggest
a general transition from magnetically controlled
accretion in Herbig Ae and late type Be stars to boundery layer accretion in Herbig Be stars \citep[see][]{cauley15,fairlamb15}.
For the particular case of VV\,Ser, attempts at measuring the magnetic field were firstly performed by \cite{hubrig09}.
This study, was however only capable of diagnosing VV\,Ser's magnetic field at a significant level of
2.7$\sigma$ (200$\pm$75\,G), and thus VV Ser was only classified as an Herbig star "suggestive" of
the presence of a magnetic field. Additional attempts were performed by \cite{alecian13}. In this case,
a magnetic field
of 561\,G was measured, although with a large uncertainty of $\pm$238 G. The difficulty in measuring the
magnetic field of VV\,Ser through spectro-polarimetry is probably due to the combination of the
faintness of this source (V=11.6, and a nearly edge-on disc, self-shadowed by a puffed-up
inner disc rim, see \citealt{pontoppidan07}), along with the large measurement uncertainties of this technique.
However, VV\,Ser shows inverse P-Cygni profiles in several optical lines \citep[see][]{mendigutia11, cauley15}, as well
as redshifted absorption components in the Pa$\delta$ and Br$\gamma$ lines observed in our LBT NIR spectra (see Fig.\,\ref{fig:LBT-obs}).
For these reasons, there is the possibility that VV Ser is weakly magnetised and has a compact
magnetosphere and an accretion driven wind. Therefore, in the following sections we explore this possibility, and further assume that the outflow
mechanisms in VV Ser are similar to those in the CTTSs which are also magnetised but
have stronger magnetic fields. In particular, we examine our spectroscopic and interferometric
data using combinations of a magnetosphere, a disc wind and a bipolar wind.
Finally, it is worth noting that the advantages of the adopted model over a simple geometric model are several. Firstly,
our modelling can provide us with estimates of basic physical parameters under our assumptions, such as the wind
mass-loss rate, the gas temperature and density, in addition to the
emission geometry. Secondly, it allows us to model the emission lines
observed with LBT (Pa$\delta$, Pa$\beta$, and Br$\gamma$) simultaneously, and in a self-consistent way.
\subsection{Model configurations }
\label{sub:model-config}
Our model sketches are shown in Fig.~\ref{fig:model-config}. The three models consider three distinct flow
components: (1)~a dipolar magnetospheric accretion zone (magnetosphere) as described in
\citet{hartmann94} and \citet{muzerolle01}, (2)~a disc wind
emerging from the equatorial plane (a geometrically thin
accretion disc) located outside of the magnetosphere (Fig.\,\ref{fig:model-config}, left) and
(3)~a bipolar outflow in the polar regions of the
star (Fig.\,\ref{fig:model-config}, right). In the following, we briefly describe each flow component and
their key parameters. Detailed descriptions of each component can be
found in \citet{kurosawa11}.
\subsubsection{Magnetosphere }
\label{subsub:MA-config}
The accretion stream through a dipolar magnetic field is described
as $r=R_{\mathrm{m}}\,\sin^{2}{\theta}$ (e.g.~\citealt{ghosh77};
\citealt{ghosh79}; \citealt{hartmann94}) where $r$ and $\theta$
are the polar coordinates; $R_{\mathrm{m}}$ is the magnetospheric
radius at the equatorial plane. The accretion funnel regions are defined
by two stream lines corresponding to the inner and outer magnetospheric
radii, that is, $R_{\mathrm{m}}=R_{\mathrm{mi}}$ and $R_{\mathrm{mo}}$
(Fig.~\ref{fig:model-config}). We adopt the density and temperature
structures along the stream lines as in \cite{muzerolle01}.
The temperature scale is normalised with a parameter $T_{\mathrm{m}}$
which sets the maximum temperature in the stream. The mass-accretion
rate $\dot{M}_{\mathrm{a}}$\footnote{To avoid confusion, from now on $\dot{M}_{\mathrm{a}}$ refers to the input model parameter and $\dot{M}_\mathrm{acc}$\ to the measured value.} scales the density of the magnetospheric
accretion funnels.
\subsubsection{Disc wind}
\label{subsub:DW-config}
Our disc wind model is an adaptation of the ``split-monopole'' wind
model by \citet{knigge95} and \citet{long02}. This simple
kinematic wind model roughly follows the basic ideas of the
magneto-centrifugal wind paradigm (e.g.~\citealt{blandford82}). The
outflow arises from the surface of the rotating accretion disc, and
has a biconical geometry. The specific angular momentum is assumed to
be conserved along stream lines, and the poloidal velocity component
is assumed to be simply radial from ``sources'' vertically displaced
from the central star. Near the disc surface where the wind emerges,
the value of the velocity toroidal component is similar to that of the local
Keplerian velocity of the disc.
\begin{table*}
\begin{minipage}{140mm}
\caption{Adopted parameters of the star and magnetosphere for VV~Ser}
\label{tab:stellar_parameters}
\begin{center}
\renewcommand*{\thefootnote}{\alph{footnote}}
\begin{tabular}{cccccccccc}
\hline
$R_{*}$ & $M_{*}$ & $T_{\mathrm{eff}}$ & $\log g$ & $P_{*}$ & $d$ & $\dot{M}_{\mathrm{a}}$ & $R_{\mathrm{mi}}$ & $R_{\mathrm{mo}}$ & $T_{\mathrm{m}}$\tabularnewline
($\mathrm{R_{\odot}}$) & ($\mathrm{M_{\odot}}$) & ($\mathrm{K}$) & (cgs) & (d) & ($\mathrm{pc}$) & ($\mathrm{M_{\odot}yr^{-1}}$) & ($R_{*}$) & ($R_{*}$) & ($\mathrm{K}$) \tabularnewline
\hline
$2.6$\footnote{From \cite{montesinos09} assuming a distance of 415\,pc} & $4.0$\footnotemark[1] & $14000$\footnotemark[1] & $4.0$\footnotemark[1] & $0.86$ & $415$\footnote{From \cite{dzib10}} & $3.3\times10^{-7}$ & $1.3$ & $1.8$ & $10000$\tabularnewline
\hline
\end{tabular}
\par\end{center}
\end{minipage}
\end{table*}
Our model has five basic parameters: (1)~the total mass-loss rate in the disc
wind ($\dot{M}_{\mathrm{dw}}$), (2)~the degree of the wind
collimation, (3)~the steepness of the radial velocity
($\beta_{\mathrm{dw}}$), (4)~the wind temperature, and (5)~the
power-law index of the local mass-loss rate per unit area
$\dot{m}(w) \propto w^{-p}$ where $w$ is the distance from the star
on the equatorial plane. The basic
configuration of the disc-wind model is shown in
Fig.~\ref{fig:model-config}. The disc wind originates from the disc
surface, and the ``source'' points ($S$), from which the stream lines
diverge, are placed at a distance $D$ above and below the centre of the
star. The angle at which the matter is launched from the disc is controlled
by changing the value of $D$. The mass-loss launching occurs between
$R_{\mathrm{wi}}$ and $R_{\mathrm{wo}}$ where the former is set to be
near the outer radius of the closed magnetosphere
($R_{\mathrm{mo}}$) and the latter to be a free parameter. The wind
density is normalised with the total mass-loss rate in the disc wind
($\dot{M}_{\mathrm{dw}}$). The temperature of the wind
($T_{\mathrm{dw}}$) is assumed as isothermal.
\begin{table*}
\caption{Model parameters for disc wind and bipolar outflow.}
\label{tab:model-param}
\begin{tabular}{lcccccccccccccccc}
\hline
& MA$^{\dagger}$ & & \multicolumn{7}{c}{Disc wind} & &
\multicolumn{6}{c}{Bipolar outflow}\tabularnewline
\cline{2-2} \cline{4-10} \cline{12-17}
& (1) & & (2) & (3) & (4) & (5) & (6) & (7) & (8) & & (9) & (10) & (11) & (12) & (13) & (14)\tabularnewline
& & & $\dot{M}_{\mathrm{dw}}$ & $R_{\mathrm{wi}}$ & $R_{\mathrm{wo}}$ & $p$ & $T_{\mathrm{dw}}$ & $\beta_{\mathrm{dw}}$ & $D$ & & $\dot{M}_{\mathrm{bp}}$ & $\theta_{\mathrm{bp}}$ & $R_{0}$ & $T_{\mathrm{bp}}$ & $V_{\infty}$ & $\beta_{\mathrm{bp}}$\\
Model & & & ($\mathrm{M_{\odot}yr^{-1}}$) & ($R_{*}$) & ($R_{*}$) & $\cdots$ & ($\mathrm{K}$) & $\cdots$ & ($R_{*}$) & & ($\mathrm{M_{\odot}yr^{-1}}$) & $\cdots$ & ($R_{*}$) & ($\mathrm{K}$) & ($\mathrm{km\, s^{-1}}$) & $\cdots$\\
\hline
A$^{*}$ & yes & & $\cdots$ & $\cdots$ & $\cdots$ & $\cdots$ & $\cdots$ & $\cdots$ & $\cdots$ & & $\cdots$ & $\cdots$ & $\cdots$ & $\cdots$ & $\cdots$ & $\cdots$\\
B & yes & & $3\times10^{-8}$ & $1.8$ & $10.0$ & $2.3$ & $10^{4}$ & $4.0$ & $2.2$ & & $\cdots$ & $\cdots$ & $\cdots$ & $\cdots$ & $\cdots$ & $\cdots$\\
C & no & & $3\times10^{-8}$ & $1.8$ & $10.0$ & $2.3$ & $10^{4}$ & $4.0$ & $2.2$ & & $\cdots$ & $\cdots$ & $\cdots$ & $\cdots$ & $\cdots$ & $\cdots$\\
D & yes & & $3\times10^{-8}$ & $5.8$ & $14.0$ & $2.3$ & $10^{4}$ & $4.0$ & $2.2$ & & $\cdots$ & $\cdots$ & $\cdots$ & $\cdots$ & $\cdots$ & $\cdots$\\
E & yes & & $4\times10^{-8}$ & $3.8$ & $12.0$ & $0.2$ & $10^{4}$ & $2.0$ & $2.2$ & & $\cdots$ & $\cdots$ & $\cdots$ & $\cdots$ & $\cdots$ & $\cdots$\\
F & yes & & $\cdots$ & $\cdots$ & $\cdots$ & $\cdots$ & $\cdots$ & $\cdots$ & $\cdots$ & & $6\times10^{-8}$ & $35^{\circ}$ & $2.4$ & $10^{4}$ & $500$ & $1.2$\\
G & no & & $\cdots$ & $\cdots$ & $\cdots$ & $\cdots$ & $\cdots$ & $\cdots$ & $\cdots$ & & $6\times10^{-8}$ & $35^{\circ}$ & $2.4$ & $10^{4}$ & $500$ & $1.2$\\
\hline
\end{tabular}
Note: ($\dagger$) MA indicates if a model includes a magnetospheric
accretion. If indicated by `yes', the parameters in Table~\ref{tab:stellar_parameters}
are used for the magnetosphere. ({*})~Model~A consists of the magnetospheric
accretion flows only.
\end{table*}
\begin{figure}
\begin{center}
\includegraphics[width=0.48\textwidth]{MA_DW_SW_new}
\end{center}
\caption{Basic model configurations of the circumstellar flows which
consist of (a)~a magnetosphere and a disc wind (left panel), or (b)~a
magnetosphere and a bipolar outflow (right panel). The density is assumed
to be axisymmetric and top-down symmetric. The components of the
models are: (1)~the continuum source (star) located at the origin of
the cartesian coordinates system, (2)~the magnetospheric accretion
flow, (3)~the geometrically thin accretion disc, (4)~the disc wind,
and (5)~the bipolar outflow. The split-monopole (with the source
displacement distance $D$) disc wind emerges from the equatorial
plane, but only within the distances from $z$-axis between
$R_{\mathrm{wi}}$ and $R_{\mathrm{wo}}$. The bipolar outflow is
launched from a sphere with radius $R_{\mathrm{0}}$, but is
restricted within the cones with the half opening angle
$\theta_{\mathrm{bp}}$. The figure is not to scale.}
\label{fig:model-config}
\end{figure}
\subsubsection{Bipolar outflow}
\label{subsub:SW-config}
As an alternative flow geometry, we also consider a
bipolar outflow which arises in the polar regions near the star. Possible scenarios in which this type of outflows could occur
are: (1)~an accretion-powered stellar
wind launched from open magnetic field lines anchored to the stellar surface
(e.g.~\citealt{decampli81,strafella98,bouret00,matt05,cranmer08,cranmer09}),
or (2)~a relatively fast magnetically driven polar outflow which
appears in between the slower conically-shaped winds
launched from the disk-magnetosphere interaction regions
(e.g.~\citealt{romanova09,lii12}).
The bipolar outflow is approximated as an outflow consisting of narrow cones with
a half-opening angle $\theta_{\mathrm{bp}}$. Here, we assume that the
flow propagates only in the radial direction, and that its velocity is described by
the classical beta-velocity law (cf.~\citealt{castor79}):
\begin{equation}
v_{r}\left(r\right)=v_{0}+\left(v_{\infty}-v_{0}\right)\left(1-\frac{R_{0}}{r}\right)^{\beta_{\mathrm{bp}}}\,,
\label{eq:beta-velocity-law}
\end{equation}
where $v_{\infty}$ and $v_{0}$ are the terminal velocity and the
velocity of the outflow at the base ($r=R_{0}$). Here, we set
$v_{0}=10\,\mathrm{km\, s^{-1}}$ which roughly corresponds to the
thermal velocity of gas around $10^{4}$~K.
Assuming that the mass-loss rate of
the outflow is $\dot{M}_{\mathrm{bp}}$ and
following the mass-flux conservation in the flows, the density $\rho_{\mathrm{pb}}$ of the outflow can be written as:
\begin{equation}
\rho_{\mathrm{bp}}\left(r\right)=\frac{\dot{M}_{\mathrm{bp}}}
{4\pi
r^{2}v_{r}\left(r\right)\left(1-\cos\theta_{\mathrm{bp}}\right)}\,.
\label{eq:sw-density}
\end{equation}
The temperature of the bipolar outflow ($T_{\mathrm{bp}}$) is assumed
isothermal as in~\citet{kurosawa11}. To avoid an overlapping of the
bipolar outflow with the accretion funnels, the base of the bipolar outflow
($R_{0}$) is set approximately at the outer radius of the
magnetosphere ($R_{\mathrm{mo}}$) (cf.~Fig.~\ref{fig:model-config}).
The rotational velocity of the flow is assigned such that the specific angular
momentum of gas is conserved along the stream lines, and its initial
value is constrained by the rotation speed of the stellar surface.
A similar bipolar outflow model was recently applied to the pre-FUor star,
V1331~Cyg \citep{petrov14}.
The bipolar outflow introduced here is rather a simple
kinematic model which does not involve a physical mechanism for the
wind acceleration.
However,
since the outflow geometry here is drastically different from that
of a disc wind model, it is useful to consider this model to
qualitatively check if the outflow in VV~Ser arises mainly from the
polar regions or the accretion disc.
\subsection{Modelling line profiles}
In this section, we will apply the models described above (i.e.
magnetospheric accretion, disc wind and bipolar outflow) to model the \hi\ line profiles obtained from the LBT
observations. Due to the complex line profiles and line variability
observed in these data, we opted to model, as a first approximation,
the average line profiles of the Br$\gamma$, Pa$\beta$\ and Pa$\delta$\ lines during
the three epochs. These data offer a higher spectral resolution
(R$\sim$7000) than the MR-AMBER data (R$\sim$1500). The origin of the
line variability will be discussed in Section\,\ref{sect:discussion}.
\subsubsection{Adopted stellar and disc parameters}
\label{subsub:adopted-param}
\begin{figure}
\begin{center}
\includegraphics[width=0.38\textwidth]{ads143-MA-demo}
\end{center}
\caption{Pa$\beta$ (solid), Pa$\delta$ (dash) and Br$\gamma$
(dash-dot) model line profiles for VV~Ser computed (at
$i=70^{\circ})$ with a small magnetosphere with
$R_{\mathrm{mi}}=1.3\,R_{*}$ and $R_{\mathrm{mo}}=1.8\,R_{*}$ and
the stellar rotation period of $P_{*}=0.84$\,d. Other model
parameters are summarised in Table~\ref{tab:stellar_parameters}. The
lines are mainly in absorption except for a very small emission
component that arises on the blue side of the profiles. The model
profiles clearly disagree with the observed profiles which display
instead a relatively strong emission peak around the line centres
(Fig.\,\ref{fig:LBT-obs}). For clarity, the continuum
emission from the ring emission around the dust sublimation radius
and photospheric absorption are excluded in these models.}
\label{fig:MA-demo}
\end{figure}
The basic stellar parameters adopted for modelling the VV\,Ser spectra from the LBT
are listed in Table\,\ref{tab:stellar_parameters}.
The atmosphere model of \citet{kurucz79} with
$T_{\mathrm{eff}}=14000$~K and $\log g=4.0$ (cgs) is used as the source
of the stellar continuum in the line radiative transfer models. A disk inclination angle $i$ of $\sim$70\degr\ is assumed \citep{pontoppidan07, eisner14}.
The speed at which the star rotates at the equator ($v_{\mathrm{eq}}$) was estimated assuming that the disc/ring normal vector coincides with the rotation axis of VV\,Ser, and that $v_{\mathrm{eq}}$ is the same as $v$ in $v\sin i$.
In the case of VV\,Ser, $v\sin i=142\,\mathrm{km\,
s^{-1}}$ (\citealt{vieira03}), and thus $v_\mathrm{eq}=151\,\mathrm{km\, s^{-1}}$ (approximately $0.3$ of the breakup
velocity).
Consequently, the rotation period
of VV~Ser is estimated to be $P_{*}=2\pi
R_{*}/v_{\mathrm{eq}}=0.86$~d. This value is in agreement with the one estimated by
\citet{hubrig09}.
Finally, a mass-accretion rate of 3.3$\times$10$^{-7}$\,M$_\mathrm{\odot}$\,yr$^{-1}$ is assumed.
To model the dust disc of VV~Ser,
a uniform geometrical ring model is used to fit the AMBER continuum
visibility data in Section~\ref{sect:interferometry}. The inner radius
of the ring is estimated to be 2.35~mas which corresponds to 0.97~au at
$d=415$~pc. We adopt the same ring geometry and dimensions as in the line
profile calculations. We also adopt the position angle (PA) and the ring
inclination angle ($i$) from our earlier analysis (Table\,\ref{tab:geometric_model}),
i.e. PA=\,66\fdg7 and $i$=70\degr, respectively. The ring is
assumed to emit as a blackbody at a temperature
$T_{\mathrm{ring}}=1400$~K.
\subsubsection{Line profiles from magnetospheric accretion models}
\label{subsub:MA-model-LBT}
In this section, we briefly discuss the effect of magnetospheric accretion
(see Section~\ref{subsub:MA-config}) on the formation of the NIR
atomic hydrogen emission lines observed in VV\,Ser.
Using the stellar parameters listed in Table\,\ref{tab:stellar_parameters}, the corotation radius ($R_{\mathrm{cr}}$) of VV~Ser becomes
$R_{\mathrm{cr}}=\left(GM_{*}\right)^{1/3}\left(P_{*}/2\pi\right)^{2/3}=2.4\,
R_{*}$. We assume that the extent of the magnetosphere is slightly
smaller than $R_{\mathrm{cr}}$, and set the inner and outer radii of
the magnetospheric accretion funnel to be $R_{\mathrm{mi}}=1.3\,
R_{*}$ and $R_{\mathrm{mo}}=1.8\, R_{*}$. These radii (in the units
of the stellar radius) are considerably smaller than those of
CTTSs (e.g.~\citealt{koenigl91};
\citealt{muzerolle04}). Consequently, the volume of the gas emitting
region/accretion funnel becomes very small. Hence, the hydrogen line
emission strengths are expected to be also very small. The weakness of
emission lines in the small and fast-rotating magnetosphere was first
pointed out by \cite{muzerolle04}, in modelling the Balmer lines of
Herbig Ae star UX~Ori (see their fig.~3).
Figure~\ref{fig:MA-demo} shows the Pa$\beta$, Pa$\delta$ and Br$\gamma$
model line profiles assuming that they are only formed in the magnetosphere. As expected, the lines are rather
weak, and mainly in absorption except for a very small emission
component on the blue side of the profiles. Very similar line shapes
are also found in the rotating magnetosphere model of
\cite{muzerolle04} (their fig.~3). The model clearly disagrees with
the observed line profiles (Fig.\,\ref{fig:LBT-obs}) which display
strong emission peaks around the line centres. In particular,
the observed Pa$\beta$ and Br$\gamma$ emission lines are roughly
symmetric around the line centres.
Although not shown here, we have
computed models with various combinations of magnetospheric
temperature $T_{\mathrm{m}}$ and mass-accretion rates
($\dot{M}_{\mathrm{a}}$). The line shapes of those models are similar to those shown in Fig.\,\ref{fig:MA-demo}.
In general, the symmetric, or almost symmetric, emission line
profiles are difficult to explain with a fast-rotating
magnetosphere model alone, especially at a high inclination angle, as
in VV~Ser. For this reason, it is most likely that an additional gas
flow component is involved in the formation of the hydrogen emission
lines.
It must be noted, however, that the results presented here may not apply to other Herbig
Ae/Be stars. To examine whether the results above are applicable to
Herbig Ae/Be stars in general, a further investigation is needed. For instance, one would need to explore much larger parameter spaces. However, this is beyond the scope of the present paper and shall be investigated in the future.
\subsubsection{Line profiles from disc wind models }
\label{subsub:DW-model-LBT}
To overcome the weakness of the line emission in the models with a
magnetospheric accretion funnel (Fig.~\ref{fig:MA-demo}), an
additional emission volume from a disc wind (see Section~\ref{subsub:DW-config}) will be added to the magnetospheric contribution.
The left
panels in Fig.~\ref{fig:DW-compare-obs} show the model line profiles,
computed at $i=70^{\circ}$ (i.e. almost edge-on), resulting from the combination of a magnetospheric
accretion funnel and a disc wind (Model~B). The main model parameters
are summarised in Table~\ref{tab:model-param}. The ratio of the wind
mass-loss rate to the mass-accretion rate
($\dot{M}_{\mathrm{dw}}/\dot{M}_{\mathrm{a}}$) is $\sim0.09$. This
model produces similar line strengths and widths as seen in the
observed Pa$\beta$, Pa$\delta$ and Br$\gamma$ lines of the LBT observations. However,
the model profiles clearly disagree with the observed profiles in
their shapes: the former are double-peaked, but the latter are
single-peaked.
This is because in our disc wind model
the \hi\ NIR lines are mainly formed near the
base of the disc wind. In this region the Keplerian rotation of the wind dominates over the radial motion. Therefore, double-peaked profiles naturally
occur when the disc wind is viewed from horizontal directions, that is, when the system has a mid to high inclination angle ($i$). This is demonstrated in Fig.~\ref{fig:DW-inc-effect}, which shows how the
Br$\gamma$ line profile depends on the inclination angle. In particular, this figure shows that the modelled Br$\gamma$ line profile becomes double peaked for $i\simgreat30^{\circ}$. Note that in our disc wind model, the Keplerian velocities are about
$400\,\mathrm{km\, s^{-1}}$ and $170\,\mathrm{km\, s^{-1}}$ at the
inner and outer radii of the wind launching regions, that is, $R=1.8\,\mathrm{R_{\odot}}$ and $10\,\mathrm{R_{\odot}}$,
respectively. Moreover, the line emission mainly originates from
the disc wind and the contribution of the magnetosphere to the line profile is very small (see Section\,\ref{subsub:MA-model-LBT}). This is illustrated in the right panels of
Fig.~\ref{fig:DW-compare-obs}, where a comparison of the line profiles produced by the
magnetosphere plus disc wind model (Model~B), with those generated by the single contributions of the disc wind model
(Model~C), and the magnetosphere model (Model~A) is shown. Therefore, in model\,B (magnetosphere + disc wind), the overall shape of the \hi\ lines is dominated by the emission from the disc wind.
Although not shown here, we have explored various combinations of the
disc wind model parameters (i.e.~$\dot{M_{\mathrm{dw}}}$,
$R_{\mathrm{wi}}$, $R_{\mathrm{wo}}$, $D$, $T_{\mathrm{dw}}$
$\beta_{\mathrm{dw}}$ and $p$ as in
Section~\ref{subsub:DW-config}; see also
Fig\@.~\ref{fig:model-config}) which control the characteristics of
the wind.
Examples of the dependency of the Br$\gamma$ profile on a few
selected models parameters (the wind launching radii $R_{\mathrm{wi}}$ and
$R_{\mathrm{wo}}$; the power-law index of local mass-loss rate per
unit area $p$) are given in Appendix~\ref{sec:appendix-dw-param}.
Even though the line strengths, line widths and the peak separation
widths vary with different combinations of the disc wind parameters,
the double peaks are always visible for a mid to high inclination angle, as is the case for VV~Ser
(assuming $i\approx70^{\circ}$). Hence, the disc wind is unlikely a major
contributor to the single-peaked emission lines (Pa$\beta$, Pa$\delta$
and Br$\gamma$) seen in VV Ser.
However, if the inclination is $\sim$70\degr\ or larger, we cannot exclude the possibility
that the innermost region of the disc wind is obscured by the outer region
of a flared disc, and thus that another flux contribution is dominant.
For these reasons, we seek an alternative flow
component which can robustly reproduce a rather symmetric and
single-peak Br$\gamma$ emission line as seen in VV\,Ser and many other
Herbig Ae/Be stars (e.g.~\citealt{rebeca06};
\citealt{brittain07}). Note that, for a relatively low inclination
angle system (nearly face-on), it may be still possible to reproduce a
single peaked Br$\gamma$ by a disc wind model
(e.g.~Fig.~\ref{fig:DW-inc-effect}; see also \citealt{weigelt11, rebeca15, ale15}).
\begin{figure}
\begin{center}
\includegraphics[width=70mm]{adw087-inc-effect}
\end{center}
\caption{The dependency of Br$\gamma$ on inclination angle ($i$) in
Model~B which uses a combination of a disc wind and magnetosphere
(Table~\ref{tab:model-param}). The line profiles are double-peaked
for the models with $i \mathrel{\copy\simgreatbox} 30^{\circ}$. Disc models in
general have difficulties reproducing the singe-peak Br$\gamma$
line profile seen in the LBT observations (Fig.\ref{fig:LBT-obs})
for the models with mid to high inclination angles.
}
\label{fig:DW-inc-effect}
\end{figure}
\subsubsection{Line profiles from bipolar outflow models }
\label{subsub:SW-model-LBT}
Another possible way to obtain a single-peak emission line profile in a nearly edge-on system is to
include a bipolar outflow in the model.
In this case, the inclination angle $i$ must be larger than the half-opening
angle of the bipolar outflow $\theta_{\mathrm{bp}}$ (see
Fig.~\ref{fig:model-config}) to avoid a strong wind absorption on the blue
side of the line profile (i.e. a P-Cygni profile).
The left panels in Fig.~\ref{fig:SW-LBT} shows the model line
profiles computed with a combination of a magnetospheric accretion
funnel and a bipolar outflow (Model~F). The lines are computed at
$i=70^{\circ}$ assuming a wind half-opening angle $\theta_{\mathrm{bp}}=35^{\circ}$. The model parameters are
summarised in Table~\ref{tab:model-param}. The ratio of the mass-loss
rate in the wind to the mass-accretion rate
($\dot{M}_{\mathrm{dw}}/\dot{M}_{\mathrm{a}}$) is about $0.18$. The
figure clearly shows that the model is capable of producing
single-peak line profiles. Furthermore, the model produces line profiles very similar to the observed Pa$\beta$, Pa$\delta$ and Br$\gamma$ line profiles (in their line strengths and widths).
As for the case of the magnetosphere-plus-disc wind model, the line emissions in this
model are mainly from the bipolar outflow. This is clearly illustrated in the right
panels of Fig.~\ref{fig:SW-LBT}, which compare the profiles from
Model~F (magnetosphere + bipolar outflow) with those computed with only
the bipolar outflow (Model~G) and only the magnetosphere (Model~A). In this
particular model (Model~F), the magnetosphere contributes only
slightly to the lines, and the overall shapes of the lines are
determined by the emission from the bipolar outflow.
The emission profiles of the Pa$\beta$ and Br$\gamma$ lines are mostly symmetric
around the line centres. However, the Pa$\delta$ line profile is slightly
asymmetric towards the blue side of the
line, that is, the blue-shifted emission is slightly stronger.
This is due to the absorption by the magnetospheric accretion
funnel which is stronger on the red side of the line. A similar trend is
also observed in the Pa$\delta$ line computed with the disc wind +
magnetosphere (Model~B) in Fig.~\ref{fig:DW-compare-obs}, which shows
stronger blue-shifted emission.
In summary, the bipolar outflow, when viewed from equatorial
directions, can form single-peak line profiles as the ones observed in the LBT spectra.
The line strengths and shapes of the observed
Pa$\beta$, Pa$\delta$ and Br$\gamma$\ line profiles are reproduced well
by Model~F (Fig.~\ref{fig:SW-LBT}; Table~\ref{tab:model-param}).
\subsection{Models for AMBER data}
\label{sub:models-AMBER}
To probe whether the same bipolar outflow plus magnetosphere model described above can reproduce the Br$\gamma$\ AMBER-VLTI spectro-interferometric observations (Section\,\ref{sect:interferometry}) in addition to the
LBT spectra, the intensity maps of the line emitting regions were computed using the same radiative transfer model employed to produce the line profiles (see Section~\ref{sect:models}).
In this way, the interferometric
quantities such as visibility, differential and closure phases can be
readily calculated from the model intensity maps.
The results are summarised in Fig.~\ref{fig:DW-SW-AMBER}. The figure
compares the model Br$\gamma$ line profiles, visibility and
differential phases with those of LBT (average Br$\gamma$\ line profile) and VLTI-AMBER
observations. For purposes of comparison, the figure also includes
the models computed with a disc wind plus a magnetosphere in addition to
those with the bipolar outflow.
Six different cases in Table~\ref{tab:model-param} are shown here:
(1)~a disc wind with small launching radii (Model~B) computed at
$i=70^{\circ}$, (2)~a disc wind with larger launching radii (Model~D) computed at $i=70^{\circ}$,
(3)~a disc wind with intermediate launching radii and a small $p$ (the
index of the power-law in the mass-loss rate per unit area; see
Appendix~\ref{sec:appendix-dw-param} and \citealt{kurosawa11})
(Model~E) computed at $i=70^{\circ}$, (4)~a bipolar outflow model
(Model~F) computed at $i=65^{\circ}$, (5)~same as (4) but computed at
$i=70^{\circ}$, and (6)~same as (4) but with $i=75^{\circ}$.
Note that model closure phases are not shown in this figure because no
closure-phase signal within the error of $20^\circ$ is measured from
our AMBER observations (see, Fig.\,\ref{fig:AMBER-obs}), and all model closure phases are smaller than 10\degr.
In cases~(1)--(3) (disc wind models), the models fit the
interferometric observations reasonably well. However, the
double-peak line profiles seen in those models do not match the
observations. The separation of the double peaks are slightly reduced
by increasing the disc wind launching radii from case~(1) (Model~B) to
case~(2) (Model~D) (Table~\ref{tab:model-param}). A further
reduction of the peak separation is achieved by reducing the value of $p$ (the
power-law for the mass-loss rate per unit area;
c.f.\,Appendix~\ref{sec:appendix-dw-param}; \citealt{kurosawa11})
from case~(2) (Model~D) to case~(3) (Model~E)
(Table~\ref{tab:model-param}). The double-peak feature is rather
persistent in the models with a disc wind
(see Section~\ref{subsub:DW-model-LBT}). On the other hand, the
bipolar outflow models (Model~F) with $i=65^{\circ}$ (case~4) and $75^{\circ}$
(case~6) reproduce reasonably well the observed line profiles, but the
visibility levels disagree with the AMBER observations. Only the model with
the bipolar outflow computed at $i=70^{\circ}$, case~(5), fits the
observed line profiles (here and also in Fig.~\ref{fig:SW-LBT}),
visibility and differential phase,
simultaneously.
In all the models, the visibility levels are slightly larger in the lines
(by $\sim0.06$) compared to those in the continuum. This agrees with the
fact that the line emitting regions are smaller than that of the
continuum emitting regions. In our models, the inner radius of the
K-band continuum emitting ring model is approximately 1.0~au
(Section\,\ref{sect:geometric_model}) which corresponds to
$\sim80\,\mathrm{R_{\odot}}$. This is much larger than the wind
launching regions of both disc wind ($1.8$--$14\,\mathrm{R_{\odot}}$)
and bipolar outflow ($2.4\,\mathrm{R_{\odot}}$)
(Table~\ref{tab:model-param}). The increase in the visibility levels across the Br$\gamma$ emission line is not clearly seen in the AMBER observations due to the relatively low S/N and spectral resolution of the data.
However, a weak increase of the visibility at the longest baseline (UT1--UT4) is observed towards the line centre (see Fig.\,\ref{fig:AMBER-obs}). The small increase in the visibility in the line centre
($\sim0.06$) with respect to the continuum seems to be in agreement
with the data, considering the levels of uncertainty/noise.
The differential phases from the AMBER observation are $0^{\circ}$
within the error of $5^{\circ}$ across the Br$\gamma$ line
without any
trend for an increase or a decrease. On the other hand, our models show
very small variations with their amplitude between $\sim1^{\circ}$ and
$\sim2^{\circ}$ across the line. These small
amplitudes are well below the noise levels of the observations. This
suggests that the models do not disagree with the observed
differential phases, that is, the amplitude of the variation in the
differential phase across the line predicted by the model do not
exceed the noise levels in the observations.
\begin{figure}
\begin{center}
\includegraphics[width=84mm]{adw087-summary}
\end{center}
\caption{Left Panels: a comparison of the mean line profiles
obtained by LBT (dashed) with the hydrogen line
profiles (Pa$\beta$, Pa$\delta$ and Br$\gamma$) computed using the
models with the combination of a disc wind and magnetosphere
(solid; Model~B in Table~\ref{tab:model-param}). Right panels: a
comparison of line profiles computed using the disc wind +
magnetosphere (solid; Model~B) with those using (1) only the disc
wind (dash-dot; Model~C) and (2)~only the magnetosphere (dot;
Model~A). All the profiles are computed at the inclination angle
$i=70^{\circ}$. In general, models with disc wind produced
double-peak profiles due to rotating motion of the disc wind. The
double peaks are always prominent at a mid to a high inclination
angle (cf.\,Fig.~\ref{fig:DW-inc-effect}). The right panels show
that the emission contribution from the magnetosphere is very
small in Model~B. }
\label{fig:DW-compare-obs}
\end{figure}
In principle, the physical parameters of the line emitting wind
regions (the wind geometry and kinematics) can be further constrained
by performing detail model fitting of the observed visibility and
differential phases across the line. However, the high noise
levels in the data prevent us from performing such an investigation.
In summary, the model with a bipolar outflow
(Model~F) observed at an inclination angle of
$i=70^{\circ}$ (the third column in Fig.~\ref{fig:DW-SW-AMBER}) gives
the best match to the observed visibility, differential phases and
the NIR hydrogen line profiles (Pa$\beta$, Pa$\delta$ and Br$\gamma$
as in Fig.~\ref{fig:SW-LBT}).
\section{Discussion}
\label{sect:discussion}
\subsection{Origin of the NIR \hi\ emission lines}
\label{sect:origin_HI}
In the previous sections, we investigated possible mechanisms responsible for the formation of the NIR \hi\ emission lines in the Herbig star VV Ser. With this goal in mind, we explored
what should be expected from three different
line emitting sources namely, a magnetosphere, a disc wind and a
bipolar outflow, and compare these results with
average \hi\ line profiles obtained with LUCIFER at LBT, and with
AMBER-MR spectro-interferometric observations.
Our modelling suggests, that in the case of VV\,Ser, the contribution of a fast rotating magnetosphere to the \hi\ NIR emission line profiles is very small in comparison with the
contribution of a disc wind or bipolar outflow.
Similar results have been previously found in other Herbig AeBe stars by analysing their NIR line profiles alone or in combination with NIR spectro-interferometric techniques \citep{weigelt11,larisa14,rebeca15, ale15}.
In contrast with these results, where a disc wind model could be used
to model the Br$\gamma$\ line profile and the spectro-interferometric
observables, in the case of VV\,Ser only a bipolar outflow
can approximately reproduce the
averaged single-peaked line profiles of the Pa$\beta$,
Pa$\delta$, and Br$\gamma$\ lines observed with the LBT, as well as, the
Br$\gamma$\ spectro-interferometric observables.
The main difference,
between VV\,Ser and the results mentioned above is the high disc inclination angle of VV\,Ser ($i\sim$70\degr). As shown in Fig.\,\ref{fig:DW-inc-effect}, our disc wind model
can only reproduce single peaked line profiles when low inclination angles ($i\lesssim$30\degr) are considered. Similar results are also found in \cite{larisa14} for the Br$\gamma$\ and H$\alpha$ lines.
This is because, the NIR \hi\ lines are formed at the base of the
disc wind, where the Keplerian rotation of the disc dominates over the
wind radial velocity.
Therefore, a disc wind can only generate a single peaked line profile at high inclination angles if the inner disc wind emitting region is obscured by an outer flared disc, or alternatively, if other components (such as a magnetosphere or a bipolar wind)
significantly contribute to the line profile. In contrast,
bipolar outflows are launched
well above the circumstellar disc
(see, sketch in Fig.\,\ref{fig:model-config}),
and thus,
single peaked line profiles are
easily
obtained for all the NIR \hi\ observed lines.
\begin{figure}
\begin{center}
\includegraphics[width=84mm]{asw163-summary}
\end{center}
\caption{Left Panels: a comparison of the mean line profiles obtained
by the LBT (dashed; see Section\,\ref{sect:spectroscopy} and Fig.\,\ref{fig:LBT-obs}) with the model hydrogen line
profiles (Pa$\beta$, Pa$\delta$ and Br$\gamma$) computed using the
models with the combination of a bipolar outflow and magnetosphere
(solid; Model~F in Table~\ref{tab:model-param}). Right panels: a
comparison of the line profiles computed using the
bipolar outflow + magnetosphere (solid; Model~F) with those using (1) only the
bipolar outflow (dash-dot; Model~G) and (2)~only the magnetosphere (dot;
Model~A). All the profiles are computed at the inclination angle
$i=70^{\circ}$. The left panels show that Model~F can reasonably and
simultaneously fit the observed Pa$\beta$, Pa$\delta$ and Br$\gamma$
profiles (mean) obtained by the LBT. The right panels
show that the emission contribution from the magnetosphere is very
small in Model~F.}
\label{fig:SW-LBT}
\end{figure}
Although the bipolar outflow model works very well
here, we would like to remind readers that the model is highly
schematic, and the exact physical process which can produce this type
of outflows is not well known. As mentioned earlier, one possible
candidate is the accretion-powered stellar wind
(e.g.~\citealt{decampli81,strafella98,bouret00,matt05,cranmer08,cranmer09});
however, these models (except for \citealt{strafella98,bouret00})
are mainly for winds in CTTSs which have stronger magnetic fields. Interestingly,
recent spectroscopic studies of Herbig Ae/Be stars by
\citet{cauley14, cauley15} have shown that about
30~per~cent of their sample display P-Cygni profiles in
HeI~10830\,\AA{} and H$\beta$, which is
a good indication for stellar wind like outflows
(e.g.~\citealt{edwards06,kwan07,kurosawa11}).
Our AMBER-MR spectro-interferometric observations of the Br$\gamma$\ line support the results obtained from the pure modelling of the LBT spectroscopic observations. That is,
regardless of the accuracy on the line profile modelling, the wind
(disc or bipolar wind) component dominates the line emission, whereas the magnetosphere do not play a major role in the line profile.
Indeed, the AMBER-MR interferometric observations of the Br$\gamma$\ line shows that even if the Br$\gamma$\ line emission is more compact than the continuum emission, the Br$\gamma$\ emission is nevertheless resolved. Therefore, the line emitting region
is not mainly formed in the unresolved magnetospheric accretion
region. Furthermore, the interferometric observables (visibilities,
differential phases and closure phase) are best reproduced when a disc
wind or bipolar outflow is considered,
the latter being the one that best reproduces the Br$\gamma$\ single line profile.
\subsection{Line profile variability}
\label{sect:line_variability}
As shown in Fig.\,\ref{fig:variance_profile}, a significant fraction of the variation in the observed lines occurs in their red wings. Therefore, variations in the contribution
of the magnetosphere to the total \hi\ line emission could be the cause
of the NIR \hi\ line variability observed in VV\,Ser (see,
Fig.\,\ref{fig:LBT-obs}). For instance, a periodic and
a non-periodic line variability can be caused by rotating non-axisymmetric
magnetospheric accretion flows in stable and unstable regimes,
respectively (e.g.~\citealt{kurosawa13}). Similarly, non-steady accretion or
an enhanced
mass-accretion rate could modify the redshifted component of the
line profiles, introducing strong redshifted absorption components to the line profiles (see Fig.\,\ref{fig:MA-demo}). This could be the cause of the redshifted adsorptions in the Pa$\delta$, Pa$\beta$\ and Br$\gamma$\ line profiles observed in February 2012 (see Fig.\,\ref{fig:LBT-obs}).
On the other hand, the complex Pa$\delta$\ line profile observed in April 2012 could be explained by an increase from a disc wind contribution to the line profile. A disc wind could also reproduce the double peaked H$\alpha$\ line profiles observed in VV\,Ser (see e.g., \citealt{mendigutia11}). This might indicate that lines such as H$\alpha$\ are optically thicker than the NIR \hi\ emission lines.
Furthermore, they are formed in regions located farther away from the disc plane and observed through the wind down to the central source.
In this context, the complex line profiles and their variability could
be explained through the coexistence of at least three different
mechanisms, namely magnetospheric accretion, a disc wind and a
bipolar outflow, the intensity and contribution to the
total line profile of which vary with time.
This would indicate that accretion, and thus, the ejection processes do not occur in a steady-state regime.
Non steady accretion has been previously used to explain the short term spectral and photometric variability of the CTTS AA\,Tau \citep{bouvier03}. In this case, the optical line profile and photometric variations were explained by the presence of a non-axisymmetric warp
in the inner disc caused by the interaction of the disc and an
inclined stellar dipole (e.g.~\citealt{romanova03,romanova13}). The variability is then related to the perturbation of the stellar magnetic field at the disc inner edge. In this regard, an increase in brightness, and the subsequent
line variability, is due to a severe reduction of the accretion flow onto the star, leading to a temporary disappearance of the disc inner warp.
However, it is not clear how such a mechanism could work in VV\,Ser. Whereas CTTSs are slow rotators as a consequence of strong magnetic fields producing a magnetic braking, Herbig AeBe stars are fast rotators with no clear
evidence of a {developed and organised magnetic field configuration \citep[e.g.,][and references therein]{hubrig11}. Although the measured variations in the EW of the \hi\ lines could be interpreted as changes in the continuum level (i.e. magnitude) of the source, they could also represented a decrease in the
line flux. Therefore, without simultaneous photometry at both optical and NIR wavelengths it is difficult to test whether VV\,Ser's variability is due to inner disc instabilities caused by enhanced/depressed accretion. Further observations, spanning a
wider wavelength and temporal range, and accompanied by simultaneous optical and NIR photometry are needed in order to disentangle the inner disc mechanism producing the line variability.
\section{Summary and conclusions}
\label{sect:conclusions}
\begin{figure*}
\begin{center}
\includegraphics[width=175mm]{DW-SW-amber-summary-6col_reb}
\end{center}
\caption{Comparisons of the LBT and AMBER observations of Br$\gamma$
with our models (six different cases):
(1)~Model~B with $i=70^{\circ}$ --- a disc wind with
small launching radii (first column),
(2)~Model~D with $i=70^{\circ}$ --- a disc wind with lager launching
radii (second column),
(3)~Model~E with $i=70^{\circ}$ --- a disc wind with intermediate
launching radii and a small $p$ (third column),
(4)~Model~F with
$i=65^{\circ}$ --- a bipolar outflow
model (fourth column),
(5)~Model~F with
$i=70^{\circ}$ --- a bipolar outflow
model (fifth column), and
(6)~Model~F with
$i=75^{\circ}$ --- a bipolar outflow
model (sixth column). See
Table~\ref{tab:model-param} for their model parameters.
The top panels show the comparisons of the mean
Br$\gamma$ profile from the LBT (dash-dot) with models (solid). The
middle and bottom panels show the comparisons of our models (solid)
and the visibility and differential phases obtained by AMBER
(Section~\ref{sect:interferometry}) with three baselines: UT1--UT2
($\mathrm{PBL}=49.20$\,m, $\mathrm{PA}=-159.67^{\circ}$), UT2--UT4
($\mathrm{PBL}=83.25$\,m, $\mathrm{PA}=-98.40^{\circ}$) and UT1--UT4
($\mathrm{PBL}=115.28$\,m, $\mathrm{PA}=-120.38^{\circ}$). For
clarity, the differential phases of UT2--UT4 and UT1--UT4 baselines
are vertically shifted by $+10^{\circ}$ and $-10^{\circ}$,
respectively. Model~F with $i=70^{\circ}$ (fifth column)
agrees reasonable well with the observed Br$\gamma$ profile, visibility
and differential phase. The same model reproduces the observed
Pa$\beta$ and Pa$\delta$ lines also well (Fig.~\ref{fig:SW-LBT}).
The disc wind models (Models~B,D and E with $i=70^{\circ}$)
fit the interferometric observations, but their line profile
shapes (double peaked) do not match the observation. Although the
bipolar outflow
models (Model~F) with $i=65^{\circ}$ and $75^{\circ}$ reproduce reasonably well
the observed line profile, their visibility levels do not match with
the observation.}
\label{fig:DW-SW-AMBER}
\end{figure*}
We have shown LBT-LUCIFER medium resolution z-, J-, and K-band spectroscopic observations covering the Pa$\delta$, Pa$\beta$, and Br$\gamma$\ lines of the Herbig star VV\,Ser at three different epochs spanning over three months.
Additionally, MR VLTI-AMBER interferometric observations of the Br$\gamma$\ line in this source are
presented as well.
The spectroscopic observations show relatively strong line variability in all the \hi\ NIR emission lines. The line profile variability is more extreme in the
Paschen lines probably because the line emitting volume of these lines is larger than that of the Br$\gamma$\ line.
Therefore, an observer would receive emission originating from different circumstellar regions (such as a wind and magnetospheric region) along the line of sight.
To investigate the physical mechanisms that are responsible for the \hi\ line
emission, we have a applied a radiative transfer model consisting of a
magnetospheric accretion region, a disc wind and a
bipolar outflow. The best model able to reproduce the
roughly symmetric and single peaked averaged line
profiles of the \hi\ lines for the three epochs is a bipolar outflow model. However, it should be noted that the bipolar outflow model presented in Section~\ref{subsub:SW-config} is highly
schematic, and the exact physical process which can produce this type
of outflows is not well known.
The contribution to the line profiles of the magnetospheric accretion region is small in comparison with that of any of our wind models. Therefore, the
NIR \hi\ emission region is probably dominated by wind emission.
This is supported by our spectro-interferometric observations of the Br$\gamma$\ line. Our results show a Br$\gamma$\ emitting region smaller than the continuum emitting region. However, the Br$\gamma$\ line emission is only resolved at the
longest baseline. This indicates that the emission is compact but nevertheless spatially resolved (i.e. consistent with wind emission).
On the other hand, episodic enhancement accretion could explain the redshifted absorption components observed in some of our data. These periods could be followed by an increase of disc-wind activity. Although it is difficult to produce single peaked
line profiles from a disc wind model alone, some of the line profiles observed in VV\,Ser, such as the H$\alpha$\ line profile observed by \cite{mendigutia11} and the triple-peaked Pa$\delta$\ line profile observed in April 2012 could be explained by the combined
effect of a double peaked disc wind profile (see
Fig.\,\ref{fig:DW-compare-obs}) plus the single-peak profile obtained
in a bipolar outflow (see Fig.\,\ref{fig:SW-LBT}).
Indeed, the AMBER visibilities, differential phases and closure phases
can be approximately reproduced by a disc
wind or bipolar outflow, although, only a bipolar outflow (i.e. gas emitted close to the polar regions) can reproduce
the single peaked Br$\gamma$\ line profile observed in VV\,Ser (see Fig.\,\ref{fig:DW-SW-AMBER}).
In summary, our results indicate a very complex structure for the inner disc region of VV\,Ser, in where several mechanisms
(i.e. magnetospheric accretion, disc wind and bipolar outflow) could coexist in a non steady-state regime, given rise to strong line variability
and increasing the complexity of our understanding of the innermost gaseous disc region.
\section*{Acknowledgments}
We thank the anonymous referee for his/her useful comments and suggestions.
This research has made use of the Jean-Marie Mariotti Center
\texttt{Aspro} service \footnote{Available at http://www.jmmc.fr/aspro}.
We thank Dmitry Shakhovskoy for the photometric follow-up of VV Ser.
R.G.L and A.C.G. were supported by Science Foundation of
Ireland, grant 13/ERC/I2907. A.K. acknowledges support from an STFC Rutherford Grant (ST/K003445/1). L.V.T. was
partially supported by the Russian Foundation for Basic Research (Project 15-02-05399). V.P.G was supported by grant RFBR (project 15-02-09191).
\bibliographystyle{mnras}
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{
"redpajama_set_name": "RedPajamaArXiv"
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\section{Introduction}
Deep reinforcement learning (RL) is poised to revolutionize how autonomous systems are built. In recent years, it has been shown to achieve state-of-the-art performance on a wide variety of complicated tasks \cite{mnih2015human,lillicrap2015continuous,schulman2015trust,van2016deep,schulman2017proximal}, where being successful requires learning complex relationships between high dimensional state spaces, actions, and long term rewards. However, the current implementations of the latest advances in this field have mainly been tailored to academia, focusing on fast prototyping and evaluating performance on simulated benchmark environments.
While interest in applying RL to real problems in industry is high~\cite{chen2019top,zhao2018recommendations,zhao2018deep,mirhoseini2017device,zheng2018drn}, the current set of implementations and tooling must be adapted to handle the unique challenges faced in applied settings. Specifically, the handling of large datasets with hundreds or thousands of varying feature types and distributions, high dimensional discrete and continuous action spaces, optimized training and serving, and algorithm performance estimates before deployment are of key importance.
Currently, several platforms have been developed that address different parts of this end-to-end applied RL challenge \cite{Bellemare2018Dopamine,caspi_itai_2017_1134899,liang2017ray,agarwal2016making}, however to our knowledge, no single system offers an end-to-end solution. Table \ref{rl_framework} outlines the features of different frameworks compared to Horizon.
\begin{table}[t]
\caption{\textbf{Comparison of Open Source RL Frameworks.}} DP = Data Preprocessing \& Feature Normalization, DT = Distributed Training, CPE = Counterfactual Policy Evaluation, EC2 = Amazon EC2 Integration.
\label{rl_framework}
\vskip 0.15in
\begin{center}
\begin{small}
\begin{sc}
\begin{tabular}{lcccr}
\toprule
Framework & DP & DT & CPE & EC2\\
\midrule
Horizon & $\surd$ & $\surd$ & $\surd$ & $\times$ \\
Garage & $\times$ & $\surd$ & $\times$ &
$\surd$ \\
Dopamine & $\times$ & $\times$ & $\times$ & $\times$ \\
Coach & $\times$ & $\surd$ & $\times$ & $\times$ \\
SageMaker RL & $\times$ & $\surd$ & $\times$ & $\surd$ \\
\bottomrule
\end{tabular}
\end{sc}
\end{small}
\end{center}
\vskip -0.1in
\end{table}
With this in mind, we introduce Horizon - an open source end-to-end platform for applied RL developed and used at Facebook. Horizon is built in Python and uses PyTorch for modeling and training \cite{paszke2017pytorch} and Caffe2 for model serving \cite{jia2014caffe}. It aims to fill the rapidly-growing need for RL systems that are tailored to work on real, industry produced, datasets.
The rest of this paper goes into the details and features of Horizon, but at a high level Horizon features:
\textbf{Data preprocessing:} A Spark \cite{zaharia2010spark} pipeline that converts logged training data into the format required for training numerous different deep RL models.
\textbf{Feature Normalization:} Logic to extract metadata about every feature including type (float, int, enum, probability, etc.) and method to normalize the feature. This metadata is then used to automatically preprocess features during training and serving, mitigating issues from varying feature scales and distributions which has shown to improve model performance and convergence \cite{ioffe2015batch}.
\textbf{Data Understanding Tool:} RL algorithms are suitable for sequential problems where some form of accumulated rewards are to be optimized. In contrary to many academic research environments that have well-defined transition and reward functions~\cite{brockman2016openai}, real world environments are not easily formulated to the standard Markov Decision Process (MDP) framework~\cite{bellman1957markovian} with properly defined states, actions, rewards, and transitions. Thus, we developed a data understanding tool that checks properties of problem formulation prior to applying any RL algorithm. In practice, the data understanding tool has accelerated data engineering iterations and provided explainable insights to RL practitioners.
\textbf{Deep RL model implementations:} Horizon provides implementations of Deep Q-networks (DQN) \cite{mnih2015human}, Deep Q-networks with double Q-learning (DDQN) \cite{van2016deep}, Deep Q-networks with dueling architecture (Dueling DQN \& Dueling DDQN) \cite{wang2015dueling} for discrete action spaces, a parametric action version of all the previously mentioned algorithms for handling very large discrete action spaces, and Deep Deterministic Policy Gradients (DDPG) \cite{lillicrap2015continuous} and Soft Actor-Critic (SAC) \cite{haarnoja2018soft} for continuous action spaces.
\textbf{Multi-Node and Multi-GPU training:} Industry datasets can be very large. At Facebook many of our datasets contain tens of millions of samples per day. Horizon has functionality to conduct training on many GPUs distributed over numerous machines. This allows for fast model iteration and high utilization of industry sized clusters. Even for problems with very high dimensional feature sets (hundreds or thousands of features) and millions of training examples, we are able to learn models in a few hours (while doing preprocessing and counterfactual policy evaluation on every batch). Horizon supports CPU, GPU, multi-GPU, and multi-node training.
\textbf{Counterfactual policy evaluation:} Unlike in pure research settings where simulators offer safe ways to test models and time to collect new samples is very short, in applied settings it is usually rare to have access to a simulator. This makes offline model evaluation important as new models affect the real world and time to collect new observations and retrain models may be days or weeks. Horizon scores trained models offline using several well known counterfactual policy evaluation (CPE) methods. The step-wise importance sampling estimator, step-wise direct sampling estimator, step-wise doubly-robust estimator \cite{dudikdoubly}, sequential doubly-robust estimator \cite{jiang2016doubly}\footnote{Two variants are implemented; one makes uses of ordinal importance sampling and the other weighted importance sampling.}, and MAGIC estimator \cite{thomas2016data} are all run as part of Horizon's end-to-end training workflow.
\textbf{Optimized Serving:} Post training, models are exported from PyTorch to a Caffe2 network and set of parameters via ONNX \cite{exchange2018onnx}. Caffe2 is optimized for performance and portability, allowing models to be deployed to thousands of machines.
\textbf{Tested Algorithms:} Testing production RL systems is a new area with no established best practices. We take inspiration from systems best practices and test our algorithms in Horizon via unit tests and integration tests. Using custom environments (i.e. Gridworld) and some standard environments from OpenAI's Gym \cite{brockman2016openai} we train and evaluate all of our RL models on every pull request.
We end the paper discussing examples of how models trained with Horizon outperformed supervised learning and heuristic based policies to send notifications and to stream videos at Facebook. We provide details into the formulation and methods used in our approach to give practitioners insight into how to successfully apply RL to their problems.
\section{Data Preprocessing}
Many RL models are trained on consecutive pairs of state/action tuples (DQN, DDPG, SAC etc.). However, in production systems data is often logged as it comes in, requiring offline logic to join the data in a format suitable for RL. To assist in creating data in this format, Horizon includes a Spark pipeline (called the \textit{Timeline} pipeline) that transforms logged data collected in the following row format:
\begin{itemize}
\item \textit{MDP ID}: A unique ID for the Markov Decision Process (MDP) chain that this training example is a part of.
\item \textit{Sequence Number}: A number representing the location of the state in the MDP (i.e. a timestamp).
\item \textit{State Features}: The features of the current step that are independent of the action.
\item \textit{Action}: The action taken at the current step. A string (i.e. `up') if the action is discrete or a set of features if the action is parametric or continuous.
\item \textit{Action Probability}: The probability that the current system took the action logged. Used in counterfactual policy evaluation.
\item \textit{Metrics}: A map from metric name to value. Used to construct a reward value during training by computing the dot product between input weights and metric values.
\item \textit{Possible Actions}: An array of possible actions at the current step, including the action chosen (left blank for continuous action domains). This is optional but enables Q-Learning (vs. SARSA).
\end{itemize}
This data is transformed into data in the row format below. Note, \textit{MDP ID}, \textit{Sequence Number}, \textit{State Features}, \textit{Action}, \textit{Action Probability}, and \textit{Metrics} are also present in the data below, but are left out for brevity.
\begin{itemize}
\item \textit{Next State
Features}: The features of the subsequent step that are action-independent.
\item \textit{Next Action}: The action taken at the next step.
\item \textit{Sequence Number Ordinal}: A number representing the location of the state in the MDP after the \textit{Sequence Number} was converted to an ordinal number.
\item \textit{Time Diff}: A number representing the ``time difference'' between the current state and next state (computed as the difference in non-ordinal sequence numbers between states). Used as an optional way to set varying time differences between states. Particularly useful for MDPs that have been sub-sampled upstream.
\item \textit{Possible Next Actions}: A list of actions that were possible at the next step. Only present if \textit{Possible Actions} were provided.
\end{itemize}
As seen above, instead of taking in a reward scalar explicitly, Horizon takes in a "metrics" map. This enables reward shaping during training and counterfactual policy evaluation over metrics.
\begin{enumerate}
\item \textit{Reward shaping}: By taking the dot product between the vector of values in the metrics map and the vector of weights in a "metrics weight" map provided by the user at training time, we compute the reward scalar value for each training observation. This allows for rapid iteration on reward shaping. The user can experiment with different reward formulas by specifying different input weights as the input to the training process without the need to regenerate data tables.
\item \textit{Counterfactual policy evaluation over metrics}: The metrics map also enables Horizon's counterfactual policy evaluation pipeline to run over each metric in the map instead of just aggregate reward. This allows for a granular estimation on the newly trained policy's performance.
\end{enumerate}
\section{Feature Normalization}
Data from recommender systems is often sparse, noisy and arbitrarily distributed \cite{adomavicius2005toward}.
Literature has shown that neural networks learn faster and better when operating on batches of features that are normally distributed \cite{ioffe2015batch}. In RL, where the recurrence can become unstable when exposed to very large features, feature normalization is even more important. For this reason, Horizon includes a workflow that automatically analyzes the training dataset and determines the best transformation function and corresponding normalization parameters for each feature. Developers can override the estimation if they have prior knowledge of the feature that they prefer to use.
In the workflow, features are identified to be of type binary, probability, continuous, enum, quantile, or boxcox. A ``normalization specification'' is then created which describes how the feature should be normalized during training.
Although we pre-compute the feature transformation functions prior to training, we do not apply the feature transformation to the dataset until during training. At training time we create a PyTorch network that takes in the raw features and applies the normalization during the forward pass. This allows developers to quickly iterate on the feature transformation without regenerating the dataset. The feature transformation process begins by grouping features according to their identity and then processing each group as a single batch using vector operations.
\section{Data Understanding Tool}
One big challenge of applied RL is problem formulation. RL algorithms are theoretically designed on the Markov Decision Process (MDP) framework~\cite{bellman1957markovian} where some sort of long-term reward is optimized in a sequential setting. MDP tasks are defined by $(\mathcal{S}, \mathcal{A}, T, R)$ tuples where $\mathcal{S}$ and $\mathcal{A}$ refer to the state and action spaces; $T:\mathcal{S} \times \mathcal{A} \rightarrow \mathcal{S}$ refers to the state transition function, which can be stochastic; and $R:\mathcal{S} \times \mathcal{A} \rightarrow \mathbb{R}$ represents the reward function which maps a transition into a real value. Since this formulation can be unfamiliar to engineers inexperienced in RL, it is easy to accidentally prepare data that does not conform well to the MDP definition. Applying RL on ill-formulated problems is a costly process: (1) online testing RL models trained on wrongly defined environments can regress online metrics; (2) engineering time may be spent debugging and tuning the RL model training process for irrelevant factors such as hyper-parameters.
In order to quickly pre-screen the problem formulation and accelerate feature engineering iterations, we developed a data understanding tool. Using a data-driven, model-based method together with heuristics, it checks whether several important properties of the problem formulation conform to the MDP framework.
First, the tool learns a model about the formulated environment based on the same dataset to be used in RL training. While there have been extensive research in model-based RL~\cite{deisenroth2011pilco,nagabandi2018neural,finn2017deep,watter2015embed} in the line of modeling environments, we use a probabilistic generative model that is capable of handling high-dimensional input and stochasticity of state transitions and rewards, inspired by recent model-based work~\cite{ha2018world}. The chosen model is a deep neural network with the input as the current state and action. To handle possible stochasticity in rewards and transitions, the last layer of the neural network is set as a Gaussian Mixture Model (GMM) layer~\cite{bishop1994mixture,variani2015gaussian} such that the model outputs a Gaussian mixture distribution of next states and rewards rather than point estimates:
\begin{equation} \label{eqn:gmm}
P(s_{t+1}|s_{t}, a_{t}) = \sum\limits_{k} \pi_k \mathcal{N}({\mu}_k, {\Sigma}_k)
\end{equation}
We omit the expression of $P(r_t|s_t, a_t)$ since it has a similar form. In Eqn.~\ref{eqn:gmm}, $k$ is a hyper-parameter controlling the number of Gaussian mixtures, ${\mu}_k$ and ${\Sigma}_k$ are the mean and covariance matrix of each Gaussian mixture. $\pi_k$, ${\mu}_k$ and $\log({\Sigma}_k)$ are computed by the neural network layers before the GMM layer based on the input $s_t$ and $a_t$. Depending on our needs, the model can be learned by fitting state transitions and rewards either jointly or separately.
Once trained, the environment model can be used to examine problem formulation and data in many ways. One usage is to calculate feature importance and select only important features for RL training. We hypothesize that any feature with no importance in predicting state transitions or rewards should be discarded in order to reduce noise and increase learning efficiency. We use a heuristic that a feature's importance is the increase of the model loss due to masking the feature. The intuition is that if the feature is important, masking it would cause the model to perform much worse making the loss increase large. The current way to mask each feature is to set that feature to its mean value. Showing feature importance is also an effective way to help engineers examine datasets.
Another usage of the learned environment model is to evaluate problem formulation based on the definition of an MDP and heuristics. (1) We first check whether transitions are predictable by action and state features by looking at feature importance. An action or state feature is an important predictive feature if it increases the model loss when being masked, based on an environment model that fits only next states. An action suggested as not important means taking the action would not exert influence on transitions, thus warranting further investigation on the design of the action space. On the other hand, if none of the state features are important in predicting next states, it indicates there is no sequential nature to the problem. (2) We check if there exists any state feature both dependent on actions and predictive of rewards. This verifies the reward is indeed determined by both actions and states in a meaningful way. When no state feature is predictive of rewards the problem would not pass the check: such problems can be reduced to multi-arm bandits where we just need to estimate the return of each action. The check also invalidates problems that pass the previous checks, but where no state feature involved in transitions is relevant to the rewards. We compute how dependent a state feature is to the actions taken by varying actions in the data and observing the extent to which the state features in the next state changes, based on the predictions of the environment model that only fits next states. We compute how predictive a state feature is of rewards by computing feature importance on a model fitting only rewards.
Although the data understanding tool is based on several heuristics that are not expected to cover all invalid problem formulations, in practice it has helped users understand the problem formulation in early stages of the RL training loop and has been effective at catching many improperly defined problems.
\section{Model Implementations}
Horizon contains implementations of several deep RL algorithms that span to solve discrete action, very large discrete action, and continuous action domains. We also provide default configuration files as part of Horizon so that end users can easily run these algorithms on our included test domains (e.g. OpenAI Gym \cite{brockman2016openai}, Gridworld). Below we briefly describe the current algorithms supported in Horizon.
\subsection{Discrete-Action Deep Q-Network (Discrete DQN)}
For discrete action domains with a tractable number of actions, we provide a Deep Q-Network implementation \cite{mnih2015human}. We chose to include DQN in Horizon due to its relative simplicity and its importance as a building block for numerous algorithmic improvements \cite{hessel2017rainbow}. In addition, we provide implementations for several DQN improvements, including double Q-learning \cite{van2016deep}, dueling architecture \cite{wang2015dueling}, and multi-step learning \cite{sutton1998reinforcement}. We plan on continuing to add more improvements to our DQN model (distributional DQN \cite{bellemare2017distributional}, and noisy nets \cite{fortunato2017noisy}) as these improvements have been shown to stack to achieve state of the art results on numerous benchmarks \cite{hessel2017rainbow}.
\subsection{Parametric-Action Deep-Q Network (Parametric DQN)}
Many domains at Facebook have have extremely large discrete action spaces (more than millions of possible actions) with actions that are often ephemeral. This is a common challenge when working on large scale recommender systems where an RL agent can take the action of recommending numerous different pieces of content. In this setting, running a traditional DQN would not be practical. One alternative is to combine policy gradients with a K-NN search \cite{dulac2015deep}, but when the number of available actions for any given state is sufficiently small, this approach is heavy-handed. Instead, we have chosen to create a variant of DQN called Parametric-Action DQN, in which we input concatenated state-action pairs and output the Q-value for each pair. Actions, along with states, are represented by a set of features. The rest of the system remains as a traditional DQN. Like our Discrete-Action DQN implementation, we also have adapted the double Q-learning and dueling architecture improvements to the Parametric-Action DQN.
\subsection{Deep Deterministic Policy Gradients (DDPG) and Soft Actor-Critic (SAC)}
Other domains at Facebook involve tuning of sets of hyperparameters. These domains can be addressed with a continuous action RL algorithm. For continuous action domains we have implemented Deep Deterministic Policy Gradients (DDPG) \cite{lillicrap2015continuous} and Soft Actor-Critic (SAC) \cite{haarnoja2018soft}. DDPG was selected for its simplicity and familiarity, while SAC was selected due to its recently demonstrated SOTA performance on numerous continuous action domains.
Support for other deep RL algorithms will be a continued focus going forward.
\section{Training}
Once we have preprocessed data and have a feature normalization function for each feature, we can begin training. Training can be done using CPUs, a GPU, or multiple GPUs across multiple machines. We utilize the PyTorch multi-GPU functionality to do distributed training \cite{paszke2017pytorch}.
Using GPU and multi-GPU training we are able to train large RL models that contain hundreds to thousands of features across tens of millions of examples in a few hours (while doing feature normalization and counterfactual policy evaluation on every batch).
Typically, the initial RL policy is trained on off-policy data generated by a non-RL production policy. Once the first RL policy is trained and deployed to a fraction of production traffic, subsequent training runs use this on-policy training data. In practice we have found that A/B test results improve as the RL model moves from learning on off-policy data to on-policy data. Figure \ref{fig:metric_improve} shows the change in the metric value of interest during a real A/B test.
\begin{figure}[htp]
\centering
\includegraphics[width=0.42\columnwidth]{figures/metrics.png}
\caption{\textbf{Real RL model A/B Test Results.} The RL model (test) outperforms the non-RL model (control) on the push notification optimization task described in section \ref{notification_section}. The x-axis shows the progression of the metric being optimized by day. Note, the performance of the RL model starts out neutral vs. the control, but quickly exceeds as it re-trains daily on data generated by itself.}
\label{fig:metric_improve}
\end{figure}
Internally, we have recurring training jobs where models are updated on a daily frequency and training starts with the previous network weights and optimizer state (for stateful optimizers, e.g. Adam \cite{kingma2014adam}). Our empirical observations of performance improving as the RL policy learns from data generated by itself is inline with findings in literature. Specifically, recent literature has shown that off-policy RL aglorithims struggle significantly when learning from fixed batches of data generated under a seperate policy due to a phenomenon coined "extrapolation error" \cite{fujimoto2018off}. Extrapolation error is a phenomenon in which unseen state-action pairs are erroneously estimated to have unrealistic values. By retraining daily on self generated data, we mitigate this problem by forcing learning to be more "on-policy", thus improving the model performance.
\section{Model Understanding And Evaluation}
There are several features in Horizon that help engineers gain insight into each step of the RL model building loop (i.e. training, and evaluation). Below we describe the tools available at each step of the process:
\begin{itemize}
\item \textbf{Training:} Training metrics are surfaced that give insight into the stability and convergence of the training process.
\item \textbf{Evaluation:} Several well known counterfactual policy evaluation estimates compute the expected performance of the newly trained RL model.
\end{itemize}
\subsection{Training: TD-loss \& MC-Loss}
\textbf{Temporal difference loss (TD-loss)} measures the function approximation error. For example, in DQN, this measures the difference between the expected value of Q given by the bellman equation, and the actual value of Q output by the model. Note that, unlike supervised learning where the labels are from a stationary distribution, in RL the labels are themselves a function of the model and as a result this distribution shifts. As a result, this metric is primarily used to ensure that the optimization loop is stable. If the TD-loss is increasing in an unbounded way, we know that the optimization step is too aggressive (e.gs. the learning rate is too high, or the minibatch size is too small).
\textbf{Monte-Carlo Loss (MC-loss)} compares the model's Q-value to the logged value (the discounted sum of logged rewards). When the logged policy is the optimal policy (for example, in a toy environment), MC-loss is a very effective measure of the model's performance. Because the logged policy is often not the optimal policy, the MC-loss has limited usefulness for real-world domains. Similar to TD-loss, we primarily monitor MC-loss for extreme values or unbounded increase.
Because RL is focused on policy optimization, it is more useful to evaluate the policy (i.e. what action a model chooses) than to evaluate the model scores directly. Horizon has a comprehensive set of Counterfactual Policy Evaluation techniques.
\subsection{Evaluation: Counterfactual Policy Evaluation}
Counterfactual policy evaluation (CPE) is a set of methods used to predict the performance of a newly learned policy without having to deploy it online~\cite{wang2017optimal,bottou2013counterfactual,dudikdoubly,jiang2016doubly,thomas2016data}. CPE is important in applied RL as deployed policies affect the real world. At Facebook, we serve billions of people every day; deploying a new policy directly impacts the experience they have using Facebook. Without CPE, industry users would need to launch numerous A/B tests to search for the optimal model and hyperparameters. These experiments can be time-consuming and costly. With reliable CPE, this search work can be fully automated using hyperparameter sweeping techniques that optimize for a model's CPE score. CPE also makes an efficient and principled parameter sweep possible by combining counter-factual offline estimates with real-world testing.
Horizon includes implementations of the following CPE estimators that are automatically run as part of training:
\begin{itemize}
\item Step-wise direct method estimator
\item Step-wise importance sampling estimator~\cite{horvitz1952generalization}
\item Step-wise doubly-robust estimator~\cite{dudikdoubly}
\item Sequential doubly-robust estimator~\cite{jiang2016doubly}
\item Sequential weighted doubly-robust estimator~\cite{thomas2016data}
\item MAGIC estimator~\cite{thomas2016data}
\end{itemize}
The first three estimators were originally designed to evaluate polices in contextual bandit problems~\cite{auer2002nonstochastic,langford2008epoch}, the special cases of RL problems where the horizon of episodes is one. The step-wise direct method (DM) learns a reward function to estimate rewards that are not logged but expected to incur by the evaluated policy. The method suffers when the learned reward function has high bias. The step-wise importance sampling (IS) estimator~\cite{horvitz1952generalization} uses action propensities of logged and evaluated policies to scale logged rewards in order to correct for different action distributions between the two policies. The step-wise IS estimator tends to have high variance~\cite{dudikdoubly} and could be biased if logged action propensities are not accurate. The step-wise doubly-robust (DR) estimator~\cite{dudikdoubly} combines the ideas of the previous two methods: (1) the bias tends to be low as long as either logged action propensities or the learned reward function is accurate; (2) the variance tends to be lower than the step-wise IS estimator under reasonable assumptions (Section 4 in~\cite{dudikdoubly}). Due to these estimators' simplicity in the concept, we still compute them (averaging over steps) when evaluating longer episodes, though they will be biased.
The last three estimators are specifically designed for evaluating policies on longer horizons. The sequential DR estimator~\cite{jiang2016doubly} inherits the advantage from the DR method that a low bias can be achieved if either action propensities or the reward function is accurate. The estimator has also been adapted to use weighted importance sampling~\cite{thomas2016data}, which is considered to ``better balance it (the bias-variance trade-off) while maintaining asymptotic consistency''. In the same line of balancing the bias-variance trade-off, the MAGIC estimator~\cite{thomas2016data} combines the DR and DM in a way that directly optimizes the mean squared error (MSE).
Incorporating the aforementioned estimators into our platform's training pipeline provides us with two advantages: (1) all feature normalization improvements tailored to training are also available to CPE (2) users of our platform get CPE estimates at the end of each epoch which helps them understand how more training affects model performance. The CPE estimators in Horizon are also optimized for running speed. The implemented estimators incur minimal time overhead to the whole training pipeline.
One of the biggest technical challenges implementing CPE stems from the nature of how batch RL is trained. To decrease temporal correlation of the training data, which is needed for stable supervised learning, a pseudo i.i.d. environment is created by uniformly shuffling the collected training data \cite{mnih2015human}. However, the sequential doubly robust and MAGIC estimators both are built based on cumulative step-wise importance weights \cite{jiang2016doubly, thomas2016data}, which require the training data to appear in its original sequence. In order to satisfy this requirement while still using the shuffled pseudo i.i.d. data in training, we sample and collect training samples during the training workflow. At the end of every epoch we then sort the collected samples to place them back in their original sequence and conduct CPE on the collected data. Such deferral provides the opportunity to calculate all needed Q-values together in one run, heavily utilizing matrix operations. As a side benefit, querying for Q-values at the end of one epoch of training decreases the variance of CPE estimates as the Q-function can be very unstable during training. Through this process we are able to calculate reliable CPE estimations efficiently. Internally, end users get plots similar to Figure \ref{fig:value_cpe} at the end of training. In the open source release we surface CPE results in TensorboardX.
\begin{figure}[htp]
\centering
\includegraphics[width=1\columnwidth]{figures/cpe_plot.png}
\caption{\textbf{Value CPE Results.} As part of training, Horizon surfaces CPE results indicating the expected performance of the newly trained policy relative to the policy that generated the training data. In this plot we see relative value estimates (y-axis) for several CPE methods vs. training time (x-axis) on a real Facebook dataset. A score of 1.0 means that the RL and the logged policy match in performance. These results show that the RL model should achieve roughly 1.5x - 1.8x as much cumulative reward as the logged system. As the number of training epochs increases, the CPE estimates improve.}
\label{fig:value_cpe}
\end{figure}
\subsection{TensorboardX}
To visualize the output of our training process, we export our metrics to tensorboard using the TensorboardX plugin \cite{tensorboardx}. TensorboardX outputs tensors from pytorch/numpy to the tensorboard format so that they can be viewed with the Tensorboard web visualization tool.
\begin{figure}[htp]
\centering
\includegraphics[width=0.45\columnwidth]{figures/magic.png}%
\hspace{.1cm}
\includegraphics[width=0.45\columnwidth]{figures/weighted_dr.png}
\caption{\textbf{TensorboardX CPE Results.} Example TensorboardX counterfactual policy evaluation results on the CartPole-v0 environment. The x-axis of each plot shows the number of epochs of training and the y-axis shows the CPE estimate. While we only display two CPE methods here (MAGIC and Weighted Doubly Robust), several other CPE methods and loss plots are displayed in the final Tensorboard dashboard post-training. In these plots a score of 1.0 means that the RL and the logged policy match in performance. Here we see the RL model should achieve roughly 1.2x - 1.5x as much cumulative reward as the logged policy.}
\label{fig:tensorboardX}
\end{figure}
\section{Model Serving}
At Facebook, we serve deep reinforcement learning models in a variety of production applications.
PyTorch 1.0 supports ONNX \cite{exchange2018onnx}, an open source format for model inference. ONNX works by tracing the forward pass of an RL model, including the feature transformation and the policy outputs. The result is a Caffe2 network and a set of parameters that are serializable, portable, and efficient. This package is then deployed to thousands of machines.
At serving time, product teams run our RL models and log the possible actions, the propensity of choosing each of these actions, the action chosen, and the reward received. Depending on the problem domain, it may be hours or even days before we know the reward for a particular sample. Product teams typically log a unique key with each sample so they can later join the logged training data to other data sources that contain the reward. This joined data is then fed back into Horizon to incrementally update the model. Although all of our algorithms are off-policy, they are still limited based on the policy that they are observing, so it is important to train in a closed loop to get the best results. In addition, the data distribution is changing and the model needs to adapt to these changes over time.
\section{Real World Deployment: Notifications at Facebook}
\subsection{Push Notifications} \label{notification_section}
Facebook sends notifications to people to connect them with the most important updates when they matter, which may include interactions on your posts or stories, updates about your friends, joined groups, followed pages, interested events etc. Push notifications are sent to mobile devices and a broader set of notifications is accessible from within the app/website. It is primarily used as a channel for sending personalized and time sensitive updates. To make sure we only send the most personally relevant notifications to people, we filter notification candidates using machine learning models. Historically, we have used supervised learning models for predicting click through rate (CTR) and likelihood that the notification leads to meaningful interactions. These predictions are then combined into a score that is used to filter the notifications. For example, this score could look like:
\begin{gather*}
\scalebox{.9}{$
score = weight_1 * P(event_1) + weight_2 * P(event_2) + ...$}
\end{gather*}
This however, didn't capture the long term or incremental value of sending notifications. There can be some signals that appear long after the decision to send or drop is made or that can't be attributed directly to the notification.
We introduced a new policy that uses Horizon to train a Discrete-Action DQN model for sending push notifications to address the problems above. The Markov Decision Process (MDP) is based on a sequence of notification candidates for a particular person. The actions here are sending and dropping the notification, and the state describes a set of features about the person and the notification candidate. There are rewards for interactions and activity on Facebook, with a penalty for sending the notification to control the volume of notifications sent. The policy optimizes for the long term value and is able to capture incremental effects of sending the notification by comparing the Q-values of the send and drop action. Specifically, the difference in Q-values is computed and passed into a sigmoid function to create an RL based policy:
\vspace{-0.2cm}
\begin{gather*}
\scalebox{.9}{$
\left.
\begin{cases}
send; & \text{if } sigmoid(Q(send) - Q(drop)) \geq threshold \\
drop; & \text{if } sigmoid(Q(send) - Q(drop)) < threshold \\
\end{cases}
\right\}
$}
\end{gather*}
If the difference between $Q(send)$ and $Q(drop)$ is large, this means there is significant value in sending the notification. If this difference is small, it means that sending a notification is not much better than not sending a notification.
As an implementation trick, we use a proportional integral derivative (PID) controller to tune the threshold used in the RL policy. This helps to keep the RL policy's action distribution inline with the previous production policy's action distribution.
The model was incrementally retrained daily on data from people exposed to the model with some action exploration introduced during serving. The model is updated with batches of tens of millions of state transitions. We observed this to help online usage metrics as we are doing off-policy batch learning. The benefit of this is shown in figure \ref{fig:metric_improve}.
We observed a significant improvement in activity and meaningful interactions by deploying an RL based policy for certain types of notifications, replacing the previous system based on supervised learning.
\subsection{Page Administrator Notifications}
In addition to Facebook users, page administrators also rely on Facebook to provide them with timely updates about the pages they manage. In the past, supervised learning models were used to predict how likely page admins were to be interested in such notifications and how likely they were to respond to them. Although the models were able to help boost page admins' activity in the system, the improvement always came at some trade-off with the notification quality, e.g. the notification click through rate (CTR).
With Horizon, a Discrete-Action DQN model is trained to learn a policy to determine whether to send or not send a notification based on the state represented by hundreds of features. The training data spans multiple weeks to enable the RL model to capture page admins' responses and interactions to the notifications with their managed pages over a long term horizon. The accumulated discounted rewards collected in the training allow the model to identify page admins with long term intent to stay active with the help of being notified. After deploying the DQN model, we were able to improve daily, weekly, and monthly metrics without sacrificing notification quality.
\subsection{More Applications of Horizon}
In addition to making notifications more relevant on our platform, Horizon is applied by a variety of other teams at Facebook. The 360-degree video team has applied Horizon in the adaptive bitrate (ABR) domain to reduce bitrate consumption without harming people's watching experience. This was due to more intelligent video buffering and pre-fetching.
While we focused our case studies on notifications, Horizon is a horizontal effort in use or being explored to be used by many organizations within Facebook.
\section{Future Work}
The most immediate future additions to Horizon will be new models \& model improvements. We will be adding more incremental improvements to our current models and plan on continually adding the best performing algorithms from the research community.
We welcome community pull requests, suggestions, and feedback.
\nocite{langley00}
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{"url":"https:\/\/lavelle.chem.ucla.edu\/forum\/viewtopic.php?f=129&t=41933","text":"## Proving the work equation\n\n$w=-P\\Delta V$\nand\n$w=-\\int_{V_{1}}^{V_{2}}PdV=-nRTln\\frac{V_{2}}{V_{1}}$\n\nModerators: Chem_Mod, Chem_Admin\n\nJeremyPark14B\nPosts: 29\nJoined: Fri Sep 28, 2018 12:19 am\n\n### Proving the work equation\n\nWill we be required to know \/ explain the integral justification for w = P delta V?\n\n705170809\nPosts: 60\nJoined: Fri Sep 28, 2018 12:26 am\nBeen\u00a0upvoted: 1 time\n\n### Re: Proving the work equation\n\nI believe that all the derivations of those formulas are fair game on the midterm since Professor Lavelle went over it in class.\n\nchaggard\nPosts: 37\nJoined: Fri Sep 28, 2018 12:19 am\n\n### Re: Proving the work equation\n\nIf you remember that it is always the integral of V1 to V2, and depending on the question, whatever are constants you move to the outside of the integral sign, then you should be fine.\n\nReturn to \u201cCalculating Work of Expansion\u201d\n\n### Who is online\n\nUsers browsing this forum: No registered users and 1 guest","date":"2019-12-14 11:56:10","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 2, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.6953572630882263, \"perplexity\": 4237.665427325474}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": false}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2019-51\/segments\/1575540586560.45\/warc\/CC-MAIN-20191214094407-20191214122407-00021.warc.gz\"}"}
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Bad Religion es una banda estadounidense de punk rock fundada en 1980 en el sur de California por Greg Graffin (voz), Jay Bentley (bajo), Jay Ziskrout (batería) y Brett Gurewitz (guitarra), a la que se le adjudica haber guiado el resurgimiento del punk rock en el mainstream, así como haber influenciado a lo largo de su trayectoria a un gran número de músicos del punk y del rock.
La banda ha contado con diferentes alineaciones a lo largo de sus años de existencia, siendo Graffin el único miembro que ha sido constante; no obstante, la banda cuenta en el con tres de sus miembros originales: Greg Graffin, Brett Gurewitz y Jay Bentley.
Ha lanzado diecisiete álbumes de estudio, dos EP, tres álbumes compilatorios, un álbum en directo y tres DVD. Su álbum Suffer ha sido valorado por algunos críticos como el álbum de punk rock más relevante de todos los tiempos, aunque nunca tuvo un puesto de popularidad en la lista Billboard. En 1993 la banda alcanzó un puesto de cartelera con su álbum Recipe for Hate, ese acontecimiento les dio fama mientras les aseguró el puesto número 14 de la lista Heatseekers de la Billboard de ese año. Su mayor éxito vino con Stranger than Fiction el primer álbum con el que consiguieron el disco de oro en Estados Unidos, desprendiéndose de él reconocidos singles como «21st Century (Digital Boy)» e «Infected». La banda se mantuvo cosechando éxitos de manera más discreta en su nueva discográfica, Warner, sin Brett Gurewitz, quien se retirara en 1994 por motivos personales. El 2001 fue un año importante para la banda ya que marcó la vuelta de Gurewitz y el regreso de Bad Religion a Epitaph, discográfica de música independiente de la cual es el dueño. Desde este «renacer» para la banda, se ha mantenido con la misma alineación durante más de diez años seguidos y cinco álbumes.
Son conocidos particularmente por su sofisticado uso del estilo, metáfora, vocabulario, uso de íconos y armonías vocales (los denominados por la banda como oozin' aahs); esto último consagrándolos como pioneros del naciente hardcore melódico. Sus letras suelen ser reflexivas en torno a sentimientos personales, ideologías de vida y responsabilidad social.
Historia
Orígenes (1979-1985)
Los orígenes de Bad Religion se remontan a finales de la década de los años 1970, cuando unos adolescentes del instituto El Camino Real High School, situado en el angelino distrito de Woodland Hills, en el Valle de San Fernando, coinciden en sus aficiones musicales y deciden formar una banda con influencias del punk del momento de bandas como The Adolescents, Black Flag o The Germs.
El grupo en ese momento lo componían Greg Graffin (voz), Jay Ziskrout (batería), Brett Gurewitz (guitarra) y Jay Bentley (bajo). La escena punk, pese al éxito de grupos antes mencionados como Black Flag o los históricos Ramones y Sex Pistols, aún era complicada para las bandas jóvenes que emergían y pedían una oportunidad. Por eso, Brett Gurewitz, alias Mr. Brett, se aventuró en la creación de un sello discográfico independiente con el que poder lanzar los discos de Bad Religion y, de paso, poder ayudar y a las bandas punk rock que comenzaban en la música. Gurewitz recuerda que la situación era «una escena gris en la que solo había bandas de colegio; por eso decidimos escribir nuestra propia historia y, de paso, ayudar a otros a escribirla. Porque no teníamos cabida, tan solo había unos pocos sellos de punk que estaban en la frontera entre lo que hacíamos y el pasado. Pero, a la vez, también había un caldo de cultivo de bandas que pedían a gritos editar sus primeros siete pulgadas. Eso es lo que nos terminó de animar».
Gurewitz fundó Epitaph, sin saber en ese momento el punto de inflexión que supondría ese modesto sello en el mundo del punk rock y del rock alternativo, estadounidense sobre todo, en el futuro. La banda graba su primer trabajo, un EP autotitulado Bad Religion, compuesto por seis canciones y lanzado mediante Epitaph en 1981. Tras ese trabajo, la banda graba su primer álbum de estudio, How Could Hell Be Any Worse?, en el que contaría con la colaboración de uno de los futuros guitarristas, Greg Hetson, que aportó un solo de guitarra en el tema Part III. En aquel momento, Hetson era guitarrista de Circle Jerks, pero compatibilizaría ambos grupos en el futuro. Durante la grabación del disco debut, comienzan a aparecer lo que sería una de las constantes en la banda californiana: los cambios en la formación. Jay Ziskrout deja la banda, tras haber grabado 8 canciones, y es sustituido por Pete Finestone, quien graba las 6 restantes. El disco tuvo una buena acogida, vendiendo más de 10 000 copias y, lo más importante, reclutando una importante legión de fanes.
En 1983 comienzan a introducir nuevos sintetizadores y teclados en el segundo disco, Into the Unknown, que les llevan a un sonido más progresivo. Sus seguidores no encajaron nada bien este cambio en la música de Bad Religion y criticaron muy duramente el álbum. Además, la formación había vuelto a cambiar, ya que Finestone dejó la banda y en su lugar entró Davy Goldman en la batería. También Jay Bentley dejó el bajo y fue sustituido por Paul Dedona. Comienzan también las primeras crisis internas y todo provoca que la banda sufra su primera ruptura. El disco está fuera del mercado y las ventas no superaron a las de How Could Hell Be Any Worse?. Un año más tarde, en 1984, Gurewitz deja la banda para tratarse de su adicción a las drogas y es reemplazado por Hetson, que ya trabajó en el disco debut de la formación. Este habla con Graffin y le propone volver a los estudios de grabación para grabar su segundo EP, Back to the Known. En este trabajo Tim Gallegos entra a ocupar el bajo en lugar de Dedona, y Finestone vuelve a la batería. Des 1984 a 1988 no se produce ninguna novedad en cuanto a grabación de nuevo material pero Finestone vuelve a marchar, es sustituido por John Albert y este, a su vez, por Lucky Lehrer.
Reunión y primer auge de Bad Religion (1986-1993)
Bentley, Finestone y Gurewitz vuelven a la banda en 1986 y se prepara la grabación de su tercer álbum, Suffer. Este disco sería lanzado en 1988 mediante Epitaph y es uno de los primeros éxitos de la banda y del movimiento punk rock californiano de finales de los años 1980. Representó un punto inflexión en el punk, a partir de una personal fusión de punk y melodías folk, Bad Religion se erigieron como creadores de un nuevo género, el hardcore melódico, que sería más adelante imitado por numerosas bandas de California y, más tarde, del resto del mundo. Al éxito de Suffer le siguieron en 1989 No Control y Against the Grain, en 1990, completando una trilogía y colocándolos en el número 1 de las bandas punk rock del momento y del hardcore melódico. En 1992 la banda grabó Generator, con algunos cambios como canciones más largas y más trabajadas y también se produjo la enésima y definitiva marcha de Finestone en la batería, ocupándola Bobby Schayer. Sin embargo, esta sería la última fuga de Finestone de la banda, ya que no volvió más.
Recipe for Hate, el séptimo álbum de la banda, se lanzó en 1993 y sería el último con Epitaph. La banda firmó por Atlantic y el disco fue distribuido por ambos sellos. Como novedad destacar el éxito del sencillo "Watch It Die", con la colaboración de Eddie Vedder, líder de Pearl Jam. El álbum obtuvo el decimocuarto lugar en el Billboard estadounidense. Sin embargo, los seguidores de Bad Religion les acusaron de «vendidos» por haberse marchado a una multinacional, Atlantic Records, que les aseguraba una mejor distribución, ya que en ese momento Epitaph estaba sobrecargada y ocupada con las bandas que tenía contratadas como NOFX, Rancid, Offspring o Pennywise. Pero los seguidores no lo vieron así y se lo reprocharon duramente. En ese mismo año, la banda grabó una canción aparte, "Leaders and Followers", para la banda sonora de la película Clerks.
Marcha de Gurewitz y de Epitaph (1994-2001)
El 1994 sería un año caliente en Bad Religion y en el punk rock. La banda lanzó Stranger than Fiction, uno de los mejores álbumes de la agrupación y del punk rock y hardcore melódico. Este sería el último álbum de grabación en el que trabajase Gurewitz en su primera, y única marcha, y el único disco de Bad Religion que recibió el disco de oro de la RIAA tras haber despachado medio millón de copias. Stranger Than Fiction cuenta también con aportaciones notables del mundo del punk rock como Tim Armstrong de Rancid y Jim Lindberg de Pennywise. Mr. Brett decidió marcharse de la banda para dedicarse exclusivamente a Epitaph, en pleno éxito con Smash, de The Offspring, el disco más vendido de la historia de la música por un sello independiente. Los seguidores de Bad Religion no le perdonaron su marcha y lo acusaron de abandonar por dinero gracias al éxito de la banda de Dexter Holland. Brian Baker, notable músico punk, sustituyó a Gurewitz tras haber pasado por bandas como Minor Threat o Dag Nasty. Además, en 1995 Epitaph publicó por su cuenta el recopilatorio All Ages, lo que provocó el primer desencuentro entre Brett y sus antiguos compañeros.
A partir de este momento, la capacidad creativa de la banda se vio seriamente afectada y todo el peso creativo recayó en Graffin. El resultado fue The Gray Race, en 1996. Las discretas ventas fueron suplidas por una espectacular gira mundial tras la cual lanzaron mediante Epic Records, en 1997, Tested, un álbum en directo que repasa lo mejor de la misma. Un año más tarde salió a la luz No Substance, décimo álbum de la banda y que tampoco gozó de éxito ni de buenas cifras.
Con The New America y a las puertas del siglo XXI, la banda comienza a retomar el vuelo. En primer lugar marchan a grabar este álbum a Kauai, Hawái y se empiezan a observar indicios de reconciliación con Mr. Brett, que colabora con la banda en una canción del álbum. The New America supondrá, también, el último disco con Atlantic. En 2001, Bad Religion vuelve a ingresar en Epitaph, y se retira el batería Bobby Schayer por una lesión en el hombro que lo apartaría definitivamente de la música. Lo sustituye el joven Brooks Wackerman, que había sido batería de The Vandals, Infectious Grooves y Suicidal Tendencies.
Regresos de Gurewitz y Epitaph (2001-presente)
En 2002 salió a la venta The Process of Belief, ya con Epitaph y Mr. Brett de nuevo en la formación, lo que provoca que la expectación por este disco sea muy alta, así como por tener los ingredientes para volver al antiguo y añorado sonido de Bad Religion. Gurewitz admite: «tuve que dejar Bad Religion porque mi vida era una locura. He regresado porque necesitaba hacer música y tenía un vacío en mi vida. Afortunadamente el grupo estaba prepararado para el reencuentro. Ahora mi vida personal está en orden y tengo la habilidad para estar en una banda de nuevo». En 2004 la banda publicó su decimotercer álbum de estudio, The Empire Strikes First, que logra el puesto 40 en el Billboard 200 de ese año. También en 2004 la banda participa en el Warped Tour junto a varios de los grupos más importantes del punk rock y del rock alternativo estadounidense del momento, se embarcan en una gira norteamericana con Rise Against y visitan Brasil junto a Pennywise.
En 2006 la banda publica su primer DVD, Live at the Palladium, que recoge dos días de concierto en la prestigiosa sala Palladium de Hollywood, entrevistas con la banda, fotos exclusivas y vídeos grabados durante sus primeros años de existencia. Un año después, la banda californiana lanza New Maps of Hell, decimocuarto álbum de estudio, con el éxito del sencillo «Honest Goodbye».
Bad Religion comenzó a componer su decimoquinto álbum, The Dissent of Man, cuyo lanzamiento se realizó en el año 2010 y el 22 de enero de 2013 se publicó el decimosexto álbum de estudio de la banda, titulado True North.
El 29 de octubre de 2013, Bad Religión lanzó su primer disco navideño, Christmas Songs.
El 3 de mayo de 2019 la banda publica el álbum Age of Unreason y acto seguido se embarca en una gira europea dentro del cartel del festival itinerante Punk In Drublic, promovido por sus contemporáneos NOFX. En la grabación del mismo ya participan Mike Dimkich y Jamie Miller a la guitarra y batería respectivamente.
Logo
El logotipo de Bad Religion ha sido llamado por los fanes como «Crossbuster». Cuenta con una cruz de color negro con una señal de prohibición de color rojo sobre ella. Fue creado por el guitarrista Brett Gurewitz que simplemente la dibujó en un trozo de papel y se la mostró al resto de la banda. Brett pensó que sería una buena forma de molestar a sus padres.
En el documental Along the Way, el líder Greg Graffin afirma que lamenta la elección de este símbolo ya que puede llegar a evitar que personas religiosas se beneficien del mensaje de la banda. Cuando se le pregunta al bajista Jay Bentley al respecto en el documental, afirma que el símbolo solo tenía la intención de «joder a nuestros padres», que era «algo fácil de poner en nuestras camisetas y también para los niños y adolescentes al pintar con aerosol en las paredes» y que cuando la gente le pregunta que significa responde «lo que tú creas que significa». El guitarrista Greg Hetson afirma en el documental que representa la lucha contra lo establecido. Brian Baker, quien se unió a la banda más tarde lo resume así: «El nombre de Bad Religion y el logotipo de Crossbuster se inició en la mente de dos jóvenes de 15 años que estaban tratando de encontrar el nombre más ofensivo. No se trata de personas que pensaban que en veinte años estarían haciendo entrevistas».
El logotipo también se usó en las portadas de sus primeros EP de 1981: en su álbum homónimo y en 1985 en Back to the Known, también en el disco New Maps Of Hell (en el dibujo del CD) y se puede encontrar en otros álbumes incluyendo a Suffer (en la parte posterior de la camiseta del niño en llamas), en No Substance (en el pecho derecho de Kristen Johnston),
en The Process of Belief (en el interior del folleto hay un trozo pequeño mezclado con todos los símbolos) y en 30 Years Live (en el cero del número 30).
Miembros
Línea de tiempo
Miembros
Greg Graffin: voz principal, teclados
Brett Gurewitz: guitarra, coros
Mike Dimkich: guitarra
Brian Baker: guitarra, coros
Jay Bentley: bajo, coros
Jamie Miller: Batería
Miembros anteriores
Greg Hetson: guitarra, coros
Paul Dedona: bajo
Tim Gallegos: bajo
Jay Ziskrout: batería
Davy Goldman: batería
John Albert: batería
Lucky Leher: batería
Pete Finestone: batería
Bobby Schayer: batería
Brooks Wackerman: batería
Discografía
Álbumes de estudio
{| border="2" cellpadding="4" cellspacing="0" style="margin: 1em 1em 1em 0; background: #f9f9f9; border: 1px #aaa solid; border-collapse: collapse; font-size: 95%;width: 70%;"
|-
!style="background: #f2f2f2;"|Año
!style="background: #f2f2f2;"|Álbum
!style="background: #f2f2f2;"|Posición en EE.UU.
!style="background: #f2f2f2;"|Discográfica
|-
| 1981
| How Could Hell Be Any Worse?
| Sin posición
| Epitaph
|-
| 1983
| Into the Unknown
| Sin posición
| Epitaph
|-
| 1988
| Suffer
| Sin posición
| Epitaph
|-
| 1989
| No Control
| Sin posición
| Epitaph
|-
| 1990
| Against the Grain
| Sin posición
| Epitaph
|-
| 1992
| Generator
| Sin posición
| Epitaph
|-
| 1993
| Recipe for Hate
| 14 (Heatseekers)
| Epitaph / Atlantic
|-
| 1994
| Stranger than Fiction| 87
| Atlantic
|-
| 1996
| The Gray Race| 56
| Atlantic
|-
| 1998
| No Substance| 78
| Atlantic
|-
| 2000
| The New America| 88
| Atlantic
|-
| 2002
| The Process of Belief| 49
| Epitaph
|-
| 2004
| The Empire Strikes First| 40
| Epitaph
|-
| 2007
| New Maps of Hell| 35
| Epitaph
|-
| 2010
| The Dissent of Man| 35
| Epitaph
|-
| 2013
| True North| 19
| Epitaph
|-
| 2019
| Age of Unreason| ??
| Epitaph
|}
EP
Bad Religion (1981)
Back to the Known (1984)
Christmas Songs (2013)
Recopilaciones
'''80-'85 (1991)
All Ages (1995)
Punk Rock Songs (The Epic Years) (2002)
Grabaciones en directo
Tested (1997)
30 Years Live (2010)
Vídeos (DVD)
Along the Way. VHS/DVD (1990)
Big Bang. VHS (1991)
The Riot. DVD (2000)
Live at the Palladium. DVD (2006)
Véase también
Punk-o-Rama
Referencias
Enlaces externos
Página web oficial de Bad Religion
Bad Religion Tribute Todo sobre Bad Religion
The Bad Religion Page Página no oficial de fanes reconocida por Bad Religion, con toda la información sobre la banda y su actividad. Enlaces a maquetas de versiones hechas por fanes.
Manifiesto Punk Escrito por el cantante Greg Graffin, traducido al castellano. Parte de una colección de ensayos de análisis sociocultural que pueden leerse en inglés en la web de Bad Religion
Biografía, discografía, wallpapers, fotos de Bad Religion Textos de Greg Graffin traducidos al castellano, como ser o no ser punk o su clásico manifiesto
Bad Religion
Música y política
Artistas de Atlantic Records
Artistas de Epitaph Records
Artistas de Sympathy for the Record Industry
Grupos de música de California
Grupos de rock de California
Grupos de música de Los Ángeles
Grupos de punk rock de Estados Unidos
Grupos de skate punk
Grupos de hardcore punk de Estados Unidos
Grupos de hardcore melódico
Grupos de música de los años 1980
Grupos de música de los años 1990
Grupos de música de los años 2000
Grupos de música de los años 2010
Grupos de música de los años 2020
Grupos de música formados en 1980
Grupos de música formados en los años 1980
|
{
"redpajama_set_name": "RedPajamaWikipedia"
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| 1,923
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I found this wedding photography competition and knew I had to pass it along to all of you! Whether or not any of these are your style, they are definitely worth checking out!
Below is one of my favorites, but then again, I'm a sucker for the father/daughter dance!
|
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"redpajama_set_name": "RedPajamaC4"
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| 7,684
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us toll free: 1-800-948-5563international: +1 (843) 849-0283
Books Tell You Why, Inc.
Legendary Authors
V. S. Naipaul
All orders shipped to destinations within the United States will ship free of charge per standard USPS mail; typical delivery times are between 5 and 14 business days. International orders ship free per standard air mail for order amounts above $500. Expedited shipping options are also available.
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Collector's Resources
The Caldecott Medal is awarded annually by the Association for Library Service to Children, a division of the American Library Association, to the artist of the most distinguished American picture book for children published that year. It was named in honor of nineteenth-century English illustrator Randolph Caldecott. Together with the Newbery Medal, it is the most prestigious American children's book award.
See a complete list of Caldecott Medal winners.
Caldecott Medal [x]
The Hello, Goodbye Window - 1st Edition/1st Printing
Juster, Norton
Illustrated by Chris Raschka. [New York]: Michael Di Capua Books/Hyperion Books for Children, 2005. Laminated Boards. First Edition; First Printing; Signed by Author & Illustrator. 4to ; [32] pages. A..... (Book #22575) More
This Is Not My Hat
Klassen, Jon
Illustrated by Jon Klassen. Somerville, MA: Candlewick Press, 2012. Hardcover. First Edition; Third Printing; Signed by Author. Oblong 8vo; [32] pages. A beautiful later printing of the first edition in..... (Book #29999) More
This Is Not My Hat - 1st Edition/1st Printing
Illustrated by Jon Klassen. Somerville, MA: Candlewick Press, 2012. Hardcover. First Edition; First Printing; Signed by Author. Oblong 8vo; [32] pages. A first printing of the first edition in Fine..... (Book #22230) More
Illustrated by Jon Klassen. Somerville, MA: Candlewick Press, 2012. Hardcover. First Edition; First Printing; Signed by Author. Oblong 8vo. A first printing of the first edition in Fine condition, little..... (Book #28012) More
Illustrated by Jon Klassen. Somerville, MA: Candlewick Press, 2012. Hardcover. First Edition; First Printing. Oblong 8vo; [32] pages. A beautiful first printing of the first edition in unread Fine condition..... (Book #29903) More
Illustrated by Jon Klassen. Somerville, MA: Candlewick Press, 2012. Hardcover. First Edition; First Printing; Signed by Author. Oblong 8vo; [32] pages. A beautiful first printing of the first edition in..... (Book #29910) More
They Were Strong And Good - 1st Edition/1st Printing
Lawson, Robert
Illustrated by Robert Lawson. New York: The Viking Press, 1940. Cloth. First Edition; First Printing. 4to; [72] pages. A beautiful first edition/first printing in Fine condition in Very Good dust-jacket..... (Book #29736) More
Always Room For One More
Leodhas, Sorche Nic [; LeClaire Gowans Alger]
Illustrated by Nonny Hogrogian. New York: Holt, Rinehart and Winston, c1965. Cloth. Signed by Illustrator. Oblong 8vo; [32] pages. A charming Holt Reinforced edition in a later, early 70s printing..... (Book #29458) More
Black And White - 1st Edition/1st Printing
Illustrated by David Macaulay. Boston: Houghton Mifflin Company, 1990. 1/4 Cloth. First Edition; First Printing. 4to ; [32] pages. A handsome first edition/first printing in Fine condition in Near Fine..... (Book #22091) More
Illustrated by David Macaulay. Boston: Houghton Mifflin Company, 1990. 1/4 Cloth. First Edition; First Printing. 4to ; [32] pages. A handsome first edition/first printing in Fine condition in pictorial dust-jacket..... (Book #22092) More
Illustrated by David Macaulay. Boston: Houghton Mifflin Company, 1990. 1/4 Cloth. First Edition; First Printing. 4to; [32] pages. A handsome first edition/first printing in Fine condition in alike dust-jacket. Gray..... (Book #22094) More
Illustrated by David Macaulay. Boston: Houghton Mifflin Company, 1990. 1/4 Cloth. First Edition; First Printing; Signed by Author. 4to ; [32] pages. An attractive first printing of the first edition..... (Book #29491) More
Mirette On The High Wire - 1st Edition/1st Printing
Illustrated by Emily Arnold McCully. New York: G. P. Putnam's Sons, 1992. Laminated Boards. First Edition; First Printing; Signed by Author & Illustrator. 4to ; [32] pages. A beautiful first..... (Book #22104) More
Illustrated by Emily Arnold McCully. New York: G. P. Putnam's Sons, 1992. Laminated Boards. First Edition; First Printing. 4to ; [32] pages. A beautiful first edition/first printing, in Fine condition..... (Book #29487) More
The Egg Tree
Milhous, Katherine
Illustrated by Katherine Milhous. New York: The Junior Literary Guild, Charles Scribner's Sons, 1950. Cloth. Small 4to; [32] pages. An attractive Junior Literary Guild edition in Fine condition, bound in..... (Book #26574) More
The Funny Little Woman - 1st Edition/1st Printing
Mosel, Arlene
Illustrated by Blair Lent. New York: E. P. Dutton and Company, Inc., c1972. Cloth. First Edition; First Printing. Square 4to; [40] pages. A charming first edition/first printing, end papers cracked..... (Book #29445) More
Ashanti To Zulu; African Traditions - 1st Edition/1st Printing
Musgrove, Margaret
Illustrated by Leo and Diane Dillon. New York: The Dial Press, c1976. Hardcover. First Edition; First Printing. 4to; [32] pages. A charming first printing of the first edition in Fine..... (Book #29792) More
Sam, Bangs & Moonshine
Ness, Evaline
Illustrated by Evaline Ness. New York, Chicago, San Francisco: Holt, Rinehart and Winston, c1966. Hardcover. Signed by Author. Small 4to; [44] pages. A beautiful early edition, in pictorial boards in..... (Book #29895) More
The Lion & The Mouse - 1st Edition/1st Printing
Pinkney, Jerry
Illustrated by Jerry Pinkney. New York: Little, Brown Books for Young Readers, 2009. Hardcover. First Edition; First Printing; Signed by Author. Oblong 4to; [32] pages. A beautiful first edition/first printing..... (Book #19582) More
Read MoreThe Hello, Goodbye Window - 1st Edition/1st Printing
Tranströmer, Tomas
17 Dikter - 1st Edition/1st Printing
Read More17 Dikter - 1st Edition/1st Printing
Girl with a Pearl Earring - 1st Edition/1st State
Read MoreGirl with a Pearl Earring - 1st Edition/1st State
Gilead - True 1st Edition/1st Printing
Read MoreGilead - True 1st Edition/1st Printing
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|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 6,113
|
Q: Versioning concept for records with relationships (foreign key) [Database] With the versioning concept of having a extra history/revision table for each table, where you want to keep track of the changes, I am wondering how to handle the relationships (foreign keys)?
Example:
Table: T_Shelf
ID, Name
Table: T_Inventory
ID, Item, FK_T_Shelf_ID
Table: T_Shelf_Rev
ID, ID_T_Shelf, Name, Date_Modified
Table: T_Inventory_Rev
ID, ID_T_Inventory, Item, (FK_T_Shelf_ID or FK_T_Shelf_Rev_ID), Date_Modified
Do I link the foreign key to the corresponding history table? Or does the approach does not work at all with relation databases?
A: Model them like so:
CREATE TABLE t_shelf (
shf_surrogate_id INTEGER NOT NULL
DEFAULT HASH(shf_business_id,shf_valid_from) NOT NULL PRIMARY KEY
, shf_business_id INTEGER NOT NULL
, shf_valid_from DATE NOT NULL
, shf_valid_to DATE NOT NULL
, shf_name VARCHAR(32)
)
CREATE TABLE inventory (
inv_surrogate_id INTEGER NOT NULL
DEFAULT HASH(inv_business_id,inv_valid_from) NOT NULL PRIMARY KEY
, shf_surrogate_id INTEGER NOT NULL FOREIGN KEY REFERENCES t_shelf
, inv_business_id INTEGER NOT NULL
, inv_valid_from DATE NOT NULL
, inv_valid_to DATE NOT NULL
, inv_item VARCHAR(32)
);
Do not separate stem and version as you are suggesting.
The valid_to date value of the currently active record is at 9999-12-31.
If you need details on how to handle this type of model - just answer here.
Some databases offer a HASH() function that returns an integer based on one or more input expressions, comma separated. I'm using that here. Otherwise, you'd be stuck to using a database sequence object.
|
{
"redpajama_set_name": "RedPajamaStackExchange"
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| 5,955
|
Mandarin-speaking butler bots heading to US real estate
Singou Technology and Juwai.com's Butler 1 robot is built for service, affordability and approachability
Photo by 수안 최 on Unsplash
Lost for words when a Chinese buyer presents themselves to you because you don't speak the language?
A robot called "Butler 1″ may be the answer. Chinese international property portal Juwai.com is partnering with Macau-based tech startup Singou Technology to bring Mandarin-speaking robots to U.S. real estate events later this year.
"The robot is essentially a carrier that lets our AI consumer service engine be present in real estate sales offices anywhere in the world," Juwai.com CEO Carrie Law told Inman. "The robot has the same AI brain and intelligence as our chatbot."
The Butler 1 robot stands 4 feet, 7 inches tall, according to Dr. Hon Chi Tin, chief executive officer of Singou Technology. Hon told Inman the robot is more approachable and affordable than other existing Singou models.
"A robot is superior to a fixed device, smart speaker or smart furniture," Hon said. "A robot has all the same benefits, plus the great advantage of being able to move and approach people just like another person would."
Earlier models of the Singou robots have so far been used to help provide security at large organizations such as universities and convention centers. They have also been used to help monitor the elderly living on their own in their homes.
Butler 1
The first Butler 1 is expected to arrive in the U.S. by May and will cost close to $2,000, according to a press release issued by Juwai.
During the training period, early robots will be used at international property industry events in China and showrooms and offices in the U.S., Australia, Canada, Malaysia and Singapore, these experiences adding to the robot's AI data.
This summer, Singou and Juwai will be training the Singou AI engine using the data and knowledge that Juwai has gathered in its five-year history of working with international Chinese buyers.
The data crunch should also improve Juwai's chatbot features and the responses its consumer service team provides in Shanghai to international property buyers, they said.
The number of robots that come to the U.S. will depend on the demand, said Juwai. China "installed" 90,000 industrial robots between 2010 and 2015, according to Machine Design magazine. China is expected to install 160,000 robots next year, many of them destined for factories, but butler bots are being built in even greater quantities, Juwai said.
Juwai is the exclusive international property partner of Tencent, the Chinese internet giant and operator of China's most popular messaging app, WeChat. Juwai.com has more than 2 million Chinese-speaking users and showcases 2.5 million listings from 89 countries.
Email Gill South
5 ways to make your chatbot seem more human
How an agent is using her Asian roots to serve international buyers
Chinese real estate investment in US predicted to drop in 2017, according to Juwai.com
More in Agent
Bobby Darin's one-time Beverly Hills home listed for $8.5M
New text and email 'gift card' scam targets agents directly
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
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| 381
|
The Influence Of Advertising In Advertising
Watching TV, listening to the radio, and streaming funny videos on the internet, these activities are big in American culture. However, think about this, how many times while watching a favorite television show does it take a break to commercial? Also, how long are those commercial breaks? Advertising companies want to get their product out there in anyway they can. Whether it be through cellular devices, televisions, and radios. Author of "Champagne Taste, Beer Budget", Delia Cleveland, explains her difficulties being dragged in my designer brands and how it's affected her life. It is as if marketers are taking over technology with commercials filled with glitz and glam. In an article written by Jay Chait, he defines the truth behind the …show more content…
Taglines are claimed to draw major attention to the product that the company is selling. A great slogan identifies the brand and is memorable."Advertising catchphrases are a dime a dozen. But only the best withstand the test of time and enter the public lexicon. "Good to the Last Drop" is one of the immortal ones." (Saturday Evening Post). Popular slogans known by thousands people are Nike:Just do it, Dunkin Doughnuts: America runs on Dunkin, and more. Many coffee drinker would remember the phrase, "Good to the Last Drop" and think of Maxwell House Coffee. According to The Saturday Evening Post the origin of The Maxwell House slogan goes way back to 1907. The phrase was coined by Theodore Roosevelt at President Andrew Jackson's estate. "Roosevelt - one of America's great coffee drinkers, rumored to consume a gallon of java a day - so enjoyed the brew at the Hermitage, he declared it "good to the last drop." The coffee was Maxwell House Coffee, named after the fancy Nashville hotel that served it. In 1917, the company began using the slogan in ads in the Post and elsewhere, and for decades it reigned as America's best-selling coffee."(Saturday Evening Post). Even vintage slogans used today can still make an impact on the modern …show more content…
Famous people from actors to athletes and models are used to promote the product. We the people idolize these celebrities, it only makes sense companies would use them as prop to gain more money. " Advertising--including movies, TV, and music videos--presents to us a world that is not our world but rather a collection of images and ideas created for the purpose of selling" (Chait). Peyton Manning is a crowd favorite among football fans. In the past couple years Manning has appeared in Papa John's, State Farm, and Direct Tv commercials. By good chance has boosted company sales. Marketers use the strategy that if people see their favorite celebrity using a service or product, they should too. Example such as Jennifer Aniston using Aveeno moisturizing wrinkle cream, thinking if they use the product the results would look similar to Jennifer Aniston. The younger generation idolize rappers and singers in music videos which believe it or not is another way of advertising. When rapper, Jay Z, started off in the "rap game" his music videos featured him wearing a flat brim New York Yankees Cap. After the video dropped everyone of multiple ages were seen wearing the notorious cap.In "Champagne Tatse, Beer Budget", the author, Delia Cleveland had problems with spending all of her hard earn money on designer labels. "I wore a designer emblem on my chest like a badge of honor and respect. But the
Negative Effects Of Rap Industry
Ordinarily, Ice-T has been in the industry for a long time and has built up his fan based by appearing on famous TV shows, it gives an advantage for GEICO to have a well known artist in their commercial. Audiences will see the commercial, and if they are fans of the ICE-T, maybe they would look into the insurance company. This brings money into the corporation and the artist, which end good for both…
Old Spice Campaign Analysis
Having a suave and charismatic yet comedic character to the advertisement appeals to both sexes and serves its purpose in forcing a conversation between both sexes (Reiss, 2010). Aside from the execution, the communication strategy played a huge role in the success of "The Man Your Man Could Smell Like". First, the tactical strategy by Old Spice is to compete against the competitor's presence in the Super Bowl, in this case the launching of Dove's Men+Care body wash campaign on the Super Bowl (Effie Worldwide, 2011, pp. 2). Old Spice adopted an efficient media strategy to create Super Bowl impact by launching the campaign around it.…
Vanilla Coffee Case Study
Every members of Vanilla have been innovators and pioneers in the hospitality industry for over 40 years. Being a coffee and a dining, Vanilla has something for everyone. it is famous for the cakes, biscuits and latest venture and also Vanilla Upstairs which has an amazing pan-Mediterranean cuisine. Everyday vanilla serves excellent soup and speaciality greek dishes. There pricing range is between $10 to $30 per plate which is afforable…
Character Analysis : Lost Dog And Rihanna Commercials
Budweiser is virtually everywhere—football games, birthday parties, barbeques—so, when the 2015 Super Bowl came along, Budweiser did its best to capture America's heart. The beer brand rolled out the Lost Dog commercial, which was positively received and raved about for years after it first aired. The much-loved commercial rightfully received seemingly endless praise because of its strong use of pathos, an appeal to emotion, and ethos, the credibility of a character. The Lost Dog commercial used a mixture of factors that contributed to its success. First, I'll talk about the use of familiar animals and their display of human-like emotions.…
Starbucks Logo Analysis
In March 2017, Starbucks announced to introduce their limited-edition of two new drinks which will be made from beans aged from years in whiskey barrels at its Seattle roastery. Thus, year by year Starbucks has proved to be one of the best coffee selling company of the world due to its whooping variety and globally…
Descriptive Essay On Coffee Shop
It is a huge building, so it is nearly impossible to miss. Next, the best coffee shop I have found in Savannah so far: The Gallery Espresso. This coffee shop is located on Chippewa Square at 234 Bull Street, and Chippewa Square is the famous bench square from Forrest Gump. The coffee shop has wi-fi access for customers and a rich blend of coffees for a decent price. The coffee shop caters mostly to customers that like coffee instead of customers that like a little coffee with their cream.…
The Pros And Cons Of Cafffeine Addiction
About 90% of Americans consume caffeine every day (Stoppler). Coffee, tea, soda, chocolate, and apples contain a common ingredient that modern day society thrives on: caffeine. Caffeine has become a huge part of pop culture: mostly marketed to children and college students as an easy way to stay up and push through the day (Temple); But should it be? We outlaw many drugs, and put age restrictions on others, yet caffeine is in mass production for public consumption. Companies like Pepsi, Coca cola, Monster, and more make their money through the addictive properties of caffeine.…
Descriptive Essay On Coffee
I experimented around for some years with different brands of coffee, settling in on canned Italian Espresso. Then, the life changing event finally happened. While living in North Berkeley in the late 1960s, I walked into what was the very first Peet 's Coffee Shop by Walnut Square and had my very first cup of the brew made of beans roasted by a process developed by Affred Peet. My coffee drinking life has never been the same. Since that fateful day in 1969, Peet 's has become a well known brand of both roasted beans and coffee shops among connoisseurs of really good coffee.…
Dada Banaspati Case Study
Dalda Banaspati, thanks to its taste and its superior promise, has won the hearts of millions of consumers, making it not only a household name in the subcontinent as synonymous with type vanaspati. Dalda in its quest to meet the changing needs of its customers; Entered the segment with the launch of cooking oil oils Dalda. In 1999, Unilever acquired International Technology to evolve Dalda Banaspati to Dalda VTF, making it the only Bansapati-free virtually transgenic Pakistan. In July 2004, Unilever Pakistan sold its brand "Dalda" Westbury Group in collaboration with Unilever Prevision Social Group, which formed a separate company under Dalda Foods (Pvt) Ltd. Dalda Foods (Pvt) Ltd has taken over 60 years of inheritance Dalda combined with continuous innovation and a deep understanding of consumers and maintaining high quality standards make it the industry's leading brand of cooking oils and fats. In a short period of…
Analysis Of The T-Mobile Drop The Balls Super Bowl Ad
When you have a celebrity promoting any product people tend to be more persuaded to buy the product. In today's culture, most people think if a celebrity trusts a product or service, then they should too. And this is exactly what T-Mobile accomplished with their commercial. Logos was the other secondary rhetorical device used in this commercial. The producers have Steve Harvey state facts about T-Mobile's service.…
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 9,381
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Munir's Disney Retrospective -- Animated Classic #18: The Sword in the Stone (1963)
Last Week's: Munir's Disney Retrospective -- Animated Classic #17: One Hundred and One Dalmatians (1961)
The Sword in the Stone was the last film Walt was alive to see, and is also his weakest (not counting the anthology films). The story of King Arthur's beginnings is retooled here as series of lessons to the future king, and while many moments are amusing and charming, the pacing is sometimes uneven, making the film a little bit slower than expected. The animation lacks the grandeur of past films but the character animation is excellent. And, while the protagonist is not very interesting, the supporting players (mainly Merlin, Archimedes and Madame Mim) are a delight from beginning to end and help elevate the picture from its uneven rhythm. Plus, the epic battle between Merlin and Madame Mim is one of the most memorable and beautifully animated sequences in all of animated film. All in all, The Sword in the Stone may not be an instant Disney classic but has enough charm and magic to delight young and old audiences. Rating: 4/5.
Next Week: Animated Classic #19: The Jungle Book (1967)
Labels: Disney, Disney Retrospective, Munir, Review, Silver Age, The Sword in the Stone, Walt Disney
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 1,760
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Grew up in Littleton, Colorado. Went to Ohio University. Journalism major , class 2017. I followed my dads footsteps coming to OU and enjoy sports hiking and road trips. I am excited to be a part of Southeast Ohio community.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 1,254
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using System;
namespace dotMigrator
{
/// <summary>
/// Holds a representation of executable code that is stored in the data store.
/// The Apply method knows how to create or replace that executable code.
/// </summary>
public class StoredCodeDefinition
{
private readonly Action<IProgressReporter> _applyAction;
/// <summary>
/// Constructs this object
/// </summary>
/// <param name="name">A case-insensitive name to uniquely identify this definition. Typically a filename.</param>
/// <param name="fingerprint">A string that can be used to compare the content between deployments. Typically a cryptographic hash.</param>
/// <param name="applyAction">The delegate that can apply the new definition to the data store.</param>
/// <param name="dependencyLevel">Used to identify the sequence this needs to be applied relative to other stored code it might depend upon. Lower numbers are applied before higher numbers.</param>
public StoredCodeDefinition(
string name,
string fingerprint,
Action<IProgressReporter> applyAction,
int dependencyLevel
)
{
_applyAction = applyAction;
Name = name;
Fingerprint = fingerprint;
DependencyLevel = dependencyLevel;
}
/// <summary>
/// Uniquely identifies this definition within the journal associated with this data store
/// </summary>
public string Name { get; }
/// <summary>
/// Uniquely identifies the <i>content</i> of this stored code definition to determine what has changed between deployments. Should be kept short. Typically a cryptographic hash.
/// </summary>
public string Fingerprint { get; }
/// <summary>
/// The level of this definition in a dependency tree. Definitions with a lower dependency level will be applied before those with a higher level.
/// </summary>
public int DependencyLevel { get; }
/// <summary>
/// Creates or replaces the stored code definition in the target data store
/// </summary>
/// <param name="progressReporter"></param>
public void Apply(IProgressReporter progressReporter)
{
_applyAction.Invoke(progressReporter);
}
}
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 9,538
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{"url":"https:\/\/topblogtenz.com\/how-to-find-pka-from-ka\/","text":"# How to calculate pKa from Ka? - ka to pka, Conversion, Formulas, Equations\n\nHome > Chemistry > How to find pKa from Ka? \u2013 (Ka to pKa)\n\npKa is the negative logarithm of the acid dissociation constant (Ka). It is a more convenient way of measuring the strength of an acidic solution than Ka.\n\nYou will learn in this article how to calculate the pKa value from Ka i.e. (Ka to pKa conversion) by applying a very simple but quite valuable chemical formula.\n\nSo without any further delay, dive into the article, and let\u2019s start reading!\n\nPage Contents\n\n## What is pKa?\n\nThe prefix p in pKa stands for power. Just like pH determines the power of hydrogen ions present in an aqueous solution. pKa measures the strength of an acidic solution as the power of the acid dissociation constant (Ka).\n\npKa is calculated by taking the negative logarithm to the base 10 of the Ka value for acid, as shown in equation (i).\n\npKa = -log10Ka\u2026\u2026\u2026\u2026. Equation (i)\n\nWeak organic acids have greater pKa values than strong mineral acids.\n\npKa is related to pKb i.e., base dissociation constant for an aqueous solution as shown in equation (ii).\n\npKa + pKb = pKw \u2026\u2026. Equation (ii)\n\nEquation (ii) can be rewritten as equation (iii) by substituting the value of pKw that stays fixed at room temperature and atmospheric pressure.\n\npKw = water dissociation constant = 14 (at 25\u00b0C).\n\npKa + pKb = 14 \u2026\u2026. Equation (iii)\n\nYou may note that Ka measures the strength of the acid itself, while pKa is an attribute associated with the strength of the aqueous solution that the acid forms upon ionization.\n\n## What is Ka?\n\nKa stands for acid dissociation constant.\n\nThe ionization equilibrium for the dissociation of a weak acid (HA) in an aqueous solution is represented as follows:\n\nThe acid dissociation constant (Ka) for the above reaction can be represented as equation (iv).\n\n$Ka = \\frac{[H_{3}O^{+}][A^{-}]}{[HA][H_{2}O]}$\u2026\u2026\u2026. Equation (iv)\n\nWhere;\n\n\u2022 [H3O+] = concentration of hydronium ions formed in the aqueous solution\n\u2022 [A] = concentration of conjugate base of the acid\n\u2022 [HA] = acid concentration at equilibrium\n\u2022 [H2O] = concentration of water\n\nAs water concentration stays constant throughout the reaction, while [H3O+] = [H+], i.e., the concentration of H+ ions released in the aqueous solution.\n\nSo, equation (iv) can be rearranged as equation (v).\n\n$Ka = \\frac{[H^{+}][A^{-}]}{[HA]}$\u2026\u2026\u2026. Equation (v)\n\nThe greater the strength of an acid, the higher the Ka value for its aqueous solution and vice versa.\n\n## What is the relationship between pKa and Ka?\n\nThis equation (pKa = -log10Ka) tells us that pKa and Ka are inversely proportional to each other. A higher Ka value results in a lower pKa value and vice versa.\n\nThis implies that a strong acid that dissociates to a large extent in an aqueous solution possesses a higher Ka value; however, it has a smaller pKa.\n\nSo pKa is also inversely related to acidic strength.\n\n## How to find pKa from Ka? \u2013 (Ka to pKa conversion)\n\npKa and Ka are interconvertible. The value of pKa can be easily calculated if the value of Ka is known by using equation (i) which is (pKa = -log10Ka).\n\nWe can substitute the value of Ka into equation (i) and take the negative logarithm of this value to find pKa.\n\npKa = -log10Ka\u2026\u2026\u2026\u2026. Equation (i)\n\nIt was highlighted at the beginning of the article that pKa is a more convenient way of measuring the acidity of a solution as compared to Ka.\n\nThis is because Ka for acid is usually calculated in magnitudes of 10 raised to the power x. While pKa is a small numerical value.\n\nFor instance, the Ka for acetic acid is 1.58 x 10-5; contrarily, its pKa is just 4.80.\n\nKa values are always positive. However, pKa values can be both positive and negative.\n\nWe have provided you with the following solved examples through which you can learn how to calculate pKa from Ka i.e. (Ka to pKa conversion) by practically using the formulas given in this article.\n\n## Solved examples of determining pKa when Ka given\n\n Example #1: The acid dissociation constant (Ka) value for propanoic acid (CH3CH2COOH) is 1.34 x 10-5. What is its pKa value? CH3CH2COOH is a weak acid that partially ionizes to yield H+ and CH3CH2COO\u2013 ions in water.As the Ka value for CH3CH2COOH is given in the question statement so we can find its pKa by applying the equation as shown below.\u2234 pKa = -log10Ka\u2234 pKa = -log10(1.34 x 10-5) = 4.87Result: The pKa value for propanoic acid (CH3CH2COOH) is 4.87.\n Example #2: The acid dissociation constant (Ka) value for nitric acid (HNO3) is 2.4 x 101. What is its pKa value? HNO3 is a strong acid that completely ionizes to give H+ and NO3\u2013 ions in an aqueous solution.As the Ka value for HNO3 is given in the question statement so we can find its pKa by applying the equation as shown below.\u2234 pKa = -log10Ka\u2234 pKa = -log10(2.4 x 101) = -1.38.Result: The pKa value for nitric acid (HNO3) is -1.38.A negative pKa signifies that HNO3 is an extremely strong acid. The proton is only weakly held to the acid, which it readily liberates in an aqueous solution.\n Example # 3: A chemist prepared 0.01 M butyric acid solution in his lab. How can you help the chemist find the pKa of the acidic solution if its pH at the equilibrium point is reported in the literature as pH= 4.63? Butyric acid, also known as butanoic acid (CH3CH2CH2COOH), is a weak acid that partially dissociates to release H+ and butanoate (CH3CH2CH2COO\u2013) ions in an aqueous solution.As the pH of the solution is given in the question statement, so we can find its [H+] at equilibrium using equation (vi).\u2234 [H+]equilibrium = 10-pH \u2026\u2026\u2026. Equation (vi)\u2234 [H+]equilibrium = 10-4.63 = 2.34 x 10-5 M.As per the balanced chemical equation shown above;\u21d2 [H+]equilibrium = [CH3CH2CH2COO\u2013]equilibrium So [CH3CH2CH2COO\u2013]equilibrium = [H+]equilibrium = 2.34 x 10-5 M.The initial butyric acid concentration is also given in the question, so[CH3CH2CH2COOH]equilibrium = [CH3CH2CH2COOH]initial \u2013 [CH3CH2CH2COO\u2013]equilibrium= 0.01 \u2013 (2.34 x 10-5) = 9.98 x 10-3 M.Now that we know the acid dissociation constant (Ka) value, we can easily find pKa by applying equation (i).\u2234 pKa = -log10Ka\u2026\u2026\u2026\u2026. Equation (i)\u2234 pKa = -log10(5.49 x 10-8) = 7.26Result: The pKa value for the butyric acid solution is 7.26.A comparatively high pKa denotes a low acidic strength.\n Example # 4: The Ka value for a weak acid is given to be 2.33 x 10-11. Which of the following options provides the correct pKa value for its acidic solution?A) 11.23\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 B) 10.93\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 C) 10.63\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 D) 11.83\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 E) 9.93 Answer: Option C (pKa = 10.63) is the correct answer.Explanation: pKa can be determined from the already given Ka value by applying equation (i).pKa = -log10Ka \u2026\u2026\u2026\u2026. Equation (i)pKa = -log10(2.33 x 10-11) = 10.63\n Example # 5: A 0.025 M solution of a weak acid dissociates to produce 0.005 mol\/L hydrogen ions at the equilibrium stage. Find its pKa. A weak acid (HA) partially dissociates to liberate H+ and A\u2013 ions in water.The concentration of hydrogen ions released at equilibrium is given in the question statement i.e., [H+] equilibrium = 0.005 M.\u2234 [H+] equilibrium = [A\u2013]equilibrium = 0.005 MThe original concentration of HA is also given in the question statement, so [HA]equilibrium = [HA]initial \u2013 [H+] equilibrium = 0.025 \u2013 0.005 = 0.02 M.As a final step, we just need to substitute the above value into equation (i) to find the required pKa value.\u2234 pKa = -log10Ka \u2026\u2026\u2026\u2026. Equation (i)\u2234 pKa = -log10(1.25 x 10-3) = 2.90Result: The pKa value for the given acidic solution is 2.90.\n\nAlso check:\n\n## FAQ\n\n### What is Ka?\n\nKa stands for acid dissociation constant.\n\nA weak acid (HA) partially dissociates to produce H+ and A ions in water. H+ ions combine with H2O molecules to form hydronium (H3O+) ions. A is known as the conjugate base of the acid. HA and A together are known as a conjugate acid-base pair.\n\nThe equilibrium constant for a reversible reaction is the ratio of the product of the concentration of products to the product of reactant concentrations.\n\nThe ionization equilibrium for the dissociation of HA in an aqueous solution can be represented as follows:\n\n\u21d2 HA + H2O \u21cc H3O+ + A\n\nThe equilibrium constant (Ka) for the above reaction can be represented as equation (i)\n\n$Ka = \\frac{[H_{3}O^{+}][A^{-}]}{[HA][H_{2}O]}$\u2026\u2026\u2026. Equation (i)\n\nWhere;\n\n\u2022 [H3O+] = concentration of hydronium ions formed in the aqueous solution\n\u2022 [A] = concentration of conjugate base of the acid\n\u2022 [HA] = acid concentration at equilibrium\n\u2022 [H2O] = concentration of water\n\nAs water concentration stays constant throughout the reaction, while [H3O+] = [H+], i.e., the concentration of H+ ions released in the aqueous solution. So, equation (i) can be rearranged as equation (ii).\n\n$Ka = \\frac{[H^{+}][A^{-}]}{[HA]}$\u2026\u2026\u2026. Equation (ii)\n\nThe greater the strength of an acid, it undergoes dissociation to a larger extent in the aqueous solution; thus, it possesses a higher Ka value.\n\nWeak organic acids such as acetic acid and citric acid have Ka values below 1. However, strong mineral acids such as HCl and HNO3 that completely dissociates to release a large number of H+ ions in an aqueous solution have Ka values above 1.\n\n### What is pKa?\n\npKa measures the strength of an acidic solution. It is the negative logarithm of the Ka value for an acid.\n\n### How is pKa related to the strength of a Bronsted acid?\n\nAs per the Bronsted-Lowry acid-base theory, an acid is defined as a proton donor. The proton is loosely held to a strong acid which can readily liberate it in an aqueous solution.\n\nHowever, weak acids strongly hold their protons, not ready to release in water.\n\nGreater the pKa value, the more strongly held the proton is by the Bronsted acid indicating a weak acidic strength and vice versa.\n\nSo pKa is inversely related to the strength of a Bronsted acid.\n\n### How is Ka related to the strength of an acid?\n\nHigher the Ka value, the greater the strength of an acid. So the acid dissociation constant is directly related to the strength of an acid.\n\nStrong acids completely ionize in water to release H+ ions. Thus, they have high Ka values.\n\nWeak acids only partially ionize in water to release a limited number of H+ ions, so they have low Ka values.\n\n### What is the relationship between pKa and Ka?\n\npKa is inversely related to Ka. The higher the Ka value of an acid, the lower its pKa and vice versa.\n\n### What is the formula to calculate pKa from Ka?\n\npKa can be calculated by taking the negative logarithm of Ka as follows;\n\n\u2234 pKa = -log10Ka.\n\n### How do you calculate Ka from pKa?\n\nKa and pKa are interconvertible chemical parameters. Ka can be calculated from pKa by taking the antilog of pKa as follows;\n\n\u2234 Ka = 10-pKa\n\n## Summary\n\n\u2022 pKa stands for the power of Ka. It measures the acidic strength of an aqueous solution.\n\u2022 It is calculated as a negative logarithm of Ka to the base 10.\n\u2022 pKa = -log10Ka.\n\u2022 The greater the strength of an acid, the lower its pKa value, and vice versa.\n\u2022 Ka denotes acid dissociation constant. It measures the extent of ionization of an acid in an aqueous solution.\n\u2022 Greater the Ka value, the higher the strength of the acid.\n\u2022 If the value of Ka for acid is known, we can easily find its pKa value by taking the negative logarithm of Ka. The formula to determine pKa from Ka is [pKa = -log10Ka].\n\n## References\n\n1. Master Organic Chemistry. (2012, May 9). Acid-Base Reactions: Ka and pKa. Retrieved from https:\/\/www.masterorganicchemistry.com\/2012\/05\/09\/acid-base-reactions-ka-and-pka\/\n2. wikiHow. (n.d.). How to Find Ka from pKa. Retrieved from https:\/\/www.wikihow.com\/Find-Ka-from-pKa\n3. Study.com. (n.d.). Converting Between Ka and pKa: Questions. Retrieved from https:\/\/study.com\/skill\/practice\/converting-between-ka-and-pka-questions.html\nDid you like it?\n\n#### Ammara Waheed\n\nAmmara Waheed is a highly qualified and experienced chemist, whose passion for Chemistry is evident in her writing. With a Bachelor of Science (Hons.) and Master of Philosophy (M. Phil) in Physical and Analytical Chemistry from Government College University (GCU) Lahore, Pakistan, with a hands-on laboratory experience in the Pakistan Council of Scientific and Industrial Research (PCSIR), Ammara has a solid educational foundation in her field. She comes from a distinguished research background and she documents her research endeavors for reputable journals such as Wiley and Elsevier. Her deep knowledge and expertise in the field of Chemistry make her a trusted and reliable authority in her profession. Let's connect - https:\/\/www.researchgate.net\/profile\/Ammara-Waheed\n\nShare it...","date":"2023-03-25 18:22:10","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 4, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.7624045014381409, \"perplexity\": 4760.923759589327}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2023-14\/segments\/1679296945368.6\/warc\/CC-MAIN-20230325161021-20230325191021-00084.warc.gz\"}"}
| null | null |
Posted on Friday June 28, 2019 By EvalartTagged Informática y Tecnología
Women have played a fundamental role in computing and information technology, in the development of some of the key components of modern information technology. The contributions of women in technology include the creation of the first computer program, the invention of computer methods and devices, the development of programs that influence the functioning of today's computers, among others.
In the early 21st century, the number of women graduating in science was rising in all the areas except in computer science. This gender gap is partly because historically many women's contributions to science have not been recognized, as well as the comparative lack of female role models in the technology industry.
Today, women represent less than 20 percent of technology jobs in the United States, even though they constitute more than half of the U.S. workforce. Worse still, women now have a lower proportion of jobs in computer science than in the 80s.
One of the main reasons women have left their IT jobs is a lack of professional growth, which is strongly linked to sexism. According to a survey conducted by The Guardian, 73% of the workers in the technology industry agrees that the industry is sexist.
However, as technology companies seek to resolve talent crisis, some companies have been implementing initiatives to shape the future of the technology industry, these initiatives include the recruitment of more women.
To make the technology industry more diverse, we must celebrate the technology pioneers of the past and the women who make a difference in today's industry. Here are 10 women who pioneered technology:
Ada Lovelace:
Recognized as the world's first computer programmer. In 1842, she wrote the first algorithm for processing numbers on the first general-purpose mechanical computer or analytical engine by Charles Bannage who, impressed by her mathematical skills, referred to her as "the enchantress of numbers". The computer language ADA bears her name.
Grace Hopper:
Known as the mother of COBOL, she is one of the most famous pioneers of computer science in the United States. In 1944, Hopper was one of the first programmers of the electromechanical computer Harvard Mark I. Later, in 1952, she developed the first compiler. Hopper popularized the concept of the machine-independent languages that drove to the development of one of the first modern programming languages, COBOL.
Jean E. Sammet:
Graduated with a master's degree in mathematics in 1949. In 1961, she became manager of IBM's Programming Center in Boston and oversaw the development of FORMAC (Formula Manipulation Compiler), the first widely used general language and the first to manipulate algebraic expressions of voltage.
Hedy Lamarr:
One of Hollywood's "Golden Age" stars co-designed in 1941 a radio-guided torpedo system based on "frequency hopping" (signal frequencies changes to avoid electrical interference by enemy devices) that became known as spectrum propagation, which later became a key element in the anti-interference devices used by the U.S. military's satellite communications control systems, as well as a key element of digital wireless mobile phone technology.
Williamina Fleming:
The head of the observatory, Edward Charles Pickering, needed someone to calculate astronomical numbers to calculate relationships and effectively measure the universe. Pickering asked his maid, Williamina Fleming, to work as a "computer" at Harvard. Fleming agreed, leading a team of more than 80 women who did the computational work that is responsible for how we understand the universe today.
Katherine Johnson:
African American mathematician whose orbital mechanics calculations as a NASA employee were key for the success of America's first and subsequent manned space flights. In 1970, she worked on the Apollo 13 moon mission. When the mission was aborted, Johnson's works on backup procedures and charts allowed the crew to return to Earth safely.
Dr. Ellen Ochoa:
Former astronaut, current director of Johnson Space Center, and pioneer of spacecraft technology for having designed optical systems for Sandia National Laboratory. She also developed a computer system designed for aeronautical expeditions at NASA's Ames Research Center. Also, she was the first Hispanic woman in space.
Sister Mary Kenneth Keller:
Was the first woman to obtain a doctorate in computer science and was present at the development of BASIC computer language in Dartmouth. Before Sister Mary, Dartmouth was considered a place of study and work "for men only".
Carol Shaw:
Considered the first woman who designed a video game. Initially, Shaw started in Atari and joined Activision, where she designed and developed the scrolling shooter video game, River Raid. She also made possible Happy Trails, Super Breakout, and 3-D Tic Tac Toe.
Joan Ball:
The inventor of dating sites, she started the first computer dating service in England in 1964. Ball's computer dating service is also the predecessor of early American computer dating services, such as Operation Match at Harvard.
Previous Post: Continuous IT Selection Processes as a Technique to Optimize Recruitment
Next Post: Honesty and Ethics test for Recruiting
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{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
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Q: How to control bldc motors with arduino when controlling with a serial connection? I am trying to control a BLDC motor (with esc) with my arduino. The arduino is reciving commands from a serial connection with a raspberry pi running a python program that repeatedly sends numbers to control the motor.
I intend to control the speed of the motors via the raspberry pi over a serial connection. So far i have never been able to spin the motor while sending data.
include <Servo.h>
Servo ESC; // create servo object to control the ESC
int incomingByte = 0;
void setup() {
Serial.begin(9600);
ESC.attach(3,1000,2000); // (pin, min pulse width, max pulse width in microseconds)
}
void loop() {
ESC.write(Serial.parseInt());
//incomingByte = Serial.parseInt();
}
import tkinter as tk
import serial
tracked_var = 0
def outputValue():
print(tracked_var)
ser.write(value.encode())
window.after(50, outputValue)
def update_tracked_variable(value):
global tracked_var
tracked_var = value
def background(color):
window.configure(bg=color)
scale = tk.Scale(window, from_=0, to=20, command=update_tracked_variable)
scale.pack()
ser = serial.Serial('/dev/ttyUSB0', 9600)
window = tk.Tk()
window.title("Drone Control")
background("black")
outputValue()
window.mainloop()
When I send the values to the arduino I get no movement from the motor.
This code was slightly changed from a simple potentiometer servo controller.
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{
"redpajama_set_name": "RedPajamaStackExchange"
}
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You can follow the discussion on 16 Effective Tips How To Have More Energy And Motivation Right Now without having to leave a comment. Cool, huh? Just enter your email address in the form here below and you're all set.
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{
"redpajama_set_name": "RedPajamaC4"
}
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{"url":"https:\/\/eccc.weizmann.ac.il\/title\/H","text":"Under the auspices of the Computational Complexity Foundation (CCF)\n\nREPORTS > A-Z > H:\nA - B - C - D - E - F - G - H - I - J - K - L - M - N - O - P - Q - R - S - T - U - V - W - X - Y - Z - Other\n\nH\nTR18-089 | 27th April 2018\nKenneth Hoover, Russell Impagliazzo, Ivan Mihajlin, Alexander Smal\n\n#### Half-duplex communication complexity\n\nRevisions: 2\n\nSuppose Alice and Bob are communicating bits to each other in order to compute some function $f$, but instead of a classical communication channel they have a pair of walkie-talkie devices. They can use some classical communication protocol for $f$ where each round one player sends bit and the other ... more >>>\n\nTR11-085 | 14th May 2011\nYijia Chen, Joerg Flum, Moritz M\u00fcller\n\n#### Hard instances of algorithms and proof systems\n\nAssuming that the class TAUT of tautologies of propositional logic has no almost optimal algorithm, we show that every algorithm $\\mathbb A$ deciding TAUT has a polynomial time computable sequence witnessing that $\\mathbb A$ is not almost optimal. The result extends to every $\\Pi_t^p$-complete problem with $t\\ge 1$; however, we ... more >>>\n\nTR17-117 | 20th July 2017\nDmitry Itsykson, Alexander Knop\n\n#### Hard satisfiable formulas for splittings by linear combinations\n\nItsykson and Sokolov in 2014 introduced the class of DPLL($\\oplus$) algorithms that solve Boolean satisfiability problem using the splitting by linear combinations of variables modulo 2. This class extends the class of DPLL algorithms that split by variables. DPLL($\\oplus$) algorithms solve in polynomial time systems of linear equations modulo two ... more >>>\n\nTR13-151 | 7th November 2013\nMark Bun, Justin Thaler\n\n#### Hardness Amplification and the Approximate Degree of Constant-Depth Circuits\n\nRevisions: 3\n\nWe establish a generic form of hardness amplification for the approximability of constant-depth Boolean circuits by polynomials. Specifically, we show that if a Boolean circuit cannot be pointwise approximated by low-degree polynomials to within constant error in a certain one-sided sense, then an OR of disjoint copies of that circuit ... more >>>\n\nTR07-102 | 4th October 2007\nAndrej Bogdanov, Muli Safra\n\n#### Hardness amplification for errorless heuristics\n\nAn errorless heuristic is an algorithm that on all inputs returns either the correct answer or the special symbol \"I don't know.\" A central question in average-case complexity is whether every distributional decision problem in NP has an errorless heuristic scheme: This is an algorithm that, for every δ > ... more >>>\n\nTR18-095 | 11th May 2018\nMarco Carmosino, Russell Impagliazzo, Shachar Lovett, Ivan Mihajlin\n\n#### Hardness Amplification for Non-Commutative Arithmetic Circuits\n\nWe show that proving mildly super-linear lower bounds on non-commutative arithmetic circuits implies exponential lower bounds on non-commutative circuits. That is, non-commutative circuit complexity is a threshold phenomenon: an apparently weak lower bound actually suffices to show the strongest lower bounds we could desire.\n\nThis is part of a recent ... more >>>\n\nTR09-072 | 3rd September 2009\nPaul Beame, Trinh Huynh\n\n#### Hardness Amplification in Proof Complexity\n\nRevisions: 2 , Comments: 2\n\nWe present a generic method for converting any family of unsatisfiable CNF formulas that require large resolution rank into CNF formulas whose refutation requires large rank for proof systems that manipulate polynomials or polynomial threshold functions of degree at most $k$ (known as ${\\rm Th}(k)$ proofs). Such systems include: Lovasz-Schrijver ... more >>>\n\nTR19-125 | 27th August 2019\nElazar Goldenberg, Karthik C. S.\n\n#### Hardness Amplification of Optimization Problems\n\nIn this paper, we prove a general hardness amplification scheme for optimization problems based on the technique of direct products.\n\nWe say that an optimization problem $\\Pi$ is direct product feasible if it is possible to efficiently aggregate any $k$ instances of $\\Pi$ and form one large instance ... more >>>\n\nTR07-130 | 3rd December 2007\nRonen Shaltiel, Emanuele Viola\n\n#### Hardness amplification proofs require majority\n\nHardness amplification is the fundamental task of\nconverting a $\\delta$-hard function $f : {0,1}^n -> {0,1}$ into a $(1\/2-\\eps)$-hard function $Amp(f)$,\nwhere $f$ is $\\gamma$-hard if small circuits fail to\ncompute $f$ on at least a $\\gamma$ fraction of the\ninputs. Typically, $\\eps,\\delta$ are small (and\n$\\delta=2^{-k}$ captures the case ... more >>>\n\nTR05-057 | 19th May 2005\nVenkatesan Guruswami, Valentine Kabanets\n\n#### Hardness amplification via space-efficient direct products\n\nWe prove a version of the derandomized Direct Product Lemma for\ndeterministic space-bounded algorithms. Suppose a Boolean function\n$g:\\{0,1\\}^n\\to\\{0,1\\}$ cannot be computed on more than $1-\\delta$\nfraction of inputs by any deterministic time $T$ and space $S$\nalgorithm, where $\\delta\\leq 1\/t$ for some $t$. Then, for $t$-step\nwalks $w=(v_1,\\dots, v_t)$ ... more >>>\n\nTR10-031 | 4th March 2010\nChristian Gla\u00dfer, Christian Reitwie\u00dfner, Heinz Schmitz, Maximilian Witek\n\n#### Hardness and Approximability in Multi-Objective Optimization\n\nWe systematically study the hardness and the approximability of combinatorial multi-objective NP optimization problems (multi-objective problems, for short).\n\nWe define solution notions that precisely capture the typical algorithmic tasks in multi-objective optimization. These notions inherit polynomial-time Turing reducibility from multivalued functions, which allows us to compare the solution notions and ... more >>>\n\nTR11-015 | 8th December 2010\nMarcel R. Ackermann, Johannes Bl\u00f6mer, Christoph Scholz\n\n#### Hardness and Non-Approximability of Bregman Clustering Problems\n\nWe prove the computational hardness of three k-clustering problems using an (almost) arbitrary Bregman divergence as dissimilarity measure: (a) The Bregman k-center problem, where the objective is to find a set of centers that minimizes the maximum dissimilarity of any input point towards its closest center, and (b) the Bregman ... more >>>\n\nTR18-178 | 9th October 2018\nLeroy Chew\n\n#### Hardness and Optimality in QBF Proof Systems Modulo NP\n\nQuantified Boolean Formulas (QBFs) extend propositional formulas with Boolean quantifiers. Working with QBF differs from propositional logic in its quantifier handling, but as propositional satisfiability (SAT) is a subproblem of QBF, all SAT hardness in solving and proof complexity transfers to QBF. This makes it difficult to analyse efforts dealing ... more >>>\n\nTR06-071 | 25th April 2006\nJohn Hitchcock, A. Pavan\n\n#### Hardness Hypotheses, Derandomization, and Circuit Complexity\n\nWe consider hypotheses about nondeterministic computation that\nhave been studied in different contexts and shown to have interesting\nconsequences:\n\n1. The measure hypothesis: NP does not have p-measure 0.\n\n2. The pseudo-NP hypothesis: there is an NP language that can be\ndistinguished from any DTIME(2^n^epsilon) language by an ... more >>>\n\nTR19-118 | 5th September 2019\nLijie Chen, Ce Jin, Ryan Williams\n\n#### Hardness Magnification for all Sparse NP Languages\n\nIn the Minimum Circuit Size Problem (MCSP[s(m)]), we ask if there is a circuit of size s(m) computing a given truth-table of length n = 2^m. Recently, a surprising phenomenon termed as hardness magnification by [Oliveira and Santhanam, FOCS 2018] was discovered for MCSP[s(m)] and the related problem MKtP of ... more >>>\n\nTR18-139 | 10th August 2018\nIgor Carboni Oliveira, Rahul Santhanam\n\n#### Hardness Magnification for Natural Problems\n\nWe show that for several natural problems of interest, complexity lower bounds that are barely non-trivial imply super-polynomial or even exponential lower bounds in strong computational models. We term this phenomenon \"hardness magnification\". Our examples of hardness magnification include:\n\n1. Let MCSP$[s]$ be the decision problem whose YES instances are ... more >>>\n\nTR18-158 | 11th September 2018\nIgor Carboni Oliveira, J\u00e1n Pich, Rahul Santhanam\n\n#### Hardness magnification near state-of-the-art lower bounds\n\nRevisions: 1\n\nThis work continues the development of hardness magnification. The latter proposes a strategy for showing strong complexity lower bounds by reducing them to a refined analysis of weaker models, where combinatorial techniques might be successful.\n\nWe consider gap versions of the meta-computational problems MKtP and MCSP, where one needs ... more >>>\n\nTR09-112 | 3rd November 2009\nDavide Bil\u00f2, Luciano Gual\u00e0, Guido Proietti\n\n#### Hardness of an Asymmetric 2-player Stackelberg Network Pricing Game\n\nConsider a communication network represented by a directed graph $G=(V,E)$ of $n$ nodes and $m$ edges. Assume that edges in $E$ are\npartitioned into two sets: a set $C$ of edges with a fixed\nnon-negative real cost, and a set $P$ of edges whose \\emph{price} should instead be set by ... more >>>\n\nTR00-062 | 25th August 2000\nVenkatesan Guruswami, Johan Hastad, Madhu Sudan\n\n#### Hardness of approximate hypergraph coloring\n\nWe introduce the notion of covering complexity of a probabilistic\nverifier. The covering complexity of a verifier on a given input is\nthe minimum number of proofs needed to satisfy'' the verifier on\nevery random string, i.e., on every random string, at least one of the\ngiven proofs must be ... more >>>\n\nTR05-127 | 5th November 2005\nVitaly Feldman\n\n#### Hardness of Approximate Two-level Logic Minimization and PAC Learning with Membership Queries\n\nRevisions: 1\n\nProducing a small DNF expression consistent with given data is a\nclassical problem in computer science that occurs in a number of forms and\nhas numerous applications. We consider two standard variants of this\nproblem. The first one is two-level logic minimization or finding a minimal\nmore >>>\n\nTR10-053 | 28th March 2010\nDana Moshkovitz, Subhash Khot\n\n#### Hardness of Approximately Solving Linear Equations Over Reals\n\nComments: 1\n\nIn this paper, we consider the problem of approximately solving a\nsystem of homogeneous linear equations over reals, where each\nequation contains at most three variables.\n\nSince the all-zero assignment always satisfies all the equations\nexactly, we restrict the assignments to be non-trivial\". Here is\nan informal statement of our ... more >>>\n\nTR99-029 | 31st August 1999\nIlya Dumer, Daniele Micciancio, Madhu Sudan\n\n#### Hardness of approximating the minimum distance of a linear code\n\nWe show that the minimum distance of a linear code (or\nequivalently, the weight of the lightest codeword) is\nnot approximable to within any constant factor in random polynomial\ntime (RP), unless NP equals RP.\nUnder the stronger assumption that NP is not contained in RQP\n(random ... more >>>\n\nTR06-019 | 24th November 2005\nJanka Chleb\u00edkov\u00e1, Miroslav Chlebik\n\n#### Hardness of asymptotic approximation for orthogonal rectangle packing and covering problems\n\nRecently Bansal and Sviridenko (Proc. of the 15th SODA'04, 189-196)\nproved that for\n2-dimensional Orthogonal Rectangle\nBin Packing without rotations allowed there is no asymptotic PTAS, unless P=NP. We show that similar\napproximation hardness results hold for several rectangle packing and covering problems even if rotations by ninety\nmore >>>\n\nTR14-051 | 12th April 2014\nSubhash Khot, Rishi Saket\n\n#### Hardness of Coloring $2$-Colorable $12$-Uniform Hypergraphs with $2^{(\\log n)^{\\Omega(1)}}$ Colors\n\nWe show that it is quasi-NP-hard to color $2$-colorable $12$-uniform hypergraphs with $2^{(\\log n)^{\\Omega(1) }}$ colors where $n$ is the number of vertices. Previously, Guruswami et al. [GHHSV14] showed that it is quasi-NP-hard to color $2$-colorable $8$-uniform hypergraphs with $2^{2^{\\Omega(\\sqrt{\\log \\log n})}}$ colors. Their result is obtained by composing a ... more >>>\n\nTR16-063 | 18th April 2016\nPavel Hubacek, Eylon Yogev\n\n#### Hardness of Continuous Local Search: Query Complexity and Cryptographic Lower Bounds\n\nRevisions: 1\n\nLocal search proved to be an extremely useful tool when facing hard optimization problems (e.g. via the simplex algorithm, simulated annealing, or genetic algorithms). Although powerful, it has its limitations: there are functions for which exponentially many queries are needed to find a local optimum. In many contexts the optimization ... more >>>\n\nTR06-109 | 29th August 2006\nJulia Chuzhoy, Sanjeev Khanna\n\n#### Hardness of Directed Routing with Congestion\n\nGiven a graph G and a collection of source-sink pairs in G, what is the least integer c such that each source can be connected by a path to its sink, with at most c paths going through an edge? This is known as the congestion minimization problem, and the ... more >>>\n\nTR18-118 | 20th June 2018\nAlexander Durgin, Brendan Juba\n\n#### Hardness of improper one-sided learning of conjunctions for all uniformly falsifiable CSPs\n\nWe consider several closely related variants of PAC-learning in which false-positive and false-negative errors are treated differently. In these models we seek to guarantee a given, low rate of false-positive errors and as few false-negative errors as possible given that we meet the false-positive constraint. Bshouty and Burroughs first observed ... more >>>\n\nTR06-061 | 5th May 2006\nVenkatesan Guruswami, Prasad Raghavendra\n\n#### Hardness of Learning Halfspaces with Noise\n\nLearning an unknown halfspace (also called a perceptron) from\nlabeled examples is one of the classic problems in machine learning.\nIn the noise-free case, when a halfspace consistent with all the\ntraining examples exists, the problem can be solved in polynomial\ntime using linear programming. ... more >>>\n\nTR17-115 | 5th July 2017\nArnab Bhattacharyya, Suprovat Ghoshal, Rishi Saket\n\n#### Hardness of learning noisy halfspaces using polynomial thresholds\n\nWe prove the hardness of weakly learning halfspaces in the presence of adversarial noise using polynomial threshold functions (PTFs). In particular, we prove that for any constants $d \\in \\mathbb{Z}^+$ and $\\epsilon > 0$, it is NP-hard to decide: given a set of $\\{-1,1\\}$-labeled points in $\\mathbb{R}^n$ whether (YES Case) ... more >>>\n\nTR06-141 | 22nd November 2006\nVenkatesan Guruswami, Kunal Talwar\n\n#### Hardness of Low Congestion Routing in Directed Graphs\n\nWe prove a strong inapproximability result for routing on directed\ngraphs with low congestion. Given as input a directed graph on $N$\nvertices and a set of source-destination pairs that can be connected\nvia edge-disjoint paths, we prove that it is hard, assuming NP\ndoesn't have $n^{O(\\log\\log n)}$ time randomized ... more >>>\n\nTR10-059 | 8th April 2010\nOlaf Beyersdorff, Nicola Galesi, Massimo Lauria\n\n#### Hardness of Parameterized Resolution\n\nParameterized Resolution and, moreover, a general framework for parameterized proof complexity was introduced by Dantchev, Martin, and Szeider (FOCS'07). In that paper, Dantchev et al. show a complexity gap in tree-like Parameterized Resolution for propositional formulas arising from translations of first-order principles.\nWe broadly investigate Parameterized Resolution obtaining the following ... more >>>\n\nTR17-147 | 3rd October 2017\nVenkatesan Guruswami, Rishi Saket\n\n#### Hardness of Rainbow Coloring Hypergraphs\n\nA hypergraph is $k$-rainbow colorable if there exists a vertex coloring using $k$ colors such that each hyperedge has all the $k$ colors. Unlike usual hypergraph coloring, rainbow coloring becomes harder as the number of colors increases. This work studies the rainbow colorability of hypergraphs which are guaranteed to be ... more >>>\n\nTR07-073 | 3rd August 2007\nParikshit Gopalan, Subhash Khot, Rishi Saket\n\n#### Hardness of Reconstructing Multivariate Polynomials over Finite Fields\n\nWe study the polynomial reconstruction problem for low-degree\nmultivariate polynomials over finite fields. In the GF[2] version of this problem, we are given a set of points on the hypercube and target values $f(x)$ for each of these points, with the promise that there is a polynomial over GF[2] of ... more >>>\n\nTR09-020 | 2nd March 2009\nVenkatesan Guruswami, Prasad Raghavendra\n\n#### Hardness of Solving Sparse Overdetermined Linear Systems: A 3-Query PCP over Integers.\n\nA classic result due to Hastad established that for every constant \\eps > 0, given an overdetermined system of linear equations over a finite field \\F_q where each equation depends on exactly 3 variables and at least a fraction (1-\\eps) of the equations can be satisfied, it is NP-hard to ... more >>>\n\nTR12-182 | 24th December 2012\nItay Berman, Iftach Haitner, Ilan Komargodski, Moni Naor\n\n#### Hardness Preserving Reductions via Cuckoo Hashing\n\nRevisions: 2\n\nA common method for increasing the usability and uplifting the security of pseudorandom function families (PRFs) is to hash\" the inputs into a smaller domain before applying the PRF. This approach, known as Levin's trick\", is used to achieve PRF domain extension\" (using a short, e.g., fixed, input length PRF ... more >>>\n\nTR07-121 | 21st November 2007\nZeev Dvir, Amir Shpilka, Amir Yehudayoff\n\n#### Hardness-Randomness Tradeoffs for Bounded Depth Arithmetic Circuits\n\nIn this paper we show that lower bounds for bounded depth arithmetic circuits imply derandomization of polynomial identity testing for bounded depth arithmetic circuits. More formally, if there exists an explicit polynomial f(x_1,...,x_m) that cannot be computed by a depth d arithmetic circuit of small size then there exists ... more >>>\n\nTR04-072 | 19th August 2004\nJohn Hitchcock\n\n#### Hausdorff Dimension and Oracle Constructions\n\nBennett and Gill (1981) proved that P^A != NP^A relative to a\nrandom oracle A, or in other words, that the set\nO_[P=NP] = { A | P^A = NP^A }\nhas Lebesgue measure 0. In contrast, we show that O_[P=NP] has\nHausdorff dimension 1.\n\n... more >>>\n\nTR03-034 | 17th March 2003\nArnold Beckmann\n\n#### Height restricted constant depth LK\n\nHeight restricted constant depth LK is a natural restriction of\nGentzen's propositional proof system LK. A sequence of LK-formulas\nhas polylogarithmic-height restricted depth-d-LK proofs iff the\nn-th formula in the sequence possesses LK-proofs where cut-formulas\nare of depth d+1 with small bottom fanin\nand of ... more >>>\n\nTR13-074 | 9th May 2013\nJohannes K\u00f6bler, Sebastian Kuhnert, Oleg Verbitsky\n\n#### Helly Circular-Arc Graph Isomorphism is in Logspace\n\nWe present logspace algorithms for the canonical labeling problem and the representation problem of Helly circular-arc (HCA) graphs. The first step is a reduction to canonical labeling and representation of interval intersection matrices. In a second step, the Delta trees employed in McConnell's linear time representation algorithm for interval matrices ... more >>>\n\nTR14-178 | 5th December 2014\nDmitry Itsykson, Alexander Knop, Dmitry Sokolov\n\n#### Heuristic time hierarchies via hierarchies for sampling distributions\n\nWe give a new simple proof of the time hierarchy theorem for heuristic BPP originally proved by Fortnow and Santhanam [FS04] and then simplified and improved by Pervyshev [P07]. In the proof we use a hierarchy theorem for sampling distributions recently proved by Watson [W13]. As a byproduct we get ... more >>>\n\nTR14-171 | 11th December 2014\nLance Fortnow, Rahul Santhanam\n\n#### Hierarchies Against Sublinear Advice\n\nWe strengthen the non-deterministic time hierarchy theorem of\n\\cite{Cook72, Seiferas-Fischer-Meyer78, Zak83} to show that the lower bound\nholds against sublinear advice. More formally, we show that for any constants\n$c$ and $d$ such that $1 \\leq c < d$, there is a language in $\\NTIME(n^d)$\nwhich is not in $\\NTIME(n^c)\/n^{1\/d}$. ... more >>>\n\nTR08-097 | 14th November 2008\nOded Goldreich, Michael Krivelevich, Ilan Newman, Eyal Rozenberg\n\n#### Hierarchy Theorems for Property Testing\n\nRevisions: 1\n\nReferring to the query complexity of property testing,\nwe prove the existence of a rich hierarchy of corresponding\ncomplexity classes. That is, for any relevant function $q$,\nwe prove the existence of properties that have testing\ncomplexity Theta(q).\nSuch results are proven in three standard\ndomains often considered in property ... more >>>\n\nTR18-098 | 17th May 2018\nOded Goldreich\n\n#### Hierarchy Theorems for Testing Properties in Size-Oblivious Query Complexity\n\nRevisions: 1\n\nFocusing on property testing tasks that have query complexity that is independent of the size of the tested object (i.e., depends on the proximity parameter only), we prove the existence of a rich hierarchy of the corresponding complexity classes.\nThat is, for essentially any function $q:(0,1]\\to\\N$, we prove the existence ... more >>>\n\nTR17-157 | 13th October 2017\nMonaldo Mastrolilli\n\n#### High Degree Sum of Squares Proofs, Bienstock-Zuckerberg hierarchy and Chvatal-Gomory cuts\n\nRevisions: 2\n\nChvatal-Gomory (CG) cuts and the Bienstock-Zuckerberg hierarchy capture useful linear programs that the standard bounded degree Lasserre\/Sum-of-Squares (SOS) hierarchy fails to capture.\n\nIn this paper we present a novel polynomial time SOS hierarchy for 0\/1 problems with a custom subspace of high degree polynomials (not the standard subspace of low-degree ... more >>>\n\nTR17-089 | 11th May 2017\nIrit Dinur, Tali Kaufman\n\n#### High dimensional expanders imply agreement expanders\n\nWe show that high dimensional expanders imply derandomized direct product tests, with a number of subsets that is *linear* in the size of the universe.\n\nDirect product tests belong to a family of tests called agreement tests that are important components in PCP constructions and include, for example, low degree ... more >>>\n\nTR13-053 | 4th April 2013\nAlan Guo\n\n#### High rate locally correctable codes via lifting\n\nRevisions: 1\n\nWe present a general framework for constructing high rate error correcting codes that are locally correctable (and hence locally decodable if linear) with a sublinear number of queries, based on lifting codes with respect to functions on the coordinates. Our approach generalizes the lifting of affine-invariant codes of Guo, Kopparty, ... more >>>\n\nTR15-068 | 21st April 2015\nSwastik Kopparty, Noga Ron-Zewi, Shubhangi Saraf\n\n#### High rate locally-correctable and locally-testable codes with sub-polynomial query complexity\n\nRevisions: 2\n\nIn this work, we construct the first locally-correctable codes (LCCs), and locally-testable codes (LTCs) with constant rate, constant relative distance, and sub-polynomial query complexity. Specifically, we show that there exist binary LCCs and LTCs with block length $n$, constant rate (which can even be taken arbitrarily close to 1), constant ... more >>>\n\nTR10-148 | 23rd September 2010\nSwastik Kopparty, Shubhangi Saraf, Sergey Yekhanin\n\n#### High-rate codes with sublinear-time decoding\n\nLocally decodable codes are error-correcting codes that admit efficient decoding algorithms; any bit of the original message can be recovered by looking at only a small number of locations of a corrupted codeword. The tradeoff between the rate of a code and the locality\/efficiency of its decoding algorithms has been ... more >>>\n\nTR15-110 | 8th July 2015\nSwastik Kopparty, Or Meir, Noga Ron-Zewi, Shubhangi Saraf\n\n#### High-rate Locally-testable Codes with Quasi-polylogarithmic Query Complexity\n\nRevisions: 1\n\nAn error correcting code is said to be \\emph{locally testable} if\nthere is a test that checks whether a given string is a codeword,\nor rather far from the code, by reading only a small number of symbols\nof the string. Locally testable codes (LTCs) are both interesting\nin their ... more >>>\n\nTR10-181 | 21st November 2010\nHamed Hatami, Shachar Lovett\n\n#### Higher-order Fourier analysis of $\\mathbb{F}_p^n$ and the complexity of systems of linear forms\n\nIn this article we are interested in the density of small linear structures (e.g. arithmetic progressions) in subsets $A$ of the group $\\mathbb{F}_p^n$. It is possible to express these densities as certain analytic averages involving $1_A$, the indicator function of $A$. In the higher-order Fourier analytic approach, the function $1_A$ ... more >>>\n\nTR96-055 | 22nd October 1996\nAlexander E. Andreev, Andrea E. F. Clementi, Jose' D. P. Rolim\n\n#### Hitting Properties of Hard Boolean Operators and their Consequences on BPP\n\nRevisions: 1 , Comments: 1\n\nWe present the first worst-case hardness conditions\non the circuit complexity of EXP functions which are\nsufficient to obtain P=BPP. In particular, we show that\nfrom such hardness conditions it is possible to construct\nquick Hitting Sets Generators with logarithmic prize.\n... more >>>\n\nTR95-061 | 27th November 1995\nAlexander E. Andreev, Andrea E. F. Clementi, Jose' D. P. Rolim\n\n#### Hitting sets derandomize BPP\n\nRevisions: 1\n\nWe show that hitting sets can derandomize any BPP-algorithm.\nThis gives a positive answer to a fundamental open question in\nprobabilistic algorithms. More precisely, we present a polynomial\ntime deterministic algorithm which uses any given hitting set\nto approximate the fractions of 1's in the ... more >>>\n\nTR13-175 | 6th December 2013\nVenkatesan Guruswami, Chaoping Xing\n\n#### Hitting Sets for Low-Degree Polynomials with Optimal Density\n\nRevisions: 1\n\nWe give a length-efficient puncturing of Reed-Muller codes which preserves its distance properties. Formally, for the Reed-Muller code encoding $n$-variate degree-$d$ polynomials over ${\\mathbb F}_q$ with $q \\ge \\Omega(d\/\\delta)$, we present an explicit (multi)-set $S \\subseteq {\\mathbb F}_q^n$ of size $N=\\mathrm{poly}(n^d\/\\delta)$ such that every nonzero polynomial vanishes on at most ... more >>>\n\nTR17-161 | 30th October 2017\nMark Braverman, Gil Cohen, Sumegha Garg\n\n#### Hitting Sets with Near-Optimal Error for Read-Once Branching Programs\n\nNisan (Combinatorica'92) constructed a pseudorandom generator for length $n$, width $n$ read-once branching programs (ROBPs) with error $\\varepsilon$ and seed length $O(\\log^2{n} + \\log{n} \\cdot \\log(1\/\\varepsilon))$. A major goal in complexity theory is to reduce the seed length, hopefully, to the optimal $O(\\log{n}+\\log(1\/\\varepsilon))$, or to construct improved hitting sets, as ... more >>>\n\nTR13-174 | 6th December 2013\nManindra Agrawal, Rohit Gurjar, Arpita Korwar, Nitin Saxena\n\n#### Hitting-sets for low-distance multilinear depth-$3$\n\nThe depth-$3$ model has recently gained much importance, as it has become a stepping-stone to understanding general arithmetic circuits. Its restriction to multilinearity has known exponential lower bounds but no nontrivial blackbox identity tests. In this paper we take a step towards designing such hitting-sets. We define a notion of ... more >>>\n\nTR14-085 | 29th June 2014\nManindra Agrawal, Rohit Gurjar, Arpita Korwar, Nitin Saxena\n\n#### Hitting-sets for ROABP and Sum of Set-Multilinear circuits\n\nWe give a $n^{O(\\log n)}$-time ($n$ is the input size) blackbox polynomial identity testing algorithm for unknown-order read-once oblivious algebraic branching programs (ROABP). The best time-complexity known for this class was $n^{O(\\log^2 n)}$ due to Forbes-Saptharishi-Shpilka (STOC 2014), and that too only for multilinear ROABP. We get rid of their ... more >>>\n\nTR05-099 | 9th September 2005\nLeslie G. Valiant\n\n#### Holographic Algorithms\n\nComplexity theory is built fundamentally on the notion of efficient\nreduction among computational problems. Classical\nreductions involve gadgets that map solution fragments of one problem to\nsolution fragments of another in one-to-one, or\npossibly one-to-many, fashion. In this paper we propose a new kind of\nreduction that allows for gadgets ... more >>>\n\nTR06-145 | 1st December 2006\nJin-Yi Cai, Pinyan Lu\n\n#### Holographic Algorithms: From Art to Science\n\nWe develop the theory of holographic algorithms. We give\ncharacterizations of algebraic varieties of realizable\nsymmetric generators and recognizers on the basis manifold,\nand a polynomial time decision algorithm for the\nsimultaneous realizability problem.\nUsing the general machinery we are able to give\nunexpected holographic algorithms for\nsome counting problems, ... more >>>\n\nTR07-020 | 11th March 2007\nJin-Yi Cai, Pinyan Lu\n\n#### Holographic Algorithms: The Power of Dimensionality Resolved\n\nValiant's theory of holographic algorithms is a novel methodology\nto achieve exponential speed-ups in computation. A fundamental\nparameter in holographic algorithms is the dimension of the linear basis\nvectors.\nWe completely resolve the problem of the power of higher dimensional\nbases. We prove that 2-dimensional bases are universal for\nholographic ... more >>>\n\nTR10-146 | 21st September 2010\nRon Rothblum\n\n#### Homomorphic Encryption: from Private-Key to Public-Key\n\nWe show that any private-key encryption scheme that is weakly\nhomomorphic with respect to addition modulo 2, can be transformed\ninto a public-key encryption scheme. The homomorphic feature\nreferred to is a minimalistic one; that is, the length of a\nhomomorphically generated encryption should be independent of the\nnumber of ... more >>>\n\nTR14-163 | 29th November 2014\nArnaud Durand, Meena Mahajan, Guillaume Malod, Nicolas de Rugy-Altherre, Nitin Saurabh\n\n#### Homomorphism polynomials complete for VP\n\nThe VP versus VNP question, introduced by Valiant, is probably the most important open question in algebraic complexity theory. Thanks to completeness results, a variant of this question, VBP versus VNP, can be succinctly restated as asking whether the permanent of a generic matrix can be written as a determinant ... more >>>\n\nTR05-085 | 5th August 2005\nAsaf Shapira, Noga Alon\n\n#### Homomorphisms in Graph Property Testing - A Survey\n\nProperty-testers are fast randomized algorithms for distinguishing\nbetween graphs (and other combinatorial structures) satisfying a\ncertain property, from those that are far from satisfying it. In\nmany cases one can design property-testers whose running time is in\nfact {\\em independent} of the size of the input. In this paper we\nmore >>>\n\nTR11-088 | 7th June 2011\nPavel Hrubes\n\n#### How much commutativity is needed to prove polynomial identities?\n\nLet $f$ be a non-commutative polynomial such that $f=0$ if we assume that the variables in $f$ commute. Let $Q(f)$ be the smallest $k$ such that there exist polynomials $g_1,g_1', g_2, g_2',\\dots, g_k, g_k'$ with $f\\in I([g_1,g_1'], [g_2, g_2'],\\dots, [g_k, g_k'] )\\,,$\nwhere $[g,h]=gh-hg$. Then $Q(f)\\leq {n\\choose 2}$, where ... more >>>\n\nTR12-167 | 16th November 2012\nPeriklis Papakonstantinou, Charles Rackoff, Yevgeniy Vahlis\n\n#### How powerful are the DDH hard groups?\n\nThe question whether Identity-Based Encryption (IBE) can be based on the Decisional Diffie-Hellman (DDH) assumption is one of the most prominent questions in Cryptography related to DDH. We study limitations on the use of the DDH assumption in cryptographic constructions, and show that it is impossible to construct a secure ... more >>>\n\nTR17-100 | 7th June 2017\nDakshita Khurana, Amit Sahai\n\n#### How to Achieve Non-Malleability in One or Two Rounds\n\nDespite over 25 years of research on non-malleable commitments in the plain model, their round complexity has remained open. The goal of achieving non-malleable commitment protocols with only one or two rounds has been especially elusive. Pass (TCC 2013, CC 2016) captured this difficulty by proving important impossibility results regarding ... more >>>\n\nTR09-132 | 8th December 2009\nLior Malka\n\n#### How to Achieve Perfect Simulation and a Complete Problem for Non-interactive Perfect Zero-Knowledge\n\nPerfect zero-knowledge (PZK) proofs have been constructed in various settings and they are\nalso interesting from a complexity theoretic perspective. Yet, virtually nothing is known about them. This is in contrast to statistical zero-knowledge proofs, where many general results have been proved using an array of tools, none of which ... more >>>\n\nTR15-055 | 13th April 2015\nSivaramakrishnan Natarajan Ramamoorthy, Anup Rao\n\n#### How to Compress Asymmetric Communication\n\nWe study the relationship between communication and information in 2-party communication protocols when the information is asymmetric. If $I^A$ denotes the number of bits of information revealed by the first party, $I^B$ denotes the information revealed by the second party, and $C$ is the number of bits of communication in ... more >>>\n\nTR12-010 | 5th February 2012\nShafi Goldwasser, Guy Rothblum\n\n#### How to Compute in the Presence of Leakage\n\nWe address the following problem: how to execute any algorithm P, for an unbounded number of executions, in the presence of an adversary who observes partial information on the internal state of the computation during executions. The security guarantee is that the adversary learns nothing, beyond P's input\/output behavior.\n\nThis ... more >>>\n\nTR12-140 | 27th October 2012\nMark Zhandry\n\n#### How to Construct Quantum Random Functions\n\nRevisions: 2\n\nIn the presence of a quantum adversary, there are two possible definitions of security for a pseudorandom function. The first, which we call standard-security, allows the adversary to be quantum, but requires queries to the function to be classical. The second, quantum-security, allows the adversary to query the function on ... more >>>\n\nTR13-183 | 22nd December 2013\nYael Tauman Kalai, Ran Raz, Ron Rothblum\n\n#### How to Delegate Computations: The Power of No-Signaling Proofs\n\nRevisions: 1\n\nWe construct a 1-round delegation scheme (i.e., argument-system) for every language computable in time t=t(n), where the running time of the prover is poly(t) and the running time of the verifier is n*polylog(t). In particular, for every language in P we obtain a delegation scheme with almost linear time verification. ... more >>>\n\nTR12-058 | 5th May 2012\nBenny Applebaum, Yuval Ishai, Eyal Kushilevitz\n\n#### How to Garble Arithmetic Circuits\n\nRevisions: 1\n\nYao's garbled circuit construction transforms a boolean circuit $C:\\{0,1\\}^n\\to\\{0,1\\}^m$\ninto a garbled circuit'' $\\hat{C}$ along with $n$ pairs of $k$-bit keys, one for each\ninput bit, such that $\\hat{C}$ together with the $n$ keys\ncorresponding to an input $x$ reveal $C(x)$ and no additional information about $x$.\nThe garbled circuit ... more >>>\n\nTR05-145 | 5th December 2005\nRonen Shaltiel\n\n#### How to get more mileage from randomness extractors\n\nLet $\\cal C$ be a class of distributions over $\\B^n$. A deterministic randomness extractor for $\\cal C$ is a function $E:\\B^n \\ar \\B^m$ such that for any $X$ in $\\cal C$ the distribution $E(X)$ is statistically close to the uniform distribution. A long line of research deals with explicit constructions ... more >>>\n\nTR05-096 | 26th August 2005\nBoaz Barak, Amit Sahai\n\n#### How To Play Almost Any Mental Game Over The Net --- Concurrent Composition via Super-Polynomial Simulation\n\nWe construct a secure protocol for any multi-party functionality\nthat remains secure (under a relaxed definition of security) when\nexecuted concurrently with multiple copies of itself and other\nprotocols. We stress that we do *not* use any assumptions on\nexistence of trusted parties, common reference string, honest\nmajority or synchronicity ... more >>>\n\nTR09-021 | 2nd March 2009\nKonstantin Makarychev, Yury Makarychev\n\n#### How to Play Unique Games on Expanders\n\nIn this note we improve a recent result by Arora, Khot, Kolla, Steurer, Tulsiani, and Vishnoi on solving the Unique Games problem on expanders.\n\nGiven a (1 - epsilon)-satisfiable instance of Unique Games with the constraint graph G, our algorithm finds an assignments satisfying at least a (1 - C ... more >>>\n\nTR06-144 | 21st November 2006\nClaire Kenyon-Mathieu, Warren Schudy\n\n#### How to rank with few errors: A PTAS for Weighted Feedback Arc Set on Tournaments\n\nSuppose you ran a chess tournament, everybody played everybody, and you wanted to use the results to rank everybody. Unless you were really lucky, the results would not be acyclic, so you could not just sort the players by who beat whom. A natural objective is to find a ranking ... more >>>\n\nTR16-023 | 23rd February 2016\nIlan Komargodski, Moni Naor, Eylon Yogev\n\n#### How to Share a Secret, Infinitely\n\nRevisions: 4\n\nSecret sharing schemes allow a dealer to distribute a secret piece of information among several parties so that any qualified subset of parties can reconstruct the secret, while every unqualified subset of parties learns nothing about the secret. The collection of qualified subsets is called an access structure. The best ... more >>>\n\nTR17-112 | 27th June 2017\nYehuda Lindell\n\n#### How To Simulate It -- A Tutorial on the Simulation Proof Technique\n\nOne of the most fundamental notions of cryptography is that of \\emph{simulation}. It stands behind the concepts of semantic security, zero knowledge, and security for multiparty computation. However, writing a simulator and proving security via the use of simulation is a non-trivial task, and one that many newcomers to the ... more >>>\n\nTR06-025 | 19th January 2006\nLeonid Gurvits\n\n#### Hyperbolic Polynomials Approach to Van der Waerden\/Schrijver-Valiant like Conjectures :\\\\ Sharper Bounds , Simpler Proofs and Algorithmic Applications\n\nLet $p(x_1,...,x_n) = p(X) , X \\in R^{n}$ be a homogeneous polynomial of degree $n$ in $n$ real variables ,\n$e = (1,1,..,1) \\in R^n$ be a vector of all ones . Such polynomial $p$ is\ncalled $e$-hyperbolic if for all real vectors $X \\in R^{n}$ the univariate polynomial\nequation ... more >>>\n\nISSN 1433-8092 | Imprint","date":"2019-10-23 11:22:37","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 2, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8188554644584656, \"perplexity\": 3214.864928430027}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": false}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2019-43\/segments\/1570987833089.90\/warc\/CC-MAIN-20191023094558-20191023122058-00438.warc.gz\"}"}
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Q: angular.js deferred doesnt work in callback Consider the following example:
.service('movieGetter', ['$q', '$timeout', function ($q, $timeout) {
this.getData = function () {
var deferred = $q.defer();
$timeout(function(){
mock.getData(function(data){
deferred.resolve(data);
});
}, 2000);
return deferred.promise;
};
}]);
For some reason this code doesn't work, when the line deferred.resolve() fires the callback at then in the constroller does't
On the other hand tthis example works fine:
.service('movieGetter', ['$q', '$timeout', function ($q, $timeout) {
this.getData = function () {
var deferred = $q.defer();
$timeout(function () {
deferred.resolve('test');
}, 2000);
return deferred.promise;
};
}]);
Fow some reason when the deferred.resolve() fires inside callback the then callback on the constroller doesn't work.
Any ideas?
Thanks!
A: As it appears, the promise API in angular is part of the scope and thus, when calling resolve inside callback angular is not in the $apply cycle and it's unaware of the function call.
To resolve this $scope.$apply() should be called right after the resolve function. If in service, and the $scope injectable is unavailable you can inject $rootScope instead.
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Who is the doctor on autopsy the last hours of?
Answred by. Alonzo Richburg
In Sport, Updates
Michael Hunter taking over as the host. The UK produced episodes featured Dr. Richard Shepherd and subsequently (after about the first ten episodes), Dr. Jason Payne-James (for about five more episodes) analyzing the official autopsy reports of various celebrities to determine their cause of death.
Simply so, What is the difference between post mortem and autopsy?
A post-mortem examination, also known as an autopsy, is the examination of a body after death. The aim of a post-mortem is to determine the cause of death. … Post-mortems provide useful information about how, when and why someone died.
Similarly, Where to watch autopsy the last hours of Andy Griffith?
There is much more to learn in Autopsy: The Last Hours of… Andy Griffith on June 6 at 8 p.m. ET/PT on REELZ. Watch REELZ on DIRECTV 238, Dish Network 299, Verizon FiOS 692, AT&T U-verse 1799 and in HD on cable systems and streaming services nationwide.
Does Hulu have autopsy?
Watch Autopsy: Confessions of a Medical Examiner Streaming Online | Hulu (Free Trial)
Furthermore, Do they remove organs when you die?
When an Autopsy Occurs
The pathologist removes the internal organs in order to inspect them. They may then be incinerated, or they may be preserved with chemicals similar to embalming fluid. … Since the organs were preserved and placed in plastic, no additional cavity embalming is needed.
Does an autopsy always show cause of death?
How long after death can an autopsy be done?
Who were Andy Taylor's girlfriends?
What is the meaning of Andy Griffith?
Can you stream reelz channel?
Where can I watch reelz TV?
Do bodies sit up during cremation?
Do they drain your blood when you die?
How long does a body last in a coffin?
Do you have to have an autopsy if you die at home?
Who decides if an autopsy is performed?
Can an autopsy be done after embalming?
Can an autopsy be done after cremation?
Who picks dead bodies from homes?
Why did Frances Bavier hate Andy?
Who does Andy Taylor marry?
Is Helen Crump still alive?
Did Aunt Bee wear a wig?
Also read How many draft picks do the Eagles have in 2021?
An autopsy is not generally necessary when the death is known to be the result of known medical conditions/diseases (ie, natural causes), adequate medical history exists, and there are no signs of foul play.
Cina says that autopsies are best if performed within 24 hours of death, before organs deteriorate, and ideally before embalming, which can interfere with toxicology and blood cultures.
While Helen Crump holds a special place in the show's history, so does the actress who portrayed Peggy McMillan. Joanna Moore plays Peggy. She played Taylor's girlfriend for four episodes of "The Andy Griffith Show." She holds a special place in fan's hearts and even holds a record on the show.
Andy had a reputation as sometimes being very mean spirited-especially when he was drunk. … Don and Andy had known each other from the hit Broadway play they both had appeared in (Andy was the star) called "No Time for Sergeants" along with also starring in the movie version.
REELZ NOW® is an on-demand online video service offered through participating TV providers that gives you the freedom to watch TV streaming live and access to full episodes of your favorite REELZ shows when and where you want to watch them. Access REELZ NOW® via our mobile apps, streaming devices and web.
REELZ is available through AT&T TV, which is a service that you might know by one of its old names, DIRECTV NOW or AT&T TV NOW. By any name, AT&T TV is a strong live TV streaming service with multiple bundles to offer. Pick one that includes REELZ and you'll be off and streaming, no cable required.
While bodies do not sit up during cremation, something called the pugilistic stance may occur. This position is characterized as a defensive posture and has been seen to occur in bodies that have experienced extreme heat and burning.
Also read Does Hulu have autopsy?
Contrary to what you might think, blood from cadavers is not only usable, but quite safe. … However, draining the blood from a body is hardly out of the ordinary; it's actually a regular part of the embalming process.
An embalmed body usually lasts in a coffin for up to 10 years, but can last from 3 to 100 years, depending on the: Skill of the embalmer. Length of time from death before embalming. Size and weight of the body.
Arrange for the body to be transported to the morgue or a funeral home/crematorium. Generally, if the deceased was elderly and was under a doctor's care, it is unlikely that an autopsy will need to be performed. If this is the case, a funeral home can transport the individual.
An autopsy may be ordered by the coroner or medical examiner to determine the cause or manner of death, or to recover potential evidence such as a bullet or alcohol content in the blood. Policy varies across the United States but typically unwitnessed, tragic, or suspicious deaths require an autopsy.
Can an autopsy be performed if the body has been embalmed? Yes, however, for the best outcome, an autopsy should be performed on an un-embalmed body after proper refrigeration. If there is a long delay (beyond one week) between the time of death and the autopsy, embalming is recommended to preserve the body tissues.
Once cremated, the body is reduced to non organic and any natural elements it contained. … This is why it is nearly impossible to determine the cause of death from cremated remains. Because of this, states require cause of death or a certified death certificate be prepared before a body can be cremated.
WHEN SOMEONE DIES AT HOME, WHO TAKES THE BODY? The answer is that it depends on how the person in question died. Typically, if the death was from natural causes and in the presence of family, a funeral home of the family's choice will go to the home and remove the dead body.
According to Griffith and Howard Morris, Bavier was extremely sensitive, and resented her role of Aunt Bee. … Andy Griffith originally told Don Knotts that he only wanted to do the show for five years.
episode "Opie Joins the Marines", made a cameo appearance in the USMC episode "Gomer Goes Home," five episodes of Mayberry R.F.D. (1968–1971) and the reunion television film Return to Mayberry (1986).
Andy Taylor (The Andy Griffith Show)
Spouse Unnamed wife (deceased) Helen Crump
Children Opie Taylor (son) Andrew Samuel Taylor, Jr. (son)
She is best known for playing Helen Crump on The Andy Griffith Show (1963–1968), Judge Cynthia Justin on Matlock (1991-1992), and Jane in The Blob (1958).
Aneta Corsaut
Born Aneta Louise CorsautNovember 3, 1933 Hutchinson, Kansas, U.S.
Died November 6, 1995 (aged 62) Studio City, Los Angeles, California, U.S.
Andy Griffith and Frances Bavier did not get along during the series. According to Griffith and Howard Morris, Bavier was extremely sensitive, and resented her role of Aunt Bee. Andy Griffith originally told Don Knotts that he only wanted to do the show for five years.
Andy flips his wig over Aunt Bee's wig.
Perhaps the biggest example comes in the season 7 episode "Aunt Bee's Crowning Glory." In it, Aunt Bee tries to wear a wig to look prettier, and everybody agrees it's a good look. … At first, Andy loses it because he thinks Aunt Bee has dyed her hair.
Who is the richest NBA player ever?
1. Michael Jordan Net Worth – $2.2 Billion. Viewed by many as the greatest player in NBA history, Jordan has turned his basketball acumen into a multi-billion dollar enterprise. Also to know is Who is the poorest NBA player? Delonte West net...
Who are the starters for the Indiana Pacers?
Who Are The Pacers Starters? The Pacers starters are Domantas Sabonis, Myles Turner, Malcolm Brogdon, TJ Warren, and Victor Oladipo. Also to know is Where did Jeff Green play last year? In 2016, he was traded to the Los Angeles Clippers. He spent...
When was the last time the Browns won a Super Bowl?
The Cleveland Browns won the Super Bowl once, in 1964. Also to know is Who was in Super Bowl 30? The Cowboys defeated the Steelers by the score of 27–17. The game was played on January 28, 1996, at Sun Devil Stadium in Tempe, Arizona, the first time...
Why Karl Malone is called mailman?
Because The Mailman always delivers! Karl Malone, is a former power forward for the Utah Jazz of the NBA and one of the game's 50 Greatest Players. The name was given to him in college by a sportswriter covering his alma mater, Louisiana Tech...
What Super Bowl did Peyton lose?
Peyton Manning lost the Super Bowl to the New Orleans Saints in 2010 and then again in 2014, to the Seattle Seahawks. Also to know is How much is a Peyton Manning rookie card worth? The 1998 Topps Chrome Peyton Manning Refractor Rookie PSA 10 Gem...
Answred by. Alonzo Richburg October 20, 2021
Who is going to the NBA Finals 2020?
Who is the famous player of basketball?
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| 1,156
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This report gives a market insight into the different types of Unnatural Amino Acids (β-Amino Acids, β-Amino Acid Derivatives, Cyclic Amino Acids & Derivatives, D-Amino Acids, D-Amino Acid Derivatives, DL-Amino Acids, DL-Amino Acid Derivatives, L-Amino Acid Derivatives and Other ) and their application areas such as R&D, Pharmaceutical, Food & Feed, Agrochemicals and Other applications. Business profiles of 58 major companies are discussed in the report. The report serves as a guide to global Unnatural Amino Acids industry covering more than 500 companies that are engaged in Unnatural Amino Acids R&D, synthesis, discovery, testing and supply of derivatives, products and services. Compilation of Worldwide Patents and Research related to Unnatural Amino Acids market size is also provided. Information related to industrial activity, corporate developments, research trends, product releases, product developments, partnerships, collaborations, and mergers and acquisitions is also covered in the report.
Modern drug discovery research is increasingly experimenting with unnatural amino acids, the non‐proteinogenic amino acids, either natural or chemically synthesized. Their unlimited structural diversity and versatile applications are being used as chiral building blocks and molecular scaffolds in building combinatorial libraries. These molecules are powerful ingredients in therapeutic peptidomimetics and are used as molecular probes which can assimilate the biological systems better. They show improved in vivo stability, better potency, oral absorption, tissue distribution, and better and selective responses. Unnatural amino acids are increasingly being used to alter the peptides tertiary structure. Drug candidates with side chain modifications meet and match their biological targets. The pharmaceutical industry accounts for almost 80% of chiral market revenues. Despite the fact that chiral drugs have been in use much before the arrival of modern medicine, it is only now that chiral drugs in the pharmaceutical industry has gained so much attention. This is largely due to the understanding that enantiomers often show different bioactivity and metabolic fates. In addition there is also a commercial reason where pharmaceutical companies have the chance to extend patent coverage after expiry of patents on racemic drugs. This can take place through the development of the chiral switch enantiomers with suitable bioactivity. Unnatural Amino Acids market is a rapidly growing market in the intermediates sector. Majority of the products utilizing these compounds are pharmaceutical intermediates (β ‐ Lactam Antibiotics). Asia ‐ Pacific region is acquiring lead position in global pharmaceuticals market with the balance gradually shifting from the US and Europe to Asia ‐ Pacific. In principle, an unnatural amino acid can be produced by procedures such as replacement of hydrogen by fluorine in a ring structure, or phenyl by another resonant ring system, or one kind of heterocyclic ring by another one, or a remnant from the framework of an amino acid by another remnant of one that is analogous in shape and size. Practically all the advantageous amino acid analogues have earlier existed as close structural isomers of amino acids that occur naturally. So far, no efficient analogs of proline, glutamic acid, aspartic acid, alanine, threonine, cysteine, serine or glycine have been accounted for. Probably, the biological sites that are involved in these amino acids are governed by particular size and shape of molecule when compared to amino acids of larger size. Some of the alterations that are performed for the production of anti ‐ metabolites from the larger sized amino acids are not tenable with smaller sized amino acids. This is because the resultant compounds lack appreciable stability as in the case of fluoroglycine or substitution of sulfur for ‐ CH2 within the molecular framework of glutamic acid or threonine. In this regard, the non ‐ existence of proline analog is intriguing, though the occurrence of azetidine ‐ 2 ‐ carboxylic acid is worth mentioning. Most of the amino acid analogues could be conceived as anti ‐ tumor, antiviral or antimicrobial. The amino acid analogues are regularly subjected to screening to find the possibility of anti metabolite activity to counteract bacteria. These experiments are all documented in detail and are useful for those who want to study the effect of analogues on proliferating bacteria. Unnatural Amino Acids market is a rapidly growing market in the intermediates sector. Majority of the products utilizing these compounds are pharmaceutical intermediates (β ‐ Lactam Antibiotics).
Synopsis of the report summarizes the global market of Unnatural Amino Acids. Market for By Type and By Application is also covered in this chapter. Historic review of Unnatural Amino Acid is also covered. List of major global companies is also included.
Market Dynamics provides information on global markets for Unnatural Amino Acids. The chapter includes global market analysis from 2010 through 2020, by geographic regions (North America, Europe, China, Asia-Pacifc and Rest of World); Type (β-Amino Acids, β-Amino Acid Derivatives, Cyclic Amino Acids & Derivatives, D-Amino Acids, D-Amino Acid Derivatives, DL-Amino Acids, DL-Amino Acid Derivatives, and L-Amino Acid Derivatives) and Application (Research & Development, Pharmaceuticals, Food & Feed, and Agrochemicals). The section includes key market trends and an industry outlook.
The chapter includes brief business profiles of major global companies; and a glance at corporate activities such as mergers and acquisitions, partnerships, new product developments/launches etc. Product price list of various major companies is also provided.
This chapter gives an insight into Unnatural Amino Acid market including definitions, segmentation and applications. The chapter also provides information on various products that contain Unnatural Amino Acids and their uses. Research activities in the field of unnatural amino acid also find a mention in this chapter.
This chapter provides the region-wise list of 520 plus companies, CROs, and CMOs that are engaged in the manufacturing, processing, trading and/or supply of Unnatural Amino Acid products and services.
This chapter provides a compilation of worldwide patents related to Unnatural Amino Acids products/technologies.
Unnatural Amino acids Market research report gives an insight into the different types of Unnatural Amino Acids (ß-Amino Acids, ß-Amino Acid Derivatives, Cyclic Amino Acids & Derivatives, D-Amino Acids, D-Amino Acid Derivatives, DL-Amino Acids, DL-Amino Acid Derivatives, L-Amino Acid Derivatives and Other ) and their application areas such as R&D, Pharmaceutical, Food & Feed, Agrochemicals and Other. The study includes historic, current, and future markets for 2010 -2022 for the global Unnatural Amino Acids market by type and applications. Regional Analysis is covered separately for North America (United States and Canada); Europe (UK, Germany, Switzerland, Italy, The Netherlands, and Rest of Europe); Asia Pacific (China, Japan, India, South Korea, Australia, and Rest of Asia Pacific); and Rest of World. The text is complemented with graphical representations of 293 exhibits. Business profiles of 58 major companies are discussed in the report. The report serves as a guide to global Unnatural Amino Acids industry covering more than 500 companies that are engaged in Unnatural Amino Acids R&D, synthesis, discovery, testing and supply of derivatives, products and services. Compilation of Worldwide Patents and Research related to Unnatural Amino Acids market size is also provided. Information related to industrial activity, corporate developments, research trends, product releases, product developments, partnerships, collaborations, and mergers and acquisitions is also covered in the report.
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# CONTENTS
Title Page
Introduction
Why sugar is bad for you
How to read food labels
Smart sugar swaps
Alternatives to sugar in cooking
Simple ways to bypass sugar
Basics
Ketchup
BBQ sauce
Apple sauce
Mayonnaise
Peanut butter
Blueberry jam
Chocolate spread
Pastry
Yoghurt
Vinaigrette
Creamy dressing
Wholemeal loaf
Breakfast
Mango & carrot smoothie
Fruit spritzer
Beetroot smoothie
Date & oat thickshake
Peanut butter & chocolate shake
Berry ripple porridge
Granola
Luxe muesli
Bircher muesli
Pancakes with sautéed peaches
Rye & berry waffles
Banana French toast
Strawberry cream cheese toast
Snacks
Cinnamon popcorn
Lime & chilli almonds
Fruit roll-ups
Berry dip with fruit crudités
Whipped banana toast
Apple crisps
Orange & saffron grissini
Doughnut balls
Apricot & coconut balls
Chocolate energy bars
Fruit & nut bars
Chocolate raisins
Stuffed dates
Freezer fudge
Baked
Date & spelt crackers
Blueberry & apple muffins
Seedy peach muffins
Banana loaf
Chocolate torte
Carrot cake
Raspberry & almond focaccia
Sweet potato scones
Peanut butter cookies
Chocolate oatmeal cookies
Thumb print biscuits
Desserts
Fruit salad & rosewater dressing
Saucy pears with pecans
Fig & mint syllabub
Chocolate mousse
Berry chia pudding
Bread & butter pudding
Apple & raspberry jelly
Fruit crumble
Apple pie
Blueberry cheesecake
Lime & coconut ice cream
Berry ice cream
Chocolate ice cream
Strawberry ice pops
Melon & apple granita
Glossary
Index
Copyright Page
7
# INTRODUCTION
This book is designed to help you reduce or even eliminate the added sugar in your diet, which most of us need to do. Added sugars should make up no more than 10 per cent, but ideally less than 5 per cent, of the calories in the food and drink we consume each day. That means no more than 70g for men and 50g for women.
How you reduce your added sugar intake is up to you. Some people go cold turkey, while others gradually cut down, but whatever you choose to do there are a few things to bear in mind.
Regardless of the amount of added sugar you currently consume, cutting down might take time to get used to. For example, you might find that home-made ketchup doesn't have the same sweet appeal as the bought stuff, or that cakes made without refined sugar lack the flavour and texture of sugary versions. My advice is to stick with it, as your brain and taste buds will adjust in time. In fact, the longer you avoid added sugar, the less you notice it.
Many so-called sugar-free recipes are laden with honey, agave or other sweet syrups, which some people praise for being 'natural' and healthier than table sugar. The fact is, these syrups are still loaded with sugar, have little nutritional value and some contain high levels of fructose, which is believed by some experts to be especially bad for human health. That's why I have not included these ingredients in this book. Neither have I used sugar substitutes like stevia or xylitol. I believe if you are trying to cut down on added sugar, it's better to avoid artificial sweeteners, as they can fuel sugar cravings.
Instead of syrups or sugar substitutes, I've used dried and fresh fruit to sweeten. Fruit is full of fibre, so the sugars it contains are absorbed slowly and don't cause spikes in blood sugar levels. I've also used fruit juice as a sweetener in a handful of recipes. While fruit juice should be consumed in moderation as a drink, I believe it's fine to use in small amounts alongside fibre-rich ingredients in cooking.
Finally, a word of caution to readers with Type 1 or Type 2 diabetes: please seek medical advice before using the recipes in this book.
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# WHY SUGAR IS BAD FOR YOU
Glucose is the body's major fuel and is broken down from carbohydrates, a combination of sugar molecules, in the food we eat. When experts talk about over-consumption of sugar, they're referring to simple sugars like sucrose (also known as added sugar or table sugar) found in foods like baked goods, sweets, desserts, soft drinks, fruit juice, honey and syrups.
Added sugar has no nutritional value and is loaded with 'empty' calories. The more calories we consume, the more likely we are to be obese, and obesity is linked to heart disease, Type 2 diabetes, tooth decay and many other serious health conditions.
Some experts believe the fructose component of added sugar is especially harmful (see diagram below). Fruit and vegetables are a small source of fructose for most people and are full of fibre, which slows down digestion of the sugars they contain.
9
# HOW TO READ FOOD LABELS
Spotting added sugar on food labels can be difficult, but follow the tips below to avoid buying sugar-loaded products.
| LOOK FOR sugar content under carbohydrates. It's often listed as 'carbohydrates (of which sugars)'.
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| MORE THAN 22.5g sugars per 100g is high, less than 5g of total sugars per 100g is low, and a figure in between is medium1.
| A LONG list of ingredients means the product is highly processed and best avoided.
| THE FIRST 4.7g of sugar per 100ml of a dairy product is naturally occurring lactose, a good sugar – the rest is added.
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| INGREDIENTS ARE often listed in descending order by weight, so if sugar is at or near the top it's probably loaded with sugar.
| FAMILIARISE YOURSELF with the different names for sugar on the adjacent table.
The list below contains some, but not all of the names for sugar used on food labels2.
Agave nectar
Barbados sugar
Barley malt
Beet sugar
Blackstrap molasses
Brown sugar
Buttered syrup
Cane crystals
Caramel
Carob syrup
Confectioners' sugar
Cane juice crystals
Cane sugar
Caster sugar
Corn sweetener
Corn syrup/corn syrup solids
Crystalline fructose
Date sugar
Demerara sugar
Dextran
Dextrose
Diastatic malt
Diatase
Ethyl maltol
Evaporated cane juice
Florida crystals
Fructose
Fruit juice/fruit juice concentrates
Fruit syrup
Galactose
Glucose/glucose solids
Golden sugar
Golden syrup
Grape sugar
High-fructose corn syrup
Honey
Hydrolysed starch
Icing sugar
Invert sugar
Lactose
Maltodextrin
Maltose
Malt syrup
Maple syrup
Molasses
Muscovado sugar
Panocha
Raw sugar
Refiners' syrup
Rice syrup
Sorghum syrup
Sugar
Sucrose
Syrup
Treacle
Turbinado sugar
Yellow sugar
1 NHS Choices website – How much sugar is good for me?
2 Harvard Institute of Public Health; _Fat Chance: The bitter truth about sugar,_ by Dr Robert Lustig
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# SMART SUGAR SWAPS
Use the table below* as a guide to replace sugar-laden products with less sugary versions. Read labels carefully, as the sugar content of a product can vary widely between brands. Also bear in mind that processed savoury food is far from sugar free. For example, 100g of barbecue crisps can contain about the same amount of added sugar as a large square of milk chocolate.
**BEVERAGES** (grams of sugar per 330ml serve)
**JAMS, SPREADS & CONFECTIONARY** (grams of sugar per 100g)
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**BREAKFAST CEREAL** (grams of sugar per 100g)
**BREAD, BISCUITS, BUNS & CAKES** (grams of sugar per 100g)
**LOW-FAT AND 'DIET' FOODS** (grams of sugar per 100g serve)
*Total sugar content according to the USDA National Nutrient Data Base for Standard Reference. Read labels carefully as sugar content varies between brands.
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**SAVOURY FOOD** (grams of sugar per 100g)
**ALCOHOLIC DRINKS** (grams of sugar per 100ml)
**TAKEAWAY AND FAST FOOD** (grams of sugar per 100g)
13
**ALTERNATIVES TO SUGAR IN COOKING**
Try replacing added sugar with the following naturally sweet options – they'll also boost flavour and compensate for lack of sweetness. Experiment with quantities according to the recipe and personal taste.
| **UNSWEETENED APPLE SAUCE**
Use instead of sugar in baked goods like biscuits, muffins and cakes, adding more of the dry ingredients to compensate if necessary. Also spoon over yoghurt or cereal instead of honey or sugar.
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| **DRIED FRUIT**
Contains lots of concentrated sugar but also valuable nutrients (counts as one of the recommended five daily servings of fruit and vegetables). Blitz fresh dates to a paste in a food processor and use instead of sugar in baked goods. If using dried dates or other dried fruit, soak in water before blitzing. Add more dry ingredients in baking to compensate if necessary.
| **MASHED BANANA**
Use instead of sugar in dense bakes like carrot cake and banana loaf. Riper bananas are sweeter, or use roasted bananas.
| **CINNAMON**
Adds gentle sweetness and flavour. Lovely stirred into coffee.
| **NUTMEG**
Adds gentle sweetness and flavour.
| **GROUND FENNEL SEEDS**
Adds gentle sweetness and flavour.
| **VANILLA**
Scraped beans from the pod, vanilla powder or unsweetened vanilla extract add sweetness. Note: some brands of vanilla extract contain added sugar.
| **COCONUT OIL**
Adds a hint of sweetness when frying food or used in baking instead of vegetable oil or butter. Add a little to smoothies.
| **COCONUT MILK**
Adds gentle sweetness when used instead of dairy milk in shakes, smoothies and cooking.
| **ALMOND MILK**
Adds gentle sweetness and creaminess to shakes, smoothies, and lovely in baking. Opt for unsweetened versions.
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# SIMPLE WAYS TO BYPASS SUGAR
Sugar is such a large part of our everyday diet that often we don't even realise we're consuming it. By paying attention to the sugar content of what we eat, and making simple dietary adjustments, it's easy to dramatically reduce our intake.
START by cutting out or reducing intake of sugary beverages, especially fizzy drinks and fruit juice, which are the most damaging ways to consume sugar. Drink milk, water, vegetable juice or diluted fruit juice instead. Try gradually reducing sugar in hot beverages until you don't add any.
WHEN baking, reduce quantities of sugar in recipes by one-third to one-half. Make puddings, cakes and biscuits a treat rather than part of your everyday diet.
RESEARCH the total sugar (especially fructose) content of the food and drink you consume – quantities vary significantly between brands. Read labels carefully.
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AVOID processed food, which is loaded with added sugar, and cook more from scratch, especially sauces, dressings and breakfast cereals. Shop in the outer aisles of the supermarket where fresh produce is generally sold.
AVOID low-fat products – manufacturers load these with added sugar to make them palatable. Instead of fruit-flavoured yoghurt, for example, buy plain yoghurt and swirl through fruit puree.
EAT lots of small meals, as many as six a day, to reduce the temptation to snack on sugary food. Identify your weaknesses and find unsweetened substitutes. For example, if you like sweet biscuits with your coffee, keep nuts or sugar-free crackers by the kettle.
FRESH fruit is a healthy choice, but contains lots of sugar, especially fructose, so enjoy in moderation and go for the less sugary kinds. The adjacent list includes fruit with less than 10g sugar per 100g, from lowest to highest. Choose cans of fruit in unsweetened juice rather than syrup.
**FRUIT**
with less than 10g sugar per 100g:
| raspberries
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| blackberries
| strawberries
| watermelon
| currants
| papayas
| cantaloupe melons
| nectarines
| mulberries
| honeydew melons
| tangerines
| pineapples
| peaches
| sour cherries
| guavas
| kiwi fruit
| apricots
| oranges
| apples
| pears
| blueberries
Ketchup • BBQ sauce • Apple sauce • Mayonnaise • Peanut butter • Blueberry jam • Chocolate spread • Pastry • Yoghurt • Vinaigrette • Creamy dressing • Wholemeal loaf
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# KETCHUP
_Makes: about 250ml • Time: 1 hour_
## YOU NEED
2 tablespoons olive oil • ½ onion, chopped • ½ red pepper, chopped
½ red apple, chopped with skin on • a generous pinch of fine sea salt
1 garlic clove, chopped • 2 tablespoons tomato purée
2 ripe tomatoes, about 250g, chopped • 60ml passata
2 tablespoons red wine vinegar • a pinch of cayenne pepper
½ teaspoon ground cinnamon • 2 cloves • ¼ teaspoon celery salt • 1 bay leaf
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Heat the oil in a large pan and gently cook the onion, pepper and apple for 15 minutes, stirring often. Season with salt, add the garlic and cook for 5 minutes more. Stir in the tomato purée, then add the remaining ingredients and gently cook, covered, for 15 minutes. Stir now and then. Uncover and cook for 5 minutes more. Discard the bay leaf and blitz the sauce in a food processor until smooth. Add more salt and pepper or vinegar to taste, then push through a sieve. Store in an airtight container in the fridge.
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# BBQ SAUCE
_Makes: about 500ml • Time: 1 hour_
## YOU NEED
400ml passata • 1 onion, chopped • 2 garlic cloves, chopped
2 tablespoons tomato purée • 2 teaspoons Dijon mustard
3 tablespoons apple cider vinegar • 1 tablespoon vegetable oil
2 tablespoons sweet smoked paprika • ½ teaspoon cayenne pepper
1 teaspoon sea salt flakes • ½ teaspoon liquid smoke (optional)
80g unsweetened pineapple chunks • 60ml unsweetened pineapple juice
1 tablespoon Worcestershire sauce (or soy sauce), or to taste
1 tablespoon raisins • about 400ml chicken stock, plus extra if needed
21
Blend together all the ingredients except the stock in a food processor until smooth. Transfer to a pan, add a splash of the stock, and gently simmer, uncovered, for 45 minutes. Stir regularly, adding a splash of stock each time to maintain a sauce-like consistency as the mixture reduces. Add more salt or pepper to taste. Store in an airtight container in the fridge.
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# APPLE SAUCE
_Makes: 500g • Time: 1–3 hours_
## YOU NEED
1kg sweet apples, cored and chopped with skin on
2 teaspoons ground cinnamon (optional)
23
Preheat the oven to 170°C/325°F/Gas 3. Place the apples in an ovenproof pan and roast, covered, for about 1 hour, or until completely soft. Stir halfway through. Alternatively, cook in a slow cooker on high for 3 hours. Transfer to a blender or food processor, add the cinnamon (if using) and blitz until smooth. Store in an airtight container in the fridge.
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# MAYONNAISE
_Makes: about 250g • Time: 10 minutes_
## YOU NEED
2 egg yolks • 1 tablespoon lemon juice, plus extra to taste
a generous pinch of sea salt flakes • 250ml vegetable oil
2 tablespoons olive oil • 1 heaped teaspoon Dijon mustard
sea salt flakes
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Beat together the egg yolks, lemon juice and salt with electric beaters or a whisk until creamy. Add the oils in a very thin stream while beating constantly until the mixture is thick and pale. Stir in the mustard and add more lemon juice or salt to taste. Store in an airtight container in the fridge.
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# PEANUT BUTTER
_Makes: about 400g • Time: 10 minutes_
## YOU NEED
400g unsalted roasted peanuts • sea salt flakes, to taste
1 tablespoon vegetable oil
27
Blitz half the peanuts in a food processor until coarsely chopped. Add the remaining peanuts and a generous pinch of salt. Process until smooth, then gradually add the oil until you achieve the desired consistency. Add extra salt to taste. Store in an airtight container in the fridge.
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# BLUEBERRY JAM
_Makes: about 600g • Time: 45 minutes_
## YOU NEED
800g blueberries, rinsed and stalks removed • 2 tablespoons lemon juice
400ml unsweetened grape juice
29
Place the blueberries in a heavy pan, mash with a potato masher, then stir in the lemon juice and grape juice. Bring to the boil, then reduce the heat and simmer, uncovered, for 30–40 minutes, or until thick and reduced to the desired consistency. Pour into sterilised jars and store in the fridge.
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# CHOCOLATE SPREAD
_Makes: about 200g • Time: 10 minutes_
## YOU NEED
100g skinless blanched hazelnuts • 1 teaspoon vanilla extract
60g pitted fresh dates • 3 tablespoons unsweetened cocoa powder
1 tablespoon hazelnut oil • 1 teaspoon milk powder
a pinch of fine sea salt • 2–3 tablespoons coconut cream
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Gently toast the hazelnuts in a dry frying pan until fragrant and starting to brown. Leave to cool a little, then transfer to a food processor and blitz to a paste. This takes a while so stick with it. Add the remaining ingredients and blitz until very smooth and creamy, adding as much coconut cream as necessary to achieve the desired consistency. Store in an airtight container in the fridge.
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# PASTRY
_Makes: enough for 1 x 25cm tart or covered pie • Time: 40 minutes_
## YOU NEED
250g plain flour, plus more for dusting • a pinch of salt
125g cold butter, diced • 1 egg
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Place the flour, salt and butter in a food processor and pulse until the mixture resembles breadcrumbs. Add the egg and pulse again until the mixture comes together. Tip onto a lightly floured work surface and shape into a smooth disc without kneading. Wrap in cling film and chill for 30 minutes before rolling.
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# YOGHURT
## YOU NEED
2 litres full-fat milk • 120ml live natural yoghurt at room temperature
35
Place the milk in a lidded, ovenproof pan and slowly heat to 80°C/175°F. Remove from the heat and cool to 45°C/115°F. Pour 200ml of the milk into a mixing bowl, stir in the yoghurt, then pour the mixture back into the milk pan. Stir, cover and wrap the pan in 2 tea towels. Switch on the oven light (don't switch the oven on), place the pan inside and leave for 4–8 hours, or until set to the desired consistency. For Greek-style yoghurt, tip into a muslin-lined colander set over a bowl and leave to drain until thick and creamy. Store in an airtight container in the fridge.
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# VINAIGRETTE
## YOU NEED
2 tablespoons red or white wine vinegar • 1 teaspoon Dijon mustard
sea salt flakes • freshly ground black pepper • 60ml vegetable oil
2 tablespoons mild extra virgin olive oil
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Place all the ingredients in a screw-top jar and shake vigorously until combined. Store in an airtight container in the fridge.
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# CREAMY DRESSING
_Makes: about 200ml • Time: 5 minutes_
## YOU NEED
150ml natural yoghurt • 2 tablespoons sour cream or crème fraîche
½ garlic clove, crushed • 1 tablespoon chopped fresh dill, chives, flat-leaf parsley or a mixture • ½ teaspoon Dijon mustard
2 tablespoons cider vinegar or white wine vinegar
90ml mild extra virgin olive oil
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Place all the ingredients in a screw-top jar and shake until completely combined. Store in an airtight container in the fridge.
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# WHOLEMEAL LOAF
## YOU NEED
250g strong wholemeal flour • 250g strong white flour, plus extra for dusting
1 teaspoon fine sea salt • 2 teaspoons fast-action dried yeast
250g vitamin C tablet, crushed to a powder • 1½ tablespoons unsalted butter, melted and cooled • 300–400ml warm water • vegetable oil, for oiling
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Preheat the oven to 200°C/400°F/Gas 6. Combine the flours, salt, yeast and vitamin C. Add the butter and stir in enough warm water to make a sticky dough. Knead for 1 minute on a floured work surface and shape into a ball. Leave to rest in a covered, oiled bowl for 2 hours, or until doubled in size. Knock back the dough, shape into a ball and leave to rest for 15 minutes. Oil a large loaf tin. On a lightly oiled work surface, flatten the dough into a rectangle the length of the tin. Tightly roll up the dough and place in the tin seam-side down. Cover with a tea towel and set aside for 45 minutes–1 hour until risen to the top of the tin. Bake for 40 minutes until golden. Cool on a wire rack before cutting.
Mango & carrot smoothie • Fruit spritzer • Beetroot smoothie • Date & oat thickshake • Peanut butter & chocolate shake • Berry ripple porridge • Granola • Luxe muesli • Bircher muesli • Pancakes with sautéed peaches • Rye & berry waffles • Banana French toast • Strawberry cream cheese toast
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# MANGO & CARROT SMOOTHIE
_Makes: about 500ml, depending on consistency • Time: 5 minutes_
## YOU NEED
80g carrots, peeled • 50g parsnips, peeled
180g mango flesh, chopped
45
If using a powerful blender or food processor, roughly chop the carrots and parsnips, otherwise grate the vegetables. Place in the bowl of the blender or food processor, add the mango and blitz until smooth. With the motor running, gradually add enough water to achieve the desired consistency. Serve immediately.
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# FRUIT SPRITZER
_Serves: 2 • Time: 5 minutes_
## YOU NEED
1 peach, finely chopped • a handful of grapes
a handful of mint leaves, plus extra to serve • ½ teaspoon grated fresh ginger
1 lemon, zest finely grated and thinly sliced
a handful of frozen berries • sparkling water
47
In a small bowl, mix together the peach, grapes, mint, ginger and lemon zest. Press the mixture against the side of the bowl with a wooden spoon to slightly crush the fruit and release the juices. Divide the mixture between 2 glasses. Add the frozen berries, mint and lemon slices. Top up with sparkling water and serve immediately.
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# BEETROOT SMOOTHIE
_Serves: 2 • Time: 5 minutes_
## YOU NEED
2 medium cooked beetroots, quartered • ½ small fennel bulb, chopped
a large handful of baby spinach • a handful of frozen berries
1.5cm piece fresh ginger, peeled and chopped, plus extra to taste
49
Place all the ingredients in a blender, add 125ml water and blitz on high power until smooth. Add more water if needed to achieve the desired consistency. Serve immediately.
50
# DATE & OAT THICKSHAKE
_Serves: 2 • Time: 5 minutes_
## YOU NEED
1 large banana • 60g pitted fresh dates
60g rolled oats • 350ml almond or dairy milk, plus extra to taste
2 tablespoons unsweetened cocoa powder • a pinch of ground cinnamon
51
Place all the ingredients in a blender and blitz until smooth. Add extra milk to achieve the desired consistency. Serve immediately.
52
# PEANUT BUTTER & CHOCOLATE SHAKE
_Serves: 2 • Time: 5 minutes_
## YOU NEED
1 large banana • 350ml almond or dairy milk, plus extra to taste
120g unsweetened peanut butter
1 heaped tablespoon unsweetened cocoa powder
53
Place all the ingredients in a blender and blitz until smooth and creamy, adding enough milk to achieve the desired consistency. Serve immediately.
54
# BERRY RIPPLE PORRIDGE
_Serves: 4 • Time: 25 minutes_
## YOU NEED
300g strawberries • 40g pitted fresh dates • 30g quinoa flakes
30g rye flakes • 30g spelt flakes • 30g buckwheat groats or flakes
40g pinhead oatmeal • 1 tablespoon chia seeds
a pinch of fine sea salt • 500ml almond or dairy milk • pistachios, to serve
55
Blitz the strawberries and dates together in a food processor until smooth, adding a splash of water to loosen if needed. Set aside. In a saucepan, combine the flakes, groats, oatmeal, chia seeds, salt and milk. Bring to the boil, stirring constantly, then reduce the heat and simmer for 20 minutes. Stir frequently during this time, adding a splash of water now and then to maintain your preferred consistency. The flakes should be tender and the mixture thick and creamy when done. Serve with the strawberry sauce swirled through and scatter with pistachios.
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# GRANOLA
_Serves: 8+ • Time: 40 minutes_
## YOU NEED
200g rolled oats • 200g quinoa flakes or other flaked grains
250g mixed nuts such as almonds, pistachios, pecans and macadamias, roughly chopped • 65g pumpkin seeds
½ teaspoon fine sea salt • 1½ teaspoons ground cinnamon
100ml melted coconut oil • 250ml unsweetened apple juice
1 large egg white • 25g desiccated coconut
125g mixed dried fruit of choice, chopped
57
Preheat the oven to 150°C/300°F/Gas 2 and line a baking tray with baking paper. In a large bowl, combine the oats, flakes, nuts, seeds, salt, cinnamon, coconut oil and apple juice. Mix well. Whisk the egg white until frothy and stir into the mixture. Spread out in the prepared baking tray and bake for 15 minutes, then mix in the coconut. Bake for 15–20 minutes more, or until golden. Leave to cool on the tray, then add in the dried fruit. Store in an airtight container.
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# LUXE MUESLI
_Serves: 8 • Time: 5 minutes_
## YOU NEED
120g rolled oats • 120g quinoa flakes • 120g spelt or rye flakes
60g almonds, chopped • 60g pecan nuts, chopped • 60g pistachios, chopped
30g pumpkin seeds • 45g sunflower seeds • 1½ tablespoons chia seeds
2 tablespoons sesame seeds • 30g coconut flakes • 60g sultanas
30g dried cherries • 60g dried mango, chopped • 30g goji berries
90g dried apricots, chopped • 2 teaspoons ground cinnamon
2 teaspoons vanilla extract • 1 teaspoon nutmeg • a pinch of fine sea salt
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In a large mixing bowl, stir together all the ingredients until evenly distributed. Store in an airtight container.
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# BIRCHER MUESLI
_Serves: 4–6 • Time: 10 minutes, plus several hours soaking_
## YOU NEED
180g rolled oats • 60g buckwheat, rye or spelt flakes
40g mixed seeds (like chia, linseed, sunflower and pumpkin) • 2 apples, cored and grated • 400ml unsweetened apple juice • 500ml milk
1 teaspoon vanilla extract • 1 teaspoon ground cinnamon
Optional extras to serve: chopped dried fruit, fresh berries, nuts and/or Greek-style yoghurt
61
Combine all the ingredients except the optional extras in a mixing bowl and stir to combine. Transfer to a lidded container and chill in the fridge for several hours, ideally overnight. Serve topped with optional extras of choice.
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# PANCAKES WITH SAUTÉED PEACHES
_Serves: 4 generously • Time: 20 minutes_
125g wholemeal flour • ½ teaspoon baking powder • a pinch of fine sea salt
1 teaspoon melted coconut or vegetable oil, plus extra for frying
1 egg • 150ml almond or dairy milk, plus extra if needed
1 teaspoon vanilla extract • 6 ripe peaches
3 tablespoons unsalted butter, plus more if needed
1 teaspoon ground cinnamon • 180ml unsweetened apple juice
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In a mixing bowl, stir together the flour, baking powder and salt. Stir in the 1 teaspoon oil, the egg, milk and vanilla. Grate 2 of the peaches and stir into the batter. Heat a little oil in a frying pan and add heaped spoonfuls of batter. Cook until golden underneath, then flip and cook for 30 seconds more. Transfer to a plate and cover with foil. Halve, stone and slice the remaining peaches, then fry them in the butter until soft. Add the cinnamon, then pour in the apple juice, stirring as it bubbles and thickens. Add more butter or apple juice if needed to make a sauce. Serve the pancakes with the peaches and sauce spooned over.
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# RYE & BERRY WAFFLES
_Serves: 4–6 • Time: 25 minutes_
## YOU NEED
300g blueberries • 100g rye flour
100g plain flour • ½ teaspoon baking powder
½ teaspoon bicarbonate of soda • 200ml milk
2 eggs, lightly beaten • 50g unsalted butter, melted and cooled
1 teaspoon vanilla extract • 120g Greek-style yoghurt, plus extra to serve
vegetable oil, for brushing • chopped hazelnuts, to serve
65
Blitz 200g of the blueberries in a food processor to make a sauce. Set aside. In a mixing bowl, stir together the flours, baking powder and bicarbonate of soda. Make a well in the centre and stir in the milk, eggs, butter, vanilla and yoghurt. Gently stir in the remaining blueberries. Heat the waffle iron, brush with oil and pour batter into the compartments. Cook according to the machine instructions, transferring the waffles to a wire rack as you go. Serve topped with yoghurt, the blueberry sauce and hazelnuts.
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# BANANA FRENCH TOAST
_Serves: 2 • Time: 15 minutes_
## YOU NEED
2 large eggs • 2 tablespoons unsalted butter, melted
a generous pinch of fine sea salt • a pinch of mace
a pinch of nutmeg • a pinch of ground cloves
¼ teaspoon ground cinnamon • finely grated zest of 1 orange
2 tablespoons orange juice • 1 large ripe banana, mashed
2 tablespoons cream cheese • 4 thick slices good-quality white bread
2 tablespoons chopped pecan nuts (optional) • 1 tablespoon vegetable oil
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In a shallow bowl, whisk together the eggs, half of the melted butter, the salt, spices, orange zest and orange juice. Set aside. In a separate bowl, beat together the banana and cream cheese. Spread 2 of the bread slices with the banana mixture, sprinkle with the pecans (if using), and top with the remaining bread to make sandwiches. Gently press down to seal. Heat the remaining butter and the oil in a frying pan until foaming. Dip the sandwiches in the egg mixture, ensuring each side is soaked but not enough to disintegrate. Fry for 2 minutes until crisp and golden underneath, then flip and cook for 1 minute more. Serve immediately.
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# STRAWBERRY CREAM CHEESE TOAST
_Serves: 4 • Time: 10 minutes_
## YOU NEED
4 thick slices sourdough or country-style bread • 200g cream cheese
200g strawberries, hulled and sliced • ground cinnamon, for sprinkling
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Toast the bread. Meanwhile, beat the cream cheese to loosen. Spread thickly on the hot toast, top with strawberry slices and sprinkle with cinnamon. Serve immediately.
Cinnamon popcorn • Lime & chilli almonds • Fruit roll-ups • Berry dip with fruit crudités • Whipped banana toast • Apple crisps • Orange & saffron grissini • Doughnut balls • Apricot & coconut balls • Chocolate energy bars • Fruit & nut bars • Chocolate raisins • Stuffed dates • Freezer fudge
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# CINNAMON POPCORN
_Serves: 2-4 • Time: 10 minutes_
## YOU NEED
50g unsalted butter, melted • 2 teaspoons vanilla extract
1½ tablespoons vegetable oil • 50g popcorn kernels
ground cinnamon, to taste
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Beat together the butter and vanilla, then set aside. In a heavy-lidded pan, heat the oil over a medium–high heat and add 4 of the popcorn kernels. Cover. When the kernels have popped, remove from the heat and add the remaining kernels. Shake, return to the heat and cover. Cook, shaking occasionally, until there are 3 seconds between pops. Remove from the heat, shake the pan and wait for stray kernels to pop. Pour over the vanilla butter, sprinkle with cinnamon and toss. Serve immediately.
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# LIME & CHILLI ALMONDS
_Makes: about 350g • Time: about 1 hour_
## YOU NEED
60ml lime juice • finely grated zest of 2 large limes
1 tablespoon melted coconut oil • 1 teaspoon sweet smoked paprika
1 teaspoon hot chilli powder • 1 teaspoon ground cinnamon
2 teaspoons fine sea salt • about 12 drops Tabasco chipotle sauce, or to taste
300g blanched almonds
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Preheat the oven to 120°C/250°F/Gas ½ and line 1 or 2 baking sheets with baking paper (you might need to cook the nuts in batches). Mix together all the ingredients except the almonds in a bowl. Add the almonds and toss to coat. Spread out in a single layer on the prepared baking sheets and bake for 45 minutes–1 hour, stirring halfway, until golden brown. Keep an eye on them to prevent burning. Leave to cool on the tray before serving.
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# FRUIT ROLL-UPS
_Makes: 2 sheets measuring 30 x 25cm • Time: 6–8 hours_
## YOU NEED
800g ripe stone fruit such as plums, peaches or apricots, chopped with skin on a squeeze of lemon • 1 banana (optional)
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Line 2 baking sheets with baking paper. Place the fruit in a pan with the squeeze of lemon and a splash of water. Gently simmer, stirring occasionally, until the fruit releases its juice. Reduce the heat to low, cover and cook for 15 minutes, stirring occasionally, until very soft. Blitz in a blender or food processor until smooth. Taste for sweetness, add some or all of the banana if needed, and blitz again. Preheat the oven to 50°C/140°F. Pour the mixture onto the prepared baking sheets and spread out evenly to a thickness of 3–5mm. Place in the oven for 6–8 hours, or until firmed into a gel that peels off the paper easily. To serve, cut into strips and roll up.
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# BERRY DIP WITH FRUIT CRUDITÉS
_Serves: 4–6 • Time: 10 minutes_
## YOU NEED
180g frozen mixed berries, defrosted • 100g pitted fresh dates
3 tablespoons melted coconut oil • 3 tablespoons coconut milk
grated zest of ½ orange • chopped fruit, for dipping
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Place the berries and dates in the bowl of a food processor and blitz until smooth. Add all the remaining ingredients except the chopped fruit and blitz until amalgamated and smooth. Serve with the chopped fruit for dipping.
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# WHIPPED BANANA TOAST
_Makes: 2 slices • Time: 10 minutes_
## YOU NEED
20g coconut oil • 1 banana • 1 teaspoon ground cinnamon
a pinch of ground nutmeg • 2 slices wholemeal bread • mixed berries, to serve
81
Melt the coconut oil in a frying pan over a medium–high heat. Slice the banana, add to the pan and cook until soft and caramelized on both sides. Sprinkle over the cinnamon and nutmeg, and cook for 1 minute more. Transfer to a mini food processor and blitz until smooth. Alternatively, mash to the desired consistency. Toast the bread, then spread with the whipped banana. Serve immediately, with the berries.
82
# APPLE CRISPS
_Makes: about 60 • Time: 4–5 hours_
## YOU NEED
4 apples • 1 teaspoon ground cinnamon
83
Preheat the oven to 110°C/225°C/Gas ¼ and line a large baking sheet with baking paper. Very thinly slice the apples crossways, ideally using a mandoline. Arrange in a single layer on the prepared baking sheet and sprinkle with the cinnamon. Cook for 4–5 hours – the exact time will depend on the thickness of the slices – flipping halfway through. The crisps should be pale brown and starting to harden. Switch off the oven and leave the crisps inside until cool. Store in an airtight container.
84
# ORANGE & SAFFRON GRISSINI
_Makes: about 40 • Time: 1 hour, plus 2 hours 40 minutes proving_
## YOU NEED
90ml orange juice, warmed • a pinch of saffron threads, chopped
10g fast-action dried yeast • about 200ml warm water
450g plain flour, plus extra for dusting • 1 teaspoon fine sea salt
finely grated zest of 1 orange • vegetable oil, for oiling and brushing
85
Combine the juice and saffron in a small bowl and set aside. In another bowl, combine the yeast and warm water and set aside for 5 minutes. In a mixing bowl, combine the flour, salt and zest, then stir in the yeast and saffron mixtures. Bring the dough together, tip onto a floured work surface and knead for 10 minutes. Set aside in a covered, oiled bowl for 20 minutes. On an oiled work surface, stretch the dough into a circle, fold in half then in half again and shape into a ball. Return to the oiled bowl, cover and set aside for 2 hours. Preheat the oven to 200°C/400°F/Gas 6. Line 2 large baking sheets with baking paper and flour a chopping board. Punch back the dough, tip onto the board and roll into a rectangle 5mm thick. Cut into 2cm strips and gently roll into pencil shapes. Transfer to the prepared baking sheets, brush with oil and set aside for 20 minutes, bake for 20 minutes, then cool on a wire rack.
86
# DOUGHNUT BALLS
_Makes: 24 • Time: 40 minutes, plus 2–3 hours proving_
## YOU NEED
1½ teaspoons fast-action dried yeast • 60ml warm water • 300g plain flour
1 teaspoon fine sea salt • about 750ml vegetable oil for deep-frying, plus extra for oiling • blueberry jam or berry dip, to serve
87
Combine the yeast and warm water and set aside for 5 minutes. In a mixing bowl, mix together the flour and salt. Add the yeast mixture, then gradually stir in up to 120ml water to make a sticky dough. Turn out onto a lightly oiled work surface and briefly knead. Transfer to an oiled bowl, cover with cling film and leave somewhere warm for 2–3 hours, or until doubled in size. Knock back the dough, knead for 1 minute, divide into 24 equal pieces, and roll into balls. Heat the 750ml vegetable oil to 175°C/350°F. Deep-fry the balls in batches for about 6 minutes, turning them over in the oil until golden. Transfer to kitchen paper with a slotted spoon. Serve hot, with the jam or dip for dipping.
88
# APRICOT & COCONUT BALLS
_Makes: about 50 • Time: 15 minutes_
## YOU NEED
120g rolled oats • 70g unsweetened peanut butter • 100g ready-to-eat dried apricots • 40g puffed rice • 20g desiccated coconut, plus extra for rolling
80–100g unsweetened apple sauce
89
Blitz the oats to a powder in a food processor, then add the peanut butter, apricots, puffed rice and coconut. Blitz until combined. Add 80g of the apple sauce and blitz until the mixture comes together, adding more apple sauce if needed. Roll heaped teaspoonfuls of the mixture into balls, then roll in the coconut. Store in an airtight container in the fridge.
90
# CHOCOLATE ENERGY BARS
_Makes: 16 squares • Time: 15 minutes, plus 2 hours chilling_
## YOU NEED
400g pitted fresh dates • 60ml melted coconut oil
2 teaspoons vanilla extract • 40g unsweetened cocoa powder
125g ground almonds • a pinch of fine sea salt
1 heaped tablespoon golden flaxseeds • 40g pistachios, roughly chopped
40g walnuts, roughly chopped • 50g dried blueberries
50g sunflower seeds • 2 tablespoons desiccated coconut
91
Blitz the dates in a blender to a paste. Add the coconut oil, vanilla and cocoa powder, and blitz again until smooth. Tip into a bowl, add the almonds, then bring the ingredients together with a wooden spoon or clean hands. Gradually work in all the remaining ingredients except the coconut until evenly dispersed. Line a 20cm square brownie tin or container with foil and tip in the mixture. Press in firmly with the back of a spoon, sprinkle with coconut and lightly press in. Chill for 2 hours, or until set, then cut into squares. Store in an airtight container in the fridge.
92
# FRUIT & NUT BARS
_Makes: 16 squares • Time: 10 minutes, plus 2 hours chilling_
## YOU NEED
225g pitted fresh dates • 150g rolled oats • 80g raisins
50g dried apples • 50g skinless blanched hazelnuts • 25g ground almonds
25g walnuts • 3 tablespoons unsweetened apple sauce
1½ teaspoons ground cinnamon • a pinch of ground nutmeg
93
Place all the ingredients in the bowl of a food processor and blitz to produce a well-combined and slightly coarse, sticky mixture. Firmly press into a 20cm square tray or brownie tin lined with cling film. Chill for 2 hours, or until set, then cut into squares. Store in an airtight container in the fridge.
94
# CHOCOLATE RAISINS
_Makes: about 350g • Time: 10 minutes, plus 2 hours chilling_
## YOU NEED
100g dark chocolate made from 100% cocoa solids, grated
80g coconut oil • 4 tablespoons double cream
1 teaspoon vanilla extract • 200g raisins
95
Line a baking sheet with greaseproof paper. Place the chocolate and coconut oil in a heatproof bowl set over a pan of gently simmering water. Stir occasionally until melted together. Remove the bowl from the pan and stir in the cream and vanilla, then the raisins. Set aside for a few minutes for the mixture to thicken slightly. Pour onto the prepared baking sheet, ensuring the raisins are in a single layer. Chill in the fridge for 2 hours, or until the chocolate has hardened. Break into pieces to serve. Store in an airtight container in the fridge.
96
# STUFFED DATES
_Makes: 24 • Time: 15 minutes_
## YOU NEED
120g soft goats' cheese • 1 teaspoon finely grated orange zest
50g nuts, such pistachios, almonds and/or walnuts, finely chopped
240g pitted fresh dates
97
Beat the goats' cheese and orange zest until smooth and creamy. Stir in the nuts until well combined. Gently pull the dates apart and stuff with the cheese mixture using a small spoon or knife. Press the dates closed and serve immediately.
98
# FREEZER FUDGE
_Makes: about 24 bars • Time: 15 minutes, plus 1–2 hours freezing_
## YOU NEED
400g pitted fresh dates • 120g tahini
120ml double cream • a generous pinch of salt
99
Line a 20cm square freezer-proof container or brownie tray with cling film. Blitz the dates to a paste in a food processor, then add the tahini, cream and salt. Blitz again until smooth and creamy. Pour into the prepared tray, spread out with a spatula and smooth the top. Transfer to the freezer for 1–2 hours, or until set, then cut into rectangles. Store in an airtight container in the fridge.
Date & spelt crackers • Blueberry & apple muffins • Seedy peach muffins • Banana loaf • Chocolate torte • Carrot cake • Raspberry & almond focaccia • Sweet potato scones • Peanut butter cookies • Chocolate oatmeal cookies • Thumb print biscuits
102
# DATE & SPELT CRACKERS
_Makes: 16 • Time: 30 minutes, plus 25 minutes freezing and cooling_
## YOU NEED
60g plain flour, plus extra for dusting • 60g wholemeal flour
½ teaspoon fine sea salt • 60g cold unsalted butter, diced
2 tablespoons spelt flakes • 40g pitted dried dates, chopped • 1 egg yolk
103
Preheat the oven to 180°C/350°F/Gas 4 and line 1 large or 2 small baking sheets with baking paper. Place the flours and salt in a mixing bowl and rub in the butter with your fingertips. Mix in the spelt and dates, then the egg and 1 tablespoon water. Turn out onto a floured work surface and lightly knead for 1 minute, then shape into a sausage 6cm in diameter. Wrap in greaseproof paper and freeze for 20 minutes. Cut the dough into 5mm slices and transfer to the baking sheet(s). Bake for 12–15 minutes until pale gold. Leave on the baking sheet(s) for 5 minutes, then transfer to a wire rack to cool. Store in an airtight container.
104
# BLUEBERRY & APPLE MUFFINS
_Makes: 12 • Time: 40 minutes_
## YOU NEED
150g plain flour • 50g wholemeal flour
1½ teaspoons baking powder • 2 teaspoons ground cinnamon
a pinch of fine sea salt • 75g unsalted butter, melted and cooled
75g unsweetened apple sauce • 100g Greek-style yoghurt
100ml milk • 1 teaspoon vanilla extract • 1 medium egg • 150g blueberries
105
Preheat the oven to 200°C/400°F/Gas 6 and line a 12-hole muffin tin with paper cases. In a mixing bowl, mix together the flours, baking powder, cinnamon and salt. In a jug, whisk together the butter, apple sauce, yoghurt, milk, vanilla and egg. Pour the wet mixture into the dry ingredients and stir just enough to combine – a few lumps are fine. Fold in the blueberries. Spoon into the prepared muffin tin and bake for 20 minutes, or until golden and an inserted skewer comes out clean. Transfer to a wire rack to cool.
106
# SEEDY PEACH MUFFINS
_Makes: 9 • Time: 40 minutes_
## YOU NEED
140g ground almonds • 40g plain flour • 20g desiccated coconut
2 teaspoons ground cinnamon • 1½ teaspoons baking powder
a pinch of fine sea salt • 20g sunflower seeds • 2 large eggs
½ ripe banana, mashed until smooth • 4 tablespoons melted coconut oil
4 tablespoons unsweetened apple sauce • 1 teaspoon almond essence
160g ripe peaches, diced, plus extra for topping
107
Preheat the oven to 180°C/350°F/Gas 4 and line 9 holes of a muffin tin with paper cases. In a mixing bowl, mix together the almonds, flour, coconut, cinnamon, baking powder, salt and sunflower seeds. In a jug, whisk together the eggs, banana, oil, apple sauce and almond essence. Pour the wet mixture into the dry ingredients and stir until just combined. Fold in the 160g peaches. Divide between the paper cases and top with more peaches. Bake for 20 minutes, or until an inserted skewer comes out clean. Cool on a wire rack.
108
# BANANA LOAF
_Makes: 1 large loaf • Time: 60 minutes_
## YOU NEED
vegetable oil, for oiling • 225g plain flour, plus extra for dusting
100g unsalted butter • 120g unsweetened apple sauce
2 large eggs • 40g Greek-style yoghurt
1 teaspoon vanilla extract • 300g ripe bananas, mashed
1 teaspoon bicarbonate of soda • a pinch of salt
1 teaspoon allspice • 2 tablespoons milk
125g raisins • 75g walnuts, chopped
109
Preheat the oven to 180°C/350°F/Gas 4. Oil and flour a 12 x 25cm loaf tin, or equivalent. In a mixing bowl, beat together the butter and apple sauce until creamy – don't worry if the mixture looks a little curdled. Gradually beat in the eggs, then the yoghurt, vanilla and bananas. Combine the flour, bicarbonate of soda, salt and allspice. Gradually stir the dry ingredients into the banana mixture, alternating with the milk. Fold in the raisins and walnuts. Pour into the prepared tin, smooth the top and bake for 40 minutes, or until an inserted skewer comes out clean. Leave in the tin for 5 minutes before turning out onto a wire rack to cool.
110
# CHOCOLATE TORTE
_Serves: 6–8 • Time: 45 minutes_
## YOU NEED
140g ground almonds • 45g unsweetened cocoa powder
½ teaspoon baking powder • a pinch of fine sea salt
200g pitted prunes • 80ml Pedro Ximénez or other sweet sherry (or grape juice)
2 tablespoons olive oil • 2 teaspoons vanilla extract • 3 large eggs
111
Preheat the oven to 170°C/325°F/Gas 3 and oil a 20cm spring-form cake tin. Mix together the almonds, cocoa, baking powder and salt. Set aside. Place the prunes and alcohol or grape juice in a small pan and simmer until 2 tablespoons of the liquid remain. Set aside to cool, then transfer to the bowl of a food processor. Add 120ml water, the olive oil and vanilla. Blitz to a paste. Transfer to a mixing bowl, add the eggs and beat until light and creamy. Add the almond mixture and stir until smooth. Pour into the prepared tin and bake for 25 minutes until cool to touch. Cool in the tin for a few minutes before releasing. Serve warm or at room temperature.
112
# CARROT CAKE
_Serves: 6–8 • Time: 1 hour_
## YOU NEED
150ml sunflower oil, plus extra for oiling • 125g plain flour, plus extra for dusting • 125g wholemeal flour • 1 teaspoon baking powder • 1 teaspoon bicarbonate of soda • a pinch of fine sea salt • 2 teaspoons ground cinnamo
½ teaspoon ground ginger • 50g walnuts, chopped • 70g sultanas
150g bananas, mashed • 3 large eggs, lightly beaten
150g pineapple, chopped • 200g carrots, grated
* * *
## FOR THE ICING
100g unsalted butter, softened • 150g cream cheese
2 teaspoons vanilla extract • 1 teaspoon ground cinnamon
90–135g unsweetened apple sauce according to taste
113
Preheat the oven to 180°C/350°F/Gas 4 and oil and flour a 22cm spring-form cake tin. In a mixing bowl, combine the flours, baking powder, bicarbonate of soda, salt, spices, walnuts and sultanas. In a jug, combine the bananas, oil and eggs. Pour the wet ingredients into the flour mixture and stir until just combined. Fold in the pineapple and carrots. Pour into the prepared tin and bake for 30–40 minutes until springy to touch. Meanwhile, beat together the butter, cream cheese, vanilla, cinnamon and apple sauce. Chill until needed. When the cake is completely cool, spread the icing over the top.
114
# RASPBERRY & ALMOND FOCACCIA
_Serves: 6–8 • Time: 45 minutes, plus 1 hour 20 minutes proving_
## YOU NEED
400g strong white bread flour, plus extra for dusting • 100g fine semolina flour
2 teaspoons fennel seeds (optional) • a pinch of fine sea salt
7g fast-action dried yeast • 300ml warm water • olive oil, for oiling and drizzling
250ml unsweetened red grape, pomegranate or apple juice
about 200g raspberries • a handful of sliced almonds
115
In a mixing bowl, stir together the flours, fennel seeds (if using) and salt. In a separate bowl, combine the yeast and warm water and set aside for 5 minutes. Make a well in the centre of the dry ingredients and stir in the yeast mixture to form a dough. Briskly knead for 10 minutes – it will be sticky at first but avoid using flour on the work surface. Set aside somewhere warm in a covered, oiled bowl for 1 hour. Meanwhile, simmer the juice until reduced to 60ml (about a quarter of the original volume), then set aside to cool. Oil a 20 x 30cm baking tray, tip in the dough and flatten out to fill the tray. Push raspberries into the top, pour over the reduced juice, sprinkle with the almonds and drizzle with oil. Cover with a tea towel and set aside for 20 minutes. Preheat the oven to 220°C/425°F/Gas 7, then bake for 20 minutes. Cool on a wire rack for 15 minutes before serving.
116
# SWEET POTATO SCONES
_Makes: 8 • Time: 40 minutes_
## YOU NEED
275g self-raising flour, plus extra for dusting • 1½ teaspoons allspice
a pinch of fine sea salt • a pinch of ground nutmeg
80g cold unsalted butter, diced • 100g dried peach, apricot or nectarine (or a mixture), chopped • 150g roasted sweet potato flesh, mashed
1 large egg • 75ml milk, plus extra if needed and for brushing
117
Preheat the oven to 220°C/425°F/Gas 7. In a mixing bowl, stir together the flour, allspice, salt and nutmeg. Rub in the butter with your fingertips, then stir in the dried fruit. In a separate bowl, mix together the sweet potato, egg and 4 tablespoons of the milk, then add to the dry ingredients. Mix to form a soft dough that holds together without crumbling. On a floured work surface, shape into a disc 2.5cm thick and stamp out circles with a 7cm cutter. Bring together the trimmings, roll out and stamp out more circles. Repeat until the dough is used up. Transfer to a baking sheet, brush with milk and bake for 12 minutes until golden. Serve warm with cream and blueberry jam.
118
# PEANUT BUTTER COOKIES
_Makes: 12 • Time: 30 minutes_
## YOU NEED
100g plain flour • 50g wholemeal flour
100g ground almonds • ½ teaspoon bicarbonate of soda
2 teaspoons ground cinnamon • a pinch of fine sea salt
75g unsalted butter, softened • 1 large egg, beaten
4 tablespoons peanut butter • 100g sultanas, chopped
2 tablespoons milk, or more or less as needed
119
Preheat the oven to 180°C/350°F/Gas 4. Stir together the flours, almonds, bicarbonate of soda, cinnamon and salt. Set aside. Beat the butter until pale and fluffy, then gradually beat in the egg and peanut butter. Stir in the flour mixture and the sultanas, adding just enough milk to make a soft dough. Roll heaped tablespoons of the mixture into balls and flatten into discs 5mm high with the tines of a fork. Bake for about 10 minutes until pale gold, then transfer to a wire rack to cool.
120
# CHOCOLATE OATMEAL COOKIES
_Makes: about 14 • Time: 30 minutes_
## YOU NEED
100g pitted fresh dates • 60g unsweetened cocoa powder • 30g ground almonds
3 egg whites • 1 tablespoon melted coconut oil
40g rolled oats • 30g desiccated coconut
121
Preheat the oven to 170°C/325°F/Gas 3 and line a baking sheet with baking paper. Place the dates, cocoa, almonds and egg whites in the bowl of a food processor and blitz until smooth. Add the coconut oil and pulse to combine. Transfer to a mixing bowl and stir in the oats and coconut. Roll tablespoons of the mixture into balls, place on the prepared baking sheet and flatten into 6cm discs. Bake for 5 minutes, flip and cook for 5 minutes more. Cool on the tray.
122
# THUMB PRINT BISCUITS
_Makes: about 30 • Time: 40 minutes_
## YOU NEED
180g unsalted butter • 230g unsweetened apple sauce
1 egg, lightly beaten • 2 teaspoons vanilla extract
finely grated zest of 1 orange • 90g ground almonds, or more if needed
180g plain flour • ¼ teaspoon fine sea salt
1 teaspoon ground cinnamon • 1 teaspoon ground ginger
about 250g blueberry jam or other sugar-free jam
123
Preheat the oven to 160°C/315°F/Gas 2–3 and line a baking sheet with baking paper. Beat together the butter and apple sauce until creamy – don't worry if the mixture looks curdled. Gradually stir in the egg, then the vanilla and orange zest. Add the almonds, flour, salt and spices, then stir to make a stiff dough-like batter. Add more almonds if too loose. Place tablespoonfuls of the mixture on the prepared baking sheet. Using damp fingers, pat into 5cm discs and make an indentation in the middle. Bake for 20 minutes, or until pale gold. Spoon a teaspoonful of jam onto each biscuit while still warm.
Fruit salad & rosewater dressing • Saucy pears with pecans • Fig & mint syllabub • Chocolate mousse • Berry chia pudding • Bread & butter pudding • Apple & raspberry jelly • Fruit crumble • Apple pie • Blueberry cheesecake • Lime & coconut ice cream • Berry ice cream • Chocolate ice cream • Strawberry ice pops • Melon & apple granita
126
# FRUIT SALAD & ROSEWATER DRESSING
_Serves: 4 • Time: 25 minutes_
## YOU NEED
250g Greek-style yoghurt • 4 tablespoons chopped mint, plus extra to serve • 4 tablespoons pomegranate molasses • 1 teaspoon rosewater
700g mixed fruit such as persimmons, plums and figs, chopped
4 tablespoons pomegranate seeds, to serve
127
Mix the yoghurt and mint together, cover and chill. Meanwhile, for the dressing, whisk together the pomegranate molasses and rosewater. Place the fruit in a bowl, toss with half the dressing and set aside for 15 minutes. Distribute the fruit between bowls, drizzle over the remaining dressing and top with the yoghurt, pomegranate seeds and mint leaves.
128
# SAUCY PEARS WITH PECANS
_Serves: 4 • Time: 20 minutes_
## YOU NEED
4 firm, ripe pears • 1 tablespoon lemon juice, plus extra to taste
3 tablespoons unsalted butter • 250ml unsweetened pineapple juice
4 tablespoons double cream, plus extra if needed
40g chopped pecans • a pinch of salt
129
Quarter, core and slice the pears. Toss with the 1 tablespoon lemon juice and set aside. Melt the butter in a frying pan until foaming, add the pears and fry over a medium–high heat until almost tender and starting to caramelise. Add the pineapple juice and stir as it bubbles up, then cook until reduced by half. Lower the heat, stir in the cream and cook to a sauce-like consistency. Stir in the pecans, salt and more lemon juice or cream to taste. Serve immediately.
130
# FIG & MINT SYLLABUB
_Serves: 4 • Time: 15 minutes_
## YOU NEED
400ml double cream • 1 teaspoon ground cinnamon
2 teaspoons vanilla extract • 1 tablespoon Pedro Ximénez sherry (or other sweet sherry or unsweetened grape juice) • 100ml natural yoghurt
4 large figs, cut into chunks • 240ml unsweetened grape juice
1 tablespoon chopped mint • 40g walnuts, chopped
131
Beat together the cream, cinnamon, vanilla and the Pedro Ximénez sherry to a soft dropping consistency – don't overbeat, as it will thicken more in the fridge. Stir in the yoghurt, then chill. Place the figs in a bowl and toss with the 240ml grape juice and mint. Set aside for 5 minutes for the flavours to mingle. To assemble, layer the figs and juice, the cream and the walnuts in glasses and serve immediately.
132
# CHOCOLATE MOUSSE
_Serves: 4 • Time: 10 minutes, plus 3 hours chilling_
## YOU NEED
200g pitted fresh dates • 400ml thick coconut milk or coconut cream
50g unsweetened cocoa powder • 1 teaspoon vanilla extract
3 tablespoons melted coconut oil • 60g raspberries, plus extra to serve whipped cream, to serve (optional)
133
Blitz the dates in a food processor to a paste. Add the remaining ingredients and blitz again until smooth. Pour into 4 ramekins, smooth the tops and chill for at least 3 hours to set. Serve topped with raspberries and cream (if using).
134
# BERRY CHIA PUDDING
_Serves: 4 • Time: 10 minutes, plus overnight chilling_
## YOU NEED
500ml almond or dairy milk • 2 large bananas
2 teaspoons vanilla extract • 80g chia seeds
160g red berries such as rasberries and/or strawberries, chopped
135
Place the milk, bananas and vanilla in a blender and blitz until smooth. Transfer to a large bowl and stir in the chia seeds. Cover with cling film and chill overnight. Spoon into bowls and serve topped with the red berries. Serve immediately.
136
# BREAD & BUTTER PUDDING
_Serves: 4-6 • Time: 40 minutes_
## YOU NEED
unsalted butter, for buttering and spreading • 8 thin slices wholemeal bread
grated zest of 1 orange • 80g dried figs, chopped
3 large eggs, lightly beaten • 350ml almond or dairy milk
50ml double cream • 1 teaspoon ground cinnamon
2 teaspoons vanilla extract • 150g bananas, mashed until smooth
137
Preheat the oven to 180°C/350°F/Gas 4 and generously butter a 1.2 litre baking dish. Butter one side of each slice of bread and cut each slice in half. Arrange half the bread in the bottom of the baking dish buttered-side up and scatter half the orange zest and half the figs on top. Arrange the remaining bread on top and scatter over the remaining zest and figs. Whisk together the eggs, milk, cream, cinnamon, vanilla and banana, and pour over the bread. Bake for 30 minutes until golden. Serve warm.
138
# APPLE & RASPBERRY JELLY
_Serves: 4 • Time: 15 minutes, plus 6 hours chilling_
## YOU NEED
250g mixed raspberries
5 gelatine leaves (or enough to set 600ml liquid)
600ml unsweetened apple juice • whipped cream, to serve
139
Distribute the raspberries between glasses that hold at least 300ml each. Set aside. Place the gelatine leaves in a heatproof bowl and add enough of the apple juice to cover. Set aside to soften for 5 minutes. Place the bowl over a pan of gently simmering water and stir until completely dissolved. Add the remaining apple juice, stir well, then pour into the glasses with the raspberries. Chill for 6 hours, or until set. Serve with whipped cream.
140
# FRUIT CRUMBLE
_Serves: 4–6 • Time: 30 minutes_
## YOU NEED
4 red apples, chopped with skin on • 8 ripe plums, chopped
700ml unsweetened white or red grape juice • 120g quinoa flakes
120g rolled oats • grated zest of 2 oranges
2 teaspoons allspice • 2 teaspoons grated fresh ginger
2 teaspoons ground cinnamon • 80g pecan nuts, chopped
¼ teaspoon fine sea salt • 6 tablespoons unsalted butter • cream, to serve
141
Preheat the oven to 180°C/350°F/Gas 4 and line a baking sheet with baking paper. Place the fruit and juice in a pan and simmer, stirring occasionally, until tender. Strain, reserve the juice, and set aside. Combine the quinoa, oats, orange zest, spices, pecans and salt in a bowl. Melt the butter in a frying pan until foaming, add the quinoa mixture and stir-fry until the butter is absorbed and the mixture starts to caramelize. Add 180ml of the reserved juice and cook, stirring constantly, until absorbed. Spread out on the prepared baking sheet and bake for 5 minutes, or until crisp. Spoon the fruit and reserved juices into bowls and top with the crumble. Serve with whipped cream.
142
# APPLE PIE
_Serves: 8 • Time: 1 hour 10 minutes, plus 30 minutes chilling_
## YOU NEED
1 quantity pastry • grated zest of ½ orange
60ml unsweetened orange juice • 6 green apples such as Granny Smith apples
2 teaspoons ground cinnamon • ½ teaspoon ground nutmeg
1 teaspoon vanilla extract • 50g raisins
1 tablespoon plain flour, plus extra for dusting
1 egg, lightly beaten with a splash of water
143
Cut the dough into 2 pieces, one slightly larger than the other. Shape into discs, wrap in cling film and chill for 30 minutes. Place the zest and juice in a bowl. Peel, quarter and core the apples, slice into the orange juice and toss. Mix in the spices, vanilla, raisins and flour. Preheat the oven to 180°C/350°F/ Gas 4. Roll out the large piece of dough and use it to line a 20cm pie tin, allowing some overhang. Add the apples and moisten the dough edge with water. Roll out the small piece of dough to make a lid. Press the edges together with a fork and trim away excess dough. Cut slits in the top, brush with the egg wash and bake for 45 minutes, or until golden. Cool in the tin for 15 minutes before serving.
144
# BLUEBERRY CHEESECAKE
_Makes: 4 • Time: 20 minutes, plus 2 hours chilling_
## YOU NEED
80g rolled oats • 60g pitted fresh dates
80g ground almonds • 3 tablespoons melted coconut oil
a pinch of fine sea salt • 280g cream cheese
2 teaspoons vanilla extract • 250ml double cream
280g blueberry jam or other sugar-free spread • a handful of blueberries
145
Place the oats in a food processor and blitz to a powder. Add the dates, almonds, coconut oil and salt, and blitz until combined. Divide between 4 x 10cm cheesecake tins (or a 20cm spring-form cake tin) and press in firmly and evenly with the back of a spoon. Chill. Meanwhile, beat together the cream cheese, vanilla and cream until thick. Spread evenly over the chilled base. Chill for 2 hours, or until set. When ready to serve, spread with the blueberry jam and top with blueberries. Release from the tin and serve immediately.
146
# LIME & COCONUT ICE CREAM
_Serves: 4–6 • Time: 20 minutes, plus up to 5 hours freezing_
## YOU NEED
2 bananas • 450ml coconut cream • 450ml double cream
grated zest of 4 limes • a generous pinch of fine sea salt
4 tablespoons desiccated coconut, lightly toasted
147
Blitz the bananas in a food processor until smooth and creamy. Transfer to a mixing bowl and add the coconut cream, cream, zest and salt. Beat until smooth and creamy, then stir in the desiccated coconut. Pour into an ice-cream maker and churn according to the machine instructions. Alternatively, place in a freezer-proof container and freeze for 3–4 hours, then blitz in a food processor. Freeze for 1 more hour then blitz again just before serving.
148
# BERRY ICE CREAM
_Serves: 4 • Time: 5 minutes_
## YOU NEED
500g frozen mixed berries • 80–120g pitted fresh dates, according to taste
120ml coconut cream or single cream
149
Place all the ingredients in the bowl of a food processor, blitz until smooth and creamy and serve immediately. Alternatively, transfer to the freezer for 30 minutes for a firmer ice cream. Store in the freezer for longer if needed, but blitz again until creamy before serving.
150
# CHOCOLATE ICE CREAM
_Serves: 2 • Time: 5 minutes_
## YOU NEED
2 frozen bananas • 2 tablespoons unsweetened cocoa powder
60ml coconut cream
151
Chop the bananas, transfer to the bowl of a food processor and blitz until broken up. Add the cocoa and coconut cream, and blitz until creamy. Serve immediately. Alternatively, transfer to the freezer for longer, if needed, but blitz again until creamy before serving.
152
# STRAWBERRY ICE POPS
_Makes: 4–6 • Time: 10 minutes, plus up to 8 hours freezing_
## YOU NEED
500g strawberries, hulled • 80g pitted fresh dates
100ml double cream • a few drops of rosewater, or to taste
153
Blitz the strawberries and dates in a blender, then add the remaining ingredients and blitz until combined. Pour into ice pop moulds and freeze for 5–8 hours, or until frozen. Run the moulds briefly under warm water to release.
154
# MELON & APPLE GRANITA
_Serves: 4 • Time: 10 minutes, plus 4 hours freezing_
## YOU NEED
750g chopped honeydew melon • 225g unsweetened apple sauce
juice of 1–2 limes • a handful of mint leaves
155
Place the melon and apple sauce in a blender and blitz until smooth. Add lime juice and mint to taste, and blitz again. Pour the mixture into a loaf tin or metal container that will fit into the freezer. Freeze for 2 hours, or until the mixture is frozen around the edges. Scrape and stir the mixture with a fork, then return to the freezer. Repeat stirring and scraping every 30 minutes for 2 hours, or until the mixture is formed of ice crystals. Serve immediately.
156
# GLOSSARY
**Artificial sweeteners** – chemically manufactured substances including aspartame, sucralose and saccharine designed to mimic the sweetness of sugar. Highly controversial, some critics claim they cause a range of health problems, while advocates say they can help control weight alongside a low-calorie diet.
**Blood sugar** – the amount of glucose present in the blood.
**Carbohydrates** – also known as 'carbs', are a source of energy. When eaten, the body converts them into glucose (blood sugar), which is used to fuel bodily functions and activity. Sugar is a type of carbohydrate.
**Empty calories** – food that supplies energy but little or no nutrition.
**Fibre** – a type of carbohydrate only found in food that comes from plants. Essential for optimum health, sources of fibre include vegetables with the skin on, wholegrain bread, wholegrain pasta and pulses.
**Fructose** – a simple sugar found in many fruit and vegetables, and only processed in the liver. Some experts believe fructose behaves more like fat than other carbohydrates and that excessive consumption can lead to sugar cravings, over-eating and health problems.
**Glucose** – also known as dextrose, is the body's preferred source of energy. It is also known as blood sugar, as it circulates in the blood.
**Insulin** – a hormone produced by the pancreas that helps the body store and use glucose.
**Lactose** – a type of sugar found in milk and other dairy products. It is regarded as a healthy sugar as it contains no fructose.
**Starch** – a form of carbohydrate made up of many sugar units bonded together. Starchy foods include bread, rice, potatoes and pasta.
**Stevia** – a naturally occurring sweetener and sugar substitute extracted from the leaves of the Stevia plant. It has no calories and is up to 200 times sweeter than sucrose.
**Sucrose** – commonly known as table sugar or added sugar, it is made up of fructose and glucose molecules.
**Type 1 diabetes** – an autoimmune condition, often inherited, where the pancreas does not produce any insulin, the hormone responsible for controlling blood sugar levels.
**Type 2 diabetes** – a condition where the pancreas does not produce enough insulin, or the body's cells don't react to insulin, the hormone responsible for controlling blood sugar levels. The rapid worldwide rise in the incidence of Type 2 diabetes is linked to obesity, lack of exercise and an increase in unhealthy diets.
**Xylitol** – a naturally occurring chemical found in plant material widely used as a sugar substitute.
157
# INDEX
#### A
##### almond milk:
###### berry chia pudding –
###### date & oat thickshake –
###### peanut butter & chocolate shake –
##### almonds:
###### chocolate torte –
###### lime & chilli almonds –
##### apples:
###### apple & raspberry jelly –
###### apple crisps –
###### apple pie –
###### apple sauce –
###### Bircher muesli –
###### blueberry & apple muffins –
###### fruit crumble –
###### melon & apple granita –
##### apricot & coconut balls –
#### B
##### bananas:
###### banana French toast –
###### banana loaf –
###### berry chia pudding –
###### bread & butter pudding –
###### chocolate ice cream –
###### date & oat thickshake –
###### peanut butter & chocolate shake –
###### whipped banana toast –
##### BBQ sauce –
##### beetroot smoothie –
##### berry chia pudding –
##### berry dip –
##### berry ice cream –
##### berry ripple porridge –
##### Bircher muesli –
##### biscuits
###### chocolate oatmeal cookies –
###### date & spelt crackers –
###### peanut butter cookies –
###### thumb print biscuits –
##### blueberries:
###### blueberry & apple muffins –
###### blueberry cheesecake –
###### blueberry jam –
###### rye & berry waffles –
###### sweet potato scones –
##### bread
###### bread & butter pudding –
###### breadsticks –
###### raspberry & almond focaccia –
###### wholemeal loaf –
##### see also toast breakfast cereal
#### C
##### cakes , –
##### carrots:
###### carrot cake –
###### mango & carrot smoothie –
##### cheesecake, blueberry –
##### chia pudding –
##### chocolate:
###### chocolate energy bars –
###### chocolate ice cream –
###### chocolate mousse –
###### chocolate oatmeal cookies –
###### chocolate raisins –
###### chocolate spread –
###### chocolate torte –
###### peanut butter & chocolate shake –
##### cinnamon popcorn –
##### coconut:
###### apricot & coconut balls –
##### coconut cream:
###### ice cream –
##### cookies see biscuits
##### crackers, date & spelt –
##### creamy dressing –
##### crudités, fruit –
##### crumble, fruit –
158
#### D
##### dates:
###### chocolate energy bars –
###### chocolate mousse –
###### chocolate oatmeal cookies –
###### date & oat thickshake –
###### date & spelt crackers –
###### freezer fudge –
###### fruit & nut bars –
###### stuffed dates –
##### doughnut balls –
##### dressings –
##### dried fruit: granola –
###### luxe muesli –
#### E
##### energy bars –
#### F
##### fig & mint syllabub –
##### focaccia –
##### food labels
##### freezer fudge –
##### French toast –
##### fruit ,
###### berry chia pudding –
###### berry dip with fruit crudités –
###### berry ice cream –
###### fruit & nut bars –
###### fruit crumble –
###### fruit roll-ups –
###### fruit salad & rosewater dressing –
###### fruit spritzer –
##### fudge, freezer –
#### G
##### granita –
##### granola –
##### grissini –
#### I
##### ice cream –
##### ice pops –
#### J
##### jams
###### blueberry jam –
###### thumb print biscuits –
##### jelly, apple & raspberry –
#### K
##### ketchup –
#### L
##### lime:
###### lime & chilli almonds –
###### lime & coconut ice cream –
#### M
##### mango & carrot smoothie –
##### mayonnaise –
##### melon & apple granita –
##### mousse, chocolate –
##### muesli –
##### muffins –
#### N
##### nuts: fruit & nut bars –
#### O
##### oats:
###### apricot & coconut balls –
###### Bircher muesli –
###### chocolate oatmeal cookies –
###### date & oat thickshake –
###### fruit & nut bars –
159
###### fruit crumble –
###### granola –
###### luxe muesli –
##### orange & saffron grissini –
#### P
##### pancakes –
##### pastry –
##### peaches:
###### fruit spritzer –
###### pancakes with sautéed peaches –
###### seedy peach muffins –
##### peanut butter –
###### peanut butter & chocolate shake –
###### peanut butter cookies –
##### pears with pecans –
##### pie, apple –
##### pineapple:
###### BBQ sauce –
##### popcorn, cinnamon –
##### porridge, berry ripple –
##### prunes:
###### chocolate torte –
#### R
##### raisins, chocolate –
##### raspberries:
###### apple & raspberry jelly –
###### raspberry & almond focaccia –
##### rye & berry waffles –
#### S
##### sauces –
##### scones, sweet potato –
##### shakes –
##### smoothies –, –
##### strawberries:
###### berry ripple porridge –
###### strawberry cream tea toast –
###### strawberry ice pops –
##### sugar 8–15
##### sweet potato scones –
##### syllabub, fig & mint –
#### T
##### thumb print biscuits –
##### toast:
###### banana French toast –
###### strawberry cream tea toast –
###### whipped banana toast –
##### tomatoes:
###### BBQ sauce –
###### ketchup –
#### V
##### vinaigrette –
#### W
##### waffles, rye & berry –
##### wholemeal loaf –
#### Y
##### yoghurt –
> My thanks to Catie Ziller and the team for all the hard work that has made this book so beautiful. It can be a tricky task to make all the pieces of the puzzle come together and they succeeded brilliantly. Special thanks go to Alice Chadwick for her gorgeous illustrations.
> Thanks go to lookslikewhite ceramics at www.lookslikewhite.com for their lovely ceramics. Other stunning pieces came from Canvas Home, ABC Carpet & Home, CB2, Muji and Kaufmann mercantile.
> I am also grateful to Magimix UK for the loan of their Cuisine 5200XL food processor, which was a huge asset while testing all the recipes.
> Finally, big hugs to Adam, Ruby and Ben – my family, test team and most valued critics. Thanks especially to Ruby for devising the Date & oat thickshake recipe, and for Ben's suggestions on muffin ingredients.
Sugar Free by Sue Quinn
First published in 2015 by Hachette Books (Marabout)
This English edition published in
2016 by Hardie Grant Books
Hardie Grant Books (UK)
5th & 6th Floors
52-54 Southwark Street
London SE1 1UN
www.hardiegrant.co.uk
Hardie Grant Books (Australia)
Ground Floor, Building 1
658 Church Street
Melbourne, VIC 3121
www.hardiegrant.com.au
The moral rights of the Sue Quinn to be identified as the author of this work has been asserted by her in accordance with the Copyright, Designs and Patents Act 1988.
Text © Sue Quinn
Photography © Victoria Wall Harris
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form by any means, electronic, electrostatic, magnetic tape, mechanical, photocopying, recording or otherwise, without the prior written permission of the Publisher.
British Library Cataloguing-in-Publication Data. A catalogue record for this book is available from the British Library.
eISBN: 978-1-74358-390-6
Publisher: Catie Ziller
Author: Sue Quinn
Photographer: Victoria Wall Harris
Design & illustration: Alice Chadwick
Food stylist: Vivian Lui
Assistant food stylist: Cybelle Tondu
For the English edition:
Publisher: Kate Pollard
Senior Editor: Kajal Mistry
Cover image: iStock
Cover Design: Hardie Grant Books
Cover Colour Production by P2D
|
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\section{Introduction}
\label{sec:intro}
Interacting ultracold gases offer unique opportunities for the modeling of realistic quantum systems
\cite{RevModPhys.80.885}. During the recent years it not only became possible to study such exotic
phenomena as BEC-BCS crossover, but also the modeling of systems inspired by the fractional quantum
Hall effect might soon be within reach \cite{Chen20051,Bloch:2012fk,Gurarie20072}. One of very
interesting and old condensed matter physics phenomena, which shows exciting physics on the one hand
and on the other hand might immensely profit from parameter adjustability offered by ultracold gas
systems is the polaron problem \cite{feynman1998statistical}. In its simplest realization it
describes electrons in a semiconductor which interact with phonons of the background lattice. The
most important feature of the model is a fundamental difference in the properties of the system for
weak and strong coupling between the fermionic and bosonic subsystem.
It turns out that polaron-like models can very effectively be simulated by fermionic impurity atoms
immersed into a BEC \cite{PhysRevA.76.011605,PhysRevB.80.184504}. Alternatively one can couple them
to a continuum of bosonic excitations of some other fermionic species
\cite{PhysRevLett.102.230402}, or even use bosonic impurities of the species different from the one constituting the BEC bath. A direct mapping of most of the results from the vintage literature
is, however, not possible for a number of reasons. First of all, the spectrum of bosonic excitations
is usually profoundly different from those in a semiconductor. The second distinction is the
coupling mechanism between the subsystems. Some less important details such as the presence and
nature of cut-off parameters might drastically alter the properties of a given system as well. But
the most important difference is at the same time an enormous advantage -- it is the adjustability
of parameters, which is far superior to that in solid state realizations. This feature makes it
possible to advance into new and as yet unexplored parameter regions. One such situation is the
semiclassical limit, in which the impurity can be considered to be an almost classical particle. Not
only is this particular parameter constellation so far poorly understood, it also allows for a
physically intuitive characterization of dynamics in super- and subsonic velocity regimes that have
mostly been investigated using involved numerical methods in similar systems before
\cite{Mathy:2012fk,PhysRevLett.97.260403}.
We consider a single fermionic impurity interacting with a gas of bosons with masses $m$ (we use
polaronic units, where the mass of the impurity $m_I$ as well as the healing length of the BEC $\xi$
and the reduced Planck constant $\hbar$ are set to unity, throughout the Letter). The Hamiltonian
reads
\begin{align}
\label{eq:hamiltonian1}
H = \frac{\vb{p}^2}{2} + \sum_\vb{k} \epsilon_\vb{k} a_\vb{k}^\dagger a_\vb{k} &+ \frac{1}{2}
\sum_{\vb{k},\vb{k}',\vb{q}} V_{BB}(\vb{q}) a_{\vb{k}'-\vb{q}}^\dagger a_{\vb{k}+\vb{q}}^\dagger
a_\vb{k} a_{\vb{k}'} \nonumber\\
&+ \sum_{\vb{k}',\vb{q}} V_{IB}(\vb{q}) \rho(\vb{q}) a_{\vb{k}'-\vb{q}}^\dagger a_{\vb{k}'},
\end{align}
where $a_\vb{k}^\dagger$ and $a_\vb{k}$ are the creation and annihilation operators for a boson with
momentum $\vb{k}$, $\vb{p}$ is the momentum operator of the impurity, $V_{BB}$ and $V_{IB}$ are
general boson-boson and impurity-boson interaction potentials, and the dispersion of the bosons is
given by
\begin{equation}
\label{eq:dispersionbosons}
\epsilon_\vb{k} = \frac{\vb{k}^2}{2m} - \mu \, .
\end{equation}
$\mu$ is the chemical potential. The momentum space density of a point particle is related to
its position operator $\vb{x}$ via
\begin{equation}
\label{eq:momentumspacedensitypointparticle}
\rho(\vb{q}) = \int \mathrm{d}^3 y \delta^3(\vb{y}-\vb{x}) e^{i \vb{q} \vb{y}}.
\end{equation}
Since we assume a dilute homogeneous gas, we perform the Bogoliubov approximation by
replacing the zero mode operators $a_0$, $a_0^\dagger$ by $c$-numbers \cite{pitaevskij2000bose}.
We furthermore use contact pseudo-potentials for the
interactions $V_{BB}(\vb{q}) = g_{BB}$, $V_{IB}(\vb{q}) = g_{IB}$, where the constants $g_{BB}$ and
$g_{IB}$ are related to the $s$-wave scattering lengths of the true potentials via the
Lippman-Schwinger equation. We then obtain a variant of the Fr\"ohlich Hamiltonian
\cite{AdvPhys.3.325,PhysRevB.80.184504}
\begin{equation}
\label{eq:hamiltonian2}
H = \frac{\vb{p}^2}{2} + \sum_\vb{k} \epsilon_\vb{k} b_\vb{k}^\dagger
b_\vb{k} + \sum_\vb{k} V_\vb{k} e^{i \vb{k} \vb{x}} \left( b_\vb{k} + b_{-\vb{k}}^\dagger \right).
\end{equation}
For reasons that will become clear below, we restrict the dispersion relation of the Bogoliubov
quasiparticles $\epsilon_\vb{k}$ and the interaction structure $V_\vb{k}$ to the expressions valid
for momenta that are smaller than the healing length in the BEC.
Therefore, we have
\begin{equation}
\label{eq:epsilonk}
\epsilon_\vb{k} = c k, \qquad V_\vb{k} = \sqrt{\alpha k},
\end{equation}
where $c = 1/(\sqrt{2} m)$ is the sound velocity in the BEC and the dimensionless coupling
constant $\alpha$ can be related to the density $n$ of the bosonic gas and the impurity-boson
interaction constant via $\alpha = n g_{IB}^2 / \sqrt{2}$.
Using the standard procedures, we can now integrate out the environmental (BEC) degrees of freedom,
see for example~\cite{weiss1999quantum}. A requirement for a semiclassical treatment is that the average
wavelength of the impurity be small compared to a typical length scale of the system
\cite{messiah2000quantum}. The latter is given by the healing length $\xi$, since it is the typical
length on which the effective potential seen by the particle varies. The wave length of the impurity
particle is in a first approximation given by $\lambda = \hbar/(v m_I)$, where $v$ is its
velocity. Since the healing length is proportional to $\hbar/(c m)$, we see that a large
impurity mass compared to the masses of the bosonic particles justifies a semiclassical
treatment. Moreover, we will mostly be interested in impurity velocities $v \geq c$, so that, for instance,
a ${}^{85}\text{Rb}$ impurity in a gas of ${}^{23}\text{Na}$ should well be described by this
theory. For the case in which $m_I < m$ however, we still expect this approximation to be valid for very fast impurities with $v \ge m c/m_I$.
Alternatively, in the strong coupling regime, where $\alpha \gtrsim 1$ the self-trapping
effects are expected to restrict the extent of the polaron wave function to a region smaller than
the healing length of the BEC \cite{PhysRevB.80.184504}, or equivalently, the strong coupling leads to
the generation of a large effective impurity mass. Apart from these effects, the dynamical aspects
of the physics can then still be captured by the classical equations of motion, provided one works
with the effective quantities.
In order to preserve the convergence of the integrals within the employed approximation, it is
necessary to employ a cutoff scheme \cite{PhysRevB.32.3515}. For reasons which become clear below we
use a Gaussian $\sim e^{-k^2/k_c^2}$ where $k_c$ is proportional to the inverse of the size of the
polaron particle. The resulting EOM in three dimensions is then given by
\begin{equation}
\label{eq:eom}
\ddot{x}_i(t) = - \int_0^t \mathrm{d} u \gamma_{ij}(t-u,r) \dot{x}_j(u)
\end{equation}
with a generalized damping kernel
\begin{widetext}
\begin{align}
\label{eq:generalizeddampingkernel}
\gamma_{ij}(s,r) = &\delta_{ij} \frac{\alpha k_c^3}{16 \pi^{3/2} c r^3} e^{- \frac{1}{4} k_c^2 c^2
s^2} \bigg\{ \left( e^{csk_c^2r} + 1 \right) \left(c^2 s^2 k_c^2 r + k_c^2 r^3 \right) -
\left( e^{csk_c^2r} - 1 \right) cs \left( 1 + k_c^2 r^2 \right) \nonumber\\
&\quad + \frac{r_j}{2r} \Big[ \left( e^{csk_c^2r} - 1 \right) \left( 3cs \left(4 + 2 k_c^2 r^2 +
k_c^4 r^4 \right) - k_c^4 r^2 c^3 s^3 \right) - \left( e^{csk_c^2r} + 1 \right) \left( 3 k_c^2
c^2 s^2 r \left( 2 + k_c^2 r^2 \right) + k_c^4 r^5 \right) \Big] \bigg\} \, ,
\end{align}
\end{widetext}
where ${\bf r = \vb{x}({\it t}) - \vb{x}({\it u})}$. The dependence of the rhs of Eq.~(\ref{eq:eom})
on $\bf r$ is a major structural difference to the case of linear coupling to the environment as in
the Caldeira-Leggett model \cite{PhysicaA.121.587}. This results in a dissipation dynamics which is
completely different. The influence of such non-Markovian dissipation scenario is weak for short
time scales and much of the dynamics can be described by an effective Caldeira-Leggett
model. However, the deviations are drastic for intermediate and long times. In this case the
solution of the initial value problem can only be found numerically \cite{masterthesis_text}. We
solve Eq.~\eqref{eq:eom} for the initial value $x(0)=0$ and $\dot{x}(0)=v_0$. As long as $v_0<c$
(subsonic initial velocity) the difference to a solution in which $r=0$ is set on the rhs of
Eq.~\eqref{eq:generalizeddampingkernel} throughout is minimal, see
Fig.~\ref{fig:numericsolution}. On the contrary, in the supersonic case $v_0 > c$ the non-Markovian
dissipation leads to drastic discrepancies. In the transient regime we observe distinct damped
oscillations which can be connected with the appealing physical picture emerging in the elementary
self-consistent harmonic approximation \cite{feynman1998statistical}, according to which the polaron
cloud is modeled as an additional mass on a spring attached to the impurity. An important point is
the fact that both approximations cover the nonperturbative regime.
\begin{figure}
\centering
\includegraphics[width=\columnwidth]{numericsolution}
\caption{
Results of the numerical solution of Eq.~\eqref{eq:eom} at short to intermediate timescales. The lower curves correspond to an initial condition $v_0= 0.5c$ whereas the upper curves represent the supersonic case $v_0= 3c$. Dashed lines are computed in the assumption ${\bf r}=0$, see text.
}
\label{fig:numericsolution}
\end{figure}
Despite its efficiency the numerical procedure is not able to produce reliable results for the
long-time asymptotics of the particle. In order to obtain it one has to rely on simplifications of
the basic equation \eqref{eq:eom}. As we have shown above, the dependence of the rhs on the details
of the particle trajectory at previous times via ${\bf r}$ is an obstacle. However, if we are
interested in the long-time limit, we can neglect fast fluctuations of the particle velocity, as
seen in the numerical simulations. Thus we can expand ${\bf r}(t,u) = {\bf v}(t)(t-u) + \dots$ and
require ${\bf v}(t)$ to be self-consistently calculated. For the long-time asymptotics one then
obtains the following EOM for the component of the displacement along the initial velocity
$\vb{v}_0$:
\begin{equation}
\label{eq:longtimeeom}
\lim_{t \to \infty} \ddot{x}(t) = \frac{\alpha}{8 \pi} \frac{c k_c^4 (c - \dot{x}(t) - |c -
\dot{x}_i(t)|)}{(c - \dot{x}(t)) \dot{x}(t)^2}
\end{equation}
It is important to note that in this effective equation for the long time behaviour of the particle
coordinate, memory effects have not been neglected, but incorporated into the $t \to \infty$ limit.
The rhs is zero for $v(t)<c$ and $\propto v(t)^{-2}$ otherwise. This means that the solution to the
initial value problem $x(0)=0$, $\dot{x}(0) = v_0$ with Eq.~(\ref{eq:longtimeeom}) is
\begin{equation}
\label{eq:longtimesolution}
x(t) =
\begin{cases}
v_0 t & \text{if } \dot{x}(t) < c \\
\frac{2 \pi}{\alpha c k_c^4} \left( v_0^4 - \left|3 v_0^3 - \frac{3 \alpha c k_c^4}{8 \pi} t\right|^{4/3}
\right) & \text{otherwise}
\end{cases}
\end{equation}
\begin{figure}
\centering
\includegraphics[width=\columnwidth]{asymptoticsolution}
\caption{Asymptotic solution to the initial value problem with $v_0=4c$. The main graph shows the evolution of the coordinate. The velocity (inset)
decays according to a power law with exponent $1/3$, until it reaches a value of $c$, after which it
remains constant and the particle moves freely. The time variable is gauged in such a way that
the transition from the supersonic to the subsonic regime occurs at $t=0$.}
\label{fig:asymptoticsolution}
\end{figure}
Especially the deceleration process of an initially supersonic impurity shows up interesting
features. As long as $v(t) > c$ the particle slows down and just above the threshold $c$ the
velocity decrease follows a power law \footnote{This power law is different for systems of different
dimensionalities.} with exponent $1/3$, see Fig.~\ref{fig:asymptoticsolution}. After $v$ drops
below $c$ it does not change any more. From the qualitative point of view this behaviour is to be
expected, being a manifestation of superfluidity in the BEC. However, the change of velocity is
smooth in previous perturbative studies \cite{PhysLettA.282.421} as opposed to our result, in which
the time derivative of $v$ shows a jump. Furthermore, the emergence of the critical velocity $c$ is
clearly a consequence of the nonlinear coupling: The long time behaviour of the corresponding EOM in
which $\vb{r}=0$ is just that of a free particle, independent of its velocity, as can easily be
shown using Laplace transform techniques.
As we have already mentioned above, $k_c^{-1}$ can be connected to the conventional polaron
radius. To see this, we note that when we take into account quadratic fluctuations around the
classical path $\vb{x}(t)$ (see e.g.~\cite{JLowTempPhys.49.609,PhysRevB.30.6419}),
Eq.~(\ref{eq:eom}) becomes a generalized Langevin equation in which a noise term $\xi_i(t)$ has to
be added to the rhs. $\vb{\xi}(t)$ is a Gaussian stochastic process with average $\langle \xi_i(t)
\rangle = 0$ and state-dependent autocorrelation function
\begin{equation}
\label{eq:noiseautocorrelation}
\langle \xi_i(t) \xi_j(u) \rangle = \text{Re} \sum_\vb{k} k_i k_j \frac{\alpha k}{2} G_\vb{k}(t-u,
\beta) e^{i \vb{k} \vb{r}},
\end{equation}
where $G_\vb{k}(t-u, \beta)$ is the real-time propagator for a boson of momentum $\vb{k}$ at inverse
temperature $\beta$. As required by the fluctuation-dissipation theorem, in the limit $\beta \to
\infty$, the rhs reduces to $\gamma_{ij}(t-u,\vb{r})/2$. When taking averages over realizations of
the noise of the full Langevin equation, $\xi_i(t)$ no longer explicitly occurs on the rhs of the
EOM, but we encounter averages of the form
\begin{equation}
\label{eq:gaussiancharacteristicfunction}
\langle e^{i \vb{k} \vb{r}} \rangle = e^{i \vb{k} \langle \vb{r} \rangle - k^2 (\langle \vb{r}^2
\rangle - \langle \vb{r} \rangle^2 )/6},
\end{equation}
where we assumed that for every $t$, $u$, the random variable $\vb{r} = \vb{x}(t) - \vb{x}(u)$ can
be appropriately approximated by having Gaussian statistics. Therefore, from
Eq.~(\ref{eq:gaussiancharacteristicfunction}), we see that a natural cutoff for the $\vb{k}$-sums is
provided by the mean square of $\vb{r}$. In a stationary situation, we would expect that $\langle
\vb{r}^2 \rangle - \langle \vb{r} \rangle^2 \to \langle \vb{x}(t) \vb{x}(u) \rangle - \langle
\vb{x}(t) \rangle \langle \vb{x}(u) \rangle$, which for $u \to t$ can be considered to be a measure
for the squared polaron radius $r_{pol}$. Therefore, in this approximation
\begin{equation}
\label{eq:cutoffpolaronradius}
k_c \approx 6/r_{pol}^2 \, .
\end{equation}
For a coupling constant $\alpha$ of the order of unity, the polaron radius in the low temperature
limit has previously been calculated to be of the order of the healing length
\cite{PhysRevB.80.184504}, justifying both our use of the low-momentum approximations
(\ref{eq:epsilonk}) and of the semiclassical approximation.
We believe, that the phenomena described above can be very conveniently measured in state-of-the-art
experiments on ultracold fermion-boson mixtures. We envisage a dilute fermionic system being trapped
in an optical lattice, which, in turn, is immersed into a BEC as is done in
e.~g. Refs.~\cite{phdthesis_schuster,PhysRevA.85.042721}.
Assuming the interwell fermion hopping to
be completely suppressed (for instance by making the lattice very deep) the lattice is then moved
through the BEC at constant velocity. The fermions are then subject to a drag force, which can be
measured as a population imbalance of the low-lying fermion states in the minimum of the potential
well by a number of well established experimental techniques.
Alternatively,
after the transients die out, one can switch off the trapping potentials and infer the force from the
velocity distributions of the freed particles.
\begin{figure}
\centering
\includegraphics[width=\columnwidth]{dragforce}
\caption{Asymptotic behavior of the drag force for $t \to \infty$ as a function of the drag velocity $v_0$. In
the subsonic regime, it is zero as expected. It jumps to finite value just above $v_0=c$,
subsequently decaying like $1/v_0^2$. Inset: drag force as a function of time for drag velocites
$v_0=0.7c$ (solid line), $v_0=c$ (dashed line), $v_0=1.2c$ (dashed-dotted line) and $v_0=2c$
(dotted line).}
\label{fig:dragforce}
\end{figure}
From the theoretical point of view such an experiment is very convenient since the particle
kinematics is fully known. Assuming the impurity/polaron to be a classical particle, the drag force
is exactly given by the rhs of Eq.~(\ref{eq:eom}) under the condition ${\bf r}(t,u) = {\bf v_0}
(t-u)$, where ${\bf v_0}$ is the drag velocity. The result of calculations is shown in the inset of
Fig.~(\ref{fig:dragforce}). While in the subsonic case the asymptotic value of the force is zero, in
the supersonic case some finite value is reached in the stationary situation \footnote{Due to a
factorized system preparation at $t=0$ and resulting polaron cloud formation process the force at
intermediate times is finite. It roughly corresponds to the situation in which the impurity is
`shot' into the BEC from the outside.}. Very interesting is the behavior of the drag force at $t
\to \infty$ as a function of $v_0$, which is given by the rhs of Eq.~(\ref{eq:longtimeeom}), see
Fig.~\ref{fig:dragforce}. It follows a $1/v_0^2$ law just beyond the sound velocity with a finite
value just above it. This is very different from the perturbative result $\sim v_0^4$ of the field
theoretical computation, see e.g.~\cite{PhysLettA.282.421}. Since a mechanical force can be
interpreted as the amount of energy radiated per unit length, it is in fact more instructive to
compare this to the famous result for Cherenkov radiation in classical electrodynamics by Frank and
Tamm \cite{franktamm}, where this quantity scales as $1-c^2/v_0^2$, $c$ being the velocity of light in
a medium. Although in our case we have the same dependence on $1/v_0^2$ which seems to be a feature
of classical dynamics, the difference is that in the BEC case, we obtain an asymptotic decoupling
from the bath for high velocities as well as the discontinuity at $v_0=c$.
The latter feature is plausible, it is clearly a signature of the nonlinear polaron coupling
mechanism since the discontinuity disappears if the coupling is linearized.
It would be very interesting to observe these effects in experiments. One possible realization could
be ${}^6\text{Li}$ fermionic impurities immersed into a BEC of ${}^{23}\text{Na}$
\cite{PhysRevB.80.184504}. In this setup the typical values for the force evaluate to $F_\infty
\approx 10^{-24}\,\text{N}$ in conventional units. This corresponds to an impurity acceleration of
the order of $10^{2} \, \text{m} / \text{s}^2$ and therefore seems to be well within reach of
experimental observation \cite{PhysRevA.85.042721,PhysRevB.80.184504}. As discussed above it might
be advantageous to replace the usually used fermion impurities by heavier ones, or even bosonic ones
like ${}^{85}\text{Rb}$. In this case the force would be of the order of $10^{-25}\,\text{N}$.
To conclude, by means of the semiclassical approximation and its extensions we have investigated the dynamics of an impurity in a BEC and interacting with its Bogolyubov modes. It turns out to crucially depend on the velocity of the wave packet and is completely different in sub- and supersonic regimes. The resulting mechanical forces can be estimated and we expect them to be measurable in the upcoming experiments.
The authors would like to thank S.~Maier, M.~Oberthaler, T.~Rentrop, T.~Schuster, R.~Scelle and A.~Trautmann for many enlightening discussions. The authors are supported by the Centre of Quantum Dynamics and HGSFP of the University of Heidelberg.
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 2,913
|
\section{Introduction}
Entanglement, that is, correlations existing in multipartite quantum
systems, is an essential feature to describe information processing
of physical systems in the most fundamental level of physics. It is
known that, none of correlation measures which have been employed to
describe correlations of classical systems suffices to describe
entanglement. Then, a number of measures to quantify entanglement of
quantum systems in the non-relativistic regime have been developed,
for instance, the criteria based on the partial transpose has been
one of major tools to not only detect but also quantify entangled
states. The measure has also been used to describe evolution of
entanglement in time, under different settings of circumstances of
given systems.
It is then of fundamental interest, also natural, to extend the
analysis to the relativistic regime, that is, entanglement of
relativistic quantum systems. In particular, the case that one of
two parties sharing entangled states moves in a uniform acceleration
has been considered \cite{ref:alsing1} \cite{ref:ball}
\cite{ref:fuentes}. Interestingly, it turns out that entanglement
behaves differently according to physical systems, whether given
systems are bosonic or fermionic. One can contrast that, in the
relativistic regime, entanglement of bosonic systems disappears in
the limit of infinite acceleration, while entanglement of fermonic
systems shows a convergent behavior
\cite{ref:fuentes}\cite{ref:alsing2}. Among others, this is one of
the most remarkable features of quantum systems, that distinguish
physical systems in terms of entanglement behavior. Moreover, in the
recent, a counterintuitive phenomenon in entanglement of
relativistic quantum systems has been shown in Ref.
\cite{ref:montero1} that entanglement can be actually amplified when
one party is moving in a uniform acceleration. After these
qualitative results on entanglement of relativistic quantum systems
have been derived, the constraint to have physical results should be
taken into account, i.e. that detectors in relativistic quantum
systems is consistent to the behavior of entanglement in the
relativistic regime. In fact, this has been made, e.g. in the case
of entanglement behavior of fermonic systems in the infinite
acceleration \cite{ref:chang}.
In this paper, we make an analysis to derive physical results in the
entanglement amplification of fermonic systems in the relativistic
regime. We apply methods shown in Refs. \cite{ref:montero2}
\cite{ref:montero3} \cite{ref:chang} and provide physical results
that entanglement of fermionic systems can be amplified in an
accelerated frame. Our result not only makes a proper analysis
itself, but also solidifies the result that phenomenon of
entanglement amplification can actually happen (within the employed
measure).
The present article is organized as follows. In Sec. II, we will
give a brief description for fermionic system in an accelerated
frame. In Sec. III, we investigate the entanglement amplification of
pure and mixed quantum states in fermionic system. In Sec. IV, we
conclude and discuss our result.
\section{Accelerated Frame}
The accelerated frame can be described by the Rindler coordinate $(\tau,\varsigma,y,z)$ instead of Minkowski coordinate $(t,x,y,z)$. In right wedge of it(called region $I$), it can be described by $\displaystyle
ct=\varsigma \sinh(\frac{a \tau}{c}),x=\varsigma \cosh(\frac{a\tau}{c}) $ and in left one of it(region $II$) the coordinate is given by $ ct=-\varsigma \sinh(\frac{a \tau}{c}),x=-\varsigma \cosh(\frac{a \tau}{c})$, where $a$ denotes the fixed acceleration of the frame and $c$ is the velocity of light. For a fixed
$\varsigma$, the coordinate displays hyperbolic trajectories in space-time.
A field in Minkowski and Rindler space-time can be expressed as $
\displaystyle \phi = N_{M}\sum_{i}(a_{i,M}v^{+}_{i,M} + b^{\dag}_{i,M}v^{-}_{i,M} ) = N_{R}\sum_{j}(a_{j,I}v^{+}_{j,I} + b^{\dag}_{j,I}v^{-}_{j,I} + a_{j,II}v^{+}_{j,II} + b^{\dag}_{j,II}v^{-}_{j,II} ) $. Here $N_{M}$ and $N_{R}$ are the normalization constants. $v^{\pm}_{i,M}$ refers to the positive and negative energy solutions of the Dirac equation in Minkowski space-time, which can be obtained with
respect to the Killing vector field in Minkowski space-time. $v^{\pm}_{i,I}$
and $v^{\pm}_{i,II}$ are the positive and negative energy solutions of the
Dirac equation in Rindler spacetime, with
respect to the Killing vector field in region $I$ and $II$.
Also $a^{\dag}_{i,\lambda}(a_{i,\lambda})$ and
$b^{\dag}_{i,\lambda}(b_{i,\lambda})$ are the creation(annihilation)
operators, satisfying the anti-commutation relations, for the
positive and negative energy solutions(particle and antiparticle),
where $\lambda $ denotes $M,I,II$. A combination of Minkowski mode,
called Unruh mode, can be transformed into monochromatic Rindler
mode and can annihilate the same Minkowski vacuum: $\displaystyle
A_{i,R/L}\equiv \cos \gamma_{i}a_{i,I/II} - \sin \gamma_{i}
b^{\dag}_{i,II/I}, $ where $\cos \gamma_{i}=(e^{\frac{-2 \pi \Omega
c}{a}}+1)^{-1/2}$. More generally, we have $\displaystyle
a^{\dag}_{i,U}=q_{L}(A^{\dag}_{\Omega ,L}\otimes I_{R}) +
q_{R}(I_{L} \otimes A^{\dag}_{\Omega ,R})$ beyond the single mode
approximation. Using this relation, in case of a Grassmann scalar,
the Unruh vacuum and the one-particle state are given by
\begin{eqnarray}
|0_{\Omega }\rangle_{U} &=& \cos^{2} \gamma_{\Omega }
|0000\rangle_{\Omega } - \sin \gamma_{\Omega }\cos \gamma_{\Omega }
|0011\rangle_{\Omega }
\nonumber\\
&+& \sin \gamma_{\Omega }\cos \gamma_{\Omega } |1100\rangle_{\Omega } - \sin^{2}
\gamma_{\Omega } |1111\rangle_{\Omega } \nonumber\\
|1_{\Omega }\rangle^{+}_{U} &=& q_{R}(\cos \gamma_{\Omega }
|1000\rangle_{\Omega } - \sin \gamma_{\Omega } |1011\rangle_{\Omega
})
\nonumber\\
&+& q_{L}(\sin \gamma_{\Omega } |1101\rangle_{\Omega } +\cos
\gamma_{\Omega } |0001\rangle_{\Omega }
\end{eqnarray}
Here we consider $q_{R}$ and $q_{L}$ as a real number and use the
notation $|pqmn\rangle_{\Omega } \equiv |p_{\Omega
}\rangle^{+}_{I}|q_{\Omega }\rangle^{-}_{II} |m_{\Omega
}\rangle^{-}_{I} |n_{\Omega }\rangle^{+}_{II} $. Actually there is
another possibility of one particle state such as
\begin{eqnarray}
|1_{\Omega }\rangle^{-}_{U} &=& q_{L}(\cos \gamma_{\Omega }
|0100\rangle_{\Omega } - \sin \gamma_{\Omega } |0111\rangle_{\Omega
})
\nonumber\\
&+& q_{R}(\sin \gamma_{\Omega } |1110\rangle_{\Omega } +\cos
\gamma_{\Omega } |0010\rangle_{\Omega }
\end{eqnarray}
From now on, for simplicity, the index $\Omega$ will be omitted. The
single-mode approximation corresponds to the case of $q_{R}=1$.
Recently it was shown that the physical ordering of the fermionic
system should be rearranged by the sequence of particle and
antiparticle in the separated
region\cite{ref:montero2}\cite{ref:montero3}\cite{ref:chang}. So in
this report, we
will use the physical structure for fermionic system.\\
\section{Entanglement amplification of quantum states in fermionic system}
\subsection{2 party pure entangled states }
At first let us consider pure entanglement between Alice and Bob.
Two parties share a pure entangled state in fermionic system and Bob
travels with a uniform acceleration. Then, the state shared is
described as
\begin{equation}
|\Phi^{+} (\alpha) \rangle = \cos \alpha |0\rangle_{M}|0\rangle_{U}
+ \sin \alpha |1\rangle_{M}|1^{+}\rangle_{U}. \label{eq6}
\end{equation}
Suppose that Bob's detector cannot distinguish between the particle
and the antiparticle. As it is explained, two regions $I$ and $II$
are causally disconnected and thus Bob does not have assess to both.
Hence, the state between Alice and Bob can be found by tracing
either regions. The state of Alice and Bob when Bob is in region $I$
is described as,
\begin{eqnarray}
\rho_{AB_{\mathrm{I}}}^{\Phi^{+}}
&=& \cos ^2 \alpha \cos ^4 \gamma |000\rangle \langle 000| \nonumber\\
&+& \frac{q_{R}}{2} \sin 2\alpha \cos ^{3} \gamma (|000\rangle \langle 110| + |110\rangle \langle 000|) \nonumber\\
&+& q_{L}^{2} \sin ^{2} \alpha \cos ^{2} \gamma |100\rangle \langle 100| \nonumber\\
&+& \frac{1}{2}(1-(1-2 q_{L}^{2}) \cos 2\gamma) \sin ^{2}\alpha
|110\rangle \langle 110| \nonumber\\
&-&\frac{q_{L}}{2} \sin 2\alpha \cos ^{2}\gamma \sin
\gamma(|001\rangle \langle 100| + |100\rangle
\langle 001|) \nonumber\\
&-& \frac{q_{R}q_{L}}{2} \sin ^{2}\alpha \sin 2\gamma (|100\rangle
\langle 111| + |111\rangle \langle 100| ) \nonumber\\
&+& \frac{1}{4} \cos ^{2}\alpha \sin ^{2} 2\gamma (|001\rangle
\langle 001| + |010\rangle \langle 010|) \nonumber\\
&+& \frac{q_{R}}{2} \sin 2\alpha \cos \gamma \sin ^{2} \gamma
(|001\rangle \langle 111| + |111\rangle \langle 001|) \nonumber\\
&+& q_{R}^{2} \sin ^{2} \alpha \sin ^{2} \gamma |111\rangle \langle 111| \nonumber\\
&+& \frac{q_{L}}{2} \sin 2\alpha \sin ^{3} \gamma (|011\rangle \langle 110| + |110\rangle \langle 011|) \nonumber\\
&+& \cos ^{2} \alpha \sin ^{4} \gamma |011\rangle \langle 011|.
\nonumber
\end{eqnarray}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=6cm]{aFig1.pdf}
\caption{\label{fig2}(Color online) Negativity of quantum state $
\rho_{AB_{\mathrm{I}}}^{\Phi^{+}}$. Part (a) and (b) show the cases
of $q_{R}=\frac{1}{\sqrt{2}}$ and $q_{R}=0.609$ respectively. The
dot-point on the line denotes the point of variation of the curve.
The small box inside the figure displays the negativity of quantum
states with $\alpha=0.785$,$\alpha=0.653$ and $\alpha=0.600$ for $
\rho_{AB_{\mathrm{I}}}^{\Phi_{+}}$. Some quantum states reveals
clearly the entanglement amplification as acceleration increases.
Here $\gamma=\frac{\pi}{4}$ denotes the infinite acceleration. }
\end{center}
\end{figure}
The entanglement of quantum state is measured by negativity, which
evaluates the sum of negative eigenvalues of the partial transposed
density matrix. The entanglement behavior at
$q_{R}=\frac{1}{\sqrt{2}}$ is depicted in Fig. 1(a). In fact similar
analysis was reported in \cite{ref:montero2} and
\cite{ref:montero4}. The entanglement of the quantum state is
decreased to the dot-point on the line. However after that point the
entanglement of the state begins to increase, as Bob moves in more
accelerated frame. It means the entanglement amplification of the
quantum state in terms of acceleration. It is very surprising
phenomena, since it is commonly believed that the entanglement may
not be generated by acceleration. Fig.1 shows that the entanglement
of some quantum states in fermionic system violates the common
belief. As seen in Fig. 1, lesser entangled the initial state is,to
more right position the point of variation moves. For the state
$\Phi^{+}(\alpha)$ the increase of entanglement happens up to
$\alpha=0.523599$ when $q_{R}=\frac{1}{\sqrt{2}}$. That is, the
amplification of entanglement can be clearly seen between
$\frac{\pi}{4}\ge \alpha \ge 0.523599$, when
$q_{R}=\frac{1}{\sqrt{2}}$. The entanglement amplification at
$q_{R}=0.609$ can be found in Fig. 1(b). In this case some quantum states in the accelerated frame reveals more entanglement than that in an inertial one.\\
We next consider the entanglement between Alice and Bob, when they
share the following state,
\begin{equation}
|\Phi^{-} (\alpha) \rangle = \cos \alpha |0\rangle_{M}|0\rangle_{U}
+ \sin \alpha |1\rangle_{M}|1^{-}\rangle_{U} \label{eq7}.
\end{equation}
As it is explained previously, Bob has inaccessible part due to his
acceleration. The state of Alice and Bob after tracing the region
$II$ can be found. Actually as far as entanglement is concerned, the
entanglement behavior of $\Phi^{+}(\alpha)$ seems to be equivalent
to that of $\Phi^{-}(\alpha)$, which was discussed in \cite{ref:montero5}.\\
We now consider pure entangled states such as Eq. (5), when Bob is
traveling with a uniform acceleration, as follows:
\begin{equation}
|\Phi^{*} (\alpha) \rangle = \cos \alpha
|0\rangle_{M}|1^{+}\rangle_{U} + \sin \alpha
|1\rangle_{M}|0\rangle_{U}. \label{eq8}
\end{equation}
As it is done before, the state that Alice and Bob share can be
obtained beyond the single-mode approximation. The state when Bob is
in region $I$ is obtained by tracing the other region,
\begin{eqnarray}
\rho_{AB_{\mathrm{I}}}^{\Phi^{*}}
&=& q_{L}^{2} \cos ^2 \alpha \cos ^2 \gamma |000\rangle \langle 000| \nonumber\\
&+& \frac{1}{2}(1-(1-2 q_{L}^{2})\cos 2\gamma) \cos ^{2} \alpha |010\rangle \langle 010| \nonumber\\
&+& \frac{q_{R}}{2}\cos ^3\gamma \sin 2 \alpha |010\rangle \langle 100|+|100\rangle \langle 010|) \nonumber\\
&+& \cos ^4\gamma \sin ^2 \alpha |100\rangle \langle 100| \nonumber\\
&-& \frac{q_{R}q_{L}}{2} \sin ^{2}\alpha \sin 2\gamma (|000\rangle
\langle 011| + |011\rangle \langle 000| ) \nonumber\\
&-& \frac{q_{L}}{2} \sin 2\alpha \cos ^2\gamma \sin
\gamma(|000\rangle\langle 101| + |101\rangle \langle 000| ) \nonumber\\
&+& q_{R}^{2} \cos ^{2} \alpha \sin ^{2} \gamma |011\rangle \langle 011| \nonumber\\
&+& \frac{q_{R}}{2} \sin 2\alpha \cos \gamma \sin
^2\gamma(|011\rangle \langle 101| + |101\rangle \langle 011| ) \nonumber\\
&+& \frac{1}{4} \sin ^2\alpha \sin
^2 2\gamma(|101\rangle \langle 101| + |110\rangle \langle 110| ) \nonumber\\
&+& \frac{q_{L}}{2}\sin ^3\gamma \sin 2 \alpha ( |010\rangle \langle 111|+|111\rangle \langle 010|) \nonumber\\
&+& \sin ^{2} \alpha \sin ^{4} \gamma |111\rangle \langle 111|.
\nonumber
\end{eqnarray}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=6cm]{aFig3.pdf}
\caption{\label{fig2}(Color online) Negativity of quantum state $
\rho_{AB_{\mathrm{I}}}^{\Phi^{*}}$. Part (a) and (b) show the cases
of $q_{R}=\frac{1}{\sqrt{2}}$ and $q_{R}=0.609$ respectively. The
dot-point on the line denotes the point of variation of the curve.
The small box inside the figure displays the negativity of quantum
states with $\alpha=0.785$,$\alpha=0.653$ and $\alpha=0.600$ for $
\rho_{AB_{\mathrm{I}}}^{\Phi^{*}}$. Some quantum states reveal
clearly the entanglement amplification as acceleration increases.
Here $\gamma=\frac{\pi}{4}$ denotes the infinite acceleration. }
\end{center}
\end{figure}
The entanglement behavior for the quantum state $\Phi^{*}(\alpha)$
at $q_{R}=\frac{1}{\sqrt{2}}$ can be seen in Fig. 2(a). We observe
the point of variation as well as the amplification of entanglement,
for certain quantum states. However, its entanglement behaves
differently from that of state $\Phi^{+}(\alpha)$. The main
difference is that the entanglement for some range of $\alpha$ does
not decrease rather increases as Bob's acceleration is getting
larger. For example, the quantum state with $\alpha=0.653$ at
$q_{R}=\frac{1}{\sqrt{2}}$, can get the maximal entanglement at the
infinite acceleration. That is, the entanglement of the quantum
state with specific $q_{R}$ and $\alpha$ has the largest value at
the infinite acceleration. It seems to be a strange property, since
the acceleration is believed to reduce the entanglement of the
quantum state. At $q_{R}=0.609$, the behavior of
entanglement can be found in Fig. 2(b).\\
\subsection*{III.b 2 party mixed entangled state }
Up to now, we have considered entanglement of pure states in
fermionic system when one of parties is traveling with a uniform
acceleration. We have observed that there is an amplification of
entanglement when a partner sharing a pure quantum state moves in
accelerated frame. In this subsection, we consider a more complicate
scenario when two parties share a mixed state. It is aimed to find
how the entanglement behavior depends on the mixedness property, and
also if its amplification is related to the mixedness. In
particular, the case when a white noise is added to a maximally
entangled states, so-called Werner state, is to be considered. The
mixedness of Werner states is parameterized by a single parameter.
So we suppose that two parties Alice and Bob prepare Werner states
in inertial frames, and then Bob moves in the uniformly accelerated
frame. That is, the initial state of Alice and Bob can be expressed
as follows,
\begin{equation}
\rho_{W}= F |\Phi_{+} (\alpha=\pi/4) \rangle \langle \Phi_{+}
(\alpha=\pi/4) | + \frac{1-F}{4}\mathbb{I}\label{eq9},
\end{equation}
where the maximally entangled state is taken from Eq. (\ref{eq6})
when $\alpha=\pi/4$.
Suppose that Bob moves in an accelerated frame. Beyond the
single-mode approximation, the state that Alice and Bob share in
Bob's region $I$ is obtained by tracing the region $II$, as follows,
\begin{widetext}
\begin{eqnarray}
\rho_{AB_{\mathrm{I}}}^{W} &=& \frac{1}{2}F q_{R} \cos ^3 \gamma
(|000\rangle \langle 110|+|110\rangle \langle 000|) + \frac{1}{8} \cos ^{2} \gamma (3-2 q_{R}^{2}+F(1-2q_{R}^{2})+(1-F)\cos 2\gamma)|100\rangle \langle 100| \nonumber\\
&+& \frac{1}{8} \cos ^{2} \gamma (3-2q_{R}^{2}-F(1-2q_{R}^{2})+(1+F)\cos 2\gamma)|000\rangle \langle 000| -\frac{F q_{L}}{2} \cos ^{2}\gamma \sin \gamma(|001\rangle \langle 100| + |100\rangle \langle 001|) \nonumber\\
&+&\frac{F q_{R}}{2} \cos \gamma \sin ^{2}\gamma(|001\rangle \langle 111| + |111\rangle \langle 001|) +\frac{F q_{L}}{2} \sin ^{3}\gamma(|011\rangle \langle 110| + |110\rangle \langle 011|) \nonumber\\
&+& \frac{1}{4} \sin ^{2} \gamma ((1+F)q_{R}^{2}+(1-F) \sin ^{2}\gamma)|111\rangle \langle 111| + \frac{1}{4} \sin ^{2} \gamma ((1-F)q_{R}^{2}+(1+F) \sin ^{2}\gamma)|011\rangle \langle 011| \nonumber\\
&-& \frac{1}{8} (1-F)q_{L}q_{R} \sin 2 \gamma (|000\rangle \langle 011| +|011\rangle \langle 000|) - \frac{1}{8} (1+F)q_{L}q_{R} \sin 2 \gamma (|100\rangle \langle 111| +|111\rangle \langle 100|)\nonumber\\
&+&\frac{1}{16} (1-F) \sin ^{2} 2\gamma|101\rangle \langle 101|+\frac{1}{16} (1+F) \sin ^{2} 2\gamma|001\rangle \langle 001| +\frac{1}{16} (2(1+F)-2(1+F)(1-2 q_{R}^{2}) \cos 2\gamma \nonumber\\
& &+(1-F)\sin ^{2} 2\gamma)|110\rangle \langle 110| +\frac{1}{16}
(2(1-F)-2(1-F)(1-2 q_{R}^{2}) \cos 2\gamma +(1+F)\sin ^{2} 2\gamma)
|010\rangle \langle 010| \nonumber
\end{eqnarray}
\end{widetext}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=6cm]{aFig4.pdf}
\caption{\label{fig3}(Color online) Negativity of quantum state $
\rho_{AB_{\mathrm{I}}}^{W}$. Part (a) and (b) show the cases of
$q_{R}=\frac{1}{\sqrt{2}}$ and $q_{R}=0.609$ respectively. The
dot-point on the line denotes the point of variation of the curve.
Some quantum states display two dot-points, implying that there are
two regions for entanglement behavior. Part (a) and (b) show clearly
the entanglement amplification as acceleration increases. Here
$\gamma=\frac{\pi}{4}$ denotes the infinite acceleration. }
\end{center}
\end{figure}
The negativity in Fig.3 depicts the entanglement amplification for
some Werner states. It implies that when the mixed states are
considered, their entanglement for certain mixed states shows the
amplification behavior. Specially the point of variation can be
found two times for the Werner state with $F=0.50$ at
$q_{R}=\frac{1}{\sqrt{2}}$. In fact it happens in the Wener state of
$F=0.50$ at $q_{R}=\frac{1}{\sqrt{2}}$ or $F=0.49$ at
$q_{R}=\frac{1}{\sqrt{2}}$ or $F=0.47$ at $q_{R}=0.609$ or $F=0.46$
at $q_{R}=0.609$. It means that there are two regions of
entanglement amplification for the states, which seems to be a
peculiar property of mixed states.\\
We now consider the mixed entangled states such as Eq. (7), when Bob
is traveling with a uniform acceleration, as follows:
\begin{eqnarray}
\rho_{WL} &=& F |\Phi_{+} (\alpha=\pi/4) \rangle \langle \Phi_{+}
(\alpha=\pi/4) | \nonumber\\
&+& \frac{1-F}{2}(|01 \rangle \langle 01 |+|10 \rangle \langle 10
|)\label{eq10},
\end{eqnarray}
where the maximally entangled state is taken from Eq. (\ref{eq6})
when $\alpha=\pi/4$. As it is done before, the state that Alice and
Bob share can be obtained beyond the single-mode approximation. The
state when Bob is in region $I$ is obtained by tracing the other
region,
\begin{eqnarray}
& &\rho_{AB_{\mathrm{I}}}^{WL} = \frac{1}{2} F q_{R} \cos ^3 \gamma
(|000\rangle \langle 110|+|110\rangle \langle 000|)\nonumber\\
&+&\frac{1}{2}
\cos\gamma^2(F(q_{L}^2)+(1-F)\cos\gamma^2)|100\rangle\langle100|\nonumber\\
&+&\frac{1}{2}\cos\gamma^2((1-F)(q_{L}^2)+F\cos\gamma^2)|000\rangle\langle000|\nonumber\\
&+&\frac{1}{16}(1+3F-4F(1-2q_{R}^2)\cos2\gamma-(1-F)\cos4\gamma)|110\rangle\langle110|\nonumber\\
&-&\frac{1}{2}F q_{L}
\cos\gamma^2\sin\gamma(|001\rangle\langle100|+|100\rangle\langle001|)\nonumber\\
&+&\frac{1}{2}F q_{R} \cos\gamma
\sin\gamma^2(|001\rangle\langle111|+|111\rangle\langle001|)\nonumber\\
&+&\frac{1}{2}F q_{L}
\sin\gamma^3(|011\rangle\langle110|+|110\rangle\langle011|)\nonumber\\
&+&\frac{1}{2}\sin\gamma^2((1-F)q_{R}^2+F\sin\gamma^2)|011\rangle\langle011|\nonumber\\
&+&\frac{1}{2}(F q_{R}^2
\sin\gamma^2+(1-F)\sin\gamma^4)|111\rangle\langle111|\nonumber\\
&-&\frac{1}{4}(1-F)q_{R}q_{L}\sin2\gamma
(|000\rangle\langle011|+|011\rangle\langle000|)\nonumber\\
&-&\frac{1}{4}F
q_{R}q_{L}\sin2\gamma(|100\rangle\langle111|+|111\rangle\langle100|)\nonumber\\
&+&\frac{1}{8}(1-F)\sin2\gamma^2|101\rangle\langle101|\nonumber\\
&+&\frac{1}{8}F\sin2\gamma^2|001\rangle\langle001|\nonumber\\
&+&\frac{1}{8}(2(1-F)(1-(1-2q_{R}^2)\cos2\gamma)+F\sin2\gamma^2)|010\rangle\langle010|\nonumber
\end{eqnarray}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=6cm]{aFig5.pdf}
\caption{\label{fig4}(Color online) Negativity of quantum state $
\rho_{AB_{\mathrm{I}}}^{WL}$. Part (a) and (b) show the cases of
$q_{R}=\frac{1}{\sqrt{2}}$ and $q_{R}=0.609$ respectively. The
dot-point on the line denotes the point of variation of the curve.
Some quantum states show clearly the entanglement amplification as
acceleration increases. Here $\gamma=\frac{\pi}{4}$ denotes the
infinite acceleration. }
\end{center}
\end{figure}
The negativity in Fig.4 shows the entanglement amplification for
some mixed quantum states of Eq. (\ref{eq10}). It implies that when
the mixed states are considered, their entanglement for certain
mixed states shows the amplification behavior. Specially the point
of variation can be found two times for $\rho_{WL}$ with $F=0.63$
at $q_{R}=\frac{1}{\sqrt{2}}$. In fact it happens in $\rho_{WL}$ of
$F=0.63$ at $q_{R}=\frac{1}{\sqrt{2}}$ or $F=0.62$ at
$q_{R}=\frac{1}{\sqrt{2}}$ or $F=0.61$ at $q_{R}=\frac{1}{\sqrt{2}}$
or $F=0.60$ at $q_{R}=\frac{1}{\sqrt{2}}$.
\section*{IV. Discussion and Conclusion } We have investigated
the amplification of entanglement of quantum states in fermionic
system when a party sharing entangled quantum state travels in
uniformly accelerated frame. Even though it has been widely believed
that the acceleration may spoil the entanglement of the system, we
showed that there can be the amplification of entanglement for some
quantum states regardless of pure or mixed one. Also it is a
surprise that some mixed states reveal two points of variation in
the line of negativity. It seems to be worthwhile to investigate why
there are more than one region of amplification of entanglement for
some mixed states.
\section*{Acknowledgment}
We would like to thank Dr. Mart\'{i}n-Mart\'{i}nez for pointing ref
\cite{ref:montero4} and Dr. Joonwoo Bae for a careful reading of the
manuscript and for valuable comments. This work is supported by
Basic Science Research Program through the National Research
Foundation of Korea funded by the Ministry of Education, Science and
Technology (KRF2011-0027142).
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Josep Gonzalvo, spanyol változatban José Gonzalvo, gyakran Gonzalvo II (Mollet del Vallès, 1920. január 16. – Barcelona, 1978. május 31.) spanyol labdarúgó, középpályás, illetve hátvéd.
Családja
Két testvére, Juli (Gonzalvo I) és Mariano (Gonzalvo III) szintén neves labdarúgók voltak a maguk korában. Josep és Mariano együtt szerepeltek az 1950-es vb-n is.
Pályafutása
Gonzalvo és testvérei a Mollet del Vallès nevű kisvárosban születtek. 1941-ben kezdődött felnőttkarrierje, katonai szolgálata idején a Ceuta játékosa volt a másodosztályban. 1943-ban a Sabadell játékosa lett, ahol idősebb testvérével, Julival játszhatott együtt. 1943. szeptember 26-án mutatkozott be az első osztályban, egy Sevilla elleni 5–2-es vereség alkalmával.
Mindössze egyetlen sabadelli szezon elteltével a korszak egyik legsikeresebb csapata, a Barcelona szerződtette, ahol bátyja után ezúttal öccse, Mariano lett a csapattársa. Katalónia fővárosában az ott töltött hat év alatt 198 összecsapáson lépett pályára, ebből közel százötven bajnoki. Összesen öt gólt szerzett a Barcelonában, ebből hármat a liga találkozóin. A hat ott töltött idény alatt három bajnoki címet ünnepelhetett a "blaugrana" színeiben. 1950-ben visszavonult, azonban két év múlva visszatért, és egy szezont eltöltött még Zaragozában.
1948 és 1950 között nyolc találkozón pályára lépett a spanyol válogatottban, valamint részt vett az 1950-es vb-n, ahol a spanyol csapat negyedik helyen végzett. A spanyolon kívül meg lett hívva a katalán nemzeti 11-be is.
1963-ban rövid időre belekóstolt az edzősködésbe, amikor korábbi csapattársát, Kubala Lászlót váltotta. Mivel tréneri megbízása csak ideiglenes volt, ezért mindössze tizenöt meccsen ült a kispadon. Ezalatt a fél év alatt is sikerült a gárdával egy kupagyőzelem.
Sikerei, díjai
Játékosként
Bajnok: 1944-45, 1947-48, 1948-49
Szuperkupa-győztes: 1945, 1949
Latin kupa-győztes: 1949
Edzőként
Kupagyőztes: 1962-63
Források
1920-ban született személyek
1978-ban elhunyt személyek
Spanyol labdarúgók
Spanyol labdarúgóedzők
Katalán labdarúgók
Labdarúgóhátvédek
Labdarúgó-középpályások
A Barcelona labdarúgói
A Real Zaragoza labdarúgói
Az 1950-es világbajnokság labdarúgói
Az FC Barcelona vezetőedzői
A La Liga edzői
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\section{Introduction}
Observations of the Cosmic Microwave Background (CMB) provide valuable
information about the early Universe. In addition to the possibility of
measuring the cosmological parameters the CMB data can provide very
important constraints on the type of the seeds that led to the structure
formation (see e.g. \cite{bon-jaf98}).
Inflationary theories predict Gaussian density perturbations
with nearly scale-invariant spectrum (e.g. \cite{tur97} and references
therein). The Gaussianity of the density perturbations results in the
Gaussianity of the CMB temperature fluctuations at the surface of last
scattering. Thus, testing the Gaussianity of the CMB fluctuations
becomes a crucial probe of inflation. On the other hand, if the seeds
for the structure formation are due to topological defects, such as
strings and textures (e.g. \cite{bra98} and references therein) then the
non-Gaussianity of the temperature fluctuations may probe fundamental
physics at high energies.
However, even if the temperature fluctuations were Gaussian at the
surface of the last scattering they may acquire small non-Gaussianity
due to subsequent weak gravitational lensing ( see e.g. \cite{sel96},
\cite{bern97}, \cite{win98}) as well as due to various astrophysical
foregrounds (see e.g. \cite{ban-etal96}). Higher resolution maps (MAP,
PLANCK) will make it even more problematic.
Establishing the Gaussian nature of the signal is also important for
practical reasons: Some current techniques for estimating the power
spectrum are optimized for the Gaussian fields only (e.g. \cite{fkp},
see also the discussion in \cite{kno-etal98} and \cite{fer-etal98}).
Standard tests for non-Gaussianity are the three-point correlation
function or bispectrum and higher order moments. However, in practice
negative results of the non-Gaussian tests can hardly be conclusive
since only infinite number of n-point correlation functions can prove
that a field is Gaussian. A distribution may appear to be Gaussian up
to very high moment and then be non-Gaussian (\cite{ken-stu77}). The
high-order correlation functions are very expensive computationally for
the large data sets ($O(N^m)$, where $m$ is the order of the correlation
function and $N$ is the number of pixels). Thus, any statistic that is
sensitive to non-Gaussianity and computationally efficient is very
useful.
Here are other well known examples of the tests sensitive to
non-Gaussianity: peak statistics (\cite{bon-efs87}, \cite{vit-jus87},
\cite{nov-jor96}),
genus curve (integral geometric characteristics) (\cite{mel89},
\cite{col88}, \cite{nas-nov95}); global
Minkowski Functionals (hereafter MFs) (\cite{got-etal90},
\cite{sch-gor98}, \cite{win-kos98}). These functionals also have
been considered for CMB polarization field by \cite{nas-nov98}.
Minkowski Functionals
(\cite{min03}) were 'properly' - i.e. in the context of differential and
integral geometry - introduced into cosmology by \cite{mec-etal94} as a
three-dimensional statistics for pointwise distributions in the universe
and then for the isodensity contours of a continuous random field by
\cite{sch-buc97}. We will discuss the MFs in the following section. Here
we just mention that in the two-dimensional case of the temperature maps
the global Minkowski Functionals are the total area of excursion regions
enclosed by the isotemperature contours, total contour length, and the
genus\footnote{In flat space the genus is equal to
the Euler-Poincar\'{e} characteristic.} or the number of isolated
high-temperature regions minus the number of isolated low-temperature
regions. Partial Minkowski Functionals are the same quantities but used
as characteristics of a single excursion region.
Kogut et al. (1996) measured the 2-point and 3-point correlation
functions and the genus of temperature maxima and minima in the
COBE DMR 4-year sky maps. They concluded that all statistics were in
excellent agreement with the hypothesis of Gaussianity.
\cite{col-etal96} measured the genus of the temperature fluctuations in
the COBE DMR 4-year sky maps and came to a similar conclusion.
Heavens (1998) computed the bispectrum of the 4-year COBE datasets
and concluded that there was no evidence for non-Gaussian behavior.
However, Ferreira, Magueijo \& G\'{o}rski (1998) studied the
distribution of an estimator for the normalized bispectrum and concluded
that the Gaussianity is ruled out at the confidence level at least of
99\%.
The first analysis of two-dimensional theoretical maps of the
temperature fluctuations that used the total area, length of the
boundary and genus for the excursion set was done by \cite{got-etal90}
although without referring to Minkowski Functionals. Then
\cite{sch-gor98} discussed the application of the MFs to the COBE maps
stressing the importance of taking into account the curvature of the
celestial sphere (the manifold supporting the random field of the
temperature fluctuations).
\cite{sch-gor98} actually applied the statistics to the COBE data and
argued for its advantage as a test of non-Gaussian signal. They concluded
that the field is consistent with a Gaussian random field on degree
scale.
\cite{sah-sat-sh98} suggested that the Partial Minkowski Functionals
(PMF) may be used as quantitative descriptors of the geometrical
properties of the elements of the large-scale structure (superclusters
and voids of galaxies). In particular, they argued that two simple
functions of the PMFs called the shapefinders can distinguish and
reasonably quantify the structures like filaments, ribbons and pancakes.
Here, we describe a new statistical tool which is sensitive to non-Gaussian
behavior of random fields. We suggest using the distribution functions of the
Partial Minkowski Functionals and the number of maxima for a given threshold
level. As an illustration we apply it to the
full sky temperature maps obtained by subtracting the galaxy
contributions from 4-year COBE observations (\cite{bennet92}, \cite{bennet94})
The main goal of the paper is the demonstration of the potentiality of this
novel technique.
The outline of the paper is as follows. In Section 2 we briefly review the
Minkowski Functionals. In Sec. 3 we outline the numerical algorithm
used for the evaluation of the Minkowski Functionals. Then, as an example of
application this method we present the first results of analysis of the
4-year COBE maps. Finally, in Sec. 4 we discuss the results and
potentiality of the method.
\section{Minkowski Functionals}
Let us consider one connected region $R_i$ of the excursion set with
$\nu(\theta,\varphi) \equiv (\Delta T(\theta,\varphi)/T)/\sigma_0 >
\nu_t$, where $\sigma_0={\langle (\Delta T/T)^2\rangle}^{1/2}$,
$\nu(\theta,\varphi)$ is the measure and $\nu_t$ is the threshold. If
the region is complex then it may require very many parameters to fully
characterize it. However, we consider only three parameters: the area of
the region, $a_i$, the length of its contour, $l_i$, and the number of
holes in it $n_{hi}$. These are three partial Minkowski Functionals. In
the following analysis we also count the number of maxima of
$\nu(\theta,\varphi)$. To obtain the global Minkowski Functionals, we
compute these quantities for all disjoint regions of the excursion set,
i.e. taking the sums $A=\Sigma a_i$, $L=\Sigma l_i$ and $G =\Sigma g_i$:
``number
of isolated $\nu > \nu_t$ regions'' $-$ ``number of isolated $\nu <
\nu_t$ regions''. The last quantity is the genus introduced into cosmology
long ago by \cite{dor70} and \cite{got-etal86}. The total area
$A(\nu_t)$ is clearly proportional to the cumulative distribution
function of the random field. At high (low) threshold levels the excursion
regions appear as isolated hot (cold) spots.
The Minkowski Functionals have several mathematical properties that make
them special among other geometrical quantities. They are
translationally and rotationally invariant, additive
\footnote{In particular, additivity means that the Minkowski Functionals
of the union of several disjoint regions can be easily obtained if
the Minkowski Functionals of every region is known.}, and have simple
and intuitive geometrical meanings. In addition, it was shown
(\cite{had57}) that all global morphological properties (satisfying
motional invariance and additivity) of any pattern in $D$-dimensional
space can by fully characterized by $D+1$ Minkowski Functionals.
Global MFs of Gaussian fields are known analytically; in the two-dimensional
flat space they are:
\begin{equation}
\begin{array}{l}
A(\nu)=\frac{1}{2}-\frac{1}{2}\Phi(\frac{\nu}{\sqrt{2}}),\\
L(\nu)=\frac{1}{8\theta_c}\nu e^{-\frac{\nu^2}{2}},\\
G(\nu)=\frac{1}{(2\pi)^{3/2}}\frac{1}{2\theta_c^2}\nu
e^{-\frac{\nu^2}{2}}.
\end{array}
\end{equation}
where $\Phi(x)=\frac{2}{\sqrt{\pi}}\int\limits_{0}^{x}e^{-x'^2}dx'$ is the
error function. Their dependence on the spectrum can be expressed only
in terms of the length scale of the field
$\theta_c=\frac{\sigma_0}{\sigma_1}$ where $\sigma_0$ and $\sigma_1$
can be calculated from the spectrum $C_l$
\begin{equation}
\begin{array}{l}
\sigma_0=1/4\pi\sum_l (2l+1)C_l,\\
\sigma_1=1/4\pi\sum_l (2l+1)(l+1)lC_l.\\
\end{array}
\end{equation}
The analytic formulae for the partial Minkowski Functionals are not
known even for Gaussian fields. However, it does not impose a principal
obstacle in their application since they can be calculated
numerically. It is worth stressing that in practical application, in
addition to the mean value of some quantity one has to know its
variance. In most cases the variance is not available in an analytic
form even if the mean value is. For instance, one can calculate
analytically the mean number of hot/cold spots but the variance of this
number can be estimated only numerically.
\section{Application to Two-dimensional Maps}
We identify all disjoint regions above a given threshold $\nu > \nu_t$ for
positive peaks and below the threshold $\nu <- \nu_t$ for negative peaks.
For every region $R_i$ we compute three Minkowski Functionals:
\noindent The area, $v_{1}^i=a_i$ \\
The perimeter $v_{2}^i=l_i$ i.e. the length of the boundary \\
The number of holes - equivalent to genus - $v_{3}^i=g_{i}$ \\
The number of maxima $v_{4}^i=n_{mi}$ within the region.
\noindent We then study the cumulative distribution functions
$F(\nu_t,v^k)$ ($ k=1,2,3,4$) of these quantities.
\subsection{Data}
We used the DMR 4--year whole sky maps, where all Galactic emission was
removed. Two independent methods were employed to separate the Galactic
foreground from the cosmic signal. The maps' construction is described
in detail in two papers (\cite{bennet92}, \cite{bennet94}), they were
released in the DMR Analyzed Science Data Sets (ASDS). The two
techniques are: One method is the so--called combination method (map
1). Here they cancel the Galactic emission by making a linear
combination of all DMR maps, then cancel the free--free emission
assuming a free--free spectral index and finally normalize the cosmic
signal in TD temperature. The subtraction method (map 2) constructs
synchrotron and dust emission maps and subtracts them from the DMR data
sets. The Galactic free--free is then removed. The analysis presented in
this paper was done for both maps and the results of the analysis were
similar.
\subsection{Numerical Algorithm}
In this subsection, we describe the numerical algorithm for
calculation of the distribution of the partial Minkowski
functionals on the sphere and application of this algorithm to
the COBE data, considered in the previous section.
\subsubsection{Maps simulations.}
In our simulations we use spherical coordinate system to assign pixels
on a sphere. Here we consider the temperature distribution on the
pixelized map as the function of two variables in the coordinate system:
$-\pi/2<\theta <\pi/2$ and $-\pi<\varphi <\pi$. In fact, this function is
defined only in the points $(\theta_{k_1},\varphi_{k_2})$, so that:
\begin{equation}
\nu_{k_1,k_2}=\nu(\theta_{k_1},\varphi_{k_2}), \hspace{0.5cm}\theta_{k_1}=
k_1h_{\theta},\hspace{0.5cm}
\varphi_{k_2}=k_2h_{\varphi}\ .
\end{equation}
We also assume, that $h_{\theta}=h_{\varphi}=h=\frac{2\pi}{M}$ where $M$
is the number of pixels in the $\varphi$ direction. The
total number of pixels is, therefore, $M^2/2$.
The original COBE maps have been
recalculated according this pixelization in the following way:
\begin{equation}
\Delta T_{data}(\theta,\varphi)=B\int\Delta T_{COBE}(\theta',\varphi')
e^{-\frac{\gamma^2}{2\gamma_0^2}}dcos(\theta')d\varphi'
\end{equation}
where $\Delta T_{COBE}$ and $\Delta T_{data}$ are temperatures defined
in the points of COBE cube pixels and in the points defined by the
variables in Eq. (3) above, $\gamma$ is the angle between the pixels,
$\gamma_0=7^0$ is the smoothing angle and B is the normalization.
The temperature fluctuations are completely characterized by the
spectrum coefficients $C_l^m$. Using this description one can write the
following expression for the temperature of the relic radiation:
\begin{equation}
\begin{array}{l}
\Delta T_{data}(\theta,\varphi)=\sum\limits_{l=2}^{\infty}
\sum\limits_{m=-l}^{m=l}C_l^mY_l^m(\theta,\varphi),\\
\nu_{data}(\theta,\varphi)=\frac{\Delta T_{data}(\theta,\varphi)}
{\langle\Delta T_{data}^2\rangle^{1/2}}
\end{array}
\end{equation}
where $Y_l^m$ are the spherical harmonics. The summation in Eq.(5) is
from l=2. The term with l=1 is the dipole component. This term has been
removed from the COBE data before analysis because the contribution of
this term in the $\Delta T$ fluctuations can not be separated from the
contribution due to the motion of the observer relative to the
background radiation.
We have simulated 1000 different Gaussian realizations of the
temperature distributions on a sphere so that we can compare the
distribution of partial Minkowski functionals in the observational data
with a random Gaussian field. This was accomplished in the following way:
\begin{equation}
\begin{array}{l}
\Delta T_{g}(\theta,\varphi)=\sum\limits_{l=2}^{\infty}
\sum\limits_{m=-l}^{m=l}a_l^mC_l^{\frac{1}{2}}Y_l^m(\theta,\varphi),\\
\nu_{g}(\theta,\varphi)=\frac{\Delta T_{g}(\theta,\varphi)}
{\langle\Delta T_{g}^2\rangle^{1/2}}
\end{array}
\end{equation}
where $a_l^m$ are independent random Gaussian numbers with zero mean
ie. $\langle a_l^m \rangle =0$ and with unit variances $\langle
(a_l^m) ^2 \rangle =1$.
The power spectrum $C_l$ in (6) were obtained using $C_l^m$ from (5) as
follows:
\begin{equation}
C_l=\frac{\sum\limits_{m=-l}^{m=l}(C_l^{m})^2}{(2l+1)}
\end{equation}
\subsubsection{Calculation of Partial Minkowski Functionals}
Let us introduce some threshold $\nu_t$ on a pixelized map of the
CMB. Each isolated hot-spot (regions with $\nu >\nu_t$) can be
considered as the cluster characterized by the area, boundary length and
Euler characteristic or equivalently by genus
(both are directly related to the number of disjoint boundaries).
For example, the
total area of the map where $\nu>\nu_t$ is the sum of the areas of all
isolated hot-spots, where $\nu>\nu_t$. The global Minkowski Functionals, i.e.
the total area, total boundary length
and total genus can be found by summation of their partial values over
all clusters on the map. Computing partial Minkowski functionals on
the pixelized map we require that the
algorithm satisfies the following convergence properties:
\begin{equation}
\begin{array}{l}
v_k^i|_p-v_k^i\rightarrow 0,\hspace{0.5cm}as\hspace{0.5cm}
h\rightarrow 0\\
\hspace{2cm}{\rm and}\\
\frac{(v_k^i|_p-v_k^i)}{v_k^i}\sim O(h^z)\hspace{0.5cm}k=1,2
\end{array}
\end{equation}
where $v_k^i|_p$ denotes k-th Minkowski functional of i-th cluster,
calculated on the pixelized map and $v_k^i$ is the exact value of this
functional on the continuous field. In the following analysis we use
linear interpolation, so that $z=1$ for our algorithm.
Pixels $(k_1,k_2)$ inside the regions where $\nu>\nu_t$ satisfy the
condition $\nu_{k_1,k_2}>\nu_t$. We define pixel $(k_1,k_2)$ inside this
region as the inner boundary pixel if the field is below the threshold
level $\nu_t$ at least in one of its four neighbors
$((k_1+1,k_2),(k_1-1,k_2),(k_1,k_2+1), (k_1,k_2-1))$ (eg.
$\nu_{k_1+1,k_2}<\nu_t$) see Fig. 4. We approximate a smooth boundary
curve by the polygon using linear interpolation of the field
between inner and outer boundary pixels (Fig. 4) and thus finding the
intersection of the boundary curve with the grid lines:
\begin{equation}
\theta_b=k_1h+h\frac{\nu_t-\nu_{k_1,k_2}}
{\nu_{k_1+1,k_2}-\nu_{k_1,k_2}},\hspace{2cm}
\varphi_b=k_2h
\end{equation}
for $\varphi$ grid lines and
\begin{equation}
\theta_b=k_1h,\hspace{2cm}
\varphi_b=k_2h+h\frac{\nu_t-\nu_{k_1,k_2}}
{\nu_{k_1,k_2+1}-\nu_{k_1,k_2}}
\end{equation}
for $\theta$ grid lines. $\theta_b$ and $\varphi_b$ denote coordinates
of the boundary points $\vec{X}_m=(\theta_b ,\varphi_b$) on the
polygon. This polygon obviously converge to the smooth boundary line as
$h\rightarrow 0$.
Then, the algorithm of cluster analysis consists of three
steps.
\begin{itemize}
\item{1)} Identifying the boundaries and computing their lengths.\\
First, we search for closed boundary lines of the level $\nu=\nu_t$.
Then, each set of boundary points is ordered by letting $\vec{X}_{m+1}^n$ to
be the nearest boundary point to the point $\vec{X}_m^n$.
The length of a closed boundary line is:
\begin{equation}
l_n=\sum\limits_{m=1}^{m=M_n+1}|\vec{X}_{m+1}^n-\vec{X}_{m}^n| \ ,
\end{equation}
where
$M_n$ is the total number of boundary points in the n-th closed
line of threshold level ($\vec{X}_{M_n+1}^n=\vec{X}_1^n$) and the norm
$|\vec{X}_{m+1}-\vec{X}_{m}|= [(\theta_{m+1}-\theta_{m})^2+
\sin^2(\frac{\theta_{m+1}+\theta_{m}}{2})(\phi_{m+1}-\phi_{m})^2]^{1/2}$.
The first point $X_1$ is arbitrary.
Different boundary lines in the map correspond to the
arrays of boundary points ($\vec{X}_m^n$) and inner boundary pixels
($\vec{Y}_m^n$). The total boundary of an isolated region $\nu >\nu_t$
may consist of a number of closed lines (two lines in Fig.4).
\item{2)} Finding all the boundaries of a connected region (cluster),
computing the total boundary length and genus.\\
We combine all closed lines which are the boundaries of the same cluster
by using arrays of inner
boundary pixels ($\vec{Y}_m^n$). Suppose, we wish to check whether
two different lines are the boundaries of the same
cluster or not. These lines correspond to two sets of inner boundary pixels
$\vec{Y}_m^{n_1}$ and $\vec{Y}_m^{n_2}$. If we take two arbitrary inner
pixels one from each set and connect them by
a path along grid lines (see Fig. 4) then the path can intersect
the boundaries $N_{int}^i$ times ($i=1,2$), where $N_{int}^i \ge 0$. If the
both numbers $N_{int}^1$ and $N_{int}^2$ are even then both
inner boundary pixels
belong to the same cluster otherwise they belong to two
different regions (clusters). Therefore all boundary lines which belong to
one cluster form its boundary with the total boundary length equal
to the sum of their lengths.
The number of closed lines for each cluster is equivalent to
the genus of this cluster. Thus we find total number of clusters and two
partial Minkowski functionals for each of them -- the length and genus.
\item{3)} Computation of the areas of clusters.\\
All pixels situated between the inner boundary pixels of a cluster
belong to the
cluster. The area of the cluster can be roughly approximated
by the total area of all these
pixels (including inner boundary pixels).
\end{itemize}
\subsection{Results}
Figures 5 and 6 show the cumulative distribution functions
$F(\nu_t,V_k)$ (where $V_k=\sum_i v_{k}^i$) for the two COBE maps
described above along with the mean Gaussian values and variances. The
mean and variance were obtained from 1000 random realizations of
Gaussian fields having the same amplitudes as shown but different sets
of random phases. In both Fig. 5 and 6 we see significant deviations from
Gaussianity. It may be interesting to note that each statistic shows
the greatest difference with the Gaussian value at different thresholds:
$F(A)$ at $\nu_t= -0.5$, $F(L)$ at $\nu_t= -1$, $F(G)$ at $\nu_t= \pm
1$, and $F(N_m)$ at $\nu_t = 0, 0.5, -1$. These differences are roughly
the same for both maps and suggest that each of the four statistics carry
different statistical information.
As one might expect, more detailed information can be obtained from the
partial Minkowski Functionals. Figures 7 through 11 show the partial
Minkowski Functionals at ten thresholds $\nu_t= \pm 2,\pm 1.5, \pm 1,
\pm 0.5$ and $\pm 0$\footnote
{The thresholds $\nu_t=+0$ and $-0$ correspond to the
excursion sets $\nu>0$ and $\nu<0$ respectively.}. Every figure shows
two curves, one for the positive ($\nu>\nu_t $, solid lines) and one for the
negative ($\nu<\nu_t $, dashed lines) thresholds, having same absolute
magnitude $\nu_t $ for each map. Thick and thin
lines correspond to COBE maps 1 and 2 respectively.
The mean Gaussian curve (that obviously
does not depend on the sign of the threshold) is the dotted line and
$1\sigma$ Gaussian variance is shown as a shaded area.
The main features of Fig. 7-11 are the following:
\begin{itemize}
\item Figure 7, $\nu_t=2$: The functions $F(a)$ and $F(l)$ show strong
non-Gaussian signal; $F(g)$ and $F(n_m)$ roughly consistent with the
Gaussianity.
\item Figure 8, $\nu_t=1.5$: All statistics shows strong non-Gaussianity.
\item Figure 9, $\nu_t=1.$: The strongest non-Gaussian signal comes from the
distribution of maxima, $F(n_m)$; other statistics are roughly compatible
with Gaussianity.
\item Figure 10, $\nu_t=0.5$: All statistics show marginal disagreement
with Gaussianity.
\item Figure 11, $\nu_t=0$: All statistics are in rough agreement with
Gaussianity.
\end{itemize}
\section{Discussion}
We suggest new statistics to test the Gaussianity of CMB maps.
These statistics are the distribution functions of the Partial Minkowski
Functionals of the excursion set for a given threshold level $\nu_t$. We
also compute the distribution function of the number of maxima in the
isolated region. The Partial Minkowski Functionals have transparent
geometrical and topological meanings of : 1) the area, 2) the perimeter
and 3)the genus of each disjoint region. Introducing these statistics is
a natural step further. It generalizes the statistical techniques used
before: the cumulative distribution function that correspond to the
total area of the excursion sets, global genus (\cite{dor70},
\cite{got-etal86}), the total length of the boundary
(\cite{got-etal90}). The set of three characteristics mentioned above is
known as global Minkowski Functional and has already been used in
cosmology (\cite{mec-etal94}, \cite{sch-buc97}, \cite{win-kos98},
\cite{sch-gor98}). \cite{sah-sat-sh98} argued that the Minkowski
Functionals can describe the morphological characteristics of isolated
regions or objects.
It is well known that Minkowski Functionals are invariant under
translations and rotations and are also additive. Due to these
properties the MFs can be used in cases of incomplete or patchy
coverage. The additivity allows to analyze large data set by splitting
them into a set of smaller subsets. Measuring the partial MF is very
efficient computationally: for a fixed threshold it requires only $O(N)$
operations, where $N$ is the number of pixels.
Clearly, computing the distribution functions of the partial MF require
much larger data sets than we used here for an illustrative purpose.
However, the upcoming MAP and Plank missions will provide the necessary
resolution. Needless to say that by knowing the partial MFs one can
easily obtain global MFs. Thus, these statistics completely incorporate
the global MFs.
We show that the reconstructions of the whole sky maps obtained by
subtraction the Galaxy contributions from the COBE maps are strongly
non-Gaussian. This was suspected by many authors who used only the
polar caps for the analysis of the cosmological signal
(e.g. \cite{col-etal96}, \cite{sch-gor98}, \cite{fer-etal98}). It is
possible that some of the non-Gaussian signal in our analysis is due
to errors in the Galaxy removal, since the Galactic signal is obviously
non-Gaussian. For instance, \cite{col-etal96} found no
deviations from Gaussianity in the genus curve while we see significant
non-Gaussianity in our genus measurements. Unfortunately, by analyzing the
Galaxy caps only we use only about half the data and in addition
split the remaining half into two disjoint regions affected by the
boundaries. Since the largest number of disjoint regions is
about ten at $\nu_t=1.5, 1$ (Fig. 9,10) in the whole sky, the analysis of
the caps only does not seem to be reasonable. This paper provides a
feasibility study in the strengths and usefulness of the Partial Minkowski
Functionals, not a definitive results regarding the non-Gaussian nature
of the COBE--DMR maps.
Acknowledgments. We are grateful to Ned Wright for criticism and useful
comments.
S. Shandarin thanks K. G\'{o}rski, V. Sahni, B. Sathyaprakash and
S. Winitzki for useful discussions of the related topics and comments.
We acknowledge the support of EPSCoR 1998 grant. DN was
supported by NSF-NATO grant 6016-0703, HF was supported in part by the
NSF-EPSCoR program and the GRF at the University of Kansas. S. Shandarin also
acknowledges the support from GRF grant at the University of Kansas and
from TAC Copenhagen.
\newpage
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
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\section{Introduction}
The attractor mechanism \cite{kallosh:attractor,strominger:attractor,kallosh:attractor2} is a ubiquitous phenomenon in gravitational theories with moduli whereby the moduli take on values at the horizon of an extremal\footnote{The attractor mechanism was recently argued to hold in a spatially averaged sense even for non-extremal black holes \cite{goldstein:hotAttr}. Implications of the attractor mechanism for near-extremal black holes were studied in \cite{larsen:nAttractor}.} (zero temperature) black hole that are independent\footnote{There are two caveats to this that we will discuss below. First, attractor moduli might depend on a choice of `area code.' Second, it is possible for only some moduli to be attracted.} of their values at infinity. It can be heuristically motivated (see, e.g., \cite{trivedi:nonSUSY}) by noting that the entropy of such a black hole -- being the logarithm of an integer -- should vary discretely, while the moduli vary continuously. Alternatively, it can be understood geometrically from the fact that extremal black holes have an infinite throat so that the physical distance to the horizon is infinite, and variations of the moduli over this distance wash away any dependence on the moduli at infinity \cite{kallosh:nonBPS}. Ultimately it follows from an analysis of the solutions of the equations of motion \cite{kallosh:attractor,strominger:attractor,kallosh:attractor2,sen:entropyFunction,kallosh:nonBPS,goldstein:nonSUSY,trivedi:nonSUSY}.
The discussion thus far has made no reference to supersymmetry, but of course the latter is intimately connected to the attractor mechanism. One reason is that the very existence of moduli is generically unnatural without supersymmetry. Another is that the study of BPS attractors is greatly simplified by the first-order Killing spinor equation.
However, one can study non-supersymmetric but extremal black holes arising as excitations of supersymmetric vacuum solutions.
This makes it natural to study extremal but non-BPS attractors in supergravity.
A particularly natural setting for such a study is in the context of string theory \cite{trivedi:nonSUSYstr}. One important reason is that the attractor mechanism implies a sort of non-renormalization theorem which, under certain conditions, allows one to compute the entropy of a weakly-coupled collection of microscopic ingredients and reliably continue the result to strong coupling where these ingredients form a black hole \cite{legalDocument}. This allows one to generalize the fantastic success of string theory in counting microstates of BPS black holes \cite{stromingerVafa} to the extremal but non-BPS case. Another good reason is that one can hope to generalize the observations of \cite{moore:arithmeticAttractors} relating arithmetic, geometry, and attractors in string theory, those of \cite{denef:attractor,denef:slag,aspinwall:unstableSlag} which pertained to geometric aspects of attractor flows, and those of \cite{sk:specialCycle,sk:cycleAuto} on special cycles. Finally, one might reasonably argue that it is especially interesting to study black holes in a theory with a known UV completion.
First questions one might ask are `How are attractor moduli distributed in moduli space?' and `How many attractors exist with entropy below some cutoff $S_*$?' Denef and Douglas \cite{douglas:distributions} attacked these problems in the BPS case, using tools (reviewed in \cite{douglas:algGeom}) that they had developed for studying flux compactifications (and which were recently applied in another context in \cite{mz:slagCounts}). They concluded that attractors are uniformly distributed in moduli space and that their count grows as a particular power of $S_*$ that depends only on the dimension of the moduli space. In particular, their results agreed with those of \cite{moore:arithmeticAttractors}, which related the growth of BPS attractors on $K3\times T^2$ to the Smith-Minkowski-Siegel mass formula. Indeed, these tools enabled the prediction of a previously-unknown constant.
The purpose of this paper is to generalize this approach to non-BPS attractors. As one might expect from the analogous results of \cite{douglas:distributions,douglas:nonSUSY} for non-supersymmetric flux vacua, our results are less elegant than in the BPS case. However, we can nevertheless make non-trivial progress. In particular, the growth of attractors with $S_*$ proves to be the same as in the BPS case. Furthermore, after restricting our attention to the simple case of one-modulus models (such as the mirror quintic), we can analytically characterize the distribution of attractors in various regions of moduli space. In contrast to the BPS case, we find a non-trivial dependence on the curvature of moduli space. We verify these predictions with numerics.
An outline of the rest of this paper is as follows. In section \ref{sec:review}, we review the attractor mechanism in the context of type IIB Calabi-Yau compactifications. In section \ref{sec:analytics}, we then analytically study the distribution of attractors. We numerically verify our predictions in the case of a one-modulus model in section \ref{sec:numerics}. We conclude in section \ref{sec:conclusion}.
\section{The attractor mechanism in type IIB Calabi-Yau compactifications} \label{sec:review}
Consider a 4d gravity theory with $U(1)$ gauge fields and moduli $\phi^i$ coupled to the gauge fields via axio-dilaton-like couplings:
\be - f_{\alpha\beta}(\phi^i) F_{\mu\nu}^\alpha F^{\beta \mu\nu} - \frac{1}{2}\tilde{f}_{\alpha\beta}(\phi^i) \epsilon^{\mu\nu\rho\sigma} F_{\mu\nu}^\alpha F^\beta_{\rho\sigma} \ .\ee
The authors of \cite{trivedi:nonSUSY} studied ans\"atze parametrized by choices of electric and magnetic charges that determine extremal black holes in such a theory. They found that solutions are associated to local minima of an effective potential, $V_{eff}(\phi^i)$. Denoting the attractor moduli that determine such a minimum by $\phi^i_0$, they showed that the horizon radius and entropy of the black hole are respectively given by
\be r_H^2 = V_{eff}(\phi^i_0) \ ,\quad S = \frac{A}{4} = \pi r_H^2 \ . \label{eq:r} \ee
In general, there will be multiple such minima \cite{moore:arithmeticAttractors,denef:attractor,denef:quinticBasin}. In these cases, we refer to the multiple basins of attraction as `area codes.' In addition, it is possible for the effective potential to be independent of some moduli. In this case, these moduli will not be attracted, and the entropy of an extremal black hole will not depend on them.
We now specialize in two steps. Our first specialization is to $\N=2$ theories with an $n$-complex-dimensional vector multiplet moduli space $\M$. (Hypermultiplet scalars do not appear in the effective potential.) $\M$ is a special K\"ahler manifold; we denote its K\"ahler potential by $K$ and its metric by $g_{i\bar\jmath} = \partial_i \partial_{\bar\jmath} K$. In addition, there is a central charge, $Z$, which is a holomorphic section of a line bundle $\Li\to \M$ whose covariant derivative is $D_i Z \equiv \partial_i Z + (\partial_i K)Z$. That is, under a K\"ahler transformation
\be K\to K - f - \bar f \ ,\ee
where $f$ is a holomorphic function on $\M$, $Z$ and $D_iZ$ transform as
\be Z \to e^f Z \ ,\quad D_i Z \to e^f D_iZ \ . \ee
The effective potential is then \cite{kallosh:critical}
\be V_{eff} = e^K\brackets{ g^{i\bar \jmath} (D_i Z)(D_{\bar\jmath} \bar Z) + |Z|^2 } \ . \label{eq:Veff} \ee
BPS attractors not only minimize this, but also satisfy
\be D_i Z = 0 \ . \label{eq:BPS} \ee
Said another way, they minimize the rescaled central charge \cite{kallosh:attractor2}
\be \Z = e^{K/2} Z \ , \label{eq:Z} \ee
in the sense that
\be D_i \Z \equiv \partial_i \Z + \frac{1}{2} (\partial_i K) \Z \equiv e^{K/2}D_i Z = 0 \ ,\ee
or
\be \partial_i|\Z|^2 = 0 \ .\ee
So, they separately minimize the two terms of \eqref{eq:Veff}. In contrast, extremal attractors need only minimize \eqref{eq:Veff}. Another important difference is that for BPS attractors critical points of $|\Z|^2$ in the interior of $\M$ are automatically local minima \cite{kallosh:critical}, since $\partial_i\partial_{\bar\jmath} \log |\Z|^2 = g_{i\bar\jmath}$ implies that the Hessian of $|\Z|^2$ at a critical point is a positive definite matrix, whereas for non-BPS critical points of $V_{eff}$ this positive definiteness is not automatic. Finally, we note the following relationships between the central charge, entropy, horizon area, and mass of a BPS black hole:
\be S = \frac{A}{4} = \pi |\Z|^2 = \pi M^2 \ .\ee
These follow from \eqref{eq:r}--\eqref{eq:Z} and the BPS bound $M=|\Z|$.
We now further specialize to $\N=2$ theories obtained via compactification of type IIB string theory on a Calabi-Yau threefold $X$. The moduli space of such a theory locally factors\footnote{This can fail globally \cite{vafa:dManifolds,katz:enhance}.} as a product of (complexified) K\"ahler and complex structure moduli spaces, and the vector multiplet moduli $\phi^i$ of interest are the complex structure moduli. The complex dimension of the complex structure moduli space is $n=h^{2,1}$. A black hole corresponds to a D3-brane wrapping a 3-cycle of $X$, and its electric and magnetic charges correspond to the homology class $\tilde\gamma \in H_3(X,\ZZ)$ representing this 3-cycle, or equivalently its Poincar\'e dual $\gamma\in H^3(X,\ZZ)$. We identify $\Li\to \M$ with the Hodge line bundle $H^{3,0}(X)\to \M$; importantly, the holomorphic 3-form $\Omega$ is then a holomorphic section of this line bundle, which is unique up to multiplication by a nowhere-vanishing holomorphic function of the $\phi^i$. The K\"ahler potential is given by
\be e^{-K}=i\int \Omega\wedge\bar\Omega \ . \label{eq:Kahler} \ee
Finally, for a black hole with charge $\gamma\in H^3(X,\ZZ)$, the central charge is
\be Z = \int \gamma \wedge \Omega \ .\ee
Importantly, $D_i\Omega$ comprise a basis for $H^{2,1}(X)$. Noting that
\be D_i Z = \int \gamma\wedge D_i\Omega \ ,\ee
we find that the BPS attractor equation \eqref{eq:BPS} (and its conjugate) states that the projection of $\gamma$ onto $H^{2,1}(X)\oplus H^{1,2}(X)$ vanishes. That is,
\be \gamma\in H^{3,0}(X) \oplus H^{0,3}(X) \ . \label{eq:niceForm} \ee
Writing this as
\be \gamma = 2\Imag(\bar S \Omega) \ , \label{eq:newEqn} \ee
where $S$ is a constant, provides an interesting reformulation of the BPS attractor condition. For, it consists of $b_3/2=h^{2,1}+1$ complex equations for the same number of unknowns (namely $S$ and $\phi^i$), whereas we started with the $h^{2,1}$ equations \eqref{eq:BPS} in $h^{2,1}$ unknowns. However, for the price of this extra complexity, we have eliminated all derivatives from the equations. We can recover the original equations by studying \eqref{eq:newEqn} in the Hodge decomposition basis for $H^3(X,\CC)$ comprised of $\Omega,D_i\Omega$, and their conjugates. However, in some circumstances it might be more convenient to study this equation in another basis, such as an integral symplectic basis. An analogue of the formulation \eqref{eq:niceForm} of the attractor equations for non-BPS black holes was obtained in \cite{kallosh:nonBPS}.\footnote{As an aside, we note that another reformulation was provided in \cite{vafa:nonSUSY}.}
We now introduce an integral symplectic basis $C^I$, $I=1,\ldots,b_3 = 2h^{2,1}+2$ for $H_3(X,\ZZ)$ and the Poincar\'e dual 3-forms $C_I$. These satisfy
\be \int C_I\wedge C_J = \int_{C^I}C_J = \Sigma_{IJ} = \begin{pmatrix}
\bf 0 & \bf 1 \\
-\bf 1 & \bf 0
\end{pmatrix} \ .\ee
Expanded in this basis, a charge vector $\gamma\in H^3(X,\ZZ)$ has integral coefficients, which are the electric and magnetic charges: $\gamma = Q^I C_I$, where
\be \int C_I\wedge \gamma = Q^J \int C_I\wedge C_J = \Sigma_{IJ} Q^J \equiv Q_I \ . \ee
Another important function of this basis is to provide convenient coordinates on $\M$, namely the periods of $\Omega$:
\be \Pi_I = \int C_I\wedge \Omega \ .\ee
The electric periods $\Pi_a$, $a=1,\ldots,h^{2,1}+1$, provide a set of projective coordinates on $\M$. The magnetic periods are then functions of the electric ones.
As in \cite{douglas:distributions}, we will find it convenient to have a third basis for $H^3(X,\CC)$ (besides the integral symplectic basis and the Hodge decomposition basis), which we will call the orthonormal basis. First, we introduce a vielbein $e^i_A$, $A=1,\ldots,h^{2,1}$, which satisfies $g_{i\bar\jmath} e^i_A e^{\bar\jmath}_{\bar B} = \delta_{A\bar B}$. Then, the orthonormal basis is comprised of $e^{K/2}\Omega$, $e^{K/2}D_A\Omega=e^{K/2} e^i_A D_i\Omega$, and their conjugates. It is so named because \eqref{eq:Kahler} and
\be ie^K\int D_i\Omega\wedge (D_j \Omega)^* = - g_{i\bar \jmath} \Rightarrow ie^K\int D_A\Omega\wedge (D_B \Omega)^* = - \delta_{A\bar B} \ee
imply that this basis diagonalizes the Hermitian form $\avg{\omega_1,\omega_2}=i\int \omega_1\wedge \bar\omega_2$, and the diagonal values are $\pm 1$ in this basis.
\section{Distributions of attractors} \label{sec:analytics}
The quantity of interest in this paper is the count $\N(S_*,\R)$ of attractor black holes with entropy at most $S_*$ and whose attractor moduli lie in the region $\R\subset\M$. We study this by mimicking the approach of \cite{douglas:distributions} to the analogous problem for BPS attractors. We write
\be \N(S_*,\R) = \sum_{\rm attractors} w(\phi^i_0) \theta(S_*/\pi-V_{eff}(\phi^i_0)) \ ,\quad w(\phi^i) = \piecewise{1}{\phi^i\in \R}{0}{\phi^i\not\in\R} \ . \ee
Then, we introduce the Laplace transform representation of the theta function:
\be \N(S_*,\R) = \lim_{\epsilon\to 0^+} \frac{1}{2\pi i} \int_{\epsilon-i\infty}^{\epsilon+i\infty} \frac{d\alpha}{\alpha} e^{\alpha S_*/\pi} \N(\alpha,\R) \ ,\quad
\N(\alpha,\R) = \sum_{\rm attractors} w(\phi^i_0)\, e^{-\alpha V_{eff}(\phi_0^i)} \ .\ee
Now, we input the attractor equations (using the notation $|dz|^2\equiv \frac{i}{2}dz\wedge d\bar z=dx\wedge dy$ for the integration measure for a complex variable $z=x+iy$):
\be \N(\alpha,\R) = \sum_{Q^IC_I\in H^3(X,\ZZ)} \int_\R |d^n\phi|^2 \, e^{-\alpha V_{eff}} \delta^{2n}(dV_{eff}) |\det d^2 V_{eff}| \, \theta(d^2V_{eff}) \ ; \label{eq:N} \ee
the final theta function schematically indicates that we require the Hessian of $V_{eff}$ to be positive definite so that our critical points are minima. The Jacobian cancels the one for the change of variables $\phi\to dV_{eff}$. Strictly speaking, these expressions require $d^2V_{eff}$ to be the Hessian obtained by differentiating with respect to the real and imaginary parts of $\phi^i$. Equivalently, we can use a unitary change of basis (in order to preserve the eigenvalues of $d^2V_{eff}$) in order to write
\be d^2V_{eff} = 2 \twoMatrix{\partial_{\bar\imath} \partial_j V_{eff}}{\partial_i \partial_j V_{eff}}{\partial_{\bar\imath} \partial_{\bar\jmath} V_{eff}}{\partial_i \partial_{\bar\jmath} V_{eff}} = 2 \twoMatrix{D_{\bar\imath}D_j V_{eff}}{D_iD_j V_{eff}}{D_{\bar\imath}D_{\bar\jmath} V_{eff}}{D_i D_{\bar\jmath} V_{eff}} \ .\ee
The second equality holds when $\partial_i V_{eff}=0$; it makes use of $\partial_i V_{eff}=D_i V_{eff}$ and the fact that when $\partial_iV_{eff}=0$ we can replace partial derivatives of $\partial_iV_{eff}$ by covariant derivatives. (Note that these covariant derivatives include appropriate Christoffel symbols, to account for cotangent space indices.) We similarly write
\be \delta^{2n}(dV_{eff}) = \prod_i \delta(D_i V_{eff}) \delta(D_{\bar\imath} V_{eff}) \ .\ee
With this, we have specified all of the ingredients in \eqref{eq:N}.
We now make a continuum approximation, which should be accurate in the regime of interest where $S_*$ is large:
\be \N(\alpha,\R) \approx \int d^{2n+2}Q\, \int_\R |d^n\phi|^2 \, e^{-\alpha V_{eff}} \delta^{2n}(dV_{eff}) |\det d^2 V_{eff}| \, \theta(d^2V_{eff}) \ .\ee
Rescaling\footnote{More precisely, we consider our integrals over $Q^I$ -- which parametrize $\RR^{2n+2}$ -- as integrals over the slice $\bar Q = Q$ of the space $\CC^{2n+2}$. We then rescale $Q\to Q/\sqrt{\alpha}$, so that $V_{eff}\to V_{eff}/\alpha$. Finally, we rotate the integration contours so that we again localize to the slice $\bar Q = Q$. Upon doing so we can again think of $Q^I$ as being real and running from $-\infty$ to $\infty$.
Note that when we first regard $Q$ as a complex variable, we must be careful to continue the integrand so that it depends holomorphically on $Q$. In particular, we must take $Q$ outside of the absolute values defining $V_{eff}$ before regarding it as complex. Otherwise, we would need to introduce another set of integration variables $Q^*$ parametrizing another copy of $\CC^{2n+2}$ and regard the integral as being over the slice $Q^*=\bar Q=Q$. We would then rescale $Q\to Q/\sqrt{\alpha}, \, Q^*\to Q^*/\sqrt{\alpha}$ and then analytically continue.
Finally, we address the presence of the theta and delta functions, which are non-analytic distributions, and which indeed are only defined when $V_{eff}$ is real. (For the theta function, this is obvious; for the delta function, a na\"ive definition for complex $V_{eff}$ would yield $4n$ real conditions for the $2n$ real integration variables $\phi$ to satisfy.) First, we use the homogeneity of these distributions under multiplication of their arguments by a non-negative number to divide these arguments by $V_{eff}$, while simultaneously multiplying the integrand by the appropriate power of $V_{eff}$ to leave the integral invariant. Then, we write the $Q$ integral in spherical coordinates, with radial coordinate $q=|Q|$. The theta and delta functions are now independent of $q$ and are not affected by the rescaling $q\to q/\sqrt{\alpha}$. The analytic continuation of $q$ now is unaffected by the theta and delta functions. Finally, once we are done with analytic continuation, it is again the case that $V_{eff}$ is non-negative, so we can again use the homogeneity of the theta and delta functions to return them to their original forms.} $Q\to Q/\sqrt{\alpha}$ rescales $V_{eff}\to V_{eff}/\alpha$ and allows us to easily determine the scaling with $S_*$:
\be \N(S_*,\R) \approx \frac{(2S_*)^{n+1}}{(n+1)!} \int_\R |d^n\phi|^2 \, \det g(\phi) \, \rho(\phi) \ , \label{eq:NS} \ee
where
\be \rho = \frac{1}{(2\pi)^{n+1} \det g} \int d^{2n+2}Q \, e^{-V_{eff}}\delta^{2n}(dV_{eff})|\det d^2V_{eff}|\,\theta(d^2V_{eff}) \ . \label{eq:density} \ee
(To perform the $\alpha$ integral yielding this answer, one can either close the contour to the left and use the Cauchy integral formula or use repeated integration by parts until the integral reduces to the Laplace transform representation of $\theta(S_*/\pi)=1$.)
We have thus answered one of our questions: the growth with $S_*$ is identical to that found in \cite{douglas:distributions} for the BPS case.
In order to study the distribution of attractors in moduli space, we would now like to simplify $\rho$. To do so, we re-write $\gamma$ in the Hodge decomposition basis:
\be \gamma = e^{K/2}\brackets{ i\bar X \Omega - i {\bar Y}^i D_i \Omega + {\rm c.c.} } \ .\ee
These coefficients are chosen so that
\be Z = \int \gamma\wedge \Omega = i Xe^{K/2} \int \Omega\wedge \bar\Omega = Xe^{-K/2} \Rightarrow X = \Z \ee
and
\be D_i Z = \int \gamma\wedge D_i\Omega = -i Y^{\bar \jmath} e^{K/2} \int D_i \Omega \wedge (D_j \Omega)^* = e^{-K/2} g_{i\bar \jmath} Y^{\bar \jmath} \Rightarrow Y_i = D_i \Z \ . \ee
In terms of these variables, we have
\be V_{eff} = Y_i \bar Y^i + |X|^2 \ .\ee
Derivatives of the effective potential may be simplified via the special geometry identities
\be D_i X = Y_i \ ,\quad D_i \bar X = 0 \ ,\quad D_i Y_j = \F_{ijk} \bar Y^k \ , \quad D_i \bar Y_{\bar \jmath} = g_{i\bar \jmath} \bar X \ , \ee
where
\be \F_{ijk} = ie^K \int \Omega \wedge D_i D_j D_k \Omega = ie^K \int \Omega \wedge \partial_i \partial_j \partial_k \Omega \ .\ee
We have the following derivatives of $V_{eff}$ at a local minimum:
\begin{align}
\partial_j V_{eff} &= D_j V_{eff} = \F_{j k \ell}\bar Y^k \bar Y^\ell + 2 Y_j \bar X = 0 \\
\partial_i \partial_j V_{eff} &= D_i D_j V_{eff} = (D_i \F_{jk\ell}) \bar Y^k \bar Y^\ell + 4 \F_{ijk} \bar X \bar Y^k \\
\partial_{\bar\imath} \partial_j V_{eff} &= D_{\bar\imath} D_j V_{eff} = 2g_{j\bar\imath}|X|^2 + 2 Y_j \bar Y_{\bar\imath} + 2 g^{k\bar m} \F_{jk\ell} \bar\F_{\bar\imath \bar m \bar n}\bar Y^\ell Y^{\bar n} \ .
\end{align}
We will shortly employ these to flesh out the expressions in \eqref{eq:density} more fully.
Finally, we adopt the orthonormal basis, where the Jacobian for the change of variables from $Q^I$ to $(X,\bar X,Y^{\bar A},\bar Y^A)$ is $2^{n+1}$ \cite{douglas:distributions}. So,
\be \rho = \frac{1}{\pi^{n+1}} \int |dX|^2\, |dY^{\bar A}|^2\, e^{-V_{eff}} \delta^{2n}(d_AV_{eff})|\det d^2_A V_{eff}|\,\theta(d^2_AV_{eff}) \ ,\ee
where
\be V_{eff} = Y_A \bar Y^A + |X|^2 \ .\ee
We have lost the factor of $1/\det g$ because the derivatives of the effective potential are now evaluated in the orthonormal frame:
\begin{align}
\delta^{2n}(d_A V_{eff}) &= \prod_A \delta(D_A V_{eff}) \delta(D_{\bar A} V_{eff}) = |\det e_A^i|^{-2} \delta^{2n}(dV_{eff}) = \det g\, \delta^{2n}(dV_{eff}) \\
d^2_A V_{eff} &= 2\twoMatrix{D_{\bar A} D_B V_{eff}}{D_A D_B V_{eff}}{D_{\bar A}D_{\bar B}V_{eff}}{D_A D_{\bar B} V_{eff}} = \twoMatrix{e_B{}^j}{}{}{e_{\bar B}{}^{\bar \jmath}} d^2V_{eff} \twoMatrix{e^{\bar \imath}{}_{\bar A}}{}{}{e^i{}_A} \\
\det d^2_A V_{eff} &= |\det e_A^i|^4 \det d^2 V_{eff} = (\det g)^{-2} \det d^2 V_{eff} \ .
\end{align}
Note that positive-definiteness of $d^2 V_{eff}$ is equivalent to that of $d^2_A V_{eff}$, since for any vector $x$,
\be x^\dagger d_A^2V_{eff} \,x = (x')^\dagger d^2 V_{eff} \,x' \ , \ee
with $x'=\twoMatrix{e^{\bar \imath}{}_{\bar A}}{}{}{e^i{}_A} x$. In the BPS case the delta function sets $Y_A=0$, the theta function is unnecessary, the determinant simply contributes $|X|^{2n}$, and the integrals are easily evaluated to give $\pi n!$. That is,
\be \rho_{BPS} = \frac{n!}{\pi^n} \ . \label{eq:bps} \ee
So, $\rho$ is independent of moduli, meaning that attractors are uniformly distributed in moduli space \cite{douglas:distributions}. We will soon see that this conclusion is altered in the non-BPS case.
In order to make progress in this more general setting, we now specialize to the case $n=1$, which includes the famous mirror quintic studied in \cite{cogp}, as well as the more general one-parameter manifolds studied in \cite{klemm:oneMod,greene:collapse,doran:oneParam,greene:tunneling}. We write $Y\equiv Y_1$, and similarly $\F\equiv \F_{111}$ and $D\F \equiv D_1\F$ (where components refer to the orthonormal basis). We then have
\begin{align}
\partial V_{eff} &= \F \bar Y^2 + 2 Y \bar X = 0 \\
\partial^2 V_{eff} &= (D\F)\bar Y^2 + 4 \F \bar X \bar Y \\
\bar\partial \partial V_{eff} &= 2|X|^2 + 2 |Y|^2 + 2 |\F|^2 |Y|^2 \ . \label{eq:diag}
\end{align}
To deal with the theta function, we notice that positivity of both eigenvalues of $d^2_A V_{eff}$ is equivalent to positivity of both the trace and the determinant. But, the trace is clearly positive, since \eqref{eq:diag} is, so the theta function simply requires positivity of the determinant.
Setting aside the BPS solutions $Y=0$ to $\partial V_{eff}=0$, we have
\be \delta^2(d_A V_{eff}) = \frac{1}{4|Y|^2} \delta\parens{X + \frac{\bar\F Y^2}{2\bar Y}} \delta\parens{\bar X + \frac{\F \bar Y^2}{2Y}} \ , \ee
which allows us to perform the $X$ integrals. We thus find
\be \rho_{non-BPS} = \frac{1}{8\pi^{n+1}} \int |dY|^2\, e^{-V_{eff}} \frac{\det d^2_A V_{eff}}{|Y|^2} \, \theta(\det d^2_A V_{eff}) \ ,\ee
where
\be \frac{\det d^2_A V_{eff}}{|Y|^2} = \parens{4 + 10 |\F|^2 + \frac{9}{4} |\F|^4 - |D\F|^2 } |Y|^2 + \brackets{ 2 (D\F) \bar\F^2 Y^2 + {\rm c.c.}} \label{eq:det} \ee
and
\be V_{eff} = \parens{1 + \frac{|\F|^2}{4}} |Y|^2 \ .\ee
As promised, we see that the non-BPS attractors are not uniformly distributed in moduli space.
We now specialize further to special loci in moduli space.
\subsection{$D\F\approx 0$} \label{sec:approx}
We first restrict to regions where we can approximate $D\F\approx 0$.\footnote{Note that $|D\F|$ is invariant under both K\"ahler transformations and multiplication of the einbein by a phase. So, $D\F\approx 0$ is a gauge invariant statement.} Then, \eqref{eq:det} is positive, and the theta function is extraneous. So, we are left with rather simple integrals over $Y$ which yield
\be \rho_{non-BPS} \approx \frac{ 4+9|\F|^2 }{2\pi \parens{4+|\F|^2}} \ . \label{eq:nbps} \ee
Furthermore, we can study corrections to this approximation by continuing to neglect the theta function, but retaining the entirety of \eqref{eq:det}, and again performing the integral over $Y$. The result is
\be \rho'_{non-BPS} \approx \rho_{non-BPS} - \frac{2 \, |D\F|^2}{\pi(4+|\F|^2)^2} \ . \label{eq:nbps2} \ee
In the model that we consider in section \ref{sec:numerics}, we have $D\F\approx 0$ near the Landau-Ginzburg point and in the large complex structure locus.
\subsection{Conifold} \label{sec:conifold}
We now study an example of a region where the theta function eliminates all candidate attractors. Our analysis closely follows that of \cite{douglas:distributions}. A natural place to look for such non-trivial behavior is near the conifold singularity common to the moduli spaces of many one-parameter threefolds. (On the other hand, since stringy effects become important at such points, this might be viewed as more of a mathematical exercise, or a proof of principle that the theta function is, in general, important.)
A natural modulus to employ in the conifold region is the period, $v$, of the vanishing cycle. The metric takes the form
\be g_{v\bar{v}} = c \ln \frac{\mu^2}{|v|^2} \equiv c \xi \ , \ee
where $\mu$ is a constant and $c = e^{K_0}/2\pi$, with $K_0 = K(v=0)$. We also have
\be \F = \frac{i}{c^{1/2}\xi^{3/2}v} \equiv \frac{1}{\epsilon}\ ,\ \ D\F = \frac{i(\xi-3)}{\epsilon^2} \ ,\ee
where $\epsilon \to 0,\xi \to \infty$ as we approach the degeneration. We then have
\begin{align}
\frac{\det(d^2_A V_{eff})}{|Y|^2} &= \parens{4 + \frac{10}{|\epsilon|^2} + \frac{9}{4|\epsilon|^4} - \frac{|\xi - 3|^2}{|\epsilon|^4}} |Y|^2 + \frac{4}{|\epsilon|^4} \Real{i(\xi-3) Y^2} \nonumber \\
&= -\frac{|\xi-3|^2 |Y|^2}{|\epsilon|^4} + \Oo(1/|\epsilon|^2) + \Oo(|\xi|/|\epsilon|^4) .
\end{align}
Since this is negative, the theta function eliminates all candidate attractors.
As suggested by the referee, it is of interest whether or not the integrated density of \emph{critical points} -- not just local minima -- of $V_{eff}$ near the conifold point is finite or not. To determine this, we study \eqref{eq:NS}, with $\R$ a small disc about $v=0$, but ignore the theta function which imposes positive-definiteness of the Hessian. We find that the density $\rho$ (without the theta function) diverges as $\xi^2$, so the integrand of \eqref{eq:NS} diverges as $\xi^3$, but this is not fast enough to give a divergent integral. Thus, as in the flux vacuum counting problems in \cite{douglas:distributions}, we do not find a non-integrable density of critical points near the conifold point.
It would be interesting to study attractors at conifold loci of multi-parameter models, as the large curvature of the moduli space
may lead to an enhanced density of attractor points (as happens with the somewhat analogous case of flux vacua).
\section{Numerical verification} \label{sec:numerics}
We turn now to numerical verification of these formulae. We focus on the mirror of an octic in $\WW\PP^4_{1,1,1,1,4}$ (corresponding to $k=8$ in \cite{klemm:oneMod}; throughout this section, we utilize the periods and other geometric quantities determined in this reference, as well as the approximations thereto employed in \cite{sk:taxonomy}). As we discussed in \S\ref{sec:conifold}, the conifold is not a good place to look for attractors. Similarly, one does not find attractors in the large complex structure locus, as the contribution to \eqref{eq:NS} is suppressed by $\det g\approx 0$\footnote{Of course, this statement is not coordinate-independent. More invariantly, $\int_{|\phi|>R} |d\phi|\, \det g \sim 1/\log(4R)$ at large $R$; in particular, this integral is finite.} (and, furthermore, the 4d supergravity approximation breaks down). However, we do find attractors near the Landau-Ginzburg point. As we now explain, $D\F\approx 0$ in this region, and so we can compare with \eqref{eq:nbps} and \eqref{eq:nbps2}.
Using the formula $\Gamma^i_{jk} = g^{i\bar\ell} \partial_j g_{k \bar\ell}$ for the Christoffel symbols of a K\"ahler manifold, and defining $\kappa_{\phi\phi\phi} = -i e^{-K} \F_{\phi\phi\phi} = \int \Omega\wedge \partial_\phi^3 \Omega$ (with $\phi$ the standard coordinate on the complex structure moduli space of the mirror octic), we have
\begin{align}
D\F &= (g_{\phi \bar\phi})^{-2} D_\phi \F_{\phi\phi\phi} = i e^{K} (g_{\phi \bar\phi})^{-2} D_\phi \kappa_{\phi\phi\phi} \\
&= i e^{K} (g_{\phi \bar\phi})^{-2} \brackets{ \partial_\phi + 2(\partial_\phi K) - 3 (g_{\phi\bar\phi})^{-1} (\partial_\phi g_{\phi\bar\phi}) } \kappa_{\phi\phi\phi} \\
&\approx 6.73 ~\phi^4 |\phi| + \Oo(|\phi|^9) \ , \label{eq:small}
\end{align}
where the final line employed formulae
from \cite{klemm:oneMod}. \eqref{eq:small} explains why $D\F\approx 0$ is a good approximation near the Landau-Ginzburg point $\phi=0$.
In order to numerically test \eqref{eq:nbps} and \eqref{eq:nbps2}, we scanned over all $(2Q_{max}+1)^4$ charge vectors $Q\in \ZZ^4$ whose components satisfied $|Q_I| \le Q_{max} \equiv 21$ and searched for local minima of the effective potential associated to each of these charges with $|\phi_0|<0.5$. The homogeneity of $S$ as a function of $Q$ makes it clear that this charge cutoff corresponds to an entropy cutoff. (More precisely, we searched for local minima in the fundamental domain $0\le \arg\phi < 2\pi/8$, as well as each of its images under a rotation by a power of $e^{i\pi/4}$, and then translated all attractors to the fundamental domain. We acted with the appropriate symplectic monodromy matrix on the charges as we did so and eliminated any duplicate attractors -- i.e., attractors with the same charge and moduli. This was computationally efficient, as it produced attractors whose charges did not satisfy $|Q_I|\le Q_{max}$, but whose entropies were nevertheless comparable to attractors whose charges did satisfy this constraint.)
On the other hand, our analytic formulae hold under the assumption that the entropy cutoff $S_*$ is large. Fortunately, as we will see, our $Q_{max}$ is large enough that these constraints are simultaneously satisfied in a window of intermediate entropies, and in this range our analytic formulae agree with the data. (As a test of the fact that the $Q_{max}$ cutoff is responsible for the failure of our analytic results at large $S_*$, we confirmed that lowering $Q_{max}$ shrank this range. We note that our choice of $Q_{max}$ was not large enough for our analytic formulae for BPS attractors to agree with the data over a sizeable window of entropies.) We discarded unphysical solutions with vanishing entropy (discussed in \cite{denef:attractor}), which we characterized as having $S<0.1$, although since our formulae do not apply in this regime this is mostly for aesthetic purposes. Finally, in order to separate BPS and non-BPS attractors, we employed the cutoff $|D_\phi \Z| = 0.1$.
Having said all of this, we now present figures \ref{fig:scatter}, \ref{fig:nonBPSscale}, \ref{fig:nonBPSscaleLogLog}, and \ref{fig:nonBPSarea}.
\begin{figure}[H]
\begin{center}
\includegraphics[width=.49\textwidth]{bps.png}
\includegraphics[width=.49\textwidth]{nonBPS.png}
\caption{Scatter plots of attractor moduli near the Landau-Ginzburg point. Our $\phi$ is the complex structure modulus of \cite{klemm:oneMod}, for which a fundamental domain is $0\le \arg\phi < 2\pi/8$.}\label{fig:scatter}
\end{center}
\end{figure}
\begin{figure}[H]
\begin{center}
\includegraphics[width=.82\textwidth]{nonBPSScaling.png}
\caption{Comparison of numerics with the analytic prediction \eqref{eq:NS}, with $\rho$ in that equation replaced by \eqref{eq:nbps}, and where $\R$ is the set $|\phi|<0.5$. We have added a $y$-intercept of $250$ to our theoretical prediction in order to account for the fact that it is only applicable at large $S_*$. Said another way, our theoretical prediction is really for $d\N(S_*)/dS_*$, and we must numerically determine the integration constant. After doing so, we find that the data fits our analytic predictions in an intermediate regime of $S_*$. At larger $S_*$, we have not found all attractors. Because of these limitations at both large and small $S_*$, this figure functions as a weak test of our prediction: it simply demonstrates that at the inflection point of our data, its slope agrees with that of the theoretical result. However, as we explain in the caption of figure \ref{fig:nonBPSarea} it at least correctly identifies the regime in which the data obeys our prediction.}\label{fig:nonBPSscale}
\end{center}
\end{figure}
\begin{figure}[H]
\begin{center}
\includegraphics[width=.82\textwidth]{nonBPSscalingLogLog.png}
\caption{Similar to figure \ref{fig:nonBPSscale}, but on a log-log scale. Unlike in figure \ref{fig:nonBPSscale}, we have not added a $y$-intercept to the theoretical prediction. This causes the theoretical prediction to be systematically smaller than the numerical results, thanks to the large number of attractors that were found with small entropy, which are not governed by our large-entropy prediction. However, one can see in this figure that the theoretical prediction is catching up to the numerics, as the total number of attractors begins to overwhelm the number of attractors with small entropies. At the same time, one can discern a trend that is dragging the data down at large $S_*$, which is due to the fact that in this regime we have not found all of the attractors.}\label{fig:nonBPSscaleLogLog}
\end{center}
\end{figure}
\begin{figure}[H]
\begin{center}
\includegraphics[width=.82\textwidth]{nonBPSarea.png}
\caption{Comparison of numerics with the analytic predictions \eqref{eq:nbps} and \eqref{eq:nbps2}. The latter two predictions are indistinguishable. In order to focus on entropies to which our predictions apply, we only include non-BPS attractors with $S_{min}=225< S< S_{max}=275$, where $S_{min}$ and $S_{max}$ are estimated from figure \ref{fig:nonBPSscale}; correspondingly, our theoretical plot is of $\N(S_{max},\R)-\N(S_{min},\R)$, where $\R=\{\phi_0 : |\phi_0| < |\phi|\}$.
We suspect that inclusion of attractors at the edges of the range $[S_{min},S_{max}]$ is responsible for the evident small systematic errors. As evidence for this, we constructed analogous plots with different choices of $S_{min}$ and $S_{max}$ and observed that the agreement between the numerics and analytic predictions worsened as we increased the size of the interval $[S_{min},S_{max}]$.}\label{fig:nonBPSarea}
\end{center}
\end{figure}
\section{Conclusion} \label{sec:conclusion}
In this paper, we have studied the distribution of the attractor moduli of non-supersymmetric extremal black holes in the complex structure moduli space of Calabi-Yau threefolds. Growth of attractors with the entropy cutoff $S_*$ was found to be identical to that of the BPS case studied in \cite{douglas:distributions}, owing to the fact that in both cases the effective potential is homogeneous of degree 2 in the charges. However, our results differed in that attractors were not found to be uniformly distributed in moduli space. We illustrated this curvature dependence concretely by focusing on the mirror octic, for which we analytically determined the distribution of attractors in various regions of moduli space. Finally, we tested our predictions near the Landau-Ginzburg point with numerics and found very satisfying agreement.
It would be nice to see some of the geometric and arithmetic connections of BPS attractors generalized to this more physical non-supersymmetric situation.
For instance, BPS attractors on $K3 \times T^2$ enjoy a close relationship to class groups and class numbers: the U-duality classes of BPS black holes
can be placed in correspondence with binary quadratic forms with discriminant related to the entropy, and the numbers of inequivalent
attractor points at a fixed value of the entropy are governed by the class numbers \cite{moore:arithmeticAttractors,sk:class}. Finding a similar arithmetic interpretation of
non-BPS attractors on $K3 \times T^2$ is a natural direction to pursue.
We hope that the study of attractors (both BPS and non-BPS) will in some sense provide a natural analogue of the mathematical notion of special cycles for moduli spaces which are not locally symmetric. On the geometric front, the problem of needing to continue weakly-coupled D-branes to a black hole which emerges at stronger coupling is an important obstacle to connecting aspects of Calabi-Yau geometry with gravity solutions, but the successes of string theory in accounting for the entropy of extremal but non-BPS black holes in special cases, as well as those of supergravity in accounting for subtle aspects of BPS spectra in string theory \cite{denef:attractor,denef:correspond}, seem to provide reason for optimism. Furthermore, mathematical tools that might be useful for studying non-BPS extremal cycles have begun to seep into the physics literature \cite{liam:nonHolo}.
\section*{Acknowledgments}
M.Z. thanks Liam McAllister for interesting suggestions. We also thank the anonymous referee for helpful comments. The research of S.K. was supported in part by a Simons Investigator Award and the National Science Foundation under grant number PHY-1720397.
\newpage
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
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\section{Introduction}
The most important challenge of quantum computing is to find quantum algorithms
that achieve exponential speedup over the best known classical solutions.
In this respect, the most extensively studied problem
is the paradigmatic hidden subgroup problem.
Stated in a group theoretical setting,
in $\mbox{\textsc{HSP}}(G,f)$
we are given explicitely a finite group $G$ and
we also have at our disposal
a function $f$ that can be queried via an oracle, and which
maps $G$ into a finite set.
We are promised that for some subgroup $H$,
$f$ is constant on each left coset of $H$
and distinct on different left cosets.
We say that $f$ {hides} the subgroup $H$.
The task is to determine the {hidden subgroup} $H$.
We measure the time complexity of an algorithm
by the overall running time when a query counts as one
computational step.
An algorithm is called {efficient}
if its time complexity
is polynomial in the logarithm of the order of $G$.
We don't know any classical algorithm of polynomial query complexity
for the HSP, even in
the restricted case of abelian groups.
In this respect, probably the most important result of
quantum computing is that the HSP can be solved
efficiently for abelian groups by quantum algorithms.
We will call this solution, for which
one can find
an excellent description for example
in Mosca's thesis~\cite{mos99}, the standard algorithm
for \mbox{\textsc{HSP}}{}.
The main quantum tool used in the standard algorithm
is Fourier sampling based on
the approximate quantum Fourier transform that can be efficiently
implemented by a quantum algorithm in case of abelian
groups~\cite{kit95}.
Among the important special cases of this general solution one can mention
Simon's xor-mask finding~\cite{sim97},
Shor's factorization
and discrete logarithm finding algorithms~\cite{sho97},
and Kitaev's algorithm~\cite{kit95} for the abelian stabilizer problem.
Since the realization of the importance of the abelian HSP,
intensive efforts have been made to solve the hidden subgroup problem also
in finite non-abelian groups. The intrinsic mathematical interest of this challenge is
increased by the fact that several famous classical algorithmic problems can be cast
in this framework, like for example
the graph isomorphism problem.
The successful efforts for solving the problem can roughly be divided into two categories.
The standard
algorithm has been extended to some non-abelian groups
by R\"otteler and Beth~\cite{rb98}, Hallgren, Russell and Ta-Shma~\cite{hrt03},
Grigni, Schulman, Vazirani and Vazirani~\cite{gsvv01} and
Moore, Rockmore, Russell and Schulman~\cite{mrrs04}
using efficient implementations
of the quantum Fourier transform
over these groups.
In a different approach, Ivanyos, Magniez and Santha~\cite{ims03} and
Friedl, Ivanyos, Magniez, Santha and Sen~\cite{fimss03} have efficiently reduced
the \mbox{\textsc{HSP}}{} in some non-abelian groups to \mbox{\textsc{HSP}}{} instances in abelian groups
using classical and quantum group theoretical tools, but not the
non-abelian Fourier transform.
All groups where the HSP has been efficiently solved are in some sense ``close"
to abelian groups. Extraspecial groups, in which we present here an efficient
quantum algorithm,
are no exception in this respect: they have the property
that all their
proper
factor groups are abelian. They form a subclass of
$p$-groups, where $p$ is a prime number,
and play an important role in the theory of this family of groups.
Extensive treatment
of extraspecial groups can be found for example in the books of Huppert~\cite{hup83} and
Aschbacher~\cite{asc00}.
Extraspecial 2-groups are heavily present in the theory of quantum error correction.
They provide a bridge between quantum error correcting codes and binary
orthogonal geometry~\cite{crss97}. They form the real subgroup of the Pauli group~\cite{crss98}
which plays a crucial role in the theory of stabilizer codes~\cite{got97}.
For general $p$, extraspecial $p$-groups give rise to
the simplest examples of Clifford codes, see~\cite{ks06}.
Efficient solutions for the HSP have already been given in several specific extraspecial groups.
Extraspecial $p$-groups are of order $p^{2k+1}$ for some integer $k$.
For odd $p$, they are of exponent $p$ or $p^2$, and
extraspecial 2-groups are of exponent 4.
The class of groups for which Ivanyos, Magniez and Santha~\cite{ims03} provide a solution
include extraspecial $p$-groups when $p$ is a fixed constant and the input size grows with $k$.
When $p$ is fixed, the smallest
extraspecial groups
are of size $p^3$. Up to isomorphism there are two extraspecial groups of order $p^3$.
Recently two independent works dealt with quantum algorithms
for the HSP in the group of exponent $p$, the Heisenberg group.
Radhakrishnan, R\"otteler and Sen~\cite{rrs05} have followed the standard algorithm
with non-abelian Fourier transform, and proved that strong Fourier sampling with a random
basis leads to a query efficient quantum solution. In a subsequent work,
Bacon, Childs and van~Dam~\cite{bcv05} devised an efficient quantum algorithm, where
a state estimation technique, called the pretty good
measurement, is used to reduce the HSP to some matrix sum problem that they could solve
classically.
In this paper we provide an efficient quantum algorithm for the HSP in any extraspecial group.
Our main contribution is an efficient algorithm in extraspecial $p$-groups of exponent $p$
when $p$ grows with the input size. A simplified version of this algorithm gives another solution
for the groups of constant exponent. The remaining case, groups of exponent $p^2$ when $p$ is
large is easily reducible to the case of groups of exponent $p$.
Our approach for groups of exponent $p$ is completely different
from the above two solutions for the Heisenberg group.
In our solution only abelian Fourier transforms and von Neumann measurements are used.
In fact, our algorithm is a series of reductions, where we repeatedly use
the standard
algorithm for abelian groups, or a slight extension of it.
In this extension, instead of a classical hiding functions we have an
efficient quantum hiding procedure at our disposal.
This procedure outputs a quantum state for every group
element so that the states corresponding to group elements coming from the same left coset of
the hidden subgroup are identical, whereas the states corresponding to group elements from different
left cosets are orthogonal. Repeated invocations of the procedure might yield different states for
the same group element.
At the end of our reductions we are faced with the problem of creating an efficient hiding
procedure in the above sense for the subgroup $HG'$ of $G$, where $G$ is an extraspecial
$p$-group of exponent $p$ when $p$ is large,
$G' = \{z^i ~:~ 0 \leq i \leq p-1 \}$
is its commutator, and $H$ is the hidden subgroup. It is easy to see, that if we could create
the coset state $\ket{aHG' }$ for some $a \in G$, then the group action multiplication from the right,
which on a given group element
$g$ would output $\ket{aHG' \cdot g}$, is a hiding procedure.
Unfortunately, we can create these states efficiently
only when $p$ is constant. In the general case, we can create efficiently only the states
$ \ket{aHG'_u}$ for a random $ 0 \leq u \leq p-1$, where
$\ket{G'_u}=
\frac{1}{\sqrt{p}} \sum_{i \in {\mathbb Z}_p} \omega^{-u i} \ket{z^i}$.
Our main technical contribution is to show that several (in fact four) copies of these states can be
combined together so that the disturbing phases cancel each other. To achieve this goal
we exploit
certain nice automorphisms
of the group to define more sophisticated group actions
that can be used for our purposes.
The structure of the paper is quite simple. After a discussion on the extension of the standard
algorithm and a basic description of extraspecial groups in Section~\ref{prelim}, our reduction
steps are presented in Section~\ref{reductions}. The summary of these reductions is stated in
Theorem~\ref{theorem:threelemmas}: An efficient hiding procedure for $HG'$ is sufficient
to solve the HSP in an extraspecial group $G$. In Section~\ref{algorithm} we establish our main
result in Theorem~\ref{theorem:main}, the existence of an efficient solution for the HSP in extraspecial
groups. The proof is given according to the three cases discussed above. The most important case
of groups of exponent $p$ when $p$ is large is dealt with in Section~\ref{important}, where in
Theorem~\ref{theorem:exponentp} we provide the hiding procedure for $HG'$.
\suppress{
Lately some new results were proved about the \mbox{\textsc{HSP}}{}, using a POVM. The first result is a negative result. Moore, Russell and Schulman showed in \cite{mrs05} that the strong Fourier transform can't solve efficiently the \mbox{\textsc{HSP}}{} in the symmetric group, even performing a POVM on the coset state, and that this result also apply to special case of the isomorphism problem. Moore and Russell generalised this result in \cite{mr05} to entangled measurements. The second result, due to Bacon, Childs and Van Dam in \cite{bcv05} is an algorithm using a POVM to solve the \mbox{\textsc{HSP}}{} in some groups: certain metacyclic groups and the groups of the form ${\mathbb Z}_p^r \rtimes {\mathbb Z}_p$ including the Heisenberg group (which is an extraspecial group). A second way to solve the \mbox{\textsc{HSP}}{} in heisenberg groups was discovered by Radhakrishnan, R\"otteler and Sen in \cite{rrs05}. The algorithm uses a random measure in random orthogonal basis.
To begin with solving the \mbox{\textsc{HSP}}{} in extraspecial groups we remarked that extraspecial groups of prime exponent where semi-direct product groups of the form ${\mathbb Z}_p^r \rtimes {\mathbb Z}_p^{r-1}$ and that the heisenberg group was one of them. Therefore we tried to use \cite{bcv05} to solve the \mbox{\textsc{HSP}}{} in extraspecial groups of prime exponent. We tried to use the pretty good measurement to reduce the \mbox{\textsc{HSP}}{} in extraspecial groups of prime exponent to the matrix sum problem like in \cite{bcv05}, but we could'nt. In the cases studied by Bacon, Childs and Van Dam, the PGM (Pretty good measurement) is a positive operator represented by a diagonal matrix and it's easy to take the inverse of the square root as we need to implement the PGM, but in our case it's only bloc diagonal.
Following the idea that Heisenberg group is an extraspecial group of prime exponent we tried to generalise the method of Radhakrishnan, R\"otteler and Sen. In there paper Radhakrishnan, R\"otteler and Sen use the strong Fourier sampling and measure in some basis almost orthogonal, but in our case we can't be enough orthogonal. In fact it's the same problem as using the method of Bacon, Childs and Van Dam, we can't find a basis where the measure is good enough because some orthogonality is missing.
It appeared that a totally different way need to be taken with a new idea. The main idea to solve the \mbox{\textsc{HSP}}{} in extraspecial groups of prime exponent $p$ is that
those groups have
many automorphisms and that the group action of those automorphism
has as eigenvectors states that are almost coset states.
}
\section{Preliminaries}\label{prelim}
\subsection{Extensions of the standard algorithm for the abelian \mbox{\textsc{HSP}}}
We will use standard notions of quantum computing for which one can consult for
example~\cite{nc00}.
For a finite set $X$, we denote by $\ket{X}$ the uniform superposition
$\frac{1}{\sqrt{|X|}}\sum_{x \in X} \ket{x}$ over $X$.
For a superposition $\ket{\Psi}$, we denote by $\mathop{\mathsf{supp}}(\ket{\Psi})$ the support of $\ket{\Psi}$,
that is the set of basis
elements with non-zero amplitude.
The general solution for the abelian $\mbox{\textsc{HSP}}$ consists essentially
of Fourier sampling of the hiding function $f$. More specifically, it involves
the creation
of the superposition $\sum_{g \in G} \ket{g}\ket{f(g)}$ and
the Fourier transform over $G$.
Clearly, for the former part it is essential to have access to a hiding function. In fact, this
requirement can be relaxed in some sense, and in this paper we will use such a relaxation.
A relaxation was already used by Ivanyos et al.~\cite{ims03} who extended the notion of the hiding
function to quantum functions. More precisely, for a finite set $X$, and a quantum function
$f : G \rightarrow {{\mathbb C}}^X$, we say that $f$ {\em hides} the subgroup $H$ of $G$ if $\ket{f(g)}$
is a unit vector for every
$g \in G$, and $f$ is constant on the left cosets of $H$,
and maps elements from different cosets into orthogonal states. The simple fact is proven
in Lemma 1 of \cite{ims03} that in the standard solution of $\mbox{\textsc{HSP}}$ for abelian groups, one
can just as well use a quantum hiding function.
The standard algorithms for the abelian $\mbox{\textsc{HSP}}$ in fact repeats
polynomially many times the Fourier sampling
involving the same (classical or quantum) hiding function.
In fact, in each iteration a random element is obtained from the subgroup orthogonal to $H$.
Our extension is based on the observation, that for the sampling, one doesn't have to use the
same hiding function in each iteration, different hiding functions will do just as well the game.
For the sake of completeness we formalize this here and state the exact conditions that will
be used in our case.
We say that a set of vectors $\{ \ket{\Psi_g} : g \in G \}$ from some Hilbert space $\cal{H}$ is
a {\em hiding set} for
the subgroup $H$ of $G$ if
\begin{itemize}
\item
$\ket{\Psi_g}$ is a unit vector for every $g \in G$,
\item
if $g$ and $g'$ are in the same left coset of $H$ then $\ket{\Psi_g} = \ket{\Psi_{g'}}$,
\item
if $g$ and $g'$ are in different left cosets of $H$ then $\ket{\Psi_g}$ and $\ket{\Psi_{g'}}$
are orthogonal.
\end{itemize}
A quantum procedure is {\em hiding} the subgroup $H$ of $G$ if
for every $g \in G$, on input $\ket{g}\ket{0}$ it outputs $\ket{g}\ket{\Psi_g}$ where
$\{ \ket{\Psi_g} : g \in G \}$ is a hiding set for $H$.
Let us underline that we don't require from a quantum hiding procedure to output
the same hiding set in different calls.
The following fact recasts
the existence of the standard algorithm for the abelian $\mbox{\textsc{HSP}}$ in the context of hiding sets. \begin{fact}\label{fact:hsp}
Let $G$ be a finite abelian group. If there exists an efficient quantum procedure
which hides the subgroup $H$ of $G$ then there is an efficient quantum algorithm for
finding $H$.
\end{fact}
\begin{proof}
It is immediate from the proof of Lemma 1 in \cite{ims03}: indeed, the exact property of the
quantum hiding function $f$ which is used there is that $\{\ket{g} \ket{f(g)} : g \in G \}$ forms
a hiding set for $H$.\qed
\end{proof}
\subsection{Extraspecial groups}
Let $G$ be a finite group. For two elements $g_1$ and $g_2$ of $G$, we usually denote their product
by $g_1g_2$. If we conceive group multiplication from the right as a group action of $G$ on itself, we
will use the notation $g_1 \cdot g_2$ for $g_1g_2$. For a subset $X$ of $G$, we will denote by
$\langle X \rangle$ the subgroup generated by $X$. The derived subgroup $G'$ of $G$ is defined as
$\langle \{ x^{-1}y^{-1}xy ~:~ x,y \in G \} \rangle$, and its center $Z(G)$ as
$\{z \in G ~:~ gz = zg \mbox{{\rm ~ for all ~}} g \in G \}$.
The Frattini subgroup $\Phi(G)$ is the intersection of all maximal subgroups of $G$.
For an integer $n$, we denote by ${\mathbb Z}_n$ the group of integers modulo $n$,
and for a prime number $p$, we denote by ${\mathbb Z}_p^*$ the multiplicative group of integers
relatively prime with $p$. A $p$-group is a finite group whose order is a power of $p$.
A $p$-group $G$ is {\em extraspecial} if $G' = Z(G) = \Phi(G)$, and its center is cyclic of prime order $p$.
If $G$ is an extraspecial $p$-group then $|G| = p^{2k+1}$ for some integer $k$.
The elements of $G$ can be encoded by binary strings of length
$O(k \log p)$,
and an efficient algorithm on that input
has to be polynomial in both $k$ and $\log p$.
The smallest non-abelian extraspecial groups are of order $p^3$. For $p=2$, we have, up to
isomorphism, two extraspecial 2-groups of order 8. These are the quaternion group $Q$, and the
dihedral group $D_4$, the symmetry group of the square in two dimensions.
The exponent of both of these groups is $p^2 = 4$.
For $p > 2$, up to isomorphism we have again two
extraspecial $p$-groups of order $p^3$. The first one is the
Heisenberg group $H_p$, which is the group of upper triangular
$3 \times 3$ matrices over the field ${\mathbb F}_p$
whose diagonal contains everywhere 1. The exponent of $H_p$ is $p$. The other one is $A_p$,
the group of applications $t \mapsto at +b$
from ${\mathbb Z}_{p^2}$ to ${\mathbb Z}_{p^2}$, where $a \equiv 1$ modulo $p$
and $b \in {\mathbb Z}_{p^2}$. The exponent of $A_p$ is $p^2$.
We give now via relations equivalent definitions of the extraspecial $p$-groups of order $p^3$.
These definitions will be useful for the arguments we will develop in our algorithms. To
emphasize the similarities between these groups, we will take three generator elements
$x,y,z$ for each of them.
The element
$z$ will always generate the center of the group. Here are the
definitions via relations:
$$Q_{} = \langle x^2 = y^2 = [x,y] = z, ~z^2 = 1 \rangle ,$$
$$D_{4} = \langle x^2 = y^2 = z^2 =1, ~[x,y] = z, ~[x,z] = [y,z] = 1 \rangle ,$$
$$H_{p} = \langle x^p = y^p = z^p =1, ~[x,y] = z, ~[x,z] = [y,z] = 1 \rangle ,$$
$$A_{p} = \langle x^{p^2} = y^p =1, ~[x,y] = z = x^p, ~[y,z] = 1 \rangle .$$
From these definitions it is clear that every element in an extraspecial group of order $p^3$
has a unique representation of the form $x^iy^jz^{\ell}$ where $i,j,\ell \in {\mathbb Z}_p$.
Extraspecial $p$-groups of order $p^{2k+1}$, for $k > 1$, can be obtained as the central product of $k$
extraspecial $p$-groups of order
$p^3$. If $G_1, \ldots, G_k$ are extraspecial $p$-groups of order $p^3$ then their
{\em central
product} ~$G_1 \central \ldots \central G_k$ is the
factor
group
$$G_1 \times \ldots \times G_k \bmod z_1 = \dots = z_k,$$
where $z_i$ is an arbitrary generator of $Z(G_i)$ for $i = 1, \ldots, k.$
Since $D_4 \central D_4 = Q \central Q$, up to isomorphism the unique extraspecial 2-groups
of order $2^{2k+1}$ are $\multicentral{i=1}{k}{D_4}$ and
$(\multicentral{i=1}{k-1}{D_4}) \central Q.$
All of these groups are of exponent $p^2 = 4$.
When $p > 2$, we have
$H_p \central A_p = A_p \central A_p$. Therefore,
up to isomorphism the unique extraspecial $p$-groups
of order $p^{2k+1}$ are $\multicentral{i=1}{k}{H_p}$ and $(\multicentral{i=1}{k-1}{H_p}) \central A_p.$
The former groups are of exponent $p$, the latter ones are of exponent $p^2$.
It follows from the above that any extraspecial group of order $p^{2k+1}$ can be generated
by $2k+1$ elements $x_1, y_1, \ldots , x_k, y_k$ and $z$. Any element of the group has a unique representation of the form $x_1^{i_1}y_1^{i'_1}\cdots x_k^{i_k}y_k^{i'_k}z^\ell$,
where $i_1,i'_1,\ldots,i_k,i'_k,\ell\in {\mathbb Z}_p$. Also,
$G'=Z(G)=\{z^\ell|\ell\in{\mathbb Z}_p\}$.
\section{Reduction lemmas}\label{reductions}
Our results leading to our main technical contribution can be the best described via
a series of reduction lemmas.
\begin{lemma}\label{lemma:firstreduction}
Let $G$ be an extraspecial $p$-group, and let us given an oracle $f$ which
hides the subgroup $H$ of $G$. Then
finding $H$ is efficiently reducible to find $HG'$.
\end{lemma}
\begin{proof}
Since $G'$ is a cyclic group of prime order,
either $G' \subseteq H$ or $G' \cap H = \{1\}$. It is simple to decide which one of this cases
holds by checking if $f(z) = f(1)$. If $G' \subseteq H$ then $H = HG'$, and therefore the algorithm
which finds $HG'$ yields immediatly $H$.
If $G' \cap H = \{1\}$ then we claim that $HG'$ is abelian. To see this, it is sufficient to show that
$H$ is abelian, since $G'$ is the center of $G$. Let
$h_1$ and $h_2$ be two elements of $H$. Then there exists $\ell \in {\mathbb Z}_p$ such that
$h_1 h_2= h_2 h_1 z^{\ell}$. This implies that $z^{\ell}$ is in $G' \cap H$
and therefore $z^{\ell} = 1$.
The restriction of the hiding function $f$ to the abelian subgroup $HG'$
of $G$ hides $H$.
Therefore the standard algorithm for solving the $\mbox{\textsc{HSP}}$ in abelian groups
applied to $HG'$ with oracle $f$ yields $H$.\qed
\end{proof}
We will show that finding $HG'$ can be efficiently reduced to the hidden subgroup problem in an abelian group.
For every element $g = x_1^{i_1}y_1^{j_1} \ldots x_k^{i_k}y_k^{j_k}z^{\ell}$ of $G$, we denote
by $\overline{g}$
the element $x_1^{i_1}y_1^{j_1} \ldots x_k^{i_k}y_k^{j_k}$.
We define now the group $\overline{G}$ whose base set is $\{ \overline{g} : g \in G\}$. Observe that
this set of elements does not form a subgroup in $G$.
To make $\overline{G}$ a group, its law is defined by
$\overline{g_1} \ast \overline{g_2}=\overline{g_1 g_2}$
for all $\overline{g_1}$ and $\overline{g_2}$ in $\overline{G}$.
It is easy to check that $\ast$ is well defined,
and is indeed a group multiplication. The group $\overline{G}$ is
isomorphic to $G/G'$ and therefore is abelian. For our purposes a nice way to think about
$\overline{G}$ as a representation of $G/G'$ with unique encoding. In fact, it is also easy to check that
$\overline{G}$ is isomorphic to ${\mathbb Z}_p^{2k}$. Finally let us observe that
$HG' \cap \overline{G}$ is a subgroup of $(\overline{G}, \ast)$ since
$HG'/G'$ is a subgroup of $G/G'$,
\begin{lemma}\label{lemma:secondreduction}
Let $G$ be an extraspecial $p$-group, and let us given an oracle $f$ which
hides the subgroup $H$ of $G$. Then
finding $HG'$ is efficiently reducible to find $HG' \cap \overline{G}$ in $\overline{G}$ .
\end{lemma}
\begin{proof}
Since $HG'=(HG' \cap \overline{G}) G'$, a generator set
of $HG'$ in $G$ is composed of a generator set of $HG' \cap \overline{G}$ in
$\overline{G}$ together with $z$.\qed
\end{proof}
The group $\overline{G}$ is abelian but we don't have a hiding function for
$HG' \cap \overline{G}$. The main technical result of our paper is that using
the hiding function $f$ for $H$ in $G$, we will be able to implement an efficient
quantum
{\em hiding procedure}
for $HG'$ in $G$.
Our last reduction lemma just states that this is sufficient for finding $HG' \cap \overline{G}$.
\begin{lemma}\label{lemma:thirdreduction}
Let $G$ be an extraspecial $p$-group, and let us given an oracle $f$ which
hides the subgroup $H$ of $G$. If we have an efficient quantum procedure (using $f$)
which hides $HG'$ in $G$ then we can find efficiently $HG' \cap \overline{G}$ in $\overline{G}$ .
\end{lemma}
\begin{proof}
The procedure which hides $HG'$ in $G$ hides also
$HG' \cap \overline{G}$ in $\overline{G}$. Since $\overline{G}$ is abelian,
Fact~\ref{fact:hsp} implies that we can find efficiently
$HG{'} \cap \overline{G}$.\qed
\end{proof}
Our first theorem
is the consequence of these three lemmas. It says that
if in an extraspecial group we succeed to transform the oracle hiding the subgroup $H$ into a
quantum procedure hiding $HG'$ then we can determine $H$. This reduction
is the basis of our algorithm.
\begin{theorem}\label{theorem:threelemmas}
Let $G$ be an extraspecial $p$-group, and let us given an oracle $f$ which
hides the subgroup $H$ of $G$. If we have an efficient quantum procedure (using $f$)
which hides $HG'$ in $G$ then $\mbox{\textsc{HSP}}(G, f)$ can be solved efficiently.
\end{theorem}
Observe that if $G' \subseteq H$ then $HG' = H$, and therefore the following corollary is immediate.
\begin{corollary}\label{corollary:threelemmas}
Let $G$ be an extraspecial $p$-group, and let us given an oracle $f$ which
hides the subgroup $H$ of $G$. If $G' \subseteq H$
then we can solve efficiently
$\mbox{\textsc{HSP}}(G, f)$.
\end{corollary}
\section{The algorithm}\label{algorithm}
We now describe the quantum algorithm which solves the $\mbox{\textsc{HSP}}$ in extraspecial groups.
In fact,
we will deal separately with three cases:
groups of constant exponent,
groups of exponent $p$ when $p$ is large, and
groups of exponent $p^2$ when $p$ is large.
The case of constant exponent is actually not new, it follows from a general
result in \cite{ims03}. Nevertheless, for the sake of completeness we show how a simplified version
of the algorithm for the second case works here.
The algorithm for extraspecial groups of exponent $p$ that goes to infinity
is our main result. Finally, the case of groups of exponent $p^2$ can be easily reduced to the
case of groups of exponent $p$. These results are summarized in our main theorem.
\begin{theorem}\label{theorem:main}
Let $G$ be an extraspecial $p$-group, and
let us given an oracle $f$ which
hides the subgroup $H$ of $G$. Then there is an efficient quantum procedure which
finds $H$.
\end{theorem}
\subsection{Groups of constant exponent}
In Theorem 9 of \cite{ims03} it is proven that in general the $\mbox{\textsc{HSP}}$ can be solved
by a quantum algorithm in polynomial time in the size of the input and the cardinality of $G'$.
This includes the case of extraspecial groups of constant exponent. Nonetheless, for the
sake of completeness we describe here an efficient procedure, similar in spirit
to the one used for the next case but much simpler.
First remark that for every $a \in G$, the set $\{ \ket{aHG' \cdot g} : g \in G \}$ is hiding for $HG'$ in $G$.
The efficient hiding procedure for $HG'$
computes, for some $a \in G$, the superposition
$ \frac{1}{\sqrt{p}} \sum _{u \in {\mathbb Z}_p} \ket{u} \ket{aHG'_u}$
which by Lemma~\ref{lemma:superposition} of Section~\ref{important}
can be done efficiently. Then the first register is measured.
This is repeated until the result of the observation is 0. Since $p$ is
constant, after a constant number of iteration the superposition
$\ket{0} \ket{aHG'_0} = \ket{0} \ket{aHG'}$ is created and finally $\ket{aHG' \cdot g}$
is computed.
Observe that this simplified approach can not work for large exponents
since $p$, the expected
number of iterations, is not polynomial in the size of the input.
\subsection{Groups of exponent $p$ when $p$ is large}\label{important}
For every $u \in {\mathbb Z}_p$, let $\ket{G'_u}=
\frac{1}{\sqrt{p}} \sum_{i \in {\mathbb Z}_p} \omega^{-u i} \ket{z^i}$
and observe that $\ket{G'_u \cdot z}=\omega^u \ket{G'_u}$.
\begin{lemma}\label{lemma:superposition}
There is an efficient quantum procedure which creates
$ \frac{1}{\sqrt{p}} \sum _{u \in {\mathbb Z}_p} \ket{u} \ket{aHG'_u}$ where $a$
is a random element from $G$.
\end{lemma}
\begin{proof}
We start with $\ket{0}\ket{0}\ket{0}$.
Since we have access to the hiding function $f$,
we can create the superposition $\frac{1}{\sqrt{|G|}}\sum_{g \in G} \ket{0} \ket{g} \ket{f(g)}$.
Observing and discharging the third
register we get $\ket{0} \ket{aH}$ for a random element~$a$.
Applying the Fourier transform over ${\mathbb Z}_p$ to the
first register gives $\ket{{\mathbb Z}_p}\ket{aH}$.
Multiplying the second register by $z^{-i}$ when $i$ is the content of the first one results in
$ \frac{1}{\sqrt{p}} \sum _{i \in {\mathbb Z}_p} \ket{-i} \ket{a H z^{i}}$. A final Fourier transform in the first register
creates the required superposition.\qed
\end{proof}
For $j=1, \ldots, p-1$, we define the automorphisms $\phi_j$ of $G$
mapping $x_i$ to $x_i^j$, $y_i$ to $y_i^j$ and $z$ to $z^{j^2}$ when
$i \in \{1, \ldots, k\}$. These maps (defined on generators)
extend in fact to automorphisms of $G$ since the elements
$x_1^j, y_1^j, \ldots x_k^j, y_k^j, z^{j^2}$
generate the group $G$ and satisfy the defining relations.
In our next lemma we claim that the states $\ket{aHG'_u}$ are eigenvectors of
the group action of multiplication from the right by $\phi_j(g)$,
whenever $g$ is from $HG'$. Moreover, the
corresponding eigenvalues are some powers of the
root of the unity, the exponent does not depend on $a$, and the dependence on $u$ and $j$
is relatively simple.
\begin{lemma}\label{lemma:action}
We have
\begin{enumerate}
\item $\forall h \in H, \exists \ell \in {\mathbb Z}_p, \forall a \in G, \forall u \in {\mathbb Z}_p, \forall j \in {\mathbb Z}_p^*, ~~
\ket{aHG'_u \cdot \phi_j(h)}=\omega^{u(j-j^2)\ell} \ket{aHG'_u},$
\item $ \forall a \in G, \forall u \in {\mathbb Z}_p, \forall j \in {\mathbb Z}_p^*, ~~
\ket{aHG'_u \cdot \phi_j(z)}=\omega^{uj^2} \ket{aHG'_u}.$
\end{enumerate}
\end{lemma}
\begin{proof}
To begin with let's remark that for $h \in H$, we have $\ket{aHG'_u \cdot h}=\ket{aHG'_u}$
and that $\ket{a H G'_u \cdot z}= \omega^u \ket{a H G'_u}$.
To prove the first part, let $h$ be an element of $H$. Then $\phi_j(h)=h^jz^{t}$ where
$t$ depends on $h$ and $j$. We will show that $t = (j-j^2)\ell$
where $\ell$ depends only on $h$. This will imply the claim.
Let $j_0$ be a fixed primitive element of ${\mathbb Z}_p^*$. Then
$\phi_{j_0}(h)=h^{j_0} z^s$, for some $ s \in {\mathbb Z}_p$.
We set $\ell=s(j_0-j_0^2)^{-1}$, and $k=h z^{\ell}$.
Then $\phi_{j_0}(k)=h^{j_0} z^{\ell(j_0-j_0^2)} z^{\ell j_0^2}=k^{j_0}$.
Therefore $\phi_{j}(k) = k^j$ and
$\phi_j(h)=\phi_j(k) \phi_j(z^{-\ell})=h^jz^{\ell(j-j^2)}$. The proof of the second part is immediate.\qed
\end{proof}
The principal idea now is to
take several copies of the states $\ket{a_iHG'_{u_i}}$ and choose
$j_i$ so that the product
of the corresponding
eigenvalues
becomes
the unity. Therefore the actions
$\phi_j(g)$, when $g$ is from $HG'$, will not modify the combined state. It turns out
that we can achieve this with four copies.
For $\overline{a}=(a_1,a_2,a_3,a_4) \in G^4$,
$\overline{u}=(u_1,u_2,u_3,u_4) \in {\mathbb Z}_p^4$,
$\overline{j}=(j_1,j_2,j_3,j_4) \in ({{\mathbb Z}_p^*})^4$ and $g \in G$, we define the quantum state
$\ket{ \Psi_g^{\overline{a}, \overline{u}, \overline{j}}}$ in ${\mathbb C}^{G^4}$ by
$$\ket{ \Psi_g^{\overline{a}, \overline{u}, \overline{j}}} =
\ket{a_1HG'_{u_1} \cdot \phi_{j_1}(g),a_2HG'_{u_2} \cdot \phi_{j_2}(g),a_3HG'_{u_3} \cdot \phi_{j_3}(g),a_4HG'_{u_4} \cdot \phi_{j_4}(g)}.$$
Our purpose is to find an efficient procedure to generate triples
$(\overline{a}, \overline{u}, \overline{j})$ such that
for
every $g \in HG'$ we have
$\ket{ \Psi_g^{\overline{a}, \overline{u}, \overline{j}}}
=
\ket{a_1HG'_{u_1},a_2HG'_{u_2},a_3HG'_{u_3},a_4HG'_{u_4}} $. We call such triples
{\em appropriate}. The reason to look for appropriate triples is that they lead to hiding
sets for $HG'$ in $G$ as stated in the next lemma.
\begin{lemma}\label{lemma:appropriate}
If $(\overline{a}, \overline{u}, \overline{j})$ is an appropriate triple then
$\{ \ket{ \Psi_g^{\overline{a}, \overline{u}, \overline{j}}} : g \in G \}$ is hiding for $HG'$ in $G$.
\end{lemma}
\begin{proof}
To see this, first observe that $HG'$ is a normal subgroup of $G$.
If $g_1$ and $g_2$ are in different cosets of $HG'$ in $G$ then
for every $j \in {\mathbb Z}_p^*$,
the elements $\phi_j(g_1)$ and $\phi_j(g_2)$ are in different cosets of
$HG'$ in $G$ since $\phi_j$ is an automorphism of $G$. Also, for every
$a \in G$ and for every $u \in {\mathbb Z}_p$ we have
$\mathop{\mathsf{supp}}(\ket{aHG'_u}) = \mathop{\mathsf{supp}} ( \ket{aHG'})$, and therefore
$\mathop{\mathsf{supp}}(\ket{aHG'_u \cdot \phi_j(b)})$ and
$\mathop{\mathsf{supp}}(\ket{aHG'_u \cdot \phi_j(b^{'})})$ are included in different cosets and are disjoint.
Thus for every $\overline{a} \in G^4,
\overline{u} \in {\mathbb Z}_p^4$ and $ \overline{j} \in ({{\mathbb Z}_p^*})^4$,
the states $\ket{ \Psi_{g_1}^{\overline{a}, \overline{u}, \overline{j}}}$ and
$\ket{ \Psi_{g_2}^{\overline{a}, \overline{u}, \overline{j}}}$ are orthogonal.
If $g_1$ and $g_2$ are in the same coset of $HG'$ then $g_1 = g g_2$ for some $g \in HG'$,
and $\phi_{j_i}(g_1) = \phi_{j_i}(g) \phi_{j_i}(g_2)$. Thus
$\ket{ \Psi_{g_1}^{\overline{a}, \overline{u}, \overline{j}}} =
\ket{ \Psi_{g g_2}^{\overline{a}, \overline{u}, \overline{j}}} =
\ket{ \Psi_{g_2}^{\overline{a}, \overline{u}, \overline{j}}}$.\qed
\end{proof}
Let us now address the question of existence of appropriate triples and efficient ways to
generate them. Let $(\overline{a}, \overline{u}, \overline{j})$ be an arbitrary element of
$G^4 \times {\mathbb Z}_p^4 \times ({\mathbb Z}_p^*)^4$, and
let $g$ be an element of $HG'$. Then $g=h z^t$ for some $h \in H$ and
$t \in {\mathbb Z}_p$, and $\phi_{j_i}(g)=\phi_{j_i}(h) \phi_{j_i}(z^t)$ for $i=1, \ldots, 4$.
By Lemma~\ref{lemma:action} there exists $\ell$ such
that $\ket{a_iHG'_{u_i} \cdot \phi_j(h)}=
\omega^{u_i(j_i-j_i^2)\ell}\ket{a_iHG'_{u_i}}$ and
$\ket{a_iHG'_{u_i} \cdot \phi_j(z^t)}= \omega^{u_i j_i^2 t}\ket{a_iHG'_{u_i}},$ and therefore
$$
\ket{ \Psi_g^{\overline{a}, \overline{u}, \overline{j}}}
= \omega^{\sum_{i=1}^4 ( u_i(j_i-j_i^2)\ell + u_i j_i^2 t ) }
\ket{a_1HG'_{u_1},a_2HG'_{u_2},a_3HG'_{u_3},a_4HG'_{u_4}}.
$$
We say that $\overline{u} \in {\mathbb Z}_p^4$ is {\it good} if the following system of
quadratic equations has a nonzero solution:
\begin{equation}
\begin{cases}
\sum_{i=1}^4 u_i(j_i-j_i^2) & =~~ 0 \\
\sum_{i=1}^4 u_ij_i^2 & =~~ 0,
\end{cases}
\end{equation}
and we call a solution $\overline{j}$ a {\em witness} of $u$ being good. It should be clear that
for every $\overline{u}$, if $\overline{u}$ is good and $\overline{j}$ witnesses that then
$(\overline{a}, \overline{u}, \overline{j})$ is an appropriate triple.
The next lemma states that a random $\overline{u}$ is good with constant probability, and that
in this case one can find efficiently $\overline{j}$ witnessing that.
\begin{lemma}\label{lemma:probability}
For every $\overline{a} \in G^4$, we have
$$\mathop{\mathsf{Pr}}{\overline{u} \in {\mathbb Z}_p^4} {
\overline{u} \mbox{~{\rm is good}}
}\geq
(p - 9)/2p.$$
Moreover, when $\overline{u}$ is good a witness $\overline{j}$ can be found efficiently.
\end{lemma}
\begin{proof}
Let us simplify system (1) to the equivalent system
\begin{equation}
\begin{cases}
\sum_{i=1}^4 u_ij_i^2 & =~~ 0 \\
\sum_{i=1}^4 u_ij_i & =~~ 0.
\end{cases}
\end{equation}
To solve (2),
we take $j_3=1$ and $j_4=-1$, and we set $v=u_3+u_4$ and $w=u_3-u_4$. We will show that
for random $(u_1,u_2,v,w) \in {\mathbb Z}_p^4$, the reduced system (3)
has a solution $(j_1,j_2) \in ({\mathbb Z}_p^*)^2$
with probability at least $(p - 9)/2p$, and that
the solution is easy to find:
\begin{equation}
\begin{cases}
u_1j_1^2+u_2j_2^2 & =~~ -v \\
u_1j_1+u_2j_2 & =~~ -w.
\end{cases}
\end{equation}
With probability at least $1 - 3p$ we have $u_1 \neq 0$, $u_2 \neq 0$, $u_1+u_2 \neq 0$.
In that case we can substitute $j_2=-\frac{w+u_1j_1}{u_2}$ in the first equation and get
in $j_1$ the quadratic equation $(u_1u_2 + u_1^2)j_1^2 +2u_1w j_1 +(w^2+ vu_2)=0$.
It is a non degenerate quadratic equation whose discriminant
$D=-4u_1u_2(w^2+(u_2+u_1)v)$ is uniformly distributed in ${\mathbb Z}_p$ since it is linear in $v$.
Therefore $D$ is a quadratic residue with probability $(p-1)/2p$,
and we can efficiently compute a square root of $D$ modulo $p$
(see, for example, subsection 13.3.1 of \cite{shoup05}).
We also have to ensure that
$j_2 \neq 0$.
If $j_2$ is zero, then $w^2=-vu_1$, which happens with probability $1/p$.
Therefore the probability of finding a solution $(j_1,j_2) \in ({\mathbb Z}_p^*)^2$ is at least
$(p-1)/2p - 4/p$.\qed
\suppress{
For $u_2 \neq 0$ let's $j_2=-\frac{w+u_1j_1}{u_2}$, we need to solve the quadratic equation in $j_1$, $(u_1u_2 + u_1^2)j_1^2 +2u_1w j_1 +(w^2+ vu_2)=0$ of discriminant $D=-4u_1u_2(w^2+(u_2+u_1)v)$. This equation has a non zero solution at least when $D$ is a non zero square. If $u_1 \neq 0$, $u_2 \neq 0$, $u_1+u_2 \neq 0$ then the equation is a non degenerate quadratic one with uniformly random discriminant as it is linear in $v$. That happens with probability at least $\frac{p-1}{2p}-\frac{3}{p}$. In those solution we're going to keep only the ones for which $j_2$ is non zero. If $j_2$ is zero, then $w^2=-vu_1$, what happens with probability $\frac{1}{p}$ when $u_1$ is non zero. The probability to find a good solution to our system of equation is then at least $\frac{1}{2}-\frac{9}{2p}$.
}
\end{proof}
\begin{theorem}\label{theorem:exponentp}
Let $G$ be an extraspecial $p$-group of exponent $p$, where $p$ grows with the input size, and
let us given an oracle $f$ which
hides the subgroup $H$ of $G$. Then there is an efficient quantum procedure which
hides $HG'$ in $G$.
\end{theorem}
\begin{proof}
We describe the efficient hiding procedure.
It computes, for some $\overline{a} \in G^4$, the superposition
$$ \frac{1}{{p}^2} \bigotimes_{i=1}^4 \sum _{u_i \in {\mathbb Z}_p} \ket{u_i} \ket{a_iHG'_{u_i}},$$
which by Lemma~\ref{lemma:superposition} can be done efficiently, and then
it measures the registers for the $u_i$. This is repeated until a good
$\overline{u} \in {\mathbb Z}_p^4$ is measured. By Lemma~\ref{lemma:probability}, this requires a
constant expected number of iterations. Also, when a good $\overline{u}$ is measured, it
finds efficiently a solution $ \overline{j} \in ({{\mathbb Z}_p^*})^4$ for system (1).
Such a triple $(\overline{a}, \overline{u}, \overline{j})$ is appropriate, and therefore by
Lemma~\ref{lemma:appropriate}
$\{ \ket{ \Psi_g^{\overline{a}, \overline{u}, \overline{j}}} : g \in G \}$ is hiding for $HG'$ in $G$.
Using the
additional input $\ket{g}$, the procedure finally computes
$ \ket{ \Psi_g^{\overline{a}, \overline{u}, \overline{j}}} $.\qed
\end{proof}
The proof of Theorem~\ref{theorem:main} in that case follows from Theorem~\ref{theorem:threelemmas} and Theorem~\ref{theorem:exponentp}.
\subsection{Groups of exponent $p^2$ when $p$ is large}
Here we deal with the group
$G = A_p \central (\multicentral{i=1}{k-1}{H_p}),$ where we start with a function $f$ hiding
some subgroup $H$.
As in Lemma~\ref{lemma:firstreduction}, we will distinguish the cases when $G' \subseteq H$
and when $G' \cap H = \{e\}$. The first case is already taken care of by
Corollary~\ref{corollary:threelemmas}.
If $G' \cap H = \{e\}$ then $H$ contains only elements whose order is at most $p$.
Indeed an element of order $p^2$ cannot be in $H$ since the $p^{\mbox{th}}$
power of such an
element is in $G'$. Therefore $H$ is a subgroup of $K = \langle
y_1, x_2, y_2, \ldots , x_{k}, y_k, z \rangle$,
where $x_1$ is the unique generator of order $p^2$ of $G$.
The subgroup $K$ is also (isomorphic to) a subgroup of
$\multicentral{i=1}{k}{H_p}$. We claim that we can extend the restriction of $f$ to $K$ into
a function $F$ defined on
the whole group
$\multicentral{i=1}{k}{H_p}$ that also hides $H$. Such an
extension can be defined for example as
$F(x_1^{i_1} y_1^{j_1} \ldots x_k^{i_k} y_k^{j_k} z^{\ell})=
(i_1,f(y_1^{j_1} \ldots x_k^{i_k} y_k^{j_k} z^{\ell}))$, and it is easy to see that it is indeed a hiding
function. Therefore the problem is reduced to the HSP in extraspecial groups of exponent $p$.
\section{Concluding remarks}
The main technical contribution of the present paper
is a quantum procedure which hides $HG'$
in an extrapsecial $p$-group $G$ where $p$ is a large
prime. We remark
that it is possible to present the proof of its correctness in terms
of irreducible representations of $G$. However,
the present approach
is shorter and it does not make use of concepts of
noncommutative representation theory. Finally, our method can in turn be extended to
finding hidden subgroups efficiently in arbitrary finite
two-step nilpotent groups, that is groups
$G$ satisfying $G'\leq Z(G)$. This extension will
be the subject of a subsequent paper.
\subsubsection*{Acknowledgment.}
The authors are grateful to P\'eter P\'al P\'alfy for
his useful remarks and suggestions.
|
{
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| 4,833
|
Indigenous Refugees
Bangladeshi Settlers
Armed Resistance
Rapes & Abductions
The indigenous Chakma refugees fetch water in the relief camp of Tripura. These refugees fled the Bangladesh military induced terror in their homeland. An exodus to India was not a new event. But for the first time, the refugees went in very large numbers and refused to be returned. The exodus in 1986 led to the establishment of six relief camps in Tripura state of India.
The Bangladesh armed forces and the Muslim settlers had committed numerous massacres and atrocities against the indigenous people of the Chittagong Hill Tracts (CHT). It was done as part of the Bangladesh Government's policy to wipe out the indigenous people from their traditional homeland and populate CHT with the Bengali Muslim settlers. The state sponsored terrorism forces the indigenous people to leave their ancestral villages and farmlands and to join the tens of thousands of homeless refugees. Thousands of them fled across the border to India and Burma to escape the racial and genocidal atrocities of the fundamentally hostile Bangladeshi regime.
Since the CHT conflict started in 1975 the indigenous refugees cross the border 3 times, in 1981 to Tripura, in 1984 to Mizoram and in 1986 to Tripura. The waves of refugees are directly related to the waves of violence against the indigenous people in the CHT. However, the origins of the refugees depend on the accessibility of their villages to the borders. Most of the refugees in Tripura come from the Khagrachari and Dighinala areas. On the other hand, the majority of those fleeing from Langadu after the attacks on 4 May 1989, were not allowed into Mizoram and so remained in the forest areas and did not attempt to make the dangerous trek across the CHT to Tripura.
1. Refugees to Tripura, 1981
As a consequence of the Bangladeshi security forces genocidal campaigns at Banraibari, Belchari, Ashalong, Gurangapara, Tabalchari in Feni valley in June and September 1981 some 18,000 indigenous people took refuge in the Tripura state of India. At that time the Bangladesh Government denied that the refugees were from Bangladesh. But the world community forced the Bangladesh Government to repatriate the refugees. The indigenous refugees agreed to go back to Bangladesh on the government's promise that they would be given full protection from repression and that they would get back their villages and farmlands in addition to sufficient financial help for their rehabilitation. It is needless to say that the Bangladeshi regime did not keep its promises.
Mr. Michael Roche (the Secretary of the Buddhist Peace Fellowship, Berkeley, California, U.S.A) visited the CHT to investigate the genocidal crimes committed by the Bangladesh Authorities against the innocent indigenous people of the CHT. He gave a very clear picture of the plight of the refugees in his report published in the Buddhist Peace Fellowship Newsletter-
"...early this year, some 18,000 of them were repatriated to Bangladesh. These tribal people were met at the border by hostile Bangladesh officials and were given the equivalent of $8 and were left to their fates. Return to their native villages is, of course, impossible for these refugees because their homes and possessions have been appropriated by Bengali settlers, so they join the tens of thousands of homeless now in the Hill Tracts. Harassed by government authorities, unable to flee the country and without any means of support, they live in limbo in a land where the quality of tribal life approached the infernal".
2. Refugees to Mizoram, 1984
In May and June 1984, the Bangladesh Army (7th and 26th Bengal), the Bangladesh Rifles (BDR - 17th Battalion) and Muslim settlers launched surprise attacks on the indigenous inhabitants of Bhusan Chara, Gorostan, Bhusan Bagh, Tarengya Ghat, Het Bhoriya, Suguri Para, Choto Harina in the Barkal sub district killing at least 300 indigenous Buddhisgt people mostly women and children, burning houses, looting valuables and destroying Buddhist temples. Bangladesh army also pursued a "scorched earth" campaign for a month between 20 September and 19 October 1984 in order to evict the villagers of Bar Kalak, Othyal Chari, Harin Hat Para, Mong Chari, Shivram Para and Bamer Subalong in the Gaba Chari area of the Subalong valley.
As a result of these massacres and scorched earth campaign, about 18,000 indigenous refugees fled to Mizoram, India. But the Mizoram state government pushed most of them back to Bangladesh. However the Indian Government has kindly given shelter to over 4,000 refugees at Tibira Ghat and Tagalak Bak in the Demagiri Sub Division of the Lunglei District of Mizoram. Those refugees who were sent back to Bangladesh could not return to their homes because their villages had already been distributed to the Muslim settlers. They took refuge in the neigboring upland forests and mountains.
On 29 April 1986, the Shanti Bahini attacked several army camps and Muslim settlements. The Far Eastern Economic Review reported in June 1986:
"..a reorganized Shanti Bahini force carried out its biggest coordinated attack on 29 April as it simultaneously raided several Bangladeshi army camps and the outposts of paramilitary Bangladesh Rifles and followed it up with swoops on new settlements of immigrant Bengali Muslims. In turn, the Muslim settlers and government forces carried out reprisals on tribal villages forcing the tribes people to flee to India on 30 April".
On 30 April 1986, the Bangladesh armed forces attacked 6 villages in Matiranga Upazilla (sub District): Khetra Mohan Para, Boga Para, Bagya Para, Sarveswar Para, Assalong Para and Talukder Para.
On the following day 1 May 1986, they invaded two villages in Khagrachari Upazilla: Mahajon Para and Pankheiya Para, and 24 villages in Panchari Upazilla: Shantipur, Latiban, Kamini Member Para, Chitta Ranjan Para, Surya Sen Para, Sachindra Karbari Para, Badidhan Karbari Para, Rangapani Chara, Napida Para, Ratan Muni Para, Golak Pudima, Joutha Khamar Para, Suta Karma Para, Kanago Para, Birendra Karbari Para, Madan Karbari Para, Rabi Singha Karbari Para, Sucharu Master Para, Pujgang Mukh, Ganesh Chandra Karbari Para, Manikya Karbari Para, Mongal Dhan Karbari Para, Dhanendu Karbari Para and Jamindhan Karbari Para. Properties were robbed, houses were burnt, women were abducted and gang raped, Buddhist temples were desecrated and destroyed, and the villagers including the Buddhist monks were tortured and murdered.
As a result of the Matiranga-Panchari-Khagrachari massacres, some 500 indigenous people mostly old age, women and children were murdered, about 50 villages were destroyed, over 40,000 people were rendered homeless, about dozen Buddhist temples including those at Kalanal, Kamini Member Para, Suta Karma Para, Shantipur (north), Shantipur (south), Rangapani Chara, Panchari and Pujgang were destroyed, many Buddhist monks were wounded and Rev. Purna Nanda Bhikkhu of Kalanal Buddhist temple was hacked to death.
The villagers fled to nearby forests for their lives. They lost all their possessions and they had nothing to live on. The only way for them to evade military atrocities was to head towards the Indian border. They had to walk for weeks without food along the most difficult jungle tracks. It was extremely risky for them to enter Tripura as the border was closely guarded by the Bangladesh Rifles (BDR).
For example, a group of 200 indigenous Tripura people mostly old men, women and children from Matiranga Upazilla were fleeing to the Tripura state of India. On 18 May 1986, the BDR rounded up these refugees at the border, took them to Taidong and Comillatilla, and prompted the Muslim settlers to massacre them. The BDR opened fire on even those refugees who managed to slip into Tripura, killing and wounding many of these refugees.
An exodus to India was not a new event. But for the first time, the refugees went in very large numbers and refused to be returned. The exodus in 1986 led to the establishment of the 6 relief camps in the State of Tripura. The camps had an average refugee population of 56,000 and at the height of the influx there were 80,000 refugees in Tripura.
For many years, the Indian Government wanted the refugees to repatriate. Indian authorities, both at the national and in the state of Tripura, where most of the refugees lived, kept camp conditions harsh to discourage the refugees from remaining in India. The Indian authorities did not permit UNHCR or International NGOs access to the indigenous Buddhist and Hindu refugees. They also pressured the refugees to leave.
Several repatriations occurred over the years, including groups of 1,850 and 3,500 refugees in 1994, but refugees often encountered poor conditions and the Bangladesh authorities did not delivered promised aid, including helping the returnees regain their land.The remaining indigenous refugees were repatriated after a treaty signed between the Jana Samhati Samiti and the Bangladesh Government on 2 December 1997.
While the refugees were in India for 12 years, their lands were usually taken over by the Muslim settlers who coveted it before the attack. Although the land is legally in the hands of the refugees, there are sometimes problems which exacerbate the difficulties of regaining land. The land documents are frequently destroyed when the houses are burnt, which means that the only records of the deeds lie with the authorities. In some cases the Muslim settlers obtain false documents for the same land and it becomes difficult for the indigenous people to prove ownership.
Refugees Pushed Back from Mizoram, India
Life is not ours: the Chittagong Hill Tracts Commission
Unlawful Killings in the CHT: Amnesty InternationalMaintained
Copyright � 2008 Chakma Buddhist Association. All Rights Reserved
|
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| 532
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{"url":"https:\/\/kerodon.net\/tag\/029K","text":"# Kerodon\n\n$\\Newextarrow{\\xRightarrow}{5,5}{0x21D2}$ $\\newcommand\\empty{}$\n\nCorollary 5.6.7.7. Suppose we are given a commutative diagram of simplicial sets\n\n$\\xymatrix@R =50pt@C=50pt{ \\operatorname{\\mathcal{D}}\\ar [rr]^-{F} \\ar [dr]_{U} & & \\operatorname{\\mathcal{E}}\\ar [dl]^{V} \\\\ & \\operatorname{\\mathcal{C}}, & }$\n\nwhere $U$ and $V$ are cocartesian fibrations. Then $F$ is an equivalence of cocartesian fibrations over $\\operatorname{\\mathcal{C}}$ (Definition 5.1.6.1) if and only if it is a categorical equivalence of simplicial sets.\n\nProof. Combine Proposition 5.1.6.5 with Corollary 5.6.7.5. $\\square$","date":"2022-05-23 14:07:27","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 2, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.7329152822494507, \"perplexity\": 517.8197924565586}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2022-21\/segments\/1652662558030.43\/warc\/CC-MAIN-20220523132100-20220523162100-00397.warc.gz\"}"}
| null | null |
\section{Introduction}
In $(3+1)$-dimensional numerical relativity an apparent horizon
in a three-dimensional spacelike slice $\Sigma_t$ is the outermost
smooth two-surface whose whose outward null expansion vanishes
\cite{thomas,thornburg}. Then an apparent horizon world-tube
is a three-surface $H$
foliated by two-surfaces $S_t \subset \Sigma_t$ with vanishing outward
null expansion.
Such surfaces have been an active topic of research in mathematical
relativity for the last 10-15 years (see \cite{AKRev,GourgRev,myRev} for
reviews or the reference section of \cite{BigPaper} for more recent papers)
and results from that work are now beginning
to be applied to numerical relativity \cite{KrishNum1,KrishNum2}.
This short paper continues this tradition by translating results from recent
papers into the language of $(3+1)$-dimensional relativity. We
first consider the recent work on slowly evolving horizons
\cite{SEH,SEH2,BigPaper}. These papers found conditions under
which a horizon can be considered to be in a quasi-equilibrium
state. Intuitively, slowly evolving horizons
are ``almost" isolated \cite{iso} and so ``nearly" null. Here we shall
focus on an expansion parameter that arose from that
work. This parameter is necessarily small for slowly evolving horizons,
but even if it isn't small it can be used to invariantly characterize
the rate of expansion of horizons.
It is to this end that we discuss it here, with a particular eye to
tracking how quickly a black hole settles down to
equilibrium after a merger or formation.
Second we consider a parameter that characterizes how
close an apparent horizon is to being extremal\cite{extremal}.
Extremality in this case is a generalization of the well-known bound
on the maximum angular momentum of a Kerr black hole relative to its
mass (or equivalently surface area). For apparent horizons this
turns out to be related to the expansion parameter and
places a bound on the maximum angular momentum relative to the
intrinsic geometry of the horizon. The immediate use
for this parameter would be to study the proximity to extremality of post-merger
black holes.
\section{Horizons in (3+1)-dimensional gravity}
Let $(M,g_{ab}, \nabla_a)$ be a four-dimensional spacetime which
is foliated by spacelike three-surfaces
$\{ (\Sigma_t, h_{ij} , D_i) \, ; t_1 \leq t \leq t_2\}$ where $h_{ij}$ is the induced metric and $D_i$ is the compatible covariant derivative.
Note the indices; throughout this paper we will
use early-alphabet latin indices for four-dimensional quantities
and mid-alphabet latin indices for those defined in the three-slices.
We use $e$ to denote the pull-back/push-forward operator
between the various spaces.
Next let $T^a$ be a compatible time-evolution vector field
generating a flow which maps the $\Sigma_t$ into each other. That is
$\Lie_T t = 1$. In the usual way this may be broken up as
\begin{eqnarray}
T^a = N \hat{u}^a + V^a \, ,
\end{eqnarray}
where $N$ is the lapse function, $V^a = e^a_i V^i$
is the spacelike shift vector field for some
$V^i \in T \Sigma_t$, and $\hat{u}^a$ is the future-pointing
timelike normal vector field to the $\Sigma_t$.
Finally we choose our sign convention so that the extrinsic curvature $K_{ij}$ of the $\Sigma_t$ in $M$ is
\begin{eqnarray}
K_{ij} = \frac{1}{N} ( \dot{h}_{ij} - \Lie_V h_{ij} )
= e_i^a e_j^b \nabla_a \hat{u}_b \, ,
\end{eqnarray}
where the dot indicates a Lie derivative with respect to $T^a$.
Now, let $S_t$ be a closed two-surface in a slice $\Sigma_t$ and
write its outward-pointing unit normal as $\hat{s}^i$. Then
future-outward and future-inward pointing null normals to
$S_t$ in $M$ can be written as
\begin{eqnarray}
\ell^a = f ( \hat{u}^a + \hat{s}^a ) \; \; \mbox{and} \; \;
n^a = \frac{1}{2f } \left( \hat{u}^a - \hat{s}^a \right) \, ,
\label{scaling}
\end{eqnarray}
where $\hat{s}^a = e^a_i \hat{s}^i$ and $f$ is an arbitrary
positive function: we have adapted the standard cross-normalization
$\ell \cdot n = -1$ so there is the only free parameter in their definition.
For $f=1$ we denote this pair of null normals as
$(\ell^a_o, n^a_o)$ as shown in Fig.~\ref{NormVect}.
\begin{figure}[t]
\begin{center}
\scalebox{0.8}{\includegraphics{NormalVectorsII}}
\caption{A two-dimensional cross-section of a spacetime $M$ foliated by spacelike three-surfaces $\Sigma_t$. $H$ is an apparent horizon world-tube which is foliated by the spacelike two-surfaces $S_t = H \cap \Sigma_t$.
}
\label{NormVect}
\end{center}
\end{figure}
We write the induced two-metric on $S_t$ as $\tilde{q}_{AB}$
(using capital Latin indices for such two-dimensional quantities)
and note that
\begin{eqnarray}
\tilde{q}^{ab} \equiv e^a_A e^b_B \tilde{q}^{AB}
= g^{ab} + \ell^a n^b + \ell^b n^a
\; \; \mbox{and} \; \;
\tilde{q}^{ij} \equiv e^i_A e^j_B \tilde{q}^{AB}
= h^{ij} - \hat{s}^i \hat{s}^j \, .
\end{eqnarray}
Then the outward and inward null expansions are, respectively,
\begin{eqnarray}
\theta_{(\ell)} = \tilde{q}^{ab} \nabla_a \ell_b = f (\tilde{q}^{ij} K_{ij} + \tilde{q}^{ij} D_i \hat{s}_j )
\; \; \mbox{and} \; \;
\theta_{(n)} = \tilde{q}^{ab} \nabla_a n_b = \frac{1}{2f} (\tilde{q}^{ij} K_{ij} - \tilde{q}^{ij} D_i \hat{s}_j ) \, .
\label{expansions}
\end{eqnarray}
As noted in the introduction, on a numerical apparent horizon
$\theta_{(\ell)} = 0$ and in practical simulations where there are known to be
black holes in the initial data, this will usually be a sufficient
condition to identify a black hole boundary. A key word in the
previous sentence is ``usually" and we will return to the
potential complications in section \ref{Sect_Extr}.
For now, however, we will assume that an apparent horizon finding algorithm
\cite{thornburg}
has been used to identify $\theta_{(\ell)} = 0$ surfaces
on each $\Sigma_t$ over some range of $t$ and
further that over that range their union is a smooth three-surface
$H$. Then we can always find a horizon evolution vector field
$\mathcal{V}^a$ that is normal to the $S_t$ and maps these surfaces
into each other. Since the $S_t \subset \Sigma_t$ we can write
\begin{eqnarray}
\mathcal{V}^a = N (\hat{u}^a + v_\perp \hat{s}^a ) \, ,
\label{FoliationV}
\end{eqnarray}
where $N$ is again the lapse and $v_\perp$ is the the ``velocity"
of the horizon relative to the foliation. For a null horizon parallel to $\ell^a$,
$v_\perp = 1$ while for a spacelike and expanding horizon $v_\perp>1$.
\section{Expansion}
\label{Sect:Exp}
We now consider the first of the physical characteristics: the rate of
expansion of the horizon. Relative to the foliation, the rate
of change of the area element $\sqrt{\tilde{q}}$ is
\begin{eqnarray}
\Lie_{\mathcal{V}} \sqrt{\tilde{q}} = \sqrt{\tilde{q}}
\left( \tilde{q}^{ab} \nabla_a \mathcal{V}_b \right)
=\sqrt{\tilde{q}} \left( N (v_\perp - 1) \tilde{q}^{ij} D_i \hat{s}_j \right) \, , \nonumber
\end{eqnarray}
where we have made use of the fact that
$\theta_{(\ell)} = 0 \Leftrightarrow \tilde{q}^{ij} K_{ij} = - \tilde{q}^{ij} D_i \hat{s}_j$
(which could also be used to rewrite the last line in terms of
$\tilde{q}^{ij} K_{ij}$).
This expansion is manifestly dependent on the lapse $N$ and so the
coordinate $t$ labelling of the hypersurfaces $\Sigma_t$. However,
if $H$ is not null there is an obvious
remedy to this problem : calculate the rate of expansion with respect to the unit
$\hat{\mathcal{V}}^a = \mathcal{V}^a / || \mathcal{V} ||$ instead of $\mathcal{V}$ itself. Then the
expansion relative to $\hat{\mathcal{V}}$ is
\begin{eqnarray}
\theta_{(\hat{\mathcal{V}})} = \alpha \sqrt{\left| \frac{v_\perp - 1}{v_\perp + 1} \right| } \tilde{q}^{ij} D_i \hat{s}_j \, ,
\end{eqnarray}
where $\alpha = \operatorname{sgn}(v_\perp-1)$.
Note that $\theta_{(\hat{\mathcal{V}})}$ goes to zero as $v_\perp \rightarrow 1$
even though $\hat{\mathcal{V}}^a$ itself diverges.
To better understand $\theta_{(\hat{\mathcal{V}})}$, we return to four-dimensions and
the formalism developed for \emph{slowly evolving horizons}
\cite{SEH,BigPaper}.
There, $\mathcal{V}^a$ was written in terms of the null normals and a
parameter $C$:
\begin{eqnarray}
\mathcal{V}^a = \ell^a - C n^a \, .
\label{HorizonV}
\end{eqnarray}
Then the foliation of the horizon fixes both a scaling of the null vectors
and $C$. Comparing with (\ref{FoliationV}) it is straightforward to see that in the
$(3+1)$-formalism these take the form:
\begin{eqnarray}
f = N (1 + v_\perp)/2 \; \; \mbox{and} \; \;
C = {N^2}(v_\perp^2-1)/2 \, .
\label{C}
\end{eqnarray}
The value of $C$ fixes the signature of the horizon:
$C > 0 \Leftrightarrow |v_\perp| > 1 \Leftrightarrow$ $H$ is spacelike,
$C = 0 \Leftrightarrow |v_\perp| = 1 \Leftrightarrow$ $H$ is null, and
$C < 0 \Leftrightarrow |v_\perp| < 1 \Leftrightarrow$ $H$ is timelike.
We can rewrite
\begin{eqnarray}
\theta_{(\hat{\mathcal{V}})} = - \alpha \sqrt{|{C}/{2}|} \theta_{(n)} \, ,
\label{Cexp}
\end{eqnarray}
where $\alpha = \operatorname{sgn}(C)$. In this form
$\theta_{(\hat{\mathcal{V}})}$ (or actually its square) is the most important of several
quantities used to decide whether or not a horizon is ``almost" isolated
and so in quasi-equilibrium with its surroundings. Among other properties
such horizons will obey approximate zeroth law and first laws of black hole
mechanics with all fluxes being calculated relative to the $\ell^a$ normals (as if they
where truly null). Some intuition for how dramatically a horizon can evolve and
still be counted as in a quasi-equilibrium state can be gained
from the examples of \cite{SEH2}.
To be mathematically certain about such a classification one needs to track
$\theta_{(\hat{\mathcal{V}})}^2$ and the other quantities point-by-point on the horizons.
However to get a quick idea of the rate of expansion (and proximity to equilibrium)
it is convenient to have a single, dimensionless, number to calculate. Such a
quantity can be obtained by integrating the square of $\theta_{(\hat{\mathcal{V}})}$
over $S_t$:
\begin{eqnarray}
\epsilon^2_{area} = \frac{1}{2} \int_{S_t} \mspace{-10mu} d^2 x \sqrt{\tilde{q}} |C| \theta_{(n)}^2
= \int_{S_t} \mspace{-10mu} d^2 x \sqrt{\tilde{q}}
\left| \frac{v_\perp - 1}{v_\perp + 1} \right| (\tilde{q}^{ij} D_i \hat{s}_j)^2 \, .
\label{epsilon_area}
\end{eqnarray}
In spherical symmetry this is proportional to $(dR_H/ds)^2$, where
$R_H= \sqrt{a/4 \pi}$ is the areal radius of $S_t$ and $s$ is the arclength
``up" the horizon along a flow line of $\mathcal{V}^a$.
\section{Apparent horizons as black hole boundaries}
\label{Sect_Extr}
\begin{figure}[t]
\begin{center}
\scalebox{0.8}{\includegraphics{HorizonBehavioursII}}
\caption{A horizon $H$ with $\theta_{(\ell)} = 0$ and $\theta_{(n)} < 0$
evolves between equilibrium states. Here, null horizons
have slopes of $\pm 45^\circ$, spacelike
horizons have slopes from $-45^\circ$ to $45^\circ$, and timelike
membranes have the steeper slopes outside of that range.
Thus before $\mathcal{A}$, $H$ is in equilibrium and null (parallel to $\ell^a$).
From $\mathcal{A} \rightarrow \mathcal{C}$ it is expanding and spacelike.
At $\mathcal{C}$ it is momentarily null (parallel to $n^a$) and $\epsilon_{area}$
diverges. From $\mathcal{C} \rightarrow \mathcal{D}$, $H$ is a timelike membrane
before becoming null again at $\mathcal{D}$.
Finally from $\mathcal{D} \rightarrow \mathcal{F}$ it is again a dynamical horizon
before becoming isolated and quiescent after $\mathcal{F}$.
Between $\mathcal{C}$ and $\mathcal{D}$, $H$ is super-extremal
while at those points it is extremal.
}
\label{HB}
\end{center}
\end{figure}
We now return to the ``usually" that followed
equation (\ref{expansions}) and consider when
we can definitively associate a black hole with an apparent horizon.
Following Penrose \cite{penrose} we take the existence of
fully trapped surfaces ($\theta_{(\ell)} < 0$, $\theta_{(n)} < 0$) as being
the key characteristic of black holes. Together with the null energy
condition (and some more technical assumptions) the existence
of trapped surfaces both implies a spacetime singularity somewhere
in their causal future and, if the spacetime is asymptotically flat,
an enveloping event horizon \cite{hawkellis}.
Then, taking the set of all points that lie on trapped surfaces as
the interior of a black hole, one would intuitively expect the
boundary of that region to be foliated by two-surfaces $S_t$
with $\theta_{(\ell)} = 0$ and $\theta_{(n)} < 0$, and further expect that slight inwards
deformations of the $S_t$ should turn them into fully trapped
surfaces. These ideas are the foundation for both the mathematical
relativity definition of an apparent horizon (the closure of the
boundary of the set of all points lying on trapped surfaces in a given $\Sigma_t$)
\cite{hawkellis}
as well as Hayward's trapping horizons
\cite{hayward}.
Though in reality things turn out to be more complicated (see for example
the discussion of ``wild" trapped surfaces in \cite{eardley} or the counter
examples in \cite{bendov}) the motivation remains valuable and $\theta_{(\ell)} = 0$
``boundaries" with trapped surfaces just inside are, at the very least, associated
with black holes and their boundaries. In preparation for discussing their
properties we quickly review deformations
(for more details see \cite{BigPaper}). A \emph{normal deformation}
to a surface $S_t$
is characterized by a deforming vector field $X^a \in T_\perp S_t$
(the normal bundle to $S_t$). Then taking any smooth extension of $X^a$ into
a neighbourhood of $S_t$ one can construct the corresponding flow and use
this to deform $S_t$; schematically $S_t \rightarrow S_t + \epsilon X$. The
deformation operator $\delta_X$ then calculates the rate of change of a quantity
during such an evolution. This operator is linear in the sense that
$\delta_{X+Y} = \delta_X + \delta_Y$ but in general $\delta_{fX} \neq f \delta_X$.
Thus, for an apparent horizon, the assumption that there be trapped surfaces
``just inside" $S_t$ corresponds to there existing an inward pointing
vector field $X^a \in T{\Sigma_t}$ such that $\delta_X \theta_{(\ell)} < 0$.
If such a two-surface exists on one slice $\Sigma_{t_o}$ then
this two-dimensional apparent horizon can necessarily be extended into
a three-dimensional, apparent horizon world-tube $H$ over some finite range
of $t$ \cite{ams}. If the null energy condition also holds, then
$H$ is necessarily spacelike or null (that is $C \geq 0$) and non-decreasing
in area if $\theta_{(n)} < 0$ \cite{ams, hayward, ak} --- this last fact follows
directly from
$ \delta_{\mathcal{V}} \sqrt{\tilde{q}} = - \sqrt{\tilde{q}} C \theta_{(n)} $.
Null regions are \emph{isolated horizons} \cite{iso} and may be regarded as
black hole equilibrium states while the spacelike and expanding regions are
\emph{dynamical horizons} \cite{ak}. On any given
$S_t$, $\mathcal{V}^a$ will be either spacelike everywhere or null everywhere \cite{ams}. That
is, transitions between isolated and dynamical horizons must happen ``all at once":
no individual $S_t$ can be partly isolated and partly dynamical.
It is possible for a horizon satisfying
$\theta_{(\ell)} = 0$, $\theta_{(n)} < 0$, and $\delta_n \theta_{(\ell)} < 0$ (note the use of the inwards null
direction for cases where there isn't a favoured inward spacelike direction)
to evolve into a
\emph{timelike membrane} on which $\delta_n \theta_{(\ell)} > 0$ \cite{bendov2,mttpaper,thornburg}.
Such a situation is shown in Fig.~\ref{HB}. Physically, evolutions of this type
correspond to situations where new horizons form outside of existing ones.
The cited examples were for spherically symmetric spacetimes but it is widely
speculated that something similar happens during at least some
of the apparent horizon ``jumps" seen in numerical relativity. For example,
if one was only tracking the outermost $\theta_{(\ell)} = 0$ surface in Fig.~\ref{HB}, it would
jump at $t = t_3$.
It is useful to compare $C$ and $v_\perp$ in this
figure. While the sign of $C$ faithfully tracks the signature of $H$, $v_\perp$
is coordinate dependent and diverges at $\mathcal{B}$ and $\mathcal{E}$
even though nothing physically significant happens there.
For $v_\perp$, the physically
significant values are $\pm 1$ not zero or infinity.
\section{Evolutions and extremality for dynamical horizons}
In the example depicted in Fig.~\ref{HB}, $C$ diverges and $H$ changes
signature when $\delta_n \theta_{(\ell)} = 0$. In spherical symmetry $\delta_n \theta_{(\ell)}$ doesn't
depend on the scaling of the null vectors, but in general one must select a ``correct"
scaling to observe this. For dynamical horizons this scaling is easy to find.
Relative to the null vectors of section \ref{Sect:Exp},
rescale so that $\bar{\ell} = \ell/C$ and
$\bar{n} = C n$ or equivalently choose $\bar{f} = 1/(N(v_\perp - 1))$. Then
since $\theta_{(\ell)} = 0$ everywhere on $H$ we have \cite{BigPaper,extremal}
\begin{eqnarray}
\delta_\mathcal{V} \theta_{\bar{\ell}} = C \delta_{\bar{\ell}} \theta_{(\bar{\ell})}
- \delta_{\bar{n}} \theta_{(\bar{\ell})} = 0 \; \; \mbox{where} \; \;
\delta_{\bar{\ell}} \theta_{\bar{\ell}} =
-\sigma_{(\bar{\ell})}^{AB} \sigma_{(\bar{\ell})AB} -
8 \pi G T_{ab} \bar{\ell}^a \bar{\ell}^b \, .
\label{dvtl}
\end{eqnarray}
$\sigma_{(\bar{\ell}) AB} = e_A^a e_B^b \nabla_a \bar{\ell}_b$ is the shear in the
$\bar{\ell}^a$ direction (note its simplified form thanks to $\theta_{(\bar{\ell})}= 0$).
One of the reasons for the scaling choice is now clear:
for general deformations $\delta_{f X} \neq f \delta_X$ but
$\delta_\ell \theta_{(\ell)}$ is a special case where multiplicative factors can
be commuted through $\delta$.
From this result it is easily seen that if the null energy condition holds and
$\delta_{\bar{\ell}} \theta_{(\bar{\ell})} \neq 0$ then
$C > 0 \Leftrightarrow \delta_{\bar{n}} \theta_{(\bar{\ell})} < 0$ (and vice versa).
This is one proof of the already mentioned result that dynamical apparent horizons
with trapped surfaces just inside are generically spacelike. Further note that if
$\delta_{\bar{n}} \theta_{(\bar{\ell})} \rightarrow 0$ then $C$ necessarily diverges.
In \cite{extremal} it has been argued that the most natural way to
define extremality for dynamical horizons is in terms of
$\delta_{\bar{n}} \theta_{(\bar{\ell})}$\footnote{However in near-isolated cases where $C \approx 0$ and so the suggested rescaling $\bar{\ell} = \ell / C$
may be numerically inappropriate,
other methods of calculating this quantity may be more useful \cite{extremal}.}. A sub-extremal horizon is one
for which $\delta_{\bar{n}} \theta_{\bar{\ell}} < 0$
(and so there are trapped surfaces just
inside) while for an extremal horizon $\delta_{\bar{n}} \theta_{\bar{\ell}} = 0$.
This definition follows by extension from isolated horizons such as Kerr where it
implies the usual restrictions on surface gravity (positive for sub-extremal,
vanishing for extremal) and, in cases where it is well-defined, angular
momentum. Note however that this characterization also applies
to highly dynamical and distorted horizons where the angular momentum
and surface gravity may not be so well-defined.
For a dynamical numerical apparent horizon $\delta_{\bar{n}} \theta_{\bar{\ell}}$ can be calculated directly as it was in \cite{extremal} but in most cases it is probably
easier to combine equations (\ref{C}) and (\ref{dvtl}) to obtain:
\begin{eqnarray}
\delta_{\bar{n}} \theta_{(\bar{\ell})}
= - \frac{1}{2} \left( \frac{v_\perp + 1}{v_\perp - 1} \right)
( || \sigma_{(\ell_o)} ||^2 + 8 \pi G T_{ab} \ell_o^a \ell_o^b)
\label{Extremal}
\end{eqnarray}
where $\ell_o^a = \hat{u}^a + \hat{s}^a$ and so
$\sigma_{(\ell_o) AB} = e_A^i e_B^j (K_{ij} + D_i \hat{s}_j )$.
Clearly
this expression goes to zero if $v_\perp \rightarrow -1$ ($H$ is null and
parallel to $-n^a$) and becomes positive for timelike membranes.
As for the expansion we can define a dimensionless parameter that tracks how
close a horizon is to extremality. We call this the \emph{extremality parameter}:
\begin{eqnarray}
e = 1 +\frac{1}{4 \pi} \int_{S_t} \mspace{-10mu} d^2 x
\sqrt{\tilde{q}} \delta_{\bar{n}} \theta_{(\ell)} = 1 - \frac{1}{8 \pi} \int_{S_t} \mspace{-10mu} d^2 x
\sqrt{\tilde{q}}
\left( \frac{v_\perp + 1}{v_\perp - 1} \right)
( || \sigma_{(\ell_o)} ||^2 + 8 \pi G T_{ab} \ell_o^a \ell_o^b) \, .
\label{e}
\end{eqnarray}
If the dominant energy condition holds $e \geq 0$ (this is most easily seen
from the alternative method of calculating quantity described in \cite{extremal}).
Thus, for sub-extremal holes $0 \leq e <1$ while for an extremal horizon
$e=1$. Super-extremal timelike membranes will have $e>1$.
Note however that the intended use of this parameter is not to determine
the signature of the horizon but rather to quantify how close a horizon is to
extremality and so a transition to a timelike membrane. If one is only interested
in signature, $v_\perp$ is sufficient.
\section{Conclusions}
This short paper has defined two dimensionless quantities
$\epsilon_{area}$ (Eq.~\ref{epsilon_area}) and $e$ (Eq.~\ref{e}) which can be used
to characterize dynamic black hole evolutions. $\epsilon_{area}$ invariantly defines the
rate of expansion: it is very small for slowly evolving horizons and vanishes only for
truly isolated horizons. As such it is well suited to tracking the approach of a dynamical
horizon to equilibrium. By contrast $e$ is probably of greatest interest in highly
dynamical situations. As noted $0 \leq e <1$ for regular sub-extremal holes, achieves
unity for extremal horizons and becomes greater than one for super-extremal timelike membranes. Thus it is well suited to tracking the approach to or aftermath of transitions
between timelike membranes and dynamical horizons --- though it should be kept in mind
that $\epsilon_{area}$ also has something to say about such situations as it diverges
whenever $e = 1$.
\section*{Acknowledgements}
This work was supported by Natural Sciences and Engineering Research Council
of Canada.
|
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"redpajama_set_name": "RedPajamaArXiv"
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| 6,258
|
{"url":"https:\/\/nrich.maths.org\/6471\/note","text":"Frieze Patterns in Cast Iron\n\nA gallery of beautiful photos of cast ironwork friezes in Australia with a mathematical discussion of the classification of frieze patterns.\n\nThe Frieze Tree\n\nPatterns that repeat in a line are strangely interesting. How many types are there and how do you tell one type from another?\n\nFriezes\n\nSome local pupils lost a geometric opportunity recently as they surveyed the cars in the car park. Did you know that car tyres, and the wheels that they on, are a rich source of geometry?\n\nReflecting Lines\n\nWhy do this problem?\n\nThis problem helps students to consolidate their understanding of how equations of the form $y=mx+c$ describe the gradient and position of lines. Students explore the effect on the equation of reflecting a straight line. Students are encouraged to visualise the movement of the graphs in order to conjecture and test their conjectures.\n\nThis is good preparation for future work on transforming the graphs of more complicated functions.\n\nPossible approach\n\nIt is useful if students have done some preliminary work plotting straight line graphs. The problems Parallel Lines and Diamond Collector offer good starting points. This problem works well alongside Translating Lines.\n\nWorking with the whole group demonstrate the interactivity. Decide on the position of one of the lines. Ask the class to describe how to create the reflection of the line in each of the axes. How can they be sure they have reflected correctly?\n\nGive students plenty of time, perhaps working in pairs at computers, to explore the effect that reflections have on the equations of lines. Clarify to the students that ultimately, the challenge is to be able to predict the new equation whenever a straight line is reflected in one of the axes.\n\nLater, bring the class together and use the interactivity to test their ability to do this. Do this a number of times with different lines, and reflections in either axis, until students are able to predict the new equation with confidence. Ask them to share insights and explanations\/justifications.\n\nHand out this card matching activity\u00a0to check that students are confident in pairing reflected graphs and identifying the line of symmetry. If students need more practice they can create their own sets of cards for their peers to pair off.\n\nIntroduce the final part of the problem: can students predict the equation of the resulting line when an original line is reflected in one axis and the image is then reflected in the other axis? Expect them to explain and justify their findings, perhaps by producing a poster for display or making a presentation to the class.\n\nKey questions\n\nWhen we reflect a graph, what changes? What stays the same?\n\nHow does this affect the equation of the graph?\nWhat is the effect of two combined reflections?\n\nPossible support\n\nEnsure that students are secure about the relationship between a line's properties and its equation. Encourage students to sketch the graphs of different equations and then use the interactivity to test their predictions.\n\nPossible extension\n\nChoose a straight line that doesn't go through the origin. Reflect in one of the axes. Reflect both lines in the other axis.\n\nWhat shape is enclosed by the four lines? What is its area?\nFind a way to predict the area from the equation of the first line, without drawing any graphs.\n\nStudents could now try the problem Surprising Transformations","date":"2021-09-22 21:09:39","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.2597426176071167, \"perplexity\": 781.5808094875106}, \"config\": {\"markdown_headings\": false, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-39\/segments\/1631780057388.12\/warc\/CC-MAIN-20210922193630-20210922223630-00295.warc.gz\"}"}
| null | null |
A Darker Shade of Magic is my first V.E. Schwab book, but it definitely won't be my last. I absolutely love her writing style- and I adore the characters she's created.
Kell is one of the last of his kind – a magician with the ability to travel between parallel worlds. From Grey London (a world without magic – much like our own), to Red London (Kell's home where magic is revered), to White London (where magic is fought and killed for). There was once a Black London, too. But it was destroyed by magic – and sealed off from the other lands.
Kell travels between words as the behest of the Maresh Empire as he carries correspondence between the royals. But, he moonlights as a smuggler, carrying trinkets from one London to the next for those willing to pay. It's a risky occupation (and considered treason in Red London). When Kell bumps into Delilah Bard, a professional thief in Grey London, she robs him – and then saves him. And, this chain of events makes them partners of sorts in an adventure neither of them were expecting.
The world in ADSOM isn't exactly ground breaking. The idea of parallel words is pretty common ins SFF. And, while the magic system is interesting, it's not extremely well-developed. However, for a first book in a series, it does what it needs to do: it introduces us to the world and makes us want more. But, the real heart of this series isn't the plot, it's the characters. They are wonderful, and flawed, and I couldn't help but to root for them.
Kell has been raised as a member of the royal family, and he considers Prince Rhy to be his brother. But, there is no blood-relation, and Kell knows nothing of his past or his family – nothing before the age of 5. So, he struggles with his identity both within the royal family and the world at large.
But, the best part of this book is without a doubt – Delilah Bard. She is smart, and tough, and unbelievably feisty. Delilah is a street-wise cut throat who steals partly to survive, and partly because it's what she does best. She doesn't even hesitate to follow Kell into the unknown just for the possibility of an adventure. Because dying doesn't scare Delilah Bard – complacency does.
While the world building isn't lacking is some areas, Schwab does a great job setting the scene. Grey London feels drab and boring, White London is terrifyingly dangerous, Red London is enticing and magical – and Black London is a riddle you want to solve. This first installment in the Shades of Magic trilogy holds so much promise. We meet some fantastic characters, and get a taste for where the series is going. And I for one, can't wait to continue.
Thanks, now you've added another title to my TBR pile! 😄😄😄😄😄 seriously, sounds like a good book that I'll be looking for!
It is amazing – and I just finished Book 2 which was even better. I hope you get a chance to read it soon!
Oh no! A second book too?? I can never stop at one in a series. I'll check it out though. Sounds really good.
That's a plus then! Nothing worse than waiting a year or two for the next book!
I just recently finished reading this book too (I'm currently about 200 pages into A Gathering of Shadows and really liking it) and I'm so excited that you are currently reading the series too! Everyone should have this book on their TBR or READ pile, to be honest. The characters are so endearing and I am just slightly worried for most of them because they keep mentioning DEATH and I am like 'NO. STOP THIS. I DON'T WANT THOSE SENTENCES COMING OUT OF YOUR MOUTH AT ANY POINT.'. Those feel like the worst kind of omens to me!
I'm totally with you there! I actually finished Book 2 last night – its amazing – but I'm terrified for what's to come in Book 3.
If anything bad happens to my adorable cinnamon rolls, I'm going to be VERY unhappy with V.E. Schwab. I just want them all to live happily ever after – is that too much to ask for?!?!
RIGHT?? Ever since the ending of Allegiant I don't trust authors anymore when it comes to last books in a series/trilogies. I remember reading the Legend trilogy and being terrified for the fate of the characters! I hope VE Schwab doesn't add to that kind of pain!
Me too! I'm even okay with semi-sad endings, but it has to be done well. However, for these characters nothing but alive and happy will do!
I 100% agree. I will probably be reading ACOL constantly crossing my fingers and wishing and hoping things work out for all of them – even Holland. The guy intrigues me!
I've heard nothing but wonderful things about Vicious! And, after reading this, I can't wait to pick up the rest of her work. I've got This Savage Song on my shelf – and it sounds really intriguing so I'm looking forward to giving that a go!
Happy to help! Haha. 😜 I hope you get a chance to pick up one of her books soon!
I've been wanting to read this! I've heard such great things about this whole series.
Sounds like a fascinating book! I am definitely adding it to my must read list. Thanks!
I'm starting A Conjuring of Light after I finish my current book – I'm so excited/nervous. I just need everything to be okay! Haha.
I hope so too. I am not halfway through and I am really hooked.
I've been a little unsure of whether I should pick up this book, but after reading your review I think I'm going to!
I bought this book a year or two ago, read about 50 pages and just kind of forgot about it. After reading your review, I think it's time to pick it back up!
|
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{"url":"http:\/\/www.chegg.com\/homework-help\/questions-and-answers\/unit-current-ampere-defined-terms-force-currents-two-10-meter-long-sections-long-wires-dis-q2369343","text":"The unit of current, the ampere, is defined in terms of the force between currents. If two 1.0-meter-long sections of very long wires a distance 1.0 m apart each carry a current of 1.0 A , what is the force between them? (If the force between two actual wires has this value, the current is defined to be exactly 1A .)\n\n### Get this answer with Chegg Study\n\nPractice with similar questions\nQ:\nItem 3 The unit of current, the ampere, is defined in terms of the force between currents. Two 1.0-meter-long sections of very long wires a distance 4.5 m apart each carry a current of 1.0 A. Part A What is the force between them? (If the force between two actual wires has this value, the current is defined to be exactly 1 A.)","date":"2016-07-24 11:01:22","metadata":"{\"extraction_info\": {\"found_math\": false, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8686673045158386, \"perplexity\": 674.1436683185042}, \"config\": {\"markdown_headings\": true, \"markdown_code\": false, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2016-30\/segments\/1469257823996.40\/warc\/CC-MAIN-20160723071023-00297-ip-10-185-27-174.ec2.internal.warc.gz\"}"}
| null | null |
{"url":"https:\/\/pressbooks.community\/t\/modular-latex-render-options\/38","text":"# Modular LaTeX Render Options\n\nI\u2019ve started a PR (#583), that exhibits the hacks we currently use at Lumen that adds a few more latex renderer options. It seems like it is similar-ish to the filter hooks used in import. Any thoughts? I\u2019ll look at it further, but some of the script tag stuff seems a little messy and like maybe there\u2019d be a better way to deal with that.\n\nYes, I think we can definitely streamline the script tag components. I\u2019d also like to diff PB-LaTeX and the current version of WP LaTex. My understanding (@brad, please correct me if I\u2019m wrong) is that PB-LaTeX is a fork of an earlier version that removes support for self-hosted LaTeX instances, but there may be some changes in the current version that are worth incorporating.\n\nyes, v1.8 I believe. I don\u2019t remember exactly what I stripped out but there were a bunch of latex rendering services. In order to get the export routine to work I had to choose one. https:\/\/github.com\/pressbooks\/pressbooks\/blob\/dev\/includes\/modules\/export\/epub\/class-pb-epub201.php#L1792\n\n1 Like\n\nAlright, the current PR is ready for review here.\n\nAnd here is our plugin\u2019s changes that utilize the hooks to pull in MathJax and Katex here.\n\n1 Like\n\nMerged! Thanks for your work on this.\n\nWow awesome! No problem ned.\n\nDo you think you can make your alternative renderers available as a small standalone plugin soon?\n\nYeah i think i can do that. The MathJax renderer we can do anyway. The other one\u2019s aren\u2019t really setup for public consumption. I\u2019ll see what I can come up with.\n\n1 Like\n\n@ned, what would you prefer the standalone plugin be named? taking suggestions.\n\nwe call our internal plugins candela-*name-here*. or we could just call it pressbooks-latex or pressbooks-mathjax.\n\n\u00af_(\u30c4)_\/\u00af\n\nI\u2019m in favour of pressbooks-mathjax just to avoid confusion between that and @brad\u2019s original pb-latex.\n\n1 Like\n\nHere\u2019s what I came up with @ned! It\u2019s tested and seems to work as expected on my local instances.\n\nhttps:\/\/github.com\/lumenlearning\/pressbooks-mathjax\n\n1 Like","date":"2022-05-26 12:14:38","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.7386892437934875, \"perplexity\": 1917.7707318925702}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2022-21\/segments\/1652662604794.68\/warc\/CC-MAIN-20220526100301-20220526130301-00759.warc.gz\"}"}
| null | null |
Q: How to verify if my network is under a man-in-the-middle attack? What happened?
When I tried to pull from one of my repos, I got the following error:
@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
@ WARNING: REMOTE HOST IDENTIFICATION HAS CHANGED! @
@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
IT IS POSSIBLE THAT SOMEONE IS DOING SOMETHING NASTY!
Someone could be eavesdropping on you right now (man-in-the-middle attack)!
It is also possible that the RSA host key has just been changed.
The fingerprint for the RSA key sent by the remote host is
SHA256:JusGXNrzFuQBPkLWthJ5pPjJQckIUe25VS0i1CMoszk.
Please contact your system administrator.
Add correct host key in /home/user/.ssh/known_hosts to get rid of this message.
Offending key in /home/user/.ssh/known_hosts:1
RSA host key for ras.mydomain.com has changed and you have requested strict checking.
Host key verification failed.
What I tried to do
*
*I did some googling, and they recommended to just remove the host and reconnect. I had my suspicions (better safe then sorry) but I went ahead carefully. ssh-keygen -R github.com removed github from known_hosts.
*Okay and now let's test the connection with ssh -T git@github.com, this was the answer:
The authenticity of host 'github.com (140.82.121.4)' can't be established.
ECDSA key fingerprint is SHA256:+QolW6mvi95EFAGeZpAjL2fOQ2rmB4uESAvNHE9IpFI.
Are you sure you want to continue connecting (yes/no/[fingerprint])?
And it seems like that the fingerprint is different than what is on their website. I might be overcomplicating this, and I don't have any company secrets in my repos, but at this point, I am curious if there is something I am missing, or if there is really something off with my network.
My conclusion
While finishing up this question it occurred to me to check out what happens if I use my cellular device to authenticate, and sure enough, running ssh -T git@github.com gave a different result.
The authenticity of host 'github.com (140.82.121.3)' can't be established.
RSA key fingerprint is SHA256:nThbg6kXUpJWGl7E1IGOCspRomTxdCARLviKw6E5SY8.
Are you sure you want to continue connecting (yes/no/[fingerprint])?
This time, I got the same fingerprint that is on the website, so to me it seems like this might indeed be a man in the middle attack. I have a home LAN with a NAS and some PCs. How should I proceed, how can I locate the man in the middle? Can there be any other explanation behind this?
Edit:
I found out what was the problem, but I still don't understand why it is happening. As I mentioned, I have a NAS that i use to back up my data from my laptop. I use SFTP to do this, and I am forwarding from port 22 on my router to the NAS. This is what caused this error, so I changed the port I use for backup.
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 1,156
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inline ULONG ref_count(IUnknown* unk) { ULONG r = unk->AddRef()-1; unk->Release(); return r; }
inline void ref_reference(IUnknown* unk) { unk->AddRef(); }
inline void ref_release(IUnknown* unk) { unk->Release(); }
#define oSAFE_RELEASE(p) do { if (p) { p->Release(); p = nullptr; } } while(false)
#define oSAFE_RELEASEV(p) do { if (p) { ((IUnknown*)p)->Release(); p = nullptr; } } while(false)
namespace ouro { namespace windows {
class scoped_handle
{
scoped_handle(scoped_handle&);
const scoped_handle& operator=(scoped_handle&);
public:
scoped_handle() : h(nullptr) {}
scoped_handle(HANDLE _Handle) : h(_Handle) { oVB(h != INVALID_HANDLE_VALUE); }
scoped_handle(scoped_handle&& _That) { operator=(std::move(_That)); }
const scoped_handle& operator=(scoped_handle&& _That)
{
if (this != &_That)
{
close();
h = _That.h;
_That.h = nullptr;
}
return *this;
}
const scoped_handle& operator=(HANDLE _That)
{
close();
h = _That;
}
~scoped_handle() { close(); }
operator HANDLE() { return h; }
private:
HANDLE h;
void close() { if (h && h != INVALID_HANDLE_VALUE) { ::CloseHandle(h); h = nullptr; } }
};
}}
// primarily intended for id classes
template<typename T> DWORD asdword(const T& _ID) { return *((DWORD*)&_ID); }
template<> inline DWORD asdword(const std::thread::id& _ID) { return *(DWORD*)&_ID; }
inline std::thread::id astid(DWORD _ID)
{
#if _MSC_VER >= oVS2015_VER
return *(std::thread::id*)&_ID;
#else
_Thrd_t tid;
ouro::windows::scoped_handle h(OpenThread(THREAD_QUERY_LIMITED_INFORMATION, FALSE, _ID));
tid._Hnd = h;
tid._Id = _ID;
return *(std::thread::id*)&tid;
#endif
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 3,288
|
Q: Change "Add To Homescreen" pop up title for PWA I am wondering: is there any way to change the default Add To Homescreen popup title?
I am not using the mini-bar banner that Chrome on Android has, because if the user accidentally dismisses it, the banner will not show again for 3 months.
Instead, I am listening to the beforeinstallprompt event and storing the prompt object in a variable. After that, I'm triggering the prompt when a button is clicked.
This works as intended and a popup is shown. But I would like to know if I can change the Add to Home Screen text to something custom?
Thank you!
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 6,073
|
{"url":"http:\/\/golem.ph.utexas.edu\/~distler\/blog\/archives\/000478.html","text":"December 1, 2004\n\nMTValidate is up to version 0.3, with some gratuitous dependencies removed and even more helpful error messages from the W3C.\n\nitex2MML is up to version 0.9. Only the binary changed, not the plugins for MovableType, WordPress or ecto. Particularly if you were having trouble using it with Markdown or Textile, you might want to check out the latest version. As usual, my distribution comes with the source code and a precompiled MacOSX binary. If James and Abiola are up to it, I\u2019ll post links to precompiled Linux and Windows binaries, when they\u2019re available.\n\nPosted by distler at December 1, 2004 12:09 AM\n\nTrackBack URL for this Entry:\u00a0\u00a0 http:\/\/golem.ph.utexas.edu\/cgi-bin\/MT-3.0\/dxy-tb.fcgi\/478\n\nHello, I have done some modfication on the wordpress itexToMML plugin to make sure that itex2MMl only convert the string between two [mathml] tags into MathML\nthe following code is my two cents:\n\nitexToMML ($text) { \/\/ customize this location$itex2MML = \u2018\/usr\/local\/bin\/itex2MML\u2019;\n\n$text = str_replace(\u201c\\r\\n\u201d, \u201c\\n\u201d,$text);\nif (ereg(\u201c^.+$mathml$.+$\u201d,$text)):\n$sptag = \u201c$mathml$\u201d;$mathmls = split($sptag,$text);\nglobal $text;$text = $mathmls[0]; for ($i = 1; $i array(\u2018pipe\u2019, \u2018r\u2019), 1 => array(\u2018pipe\u2019, \u2018w\u2019), 2 => array(\u2018pipe\u2019, \u2018w\u2019) );$itex_process = proc_open($itex2MML,$fspec, $pipes); if (is_resource($itex_process)) {\nfwrite($pipes[0],$mathmls[$i]); \/\/fwrite($pipes[0], $text); fclose($pipes[0]);\n\n$mathmls[$i] = \u201d;\nwhile (!feof($pipes[1])) {$mathmls[$i] .= fgets($pipes[1], 1024);\n}\nfclose($pipes[1]); fclose($pipes[2]);\nproc_close($itex_process);$mathmls[$i] = str_replace(\u201cnn\u201d, \u201cn\u201d,$mathmls[$i]);$text .= $mathmls[$i];\n$text .=$mathmls[$i+1]; } } endif; return$text;\n\n}\n\nPosted by: Gong Y. Liao on February 19, 2005 11:37 PM | Permalink | Reply to this\n\nThe line\n$mathmls[$i] = str_replace(\u201c\\n\\n\u201d, \u201c\\n\u201d, $mathmls[$i]);\nis used for avoiding the bug of the markdown plugin that can\u2019t handle correctly tags\ninserted in a paragraph and that contain an empty line.\n\nPosted by: Gong Y. Liao on February 19, 2005 11:51 PM | Permalink | Reply to this\n\nWordPress modifications\n\nAre you using my latest release of itex2MML? Only rather old versions produce blank lines that could screw up Markdown.\n\nIndeed, the current version of Markdown (distributed with WordPress 1.5) requires no modifications at all, in order to work with my itexToMML plugin.\n\nThe Texturize filter has some real problems, though, and that has delayed my releasing a new version to go with WordPress 1.5.\n\nI\u2019m also unclear why, in a entry which had, say, 20 equations in it, you would want to spawn 20 processes (with bidirectional pipes) to process it, when you could process the entire post with a single itex2MML instance.\n\nPosted by: Jacques Distler on February 20, 2005 12:09 AM | Permalink | PGP Sig | Reply to this\n\nRe: WordPress modifications\n\nOh, sorry, my bargain English made some misunderstandings\nthe block [mathml] [mathml] can be used as:\n[mathml] 3 itex blocks [mathml] or [mathml] 1 itex block[mathml] + [mathml]2 itex block[mathml]\n\nthe orignal intention to make the modifcation ( may be i should use other words, 150 is my tofel best) is to avoid the situation that the itex2mml plugin may conflict with other plugins like http:\/\/scott.yang.id.au\/2004\/05\/syntax-hilight-enscript\/\nso, in the situation that a post with (top to down )1 itex block + 1 c++ code block + 1 perl code block + 2 itex block + 1 matlab code block + plain text block, if the post regarded as a single string, and the plugins may influence the blocks that have no matter of itex or something else.\n\nAnd the last update of itex2MML binary makes the line to strip the \u201c\\n\\n\u201d is not needed any more.\n\nThanx for your patient on my bargain English and your great works for web-based publishing.\n\nPosted by: Gong Y. Liao on February 20, 2005 12:48 AM | Permalink | Reply to this\n\nPlugin compatibility\n\nThanx for your patient on my bargain English and your great works for web-based publishing.\n\nNo apologies necessary. Your English is much better than my Chinese.\n\nThe orignal intention to make the modifcation ( may be i should use other words, 150 is my tofel best) is to avoid the situation that the itex2mml plugin may conflict with other plugins\n\nI see. In an ideal world, the itexToMML plugin would always execute first and other plugins would be written to ignore all content between $...$.\n\nJohn Gruber, the author of Markdown, was very happy to incorporate the small changes to Markdown to make it work well with itex2MML. I think most plugin authors would be willing to do the same with their plugins.\n\nIn the particular case of Scott Yang\u2019s plugin, I don\u2019t see where the conflict is. His plugin only acts on blocks of the form\n\n<pre lang=\"..\">...<\/pre>\n\nI would not expect there to be MathML in those blocks.\n\nThe only thing you might have to worry about is the appearance of \u201c$\u201d in your text. That character is special to itex2MML. If you are displaying , say, Perl code, you\u2019d have write \u201c$\u201d instead of \u201c$\u201d, to prevent itex2MML from thinking you want to start an equation.\n\nMovableType is nicer, in that way, as you can decide on a post-by-post (and comment-by-comment) basis whether to apply itex2MML filtering.\n\nPosted by: Jacques Distler on February 20, 2005 1:22 AM | Permalink | PGP Sig | Reply to this","date":"2014-03-11 06:37:47","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 3, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.20711064338684082, \"perplexity\": 5130.675156013434}, \"config\": {\"markdown_headings\": false, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.3, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2014-10\/segments\/1394011143926\/warc\/CC-MAIN-20140305091903-00045-ip-10-183-142-35.ec2.internal.warc.gz\"}"}
| null | null |
Mario Traxl (born 30 May 1964) is an Austrian former cyclist. He won the Austrian National Road Race Championships in 1989 and 1994. He also rode in two events at the 1988 Summer Olympics.
References
External links
1964 births
Living people
Austrian male cyclists
People from Mödling District
Cyclists at the 1988 Summer Olympics
Olympic cyclists of Austria
Sportspeople from Lower Austria
|
{
"redpajama_set_name": "RedPajamaWikipedia"
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| 7,752
|
\section*{Introduction}
A data tree is an unranked ordered tree where each node carries a label from a
finite alphabet and a datum from some infinite domain. Together with the
special case of data words, they have been considered in the realm of program
verification, as they are suitable to model the behavior of concurrent,
communicating or timed systems, where data can represent \textit{e.g.}, process
identifiers or time stamps~\cite{Alur12AAA,BCGK12fossacs,Bouyer02ipl}. Data
trees are also a convenient model for XML documents~\cite{BojanczykMSS09jacm},
where data represent attribute values or text contents. Therefore finding
decidable logics for this model is a central problem as it has applications in
most reasoning tasks in databases and in verification.
Several logical formalisms and models of automata over data trees have been
proposed. Many of them were introduced in relation to \xpath, the standard
formalism to express properties of XML documents. Although satisfiability of
\xpath in the presence of data values is undecidable, automata models were
introduced for showing decidability of several
data-aware fragments~\cite{FS11,BojanczykMSS09jacm,Fig10,F09,JL08}.
As advocated in~\cite{BojanczykMSS09jacm}, the logic
\fotwo can be seen as a relevant fragment of \xpath.
Here \fotwo refers to the two-variable fragment of first
order logic over unranked ordered data trees, with predicates for the child and the next
sibling relations ($+1$), predicates for the descendant and following sibling
relations ($<$) and a predicate for testing data equality between two nodes ($\sim$).
Over data words, \fotwo was shown to be decidable by a reduction to Petri Nets or,
equivalently, Vector Addition Systems with States (\vass)~\cite{BDMSS11}.
It is also shown in~\cite{BojanczykMSS09jacm} that reachability for
Branching Vector Addition Systems with States, \bvass,
reduces to satisfiability of \fotwo over data trees.
The model of \bvass, extends \vass with a natural branching feature for running
on trees, see~\cite{acl10} for a survey of the various formalisms equivalent to
\bvass. As the reachability of \bvass is a long standing open problem, showing
decidability of finite satisfiability for \fotwo seems unlikely in the near future.
This paper is a continuation of the work of~\cite{BDMSS11,BojanczykMSS09jacm}.
We introduce a model of counter automata, denoted \ebvass, and show that
satisfiability of \fotwo is inter-reducible to reachability in \ebvass.
This model extends \bvass by allowing new features for merging counters.
In a \bvass the value of a counter at a node $x$ in a binary tree
is the sum of the values of that counter at the children of $x$,
plus or minus some constant specified by the transition relation.
In \ebvass constraints can be added modifying this behavior. In particular
(see Section \ref{sec-dad-counter} for a more precise definition) it can enforce the
following at node $x$:
one of the counters of its left child and one
of the counters of its right child are decreased by the same arbitrary number $n$,
then the sum is performed as for \bvass, and finally,
one of the resulting counters is increased by $n$.
The reduction from \fotwo to \ebvass goes via a new
model of data tree automata, denoted \dad.
Our first result (Section~\ref{sec-fotwo-dad}) shows that languages of data trees
definable in \fotwo are also recognizable by \dad.
Moreover the construction of the automaton from the formula is effective.
Our automata model is a non-trivial extension
from data words to data trees of the Data Automata (DA) model
of~\cite{BDMSS11}, chosen with care in order to be powerful enough to capture the logic
but also not too powerful in order to match its computational power.
The obvious extensions of DA to data trees are either too weak to capture \fotwo
or too expressive and undecidable (see Proposition~\ref{prop-undecid}).
Here we consider the strongest of these extensions, called $\wdad$,
which is undecidable,
and restrict it into a model called \dad
with an associated emptiness problem is equivalent to satisfiability of \fotwo.
Our second result (Section~\ref{sec-dad-counter}) shows that the emptiness
problem for \dad reduces to the reachability problem for \ebvass. Finally we
show in Section~\ref{sec-counter-fotwo} that the latter problem can be reduced
to the satisfiability of \fotwo, closing the loop. Altogether, this implies
that showing (un)decidability of any of these problems would show
(un)decidability of the three of them.
Although this question of (un)decidability remains open,
the equivalence shown in this paper between the decidability of these three problems,
the definition of the intermediate model \dad and the techniques used for proving
the interreductions provides
a better understanding of the three problems,
and in particular of the emptiness of the branching vector addition systems with states.
{\bf Related work.}
There are many other works introducing automata or logical formalism for data
words or data trees. Some of them are shown to be decidable using counter automata,
see for instance~\cite{DL-tocl08,JL08}. The link between counter automata and
data automata is not surprising as the latter
only compare data values via equality.
Hence they are invariant under permutation of the data domain and therefore,
often, it is enough
to count the number of data values satisfying some properties instead of
knowing their precise values.
\section{Preliminaries}\label{sec:prelim}
In this paper $\A$ or $\B$ denote finite alphabets while $\D$ denotes an infinite
data domain. We use $\E$ or $\F$ when we do not care whether the alphabet is
finite or not. We denote by $\E_\#$ the extension of an alphabet $\E$ with a new symbol $\#$
that does not occur in $\E$.
\paragraph{Unranked ordered data forests.}
We work with finite unranked ordered trees and forests over an alphabet~$\E$,
defined inductively as follows: for any $a \in \E$, $a$ is a tree. If
$\tree_1,\cdots,\tree_k$ is a finite non-empty sequence of trees then
$\tree_1 + \cdots + \tree_k$ is a forest. If $\stree$ is a forest and $a \in \E$, then
$a(\stree)$ is a tree. The set of trees and forests over $\E$ are respectively
denoted $\Trees(\E)$ and $\Forests(\E)$. A tree is called unary
(resp. binary) when every node has at most one (resp. two) children.
We use standard terminology for trees and forests defining nodes, roots,
leaves, parents, children, ancestors, descendants, following
and preceding siblings.
Given a forest $\tree \in \Forests(\E)$, and a node $x$ of $\tree$, we denote
by $\tree(x)$ the label of $x$ in $\tree$.
We say that two forests $\tree_1 \in \Forests(\E_1)$
and $\tree_2 \in \Forests(\E_2)$
\emph{have the same domain} if there is a bijection from the
nodes of $\tree_1$ to the nodes of $\tree_2$
that respects the parent and the next-sibling relations.
In this case we identify the nodes of $\tree_1$ with
the nodes of $\tree_2$ and the difference between $\tree_1$ and $\tree_2$ lies
only in the label associated to each node.
Given two forests $\tree_1 \in \Forests(\E_1)$,
$\tree_2 \in \Forests(\E_2)$ having the same domain,
we define $\tree_1 \otimes \tree_2 \in \Forests(\E_1\times\E_2)$
as the forest over the same domain
and such that for all nodes $x$,
$\tree_1 \otimes \tree_2 (x) = \langle \tree_1(x),\tree_2(x)\rangle$.
The set of \emph{data forests} over a finite alphabet $\A$
and an infinite data domain $\D$ is defined as $\Forests(\A {\times} \D)$.
Note that every
$\tree \in \Forests(\A {\times} \D)$
can be decomposed into
$\atree \in \Forests(\A)$
and $\dtree \in \Forests(\D)$ such that $\tree = \atree \otimes \dtree$.
\paragraph{Logics on data forests.}
A data forest of $\Forests(\A {\times} \D)$ can be seen as a relational model for
first order logic. The domain of the model is the set of nodes in the
forest. There is a unary relation $a(x)$ for all $a \in \A$ containing
the nodes of label $a$. There is a binary relation $x \dataeq y$ containing all
pairs of nodes carrying the same data value of $\D$,
and binary relations $\NS(x,y)$ ($y$ is the sibling immediately next to $x$),
$\PC(x,y)$ ($x$ is the parent of $y$), and $\SFS$, $\SAD$ which are the non
reflexive transitive closures respectively of $\NS$ and $\PC$, minus
respectively $\NS$ and $\PC$ (\textit{i.e.}, they define two or more navigation steps).
The reason for this non-standard definition of $\SFS$ and $\SAD$ is that it
will be convenient that equality, $\NS$, $\PC$, $\SFS$ and $\SAD$ are disjoint
binary relations. We will often make use of the macro, $x \parallel y$, and say
that $x$ and $y$ are \emph{incomparable}, when none of $x = y$, $\NS(x,y)$,
$\PC(x,y)$, $\SFS(x,y)$ and $\SAD(x,y)$ holds.
Let \fotwo be the set of first order sentences with two variables built on top
of the above predicates. Typical examples of properties definable in \fotwo are
key constraints (all nodes of label $a$ have different data values), $\forall x
\forall y ~a(x) \land a(y) \land x \sim y \ra x=y$, and downward inclusion
constraints (every node $x$ of label $a$ has a node $y$ of label $b$ in its
subtree with the same data value),
$\forall x \exists y ~a(x) \ra \bigl(b(y) \land x \sim y \land (\SAD(x,y) \lor \PC(x,y))\bigr)$.
We also consider the extension \emsotwo of \fotwo with existentially quantified
monadic second order variables. Every formula of \emsotwo has the form
$\exists R_1\ldots \exists R_n\; \phi$ where $\phi$ is a \fotwo formula called
the \emph{core}, involving the variables $R_1, \ldots, R_n$ as unary
predicates. The extension to full monadic second order logic is denoted
$\mso(<,+1,\dataeq)$.
We write $\mso(<,+1)$ for the set of formulas not using the $\sim$ predicates.
These formulas are ignoring the data values, \textit{i.e.},
they are classical monadic second-order formulas over forests.
\paragraph{Automata models for forests.}
We will informally refer to automata and transducers
for forests and unranked trees over a finite alphabet.
The particular choice of a model of automata is not relevant here
and we refer to~\cite[Chapters~1,6,8]{tata} for a detailed description.
A set of forests accepted by an automaton is called a \emph{regular language}
and regular languages are exactly those definable in $\mso(<,+1)$.
\paragraph{Automata models for data forests.}
Given a data forest $\tree = \btree \otimes \dtree \in \Forests(\B {\times} \D)$
and a data value $d \in \D$, the \emph{class forest}\label{def:class-forest}
$\tree[d]$ of $\tree$ associated to the datum $d$
is the forest of $\Forests(\B_\#)$ having the same domain as $\tree$
and such that $\tree[d](x)=\btree(x)$ if $\dtree(x)=d$ and $\tree[d](x)=\#$ otherwise.
\begin{figure}[h!]
\hspace{-8.7 cm}\begin{tikzpicture}
[level distance=7mm,
level 1/.style={sibling distance=28mm},
level 2/.style={sibling distance=9mm}]
\node {$(a,1)$}
child { node {$(b,1)$}
child { node {$(c,1)$} }
child { node {$(b,1)$} }
child { node {$(a,1)$} }
}
child { node {$(b,1)$}
child { node {$(a,2)$} }
child { node {$(b,2)$} }
child { node {$(a,1)$} }
};
\hspace{6cm}
\node {$a$} [level distance=7mm,
level 1/.style={sibling distance=15mm},
level 2/.style={sibling distance=5mm}]
child { node {$b$}
child { node {$c$} }
child { node {$b$} }
child { node {$a$} }
}
child { node {$b$}
child { node {$\#$} }
child { node {$\#$} }
child { node {$a$} }
};
\hspace{4cm}
\node {$\#$}[level distance=7mm,
level 1/.style={sibling distance=15mm},
level 2/.style={sibling distance=5mm}]
child { node {$\#$}
child { node {$\#$} }
child { node {$\#$} }
child { node {$\#$} }
}
child { node {$\#$}
child { node {$a$} }
child { node {$b$} }
child { node {$\#$} }
};
\end{tikzpicture}
\caption{A forest $\tree$ followed by its class forests
$\tree[1]$ and $\tree[2]$}
\label{fig-class-forest}
\end{figure}
\noindent We now define two models of automata over data trees. The first and most general
one is a straightforward generalization to forests of the automata model over
data words of~\cite{BDMSS11}. The second one adds a restriction in order to
avoid undecidability.
\paragraph{General Data Forest Automata model: \wdad.}
A \wdad is a pair $(\Aa,\Ba)$ where $\Aa$ is a non-deterministic
letter-to-letter transducer taking as input a forest in $\Forests(\A)$ and
returning a forest in $\Forests(\B)$ with the same domain, while $\Ba$ is a
forest automaton taking as input a forest in $\Forests(\B_\#)$. Intuitively a
\wdad works as follows on a forest $\tree=\atree\otimes\dtree$: first the
transducer $\Aa$ relabels the nodes of $\atree$ into $\btree$ and the forest
automaton $\Ba$ has to accept all class forests of~$\btree\otimes\dtree$.
More formally a data forest $\tree=\atree\otimes\dtree \in \Forests(\A\times\D)$
is accepted by $(\Aa,\Ba)$ iff
\begin{enumerate}
\item there exists $\btree \in \Forests(\B)$ such that
$\btree$ is a possible output of $\Aa$ on $\atree$ and,
\item for all $d\in\D$,
the class forest $(\btree\otimes\dtree)[d] \in \Forests(\B_\#)$ is accepted by $\Ba$.
\end{enumerate}
\noindent
Over data words this model was shown to be decidable~\cite{BDMSS11}.
Unfortunately it is undecidable over data trees.
\begin{proposition}\label{prop-undecid}
Emptiness of \wdad is undecidable.
\end{proposition}
\begin{proof}
We show that \wdad can simulate the Class Automata
of~\cite{BojanczykLasota10lics}. This latter model has an undecidable
emptiness problem, already when restricted to data words,
\textit{i.e.}, forests of the form $\langle a_{1}, d_1\rangle + \ldots + \langle a_{m}, d_m\rangle$.
It captures indeed the class of languages of words - without data - recognized by counter automata.
Like Data Automata, Class Automata are defined as pairs made of one transducer~$\Aa$ and one word automaton~$\Ba$.
However,
the $\Ba$ part in the Class Automata model has access to the label of the nodes that are not in the
class, while it sees only $\#$ in the Data Automata case.
This extra power implies undecidability.
\newcommand\classproj{\llbracket d \rrbracket}
\newcommand\classtreeprime{\tree'\classproj}
\newcommand\classword{\wtree\classproj}
We assume two finite alphabets $\A$ and $\B$, writing the latter
\textit{in extenso} as $\B = \{ b_1,\ldots, b_n \}$.
A \emph{class automaton} over
$\A \times \D$ is a pair $\Ca = (\Aa, \Ba)$ where $\Aa$ is a non-deterministic
letter-to-letter word transducer from $\A$ into $\B$ and $\Ba$ is a word
automaton taking as input words over the alphabet $\B \times \{ 0,1 \}$.
In order to define the acceptance of data words by class automata,
we shall use a notion of class word associated to a data word $\wtree = \btree\otimes\dtree$
and a value $d \in \D$, denoted $\classword$, defined as
the word having the same domain as $\wtree$
and such that, for every node $x$ of $\wtree$,
$\classword(x) = \langle \btree(x), 1\rangle$ if $\dtree(x) = d$
and
$\classword(x) = \langle \btree(x), 0\rangle$ otherwise.
A data word $\wtree = \atree\otimes\dtree$ is accepted by $\Ca$ iff
\begin{enumerate}
\item there exists a word $\btree$ over $\B$ such that
$\btree$ is a possible output of $\Aa$ on $\atree$ and,
\item for all $d\in\D$, the class word $(\btree\otimes \dtree)\classproj$
is accepted by $\Ba$.
\end{enumerate}
Given a class automaton $\Ca= (\Aa, \Ba)$ over $\A\times\D$, we construct a \wdad $\Ca'$ such that $\Ca$
accepts a data word iff $\Ca'$ accepts a data tree.
The idea of the reduction is that we replace each letter $b_i$ by a tree of
depth $i$. Hence, even if $b_i$ is replaced by $\#$ during the run of $\Ca'$ (conversion to class word),
this label can still be recovered.
Let $\mathbb{O}$ be a new alphabet containing the two symbols $b$ and $\#$.
For any symbol $s$ and $1 \leq i \leq n$, let $s^i$ be the unary data tree of depth $i$
defined recursively by: $s^1 = s$ and $s^{i+1} = s(s^i)$.
We associate to a data word $\wtree = \langle b_{i_1}, d_1\rangle + \ldots +
\langle b_{i_m}, d_m\rangle$ a data forest
$\hat{\wtree} \in \Forests(\mathbb{O} \times \D)$ defined by
$\hat{\wtree} = \bigl(\langle b,d_1\rangle^{i_1+1} + \ldots + \langle b, d_m\rangle^{i_m+1}\bigr)$.
From the word automaton $\Ba$ we can construct a forest automaton $\Ba'$ accepting exactly the set of
class forests $\hat{\wtree}[d]$ such that $\wtree\classproj$ is accepted by
$\Ba$, for all $d\in\D$.
The best way to see this is to use $\mso(<,+1)$ logic. The language recognized
by $\Ba$ can be defined by a formula $\varphi$ of $\mso(<,+1)$. The formula
corresponding to $\Ba'$ is constructed by replacing in $\varphi$ each atom of
the form $\langle b_i,1\rangle$ by $b_i(x)$ and each atom of the form $\langle
b_i,0\rangle$ by a formula testing that $x$ has label $\#$ and that the
subtree rooted at $x$ has depth $i$.
\medskip
From there it is now easy to construct an $\Aa'$ such that the \wdad $(\Aa',\Ba')$
accepts a data forest iff the class automaton $\Ca=(\Aa,\Ba)$ accepts a data word.
\end{proof}
\paragraph{Restricted Data Forest Automata model: \dad.}
The second data tree automata model we consider is defined as \wdad with a
restriction on $\Ba$. The restriction makes sure that $\Ba$ ignores repeated
and contiguous occurrences of $\#$ symbols. This ensures that for each class
forest $\tree[d]$, not only the automata cannot see the label of a node whose
data value is not $d$, but also can not see the shape of subtrees of nodes
whose data value differs from $d$. In particular it can no longer count the number
of $\#$ symbols in a subtree and the undecidability proof of
Proposition~\ref{prop-undecid} no longer works.
A set $L \subseteq \Forests(\B)$ is called $\#$-\emph{stuttering}
iff it is closed
under the rules depicted in Figure~\ref{fig-rules}.
Intuitively these rules should be understood as follows:
if a subforest is matched by a left-hand side of a rule
(when the variables $x$ and $y$
are replaced by (possibly empty) forests),
then replacing this subforest by the corresponding right-hand side
(with the same variable replacement)
yields a forest also in $L$,
and the other way round.
\begin{figure}[h!]
\footnotesize
\[\hspace{-8 pt}
\begin{array}{rclcrclcrclrclc}
\begin{minipage}[t]{10mm}
\vspace{-3.5mm}
\hspace{4mm}\begin{tikzpicture}
[level distance=7mm,
level 1/.style={sibling distance=10mm},
level 2/.style={sibling distance=5mm}]
\node {$\#$}
child { node {$\#$}
child { node {$x$} }
};
\end{tikzpicture}
\end{minipage}
&
\vspace{-0mm}\longleftrightarrow
&
\begin{minipage}[t]{5mm}
\vspace{-3.5mm}
\begin{tikzpicture}
[level distance=7mm,
level 1/.style={sibling distance=10mm},
level 2/.style={sibling distance=5mm}]
\node {$\#$}
child { node {$x$} };
\end{tikzpicture}
\end{minipage}
& ~~ &
\begin{minipage}[t]{5mm}
\vspace{-3.5mm}
\begin{tikzpicture}
[level distance=7mm,
level 1/.style={sibling distance=10mm},
level 2/.style={sibling distance=5mm}]
\node {$\#$}
child { node {$x$} };
\end{tikzpicture}
\end{minipage}
+ \; \#
&
\vspace{-0mm}\longleftrightarrow
&
\begin{minipage}[t]{5mm}
\vspace{-3.5mm}
\begin{tikzpicture}
[level distance=7mm,
level 1/.style={sibling distance=10mm},
level 2/.style={sibling distance=5mm}]
\node {$\#$}
child { node {$x$} };
\end{tikzpicture}
\end{minipage}
& \quad &
\# \; +
\begin{minipage}[t]{5mm}
\vspace{-3.5mm}
\begin{tikzpicture}
[level distance=7mm,
level 1/.style={sibling distance=10mm},
level 2/.style={sibling distance=5mm}]
\node {$\#$}
child { node {$x$} };
\end{tikzpicture}
\end{minipage}
&
\vspace{-0mm}\longleftrightarrow
&
\begin{minipage}[t]{5mm}
\vspace{-3.5mm}
\begin{tikzpicture}
[level distance=7mm,
level 1/.style={sibling distance=10mm},
level 2/.style={sibling distance=5mm}]
\node {$\#$}
child { node {$x$} };
\end{tikzpicture}
\end{minipage}
& \quad &
\begin{minipage}[t]{5mm}
\vspace{-3.5mm}
\begin{tikzpicture}
[level distance=7mm,
level 1/.style={sibling distance=10mm},
level 2/.style={sibling distance=5mm}]
\node {$\#$}
child { node {$x$} };
\end{tikzpicture}
\end{minipage}
+ y
&
\vspace{-0mm}\longleftrightarrow
&
y +
\begin{minipage}[t]{5mm}
\vspace{-3.5mm}
\begin{tikzpicture}
[level distance=7mm,
level 1/.style={sibling distance=10mm},
level 2/.style={sibling distance=5mm}]
\node {$\#$}
child { node {$x$} };
\end{tikzpicture}
\end{minipage}
\end{array}
\]
\caption{Closure rules for $\#$-stuttering sets. $x$ represents an arbitrary forest.}
\label{fig-rules}
\end{figure}
For instance if $L$ is $\#$-stuttering and contains the trees $\tree[1]$ and
$\tree[2]$ of Figure~\ref{fig-class-forest}, then it should also contain the
trees in Figure~\ref{fig-class-closure}.
\begin{figure}
\[
\begin{tikzpicture}[baseline]
\node {$a$} [level distance=7mm,
level 1/.style={sibling distance=15mm},
level 2/.style={sibling distance=5mm}]
child { node {$b$}
child { node {$c$} }
child { node {$b$} }
child { node {$a$} }
}
child { node {$b$}
child { node {$\#$} }
child { node {$a$} }
};
\end{tikzpicture}
\quad\!
\begin{tikzpicture}[baseline]
\node {$\#$}[level distance=7mm,
level 1/.style={sibling distance=15mm},
level 2/.style={sibling distance=5mm}]
child { node {$\#$}
child { node {$\#$} }
child { node {$\#$} }
}
child { node {$\#$}
child { node {$a$} }
child { node {$b$} }
child { node {$\#$} }
};
\end{tikzpicture}
\quad\!
\begin{tikzpicture}[baseline]
\node {$\#$}[level distance=7mm,
level 1/.style={sibling distance=15mm},
level 2/.style={sibling distance=5mm}]
child { node {$\#$}
child { node {$\#$} }
}
child { node {$\#$}
child { node {$a$} }
child { node {$b$} }
child { node {$\#$} }
};
\end{tikzpicture}
\quad\!
\begin{tikzpicture}[baseline]
\node {$\#$}[level distance=7mm,
level 1/.style={sibling distance=15mm},
level 2/.style={sibling distance=5mm}]
child { node {$\#$} }
child { node {$\#$}
child { node {$a$} }
child { node {$b$} }
child { node {$\#$} }
};
\end{tikzpicture}
\quad\!
\begin{tikzpicture}[baseline]
\node {$\#$}[level distance=7mm,
level 1/.style={sibling distance=15mm},
level 2/.style={sibling distance=5mm}]
child { node {$\#$}
child { node {$a$} }
child { node {$b$} }
child { node {$\#$} }
};
\end{tikzpicture}
\quad\!
\begin{tikzpicture}[baseline]
\node {$\#$}[level distance=7mm,
level 1/.style={sibling distance=5mm},
level 2/.style={sibling distance=5mm}]
child { node {$a$} }
child { node {$b$} }
child { node {$\#$} };
\end{tikzpicture}
\]
\caption{Closure of $\{ \tree[1], \tree[2] \}$ of Figure~\ref{fig-class-forest}.}
\label{fig-class-closure}
\end{figure}
\medskip Typical examples of $\#$-stuttering languages are those testing that
no two nodes of label $a$ occur in $\tree[d]$ (key constraint) or that each
node of label $a$ has a descendant of label $b$ in $\tree[d]$ (inclusion
constraint). Other typical $\#$-stuttering languages are those defined by
formulas of the form $\forall x \forall y\; a(x) \wedge b(y) \wedge x \dataeq y
\to \neg \SFS(x, y)$. Indeed the $\#$-stuttering rules do not affect the
relationship between pairs of nodes not labeled by~$\#$.
Typical examples of languages that are not $\#$-stuttering are
those counting the number of nodes of label~$\#$.
Note that $\#$-stuttering
languages are closed under union and intersection.
\medskip
We define \dad as those \wdad $(\Aa,\Ba)$ such that the language recognized by $\Ba$ is $\#$-stuttering.
\medskip
We conclude this section with the following simple lemma whose proof is a
straightforward Cartesian product construction. We use the term \emph{letter
projection} for a relabeling function defined as $h : \A' \to \A$, where $\A$
and $\A'$ are alphabets.
\begin{lemma} \label{lem:conjunction-disjunction}
The class of \dad languages is closed
under union, intersection and letter projection.
\end{lemma}
\section{From \texorpdfstring{\fotwo}{FO2} to \texorpdfstring{\dad}{DTA}}
\label{sec-fotwo-dad}
In this section we show the following result.
\begin{theorem}\label{th-fotwodad}
Given a formula $\phi$ in \fotwo, there exists a \dad,
effectively computable from $\phi$,
accepting exactly the set of data forests satisfying~$\phi$.
\end{theorem}
The proof works in two steps.
In the first step we provide a normal form for sentences of \fotwo
that is essentially an \emsotwo formula
whose core is a conjunction of simple formula of \fotwo.
In a second step,
we show that each of the conjunct can be translated into a \dad,
and we conclude using
composition of these automata by intersection,
see Lemma~\ref{lem:conjunction-disjunction}.
\subsection{Intermediate Normal Form} \label{app:normal-form}
We show first that every \fotwo formula $\phi$ can be transformed into an equivalent \emsotwo formula
in \emph{intermediate normal form}:
\begin{equation*}
\exists R_1\cdots \exists R_k \bigwedge_i \chi_i
\end{equation*}
where each $\chi_i$ has one of the following forms:
\begin{eqnarray}
& \forall x \forall y & \alpha(x) \wedge \beta(y) \wedge \delta(x, y) \to \gamma(x, y)
\label{eq:inf-fafa}\\
& \forall x \exists y & \alpha(x) \to (\beta(y) \wedge \delta(x, y) \wedge
\epsilon(x, y))
\label{eq:inf-faex}
\end{eqnarray}
where each of $\alpha$ and $\beta$ is a \emph{type},
that is, a conjunction of unary predicates or their negation
(these unary predicates are either from \A or from $R_1,\ldots,R_k$,
\textit{i.e.}, introduced by the existentially quantified variables),
$\delta(x, y)$ is either $x \dataeq y$ or $x \not\dataeq y$,
$\gamma(x, y)$ is one of
$\neg \SFS(x, y)$, $\neg \SAD(x, y)$
or $\neg (x \parallel y)$,
and
$\epsilon(x, y)$ is one of
$x = y$,
$\NS(x, y)$,
$\NS(y, x)$,
$\PC(x, y)$,
$\PC(y, x)$,
$\SFS(x, y)$,
$\SFS(y, x)$,
$\SAD(x, y)$,
$\SAD(y, x)$,
$x \parallel y$ or $\mathit{false}$.
This normal form is obtained by simple syntactical manipulation
similar to the one given in~\cite{BDMSS11} for the data words case, and detailed below.
\paragraph{\bf Scott normal form.}
We first transform the formula $\phi$ into Scott Normal Form
obtaining an \emsotwo formula of the form:
\[
\psi =
\exists R_1 \ldots \exists R_m\; \forall x \forall y\; \chi \wedge
\bigwedge_{i} \forall x \exists y\; \chi_i
\]
where $\chi$ and every $\chi_i$ are quantifier free,
and $R_1, \ldots R_m$ are new unary predicates (called monadic).
This transformation is standard:
a new unary predicate $R_\theta$ is introduced
for each subformula $\theta(x)$ with one free variable for marking the
nodes where the subformula holds. The subformula $\theta(x)$ is then
replaced by $R_\theta(x)$ and a conjunct
$\forall x \bigl(R_\theta(x) \leftrightarrow \theta(x)\bigr)$ is added.
This yields a formula in the desired normal form.
\paragraph{\bf From Scott to intermediate normal form.}
We show next that every conjunct of the core of the formula $\psi$ in Scott Normal Form
can be replaced by an equivalent conjunction of formulas of the
form~\eqref{eq:inf-fafa} or~\eqref{eq:inf-faex}, possibly by adding
new quantifications with unary predicates upfront.
\paragraph{\bf Case $\forall x \forall y\; \chi$.}
Recall that with our definition, the binary relations $\NS$, $\SFS$,
$\PC$, $\SAD$, $\parallel$ and $=$ are pairwise disjoint.
Hence we can rewrite $\forall x \forall y\; \chi$ into an equivalent \fotwo formula
in the following form,
\[
\forall x \forall y \left(\!%
\begin{array}{rrcl}
& x = y & \!\to\! & \psi_{=}(x,y)\\
\!\wedge\! & x \parallel y & \!\to\! & \psi_{\parallel}(x,y) \bigr)
\end{array}
\begin{array}{rrcl}
\!\wedge\! & \NS(x, y) & \!\to\! & \psi_{\!\to\!}(x,y)\\
\!\wedge\! & \PC(x, y) & \!\to\! & \psi_{\downarrow}(x,y)
\end{array}
\begin{array}{rrcl}
\!\wedge\! & \SFS(x, y) & \!\to\! & \psi_{\rightrightarrows}(x,y)\\
\!\wedge\! & \SAD(x, y) & \!\to\! & \psi_{\downdownarrows}(x,y)
\end{array}\!%
\right)
\]
where every subformula $\psi_*$ is quantifier free and only involves the predicate
$\dataeq$ together with unary predicates.
They can be obtained from $\chi$
via conjunctive normal form and De Morgan's law.
The resulting formula is equivalent to the conjunction
\[
\begin{array}{cll}
& \forall x \exists y & \bigl( x = y \wedge \psi_{=}(x,y)\bigl)\\
\wedge & \forall x \exists y &
\bigl( \neg\last(x) \to (\NS(x, y) \wedge \psi_{\to}(x,y)) \bigr)\\
\wedge & \forall x \exists y &
\bigl( \neg\leaf(x) \to (\PC(x, y) \wedge \psi_{\downarrow}(x,y)) \bigr)\\
\wedge & \forall x \forall y & \SFS(x, y) \to \psi_{\rightrightarrows}(x,y)\\
\wedge & \forall x \forall y & \SAD(x, y) \to \psi_{\downdownarrows}(x,y)\\
\wedge & \forall x \forall y & x \parallel y \to \psi_{\parallel}(x,y)\\
\end{array}
\]
where $\leaf(x)$ is a new predicate denoting the leaves of the forest and
$\last(x)$ is also a new predicate denoting nodes having no right sibling. The
predicate $\leaf$ is specified by the following formulas, that have the desired form.
\[
\begin{array}{ll}
\forall x \forall y & \PC(x,y) \land \leaf(x) \to \mathit{false}\\
\forall x \exists y & \lnot\leaf(x) \to \PC(x, y)
\end{array}
\]
Similar formulas specify the predicate $\last$.
\noindent
The first three conjuncts, with quantifier prefix $\forall x \exists y$, will be
treated later when dealing with the second case.
\noindent
For the next three conjuncts, putting $\neg\psi_{\rightrightarrows}$, $\neg \psi_{\downdownarrows}$,
$\neg\psi_{\parallel}$ in disjunctive normal form
(with an exponential blowup),
we rewrite $\psi_{\rightrightarrows}$, $\psi_{\downdownarrows}$,
$\psi_{\parallel}$ as a conjunction of formulas of the form $\neg(\alpha(x)
\wedge \beta(y) \wedge \delta(x,y))$,
where
$\alpha$, $\beta$, and $\delta$ are as in (\ref{eq:inf-fafa}).
By distribution of conjunction over implication, and by contraposition,
we obtain for the 3 cases an equivalent conjunction of formulas of the
following form (matching the desired form~\eqref{eq:inf-fafa})
\[
\begin{array}{ll}
\forall x \forall y &
\alpha(x) \wedge \beta(y) \wedge \delta(x,y) \to \neg \SFS(x, y)\\
\forall x \forall y &
\alpha(x) \wedge \beta(y) \wedge \delta(x,y) \to \neg \SAD(x, y)\\
\forall x \forall y &
\alpha(x) \wedge \beta(y) \wedge \delta(x,y) \to \neg (x \parallel y)\\
\end{array}
\]
\paragraph{\bf Case $\forall x \exists y\; \chi$.}
We first transform $\chi$ (with an exponential blowup)
into an equivalent disjunction of the form
\[
\chi' = \bigvee_j \alpha_j(x) \wedge \beta_j(y) \wedge \delta_j(x,y) \wedge \epsilon_j(x,y)
\]
where $\alpha_j$, $\beta_j$, $\delta_j$ and $\epsilon_j$
are as in (\ref{eq:inf-faex}).
Next, in order to eliminate the disjunctions, we add a new
monadic second-order variables $R_{\chi, j}$, that we existentially quantify
upfront of the global formula, and transform $\forall x \exists
y\; \chi'$ into the conjunction
\[
\bigwedge_j
\forall x \exists y\; (\alpha_j(x) \wedge R_{\chi, j}(x)) \to (\beta_j(y) \wedge \delta_j(x,y) \wedge \epsilon_j(x,y))
\wedge
\forall x \exists y\; \bigl(\bigvee_j R_{\chi, j}(x)\bigr)
\]
The first conjuncts express that
if $R_{\chi, j}(x)$ holds, then there exists a node $y$
such that the corresponding conjunct of $\chi'$ holds,
and the last conjunct expresses that
for all node $x$, at least one of the $R_{\chi, j}(x)$ must hold and can be
rewritten as $\forall x \exists y\; \bigl(\bigwedge \lnot R_{\chi, j}(x) \to
\mathit{false}\bigr)$. Now all the conjuncts are as in \eqref{eq:inf-faex} and
we are done.
\subsection{Case analysis for constructing \texorpdfstring{\dad}{DTA} from intermediate normal forms}
We now show how to transform a formula in intermediate normal form into a \dad.
Let \A be the initial alphabet and let $\A'$ be the new alphabet formed
by combining letters of \A with the newly quantified unary predicates $R_1,\ldots, R_k$.
By closure of \dad under intersection and letter projection (Lemma~\ref{lem:conjunction-disjunction}),
it is enough to construct a \dad automaton for each simple formula of the form~\eqref{eq:inf-fafa}
or~\eqref{eq:inf-faex}, accepting the data forests in $\Forests(\A'\times \D)$ satisfying the formula.
We do a case analysis depending on the atoms involved in the formula of the
form~\eqref{eq:inf-fafa} or~\eqref{eq:inf-faex}.
For each case we construct a \dad $(\Aa,\Ba)$
recognizing the set of data forests satisfying the formula.
The construction borrows several ideas from the data word case~\cite{BDMSS11}, but
some extra work is needed as the tree structure is more complicated.
In the discussion below, a node whose label satisfies the type $\alpha$ will
be called an \emph{$\alpha$-node}.
Many of the cases build on generic constructions that we described
in the following remark.
\begin{remark}\label{remark-color-class}
A \dad $(\Aa,\Ba)$ can be used to distinguish one
specific data value, by recoloring, with $\Aa$, all the nodes carrying the
data value, and checking, with $\Ba$, the correctness of the recoloring. We
will then say that $(\Aa,\Ba)$ \emph{marks a data value using the new color
$c$}. This can be done as follows. The transducer $\Aa$ marks
(i.e. relabel the node by adding to its current label an extra color) a node $x$ with
this data value with a specific new color $c'$. At the same time it guesses
all the nodes sharing the same data value as $x$ and marks each of them with
a new color $c$. Then, the forest automaton $\Ba$ checks, for every data
value, that either none of the nodes are marked with $c$ or $c'$, or that all
nodes not labeled with $\#$ are marked with $c$ or $c'$ and that $c'$ occurs
exactly once in the same class forest. Note that this defines a
$\#$-stuttering language. It is now clear that for the run to be accepting,
$\Aa$ must color exactly one data value and that all the nodes carrying this
data value must be marked with $c$ or $c'$. The transducer $\Aa$ can then
build on this fact for checking other properties.
\end{remark}
\noindent
A generic example of the usefulness of this remark is given below.
Once an arbitrary data value is marked with a color $c$,
then a property of the form
$\forall x \forall y\; \alpha(x) \wedge \beta(y) \wedge x \not\dataeq y \to \gamma(x, y)$
is a conjunction of
$\forall x \forall y\; \alpha(x) \land c(x) \wedge \beta(y) \wedge \lnot c(y) \to \gamma(x,y)$
with
$\forall x \forall y\; \alpha(x) \land \lnot c(x) \wedge \beta(y) \wedge x \not\dataeq y
\to \gamma(x, y)$.
The first part,
$\forall x \forall y\; \alpha(x) \land c(x) \wedge \beta(y) \wedge \lnot c(y)
\to \gamma(x, y)$
is now a regular property and can therefore be tested by $\Aa$.
Hence it is enough to consider the case where $x$ does not carry the marked data value.
The same reasoning holds if two data values are marked or if the formula starts with a
$\forall x \exists y$ quantification.
We will use this fact implicitly in the case analysis below.
Given a data forest, a \emph{vertical path} is a set of nodes containing exactly
one leaf and all its ancestors and nothing else. A \emph{horizontal path} is a
set of nodes containing one node together with all its siblings and nothing else.
\medskip\noindent
We start with formulas of the form~\eqref{eq:inf-fafa}.
\paragraph{\bf Case 1:}
$\forall x \forall y\; \alpha(x) \wedge \beta(y) \wedge x \dataeq y \to \gamma(x, y)$,
where $\gamma(x, y)$ is as in (\ref{eq:inf-fafa}).
These formulas express a property of pairs of nodes with the same data value.
We have seen that those are $\#$-stuttering languages that can be tested
by the forest automaton $\Ba$ solely (\textit{i.e.}, by a \dad with $\Aa$ doing
nothing).
\paragraph{\bf Case 2:}
$\forall x \forall y\; \alpha(x) \wedge \beta(y)
\wedge x \not\dataeq y \to \neg \SFS(x, y)$.
This formula expresses that a data forest cannot contain
an $\alpha$-node having a $\beta$-node with a different data value
as a sibling to its right, except if it is the next-sibling.
Let $X$ be an horizontal path in a data forest $\tree$ containing at least one
$\alpha$-node, and let $x$ be the leftmost $\alpha$-node in $X$.
Let $d$ be the data value of $x$.
Consider an $\alpha$-node $x'$ and a $\beta$-node $y'$ that make the formula
false within $X$, in particular we have $\SFS(x',y')$. Then, if $y'$ has a data
value different from $d$ we already have $\SFS(x,y')$ and the formula is
also false for the pair $(x,y')$.
Hence the validity of the formula within $X$ can be tested over pairs $(x',y')$ such that
either $x'$ or $y'$ has data value $d$.
\noindent
With this discussion in mind we construct $(\Aa,\Ba)$ as follows. In every horizontal path $X$
containing one $\alpha$-node, the transducer $\Aa$ identify the leftmost
occurrence $x$ of an $\alpha$-node in $X$, and marks it with a new color $c'$,
and marks all the nodes of $X$ with the same data value as $x$ with a color $c$.
As in Remark~\ref{remark-color-class}, the forest automaton $\Ba$ checks that the
guesses are correct, \textit{i.e.} it accepts only forests in which every horizontal
path $X$ satisfy one of the following conditions:
$X$ contains one occurrence of the color $c'$
and all other nodes of $X$ not labeled with $\#$ are marked with $c$,
or $X$ contains none of the colors $c$ and $c'$ at all.
All these properties define regular and $\#$-stuttering languages,
and hence can be checked by a forest automaton $\Ba$.
Assuming this, the transducer $\Aa$ rejects if there are some unmarked
$\beta$-nodes occurring as a right sibling (except for the next-sibling) of a
marked $\alpha$-node or there is an unmarked $\alpha$-node as
left sibling, except for the previous sibling, of a marked $\beta$-node.
As explained in Remark~\ref{remark-color-class}, this is a regular property.
\paragraph{\bf Case 3:}
$\forall x \forall y\; \alpha(x) \wedge \beta(y) \wedge x \not\dataeq y \to \neg \SAD(x, y)$.
The property expressed by this formula is similar to the previous case,
replacing the right sibling relationship with the descendant relationship.
Let $X$ be a vertical path in a data forest $\tree$ containing at least one
$\alpha$-node, and let $x$ be the $\alpha$-node in $X$ the closest to
the root. Let $d$ be the data value of $x$.
Consider an $\alpha$-node $x'$ and a $\beta$-node $y'$ that make the formula
false within $X$, in particular we have $\SAD(x',y')$. Then, if $y'$ has a data
value different from $d$ we already have $\SAD(x,y')$ and the formula is
also false for the pair $(x,y')$.
Hence the validity of the formula within $X$ can be tested over pairs $(x',y')$ such that
either $x'$ or $y'$ has data value $d$.
\noindent
The construction of $(\Aa,\Ba)$ is similar to the previous case, except that different
vertical paths may share some nodes.
The transducer $\Aa$ marks all the $\alpha$-nodes
that have no $\alpha$-node as ancestor, with a new color $c'$.
Then, for every node $x$ marked $c'$, $\Aa$ guesses all the
nodes inside the subtree rooted at $x$ having the same data value as
$x$ and mark them with a new color $c$.
As in Remark~\ref{remark-color-class}, the forest automaton $\Ba$ checks that the guesses of
colors are correct for each vertical path (see also the previous case).
Assuming this, the transducer $\Aa$ rejects if there are an unmarked
$\beta$-node that is a descendant, but not a child, of a
marked $\alpha$-node or there is an unmarked $\alpha$-node as
an ancestor, except for the parent, of a marked $\beta$-node.
This is a regular property that can be checked by $\Aa$ in conjunction with the marking,
following the principles of Remark~\ref{remark-color-class}.
\paragraph{\bf Case 4:}
$\forall x \forall y\; \alpha(x) \wedge \beta(y) \wedge x \not\dataeq y \to
\neg (x \parallel y)$.
The formula expresses that every two nodes of type respectively $\alpha$ and
$\beta$ and with different data values cannot be incomparable.
Recall that two nodes are incomparable if they are not ancestors and not siblings.
\paragraph{\bf Subcase 4.1:} There exist two $\alpha$-nodes that are incomparable.
Let $x_1$ and $x_2$ be two incomparable $\alpha$-nodes and let $z$
be their least common ancestor
(see Figure~\ref{fig:case41a}).
\input{fig41.tex}
We can choose $x_1$ and $x_2$ such that none of the
$\alpha$-nodes are incomparable with $z$ or sibling of~$z$, because if this was not
the case then there is an $\alpha$-node $x_3$ incomparable with $z$ or sibling of~$z$,
and therefore $x_3$ is incomparable with $x_1$, and we can replace $x_2$ with
$x_3$, continuing with their least common ancestor,
a node which is strictly higher than $z$.
Let $z_1$ and $z_2$ be the children of $z$
that are respectively ancestors of $x_1$ and $x_2$.
Note that by construction, $z_1\neq z_2$.
If $x_1=z_1$ and there is an $\alpha$-node $x_3$ in the subtree of $z$,
different from $x_1$ and incomparable with $z_2$,
then we replace $x_1$ by $x_3$ and proceed.
In other words we ensure that if $x_1 = z_1$
then there is no $\alpha$-node incomparable with $z_2$ in the subtree of $z$.
We proceed similarly
to enforce that if $x_2=z_2$ then there is no
$\alpha$-node incomparable with $z_1$ in the subtree of $z$.
Notice that we cannot have at the same time $x_1 = z_1$ and $x_2 = z_2$
because we assumed $x_1$ and $x_2$ to be incomparable.
All these properties can be specified in $\mso(<,+1)$ and therefore can be tested
by a forest automaton.
Let $d_1$ and $d_2$ be the respective data values of $x_1$ and $x_2$ (possibly $d_1=d_2$).
Consider now a $\beta$-node $y$ whose data value is neither $d_1$ nor $d_2$.
If $y$ is incomparable with $z$ or sibling of $z$, then the formula cannot be true as
it is contradicted by $(x_1,y)$. If $y$ is an ancestor of $z$ then, as no
$\alpha$-node is incomparable with $z$, none is incomparable with $y$.
Hence the formula can only be true with such $y$.
Assume now that $y$ is inside the subtree of~$z$.
If $y = z_1$ and $x_2 \neq z_2$, then the formula is contradicted by $(x_2, y)$.
If $y = z_1$ and $x_2 = z_2$, then, by hypothesis,
there is no $\alpha$-node incomparable with $y$ in the subtree of $z$,
and there is no $\alpha$-node incomparable with $y$ outside the subtree of $z$,
hence altogether, the formula holds for $y$.
If $y \neq z_1$ and $y$ is a descendant of $z_1$,
then the formula is contradicted by $(x_2, y)$.
The cases where $y$ is descendant of $z_2$ are symmetric:
in this case, the formula can only be true if $y = z_2$ and $x_1 = z_1$.
In the remaining cases $y$ is in the subtree of $z$ and not in the subtrees of
$z_1$ and $z_2$, making the formula false. Indeed, in each of these cases, either
$(x_1, y)$ or $(x_2, y)$ contradicts the formula.
To summarize, the only cases making the formula true
are when $y$ is an ancestor of $z$,
or $y = z_1 \wedge x_2 = z_2$,
or $y = z_2 \wedge x_1 = z_1$.
With this discussion in mind, this case can be solved as follows:
The transducer $\Aa$ guesses the nodes of $x_1$, $x_2$, $z_1$, $z_2$ and $z$
and checks that they satisfy the appropriate properties.
Moreover, $\Aa$ guesses whether $d_1=d_2$
and marks the data values of $x_1$ and $x_2$ accordingly
with one or two new colors.
The forest automaton $\Ba$ will then check that the data values are marked
appropriately as in Remark~\ref{remark-color-class}.
Moreover $\Aa$ checks that for all marked $\beta$-nodes there is no
$\alpha$-node incomparable with it and with a different data value, a regular
property as explained in Remark~\ref{remark-color-class}.
It now remains for $\Aa$ to check that every unmarked $\beta$-node~$y$ behaves
according to the discussion above:
$y$ is an ancestor of $z$ or $y = z_1$ and $x_2 = z_2$ or $y = z_2$ and $x_1 = z_1$.
This is a regular property testable by $\Aa$.
\paragraph{\bf Subcase 4.2:} There are no two incomparable $\alpha$-nodes.
Let $x$ be an $\alpha$-node such that no $\alpha$-node is a descendant of $x$.
By hypothesis, all $\alpha$-nodes are either ancestors or siblings of $x$.
Let $d$ be the data value of $x$.
We distinguish between several subcases depending on whether
there are other $\alpha$-nodes that are siblings of $x$ or not.
If there is an $\alpha$-node $x'$ that is a sibling of $x$, then let $d'$
be its data value (possibly $d=d'$). Consider
now a $\beta$-node $y$ whose data value is neither $d$ nor $d'$.
Then, in order to make the formula true, $y$ must be an ancestor or a sibling of $x$.
In this case, the transducer $\Aa$ guesses the nodes $x$ and $x'$ and marks the
corresponding data values with one or two new colors (according to whether $d = d'$
or not). The forest automaton $\Ba$ will then check that the data values are marked
correctly as explained in Remark~\ref{remark-color-class}.
For the marked $\beta$-nodes, the property expressed by the formula
is regular and can also be checked by $\Aa$.
It remains for $\Aa$ to check that every unmarked $\beta$-nodes is
either an ancestor of $x$ or a sibling of $x$.
Now, if there are no $\alpha$-nodes that are sibling of $x$,
and $y$ is a $\beta$-node whose data value is not $d$,
then in order to make the formal true, $y$ cannot be incomparable with $x$,
and therefore, $y$ can be an ancestor, a descendant or a sibling of $x$.
In this second case, the transducer $\Aa$ guesses the node $x$,
marks its data value using a new color.
The forest automaton $\Ba$ will then check that the data values were marked
correctly as explained in Remark~\ref{remark-color-class}.
The transducer $\Aa$ checks that all marked $\beta$-nodes make the formula true
(a regular property),
and that all unmarked $\beta$-nodes are not incomparable with $x$.
\medskip
We now turn to formulas of the form \eqref{eq:inf-faex}.
\paragraph{\bf Case 5:} $\forall x \exists y\; \alpha(x) \to (\beta(y) \wedge x \dataeq y
\wedge \epsilon(x, y))$, where $\epsilon(x, y)$ is as in \eqref{eq:inf-faex}.
These formulas express properties of nodes with the same data value.
Moreover they express a regular property over all $\tree[d]$.
Therefore can be treated by the forest automaton $\Ba$ as for the case 1.
\paragraph{\bf Case 6:}
$\forall x \exists y\; \alpha(x) \to (\beta(y) \wedge x \not\dataeq y \wedge \NS(x, y))$.
This formula expresses that every $\alpha$-node has a next sibling of type $\beta$
with a different data value.
The transducer $\Aa$ marks every $\alpha$-node $x$,
with a new color $c$ and checks that the next-sibling of $x$ is a $\beta$-node.
The forest automaton $\Ba$ accepts only the forests such that
for every node marked with $c$, its right sibling is labeled with~$\#$.
\paragraph{\bf Cases 7, 8, 9:}
The formulae of form
$\forall x \exists y\; \alpha(x) \to (\beta(y) \wedge x \not\dataeq y
\wedge \epsilon(x, y))$
where $\epsilon(x, y)$ is one of $\NS(y, x)$, $\PC(x, y)$, $\PC(y, x)$
are treated similarly.
\paragraph{\bf Case 10:}
$\forall x \exists y\; \alpha(x) \to (\beta(y) \wedge x \not\dataeq y \wedge \SFS(x, y))$.
This formula expresses that every $\alpha$-node
must have a $\beta$-node as a right sibling, but not as its next-sibling,
and with a different data value.
Let $X$ be an horizontal path. Let $y$ be the rightmost $\beta$-node of $X$
and $d$ be its data value.
Consider now an $\alpha$-node $x$ of $X$ with a data value different from $d$.
Then either $x$ is at the left of the previous-sibling of $y$,
and $y$ can serve as the desired witness,
or $x$ has no witness and the formula is false.
The transducer $\Aa$, for each horizontal path $X$ containing an
$\alpha$-node, marks its rightmost $\beta$-node $y$ with a new color $c'$,
guesses all the nodes of $X$ with the same data value as $y$ and marks them
with a new color $c$.
Then it checks that every unmarked $\alpha$-node of $X$
occurs at the left of the previous-sibling of $y$.
The forest automaton $\Ba$ checks that the guesses are correct
as in Remark~\ref{remark-color-class}:
for each horizontal paths, either all elements are marked with $c$ or $c'$, or none.
\paragraph{\bf Cases 11, 12, 13:}
The constructions for the formulae
$\forall x \exists y\; \alpha(x) \to (\beta(y) \wedge x \not\dataeq y
\wedge \epsilon(x, y))$
where $\epsilon(x, y)$ is one of $\SFS(y, x))$, $\SAD(x, y))$, and $\SAD(y, x))$
are similar.
\paragraph{\bf Case 14:}
$\forall x \exists y\; \alpha(x) \to (\beta(y) \wedge x \not\dataeq y \wedge x \parallel y)$.
This formula expresses that every $\alpha$-node
must have a incomparable $\beta$-node with a different data value.
\paragraph{\bf Subcase 14.1:}
There exist two $\beta$-nodes that are incomparable.
Let $y_1$ and $y_2$ be two incomparable $\beta$-nodes and let $z$ be their least
common ancestor. Using the same reasoning as in subcase 4.1, we can choose
$y_1$ and $y_2$ such that none of the $\beta$-nodes is incomparable with $z$ or a
sibling of $z$. Let $z_1$ and $z_2$ be the children of $z$ that are the
ancestors of $y_1$ and $y_2$ respectively. By construction, $z_1\neq z_2$.
Using the same trick as in subcase 4.1,
we can ensure that if $y_1 = z_1$ then there is no $\beta$-node
incomparable with $z_2$, and
if $y_2 = z_2$ then there is no $\beta$-node incomparable with $z_1$.
Moreover, we cannot have at the same time $y_1=z_1$ and $y_2=z_2$.
Recall that all these properties can be tested by a forest automaton.
Let $d_1$ and $d_2$ be the respective data values of $y_1$ and $y_2$ (possibly $d_1=d_2$).
Consider now an $\alpha$-node $x$ whose data value is neither $d_1$ nor $d_2$.
If $x$ is incomparable with $z$ or a sibling of $z$, then $y_1$ is a witness for $x$.
If $x$ is an ancestor of $z$ then by hypothesis there is no $\beta$-node incomparable
with $x$ and hence the formula is false.
Assume now that $x$ is in the subtree rooted at $z$.
If $x = z_1$ and $y_2 \neq z_2$, then $y_2$ is a $\beta$-node
incomparable with $x$ with a different data value, hence a witness for $x$ in the formula.
If $x = z_1$ and $y_2 = z_2$,
then by hypothesis, there is no $\beta$-node incomparable with $x$
in the subtree of $z$, and since there are neither $\beta$-nodes incomparable with $x$
outside the subtree of $z$, the formula must be false.
If $x \neq z_1$ and $x$ is a descendant of $z_1$,
then $y_2$ is a witness for $x$.
The cases where $x$ is a descendant of $z_2$ are symmetric.
In the remaining cases, $x$ is in the subtree of $z$
and not a descendant of $z_1$ or $z_2$.
In each of these cases, either $y_1$ or $y_2$ is a witness for $x$.
With this discussion in mind, this case can be solved as follows:
The transducer $\Aa$ guesses the nodes of $y_1$, $y_2$, $z_1$, $z_2$ and $z$
and checks that they satisfy the appropriate properties.
Moreover, $\Aa$ guesses whether $d_1=d_2$ and marks accordingly the data values
of $z_1$ and $z_2$ with one or two new colors.
The forest automaton $\Ba$ will then check that the data values are marked appropriately,
as in Remark~\ref{remark-color-class}.
Moreover $\Aa$ checks that for every marked $\alpha$-node,
there exists a $\beta$-node making the formula true.
It remains for $\Aa$ to check the three following properties:
no unmarked $\alpha$-node occurs above $z$,
if $y_1=z_1$ then $z_2$ is not an unmarked $\alpha$-node,
and if $y_2=z_2$ then $z_1$ is not an unmarked $\alpha$-node.
\paragraph{\bf Subcase 14.2:} There are no two $\beta$-nodes that are incomparable.
Let $y$ be an $\beta$-node such that no $\beta$-node is
a descendant of $y$. By hypothesis, all $\beta$-nodes are either ancestors
or siblings of $y$. Let $d$ be the data value of $y$.
We distinguish between several subcases depending on whether there are $\beta$-nodes
that are siblings of $y$ or not.
If there exists a $\beta$-node $y'$ that is a sibling of $y$,
let $d'$ be its data value (possibly $d = d'$).
Consider an $\alpha$-node $x$ whose data value is neither $d$ nor $d'$.
If $x$ is incomparable with $y$, then $y$ is a witness for $x$.
If $x$ is an ancestor or a sibling of $y$,
then the formula cannot be true, because by hypothesis
every $\beta$-node cannot be incomparable with $x$.
If $x$ is
a descendant of $y$, then $y'$ makes the formula true for that $x$.
Consider now the case where there are no $\beta$-node that are sibling of $y$.
Note that $y$ can have $\beta$-nodes among its ancestors.
Let $x$ be a $\alpha$-node that has data value different from $d$.
If $x$ is not incomparable with $y$ then the formula must be false.
Otherwise, $y$ is a witness for $x$.
The transducer $\Aa$ guesses the $\beta$-node $y$ and marks its data value using a new color.
Then it checks whether there is an $\beta$-node $y'$ that is a sibling of $y$.
If yes, it guesses whether the value at $y'$ is the same as the value at $y$ or not,
and marks the data value of $y'$ using a new color.
The forest automaton $\Ba$ will then check that the data values are marked appropriately.
For marked $\alpha$-nodes, $\Aa$ checks the regular property making the formula true.
It now remains for $\Aa$ to check, in both cases,
that every unmarked $\alpha$-node $x$
satisfy the appropriate condition described above,
\textit{i.e.},
that $x$ is incomparable with $y$ or a descendant of $y$
if there exists a sibling $y'$
and that $x$ is incomparable with $y$ otherwise.
\paragraph{\bf Case 15:}
$\forall x \exists y\; \alpha(x) \to \mathit{false}$.
It is sufficient to test with $\Aa$ that no $\alpha$-node is present in the forest.
\section{From \texorpdfstring{\dad}{DTA} to \texorpdfstring{\ebvass}{EBVASS}}\label{sec-dad-counter}
In this section we show that the emptiness problem of \dad can be reduced to
the reachability of a counter tree automata model that extends \bvass, denoted~\ebvass.
An \ebvass is a tree automaton equipped with counters. It runs on
binary trees over a finite alphabet. It can increase or decrease its
counters but cannot perform a zero test. For \bvass, when going up in the
tree, the new value of each counter is the sum of its values at the left and
right child. An \ebvass can change this behavior using simple arithmetical
constraints.
The general idea of the reduction is as follows.
\label{sketch:sec-dad-counter}
Let $(\Aa,\Ba)$ be a \dad.
We want to construct
an automaton that recognizes exactly the projections of the data forests
accepted by $(\Aa,\Ba)$. Because this automaton does not have access to the data
values, the main difficulty is to simulate the runs of $\Ba$ on all class
forests. We will use counters for this purpose. The automaton will maintain the
following invariant: At any node~$x$ of the forest, for each state~$q$ of
$\Ba$, we have a counter that stores the number of data values~$d$ such that
$\Ba$ is in state $q$ at $x$ when running on the class forest associated to
$d$. In order to maintain this invariant we make sure that the automata
model has the appropriate features for manipulating the counters. In
particular, moving up in the tree, in order to simulate $\Ba$,
the automaton has to decide which data value occurring
in the left subtree also appears in the right subtree.
At the current node, each data value is associated to a state of $\Ba$
and, by the invariant property, a counter. In order to maintain the invariant for data
values occurring in both subtrees, for each pair $q,q'$ of states of $\Ba$, the
automaton guesses a number~$n$ (the number of data values being at the same
time in state $q$ in the left subtree and in state $q'$ in the right subtree),
removes $n$ from both associated counters and adds $n$ to the counter
corresponding to the state resulting from the application of the transition function of
$\Ba$ on $(q,q')$. This preserves the invariant property and a BVASS cannot do it, so we explicitly add this feature to our model. Once we
have done this, the counters from both sides are added like a BVASS would do.
The $\#$-stuttering property of the language of $\Ba$ will ensure that this last operation
is consistent with the behavior of $\Ba$.
This is essentially what we do. But of course there are some nasty details. In
particular \dad run over unranked forests while \ebvass run over binary trees.
We start by defining the counter tree automata model and then we present
the reduction.
\subsection{Definition of \ebvass}
An \ebvass is a tuple $(Q,\A,q_0,k,\delta,\chi)$
where \A is a finite alphabet, $Q$ is a finite set of states, $q_0 \in Q$ is the initial
state, $k\in\N$ is the number of counters, $\chi$ is a finite set of constraints of
the form $\merc{i_1}{i_2}{i} $with $1\leq i_1,i_2,i\leq k$, and $\delta$ is the set of transitions which are
of two kinds: $\epsilon$-transitions (subset denoted $\delta_\epsilon$) and
up-transitions (subset denoted $\delta_\text{u}$).
An $\epsilon$-transition is an element of $(Q\times\A) \times (Q\times U)$
where $U=\set{I_i,D_i~:~1\leq i \leq k}$ is the set of possible counter
updates: $D_i$ stands for \emph{decrement counter $i$} and $I_i$ stands for
\emph{increment counter $i$}. We view each element of $U$ as a vector over
$\set{-1,0,1}^k$ with only one non-zero position.
An up-transition is an element of $(Q\times\A\times Q) \times Q$.
Informally, an $\epsilon$-transition may change the current state and increment
or decrement one of the counters. An up-transition depends on the label of the
current node and, when the current node is an inner node, on the states reached
at its left and right child. It defines a new state and the new value of each
counter is the sum of the values of the corresponding counters of the children.
Moreover, the behavior of up-transitions can be modified by the constraints
$\chi$. Informally a constraint of the form $\merc{i_1}{i_2}{i}$ modifies this
process as follows: before performing the addition of the counters,
two positive numbers
$n_1$ and $n_2$ are guessed
(possibly of value $0$), the counter $i_1$ of the left child and the counter
$i_2$ of the right child are decreased by $n_1$, the counter~$i_2$ of the left
child and the counter $i_1$ of the right child are decreased by~$n_2$ and, once
the addition of the counters has been executed, the counter~$i$ is increased by
$n_1 + n_2$. Note that $n_1$ and $n_2$ must be so that all intermediate values
remain positive. This is essentially what is explained in the sketch above
except that we cannot distinguish the left child from the right child. This
will be a property resulting from $\#$-stuttering languages when coding them into binary
trees.
We now make this more precise.
A \emph{configuration} of an \ebvass is a pair $(q,v)$ where $q\in Q$
and $v$ is a valuation of the counters, seen as a vector of $\N^k$.
The initial configuration is $(q_0,v_0)$ where $v_0$ is the function setting all counters to~$0$.
There is an $\epsilon$-\emph{transition} of label $a$ from $(q,v)$ to $(q',v')$ if
$(q,a,q',u) \in \delta_\epsilon$ and $v'=v+u$
(in particular this implies that $v+u\geq 0$).
We write $(q,v) \xrightarrow{a}_\epsilon (q',v')$, if $(q',v')$ can be reached from
$(q,v)$ via a finite sequence of $\epsilon$-transitions of label $a$.
Given a binary tree $\atree\in\Trees(\A)$, a \emph{run} $\rho$ of a \ebvass is a
function from nodes of $\atree$ to configurations verifying for all leaf $x$,
$\rho(x)=(q_0,v_0)$ and for all nodes $x,x_1,x_2$ of $\atree$ with $x_1$ and
$x_2$ the left and right child of $x$, and $\rho(x)=(q,v),
\rho(x_1)=(q_1,v_1), \rho(x_2)=(q_2,v_2)$ there exist $(q'_1,v'_1), (q'_2,v'_2)$
such that:
\begin{enumerate}
\item $(q_1,v_1) \xrightarrow{\atree(x_1)}_\epsilon (q'_1,v'_1)$,
$(q_2,v_2) \xrightarrow{\atree(x_2)}_\epsilon (q'_2,v'_2)$,
\item $(q'_1,\atree(x),q'_2,\; q) \in \delta_{\text{u}}$,
\item for each constraint $\theta \in \chi$ of the form $\merc{i_1}{i_2}{i}$
there are two numbers $n^1_\theta$ and $n^2_\theta$ (they may be $0$)
and vectors $u_{\theta,1},u_{\theta,2},u_\theta \in\N^k$, having
$n^1_\theta$ and $n^2_\theta$ at positions $i_1,i_2$ for $u_{\theta,1}$, having
$n^2_\theta$ and $n^1_\theta$ at positions $i_1,i_2$ for $u_{\theta,2}$,
$n^1_\theta+n^2_\theta$ at position $i$ for $u_\theta$
and all other positions set to zero,
\item \label{item:ebvass-decrement}
$v''_1 = v'_1 - \displaystyle\sum_{\theta\in\chi} u_{\theta,1} \geq 0$, and
$v''_2 = v'_2 - \displaystyle\sum_{\theta\in\chi} u_{\theta,2} \geq 0$, and
$v = v''_1 + v''_2+ \displaystyle\sum_{\theta\in\chi} u_\theta$.
\end{enumerate}
\noindent
We stress that it will be important for coding the automata into the logic
(Section~\ref{sec-counter-fotwo}) that $\chi$ is independent of the current state of the automaton.
Without the constraints of $\chi$ we have the usual notion of
\bvass~\cite{acl10}.
It does not seem possible in general to simulate directly a constraint
$\merc{i_1}{i_2}{i}$ with BVASS transitions. One could imagine using an
arbitrary number of $\epsilon$-transitions decreasing the counters $i_1$ and
$i_2$ while increasing counter $i$, after the merging operation summing up the
counters. However, it is not clear how to do this while preserving the
positiveness of the corresponding decrements before the merge
(Step~\ref{item:ebvass-decrement} above).
\medskip
\noindent
The \emph{reachability} problem for an \ebvass, on input $q\in Q$,
asks whether there is a tree and a run on that tree reaching
the configuration $(q,v_0)$ at its root.
\subsection{Reduction from \texorpdfstring{\dad}{DTA} to \texorpdfstring{\ebvass}{EBVASS}}
\begin{theorem}\label{prop-reduct}
The emptiness problem for \dad reduces to the reachability problem for
\ebvass.
\end{theorem}
\begin{proof}
We first take care of the binary trees versus unranked forest issue.
It is well known that forests of $\Forests(\E)$
can be transformed into binary trees in $\Trees(\E_\#)$
using the first-child/right-sibling encoding, denoted by $\fcns$,
and formally defined as follows (for $a \in \E$ and $\stree, \stree' \in \Forests(\E)$):
\[
\begin{array}{rcl}
\fcns(a) & = & a(\# + \#)\\
\fcns(a(\stree)) & = & a( \fcns(\stree) + \#)\\
\fcns(a + \stree) & = & a(\# + \fcns(\stree))\\
\fcns(a(\stree) + \stree') & = & a( \fcns(\stree) + \fcns(\stree')).
\end{array}
\]
This transformation effectively preserves regularity:
for each automaton $\Ba$ computing on $\Forests(\E)$
there exists an automaton $\Ba'$ on binary trees of $\Trees(\E_\#)$,
effectively computable from $\Ba$,
recognizing exactly the $\fcns$ encoding of the forests recognized by $\Ba$.
This automaton $\Ba'$ is called the $\fcns$ \emph{view} of~$\Ba$.
Note that we use the same $\#$ symbol in the \fcns construction and
for class forests. This simplifies the technical details of the proof. In
particular we can assume that our tree automata start with a single initial
state at the leaves of the tree.
\medskip
We show that given a \dad $\Da$, one can construct an \ebvass $\Ea$ with a
distinguished state $q$ such that for all $\atree \in \Forests(\A)$, there is
a run of $\Ea$ on $\fcns(\atree)$ reaching $(q, v_0)$ at its root iff
$\atree\otimes\dtree$ is accepted by $\Da$ for some~$\dtree$.
\medskip
Before explaining the construction of $\Ea$ we first show the consequences of
the fact that the second component of $\Da$
recognizes a $\#$-stuttering language on its \fcns view $\Ba$.
The \fcns view of the rules of Figure~\ref{fig-rules} are depicted in
Figure~\ref{fig-rules-fcns}: One obtains the same result by application of \fcns and then of a rule of Figure~\ref{fig-rules-fcns}
than by application of the corresponding rule of Figure~\ref{fig-rules} and then of \fcns.
This can be enforced using the following syntactic restrictions on the \fcns view $\Ba$ that will be useful in our proofs.
In the definition of these restrictions,
we use the notation $(p_1,b,p_2) \ra p$
for a transition of $\Ba$ from the states $p_1$, $p_2$
in the left and right child of a node of label $b$, moving up with state $p$.
We assume without loss of generality that the states of $\Ba$ permit to
distinguish the last symbol read by $\Ba$. More precisely, we assume that the
set of states of $\Ba$ is split into two kinds: the $\#$-states and the
non-$\#$-states. The states of the first kind are reached by $\Ba$ on nodes
labeled with symbol $\#$, while the states of the second kind are reached by
$\Ba$ on nodes with label in $\B$. We say that $\Ba$ is
\emph{$\#$-stuttering} if $\Ba$ is deterministic and has a specific $\#$-state
$p_\#$ that it must reach on all leaves of label $\#$, and verifies the
following properties:
\begin{enumerate}
\item if a transition rule of the form $(p_1, \#, p_\#) \to p_2$
is applied at a $\#$-node that is the left-child of another $\#$-node, then $p_1=p_2$
\item if a transition rule of the form $(p_\#, \#, p_1) \to p_2$ is applied at a $\#$-node that is the right-child of another $\#$-node, then $p_1=p_2$
\item all transition rules of the form $(p_\#, \#, p_1) \to p_2$ with $p_1$ a $\#$-state
verify $p_1=p_2$.
\item \label{it-commutativity}
all transition rules of the form $(p_1, \#, p_2) \to p$ are ``commutative'',
\textit{i.e.}, $(p_2, \#, p_1) \to p$ must then also be a rule.
\end{enumerate}
\begin{figure}
\small
\[
\begin{array}{rclcrclcrclrclc}
\begin{minipage}[t]{7mm}
\vspace{-4mm}
\begin{tikzpicture}
[level distance=7mm,
level 1/.style={sibling distance=8mm},
level 2/.style={sibling distance=5mm}]
\node {$\#$}
child { node {$\#$}
child { node {$x$} }
child { node {$\#$} }
}
child { node {$y$} };
\end{tikzpicture}
\end{minipage}
&
\vspace{-0mm}\,\,\,\,\,\,\,\longleftrightarrow
&
\begin{minipage}[t]{7mm}
\vspace{-3.5mm}
\begin{tikzpicture}
[level distance=7mm,
level 1/.style={sibling distance=4mm}]
\node {$\#$}
child { node {$x$} }
child { node {$y$} };
\end{tikzpicture}
\end{minipage}
& &
\begin{minipage}[t]{8mm}
\vspace{-3.5mm}
\begin{tikzpicture}
[level distance=7mm,
level 1/.style={sibling distance=7mm},
level 2/.style={sibling distance=4mm}]
\node {$\#$}
child { node {$x$} }
child { node {$\#$}
child { node {$\#$} }
child { node {$y$} }
};
\end{tikzpicture}
\end{minipage}
&
\vspace{-0mm}\,\,\,\longleftrightarrow
&
\begin{minipage}[t]{10mm}
\vspace{-3.5mm}
\begin{tikzpicture}
[level distance=7mm,
level 1/.style={sibling distance=5mm}]
\node {$\#$}
child { node {$x$} }
child { node {$y$} };
\end{tikzpicture}
\end{minipage}
& &
\begin{minipage}[t]{10mm}
\vspace{-3.5mm}
\begin{tikzpicture}
[level distance=7mm,
level 1/.style={sibling distance=8mm},
level 2/.style={sibling distance=5mm}]
\node {$\#$}
child { node {$\#$} }
child { node {$\#$}
child { node {$x$} }
child { node {$y$} }
};
\end{tikzpicture}
\end{minipage}
&
\vspace{-0mm}\,\,\longleftrightarrow
&
\begin{minipage}[t]{10mm}
\vspace{-3.5mm}
\begin{tikzpicture}
[level distance=7mm,
level 1/.style={sibling distance=5mm}]
\node {$\#$}
child { node {$x$} }
child { node {$y$} };
\end{tikzpicture}
\end{minipage}
& &
\begin{minipage}[t]{10mm}
\vspace{-3.5mm}
\begin{tikzpicture}
[level distance=7mm,
level 1/.style={sibling distance=8mm},
level 2/.style={sibling distance=5mm}]
\node {$\#$}
child { node {$x$} }
child { node {$y$}};
\end{tikzpicture}
\end{minipage}
&
\vspace{-0mm}\!\!\!\!\longleftrightarrow
&
\begin{minipage}[t]{10mm}
\vspace{-3.5mm}
\begin{tikzpicture}
[level distance=7mm,
level 1/.style={sibling distance=5mm}]
\node {$\#$}
child { node {$y$} }
child { node {$x$} };
\end{tikzpicture}
\end{minipage}
\end{array}
\]
\caption{\fcns view of the $\#$-stuttering closure rules. $x$ and $y$ are
arbitrary binary trees.}
\label{fig-rules-fcns}
\end{figure}
\noindent From these definitions, it is straightforward to see that
for a set $L \subseteq \Forests(\B)$, the following properties are equivalent
\begin{itemize}
\item $L$ is an $\#$-stuttering language,
\item $\fcns(L)$ is closed under the rules in Figure~\ref{fig-rules-fcns},
\item there exists an $\#$-stuttering automaton recognizing $\fcns(L)$.
\end{itemize}
\medskip
We now turn to the construction of $\Ea$.
Let $\Aa = (Q_\Aa, \A, \B, q^0_{\Aa}, F_\Aa, \Delta_\Aa)$
and $\Ba = (Q_\Ba, \B_\#, q^0_{\Ba}, F_\Ba, \Delta_\Ba)$
be the $\fcns$ views of the two components of $\Da$.
The automaton $\Ba$ is $\#$-stuttering (\textit{i.e.} there is a distinction in its
states between $\#$-states and non-$\#$-states, and the existence of a
$\#$-state $p_\# \in Q_\Ba$ on which $\Ba$ evaluates the tree with a single
node labeled with $\#$) and we also assume without loss of generality that it
is deterministic and complete, \textit{i.e.}, for every $\btree \in
\Trees(\B_\#)$, $\Ba$ evaluates into exactly one state of $Q_\Ba$.
Here $Q_\Aa$ and $Q_\Ba$ (resp. $F_\Aa$, $F_\Ba$) are the respective state sets
(resp. final state sets) of $\Aa$ and $\Ba$,
$\A$ is the input alphabet of $\Aa$,
$\B$ is the output alphabet of $\Aa$ and input alphabet of $\Ba$
(with the symbol~$\#$),
and $\Delta_\Aa$, $\Delta_\Ba$ are the sets of transitions.
We will use the notation
$(r_1, a, r_2,\; r, b)$,
for a transition of $\Aa$ from the states $r_1$, $r_2$ in the left and right child
of a node of label $a$, renaming this node with $b$ and moving up with state $r$.
In the following, we write explicitly the set of states of $\Ba$
as $Q_\Ba = \{ p_\#,p_1,\ldots,p_k \}$.
For any data tree $\tree\in\Trees(\B_\# \times\D)$, and any data value $d$ occurring in $\tree$,
the state of $Q_\Ba$ corresponding to the evaluation of $\Ba$ on the class forest $\tree[d]$
is called \emph{the $\Ba$-state associated to $d$ in $\tree$}.
When $d$ is the data value at the root of $\tree$,
this state is called the \emph{\rootstate{}} of $\tree$.
Note that for all $\tree$ the \rootstate{} of $\tree$ exists and is unique,
since $\Ba$ is assumed to be deterministic and complete,
and that it is always a non-$\#$-state.
We now construct the expected \ebvass $\Ea = (Q,\A,q_0,k,\delta,\chi)$
with $k = |Q_\Ba|-1$.
We set $Q = Q_\Aa \times Q_\Ba \times Q_0$,
where $Q_0$ is a finite set of auxiliary control states.
The initial state $q_0$ is the tuple formed with $q^0_{\Aa}$, the initial state of $\Aa$,
$q^0_{\Ba}$, the initial state of $\Ba$, and a specific state of $Q_0$.
The first and second components of a state $q\in Q$
are respectively called the $\Aa$-state and the
\rootstate of $q$.
The transitions of the \ebvass $\Ea$ are constructed in order to ensure
the following invariant:
\medskip
\noindent
\hspace{-1mm}$(\star)$%
\hspace{2mm}\parbox[t]{128mm}{$\Ea$ reaches the configuration $(q,v)$ at the
root of a tree $\atree \in \Trees(\A)$
iff there exists a data tree $\tree=\atree\otimes\dtree$
and a possible output $\btree \in \Trees(\B)$ of $\Aa$ on $\atree$
witnessed by a run of $\Aa$ whose state at the root of $\atree$ is the $\Aa$-state of~$q$,
and moreover for all $i$, $1 \leq i \leq k$,
$v_i$ is the number of data values having $p_i$ as associated $\Ba$-state
in $\btree\otimes\dtree$.}
\medskip
\noindent Note that the counters ignore the number of data values having $p_\#$ as associated $\Ba$-state
(which will always be infinite).
A consequence of $(\star)$
is that:
$(\diamond)$ there is only one non-$\#$-state $p_i \in Q_\Ba$ such that $v_i \neq 0$, and actually $v_i = 1$.
We will refer to this state $p_i$ as the \emph{\rootstate} of $v$,
and the construction of $\Ea$ will ensure that $p_i$ is also the \rootstate of $q$.
If we can achieve the invariant $(\star)$ then we are done.
Indeed, we can add to $\Ea$ some $\epsilon$-transitions which,
when reaching a state $q$ containing a final $\Aa$-state,
decrement the counters corresponding to final states of $\Ba$ (and only those).
Then, $\Ea$ reaches a configuration $(q,v_0)$ with the $\Aa$-state of $q$ being
a final state of $\Aa$ iff there exists a data tree accepted by~$\Da$.
Notice that the property $(\star)$ is invariant under permutations of $\D$.
Hence if a tree $\dtree$ witnesses the property $(\star)$, then any tree
$\dtree'$ constructed from $\dtree$ by permuting the data values is also a
witness for $(\star)$. This observation will be useful for showing the
correctness of the construction of $\Ea$.
Before defining the transition relation of $\Ea$ we sketch with more details its
construction.
The automaton $\Ea$ needs to maintain the invariant $(\star)$. One direction
will be immediate: if $\Da$ has an accepting run on $\atree\otimes\dtree$ then
$\Ea$ is constructed so that it has an accepting run on $\atree$ satisfying
$(\star)$ as witnessed by $\dtree$. For the converse direction, we need to
construct from a run of $\Ea$ on $\atree$ a tree $\dtree$ such that
$\Da$ has a run on $\atree \otimes \dtree$ as in $(\star)$.
The simulation of $\Aa$ is straightforward as $\Ea$ can simulate any regular
tree automaton. The simulation of $\Aa$ is done using the $\Aa$-state of the
states of $\Ea$: for every $\epsilon$-transition $(q,a,\; q',u)$ of $\Ea$, the
$\Aa$-states of $q$ and $q'$ must coincide, and for every up-transition
$(q_1, a, q_2,\; q)$ of $\Ea$, there exists a transition of $\Aa$ of the form
$(r_1, a, r_2,\; r, b)$, for some $b \in \B$ such that $r_1,r_2$ and $r$ are
the respective $\Aa$-states of $q_1$, $q_2$ and $q$. In other words, the
$\Aa$-state of $\Ea$ always is the state of $\Aa$ at the current node.
Let's now turn to the simulation of $\Ba$ and the invariant $(\star)$.
This invariant will be shown by induction in the depth of the tree.
Let us assume that $\Ea$ reached the configuration $(q,v)$
at the root $x$ of a tree $\atree$.
If $x$ is a leaf node, then by definition of \ebvass,
$q$ is the initial state $q_0$ of $\Ea$
and $v = v_0$,
hence $(\star)$ holds.
If $x$ is an inner node, then $\atree=a(\atree_1,\atree_2)$ for some letter
$a\in \A$. By induction on the depth, we have trees $\dtree_1$
and $\dtree_2$ such that there is a run of $\Da$ on $\atree_1\otimes\dtree_1$ and $\atree_2\otimes\dtree_2$ satisfying $(\star)$.
From the remark above on the invariance of $(\star)$ under permutations of $\D$,
we can assume that $\dtree_1$ and $\dtree_2$
do not share any data value.
We need to set the transitions of $\Ea$ such that from $\dtree_1$, $\dtree_2$,
we can construct a tree $\dtree$ such that $\Da$ also has
a run on $\atree\otimes\dtree$ as in ($\star$). The tree $\dtree$ will
be of the form $d(\dtree'_1,\dtree_2')$ for some $d\in \D$, where $\dtree'_1$
and $\dtree'_2$ are constructed from $\dtree_1$ and $\dtree_2$ by permuting
the data values. The permutation will identify some data values of $\dtree_1$
with some data values of $\dtree_2$. The number of data values we identify is
given by the $n$ in the constraints of $\Ea$ as explained in the initial
sketch on page~\pageref{sketch:sec-dad-counter}.
This $n$ is therefore given by the run of $\Ea$ and we will see that it does not
matter which data values we actually choose, it is only important that we pick
$n$ of them. The constraints make sure that this is consistent with the runs of $\Ba$.
For this purpose we define $\chi$ as the set of constraints of the form
$\merc{j_1}{j_2}{j}$ such that there exists a transition $(p_{j_1},\#, p_{j_2})
\to p_j$ of $\Ba$ where $p_{j_1}$, $p_{j_2}$, and $p_j$ are $\#$-states in
$Q_\Ba \setminus \{ p_\#\}$. Note that the commutativity rule in the
definition of $\#$-stuttering languages implies that whenever we have a
constraint $\merc{j_1}{j_2}{j}$ then both $(p_{j_1},\#, p_{j_2}) \to p_j$ and
$(p_{j_2},\#, p_{j_1}) \to p_j$ are transitions of $\Ba$.
This does maintain $(\star)$ assuming that $d$, the data value expected at $x$,
is not among the data values we identify (in the transitions used to construct
$\chi$ the root symbol is $\#$). This data value $d$ has to be treated
separately and we have several cases depending on whether $d$ is completely new
(does not occur in~$\dtree'_1$ and~$\dtree'_2$), or occurs in~$\dtree'_1$ but
not in~$\dtree'_2$, or the other way round, or it occurs in both subtrees. Actually it
will also be necessary to consider separately the cases where~$d$ occurs at the
root of~$\dtree_1'$ or~$\dtree'_2$.
This last choice is guessed by $\Ea$ and can therefore be read from the run
of $\Ea$. We can then choose $d$ consistently with the guess of $\Ea$. Again
the precise value of $d$ is not important. It is only important that its
equality type with the other data values is consistent with the choice made by
$\Ea$. This makes finitely many cases and we define the transition function of
$\Ea$ as the union of corresponding family of transitions. Each of them
involving disjoint intermediate states they don't interfere between each
other. We therefore define them separately and immediately after prove that they
do maintain $(\star)$ for their case.
\medskip
\paragraph{\bf 1.}
\emph{$\Ea$ guessed that the data value of the current node
is equal to the data value of both its children}.
\noindent
To handle this case, for each transition $\tau=(p_{i_1},b,p_{i_2}) \ra p_{i}$ of $\Ba$,
where none of $p_{i_1},p_{i_2},p_i$ are $\#$-states, $\Ea$ has the following transitions:
\begin{description}
\item[\rm $\epsilon$-transitions:] \quad\\
from a state $q_1$ of $\Ba$-state $p_{i_1}$
it decreases counter $i_1$
and moves to a state $q_\tau^1$\\
from a state $q_2$ of $\Ba$-state $p_{i_2}$
it decreases counter $i_2$
and moves to state $q_\tau^2$\\
from a state $q_\tau$
it increases counter $i$
and moves to a state $q$ of $\Ba$-state $p_i$
\item[\rm up-transition:]
$(q_\tau^1,a,q_\tau^2,q_\tau)$.
\end{description}
The state $q_\tau^1$ (resp. $q_\tau^2$, $q_\tau$)
differs from $q_1$ (resp. $q_2$, $q$)
only by its third component (in $Q_0$), that contains $\tau$.
We shall use the same convention for the states introduced in the
following construction cases.
\paragraph{\bf Correctness.}
Let us show that if $\Ea$ makes an up-transition $(q^1_\tau,a,q^2_\tau,q_\tau)$
at the root of $\atree \in \Trees(\A)$ we can construct $\dtree$ such that $\Da$
has a run on $\atree\otimes\dtree$ satisfying~$(\star)$.
This up-transition can only occur if we had $\epsilon$-transitions from $q_1$ to
$q_\tau^1$ in the left subtree and from $q_2$ to
$q_\tau^2$ in the right subtree where $p_{i_1}$ and $p_{i_2}$ are the
$\Ba$-states of $q_1$ and $q_2$.
Let $x$ be the root of the tree $\atree\otimes\dtree$ where this transition
occurred. We have $\atree = a(\atree_1,\atree_2)$.
By induction hypothesis we have trees
$\dtree_1$ and $\dtree_2$
and possible outputs $\btree_1, \btree_2 \in \Trees(\B)$ of $\Aa$
on respectively $\atree_1$ and $\atree_2$
such that there is a run of $\Da$ on
$\tree_1 = \atree_1\otimes\dtree_1$ and $\tree_2 = \atree_2\otimes\dtree_2$ satisfying~$(\star)$.
We first apply a bijection on the labels of $\dtree_1$ in order for the data
value of its root to match the one of the root of $\dtree_2$. Let $d$ be this
data value.
For each constraint $\theta=\merc{k_1}{k_2}{k} \in \chi$
we let $n^1_\theta$ and $n^2_\theta$ be the numbers used by the run of $\Ea$ when using
the above up-transition. By induction hypothesis $(\star)$, and semantics of the
constraints (making sure the counters are big enough) there are at least
$n^1_\theta$ (resp. $n^2_\theta$) distinct data values different from $d$
(because the up-transition is applied \emph{after} we decreased the counter $k_1$ by $n^1_\theta$)
in $\dtree_1$ having $p_{k_1}$ (resp. $p_{k_2}$) as associated
$\Ba$-state in $\tree_1 = \btree_1\otimes\dtree_1$,
and similarly for $\tree_2 = \btree_2\otimes\dtree_2$.
We pick such data values in each subtree
and call them the data values associated to $\theta$.
We do this for all constraints $\theta$
and we choose the associated data values such that they are all distinct.
We now apply to $\dtree_2$ a permutation on the data values
such that for all $\theta$ the data values associated to $\theta$ in $\dtree_2$
are identified with the ones for $\dtree_1$ and such that all other
data values are distinct. In order to simplify the notations we call the
resulting tree also $\dtree_2$. We then set $\dtree$ as $d(\dtree_1,\dtree_2)$
and $\tree'=\btree\otimes\dtree$ where $\btree = b(\btree_1, \btree_2)$
is an output of $\Aa$ on $\atree$ compatible with the transition.
Let $e$ be an arbitrary data value occurring in $\dtree$.
If $e = d$, the root symbol of the class forest $\tree'[e]$
is $a$ and the counter $i$ is increased by 1 by the last $\epsilon$-transition.
By induction hypothesis and its consequence $(\diamond)$,
$v_i = 1$ and for all other non-$\#$-states
the corresponding value via $v$ will be 0.
Hence $p_i$ is the new \rootstate of $v$.
It is also the \rootstate of $q$ by construction
If $e \neq d$ we consider 3 subcases.
If $e$ occurs in both $\dtree_1$ and $\dtree_2$
then the class forest $\tree'[e]$ has the form $\#(\stree_1,\stree_2)$
for some forests $\stree_1$ and $\stree_2$
containing each at least one symbol other than $\#$ (not at the root node).
Let $p_{j_1}$ and $p_{j_2}$ be the states reached by $\Ba$ when evaluating $\stree_1$ and $\stree_2$.
They are the $\Ba$-states associated to $e$ in $\tree'_1$ and $\tree'_2$,
(resp. the left- and right subtrees of $\tree'$),
and both are $\#$-states in $Q_\Ba \setminus \{ p_\# \}$.
By construction of $\dtree$, there are at least
$n_\theta=n_\theta^1+n_\theta^2$ such data values $e$,
where $\theta = \merc{j_1}{j_2}{j}$
and $p_j$ is the unique state of $\Ba$ such that
$(p_{j_1}, \#, p_{j_2}) \to p_{j}$ is a transition of $\Ba$ (and
therefore also $(p_{j_2}, \#, p_{j_1}) \to p_j$ is also a transition).
These $n_\theta$ data values will contribute to an increase of $v_j$
by $n_\theta$ as expected.
Assume now that $e$ occurs in $\dtree_1$ but not in $\dtree_2$ (the remaining
case being symmetrical). Then $\tree'[e]$ has the form $\#(\stree_1,\stree_2)$
where $\stree_1$ contains at least one symbol other than $\#$ (not at root node),
and all nodes of $\stree_2$ are labeled~$\#$.
By the hypothesis that $\Ba$ is $\#$-stuttering,
the $\Ba$-state associated to $e$ in $\tree'$ is the same as the one
associated to $e$ in $\tree'_1$,
and the $\Ba$-state associated to $e$ in $\tree'_2$ is $p_\#$.
This is consistent with the behavior of $\Ea$
that propagates upward the value of the counter corresponding to this state,
after applying the constraints.
Altogether this shows that $\tree = \atree\otimes\dtree$ verifies $(\star)$.
\tikzset{
itria/.style={
draw,shape border uses incircle,
isosceles triangle,shape border rotate=90,yshift=-0.7cm},
rtria/.style={
draw,dashed,shape border uses incircle,
isosceles triangle,isosceles triangle apex angle=90,
shape border rotate=-45,yshift=0.2cm,xshift=0.5cm},
ritria/.style={
draw,dashed,shape border uses incircle,
isosceles triangle,isosceles triangle apex angle=110,
shape border rotate=-55,yshift=0.1cm},
letria/.style={
draw,dashed,shape border uses incircle,
isosceles triangle,isosceles triangle apex angle=110,
shape border rotate=235,yshift=0.1cm}
}
\begin{figure}
\small
\[
\begin{array}{ccc}
\tree'=\btree\otimes\dtree =
\hspace{-8mm}
\begin{minipage}[t]{24mm}
\vspace{-3.5mm}
\begin{tikzpicture}
[level distance=7mm,
level 1/.style={sibling distance=12mm},
level 2/.style={sibling distance=4mm}]
\node {$(b, d)$}
child { node {$(b_1, d)$} { node[itria] {} } }
child { node {$(b_2, d)$} { node[itria] {} } };
\end{tikzpicture}
\end{minipage}
&
\tree'[d] =
\hspace{-8mm}
\begin{minipage}[t]{24mm}
\vspace{-3.5mm}
\begin{tikzpicture}
[level distance=7mm,
level 1/.style={sibling distance=12mm},
level 2/.style={sibling distance=4mm}]
\node {$b (p_i)$}
child { node {$b_1 (p_{i_1})$} { node[itria] {} } }
child { node {$b_2 (p_{i_2})$} { node[itria] {} } };
\end{tikzpicture}
\end{minipage}
\end{array}
\]
\caption{Proof of Theorem~\ref{prop-reduct}, Case 1.
The $\Ba$-states are displayed in parentheses in the class tree $\tree'[d]$.}
\label{fig-reduct1}
\end{figure}
\paragraph{\bf 2.} \emph{$\Ea$ guessed that the data value $d_1$ of
the current node is equal to the data value of its left child but different
from the data value $d_2$ of its right child.
Moreover $\Ea$ guessed that the $\Ba$-state associated to $d_1$ in the right
subtree is $p_{k_2}$, and that the data value $d_2$ of the right child
also appears in the left subtree, with $p_{k_1}$ as $\Ba$-state associated to $d_2$ in this left subtree.
Note that both $p_{k_1}$ and $p_{k_2}$ must be $\#$-states in $Q_\Ba \setminus \{ p_\#\}$.}
\noindent
To handle this case for all transitions $\tau=(p_{i_1},b,p_{k_2}) \ra p_{i}$
and $\tau'=(p_{k_1},\#,p_{i_2})\ra p_j$ of
$\Ba$, where none of $p_{i_1},p_{i_2}, p_i$ are $\#$-states but
$p_j$ (like $p_{k_1}$ and $p_{k_2}$) are $\#$-states,
$\Ea$ has the following transitions:
\begin{description}
\item[\rm $\epsilon$-transitions:] \quad\\
from a state $q_1$ of $\Ba$-state $p_{i_1}$
it decreases the counters $i_1$ and $k_1$
and moves to state $q_{\tau,\tau'}^1$\\
from a state $q_2$ of $\Ba$-state $p_{i_2}$
it decreases the counters $i_2$ and $k_2$
and moves to state $q_{\tau,\tau'}^2$\\
from a state $q_{\tau,\tau'}$
it increases counters $i$ and $j$
and moves to a state $q$ of $\Ba$-state $p_i$
\item[\rm up-transition:]
$(q_{\tau,\tau'}^1,a,q_{\tau,\tau'}^2,q_{\tau,\tau'})$.
\end{description}
\paragraph{\bf Correctness.}
We argue as in the previous case with the following modifications.
From $\dtree_1$ and $\dtree_2$ we first apply a bijection making sure that the
data values $d_1$ and $d_2$ of their roots are different and that $d_1$ has
$\Ba$-state $p_{k_2}$ in $\btree_2 \otimes \dtree_2$
and $d_2$ has $\Ba$-state $p_{k_1}$ in $\btree_1 \otimes \dtree_1$,
where $\atree = a(\atree_1,\atree_2)$ and
$\btree_1, \btree_2 \in \Trees(\B)$ are possible outputs of $\Aa$
on respectively $\atree_1$ and $\atree_2$ from the induction hypothesis.
For each $\theta \in \chi$ we select the associated data values making sure
they are neither $d_1$ nor $d_2$. The decrement in the $\epsilon$-transitions make sure
that this is always possible. We then perform the same identification as in the
previous case.
The same argument as above shows that the resulting tree $\dtree=d_1(\dtree_1,\dtree_2)$ has the desired properties.
\begin{figure}
\small
\[
\begin{array}{ccc}
\tree'=\btree\otimes\dtree =
\hspace{-8mm}
\begin{minipage}[t]{24mm}
\vspace{-3.5mm}
\begin{tikzpicture}
[level distance=7mm,
level 1/.style={sibling distance=12mm},
level 2/.style={sibling distance=4mm}]
\node {$(b, d_1)$}
child { node {$(b_1, d_1)$} { node[itria] {} } }
child { node {$(b_2, d_2)$} { node[itria] {} } };
\end{tikzpicture}
\end{minipage}
&
\tree'[d_1] =
\hspace{-8mm}
\begin{minipage}[t]{24mm}
\vspace{-3.5mm}
\begin{tikzpicture}
[level distance=7mm,
level 1/.style={sibling distance=12mm},
level 2/.style={sibling distance=4mm}]
\node {$b (p_i)$}
child { node {$b_1 (p_{i_1})$} { node[itria] {} } }
child { node {$\# (p_{k_2})$} { node[itria] {} } };
\end{tikzpicture}
\end{minipage}
&
\tree'[d_2] =
\hspace{-8mm}
\begin{minipage}[t]{24mm}
\vspace{-3.5mm}
\begin{tikzpicture}
[level distance=7mm,
level 1/.style={sibling distance=12mm},
level 2/.style={sibling distance=4mm}]
\node {$\# (p_j)$}
child { node {$\# (p_{k_1})$} { node[itria] {} } }
child { node {$b_2 (p_{i_2})$} { node[itria] {} } };
\end{tikzpicture}
\end{minipage}
\end{array}
\]
\caption{Proof of Theorem~\ref{prop-reduct}, Case 2.}
\label{fig-reduct2}
\end{figure}
\paragraph{\bf 3.}
\emph{$\Ea$ guessed that the data value $d_1$ of the
current node is equal to the data value of its left child but different
from the data value
of its right child.
Moreover $\Ea$ guessed that $d_1$ also appear in
the right subtree of the current node, with $p_{k_2}$ as associated $\Ba$-state in this right subtree,
and that the data value
of the right child of the current node does not appear in the left subtree.
Note that $p_{k_2}$ must be a $\#$-state in $Q_\Ba \setminus \{ p_\#\}$.}
\noindent
To handle this case for all transitions $\tau=(p_{i_1},b,p_{k_2}) \ra p_{i}$
and $\tau'=(p_{\#},\#,p_{i_2})\ra p_j$ of
$\Ba$, where none of $p_{i_1},p_{i_2}, p_i$ are $\#$-states but
$p_{k_2}$ and $p_j$ are $\#$-states,
$\Ea$ has the following transitions:
\begin{description}
\item[\rm $\epsilon$-transitions:] \quad\\
from a state $q_1$ of $\Ba$-state $p_{i_1}$
it decreases the counter $i_1$
and moves to state $q_{\tau,\tau'}^1$\\
from a state $q_2$ of $\Ba$-state $p_{i_2}$
it decreases the counter $i_2$
and $k_2$ and moves to state $q_{\tau,\tau'}^2$\\
from a state $q_{\tau,\tau'}$
it increases the counters $i$ and $j$
and moves to a state $q$ of $\Ba$-state $p_i$
\item[\rm up-transition:]
$(q_{\tau,\tau'}^1,a,q_{\tau,\tau'}^2,q_{\tau,\tau'})$.
\end{description}
\paragraph{\bf Correctness.}
We argue as in the previous cases with the following modifications.
From $\dtree_1$ and $\dtree_2$ we first apply a bijection making sure that the
data values $d_1$ and $d_2$ of their roots are different and that $d_1$ has
$\Ba$-state $p_{k_2}$ in $\btree_2 \otimes \dtree_2$
and $d_2$ does not appear in $\dtree_1$ ($\btree_2$ is as in previous cases).
For each $\theta \in \chi$ we select the associated data values making sure
they are neither $d_1$ nor $d_2$. The decrement in the $\epsilon$-transitions make sure
that this is always possible. We then perform the same identification as in the
previous case.
As before we show that the resulting tree $\dtree=d_1(\dtree_1,\dtree_2)$ has the desired properties.
\begin{figure}
\small
\[
\begin{array}{ccc}
\tree'=\btree\otimes\dtree =
\hspace{-8mm}
\begin{minipage}[t]{24mm}
\vspace{-3.5mm}
\begin{tikzpicture}
[level distance=7mm,
level 1/.style={sibling distance=12mm},
level 2/.style={sibling distance=4mm}]
\node {$(b, d_1)$}
child { node {$(b_1, d_1)$} { node[itria] {} } }
child { node {$(b_2, d_2)$} { node[itria] {} } };
\end{tikzpicture}
\end{minipage}
&
\tree'[d_1] =
\hspace{-8mm}
\begin{minipage}[t]{24mm}
\vspace{-3.5mm}
\begin{tikzpicture}
[level distance=7mm,
level 1/.style={sibling distance=12mm},
level 2/.style={sibling distance=4mm}]
\node {$b (p_i)$}
child { node {$b_1 (p_{i_1})$} { node[itria] {} } }
child { node {$\# (p_{k_2})$} { node[itria] {} } };
\end{tikzpicture}
\end{minipage}
&
\tree'[d_2] =
\hspace{-8mm}
\begin{minipage}[t]{24mm}
\vspace{-3.5mm}
\begin{tikzpicture}
[level distance=7mm,
level 1/.style={sibling distance=12mm},
level 2/.style={sibling distance=4mm}]
\node {$\# (p_j)$}
child { node {$\# (p_\#)$} }
child { node {$b_2 (p_{i_2})$} { node[itria] {} } };
\end{tikzpicture}
\end{minipage}
\end{array}
\]
\caption{Proof of Theorem~\ref{prop-reduct}, Case 3. The node without subtree in the class tree $\tree'[d_2]$ is a leaf.}
\label{fig-reduct3}
\end{figure}
\paragraph{\bf 4.}
\emph{$\Ea$ guessed that the data value $d$ of the
current node is different from the ones of its children but appear in both
subtrees, with $p_{k_1}$ and $p_{k_2}$ as associated $\Ba$-states repectively in left and right subtrees.
Moreover $\Ea$ guessed that the data values of both children of the current node
are equal.
Note that $p_{k_1}$ and $p_{k_2}$ must be \#-states in $Q_\Ba \setminus \{ p_\#\}$.}
\noindent
To handle this case for all transitions $\tau=(p_{k_1},b,p_{k_2}) \ra p_{i}$
and $\tau'=(p_{i_1},\#,p_{i_2})\ra p_j$ of
$\Ba$, where none of $p_{i_1},p_{i_2}, p_i$ are $\#$-states but
$p_{k_1},p_{k_2}$ and $p_j$ are $\#$-states, $\Ea$ has the following transitions:
\begin{description}
\item[\rm $\epsilon$-transitions:]\quad\\
from a state $q_1$ of $\Ba$-state $p_{i_1}$
it decreases the counters $i_1$ and $k_1$
and moves to state $q_{\tau,\tau'}^1$\\
from a state $q_2$ of $\Ba$-state $p_{i_2}$ it
decreases the counters $i_2$ and $k_2$
and moves to state $q_{\tau,\tau'}^2$\\
from a state $q_{\tau,\tau'}$
it increases the counters $i$ and $j$
and moves to a state $q$ of $\Ba$-state $p_i$
\item[\rm up-transition:]
$(q_{\tau,\tau'}^1,a,q_{\tau,\tau'}^2,q_{\tau,\tau'})$.
\end{description}
\paragraph{\bf Correctness.}
We argue as in the previous cases with the following modifications.
From $\dtree_1$ and $\dtree_2$ we first apply a bijection making sure that the
data value $d_1$ of their roots are equal and that $\dtree_1$ and $\dtree_2$ share a common
data value $d\neq d_1$ of $\Ba$-state $p_{k_2}$ in $\btree_2 \otimes\dtree_2$
and $\Ba$-state $p_{k_1}$ in $\btree_1 \otimes \dtree_1$.
For each $\theta \in \chi$ we select the associated data values making sure
they are neither $d_1$ nor $d$. The decrement in the $\epsilon$-transitions make sure
that this is always possible. We then perform the same identification as in the
previous case.
The rest of the argument is similar after setting $\dtree=d(\dtree_1,\dtree_2)$.
\begin{figure}
\small
\[
\begin{array}{ccc}
\tree'=\btree\otimes\dtree =
\hspace{-8mm}
\begin{minipage}[t]{24mm}
\vspace{-3.5mm}
\begin{tikzpicture}
[level distance=7mm,
level 1/.style={sibling distance=12mm},
level 2/.style={sibling distance=4mm}]
\node {$(b, d)$}
child { node {$(b_1, d_1)$} { node[itria] {} } }
child { node {$(b_2, d_1)$} { node[itria] {} } };
\end{tikzpicture}
\end{minipage}
&
\tree'[d] =
\hspace{-8mm}
\begin{minipage}[t]{24mm}
\vspace{-3.5mm}
\begin{tikzpicture}
[level distance=7mm,
level 1/.style={sibling distance=12mm},
level 2/.style={sibling distance=4mm}]
\node {$b (p_i)$}
child { node {$\# (p_{k_1})$} { node[itria] {} } }
child { node {$\# (p_{k_2})$} { node[itria] {} } };
\end{tikzpicture}
\end{minipage}
&
\tree'[d_1] =
\hspace{-8mm}
\begin{minipage}[t]{24mm}
\vspace{-3.5mm}
\begin{tikzpicture}
[level distance=7mm,
level 1/.style={sibling distance=12mm},
level 2/.style={sibling distance=4mm}]
\node {$\# (p_j)$}
child { node {$b_1 (p_{i_1})$} { node[itria] {} } }
child { node {$b_2 (p_{i_2})$} { node[itria] {} } };
\end{tikzpicture}
\end{minipage}
\end{array}
\]
\caption{Proof of Theorem~\ref{prop-reduct}, Case 4.}
\label{fig-reduct4}
\end{figure}
\medskip\noindent\textbf{5.} \emph{$\Ea$ guessed that the data value $d$ of the
current node is different from the ones of its children but appear in
both subtrees, with $p_{k_1}$ and $p_{k_2}$ as associated $\Ba$-states in respectively the left and right subtree.
Moreover $\Ea$ guessed that the data values
of both children of the current node are
distinct but appear in the other subtree with respective associated $\Ba$-state $p_{\ell_1}$ and $p_{\ell_2}$.
Note that $p_{k_1}$, $p_{k_2}$, $p_{\ell_1}$, $p_{\ell_2}$ must be \#-states.}
To handle this case for all transitions
$\tau = (p_{k_1},b,p_{k_2}) \ra p_{i}$,
$\tau_1=(p_{i_1},\#,p_{\ell_1})\ra p_{j_1}$ and
$\tau_2=(p_{\ell_2},\#,p_{i_2})\ra p_{j_2}$ of $\Ba$,
where none of $p_{i_1},p_{i_2}, p_i$ are $\#$-states but
$p_{k_1},p_{k_2},p_{\ell_1},p_{\ell_2},p_{j_1},p_{j_2}$ are $\#$-states, $\Ea$ has the following
transitions:
\begin{description}
\item[\rm $\epsilon$-transitions:]\quad\\
from a state $q_1$ of $\Ba$-state $p_{i_1}$
it decreases the counters $i_1$, $k_1$ and $l_2$
and moves to state $q_{\tau,\tau_1,\tau_2}^1$\\
from a state $q_2$ of $\Ba$-state $p_{i_2}$
it decreases the counters $i_2$, $k_2$ and $l_1$
and moves to state $q_{\tau,\tau_1,\tau_2}^2$\\
from a state $q_{\tau,\tau_1,\tau_2}$
it increases the counters $i$, $j_1$ and $j_2$
and moves to a state $q$ of $\Ba$-state $p_i$
\item[\rm up-transition:]
$(q_{\tau,\tau_1\,\tau_2}^1,a,q_{\tau,\tau_1,\tau_2}^2,q_{\tau,\tau_1,\tau_2})$.
\end{description}
\paragraph{\bf Correctness.}
We argue as in the previous cases with the following modifications.
From $\dtree_1$ and $\dtree_2$ we first apply a bijection making sure that the
data values $d_1$ and $d_2$ of their roots are distinct and that $d_1$ has
$\Ba$-state $p_{\ell_1}$ in $\btree_2\otimes\dtree_2$ and $d_2$ has $\Ba$-state $p_{\ell_2}$ in
$\btree_1\otimes\dtree_1$. Moreover $\dtree_1$ and $\dtree_2$ share a common data value $d$
distinct from $d_1$ and $d_2$ of $\Ba$-state $p_{k_2}$ in $\dtree_2$ and
$\Ba$-state $p_{k_1}$ in $\dtree_1$.
For each $\theta \in \chi$ we select the associated data values making sure
that they are neither $d$, $d_1$ nor $d_2$. The decrement in the $\epsilon$-transitions make sure
that this is always possible. We then perform the same identification as in the
previous case.
The rest of the argument is similar after setting $\dtree=d(\dtree_1,\dtree_2)$.
\begin{figure}
\small
\[
\begin{array}{cccc}
\tree'=\btree\otimes\dtree =
\hspace{-8mm}
\begin{minipage}[t]{24mm}
\vspace{-3.5mm}
\begin{tikzpicture}
[level distance=7mm,
level 1/.style={sibling distance=12mm},
level 2/.style={sibling distance=4mm}]
\node {$(b, d)$}
child { node {$(b_1, d_1)$} { node[itria] {} } }
child { node {$(b_2, d_2)$} { node[itria] {} } };
\end{tikzpicture}
\end{minipage}
&
\tree'[d] =
\hspace{-8mm}
\begin{minipage}[t]{24mm}
\vspace{-3.5mm}
\begin{tikzpicture}
[level distance=7mm,
level 1/.style={sibling distance=12mm},
level 2/.style={sibling distance=4mm}]
\node {$b (p_i)$}
child { node {$\# (p_{k_1})$} { node[itria] {} } }
child { node {$\# (p_{k_2})$} { node[itria] {} } };
\end{tikzpicture}
\end{minipage}
&
\tree'[d_1] =
\hspace{-6mm}
\begin{minipage}[t]{24mm}
\vspace{-3.5mm}
\begin{tikzpicture}
[level distance=7mm,
level 1/.style={sibling distance=12mm},
level 2/.style={sibling distance=4mm}]
\node {$\# (p_{j_1})$}
child { node {$b_1 (p_{i_1})$} { node[itria] {} } }
child { node {$\# (p_{\ell_1})$} { node[itria] {} } };
\end{tikzpicture}
\end{minipage}
&
\tree'[d_2] =
\hspace{-6mm}
\begin{minipage}[t]{24mm}
\vspace{-3.5mm}
\begin{tikzpicture}
[level distance=7mm,
level 1/.style={sibling distance=12mm},
level 2/.style={sibling distance=4mm}]
\node {$\# (p_{j_2})$}
child { node {$\# (p_{\ell_2})$} { node[itria] {} } }
child { node {$b_2 (p_{i_2})$} { node[itria] {} } };
\end{tikzpicture}
\end{minipage}
\end{array}
\]
\caption{Proof of Theorem~\ref{prop-reduct}, Case 5.}
\label{fig-reduct5}
\end{figure}
\paragraph{\bf 6.}
\emph{$\Ea$ guessed that the data value $d$ of the
current node is different from the ones of its children but appear in both
subtrees, with $p_{k_1}$ and $p_{k_2}$ as associated $\Ba$-states in respectively the left and right subtree.
Moreover $\Ea$ guessed that the data value
of the right child of the current node appear in its
left subtree, with $p_{\ell_1}$ as associated $\Ba$-state in this left subtree,
and that the data value
of the left child does not appear in the right subtree.
Note that $p_{k_1}$, $p_{k_2}$ and $p_{\ell_1}$ must be \#-states in $Q_\Ba \setminus \{ p_\#\}$.}
\noindent
To handle this case for all transitions
$\tau = (p_{k_1},b,p_{k_2}) \ra p_{i}$,
$\tau_1 = (p_{i_1},\#,p_{\#})\ra p_{j_1}$ and
$\tau_2 = (p_{\ell_1},\#,p_{i_2})\ra p_{j_2}$ of $\Ba$,
where none of $p_{i_1},p_{i_2}, p_i$ are $\#$-states but
$p_{k_1},p_{k_2},p_{\ell_1},p_{j_1},p_{j_2}$ are $\#$-states, $\Ea$ has the following transitions:
\begin{description}
\item[\rm $\epsilon$-transitions:]\quad\\
from a state $q_1$ of $\Ba$-state $p_{i_1}$
it decreases the counters $i_1$, $k_1$ and $l_1$
and moves to state $q_{\tau,\tau_1,\tau_2}^1$\\
from a state $q_2$ of $\Ba$-state $p_{i_2}$
it decreases the counters $i_2$, $k_2$
and moves to state $q_{\tau,\tau_1,\tau_2}^2$\\
from a state $q_{\tau,\tau_1,\tau_2}$
it increases the counters $i$, $j_1$ and $j_2$
and moves to a state $q$ of $\Ba$-state $p_i$
\item[\rm up-transition:]
$(q_{\tau,\tau_1\,\tau_2}^1,a,q_{\tau,\tau_1,\tau_2}^2,q_{\tau,\tau_1,\tau_2})$.
\end{description}
\paragraph{\bf Correctness.}
We argue as in the previous cases with the following modifications.
From $\dtree_1$ and $\dtree_2$ we first apply a bijection making sure that the
data values $d_1$ and $d_2$ of their roots are distinct and that $d_1$ does not
appear in $\dtree_2$ and $d_2$ has $\Ba$-state $p_{\ell_1}$ in
$\btree_1\otimes\dtree_1$. Moreover $\dtree_1$ and $\dtree_2$ share a common data value $d$
distinct from $d_1$ and $d_2$ of $\Ba$-state $p_{k_2}$ in $\btree_2\otimes\dtree_2$ and
$\Ba$-state $p_{k_1}$ in $\btree_1\otimes\dtree_1$.
For each $\theta \in \chi$ we select the associated data values making sure
that they are neither $d$, $d_1$ nor $d_2$. The decrement in the $\epsilon$-transitions make sure
that this is always possible. We then perform the same identification as in the
previous case.
The rest of the argument is similar after setting $\dtree=d(\dtree_1,\dtree_2)$.
\begin{figure}
\small
\[
\begin{array}{cccc}
\tree'=\btree\otimes\dtree =
\hspace{-8mm}
\begin{minipage}[t]{24mm}
\vspace{-3.5mm}
\begin{tikzpicture}
[level distance=7mm,
level 1/.style={sibling distance=12mm},
level 2/.style={sibling distance=4mm}]
\node {$(b, d)$}
child { node {$(b_1, d_1)$} { node[itria] {} } }
child { node {$(b_2, d_2)$} { node[itria] {} } };
\end{tikzpicture}
\end{minipage}
&
\tree'[d] =
\hspace{-8mm}
\begin{minipage}[t]{24mm}
\vspace{-3.5mm}
\begin{tikzpicture}
[level distance=7mm,
level 1/.style={sibling distance=12mm},
level 2/.style={sibling distance=4mm}]
\node {$b (p_i)$}
child { node {$\# (p_{k_1})$} { node[itria] {} } }
child { node {$\# (p_{k_2})$} { node[itria] {} } };
\end{tikzpicture}
\end{minipage}
&
\tree'[d_1] =
\hspace{-6mm}
\begin{minipage}[t]{24mm}
\vspace{-3.5mm}
\begin{tikzpicture}
[level distance=7mm,
level 1/.style={sibling distance=12mm},
level 2/.style={sibling distance=4mm}]
\node {$\# (p_{j_1})$}
child { node {$b_1 (p_{i_1})$} { node[itria] {} } }
child { node {$\# (p_\#)$} { } };
\end{tikzpicture}
\end{minipage}
&
\tree'[d_2] =
\hspace{-6mm}
\begin{minipage}[t]{24mm}
\vspace{-3.5mm}
\begin{tikzpicture}
[level distance=7mm,
level 1/.style={sibling distance=12mm},
level 2/.style={sibling distance=4mm}]
\node {$\# (p_{j_2})$}
child { node {$\# (p_{\ell_1})$} { node[itria] {} } }
child { node {$b_2 (p_{i_2})$} { node[itria] {} } };
\end{tikzpicture}
\end{minipage}
\end{array}
\]
\caption{Proof of Theorem~\ref{prop-reduct}, Case 6.}
\label{fig-reduct6}
\end{figure}
\paragraph{\bf 7.}
\emph{$\Ea$ guessed that the data value $d$ of the
current node is different from the ones of its children but appears in both
subtrees with $p_{k_1}$ and $p_{k_2}$ as associated $\Ba$-states.
Moreover it guessed that the data values of both children of the current node do not appear elsewhere.
Note that $p_{k_1}$, $p_{k_2}$ must be \#-states in $Q_\Ba \setminus \{ p_\#\}$.}
\noindent
To handle this case for all transitions
$\tau = (p_{k_1},b,p_{k_2}) \ra p_{i}$,
$\tau_1 = (p_{\#},b,p_{p_2})\ra p_{j_1}$ and
$\tau_2 = (p_{i_1},b,p_{\#})\ra p_{j_2}$ of $\Ba$,
where none of $p_{i_1},p_{i_2}, p_i$ are $\#$-states but
$p_{k_1},p_{k_2},p_{j_1},p_{j_2}$ are $\#$-states, $\Ea$ has the following
transitions:
\begin{description}
\item[\rm $\epsilon$-transitions:]\quad\\
from a state $q_1$ of $\Ba$-state $p_{i_1}$
it decreases the counters $i_1$, $k_1$
and moves to state $q_{\tau,\tau_1,\tau_2}^1$\\
from a state $q_2$ of $\Ba$-state $p_{i_2}$
it decreases the counters $i_2$, $k_2$
and moves to state $q_{\tau,\tau_1,\tau_2}^2$\\
from a state $q_{\tau,\tau_1,\tau_2}$
it increases the counters $i$, $j_1$ and $j_2$
and moves to a state $q$ of $\Ba$-state $p_i$
\item[\rm up-transition:]
$(q_{\tau,\tau_1\,\tau_2}^1,a,q_{\tau,\tau_1,tau_2}^2,q_{\tau,\tau_1,\tau_2})$.
\end{description}
\paragraph{\bf Correctness.}
We argue as in the previous cases with the following modifications.
From $\dtree_1$ and $\dtree_2$ we first apply a bijection making sure that the
data values $d_1$ and $d_2$ of their roots are distinct and that $d_1$ does not
appear in $\dtree_2$ and $d_2$ does not appear in
$\dtree_1$. Moreover $\dtree_1$ and $\dtree_2$ share a common data value $d$
distinct from $d_1$ and $d_2$ of $\Ba$-state $p_{k_2}$ in $\dtree_2$ and
$\Ba$-state $p_{k_1}$ in $\dtree_1$.
For each $\theta \in \chi$ we select the associated data values making sure
that they are neither $d$, $d_1$ nor $d_2$. The decrement in the $\epsilon$-transitions make sure
that this is always possible. We then perform the same identification as in the
previous case.
The rest of the argument is similar after setting $\dtree=d(\dtree_1,\dtree_2)$.
\begin{figure}
\small
\[
\begin{array}{cccc}
\tree'=\btree\otimes\dtree =
\hspace{-8mm}
\begin{minipage}[t]{24mm}
\vspace{-3.5mm}
\begin{tikzpicture}
[level distance=7mm,
level 1/.style={sibling distance=12mm},
level 2/.style={sibling distance=4mm}]
\node {$(b, d)$}
child { node {$(b_1, d_1)$} { node[itria] {} } }
child { node {$(b_2, d_2)$} { node[itria] {} } };
\end{tikzpicture}
\end{minipage}
&
\tree'[d] =
\hspace{-8mm}
\begin{minipage}[t]{24mm}
\vspace{-3.5mm}
\begin{tikzpicture}
[level distance=7mm,
level 1/.style={sibling distance=12mm},
level 2/.style={sibling distance=4mm}]
\node {$b (p_i)$}
child { node {$\# (p_{k_1})$} { node[itria] {} } }
child { node {$\# (p_{k_2})$} { node[itria] {} } };
\end{tikzpicture}
\end{minipage}
&
\tree'[d_1] =
\hspace{-6mm}
\begin{minipage}[t]{24mm}
\vspace{-3.5mm}
\begin{tikzpicture}
[level distance=7mm,
level 1/.style={sibling distance=12mm},
level 2/.style={sibling distance=4mm}]
\node {$\# (p_{j_1})$}
child { node {$b_1 (p_{i_1})$} { node[itria] {} } }
child { node {$\# (p_\#)$} { } };
\end{tikzpicture}
\end{minipage}
&
\tree'[d_2] =
\hspace{-6mm}
\begin{minipage}[t]{24mm}
\vspace{-3.5mm}
\begin{tikzpicture}
[level distance=7mm,
level 1/.style={sibling distance=12mm},
level 2/.style={sibling distance=4mm}]
\node {$\# (p_{j_2})$}
child { node {$\# (p_\#)$} { } }
child { node {$b_2 (p_{i_2})$} { node[itria] {} } };
\end{tikzpicture}
\end{minipage}
\end{array}
\]
\caption{Proof of Theorem~\ref{prop-reduct}, Case 7.}
\label{fig-reduct7}
\end{figure}
\paragraph{\bf 8.}
\emph{$\Ea$ guessed that the data value $d$ of the
current node is different from the ones of its children and does not appear
in the subtrees. Moreover $\Ea$ guessed that the data values of both
children of the current node are equal.}
\noindent
To handle this case for all transitions
$\tau = (p_{\#},b,p_{\#}) \ra p_{i}$,
$\tau' = (p_{i_1},\#,p_{i_2})\ra p_{j}$ of $\Ba$,
where none of $p_{i_1},p_{i_2},
p_i$ are $\#$-states, $\Ea$ has the following transitions:
\begin{description}
\item[\rm $\epsilon$-transitions:]\quad\\
from a state $q_1$ of $\Ba$-state $p_{i_1}$
it decreases the counters $i_1$
and moves to state $q_{\tau,\tau'}^1$\\
from a state $q_2$ of $\Ba$-state $p_{i_2}$
it decreases the counter $i_2$
and moves to state $q_{\tau,\tau'}^2$\\
from a state $q_{\tau,\tau'}$
it increases the counters $i$, and $j$
and moves to a state $q$ of $\Ba$-state $p_i$
\item[\rm up-transition:] $(q_{\tau,\tau'}^1,a,q_{\tau,\tau'}^2,q_{\tau,\tau'})$.
\end{description}
\paragraph{\bf Correctness.}
We argue as in the previous cases with the following modifications.
From $\dtree_1$ and $\dtree_2$ we first apply a bijection making sure that the
data values of their roots are equal (let us call it $d_1$).
For each $\theta \in \chi$ we select the associated data values making sure
it is not $d_1$. The decrement in the $\epsilon$-transitions make sure
that this is always possible. We then perform the same identification as in the
previous case.
The rest of the argument is similar after setting
$\dtree=d(\dtree_1,\dtree_2)$, where $d$ is a fresh new value.
\begin{figure}
\small
\[
\begin{array}{ccc}
\tree'=\btree\otimes\dtree =
\hspace{-8mm}
\begin{minipage}[t]{24mm}
\vspace{-3.5mm}
\begin{tikzpicture}
[level distance=7mm,
level 1/.style={sibling distance=12mm},
level 2/.style={sibling distance=4mm}]
\node {$(b, d)$}
child { node {$(b_1, d_1)$} { node[itria] {} } }
child { node {$(b_2, d_1)$} { node[itria] {} } };
\end{tikzpicture}
\end{minipage}
&
\tree'[d] =
\hspace{-8mm}
\begin{minipage}[t]{24mm}
\vspace{-3.5mm}
\begin{tikzpicture}
[level distance=7mm,
level 1/.style={sibling distance=12mm},
level 2/.style={sibling distance=4mm}]
\node {$b (p_i)$}
child { node {$\# (p_\#)$} { } }
child { node {$\# (p_\#)$} { } };
\end{tikzpicture}
\end{minipage}
&
\tree'[d_1] =
\hspace{-6mm}
\begin{minipage}[t]{24mm}
\vspace{-3.5mm}
\begin{tikzpicture}
[level distance=7mm,
level 1/.style={sibling distance=12mm},
level 2/.style={sibling distance=4mm}]
\node {$\# (p_{j})$}
child { node {$b_1 (p_{i_1})$} { node[itria] {} } }
child { node {$b_2 (p_{i_2})$} { node[itria] {} } };
\end{tikzpicture}
\end{minipage}
\end{array}
\]
\caption{Proof of Theorem~\ref{prop-reduct}, Case 8.}
\label{fig-reduct8}
\end{figure}
\paragraph{\bf 9.}
\emph{$\Ea$ guessed that the data value $d$ of the
current node is different from the ones of its children and does not appear in both subtrees.
Moreover $\Ea$ guessed that the data values of both children of the current node (say $d_1$ and $d_2$)
are distinct but appear in the other subtree with respective associated $\Ba$-state $p_{\ell_1}$
and $p_{\ell_2}$.
Note that $p_{\ell_1}$, $p_{\ell_2}$ must be $\#$-states in $Q_\Ba \setminus \{ p_\#\}$.}
\noindent
This case is treated as before with the expected transitions.
\begin{figure}
\small
\[
\begin{array}{cccc}
\tree'=\btree\otimes\dtree =
\hspace{-8mm}
\begin{minipage}[t]{24mm}
\vspace{-3.5mm}
\begin{tikzpicture}
[level distance=7mm,
level 1/.style={sibling distance=12mm},
level 2/.style={sibling distance=4mm}]
\node {$(b, d)$}
child { node {$(b_1, d_1)$} { node[itria] {} } }
child { node {$(b_2, d_2)$} { node[itria] {} } };
\end{tikzpicture}
\end{minipage}
&
\tree'[d] =
\hspace{-8mm}
\begin{minipage}[t]{24mm}
\vspace{-3.5mm}
\begin{tikzpicture}
[level distance=7mm,
level 1/.style={sibling distance=12mm},
level 2/.style={sibling distance=4mm}]
\node {$b (p_i)$}
child { node {$\# (p_\#)$} { {} } }
child { node {$\# (p_\#)$} { {} } };
\end{tikzpicture}
\end{minipage}
&
\tree'[d_1] =
\hspace{-6mm}
\begin{minipage}[t]{24mm}
\vspace{-3.5mm}
\begin{tikzpicture}
[level distance=7mm,
level 1/.style={sibling distance=12mm},
level 2/.style={sibling distance=4mm}]
\node {$\# (p_{j_1})$}
child { node {$b_1 (p_{i_1})$} { node[itria] {} } }
child { node {$\# (p_{\ell_1})$} { node[itria] {} } };
\end{tikzpicture}
\end{minipage}
&
\tree'[d_2] =
\hspace{-6mm}
\begin{minipage}[t]{24mm}
\vspace{-3.5mm}
\begin{tikzpicture}
[level distance=7mm,
level 1/.style={sibling distance=12mm},
level 2/.style={sibling distance=4mm}]
\node {$\# (p_{j_2})$}
child { node {$\# (p_{\ell_2})$} { node[itria] {} } }
child { node {$b_2 (p_{i_2})$} { node[itria] {} } };
\end{tikzpicture}
\end{minipage}
\end{array}
\]
\caption{Proof of Theorem~\ref{prop-reduct}, Case 9.}
\label{fig-reduct9}
\end{figure}
\paragraph{\bf 10.}
\emph{$\Ea$ guessed that the data value $d$ of the
current node is different from the ones of its children and does not appear in both subtrees.
Moreover $\Ea$ guessed that the data value $d_2$ of the right child
in its left subtree with $p_{\ell_1}$ as associated $\Ba$-state in this left subtree
and that the data value $d_1$ of
the left child does not appear in the right subtree.
Note that $p_{\ell_1}$ must be a $\#$-states in $Q_\Ba \setminus \{ p_\#\}$.}
\noindent
This case is treated as before with the expected transitions.
\begin{figure}
\small
\[
\begin{array}{cccc}
\tree'=\btree\otimes\dtree =
\hspace{-8mm}
\begin{minipage}[t]{24mm}
\vspace{-3.5mm}
\begin{tikzpicture}
[level distance=7mm,
level 1/.style={sibling distance=12mm},
level 2/.style={sibling distance=4mm}]
\node {$(b, d)$}
child { node {$(b_1, d_1)$} { node[itria] {} } }
child { node {$(b_2, d_2)$} { node[itria] {} } };
\end{tikzpicture}
\end{minipage}
&
\tree'[d] =
\hspace{-8mm}
\begin{minipage}[t]{24mm}
\vspace{-3.5mm}
\begin{tikzpicture}
[level distance=7mm,
level 1/.style={sibling distance=12mm},
level 2/.style={sibling distance=4mm}]
\node {$b (p_i)$}
child { node {$\# (p_\#)$} { {} } }
child { node {$\# (p_\#)$} { {} } };
\end{tikzpicture}
\end{minipage}
&
\tree'[d_1] =
\hspace{-6mm}
\begin{minipage}[t]{24mm}
\vspace{-3.5mm}
\begin{tikzpicture}
[level distance=7mm,
level 1/.style={sibling distance=12mm},
level 2/.style={sibling distance=4mm}]
\node {$\# (p_{j_1})$}
child { node {$b_1 (p_{i_1})$} { node[itria] {} } }
child { node {$\# (p_\#)$} { } };
\end{tikzpicture}
\end{minipage}
&
\tree'[d_2] =
\hspace{-6mm}
\begin{minipage}[t]{24mm}
\vspace{-3.5mm}
\begin{tikzpicture}
[level distance=7mm,
level 1/.style={sibling distance=12mm},
level 2/.style={sibling distance=4mm}]
\node {$\# (p_{j_2})$}
child { node {$\# (p_{\ell_1})$} { node[itria] {} } }
child { node {$b_2 (p_{i_2})$} { node[itria] {} } };
\end{tikzpicture}
\end{minipage}
\end{array}
\]
\caption{Proof of Theorem~\ref{prop-reduct}, Case 10.}
\label{fig-reduct10}
\end{figure}
\paragraph{\bf 11.}
\emph{We omit the symmetric cases.}
\end{proof}
\section{From \texorpdfstring{\ebvass}{EBVASS} to \texorpdfstring{\fotwo}{FO2}}\label{sec-counter-fotwo}
We show in this section that reachability of \ebvass
can be expressed as a sentence of \fotwo.
This concludes the loop of reductions, showing that
reachability for \ebvass, satisfiability of \fotwo and emptiness of \dad
are equivalent as decision problems.
The proof essentially mimics the reduction from \bvass to \fotwo described
in~\cite{BojanczykMSS09jacm} with
extra material in order to handle the extra features.
\begin{theorem}\label{thm-bvass-fodeux}
The reachability problem for \ebvass reduces to the satisfiability problem for \fotwo.
\end{theorem}
\begin{proof}
Given an \ebvass $\Ea=(Q,\A,q_0,k,\delta,\chi)$ and a state $q\in Q$,
we compute a sentence $\phi \in \fotwo$ such that $\phi$ has a model
iff the configuration $(q,v_0)$ is reachable in some tree
(where $v_0$ is the function setting all counters to $0$).
\noindent
We associate to $\Ea$ the following finite alphabet
$\A_\Ea = \delta \cup\{ D_i, I_i \mid 1\leq i \leq k\}
\cup \{ T_\theta, L_\theta, R_\theta \mid \theta \in \chi \}$.
Intuitively $D_i$ says that the counter
$i$ has been decreased, $I_i$ says that the counter $i$ has been increased,
$\delta$ encodes the transition relation, and the letters $L_\theta$, $R_\theta$ and $T_\theta$ will be used to enforce
the constraint $\theta$.
The formula $\phi$ we construct accept all binary data trees
of $\Trees(\A_\Ea\times \D)$ encoding runs of $\Ea$. It turns out that $\phi$
accepts more trees but any accepted trees of $\phi$ can be transformed into an accepting
run of $\Ea$ with simple transformations.
\noindent
We start with the encoding of a single transition $\mu \in \delta$.
\noindent
If $\mu$ is an $\epsilon$-transition then we encode it with two nodes
$x,y$ where $y$ is the unique child of $x$ and the label of $x$ is $\mu$ while
the label of $y$ is $D_i$ (resp. $I_i$)
if $\mu$ was decreasing (resp. increasing) counter $i$.
\noindent
If $\mu$ is an up-transition, then we encode
it as a subtree of the following form:
\begin{itemize}
\item The root has label $\mu$,
\item below the root there is a (vertical) sequence of nodes of arity one whose
labels form a word of
$\displaystyle\sum_{\theta = \merc{i_1}{i_2}{i}\in\chi} (I_iT_\theta)^*$,
where $\sum$ denotes concatenation,
\item the last node of that sequence has arity two and two branches starts from that node,
\item the sequence of labels of the left branch forms a word of
$\displaystyle\sum_{\theta=\merc{i_1}{i_2}{i}\in\chi} (D_{i_1}L_\theta D_{i_2}R_\theta)^*$,
\item the sequence of labels of the right branch forms a word of
$\displaystyle\sum_{\theta=\merc{i_1}{i_2}{i}\in\chi} (D_{i_1}R_\theta D_{i_2}L_\theta)^*$,
\item for all $\theta$ the number of occurrences of $L_\theta, R_\theta$ and
$T_\theta$ are the same.
\end{itemize}
A tree satisfying all these items, except maybe the last one, is said to be a \emph{pseudo-encoding} of the up-transition $\mu$.
Notice that pseudo-encodings of up-transitions form a regular tree language.
\noindent
From there, the encoding of a run is obtained in the obvious way by concatenating
encodings of transitions.
The formula $\phi$ essentially describes this construction. It first enforces
that the tree has the desired shape:
\begin{itemize}
\item The tree is a repetition of a sequence of the form: a pseudo-encoding
of one up-transition followed by the encodings of several $\epsilon$-transitions,
\item the sequencing is valid: if $\mu$ and $\nu$ are consecutive transitions
in the tree then the starting state of one is the ending state of the other,
\item the initial state $q_0$ can be found at the leaves
and the state $q$ is reached at the root.
\end{itemize}
Note that the above three conditions can be checked by a standard tree
automaton over $\A_\Ea$, and therefore can be expressed in $\emso^2(\descendant,\neighbor)$.
Therefore, by setting $\A=\A_c\times\A'$ for a
suitable $\A'$ matching the existential part of the $\emso$ formula,
the property above can be expressed in $\fo^2(\descendant,\neighbor)$.
The formula $\phi$ now needs to make sure that no counter ever gets negative and that
pseudo-encodings of up-transitions are actually real encodings.
This is where
data values are needed:
The formula $\phi$ enforces that
\begin{enumerate}[label=\enspace(\arabic*)]
\item \label{it:Di}
no two nodes with label $D_i$
can have the same data value, for $1 \leq i \leq k$,
\item \label{it:Ii}
no two nodes with label $I_i$
can have the same data value, for $1 \leq i \leq k$,
\item \label{it:DiIi}
for all $i\in[k]$, every node with label $D_i$ has a descendant
with label $I_i$ and with the same data value,
\item \label{it:IiDi}
for all $i\in[k]$, every node with label $I_i$ has an ancestor
with label $D_i$ and with the same data value.
\end{enumerate}
These four conditions enforce that the counters never get negative and that
they are all set to $0$ at the root. It remains to enforce that all
pseudo-encodings can be transformed into real encodings.
This is done with the following conditions.
\enlargethispage{\baselineskip}
\begin{enumerate}[label=\enspace(\arabic*)]
\setcounter{enumi}{4}
\item \label{it:Ttheta}
no two nodes with label $T_\theta$, for $\theta \in \chi$,
can have the same data value,
\item \label{it:Ltheta}
no two nodes with label $L_\theta$, for $\theta \in \chi$,
can have the same data value,
\item \label{it:Rtheta}
no two nodes with label $R_\theta$, for $\theta \in \chi$,
can have the same data value,
\item \label{it:TthetaLRtheta}
every node with label $T_\theta$ has a descendant with label $L_\theta$
and a descendant with label $R_\theta$
both with the same data value,
\item \label{it:LRthetaTtheta}
every node with label $L_\theta$ or $R_\theta$ has an ancestor with label $T_\theta$
and with the same data value,
\item \label{it:LRtheta}
two nodes of label $L_\theta$ and $R_\theta$ with the same data value
are not comparable with the ancestor relationship.
\end{enumerate}
It now remains to show that $\phi$ has the desired property.
\begin{lemma}\label{lemma-ebvass-fo}
$\phi$ has a model iff $(q, v_0)$ is reachable by $\Ea$.
\end{lemma}
\begin{proof}
{\bf From reachability to models of $\phi$.}
Assume that $(q, v_0)$ is reachable and let $\rho$ be a run of $\Ea$ witnessing this fact.
Let $\atree$ be the tree constructed from $\rho$ by concatenating the sequences
of encodings of transitions of $\rho$ as explained above.
The binary tree $\atree$ certainly satisfies the ``regular'' part of $\phi$.
We now assign the data values so that
the remaining part of $\phi$ is satisfied. This is done in the obvious way:
each time a counter $i$ is decremented, as the resulting value is positive,
this means that a matching increment was performed before. Similarly, each time
a constraint $\theta$ is used in a transition $\mu$, we assign one distinct
data value per triple $L_\theta,R_\theta,T_\theta$
occurring in the encoding of
$\mu$. The formula was constructed to make the resulting tree a model of $\phi$.
{\bf From models of $\phi$ to reachability.}
Assume now that $\tree=\atree\otimes \dtree \models \phi$.
Unfortunately, it may happen that $\atree$
does not encode a run of $\Ea$ because
some section corresponds to a pseudo-encoding of an up-transition,
instead of an expected real encoding.
However, we show that from $\tree$ we can construct another tree
$\tree'=\atree'\otimes\dtree'$ such that $\tree' \models \phi$
and $\atree'$ encodes a real run of $\Ea$.
To see this, let us consider a node $x$ of $\tree$
with label $T_\theta$,
where $\theta = \merc{i_1}{i_2}{i}$, and let $d = \dtree(x)$.
Let $x_1$ and $x_2$ be two descendants of $x$
with respective labels $L_\theta$ and $R_\theta$
and such that $d = \dtree(x_1) = \dtree(x_2)$.
Let $z$ be the least common ancestor of $x_1$ and $x_2$.
The existence of $x_1$ and $x_2$ is guaranteed by $\phi$
(conditions \ref{it:Ttheta}--\ref{it:TthetaLRtheta}).
The sentence $\phi$ also ensures
that $x$ is an ancestor of $z$
(conditions \ref{it:LRthetaTtheta}--\ref{it:LRtheta}).
By construction the subtree at $z$ must correspond to
a pseudo-encoding of an up-transition $\mu'$.
We now move (down) $x$ and its parent
(that must have label $I_i$)
right above $z$ within the coding of $\mu'$.
Similarly we move (up) $x_1$ and its parent
(that must have label $D_{i_1}$)
right below $z$, and similarly for $x_2$.
The reader can verify that the
resulting tree is still a model of $\phi$: the regular conditions remain
obviously satisfied.
Conditions \ref{it:Di}--\ref{it:IiDi}
are still valid because the node of label $I_{i_1}$
matching the parent of $y$ was already below the initial position of
$y$ and its new position is upward in the tree.
Finally conditions \ref{it:Ttheta}--\ref{it:LRtheta}
remain valid by construction.
Repeating this argument eventually yields a model $\tree'=\btree\otimes\dtree'$
of $\phi$ such that $\btree$ is a correct sequencing of encodings of
transitions a $\Ea$.
This encoding is actually a real run because
conditions \ref{it:Di}--\ref{it:IiDi}
of $\phi$ immediately enforces that no counter is ever negative
\end{proof}
Theorem~\ref{thm-bvass-fodeux} is now immediate from Lemma~\ref{lemma-ebvass-fo}.
\end{proof}
\section{Conclusion}\label{sec-conclusion
We have seen that satisfiability of \fotwo, emptiness of \dad and reachability
of \ebvass are equivalent problems in terms of decidability. The main open
problem is of course whether they are all decidable or not.
The use of the \ebvass constraints of the form
$\merc{i_1}{i_2}{i}$
is crucial for the construction of Section~\ref{sec-dad-counter}.
Their semantics cannot be directly simulated with the usual BVASS,
but it is not clear whether \ebvass are strictly more expressive than BVASS,
and whether this extension is needed in order
to capture the expressive power of \fotwo on data trees.
In our definition of \ebvass the constraints of the form $\merc{i_1}{i_2}{i}$
have a ``commutative'' semantics.
Without commutativity, \textit{i.e.}, the rule modifies
only counter $i_1$ on the left child and counter $i_2$ on the right child,
the automata model is more powerful.
In order to describes its runs as in the
proof of Theorem~\ref{thm-bvass-fodeux}, the logic needs to be able to enforce
that a $L_\theta$ must be to the left of the $R_\theta$ with the same data value.
This can be done by adding the document order predicate into the logic.
A close inspection of the proof of Theorem~\ref{th-fotwodad} and
Theorem~\ref{prop-reduct} then shows that the extension of \fotwo with the
document order predicate can be captured by a \dad without the commutativity
rule and that such automata can be captured by the non-commutative version of
\ebvass.
In~\cite{BjSch10} it was shown that, over data words, the Data Automata model
of~\cite{BDMSS11} is more expressive than the Register Automata
of~\cite{KF94}. It is not obvious that our automata model \dad extends the
expressive power of the straightforward extension of register automata to data
trees. This remains to be investigated.
\bibliographystyle{abbrv}
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
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emotional support animal lawsuit nj
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"And a housing provider cannot second guess a treating physician's determination that an emotional support animal is necessary to allow a resident with a disability an equal opportunity to enjoy her home. The difference between a legitimate Emotional Support Animal and a pet is a letter from a licensed therapist. Emotional Support Animals in New York Apartments and Co-Ops. Unlike service dogs that are used to guide the deaf or the blind and are highly trained, there is no uniform training for emotional service dogs and no certification process. Emotional support animals are animals that are meant to be companions for someone who suffers from an emotional or mental type of disability. Because state laws treat companion animals like property, it can be difficult—but not impossible—to get fair compensation for your loss when a pet dies or suffers as a result of a vet's careless or incompetent treatment. ... Wolf and the law firm found another case involving Megan McFadden and her dog that served as an emotional support animal. All rights reserved (About Us). One company that provides supplies and services for support animals, the National Service Animal Registry, told the New York Times last year that it that it listed almost 200,000 animals, up from 2,400 in 2011. The Defendants moved to dismiss for failure to state claims upon which relief could be granted. On its website, the business lays out its philosophy that declares "We believe in teamwork.". Learn more about The Fair Housing Act and Air Carrier Access Act. Ass'n, 836 F. Supp. Emotional support animals are typically cats and dogs, but may be members of other animal species. However, a housing provider may impose reasonable conditions on approvals For an occupant with a disability whose medical provider prescribes an emotional support, therapy or assistance animal, reasonable accommodations may include granting an exception to a policy that bans pets or imposes weight or size restrictions. 2d 800 (N.D. Ill. 2011). Orlando is seeking a jury trial and unspecified damages for lost wages, plus pain and suffering. What are the laws protecting Emotional Support Animal owners? Service dogs are considered a "reasonable accommodation" under the Americans With Disabilities Act and can go just about anywhere – into restaurants, onto planes, or in workplaces – but legal disputes remain regarding the rights of people with emotional-support animals. Service Animal Scams: A Growing Problem A cottage industry has developed around fake emotional support animals. The suit argues that Brannan is liable for all damages incurred and is seeking $100,000 for past and future medical costs as well as $1 million for the girl's pain and suffering. Your California Privacy Rights / Privacy Policy. Therefore, the governing board of a community association should seek the advice of legal counsel before denying the request of a resident for a physical assistance or emotional support animal. Frank Orlando, 42, worked for Dobco Inc. of Wayne as a project superintendent on the grounds of Ramapo College in Mahwah, according to the suit, filed July 3 in Superior Court of Passaic County. These disabilities include anxiety and depression as the most common types, but many more could fall into the category. The owners of emotional support animals will also need to offer a document, signed by a doctor or licensed mental health professional, verifying that the creature will behave. By Shawn Chitnis June 5, 2019 at 12:15 pm. The U.S. He asked his employer, Dobco, Inc. of Wayne, to allow him to bring the dog to Ramapo College, where the company was doing a major expansion of the George T. Potter Library, according to the suit filed this week in Passaic County Superior Court. The lawsuit Sara Manzke filed alleged the town and county have violated the Fair Housing Act which requires reasonable accommodations be made for individuals with physical disabilities. © 2020 www.njherald.com. Emotional Support Animal Laws NY - https://petpartnersofsyracuse.org - Emotional Support Animal Laws NY - Apply for an ESA Letter Landlord To Pay $1M In Emotional Support Animals Lawsuit. An emotional support animal letter is a signed statement from the tenant's mental health practitioner proving that the animal companion is essential to their wellbeing and recovery. Emotional Support Animal Qualification Requirements. Orlando is seeking a jury trial and unspecified damages for lost wages, plus pain and suffering. One company that provides supplies and services for support animals, the National Service Animal Registry, told The New York Times last year that it listed almost 200,000 animals… Emotional Support Animals (ESA) The Rights of owning an ESA's. Read on to learn more about getting an emotional support animal in New Jersey Rather, it is an animal that the resident has claimed is required under the law for the physical assistance or emotional support for the disability that the resident is afflicted with. But Dobco made no "reasonable accommodation" for Orlando, and he was terminated in January, according to the complaint. Woman sues American Airlines, claims emotional support dog was locked in aircraft restroom The passenger, Avigail Diveroli, said the dog helps her battle severe anxiety. "However, some state or local governments have laws that allow people to take emotional support animals into public places. Marlin Jackson of Alabama filed the lawsuit over the June 2017 incident on Friday. Note to readers: if you purchase something through one of our affiliate links we may earn a commission. Emotional support animals will no longer be considered service animals on flights, DOT decides Revision to Air Carrier Access Act followed over 15K comments on proposal You can usually be compensated for additional vet bills. For A.J. © 2020 Advance Local Media LLC. "An airline may treat an emotional support animal as a pet." It doesn't mean there will be a flying zoo in the skies. An emotional support animal that helps a person stay calm or has other positive effects is not a service dog because it is generally not trained to do specific work, Sweet said. On Jan. 5, Orlando was fired, the suit claims. Plaintiffs brought the instant suit contending that their Condo Board's refusal to accommodate the need for an emotional support animal forced them to sell their condo. The intended purpose of the emotional support animal is to ease the patient's psychological disability or emotional trauma. Our journalism needs your support. Find NJ.com on Facebook. Choose your city to get emotional support animal letter and find out about special discounts and coupons. Posted Jun 11, 2014 Service dogs are allowed access to all public places such as movie theaters, hospitals, and restaurants. Emotional support animals are one of the safest and most effective support options for people who are suffering from psychiatric disorders such as depression, panic attacks, postpartum and anxiety. Brittany Williams-Goldstein, a Ramapo spokeswoman, said the school did contract with Dobco in 2019 for the library project but "does not have any knowledge of the lawsuit.". Through this support option, more and more patients have made notable progress on improving their mental condition. MEEKER, Colo. (CBS4) – … Animals. No matter your disability or disorder, an emotional support animal will serve as the perfect non-judgemental treatment you need to get through the day. They are one of the leading online destinations for information on Service Animals, Emotional Support Animals, and the laws surrounding ownership of each. MADISON -- A town of Ixonia woman has taken her fight to federal court to keep the emotional support miniature goats and geese on her property that the town and Jefferson County said violates zoning ordinances. A man who was severely mauled by an emotional support animal on a Delta flight in 2017 is suing the airline and the dog's owner for damages. At EZCare Clinic New Jersey, our mental health physicians will be more than happy to prescribe a legitimate ESA letter for you. Service Animal Scams: A Growing Problem A cottage industry has developed around fake emotional support animals. HUD defines an emotional support animal as an animal that "provides emotional support that alleviates one or more identified symptoms or effects of a person's disability." Orlando declined to be interviewed when reached by phone on Wednesday. The lawsuit claims supervisors at Dobco refused to accommodate the animal and refused to discuss the need for an emotional support dog at the job site. These animals do not need specialized training. They cited a "no pets" policy, although the nine-year resident of the 16-unit apartment building had a prescription from her doctor for the emotional support animal, the attorney general said. In January, we explained that federal (and most states') public accommodation laws do not require businesses and organizations to accommodate disabled individuals with regard to their requested use … Due to this distinction, your emotional support animal is not protected by the same laws that govern service animals. Lawsuit Regarding Use of Emotional Support Dog Claims Employment Discrimination . The Justice Department announced today that it has filed a lawsuit alleging that a Philadelphia condo association has violated the Fair Housing Act by discriminating against persons with disabilities who need assistance animals, including emotional support and service animals. What is an emotional support animal? Equal Employment Opportunity Commission (EEOC) is taking the position that an emotional support animal may be a required reasonable accommodation in the workplace. Although chickens are not commonly thought of as therapy animals, chickens can qualify as emotional support animals. US Service Animals was founded in 2015 with the mission of educating and assisting people with disabilities through the use of animals. Emotional Support Animal (ESA) To qualify for an ESA Letter typical qualifying conditions are (but not limited to) post-traumatic stress disorder, anxiety, depression. Lawsuit Claims 'Emotional Support Animal' Mauled 5-Year-Old at Portland Airport Airlines & Airports Patrick Clarke February 28, 2019 PHOTO: A service dog sitting on an airplane seat. Your support helps us cover local news. The lawsuit claims Dobco violated Orlando's civil rights under New Jersey's Law Against Discrimination by failing to offer reasonable accommodations for his dog and by unlawfully terminating his employment. Under the ADA and New Jersey law… There are a few exceptions to this general rule: When a pet has no market value (like a mutt adopted from the shelter), some states recognize that the damages for its loss should be the actual value to the owner, which can include sentimental value (for example, see … Emotional support animals are able to provide you with comfort, love, and relaxation, along with real health benefits. There are many individuals who might benefit from an emotional support animal. Some … Although these animals often have therapeutic benefits, they are not individually trained to perform specific tasks for their handlers. "Mr. Orlando also made it known to defendant Dobco that he was requesting an accommodation to permit the dog to be with him during work hours, specifically to assist with plaintiff's disability," the lawsuit says. Orlando says in the suit the reason for his termination was that supervisors "did not want to address the issue of his emotional support dog.". Emotional support animals provide comfort and a sense of security to those that might suffer from emotional illness or disabilities. It's true. On Jan. 5, Orlando was fired, the suit claims. US Service Animals was founded in 2015 with the mission of educating and assisting people with disabilities through the use of animals. Commentary Suit Against Association for Emotional Support Animal Denial Sends Message to Fla. Condos, HOAs These new policies and signs have … "Dobco Group is only as successful as the individual members of its team" and "encourages employees to further their personal capabilities and self-esteem through each project," the company says. You also cannot impose weight, breed or size restrictions on the animal. The laws that protect other support animals apply to chickens as well. In this post, we are going to think outside the ESA box to answer the question; can my chicken be an emotional support chicken? But if your pet dies or is permanently disabled, you can usually only be compensated for the animal's market value. Dobco did not return repeated phone calls. You can, however, charge residents a fee if the emotional support animal causes damage to your rental property provided it is your customary practice to charge tenants a fee for any damage they … Please subscribe today to NJ.com. A New Jersey woman with an emotional disability and lives at an apartment complex in Vineland, N.J., wanted to get a Yorkshire terrier puppy as an emotional support dog and followed Federal Law and obtained an emotional support animal letter of recommendation touting the benefit, but the property had a "no pets" policy and denied her request. While Emotional Support Animals or Comfort Animals are often used as part of a medical treatment plan as therapy animals, they are not considered service animals under the ADA. "Because they have not been trained to perform a specific job or task, they do not qualify as service animals under the ADA," the U.S. Justice Department says online. Can your chicken qualify as an emotional support chicken? Filed Under: Meeker News. They allow the individual not to feel so alone or deal with stressful situations more easily. His attorney, Robert A. Diehl, also declined to comment. The feeling of love and companionship individuals receive from a dog or a cat can actually help improve certain conditions without any invasive procedures and treatments. Our Medical Doctors offer ESA Letters in New Jersey. Landlord To Pay $1M In Emotional Support Animals Lawsuit. Emotional Support Animal Letters for Housing. During his employment, which began in September 2019, Orlando disclosed to his bosses that he was receiving treatment to address mental health issues, including bipolar and personality disorders, the suit states. Housing providers cannot charge their tenants any fees or deposits for an ESA, or impose weight or breed restrictions on the animal. All information about Emotional Support Animals in New Jersey. Emotional support animals are one of the best support options available. Emotional Support Animals Do Not Have the Same Rights as Service Animals Animals have long been used to medically assist humans with various needs, such as a service dog to aid a blind or visually impaired person with navigation and protection, or an emotional support animal to provide affection and companionship as part of a treatment plan for anxiety issues. "The use of the emotional support dog was prescribed by (Orlando's) treating physician," the suit states. Anthony G. Attrino may be reached at [email protected] What is an emotional support animal? In the circumstance that a landlord or property manager does not permit your emotional support animal on their property or charge you a pet-deposit or a pet-related fee, you should file a complaint against the landlord or management property for discriminating against your right to an ESA according to the Fair Housing Amendments Act (FHAA), with enforcement by Housing and Urban Development (HUD). Registration on or use of this site constitutes acceptance of our User Agreement, Privacy Policy and Cookie Statement, and Your California Privacy Rights (each updated 1/1/20). An emotional support animal is not a pet, rather it is a companion animal that provides therapeutic benefit to an individual with a disability which significantly limits … Emotional support animals are one of the safest and most effective support options for people who are suffering from psychiatric disorders such as depression, panic attacks, postpartum and anxiety. Emotional support animals are typically cats and dogs, but may be members of other animal species. The Colorado Springs-based registry is one of many online companies that will sell certificates and a vest that make emotional-support animals appear official. Emotional support animals have been in the news quite a bit during the last couple of years. These support animals provide companionship, relieve loneliness, and sometimes help with depression, anxiety, and certain phobias, but do not have special training to perform tasks that assist people with disabilities. Unless you lost a trained service animal or champion show dog, the replacement cost probably won't amount to much. At USA Service Dog & Emotional Support Animal Registration we offer free registration and Service Dog & ESA Vests, ID Cards, ESA Letter & more. The case is potentially important because of the dramatic rise in recent years in the number of people relying on emotional support animals – and the unclear legal framework surrounding the practice. Under New York law, you have the right to live with your emotional support animal in rental units, condos, co-ops and other types of housing, even if the building has a strict "no pets" policy. ", Email: [email protected] Twitter: @richardcowen123. and how does one get an ESA in the state of New Jersey? "There is no requirement under the LAD that emotional support animals receive specialized training," said Director Wainer Apter. MADISON -- A town of Ixonia woman has taken her fight to federal court to keep the emotional support miniature goats and geese on her property that the town and Jefferson County said violates zoning ordinances. The material on this site may not be reproduced, distributed, transmitted, cached or otherwise used, except with the prior written permission of Advance Local. Emotional Support Animals are allowed access only to apartments (including those with no-pet policies) and on airplanes. Animals. Subscribe to NJ.com », Anthony G. Attrino | NJ Advance Media for NJ.com. An emotional support animal letter is a signed statement from the tenant's mental health practitioner proving that the animal companion is essential to their wellbeing and recovery. The project superintendent who oversaw early stage construction of the $40 million library expansion at Ramapo College has sued his former employer, claiming he has a mental illness but was not allowed to bring his emotional support dog to the job site. and how does one get an ESA in the state of New Jersey? They are one of the leading online destinations for information on Service Animals, Emotional Support Animals, and the laws surrounding ownership of each. The Animal Legal Defense Fund filed a lawsuit against the United States Department of Agriculture (USDA) under the Freedom of Information Act (FOIA) over the agency's critical redactions in a contract between the USDA's Wildlife Services program and a Colorado slaughterhouse, outlining plans for slaughtering geese rounded up in parks across Denver. Orlando was told by the head of the company's human resources department "that he was terminated because the defendant did not want to address the emotional support dog," the lawsuit says. Posted Jun 11, 2014 Airlines for America, an airline trade association, estimated that the number of passengers flying with emotional support animals in 2018 increased by 14%, … A passenger traveling on a 2017 Delta flight is suing the airline and a pet owner, claiming that an emotional support dog bit him in an attack that left permanent damage to his face. Was terminated in January, according to emotional support animal lawsuit nj complaint to all content you upload otherwise. Growing Problem a cottage industry has developed around fake emotional support animals provide and! Will be more than happy to prescribe a legitimate emotional emotional support animal lawsuit nj animals one get an ESA the! Alone or deal with stressful situations more easily of years only to apartments ( those! 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Nj Advance Media for NJ.com 2014 Landlord to Pay $ 1M in emotional support animals in New apartments! Local governments have laws that protect other support animals are animals that are meant to be interviewed when reached phone... And more patients have made notable progress on improving their mental condition made notable progress on improving their mental.! Of emotional support animals a phone call or email seeking comment on Friday of other animal species the! Breed restrictions on the animal 's market value include anxiety and depression as the most common types, may... The LAD that emotional support animal need specialized training registry is one of many online that! S accusing the airline and the law firm found another case involving Megan McFadden and her that... Law firm found another case involving Megan McFadden and her dog that served as an emotional support animal be than! The replacement cost probably won ' t amount to much trial and damages... Industry has developed around fake emotional support animals receive specialized training or breed restrictions the..., Orlando was fired, the business lays out its philosophy that declares `` we believe in teamwork ``! However, a Housing provider may impose reasonable conditions on approvals emotional support animal usually compensated. Prescribe a legitimate ESA letter | ESA CertificationEmotional support animals are typically cats and dogs, but many could! Reportedly told Alaska Airlines that the dog was prescribed by ( Orlando s... S ) treating physician, " said Director Wainer Apter for additional vet bills ESA but... Conditions on approvals emotional support animals in New York apartments and Co-Ops our affiliate links we may a... Type of disability also declined to comment " said Director Wainer Apter more easily who suffers from an support. 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2020 emotional support animal lawsuit nj
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Frühlingsnacht (1840) Op.39 no.12
Liederkreis (Op.39)
Frühlingsnacht
Überm Garten durch die Lüfte
Hört' ich Wandervögel zieh'n,
Das bedeutet Frühlingsdüfte,
Unten fängt's schon an zu blühn.
Jauchzen möcht' ich, möchte weinen,
Ist mir's doch, als könnt's nicht sein!
Alte Wunder wieder scheinen
Mit dem Mondesglanz herein.
Und der Mond, die Sterne sagen's,
Und im Traume rauscht's der Hain
Und die Nachtigallen schlagen's:
Sie ist Deine, sie ist Dein!
Over the garden, through the air
I heard birds of passage fly,
A sign that spring is in the air,
Flowers already bloom below.
I could shout for joy, could weep,
For it seems to me it cannot be!
All the old wonders come flooding back,
Gleaming in the moonlight.
And the moon and stars say it,
And the dreaming forest whispers it,
And the nightingales sing it:
'She is yours, is yours!'
Translations by Richard Stokes, author of The Book of Lieder (Faber, 2005)
Robert Schumann was a German composer and influential music critic. He is widely regarded as one of the greatest composers of the Romantic era. Schumann left the study of law, intending to pursue a career as a virtuoso pianist. He had been assured by his teacher Friedrich Wieck that he could become the finest pianist in Europe, but a hand injury ended this dream. Schumann then focused his musical energies on composing.
Schumann's published compositions were written exclusively for the piano until 1840; he later composed works for piano and orchestra; many Lieder (songs for voice and piano); four symphonies; an opera; and other orchestral, choral, and chamber works. Works such as Kinderszenen, Album für die Jugend, Blumenstück, the Sonatas and Albumblätter are among his most famous. His writings about music appeared mostly in the Neue Zeitschrift für Musik (New Journal for Music), a Leipzig-based publication which he jointly founded.
In 1840, Schumann married Friedrich Wieck's daughter Clara, against the wishes of her father, following a long and acrimonious legal battle, which found in favor of Clara and Robert. Clara also composed music and had a considerable concert career as a pianist, the earnings from which formed a substantial part of her father's fortune.
Schumann suffered from a lifelong mental disorder, first manifesting itself in 1833 as a severe melancholic depressive episode, which recurred several times alternating with phases of 'exaltation' and increasingly also delusional ideas of being poisoned or threatened with metallic items. After a suicide attempt in 1854, Schumann was admitted to amental asylum, at his own request, in Endenich near Bonn. Diagnosed with "psychotic melancholia", Schumann died two years later in 1856 without having recovered from his mental illness.
Taken from wikipedia. To read the rest of the article, please click here.
Joseph Freiherr von Eichendorff was a German poet, novelist, playwright, literary critic, translator, and anthologist. Eichendorff was one of the major writers and critics of Romanticism. Ever since their publication and up to the present day, some of his works have been very popular in Germany.
Eichendorff first became famous for his novella Aus dem Leben eines Taugenichts (Memoirs of a Good-For-Nothing) and his poems. The Memoirs of a Good-For-Nothing, a typical romantic novella, whose main themes are wanderlust and love. The protagonist, the son of a miller, rejects his father's trade and becomes a gardener at a Viennese palace where he subsequently falls in love with the local duke's daughter. As, with his lowly status, she is unattainable for him, he escapes to Italy - only to return and learn that she is the duke's adopted daughter, and thus within his social reach. With its combination of dream world and realism, Memoirs of a Good-For-Nothing is considered to be a high point of Romantic fiction. One critic stated that "Eichendorff's 'Good-For-Nothing' is the "personification of love of nature and an obsession with hiking." Thomas Mann called Eichendorff's Good-For-Nothing a combination of "the purity of the folk song and the fairy tale."
Many of Eichendorff's poems were first published as integral parts of his novellas and stories, where they are often performed in song by one of the protagonists. The novella Good-For-Nothing alone contains 54 poems.
25 Oct 2018: Die schöne Magelone: Thomas Oliemans & Malcolm Martineau
23 Oct 2016: Mastercourse 2016 (for T&Ts)
15 Oct 2016: The Life & Times of Robert Schumann Session I
22 Oct 2019: 61. Forest Twilight: Sophie Karthäuser, Stephan Loges & Eugene Asti
19 Apr 2018: Rycote Park - Jessica Dandy, Julien van Mellaerts & Sholto Kynoch
19 Oct 2017: La Bonne Chanson: Mark Padmore & Imogen Cooper
26 Oct 2016: Eichendorff Liederkreis: Felicity Lott & Eugene Asti
19 Oct 2016: Clara's Piano: Bryony Williams, John Mark Ainsley & David Owen Norris
19 Oct 2016: Sarah Walker: Song Cycle
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ANKARA, 6 December 2012: A four member parliamentary delegation of Senators from Pakistan was was warmly received by the Turkish President Mr. Abdullah Gul here today.
Led by Chairman of Senate Standing Committee on Foreign Affairs, Kashmir & Gilgit Baltistan Haji Muhammad Adeel, the delegation included Senator Syed Muzafar Hussain Shah, Senator Maulana Abdul Ghafoor Haideri, Senator Sehar Kamran and Mr. Amjad Pervez, Secretary of the Committee.
President Gul said that the visit of Senate Parliamentary delegation is very important and meaningful for further enhancing the existing extra-ordinary good relations between Pakistan and Turkey. He said both the countries have traditions of supporting each other at international fora on various issues. Referring to the visit of the delegation to Turkish Republic of Northern Cyprus, he thanked them for the support for a peaceful and lasting solution of the Cyprus issue.
On Kashmir issue, President Gul stated that there is a great deal of awareness about the Kashmir issue in Turkey. He said Kashmir issue was a product of the unjust international system. Commending Pakistan for its positive stand on the issue, Mr. Gul expressed the hope that the dialogue between the leadership of Pakistan and India would lead to an amicable solution.
On bilateral economic and commercial relations, President Gul said that the two countries are working on multiple tracks to boost trade and investment links. Mentioning 'Gul train' he said with efficient operation and reduction in its duration, the cargo train can play an important role in augmenting trade links between the two countries and beyond.
Referring to the forthcoming 7th trilateral Afghanistan-Pakistan-Turkey summit being held in Ankara, President Gul said he is looking forward to meet President Zardari. He said that he was fully aware with Pakistan's difficulties arising out of instability in Afghanistan and the three countries are working through trilateral process to bring peace, stability and development in Afghanistan.
Senators thanked President Gul for his strong support and friendship with Pakistan. They informed that the long-lasting special relations of Pakistan and Turkey enjoy all the support across the political divide.
Haji Adeel also showed gratitude for Turkey's solidarity and assistance during natural disasters in Pakistan. He said Pakistan and Turkey are two important Muslim countries and can play a critical role for resolution of outstanding disputes like Cyprus, Kashmir and Palestine through concerted and united efforts of the Islamic world.
The visiting delegation also met with Speaker of Turkish Grand National Assembly (TGNA) Mr. Cemil Çiçek (pronounced as Jamil Chichek). Mr. Cemil Çiçek said such an exchange of parliamentary delegations will help boost our relations and shall help in evolving joint strategies to tackle common issues.
Haji Adeel said Turkey is our second home and appreciated Turkish support for the cause of oppressed people of Indian Occupied Kashmir.
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Less of a stink in diabetes patients?
Published: Monday, March 16, 2009 - 09:34 in Health & Medicine
Hydrogen sulfide (H2S) is commonly associated with smell of rotten eggs, stink bombs and blocked drains but lower blood levels of the gas are possibly linked to cardiovascular complications in some male patients with type II diabetes, according to research recently presented by researchers at the Peninsula Medical School in the South West of England at the Annual Diabetes UK Professional Conference in Glasgow this week and published in Diabetic Medicine. H2S is produced naturally within our bodies, along with other chemical compounds such as nitric oxide, where it is believed to help regulate blood pressure. Research shows that a balance between these compounds relates to good health, whereas an imbalance could indicate disease. In the case of diabetes, common complications of the disease are high blood pressure and microvascular dysfunction, which leads to damage of the tiny blood vessels (microvessels) that deliver blood, oxygen and nutrients to the eyes, skin, nerves and kidney.
Dr. Matt Whiteman of the Peninsula Medical School and colleagues from the Peninsula National Institute for Health Research (NIHR) Clinical Research Facility have compared the levels of H2S in blood samples taken from healthy people and male patients with type II diabetes and found markedly decreased levels of H2S in the diabetes patients. Lower H2S levels were associated with clinical markers of impaired microvessel function suggesting that a loss of this blood pressure lowering gas could be a contributing factor in the development of vascular complications in patients with diabetes.
Previous work on H2S has almost exclusively been carried out on animals in the laboratory however work carried out at PMS in the recently opened Peninsula NIHR Clinical Research Facility has been the first to investigate the role of H2S in any disease in humans. Dr. Whiteman commented: "Our previous work in the test tube has shown the potential for H2S to mediate blood pressure regulation. However, this is the first study examining H2S levels in a human disease with relevant clinical indices of vascular health."
He added: "It would appear that in this study, male patients with diabetes have lower levels of H2S in their blood compared to otherwise healthy males of the same age. Lower levels of H2S could effect how blood vessels dilate. Although these are early days in a new field of research, manipulation of H2S levels by novel or existing pharmacological or even dietary means in the future could help treat or prevent cardiovascular complications caused by diabetes and other related conditions."
Source: The Peninsula College of Medicine and Dentistry
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DEC. 1 MEN'S BASKETBALL: Syracuse holds off Cornell
MARK FRANK / Associated Press
Dec 2, 2018 at 8:01 PM Dec 2, 2018 at 8:01 PM
SYRACUSE, N.Y. (AP) — Round one of the Boeheims versus Boeheim went to Syracuse but it wasn't easy. The Orange just managed to avoid a huge upset against Cornell Saturday.
Brothers Buddy Boeheim of Syracuse and Jimmy Boeheim of the Big Red played against each other for the first time in their collegiate careers. Their father, Hall of Fame coach Jim Boeheim, didn't have much time to enjoy the family affair as he watched his team struggle to a 63-55 win for its 39th straight victory against its upstate foe.
Tyus Battle scored 26 points and Oshae Brissett had 19 as Syracuse (5-2) held off Cornell (4-4) to remain unbeaten at home.
"There's a lot of things we're not doing well," Jim Boeheim said. "Tyus and Oshae played well enough for us to win. Otherwise there wasn't a lot of good things. I can't tell you how disappointing it is. Really bad."
The effort was particularly disturbing coming off his team's impressive road win at Ohio State.
"It's not fun to watch. I don't like watching it," Boeheim added. "And that's disappointing coming off Wednesday night where we did a lot of things well and we come out here and play like this. I can't tell you how disappointing it is."
It was so disappointing he couldn't even take pleasure watching his sons play against each other.
"I was so worried about the game when it was going on, I wasn't really thinking about that (his kids). Their mother can think about that," Boeheim said, who added Jimmy was "good" and "is on the verge of really playing well and helping" his team. Jimmy Boeheim scored nine points and registered six rebounds and four assists. Buddy hit a three-pointer.
Matt Morgan paced Cornell with 26 points, 16 in the second half. He was 6-of-10 from 3 and 9-of-14 overall. Josh Warren added eight.
"We put up a fight and that's what we wanted to come in and do," Morgan said. "Control the pace of the game, control the tempo. "They just hit shots towards the end but I'm proud of the way we fought. Nothing much more than you could ask for."
Syracuse took its biggest lead at 39-24 on a three-pointer by Battle but Cornell stormed back, going on a 12-2 run over the next four minutes to close the gap to 41-36 with a little more than 13 minutes to go. Brissett's consecutive threes, sandwiched around two foul shots by Jimmy Boeheim, gave the Orange a 47-38 lead but Cornell closed to 47-45 on two threes by Morgan and a free throw by Steven Julian.
Cornell took its first lead at 48-47 on a three-pointer by Morgan with 7:53 to go. A layup by Marek Dolezaj gave the Orange a 49-48 lead but two free throws by Morgan put Cornell in front, 50-49 with 6:16 to go. A three-pointer and layup by Battle on a Cornell turnover extended Syracuse's margin to 54-50 with 3:50 remaining.
Elijah Hughes' lay-in and a desperation three by Frank Howard, his only points of the game, gave the Orange a 59-52 lead. Battle closed out Syracuse's scoring on a fall-back jumper.
"It was a good fight," said Cornell coach Brian Earl. "We fought hard the whole time. We could've folded. We probably would've folded in the past but we didn't. It was a pretty good step forward. We just came up short against a good team."
For the Orange, the game was a wake-up call.
"We weren't ready to play and when we do that anyone can make it a game with us," Battle said. "If we play Tuesday (against Northeastern) like we did tonight, we'll lose.
Syracuse had a 33-24 halftime lead. Battle and Brissett accounted for 27 of the Orange's 33 first-half points.
Matt Morgan has now scored in double figures in 59 straight games.
COMING UP EMPTY
After scoring 17 and 18 points in his last two games, Syracuse's Elijah Hughes had just four points.
The Orange got only 18 points from players not named Tyus Battle and Oshae Brissett.
CORNELL: There are no moral victories but the Big Red should feel pretty good about itself, not just hanging around Syracuse but taking the lead late in the game, threatening to break Syracuse's 38-game winning streak against the Big Red.
SYRACUSE: The Orange have work to do. After an impressive road win against Ohio State, Syracuse looked sluggish on offense with only Battle and Brissett doing any damage.
Cornell has a two-week layoff until the Big Red travels to Niagara for a Dec. 16 matchup.
Syracuse hosts Northeastern Tuesday night, its second in a stretch of seven consecutive games at home.
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\section{Introduction}
The application of complex networks in a broad range of social and biological systems has been the subject of much interest recently \cite{castellano09, dunne02, jeong00, negyessy06, cancho01}. These applications involve -- among others -- the description of ``small-world'' property of the networks \cite{watts98} or the consequences of scale-free degree distributions \cite{barabasi02}. Many aspects of the real systems can be studied in the framework of undirected networks \cite{newman10,newman03,pastorsatorras01,pastorsatorras04}. The most important property of the network is the degree distribution $p_k$ which is the probability of a randomly chosen node having $k$ edges \cite{barabasi02}. Other features of the network can be understood through the degree distribution (average length of the shortest path between nodes, average number of edges between a node's neighbors \cite{newman01}, the characteristics of epidemics on the network \cite{pastorsatorras01} or robustness against failures and attacks \cite{barabasi00}).
However, most of the real networks are directed, i.e., the connection between two units of the system is not symmetric. Many structural properties of a directed network can be derived from undirected networks in a straightforward way \cite{newman10}, but the appearance of directionality also opens the door to features that are essentially different from those in undirected graphs (Fig.~\ref{fig:directed_network}).
\begin{figure}[!h]
\centering
\mbox{
\subfloat[\textbf{Undirected graph}]{\includegraphics[width=8cm]{Fig1a.eps}}
\subfloat[\textbf{Directed graph}]{\includegraphics[width=8cm]{Fig1b.eps}}}
\mbox{
\subfloat[\textbf{Giant component}]{\includegraphics[width=8cm]{Fig1c.eps}}
\subfloat[\textbf{Giant components}]{\includegraphics[width=8cm]{Fig1d.eps}}}
\caption{The difference between undirected (a) and directed (b) graphs. On large scale, the structure of the undirected graph (c) can be described by the largest connected component (the \emph{giant component} or GC) and the \emph{small components} (SC) \cite{bollobas01}. In the case of a directed graph (d), the giant components are best summarized in the ``bow-tie'' diagram \cite{broder00,dorogovtsev01}: the primary core is the \emph{giant strongly connected component} ($\mathcal{G}_{S}$). Inside the $\mathcal{G}_{S}$, every node can reach every other. There are nodes that can reach the whole $\mathcal{G}_{S}$ but not vice verse (IN) and together with the $\mathcal{G}_{S}$ they form the \emph{giant in component} ($\mathcal{G}_{in}$). The similar is true for the \emph{giant out component} ($\mathcal{G}_{out}$) but in the reversed direction. There are nodes that connect the $\mathcal{G}_{in}$ and $\mathcal{G}_{out}$ components but are not in the $\mathcal{G}_{S}$, they form the \emph{tubes}. There are also \emph{tendrils} that attach to the $\mathcal{G}_{in}$ and $\mathcal{G}_{out}$ components. The rest of the nodes are in the small \emph{disconnected components} (DC).}
\label{fig:directed_network}
\end{figure}
In the presence of directed edges, the organization level of the nodes on a large scale can be very complex and \emph{flow hierarchy} can emerge. It is a global structure of the network that is the result of the different roles of the nodes (see Fig.~\ref{fig:hierarchy_types} for the comparison of different hierarchy types).
\begin{figure}
\centering
\mbox{
\subfloat[\textbf{Order hierarchy}]{\includegraphics[width=10cm]{Fig2a.eps}}}
\mbox{
\subfloat[\textbf{Nested hierarchy}]{\includegraphics[width=10cm]{Fig2b.eps}}}
\mbox{
\subfloat[\textbf{Flow hierarchy}]{\includegraphics[width=10cm]{Fig2c.eps}}}
\caption{The three different types of hierarchy. (a) \emph{Order hierarchy} is simply a rank assigned to each unit making them an ordered set. (b) \emph{Nested hierarchy} is the hierarchy of the nested clusters of nodes. (c) In a (complete) \emph{flow hierarchy}, nodes can be layered in different levels so that the nodes that are influenced by other nodes (via an out-edge) are at lower levels. As the figures illustrate, each type can be transformed into a flow hierarchy. In the order hierarchy one can introduce a directed edge between every pair of adjacent nodes in the hierarchy. In the nested hierarchy one can assign a virtual node to each cluster and link a cluster to its contained clusters.}
\label{fig:hierarchy_types}
\end{figure}
As the growing number of findings show, hierarchy is a frequently appearing property of real networks, especially of networks describing social interactions \cite{nagy10,fushing11,ma04,huseyn84,pumain06}. The concept of hierarchy has led to different definitions (Fig.~\ref{fig:hierarchy_types}) and also to algorithms for measuring it in both directed and undirected networks \cite{lane06,wimberley09,carmel02,trusina04,rowe07,memon08}. In this paper we investigate \emph{flow hierarchy} by a corresponding measure, the \emph{global reaching centrality} ($G_R$), that has the intention to quantify that \cite{mones12}. In the following sections we show that the behavior of the $G_R$ is different below and above the critical average degree $k_c$, i.e., in the absence and presence of the giant components. We also give an approximation to its dependence on the average degree for different random network models when there are no degree correlations. In the last section we study the effects of degree correlations.
\section{Reaching centralities in uncorrelated random networks}
\subsection{Local and global reaching centrality}
Given a directed graph $G(V,E)$ with $N=|V|$ vertices and $M=|E|$ edges, the \emph{local reaching centrality} of node $i$ is defined as the number of reachable nodes via out-degrees divided by the total number of nodes:
\eq{c_R(i)=\frac{|S_i|}{N-1}=\frac{C_R(i)}{N-1}}{eq:cR_def}
where $S_i=\{j\in V|0<d^{out}(i,j)<\infty\}$ is the set of nodes that has finite, non-zero out-distance from node $i$. We will denote the size of the reachable set (i.e., the local reaching centrality without normalization) by $C_R$. The global reaching centrality of the graph is the normalized sum of the distances from the maximum local reaching centrality:
\eq{G_R=\frac{1}{N-1}\sum_i\Big[c_R^{max}-c_R(i)\Big]}{eq:grc_def1}
The normalization factor is the maximum possible value of the sum in a graph with $N$ nodes (this can be achieved in a star graph). The definition of the $G_R$ can be written in a more expressive form:
\eq{G_R=\frac{N}{(N-1)^2}\Big[C_R^{max}-\langle C_R\rangle\Big]}{eq:grc_def2}
Hence, the $G_R$ is proportional to the difference between the average and the maximum size of the reachable sets.
\subsection{Generating function method in directed networks}
The calculation of the reachable set of a node is equivalent to the problem of finding the out-component, which is the union of the reachable set and the node itself. The out-component can be determined by the generalization of the generating function formalism developed by Newman et al. \cite{newman01, newman10} to directed networks. Assuming that our graph has joint degree distribution $p_{ij}$, that is the probability of a randomly chosen node having $i$ in-degree and $j$ out-degree, the corresponding double generating function can be defined as
\eq{g_{00}(x,y)=\sum_{i,j=0}^\infty p_{ij}x^iy^j}{eq:g00_def}
and the generating functions for the excess in- and out-degree distributions \cite{newman10}:
\eq{g_{10}(x,y)=\frac{1}{\langle k\rangle}\partial_xg_{00}(x,y)}{eq:g10_def}
\eq{g_{01}(x,y)=\frac{1}{\langle k\rangle}\partial_yg_{00}(x,y)}{eq:g01_def}
Let $\pi_s^{out}$ denote the probability that a randomly chosen node has out-component of size $s$ and $\rho_s^{out}$ the probability that a randomly chosen edge points to an out-component of size $s$. Their generating functions are:
\eq{h_0(y)=\sum_{s=1}^\infty \pi_s^{out}y^s}{eq:h0_def}
\eq{h_1(y)=\sum_{s=1}^\infty \rho_s^{out}y^s}{eq:h1_def}
If we assume that the graph is \emph{locally tree-like} (i.e., loops are infrequent), they satisfy the following equations \cite{newman10}:
\eq{h_0(y)=yg_{00}[1,h_1(y)]}{eq:h0_eq}
\eq{h_1(y)=yg_{10}[1,h_1(y)]}{eq:h1_eq}
Using these equations for the generating functions, it is possible to derive a closed formula for the out-components in directed graphs (for the details see Appendix A):
\eq{\pi_s^{out}=\frac{\langle k\rangle}{(s-1)!}\Bigg[\frac{\mathrm{d}^{s-2}}{\mathrm{d} y^{s-2}}\bigg(g_{01}(1,y)g_{10}(1,y)^{s-1}\bigg)\Bigg]_{y=0}}{eq:pi_formula}
Thus, if we know the joint degree distribution, we can calculate $P(C_R)$ (and thus the distribution of the local reaching centralities as well, since it differs from $P(C_R)$ only by a scale factor). In order to calculate $P(C_R)$, we have to determine the out-components and apply the $s=C_R+1$ substitution. With the knowledge about $P(C_R)$, we are able to calculate the $G_R$ at different average degrees.
It is important to note that Eq.~(\ref{eq:pi_formula}) describes only the \emph{small} reaching centralities, i.e., the distribution of local reaching centralities of the nodes outside the giant components. Above the critical average degree, where the giant components are already present, a significant fraction of the nodes can reach finite fraction of the whole network. In this regime, there are three type of nodes besides the ones with small reaching centrality: the nodes inside the $\mathcal{G}_{S}$, $\mathcal{G}_{in}$ and $\mathcal{G}_{out}$, each type can reach differenct fraction of the graph. Thus, in the distribution of the local reaching centrality above the percolation threshold, a peak with finite width appears at large values.
Before applying these equations to random networks with different degree distributions, we determine the $G_R$ for the case of a hierarchical tree.
\subsection{Hierarchical tree}
\subsubsection{Local reaching centralities}
In a tree graph with $N$ vertices and branching number of $d$, nodes in the same level have the same local reaching centrality. Let us denote the size of reachable set of a node in the $\ell$-th level by $C_R^{(\ell)}$. The number of nodes and the size of the reachable set in the $\ell$-th level are the following (see Fig.~\ref{fig:tree_levels}):
\eq{k_\ell=d^\ell}{eq:tree_kl}
\eq{C_R^{(\ell)}=\frac{N-\sum_{j=0}^\ell d^j}{d^\ell}=\frac{N-\frac{d^{\ell+1}-1}{d-1}}{d^\ell}}{eq:tree_CRl}
\begin{figure}
\centering
\includegraphics[width=10cm]{Fig3.eps}
\caption{The number of nodes and size of reachable sets in the different levels.}
\label{fig:tree_levels}
\end{figure}
The probability that a randomly chosen node has a reachable set of size $C_R^{(\ell)}$ is $k_\ell/N$. Substituting Eq.~(\ref{eq:tree_kl}) in Eq.~(\ref{eq:tree_CRl}) gives:
\eq{P\big(C_R^{(\ell)}\big)=\frac{N(d-1)+1}{N(d-1)C_R^{(\ell)}+Nd}}{eq:tree_PCR}
In the asymptotic limit of $N\to\infty$, we get the following approximation for the probability of the normalized local reaching centrality (we also omit the $\ell$ index, since in the mentioned limit, the allowed discrete values of $C_R^{(\ell)}/(N-1)$ are becoming dense in $[0;1]$ and $c_R^{(\ell)}$ becomes continuous) :
\eq{P(c_R)\approx\frac{1}{Nc_R+\frac{d}{d-1}}}{eq:tree_PcR}
Comparison with numerical results is plotted in Fig.~\ref{fig:cr_tree}.
\begin{figure}
\centering
\includegraphics[angle=-90,width=10cm]{Fig4.eps}
\caption{Theoretical and measured distribution of the local reaching centrality in the hierarchical tree. The dots are the results from graphs with $d=2$ (red squares) and $d=3$ (black circles), the corresponding number of nodes are $N_2=32767$ and $N_3=29524$.}
\label{fig:cr_tree}
\end{figure}
In the simulations, trees with branching number of 2 and 3 are used, the corresponding number of levels are 15 and 10. The numerical results show satisfactory agreement with Eq.~(\ref{eq:tree_PcR}).
\subsubsection{Global reaching centrality}
Using the equations for the number of nodes and size of reachable sets in the $\ell$-th level, we can easily calculate the size of the reachable sets:
\eq{\langle C_R\rangle=\sum_{\ell=0}^{L-1}P\big(C_R^{(\ell)}\big)\cdot C_R^{(\ell)}=\sum_{\ell=0}^{L-1}\bigg(1-\frac{d^{\ell+1}-1}{N(d-1)}\bigg)}{eq:tree_CR_av1}
where $L$ denotes the number of levels (the level of the root is zero). This number can be determined by the constraint that the sum of the nodes in all levels gives the number of nodes:
\eq{\sum_{\ell=0}^{L-1}d^\ell=\frac{d^L-1}{d-1}=N}{eq:tree_L_def}
Arranging for $L$ and simplifying it:
\eq{L=\frac{\ln[N(d-1)+1]}{\ln d}}{eq:tree_L_eq}
Calculating the sum in the right hand side of Eq.~(\ref{eq:tree_CR_av1}) gives:
\eq{\langle C_R\rangle=L\bigg(1+\frac{1}{N(d-1)}\bigg)-\frac{d}{(d-1)}}{eq:tree_CR_av2}
Substituting $L$ into the last equation and using Eq.~(\ref{eq:grc_def2}) we get:
\begin{equation}
G_R=\frac{N}{(N-1)^2}\Bigg[\underbrace{N-1}_{C_R^{max}}-\underbrace{\frac{\ln[N(d-1)+1]}{\ln d}\bigg(1+\frac{1}{N(d-1)}\bigg)+\frac{d}{(d-1)}}_{\langle C_R\rangle}\Bigg]
\label{eq:tree_grc}
\end{equation}
In the asymptotic case of $N\to\infty$:
\eq{G_R=1+\frac{2d-1}{N(d-1)}-\frac{\ln[N(d-1)+1]}{N\ln d}}{eq:tree_grc_asymptotic}
In Fig.~\ref{fig:grc_tree} we show the comparison of Eq.~(\ref{eq:tree_grc}) with the simulations.
\begin{figure}
\centering
\includegraphics[angle=-90,width=10cm]{Fig5.eps}
\caption{Comparison of the measured $G_R$ with the theoretical prediction. The dots are the $G_R$ of trees with $N=10^5$ nodes. Because of the fixed number of nodes, the number of levels are approximated by Eq.~(\ref{eq:tree_L_def_modified}), which neglects the lowermost nodes in the total number of nodes. The deviations from the theoretical curve depends on the branching number. For branching numbers with an integer power close to $10^5$, the theoretical curve is more accurate.}
\label{fig:grc_tree}
\end{figure}
In the numerical results, the number of nodes is $10^5$ for every branching number. Thus, Eq.~(\ref{eq:tree_L_def}) for the number of levels does not hold exactly: there are less nodes in the last level than expected. This fact is taken into account by summing up only to $L-2$ in Eq.~(\ref{eq:tree_L_def}):
\eq{\sum_{\ell=0}^{L-2}d^\ell=N}{eq:tree_L_def_modified}
This means that in the expression of $L$, the number of nodes is replaced by a reduced number (which is the nodes at the lowermost level). This modification gives a better agreement with the numerical calculations for large branching numbers. From Eq.~(\ref{eq:tree_L_def}), it is also clear that the approximation is more accurate if a branching number has an integer power close to $10^5$. This can be observed in Fig.~\ref{fig:grc_tree} as well.
\subsection{Erd\H{o}s--R\'{e}nyi graph}
\subsubsection{Local reaching centralities}
In the case of uncorrelated in- and out-degrees, the joint degree distribution of an Erd\H{o}s--R\'{e}nyi (ER) graph \cite{erdos60,bollobas01} is the product of two independent Poisson distributions:
\eq{p_{ij}=e^{-2\langle k\rangle}\frac{\langle k\rangle^{i+j}}{i!j!}}{eq:ER_pij}
where $\langle k\rangle$ denotes the average degree. The double generating function has the form:
\eq{g_{00}(x,y)=e^{\langle k\rangle(x+y-2)}}{eq:ER_g00}
which is also the generating function of the excess degree distributions in this case. Now, using Eq.~(\ref{eq:pi_formula}) we get:
\eqarray{\pi_s^{out} & = & \frac{\langle k\rangle}{(s-1)!}\Bigg[\frac{\mathrm{d}^{s-2}}{\mathrm{d} y^{s-2}}\bigg(e^{\langle k\rangle s(y-1)}\bigg)\Bigg]_{y=0}= \nonumber \\
& = & \frac{\langle k\rangle^{s-1}s^{s-2}}{(s-1)!}e^{-\langle k\rangle s}}{eq:ER_pi}
And for the size of small reachable sets (without the giant components):
\eq{P(C_R)=\frac{\langle k\rangle^{C_R}(C_R+1)^{C_R-1}}{C_R!}e^{-\langle k\rangle(C_R+1)}}{eq:ER_PCR}
Fig.~\ref{fig:cr_er} shows this result compared with the numerical distributions.
\begin{figure}
\centering
\includegraphics[angle=-90,width=10cm]{Fig6.eps}
\caption{Distribution of the small reachable set sizes for the ER graph, based on the assumption that the graph is locally tree-like. Below the transition point (red squares), there is no node that can reach any finite part of the graph. This changes when the $\mathcal{G}_{S}$ appears at $\langle k\rangle=1$ (gray circles). The numerical results are the averages of 1000 independent calculations on networks with $N=10^4$. Note that Eq.~(\ref{eq:ER_PCR}) describes the distribution of the small components, thus the emerging $\mathcal{G}_{S}$ (the peak at large reachable sets) is out of its scope.}
\label{fig:cr_er}
\end{figure}
It is important to understand the limits of Eq.~(\ref{eq:ER_PCR}). It is only the distribution for the size of the \emph{small reachable sets}, i.e., it does not contain the $\mathcal{G}_{S}$\footnote{However, the integrated size of the giant components is encoded in the distribution, since it is normalized to \mbox{$N-|\mathcal{G}_{W}|$}, where $\mathcal{G}_{W}$ is the \emph{giant weakly connected component}.}. This can be seen on the plots. Before the transition, all of the nodes are in separated small components and the reaching centrality distribution vanishes very quickly. Above the transition point, they start to aggregate in the $\mathcal{G}_{S}$. Note that in this regime, where the giant component appears, a large amount of nodes have a large reachable set. More precisely, the nodes in the $\mathcal{G}_{in}$ component can reach every node in $\mathcal{G}_{out}$. This is clearly seen in Fig.~\ref{fig:cr_er}: the peak has a finite width, corresponding to the three different giant components.
\subsubsection{Global reaching centrality}
We have to distinguish between the graph without the $\mathcal{G}_{S}$ and with the $\mathcal{G}_{S}$ \cite{newman10}. Below the transition point $k_c$, there are only small components. All of the nodes can reach only infinitesimal part in the graph, thus having an average reachable set size of order unit ($\langle C_R\rangle=\mathcal{O}(1)$). In this regime, the $G_R$ is dominated by the maximum value of the local reaching centrality. Since most of the nodes can reach very few other nodes and the distribution vanishes quickly, we can assume that the largest reachable set belongs to only one node (and that the corresponding out-component has the smallest relative frequency). Given a graph with $N$ nodes, this condition translates as $P(C_R)\approx1/N$ for $C_R=C_R^{max}$. Thus, finding the reachable set size that has only one realization can lead us to find the largest component. In the $C_R^{max}\gg1$ limit we can use the Stirling-formula to approximate $P(C_R)$:
\eq{P(C_R)\approx e^{1-\langle k\rangle}\frac{\big(\langle k\rangle e^{1-\langle k\rangle}\big)^{C_R}}{\sqrt{2\pi}(C_R+1)^{3/2}}}{eq:ER_PCR_asymptotic}
Writing the $P(C_R)\approx1/N$ condition and rearranging it for $C_R$ we get the following exponential equation:
\eq{\Bigg(\frac{\sqrt{2\pi}}{Ne^{1-\langle k\rangle}}\Bigg)^{2/3}(C_R+1)=\exp\bigg[\frac{2}{3}(\ln \langle k\rangle+1-\langle k\rangle)C_R\bigg]}{eq:ER_CRmax_eq}
This equation can be solved in terms of the \emph{Lambert W} function \cite{corless96}. The equation of the form
\eq{A(x-R)=e^{-Bx}}{eq:ER_exponential_equation}
has the solution of $x=R+\frac{1}{B}W\Big[\frac{Be^{-Br}}{A}\Big]$. Now we have
\eq{A=\Big(\frac{\sqrt{2\pi}}{Ne^{1-\langle k\rangle}}\Big)^{2/3}}{eq:ER_A}
\eq{B=\frac{2}{3}(\ln \langle k\rangle+1-\langle k\rangle)}{eq:ER_B}
\eq{R=-1}{eq:ER_R}
so the final expression for the largest local reaching centrality:
\begin{equation}
C_R^{max}=-\frac{W\bigg[\frac{2}{3}(\ln \langle k\rangle+1-\langle k\rangle)e^{-\frac{2}{3}(\ln \langle k\rangle+1-\langle k\rangle)}\Big(\frac{\sqrt{2\pi}}{Ne^{1-\langle k\rangle}}\Big)^{-2/3}\bigg]}{\frac{2}{3}(\ln \langle k\rangle+1-\langle k\rangle)}-1
\label{eq:ER_CRmax}
\end{equation}
Now we turn our attention to the case when the $\mathcal{G}_{S}$ is already present. In this case, for a good approximation, we can ignore those nodes that are not in the bow-tie (they are relevant only in the average local reaching centrality, but they have only an infinitesimal contribution). Thinking of the ``bow-tie'' picture, we can assume that there are some nodes that can reach the whole bow-tie. Thus, $C_R^{max}\approx|\mathcal{G}_{in}|+|\mathrm{\mathcal{G}_{out}}|-|\mathcal{G}_{S}|$. The average is slightly different and nontrivial, but let assume that it is equivalent to the size of the giant out-component $\mathcal{G}_{out}$. If we assume that most of the nodes are gathering in the $\mathcal{G}_{S}$, it is also reasonable that the average size of reachable sets is dominated by the nodes in the $\mathcal{G}_{S}$ and they can reach the whole $\mathcal{G}_{out}$ component (see Fig.~\ref{fig:directed_network}d). Using these assumptions, the size of the reachable sets is approximately $|\mathrm{\mathcal{G}_{out}}|$. The relative sizes of these components are quite the same as the local reaching centrality. In the generating function formalism they are given by:
\eq{\frac{|\mathcal{G}_{S}|}{N}=S=1-g_{00}(u,1)-g_{00}(1,v)+g_{00}(u,v)}{eq:ER_gscc_eq}
\eq{\frac{|\mathcal{G}_{in}|}{N}=I=1-g_{00}(u,1)}{eq:ER_gin_eq}
\eq{\frac{|\mathrm{\mathcal{G}_{out}}|}{N}=O=1-g_{00}(1,v)}{eq:ER_gout_eq}
where $u$ and $v$ are the smallest non-zero solutions of the following equations \cite{newman10}:
\eq{u=g_{01}(u,1)}{eq:ER_u_eq}
\eq{v=g_{10}(1,v)}{eq:ER_v_eq}
Since the generating function is symmetrical in its variables, we have $u=v$. Using Eq.~(\ref{eq:ER_g00}), the solution can be written in terms of the Lambert W function giving:
\eq{u(\langle k\rangle)=-\frac{1}{\langle k\rangle}W(-\langle k\rangle e^{-\langle k\rangle})}{eq:ER_u_result}
And for the $G_R$ above the phase transition:
\eq{G_R=I-S=g_{00}[u(\langle k\rangle),1]-g_{00}[u(\langle k\rangle),u(\langle k\rangle)]}{eq:ER_grc}
The theoretical curve and the measurements are shown in Fig.~\ref{fig:grc_er}.
\begin{figure}
\centering
\includegraphics[angle=-90,width=10cm]{Fig7.eps}
\caption{Global reaching centrality in the ER graph. The dots are the average of 1000 independent calculations on networks with $N=10^4$. The errors are comparable to the size of the dots. The lines show the different approximations in the two regimes: below the percolation threshold (solid green line) and above it (dashed blue line). Both approximations tend to deviate from the numerical values near the transition point.}
\label{fig:grc_er}
\end{figure}
The theoretical curve in the $k_c<\langle k\rangle<2$ range is a little below the numerical results. This is in good accordance with the assumptions used in deriving Eq.~(\ref{eq:ER_grc}): the average reachable set is approximated by the $\mathcal{G}_{out}$ component, however at small average degrees, there are many small out-components that decrease the average. The relative sizes of the giant components are depicted on Fig.~\ref{fig:er_giant_components}.
\begin{figure}
\centering
\includegraphics[angle=-90,width=10cm]{Fig8.eps}
\caption{The relative sizes of the giant components of the bow-tie diagram in the ER network (Fig.~\ref{fig:directed_network}d). Although $\mathcal{G}_{out}$ (dashed blue line) grows quickly with the average degree, at low edge densities ($\langle k\rangle<2$) both components contain less than 80\% of the nodes.}
\label{fig:er_giant_components}
\end{figure}
It is clearly seen that near the critical average degree, an appreciable portion of the nodes is outside of the giant components and they all have very small reachable set. Thus, the difference between the largest and average reaching centrality is larger in the real network, resulting in a larger $G_R$. The theoretical curve below $k_c$ predicts lower $G_R$, which indicates that the distribution of $P(C_R)$ described by Eq.~(\ref{eq:ER_PCR}) is no more valid for the whole network when approaching the critical average degree.
\subsection{Exponential network}
\subsubsection{Local reaching centralities}
In this section we calculate $P(C_R)$ and the $G_R$ for the exponential network, motivated by the finding that the distribution of many real world networks can be well fitted by an exponential \cite{amaral00}. An uncorrelated exponential network has joint degree distribution of the form
\eq{p_{ij}=(1-e^{-1/\kappa})^2e^{-(i+j)/\kappa}}{eq:EXP_pij}
where the average degree can be obtained from the $\kappa$ parameter: $\langle k\rangle=(e^{1/\kappa}-1)^{-1}$. The double generating function and its derivatives are:
\eq{g_{00}(x,y) = \frac{(e^{1/\kappa}-1)^2}{(e^{1/\kappa}-x)(e^{1/\kappa}-y)}}{eq:EXP_g00}
\eq{g_{10}(x,y)=\frac{1}{\langle k\rangle}\frac{(e^{1/\kappa}-1)^2}{(e^{1/\kappa}-x)^2(e^{1/\kappa}-y)}}{eq:EXP_g10}
\eq{g_{01}(x,y)=\frac{1}{\langle k\rangle}\frac{(e^{1/\kappa}-1)^2}{(e^{1/\kappa}-x)(e^{1/\kappa}-y)^2}}{eq:EXP_g01}
By the formula for the out-components we have:
\eq{\pi_s^{out} = \frac{1}{\langle k\rangle^s(s-1)!}\frac{(2s-2)!}{s!}e^{-\frac{2s-1}{\kappa}}}{eq:EXP_pi1}
Substituting $e^{1/\kappa}=\frac{\langle k\rangle+1}{\langle k\rangle}$ we get:
\eq{\pi_s^{out}=\frac{(2s-2)!}{\langle k\rangle^s(s-1)!s!}\bigg(\frac{\langle k\rangle}{\langle k\rangle+1}\bigg)^{2s-1}}{eq:EXP_pi2}
Translating this to the small reachable sets (see Fig.~\ref{fig:cr_ex} for comparison with numerical calculations):
\eq{P(C_R)=\frac{(2C_R)!}{\langle k\rangle^{C_R+1}C_R!(C_R+1)!}\bigg(\frac{\langle k\rangle}{\langle k\rangle+1}\bigg)^{2C_R+1}}{eq:EXP_PCR}
\begin{figure}
\centering
\includegraphics[angle=-90,width=10cm]{Fig9.eps}
\caption{Distribution of the small reachable set sizes in the exponential graph. Numerical results are the average of 1000 measurement on networks with $N=10^4$. The emergence of the giant components (which are not included by the analytical distribution) can be clearly seen at $\langle k\rangle=1$ (gray circles) and $\langle k\rangle=1.3$ (purple triangles).}
\label{fig:cr_ex}
\end{figure}
\subsubsection{Global reaching centrality}
The first task is to find the smallest solution of the $u=g_{01}(u,1)$ and $v=g_{10}(1,v)$ equations. Since we assume uncorrelated exponential distributions, we have $u=v$. The equation
\eq{u=g_{01}(u,1)=\frac{1}{\langle k\rangle(e^{1/\kappa}-u)}}{eq:EXP_u_eq}
is quadratic in $u$ and has two solutions: $u_1=1$ and $u_2=1/\langle k\rangle$, thus for $\langle k\rangle<1$ there are no giant components and we can use the ``rarest component'' assumption as before with the ER graph. For this to do, we have to solve the following equation for $C_R$:
\eq{\frac{(2C_R)!}{\langle k\rangle^{C_R+1}C_R!(C_R+1)!}\bigg(\frac{\langle k\rangle}{\langle k\rangle+1}\bigg)^{2C_R+1}=\frac{1}{N}}{eq:EXP_CRmax_eq1}
Using the Stirling-formula (without going into the details), this equation can be approximated by the following:
\begin{equation}
\bigg(\frac{(\langle k\rangle+1)\sqrt{\pi}}{Ne}\bigg)\bigg(\frac{C_R+1}{C_R}\bigg)^{C_R}(C_R+1)^{3/2}=e^{\frac{2}{3}\ln\Big(\frac{4\langle k\rangle}{(\langle k\rangle+1)^2}\Big)C_R}
\label{eq:EXP_CRmax_eq2}
\end{equation}
We assume that the rarest component is much larger than one, thus $\big(\frac{C_R+1}{C_R}\big)^{C_R}\approx e$. This reduces our equations and we can rewrite it:
\eq{AC_R=e^{-BC_R}}{eq:EXP_exponential_equation}
Where we used the following shorthand notations:
\eq{A=\bigg(\frac{(\langle k\rangle+1)\sqrt{\pi}}{N}\bigg)^{2/3}}{eq:EXP_A}
\eq{B=-\frac{2}{3}\ln\bigg(\frac{4\langle k\rangle}{(\langle k\rangle+1)^2}\bigg)}{eq:EXP_B}
And neglected the additional $1$ in the left hand side. The solution of Eq.~(\ref{eq:EXP_CRmax_eq2}) is then:
\eq{C_R^{max}=\frac{1}{B}W\bigg(\frac{B}{A}\bigg)}{eq:EXP_CRmax}
If $\langle k\rangle>1$, this approximation fails because of the appearance of the giant components. Using the solution of Eq.~(\ref{eq:EXP_u_eq}), the relative sizes of the parts in the bow-tie diagram are:
\eq{S=\bigg(1-\frac{1}{\langle k\rangle}\bigg)^2}{eq:EXP_S}
\eq{I=1-\frac{1}{\langle k\rangle}}{eq:EXP_I}
\eq{O=1-\frac{1}{\langle k\rangle}}{eq:EXP_O}
By the same argument as with the ER graph, we get for the $G_R$:
\eq{G_R=1-\frac{1}{\langle k\rangle}-\bigg(1-\frac{1}{\langle k\rangle}\bigg)^2}{eq:EXP_grc}
This result is shown on Fig.~\ref{fig:grc_ex} along with the numerical results.
\begin{figure}
\centering
\includegraphics[angle=-90,width=10cm]{Fig10.eps}
\caption{Global reaching centrality of the exponential graph and the predicted curves in the different regimes of $\langle k\rangle$. Every numerical point is the average of 1000 independent runs on networks with $N=10^4$. The magnitude of the errors is in the order of the dot sizes.}
\label{fig:grc_ex}
\end{figure}
The same argument can be applied for the exponential network as in the previous section. The predicted curves fit well in the very small and in the large average degree regimes.
\subsection{Scale-free network}
Without exponential cutoff, the probability distribution and double generating function of a scale-free network \cite{goh01,chung02} are the following:
\eq{p_{ij}=\frac{(ij)^{-\gamma}}{\zeta(\gamma)^2}}{eq:SF_pij}
\eq{g_{00}(x,y)=\frac{\mathrm{Li}_\gamma(x)\mathrm{Li}_\gamma(y)}{\zeta(\gamma)^2}}{eq:SF_g00}
and the generating function of the excess degree distributions:
\eq{g_{10}(x,y)=\frac{\mathrm{Li}_{\gamma-1}(x)\mathrm{Li}_\gamma(y)}{\langle k\rangle x\zeta(\gamma)^2}}{eq:SF_g10}
\eq{g_{01}(x,y)=\frac{\mathrm{Li}_\gamma(x)\mathrm{Li}_{\gamma-1}(y)}{\langle k\rangle y\zeta(\gamma)^2}}{eq:SF_g01}
Newman showed in \cite{newman10} that the condition for the existence of the giant components is
\eq{\partial_x\partial_yg_{00}(x,y)|_{x,y=1}>\langle k\rangle}{eq:SF_giant_comp_condition1}
For the scale-free network, this equation reads as
\eq{\frac{\mathrm{Li}_{\gamma-1}(x)\mathrm{Li}_{\gamma-1}(y)}{xy\zeta(\gamma)^2}\bigg|_{x,y=1}>\langle k\rangle}{eq:SF_giant_comp_condition2}
Now, if make use of the relation between the exponent and the average degree: $\langle k\rangle=\frac{\zeta(\gamma-1)}{\zeta(\gamma)}$, and substitute $x=1$, $y=1$ we get:
\eq{\langle k\rangle^2>\langle k\rangle}{eq:SF_giant_comp_condition3}
or equivalently
\eq{\langle k\rangle>1}{eq:SF_giant_comp_condition4}
So, there is a giant component if the average degree is larger than one. But if we look at the function
\eq{\frac{\zeta(\gamma-1)}{\zeta(\gamma)}}{eq:SF_k_av}
we can conclude that this condition gives giant components for any $\gamma\ge2$. Numerical simulations show that this is not the case (see Fig.~\ref{fig:cr_sf}).
\begin{figure}
\centering
\includegraphics[angle=-90,width=10cm]{Fig11.eps}
\caption{Distribution of the reachable set sizes in the scale-free graph. The data points are the average of 1000 distributions on networks with $N=10^4$. The giant components emerge at $\gamma=2$ (blue circles) and they vanish above this threshold (green triangles).}
\label{fig:cr_sf}
\end{figure}
If we substitute $g_{00}(x,y)$ and its derivatives in Eq.~(\ref{eq:grc_def2}) and Eq.~(\ref{eq:ER_u_eq})-(\ref{eq:ER_v_eq}) we observe that there are giant components of unit size for every exponent larger than two, since the formula
\eqarray{\pi_s^{out} & = & \frac{\langle k\rangle}{(s-1)!}\Bigg[\frac{\mathrm{d}^{s-2}}{\mathrm{d} y^{s-2}}\bigg(g_{01}(1,y)g_{10}(1,y)^{s-1}\bigg)\Bigg]_{y=0} \nonumber \\
& = & \frac{1}{\zeta(\gamma)^s(s-1)!}\Bigg[\frac{\mathrm{d}^{s-1}}{\mathrm{d} y^{s-1}}\bigg(\mathrm{Li}_\gamma(y)^s\bigg)\Bigg]_{y=0}}{eq:SF_pi}
gives exactly zero for any $s$ and the equation
\eq{u=g_{01}(u,1)=\frac{\mathrm{Li}_\gamma(u)}{\zeta(\gamma)}}{eq:SF_u_eq}
has always two solutions: $u_1=0$ and $u_2=1$.
These show the limitations of the generating function formalism in directed networks. The limits of the method is already well-known in some cases of undirected scale-free networks as well \cite{newman03}. In the undirected case, networks with small exponents tend to have many hubs, and the clustering coefficient also increases remarkably \cite{newman03}. Large clustering coefficient means, that the graph is not locally tree-like, which is the main assumption of the applied method. Eq.~(\ref{eq:SF_pi})-(\ref{eq:SF_u_eq}) point out that, for directed networks, the method can be barely applied to scale-free networks.
However, it is possible to give a qualitative approximation for the $G_R$ in the case of $\gamma>2$ (this is the most important regime in terms of real networks \cite{barabasi02}). We use our observation from the simulations that there is no $\mathcal{G}_{S}$, and that in scale-free networks, very large degrees can appear. Since a large amount of the nodes have few out-degrees, the $G_R$ is obviously dominated by $C_R^{max}$. Let us assume that the network breaks down into small components whose are the neighborhoods of the nodes with large out-degrees (i.e., every component gathers around a hub). In this case, the largest reachable set is the largest out-degree. In a scale-free network with degree distribution of $p_k\propto k^{-\gamma}$, the largest degree is well approximated by $k_{max}\approx N^{\frac{1}{\gamma-1}}$ \cite{cohen00}. Using this approximation for the out-degrees and not taking into account the in-degrees we get:
\eq{G_R\simeq N^{\frac{2-\gamma}{\gamma-1}}}{eq:SF_grc}
Comparison of the real $G_R$ and this approximation is shown in Fig.~\ref{fig:grc_sf}.
\begin{figure}
\centering
\includegraphics[angle=-90,width=10cm]{Fig12.eps}
\caption{Global reaching centrality of the scale-free graph. Numerical results are the average of 1000 independent calculations on networks with $N=10^4$. Errors have a magnitude of the dot sizes. The largest degree approximation fits well above $\gamma>3$ and gives a lower value below it.}
\label{fig:grc_sf}
\end{figure}
For large exponents, Eq.~(\ref{eq:SF_grc}) fits well to the numerical results. Below $\gamma=3$, it becomes less accurate. Note that the lower the exponent is the more portion of the nodes has large degrees. The predicted $G_R$ becomes larger than the real value at some point ($\gamma\approx2.3)$, that is the number of large hubs increases which results in larger average reaching centrality as well.
It is worth to stop here and understand the non-monotonic dependence of the $G_R$ on the exponent. For large exponents, the scale-free network tends to behave similar as the Erd\H{o}s--R\'{e}nyi graph. Thus, it becomes more homogeneous. Its average degree also decreases and instead of the hubs, more and more small, disconnected components appear. As the network becomes more fragmented, both the average and maximum reaching centrality decreases, which results in a very small $G_R$. In the case of small exponents, it is known that the clustering coefficient of undirected scale-free networks significantly increases \cite{newman03}. This phenomenon is likely to be present in the directed case as well. With large clustering, the number of \emph{directed circles} also increases. However, the nodes in a directed circle have exactly the same reachable set, and thus similar local reaching centrality. This tendency of equalization in the local reaching centralities affects the heterogeneity of the distribution, and enables multiple nodes to reach (or approach closely) the maximum reaching centrality. The result is again a decreasing $G_R$.
\section{Effects of correlations}
\subsection{Degree-correlations}
In the above sections we assumed that the joint probability distribution of the in- and out-degrees is simply the product of two independent distributions, i.e., there are no degree-correlations. However, it is known that there are such correlations in real networks \cite{newman03b}. It is also known that these correlations have markable effects on the different properties of networks (percolation thresholds, epidemic thresholds, etc) \cite{newman02,boguna03}. In this paper, we numerically study the effect of two types of correlations on the $G_R$: one-point correlations and directed assortative mixing. One-point correlation is the Pearson correlation between the in- and out-degree of the nodes:
\eq{\rho=\frac{\langle k_{in}k_{out}\rangle_V-\langle k_{in}\rangle_V\langle k_{out}\rangle_V}{\sigma_V(k_{in})\sigma_V(k_{out})}}{eq:Corr_rho_def}
The brackets denote averages over the nodes and $\sigma_V(k)=\sqrt{\langle k^2\rangle_V-\langle k\rangle_V^2}$ is the standard deviation of the corresponding degrees. Somewhat similarly, one can define the Pearson correlation between the out-degree of the start of an edge and the in-degree of its end term \cite{newman03b}:
\eq{r=\frac{\langle j_{in}k_{out}\rangle_E-\langle j_{in}\rangle_E\langle k_{out}\rangle_E}{\sigma_E(j_{in})\sigma_E(k_{out})}}{eq:Corr_r_def}
Here $j_{in}$ is the in-degree of the node an edge points to and $k_{out}$ is the out-degree of the node that edge comes from. The averages run over the edges. We will refer to this quantity as two-point correlation or directed assortativity, since it is a plausible generalization of the assortativity in undirected networks. Table~\ref{tab:real_network_correlations} shows the two correlations in several real networks.
\begin{table}
\centering
\begin{tabular}{lccc}
Network & $\langle k\rangle$ & $\rho$ & $r$ \\
\hline
\multicolumn{3}{l}{\bf Food networks} & \\
Ythan \cite{dunne02} & 4.452 & 0.168 & -0.249 \\
LittleRock \cite{martinez91} & 13.628 & -0.138 & -0.394 \\
Grassland \cite{dunne02} & 1.557 & -0.179 & -0.233 \\
\multicolumn{3}{l}{\bf Electric} & \\
s1488 \cite{circuits} & 2.085 & -0.274 & 0.218 \\
s5378 \cite{circuits} & 1.467 & -0.137 & 0.151 \\
s35932 \cite{circuits} & 1.683 & -0.074 & 0.088 \\
\multicolumn{3}{l}{\bf Trust} & \\
WikiVote \cite{leskovec10} & 14.573 & 0.318 & -0.083 \\
College \cite{vanduijn03,milo04} & 3 & 0.053 & -0.159 \\
Prison \cite{vanduijn03,milo04} & 2.716 & 0.201 & 0.129 \\
\multicolumn{3}{l}{\bf Regulatory} & \\
TRN-Yeast-1 \cite{balaji06} & 2.899 & 0.025 & -0.173 \\
TRN-Yeast-2 \cite{milo02} & 1.568 & -0.236 & -0.220 \\
TRN-EC \cite{milo02} & 1.239 & -0.082 & 0.085 \\
\multicolumn{3}{l}{\bf Metabolic} & \\
\emph{C. elegans} \cite{jeong00} & 2.442 & 0.924 & -0.174 \\
\emph{E. coli} \cite{jeong00} & 2.533 & 0.923 & -0.167 \\
\emph{S. Cerevisiae} \cite{jeong00} & 2.537 & 0.923 & 0.182 \\
\end{tabular}
\caption{The one- and two-point correlations of real networks along with their references. With the exception of the metabolic networks, most of them have small correlations.}
\label{tab:real_network_correlations}
\end{table}
\subsection{One-point correlations}
\subsubsection{Numerical results}
In order to study the effect of the one-point correlation, we generated the in- and out-degree lists for the network with a given distribution and average degree. After randomizing both lists, we fixed the out-degree list while we successively swapped randomly chosen elements in the in-degrees. After every swap, we calculated $\rho(k_{in},k_{out})$ and accepted the new list whenever the correlation increased (decreased). We measured the $G_R$ when the difference between the correlation of the current state and the last measured state was larger than 0.01 (this is the resolution of the measured $G_R(\rho)$ function). The dependence of the $G_R$ on the one-point correlation is shown in Fig.~\ref{fig:one_point_corr}.
\begin{figure}
\centering
\mbox{
\subfloat[\textbf{Erd\H{o}s--R\'{e}nyi}]{\includegraphics[angle=-90,width=8cm]{Fig13a.eps}}
\subfloat[\textbf{Exponential}]{\includegraphics[angle=-90,width=8cm]{Fig13b.eps}}}
\mbox{
\subfloat[\textbf{Scale-free}]{\includegraphics[angle=-90,width=8cm]{Fig13c.eps}}}
\caption{The $G_R$ versus the one-point correlations for different average degrees in Erd\H{o}s--R\'{e}nyi and exponential graph and for different exponents in the scale-free network. Every point on the plots is the average of at least 200 independent simulations on networks with $N=10^4$ nodes. In the case of the scale-free network, only a small negative degree-correlation is accessible through random optimization.}
\label{fig:one_point_corr}
\end{figure}
It is clearly seen that the behavior of the $G_R$ varies and depends strongly on the average degree. In the ER and exponential graphs, even the monotonity of the curves change. In the scale-free network, the $G_R$ saturates at some level of correlation and the exponent effects only the threshold above which further correlations do not change the $G_R$.
\subsubsection{A qualitative approach}
In this section, we present a simple argument to understand the direction of change if small correlations are present in the graph. It is important to emphasize, that the analytic expression for the effects of correlations is out of the scope of this paper and we intend to give only a rather qualitative insight of the behavior. For this, let us consider the following joint degree distribution:
\eq{p_{jk}=p_jp_k+\rho\sigma_p^2m_{jk}}{eq:1pCorr_modified_pij}
Where the only criteria for the $m_{jk}$ matrix are:
\eq{\sum_{j=0}^\infty m_{jk}=\sum_{k=0}^\infty m_{jk}=0}{eq:1pCorr_mij_crit1}
\eq{\sum_{j,k=0}^\infty jkm_{jk}=1}{eq:1pCorr_mij_crit2}
With these conditions, the one-point degree-correlation of the above joint degree distribution is exactly $\rho$ \cite{newman03b}. Note that we assumed the same distribution for the in- and out-degrees ($\sigma_V(k_{in})=\sigma_V(k_{out})=\sigma_p$). The generating function of the modified distribution:
\eq{g_{00}(x,y)=g_{00}^p(x,y)+\rho\chi_{00}(x,y)}{eq:1pCorr_modified_g00}
where the $g_{00}^p$ is the generating function of the original joint degree distribution and we introduced the following function:
\eq{\chi_{00}(x,y)=\sigma_p^2\sum_{j,k=0}^\infty x^jy^km_{jk}}{eq:1pCorr_khi00_def}
Above the critical average degree, we have to solve
\eq{u=g_{01}^p(u,1)+\frac{\rho}{\langle k\rangle}\partial_y\chi_{00}(u,1)}{eq:1pCorr_modified_u_eq}
and the $G_R$ is given by the modified generating function:
\eq{G_R=g_{00}(u,1)-g_{00}(u,u)}{eq:1pCorr_modified_grc}
The exact solution of Eq.~(\ref{eq:1pCorr_modified_u_eq}) depends on the actual choice of $m_{jk}$ and in most cases not possible to find in closed form. However, for small correlations ($\rho\ll1$), we can describe the change in the $G_R$ at given average degree. In this case, the solution of Eq.~(\ref{eq:1pCorr_modified_u_eq}) is very close to the solution of the original equation without the correlations: $u=u_0+u_\rho$. Expanding both sides and keeping only the linear terms in $\rho$ and $u_\rho$, we get:
\eq{u_\rho=\frac{1}{\langle k\rangle}\frac{\partial_y\chi_{00}(u_0,1)}{1-\partial_xg_{01}^p(u_0,1)}\rho=\beta(u_0)\rho}{eq:1pCorr_urho_def}
The coefficient $\beta(u)$ is negative above the transition point for the model networks we are interested in (for the proof, see Appendix B). In the linear approximation, the $G_R$ looks like:
\eq{G_R=G_R^{(0)}+G_R^{(\rho)}}{eq:1pCorr_grc_result}
where
\eq{G_R^{(0)}=g_{00}^p(u_0,1)-g_{00}^p(u_0,u_0)}{eq:1pCorr_grc0_def}
and
\eq{G_R^{(\rho)}=\bigg[\beta(u_0)(1-2u_0)\cdot\frac{\mathrm{d} g_0^p(x)}{\mathrm{d} x}\Big|_{x=u_0}-\chi_{00}(u_0,u_0)\bigg]\rho}{eq:1pCorr_grcrho_def}
In the derivation of $G_R^{(\rho)}$, we used the observations that when the joint degree distribution factorizes, the generating function is also a product of the single distributions, i.e.,
\eq{g_{00}^p(x,y)=g_0^p(x)g_0^p(y)}{eq:1pCorr_g00p_factoring}
and also
\eq{g_0^p(u_0)=\sum_{j=0}^\infty p_ju_0^j=\frac{1}{\langle k\rangle}\sum_{j,k=0}^\infty ku_0^jp_{jk}=g_{01}^p(u_0,1)=u_0}{eq:1pCorr_g0p_equal_u0}
Now we have to interpret the result we obtained for the change in the $G_R$. First, for simplicity, let us choose the $m_{jk}$ as proposed in \cite{newman03b}:
\eq{m_{jk}=\frac{(p_j-\phi_j)(p_k-\phi_k)}{\big(\langle k\rangle-\langle k\rangle_\phi\big)^2}}{eq:1pCorr_mij_example}
where $\phi_j$ is an arbitrary normalized distribution and $\langle k\rangle_\phi$ is its average. Moreover, choose the $\phi_j$ distribution such that $\langle k\rangle_\phi=1$ which is the critical point of the ER and exponential networks. In this case $\chi_{00}(u_0,u_0)\ge0$ and also note that
\eq{\beta(u_0)<0}{eq:1pCorr_beta_negative}
\eq{\frac{\mathrm{d} g_0^p(x)}{\mathrm{d} x}\Big|_{x=u_0}>0}{eq:1pCorr_dg0p_dx_positive}
above the transition point. The behavior of $G_R^{(\rho)}$ is governed by the relation of the two terms in the right hand side of Eq.~(\ref{eq:1pCorr_grcrho_def}). It is easy to check that near the critical point ($u_0\approx1$), the second term is very close to zero, and $G_R^{(\rho)}$ is dominated by the first term which is positive. This means that when the average degree is small, but the graph already has giant components of finite size, small one-point correlations increase its hierarchical structure, as in Fig.~\ref{fig:one_point_corr}. For large average degrees, $u_0\to0$ and both terms in Eq.~(\ref{eq:1pCorr_grcrho_def}) becomes negative, resulting in a decreasing effect of small correlations, in good accordance with the numerical results (see Fig.~\ref{fig:one_point_corr}a and Fig.~\ref{fig:one_point_corr}b). In the regime where the $G_R$ has a maximum ($u_0=\frac{1}{2}$), Eq.~(\ref{eq:1pCorr_grcrho_def}) predicts a negative coefficient for $\rho$, but as Fig.~\ref{fig:one_point_corr}b shows, this is not the case for the exponential network. This discrepancy suggests that the change in the slope near this point is not trivial and strongly depends on the details of the addition of correlations.
Below the transition point, there are no giant components and the $G_R$ is dominated by the largest reachable set.
\begin{figure*}
\centering
\subfloat[]{\includegraphics[width=5cm]{Fig14a.eps}}
\subfloat[]{\includegraphics[width=5cm]{Fig14b.eps}}
\subfloat[]{\includegraphics[width=5cm]{Fig14c.eps}}
\caption{The largest reachable set below the transition point (a) and one of the nodes with large out-degree in the largest reachable set (\textbf{A}). Without degree-correlations, the expected number of in-degrees of \textbf{A} is the average degree and the maximum out-degree of its in-neighbors is also moderate (b). With degree-correlations, the nodes with large out-degree has large in-degree as well (c). And with increasing number of in-neighbors the expected maximum out-degree of its neighbors increases as well.}
\label{fig:one_point_corr_below_transition}
\end{figure*}
We can assume that the node with the largest reachable set (node \textbf{C} on Fig.~\ref{fig:one_point_corr_below_transition}a) or some of its out-neighbors have large out-degree, since this increases the probability of reaching more other nodes. Consider this neighbor with the large out-degree (node \textbf{A} in Fig.~\ref{fig:one_point_corr_below_transition}a). In the case of negative or zero correlations, the expected maximum of the out-degree of its in-neighbors is small (Fig.~\ref{fig:one_point_corr_below_transition}b). But in the presence of positive one-point correlations, the number of in- and out-edges tend to be similar, in other words, the node in question has large in-degree as well. In this case, the expected maximum of the out-degree of its in-neighbors (and thus of the candidate node for the largest local reaching centrality) increases and there are more reachable nodes. The scale-free network is a special case in the sense that the largest reachable set is with good approximation the neighborhood of a hub. Because of the correlations, this hub tends to have many in-neighbors as well and it is more likely to have a neighbor with many links (Fig.~\ref{fig:one_point_corr_below_transition}d). The numerical results in Fig.~\ref{fig:one_point_corr}c suggest that the maximum out-degree of the nearest neighbors reaches its saturation level at relatively small correlations.
\subsection{Two-point correlations}
The two-point correlation of the type we investigate in this paper is the generalization of the assortativity to directed networks \cite{newman03b}. In order to introduce this correlation in our calculations, let $\mathcal{P}(j_{in},j_{out};k_{in},k_{out})$ denote the probability that a randomly chosen edge starts at a node with $j_{in}$ in- and $j_{out}$ out-degree and points to a node with $k_{in}$ in- and $k_{out}$ out-degree. This probability satisfies the following equations:
\begin{equation}
\sum_{j_{in},j_{out}=0}^\infty\mathcal{P}(j_{in},j_{out};l_{in},l_{out})=\sum_{k_{in},k_{out}=0}^\infty\mathcal{P}(l_{in},l_{out};k_{in},k_{out})=p_{l_{in}l_{out}}
\label{eq:2pCorr_P_to_pij}
\end{equation}
which also create its connection to the joint degree distribution. Without two-point correlations (and other correlations), the two-node joint distribution factorizes:
\eq{\mathcal{P}^0(j_{in},j_{out};l_{in},l_{out})=p_{j_{in}}p_{j_{out}}p_{k_{in}}p_{k_{out}}}{eq:2pCorr_P_without_corr}
We can modify it by adding a correlation between $p_{j_{out}}$ and $p_{k_{in}}$:
\begin{equation}
\mathcal{P}^r(j_{in},j_{out};k_{in},k_{out})=p_{j_{in}}p_{k_{out}}\big[p_{j_{out}}p_{k_{in}}+r\sigma(p_{j_{out}})\sigma(p_{k_{in}})m_{j_{out}k_{in}}\big]
\label{eq:2pCorr_P_with_corr}
\end{equation}
However, if we recover the joint degree distribution, the added term vanishes:
\eqarray{p^r_{l_{in}l_{out}} & = & \sum_{j_{in},j_{out}=0}^\infty\mathcal{P}_r(j_{in},j_{out};l_{in},l_{out}) \nonumber \\
& = & p^0_{l_{in}l_{out}}}{eq:2pCorr_pijr_equals_pij0}
because the sum of any row or column of the matrix $m_{j_{out}k_{in}}$ must be zero (Eq.~(\ref{eq:1pCorr_grcrho_def})). This means that the assortativity defined by Eq.~(\ref{eq:Corr_r_def}) does not affect the $G_R$ directly (via the joint degree distribution). Fig.~\ref{fig:two_point_corr} depicts the numerical results that were produced by the same protocol as in the previous subsection.
\begin{figure}
\centering
\mbox{
\subfloat[\textbf{Erd\H{o}s--R\'{e}nyi}]{\includegraphics[angle=-90,width=8cm]{Fig15a.eps}}
\subfloat[\textbf{Exponential}]{\includegraphics[angle=-90,width=8cm]{Fig15b.eps}}}
\mbox{
\subfloat[\textbf{Scale-free}]{\includegraphics[angle=-90,width=8cm]{Fig15c.eps}}}
\caption{The effect of two-point correlations to the $G_R$ for the random graph models. Every point is an average at least 100 independent measure on networks with $N=1000$.}
\label{fig:two_point_corr}
\end{figure}
In the case of the ER and exponential networks, a small decrease in the $G_R$ can be observed, regardless of the average degree. The SF network has a non-monotonous behavior, but for larger assortativity, a decreasing in the $G_R$ can be seen. These results point out that, although two-point correlation does not affect the joint degree distribution directly, it changes the hierarchical structure of the network a little. This small effect can be understood if we look at the different typical structures around an edge (Fig.~\ref{fig:two_point_corr_explain}).
\begin{figure}
\centering
\mbox{
\subfloat[$\boldsymbol{r}\boldsymbol{>}\boldsymbol{0}$]{\includegraphics[width=6cm]{Fig16a.eps}}
\subfloat[$\boldsymbol{r}\boldsymbol{>}\boldsymbol{0}$]{\includegraphics[width=6cm]{Fig16b.eps}}}
\mbox{
\subfloat[$\boldsymbol{r}\boldsymbol{<}\boldsymbol{0}$]{\includegraphics[width=6cm]{Fig16c.eps}}
\subfloat[$\boldsymbol{r}\boldsymbol{<}\boldsymbol{0}$]{\includegraphics[width=6cm]{Fig16d.eps}}}
\caption{The illustration of the two limiting cases of two-point correlations $r$ defined by Eq.~(\ref{eq:Corr_r_def}). The edges that are correlated are shown in red. In the case of $r>0$, the reachable sets of hubs tend to be similar (a) and bottlenecks emerge (b), causing an increase in the overlap of reachable sets. In negatively correlated networks ($r<0$), hubs can have their own reachable sets (c) and nodes with large in-degree tend to be reachable from independent parts of the network (d), decreasing the overlap between reachable sets.}
\label{fig:two_point_corr_explain}
\end{figure}
In the case of large two-point correlations, the nodes with large out-degree (those that are expected to have larger reachable set) have out-neighbors with also large in-degrees (Fig.~\ref{fig:two_point_corr_explain}a). This means that the nodes they can directly reach are also reachable from many other nodes (that also have large out-degrees). This reduces the difference between the local reaching centralities among nodes with large $C_R$ or, in other words, introduces higher $c_R(i)$ in the definition of $G_R$ (see Eq.~(\ref{eq:grc_def1})). Positive two-point correlation also introduces bottlenecks in the network (Fig.~\ref{fig:two_point_corr_explain}b). These structures accumulate many nodes on the in-edges that has similar reachable set, thus also reducing the differences. On the other hand, if the graph has negative two-point correlations, nodes with large out-degree can reach their out-neighbors uniquely (Fig.~\ref{fig:two_point_corr_explain}c). Nodes that are reachable from independent directions also emerge (Fig.~\ref{fig:two_point_corr_explain}d). These nodes have in-neighbors with small out-degree. Both effects decrease the ratio of overlapping reachable sets which results in a reduced similarity in the $C_R$ values.
\section{Discussion}
The global reaching centrality ($G_R$) is a measure constructed to provide a characteristic number for the flow hierarchy of a directed network. In this paper we investigated the behavior of this measure and its dependence on the joint degree distribution. We have shown that the hierarchical structure of a random network strongly depends on the existence of the giant strongly connected component ($\mathcal{G}_{S}$) and other giant components in the network. In the regime of low average degree, the $G_R$ is dominated by the node with the largest reachable set that can be approximated from the distribution of the local reaching centralities. This distribution is connected to the distribution of small out-components in a network and can be analytically determined using the generating function method generalized to directed networks. In the presence of the $\mathcal{G}_{S}$, the $G_R$ can be well approximated by the difference in the sizes of the giant in-component ($\mathcal{G}_{in}$) and the $\mathcal{G}_{S}$, and both can be calculated exactly for some network models with given degree distribution. Using the approximations for the $G_R$, we calculated its dependence on the average degree for different network models: a directed random tree, the Erd\H{o}s--R\'{e}nyi graph (ER), the exponential the scale-free (SF) network. The results show that in the sense of hierarchy, there is an optimal average degree at which the $G_R$ has a maximum value. It is a result of the competition between the size of the largest reachable set (which can be found by nodes in the $\mathcal{G}_{in}$) and the average size of reachable sets (which is dominated by the nodes in the $\mathcal{G}_{S}$). Near to the transition point, the size of the $\mathcal{G}_{in}$ is close to the size of the $\mathcal{G}_{S}$ and the difference is increasing since the $\mathcal{G}_{in}$ grows faster in the beginning. In the limit of large average degree, the sizes of both giant components tend to become equal, since even the two set of nodes tend to be the same.
We also investigated the dependence of the $G_R$ on two types of degree-correlations: one-point correlation (in-degree and out-degree of a node) and two-point correlation (the out-degree of the source and the in-degree of the target of a directed edge). Numerical results show that the hierarchical structure changes systematically with the one-point correlation. This is in accordance with the fact that the $G_R$ can be expressed with the joint degree distribution, and latter is directly affected by the one-point correlations. We have pointed out that in the two limiting case of the average degree, the qualitative effect of small correlations can be understand by the addition of a correlation term to the uncorrelated joint degree distribution. When the average degree is very low, small correlations have a positive effect on the $G_R$. This is not true for denser graph, in which correlations decrease the $G_R$. There is also a regime of the average degree in which a given level of correlations can maximize the hierarchy.
Both numerical and analytical results suggest that two-point correlation (which is the generalization of the assortativity for directed networks) does not effect the $G_R$ directly. However, a small negative effect can be observed. It can be understood by looking at the effect of the two-point correlation on the neighborhood of an edge.
The results on the random network models have shown a deeper insight of the behavior of the $G_R$ but we have to keep in mind that they are only the first steps in the understanding of hierarchy. The main message of the results is that hierarchy is sensible to the edge density of a network and tends to emerge more likely in sparse networks. This is in good accordance with the observation that most of the real world networks are in the range of low density and many of them has an inherent hierarchical structure. The results also point out that correlations can have a large effect and can change the the hierarchical structures fundamentally (they can produce a finite magnitude of $G_R$ even if the network would have an infinitesimal $G_R$ otherwise). This is another indicator of the well-known fact that one has to take into account the presence of correlations when dealing with real networks.
\section*{Acknowledgement}
The author would like to thank Tam\'{a}s Vicsek, P\'{e}ter Pollner and Gergely Palla for the fruitful conversations that facilitated the interpretation of the results and for their advices during the preparation of the manuscript. This research was fully supported by the EU ERC FP7 COLLMOT Grant No: 227878.
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 2,910
|
\section{Introduction}
In one of the most significant achievements of cold atom physics in recent years, a degenerate gas of ultracold atoms loaded into an optical lattice formed far off resonance lasers was demonstrated to undergo a quantum phase transition from a superfluid into the Mott insulator phase \cite{Bloch}. In the Mott insulator a perfectly regular lattice at half the laser wavelength with a fixed number of atoms per site is achieved. This quantum phase transition from the superfluid into the Mott insulator was predicted and described by the Bose-Hubbard model \cite{Jaksch,Fisher}. As the Mott insulator phase can be considered as an artificial crystal with parameters well controllable in time and space, this generates a close connection between cold atom optics and solid state physics, which has generated a plethora of subsequent work generalizing the model and identifying more and more solid state phenomena to be studied in such configurations \cite{Zoller}. Furthermore, strong resonant light-matter coupling for a Bose-Einstein Condensate in an optical cavity has been achieved recently \cite{Esslinger}.
In previous work \cite{ZoubiA} we exhibited the similarities of such artificial crystals and molecular or noble atom crystals, where one gets the so called Frenkel-excitons. In particular for the special case of identical ground and excited state optical lattice potentials the Mott insulator phase allows the formation of such excitons as collective electronic excitations in the whole optical lattice \cite{Zoubi,Agranovich}. If the optical lattice is placed between cavity mirrors with a single cavity mode close to resonance with the excitons, coherent superpositions of excitons and cavity photons can form. In the strong coupling regime the corresponding system eigenstates then are cavity polaritons, which have very similar behavior in solid state and cold atom systems \cite{Zoubi,Kavokin}. Going beyond the analogous solid state case, very interesting new physics appears in the case of lattices with two atoms per site, where the on-site resonant excitations form symmetric (bright) and antisymmetric (dark) superposition states of individual excitations \cite{ZoubiB}. While the symmetric states radiate and via dipole-dipole coupling will form excitons and thus cavity polaritons, the antisymmetric states have no dipole moment, so that their excitations are long lived and stay localized at one site. Lattice asymmetries can lead to coupling between bright and dark states and produce strongly polarization dependent spectra.
Optical lattices are spatially and externally described by the laser field and thus almost perfect over long distances. Nevertheless due to imperfections in the dynamical formation of the Mott insulator, the appearance of some defects in the Mott insulator phase is unavoidable \cite{Bloch} and there are missing or extra atoms at some sites. Such defects might create decisive errors when using such lattices for quantum information processing or for observing even more exotic quantum phases in such systems and some suggestion to repair such defects were already presented \cite{Rabl}. On the other hand they are hard to detect by direct observations of the atomic distribution.
In this paper we investigate the effect of such defects on the dynamical properties of excitons and cavity polaritons. We concentrate in the case of a low defect number, where the exciton and cavity polariton picture still holds and these quasi-particles are only scattered by single defects. Namely, the distance between each two defects is enough large for the formation of coherent excitons and cavity polaritons, which propagate as free quasi-particles between each two scattering processes. In principle defects can move by hopping among the lattice sites, but the corresponding time scale is so long that they can be considered frozen. Introducing more and more defects with faster hopping would then correspond to the transition from the Mott to a superfluid atomic phase in the lattice, which will not be considered here.
Here we treat defects related to a missing atom: in the case of one atom per site this corresponds to vacant sites and while for two atoms per site a defect is a singly occupied site. Interestingly in calculating the exciton and cavity polariton elastic scattering amplitude of such defects, the two case behave even qualitatively very different. As a consequence of this defect scattering we show how cavity polaritons can be used as observation tool to detect defects in the Mott insulator phase.
The paper is organized as follows. In section 2 we investigate the exciton scattering off a vacancy in an optical lattice in the Mott insulator with filling factor one, which is generalized to the scattering of cavity polaritons in section 3. The scattering of excitons and cavity polaritons off a defect in the Mott insulator case with two atoms per site is treated in section 4, where also we treat the special case of an optical lattice with asymmetric sites.
\section{Exciton scattering of a vacancy in an optical lattice}
Let us consider first a $2D$ optical lattice at the magic wavelength filled with one 2-level atom per site in the Mott-insulator phase. Including dipole-dipole interactions resonant excitations of the atoms can be represented as quasi-particles called Frenkel excitons \cite{ZoubiA}. A single atom missing at the origin (${\bf r}_i={\bf 0}$) then creates an impurity in the artificial lattice of ultracold atoms, which for sufficient lattice depth stays localized and will not hop among the lattice sites as shown in figure (1). We will now consider scattering of these excitons at such a missing atom (hole). As the scattering time is much shorter than the hopping time, the impurity assumed to be localized during the scattering process.
Adding the impurity to the ideal atom crystal just needs a small change in the system Hamiltonian $H=H_0+V$ derived in Ref.\cite{ZoubiA}, whose components now read:
\begin{equation}
H_0=\sum_{\bf k}\hbar\omega_{ex}(k)\ B_{\bf k}^{\dagger}B_{\bf k}\ ,\ V=-\hbar\omega_A\ B_0^{\dagger}B_0.
\end{equation}
$H_0$ represents free excitons due to the resonant electronic excitation transfer among lattice sites induced by dipole-dipole interactions including the lattice symmetry. $B_{\bf k}^{\dagger}$ and $B_{\bf k}$ are the creation and annihilation operators of an exciton with in-plane wave vector ${\bf k}$, respectively, and $\omega_{ex}(k)$ is the exciton dispersion. $V$ is the impurity Hamiltonian at the origin, where $\hbar\omega_A$ is the atomic transition energy.
For an exciton the impurity thus appears as a potential well located at the origin, with depth $\hbar\omega_A$ and radius $a$. Here we will not try to find the self-consistent eigenstates of $H$ but to consider only the scattering problem. We can neglect trapping of an exciton in the impurity potential as a vacant site cannot absorb the trapping energy. Hence we consider only the scattering process of an exciton off the impurity.
\begin{figure}[h!]
\centerline{\epsfxsize=8.0cm \epsfbox{Plot1.eps}}
\caption{An impurity in $1D$ optical lattice.}
\end{figure}
In the following we calculate the scattering amplitude of an exciton of an impurity. The initial exciton has wave vector ${\bf k}$ very far from the impurity, is scattered elastically and found with wave vector ${\bf k'}$ also very far, and for elastic scattering we have $|{\bf k'}|=|{\bf k}|$. As the impurity is very deep with depth $\hbar\omega_A$, in order to calculate the scattering amplitude we need to go beyond the Born approximation \cite{Taylor} even though the perturbation is confined to a radius $a$.
The eigenstates of the free exciton Hamiltonian are $H_0|\phi_{\bf k}\rangle=E(k)|\phi_{\bf k}\rangle$, and the full Hamiltonian eigenstates obey $H|\psi\rangle=E|\psi\rangle$. The excitation eigenstates in the quasi-momentum space $|\phi_{\bf k}\rangle$ are related to the lattice space eigenstates by $|\phi_{\bf k}\rangle=\frac{1}{\sqrt{N}}\sum_ie^{i{\bf k}\cdot{\bf r}_i}\ |\phi_i\rangle$, where $N$ is the number of lattice sites. The eigenstates form a complete basis, with the closure relation $\sum_i|\phi_i\rangle\langle\phi_i|=\hat{1}$. A general state $|\psi\rangle$ can be expanded by $|\psi\rangle=\sum_i\psi_i\ |\phi_i\rangle$, with the expansion amplitude $\psi_i=\langle\phi_i|\psi\rangle$.
In the scattering problem the incoming exciton is prepared in a delocalized unperturbed exciton state $|\phi_{\bf k}\rangle$ and the scattered exciton is observed also very far from the impurity. Hence, the whole system eigenstates $|\psi\rangle$ needs to obey the boundary condition $|\psi\rangle\rightarrow|\phi_{\bf k}\rangle$ as $V\rightarrow 0$. The required solution is given by the Schwinger-Lippmann equation \cite{Taylor}
\begin{equation}
|\psi\rangle=|\phi_{\bf k}\rangle+G_0V|\psi\rangle,
\end{equation}
where
\begin{equation} \label{Green}
G_0=\lim_{\eta\rightarrow 0_+}\left(\frac{1}{E-H_0+i\eta}\right).
\end{equation}
The sign of $+i\eta$ is chosen in such a way to ensure that the scattered exciton propagates away from the impurity. In multiplying the equation from the left by the bra vector $\langle\phi_i|$, and in inserting the above identity operator between $G_0$ and $V$, we get
\begin{equation}
\langle\phi_i|\psi\rangle=\langle\phi_i|\phi_{\bf k}\rangle+\sum_j\langle\phi_i|G_0|\phi_j\rangle\langle\phi_j|V|\psi\rangle.
\end{equation}
The calculations using the above definitions yields:
\begin{equation}
\psi_i=\frac{1}{\sqrt{N}}e^{i{\bf k}\cdot{\bf r}_i}-\frac{E_a}{N}\sum_{\bf k'}\lim_{\eta\rightarrow 0_+}\frac{e^{i{\bf k'}\cdot{\bf r}_i}}{E-E(k')+i\eta}\ \psi_0,
\end{equation}
where $E_a=\hbar\omega_A$. This represents the scattered wave amplitude at site $i$ very far from the impurity. The first term is for the non-scattered wave, and the second is for the scattered wave. For the impurity site amplitude, at ${\bf r}_0={\bf 0}$, we get
\begin{equation}
\psi_0=\frac{1}{\sqrt{N}}\left\{1+\frac{E_a}{N}\sum_{\bf k'}\lim_{\eta\rightarrow 0_+}\frac{1}{E-E(k')+i\eta}\right\}^{-1}.
\end{equation}
As the scattering is elastic the energy $E$ can be replaced by the incident exciton energy and we have $E=E(k)$. We get
\begin{equation}
\psi_i=\frac{1}{\sqrt{N}}\left\{e^{i{\bf k}\cdot{\bf r}_i}+\frac{E_aI_{os}}{1-E_aI_{st}}\right\},
\end{equation}
where we defined the oscillating and static summations
\begin{eqnarray}
I_{os}&=&-\frac{1}{N}\sum_{\bf k'}\lim_{\eta\rightarrow 0_+}\frac{e^{i{\bf k'}\cdot{\bf r}_i}}{E(k)-E(k')+i\eta}, \nonumber \\
I_{st}&=&-\frac{1}{N}\sum_{\bf k'}\lim_{\eta\rightarrow 0_+}\frac{1}{E(k)-E(k')+i\eta}.
\end{eqnarray}
Our main aim now is to calculate the two sums in the case of small wave vector scattering excitons, that is $ka\ll 1$. For this we can use the parabolic approximation for the dispersion of the excitons, $\omega_{ex}(k)=\omega_{ex}(0)+\frac{\hbar k^2}{2m_{ex}}$, where $m_{ex}$ is the exciton effective mass. For isotropic atoms in a square lattice of cubic symmetry, and in including only nearest neighbor interactions with coupling parameter $J$, we get $m_{ex}=-\hbar/(2Ja^2)$, and $\omega_{ex}(0)=\omega_A-2J$. For a large enough $2D$ optical lattice, the sum over ${\bf k'}$ can be approximated by a $2D$ integral given by
\begin{equation}
\frac{1}{N}\sum_{\bf k'}\rightarrow \left(\frac{a}{2\pi}\right)^2\int d^2k'.
\end{equation}
We get the two integrals
\begin{eqnarray} \label{INT}
I_{os}&=&-\frac{2m_{ex}}{\hbar^2}\left(\frac{a}{2\pi}\right)^2\int d^2k'\lim_{\eta\rightarrow 0_+}\frac{e^{i{\bf k'}\cdot{\bf r}_i}}{k^2-k'^2+i\eta}, \nonumber \\
I_{st}&=&-\frac{2m_{ex}}{\hbar^2}\left(\frac{a}{2\pi}\right)^2\int d^2k'\lim_{\eta\rightarrow 0_+}\frac{1}{k^2-k'^2+i\eta}.
\end{eqnarray}
as shown in the appendix. The scattered exciton, following the definition in \cite{Petrov}, is given by
\begin{equation}
\psi_i=\frac{1}{\sqrt{N}}\left\{e^{i{\bf k}\cdot{\bf r}_i}-f(k)\sqrt{\frac{i\pi}{2kr}}e^{ikr}\right\},
\end{equation}
where $r=|{\bf r}_i|$ is the distance of the $i$ site from the origin. We defined the scattering amplitude by
\begin{equation}
f(k)=\frac{\frac{\pi E_a}{2\Delta_{ex}}}{1+\frac{\pi E_a}{2\Delta_{ex}}\left[\ln\left(\frac{ka}{\pi}\right)-i\frac{\pi}{2}\right]},
\end{equation}
and the effective exciton band width is defined by
\begin{equation} \label{EXBAND}
\Delta_{ex}=\frac{\hbar^2\pi^2}{2m_{ex}a^2}.
\end{equation}
The dipole-dipole interaction energy between different sites in optical lattices is small, and hence the excitons have a small band width. In our case we have the limit of $ E_a\gg\Delta_{ex}$ so that the scattering amplitude is $f(k)\approx\frac{1}{\ln\left(\frac{ka}{\pi}\right)}$, which exactly reproduces the result for the scattering off a hard disk of radius $a$ \cite{Lapidus}, with the scattering cross section defined by $\sigma(k)=2\pi|f(k)|^2$.
We thus conclude that an impurity generated by a missing atom in an optical lattice acts effectively like a hard disk of radius $a$. As the scattering is elastic, for an incident exciton with a fixed and small wave vector ${\bf k}$ we get a scattered exciton with a wave vector ${\bf k'}$, which equals in magnitude to the incident one, namely $|{\bf k}|=|{\bf k'}|=k$. Hence if a big number of incident excitons with identical wave vector are scattered off the impurity, we get a ring of radius $k$ of scattered excitons.
The scattering amplitude is plotted in figure (2) as a function of wave vectors, $k$, for lattice constant $a=2000\ \AA$. The singularity at $k=0$ is the $2D$ signature.
\begin{figure}[h!]
\centerline{\epsfxsize=8.0cm \epsfbox{Plot2.eps}}
\caption{The scattering amplitude vs. wave vector $k$, for zero detuning.}
\end{figure}
\section{Cavity polariton scattering of a vacancy in an optical lattice}
Let us now add cavity mirrors to our lattice as described in \cite{ZoubiA}, where in the strong coupling regime, the system eigenstates are cavity polaritons. As polariton is a coherent superposition of an exciton and a photon it can scatter of the impurity due its excitonic part. The corresponding Hamiltonians then read:
\begin{equation}
H_0=\sum_{{\bf k}r}\hbar\Omega_r(k)\ A_{{\bf k}r}^{\dagger}A_{{\bf k}r},\ V=-E_a\ B_0^{\dagger}B_0,
\end{equation}
where $\Omega_{\pm}(k)$ are the upper and lower polariton branch dispersions, given by: $\Omega_{\pm}(k)=\frac{\omega_{cav}(k)+\omega_{ex}(k)}{2}\pm\Delta_k$. Here $\Delta_k=\sqrt{\delta_k^2+|g_k|^2}$, and the exciton-photon detuning is defined by $\delta_k=\frac{\omega_{cav}(k)-\omega_{ex}(k)}{2}$. The parameter $g_{\bf k}$ is for the exciton-photon coupling, which is taken to be of the electric dipole interaction. The cavity-photon dispersion is given by $\omega_{cav}(k)=\frac{c}{\sqrt{\epsilon}}\sqrt{k^2+\left(\frac{\pi}{L}\right)^2}$, where $L$ is the distance between the cavity mirrors, and $\epsilon$ is the cavity medium dielectric constant, which here taken to be a vacuum with $\epsilon=1$. The polariton operators are defined by $A_{{\bf k}\pm}=X_k^{\pm}\ B_{\bf k}+Y_k^{\pm}\ a_{\bf k}$, with $a_{\bf k}$ the cavity photon operator. $X_k^{\pm}$ and $Y_k^{\pm}$ are the exciton and photon amplitude, respectively, which are given by $X_k^{\pm}=\pm\sqrt{\frac{\Delta_k\mp\delta_k}{2\Delta_k}}$, and $Y_k^{\pm}=\frac{g_k}{2\Delta_k(\Delta_k\mp\delta_k)}$ (more details are found in Ref.\cite{ZoubiA}).
As next step we now calculate the polariton scattering off such impurity. Again the scattering is elastic so that an incident polariton in branch $r$ with wave vector ${\bf k}$ will scatter into a polariton with wave vector ${\bf k'}$ in the same branch.
The free eigenstates obey $H_0|\phi^{pol}_{{\bf k}r}\rangle=E_r(k)|\phi^{pol}_{{\bf k}r}\rangle$, and the whole system eigenstates obey $H|\psi\rangle=E|\psi\rangle$, where $E_r(k)=\hbar\Omega_r(k)$. The cavity photon eigenstate is defined by $a_{\bf k}^{\dagger}|vac\rangle=|\phi_{\bf k}^{cav}\rangle$, and the exciton eigenstate in quasi-momentum space is defined by $B_{\bf k}^{\dagger}|vac\rangle=|\phi_{\bf k}^{ex}\rangle$. The $r$ polariton branch eigenstate is defined by $A_{{\bf k}r}^{\dagger}|vac\rangle=|\phi_{{\bf k}r}^{pol}\rangle$, and in terms of exciton and photon states we get $|\phi_{{\bf k}\pm}^{pol}\rangle=X_k^{\pm}\ |\phi_{\bf k}^{ex}\rangle+Y_k^{\pm}\ |\phi_{\bf k}^{cav}\rangle$. In terms of real lattice space, we get $|\phi_{{\bf k}\pm}^{pol}\rangle=\frac{X_k^{\pm}}{\sqrt{N}}\sum_ie^{i{\bf k}\cdot{\bf r}_i}\ |\phi_i^{ex}\rangle+Y_k^{\pm}\ |\phi_{\bf k}^{cav}\rangle$. A general state $|\psi\rangle$ can be expanded as $|\psi\rangle=\sum_{\bf k}\psi_{\bf k}^{cav}\ |\phi_{\bf k}^{cav}\rangle+\sum_i\psi_i^{ex}\ |\phi_i^{ex}\rangle$.
As above the scattered polariton state is given by the Schwinger-Lippmann equation $|\psi\rangle=|\phi^{pol}_{{\bf k}r}\rangle+G_0V|\psi\rangle$, where we used the free Green function operator in Eq.(\ref{Green}). We multiply the equation from the left by the lattice exciton eigenstate $\langle\phi_i^{ex}|$, and insert the previous identity operator between $G_0$ and $V$, to get
\begin{equation}
\langle\phi_i^{ex}|\psi\rangle=\langle\phi_i^{ex}|\phi^{pol}_{{\bf k}r}\rangle+\sum_j\langle\phi_i^{ex}|G_0|\phi_j^{ex}\rangle\langle\phi_j^{ex}|V|\psi\rangle.
\end{equation}
Using the above definitions, we get the scattered polariton excitonic part amplitude by
\begin{equation}
\psi_i^{ex}=\frac{X_k^r}{\sqrt{N}}e^{i{\bf k}\cdot{\bf r}_i}-\frac{E_a}{N}\sum_{{\bf k'}s}\lim_{\eta\rightarrow 0_+}\frac{|X_{k'}^s|^2\ e^{i{\bf k'}\cdot{\bf r}_i}}{E_r(k)-E_s(k')+i\eta}\ \psi_0^{ex},
\end{equation}
where due to energy conservation we replaced the energy $E$ by the initial energy $E_r(k)$, and $|X_{k'}^s|^2$ is the exciton weight in the polariton. For the impurity site amplitude we have
\begin{equation}
\psi_0^{ex}=\frac{X_k^r}{\sqrt{N}}\left\{1+\frac{E_a}{N}\sum_{{\bf k'}s}\lim_{\eta\rightarrow 0_+}\frac{|X_{k'}^s|^2}{E_r(k)-E_s(k')+i\eta}\right\}^{-1}.
\end{equation}
We thus obtain
\begin{equation}
\psi_i^{ex}=\frac{X_k^r}{\sqrt{N}}\left\{e^{i{\bf k}\cdot{\bf r}_i}+\frac{E_aI_{os}}{1-E_aI_{st}}\right\},
\end{equation}
where we defined oscillating and static sums. For a large optical lattice size the $k$-space can be assumed continuous and the sums converted to the integrals
\begin{eqnarray}
I_{os}&=&-\sum_s\left(\frac{a}{2\pi}\right)^2\int d^2k'\lim_{\eta\rightarrow 0_+}\frac{|X_{k'}^s|^2\ e^{i{\bf k'}\cdot{\bf r}_i}}{E_r(k)-E_s(k')+i\eta}, \nonumber \\
I_{st}&=&-\sum_s\left(\frac{a}{2\pi}\right)^2\int d^2k'\lim_{\eta\rightarrow 0_+}\frac{|X_{k'}^s|^2}{E_r(k)-E_s(k')+i\eta}. \nonumber \\
\end{eqnarray}
We calculate first the oscillating integral in case of scattering of small wave vector polaritons, that is in the limit $ka\ll1$ in the lower branch. In this limit the polariton dispersion can considered approximately parabolic with a polariton effective mass of $m_p$. This is of the order of the cavity photon effective mass $m_p\approx (\hbar\pi)/(cL)$. Hence, the lower polariton branch dispersion is taken to be $E_-(k)=E_-(0)+\frac{\hbar^2k^2}{2m_p}$. The scattered states will also have small wave vectors due to the energy conservation. As the upper branch has higher energies its contributions are negligibly small here. Anyway the upper branch for larger wave vectors is mainly photonic with small excitonic part and thus only weakly contributes to the scattering of impurities. We consider the case around zero detuning between the excitons and photons. Therefore the excitonic weight $|X_{k}^-|^2$ will change from half around zero wave vector up to one for large wave vectors, where the lower branch became excitonic. The weight $|X_{k}^-|^2$ is a smooth function of $k$, and in the present case can be taken out of the integral, and to be fixed with the initial polariton excitonic weight value. From here on we neglect the contribution of the upper polariton branch, both as initial and scattered states, and also as intermediate scattering state. We will drop the branch index and summation, and all the parameters will be only for the lower branch.
The integral now reads:
\begin{eqnarray}
I_{os}=-X_{k}^2\ \frac{2m_p}{\hbar^2}\left(\frac{a}{2\pi}\right)^2\int d^2k'\lim_{\eta\rightarrow 0_+}\frac{e^{i{\bf k'}\cdot{\bf r}_i}}{k^2-k^{'2}+i\eta}.
\end{eqnarray}
This is similar to the case of excitons of the previous section except for the factor $|X_{k}^r|^2$ and involving the much smaller polariton effective mass in place of the exciton mass. Hence we have $m_p\ll m_{ex}$ and the integration (see the appendix) gives
\begin{equation}
I_{os}=-\frac{\pi X_k^2}{2\Delta_p}\sqrt{\frac{i\pi}{2kr}}e^{ikr},
\end{equation}
where we defined the polariton effective band width $\Delta_p=\frac{\hbar^2\pi^2}{2m_{p}a^2}$.
We turn now to the second static integral. Here no oscillating exponent appears, and hence all wave vectors along the lower branch contribute, so that the intermediate scattering state can be anywhere along the lower branch. Again for energy reasons we neglect the contribution of the upper branch. The integral then can be simplified by using a model for the lower branch dispersion in place of the real one \cite{ZoubiC}. The lower branch is divided into two parts. The first part between $0\leq k\leq k_0$ is taken to be of a parabolic dispersion with a polariton effective mass, where $E(k)=E(0)+(\hbar^2k^2)/(2m_p)$; and the second part between $k_0\leq k\leq \pi/a$, where $\pi/a$ is the Brillouin boundary, is taken to be dispersion less with energy equal to the exciton energy at zero wave vector, where we have $k_0\ll\pi/a$. The intersection point between the two parts is fixed by $\hbar^2k_0^2/(2m_p)=E_0-E(0)$. The integration as shown in the appendix gives
\begin{equation} \label{ST}
I_{st}=-\frac{\pi X_k^2}{2\Delta_p}\left[\ln\left(\frac{k}{k_0}\right)-i\frac{\pi}{2}\right]+\frac{\pi}{4\Lambda_k},
\end{equation}
where $\Lambda_k=E_0-E(k)$. The first term is the contribution of the parabolic part and the second originates from the flat part. The $Ln(k/k_0)$ is large in the limit $ka\ll 1$, but for a laterally confined $2D$ optical lattice, and for the smallest wave vector $k_m$ which is different from zero, due to the fact $\Delta_p\gg E_a$, the term $\frac{\pi X_{k_m}^2}{2\Delta_p}\ln\left(\frac{k_m}{k_0}\right)$ is much smaller than one and can be neglected. Hence $I_{st}\approx\pi/(4\Lambda_k)$.
The scattered polariton excitonic part reads
\begin{equation}
\psi_i^{ex}=\frac{X_k}{\sqrt{N}}\left\{e^{i{\bf k}\cdot{\bf r}_i}-f(k)\sqrt{\frac{i\pi}{2kr}}e^{ikr}\right\},
\end{equation}
where the scattering amplitude is given by
\begin{equation}
f(k)=\frac{X_k^2\left(\frac{\pi E_a}{2\Delta_p}\right)}{1-\left(\frac{\pi E_a}{4\Lambda_k}\right)}.
\end{equation}
As $E_a>\Lambda_k$, we have $(\pi E_a)/(4\Lambda_k)>1$, and the scattering amplitude is negative, that is $f(k)<0$. Again the above impurity effective potential is repulsive for the polaritons.
In the case of zero detuning, that is $\delta_0=0$, we have for small wave vectors $X_k^2= 1/2$, and $\Lambda_k$ is of the order of the exciton-photon coupling, $|g_k|$, where $E_a\gg\Lambda_k$, and we get $f(k)\approx-\Lambda_k/\Delta_p$. This scattering amplitude equals that of the scattering from an effective potential of a square barrier potential of height $\Lambda_k$ and width $a$.
For the case of negative detuning, in the limit of $E_a\gg\delta_0$, where $\Lambda_k$ is of the order of the exciton-photon detuning, the scattering amplitude is $f(k)\approx-(2X_k^2\Lambda_k)/\Delta_p$. This scattering amplitude equals that of the scattering from an effective potential of a square barrier potential of height $2X_k^2\Lambda_k$ and width $a$. Hence we find that the scattering amplitude can be controlled by changing the exciton-photon detuning.
Lets insert some numbers: for an atomic energy $E_a=2\ eV$, exciton-photon coupling $\hbar|g|=0.0001\ eV$, and lattice constant $a=2000\ \AA$, the scattering amplitude is plotted in figure (3) as a function of the exciton-photon detuning, for approximately normal incident waves, where we used $k=10^{-6}\ \AA$. It is clear that maximum scattering is obtained for zero detuning. As the detuning increases, both positive or negative, the $k\approx 0$ polaritons become more photonic and they scattered off the impurity much less. As the atomic energy $E_a$ is much larger than the coupling energy $\hbar g$, the scattering amplitude only shows a negligibly small asymmetry for negative and positive detunings, but we expect a clear resonance of the scattering amplitude around resonance $\delta_0$. Considering a stream of incident polaritons with the same wave vector ${\bf k}=k\hat{\bf k}$ we then should see a ring of radius $k$ of scattered polaritons.
\begin{figure}[h!]
\centerline{\epsfxsize=8.0cm \epsfbox{Plot3.eps}}
\caption{The scattering amplitude vs. exciton-photon detuning, for $k\approx 0$ polaritons.}
\end{figure}
\section{Exciton and polariton scattering of a vacancy in two-atoms per site optical lattices}
We will now go one step further and study the scattering of excitons and polaritons in a doubly occupied optical lattice where one atom is missing in one site (called the origin site). The corresponding exciton polariton picture for an ideal lattice is discussed in Ref.\cite{ZoubiB}. Here resonant electronic excitation transfer occurs among the two on-site atoms with transfer parameter $J_0$ and also among the nearest neighbor sites with transfer parameter $J_1$. The on-site interaction can be diagonalized to form symmetric and antisymmetric localized excitation with frequencies $\omega_{s}=\omega_A+J_0$, and $\omega_{a}=\omega_A-J_0$, respectively. Only the symmetric states have a significant dipole moment and thus form excitons through resonant coupling. The symmetric exciton dispersion in the limit $ka\ll1$ then reads $\omega_s(k)=\omega_A+J_0+8J_1+\frac{\hbar k^2}{2m_{eff}}$, with the effective mass $m_{eff}=-\hbar/(4J_1a^2)$ and up to a rescaling is analogous to the previous case. Naturally within a cavity only the symmetric excitons are coupled to the photons to form cavity polaritons (for details see \cite{ZoubiB}). At first sight there seems to be nothing new in this case. However, we will show that the defect, plotted schematically in figure (4), which in this case constitutes a single atom as compared to two, here acts substantially different from the simple no atom hole in the case of a single occupied lattice. Physically this can be understood from the fact that a single atom can store almost the same amount of energy as a pair if only one photon excitations are considered.
Let us now calculate the scattering amplitude of excitons and polaritons of this impurity. The scattering is for the symmetric excitons, and for the polariton excitonic part. The antisymmetric states are not involved in the scattering process, as they are on-site localized and posses no dipole moment.
\begin{figure}[h!]
\centerline{\epsfxsize=8.0cm \epsfbox{Plot4.eps}}
\caption{An impurity in $1D$ optical lattice.}
\end{figure}
Again we concentrate on the scattering of long wave length excitons with a parabolic dispersion described by an effective mass. The scattering amplitude is found to be
\begin{equation}
f(k)=\frac{\frac{\pi J_0}{2\Delta_{ex}}}{1+\frac{\pi J_0}{2\Delta_{ex}}\left[\ln\left(\frac{ka}{\pi}\right)-i\frac{\pi}{2}\right]}.
\end{equation}
For negative on-site energy transfer, $J_0<0$, the scattering is of an effective potential of a square barrier of height $|J_0|$ and width $a$. One need to compare between the on-site transfer parameter $|J_0|$ and the exciton band width $\Delta_{ex}$. In the limit of $|J_0|\gg\Delta_{ex}$ the scattering is identical to that from an effective potential of a hard disk with radius $a$ (see figure (2)), that is $f(k)\approx\frac{1}{\ln\left(\frac{ka}{\pi}\right)}$.
For polaritons the scattering of the impurity is only for their excitonic part. We consider the scattering of long wave length lower branch polaritons with a parabolic dispersion and an effective polariton mass $m_p$. The scattering amplitude is given by
\begin{equation}
f(k)=\frac{X_k^2\left(\frac{\pi J_0}{2\Delta_p}\right)}{1-\left(\frac{\pi J_0}{4\Lambda_k}\right)}.
\end{equation}
Here $\Lambda_k=E_0-E(k)$, where $E_0=\hbar\omega_A+\hbar J_0$, and where $J_0\gg J_1$.
In the limit of $|J_0|\gg\Lambda_k$ we get $f(k)\approx -X_k^2\left(\frac{2\Lambda_k}{\Delta_p}\right)$, where, for $J_0<0$, the scattering acts like a square barrier of height $2X_k^2\Lambda_k$ and width $a$. Similarly in the opposite limit of $|J_0|\ll\Lambda_k$ we get $f(k)\approx X_k^2\left(\frac{\pi J_0}{2\Delta_p}\right)$, and the scattering, for $J_0<0$ mimics a square barrier of height $\pi |J_0|X_k^2/2$ and width $a$. As shown in the previous chapter, the polariton scattering of an impurity can be modulated by controlling the exciton-photon detuning. As we change $\delta_k$, then $X_k^2$ and $\Lambda_k$ are strongly changed, and as a result the scattering amplitude $f(k)$ and the effective potential strength are changed.
Introducing the numerical examples used in the previous section with transfer energy $\hbar J_0=-0.001\ eV$ the scattering amplitude is plotted in figure (5) as a function of the exciton-photon detuning, for incident waves, namely $k\approx 0$. It is clear that maximum scattering is obtained for zero detuning. As here the transfer energy $\hbar J_0$ is smaller than, and close to, the coupling energy $\hbar g$, the scattering amplitude asymmetry for negative and positive detuning is much more pronounced relative the case of the previous section. For $k=0$, at zero detuning, the lower branch polariton is half exciton and half photon. For negative detuning, at $k=0$, the lower branch polariton is more photonic than excitonic; while for positive detuning the opposite the lower branch polariton is more excitonic than photonic. Therefore, the positive detuning scattering amplitude is larger than the negative one.
\begin{figure}[h!]
\centerline{\epsfxsize=8.0cm \epsfbox{Plot5.eps}}
\caption{The scattering amplitude vs. exciton-photon detuning, for $k\approx 0$ polaritons.}
\end{figure}
\subsection{An impurity in an asymmetric optical lattice}
One of the most interesting phenomena for excitons in doubly occupied lattices appears in the case of asymmetric optical lattice sites \cite{ZoubiB}. We get a strong polarization dependence of the exciton and polariton energies. Here we discuss
the consequence of this for their scattering amplitudes off impurities.
If one of the orthogonal pairs of counter propagating lasers forming the lattice potentials has a different intensity, the potential is elongated in one direction, e.g. $x$. Hence the two atoms at one site will have a larger average distance $R$ in the $x$ direction as shown in figure (6). The atomic transition dipole induced by the cavity photon is assumed to be in the (x,y)-plane $\vec{\mu}=\mu(\cos\theta,\sin\theta)$, where $\theta$ is the angle between the dipole $\vec{\mu}$ and the $x$ axis. The resonance dipole-dipole interaction between the two on-site atoms is $\hbar J_0(\theta)=\hbar \bar{J}\ \left(1-3\cos^2\theta\right)$, where $\hbar \bar{J}=\frac{\mu^2}{4\pi\epsilon_0R^3}$. We have $\hbar J_0(\theta=0)=-2\hbar \bar{J}$, and $\hbar J_0(\theta=90)=\hbar \bar{J}$, with $\hbar J_0(\theta\approx 54.74)=0$. The detuning energy between symmetric and antisymmetric states thus will change sign at some angle, where the polarization even vanishes.
\begin{figure}[h!]
\centerline{\epsfxsize=5.0cm \epsfbox{Plot6.eps}}
\caption{An asymmetric optical site.}
\end{figure}
The long wave length polariton scattering amplitude as a function of the relative transition dipole direction now is
\begin{equation} \label{SSS}
f_k(\theta)=\frac{X_k^2(\theta)\left(\frac{\pi J_0(\theta)}{2\Delta_p}\right)}{1-\left(\frac{\pi J_0(\theta)}{4\Lambda_k(\theta)}\right)}.
\end{equation}
We plot this scattering amplitude as a function of $\theta$ for different values of $\bar{J}$, and for $k\approx 0$, again using the numerical values of section 3. We also have $E_c(0)=E_A+J(0)$, and $\hbar J_1=10^{-7}\ eV$. In figure (7) the plot is for $\hbar\bar{J}=10^{-4}\ eV$, where $\hbar|g|=\hbar\bar{J}$. Figure (8) is for $\hbar\bar{J}=5\times 10^{-4}\ eV$, where $\hbar|g|<\hbar\bar{J}$.
Note that the scattering amplitude changes sign at $\theta\approx 54.74$ and we can turn of scattering by using this proper angle. In figure (9) we plot this for $\hbar\bar{J}=10^{-3}\ eV$. Here two resonances appear. Figure (10) is for $\hbar\bar{J}=5\times 10^{-3}\ eV$. Now the resonances tend to the negative-positive crossover angle.
The negative scattering amplitude corresponds to a repulsive effective potential, and polaritons scattered away of the impurity. While the positive scattering amplitude corresponds to an attractive potential. Here even the formation of bound states could be expected, allowing for localized polaritons. The bound state signature appears in the pole of the scattering amplitude of Eq.(\ref{SSS}) but by including the $Ln$ term of Eq.(\ref{ST}) in the denominator. We get a shallow bound state that falls inside the polariton line width, and which presents as a resonance scattering state inside a continuum.
\begin{figure}[h!]
\centerline{\epsfxsize=8.0cm \epsfbox{Plot7.eps}}
\caption{The scattering amplitude vs. $\theta$, for $k\approx 0$ polaritons, with $\hbar\bar{J}=10^{-4}\ eV$.}
\end{figure}
\begin{figure}[h!]
\centerline{\epsfxsize=8.0cm \epsfbox{Plot8.eps}}
\caption{The scattering amplitude vs. $\theta$, for $k\approx 0$ polaritons, with $\hbar\bar{J}=5\times 10^{-4}\ eV$.}
\end{figure}
\begin{figure}[h!]
\centerline{\epsfxsize=8.0cm \epsfbox{Plot9.eps}}
\caption{The scattering amplitude vs. $\theta$, for $k\approx 0$ polaritons, with $\hbar\bar{J}=10^{-3}\ eV$.}
\end{figure}
\begin{figure}[h!]
\centerline{\epsfxsize=8.0cm \epsfbox{Plot10.eps}}
\caption{The scattering amplitude vs. $\theta$, for $k\approx 0$ polaritons, with $\hbar\bar{J}=5\times 10^{-3}\ eV$.}
\end{figure}
\section{Summary}
We demonstrated that defects in an optical lattice in the Mott insulator phase will change the dynamics of resonant excitons and cavity polaritons. For a very low density of defects, the exciton and polariton pictures still hold and the defect simply acts as a scatterer for such quasi-particles. We calculated the scattering amplitude for excitons and polaritons showing that the defects can be approximated by effective potentials. In the case of one atom per site the vacancy scattering effective potential for excitons is a hard disk of a radius equal to the lattice constant $a$, which is quite different for polaritons, where only the excitonic part contributes significantly to the scattering. The scattering effective potential for long wave length polaritons just is a square barrier of height $2|X_k|^2\Lambda_k$ and width $a$, where $|X_k|^2$ is the exciton weight in the cavity polariton, and which appears here as the scattering is only for the polariton excitonic part. For the case of zero exciton-photon detuning, and in the limit $ka\ll1$, we have $|X_k|^2=1/2$, and $\Lambda_k$ is of the order of the Rabi splitting. While for large negative detuning we have $|X_k|^2\ll1$, and $\Lambda_k$ is of the order of the exciton-photon detuning. As $|X_k|^2$ and $\Lambda_k$ are a function of the detuning, hence the scattering amplitude can be controlled by changing the detuning, with a scattering resonance at zero detuning.
In the case of a two atoms per site lattice with a defect represented by a single atom site, we found two distinct cases. If the on site dipole-dipole coupling $J_0$ is larger than the Rabi splitting, we got similar results as in the case of one atom per site. But if $J_0$ is smaller than the Rabi splitting, hence the polariton scattering effective potential is identical to the scattering of a square barrier of height $J_0$ and width $a$. The parameter $J_0$ can be easily controlled in changing the photon polarization, as we presented for the case of asymmetric optical lattice sites. Also we showed that at a fixed angle $J_0$ can change sign from positive to negative, and then also the scattering amplitude changes sign.
We conclude that cavity polaritons can be used as a useful tool to observe defects in an optical lattice. As the polariton is part exciton and part photon, where the photon part can be controlled externally, the above results suggest that one can recognize the kind of defect in each case. For example in transmission or reflection experiments, for an incident field with a fixed wave vector $k$, in the transmitted or reflected signals we get a scattering ring of radius $k$ with the appropriate intensity which obtained from the scattering cross section.
\begin{acknowledgments}
The work was supported by the Austrian Science Fund (FWF), through the Lise-Meitner Program (M977).
\end{acknowledgments}
|
{
"redpajama_set_name": "RedPajamaArXiv"
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| 461
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Every Hurricane from the Past 170 Years, Mapped
Should you pilot a small, rickety craft across international waters this summer, it would be wise to consult this unusual map of foul ocean weather.
John Metcalfe, The Atlantic Cities
This article is from the archive of our partner .
MORE FROM THE ATLANTIC CITIES
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Seattles New Streetlights Are 40-Foot-Tall Singing Flowers
Should you pilot a small, rickety craft across international waters this summer, it would be wise to consult this unusual map of foul ocean weather. The gusty cartography plots the paths all the tropical cyclones recorded in the past 170 years. Brighter areas show where they have overlapped in space, representing areas of historically frequent hurricane activity—tumultuous ocean zones probably best to steer around.
Visualization super-nerds at NOAA (that's meant in the most flattering way) conjured this top-down look at hurricanes and Pacific cyclones using storm-track records from the National Climatic Data Center. The records date back to 1842 and include both satellite data and first-person accounts from (no doubt really stressed) mariners. Though the U.S. government stocks such information on 11,967 tropical cyclones, that number is probably smaller than what has actually blown across the seas over the ages. Satellites nowadays keep a laser bead on these powerful storms, but back when sailors were responsible for snitching on them, one could flail about in the middle of the ocean without many people noticing.
This key shows where on the map the highest points of overlap are:
NOAA has a few things to note about why history's tempests tend to repeat themselves:
By coloring how many times any storm track overlapped another, certain patterns arise in the density of storms affecting a given area. Cyclone tracks overlapped the most in the western Pacific and Bay of Bengal (India), where typhoon season never ends since waters are always warm enough to sustain cyclone formation. The frequency of track overlaps is much lower in the Western Hemisphere than in the Eastern Hemisphere, however, a related map showing storm intensity seen here shows an interesting contrast.
Here's that related map of cyclone strength, broken down into eastern and western hemispheres. Again, areas of brighter hues represent higher values (in this case, wind speeds). First the Americas:
And now Asia, Africa, and Australia:
One takeaway: People living on the western coast of Central America and on the sprawling eastern and southern contours of North America, including around the Gulf of Mexico, have a good chance in their lifetimes of encountering extra-ferocious hurricanes. The range of intense cyclones on the other side of the globe is more limited. As NOAA notes, there the "strongest cyclones seem to group near the Philippines."
Images courtesy of NOAA
This article is from the archive of our partner The Wire.
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}
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Talking with your clients about their values and passions in life is a meaningful way to strengthen your client relationships. It can also be enjoyable, and a natural part of building your clients' trust in you.
Why ask about charitable giving?
The short answer is because your clients would like you to! A study by the Charities Aid Foundation surveyed wealthy individuals in the UK and found that two-thirds believe professional advisers could and should provide more advice relating to charitable giving. What's more, two-fifths of wealthy people in the UK are already taking philanthropy advice.
So, if your services don't include the advice of a philanthropic adviser, clients may well start looking for someone who does.
Talking with someone about their values doesn't have to be a serious, awkward conversation. In fact, it can be quite interesting! It's also an important opportunity to learn more about your clients and invite further, more meaningful interactions going forward.
I'm pleased with what we've accomplished together in preparing you for retirement. We've met your financial objectives and I hope you feel secure about your financial plan.
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Even if your clients haven't given the topic much thought, you're at least opening the door to further discussion. Show them that you're there to listen and provide them with advice and resources when they're ready.
Now that you've raised the topic of charitable giving with your clients, it's up to you to follow up.
While philanthropy is important to a lot of people in principle, it can easily fall to the bottom of a busy person's to-do list. If they've expressed genuine interest in developing a charitable giving strategy, your clients will expect you to follow up with resources and next steps.
Here's when you can bring in a philanthropic adviser like Thoughtful Philanthropy. We can arrange an introductory phone call with your client or even just send a questionnaire to start them on the path of identifying their charitable interests.
You've worked hard to build a relationship with your clients, who know and trust your professional experience. But you can't be an expert in everything. Increasingly, middle-and-higher income individuals and families are looking for professional advice on using their wealth to support their values—from environmental protection to education. By incorporating conversations and expertise on charitable giving into your service package, you better serve the whole person. This increases the chances those clients will stick with you—and recommend you—in the long term.
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{
"redpajama_set_name": "RedPajamaC4"
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Buddhism
# Buddhism
# A Short History
EDWARD CONZE
A Oneworld Book
Copyright © Muriel Conze 1980, 1982, 1993
First published by Oneworld Publications in 1993
This ebook edition published by Oneworld Publications in 2014
All rights reserved
Copyright under Berne Convention
A CIP record for this title is available
from the British Library
ISBN 978–1–85168–568–4
eISBN 978–1–78074–669–2
Cover design by Simon McFadden
Oneworld Publications
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England
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## Contents
Introduction
**ONE** The First Five Hundred Years: 500–0 BC
**TWO** The Second Period: AD 0–500
**THREE** The Third Period: AD 500–1000
**FOUR** The Last One Thousand Years: AD 1000–1978
Bibliography
Index
## Introduction
### THE HISTORICAL CONTEXT AND THE EPOCHS OF BUDDHIST HISTORY
_A_. Buddhism claims that a person called "The Buddha", or "The Enlightened One", rediscovered a very ancient and longstanding, in fact an ageless, wisdom, and that he did so in Bihar in India, round about 600 or 400 BC – the exact date is unknown. His re-formulation of the perennial wisdom was designed to counteract three evils.
1. _Violence_ had to be avoided in all its forms, from the killing of humans and animals to the intellectual coercion of those who think otherwise.
2. The " _self_ ", or the fact that one holds on to oneself as an individual personality, was held to be responsible for all pain and suffering, which would in the end be finally abolished by the attainment of a state of self-extinction, technically known as "Nirvana".
3. _Death_ was an error which could be overcome by those who entered the "doors to the Deathless", "the gates of the Undying".
Apart from providing antidotes to these three ills, the Buddha formulated no definite doctrines or creeds, but put his entire trust into the results obtained by training his disciples through a threefold process of moral restraint, secluded meditation and philosophical reflection.
As to the first point, that of _violence_ – the technical term for "non-violence" is _ahimsá_ , which means the avoidance of harm to all life. In this respect Buddhism was one of the many movements which reacted against the technological tyrannies which had arisen about 3000 bc, whose technical projects and military operations had led to widespread and often senseless violence and destruction of life.
From its very beginning the growth of civilization has been accompanied by recurrent waves of disillusion with power and material wealth. About 600 BC onwards one such wave swept through the whole of Asia, through all parts of it, from China to the Greek islands on the coast of Asia Minor, mobilizing the resources of the spirit against the existing power system.
In India the reaction arose in a region devoted to rice culture, as distinct from the areas further West with their animal husbandry and cultivation of wheat. For the last two thousand years Buddhism has mainly flourished in rice-growing countries and little elsewhere. In addition, and that is much harder to explain, it has spread only into those countries which had previously had a cult of Serpents or Dragons, and never made headway in those parts of the world which view the killing of dragons as a meritorious deed or blame serpents for mankinds ills.
As to the second point, concerning the _self_ , in offering a cure for individualism Buddhism addresses itself to an individualistic city population. It arose in a part of India where, round Benares and Patna, the iron age had thrown up ambitious warrior kings, who had established large kingdoms, with big cities, widespread trade, a fairly developed money economy and a rationally organized state. These cities replaced small-scale tribal societies by large-scale conurbations, with all the evils of depersonalization, specialization and social disorganization that that entails.
Most of the Buddha's public activity took place in cities and that helps to account for the intellectual character of his teachings, the "urbanity" of his utterances and the rational quality of his ideas. The Buddha always stressed that he was a guide, not an authority, and that all propositions must be tested, including his own. Having had the advantage of a liberal education, the Buddhists react to the unproven with a benevolent scepticism and so they have been able to accommodate themselves to every kind of popular belief, not only in India, but in all countries they moved into.
As to the third point, concerning _death_ ; there is something here which we do not quite understand. The Buddha obviously shared the conviction, widely held in the early stages of mankind's history, that death is not a necessary ingredient of our human constitution, but a sign that something has gone wrong with us. It is our own fault; essentially we are immortal and can conquer death and win eternal life by religious means. The Buddha attributed death to an evil force, called _Mára_ , "the Killer", who tempts us away from our true immortal selves and diverts us from the path which could lead us back to freedom. On the principle that "it is the lesser part which dies" we are tied to Mára's realm through our cravings and through our attachment to an individual personality which is their visible embodiment. In shedding our attachments we move beyond "death's realm", "beyond the death-king's sight" and win relief from an endless series of repeated deaths, which each time rob us of the loot of a lifetime.
_B_. Buddhism has so far persisted for about 2,500 years and during that period it has undergone profound and radical changes. Its history can conveniently be divided into four periods. The first period is that of the old Buddhism, which largely coincided with what later came to be known as the "Hínayána"; the second is marked by the rise of the Maháyána; the third by that of the Tantra and Ch'an. This brings us to about AD 1000. After that Buddhism no longer renewed itself, but just persisted, and the last 1,000 years can be taken together as the fourth period.
Geographically, first period Buddhism remained almost purely Indian; during the second period it started on its conquest of Eastern Asia and was in its turn considerably influenced by non-Indian thought; during the third, creative centres of Buddhist thought were established outside India, particularly in China. Philosophically, the first period concentrated on psychological questions, the second on ontological, the third on cosmic. The first is concerned with individuals gaining control over their own minds, and psychological analysis is the method by which self-control is sought; the second turns to the nature (svabháva) of true reality and the realization in oneself of that true nature of things is held to be decisive for salvation; the third sees adjustment and harmony with the cosmos as the clue to enlightenment and uses age-old magical and occult methods to achieve it. Soteriologically, they differ in the conception of the type of man they try to produce. In the first period the ideal saint is an Arhat, or a person who has non-attachment, in whom all craving is extinct and who will no more be reborn in this world. In the second it is the Bodhisattva, a person who wishes to save all his fellow-beings and who hopes ultimately to become an omniscient Buddha. In the third it is a Siddha, a man who is so much in harmony with the cosmos that he is under no constraint whatsoever and as a free agent is able to manipulate the cosmic forces both inside and outside himself.
Other religions may perhaps have undergone changes as startling as these, but what is peculiar to Buddhism is that the innovations of each new phase were backed up by the production of a fresh canonical literature which, although clearly composed many centuries after the Buddha's death, claims to be the word of the Buddha Himself. The Scriptures of the first period were supplemented in the second by a large number of Maháyána Sútras and in the third by a truly enormous number of Tantras. All these writings are anonymous in the sense that their authors are unknown and the claim that they were all spoken by the Buddha Himself involves, as we shall see (ch. 2 sec. 1), a rather elastic conception of the Buddha.
At any given time the newer developments did not entirely supersede the older ones. The older schools coexisted with the new ones, although they were often profoundly modified by them. The old Buddhism of the first period absorbed in the second a good many of the tenets of the Maháyána and the contact between the Tantras and the Maháyána led to a synthesis which took place in the universities of Bengal and Orissa during the Pála period (see ch. 3 sec. 1). In my account I will concentrate on the creative impulses and they will be my guide.
The division of Buddhist history into periods of 500 years does not only agree with the facts, but it is mentioned in many Buddhist writings dating from the beginning of the Christian era. These five periods of 500 years are enumerated as marking the continued degeneration of the doctrine. Like everything else, the Buddhist order and doctrine is bound to decay, in each period its spirituality will be diminished, and after 2,500 years it will be near its extinction (see ch. 4 sec. 9). Whether or not observation bears out this diagnosis of a continuous decay, it had a profound influence on the mentality of the Buddhists in later ages, and we will hear of it again and again. The story of Buddhism is indeed not only a splendid, but also a melancholy one.
To the modern historian, Buddhism is a phenomenon which must exasperate him at every point and we can only say in extenuation that this religion was not founded for the benefit of historians. Not only is there an almost complete absence of hard facts about its history in India; not only is the date, authorship and geographical provenance of the overwhelming majority of the documents almost entirely unknown, but even its doctrines must strike the historian as most unsatisfactory, and elusive. Buddhists tend to cancel out each statement by a counter-statement and the truth is obtained not by choosing between the two contradictory statements, but by combining them. What then, apart from their characteristic terminology, is common to all this variety of diverse teachings, what are the common factors which allow us to call all of them "Buddhist"?
1. Among the more stable factors the _monastic organization_ is the most obvious and conspicuous. Its continuity is the basis which supports everything else (see ch. 1 sec. 2).
2. Next we have as a constant element a traditional set of _meditations_ which have moulded all generations of Buddhists and which are bound to exert a fairly uniform effect on everyone who subjects himself to their influence (see ch. 1 sec. 3).
3. Thirdly, all Buddhists have had one and the same _aim_ , which is the "extinction of self", the dying out of separate individuality, and their teachings and practices have generally tended to foster such easily recognizable spiritual _virtues_ as serenity, detachment, consideration and tenderness for others. In the Scriptures, the Dharma has been compared to a _taste._ The word of the Buddha is there defined as that which has the taste of Peace, the taste of Emancipation, the taste of Nirvana. It is, of course, a peculiarity of tastes that they are not easily described, and must elude those who refuse actually to taste them for themselves.
4. Throughout its history, Buddhism has the unity of an _organism_ , in that each new development takes place in continuity from the previous one. Nothing could look more different from a tadpole than a frog and yet they are stages of the same animal, and evolve continuously from each other. The Buddhist capacity for metamorphosis must astound those who only see the end-products separated by long intervals of time, as different as chrysalis and butterfly. In fact they are connected by many gradations, which lead from one to the other and which only close study can detect. There is in Buddhism really no innovation, but what seems so is in fact a subtle adaptation of pre-existing ideas. Great attention has always been paid to continuous doctrinal development and to the proper transmission of the teachings. These are not the anarchic philosophizings of individualists who strive for originality at all costs. Instead, we have groups of teachers, known as "sects" or "schools", and lines of masters which maintain continuity over many centuries.
## **ONE**
## The First Five Hundred Years: 500–0 BC
### THE PECULIARITIES OF THE FIRST PERIOD
The absence of hard facts is particularly marked for the first period. One, and only one, date is really certain and that is the rule of the emperor Aśoka (274–236) whose patronage transformed Buddhism from a small sect of ascetics into an all-Indian religion. Even the date of the Buddha's life is a matter of conjecture. Indian tradition often tells us that His death took place 100 years before Aśoka. Modern scholars have on the whole agreed to place His life between 563 and 483 BC. With some reluctance I have here followed their chronology.
The nature of our documents gives rise to further uncertainties. During this entire period the Scriptures were transmitted orally and they were written down only towards the end of it. Of the actual words of the Buddha nothing is left. The Buddha may have taught in Ardhamagadhi, but none of His sayings is preserved in its original form. As for the earliest Canon, even its language is still a matter of dispute. All we have are translations of what may have been the early Canon into other Indian languages, chiefly Páli and a particular form of Buddhist Sanskrit. Always without a central organization, Buddhism had divided itself at some unspecified time into a number of sects, of which usually eighteen are counted. Most of these sects had their own Canon. Nearly all of them are lost to us, either because they were never written down, or because the depredations of time have destroyed the written record. Only those are left which after the collapse of Buddhism in India about AD 1200 had by some chance got into some region outside India, like Ceylon, Nepal, or Central Asia, or which had been previously translated into Chinese or Tibetan. We therefore possess only a small portion of what actually circulated in the Buddhist community during the first period. What is more, the selection of what is preserved is due more to chance than considerations of antiquity and intrinsic merit.
And that which we have may have been composed at any time during the first 500 years. First of all it must state quite clearly that there is no objective criterion which would allow us to single out those elements in the record which go back to the Buddha Himself. Some modern European books abound in confident assertions about what the Buddha Himself has personally taught. They are all mere guesswork. The "original gospel" is beyond our ken now. The farthest we can get back in time is the period when the community split up into separate sects. What we can do is to compare the documents of the various sects, say a Theravádin _Dhammapáda_ from Ceylon with a Sarvástivádin _Udánavarga_ found in the sands of Turkestan. Where we find passages in which these two texts, the one in Pali and the other in Sanskrit, agree word by word, we can assume that they belong to a time antedating the separation of the two schools, which took place during Aśoka's rule. Where they do not agree, we may infer their post-Aśokan date in the absence of evidence to the contrary. So far no one has yet systematically undertaken such a comparison and until that is done we are unable to clearly distinguish the doctrines of the first one or two centuries, from those of post-Aśokan times. It is not even quite certain when and under what circumstances these separations of the sects took place, since all the works we have on the subject are five centuries later than the events they report and the data are everywhere distorted by sectarian bias. But whether our knowledge gets us to within one century of the neighbourhood of the Nirvana, or to within two or three centuries only, there is an initial period which is shrouded in mystery and to which we cannot penetrate.
In the next two sections I will try to explain the doctrines which marked the Buddhism of the first period as far as it can be inferred with some probability. They first concern monastic discipline, and then the basic theory of salvation and the way to it.
### THE MONASTIC DISCIPLINE
The oldest documents which we can place with some degree of certainty before Aśoka happen to deal with monastic discipline (Vinaya). From fairly early times onwards the traditions concerning the Buddha's teachings were grouped under two principal headings called respectively Dharma and Vinaya. The Vinaya proved the more stable and uniform element of the two, much less subject to disagreements and re-formulations. Discussions on the Vinaya are seldom heard of and even at later times school formations rarely implied modifications in the Vinaya, except in quite external and superficial matters, such as dress, etc. Even when with the Maháyána quite new schools arose on dogmatic grounds, they adhered for a long time as far as the Vinaya was concerned to one of the older Hínayána schools. In actual practice there has been, of course, much plain disregard of the more onerous rules in the long history of the order, but as for their formulation it seems to have reached its final form already in the fourth century BC. At that time a great work, the _Skandhaka_ , was produced, which divided and arranged the enormous material accumulated by then according to a well conceived plan. It regulates the fundamental institutions of Buddhist monastic life, the admission to the order, the confession ceremonies, the retirement during the rainy season, and it discusses clothing, food and drugs for the sick, as well as the rules to be observed in the punishment of offenders.
Older still are the approximately 250 rules of the _Prátimoksha_ , a classification of ecclesiastical offences, of which we possess about a dozen different recensions, which agree on all essentials. These rules must be recited every fortnight in front of a chapter of the monks. Among all the texts of the Scriptures there is none that has enjoyed among Buddhists an authority as uncontested, widespread and lasting as these Pratimoksha rules, and it is therefore necessary to give the reader some idea of their contents.
First of all they list four offences which deserve expulsion, i.e. sexual intercourse, theft, murder, and the false claim to either supernatural powers or high spiritual attainments. Then follow thirteen lighter offences, which deserve suspension, and of which five concern sexual misconduct, two the building of huts, and the remaining six dissensions within the Order. The recitation then continues to enumerate two sexual offences which are "punishable according to the circumstances", and after that come thirty offences which "involve forfeiture" of the right to share in garments belonging to the Order and which, in addition, make the offender liable to an unfavourable rebirth. They forbid, among other things, the handling of gold and silver as well as trading activities, or the personal appropriation of goods intended for the community. Next there are ninety offences which, unless repented and expiated, will be punished by an unfavourable rebirth. They concern such things as telling lies, belittling or slandering other monks, they regulate the relations with the laity by forbidding "to teach the Scriptures word by word to an unordained person", to tell laymen about the offences committed by monks, and so on. For the rest they concern a huge variety of misdemeanours, e.g. they forbid to destroy any kind of vegetation, to dig the earth, to drink alcoholic beverages, or to have a chair or bed made with legs higher than eight inches. The obviously very archaic document then further gives four offences requiring confession, followed by thirteen rules of decorum, and it concludes with seven rules for the settling of disputes.
The purpose of the Vinaya rules was to provide ideal conditions for meditation and renunciation. They try to enforce a complete withdrawal from social life, a separation from its interests and worries, and the rupture of all ties with family or clan. At the same time the insistence on extreme simplicity and frugality was meant to ensure independence, while the giving up of home and all property was intended to foster non-attachment. Originally, the Order seems to have been conceived as composed of wandering beggars, who ate food obtained as alms in their begging bowls, wore clothes made from rags picked up on rubbish heaps and dwelt in the forest, in caves or at the foot of trees. Only during the rainy season must they cease roaming about and stay in one and the same place. At all times a minority continued to aspire after the rigours of this primitive simplicity, but, generally speaking, with the increasing prosperity of the religion the monks settled down in monasteries which gave aloofness from social concerns without some of the inconveniences of the hand-to-mouth existence originally envisaged. The text of the Vinaya being fixed once and for all, its further history is one of constant compromises between its sacrosanct provisions on the one hand, and social realities and human fallibility on the other.
### THE BASIC DOCTRINES
So much about the practices of the monks. What then were the doctrines common to all the Buddhists of the first period, and shared not only by them but by all later Buddhists however much they might modify them by additions and reservations? They can be grouped under two main headings. They first of all propound a _theory of salvation_ , showing the need for it, its nature and the methods necessary to attain it. They secondly concern the _three_ " _Jewels_ " or "Treasures", i.e. the Buddha, the Dharma and the Samgha.
In its core, Buddhism is a _doctrine of salvation._ The need for it arises from the hopelessly unsatisfactory character of the world in which we find ourselves. Buddhists take an extremely gloomy view of the conditions in which we have the misfortune to live. It is particularly the impermanence of everything in and around us that suggests the worthlessness of our worldly aspirations which in the nature of things can never lead to any lasting achievement or abiding satisfaction. In the end death takes away everything we managed to pile up and parts us from everything we cherished. How futile is the search for security in such surroundings, for happiness with such unsuitable materials! The joys and pleasures of the children of the world are exceedingly trivial and their choices and preferences betray little wisdom. They behave rather like the small child who finds a marble of exceeding beauty with a green spot on it, is overjoyed at having found it, and who, so as to make quite sure of not losing it again, proceeds straightaway to swallow the marble, with the result that his stomach has to be pumped out. Further, who would not be frightened if he realized all the pains and terrors to which he exposes himself by having a body! Suffering without end in a futile round of rebirths after rebirths ( _samsára_ ), that is the lot of ordinary people and the revulsion from it is the spur to salvation. The Buddhist ascetics were men who in fear of birth and death had left home life to gain salvation.
If next we ask for the cause of this unsatisfactory state of affairs, we are told that it is not imposed upon us by any outside force, by some fate or malevolent deity, but that it is due to some factor in our own mental constitution. This factor is variously described as "craving", the "belief in a separate self", "ignorance" or adherence to the "perverted views". Not only the craving for sense-pleasures, for money, social position or power is apt to put us in bondage to the forces which we vainly hope to use for our own ends, but any form of desire whatsoever is condemned by Buddhists as destructive of our inward freedom and independence. From another angle we may say that the whole of our unhappiness stems from the habit of trying to appropriate some part of the universe as if it were our "own" and to say of as many things as we can that "this is mine, I am this, this is myself". It is a fundamental teaching of Buddhism that this word "self" does not correspond to a real fact, that the self is fictitious and that therefore by our self-seeking we sacrifice our true welfare to a mere fiction. Finally, Buddhism differs from Christianity in that it sees the root cause of all evil in "ignorance" and not in "sin", in an act of intellectual misapprehension and not in an act of volition and rebellion. As a working definition of ignorance we are offered the four "perverted views" ( _viparyása_ ) which make us seek for permanence in what is inherently impermanent, ease in what is inseparable from suffering, selfhood in what is not linked to any self, and delight in what is essentially repulsive and disgusting.
The situation would, of course, be entirely hopeless if this world of suffering and Samsára comprised the whole extent of reality. In fact this is not so, and beyond it there is something else, which is called Nirvana, a transcendental state which is quite beyond the ken of ordinary experience, and of which nothing can be said except that in it all ills have ceased, together with their causes and consequences. Buddhists are less intent on defining this Nirvana, than on realizing it within themselves. And they are very much averse to making positive statements about the man who has gone to Nirvana. This world is often compared to a house on fire, which everyone in his senses will try to escape from. But if the samsaric world is like a fire, then Nirvana is like the state which results from the extinction of that fire. As we read in the _Sutta Nipáta_ (1074, 1079), one of our more ancient texts:
As flame flung on by force of wind
Comes to its end, reaches what none
Can sum; the silent sage, released,
From name-and-form, goes to the goal,
Reaches the state that none can sum.
When all conditions are removed,
All ways of telling also are removed.
Since the causes of all evil lie within ourselves, we ourselves can, by our own efforts, rid ourselves of them, if we only know how to go about it. Like a good physician the Buddha has given us a profusion of remedies for the great variety of our ailments. On their lower levels the Buddhist methods of salvation are similar to those found in other religions. A man must first of all bring some _morality_ into his daily life, and he must observe the "five precepts" which forbid killing, stealing, sexual misconduct, lying and the use of intoxicants. Next he must take care how he earns his living. Butchers, fishermen, or soldiers, for instance, break the first precept all the time, and little spirituality can be expected of them. Other occupations are less perilous to the soul, but the safest and most fruitful is that of a homeless and propertyless monk who relies on others for all his material needs.
But once the moral foundations are laid, the remainder of the Buddhist efforts consist in mental training, in _meditations_ of various kinds. Meditation is a mental training which is carried out for three distinct, but interconnected, purposes:
1. It aims at a withdrawal of attention from its normal preoccupation with constantly changing sensory stimuli and ideas centred on oneself.
2. It aims at effecting a shift of attention from the sensory world to another, subtler realm, thereby calming the turmoils of the mind. Sense-based knowledge is as inherently unsatisfactory as a sense-based life. Sensory and historical facts as such are uncertain, unfruitful, trivial, and largely a matter of indifference. Only that is worth knowing which is discovered in meditation, when the doors of the senses are closed. The truths of this holy religion must elude the average worldling with his sense-based knowledge, and his sense-bounded horizon.
3. It aims at penetrating into the suprasensory reality itself, at roaming about among the transcendental facts, and this quest leads it to Emptiness as the one ultimate reality.
In Buddhist terminology, the first preliminary step is known as "mindfulness" ( _smrti_ ), which is followed then by "ecstatic trance" ( _samádhi_ ) and "wisdom" ( _prajñá_ ). The relation of the three is indicated by the following diagram:
This is the classification of the meditations according to their purpose. From another point of view they can be classified according to their subjects or topics. A considerable number of such topics were offered to the aspirant, and his choice among them depends on his mental endowments and proclivities. So vast is the range of possibilities offered that they cannot possibly be even enumerated here. There we have relatively simple breathing exercises of the Yogic type, a survey of the "thirty-two parts of the body", the contemplation of corpses in various degrees of decomposition, an introspective awareness of our mental processes as they go along, be they feelings, thoughts, or the hindrances to concentration, or the factors which make for enlightenment. Then there is the cultivation of the social emotions, such as friendliness and compassion, the recollection of the virtues of the three Jewels, the meditation on death and the aspiration for Nirvana. A favourite subject of meditation are the twelve links of the chain of conditioned co-production ( _pratítyasamutpáda_ ), which shows how ignorance leads to the other factors of worldly existence ending in old age and death and how, conversely, the extinction of ignorance must lead to the extinction of all these factors. Other meditations again try to impress on our minds the facts of the impermanence of all conditioned things, to show up the full extent of suffering, demonstrate the inanity of the term "self", to foster insight into emptiness and to reveal the characteristic features of the path which leads to salvation. In fact, there seems to be almost no limit to the number of meditational devices which are attested for the first period of Buddhism, although it was apparently only in the second period that some systematic order was imposed upon them.
Now as to the _Three Jewels. The Buddha_ is essential to this religion as its founder who guarantees the truth and reliability of the teaching by the fact that He is "fully enlightened". He has awoken to the nature and meaning of life and has found a definite way out of it. He differs from all other people in that He has by Himself found the truth, and that He knows everything that is necessary to salvation. Whether He knew also all other things, i.e. whether he was omniscient in the full sense of the term, was a matter of dispute among the sects. There was, however, general agreement that He knew everything needful for the attainment of final peace and that therefore He could in spiritual matters act as a sure and infallible guide.
The word "Buddha" itself is, of course, not a proper name but a title, or epithet, which means the "Enlightened One". It refers to the condition of a man who was a completely unobstructed channel for the spiritual force of Dharma, or Reality. The personal name of the historical Buddha was Gautama, or Siddhártha, and after His tribe He is often called Śákyamuni, "the sage from the tribe of the Śákyas". With the historical individual the Buddhist religion is not greatly concerned. His value to the religion lay in His transmission of the spiritual teachings about Dharma. A duality of this kind is normal in authoritative Asian religious leaders. In recent years we have met it again in Mohandas Karamchand Gándhi, who at the same time was the Mahátma, the "Great-souled One", a word for the spiritual force which worked through that particular individual.
In this way the individual, called Gautama or Śákyamuni, somehow coexists with the spiritual principle of Buddhahood, which is variously called the "Tathágata", or "the Dharmabody" or "the Buddha-nature". The Buddhists have, however, always maintained that the exact relation between His individual and His spiritual sides cannot be defined. They have also consistently opposed the tendencies of the unregenerate to put their faith into a living actual person and have done everything to belittle the importance of the Buddha's actual physical existence. It is the Buddha Himself who is reported to have said to Vakkali: "What is there, Vakkali, in seeing this vile body of mine? Whoso sees the spiritual Law, or Dharma, he sees me; whoso sees me sees the spiritual Dharma. Seeing Dharma, Vakkali, he sees me; seeing me, he sees Dharma."
As the manifestation of a type, the "historical Buddha" is not an isolated phenomenon, but one of a series of Buddhas who appear in this world throughout the ages. Knowledge of the non-historical Buddhas seems to have grown as time went on. Originally there were seven, then we hear of twenty-four, and so the number steadily increased. The "seven Buddhas", i.e. Śákyamuni and His six predecessors, are frequently represented in art – in Bharhut and Sanchi by Their stúpas and Bodhi-trees, in Gandhara, Mathura and Ajanta during our second period in human form, each nearly indistinguishable from the other. It was only towards the end of the first period that interest shifted to two other non-historical Buddhas. With the development of the Bodhisattva-theory (see ch. 2 sec. 1) comes Dípankara, Śákyamuni's twenty-fourth predecessor, under whom He first resolved to become a Buddha. With the spread of pessimism about the continued vitality of Śákyamuni's message comes the cult of Maitreya, the future Buddha, under whom the Dharma will reappear with new vigour.
This period had little interest in the biography of the Buddha Śákyamuni as a person. It would be difficult to reconstruct the facts of His life from the details we have. Interest concentrated on the two periods of His life which had the greatest significance for the believer, i.e. to the period of His enlightenment which marked His victory over ignorance, and to His last days, when He attained His final Nirvana, and consummated His victory over death and the world. For the rest it appears that the greater part of what we believe to know of His life was at first a part of the Vinaya tradition, that it consisted of an account which began with His genealogy and miraculous birth, and went on beyond His final Nirvana to the legendary first Council of Rájagrha where the Canon of the Sacred Scriptures is said to have been compiled, and ended with the so-called second council of Vaiśalí where controversial points of disciplinary practice were discussed. The story of His life was at first a collection of precedents, which were invoked to justify the Vinaya rules. In addition, many stories and legends gradually grew up in connection with some holy place or shrine, to account for its sanctity. Little attempt was made to weave all these stories into one consecutive biography. At present we are not in a position to decide which ones of them are trustworthy historical information and which ones are the pious inventions of a later age. Nothing was in any case more alien to the mentality of the monks of this first period than to make such distinctions between these two orders of facts.
Our description of the Buddha would be incomplete if we failed to mention that alone among mortals of His age He had in addition to His normal physical body, as it appeared to common people, still a kind of "ethereal" body, which only the elect could see with the eye of faith and which Buddhist art tried to reproduce to the best of its abilities. The "ethereal" body is sixteen feet high, and it possesses the thirty-two "marks of the superman". For instance, the Buddhas have wheels engraved on Their feet, webs between Their fingers, a cowl on Their heads, a halo and an aureole round Their heads and bodies, a tuft of white curly hair between Their eyebrows, and so on and so on. In the form in which we have it, this tradition is obviously post-Aśokan. Parts of it may, however, go back much further, to ancient and even pre-Buddhist traditions about manly beauty, and to the age-old art of predicting a person's destiny, nature and future from such signs and prognostics.
A Buddha's body differs from that of other people not only by the possession of the thirty-two marks, but in addition it has the peculiar property that its bony parts are indestructible. At the cremation of the Buddha Śákyamuni they were not reduced to ashes, and they formed the relics which were distributed among the believers, and were preserved from generation to generation, like the Buddha's tooth now in Kandy.
_Dharma_ , the second of these Treasures, comprises all the mysteries of the Buddhist faith, and cannot easily be explained in a few words. Buddhists in Asia normally did not describe themselves as "Buddhists", but as "followers of the Dharma". This "Dharma" is the name for an impersonal spiritual force behind and in everything. Being spiritual and not of this world, it is rather elusive and not easy to define or get hold of. Judged by logical standards the word is extremely ambiguous. But since the Dharma is the subject-matter of all Buddhist teachings, it is necessary to list its main meanings, and to show their interconnection:
1. First of all it is a word for the _one ultimate reality._ One spiritual reality underlies all that we perceive in and around us. It is real as contrasted with the illusory things of the commonsense world, to it we should turn as we should turn away from them, for it alone brings true satisfaction. And it is not external to worldly things and events, but in some ways immanent to them, and the directing Law within them.
2. Secondly, by an easy transition, it means that ultimate reality as interpreted or stated in the Buddha's teaching, and in this subjective form it means " _Doctrine_ ", "Scripture", or "Truth".
3. Thirdly, Dharma, in both the first and second sense, may be reflected in our lives, may manifest itself in our actions, insofar as we act in accordance with it. The word thus assumes the meaning of " _righteousness_ " and "virtue".
4. It is in its fourth sense that the word becomes rather subtle and assumes a meaning which constitutes the specific contribution of Buddhist thought, containing at the same time within it all the tensions that have caused it to develop. Buddhist writings everywhere are replete with references to " _dharmas_ " in the plural and they become unintelligible unless the specific meaning of this term is appreciated. The word is here used in a scientific sense, which results from considering things and events in their relation to the Dharma in sense 1, i.e. from studying them as they are in their own ultimate reality. Nearly all scientific and philosophical systems agree in rejecting the appearance of the commonsense world as a false artificial construction, replacing it by an explanation of events based on intelligible entities of various kinds. The most obvious example is the atomic system. Behind the sensory appearance of the material world this system postulates another world, composed of atoms, fairly invisible and adequately grasped only by mathematical formulas. These atoms are that which is physically really there, a thorough understanding of their behaviour allows us to control the physical universe, and we can deduce from them the physical properties of things which our senses perceive. Likewise, the Buddhists assume that our commonsense view of the world is hopelessly distorted by ignorance and craving, and that neither the units into which we divide it, i.e. the "things" we believe to perceive, nor the connections we postulate between them, have much validity. What are "atoms" to the modern physicists, are the "dharmas" to the Buddhists. A systematic classification of all dharmas had to wait for the second period, just as in this matter of atoms a long time passed between their initial conception by Demokritos and their more precise study by Mendeleyev and Bohr. What we have in this period are various numerical lists of dharmas – such as the five "skandhas", i.e. form, feelings, perceptions, volitional impulses and consciousness, which were said to constitute the whole range of a human personality. Or the six external and internal sense-fields, i.e. eye, ear, nose, tongue, touch-organ and mind, as well as sight objects, sound-, smell-, taste-, touch- and mind-objects, which constitute the whole range of our possible experience. A "dharma" is an impersonal event, which belongs to no person or individual, but just goes along on its own objective way. It was regarded as a most praiseworthy achievement on the part of a Buddhist monk if he succeeded in accounting to himself for the contents of his mind with the help of these impersonal dharmas, of which tradition provided him with definite lists, without ever bringing in the nebulous and pernicious word "I". No other religion has included anything like this in the mental training of its adherents and the originality of Buddhism is to be found largely in what it has to say about these elusive dharmas.
With regard to the _Samgha_ , or "community", a visible and invisible Church are distinguished. The _visible_ community consists first of all of the monks and nuns, and then in a wider sense it also comprises the laymen and laywomen who support the monks, have taken their refuge with the three Jewels, and promise to observe the five precepts. Within this community a small elite constituted the _true Samgha._ The wearing of the yellow robe merely shows that a man had exceptionally fine opportunities for spiritual attainment, but it does not render his spiritual success absolutely certain. As for the laymen, their status in the community was a most uncertain one, and for many of the monks they seemed to carry almost no weight at all. The true Samgha, the invisible Church, consisted of the _Áryans_ , the "noble" or "holy" ones, men who were contrasted with the common worldlings, also known as the "foolish common people" (bála-prthag-janá).
The difference between these two classes of persons is fundamental to Buddhist theory. They are held to occupy two distinct planes of existence, respectively known as the "worldly" and the "supramundane".The saints alone are truly alive, while the worldlings just vegetate along in a sort of dull and aimless bewilderment. Not content with being born in the normal way, the saints have undergone a spiritual rebirth, which is technically known as "winning the Path". In other words, they have detached themselves from conditioned things to such an extent that they can now effectively turn to the Path which leads to Nirvana. The worldling's vision of Nirvana is obstructed by the things of the world which he takes far too seriously. Through prolonged meditation he can, however, reach a state where each time a worldly object rises up in front of him, he rejects it wholeheartedly as a mere hindrance, or nuisance. Once this aversion has become an ingrained habit, he can at last take Nirvana, the Unconditioned, for his object. Then "he ceases to belong to the common people", he "becomes one of the family of the Áryans". Thereafter he is less and less impelled by the motives of ordinary people, i.e. by motives which are a compound of self-interest and a misguided belief in the reality of sensory things and which contain a strong dosage of greed, hate and delusion. The contrast with the vision of Nirvana reveals the insignificance and triviality of all these worldly concerns and Nirvana itself increasingly becomes the motivating force behind whatever is done.
Four kinds of saints are normally distinguished. The lowest is called a "Streamwinner", to indicate that he has won contact with the Path which leads to the Unconditioned. The saints are characteristically distinguished by the number of times they have to return to this world after death – the first kind must come back seven times at the most, the second only once, and the fourth, the Arhat, the finest and final product of this training, need never come back at all. The true Samgha is the community of all these saints, but the Arhats are those most highly prized.
### THE SECTS AND THEIR DISPUTES
The Buddhist community did not remain united for long and soon fell apart into a number of sects. Indian Buddhist tradition generally speaks of "eighteen" such sects, but that is a mere traditional number and in fact more than thirty are known to us, at least by name. The Buddha appointed no successor and Buddhism has never known a central authority like that of the Pope or the Khalif. As different communities fixed themselves in different parts of India, local traditions developed, though in spite of all geographical and doctrinal divisions the different sects generally speaking remained in constant communion with each other. Not only did individual monks constantly travel from one centre to another, but the institution of regular pilgrimages of masses of monks and laymen to the holy places of Magadha, which were hallowed by the life of the Buddha and by the relics of His body, caused a constant intermingling of the most diverse elements. The problems which the sects discussed remained thus roughly the same for all and so were the assumptions on which the solutions were based. Through constant contact all Buddhists thus remained mutually intelligible.
The different sects tended to have their own organization and Scriptures. In many monasteries members of different sects nevertheless lived together in perfect amity; it was generally recognized that the goal may be reached by different roads and the sects showed great tolerance to each other, although occasional sharp religious invective was of course not entirely unknown. They all shared one common Dharma, although it is important to realize that the verbal formulation of this Dharma did not exist in a brief, handy and unambiguous form. It was transmitted orally, to prevent it from reaching those unfit to receive it, but there was so much of it that no one person could keep it all in mind. In consequence different parts of the Scriptures were handed to specialists who knew by heart, say, the Vinaya or the Sútras, or a part of the Sútras, or the Abhidharma, and so on. The reciters of each part of the Scriptures formed separate corporations with privileges of their own and their very existence would add to the divisions within the Order.
Nor must we forget that this Order, however much it might resent the fact, was not a self-contained entity, but had to coexist with laymen on whom it was economically dependent. There was thus a constant tension between those who regarded the Dharma as a means for the production of a small elite of Arhats living in monastic seclusion in strict observance of the Vinaya rules, and those who wished to increase the chances of salvation for the ordinary people, while combating the authority of the Arhats and working for a relaxation of the monastic precepts.
Finally we must mention philosophy as one of the most potent causes of sectarian divisions. It is not difficult to see why philosophy should have played a decisive role in the development of Buddhism. Salvation on its higher levels was made dependent on the meditational awareness of the actual facts governing our mental processes. In the course of carrying out these meditations, the monks came up against problems which everywhere form the field of philosophy, such as the nature and classification of knowledge, the problems of causality, of time and space, of the criteria of reality, of the existence or non-existence of a "self" and so on. Now it is a fact of observation that philosophy differs from all other branches of knowledge in that it allows of more than one solution to each problem. It is in the nature of things that the differences of opinion should have multiplied the more the Buddhists went into the philosophical implications of their doctrine.
It would be clearly impossible here to enumerate the literally hundreds of points of dispute among the Buddhists, or even to give an account of all the sects. It will be sufficient to say a few words about the four or five chief sects, and leave the sub-sects to look after themselves. The diagram on p. 19 shows the affiliations between the main branches of the Order.
The first schism, between _Mahásanghikas_ and _Sthaviras_ , was occasioned by the question of the status of the Arhats. A teacher by the name of Mahádeva arose, who claimed that in five points the Arhats fell short of the god-like stature which some sections of the community attributed to them. They could, among other things, have seminal emissions in their sleep, and that fact, so he argued, indicated that they are still subject to the influence of demonic deities who appear to them in their dreams. They are also still subject to doubts, ignorant of many things, and owe their salvation to the guidance of others. His thesis led to a dispute in which the majority took the side of Mahádeva, whose school in consequence called themselves the Mahásanghikas. His adversaries took the name of Sthaviras, "the Elders", claiming greater seniority and orthodoxy. The Mahásanghikas continued to exist in India until the end and important doctrinal developments took place within their midst. All these were ultimately determined by their decision to take the side of the people against the saints, thus becoming the channel through which popular aspirations entered into Buddhism.
Their most important theories concern Buddhology and philosophical theory. As for the _Buddha_ , they regarded everything personal, earthly, temporal and historical as outside the real Buddha, Who was transcendental, altogether supramundane, had no imperfections and impurities whatsoever, was omniscient, all-powerful, infinite and eternal, forever withdrawn into trance, never distracted or asleep. In this way the Buddha became an ideal object of religious faith. As for the historical Buddha, He was a magical creation of the transcendental Buddha, a fictitious creature sent by Him to appear in the world and to teach its inhabitants. While on the one side intent on glorifying the otherworldliness of the Buddha, the Mahásanghikas at the same time tried to increase the range of His usefulness to ordinary people. The Buddha has not disappeared into Nirvana, but with a compassion as unlimited as the length of His life, He will until the end of time conjure up all kinds of messengers who will help all kinds of beings in diverse ways. His influence is not confined to those few who can understand His abstruse doctrines. As a Bodhisattva, i.e. during the very long period which precedes His Buddhahood, He is even reborn in the "states of woe", becomes of His own free will an animal, a ghost or a dweller in hell and in many ways furthers the weal of those beings who live in conditions in which wisdom teaching must fall on deaf ears. Nor are Buddhas found on this earth alone, but they fill the entire universe, and exist here and there everywhere, in all the world systems.
Two of the _philosophical theories of the Mahásanghikas_ are of outstanding importance:
1. They taught that thought, in its own nature, its own being, in its substance, is perfectly pure and translucent. The impurities are accidental to it, never enter into or affect its original purity, and remain "adventitious" to it.
2. The Mahásanghikas were in the course of time led to an increasing scepticism about the value of verbalized and conceptualized knowledge. Some of them taught that all worldly things are unreal, as a result of the perverted views. Only that which transcends worldly things and can be called "emptiness", being the absence of all of them, is real. Others said that everything, both worldly and supramundane, both absolute and relative, both Samsára and Nirvana, is fictitious and unreal and that all we have got is a number of verbal expressions to which nothing real corresponds. In this way the Mahásanghikas early implanted the seeds which came to fruition in Maháyána Buddhism in the second period.
The second split, between the _Pudijalavádins_ and the _Sthaviras_ , concerned the question of pudgala, or "person". At the beginning of their history the "Personalists" were called _Vatsíputríyas_ , after their founder, whereas later on they were better known as the _Sammitíyas._ Although barely orthodox they were at times strong in numbers, as we can see from the fact that Yüan Tsang in the seventh century counted 66,000 Personalist monks, out of a total of 250,000 in the whole of India. It was a fundamental dogma of Buddhist philosophy that personality is a token of falsehood and that no idea of "self", in whichever form it might appear, ought to have a place in the conception of reality as it actually is. The Personalists challenged this position and claimed that in addition to the impersonal dharmas there is still a Person to be reckoned with. They could adduce much scriptural authority in favour of their views. They were, for instance, fond of quoting the remark: "One person, when He is born in the world, is born for the weal of the many. Who is that one person? He is the Tathágata." Their opponents had to admit these and many other passages, but they maintained that they do not mean what they say, since in them the Buddha only conformed to the linguistic usage of an ignorant world.
The Personalists on the other hand taught that the Person is a reality in the ultimate sense, which provides a common factor or link for the successive processes occurring in a self-identical individual, over many lives, up to Buddhahood. At the same time the Pudgalavádins took great care to define the relation of the Person to the skandhas in such a way as not to contradict the essential principles of the Buddha's teaching and so as to exclude the "erroneous belief in a self". "The Person is neither identical with the skandhas, nor is he in the skandhas, nor outside them", so they taught. He provides, as we would put it, a kind of "structural unity" for the psycho-physical elements. As such he is "ineffable", indefinable in every respect whatsoever. A man's true, transcendental Self is indeed so subtle that only the Buddhas can see it. The Pudgalavádins represented the reaction of commonsense against the improbabilities of the dharmas-theory in its more uncompromising forms. They provided over the centuries a constant irritant to disputants of other sects and in some ways they were the forerunners of Maháyána philosophy. There exists a close analogy between the _pudgala_ and the Suchness, or Emptiness, of the Mádhyamikas, and the "Store-consciousness" of the Yogácárins had many of the functions which the Personalists assigned to the _pudgala_.
Thirdly, the split between _Sarvástivádins_ and _Vibhajyavádins_ was occasioned by the pan-realistic ontological doctrine of Kátyáyaníputra, who taught that not only the present, but also past and future events are real. It appears that Aśoka sided with the Vibhajyavádins and that in consequence the Sarvástivádins went North and converted Kashmir, which remained their centre for more than a thousand years. When we consider the basic practice of Buddhist meditation, it is not surprising that the problem of the existence of past and future events should have seemed so important. Among the unsatisfactory features of this world the pride of place belonged to impermanence and it was the task of the Yogin to impress its full extent on his mind so as to further his distaste for worldly things. In this connection he had to take an event, or dharma, and see its "rise and fall", i.e. how it "comes, becomes, goes". Now, once a monk had got used to contrasting the past with the present and future, he might well become curious to know whether only the present really exists, or also the past and future. If only the present exists, this raises the further point of its duration, which many regarded as lasting just one single instant. In that case no thing will endure for any length of time, and one must assume that it is annihilated and re-created from instant to instant. This raises difficulties not only for the commonsense, but according to Kátyáyaníputra, also for the Buddhist doctrine of karma and retribution. For if a past action, which has ceased to exist immediately after taking place should lead to a reward or punishment many years later, then in that case something which does not exist is operative, has an effect, at a time when it does not exist. Likewise, so Kátyáyaníputra thought, the knowledge of past and future objects, as attested by memory and prediction, would be impossible, since no knowledge is possible without an actual object in front of the mind. In consequence he evolved the pan-realistic theory, which became the peculiar thesis of the Sarvástivádins. It avoided the difficulties mentioned above only to introduce many others in their stead and a vast superstructure of auxiliary hypotheses was required to make it tenable. In spite of their addiction to a rather tortuous scholasticism, the Sarvástivádins became the most significant school on the Indian subcontinent.
As the result of the emergence of an interest in philosophical questions we have the first instance of a whole class of canonical literature being created to meet a new situation. The _Abhidharma_ books were clearly composed after the third division of the schools. The contents of the seven Abhidharma books of the Sarvástivádins differ greatly from those of the seven books of the Theravádins, who are an offshoot of the Vibhajyavádins. Some sects, like the Sautrántikas, went so far as to contest the authenticity of all Abhidharma works. A great mental effort went, from about 200 BC onwards, into the production of these books, which are technical handbooks of meditation, teaching what events can be regarded as elementary, how others are composed of them, how they condition each other, etc.
Before we leave the schools, we may mention a few more points of disagreement on questions of a more general interest. The elusive concept of Nirvana came in for some discussion. If it is unconditioned, does it exist, and can it have effects? Is it the only unconditioned thing, or is space also unconditioned? Is there any difference between the Nirvana of the Buddhas and that of other people, and what is it? There was also much interest in determining the criteria of a _definite achievement_ , which cannot again be lost. There was therefore much debate on when and whether the Arhats and other saints can "fall back" and from when onwards their salvation is assured. On the subject of _death_ , always present in the minds of these ascetics, one wondered whether the hour of death is definitely fixed by karma, or whether a premature and untimely death is possible. There was also disagreement on what follows on death: five schools believed that death is instantly followed by rebirth in another organism, whereas five other schools taught that death would be followed by an "intermediary existence" of up to forty-nine days, during which in most cases the new incarnation slowly prepared itself. In the case of certain saints this interval is used for the attainment of the Nirvana which escaped them during this life.
### THE LAITY
We have now sketched the basic opinions and aims of the homeless monks who constitute the essential core of the Buddhist world. But what about those Buddhists who were not monks, what about the laity without whom the monks could not possibly carry on their meditations? What is their place in the scheme of things? What are they given to do? And what do the monks do for them?
If a layman feels tied to his home and unable to escape from it into the homeless life, it is due to his deficiency in a quality called "merit", which depends on what he has done in the past and which circumscribes his access to spiritual opportunities. A number of exceptional cases are recorded of laymen having won deathlessness without previously entering the Order. Generally speaking, however, their salvation is out of the question at present, and can be assured only on condition that by a future life they have accumulated sufficient "merit" to make the jump into the social freedom of the monastic life. The layman's one and only religious task at present can be to increase his store of merit. The Buddhist religion offers him four avenues for doing so:
1. He must observe the five precepts (see p. 8), or at least some of them. On feast days, every fortnight, he may add to them another three, i.e. he fasts, avoids worldly amusements, and uses neither unguents nor ornaments. A few observed still two more precepts, i.e. they did not sleep on a high, big bed and they accepted no gold or silver.
2. He must have devotion for the Three Treasures (see p. 10) and faith is the virtue apposite to a householder's state of life. But this faith is not an exclusive one and does not entail a rejection of his ancestral beliefs and of the Brahmanic religious usages of his social environment. The Triple Jewel is not a jealous God and is not displeased by the worship of the deities of a man's country or caste.
3. He must be generous, especially to the monks, and give as much as possible to them, not only for their upkeep, but also for religious buildings inhabited by no one. To some extent the merit produced by gifts depends on the spiritual endowments of the recipient, and therefore the sons of Śákyamuni, and in particular the Arhats, are the best possible "field for planting merit".
4. He may worship the relics of the Buddha (see p. 13). The actual attitude of the Buddhists to these teeth and bones is difficult to describe in terms readily understood in the West. It is obviously impossible for them to "pray" to the Buddha, for the reason that He is no longer there, being in Nirvana, i.e. extinct as far as this world is concerned. It is even doubtful whether the word "worship" is a very suitable one. Before the advent of modern industrialism men everywhere looked upon the world as a mysterious realm of boundless possibilities, full of invisible forces, meaningful and replete with significant hints. The posture of namaskára, in which the folded extended palms are held forth, is the customary mode of greeting in India. Bigotry, servility and superstitious idolatry do not enter into it. All these things rest very lightly on the true believer and do not constrain his inner freedom. The fervour of the faithful filled the Buddhist world with innumerable shrines (caitya) and Stúpas, which became the object of the special devotion of householders. The creation and cult of Buddha images is, however, fairly late, and unlikely to go back before the first century AD.
If a layman well observes these four duties, he will be happy in this life, and after his death he will be reborn in heaven, or in paradise. The Emperor Asoka well exemplifies the character of Buddhism as understood by the laity. Among Buddhist doctrines he regarded as the two most important ones the avoiding of doing harm to others (ahimsá) and the active benevolence towards them (maitrí). His edicts contain many moral exhortations to the practice of the simple virtues and we also hear much about the need for piety. But there is nothing in them about the deeper ideas or fundamental tenets of the faith. There is no mention of the four holy Truths, the eightfold path, the chain of causation, or even of Nirvana, or of the supernatural qualities of a Buddha.
What benefits then does the monk bestow upon the laymen? He increases both their spiritual and their material welfare. He promotes the first by sermons on those aspects of the doctrine which are intelligible and relevant to the laity, as well as by the example of a holy life which will give courage and zest to those still tied to the world and can give them a glimpse of the freedom and serenity they may achieve in a future life. In the course of time a vast literature of Birth stories (játaka), which tell of the Buddha's previous lives, animal as well as human, and of edifying tales (avadána) was composed for the benefit of the laity. These stories were listened to with avidity, but they had less authority than the more metaphysical teachings. Their message concerns chiefly the virtues of secular life. They constantly stress the doctrine of karma and rebirth and also foster a tenderness towards all that lives. In Bharhut, Bodhgaya, Sanchi, Nagarjunikonda and Ajanta many of the Jataka tales have been illustrated in sculpture and painting.
It was also a belief of Buddhist Asia that the material well-being of the people, their economic prosperity and their freedom from famine, epidemics and wars, was largely the work of the monks. For the welfare of a nation depends chiefly on the benevolence of occult and spiritual forces, which the monks alone can know about and which they alone can propitiate. All is well with a people which respects the monks, showing its reverence for the Buddhas by generous gifts to the monasteries and for temples and shrines, but a nation which turns its back on the religion is doomed to perish in misery. These were the beliefs which helped to maintain the monastic institutions.
The voluntary and sporadic support of a population tied to them by links as tenuous as these would, however, not have kept the Order going for long. The secret behind its social survival over the centuries lay in the ability of the Buddhists, repeated over and over again, to enlist the support of Asian rulers, who maintained the monastic institutions out of government funds. In default of this, the monks were driven to become large property owners in their own right and to dispense altogether with the capricious rewards of begging from house to house. This is also a solution, but it imperils aloofness from the things of this world and is apt to draw the monks back into the arena of social strife.
Nevertheless relations with the laity were always precarious and there at its base was the Achilles heel of the whole soaring edifice. If Buddhism departed from the tenets of the first period, it was largely the work of the laity. It was their pressure which did much to bring about the reforms of the second and third period, reforms which therefore appeared to the strict monastic party as a degeneration. The Maháyána gave much greater weight to the laymen. It could count on much popular support for its opinion that people are as important as dharmas, for its attacks on the selfishness of monks who think only of their own welfare, for its constant censure of "haughty" and "conceited" monks and for its stories of wealthy householders, such as Vimalakírti, who surpassed the oldest and most venerable monks in the splendour of their spiritual attainments. The same kind of popular pressure would induce the monks to become more manifestly useful to laymen. In the third, Tantric, period they inserted themselves into their magical beliefs and acted as astrologers, exercisers, weather makers, doctors, etc. That is why the story of Buddhism becomes unintelligible unless due weight is given to the desires of the dumb common people. The stone which the builders had rejected became the cornerstone after all.
### EXPANSION
During this period, Buddhism remained on the whole a purely Indian religion. The emperor Asoka, about 250 BC, sent some missions to the successors of Alexander the Great, i.e. to the Greek kingdoms of the diadochs in Egypt, Macedon, Cyrene and Epirus. These missions have left no trace and they may very well have been ineffective. The rather dim awareness of Buddhism which we find in Greek authors can be accounted for by later contacts which took place in connection with the trade which flourished in Roman times between India and the Mediterranean.
It was only in Ceylon that Asoka's missionary activity bore fruit. Once brought there about 240 BC by Mahinda, Asoka's son, Buddhism has existed in Ceylon for a longer stretch of time than anywhere else. From that time onwards Buddhism has been the state religion of Ceylon. Only Buddhists had a legitimate right to be kings and the island of Lanká was held to belong to the Buddha Himself. It was the king's duty to protect the Order of monks and great benefits accrued to the monasteries in the form of donations, prestige and protection from interference. The kings, although mostly laymen, were also the final judges in any dispute which might arise among the Buddhists. The monks in their turn generally helped the kings and won popular support for their wishes. This close connection of the Samgha with the state had its disadvantages. From the second century BC onwards it not only infused a spirit of nationalism into the Buddhism of Ceylon and made the monks prone to political intrigue, but it also led them to enthusiastically support the national wars of their kings. They assured king Dutta Gámaní (101–77 BC) that the killing of many thousands of enemies was of no account, because as unbelievers they were really no more than animals. They accompanied the army of the same king, "since the sight of bhikkhus is both blessing and protection for us", and the king himself had a relic of the Buddha put into his spear.
For a long time Ceylonese Buddhists continued to be in lively contact with India over the ports of Bharukaccha and Súrpáraka in the West. Gradually the whole Canon came to Ceylon and towards the end of our period, or even later, also new works composed in Páli in India by the mother-sect, such as the first part of the "Questions of King Milinda" and the "Niddesa". During the first century BC the Canon and Commentaries, so far transmitted orally, were written down at Aluvihára, "so that the Dharma might endure". War and famine had depopulated the country and the oral transmission of the Pitakas was in danger. The holy language of the Canon was Páli, whereas the Commentaries were in Sinhalese. Ceylon became the home of a school known as the Theravádins – of great interest in the history of Buddhism partly because their Canon is preserved in its entirety and partly because in their geographical isolation they remained relatively unaffected by many of the later developments. It is not, however, very clear what Continental school they were derived from. Probably they were akin to the Indian Vibhajyavádins, and an offshoot of one of their branches.
## **TWO**
## The Second Period: AD 0–500
### THE MAHAYANA IN INDIA
About the beginning of the Christian era a new trend took shape in Buddhism, known as the Maháyána, literally "the great vehicle". It was prepared by the exhaustion of the old impulse which produced fewer and fewer Arhats, by the tensions within the doctrines as they had developed by then and by the demands of the laity for more equal rights with the monks. Foreign influences also had a great deal to do with it. The Maháyána developed in North-West India and South India, the two regions where Buddhism was most exposed to non-Indian influences, to the impact of Greek art in its Hellenistic and Romanized forms and to the influence of ideas from both the Mediterranean and the Iranian world. This cross-fertilization incidentally rendered the Buddhism of the Maháyána fit for export outside India. So that it should be able to travel outside India, Buddhism had first to be somewhat modified by foreign influences, had to undergo a preliminary phase of de-Indianization. Before it could be received by alien cultures it had first to receive an impression from them. Roughly speaking only in its modified Maháyána form has it been able to live outside India. In due course the Maháyána has conquered the entire northern half of the Buddhist world, and the Buddhists of Nepal, Tibet, Mongolia, China, Korea and Japan are nearly all Maháyánists.
The Maháyána developed in two stages: first in an unsystematic form, which went on between 100 BC and AD 500, and then, after AD 150, in a systematized philosophical form, which led to two distinct schools, the Mádhyamikas and the Yogácárins.
We must first of all explain the main features of the _early Maháyána._ About 100 BC a number of Buddhists felt that the existing statements of the doctrine had become stale and useless. In the conviction that the Dharma requires ever new re-formulations so as to meet the needs of new ages, new populations and new social circumstances, they set out to produce a new literature. The creation of this literature is one of the most magnificent outbursts of creative energy known to human history and it was sustained for about four to five centuries. Repetition alone, they believed, cannot sustain a living religion. Unless counterbalanced by constant innovation, it will become fossilized and lose its life-giving qualities.
So far the Maháyánistic attitude seems quite logical. What is more difficult to understand is that they insisted in presenting these new writings, manifestly composed centuries after the Buddha's death, as the very words of the Buddha Himself. In order to make room for the new dispensation, they followed the Mahásanghikas in minimizing the importance of the historical Buddha Śákyamuni, whom they replaced by the Buddha who is the embodiment of Dharma ( _dharmakáya_ ). In the "Lotus of the Good Law" we are told that the Buddha, far from having reached His enlightenment at Bodhgáya, about 500 BC or whenever the date may have been, abides for aeons and aeons, from eternity to eternity, and that He preaches the Law at all times in countless places and innumerable disguises. In the "Diamond Sútra" occurs the famous verse:
Those who by my form did see me,
And those who followed me by voice,
Wrong the efforts they engaged in,
Me those people will not see!
From the Dharma-body should one see the Buddhas,
From the Dharma-bodies comes their guidance.
The conception of the Buddha as the timeless embodiment of all Truth allowed for a successive revelation of that truth by Him at different times. Not content with this, the Maháyánists tried to link their own new writings with the historical Buddha by a number of mythological fictions. They asserted that they had been preached by the Buddha in the course of His life on earth, that parallel to the Council at Rájagrha, which codified the Sútras of the Hínayána, the Maháyána Sútras had been codified by an assembly of Bodhisattvas on the mythical mountain of Vimalasvabháva; that the texts had been miraculously preserved for five centuries and stored away in the subterranean palaces of the Nágas, or with the king of the Gandharvas, or the king of the Gods. Then, as Nágárjuna puts it, "five hundred years after the Buddha's Nirvana, when the Good Law, after having gradually declined, was in great danger", these treasures from the past were unearthed, revealed and made known, so as to revivify the doctrine.
What then were the main doctrinal innovations of the Maháyána? They can be summarized under five headings:
1. As concerns the goal there is a shift from the Arhat-ideal to the Bodhisattva-ideal;
2. A new way of salvation is worked out, in which compassion ranks equal with wisdom, and which is marked by the gradual advance through six "perfections" ( _páramitá_ );
3. Faith is given a new range by being provided with a new pantheon of deities, or rather of persons more than divine;
4. "Skill in means" ( _upáyakaus_ O _alya_ ), an entirely new virtue, becomes essential to the saint, and is placed even above wisdom, the highest virtue so far;
5. A coherent ontological doctrine is worked out, dealing with such items as "Emptiness", "Suchness", etc.
We will now consider these five points one by one.
1. The goal of Arhatship, which had motivated Buddhism in the first period, is now relegated to the second place. The Maháyánistic saint strives to be a "Bodhisattva" – from _bodhi_ , "enlightenment", and _sattva_ , "being" or "essence". A Bodhisattva is distinguished by three features: ( _a_ ) In his essential being he is actuated by the desire to win the full enlightenment of a Buddha, which, from this point of view, implies complete omniscience, i.e. the knowledge of all things at all times in all their details and aspects, ( _b_ ) He is dominated by two forces, in equal proportion, i.e. by compassion and wisdom. From compassion he selflessly postpones his entrance into the bliss of Nirvana so as to help suffering creatures. From wisdom he attempts to win insight into the emptiness of all that is. He persists in his compassionate solidarity with all that lives although his wisdom shows him that living beings and all their woes are purely illusory, ( _c_ ) Although intent on ultimate purity, a Bodhisattva remains in touch with ordinary people in having the same passions they have. His passions, however, do not either affect or pollute his mind.
2. A Bodhisattva's compassion is called "great", because it is boundless and makes no distinctions. A Bodhisattva resolves to become the saviour of all, whatever may be their worth or their claim to his attention. In the first period the wisdom of the saints had been fully emphasized, but now their selfless desire to make others happy is said to rank equal in value with it. Enlightenment is the thorough and complete understanding of the nature and meaning of life, the forces which shape it, the method to end it, and the reality which lies beyond it. This enlightenment, the Maháyánists agreed, does not automatically entail the desire to assist others. Among the enlightened they distinguished three types, two of them "selfish", one "unselfish". The "selfish" types are the Arhats and Pratyekabuddhas, who are said to represent the idea of the Hínayána, of the "inferior vehicle". They are described as aloof from the concerns of the world and intent on their own private salvation alone. The "unselfish" ones are the Buddhas, and the pursuit of the unselfish quest for enlightenment on the part of a Bodhisattva is called the "Buddha-vehicle", or the "Great Vehicle" (maháyána).
A Bodhisattva must be a patient man. He wants to become a Buddha, but his distance from the transcendental perfection of a supreme Buddha, Who both knows and is everything, will obviously be nearly infinite. In one life it could not possibly be traversed. Countless lives would be needed and a Bodhisattva must be prepared to wait for aeons and aeons before he can reach his goal. Yet, he is separated from Buddhahood only by one single small obstacle, i.e. his belief in a personal self, his assumption that he is a separate Individual, his inveterate tendency towards "I-making and Mine-making" ( _ahamkárama-makára_ ). To get rid of himself is the Bodhisattva's supreme task. By two kinds of measures he tries to remove himself from himself – actively by self-sacrifice and selfless service, cognitively by insight into the objective non-existence of a self. The first is due to his compassion, the second to wisdom, defined as the ability to penetrate to the true reality, to the "own-being" of things, to what they are in and by themselves. It is believed that action and cognition must always go hand in hand to bring forth their spiritual fruits.
The unity of compassion and wisdom is acted out by the six "perfections", or _páramitá_ , the six "methods by which we go to the Beyond". A person turns into a Bodhisattva when he first resolves to win full enlightenment for the benefit of all beings. Thereafter, until his attainment of Buddhahood, aeons and aeons are devoted to the practice of the Páramitás. So important is this concept that the Maháyána often refers to itself as the "Vehicle of the Páramitás". The six are: the perfections of giving, morality, patience, vigour, meditation and wisdom. The first enjoins generosity, a willingness to give away all that one has, even one's own body, and the second the scrupulous observance of the moral precepts, even at the risk of one's own life. As for "patience", the Maháyána has much more to say about it than the Hínayána and it uses the word in a wider sense than is usual. As a moral virtue it means the patient endurance of all kinds of suffering and hostility and the absence of any feeling of anger or discontent when meeting with them. In addition, "patience" is here also considered as an intellectual virtue and as such it means the emotional acceptance, before one has fathomed the whole of their depth, of the more incredible and anxiety-producing ontological doctrines of the Maháyána, such as the non-existence of all things. Vigour means that the Bodhisattva indefatigably persists in his work over the ages and never feels discouraged; his perfection of meditation enables him to gain proficiency in trances "numerous as the sands of the Ganges". The perfection of wisdom finally is the ability to understand the essential properties of all processes and phenomena, their mutual relations, the conditions which bring about their rise and fall, and the ultimate unreality of their separate existence. At its highest point it leads right into the Emptiness which is the one and only reality.
3. Another distinctive contribution of the Maháyána is the distinction of ten stages which the Bodhisattva must traverse on his way to Buddhahood. This aspect of the doctrine reached its final formulation in the third century in the "Sútra on the Ten Stages". The first six of these stages correspond to the six "perfections" and each of them is marked by the intensive practice of one of them. The sixth stage therefore corresponds to the perfection of wisdom and with it the Bodhisattva has by his understanding of emptiness come "face to face" ( _abhimukhí_ ) with Reality itself. At that point he would be able to escape from the terrors of this world of birth-and-death and he could, if he wanted to, enter into Nirvana. Out of compassion he nevertheless makes no use of this possibility, but stays on in the world for a long time so as to help those in it. Although in the world, he now is no longer of it. During the last four stages a Bodhisattva gains what the texts call "sovereignty over the world", and he becomes a kind of supernatural being endowed with miraculous powers of many kinds. From the ordinary Bodhisattvas as they exist on the first six stages, the "celestial Bodhisattvas" of the last four stages differ in that they were well suited to becoming objects of a religious cult. Soon the faithful increasingly turned to all kinds of mythical Bodhisattvas, such as Avalokiteśvara, Mañjuśrí, Maitreya, Kshítigarbha, Samantabhadra and others. Though conceived in India some of these Bodhisattvas show strong non-Indian, and particularly Iranian, influences.
The development of mythical Bodhisattvas was accompanied, and even preceded, by that of mythical Buddhas, who were held to reside in the heavens in all the ten directions. In the East lives Akshobhya, the "Imperturbable". In the West is the kingdom of the Buddha of "Infinite Light", Amitábha, not always clearly distinguished from Amitáyus, the Buddha who "has an infinite life-span". Amitáyus is a counterpart to the Iranian Zurvan Akaranak ("Unlimited Time"), just as the cult of Amitábha owed much to Iranian sun worship and probably originated in the Kushana Empire in the borderland between India and Iran. There are many other celestial Buddhas, in fact infinitely many, and most of them have a "kingdom" of their own, a world which is not of this world, a land which is "pure" because free from defilements and adverse conditions.
4. Next we must say a few words about the "skill in means", a virtue which is indispensable to a Bodhisattva at all times, but which he possesses in its fullness only late, on the seventh stage, after the "perfection of wisdom" has thoroughly shown him the emptiness of everything that seems to be. "Skill in means" is the ability to bring out the spiritual potentialities of different people, by statements or actions which are adjusted to their needs and adapted to their capacity for comprehension. If the truth be told, all that we have described so far as constituting the doctrine of the Maháyána is just "skill in means" and nothing more. It is a series of fictions elaborated to further the salvation of beings. In actual fact there are no Buddhas, no Bodhisattvas, no perfections, and no stages. All these are products of our imagination, just expedients, concessions to the needs of ignorant people, designed to ferry them across to the Beyond. Everything apart from the One, also called "Emptiness" or "Suchness", is devoid of real existence, and whatever may be said about it is ultimately untrue, false and nugatory. But nevertheless it is not only permissible, but even useful to say it, because the salvation of beings demands it.
5. So far we have spoken about the way to the Beyond. Now we come to the Beyond itself. Wisdom teachings about ontology, or the nature of reality, constitute the inner core of the Maháyána doctrine. These teachings are extremely subtle, abstruse and elusive and defy any attempt at summarizing them, because they are not meant as definite statements about definite facts and because it is said expressly that they do not explain anything, do not say anything in particular, for the ultimate transcendental reality is held to lie beyond the grasp of intellectual comprehension and verbal expression. Be that as it may, the peculiar ontological doctrines of the Maháyána developed logically from the philosophy of the Mahásanghikas and in direct and conscious opposition to that of the Sarvástivádins. Four basic propositions are common to all Maháyánists:
1. All dharmas are "empty" in the sense that each one is nothing in and by itself. Any dharma is therefore indistinguishable from any other dharma. In consequence all dharmas are ultimately non-existent and the same.
2. This Emptiness can be called "Suchness", when one takes each thing "such as it is", without adding anything to it or subtracting anything from it. There can be only one Suchness and the multiple world is a construction of our imagination.
3. If all is one and the same, then also the Absolute will be identical with the Relative, the Unconditioned with the conditioned, Nirvana with Samsára.
4. True Knowledge must rise above the duality of either subject and object, or of affirmation and negation.
These four propositions get near to the Beyond, but they do not quite reach it. The inmost sanctum of the whole doctrine is filled with nothing but silence.
We now come to the _systematized Maháyána_ , which falls into two main philosophical schools, the Mádhyamikas and the Yogácárins. The _Mádhyamika_ school was founded by Nágárjuna ( _c_ AD 150), a South Indian and one of the greatest minds India has produced. The school persisted for many centuries and has had a vigorous life also in China and Tibet. The Mádhyamika philosophy is primarily a logical doctrine which aims at an all-embracing scepticism by showing that all statements are equally untenable. This applies also to statements about the Absolute. They are all bound to be false and the Buddha's "thundering silence" alone can do justice to it. Soteriologically, everything must be dropped and given up, until absolute Emptiness alone remains, and then salvation is gained.
At the time of Nágárjuna the shadowy beginnings of _Yogácárin_ thinking could already be discerned, but the philosophy itself was clearly formulated only in the fourth century. Vasubandhu and Asanga are the greatest names here and modern historical research has so far not succeeded in sorting out the many conflicting data we have on their chronology, writings and activities. The Yogácárins propounded a primarily psychological theory and believed that the Absolute can usefully be described as "Mind", 'Thought" or "Consciousness".
Theirs was a metaphysical idealism, according to which consciousness creates its objects out of its own inner potentialities. Mind can, however, exist quite by itself, without any object whatever. Soteriologically, the Yogácárins aimed at achieving "an act of cognition which no longer apprehends an object". Salvation is won when we can produce in ourselves an act of thought which is "Thought-only", pure consciousness, and altogether beyond the division between subject and object.
The two systems were clearly quite distinct in their interests and intentions. The polemics which they occasionally directed against each other had therefore little effect and occupy little space in their writings. On the whole each school was content to elaborate its own tenets, without paying too much attention to its rivals. To the Mádhyamikas, the Yogácárin doctrine appeared as a quite incomprehensible perversity, whereas the Yogácárins regarded the Mádhyamika doctrine as a preliminary stage of their own, which however missed the true and esoteric core of the Buddha's teaching.
The Yogácárin school is further noteworthy for having elaborated the final formulation of the doctrine of the _three Bodies of the Buddha._ The Buddha is said to exist on three distinct levels. As the Dharma-body He is the Absolute, Truth and Reality itself. In His "communal body", or His "enjoyment body" ( _sámbhoga-káya_ ), the Buddha shows Himself to the celestial Bodhisattvas and other superhuman beings and preaches in unearthly realms the Dharma to them, generating joy, delight and love for it. Finally there is the fictitious, or conjured up body ( _nirmána-káya_ ), which is the one that human beings see appearing at certain times on earth and which is a phantom body sent by the real Buddha to do His work in the world. By way of scholastic refinement, many Yogácárins still added a fourth Body, the Substantial Body ( _svábhávika-káya_ ), which is the basis of the other three.
Yet a note of caution must here be sounded. It is generally said that this doctrine of the Three Bodies was first formulated by the Yogácárins about AD 300, but basically there is nothing really new about it. All three bodies had been known centuries before. The identification of one side of the Buddha with the Dharma had often been made in the first period and is of the essence of Buddhism. As to the second body, there had been a long-standing tradition about the "thirty-two marks of the superman" (see p. 12), which were obviously not attributes of the body visible to all, but adhered to some glorified body which is visible only to the eyes of faith and manifests itself only to the community of the saints. Although the assumption of such a "glorified" body had been made for a long time, all references to it until about AD 300 are vague and elusive. It may be that the doctrine on this subject was not fully developed before the third century. It may also be, however, that this was regarded as a particularly sacred, and therefore secret, subject, which could be explained only orally to those who were spiritually qualified to hear of it, while the remainder had to content themselves with a few vague hints. It is likely that the continuous decline of which we spoke before (p. x) was accompanied by an increasing profanization of the doctrine. In early times, as we saw (p. 4), a monk was even forbidden to recite the actual text of the Sútras to laymen. We hear of Anáthapindada, one of the greatest early benefactors of the Order, that only on his deathbed, after having for many years honoured the Lord and helped the Samgha, he was allowed to hear from Sáriputra a sermon on the unsatisfactory nature of sense-objects, because, as Sáriputra told him, such subjects were reserved for the yellow-robed monks and were not normally taught to the men in white robes, to the laymen. Later on, first the Sútras ceased to be secret and further on also the more secret teachings hidden behind them were divulged one by one. As a matter of fact the Yogácárins always claimed that all they did was to explain the "esoteric" meaning, known all along, but never broadcast to all and sundry.
If this is so, then what in the history of Buddhist thought seems to be doctrinal innovation may very often be nothing but the gradual shifting of the line between esoteric and exoteric teachings. At first, even up to Aśoka, the bulk of the doctrine, except for some moral maxims and so on, was esoteric. By the time of the Tantra, in the third period, even the most esoteric doctrines were written down. This process can be understood as one of compensation for the increasing admitted failure to achieve the spiritual goals aimed at. The monks who were unable to succeed inwardly in their self-realization would then indulge in the extroverted activity of spreading their doctrines among the general population. From the fact that a statement is attested only at a later date we cannot therefore conclude with any cogency that it was actually invented at that time. It is just as possible that it ceased at that time to be the prerogative of the initiated and became more or less public property.
### HINAYANA DEVELOPMENTS IN INDIA
In spite of the growth of the Maháyána, the old Hínayána schools held their own. The new developments naturally had some influence on them. They adopted some Maháyána theories, either by direct borrowing or because they were exposed to the same influences which shaped the Maháyána. The idea of a Bodhisattva now becomes prominent in the vast popular Játaka literature which tells stories about the Buddha's former lives. Originally these tales were fables, fairy-tales, anecdotes, etc., taken from the vast fund of Indian folklore. These current tales were then adapted to Buddhist uses by being represented as incidents in the lives of the historical Buddha. For a long time they were just told to illustrate the glory and spiritual stature of the Lord ( _Bhaijavan_ ). Only at a later age were they recast into the form of stories about the Bodhisattva. In connection with the Játakas a set of ten "perfections" was elaborated, parallel to the six perfections of the Maháyána. Also the compassion and the loving-kindness, which in older literature is a minor and very subordinate virtue, becomes more prominent in these tales of the Bodhisattva's deeds, the "Bodhisattva" always being the Buddha in His previous lives. Likewise the doctrine of "emptiness" is now stressed more than it was in the past. A recognition of the fact that the times are bad and the days for the Arhats have passed, gives greater respectability to the aspiration after the secondary goals, such as the rebirth among the gods, or with Maitreya, the future Buddha, now in the Tushita heaven. But on the whole these concessions are made rather grudgingly. Our Hínayána sources practically never mention the Maháyánists, either positively or negatively. They were somewhat incredulous of all these innovations and they refused to take seriously the claim that the many new Maháyána works gave the Buddha's actual words. In fact they rejected these works as just so many "concoctions" and unworthy of serious consideration. The eloquent testimony of the complete and total silence of all Hínayána doctors on the subject of the Maháyána shows clearly what they thought of all this splendour.
Undeterred by the Maháyána, the Hínayánists went on with their own doctrinal development, which consisted in working out the logical implications of their Abhidharma. The elaboration and systematization of the Abhidharma occupied the first four centuries of our era. After that time it was completed for the two principal schools of which we have any precise knowledge, i.e. by Vasubandhu for the Sarvástivádins and by Buddhaghosa for the Theravádins. About AD 400 the Hínayánists reached the perfection of which they were capable. After that there was no more to come and the Indian Hínayána, although it persisted for another 800 years, has left us few records of further creative intellectual activity. Vasubandhu himself felt that he had reached the end of an epoch and he concludes his "Abhidharmakośa" with the famous words,
The times are come
When flooded by the rising tide of ignorance
Buddha's religion seems to breathe its last.
The creation of the Abhidharma was one of the greatest achievements of the human intellect. On pp. 13–15 I have explained to some extent the sense in which the word "dharmas" was used. In our second period one attempted to determine systematically how many kinds of "dharmas", or ultimate constituents of experience, had to be assumed. The Sarvástivádins arrived at a list of 75 dharmas, whereas the Theravádins believed that 174 were necessary. The difference between the two lists is much less serious than it appears to be. The Theravádin list is so much longer chiefly because they sub-divided one item of the Sarvástivádins (i.e. no. 14, Thought) into the 89 kinds of consciousness. Otherwise the lists mainly differ in their arrangement, order of enumeration and terminology, as well as in a number of trifling details too wearisome to enumerate here. The basic factors were already worked out while the two schools were still united and only the final touches were added at a later period.
The astounding range of Abhidharma studies can be appreciated when we look at the topics which Vasubandhu discusses in his _Abhidharmakos_ O _a._ It falls into eight chapters, dealing with the elements, the powers and faculties, cosmology, i.e. the origin, arrangement and destruction of the universe, with karma, the passions, the various kinds of saints and the paths which lead to salvation, concluding with a survey of sacred cognition and meditational attainments. In addition an appendix is devoted to the refutation of the views of Buddhists and non-Buddhists who postulate the existence of an ego, the abolition and eradication of all such views being Vasubandhu's main object in the composition of his treatise.
The final synthesis was preceded by many lengthy and extensive discussions of which we have for the Sarvástivádins some documents left. In the first century of our era they fixed their Canon, about AD 100 there is the _Vibháshá_ , a commentary to the Abhidharma, and about AD 200 the enormous _Mahávibhásha_ , a commentary to the _Jñánaprasthána_ composed by 500 Arhats of Kashmir, which gives the name of _Vaibháshika_ to the most orthodox school of the Sarvástivádins. The word vibháshá can be translated as "option" and the works just mentioned derived their name from the fact that different opinions of the leading teachers of the school are carefully recorded, so that the reader may be able to choose those which seem most likely to him. The chief adversaries of the Vaibháshikas were the Sautrántikas who did not believe that the seven basic Abhidharma texts had been preached by the Buddha, and regarded the statements on Abhidharma which are scattered in the Sútras as the only reliable scriptural basis for that subject. The doctrines of the Sautrántikas are often simpler and more obviously reasonable than those of the Sarvástivádins. The controversies between the two schools dealt with such subjects as the possibility of self-consciousness, or that of the direct perception of objects. Or one debated in what sense external objects really exist, or what it is that does the "seeing" (the eyes, or the consciousness, or mind), or whether destruction has a cause or comes about automatically of itself in the very nature of things. Vasubandhu made many concessions to the Sautrántika point of view, and his _Kos_ O _a_ was in consequence assailed by the orthodox Vaibháshikas. He found an able and powerful opponent in Samghabhadra, who commented on the _Kos_ O _a_ from the traditional point of view. Nevertheless the _Kos_ O _a_ was increasingly recognized as the last word on the subject and numerous commentaries testify to its enduring popularity in subsequent centuries.
The creative activities of the Hínayána were, however, not entirely confined to the Abhidharma. Constant additions were made to the Birth Stories and Edifying Tales. The life and personality of the Buddha claimed the attention of the devotees. _As_ O _vaghosa_ ( _c_. 100), a very fine poet, used the devices of Indian Sanskrit poetics to popularize the life of the Buddha by his _Buddhacarita_ , into which he introduced much Hindu learning. His work is marked by great devotional feeling, but there is no reason to assume that Aśvaghosa was a Maháyánist in any precise sense of the term and his views show more affinity to those of the Mahásanghikas than to any other known school. Aśvaghosa also wrote dramas, which have since his time been favourite means of popularizing Buddhist sentiments. In Burma and Tibet some of the longer Játakas, like the famous story of Vessantara, who gave away all he had, are still popular subjects of dramatic performances. In the fifth century a biography of the Buddha from the period aeons ago when he first decided to attain Buddhahood, down to the beginning of His teaching, was compiled in Ceylon, in the form of an introduction to the Pali Játaka book. We also have Mátrcetas ( _c_. 150) "Hymn in 150 Verses", lauding "the Buddha's great and profound virtues", which was taught to all monks. Piety and not wisdom was the aim of this kind of literature.
### NEPAL AND KASHMIR
In _Nepal_ the religion seems to have existed for a long time, probably from the beginning of Buddhism onwards. Little is, however, known of the period before the seventh century ad, and the Buddhism of Nepal was in all probability not substantially different from that of Northern India. In the legendary history of the _Svayambhúpurána_ a great role is assigned to Mañjuśrí, who came from China to Svayambhú, made the great lake disappear which up to then had filled the valley, founded the city of Kathmandu and placed there as a ruler the king Dharmíkara whom he had brought with him from Mahá-Cína. The Buddha Himself was born in Nepal, at Lumbiní, and Aśoka is known to have visited His birthplace, where he erected an inscribed pillar.
Although probably known in _Kashmir_ before Aśoka, Buddhism really made its influence felt only during his rule, when Kashmir formed part of his Empire. The _bhikshu_ Madhyántika was sent to convert the country. Aśoka is said to have built 500 monasteries for the Arhats, and to have given the valley itself as a gift to the Samgha. Thereafter the fate of Buddhism fluctuated with the attitude of the rulers.
Under Kanishka a Council is said to have been held which fixed the Sarvástivádin Canon. From that time onwards the Sarvástivádin writings were normally in Sanskrit, and this fact by itself would increase the relative weight of the Brahmin converts who alone would be fully conversant with the complications of this language. After the Kushana kings a Hindu reaction set in, under King Kinnara many monasteries were destroyed, the rulers in general were Shivaites, and royal patronage was therefore withdrawn. During our period Kashmir gained a high reputation as a centre of Buddhist learning and nearly all the great Buddhist scholars between Aśvaghosa and Asanga are reported to have resided there at some time or other. Harivarman about 250 wrote his _Satyasiddhi_ , an interesting synthesis of Maháyána and Hínayána views. Kashmiri monks went to Khotan, China and the Andhra country, and it was a Kashmiri monk, Gunavarman, who converted Java at the beginning of the fifth century.
### CEYLON
At the beginning of our period a most significant discussion took place about the question whether learning or practice is the more important. The Dhammakathikas who stressed learning rather than practical realization were victorious and as a result the whole character of Ceylonese Buddhism changed. The learned monks were greatly honoured and in consequence all able and intelligent monks applied themselves to book-learning. The full-time practice of meditation was normally taken up by elderly monks of weak intellect and feeble physique. Book-learning soon included not only the Tipitaka, but also languages, grammar, history, logic, medicine, etc., the Buddhist monasteries became centres of learning and culture, and they were also made artistically attractive. In the first century BC Saddhátissa, the king's brother, had asked the monks to name even one holy man who deserved his veneration. The Sinhalese commentaries, on the other hand, assume that at that time the island was full of Arahats and for a long time afterwards many monks continued to live a strictly disciplined and austere spiritual life. As we know from Fa Hien and Yüan Tsang, Ceylon enjoyed a high reputation in other Buddhist lands.
During the fifth century three scholars, all non-Ceylonese from Southern India, translated the old Sinhalese commentaries into Páli. They were Buddhadatta, Buddhaghosa and Dhammapála. The most famous of them, Buddhaghosa, gave in his "Path to Purity" (Visuddhimagga) a splendid survey of Buddhist doctrine. The book is a compendium of the Tipitaka, one of the great masterpieces of Buddhist literature which describes authoritatively, lucidly and in great detail the principal meditational practices of the Buddhist Yogin. At the end of the fifth century also a council revised the text of the Tipitaka. From this time onwards the doctrine and tradition of the Theravádins has been definitely fixed. And about 400 the Páli Suttas had for the first time been translated into Sinhalese.
For its vitality the Buddhism of Ceylon continued to depend on its contact with India, but the nature of this contact had altered in the second period. The communications with the Western ports were now abandoned, and communications went through the ports at the mouth of the Ganges. In this way the influence of the monks of Magadha, particularly the Múlasarvástivádins, made itself felt.
There was during this period much discord and controversy between the two principal monasteries, the Mahávihára and the Abhayagirivihára, the latter having been founded in 24 bc. The Abhayagiri monks had a more democratic attitude to laymen, had more contact with India, were liberal in their views, welcomed new ideas from abroad, and were more progressive than the conservative Mahávihára monks. Soon after their foundation they received Vatsíputríya monks (see p. 21) from India. Later on they added to the basic Theraváda a superstructure of Maháyána doctrines and scriptures. At the end of the third century we hear of a new school among them, called Vaitulyaváda. This was probably a form of Maháyána, and in the fourth century Sanghamitra, an Indian Maháyánist "versed in the exorcism of spirits", won the support of the king, and the Mahávihára was closed for a time. But Sanghamitra was soon killed by a carpenter, and after 362 the Mahávihára began to function again. At this time, in AD 371, the left eye tooth of the Buddha was brought to Ceylon from Dantapura in Kalinga, and this precious relic was entrusted to the Abhayagiri monastery which because of its Maháyána leanings was more willing to encourage bhaktic piety. In the beginning of the fifth century Fa Hien counted 60,000 monks in Ceylon, of whom 5,000 belonged to the Abhayagiri, and 3,000 to the Mahávihára. The Ceylonese orthodoxy has succeeded in suppressing the entire literature of the Abhayagirivádins, but one of their works is preserved in a Chinese translation. It is Upatissa's _Vimuttimaijga_ , which has the same theme as Buddhaghosa's "Path to Purity", and was written before his time. It is curious to observe that it does not depart from Theravádin doctrines on any fundamental issues.
### EXPANSION INTO GREATER ASIA
Five whole centuries had to elapse before Buddhism had penetrated the Indian subcontinent, about as long as it took Rome to conquer the Italian peninsula. Now, about 500 years after the Buddha's Nirvana, His religion could begin to expand into Greater Asia. Gandhára, in the North-West of India, was the birthplace of Buddhism as a world religion. It was from here that the monks in the saffron robe gradually filtered into Central Asia, and from there into China, and further on. And it was chiefly the Maháyána form of Buddhism which took root outside India.
We must give some explanation why the Maháyánists were so much more effective missionaries than the Híayánists. It was not that the latter were deficient in missionary zeal, but they were handicapped by the fact that they were rather inflexible literalists, whereas the Maháyána claimed much greater freedom in interpreting the letter of the Scriptures. This applied to both monastic rules and doctrinal propositions. For instance, if the rules about eating meat are strictly interpreted, nomadic populations will remain without the consolations of the Dharma, because among them the Vinaya rules cannot be strictly observed. Maháyána monks quickly found a way round unworkable rules, and reinterpreted them to fit the circumstances. Of particular importance for the success of their missionary enterprises was their attitude to the Vinaya rule which forbids monks to practise medicine. The history of Christian missions in recent centuries shows that, violence apart, the medical missionaries effected more conversions than anyone else. The sword was the one method which the Buddhists disdained to use, but the scalpel, the herb and the potion opened to the Maháyánists the houses of the poor and rich alike. They convinced themselves that compassion and their responsibilities to their fellow-men counted for more than a well-meant monastic rule and they zealously gave themselves over to the study and practice of medicine, which formed part of the curriculum for instance at Nalanda University and also at the monastic institutions of Tibet.
The same latitudinarianism was practised with regard to doctrinal questions. Great care was taken to minimize the differences between Buddhist and non-Buddhist opinions, to absorb as much of the pre-existing views of their converts as was possible, be they Taoist, Bon, Shinto, Manichean or shamanistic. This latitudinarianism is of course in danger of lapsing into laxity in the moral and into arbitrary conjectures in the doctrinal field. The latter danger was on the whole more effectively avoided than the former and the best Maháyána literature contains little, if anything, that to any fair-minded Buddhist can appear as positively unorthodox. There was one factor which limited and restrained the "skill in means" of these men, and that was the fact that before they wrote their books their minds had been remoulded and disciplined by many years of meditation on traditional lines.
_China_ was the first large country to be penetrated by Buddhist thought. As in Japan and Tibet later on, Buddhism went through five stages, which will act as our guides for the arrangement of our material.
1. There was first a period of consolidation, marked by translations of the basic texts.
2. This was followed by a preliminary attempt at coming to terms with the material. Buddhism did not move into a spiritual vacuum, but everywhere it encountered people formed by some previous tradition – by Taoism and Confucianism in China, Shinto in Japan, Bon in Tibet.
3. After this, the next, or third phase, is marked by a more mature assimilation of the doctrine, but still largely in dependence on Indian models. In China, for instance, this took the form of either numerous, generally brief, commentaries, or of original doctrinal treatises which were passed off as translations from the Sanskrit. Two of these are very well known. The one is the famous "Awakening of Faith", wrongly attributed to Aśvaghosa, and the other the so-called Súrangama Sútra, said to have been brought from Nalanda, but actually written in China by Fang Jong.
4. We now come to the fourth phase, which is perhaps the most important of all and normally took 600 years to reach. A truly Chinese, Japanese and Tibetan Buddhism, which no longer did violence to the national character, asserted itself – in China with the Ch'an sect, in Japan in the Kamakura period, in Tibet with the Kahgyudpas and Gelugpas.
5. Then finally there is the period of decay. The first phase, as we saw, was one of bare copying; in the second one asserted one's independence, somewhat wilfully, as a child in its second year; in the third one attained some true independence, without however quite daring to, as in adolescence; in the fourth phase the native genius at last fully asserted itself. This child had grown up. The creative manhood of Buddhism lasted for several centuries. Manhood is followed by old age, and after a time the creative powers of Buddhism waned.
### CENTRAL ASIA
Spreading from the Indo-Greek Bactrian kingdoms, Buddhism had by the second century BC been well established in Central Asia. Khotan, Kucha, Turfan, etc., were at that time flourishing centres of culture, owing to the caravan routes which went through them. The establishment of Buddhism on the great silk routes was an event of decisive importance for its future propagation in Eastern Asia. Among the schools, the Sarvástiváda and Maháyána were most strongly represented. They brought their Scriptures with them and in the course of the twentieth century European travellers have made many invaluable finds in the sands of Turkestan, which yielded both Indian books imported into Central Asia and translations of the Scriptures into the local languages, such as Sogdian, Khotanese, Kuchean, etc. We have also, in Kuchean, several works written in Kucha itself, imitating the Buddhist Sanskrit writings of India, but no really original works of local origin have come down to us. In addition these expeditions, carried out between 1900 and 1915, have brought to light a highly eclectic Buddhist art which offers a curious blend of Greco-Buddhist influences from Gandhara with others from the Roman Empire, and from Arsaco-Sassanid and Chinese Art. Through it the Greco-Buddhist art spread to China, where it led to the Wei art of the fifth century. In these cosmopolitan centres of intercontinental trade Buddhism was exposed to new religious influences which it had not encountered so far. It not only met with Christianity in its Nestorian form, but also with the Manicheans who were very active in that area, particularly among the Sogdians, and who left some traces on the Buddhist doctrines evolved there.
### CHINA
From Central Asia Buddhism was brought, by a natural transition, to China, which had conquered that region in the first century BC and kept it until the end of the Han dynasty (AD 220). The beginnings are said to go back to somewhere between 70 and 50 bc, and the religion slowly spread under the Han dynasty. But at first it was a foreign religion of the non-Chinese populations in China's outlying marches. In 148 a Parthian, Ngan Che Kao, and in 170 an Indian, Tshou Cho-fo, and a Yueh-chi, Tche tsh'an, arrived in China from Central Asia and established a monastery in Lo-yang, the capital of the Han. It was only in the period of disunity (221–589) which followed on the collapse of the Han, that Buddhism really became a major force in China itself. Only in 355 were Chinese for the first time permitted to become monks, at least in the realm of the Eastern Ts'in rulers. In the second century foreigners from Central Asia – Parthians, Sogdians, Indians, etc. – did some translations. In the third and fourth centuries Buddhism gained momentum among the people and at the Court, and some emperors clearly favoured it. By AD 400 1,300 works had been translated. Then came Kumárajíva, whose translations, made with the help of Chinese literati, were classical works and are still being read. By 500 Buddhism was firmly established throughout the whole of China and in a flourishing condition, with countless monasteries, temples, and sculptured grottoes for the monks.
This was a remarkable success for a religion which offended Chinese official sentiment at many points, for it seemed indifferent to the perpetuation of the family, showed little loyalty to the country and seemed to encourage baseless superstitions. The Buddhist clergy, on the ground that they had withdrawn from the world, refused to make the socially recognized signs of outward respect to the Son of Heaven and his representatives. All through its history, in fact, the Buddhist Church tended to develop into a state within the state. Their opponents blamed them for enjoying the benefits of the rule of the Son of Heaven without doing anything in return. The Buddhists claimed that on the contrary it is the monk, if anyone, who dispenses munificence, for enormous benefits accrue to the whole of society from his practice of the way of the Buddha. In fact, the benefits bestowed by the Son of Heaven are as but a drop of water when compared to the favours dispensed on all mankind by the Buddhist clergy. The state, however, always insisted on controlling the Buddhist Church through the Ministry of Worship and saw to it that to some extent the monks lived up to their claim that they were sacrificing themselves for the good of the people.
The traditionalist opponents also stressed the foreign origin of Buddhism, which came from "barbarian lands", and the doctrine of reincarnation seemed to them quite incredible because they believed that when a man dies his soul also perishes. The problem of survival after death aroused intense interest at the time. In their polemics the Chinese Buddhists were apt to stray away from the orthodox denial of an individual soul and to postulate some enduring "spiritual something of the finest essence", which transmigrates from existence to existence. They quoted either Lao Tzu or the Yellow Emperor as having said that "the body suffers destruction, but the soul undergoes no change. With its unchangingness it rides upon changes and thus passes through endless transformations." This did not really well agree with Buddhism as it had been understood up to then.
The success was of course largely due to the fact that Buddhism contained a message which the indigenous teachers could not provide. For, as Seng-yu expressed it in the fifth century, "none of them have measured the shape of Heaven or peered into the mind of the Sage". Both the ruling classes and the people supported the new religion. The Emperors would be pleased to number as many peace-loving Buddhists as possible among their subjects, because Chinese society never knew universal conscription, and has always valued Peace very highly. The ruling layers of society would find the Buddhist priests more amenable than their Taoist rivals who were continually fomenting rebellions among the peasantry and whose churches were supported by contributions of the members who constituted them. The Buddhists, on the other hand, relied on the donations of wealthy laymen, and could therefore be relied upon not to pursue unwelcome political schemes of their own. The masses, finally, were greatly attracted to the Bodhisattva ideal which opened the highest possibilities even for those low on the social scale; the Buddhist pantheon, with merciful deities like Kuan Yin and others, brought encouragement and comfort; and from the support of the Buddha and Samgha they expected rewards in an after-life. It was widely believed in China that thereby one could influence Yama, the God of the Nether World. Some Buddhist priests, like for instance Buddha Mátanga in the third century, performed miracles, prophesied and cured diseases by means of their spells.
The development of Chinese Buddhist thought was largely determined by the choice of the sacred texts which were translated into Chinese. Among the first and most influential were the Sútras on Prajñápáramitá. The mentality of the Chinese is said to be rationalistic, positivistic, matter-of-fact and anti-metaphysical. That this is only one side of their national character is shown by the enthusiastic reception which they gave to the highly metaphysical Prajñápáramitá literature from Han times onwards. The Bible was not studied with greater avidity in Protestant Europe than these very abstract writings on perfect wisdom and emptiness in China. Other works which gained a great popularity, and often became the nucleus of separate schools, were the _Lotus of the Good Law_ (translations 250 onwards), which attracted the Chinese by the splendour of the scenery and by its parables, the story of _Vimalakírti_ (translations 188 onwards), which fascinated by the noble picture of a "white-robed" layman who took the sickness of the world upon himself, and the Nirvana Sútra (translation of 423) which seemed interesting for its teaching about the Buddha-nature within each of us. Between 200 and 450 there developed a strong interest in the technical details of Buddhist meditation, and many handbooks were translated during that period.
The rise of Buddhism coincided with the revival of Taoism, and many Chinese stressed the similarity in outlook between these intellectual trends. Few doubted that the Truth as it had been seen by the Buddha and the sages of China, by Lao-tzu and Chuang-tzu in particular, was one and the same. Until the fifth century, many Taoists considered Buddhism as one more method of reaching Taoist goals. In the third century Wang Fo wrote a famous pamphlet, in which he represented Buddhism as the result of "the conversion of the Barbarians by Lao-tzu".
Taoist terminology was often deliberately used to explain Buddhist concepts and in any case many of the Chinese equivalents of Sanskrit technical terms had first been used with a Taoist meaning, which to some extent influenced their use also in Buddhist contexts. A word like tao, used to translate _márga_ ,or "Path", would automatically carry with it many Taoist connotations and overtones quite unforeseen and unintended in the Sanskrit scriptures of India. _Shou-yi_ , the equivalent of _satipatthána_ , was often equated with the Taoist _Shou-yi_ , meaning the retention of the flame of life; or _nairátmya_ , translated as the "absence of _sben_ (body)", was easily misunderstood as existence without a body, or in a spirit body; and "Emptiness" was identified with _pen-wu_ , the "Original Non-existence" of Lao-tzu, the "Void filled to the brim", which, like a womb, carries all existence within it. To a representative thinker like Hui-Yüan the Dharmakáya is equivalent to the Highest Being, Personified Nature, the Sage or Great Man of the Neo-Taoists, the Buddha, the Spirit in the Centre of Existence, and the World Soul. Buddhist ideas were freely interpreted by the use of phrases taken from Lao-tzu, Chuang-tzu and the _Book of Changes_ and it was quite usual to read the Taoist world-view into the Buddhist system. Less pronounced was the influence of Confucianism, which nevertheless made itself felt in the translation of the Sútras. During this period great care was taken to alter any sentiments or phrases which would offend the Confucian sense of propriety in such matters as family ethics, the relation between the sexes and the attitude to social superiors.
The main problem which interested the indigenous Buddhists during this period was taken from the Taoist tradition and concerned the relationship of being ( _yu_ ) and non-being ( _wu_ ), which later they identified with the "emptiness" ( _Súnyatá_ ) of the Sanskrit writings. The discussion of this problem led to the emergence of " _the seven schools_ ". Among these Tao-an's (312–85) School of Original Non-being taught that "non-being lies prior to the myriad kinds of evolution, and emptiness is at the beginning of the multitudinous shapes of physical things". The variations of this doctrine are counted as the second school. The third concentrated on the question of the emptiness of matter. The fourth teaches "the non-being of mind" which means "that the sage lacks any deliberate mind toward the ten thousand things; it does not mean that these things themselves are ever non-existent". This leads to the demand that we should "stop the activities of the mind within, and not let it be impeded by external matter", which is re-echoed in Chinese Buddhism again and again. The fifth, the "school of stored impressions", maintains that all phenomena are apparitions in a dream caused by mind and consciousness and will cease, together with the source, when we awaken from this dream. "Then the triple world is seen to be empty, and although the mind is extinguished, there is nothing it cannot produce." The sixth, called the "school of phenomenal illusion", taught that "all dharmas are equally illusory and, being so, constitute what pertains to ordinary truth. But the spirit ( _shen_ ) of the mind is genuine and not empty, and as such pertains to the highest truth. For if this spirit were likewise empty, to whom could the Buddhist doctrine be taught and who would be there to cultivate its path, renounce the world and become a Sage? Hence we know that the Spirit is not empty." The seventh "school of causal combination" finally asserted that being, or worldly truth, results from the combination of causes and their disconnection leads to non-being, which is the highest truth.
About 400 _Kumárajíva_ 's scholarly work consolidated Buddhism and gave it greater prestige. He came from Kucha, born in 344 of an Indian father. Carried off as war booty to China in 384, he lived for fifteen years in Leang-chou in Kansu, and was taken in 402 to the capital of Chang-an, where he became Kuo-Shih, or Director of Religious Instruction, and died in 413. He enlisted the patronage of the emperor Yao Hsing, and translated more than a hundred works. Originally he was a Sarvástivádin monk, but later, while still in Kucha, he was converted to the doctrines of Nágárjuna.
His two most important disciples were Seng-chao (384-414) and Chu Tao-sheng ( _c_. 360-434). Seng-chao's writings, collected under the title "Book of Chao", represent an interesting combination of Buddhism and Neo-Taoism. On this period the basic oppositions within Buddhist thinking were considered equivalent to those of Neo-Taoism. The contrast between the Absolute ( _bhútatathatá_ ) and the temporal sequence of production and stopping seemed to correspond to that between non-being ( _wu_ ) and being ( _yu_ ); that between permanence and impermanence to that between quiescence ( _ching_ ) and movement ( _tung_ ); and the contrast between Nirvána and Samsára to that of non-activity ( _wu wei_ ) and having activity ( _yu wei_ ). Sengchao discussed the Buddhist philosophy of the Maháyána on the basis of these equivalences and his views are the first formulated indigenous Chinese Buddhist philosophical system which has come down to us.
Tao-sheng sounded one of the leitmotifs of Chinese Buddhism when he said: "Ever since the transmission of the scriptures eastward (i.e. to China), their translators have encountered repeated obstacles, and many have been blocked by holding too narrowly to the text, with the result that few have been able to see the complete meaning. Let them forget the fish-trap and catch the fish. Then one may begin to talk with them about the Way ( _Tao_ )." One of the questions which agitated the Chinese Buddhists of that time was that of the destiny of the Icchantikas. Are there any beings called _icchantikas_ (a word of unknown etymological derivation), who are forever excluded from Buddhahood? Tao-sheng asserted, in opposition to most other scholars, that the _icchantikas_ also possess the Buddha-nature and are therefore capable of achieving Buddhahood, During his own lifetime a fuller text of the _Great Nirvana Sútra_ reached China and confirmed his views.
Tao-sheng also taught that "Buddhahood is achieved through instantaneous enlightenment". To his contemporaries this teaching appeared to be a "new doctrine", and the denial of a gradual enlightenment continued to be one of the special features of Chinese Buddhism. In the fifth century already Lu-cheng (425–94), a scholar-official, ascribed this difference in emphasis to a difference in national psychology. "The people of China have a facility for comprehending Truth intuitively or 'mirroring' it, but difficulty in acquiring learning. Therefore they close themselves to the idea of accumulating learning, but open themselves to that of one final ultimate. The Hindus, on the other hand, have a facility for acquiring learning, but difficulty in comprehending Truth intuitively. Therefore they close themselves to the idea of instantaneous comprehension, but open themselves to that of gradual enlightenment." In fact, Indian Buddhists had made a distinction between "gradual" and "sudden" enlightenment, but had regarded the second as the final stage of the first and nobody had thought of taking sides for one or the other. Tao-sheng now argues that, since the absolute emptiness of Nirvana is absolutely and totally different from all conditioned things, the enlightenment which mirrors it must also be totally different from all mental stages which are directed on other things. In consequence, enlightenment, if it is to be achieved at all, can be achieved only in its totality, and not in a gradual or piecemeal fashion. Many preparatory stages must, of course, precede the final flash of insight, but those ought to be called "learning"; they remain inside phenomenal existence and are not a part of the actual experience of enlightenment itself. For "when the single enlightenment comes, all the myriad impediments are equally brought to an end". The final vision is the total extinction of all ties, final liberation from them, for "what is genuine, that is permanent; what is temporary is false". From Tao-sheng's time onwards this theme was constantly debated in China and the theoreticians were divided into supporters of "gradual" or "instantaneous" enlightenment respectively.
So far about metaphysics. Popular faith, in its turn, was preoccupied with rebirth in Paradise. There were at that time three principal Paradises – that of the Buddha Akshobhya in the East, that of Amitábha in the West, and that of Maitreya at a future time on earth. The cult of _Akshobbya_ is attested for Han times, and the faithful were advised to imitate him in never feeling wrath or anger for any being, in order that they may be reborn in Abhirati, His kingdom far away on a star in the East. In the course of time the cult of _Amitábha_ proved more popular. It is said to have been first made known by the translations and preachings of the Arsacid prince An-Shih-Kao about AD 150. At the end of the fourth century, Hui-Yüan (334–416), a former Taoist, who even after his conversion to Buddhism still used Chuang-tzu's writings to explain his new faith, made the Lu-Feng monastery in Hupeh into a centre of the cult. In 402 a group of 124 persons was formed who prayed to be reborn in Amidas Paradise. This group was later on called the "Fellowship of the White Lotus" and was the prototype of the later Ching-t'u movement. Like the other Chinese schools, the Ching-t'u or "Pure Land" school was really founded only after AD 500. Akshobhya and Amitábha are cosmic Buddhas known only to the Maháyána. _Maitreya_ , on the other hand, is the future Buddha due to appear on this earth, and he is known to both Maháyánists and Hínayánists. Sútras describing the splendour of the earth at the time of His coming were translated into Chinese in this our second period, but Maitreya's greatest popularity in China lay between _c._ AD 400 and 650 and His cult seems to have been largely stimulated by the Yogácárin school.
## **THREE**
## The Third Period: AD 500–1000
### INDIA
The most important event in India in this third period is the emergence of the _Tantra._ In addition we will have to say a few words about the _Pála synthesis_ of Maháyána thought, the development of _logic_ , and the doings of the _Hínayánists._
The _Tantra_ is the third, and last, creative achievement of Indian Buddhist thought. It went through roughly three phases. The first may be called _Mantrayána._ It began in the fourth century, gained momentum after AD 500, and what it did was to enrich Buddhism by the appurtenances of magical tradition, utilizing them for the purpose of facilitating the search for enlightenment. In this way many mantras, mudrás, mandalas and new deities were more or less unsystematically introduced into Buddhism. This was, after 750, followed by a systematization, called the _Vajrayána_ , which co-ordinated all previous teachings with a group of Five Tathágatas. In the course of time, further trends and systems made their appearance. Noteworthy among them is the _Sahajayána_ , which, like the Chinese Ch'an school, stressed meditational practices and the cultivation of intuition, taught by riddles, paradoxes and concrete images, and avoided the fate of turning into a dead scholasticism by holding on to no rigidly defined tenets. Towards the end of our period, in the tenth century, we have the _Kálacakra_ , "Wheel of Time", which is marked by the extent of its syncretism and by its emphasis on astrology.
This new movement arose in the South and the North-West of India. Non-Indian influences, from China, Central Asia and the border lands round India, played a great part in shaping it. There was also much absorption of ideas from aboriginal tribes within India itself. The Tantra endeavoured to assign an honoured, though subordinate, role to all the spirits, sprites, fairies, fiends, demons, ogres and ghosts which had haunted the popular imagination, as well as to the magical practices so dear to all nomadic and agricultural populations. This further step in popularizing the religion aimed at providing it with a more solid foundation in society. But as far as the elite was concerned, there was the important difference that non-Buddhists use magic to acquire power, whereas the Buddhists do so to free themselves from the powers alien to their own true being.
The Tantra departed from the early Maháyána in its definition of the goal and of the ideal type of person and also in its method of teaching. The aim is still Buddhahood, though no longer at a distant future, aeons and aeons hence, but Buddhahood right now, "in this very body", "in the course of one single thought", achieved miraculously by means of a new, quick and easy way. The ideal saint is now the _Siddha_ , or magician, who has, however, some resemblance to a Bodhisattva as he was said to be after the eighth stage (see pp. 35–6), with his wonder-working powers fully developed.
As for the method of teaching, the Maháyána had stated its doctrines in _Sútras_ and _S_ O _ástras_ which were public documents, available to anyone sufficiently interested to procure, and sufficiently intelligent to understand them. In their stead we now witness the composition of a new vast canonical literature of _Tantras_ , which are secret documents destined only for a chosen few who are properly initiated by a _guru_ , or teacher, and which are phrased in a deliberately mysterious and ambiguous language, meaningless in itself without the oral explanations of a teacher who had been properly initiated into its secrets. The secret has been well kept, and although thousands of Tantras are still extant, modern scholars seldom have a clue to their meaning, partly because, hypnotized by the "scientific" assumptions of their own age, they have little sympathy with magical modes of thinking. The general principles of Tantric teaching can be inferred with some certainty, but the concrete detail, which is bound up with actual yogic practices and constituted the real message, eludes our grasp. Unlike the early Maháyánists (see p. 31), the Tantric authors no longer link their scriptures with Śákymuni, but frankly assign them to some mythical Buddha who is said to have preached them at some remote and distant past.
The foundations for these new literary conventions were laid already in the Yogácára school. That school systematizes the experiences gained in the course of an excessively introverted transic meditation, and the Yogins were convinced that the visions they had in trance had much greater reality than what we call "facts", than dates or localities, than individuals, their names and biographies. In consequence they tell us that certain works are due to the inspiration of, say, "Maitreya" and forget to mention the individual name of the human author who took down the inspiration. They thus cause great difficulties to modern historical research, though in their own view they tell us all that is essential and needful. The Yogácárins had also for a long time shown a keen interest in the more secretive modes of conveying information, and Asanga's _Maháyána-samgraha_ contains a fine classification of the permissible ways by which a "hidden meaning" may be conveyed, when one says something different from what one really wants to say. It was in fact from the Yogácára branch of the Maháyána that the Tantric ideas and practices originated.
The new trend was bound to weaken the monastic system. By fostering the development of small conventicles of disciples who owed absolute submission to their _guru_ it favoured the dispersal of the Samgha into self-sufficient bands of Yogins, many of whom believed that they were spiritually so developed as not to need the restraint of the monastic rules any longer, while others by their unconventional behaviour liked to cock a snook at the sheltered lives of the ordinary monks.
The mantrayanic development was originally a natural reaction against the increasingly adverse historical trends which threatened to suffocate Indian Buddhism. In their defence and for their protection its adherents now more and more mobilized magical and occult powers and invoked the help of more and more mythological beings, whose actual reality was attested to them in the practice of transic meditation. Among these great attention was paid to the "wrathful" deities, like the "Protectors of the Dharma", also called _vidyárájá_ , "kings of the sacred lore", who are inherently well-meaning, but assume a terrifying appearance to protect the faithful. It is also interesting to note that in their search for security the Buddhists of that time more and more relied on feminine deities. Already about AD 400 Tárá and Prajñápáramitá had been adored as celestial Bodhisattvas. They were soon joined by the "Five Protectresses", with Mahámáyurí, "the great Pea Hen", at their head. Later on the practitioners of advanced mystical meditation evolved a whole pantheon of feminine deities, like Cundá, Vasudhará, Usnísavijayá, Vajravárahí, Buddhalocaña, and others; the practitioners of the magical arts were especially devoted to the "Queens of the sacred Lore" and to the dákinís, or "sky walkers"; and the general population was encouraged to turn for their own specific interests to goddesses who gave children, protected from the small-pox and so on. After 700 the so-called "left-handed" Tantra added consorts of the Buddhas and Bodhisattvas. These were called _Vidyás_ of _Prajñás_ , corresponding literally to the _Ennoias_ and _Sophias_ of the Gnostics. A seemingly erotic ritual often accompanied the cult of the vidyás, and this aspect of the Tantra has greatly bemused the more unsophisticated European enquirers. Nothing need be said about it here, because the actual facts of this ritual are totally unknown to us.
The belief in the occult, in magic and miracles, has at all times been an integral part of Buddhism, though more by way of recognizing an established fact than as a matter of urgent practical importance. But as the spiritual potency of the Dharma waned and as history was felt to become more and more adverse, greater reliance was placed on magic to ward off dangers and secure help. We find that after AD 300 sporadically _mantras_ of all kinds are slowly incorporated into the holy writings. These were also called _dháranís_ , from the root _dhr_ , because they are intended to "uphold" or "sustain" the religious life. Then, after AD 500, all the customary procedures of magic were resorted to, rituals as well as magical circles and diagrams. These were employed to both guard the spiritual life of the elite, and to give to the unspiritual multitude that which it desired. Mudrás, or ritual gestures, often reinforced the efficacy of the spells.
Moreover there are the _mandalas_ , the harmonious beauty of which still appeals to our aesthetic sense. Magical circles, which mark off a sacred or ritually pure spot, are, of course, as old as magic and go back well into prehistoric times. The peculiar Buddhist arrangement of mandalas seems, however, to have developed in Central Asia and owes much to the pattern of the Chinese TLV mirrors of the Han dynasty. The mandala expresses cosmic and spiritual forces in a mythological, or personified, form, representing them by the images of deities, shown either in their visual appearance, or by the syllable which allows us to evoke them and which constitutes their occult principle. These symbols, properly read, allow us to give expression to deeply hidden fears, primordial impulses and archaic passions. Through them we can chain, dominate and dissolve the forces of the universe, effect a revulsion from all the illusory things of the samsaric world, and achieve reunion with the light of the one absolute Mind. Mandalas are a special form of age-old diagrams of the cosmos, considered as a vital process which develops from one essential principle and which rotates round one central axis, Mount Sumeru, the axis _mundi._ Such diagrams were reproduced not only in mandalas, but also in ritual vases, royal palaces, Stupas and Temples. Owing to the equivalence of macrocosm and microcosm, the drama of the universe is reproduced in each individual, whose mind, as well as whose body, can be regarded as a _mandala_ , as the scene of the quest for enlightenment. The construction and designing of _mandalas_ , and the evocation of deities, were naturally governed by strict rules and well defined ritual observances.
The creative outburst of the early Tantra led to a complete chaos of assumptions about cosmic and spiritual forces and it was the _Vajrayána_ which imposed order on the vast inchoate mass of traditions which had evolved. It adopted a fivefold division of all cosmic forces, each class being in a sense presided over by one out of five Tathágatas. The names of the Five Tathágatas were Vairocana, Akshobhya, Ratnasambhava, Amitábha and Amoghasiddhi. A complicated and most intricate system of magical correspondences, identifications, transformations and transfigurations then link all the forces and facts of the universe with these five "families". The body in particular is regarded as a microcosm, which embodies the entire universe and is the medium for realizing the truth, very largely by methods which form a part of what is nowadays known as _Hathayoga_ in India. We hear much about parallelisms between the visible, the audible and the touchable, and everything is designed to unite the powers of mind, speech and body for the purpose of realizing the final state of completeness, or enlightenment. The Vajrayána has been well defined as "the art of living which enables us to utilize each activity of body, speech and mind as an aid on the Path to Liberation", and in this way it is astonishingly akin to the contemporary Ch'an school. The true meaning of Vajrayána teachings is, however, not always easy to ascertain, because here it has become a convention to clothe the highest into the form of the lowest, to make the most sacred appear as the most ordinary, the most transcendent as the most earthly, and the sanest knowledge is disguised by the most grotesque paradoxes. This is a deliberate shock therapy directed against the over-intellectualization of Buddhism at that time. The abundant sexual imagery in particular was intended to shock monkish prudery. Enlightenment, the result of a combination of wisdom and skill in means, is represented by the union of female and male in the ecstasy of love. Their becoming one in enlightenment is the highest indescribable happiness ( _mahásukha_ ).
The further development of Buddhism in Northern India was greatly influenced by the accidents of royal patronage. In the seventh century, King Harshavardhana, a lesser Aśoka, patronized Buddhism, preferring first the Sammitíyas, and then, perhaps as a result of Yüan-tsang's visit in 630–44, the Maháyána, though Śhivaism may have been his own personal religion. It was, however, the _Pála_ dynasty of Bengal (750–1150) who by their support of the great Buddhist universities determined the history of Buddhism for centuries to come. From the sixth to the ninth centuries, Nalanda had been the centre of living thought for the entire Buddhist world. Under the Pála dynasty new centres were founded in Eastern India, especially Vikramaśíla, and Odantapuri. These together with Jaggadala and Somarúpa were the focal points from which Buddhist culture radiated over Asia during the ninth to twelfth centuries.
I-Tsing, who visited Nalanda about AD 700, said of the sects there that "they rest in their own places, and do not get themselves embroiled with one another". In fact, the official Buddhism of the period became a mixture of _Prajñápáramitá_ and _Tantra._ King Dharmapála ( _c_. 770–810), immediately on ascending the throne, greatly honoured the teacher Haribhadra, a leading authority on _Prajñápáramitá_ and _Abhisamayálankára_ , while not at the same time neglecting the interpreters of the _Guhyasamája_ , a celebrated Tantric text. The monks of these universities combined metaphysics and magic almost like the _Gerbert of Rheims_ and _Albert the Great of_ mediaeval folklore. Their range of interest is well typified by what Táranátha reports of one of them. "By constantly looking on the face of the holy Tárá he resolved all his doubts. He erected eight religious schools for the _Prajñápáramitá_ , four for the exposition of _Guhyasamája_ , one each for each one of three kinds of Tantra, and he also established many religious schools with provisions for teaching the _Mádhyamika_ logic. He conjured up large quantities of the elixir of life, and distributed it to others, so that old people, 150 years old and more, became young again." This _Pála synthesis_ of Maháyána thought has shown an astounding vitality. Though destroyed by the Muslims in Bengal, it spread to Java and Nepal, and in Tibet it continued as a living tradition up to recent years.
As the Buddhists preceded the Hindus in the development of Tantras, so also in that of _logic._ The social standing, as well as the income, of religious groups in the Indian Middle Ages depended to some extent on the showing they could make in the religious disputations which were about as popular at that time as tournaments were in the European Middle Ages. In this context, a knowledge of the rules by which valid can be distinguished from invalid inferences would be a definite advantage. Just as the disputes of the Greek sophists led to the logical systems of the Socratic schools, so disputes of the Indian religious sects led to the formulation of logical and epistemological theories among the Buddhists. This new trend goes back to Nágárjuna, but the first Buddhist to teach an articulate system of logic was Dinnága ( _c_. 450), a pupil of Asanga. He also initiated systematic epistemological studies among the Buddhists, discussing the sources of knowledge, the validity of perception and inference, as well as the object of knowledge, and the reality of the external world. In the course of this third period these logical studies reached great maturity with Dharmakfrti ( _c_. 600–50) and Dharmottara ( _c_. 850), who dealt with many of the problems which have occupied modern European philosophy, such as the problem of solipsism and the existence of other minds. This interest continues right to the end of Buddhism in India, and it was from there carried to Tibet and to a lesser extent to China and Japan. The logical studies of the Yogácárins developed quite naturally from some of the questions which the Vaibháshikas (see p. 43) had asked themselves and they kept Buddhist philosophical thinking abreast, and often ahead, of the time.
In India itself the Maháyánists appear to have remained numerically a minority. In AD 640, for instance, out of 250,000 monks counted by Yúan-tsang, only 70,000 to 100,000 belonged to the Maháyána. It must seem definitely unfair therefore that I can find nothing to say about the Hínayánists, and that all the space is given to their Maháyána rivals. This disproportion is perhaps due to a fault in perspective which affects most historical works. The continuing tradition, however praiseworthy, is taken for granted and passed over without comment. The life sprouting out at the growing points gets all the limelight. By way of correction it is sometimes good to remember that at any given time the majority of Buddhists were virtuous people who just carried on in the old ways, and who have no news value, just as virtuous women are said to have none.
### NEPAL AND KASHMIR
The Buddhism of _Nepal_ continued to flourish as an offshoot of that of Northern India, and Patan became a replica of one of the Pála universities. Between the seventh and ninth centuries close ties were developing with Tibet, and many Tibetans came to Nepal to learn about the Buddhism of India. It was in Nepal that Śántaraksita encountered Padmasambhava when he conveyed to him the invitation of the king of Tibet.
At the beginning of this period, the Samgha of _Kashmir_ suffered a serious setback from the invasions of the Huns, who under Mihirkula ( _c_. 515) devastated the country and persecuted the monks. After their departure Meghavahana, a Buddhist ruler, forbade all slaughter of animals, while compensating butchers and fishermen for the resulting loss. This king erected many religious buildings and his successors continued to patronize the Church. Yüan-tsang remained for two years in Kashmir. He found about 5,000 monks, but noted that "at the present time this kingdom is not much given to the faith". New prosperity began in the seventh and eighth centuries with the Karkota rulers. The faith revived again, though in a form which brought it nearer to Hindu cults. This shows itself in Sarvajñamitra, and his Hymns in praise of Tárá. Sorcery and miracle-working spread and the monks practised how to make or stop rain, how to check the flow of flooded rivers, etc. The spread of Tantrism and Devotionalism brought Buddhism nearer to Śivaism, which in its turn in the ninth and tenth centuries developed, with Vasugupta and others, firm philosophical foundations. About 1000 we have Kshemendra, who wrote Avadánas, Buddhist legends resembling Brahminic Mahátmyas. In the ninth century many Kashmiri monks went to Tibet.
### CEYLON
At this time the Theravádin sect managed to expand beyond Ceylon itself on the route between Ceylon and the places of pilgrimage in Magadha, and many were found in Southern India and in the region of the two ports through which they went, i.e. the Ganges delta (Támralipti) in the East and Bharukaccha in the West. In Ceylon itself the Abhidhamma was greatly honoured, but at the same time magical practices began to be encouraged. About 660 we hear for the first time of the chanting of _Paritta_ as a ceremony, which became a regular feature of later Buddhism in Ceylon.
For a time the Maháyána was fairly strong, and both Prajnaparamita and Tantra had their centres in the island. The Indikutasaya Copper Plates have preserved for us parts of one of the large Prajñápáramitá Sútras in Sinhalese script of the eighth or ninth century. The Abhayagiri continued to import many Maháyána features and its relations to the Mahávihára remained unfriendly. About 620 the members of the Mahávihára refused the king's request that they should hold the _uposatha_ -ceremony together with those of the Abhayagiri, and about 650 the Mahávihára were so incensed with the king for the favours he bestowed on the Abhayagiri that they applied to him the "turning down of the alms-bowl", an act equivalent to the excommunication of a layman. In 536 a book called _Dharmadhátu_ was brought to Ceylon, which probably dealt with the Three Bodies of the Buddha and this book was greatly honoured by the king and became an object of ritual worship. In the ninth century Vajrayána tenets were spread by an Indian monk residing in Abhayagiri and the king was greatly attracted to the teaching. In the words of the Chronicle, "it also became prevalent among the foolish and ignorant people of this country" and led to the formation of a special order of monks clad in dark blue robes. During the seventh century an ascetic reaction against the generally comfortable life of the monks made itself felt at the Abhayagiri. Those who strove to revive the rigours of old separated themselves in the ninth century and as _Pamsukúlikas_ they were prominent for centuries, deriving their name from the ancient practice of wearing robes made from rags collected on rubbish heaps. In the Polonnaruva period, from the end of the eighth century onwards, Hindu influences on Buddhist practices began to come in.
### CENTRAL ASIA
Under the T'ang dynasty, Central Asia once more became an intermediary between China and India, for between 692 and _c_. 800 it was again part of the Chinese empire. The Tibetans held sway for some time and many valuable Tibetan documents from Tun-huang, etc., dating from the seventh to tenth centuries, have been recovered in recent years. The empire of the Uigurs, at its height between 744 and 840, is also of some importance for the history of Buddhism. Defeated in 840 by the Kirghiz, the Uigurs then founded a new kingdom in the region of Turfan, Bechbaliq, Karachar and Kucha, which persisted in Turfan and some other areas until the fourteenth century. The Uigurs, from the eighth century onwards Manicheans, were in the ninth century converted to Buddhism and an abundance of Buddhist works was translated into Uigur from the Sanskrit, Kuchean, Khotanese and Chinese. Generally speaking, however, after 900 Turkish Islamic populations displaced the Buddhist Indo-Europeans in Central Asia.
### SOUTH-EAST ASIA
Buddhism reached South-East Asia as the result of the colonizing activities of Hindus, who not only founded trading stations, but also brought their cults and culture with them. From the third century onwards the area, also known as "Further India", was increasingly ruled by dynasties which could either claim Indian descent, or which were at least motivated by the ideals of Hindu civilization.
By the fifth and sixth century both Maháyána and Hínayána Buddhism had filtered into _Burma._ At first it came from the Pallava country of Southern India (Magadha) and the Sarvástivádins may well have established themselves for a time. From the ninth century onwards, Pála Buddhism was imported from Bihar and Bengal. It led in Burma to the formation of a powerful organization of monks who called themselves "Aris" (from _árya_ , "noble"). We have no information about their metaphysical teachings, but we know that they worshipped the Maháyána pantheon, were addicted to Tantric practices, justified doctrinal innovations by occasionally discovering some "hidden scripture" and absorbed many local customs, for instance the _jus primae noctis_ , which they considered as an act of religious worship.
Turning to _Indo-China_ , we find that in Cambodia about AD 400 already the reigning house, the nobility and the priesthood are Hindus. We also find a mixture of Śivaism and Maháyána first in Fu-nan, and then, after 540, in the Khmer kingdom, of which Angkor became the capital in 802. The Khmers erected many huge buildings, some of which were devoted to Maháyána deities, among whom Lokeśvara and Bhaisajyaguru were specially popular. Up to about AD 1000 the syncretism of Śivaism and Maháyána also dominated the Champa kingdom, although the Maháyána element was less strong there, and also the Sammitíyas and Sarvástivádins were represented. The influence of Śrívijaya greatly strengthened the Maháyána during the ninth century also in Indo-China.
_Indonesia_ was likewise ruled by Indian emigrants, and a Buddhism imported from South-East India is attested there from the fifth century onwards. The imperial power of Śrívijaya after 675 replaces by Buddhism the Brahminism prevalent until then. In Sumatra the Sarvástivádins were strong in the seventh century. Later on the Vajrayána was brought in from the Pála Universities. The same happened in Central Java under the Śailendra dynasty from the eighth century onwards, although Śivaism always remained fairly strong. The Śailendras filled the Kedu plain with beautiful temples, adorned with exceptionally fine sculptures. The most famous of these is the gigantic Borobudur, a Stúpa built in the sixth century, which is a _mandala_ in stone, and symbolizes the cosmos as well as the way to salvation. Those who walk in _pradaksiná_ through its galleries will thereby ritually undergo the process of moving out of Samsara into Nirvana, ascending through the three levels of the triple world to the supramundane transcendental realm. Some of the great Maháyána texts are here illustrated on bas-reliefs, i.e. the _Játakamálá, Lalitavistara, Gandavyúha_ and _Karmavibhanga._
### CHINA AND KOREA
The three centuries between 500 and 800 were the most prosperous and creative years for Chinese Buddhism. The religion was now assimilated, and became an integral part of national life. Eight indigenous schools arose during this period. They were (1) the Lü-tsung, founded by Tao-Hsüan (595–667); (2) the San-lun, founded by Chi-tsang (549–623); (3) the Weih-shih, founded by Yüan-tsang (596–664); (4) the Mi-tsung, founded by Amoghavajra (705–74); (5) the Hua-yen tsung, founded by Tu-shun (557–640); (6) the Tien-t'ai, founded by Chih-k'ai (538–597); (7) the Ching-t'u, founded by Shan-tao (613–81); and (8) the Ch'an school, said to have been founded by Bodhidharma about 520.
The first school, or _Vinaya_ sect, had no doctrinal significance, its purpose being to work for a stricter observance of the Vinaya rules, particularly as regards ordination and the begging of food. The school had some success in raising the standards of monastic strictness, but it soon passed to the periphery of the Buddhist world.
The next three schools are Indian scholastic systems, which remained more or less foreign bodies in Chinese Buddhism and did not endure for more than a few centuries. The _San-lun_ is the Chinese form of the Mádhyamikas. It is based, as the name says, on "three treatises", one by Nágárjuna and two by Áryadeva, and continues the work done by Kumárajíva about 400. Chi-tsang, its founder, was a most prolific writer of books, chiefly commentaries and encyclopaedias. The general purpose of the school is to discard all views, so that emptiness may prevail.
The _Weih-Shih_ is the Chinese form of the Yogácárins and its basic textbook is the _Ch'eng Weih-shih tun_ , "The Completion of the Doctrine of mere ideation". The great pilgrim Yüan-tsang had brought with him from Nálandá ten commentaries to Vasubandhus "Thirty Stanzas", and he combined them into one work, generally giving preference to the interpretations of Dharmapála (sixth century). It is the purpose of this school to discard all objects, to see that they all "are mental representations dependent upon the evolutions of consciousness", and to merge into the one Mind in which everything is mere ideation. Its tenets and attitudes were, however, not in harmony with the general tendencies of Chinese mentality. In K'uei-chi (632–82), Yüan-tsang's leading disciple, this school attracted another first-class mind, but soon it degenerated into scholastic disputes about the "seventh", "eighth" and "ninth" consciousness, which generally did nothing but reflect divergent Indian traditions, not always clearly understood.
The _Mi-tsung_ , or "School of the Mysteries", is the Chinese form of the Tantra. It is also known as Chen-yen, the school of the "Mantras". In the eighth century, three Indians, Śubhákarasimha (637–735), Vajrabodhi (670–741) and Amoghavajra (705–74), imported into China Tantric systems of the non-Shaktic type, and won great influence at the Court of the T'ang emperors. They there established a great variety of rites, partly designed to avert catastrophes from the Empire, and partly to favourably influence the fate of people after their death. The school lasted not much longer than a century, and in later times the Tantric tradition in China fell into the hands of Lama monks from Tibet.
The next three schools attained a greater degree of assimilation. First among these is the _Hua-yen-tsung_ , literally the "Wreath" school, which represents the link between Yogácára and Tantra, in that it gives a cosmic interpretation to the ontological ideas of the Yogácárins. It is derived from a study of the Indian _Avatamsaka Sútra._ Here the sameness, or identity, of everything is interpreted as the interpenetration of every element in the world with every other element. The one principle of the cosmos is present in all beings and in all things, in the sense that everything harmonizes with everything else. Each particle of dust contains all the Buddha-lands, and each thought refers to all that was, is and will be. The sensory universe is a reflex of the eternal and the mysteries of the truth can be beheld everywhere. Unlike the Tantra this school did not aim at the manipulation and control of cosmic forces by magical means, but was content with the contemplation and aesthetic appreciation of the interplay of these forces. This doctrine greatly influenced the attitude to nature in the Far East, and also inspired many artists in China and later on in Japan. The Hua Yen school, founded about 630, lasted until about AD 1000.
One of its greatest teachers was _Fa-tsang_ (643–712), the descendant of a Sogdian family and originally a disciple of Yüan-tsang, who wrote an important work called "Meditation which extinguishes false imaginations, and by which one returns to the source". With the Yogácárins he speaks of one mind which makes possible the world of particulars. But then he goes beyond the Yogácárin doctrine by claiming that everything has the following three marks, or characteristics:
1. Existentially, each particular object, each "particle of dust", contains in itself the whole realm of reality (dharmadhátu) in its entirety;
2. Creationally it can generate all possible kinds of virtue, and any object may therefore reveal the secrets of the entire world;
3. In each particle the emptiness of true reality is perceivable.
Six kinds of contemplation are recommended to the disciple:
1. To look into the serenity of Mind to which all things return;
2. To realize that the world of particulars exists because of the One Mind;
3. To observe the perfect and mysterious interpenetration of all things;
4. To observe that there is nothing but Suchness;
5. To observe that the mirror of Sameness reflects the images of all things, which thereby do not obstruct each other;
6. To observe that, when one particular object is picked up, all the others are picked up with it.
The _T'ien-t'ai_ school is so called because its founder, Chih-k'ai, lived and taught in the T'ien-t'ai mountains in Chekiang. It is also known as the _Fa-hua_ , or "Lotus" school, because it took the _Saddharmapundaríka_ as its basic text. Chih-k'ai wrote some extremely valuable treatises on the art of meditation. In its doctrines the T'ien-t'ai aimed at a syncretism of all the different Maháyána schools and in its general policy it tended to promote social order in collaboration with the secular authorities. Its mentality is akin to that of the Yellow Church of Tibet, although Chinese conditions produced constant checks on its political influence. In its profound and complicated philosophical teachings the T'ien-t'ai shows strong traces of the influence not only of the Weih-shih and Hua-yen schools, but also of the _Awakening of Faith in the Maháyána_ , a work falsely ascribed to Aśvaghosha, which may very well have originated in China. The T'ien-t'ai had a strong preference for calling the Absolute "true or genuine Suchness" or also the "Womb of the Tathágata", which contains within itself all the pure and impure potentialities and is thus capable of generating both this-worldly and other-worldly things.
This dualistic theory is special to the T'ien't'ai school. All things and events of the phenomenal world are "harmoniously integrated", and there is no barrier between one thing and another. The T'ien-t'ai tend to ascribe a greater degree of reality to the phenomenal world than the Indian schools would allow. In their concern with social activity they emphasized that Nirvana eliminates all ills but not likewise "the great functioning" of the universe. According to them even the Buddhas can work and stay within the circle of birth and death, because even after enlightenment they retain their impure potentialities, which cannot ever be destroyed and therefore they may, like ordinary people, be engaged in impure or mundane acts. And because every single thing contains the absolute Mind in its totality, not only, as Tao-sheng had said (see p. 58), all sentient beings have the Buddha-nature in them, but also, as Chan-jan (711–82), the ninth patriarch of the T'ien-t'ai explained, "even inanimate things possess the Buddha-nature", "and why should exception be made of even a tiny particle of dust?"
In the Ching-t'u ("Pure Land") school _Amidism_ , which had for centuries existed as a popular trend (see p. 59), became more strictly organized. This school was founded by Tao-ch'o (562–645), and consolidated by Shan-tao (613–81). These two were followed by a few more outstanding figures, called "patriarchs", the last of whom, Shao-k'ang, died in 805. After the ninth century Amidism ceases to have a separate corporate existence as a sect and becomes an influence which pervades all forms of Buddhism in China.
Amidism taught that the power inherent in the name of the Buddha Amitábha can remove all obstacles to salvation and that the mere utterance of His name (O-mi-to-fo) can assure rebirth in His kingdom. The legend of Amitábha is based chiefly on the _Sukhávatívyúha_ , a Sanskrit text of the first century AD. It tells us that inconceivable aeons ago the Bodhisattva Dharmákara made forty-eight vows, among them the promise that all who call on his name shall be saved; that later on he became the Buddha Amitábha; and that finally, ten aeons ago, in accordance with his vows, he established the Pure Land or Western Paradise which lies one million billion Buddha-lands away. This sect honoured Amitábha by multiplying copies of His statues as well as of the Sútras which deal with Him, and also by paintings which depict and by hymns which sing the splendours of the Pure Land. A study of the dated inscriptions at Long-men shows that the cult of Amitábha flourished there particularly between 647 and 715. The Amidists also worshipped Kuan-yin, the Indian Avalokiteśvara, who in the course of time changed his sex in China, and became a feminine deity.
The strength of Amidism lies in its democratic spirit. The intellectualism of religious aristocrats who retire into solitary mountain places is quite beyond the reach of the common people who must live in the bustle of ordinary life. A religion which appeals to the masses must above all aim at extreme simplification, and the great merit of the Ching-t'u teaching, according to its propounders, is that it is simple and easy to follow. All that is required by way of virtue is just faith, and the Ching-t'u authors seem to assume that that is more commonly found than the capacity for trance or wisdom.
The most important of all Chinese schools is, however, the _Ch'an_ school. It is the fourth and last of the original recreations of the Buddha's thought, the first three being the Abhidharma, the Maháyána and the Tantra. With the Tantra Ch'an is nearly contemporary and the two have much in common. The history of the Ch'an school begins with Hui-neng (638–713), also known as the "sixth Patriarch". Before Hui-neng we have a kind of pre-history of Ch'an, which is said to begin with Bodhidharma, a more or less legendary Southern Indian who came to China at the beginning of the sixth century and spent nine years in Lo-yang, the capital, in "wall-gazing". The importance of Bodhidharma lies in providing the Ch'an sect with a concrete link with the Indian tradition, a link which the school in spite of its profound originality greatly cherished. The Buddha Śákyamuni, so we are told, had given the secret doctrine to Mahákáśyapa, and from him it was transmitted to one "patriarch" after the other, but "from mind to mind, without the use of written texts", until it reached Bodhidharma, the twenty-eighth of the line. Between Bodhidharma and Hui-neng we have four more "patriarchs" who taught a Buddhism strongly tinged with Taoism in the tradition of Tao-sheng (see pp. 57–9). Among them the third patriarch, Seng-tsan (died 606), is noteworthy for his superb poem on "Believing in Mind", which is one of the great classics of Buddhist literature. These patriarchs had, however, little influence on society in general, because they lived in poverty without a fixed residence and generally made it a rule not to spend more than one night in any one place.
History further records that the interpretation of the teachings of these patriarchs led to a rift between a Northern branch, headed by Shen-hsiu ( _c_. 600–706), and a Southern branch, headed by Hui-neng, of Canton, the main point in dispute being the question of "gradual" and "sudden" enlightenment. The Northern followers of "gradual enlightenment", who assumed that our defilements must be gradually removed by strenuous practice, soon died out. What we call the Ch'an school consists of Hui-neng's numerous disciples. Organizationally, Ch'an became independent only at the time of Pochang Huai-hai (720–814). Up to then, most Ch'an monks had lived in monasteries of the Lü-tsung under the regulations of its Vinaya. Now Po-chang made a new set of rules for Ch'an monks, which tried to revive the austerity and simplicity of living conditions in the early Order, and also combined the Buddhist Vinaya with Confucian rules of etiquette. The regulations of all Ch'an monasteries are derived from Po-chang. He introduced an innovation which did much to ensure the survival and social success of his sect. The monks went on their begging round each morning, but in addition they were expected to work. "A day without work, a day without eating" was Po-chang's watchword. This was something unheard of so far. The Ch'an school has had two periods of vigorous development, the first in the Tang, the second in the Sung period. The second phase belongs to chapter IV, and here we confine ourselves to the first.
It had long been a problem whether learning or practical realization is more important. The Ch'an sect, as against the Ceylonese Dhammakathikas (see p. 46), uncompromisingly decided in favour of practical realization. They found a situation in which the fervour of the faithful had so multiplied the means of salvation, in the form of Sútras, commentaries, philosophical subtleties, images and rites, that the goal itself was apt to be lost sight of; the spiritual life was in danger of being choked by the very things which were designed to foster it. In their reaction against the overgrown apparatus of piety they advocated a radical simplification of the approach to enlightenment. They never tired of denouncing the misuse of this apparatus, which could so easily have become an end in itself. In particular they set themselves against the excessive worship paid to the scriptural traditions and insisted that salvation could not be found by the study of books. That did not mean that they studied no books at all. On the contrary their own sayings are saturated with references to such works as the _Vajracchediká Sútra_ , and the _Lankávatára Sútra_ , the two favourites of the school in its early days. But they felt strongly that the study of these Sútras should play only quite a subordinate role compared with the demands of meditation ( _Ch'an_ means _dhyána_ ) and spiritual realization. The complicated cosmological and psychological theories of the other Buddhist schools are rejected as just so much "rubbish" and "useless furniture".
By way of protest against the excesses of devotion and the current misunderstandings of the Buddha's role, a famous Ch'an master of the Tang dynasty, Tan-hsia T'ien-jan, in the eighth century, when he was cold, burned a statue of the Buddha and warmed himself by it. Because a definite fixation of the affections on a definite object might act as a fetter, another Ch'an master coldly informs us that, if you meet the Buddha, you ought to kill Him if He gets in your way. Less drastic are the replies of another Ch'an master Nan-yuan Hui-yung, to the question, "What is the Buddha?" He just said, "What is not the Buddha?", or "I never knew Him", or "Wait until there is one, then I will tell you". All this hardly gives the mind very much to rest upon. Ch'an was intent on restoring Buddhism as a spiritual doctrine. Spiritual things have their own laws, their own dimensions, and their own mode of being. This makes them rather indefinite for mundane perception, and it has been rightly said that the spirit can be apprehended only by the eyes of the Spirit.
The Ch'an school well knew that it represented a quite new departure. Just as the Tantric followers of Padmasambhava regarded him as a second Buddha, equal in authority to Śákyamuni, so in the same spirit the Ch'an Buddhists deliberately called a collection of Hui-neng's sermons a "Sútra", a term reserved for the Buddha's own utterances. Because the Ch'an school abhorred all intellectualization and systematizations, its own literature, insofar as it had any, widely departed from the Indian models. A few Ch'an monks seem to have composed sermons and didactic hymns, but the great majority of the T'ang masters refused to write down anything at all. They confined themselves to a few brief and cryptic sayings, which at a later age were collected as "Sayings of the Ancient Worthies". So much did they distrust the distorting effect of words, that they tried to induce enlightenment in their pupils not only by nonsensical remarks, but by beating them at appropriate moments with a stick, pulling their noses, or making rude and inconsequential noises, like Ma-tsus famous "Ho", etc. Their method of teaching was technically known as "strange words and stranger actions". Because no written work can contain them, these teachings were held to be something outside the scriptures. They are regarded as instances of the "Buddha-mind" speaking directly to the "Buddha-mind", and they transmit the "Seal of Mind" directly from teacher to pupil.
It is, of course, not easy to distil from such unpromising material a rationally formulated philosophical doctrine. But, attempting the impossible, one may well say that these were the chief tenets of Ch'an. First of all, there is the famous teaching that "Buddhahood is achieved through instantaneous enlightenment". As practical people, the Ch'an Buddhists were not, however, so much interested in theories about enlightenment, as in its practical achievement. The Hínayána had much to say about "enlightenment", but could no longer produce any fully enlightened people, be they Arhats or Buddhas. Nor was the traditional Maháyána in any better position and had to justify its apparent sterility by asserting that any given Bodhisattva would have to still pass through aeons and aeons of preparation before he could become a Buddha. In the seventh and eighth centuries a number of Buddhists became rather impatient with doctrines which deferred the attainment of the goal to an indefinite future and insisted on quicker results. This led to the Tantra devising methods for winning Buddhahood "in this very body", and to the Ch'an working for enlightenment "in this very life". The Ch'an claimed that within their ranks numerous people attained "enlightenment" all the time, but for this they did not use the traditional term _p'u-t'i_ , which corresponds to _bodhi_ , but a new word, _wu_ , "comprehension, awareness", better known in its Japanese form as _satori._ Its relation to "enlightenment" in its traditional Indian sense and to the Buddha's omniscience has never to my knowledge been clarified, although the Ch'an Patriarchs are referred to as "venerable Buddhas". This signifies that in the history of Buddhism a new type of "saint" had arisen. After the Arhats, Pratyekabuddhas, Bodhisattvas and Siddhas we now have the Ch'an _Róshis_ as a fifth type.
Secondly, the highest principle is inexpressible. Again, Ch'an was not content to just say so, as many Buddhist philosophers had done before them, but it tried to make the insight into this truth into a concrete experience, by evolving methods of "stating it through non-statement", by in other words designing some extraordinary and on the face of it quite irrelevant kind of statement which would do justice to it. Like for instance,
In the square pool there is a turtle-nosed serpent.
Ridiculous indeed when you come to think of it!
Who pulled out the serpent's head?
Analogously, "cultivation must be carried out by non-cultivation". Just as a mirror cannot be made by grinding a brick, so a Buddha cannot be made by practising meditations. This does not mean that all meditation should be discarded, but that it should be carried out without any striving, self-assertion or deliberate purpose, thus exhausting the old karma and creating no new karma. One must be established in "no-thought" which means "to be in thought yet devoid of thought" and to "stop the mind dashing hither and thither". As a result of this kind of cultivation, a man gains enlightenment, he has no more doubts and all his problems are suddenly solved, not because he has found a solution for them, but because they have ceased to be problems for him. And although his new-found knowledge is different from the ignorance of ordinary people, nevertheless, in the last resort, he has gained nothing at all, and the life of the sage is not different from that of ordinary men. As Yi-hsuan (died 867) put it: "Only do ordinary things with no special effort: relieve your bowels, pass water, wear your clothes, eat your food, and, when tired, lie down! Simple fellows will laugh at you, but the wise will understand." So "there is really nothing much in the Buddhist teaching". The secret which the Buddha gave to Mahákásyapa is really an open secret, and there is nothing to it, except that the mass of people fail to understand it.
Once enlightened, the sage can without any effort combine a mysterious aloofness with a constant response to the calls of the world. Non-activity has become identical with action, and, as P'ang-yun put it, "spirit-like understanding and divine functioning lies in carrying water and chopping wood". To conclude with a saying of Hai-yun: "To eat all day yet not to swallow a grain of rice; to walk all day yet not tread an inch of ground; to have no distinction during that time between object and subject, and to be inseparable from things all day long, yet not be deluded by them, this is to be the man who is at ease in himself." Ch'an is a very profound doctrine indeed. Although the cultural background and social conditions of the China of the Tang differed in almost every way from those of the India of the Buddha Śákyamuni, rarely have Buddhists at any time come as near to the spirit of their Founder as the great masters of the Ch'an school.
So far about the intellectual developments of the period. Outwardly also under the Tang the Buddhist Church attained a position of greater brilliance, wealth and power than it has probably experienced at any other time during its long history. This success was, however, bought at a heavy price. The prosperity of the monasteries threatened to ruin the economy of the country. The vast monastic establishments were economically unproductive, and had to be maintained by the lay community, i.e. by the Imperial Court, by aristocratic families or by villages; the expensive architectural enterprises deflected huge numbers of the rural population from work in the fields, and finally the metallic reserves of the country were drained away, being used to cast images and other ritual objects. This process led to the great persecution of 845. The Government confiscated the property of the monasteries, forced the monks and nuns to return to secular life, and seized the works of art in order to use the metal for more secular purposes.
Buddhism came to _Korea_ officially in AD 372, and by about 525 it had penetrated the entire country. Between 550 and 664 it became the state religion and steadily grew in power, with the monks periodically dominating the rulers. Kings, princes and princesses often became bonzes and everywhere magnificent temples, statues and other monuments were erected. There were no notable developments in doctrine. Korean Buddhism was chiefly significant by acting as an intermediary between China and Japan. Apart from that it was noteworthy for the fervour with which it was practised, and for centuries all the surplus wealth of the country was expended on religious purposes.
### JAPAN
About 550 Buddhism came to Japan from Korea, as one of the constituent elements of Chinese civilization and a great statesman, Shotoku Taishi (523–621), adopted it as a kind of religion. Soon it fused with the indigenous Shintó which had at first fiercely opposed it. At first it was said, as in Tibet of the indigenous deities, that the Shintó gods are the guardians and protectors of Buddhism. Then the pantheon of the two schools was slowly identified and it was taught that they were just the same deities under different names. In the ninth century this amalgamation received the name of Ryóbu Shintó. The Ryóbu Shintó is a remarkable achievement not only for the reason that it effectively fused the two religions for the time being, but also because it fused them in such a way that 1,000 years later it was quite easy to separate them again.
This was a period of copying. Before 700 four "sects" were introduced, which were not however corporations pledged to support particular doctrines, but simply philosophical schools which expounded certain textbooks. They were the _Jójitsu_ (625) based on Kumárajíva's translation of Harivarman's "Satyasiddhi"; the _Sanron_ (625) which studied the three works of Nágárjuna and Áryadeva which were the basis of the Chinese San-lun school; the _Hossó_ (654) which has for its textbook the Yuishiki, which expounds the principles of Vijñánaváda after Yüan-tsang and K'uei-ki; and the _Kusha_ (658) which was devoted to the exposition of Vasubandhu's Abhidharmakośa. Then came the Hua-yen (730), now called _Kegon_ , which lasted for many centuries, and worshipped Vairocana, as Roshana or Birushana; and also the Vinaya sect (753) which was called _Risshú_ tried to introduce stricter rules of ordination, and declined soon.
Much more substantial were the sects introduced during the Heian period (794–1186), which was dominated by the _Tendai_ and _Shingon_ who had their centres on two mountains. The one was founded by Dengyó Daishi (767–822) who had brought the T'ien-t'ai doctrine from China, the other by Kóbó Daishi (774–835) who had learned the mysteries of the Chén-yen in Chang-an. The sacred Tendai mountains of Hieizan near the new capital of Kyótó were soon covered by no fewer than 3,000 temples or halls. The Tendai not only had a great influence on art, but all later sects arose from within it, in the sense that their founders had for a time belonged to this sect. Kóbó Daishi on his return from China not only became a great favourite at the imperial court, but he also impressed the popular imagination more than any other Japanese teacher has done. For the people he is the hero of countless legends, for his followers a manifestation of Vairocana not yet dead, but awaiting within his tomb the coming of the future Buddha.
The centre of the Shingon sect was on the lonely mountain of Kóyasan, and the performance of ritual has been its main activity, apart from the execution of paintings and sculptures of Tantric deities. Not all the monks of Tendai and Shingon resided in monasteries, and there was a strong movement within both schools to revive the ardours of the early Buddhist community, when the monks actually dwelled in the forest. There was a considerable number of Yama-bushi, "those who sleep on mountains", or Shugenja, "those who practise austerities", who lived alone or in little groups in the wild mountains and forests. On the whole, both Tendai and Shingon chiefly addressed themselves to the educated classes and their popular appeal was not very strong. To those who desired an easier way they held out the invocation of Amida's name which would lead to rebirth in the Western Paradise. Both the Nara and Heian sects built special halls for recitation of the _Nembutsu_ , accompanied by hymns and musical services. At the same time during the tenth century itinerant preachers brought the message of Amida's saving grace to the masses in a language which they could understand.
Buddhism took on the colouring of the social conditions in which it lived. The esteem in which the religion was held was to a large extent a tribute to its beneficial magical effects on the welfare of the nation. Monasteries were by their very presence preserved from the noxious influences which arise out of the earth in certain places, and the recital of the great Maháyána Sútras was regularly carried out for the purpose of averting plagues, earthquakes, and other disasters. The moral precepts, on the other hand, were not always closely observed. In the Heian period there were violent quarrels between the monasteries, who had become huge territorial magnates, and behaved as feudal institutions usually do. Organized bodies of mercenaries commanded by priests burned down each other's monasteries, and appeared in armed bands in Kyoto to force the hands of the government. Aesthetic culture was the chief note of the age, and much of its wonderful art has survived.
### TIBET
In Tibet Buddhism is said to have begun about 650, but it made real headway only a century later. At first it met with fierce resistance from the shamans of the native Bon religion, who had the support of the greater part of the nobility. The patronage of the king, however, enabled the Buddhists gradually to establish themselves, and under King Ral-pa-can (817–36) they reached the height of their influence. In 787 the first monastery was completed at bSam Yas and soon after the first monks were ordained by Śántarakshita. Everywhere temples were erected, many teachers invited from India, a script was invented and numerous works were translated. Great endeavours were made to ensure the accuracy of the translations and the terminology was standardized about 825 by a commission consisting of Indian pandits and Tibetan Lotsabas, which published the _Mahávyutpatti_ for the guidance of translators. The Bon rivals seemed defeated, the monks seized the effective rule of the country, but then under gLang-dar-ma (836–42) a persecution wiped out everything that had been gained. For about one century Buddhism once more vanished from Tibet.
The period under review is for Tibet one of reception. In the course of it four principal systems, or lines of thought, were introduced:
1. From the West, from the Swat valley, came the Tantric ideas of _Padmasambhava_ , who himself stayed in Tibet for a short while. Padmasambhava's mentality had considerable affinities with that of the Bon and he had a striking success in Tibet. He expounded some kind of Vajrayánic system, but we do not know exactly which one. The impression he made on Tibet was chiefly based on his thaumaturgical activities and the legend has quite overgrown the historical facts. The school of the _Nyincjmapa_ , or "Ancient Ones", goes back to Padmasambhava and has persisted continuously up to today.
2. From the South came the _Pála Synthesis_ of the Maháyána, brought by some of the leading scholars of the universities of Magadha. This combination of Prajñápáramitá and Tantra has become the central tradition of Tibetan Buddhism, and has renewed itself again and again up to the present day. It has always attached a special value to the _Abhisamayálankára_ , an Indian work of the fourth century, which arranges the contents of the "Prajñápáramitá in 25,000 Slokas" in definite numerical lists, that make it possible to memorize the text as a preliminary step to meditation on it, while at the same time interpreting it in the spirit of the Mádhyamikas with some admixture from the more moderate Yogácárin tradition. Frequently commented upon already in India, the Abhisamayálankára now in Tibet became the cornerstone of the more advanced non-Tantric training and innumerable commentaries have been composed on it by the learned men of Tibet.
3. Thirdly, from the South-West the Sarvástivádins also attempted to gain a foothold in Tibet. Quite early on the king invited them to establish a monastery, but their settlements soon withered away, the surrounding population remaining indifferent to a teaching which lacked in magical practices. Although they could not maintain themselves for long in this world of magic and witchcraft, the Sarvástivádins have nevertheless exerted a considerable influence on the thought of Tibet, because their literature is practically the only version of the older type of Buddhism to find its way into the Canon of translated scriptures.
4. The fourth influence came from the East. Numerous Chinese monks of the Ch'an Sect appeared in Tibet and attempted to convert its inhabitants to their tenets. They soon came into conflict with the Indian pandits of the Pála orthodoxy, and were decisively defeated at the famous Council of bSam Yas in 793–4. After that they had to leave the country, or go underground, and their influence on later Tibetan history is negligible.
## **FOUR**
## The Last One Thousand Years: AD 1000–1978
### INDIA: THE COLLAPSE AND ITS CAUSES
In India itself, Buddhism came to an end about 1200, though in some districts, as in Magadha, Bengal, Orissa and South India, it lingered on for a further 200 or 300 years.
The main cause which precipitated its disappearance was, of course, the Mohammedan invasions. In their fanatical hatred for what seemed to them "idolatry", these ruthless conquerors burned down the flourishing monasteries and universities of Sind and Bengal, and killed the monks, who offered no resistance, partly in obedience to their vows, and partly because they believed that astrological calculations had shown that the Muslims would in any case conquer Hindustan. On further consideration Muslim savagery cannot, however, be the whole explanation and that for two reasons: Firstly, Hinduism and Jainism, subjected to the same fury, managed to carry on. Secondly, in regions which were not touched by the Muslim invasions, as in Nepal and South India, Buddhism also steadily died out, though much more slowly. Hence the cause of this decline must be sought as much within Buddhism as without it.
As a _social force_ an unworldly religion can only survive if by some accident it is able to enlist the support of some powerful or wealthy section of society. If the Jains alone among the numerous ancient sects of India are still a power in that country, it is because by some accident wealthy merchants are numbered among its adherents, merchants who regard it as an honour to support the ascetics. Buddhism has generally relied on the support of kings and where that was wanting it has usually been in difficulties. It has, as we saw (p. 24), never succeeded in doing very much for the average lay follower, and therefore the monks cannot normally live on their voluntary patronage. The Buddhist laity never formed a corporate social entity, or a homogenous group living apart from the followers of the Brahminical sects, and it had throughout conformed to the Brahminical caste system and followed Brahminical rites in ceremonies at birth, marriage and death. So any weakening of the monasteries would automatically lead to the absorption of the lay followers into the closely knit social structure of Brahminism. The Jains survived because a living community existed between monks and laymen, but the Buddhists were lacking in that. The international character of Buddhism, which had enabled it to conquer Asia, also favoured its extinction in India. The Buddhist religion had always inculcated indifference to the particular country in which the monks were living, and so the surviving monks left the country in which they could no longer practise their monastic rules, and went to Nepal, Tibet, China, etc. Their less flexible and more earthbound Hindu and Jain brethren stood their ground, and in the end they survived where they were.
As a _spiritual force_ Buddhism had played itself out. There is no reason to believe that after 1,000 the Buddhist monks were any lazier or more corrupt than at any time, and in any case the history of religion knows numerous cases where corruption has been healed by reformation. In fact, when we see the calibre of the men whom the Indian foundations could still send to Tibet, it is difficult to believe in their depravity or degeneracy. But what had ceased was the creative impulse. The Buddhists had nothing new to say any more. By analogy with what happened in the first and sixth centuries, a new outburst of creative activity was due in the eleventh, and was necessary to the rejuvenation of the religion. It failed to take place.
What had of course happened was that in the course of 1,700 years of co-existence the Hindus had taken over a great deal from the Buddhists and the Buddhists likewise from the Hindus. In consequence the division between them had increasingly diminished and it was no great thing for a Buddhist to be absorbed into the largely Buddhified Hindu fold. The Buddha and some Buddhist deities were incorporated into the Hindu pantheon. The philosophy of Nágárjuna had been absorbed into the Vedánta by Gaudapáda, Śánkara's teacher, just as the Vaishnavas of later times were greatly indebted to the Buddhists. The Buddhist Tantras had provoked their Hindu counterparts, which abound with references to Maháyána deities. There had been a constant assimilation in the iconography and mythology of the two religions. It is a law of history that the co-existence of rival views must lead to some form of eclecticism. This is merely the reproduction of the effects of osmotic pressure in the intellectual field. So it was in the Greco-Roman world with the philosophical systems, and so with the political parties in England in the fifties, their main difficulty being to find something to disagree on. The same happened to Hinduism and Buddhism. The separate existence of Buddhism no longer served a useful purpose. Its disappearance thus was no loss to anyone. We must also not forget the Buddhist conviction that this is a period of religious decline. In Orissa the Buddhists said that in the inauspicious Kali Yuga the Buddhists must disguise themselves and worship Hari, waiting patiently for the time when the Buddhas will reappear.
Hostile critics generally scrutinize the collapse of Buddhism in India on the assumption that there must have been something wrong with it. "It is always so easy to flog a dead horse," as one of these historians himself admits, and Darwinian preconceptions about the "survival of the fittest" may mislead when applied to religions. Everything has its duration, its allotted life-span – trees, animals, nations, social institutions, and religions are no exception. What Buddhism in India died from was just old age, or sheer exhaustion. Nor had it ever believed that it was exempt from the impermanence of all conditioned things which it had preached so often. In fact, in their wisdom, its teachers had foreseen the coming end. For centuries the fall of the Order had been predicted for a period about 1,500 years after the Buddha's Nirvana and Yüan-tsang not only recounts many legends current in many places in India in the seventh century which showed an expectation of the coming end, but he himself had, amidst the grandeurs of Nálandá, a dream to the effect that fire would devastate this celebrated centre of learning, and that its halls would one day be deserted. So when the end came it was in no way unexpected and all that was left was to disappear gracefully from the scene.
### NEPAL AND KASHMIR
The Moslem persecutions induced many monks and scholars of Northern India to flee to Nepal, bringing their books and holy images with them. Nepal thus became a repository of Pala Buddhism. Nevertheless even the arrival of the refugees from India failed to infuse new vigour into the Buddhism of Nepal, and after AD 1000 it presents a picture of increasing decay. Royal patronage kept the Samgha alive for some time, and for a few centuries the country remained a centre of Buddhist culture. Scholars can determine the extent of the decadence by the condition of the Sanskrit manuscripts. These are very good about AD 1200, they become fair in the seventeenth century, and in the nineteenth they become so careless and slovenly that little reliance can be placed on them. Likewise the quality of the art goes steadily down and down. With the collapse of Buddhism in India the Buddhists of Nepal had to rely on their own strength. Reduced to one small valley, they capitulated to Hinduism within a hundred years or so. In the course of the fourteenth century the monks decided that the monastic rules were too difficult to keep, and they transformed themselves into a Hindu caste, calling themselves the _banras_ ("honourable ones"). They gave up their celibacy, moved into the _viháras_ with their families, and have ever since continued to earn their living as metal workers. Deprived of its elite, Nepalese Buddhism could only preserve some of the outward forms of the religion. A number of deities are worshipped in the manner of Hindu gods and for centuries lay Buddhism alone has prevailed in Nepal. The most popular deities are Matsyendranáth, "Lord Indra of the Fish", a deified Yogin, identified with Lokeśvara, and also Tárá, the "Saviouress", who, however, as the centuries passed on, has lost ground to the Śivaite Kálí.
In the popular cult the dividing lines from Hinduism have become more and more blurred. In some cases the same image does service for both, e.g. the Hindu looks upon Mahákála as Śiva or Vishnu, the Buddhist as Vajrapáni; or Hindu pilgrims at Tundiktel worship the guardian deity of Nepal, Buddhists the same image as Padmapáni.
Not that all scholarship and intellectual life has been completely extinct. Hodgson, the British Resident, tells us that early in the nineteenth century there were four philosophical schools, called the Svábhávikas, Aiśvarikas, Kármikas and Yátnikas. But, like so many other English Proconsuls, he had no taste for philosophy, refused to be drawn into "the interminable absurdities of the Bauddha system", and his account of their differences gives little sense. Curiously enough, no one since has tried to determine the points in dispute. The conquest of the country by the Gurkhas in 1768 reduced the Buddhist Newars to the status of a subject race, and that was the final blow which further accelerated the decay which was the inevitable consequence of the disappearance of the Samgha of homeless monks. In recent years missionaries from both Ceylon and Tibet have attempted to found a new Samgha in Nepal, and any revival of the religion will depend on the success of their endeavours.
In Kashmir, the last centuries of Hindu rule were on the whole years of misrule, and the years between 855 and 1338 represent a period of continuous decline and of political disintegration. Buddhism and Śivaism fused and Buddhists and Śivaites often lived together in the same religious foundations. After 1000, many Kashmiri scholars and craftsmen went to Tibet, Ladakh, Cuge and Spiti, and between 1204–13 Śákyasríbhadra, "the Great Kashmiri Scholar" was prominent in Tibet. The year 1339 marked the beginning of Muslim rule. At first that was tolerant to the Buddhists, but about 1400 the persecution began in earnest, images, temples and monasteries were systematically destroyed, religious ceremonies and processions were forbidden, and about 1500 Buddhism came to an end as a distinct faith, not without leaving strong traces on the Hinduism in that region and fainter traces even on the Muslims. For the rest everything was totally wrecked.
### CEYLON
In 1160 a council at Anurádhapura terminated the dissensions between the Mahávihára and its rivals by the suppression of the latter. Soon after 1200 there was a collapse, not so much of Buddhism, as of the social system which supported it. Invasions from India weakened the central power, which could no longer enforce the irrigation works and soon Muslim pirates and even Chinese eunuchs ruled over large stretches of the land. The economic basis of the Samgha in this way became extremely precarious. Later on, beginning in the sixteenth century, the Portuguese persecuted Buddhism, claimed to have destroyed the Sacred Tooth, and forced many Ceylonese to become Roman Catholics. Then followed the Dutch, and finally the English (until 1948). The long centuries of European rule did great harm to the Buddhist cause. The Samgha often died out completely, and monks had to be repeatedly imported from Burma and Siam, in the seventeenth, eighteenth and nineteenth centuries. The revival began about 1880, first stimulated by the Theosophical Society, and then carried out under the impulse of awakening nationalism. Since that time Ceylonese Buddhists have become increasingly active and have done a great deal of valuable scholarly work, though generally within the limits of a rather narrow orthodoxy, and in 1950 they took the lead in trying to bring all Buddhist countries together, and set up the World Fellowship of Buddhists.
### SOUTH-EAST ASIA
At the beginning of this period the Buddhism of _Burma_ changes its character, and draws its inspiration henceforth from Ceylon. In 1057 King Anawrahta of Págan conquers Thaton to take possession of the Páli Tipitaka and the relics stored there. He then has monks and scriptures brought from Ceylon, and the chronicles assure us that he "drove out" the Ari priests of the Vajrayána. There is, however, much evidence for the persistence of the Maháyána after that date. Archaeology has shown that it was during the suzerainty of the Anawrahta dynasty (1044–1283) that the Maháyána flourished most, side by side with the more popular Theraváda. Many sculptures of Maháyána deities date back to that time, Maháyána texts were found in the monasteries up to the fifteenth century, and unmistakably Tantric paintings can still be seen on the walls of temples near Págan, first in the style of Bengal, and later in that of Nepal. The Aris were certainly abhorrent to the Theravádins, because they ate meat, drank spirits, used spells to remove guilt, practised animal sacrifices and indulged in erotic practices, but nevertheless they continued to exist until the end of the eighteenth century.
The patronage of the Court went, however, to the Theravádins, and Págan, until its destruction by the Mongols in 1287, was a great centre of Buddhist culture, and witnessed during three centuries one of those outbursts of devotion of which we have seen other examples in China, Korea and Tibet. For eight miles the land was filled with 9,000 pagodas and temples, among which the most famous is the Ananda temple of the eleventh century. The 547 Játaka stories are here represented on glazed plaques.
After the collapse of the central dynasty Burma was for 500 years divided into warring kingdoms, but the Theraváda tradition continued, though less splendidly than before. The end of the fifteenth century saw the final triumph of the Sinhalese school, when king Dhammaceti of Pegu reintroduced a canonically valid monastic succession from Ceylon. In 1752 Burma was united again, after 1852 the dynasty vigorously patronized the Samgha and a Council at Mandalay in 1868–71 corrected the text of the Tipitaka, which was then incised on 729 marble slabs. The coming of the English in 1885 did much harm to the Samgha by destroying the central ecclesiastical authority. In the struggle for independence the monks played a prominent part. During recent years attempts have been made to combine Buddhism with Marxism, and also a new method of meditation has been advocated which by employing Tantric practices is said to lead to speedier results.
Burmese Buddhism is bent on preserving Theraváda orthodoxy and it has made no creative contribution to Buddhist thought. Disputes have always been confined to the externalities of the Vinaya and the extensive literature consists of works on grammar, astrology and medicine, of commentaries and of adaptations of Játakas. The thirty-seven Nats, or "spirits", are universally asked for their favours, but the chief means of acquiring merit is to build a pagoda, with the result that the country is covered with them. The Samgha is not estranged from the people, monasteries and shrines are placed near the centres of habitation, so as to be easily accessible to laymen, every layman becomes a novice for a time, and receives some education in the monasteries. The population, 85 per cent Buddhist, has been distinguished by its high degree of literacy for a long time. Buddhism has been a great civilizing force in the life of Burma, has helped to tone down racial rivalries, fostered a democratic social life by minimizing the importance of wealth and caste, brought much beauty and knowledge with it, and above all, it has created a singularly cheerful, polite and likeable people.
Theraváda Buddhism during our period likewise took over in _Thailand_ and Indo-China. The Thais brought from their home in China some form of Buddhism, but in the fourteenth century the Ceylonese Theraváda was established. The capitals – first Ayuthia (1330–1767) and then Bangkok (after 1770) – are large, magnificent Buddhist cities with immense religious edifices and great Buddhas. Buddhism is the state religion, all indigenous culture is bound up with it and the king is the "Protector of Dhamma" not only in word but also in deed. Tradition is strictly followed and the rhythmical recitation of Páli texts is greatly stressed. Petitions, as in Burma, are not directed to the Buddha but to local genii and tree spirits.
Whereas in the eleventh century the Tantrayána still flourished in _Cambodia_ , after 1300 the Theraváda as a result of the Thai pressure slowly replaced it and in the fifteenth century the Ceylonese orthodoxy was imported. Also here the education is in the hands of the monks and Buddhism has proved itself an elevating and ennobling influence, and has produced a mild, kindly and helpful people. The _Neaca-ta_ , or spirits of the land, also play their part and there is some blending of influences from China (e.g. the presence of Mi-lei-fo in the temples) and from India (e.g. the Nágas, Garudas and four-faced Śivas found in architecture). The history of Buddhism in _Laos_ is shrouded in legend. It seems to have been introduced in the fourteenth century by Khmer immigrants, and at present is of the Siamese type, with greater emphasis on the Nágas. _Annam_ finally, independent since 1000, is culturally a part of China, and the Maháyána has existed there for a long time.
In _Indonesia_ Tantric Buddhism persisted until it was suppressed by Islam, in Sumatra at the end of the fourteenth century, in Java from the fifteenth century onwards. Its final collapse was preceded by a slow decline in the Hindu impact on the culture and a re-assertion of the more indigenous elements. The Tantrism prevalent in this period was an extremist form, which enjoined the practice of the five makáras, "free from all sensualities", and regarded Vairocana as the primordial Buddha. It syncretized the Kálacakra with the devotion to Śiva Bhairava into a cult of _S_ O _iva-buddha_ and, in keeping with the native Indonesian tradition, it was chiefly devoted to the redemption of the souls of the dead. Some of the loveliest pieces of Buddhist sculpture were made in Java under the dynasty of Singhasari (1222–92), which represented its kings on statues as Amoghapáśa, Aksobhya, etc., and its queens as Prajñápáramitá, etc.
### CHINA AND KOREA
Although the Sung emperors were on the whole well disposed towards Buddhism, its vigour declined during this period. After about AD 1000 two schools ousted all the others, the Amidism of Faith, and the meditational school of Ch'an. Within Ch'an, five lines of transmission, called the "Five Houses", had taken shape. All Ch'an Buddhists alike believe that one's own heart is the Buddha, but there are obviously great differences in the hearts of men and these must inevitably reflect themselves in different methods and approaches. What therefore differentiated the "Five Houses" were less differences in doctrine than differences in style. Three of the five, the _Wei-yanci-tsung_ , the _Yün-men-tsung_ and the _Fa-yen-tsunij_ , died out already by the middle of the Sung period. Characteristic of the Wei-yang sect was a special method of teaching by drawing various circles in the air or on the ground; the Yün-men sect generally resembled the Lin-chi, but one of its special devices was the reply to questions with one single word of one syllable; the Fa-yen was more favourable to the study of the Sútras than the other Ch'an sects and the influence on it of the Hua-yen doctrines was particularly marked.
The two schools which have survived to the present day are the _Ts'ao-tung-tsung_ , founded by Tung-shan Liang-chieh (807–69), and the _Lin-chi-tsung_ , which goes back to his contemporary Lin-chi-I-hsüan (died 867). The differences between these two, which had been just distinctive tendencies so far, hardened into different sects in the proper sense of the term only about 1150. The Ts'ao-tung was always characterized by quietism and Hung-chih Cheng-chüeh (died 1157) gave it the special name of _Mo-chao cb'an_ "silent-illumination Ch'an". This indicated that the school stressed the quiet sitting still in silent meditation, by or in which enlightenment, or spiritual insight into absolute emptiness, is attained. The founder of this sect was mild and gentle in his methods. He also bequeathed to his school a special doctrine concerning the "Five Ranks", which distinguishes five stages of the movement towards enlightenment in a thoroughly Chinese manner which was greatly indebted to the Book of Changes, and the stages were represented by white and black circles. Four doctrines are mentioned as characteristic of the Ts'ao-tung: (1) All beings have the Buddha-nature at birth and consequently are essentially enlightened; (2) They can enjoy fully the Bliss of the Buddha-nature while in a state of quiet meditation; (3) Practice and knowledge must always complement one another; (4) The strict observance of religious ritual must be carried over into our daily lives. The founder of the Lin-chi sect by contrast favoured the use of rudeness and abruptness and the "shout and the stick" played a great part in the practices of this school. It was the most hostile of them all to rationalization and the most emphatic in stressing the suddenness and directness of Ch'an experience.
During the Sung the Ch'an school became a cultural factor of great importance. Many Ch'an monks were found among the painters of the period, and its influence on art was considerable. Even the Neo-Confucian Renaissance of Chu-hsi and others owed much to Ch'an Buddhism, just as the Vedantic Renaissance of śankara had been greatly indebted to Maháyána Buddhism. The practice of _tso-ch'an_ , quiet contemplation, so important in Ch'an, found its way into the practices of Confucianism as _ching-tso_ , or "quiet-sitting". This outward success brought its dangers and led to a deep crisis within Ch'an. The Tang masters had always avoided the capital, but now the Ch'an monasteries maintained excellent relations with the Court and meddled much in politics. Magnificent Ch'an monasteries arose throughout the country and became focal points of social and cultural life. Many concessions were made to intellectualism and to the study of the Sútras, and within the Ch'an camp a vigorous controversy arose about their importance.
Most radical in its rejection of the authority of the Sútras was the Lin-chi, which countered the impending decadence by evolving the _kung-an_ system. The word _Kung-an_ consists of two characters, for "government" and "legal case" and denotes a precedent or authoritative model. In practice a _kung-an_ is a riddle, usually connected with a saying or action of one of the Tang masters. Collections of such _kung-ans_ were now published and to each was added an explanation which deliberately never explained anything at all. The first example of this new literary genre was a collection of 100 riddles, called the _Pi-yen-lu_ , which appeared in 1125. The other famous collection is the "Careless Gate", or _Wu-men-kuan_ , comprising 48 cases, and which appeared more than a century later. In opposition to the quietism advocated by the Ts'ao-tung, the Lin-chi advocated ceaseless activity on the chosen _kuncf-an_ which must be carried on until sudden enlightenment supervenes. As Ta-hui tsung-kao (1089–1163) put it: "Just steadily go on with your _kung-an_ every moment of your life! Whether walking or sitting, let your attention be fixed upon it without interruption. When you begin to find it entirely devoid of flavour, the final moment is approaching: do not let it slip out of your grasp! When all of a sudden something flashes out in your mind, its light will illuminate the entire universe, and you will see the spiritual land of the Enlightened Ones fully revealed at the point of a single hair and the wheel of the Dharma revolving in a single grain of dust." In Sung times systematic method thus replaced the individualistic spontaneity of the T'ang masters. But it was this systematization and to some extent mechanization which assured the survival of Ch'an.
Whenever philosophical schools coexist for any length of time, the result will be an increasing syncretism between them. In many ways Ch'an was combined with Huayen and T'ien-t'ai, and the practice of the _Nembutsu_ was often brought in to strengthen the Ch'an meditation. During the Yüan and Ming dynasties a fairly complete fusion of the different trends of Chinese Buddhism actually took place. The Ming and Manchus favoured Confucianism, but tolerated, and occasionally encouraged Buddhism. Two emperors, Yung-cheng (1723–35) and Ch'ien-lung (1736–95), tried to create a type of Buddhism which combined Chinese Buddhist (Fo-ist) and Lamaist elements, thus appealing to Chinese on the one hand, and Tibetans and Mongols on the other. The Yung-ho-kung, the Lamaist Cathedral in Peking, is a visible monument to these endeavours and in it the deities proper to these two types of Buddhist cult are carefully blended. Even Kuan Ti, the Chinese War God, and Confucius are there enlisted among the Bodhisattvas. The prosperity of the monasteries has never recovered from the Taiping rebellion of the "long-haired Christians", who for fifteen years (1850–65) devastated sixteen provinces, destroyed 600 cities, and thousands of temples and monasteries. Nevertheless, until the present day Buddhism has remained a by no means negligible factor in the cultural and religious life of China.
In _Korea_ , Buddhism reached the height of its power under the Koryo dynasty, particularly between 1140 and 1390. The founder of the dynasty was a pious Buddhist, who attributed his success to the Buddha's protection. His successors never wavered in their support of the religion. Each king chose a bonze as his "preceptor", or advisor. The holy scriptures were carried in front of the kings when they travelled. Fine editions of the Canon were printed at the expense of the state, one of them comprising 81,258 leaves. For long stretches of time the government was entirely in the hands of the bonzes. Up to the twelfth century the aristocracy had been the main support of Buddhism, but now it became the religion of the common people as well. Strong magical elements entered into Buddhism, as has happened to this religion wherever it became really popular. Many bonzes became experts in prolonging life, in working miracles, evoking spirits, distinguishing between auspicious and inauspicious times and places, and so on. In 1036 an edict abolished the death penalty and decreed that out of four sons one must become a monk. The Koryo dynasty expended much wealth on magnificent religious ceremonies and buildings, and innumerable works of art were created under it. During the Yüan dynasty, especially after 1258, Lamaism exerted a considerable influence. In the fourteenth century the Buddhists dominated Korea almost completely. In 1310 it was decreed that the monks need not salute anyone whereas everyone else must show respect to them. Those who had chosen the religious life were exempt from all material cares.
The excessively privileged position of the Church came to an abrupt end with the change of the dynasty in 1392. Confucianism now gained the upper hand, the monks were deprived of official support and a share in political life, their lands were confiscated, they were forbidden to pray at funerals, the twenty-three convents existing in Seoul were closed, and Buddhism was generally discouraged. As a religion of the masses it nevertheless persisted, away from the cities, in the rather inaccessible Diamond Mountains. Doctrinally, this Buddhism was the usual Chinese mixture of Ch'an, Amidism and local superstitions. Between 1910 and 1945 the Japanese fostered Buddhism, but it remained in a rather debilitated condition. In 1947, about 7,000 monks were counted in Korea.
### JAPAN
During this period a second flowering of Buddhism took place in Japan. Between 1160 and 1260 new sects arose which entirely changed its character, and Japanese Buddhism now reached the height of its originality and creative power. In the Kamakura period (1192–1335) the Amida schools and Zen came into the foreground, just as they did in China after AD 1000.
The first _Amida_ sect, known as the Yúzú Nembutsu, was founded already in 1124 by Ryónin, who saw the way to salvation in the constant recitation of the "Nembutsu", i.e. of the formula _Namu Amida Butsu_ , up to 60,000 times a day. He also taught that this invocation was infinitely more meritorious if repeated on behalf of others than for one's own selfish ends. His sect, though still in existence, never commanded a large following. Far more influential was the Jódó, or "Pure Land", school, founded by Hónen (1133–1212), an exceptionally learned and gentle priest. In 1175, at the age of forty-three, Shan-tao's works led him to the conclusion that the traditional Buddhist moral and mental disciplines were no longer effective in this age of decay. Whatever in such an age we may do by our own efforts ( _jiriki_ ) is of no avail. Peace can only be found through the strength of another ( _tariki_ ), in self-surrender and in reliance on a higher power, that of the Buddha Amitábha. Hónen therefore abandoned all other religious practices, and devoted himself exclusively to the recitation of Amida's name. All that matters is to "repeat the name of Amida with all your heart – whether walking or standing still, whether sitting or lying, never cease to practise it for even a moment!" In these evil days the only way to obtain salvation is to strive to be reborn in Amida's "Western Paradise" (Jó-dó), and the "holy path" (shó-dó), consisting of good works and religious exercises, no longer works. A simple faith in Amida is all that is needed. It will carry even the greatest sinner into Amida's Blessed Land. Hónen drew, however, no antinomian inferences from this assertion and enjoined his followers to avoid sin, to observe the monastic regulations, and also to show no disrespect to the other Buddhas and to the Sútras. His teaching had an instantaneous success at the Court, among the aristocracy, the Samurai and the clergy, and the new movement maintained itself easily against the hostility of the older sects. The Jódó school has continued to the present day without much modification. But in the fourteenth century the seventh patriarch Ryóyó Shógei made an interesting and influential re-interpretation. Rebirth in the Pure Land, so he said, does not mean that one is transported into another region, but the Pure Land is everywhere, and to go there is a change of mind and condition, and not of place. This is very much in agreement with the tradition of Maháyána.
A further simplification of Amidism was effected by Shinran (born 1173), one of Hónen's disciples, and the founder of the _Shin_ sect, the word _shin_ being an abbreviation of Jódó Shinshú, "the True Jódó Sect". Shinran broke with the monastic traditions, got married and advised his followers to do likewise. He regarded the constant repetition of the _Nembutsu_ as unnecessary, and asserted that to call on Amida once only with a believing mind was sufficient to secure birth in His Paradise. The faith in Amida is, however, Amida's own free gift. As to the problem of morality, Shinran maintained that a wicked man is more likely to get into Amida's Land than a good man, because he is less likely to trust in his own strength and merits. The clergy of this sect disclaimed all learning, but as the teachings lend themselves to misunderstanding, great theological subtleties were evolved in the course of time. The devotional practices of this and other Amida schools led to the multiplication of images of Amida, to whom also hymns ( _wasan_ ) in Japanese were written. Shinran aimed at breaking down the barriers between religion and the common people, and in fact the Shinshú became one of the most popular sects and has remained so to the present day.
Less successful was the third Amidist sect, founded by Ippen in 1276, and called the Ji, or "the Time", to indicate that it was the proper religion for these degenerate times. In the tradition of the Ryóbu-Shintó he identified a number of Shintó deities with Amida, but as for the _Nembutsu_ Ippen even regarded faith as unnecessary, for is it not an activity of the corrupt human mind? The recitation of Amida's name is effective as a result of the sound alone, _ex opere operate_ , as it were.
The fourth devotionalist sect, founded in 1253 by Nichiren, the son of a fisherman, differs from all other Buddhist schools by its nationalistic, pugnacious and intolerant attitude and it is somewhat doubtful whether it belongs to the history of Buddhism at all. The patriotic fervour of Nichiren is accounted for by the fact that nationalist sentiments had at that time been greatly inflamed by the longstanding threat of Mongol invasion, which was finally dispelled by the repulsion of Khubilai's armadas in 1274 and 1281. Nichiren replaced the _Nembutsu_ with the formula Namu _Myóhó Renge-kyó_ , "Homage to the Sútra of the Lotus of the Good Law", and declared that this phrase alone was suitable for this, the last period of Buddhism, which is that of _mappó_ , "the destruction of the Law", and which according to him began about AD 1050. Nichiren always spoke with the vehemence of a Hebrew prophet and demanded the suppression of all sects except his own. "For the Nembutsu is hell; the Zen are devils; Shingon is a national ruin, and the Risshú are traitors to the country." On this occasion Buddhism had evolved its very antithesis out of itself.
As for the _Zen_ school, Eisai (1141–1215) introduced the Lin-chi sect into Japan, where it became known as _Rimai_ , and attained a great success, whereas the Ts'ao-tung, or Sóto, was first introduced by Dógen (1200–33), and then organized and popularized by Keizan Jokin (1268–1325). Dógen's principal work, "The Eye of the True Law", was written in Japanese, so that all could read it. He insisted that, although his generation clearly belonged to the decline of Buddhism, this was no reason for heroic spirits to aim at less than insight into the highest Truth. Against the intellectualist distortions of Buddhism he maintained that "attainment of the Way can only be achieved with one's body". _Zazen_ , or "sitting cross-legged", is not a set of meditational practices in which one waits for enlightenment to come, but enlightenment is an inherent principle of Zen meditation from the outset, and it should be carried out as an absolutely pure religious exercise from which nothing is sought and nothing is gained. Everything is the Buddha-nature, and that in its turn is nothing more than "the chin of the donkey or the mouth of a horse". The Sótó sect claims that in Japan it went beyond the developments the parent sect had reached in China, and it gives as an instance of this its belief that, because man is already enlightened from birth, all daily activities should be regarded as post-enlightenment exercises, which should be performed as acts of gratitude to the Buddha ( _gyojiho-on_ ).
Zen soon spread among the Samurai, particularly in its Rinzai form, in accordance with the proverbial saying that "Rinzai is for a general, and Sótó for a farmer". In this way Zen led to the cult of _Bushido_ , the "Way of the Warrior", and this close association with the soldier class is one of the more astonishing transformations of Buddhism. Zen did much to stimulate the innate Japanese sensitiveness to beauty ( _mono-no-aware_ ). As Ch'an had done in China, so Zen in Japan from the end of the Kamakura period onwards greatly stimulated not only architecture, sculpture, painting, calligraphy and pottery, but also poetry and music. The close bonds between Zen and the Japanese national character have often been stressed. Buddhist literature was further enriched by two new literary forms, the Noh drama and the so-called "farewell songs". In a culture dominated by the Samurai, death was an ever-present reality, and to overcome the fear of death became one of the purposes of Zen training. Under the Ashikaga Shoguns (1335–1573) Zen had the support of the government. Its cultural influence was then at its height and it could spread among society in general because it emphasized concrete action rather than speculative thought. Actions must be simple, and yet have depth, and "simple elegance" ( _wabi_ or _sabi_ ) became the accepted ideal of conduct. In the sixteenth century the tea ceremony was systematized by Zen masters. At the same time many artists believed that "Zen and art are one", Sesshu (1420–1506) being the best-known among them.
After 1500 things were no longer going so well with Japanese Buddhism. Its creative power had waned, and now its political power was broken. Nobunaga destroyed the Tendai stronghold on Hieizan in 1571, and Hideyoshi the great Shingon centre at Negoro, in 1585. Under the Tokugawa (1603–1867) there was a revival of Confucianism and later on, in the eighteenth century, of militant Shintoism. Buddhism receded into the background, the organization and activities of the monks were carefully supervised by the government, which assured the income of the Church while doing everything to prevent any independent life from developing in it. Buddhism sank into a torpid condition. The traditions of the sects, were, however, maintained. The Zen sect alone showed some vitality. In the seventeenth century Hakuin introduced new life into the Rinzai sect, which regarded him as its second founder; the poet Basho evolved a new style of poetry; and in 1655 a third Zen sect, the Óbaku, was imported from China and has always retained marked Chinese characteristics.
In 1868 Buddhism was to a great extent disendowed and for a short time it seemed that it would die out altogether. After 1890, however, its influence has again increased steadily and in 1950 two-thirds of the population were connected with one or the other of the chief sects. The adaptation to modern life and to the competition with Christianity has gone further than in any other Buddhist country so far. In recent years, Japanese Zen has aroused great interest in Europe and America and in D. T. Suzuki it has found a very fine interpreter.
### TIBET
About the year 1000 a revival of Buddhism took place, initiated by a few enthusiasts who lived in the utmost East and West of the country, where the pressure of persecution was least felt. They soon re-established contact with India and Kashmir, which some of them visited themselves, and also Indian teachers were again invited. The most outstanding personality among these revivers was Rin-chen bzang-po (958–1055), who was prominent not only as a translator, but also as a builder of temples and monasteries in Western Tibet. Of decisive importance was also the coming of Atíśa in 1042, who left Vikramaśílá at the invitation of the king of Western Tibet, and later on established the Pála Maháyána also in Central Tibet. The year 1076 saw a great council in mTho-ling, in West Tibet, where lamas from all parts of Tibet met, and this year can be regarded as marking the final establishment of Buddhism in Tibet.
Atíśa's services were not confined to the re-establishment of the religion throughout the length and breadth of the country. He also created a system of chronology which is still used in Tibet, and which defines each year by its position in a cycle of sixty years, which results from combining five elements, viz. earth, iron, water, wood and fire with the twelve animals of the zodiac, i.e. dog, boar, mouse, ox, tiger, hare, dragon, serpent, horse, sheep, monkey and bird. Without this chronological system the work of the historians, which later on forms one of the glories of Tibetan literature, would have been impossible. This was not all. It is one of the difficulties of Buddhism as a doctrine that it is so profuse in its teachings and methods, that a guide to them and a classification is desirable. Atíśa provided this in his "Lamp illuminating the road to enlightenment", in which he distinguishes the practices according to three levels of spiritual development. The lowest are those who seek happiness in this world and consider only their own interest; the second are those who are also intent on their own interest, but more intelligently, by leading a virtuous life, and seeking for purification; the last are those who have the salvation of all at heart. The full fruits of this manual came only 300 years later, with Tsong-kha-pa.
The next 400 years saw the formation of Tibetan sects, founded by Tibetans themselves and adjusted to their mental and social conditions. Each of them excelled in one of the things which make up the Buddhist spiritual life. The sects differ in their monastic organization, in their dress, in the tutelary deities, in their interpretation of the Ádi-Buddha, in the methods of meditation they prefer and so on. But they have interacted on one another, and much mutual borrowing has taken place.
The first of these sects were the _Bka-ijdam-pa_ , founded by 'Brom ston, a pupil of Atíśa, about 1050. They derived their name from the fact that they followed the "authoritative word" of Atíśa as laid down in his book on the "Road to Enlightenment". They represent the central tradition of Tibetan Buddhism, and form the link between the Indian pandits of the first period and the Yellow Church which dominated Tibet after 1400. They paid great attention to morality and monastic discipline, were strictly celibate, and produced many saintly and learned men.
A much closer contact with the life of the people was achieved by the _bKa-rclyud-pa._ Founded by Mar-pa (1012–97) they became in the course of time the most Tibetan of all the sects. For some time they possessed some worldly power, but always less than the Saskyapa and Gelugpa. They aimed not so much at theoretical knowledge as at its practical realization. They are still one of the strongest "unreformed" sects, and regard marriage as no bar to sanctity. The biographies of their teachers show us no stock saints, but human beings as they actually are, with all their imperfections and foibles. From their ranks came Mila-ras-pa (1040–1123), Tibet's greatest and most popular saint and poet, a direct disciple of Marpa. Everyone in Tibet has heard some of his famous "One Hundred Thousand" songs, and everyone is familiar with the main events of his life. How he learned the black arts and revenged himself on his family's enemies by making a house collapse on them, and smashing their fields with a hailstorm. How he soon realized his guilt, feared to be reborn in hell, and sought purification by the "direct methods" of the Vajrayána. How in his thirty-eighth year he found Marpa, who for six years tormented him, so as to allow him to work off his evil deeds. How, when he was forty-four, he was held ripe for initiation, and how he then spent the remaining thirty-nine years of his life as a hermit on the high Himalayas near the Nepalese border, or wandering about and converting people, until he died from drinking poisoned milk, the gift of a jealous lama. Some of the most dramatic scenes of his life took place in the first years after his initiation, when he lived alone in a cave, ate only herbs until he turned green, and never wore more than his thin cotton cloth in the icy cold of the winter. His indifference to property and comfort, as well as his benevolence towards all that lives, never left him. The rich literature of this sect consists largely of short books aiming at teaching the practice of various kinds of Yoga. In their desire to be practical they have always given special attention to _gtum-mo_ , the art of creating "magical heat", without which life in the hermitages would be impossible. This is also something which the average person can appreciate, and which can convince him of the truth and effectiveness of Yoga.
A special form of the Prajñápáramitá doctrine was confined to a small elite, to the _Shi-byed-pa_ ("The Pacifiers") founded about 1090, who had a far greater religious than social significance. They were less well organized than the other sects, and consisted of loose groups of Yogins or hermits or mystics, who devoted themselves to solitary meditation. Their teaching was originally inspired by Pha-dam-pa, an Indian teacher from South India, who in his turn owed much to the doctrines of Áryadeva, the Mádhyamika. It is a Tantric adaptation of the essential spiritual message of Buddhism. The spiritual life consists of two stages: (1) purification, by cutting off the passions, and (2) pacification, which consists in the removal of all suffering and the attainment of even-mindedness. For the first they relied on meditational practices which aimed at driving away the evil spirits which tempt us to commit unwholesome thoughts and for the second they relied largely on the repetition of mantras, such as that of the "Heart Sútra" which appeases all ill, or of short sayings, such as "illness", "joy", "death", and "pleasure". The greater splendours of priestly power should not blind us to the quiet work of these unworldly people.
More worldly were the _Sa-skya-pa_ , who derive their name from the monastery of Saskya which had been founded in 1073. They provided the counterweight to the Bka-gdam-pa and Shi-byed-pa by excelling in social organization. After the destruction of the monarchy, Tibet was without a central authority. The Saskya abbots now took over the reins of government, each one handing the rule to his sons. 'Phags-pa (1235–80) was one of the most prominent among these new hereditary rulers of the whole of Tibet and his position as such was recognized by the emperor Khubilai. The sect has produced many men of great learning, it is still in existence, but it lost its worldly power long ago. The power was bought by an increase in worldliness and the monks of the great monasteries, like those of Japan at the same time, formed themselves into great hordes who fought battles among themselves, sacked each other's monasteries, and behaved in a manner unworthy of their professed teachings.
We are not really sufficiently informed about the very powerful _Nying-ma-pa_ sect, the followers of Padmasambhava, to know how they survived the long persecution. Quite possibly many of them did so in the guise of Bon priests. Nor can we be sure what in their doctrines is actually due to later developments and what to Padmasambhava himself. The organization of the sect seems to go back to 1250, and is the work of Gu-ru Chos dbyang. The Nyingmapas themselves distinguish two stages of their tradition, the sayings ( _bka'-ma_ ) of the Indian masters, and the "Buried Treasures" ( _gter-ma_ ), which were scriptures hidden by Padmasambhava or the Ádibuddha. Between 1150 and 1550 a considerable number of _gtermas_ were unearthed, and their discovery made it easy to camouflage religious innovation. The biography we have of Padmasambhava was thus "discovered" about 1350. Many of these _gtermas_ do, however, preserve traditions of great antiquity, as is particularly obvious in the famous "Book of the Dead" ( _bar do thos grol_ ).
The Nyingmapa distinguish six kinds of _bardo_ , or of experiences which are "intermediary" in the sense that they are somewhere in between this world of ordinary sensory awareness on the one hand, and the purely spiritual realm of Nirvana on the other. The first three occur (l) in the womb during the months which precede birth, (2) in certain kinds of controlled dreams, and (3) during deep trance. The other three _bardos_ are in addition "intermediary" in the sense that they take place in the interval between death and reconception, which is said to last forty-nine days (see p. 24). During that time the ordinary physical body is replaced by a kind of subtle or "ethereal" body. The "Book of the Dead" graphically describes in some detail the visions which are likely to befall those steeped in the traditions of Lamaism during that period. This work has preserved some of the ancient Stone-age knowledge about life after death and shows surprising similarities to other traditions found in Egyptian, Persian and Christian writings. Very old is also the ceremony of _gCod_ , about which we know from a description of a fourteenth century author, and which aims at "cutting off" all attachment to self by offering one's body to the greedy demons on a lonely and deserted site.
The Nyingmapa differ from the other sects in that they utilize that which is generally discarded, like anger or lust, and also the physical body, which is generally looked upon as a shackle and a source of evil, is used here as a means to further an enriched life of the spirit. On the whole their ideas are in keeping with those of the left-handed Tantra in India. The order of their practice is (1) the mental creation of tutelaries ( _yi-dam_ ) with the help of mantras, visions and the "sky walkers" (see p. 64); (2) the control of the occult body, with its arteries, semen virile, etc.; (3) the realization of the true nature of one's own mind. Samantabhadra, the celestial Bodhisattva corresponding to Vairocana, is the source of the highest revelation about the third stage. "Suchness, including yourself, is not intrinsically entangled – so why should you try to disentangle yourself? It is not intrinsically deluded – so why should you seek the truth apart from it?" The repression involved in Buddhist morality is thus rejected. A well-rounded personality does not suppress lust, anger, etc., but puts them into their proper place. In its highest teachings this school has great affinity with the Ch'an sect, in that the highest form of Yoga consists in realizing the true nature of one's own mind. Like the Ch'an school it also speaks of enlightenment in a somewhat non-Indian sense (see p. 81). The man who has won Nirvana here and now, and whose actions are free from causation, is able to make his body vanish in a rainbow. The Nyingmapa concentrated on esoteric teaching and personal realization, and preferred intuitive insight to communicable knowledge. Until about a century ago they had no academic studies in the Gelugpa sense. Then they were in some places introduced in imitation of their rivals.
This sect has continually struggled for power against the others, and although it has several times attempted to gain control of the country, it could never hold it. This was due less to the greater spiritual power of their more virtuous rivals, than to their superior political gifts. So great is the hold of the Nyingmapa over the people that the other sects must make concessions to them. Many of their magical practices are suspect to the other Buddhists not so much because they regard them as ineffective, but because they seem to show an undue concern for worldly well-being. When the Gelugpas want to foresee the future, they normally do not do so themselves but employ an oracle-priest belonging to the ranks of the "Ancient Ones". The Nyingmapas have absorbed many Bon teachings, and it is in their midst that Buddhism and Bon continuously interact. The fact that they go down to the lowest has often been held against them. There is, however, no reason to doubt that in spite, or perhaps because, of that they were as capable of winning the highest as their "purer" colleagues were.
The victory over the Nyingmapa finally went to the _Dge-lugs-pa_ , "The Virtuous Ones", the sect founded by Tsong-kha-pa (1327–1419), the last great thinker of the Buddhist world. He was a reformer who carried on Atíśa's work, insisted on the observance of the moral precepts and monastic rules, strictly regulated the daily routine of the monks, reduced the weight of magic by stressing the spiritual side of Buddhism and founded the "Yellow Church", which ruled Tibet until 1950. He was a very great scholar and in every way he tried to find a position between the extremes, to avoid one-sidedness and to attain an encyclopaedic universality. His influence was perpetuated by many pupils, by the foundation of rich and powerful monasteries and by the sixteen volumes of his Collected Works. Among these we must mention two compendia which show the way to salvation, the one through the six Maháyánistic perfections, the other through Tantric practices. The first, "The Steps which lead to Enlightenment", is modelled on Atíśa's manual (see p. 109) but greater attention is accorded to those who are not particularly gifted. After his death Tsong-kha-pa became the object of a fervent religious cult, and he is believed to reside now in the Tusita heavens, as future Buddhas do.
Apart from the formation of indigenous schools, three great achievements are to the credit of the Tibetan Buddhism of this period. First there is the _codification_ of _the canonical literature_ in two gigantic collections, the Kanjur ( _bka-'gyur_ ) for the Sútras in the thirteenth, and the Tanjur ( _bstan 'gyur_ ) for the Sástras in the fourteenth century. The Kanjur was printed for the first time in Peking about 1411, and both collections were printed in Tibet for the first time in sNarthang in 1731 and 1742 respectively. Many other editions followed, and the Canon in the comprehensive, accurate, authoritative and easily accessible form which it achieved between the thirteenth and eighteenth centuries has formed the backbone of all Buddhist studies in Tibet.
Secondly there is the production of an enormous indigenous literature – of manuals, commentaries, sub-commentaries and so on. In one field of literature the Buddhists of Tibet have excelled all others, and that was the writing of History. This historical interest is connected with the way in which the Tibetans see the development of Buddhism in relation to the historical Buddha. The full import and meaning of the Buddha's Dharma, so they believe, has revealed itself over many centuries, and the many facets of its infinite richness were grasped by His followers only very slowly, over a period of 1,500 years. It is a curious fact that it was not an Indian but a Tibetan who wrote the best history of Buddhism in India. Bu-ston's (1322) "History of Buddhism in India and Tibet" (chos-'byun) is indeed a masterpiece of its kind, comprehensive and marked by deep philosophical understanding. The first volume gives a survey of the Scriptures; the second deals with the "twelve principal events in the life of the Buddha Śákyamuni", followed by the "three rehearsals of the doctrine", and so on up to the "prophecies about the disappearance of the doctrine" in India, and its continuation in Tibet, the third volume gives an introduction to the Narthang edition of the Canon, followed by a systematic table of contents. Many other first-class works deal either with the history of Buddhism in Tibet, or that of the different sects.
Thirdly, the Buddhist Church became firmly rooted in the life of the people. In the course of the fifteenth century the disciples of Tsong-kha-pa adapted to the needs of social organization the old Buddhist doctrine according to which the Buddhas, saints and Bodhisattvas could conjure up phantom bodies, which to all intents and purposes are indistinguishable from ordinary bodies, and which they use as a kind of puppet to help and convert others. They are in no way "incarnations" of the saint in question, but free creations of his magical power, which he sends out to do his work, while he himself remains uncommitted. In the fifteenth century the Gelugpas gave a concrete form to this teaching by claiming that certain Bodhisattvas (like Avalokiteśvara and Maitreya) and Buddhas (like Amitábha) would send into certain places, such as Lhasa, Urga, and so on, a certain number of phantom bodies ( _sprul-sku, Tulku_ , see p. 39) to act as their priestly rulers. In addition they thought it possible to rediscover the phantom body of the deceased ruler in a child conceived forty-nine days after his death. The rule of the _Tulkus_ , carefully chosen by skilled monks on the basis of rules as elaborate as those which enable the Congregation of Rites to distinguish genuine from spurious miracles, was the distinguishing feature of the Lamaist world during the last 450 years. It brought with it a great measure of social stability and up to 1950 protected Buddhism effectively from the inroads of modern civilization. What is more, Lamaism has proved surprisingly immune against the upsurge of popular cupidity which accompanied the breakdown of the old order in Asia. In Lamaist Ladakh the loyal tenants of monastic lands in 1953 resisted the expropriation of the monks. The Indian State Government sent a Commission which reported that "it was rather surprising that the tenants who were likely to gain by the operation of the Act (abolishing the big landed estates) on the lands attached to the _gumpas_ have unanimously decided that these lands should remain attached to the _gumpas_ and be free from the operation of the Abolition Act" (pp. 30–1 of the _Report of the Waiir Committee_ ).
The Buddhists had often before attempted to combine both secular and spiritual power in their hands. This was the first time they succeeded in doing so. The advantages are obvious. Conditions favourable to a religious life can be assured, militarism reduced to a minimum, animals protected, acquisitiveness discouraged, noise and unrest suppressed. The undisputed rule of the Lamas was backed up by the universality of their intellectual interests, which can be seen in the programme of studies pursued by the Gelugpas, by a pantheon which was extensive and comprehensive, and by the omnipresence of the objects of faith.
Nevertheless, in spite of this outward success, a religious decline set in after the seventeenth century. The Great Fifth Dalai Lama's (1617–1715) habitual reliance on violence boded ill for the future. The Lamaist system gradually became fossilized. Up to the eighteenth century foreign influences had been welcomed and encouraged. From then onwards the country was shut off and this measure not only reflected the policy of the Peking government, but also a certain inward timidity. The decline shows itself clearly in the works of art, which from now on show more mechanical competence than creative genius. Rare, though still discernible, are the traces of the qualities which had marked Tibetan art at its height – with its fire and almost magical fascination, its overpowering compassion and horror, its ethereal lightness and demonic compulsion, and its nearly superhuman skill in the handling of proportions and colours. For a long time geographical inaccessibility and the rivalry of the powers prevented the country from being conquered. Now modern civilization flows in. Roads, medicine, land reform and the development of natural resources have begun their work, with consequences quite disastrous to religious traditions.
### MONGOLIA
The Mongols were twice converted by the Tibetan hierarchs, first in 1261 by the Saskya ruler 'Phags-pa, then again in 1577 by the Dalai Lama. In the interval between 1368 and 1577 they had reverted to their native shamanism. It was the Tibetans' ability to work magic which most impressed the Mongols. Marco Polo tells us wonderful things about the various magical tricks the Lamas performed at the court of the Great Khan, and later on, when the Dalai Lama journeyed to Altan Chagan, ruler of the Eastern Mongols, he everywhere showed his magical powers, forced rivers to flow uphill, made springs well up in the desert, and the traces of his horse's hooves formed the _Om mani padme húm._ As a result of the Mongol conversion to Buddhism the Lamas took over many of the magical rites which formerly the shamans had performed. Buddhist respect for life was enforced by legislation forbidding the shamanistic sacrifices of women, slaves and beasts, and restricting hunting.
In consequence of the first conversion, Lamaism shared in the wealth of the Mongol Empire, could establish many monasteries and sanctuaries in China, particularly in Peking, and acquired great power under the Yüan dynasty (1260–1368). The second conversion was followed by a religious fervour which shows what hold the Buddhist religion can have over the mind of a nation. There seemed to be no limits to the piety of the Mongol people. The holy scriptures were translated into Mongol and many thousands of often splendid monasteries were built, which contained up to 45 per cent of the male population and were not infrequently centres of considerable intellectual activity. In the thirteenth century the conquest of Iran by the Mongols had led to the establishment of centres of Buddhist culture in Iranian lands for about half a century before the Il-khanid rulers became Muslims in 1295. After their second conversion the Mongols spread Buddhism to other nomadic populations, like the Buryats and Kalmuks. Urga became a great centre of Lamaism. The last Hutuktu died in 1924, and his functions were taken over by the Mongolian People's Republic. For 300 years the devotion of the Mongols to Buddhism had been distinguished by the intensity of its fervour, and because their deep faith had not counted the cost a certain degree of national exhaustion ensued, as in the parallel case of Korea in the fourteenth century. It is only natural that now they should have turned to something else.
### THE PRESENT SITUATION
During the last century Buddhism had to spend most of its energies in maintaining itself, not without difficulties, against the driving forces of modern history. Nowhere has it had the initiative. In the 1950s many Asian Buddhists celebrated the 2,500th anniversary of the Buddha's enlightenment, which was known as the "Buddha Jayanti", because it implied His "victory" over Mara, who personifies death, evil and this world. The event was marked by great enthusiasm which did not, however, concern Buddhism as a spiritual but as a social force. More so perhaps even than Europeans, Asians as a mass have at present withdrawn their interests from religious matters. Social and political issues seem to them so much more urgent. Buddhism is the only factor common to all Asian culture, at least from the Indus and Hindu Kush to Kyoto and Java. All those who dwell in Asia can take pride in a religion which is not only five centuries older than that of the West, but has spread and maintained itself with little recourse to violence and has remained unstained by religious wars, holy inquisitions, sanguinary crusades or the burning of women as witches. Nationalistic self-assertion is a prime motive at this stage of history and the achievements of the Buddhists are certainly something to be proud of. India cherishes the Buddha as one of her greatest religious teachers and Aśoka, the Buddhist emperor, as one of her most outstanding rulers. Not only in India, but also in China, Japan and Ceylon, the most brilliant periods of history were precisely those in which Buddhism flourished most. Splendid buildings and works of art in profusion, as well as a vast, subtle and often beautiful literature testify to the continuous outpouring of cultural values of a high order. From the Buddhist point of view all these things are, of course, mere trifles, accidental byproducts of intense spiritual contemplation. But they are splendid trifles.
Prophecies dating from the beginning of the Christian era have given 2,500 years as the duration of the teaching of the Buddha Śákyamuni. After that even the monks "will be strong only in fighting and reproving" and the holy doctrine will become more and more invisible. It is also a fact of observation that, like the other traditional religions, Buddhism has suffered severely from the impact of industrial civilization which has nearly completed its work of destruction in the twenty years which have passed since the Buddha Jayanti.
The bulk of the Northern Buddhists have now passed under Communist control – first Outer Mongolia (1924), then China (1949), then Tibet (1950), and finally Indo-China (1945, 1971). The effects of anti-religious totalitarian regimes are bound to be unfavourable. In Mongolia the religion is practically extinct. In China the monks, persecuted already under the Kuomintang, are exhorted to take an interest in the masses, and to live up to their vow to "benefit all living beings" in ways which they had never intended. Buddhist monuments are treated as museum pieces, Buddhist beliefs as deplorable superstitions which, however, are somehow associated with the great days of the Tang dynasty and of Chien-lung, while also providing valuable links with Japan and other Asian countries.
In Tibet the Dalai Lama had to flee in 1959, taking nearly 70,000 of his supporters with him to India. The holy land of Tibet has ceased to exist, its feudal social structure is being dismantled root and branch, its priestly artefacts, such as books, images and paintings, are destroyed or removed, and its inhabitants ushered into the satisfactions of an industrializing militarized society. Its purpose is no longer to uphold the Faith, but to guard the Chinese People's Republic against attacks from India, the Soviet Union or the United States. The influence of Marxism spreads also further South. Even in Burma and Sri Lanka many monks are sufficiently in contact with the ordinary "man in the village" to have turned left and to work for a synthesis of Buddhism and Socialism.
On many issues Communists and Buddhists are bound to clash: universal military service is abhorrent, particularly when applied to monks; Buddhist otherworldliness frowns on the uncontrolled growth of applied science and technology; and the mere building of railways, motor roads and airfields, with all that it entails, is detrimental to calm and serenity. The central conflict, however, concerns monastic institutions, without which Buddhism cannot exist. In a society dedicated to the production of material wealth an order of contemplative monks must appear anomalous and parasitical and its economic basis will be pretty precarious. The fate of a harassed and barely tolerated minority – that is what is in store for the Buddhists of those countries. So at least is the outlook on the plane of social reality. On the plane of ideas it may well be different. The doctrinal similarities between Maháyána Buddhism and dialectical materialism are surprisingly close and by a process of osmosis both sides will learn from each other in due course.
Likewise outside the Communist area the damage done has been severe. In their desire to spread the blessings of their plutocratic democracy to the Far East the Americans used all the resources of their technology to devastate first Japan, then Korea, then Vietnam, and after that Laos and Cambodia. The last, in particular, had been quite a showcase of Buddhism. Although a neutral, it was bombed back into the Stone Age, all the refinements of civilization were blotted out and for the time being it has fallen into the hands of rather primitive mountain tribes. In Burma U Nu's shortlived attempt to revive the royal Buddhism of a glorious past was superseded by a humdrum military dictatorship. In Thailand the monarchy and their supporters were so afraid of communists that the country was handed over to a military dictatorship, Buddhist monks were seen to sprinkle holy water on American tanks and tens of thousands of USAF troops were invited to pulverize their neighbours with B-52s. This has assured the ultimate triumph of communism also there.
In Japan our industrial age has put a premium on those sects, Zen, Shin and Nichiren, which have most radically departed from tradition. Shin, the numerically most successful sect, has reduced Buddhist doctrines and practices to a point where they become hardly perceptible. The threatened American invasion of 1853 had been followed twenty years later by the disestablishment of the Buddhist Church and the burning or confiscation of innumerable temples, while the actual invasion of 1945 brought financial ruin to the monasteries through MacArthur's "land reform" of 1947–50, led to a "general trend towards profanity" and to widespread religious apathy. It also brought about an enormous growth of nationalistic Buddhism. The latest census of Japan shows the Nichiren groups to number 30 million out of 75 million Buddhists. Of these more than one half belong to the "True Nichiren Sect", which grew with amazing rapidity from 350,000 members in 1955 to 15,700,000 in 1968. They are lay movements of the Nichiren line, which are run by and for merchants and craftsmen, all humble, common, ordinary people intent on improving the quality of their daily lives. The largest are the Sóka-gakkai, Reiyú-kai and Risshó-kósai-kai, founded respectively in 1930, 1925 and 1938. In appearance and behaviour these people are not unlike Kiwanis or Shriners, though as Japanese they are blessed with better taste and aesthetic judgment and as Maháyána Buddhists they are exposed to the reverberations of a very high spirituality. This is one of Buddhism's more successful attempts to come to terms with the "American Century". One may well doubt whether capitalism has been any more kind to the Buddhists than communism.
On the credit side what is chiefly to be noted is the considerable work done in recent years, in Burma, Thailand, Japan and Ceylon, to keep alive and to revive the ancient methods of meditation. It is in the seclusion of the meditation centres that the old faith will be recharged, and confer new benefits on the world.
While the strongholds of Buddhism in the East were being destroyed one by one, it was some compensation that the religion has slowly but steadily spread to the capitalist countries of the West. There it has been absorbed on three different levels – the philosophical, the scholarly and the sectarian.
1. The philosophical reception began with Arthur Schopenhauer in 1819 and has continued at a fairly steady pace since. Although he had access to very few original documents, Schopenhauer reproduced the Buddhist system of thought from Kantian antecedents with such an accuracy that one may well believe that he remembered it from a previous life. He in his turn greatly influenced musicians like Richard Wagner, philosophers like Bergson, and many other creative people in Western Europe. From quite another angle the genius of Helena Petrovna Blavatsky introduced the West to many of the basic teachings of Maháyána Buddhism and her Theosophical Society has fostered further research in many ways. In more recent years such divers philosophers as Rickert, Jaspers, Wittgenstein and Heidegger have testified to their having been influenced by Buddhism, and over the last twenty years there has grown up a vast literature on the relationship between various Buddhist thought systems and those of modern European thinkers. It is of such a consistently high quality that it cannot fail to leave its mark on Western, as well as Eastern, philosophical thought. One day the West, tired of being critical, will become creative again; and the East, now so cowed, will once again raise its head.
2. For 150 years the countless documents of Buddhist history, whether literary or artistic, have attracted the attention of many scholars. To some extent this interest was prompted by the administrative needs of imperialist governments who found Buddhists among their newly conquered subjects. In this way the Russians came to study the views of their Siberian Buddhists; puzzled by the Ceylonese attitude to land tenure the English in Ceylon, among them the Rhys Davids, turned to their religious books for an answer; the French did exceptionally fine work through the École Française d'Extrême Orient which was based in Saigon; lately even the Americans had attached to their Army a school of Oriental languages which first trained many of the Orientalists now at work in American universities, whose graduate students live on grants from the N(ational) D(efence) E(xpense) A(ccount), and who are heavily subsidized by CIA, FBI and the large Foundations. But this was not all. Just as Buddhism proved to be the most exportable form of Indian culture, so no form of Asian thinking has evoked more interest in Europe. No other religion has attracted such a galaxy of scholarly talent, not only first-class philologists drawn to the often difficult languages in which the Buddhists expressed themselves, but first-class minds bent on interpreting the subtleties and profundities of Buddhist thought. It took a long time to get to the bottom of Buddhist thinking or to even understand the terminology they employed. At first we were in the position of Egyptologists who, with all the priests dead, have to guess wildly and who have managed to reduce to a farrago of absurdities what to the best Greeks was the highest wisdom. Likewise to the first interpreters – proconsuls, missionaries, military men and financial administrators – the Buddhist religion seemed to be ludicrous nonsense. There were a few exceptions, of course, like R. C. Childers ( _c_. 1870), and, following in his footsteps, after a time the proud conquerors of Asia unbent and tried to learn from Buddhist monks who survived in Japan, Ceylon and Siberia. By the 1930s things began to fall into shape, and we can now be fairly confident to catch the spiritual meaning which the Buddhist authors wished to convey.
3. From the stratospheric heights of philosophy and the mountainous terrain of scholarship we now descend to the low-flying flatlands of popular sectarian Buddhism. Buddhist societies have sprung up for nearly eighty years, chiefly in Protestant countries. There they form one of the smaller Nonconformist sects. They try to outshine active Christian Love with their more non-violent _Mettá_ , to determine the meaning of the Holy Scriptures from often inaccurate English translations without much recourse to the originals, and to add meditation and some exotic glamour to good works, a blameless life and a ceaseless denigration of the intellect. Over the last twenty years these groups and conventicles have rapidly grown in numbers and financial weight. At first they took their inspiration almost exclusively from what they could learn about the Páli scriptures which, as good Protestants, they believed to be the original Gospel, the Buddha-dhamma in its pristine purity; then, in the wake of the magnificent publications of Daisetz Taitaro Suzuki in the thirties, there has been a flood of what describes itself as "Zen"; Conze and others added a fuller knowledge of the Prajñápáramitá and other early Maháyána texts; and since 1950 there have been many attempts to add also some Tantra to the mixture. In America side by side with the organized Buddhist groups a few gifted individuals, like Alan Watts and Gary Snyder, liberally scattered a variety of unco-ordinated ideas like seed-pods in all directions. In the sixties they had some influence on the "counter culture" which fed on the revulsion against the strains of a technological consumer society and the horrors of the war in Vietnam. Generally speaking, however, sectarian Buddhists keep themselves to themselves and have little impact on the world in general. No one can at present estimate their potentialities. Everything about them is obscure – whether it be their numbers, their financial resources, the social origin of their members, their motivation, their spiritual maturity, their doctrinal stance or the range of their influence. So why pry into the future?
Disinterestedness and self-effacement have been the most effective weapons of the Buddhists in the past. They would sadly depart from the outlook of their spiritual forebears if now they were to start worrying about whether Buddhist institutions can maintain a foothold in our present world. When asked "how a drop of water could be prevented from ever drying up", the Buddha replied, "by throwing it into the sea". It is for sayings such as this that he has been revered as the Enlightened One.
## Bibliography
### BUDDHISM IN GENERAL
Bu-ston, _History of Buddhism_ , trsl. H. Obermiller, 2 vols, 1931–2. – A. Coomaraswamy, _Buddha and the Gospel of Buddhism_ (1916), ed. L. Coomaraswamy, 1964. – E. Conze, _Buddhism_ , 1951. – R. Robinson, _The Buddhist Religion_ , 1970. – J. B. Pratt, _The Pilgrimage of Buddhism_ , 1928. – E. Conze, _Buddhist Scriptures_ , 1959. – E. Conze, I. B. Horner, D. Snellgrove, A. Waley, _Buddhist Texts through the Ages_ , 1954. – S. Beyer, _The Buddhist Experience_ , 1974.
### BASIC CONCEPTS
Bh. Nyanatiloka, _The Word of the Buddha_ , 9th ed., 1948. – E. Conze, _Buddhist Meditation_ , 1956. – _Buddhist Thought in India_ , 1962. – K. N. Jayatilleke, _Early Buddhist Theory of Knowledge_ , 1963. – L. de la Vallée Poussin, _Nirvana_ , 1925. – H. V. Guenther, _Philosophy and Psychology in the Abhidharma_ , 1957.
### ART
D. Seckel, _The Art of Buddhism_ , 1963 (Bibl.). – A. Coomaraswamy, _The Elements of Buddhist Iconography_ , 1935. – E. Gombaz, L'évolution du Stúpa en Asie, in: _Mélanges Chinois et Bouddhiques_ , 1932–6. – J. Eracle, _L'art des thanka et le Bouddhisme Tantrique_ , 1970. – D. L. Snellgrove, ed. _The Image of the Buddha_ , 1977.
### INDIA
The first period: E. Lamotte, _Histoire du Bouddhisme Indien._ 1958. – E. J. Thomas, _The Life of the Buddha as Legend and History_ , 1927. – A. Foucher, _La vie du Bouddha_ , 1949. – H. Oldenberg, _Buddha_ , 13th ed., ed. H. von Glasenapp, 1959. – A. Bareau, _Les sectes bouddhiques du petit véhicule_ , 1955. – E. Mookerji, _Asoka_ , 3rd ed., 1962. – G. Woodcock, _The Greeks in India_ , 1966.
The second period: Har Dayal, _The Bodhisattva Doctrine in Buddhist Sanskrit Literature_ , 1932. – N. Dutt, _Aspects of Mahayana Buddhism_ , 1930. – D. T. Suzuki, _Studies in the Lankavatara Sutra_ , 1930. – _On Indian Mahayana Buddhism_ (ed. E. Conze), 1968. – T. R. V. Murti, _The Central Philosophy of Buddhism_ , 1955. – R. Robinson, _Early Madhyamika in India and China_ , 1966. – E. Lamotte, _Le traité de la grande vertu de sagesse_ , 5 vols, 1944–79. – _The travels of Fah-hien_ , trsl. H. A. Giles, 1876. – Th. Watters, _On Yuan Chwang's Travels in India_ , 2 vols, 1904–5.
The third period: S. B. Dasgupta, _Obscure Religious Cults as Backgrounds of Bengali Literature_ , 2nd ed., 1962. – _An Introduction to Tantric Buddhism_ , 1950. – G. Tucci, _Tibetan Painted Scrolls_ , 2 vols, 1949 (esp. vol. 1, 209–249). – _The Theory and Practice of the Mandala_ , 1961. – D. L. Snellgrove, _The Hevajra Tantra_ , 2 vols, 1959. – H. Guenther, _Jewel Ornament of Liberation_ , (Sgam-po-pa), 1959. – P. Mus, _Barabudur_ , 2 vols, 1935. – Th. Stcherbatsky, _Buddhist Logic_ , 2 vols, 1930–2.
The fourth period: R. C. Mitra, _The decline of Buddhism in India_ , 1954.
### NEPAL
D. L. Regmi, _Ancient Nepal_ , 1960. – S. Kramrisch, _The Art of Nepal_ , 1964.
### KASHMIR
J. N. and P. N. Ganhar, _Buddhism in Kashmir and Ladakh_ , 1956.
### CEYLON
W. Rahula, _History of Buddhism in Ceylon: the Anuradhapura Period_ , 1956. – E. W. Adikaram, _Early History of Buddhism in Ceylon_ , 1946. – B. L. Smith, _Tradition and change in Theravada Buddhism_ , 1973. – R. F. Gombrich, _Precept and Practice: Traditional Buddhism in the_ _Rural Highlands of Ceylon_ , 1971. – W. Rahula, _The Heritage of the Bhikkhu_ , 1974.
### SOUTH-EAST ASIA
G. Coedès, _Indianized States of Indo-China and Indonesia_ , 1968. – R. C. Lester, _Theravada Buddhism in South East Asia_ , 1973. – G. E. Harvey, _History of Burma_ , 1925. – S. J. Tambiah, _World Conqueror and World Renouncer_ , 1976. – N. Ray, _Sanskrit Buddhism in Burma_ , 1936. – R. Butwell, _U Nu of Burma_ , 2nd ed. 1970. – E. Sarkisyanz, _Buddhist Backgrounds of the Burmese Revolution_ , 1965. – D. E. Smith, _Religion and Politics in Burma_ , 1968. – H. H. Prince Dhani-Nivat, _A History of Buddhism in Siam_ , 1965. – K. Wells, _Thai Buddhism, its Rites and Activities_ , 1960. – J. Hamilton-Merritt, _A Meditator's Diary_ , 1976. – A. H. Brodrick, _Little Vehicle: Cambodia and Laos_ , 1949.
### CENTRAL ASIA
A. Stein, _Serindia_ , 5 vols, 1921. – A. Giles, _Six centuries at Tun Huang_ , 1944. – K. Saha, _Buddhism and Buddhist Literature in Central Asia_ , 1970. – P. Demiéville, _Récents travaux sur Touen-Houang_ , 1970.
### CHINA
K. S. Ch'en, _Buddhism in China_ (Bibl.), 1964. – E. Zuercher, _The Buddhist Conquest of China_ , 2 vols, 2nd ed. 1972. – Fung Yu-lan, _A History of Chinese Philosophy_ , II, 1953, 237–433. – W. Liebenthal, _Chao Lun. The treatises of Seng-chao_ , 1968. – D. T. Suzuki, _Essays in Zen Buddhism_ , 3 vols, 1927–32. – H. Dumoulin, _A History of Zen Buddhism_ , 1963. – J. Gernet, _Les aspects économiques du Bouddhisme dans la société chinoise du 5' au 10' siècles_ , 1956. – J. Prip-Møller, _Chinese Buddhist Monasteries_ , 1937. – H. Welch, _The Practice of Chinese Buddhism_ , 1900–1950, 1967. – A. Wright, _Buddhism in Chinese History_ , 1959.
### KOREA
C. Osgood, _The Koreans and their Culture_ , 1951. – F. Starr, _Korean Buddhist History_ , 1918.
### JAPAN
Ch. Eliot, _Japanese Buddhism_ , 1935. – Steinilber-Oberlin, _The Bud-dhist Sects of Japan_ , 1938. – D. T. Suzuki, _Zen and Japanese Culture_ , 1959. – M. W. de Visser, _Ancient Buddhism in Japan_ , 2 vols, 1928, 1935. – H. Nakamura, _Ways of Thinking of Eastern Peoples: India-China-Tibet-Japan_ , 1964. – M. Anesaki, _Nichiren, the Buddhist Prophet_ , 1916. – N. Brannen, _Soka Gakkai_ , 1968.
### TIBET
H. Hoffman, _The religions of Tibet_ , 1961. – C. Ben, _The religion of Tibet_ , 1931. – P. Demiéville, _Le Concile de Lhasa_ , 1952. – H. W. Evans-Wentz, _Tibet's Great Yogi Milarepa_ , 1928. – _The hundred thousand Songs of Milarepa_ , trsl. Garma C. C. Chang, 2 vols, 1962. – G. Roerich, _The Blue Annals_ , 2 vols, 1949–53. – D. L. Snellgrove, _Buddhist Himalayas_ , 1957.
### MONGOLIA
S. Camman, _The Land of the Camel_ , 1951. – E. D. Philips, _The Mongols_ , 1969. – C. R. Bawden, _The Jebtsundampa Khutuktus of Urga_ , 1961.
### EUROPE AND AMERICA
H. de Lubac, _La rencontre du Bouddhisme et de I'Occident_ , 1952. – J. W. de Jong, _A brief history of Buddhist Studies in Europe and America_ , 1976. – W. Peiris, _The Western Contribution to Buddhism_ , 1973. – E. McCloy Layman, _Buddhism in America_ , 1976. – C. Humphreys, _Sixty Years of Buddhism in England_ , 1968. – I. P. Oliver, _Buddhism in Britain_ , 1979.
### COMPARATIVE STUDIES
K. N. Upadhyaya, _Early Buddhism and the Bhagavad Gita_ , 1971. – J. E. Carpenter, _Buddhism and Christianity_ , 1923. – J. W. Boyd, _Satan and Mara. Christian and Buddhist Symbols of Evil_ , 1975. – C. Gudmunsen, _Wittgenstein and Buddhism_ , 1977.
Most of the books mentioned have been reprinted several times. The date given is that of the first publication, except where I believe that one particular edition is preferable.
The books in French cover essential topics which no one has adequately treated in English.
Further study will, of course, involve the original documents. If these are read in translation one should remember that they are rarely accurate if made before 1940, by which date Buddhist terminology was at last being understood.
## Index
Abhayagiri , 70–1
Abhidharma Abhidhamma] , , [42–4, ,
Abhidharmakośa , ,
Abhirati
Abhisamayálankára ,
ahimsá (non-violence) vii,
Aiśvarikas
Altan Chagan
Amida, _see_ Buddha(s)
Amidism 77–8, , , 104–6
Ching-t'u , 77–8
Ji
Jódó 104–5
Shinshú [Shin] ,
Yúzú Nembutsu
_see also_ Nichiren
Amoghavajra ,
Anáthapindada
Anawrahta (Burmese dynasty)
Annam
Arhat, _see_ saints
Aris
art
Arsaco-Sassanid
Buddhist , , , , , , , ,
Chinese ,
Greek
Indonesian
Japanese ,
Korean
Nepalese
Tibetan ,
Áryans ,
Áryadeva , ,
Asanga , , ,
Ashikaga Shoguns
Asia vii, , , , , ,
Asia Minor vii
Central Asia , , 50–2, , , 71–2
Eastern Asia ix,
South-East Asia 72–3, 96–9
Aśoka (Indian emperor) , , , , , , , , ,
Aśvaghosa , ,
Atíśa , ,
Avadánas ,
Avalokiteśvara , ,
'Awakening of Faith' ,
Basho
Bengal x, , , , ,
Bergson, Henri
Bhaisajyaguru
Bible
Blavatsky, Helena Petrovna
Bodhidharma ,
Bodhisattvas, _see_ saints
Bohr, Niels
Bon , , , ,
Book of Changes ,
Brahmanism , , , ,
'Brom ston
Buddha(s) 10–11, , , , , , , , , , , , , , , , ,
Ádi-Buddha ,
Akshobhya , , ,
Amitábha [Amida] , , , , ,
Amitáyus
the Buddha Gautama, Śákyamuni, Siddhártha] [vi, viii, , , , , , 10–13, , 19–20, , , , , , , , , , , , , , , , , , , , , , , , , , , , ,
Dharmakáya ,
Dípankara
future Buddha(s) ,
Maitreya , , , 59–60, ,
mythical Buddhas ,
Buddha-dhamma
Buddhadatta
Buddhaghosa , ,
Buddhahood , , , , , , , ,
Buddha Jayanti ,
Buddha Mátanga
Burma , , 95–8, ,
Bushido, _see_ Zen
Bu-ston
Cambodia , ,
canonical literature ix–x, 1–3, , , , , , 49–50, 62–3, ,
Avatamsaka Sútra
Buddhacarita
'Diamond Sútra' 31–2
Gandavyúha
'Heart Sútra'
Hínayána Sútras
Játakamálá
Jñánaprasthána
Kanjur
Karmavibhanga
Kośa
Lalitavistara
Lankávatára Sútra
Lotus of the Good Law
Maháyána texts ix–x, , , , , , ,
Nirvana Sútra ,
Pitakas
Prajñápáramitá Sútras ,
Saddharmapundaríka
Sarvástivádin Canon
Śástras ,
Śúrangama Sútra
'Sútra on the Ten Stages'
Sútras , , , , , , , , , , , ,
Sutta Nipáta
Tanjur
Tantras x, , 61–3,
Vajracchediká Sútra
Vibháshá
Visuddhimagga
_see also_ Abhidharma
Ceylon , 28–9, , 46–8, 70–1, 95–6, , , ,
Champa (kingdom)
Ch'an ix, , , , , 78–84, , 99–102, , ,
Fa-yen-tsung
Lin-chi-tsung [Rinzai] ,
Ts'ao-tung-tsung Sótó] [99–100,
tso-ch'an
Wei-yang-tsung
Yün-men-tsung
_see also_ doctrine, in third period
Chan-jan
Ch'eng Weih-shih Lun
Chen-yen ,
Ch'ien-lung (Chinese emperor) ,
Chih-k'ai ,
Childers, R. C.
China vii, ix, , , , , , , , 52–60, , , , 73–85, , , , , 99–103, , , ,
Chinese People's Republic
Ching-t'u , , 77–8
Chi-tsang
Chos dbyang
Christianity , 48–9, , , ,
Chuang-tzu , ,
Chu-hsi
Chu Tao-sheng , 58–9, ,
Communism 120–2
Confucianism , , , , , ,
ching-tso
Neo-Confucianism
Confucius
Conze, Edward
Council of bSam Yas
Council of Rájagrha ,
Council of Vaiśalí
Dalai Lama 117–18,
Davids, Rhys
death vi, viii, , 23–4, , , , , 112–13
deities , , , , , , , , ,
feminine ,
Lamaist
Maháyána , ,
Shintó ,
Tantric
Dengyó Daishi
Dhammaceti (Burmese king)
Dhammapála
dháranís (mantras)
Dharma xi, , , , , 13–15, , , , , , , , , , , , , ,
Dharmadhátu ,
Dharmákara (Bodhisattva)
Dharmakírti
Dharmapála (Indian king) ,
Dharmíkara (Nepalese king)
Dharmottara
Dinnága
doctrine x, 5–16, , 31–44, , 49–50, , , 56–9, 76–7, 80–4, ,
ahimsá
assimilation of
Ch'an 82–4
degeneration of x
development of xi–xii, , , ,
in first period 5–16
interpretation of ,
Maháyána 32–41,
maitrí
seven schools
Tantra 62–3, 66–7
Theraváda ,
in third period 40–1
Ts'ao-tung
Dógen
Dutta Gámaní (king of Ceylon)
eightfold path
Eisai
emptiness , , , , , , 36–8, , , , , , , , ,
English , , ,
enlightenment ix, , , , , , , , , , , 79–80, , , , , 106–7, , ,
Fa Hien ,
Fa-hua
_see also_ Tien-t'ai
Fang Jong
Fa-tsang
Fellowship of the White Lotus
five precepts , ,
Five Protectresses
French
Gandhára ,
Gándhi, Mohandas Karamchand (the Mahátma)
Gaudapáda
gLang-dar-ma
Guge
Guhyasamája, _see_ Tantra
Gunavarman
Gurkhas
gurus ,
Hai-yun 83–4
Hakuin
Han (Chinese dynasty) , , ,
Hari
Haribhadra
Harivarman ,
Harshavardhana (Indian king)
Hathayoga
Heian period (Japan) , ,
_see also_ sects
Heidegger, Martin
Hideyoshi
Hínayána viii, , , , 41–4, , ,
_see also_ canonical literature; doctrine, in first period
Hínayánists , , , ,
Hinduism , , , , , 93–4
Hindus , , , , ,
Hónen 104–5
Hua-yen-tsung , , , ,
_see also_ sects
Hui-neng , ,
Hui-Yüan ,
Hung-chih Cheng-chüeh
Il-khanid (Iranian dynasty)
impermanence , , , , ,
India vi, vii, viii, ix, x, , 16–17, , , , , , 30–44, , , , , , , 61–9, , , , , , , , , 90–3, , , , , , , 119–20
Indikutasaya Copper Plates
individualism vii, viii, xii,
_see also_ self
Indo-China , ,
Indonesia , 98–9
Ippen
Iran , ,
Islam , , , , , ,
I-Tsing
Jaggadala
Jainism 90–1
Japan , , , , 85–7, 103–8, , , , ,
Jaspers, Karl
Játakas , , ,
Java , , , , ,
Kahgyudpas
Kálacakra, _see_ Tantra
Kálí
Kali Yuga
Kamakura period (Japan) , ,
Kanishka
Karkota (Kashmiri dynasty)
karma , , , ,
Kármikas
Kashmir , , 45–6, 69–70, , ,
Kátyáyaníputra 22–3
Keizan Jokin
Khmers ,
Khotan
Khubilai (Mongol emperor) ,
Kinnara (Kashmiri king)
Kirghiz
Kiwanis
Kóbó Daishi
Korea , 84–5, , , 102–3, ,
Koryo (Korean dynasty) 102–3
Kshemendra
Kshítigarbha
Kuan Ti
Kuan Yin ,
K'uei-chi
K'uei-ki
Kumárajíva , , ,
kung-an
Kuomintang
Kushana (empire) ,
Ladakh ,
laity , 24–8, , , , , , , , ,
Lamaism , , , 117–18
Lamas
languages
Ardhamagadhi
Chinese , , ,
English
Japanese ,
Khotanese ,
Kuchean ,
Mongol
Sogdian
Tibetan
Uigur
_see also_ Páli; Sanskrit; Sinhalese
Laos ,
Lao-tzu ,
Lin-chi-I-hsüan
logic
Lokeśvara ,
Lotsabas
Lu-cheng
Lu-Feng (monastery)
Lü-tsung ,
Madhyántika
Magadha , , , , ,
magic ix, , , , , , 64–7, , , , , , , ,
Mahádeva
Mahákála
Mahákáśyapa ,
Mahátmyas
Mahávihára , ,
Mahávyutpatti
Maháyána ix, x, , , , , 30–41, , , , , , , , , , , , , , , 76–7, , , , , , , , , , , , ,
_see also_ canonical literature; doctrine, in second period
Maháyánists , , , , 48–9, , , ,
Mahinda
maitrí (benevolence)
makáras
Manchu (Chinese dynasty)
mandalas , 65–6,
Manicheans , ,
Mañjuśrí ,
mantras , , , ,
Mantrayána, _see_ Tantra
Mára viii,
Marpa [Mar-pa]
Marxism ,
Mátrceta
Ma-tsu
Matsyendranáth
meditation vii, , 8–10, , , , , , , , , , , , , , , , , , , , , ,
mystical
transic ,
Meghavahana
Mendeleyev, Dmitry Ivanovich
Mihirkula
Mila-ras-pa 110–11
Mi-lei-fo
Ming (Chinese dynasty)
Mi-tsung ,
monasticism xi, 3–24, , , , , 63–4, , 79–80, , , 88–9, , , , , , , , , , , ,
Mongolia , 118–19,
Outer Mongolia
Mongols , , ,
monks , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , ,
mudrás ,
Múlasarvástivádins
Muslims, _see_ Islam
Nágas ,
Nágárjuna , , , , , ,
Nálandá , , , ,
Nan-yuan Hui-yung
Neaca-ta
Nembutsu , , , ,
Nepal , , 45–6, , , 93–4,
Newars
Ngan Che Kao
Nichiren 105–6,
Reiyú-kai
Risshó-kósai-kai
Sóka-gakkai
Nirvana xi, , , , , , , , , , , , ,
of the Buddha , , , , , , , ,
Nobunaga
Odantapuri
Padmapáni
Padmasambhava , , ,
Pála (Indian dynasty) x, , , , , , , , , ,
Páli , , , , , , , ,
Pallava (Indian dynasty)
Pamsukúlikas
P'ang-yun
paradise ,
Amida's Paradise ,
Pure Land , 77–8,
Western Paradise , ,
Páramitás six perfections] , [34–5,
Paritta
persecution , , , , , , 107–8, ,
Personalists 21–2
Sammitíyas , ,
Vatsíputríyas ,
Pha-dam-pa 'Phags-pa ,
philosophy 18–23, , , 82–3, , ,
Pi-yen-lu
Po-chang Huai-hai 79–80
Polonnaruva
Prajñápáramitá , , , , , , , ,
Prátimoksha
Pratyekabuddhas, _see_ saints
Pure Land, _see_ paradise
Ral-pa-can (king of Tibet)
rebirth ix, , , , , , , , ,
_see also_ Samsára
reincarnation
relics of the Buddha , , , , ,
Rickert, Heinrich
Rin-chen bzang-po
Rinzai, _see_ Ch'an, Zen
Roshana
Róshis, _see_ saints
Ryónin
Ryóyó Shógei
Saddhátissa
Sahajayána, _see_ Tantra
Śailendra (Javan dynasty)
saints 15–16, , , , , , , ,
Arhats Arahants] [ix, , , , , , , , , , ,
Bodhisattvas ix, , , 32–7, , , , , , , , , ,
Pratyekabuddhas ,
Róshis
Siddhas ix, ,
salvation ix, , , 6–8, , , , , , , , , , , , , , , , ,
Śákyasríbhadra
Samantabhadra ,
Samgha , , , , , , , , , , ,
Samghabhadra
Sammitíyas, _see_ Personalists
Samsára , , , , ,
Samurai ,
Sanghamitra
Śánkara ,
San-lun , ,
Sanskrit , , , , , , , , , ,
Śántarakshita ,
Sáriputra
Sarvajñamitra
Satyasiddhi ,
Schopenhauer, Arthur
sects xii, , , , 16–24, , , 85–6, 104–7, , 109–15, 124–5
Bka-gdam-pa ,
bKa-rgyud-pa
Dge-lugs-pa 114–15
Dhammakathikas ,
Gelugpa , , , ,
Heian
Hossó
Hua-yen [Kegon]
Jójitsu
Kusha
Mádhyamikas , , 38–9, ,
Mahásanghikas , , , , ,
Nara
Nyingmapa Nying-ma-pa] [112–14
Óbaku
Pudgalavádins
Risshú ,
Sanron
Sarvástivádins , , , , , 43–4, , , , , , 88–9
Saskyapa [Sa-skya-pa] ,
Sautrántikas , ,
Shi-byed-pa
Shingon , ,
Sthaviras , ,
Tendai 85–6
Theravádins , , , , ,
Vaibháshikas , ,
Vibhajyavádins , ,
Vinaya
self vi, vii, xi, 6–7, , , , 33–4,
Seng-chao
Seng-t'san
Seng-yu
Sesshu
seven schools
shamanism , ,
Shan-tao , ,
Shao-k'ang
Shen-hsiu
Shin, _see_ Amidism
Shinran
Shintó , , ,
Ryóbu-Shintó ,
Shotoku Taishi
Shugenja
Siberia
Siddhas, _see_ saints
Singhasari (Javan dynasty)
Sinhalese , , , ,
Siva ,
Sivaism [Shivaism] , , , , ,
Skandhaka
Snyder, Gary
Somarúpa
Son of Heaven
Sótó, _see_ Ch'an, Zen
Spiti
Sri Lanka
_see also_ Ceylon
Srívijaya
Subhákarasimha
suchness , , , , ,
Sukhávatívyúha
Sumatra ,
Sung (Chinese dynasty) , , ,
Sútras, _see_ canonical literature
Suttas
Suzuki, Daisetz Taitaro ,
Svábhávikas (school)
Svayambhúpurána
Ta-hui tsung-kao
T'ang (Chinese dynasty) , , , , , ,
Tan-hsia T'ien-jan
Tantra ix, x, 40–1, 61–3, , , 67–8, , , , , , , , , , , , , , ,
Guhyasamája ,
'left-handed' ,
Kálacakra ,
Mantrayána
Sahajayána
Vajrayána , , , , , ,
_see also_ canonical literature; doctrine, in third period
Tantrayána
Tao-an
Tao-ch'o
Tao-Hsüan
Taoism , , , , ,
Neo-Taoism ,
Tao-sheng, _see_ Chu Tao-sheng
Tárá , , ,
Táranátha
Tathágatas , ,
Akshobhya
Amitábha
Amoghasiddhi
Ratnasambhava
Vairocana
Tche tsh'an
ten perfections
Thailand [Siam] , , ,
Theosophical Society ,
Theraváda , , ,
thirty-two marks of the superman , 39–40
Three Bodies of the Buddha ,
Three Jewels Treasures] , [10–16,
Tibet , , , , , , , , , , , , 87–9, , , , , 108–18, 120–1
T'ien-t'ai , 76–7, ,
Tipitaka , ,
Tokugawa (Japanese dynasty)
Tshou Cho-fo
Ts'in (Chinese dynasty)
Tsong-kha-pa , 114–15,
Tung-shan Liang-chieh
Turkestan ,
Tushita heaven ,
Tu-shun
Uigurs
United States of America , , ,
U Nu
Upatissa
Urga ,
Vairocana , , , ,
Vaishnavas
Vaitulyaváda
Vajrabodhi
Vajrapáni
Vajrayána, _see_ Tantra
Vakkali
Vasubandhu , , , , ,
Vasugupta
Vatsíputríyas, _see_ Personalists
Vedánta ,
Vessantara
Vietnam ,
Vijñánaváda
Vimalakírti ,
Vimuttimagga
Vinaya , 4–5, , , , , , ,
violence vi, vii, , , , , , ,
Vishnu
Wang Fo
Watts, Alan
Weih-shih ,
Wittgenstein, Ludwig
World Fellowship of Buddhists
Wu-men-kuan
Yama
Yama-bushi
Yao Hsing (Chinese emperor)
Yátnikas
Yellow Church of Tibet , ,
Yellow Emperor
Yi-hsuan
Yoga , , ,
Yogácára , , 38–9, , , , , , , ,
Yogins , , , , ,
Yüan (Chinese dynasty) , ,
Yüan-tsang , , , , , , , ,
Yuishiki
Yung-cheng (Chinese emperor)
Zen , 106–7, , ,
Bushido Óbaku
Rinzai [Lin-chi] ,
Sótó Ts'ao-tung] [106–7
Zurvan Akaranak
|
{
"redpajama_set_name": "RedPajamaBook"
}
| 5,351
|
\section{Introduction}
The most accurate way amongst today's standard approaches
to account for relativistic effects
in molecules is to solve the Dirac equation for the large (LC)
and small two-component (SC) part of the wave function.\cite{Dyall2007}
Employing the full four-component (4C) methodology of the Dirac equation
yields solutions for both positronic and electronic states.
An accurate approximation to the Dirac equation
that gives electronic --- positive energy --- solutions only is the
exact (X) two-component (2C) method,\cite{Ilias2005,*Kutzelnigg2005,*Kutzelnigg2006,*Ilias2007}
in which the Dirac Hamiltonian is reduced to a 2 x 2 matrix form.
While exact for a given one-body operator, the X2C method usually includes the approximation of
omitting the picture-change transformation of two-electron integrals.
Especially for correlated calculations, this makes the algorithm very efficient as molecular integrals
then require evaluation of only LC atomic-orbital (AO) two-electron integrals.
Since the SC AO basis can be up to 3~times larger than the LC AO basis,
if the unrestricted kinetic balance condition is employed,
the overhead of the integral calculation and transformation
is then reduced immensely.\cite{Peng2007,*Liu2009,*Sikkema2009}
With a relativistic 2C Hamiltonian the overhead of
the Dirac equation is thus reduced, but accurate wave function methods
still feature a steep scaling of the computational work with the
system size $N$, e.g.\
second-order M{\o}ller--Plesset perturbation theory\cite{Moeller1934} (MP2)
scales with $\mathcal{O}(N^5)$.
To overcome this computational bottleneck, several reduced scaling
approaches were proposed for MP2 over the years.\cite{Haeser1992,Haeser1993,Ayala1999,Doser2009,Maurer2014,*Hetzer2000,*Jung2004,*Yang2011,*Schmitz2013}
One of the most successful approaches originates from
Alml{\"o}f\cite{Almloef1991,Haeser1992} and H{\"a}ser\cite{Haeser1993}
where the MP2 correlation energy
is formulated purely in the AO basis by means of
a numerical Laplace transformation (LT)
of orbital-energy denominators.
By employing estimates for integral screening,
low-order scaling implementations
were proposed by H{\"a}ser\cite{Haeser1993} and Ayala and Scuseria.\cite{Ayala1999}
Ochsenfeld and his co-workers showed how to achieve linear scaling
of all computationally demanding steps by accounting for the distance-dependent decay of
integrals,\cite{Lambrecht2005a,Doser2009,Maurer2013}
and their implementation currently allows for calculations on molecules with 1000~atoms and more on a
single core.\cite{Maurer2013}
The same authors have also presented a promising computational performance
for large AO basis sets that include high angular momentum and / or diffuse basis functions
when the LT AO-based approach is combined with Cholesky
decomposition of two-electron integrals.\cite{Maurer2014}
Alternatively, the performance of the LT AO-based approach when large basis sets are employed
can also be remedied with a modern formulation of explicitly correlated MP2-F12\cite{Klopper1987,*Kutzelnigg1991,*Klopper2006a,Li2012,*Tenno2012}
in the AO basis, which became available recently.\cite{Hollman2013}
In the current work,
we present for the first time formulae for LT AO-based MP2 correlation energy
for relativistic 2C Hamiltonians in a Kramers-restricted (KR) formalism.
The additional spin orbit (SO)-induced complexity of the formulae is discussed by comparing
with non-relativistic (NR) LT AO-MP2 and conventional KR spinor-based approaches.
Furthermore, we present an adaptation of the Schwarz-type estimates,
which are employed to screen shell quadruple contributions to the MP2 correlation energy,
to the 2C formalism.
Those Schwarz-type estimates\cite{Haeser1993} pave the way to develop a linearly scaling
2C LT AO-MP2 implementation once they are combined with the proper
distance-dependence terms.\cite{Maurer2013}
With a proof-of-principle implementation we analyze the
effect of the nuclear charge and the separation of electronic charge distributions
on the correlation energy contributions.
\section{Theory} \label{theory}
\subsection{MP2 energy for 1C, 2C, and 4C Hamiltonians}
The MP2 correlation energy is given by
\begin{align} \label{emp2}
E_{\text{MP2}\xspace}
&= - \frac{1}{4} \sum_{IJAB} \frac{1}{\Delta_{AIBJ}} | (IA||JB) |^2 \\
&= - \frac{1}{2} \sum_{IJAB} \frac{1}{\Delta_{AIBJ}}
\left( (BJ|AI) - (AJ|BI) \right) (IA|JB) \label{emp2b} \\
&= E_J - E_K
\text{.}
\end{align}
In Eq.\ \eqref{emp2}, $(IA||JB)$ are anti-symmetrized two-electron integrals $(IA|JB)$
that involve active occupied ($I,J$) and
active virtual ($A,B$) spinors;
$\Delta_{AIBJ}$ is the denominator
\begin{align}\label{denom}
\Delta_{AIBJ} = \varepsilon_A-\varepsilon_I+\varepsilon_B-\varepsilon_J
\end{align}
that comprises real orbital energies $\varepsilon_P$ with $P=I,A,J,\text{ and }B$.
Note that Eq.\ \eqref{emp2} is valid for both NR and relativistic
Hamiltonians when spin orbitals and 4C (or 2C) spinors are
employed, respectively. This equation furthermore only assumes a single
determinant reference wave function and is therefore applicable to both restricted and
unrestricted Hartree--Fock wave functions. In practice, one usually deals with closed-shell
systems and it is therefore efficient to make use of Kramers symmetry\cite{Kramers1930}
in the Hartree--Fock self-consistent field procedure. Spinor energies are then doubly degenerate and
the number of unique variational parameters is reduced by a factor of two as the expansion
coefficients for pairs of spinors are related. We will assume such a restricted optimization
and label two spinors that form a Kramers pair by the lowercase symbols $p$ and $\tilde{p}$.
These spinors can be expressed in a set of real AO basis functions $\chi_\mu$ as
\begin{align}\label{LCAO}
\phi_p &=
\begin{pmatrix}
\phi_p^{\alpha} \\
\phi_p^{\beta}
\end{pmatrix}
=
\begin{pmatrix}
\sum_{\mu} \chi_{\mu} C_{\mu p}^{\alpha} \\
\sum_{\mu} \chi_{\mu} C_{\mu p}^{\beta}
\end{pmatrix}
&
\phi_{\tilde{p}} &=
\begin{pmatrix}
\phi_{\tilde{p}}^{\alpha} \\
\phi_{\tilde{p}}^{\beta}
\end{pmatrix}
=
\begin{pmatrix}
\sum_{\mu} \chi_{\mu} (-C_{\mu p}^{\beta *} ) \\
\sum_{\mu} \chi_{\mu} ( C_{\mu p}^{\alpha *})
\end{pmatrix}
\text{;}
\end{align}\\
a form which clearly displays the Kramers relation between the coefficients.
This expansion is valid for NR, scalar-relativistic (SR), and SO relativistic spinor optimization and can
be defined to encompass both 2C and 4C spinors. In the latter case, the basis set is
divided into separate sets of LC and SC expansion functions and coefficients,
which describe respectively the upper and lower components of the 4C spinor.
In the X2C approximation, that we focus on in the current work, the Dirac--Coulomb Hamiltonian
is reduced to an effective 2C form and picture change corrections on the two-electron operator are neglected.
With these approximations AO integrals reduce to their familiar NR form
\begin{align}
(\kappa\lambda|\mu\nu)=\int \int \chi_{\kappa}(\mathbf{r}_1) \chi_{\lambda}(\mathbf{r}_1) \frac{1}{r_{12}} \chi_{\mu}(\mathbf{r}_2) \chi_{\nu}(\mathbf{r}_2) d\mathbf{r}_1 d\mathbf{r}_2
\end{align}
and can be evaluated using standard techniques.
Relativity is manifest only in the MO coefficients, with scalar relativistic effects merely changing their value but not changing
the structure of the coefficient matrices. NR and SR
approaches have real, block diagonal, coefficient matrices
$\mathbf{C}_p^{\alpha}=\mathbf{C}_{\tilde{p}}^{\beta}; \mathbf{C}_p^{\beta}=\mathbf{C}_{\tilde{p}}^{\alpha}=\mathbf{0}$,
while SO approaches yield complex matrices for which $\mathbf{C}_p^{\beta}\neq 0$. It is the latter effect
which makes relativistic correlated calculation more expensive than their NR counterparts.
\subsection{LT AO-based MP2 for 1C Hamiltonians}
By means of the (numerical) LT,
it has been shown initially by Alml{\"o}f and H{\"a}ser\cite{Almloef1991,Haeser1992,Haeser1993} that
an expansion of the orbital-energy denominator (Eq. \eqref{denom}) according to
\begin{align} \label{laplace}
\frac{1}{\Delta_{aibj}} &= \int_0^{\infty} \exp(-\Delta_{aibj}\, t) dt
\approx \sum_{z=1}^{n_z} \omega_{z}\, \exp(-\Delta_{aibj}\, t_{z})
\end{align}
results in a formulation for the Coulomb $(J)$ and
exchange contribution $(K)$,\cite{Haeser1993,Ayala1999,Lambrecht2005a,Surjan2005}
\begin{align}\label{emp2lap}
& E_{\text{MP2}\xspace} = \sum_{z=1}^{n_z} e_J^{(z)} - e_K^{(z)}
\text{,}
\end{align}
solely in terms of intermediates in the AO basis.
In Eqs.\ \eqref{laplace} -- \eqref{emp2lap} $n_z$ denotes a pre-defined number of quadrature points
represented by $\{\omega_{z},t_{z}\}$.
For the NR Hamiltonian and restricted HF reference wave functions,
occupied
\begin{align} \label{psdeno_nr}
\mathbf{\underline{P}}^{(z)}
&= |\omega_z|^{1/4}\, \mathbf{C}^o \, \exp(+\mathbf{\boldsymbol\varepsilon}^o t_z)\, (\mathbf{C}^o)^{T} \notag \\
&= |\omega_z|^{1/4}\, \exp(+t_z\, \mathbf{P}\, \mathbf{F})\, \mathbf{P}
\end{align}
and virtual pseudo-density matrices
\begin{align} \label{psdenv_nr}
\mathbf{\bar{P}}^{(z)}
&= |\omega_z|^{1/4}\, \mathbf{C}^v\, \exp(-\mathbf{\boldsymbol\varepsilon}^v t_z)\, (\mathbf{C}^v)^{T} \notag \\
&= |\omega_z|^{1/4}\, \exp(-t_z\, \mathbf{Q}\, \mathbf{F})\, \mathbf{Q}
\end{align}
are used to transform the two-electron integrals to write the $J$ and $K$ contributions
\begin{align}
e_J^{(z)} & = 2\, \sum_{\mu \nu \kappa \lambda}
(\underline{\mu} \bar{\nu} | \kappa \lambda)^{(z)}
(\mu \nu | \underline{\kappa} \bar{\lambda})^{(z)} \text{,} \\
e_K^{(z)} & = \phantom{2}\, \sum_{\mu \nu \kappa \lambda}
(\underline{\mu} \bar{\nu} | \kappa \lambda)^{(z)}
(\mu \bar{\lambda} | \underline{\kappa} \nu)^{(z)}
\end{align}
in terms of half-transformed integrals (HTI)
\begin{align}
(\underline{\mu} \bar{\nu} | \kappa \lambda)^{(z)} &=
\sum_{\mu'} \underline{P}_{\mu'\mu}^{(z)} \left( \sum_{\nu'} \bar{P}_{\nu\gn'}^{(z)} (\mu' \nu' | \kappa \lambda) \right) \text{,} \label{htinr1} \\
(\mu \bar{\lambda} | \underline{\kappa} \nu)^{(z)} &=
\sum_{\kappa'} \underline{P}_{\kappa'\kappa}^{(z)} \left( \sum_{\lambda'} \bar{P}_{\lambda\gl'}^{(z)} (\mu \lambda' | \kappa' \nu) \right)
\text{.} \label{htinr2}
\end{align}
In Eqs.\ \eqref{psdeno_nr} -- \eqref{psdenv_nr},
$\mathbf{F}$ is the Fock matrix and $\mathbf{\boldsymbol\varepsilon}$ the orbital-energy vector;
$o$ and $v$ indicate the set of
all active occupied and virtual orbitals, respectively.
In Eqs.\ \eqref{htinr1} -- \eqref{htinr2} and in the following
$\mu$, $\nu$, $\kappa$, and $\lambda$ denote scalar AO basis functions.
Since the two density matrices $\mathbf{P}$ and $\mathbf{Q}$
are related through the constant AO overlap matrix $\mathbf{S}$ by
\begin{align}
& \mathbf{P} = \mathbf{C}^o \, (\mathbf{C}^o)^{T} \text{,} \\
& \mathbf{P} + \mathbf{Q} = \mathbf{S}^{-1}
\text{,}
\end{align}
the NR MP2 energy in Eq.\ \eqref{emp2lap} is a functional of the
HF density matrix $\mathbf{P}$.\cite{Surjan2005}
To simplify the formulae, the index $z$ that denotes the
quadrature point is omitted in the following when appropriate.
\subsection{LT AO-based MP2 for 2C Hamiltonians}
We can repeat this procedure for relativistic spinors in which we use the
Kramers' symmetry of the MO coefficients to reduce the number of operations.
If spinors are generated in a KR algorithm, the full spinor set
is subdivided in two sets of spinors with related coefficients (Eq. \eqref{LCAO}).
This then leads to the classification of 16 different sub-blocks
of two-electron integrals $(IA|JB)$:
\begin{align} \label{intblock}
& (ia|jb) \, (\tilde{i}\tilde{a}|jb) \, (\tilde{i} a|\tilde{j} b) \, (\tilde{i} a|j\tilde{b}) \notag \\[2ex]
& (ia|j\tilde{b}) \, (ia|\tilde{j} b) \, (i\tilde{a}|jb) \, (\tilde{i} a|jb) \notag \\[2ex]
& (\tilde{i}\tilde{a}|\tilde{j}\tilde{b}) \, (ia|\tilde{j}\tilde{b}) \, (i\tilde{a}|j\tilde{b}) \, (i\tilde{a}|\tilde{j} b) \notag \\[2ex]
& (\tilde{i}\tilde{a}|\tilde{j} b) \, (\tilde{i}\tilde{a}|j \tilde{b}) \, (\tilde{i} a|\tilde{j}\tilde{b}) \, (i\tilde{a}|\tilde{j}\tilde{b}) \text{,}
\end{align}
for which it is easy to show that the last 8 integral blocks are the complex conjugate
of the first 8. Furthermore, the integrals on the second and the fourth line are zero if
the system under consideration has (at least) a two-fold element of symmetry (mirror plane or
rotation axis).
The Coulomb energy
\begin{align} \label{ecoul1}
E_J = \frac{1}{2} \sum_{JIBA} \frac{1}{\Delta_{AIBJ}} &
(BJ|AI) (IA|JB) \\
= \sum_{jiba} \frac{1}{\Delta_{aibj}} \Big(
& (ai|bj)(ia|jb) + (\tilde{a}\tilde{i}|bj)(\tilde{i}\tilde{a}|jb) \notag \\
+ & 2 (a\tilde{i}|bj)(\tilde{i} a|jb) + 2 (\tilde{a} i|bj)(i\tilde{a}|jb) \notag \\
+ & (a\tilde{i}|b\tilde{j})(\tilde{i} a|\tilde{j} b) + (a\tilde{i}|\tilde{b} j)(\tilde{i} a|j\tilde{b}) \Big)
\end{align}
comprises 6 contributions that are real even without exploiting Kramers symmetry
because one of the integrals in each of the products in Eq. \eqref{ecoul1}
is the complex conjugate of the one it is multiplied with.
In the KR formalism, the exchange energy
\begin{align} \label{eexch1}
E_K
= \sum_{jiba} \frac{1}{\Delta_{aibj}} \Big(
& \re{(bi|aj)(ia|jb)} + \re{(b\tilde{i}|\tilde{a} j)(\tilde{i}\tilde{a}|jb)} \notag \\
+ & 2 \re{(b\tilde{i}|aj)(\tilde{i} a|jb)} + 2 \re{(bi|\tilde{a} j) (i\tilde{a}|jb)} \notag \\
+ & \re{(b\tilde{i}|a\tilde{j})(\tilde{i} a|\tilde{j} b)} + \re{(\tilde{b} \tilde{i}|aj)(\tilde{i} a|j\tilde{b})} \Big)
\end{align}
comprises 6 real contributions as the integral products in \eqref{eexch1}
appear in complex conjugate pairs with imaginary parts canceling each other.
The spinor-based integral products in Eqs.\ \eqref{ecoul1} and \eqref{eexch1}
can be factorized in terms of two-electron integrals
and density matrices as for the NR case.
Here, we only show the working equations in their most condensed
formulation of 2C AO-based MP2.
For a complete derivation we refer to the supporting information.\cite{si}
Before proceeding, we introduce quaternion algebra\cite{Saue1997,*Saue1999} for the KR formalism as
it is the most compact notation and results in working equations
that feature the least number of computational operations.
The quaternion spinor coefficients are given by
\begin{align}\label{qspinor}
{^q}\mathbf{C}
&= \mathbf{C}^{\alpha} - (\mathbf{C}^{\beta})^*\, j \notag \\
&= \re{\mathbf{C}^{\alpha}} + \im{\mathbf{C}^{\alpha}}\ i
- \re{\mathbf{C}^{\beta}}\ j + \im{\mathbf{C}^{\beta}} \ k \notag \\
&= \mathbf{C}^0 + \mathbf{C}^1\ i + \mathbf{C}^2\ j+ \mathbf{C}^3\ k
\end{align}
and from Eq.\ \eqref{qspinor} the quaternion density matrices
${^q}\mathbf{P}$ and ${^q}\mathbf{Q}$ can be constructed by
\begin{align}
& {^q}\mathbf{P} = {^q}\mathbf{C}^o \, ({^q}\mathbf{C}^o)^{\dag}
= \mathbf{P}^0 + \mathbf{P}^1\ i + \mathbf{P}^2\ j+ \mathbf{P}^3\ k \text{,} \label{deno} \\
& {^q}\mathbf{P}+ {^q}\mathbf{Q} = \mathbf{S}^{-1} \label{denv}
\text{,}
\end{align}
where $\mathbf{P}^0$,$\mathbf{Q}^0$ and
$\mathbf{P}^{q_1}$,$\mathbf{Q}^{q_1}$ with $q_1 = 1,\ldots,3$
are real symmetric and anti-symmetric matrices, respectively.
As for the NR Hamiltonian,\cite{Surjan2005} the MP2 energy is a functional
of the quaternion HF density matrix ${^q}\mathbf{P}$, which facilitates a
formulation and implementation without spinors purely in the AO basis.
For relativistic 2C Hamiltonians, the Coulomb-
\begin{align} \label{ecoul}
e_J^{(z)} = 2\, \sum_{\mu\nu\kappa\lambda} \sum_{\mu'\nu'\kappa'\lambda'} \Big(
& \underline{P}^0_{\mu' \mu} \bar{P}^0_{\nu \nu'} - \underline{P}^1_{\mu' \mu} \bar{P}^1_{\nu \nu'}
- \underline{P}^2_{\mu' \mu} \bar{P}^2_{\nu \nu'} - \underline{P}^3_{\mu' \mu} \bar{P}^3_{\nu \nu'} \Big) \notag \\
\Big(
& \underline{P}^0_{\kappa' \kappa} \bar{P}^0_{\lambda \lambda'} - \underline{P}^1_{\kappa' \kappa} \bar{P}^1_{\lambda \lambda'}
- \underline{P}^2_{\kappa' \kappa} \bar{P}^2_{\lambda \lambda'} - \underline{P}^3_{\kappa' \kappa} \bar{P}^3_{\lambda \lambda'} \Big) \notag \\
& (\mu'\nu'|\kappa'\lambda') (\mu\nu|\kappa\lambda) \\
= 2\, \sum_{\mu\nu\kappa\lambda} \sum_{\mu'\nu'\kappa'\lambda'} \Big(
& \re{{^q}\mathbf{\underline{P}}_{\mu' \mu}\, {^q}\mathbf{\bar{P}}_{\nu \nu'}}
\re{{^q}\mathbf{\underline{P}}_{\kappa' \kappa}\, {^q}\mathbf{\bar{P}}_{\lambda \lambda'}} \Big)
(\mu'\nu'|\kappa'\lambda') (\mu\nu|\kappa\lambda) \\
= 2\, \sum_{\mu\nu\kappa\lambda}
& \re{ ({^q}\underline{\boldsymbol\mu} {^q}\bar{\boldsymbol\nu} | \kappa \lambda) }
\re{ (\mu\nu | {^q}\underline{\boldsymbol\kappa} {^q}\bar{\boldsymbol\lambda}) }
\end{align}
and exchange contributions
\begin{align} \label{eexch}
e_K^{(z)} = \sum_{\mu\nu\kappa\lambda} \sum_{\mu'\nu'\kappa'\lambda'} \Big[
\Big(
& \underline{P}^0_{\mu' \mu} \bar{P}^0_{\lambda \nu'} - \underline{P}^1_{\mu' \mu} \bar{P}^1_{\lambda \nu'}
- \underline{P}^2_{\mu' \mu} \bar{P}^2_{\lambda \nu'} - \underline{P}^3_{\mu' \mu} \bar{P}^3_{\lambda \nu'} \Big) \notag \\
\Big(
& \underline{P}^0_{\kappa' \kappa} \bar{P}^0_{\nu \lambda'} - \underline{P}^1_{\kappa' \kappa} \bar{P}^1_{\nu \lambda'}
- \underline{P}^2_{\kappa' \kappa} \bar{P}^2_{\nu \lambda'} - \underline{P}^3_{\kappa' \kappa} \bar{P}^3_{\nu \lambda'} \Big) \notag \\
- \Big(
& \underline{P}^0_{\mu' \mu} \bar{P}^1_{\lambda \nu'} + \underline{P}^1_{\mu' \mu} \bar{P}^0_{\lambda \nu'}
- \underline{P}^2_{\mu' \mu} \bar{P}^3_{\lambda \nu'} + \underline{P}^3_{\mu' \mu} \bar{P}^2_{\lambda \nu'} \Big) \notag \\
\Big(
& \underline{P}^0_{\kappa' \kappa} \bar{P}^1_{\nu \lambda'} + \underline{P}^1_{\kappa' \kappa} \bar{P}^0_{\nu \lambda'}
- \underline{P}^2_{\kappa' \kappa} \bar{P}^3_{\nu \lambda'} + \underline{P}^3_{\kappa' \kappa} \bar{P}^2_{\nu \lambda'} \Big) \notag \\
- \Big(
& \underline{P}^0_{\mu' \mu} \bar{P}^2_{\lambda \nu'} + \underline{P}^1_{\mu' \mu} \bar{P}^3_{\lambda \nu'}
+ \underline{P}^2_{\mu' \mu} \bar{P}^0_{\lambda \nu'} - \underline{P}^3_{\mu' \mu} \bar{P}^1_{\lambda \nu'} \Big) \notag \\
\Big(
& \underline{P}^0_{\kappa' \kappa} \bar{P}^2_{\nu \lambda'} + \underline{P}^1_{\kappa' \kappa} \bar{P}^3_{\nu \lambda'}
+ \underline{P}^2_{\kappa' \kappa} \bar{P}^0_{\nu \lambda'} - \underline{P}^3_{\kappa' \kappa} \bar{P}^1_{\nu \lambda'} \Big) \notag \\
- \Big(
& \underline{P}^0_{\mu' \mu} \bar{P}^3_{\lambda \nu'} - \underline{P}^1_{\mu' \mu} \bar{P}^2_{\lambda \nu'}
+ \underline{P}^2_{\mu' \mu} \bar{P}^1_{\lambda \nu'} + \underline{P}^3_{\mu' \mu} \bar{P}^0_{\lambda \nu'} \Big) \notag \\
\Big(
& \underline{P}^0_{\kappa' \kappa} \bar{P}^3_{\nu \lambda'} - \underline{P}^1_{\kappa' \kappa} \bar{P}^2_{\nu \lambda'}
+ \underline{P}^2_{\kappa' \kappa} \bar{P}^1_{\nu \lambda'} + \underline{P}^3_{\kappa' \kappa} \bar{P}^0_{\nu \lambda'} \Big) \Big] \notag \\
& (\mu'\nu'|\kappa'\lambda') (\mu\nu|\kappa\lambda) \\
= \sum_{\mu\nu\kappa\lambda} \sum_{\mu'\nu'\kappa'\lambda'}
& \re{{^q}\mathbf{\underline{P}}_{\mu' \mu}\, {^q}\mathbf{\bar{P}}_{\lambda \nu'}\,
{^q}\mathbf{\underline{P}}_{\kappa' \kappa}\, {^q}\mathbf{\bar{P}}_{\nu \lambda'} }
(\mu'\nu'|\kappa'\lambda') (\mu\nu|\kappa\lambda) \\
= \sum_{\mu\nu\kappa\lambda}
& \re{ ({^q}\underline{\boldsymbol\mu} {^q}\bar{\boldsymbol\nu} | \kappa \lambda)
(\mu {^q}\bar{\boldsymbol\lambda} | {^q}\underline{\boldsymbol\kappa} \nu) }
\end{align}
are expressed in terms of two-electron integrals and occupied
\begin{align} \label{psdeno}
{^q}\mathbf{\underline{P}}^{(z)}
&= |\omega_z|^{1/4}\, {^q}\mathbf{C}^o \, \exp(+\mathbf{\boldsymbol\varepsilon}^o t_z)\, ({^q}\mathbf{C}^o)^{\dag} \notag \\
&= |\omega_z|^{1/4}\, \exp(+t_z\, {^q}\mathbf{P}\, {^q}\mathbf{F})\, {^q}\mathbf{P}
\end{align}
and virtual quaternion pseudo-density matrices
\begin{align} \label{psdenv}
{^q}\mathbf{\bar{P}}^{(z)}
&= |\omega_z|^{1/4}\, {^q}\mathbf{C}^v\, \exp(-\mathbf{\boldsymbol\varepsilon}^v t_z)\, ({^q}\mathbf{C}^v)^{\dag} \notag \\
&= |\omega_z|^{1/4}\, \exp(-t_z\, {^q}\mathbf{Q}\, {^q}\mathbf{F})\, {^q}\mathbf{Q}
\text{.}
\end{align}
Apart from using quaternion rather than scalar Fock and density matrices,
the working equations to compute the SO 2C MP2 energy (Eqs.\ \eqref{ecoul} -- \eqref{eexch})
and the pseudo-density matrices (Eqs.\ \eqref{psdeno} -- \eqref{psdenv})
are identical to their NR counterparts.
The equations for computing the NR and spin-free (SF) MP2 energy
are identical because for the latter only the real part of the
quaternion pseudo-densities will be non-zero. The quaternion formalism therefore
leads to an easy identification of SO contributions to the MP2 energy: these
are due to the imaginary parts of the pseudo-densities.
\subsection{Schwarz-type integral estimates}
In his seminal work on the LT AO-based MP2 H{\"a}ser
introduced integral estimates that are employed
for a Schwarz-type screening of transformed integrals.\cite{Haeser1993}
Due to the similarity of the working equations for NR and 2C MP2,
the original Schwarz-type screening can be extended easily
to discard contributions of AO quadruple to the Coulomb
\begin{align} \label{scrj}
& | (\underline{\mu}^{q_1} \bar{\nu}^{q_1} | \kappa \lambda)
(\mu\nu | \underline{\kappa}^{q_1} \bar{\lambda}^{q_1}) |
\le Z_{\mu \nu}^{q_1 q_1}\, Q_{\kappa \lambda} \, Q_{\mu \nu} \, Z_{\kappa \lambda}^{q_1 q_1}
\end{align}
and the exchange contribution
\begin{align} \label{scrk}
& | (\underline{\mu}^{q_1} \bar{\nu}^{q_2} | \kappa \lambda)
(\mu \bar{\lambda}^{q_2} | \underline{\kappa}^{q_1} \nu) |
\le Z_{\mu \nu}^{q_1 q_2}\, Q_{\kappa \lambda} \, Y_{\mu \lambda}^{q_2} \, X_{\kappa \nu}^{q_1}
\end{align}
to the 2C MP2 correlation energy.
The (quaternion pseudo-)Schwarz estimates in Eqs. \eqref{scrj} -- \eqref{scrk}
are given by:
\begin{align}
\left(Q_{\mu \nu} \right)^2 &=
(\mu \nu| \mu \nu) \text{,} \label{estq} \\
\left(X_{\mu \nu}^{q_1} \right)^2 &=
\underline{P}_{\mu' \mu}^{q_1} \underline{P}_{\kappa' \mu}^{q_1} (\mu' \nu|\kappa' \nu) \text{,} \label{estx} \\
\left(Y_{\mu \nu}^{q_1} \right)^2 &=
\bar{P}_{\nu \nu'}^{q_1} \bar{P}_{\nu \lambda'}^{q_1} (\mu \nu'|\mu \lambda') \text{,} \label{esty} \\
Z_{\mu \nu}^{q_1 q_2} &=
\min( \sum_{\nu'} X_{\mu \nu'}^{q_1} |\bar{P}_{\nu\gn'}^{q_2}| ,
\sum_{\mu'} |\underline{P}_{\mu'\mu}^{q_1}| Y_{\mu' \nu}^{q_2} )
\label{estz} \text{.}
\end{align}
To keep the screening procedure computationally efficient
and also retain the rotational invariance of the MP2 energy,
the Coulomb (Eq. \eqref{scrj}) and exchange contributions
(Eq. \eqref{scrk}) should
be screened at the level of shells rather than individual
AO basis functions.
Thus, for the estimates $\mathbf{Q}$, ${^q}\mathbf{X}$,
${^q}\mathbf{Y}$, and ${^{q, q}}\mathbf{Z}$
the maximum or Frobenius norm computed for all
basis functions that are associated with a shell pair
are employed for screening.
The Schwarz-type screening of Ref.\ \onlinecite{Haeser1993}
allows for an $\mathcal{O}(N^2)$ scaling with the system size $N$.
However, as it was shown for the NR LT AO-based MP2\cite{Doser2009,Maurer2013}
efficient linearly scaling implementations ($\mathcal{O}(N)$)
are only in reach if one accounts for the physically
correct decay behavior of two charge distributions separated by $R$.
For the exchange term $E_K$ fast exponential decay is expected.
The familiar $R^{-6}$ decay of $E_J$ at large $R$ is due to the
orthogonality of the occupied and virtual orbital space
which causes the zeroth-order moments of the multipole expansion
of $1/R$ to vanish.\cite{Ayala1999,Lambrecht2005a}
This holds for 2C LT AO-based MP2 as well and can be expressed
through an analogous orthogonality condition:
\begin{align} \label{zeroovlp}
0 = {^q}\mathbf{ \underline{P}}^{(z)} \, \mathbf{S}\, {^q}\mathbf{ \bar{P}}^{(z)}
\text{.}
\end{align}
Consequently, the efficient distance dependence adaptation of
H{\"a}ser's integral estimates proposed by Ochsenfeld and
his co-workers\cite{Maurer2013}
can be easily adapted to the 2C LT AO-based MP2
implementation to achieve linear scaling eventually.
\section{Computational details}
The LT AO-based MP2 energy formulation
for relativistic 2C Hamiltonians was implemented in a
development version of DIRAC.
The two-electron integrals were computed with routines provided
by the InteRest library.\cite{Repisky2013}
For all HF calculations the molecular mean field X2C Hamiltonian\cite{Sikkema2009}
was used.
For the preceding 4C HF calculations only the LL and LS type
two-electron integrals were calculated.\cite{Visscher1997}
Point-group symmetry was exploited at the HF level for
the HX molecules, only.
Nuclei were treated as Gaussian charge distributions.\cite{Visscher1997b}
For HX (X = F, Cl, Br, I, and At)
we froze 2, 10, 18, 36, and 54~core electrons and 2, 6, 26, 40, and 96~anti-core
electrons, respectively, and employed the all-electron double-zeta basis
set of Dyall.\cite{Dyallunpub,*Dyall2006,*Dyall2012}
Experimental equilibrium bond distances\cite{nistdiatom} were used for (HX, X=F,Cl,Br, and I);
0.9168~{\AA} (F), 1.2746~{\AA} (Cl), 1.4144~{\AA} (Br), and 1.6092~{\AA} (I).
The HAt bond distance 1.7075~{\AA} was taken from
an all-electron calculation of Peterson et al.\cite{Peterson2003}
The geometry of Hg-porphyrin was optimized with symmetry constraints
of the $D_{2h}$ point group by using the
Turbomole package\cite{TM-V7.0} and is provided in the supporting information.\cite{si}
For the energy and gradient calculation we employed the dispersion-corrected\cite{Grimme2006,*Grimme2010} (D3)
PBE density functional\cite{Perdew1996} and the def2-TZVP basis set.
For the same calculation, an effective core potential\cite{Andrae1990}
for Hg with 60 core electrons
and multipole accelerated density fitting\cite{Eichkorn1995,*Eichkorn1995a,*Sierka2003}
were used for reasons of performance.
For the AO-based MP2 calculation of Hg-porphyrin we used the SVP\cite{Schaefer1992}
(H,C, and N) and all-electron double-zeta basis\cite{Dyall2012a}
sets (Hg) and froze 60~core and 24~anti-core electrons.
In case of Ba\tief{2} the all-electron double-zeta basis\cite{Dyall2012a} was employed
and the 72~core and 24~anti-core electrons were frozen.
The Laplace parameters $\omega_{z}$ and $t_{z}$
were obtained by the minimax approximation\cite{Takatsuka2008,*Helmich2016}
for a fixed number of quadrature points ($n_z=18$ for HX, $n_z=27$ for Ba\tief{2}, and
$n_z=1$ for Hg-porphyrin).
The errors in MP2 correlation energies for the diatomic molecules
caused by the numerical quadrature were always lower than $10^{-8}$~a.\ u.
as was
verified by comparison with a reference (MO-based) implementation\cite{Laerdahl1997}.
For Hg-porphyrin only the quaternion Schwarz-type estimates were computed, the
MP2 correlation energy was not determined.
\section{Results and discussion}
\subsection{Comparison with spinor-based implementations}
Compared to the NR formulation, the LT AO-based
formulation of MP2 energies for relativistic 2C Hamiltonians
requires 16 times more operations for the computation of HTIs.
Contraction of HTIs to the MP2 energy has essentially the same scaling as NR for
the 2C Coulomb contributions $e_J^{(z)}$, and requires a 4 times larger
effort for 2C exchange contributions $e_K^{(z)}$.
The ``SO factor'' of 16 in the time-determining
transformation step of our purely AO-based formulation
is similar to the factor of 16 found for the first half-transformation in the conventional
KR spinor-based approach\cite{Laerdahl1997,*Thyssen2008}.
In both cases this arises from the need to use
a quaternion multiplication in the transformation of the second index,
which takes $4\times 4=16$ terms
more operations than multiplication of real matrices.
In the conventional formalism, also a second half-transformation
is required in which the quaternion unit of the
second electron becomes active.
This leads ultimately to
a factor of $16\times 4= 64$ if no symmetry can be used.
In practice, one finds that for a spinor-based MP2 implementation
the most expensive step is often the initial quarter transformation,
which has a theoretical scaling factor of only 4.
Furthermore, only part of the spinors are taken as
active in correlation calculation, thereby reducing the
size of matrices as the index transformation proceeds.
Such reductions are particularly effective for heavy
elements in which a number of core orbitals (and the associated
virtuals with high energies) can be frozen.
For larger molecules, in which typically also many lighter elements
are present, the reduction in matrix size is smaller and the later
steps of the index transformation become important. For
such systems the AO-based formalism of the LT
should therefore become competitive, also because integral screening
can be very effective with the highly localized densities of heavy elements.
It was shown for NR LT AO-based MP2
that integral screening leads to low-order\cite{Haeser1993,Ayala1999,Maurer2014}
or even linearly scaling implementations\cite{Doser2009,Maurer2013}
for medium- and large-sized systems.
Thus, screening and the better SO scaling of the LT AO-based approach
has the potential for early break-even points with spinor-based approaches.
\subsection{Effect of the nuclear charge on the energy contributions}
Our current implementation does not exploit any sparsity
and has a hard $\mathcal{O}(N^5)$ scaling with the system size $N$.
To show the potential of screening on the computational work,
we analyze the 16~components of
$|({^q}\underline{\boldsymbol\mu} \, {^q}\bar{\boldsymbol\nu} | \kappa \lambda)|^2$
from Eqs.\ \eqref{ecoul} -- \eqref{eexch}
for the halogen hydrides HX (X = F, Cl, Br, I, and At)
in Fig.\ \ref{fig1}.
Note that if the nuclei of a linear molecule are located
at one of the Cartesian coordinate axes, two of the three imaginary quaternion parts
will be identical for symmetry reasons.
For HX in Fig.\ \ref{fig1} as well as Ba\tief{2} in Figs.\ \ref{fig2} -- \ref{fig3}
we chose the z-axis as molecular axis; thus $q=2$ and $q=3$ are equivalent.
The real or SF parts of the quaternion pseudo-densities ${^q}\mathbf{\underline{P}}$ and ${^q}\mathbf{\bar{P}}$
are much larger then the imaginary or SO parts, which allows for the following grouping
of HTIs according to the 16~different combinations termed $(q_1,q_2)$
of ${^q}\mathbf{\underline{P}}$ and ${^q}\mathbf{\bar{P}}$:
(I) only SF densities;
(II) one SF and one SO density;
(III) two SO densities.
As can be seen from Fig.\ \ref{fig1},
the difference is most distinct for the lightest hydride X=F where
(I) and (II) differ roughly by a factor of $10^{-6}$
while (I) and (III) differ by $10^{-12}$.
For such a light molecule, the energy contributions from HTIs that
contain only SO densities
are neglected without loss of accuracy if screening is exploited.
Since the mixed SF-SO density contributions are small as well,
the SF formalism suffices to describe the
2C MP2 energy sufficiently accurate for such a light molecule
--- the relative deviation to SO 2C MP2 is $2.8\times 10^{-6}$ only.
The difference between (I) and (II)
HTIs and (II) and (III) HTIs decreases by one and two orders of magnitude,
respectively, each time we compare with a heavier homologue.
For the heaviest halogen hydride HAt the SF-only
HTIs and the mixed SF-SO HTIs differ by a factor of $10^{-2}$
while the former and the SO-only HTIs differ roughly by $10^{-4}$.
For HAt the relative deviation between SF and 2C MP2 is
much larger ($2.5\times 10^{-3}$) than for X=F.
Thus, the SF approximation shows only limited accuracy for this small molecule that
is dominated by the heavy element. For larger molecules in which one or more heavy
atoms are present a complete neglect of SO coupling
may likewise lead to significant errors. However, as all HTIs are expressed in the AO basis,
it is still possible to obtain considerable savings by only neglecting SO contributions for
pseudo density matrix elements of the light elements. Such savings are not possible in
conventional MO-based electron correlation treatments.
\subsection{Distance dependence of the energy contributions and estimates}
Besides the nuclear charge, the inter-electronic distance
has a substantial effect on screening and its utilization results
eventually in a linearly scaling relativistic MP2 implementation.\cite{Doser2009,Maurer2013}
First, this distance behavior is investigated by
means of the contributions to the interaction energy of Ba\tief{2} in Fig.\ \ref{fig2}.
$E_J$ shows the typical $R^{-6}$ decay of the dispersion
energy as explained in Sec. \ref{theory},
the 4 contributions to $E_K$ decay more rapidly than the Coulomb
contribution; but the expected exponential scaling
is hard to observe as the values result from taking
differences between small numbers.
Amongst the 4 exchange contribution, the one that includes the SF-only
HTIs is clearly the largest while the other 3 contribute only little.
It is also clear that the decay of the already small SO contributions $E_K(q=1,2=3)$ is at least
as fast as the SF $E_K(0)$ contribution.
Individual elements of the ${^q}\mathbf{X}$ estimates are shown in Fig.\ \ref{fig3}
for selected points of the Ba\tief{2} potential curve from Fig.\ \ref{fig2}.
Like in case of the halogen hydrides,
the SF part of the ${^q}\mathbf{X}$ estimates is largest
in magnitude, that is,
the largest element in $\mathbf{X}^0$ is always more than a factor of 30
larger than in $\mathbf{X}^{q_1}$ with $q_1 = 1,2=3$.
As the inter-atomic distance increases, the largest elements of
the two intra-atomic blocks remains almost constant whereas
the largest element of the two inter-atomic blocks decreases
and is at R=50~a.\ u.\ less than $1.4\times 10^{-6}$, $6.1\times 10^{-10}$,
and $1.4\times 10^{-7}$ for $\mathbf{X}^{q_1}$ with $q_1 = 0,1,2=3$, respectively.
Thus, individual elements of the SF and SO pseudo-Schwarz estimates, which are used to
screen contributions to the 2C MP2 energy, become smaller in magnitude
as the inter-atomic distance increases.
If contributions to the 2C MP2 energy are screened by means of SF and SO
pseudo-Schwarz estimates in Eqs.\ \eqref{estx} -- \eqref{estz},
reduced- or even linear-scaling implementations can be designed
as for NR AO-based MP2\cite{Doser2009,Maurer2013,Maurer2014}.
Like for HTIs in Fig.\ \ref{fig1} and for the contributions to the exchange interaction
energy in Fig.\ \ref{fig2} the SO part of the estimates $\mathbf{X}^{q_1}$ with $q_1 = 1,\ldots,3$
is much smaller than the SF part, too.
This will result in a much more efficient computation of the SO, rather than the SF,
energy contributions once screening is exploited.
Therefore, in practice, it is expected that the inherent ``SO factor'' of 4 and 16
for the integral contraction and transformation, respectively,
is reduced significantly as there are relatively more SO contributions that fall
below threshold at larger distances than SF contributions.
\subsection{
Combined effect of the nuclear charge and
the inter-electronic distance on screening
}
To illustrate the joint effects of the nuclear charge
from different elements and the inter-electronic distances,
we calculated the estimates ${^q}\mathbf{X}$, ${^q}\mathbf{Y}$,
and some of ${^{q,q}}\mathbf{Z}$ for Hg-porphyrin as depicted in Fig.\ \ref{fig4}.
Note that as for the linear molecules HX and Ba\tief{2}
two of the three imaginary quaternion parts are identical ($q=2$ and $q=3$)
because the x- and y-axis of the molecular coordinate system
coincide with the $C_2$ symmetry elements of the $D_{2h}$ point group.
Since molecules that are mainly composed of a very few heavy metal elements
surrounded by organic ligands are highly relevant for synthetic and
bio- organic and inorganic chemistry,
Hg-porphyrin is an ideal example to investigate.
As expected, the shell pairs of light elements in porphyrin make only significant
contributions to the SF part of the estimates ($q=0$).
Consequently, the light elements will mainly contribute to SF part of the 2C MP2 energy
while Hg dominate the SO part of the 2C MP2 energy.
The largest element in any of the estimates is always one of the Hg-Hg shell pairs,
except for $\mathbf{Y}^0$ where the maximum value is one of the N-N shell pairs.
The H-H shell pairs contribute the least to the estimates,
especially for the SO type estimates.
Furthermore, it can be observed that
the closer the light atoms are to Hg the larger are their estimates.
For example, consider the C-C blocks,
where the 8 C atoms that are neighbors of the N atoms
have larger estimates than the remaining 12 C atoms located
at the outside and bridges of the porphyrin ring.
Since the estimates are employed to screen contributions of shell
quadruple to the MP2 correlation energy, we can conclude that
the largest contributions, both SF and SO, to the correlation energy
originate from the Hg and N atoms and the least from the H atoms.
A more detailed analysis and also quantification of the number of
screened shell quadruples is beyond the scope of the
present work and can be done once the distance-dependent extension
of the pseudo-Schwarz estimates is available.
\section{Conclusions}
We presented a formulation that is ready for combining
linear-scaling techniques for wave-function
methods with relativistic methods
that solve the Dirac equation explicitly.
Working equations are given for the LT AO-based
MP2 for relativistic 2C Hamiltonians in the KR
formalism and compared to their NR counterparts.
By an analysis of the norm of HTIs
it is shown that for light molecules contributions
that arise from taking SO coupling into account
can be easily neglected by screening.
For molecules with heavy atoms those SO contributions are important and
will not be completely neglected when screening is exploited.
Furthermore, we have shown that the relativistic 2C Coulomb and exchange contributions
to the correlation energy
feature the same decay properties with an increasing separation
of charge distributions as their NR counterparts.
An adaptation of distance-dependent integral estimates developed
for NR MP2 to quaternion-based HTIs will therefore result in
a linearly scaling 2C MP2 implementation with early break-even points
compared to conventional spinor-based implementations.
Schwarz-type screening estimates can be adapted easily
to the 2C LT AO-based MP2 formalism.
Both SF- and SO-type estimates become negligible for large inter-electronic
distances.
For light elements only the SF-type estimates show sizable
contributions,
which makes the 2C LT AO-based MP2 formalism attractive
for calculation on large metal-organic complexes
once a linearly scaling implementation is available.
\section{Acknowledgments}
Financial support from the German research foundation DFG
through grant number HE 7427/1-1 is gratefully acknowledged.
MR acknowledges support from the Research Council of Norway
through a Centre of Excellence Grant (No. 179568/V30).
The authors thank Trond Saue for helpful discussions
on the quaternion formulation of the Dirac--Hartree--Fock method.
|
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Willshire es una villa ubicada en el condado de Van Wert en el estado estadounidense de Ohio. En el Censo de 2010 tenía una población de 397 habitantes y una densidad poblacional de 410,95 personas por km².
Geografía
Willshire se encuentra ubicada en las coordenadas . Según la Oficina del Censo de los Estados Unidos, Willshire tiene una superficie total de 0.97 km², de la cual 0.96 km² corresponden a tierra firme y (0.54%) 0.01 km² es agua.
Demografía
Según el censo de 2010, había 397 personas residiendo en Willshire. La densidad de población era de 410,95 hab./km². De los 397 habitantes, Willshire estaba compuesto por el 97.73% blancos, el 1.01% eran afroamericanos, el 0.5% eran amerindios, el 0% eran asiáticos, el 0.25% eran isleños del Pacífico, el 0% eran de otras razas y el 0.5% pertenecían a dos o más razas. Del total de la población el 0.76% eran hispanos o latinos de cualquier raza.
Referencias
Enlaces externos
Villas de Ohio
Localidades del condado de Van Wert
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
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\section{Supplementary Material}
\subsection{Sound absorption and attenuation in a liquid}
Fluid viscosity will cause sound absorption and attenuation in a liquid. To
discuss this effect, we begin with linearlized Navier-Stokes equation,
\begin{equation}
\rho \frac{\partial \mathbf{u}}{\partial t}=-\nabla p+\left( \frac{4}{3}\eta
+\chi \right) \nabla \left( \nabla \cdot \mathbf{u}\right) -\eta \nabla
\times \nabla \times \mathbf{u,} \label{LNSE}
\end{equation}%
where $\rho $ is the fluid density, $\mathbf{u}$ is the flow velocity, $p$
is the pressure, $\eta $ and $\chi $ are the shear and compressional
viscosities respectivley. The instantaneous density $\rho $ may be further
written as $\rho =\rho _{0}\left( 1+s\right) $, where $s$ is a small
fraction and $\rho _{0}$ is a constant. Then equation of coninuity has the
following form
\begin{equation}
\nabla \cdot \mathbf{u}=-\frac{\partial s}{\partial t}.
\end{equation}%
The acoustic pressure $p$ is found to be of the form%
\begin{equation}
p=\left( \frac{\partial p}{\partial \rho }\right) _{\rho _{0}}\rho
_{0}s=\rho _{0}v_{s}^{2}s
\end{equation}%
in terms of $s$ and the sound velocity $v_{s}$. So that we have a lossy wave
equation
\begin{equation}
\left( 1+\tau _{s}\frac{\partial }{\partial t}\right) \nabla ^{2}p=\frac{1}{%
v_{s}^{2}}\frac{\partial ^{2}p}{\partial t^{2}},
\end{equation}%
with a relaxation time given by Eqs.(10). If we assume monofrequency motion,
the above wave quations is reduced to a lossy Helmholtz equation%
\begin{equation}
\nabla ^{2}p+k^{2}p=0,
\end{equation}%
where $k=\frac{\omega }{v_{s}}\frac{1}{\left( 1+i\omega \tau _{s}\right)
^{1/2}}$. The solution for $\alpha =-$Im$k$ reads
\begin{equation}
\alpha =\frac{1}{\sqrt{2}}\frac{\omega }{v_{s}}\left[ \frac{\sqrt{1+\left(
\omega \tau _{s}\right) ^{2}}-1}{1+\left( \omega \tau _{s}\right) ^{2}}%
\right] ^{1/2}.
\end{equation}%
In the limit $\omega \tau _{s}\ll 1$, we have the sound attenuation
coefficient in Eq.(11).
\subsection{Screened spinon phonon coupling for longitudinal mode}
Without the loss of generality, the spinon phonon coupling $M_{\mathbf{k}%
\lambda }\left( \mathbf{q}\right) $ for longitudinal sound can be written in
terms of spherical harmonic functions,%
\begin{equation}
M_{\mathbf{k}\lambda }\left( \mathbf{q}\right) =\frac{1}{3}%
f(k,q)+\sum\limits_{l\geq 1,m}a_{lm}Y_{lm}\left( \theta ,\phi \right) ,
\label{MkE}
\end{equation}%
where $f(k,q)=\frac{k^{2}q}{m\sqrt{2\rho _{ion}\omega _{\mathbf{q}\lambda }}}
$, $\theta $ is the angle between $\mathbf{k}$ and $\mathbf{q}$, $\phi $ is
the azimuthal angle of $\mathbf{k}$. For longitudinal mode, the Thomas Fermi
screening length $k_{\text{TF}}^{-1}$ is much shorter than $q^{-1}$. We
shall show that the monople part $\frac{1}{3}f(k,q)$ will be screened by
charge fluctuation, resulting in an effective coupling matrix $\tilde{M}_{%
\mathbf{k}\lambda }\left( \mathbf{q},\omega \right) $ containing only higher
order terms in multipole expansion (\ref{MkE}) and a term of order of $%
v_{s}/v_{F}$.
\begin{figure}[hpbt]
\includegraphics[width=7.6cm]{fig3.eps}
\caption{(a) Screening effect of spinon density-density interaction $U$,
zigzag lines denote unscreened interaction $U^{(0)}$, double zigzag lines
denote screened interaction $U$, the bubble is for the polarization function
$P$. (b) The bare spinon phonon coupling. (c) Screened part of spinon phonon
coupling. }
\label{fig3}
\end{figure}
We firstly consider screening effect of the bare spinon density-density
interaction $U^{(0)}\left( \mathbf{q},\omega \right) $, which gives rise to
the screened interaction%
\begin{equation}
U\left( \mathbf{q},\omega \right) =\frac{U^{\left( 0\right) }\left( \mathbf{q%
},\omega \right) }{1-P\left( \mathbf{q},\omega \right) U^{\left( 0\right)
}\left( \mathbf{q},\omega \right) },
\end{equation}%
where $P$ is the polarization function in an impure fermi system which is
given by the bubble diagram in Fig.3(a). The screening of spinon phonon
coupling is very similar to that of $U$. These two can be evaluated through
the same vertex function. We divide the screened spinon phonon coupling $%
\tilde{M}_{\mathbf{k}\lambda }\left( \mathbf{q},\omega \right) $ into two
parts,%
\begin{equation}
\tilde{M}_{\mathbf{k}\lambda }\left( \mathbf{q},\omega \right) =M_{\mathbf{k}%
\lambda }\left( \mathbf{q}\right) +M_{\mathbf{k}\lambda }^{(1)}\left(
\mathbf{q},\omega \right) ,
\end{equation}%
where $M_{\mathbf{k}\lambda }^{(1)}$ in Matsubara frequency is given by
\begin{equation}
M_{\mathbf{k}\lambda }^{(1)}\left( \mathbf{q},i\omega _{n}\right) =\frac{2}{%
\beta }\sum_{ik_{m},\mathbf{k}}M_{\mathbf{k}\lambda }\left( \mathbf{q}%
\right) \mathcal{G}\left( \mathbf{k+q},ik_{m}\right) \mathcal{G}\left(
\mathbf{k},i\omega _{n}+ik_{m}\right) U\left( \mathbf{q},i\omega _{n}\right)
\gamma \left( \mathbf{q},\mathbf{k},ik_{m},i\omega _{n}+ik_{m}\right) ,
\end{equation}%
as shown in Fig.3(c). The vertex function $\gamma $ is the solution of the
following equation,%
\begin{eqnarray}
\gamma \left( \mathbf{q,k},ik_{m},i\omega _{n}+ik_{m}\right)
&=&1+n_{imp}\sum_{\mathbf{k}^{\prime }}\mathcal{G}\left( \mathbf{k}^{\prime }%
\mathbf{+q},ik_{m}\right) \mathcal{G}\left( \mathbf{k}^{\prime },i\omega
_{n}+ik_{m}\right) \notag \\
&&\times T_{\mathbf{k+q,k}^{\prime }\mathbf{+q}}\left( ik_{m}\right) T_{%
\mathbf{k}^{\prime }\mathbf{k}}\left( i\omega _{n}+ik_{m}\right) \gamma
\left( \mathbf{q,k}^{\prime },ik_{m},i\omega _{n}+ik_{m}\right) ,
\end{eqnarray}%
where $T_{\mathbf{k}^{\prime }\mathbf{k}}$ is the transition matrix due to
multiple impurity scattering and $n_{imp}$ is the impurity density.
To proceed we shall make use of the following approximations,%
\begin{eqnarray}
\mathcal{G}_{\text{adv}}\left( \mathbf{k+q},\epsilon \right) \mathcal{G}_{%
\text{ret}}\left( \mathbf{k},\epsilon +\omega \right) &\simeq &\frac{2i\pi
\delta \left( \epsilon -\xi _{\mathbf{k}}\right) }{qv_{F}\cos \theta +\omega
+i/\tau }, \\
\int \frac{d\epsilon }{2\pi i}n_{F}\left( \epsilon \right) \mathcal{G}_{%
\text{ret}}\left( \mathbf{k+q},\epsilon \right) \mathcal{G}_{\text{ret}%
}\left( \mathbf{k},\epsilon +\omega \right) &\simeq &-\frac{\partial
n_{F}\left( \xi _{\mathbf{k}}\right) }{\partial \xi _{\mathbf{k}}}, \\
\int \frac{d\epsilon }{2\pi i}n_{F}\left( \epsilon \right) \mathcal{G}_{%
\text{adv}}\left( \mathbf{k+q},\epsilon \right) \mathcal{G}_{\text{adv}%
}\left( \mathbf{k},\epsilon -\omega \right) &\simeq &\frac{\partial
n_{F}\left( \xi _{\mathbf{k}}\right) }{\partial \xi _{\mathbf{k}}}.
\end{eqnarray}%
For $l\geq 1$, one sees that%
\begin{equation}
\int d\Omega Y_{lm}\left( \theta ,\phi \right) \int \frac{d\epsilon }{2\pi i}%
n_{F}\left( \epsilon \right) \mathcal{G}_{\text{ret(adv)}}\left( \mathbf{k+q}%
,\epsilon \right) \mathcal{G}_{\text{ret(adv)}}\left( \mathbf{k},\epsilon
+\omega \right) =0.
\end{equation}%
With the help of optical sum rule and using the relation
\begin{equation*}
\frac{1}{2\tau }=-n_{imp}\text{Im}T_{\mathbf{kk}},
\end{equation*}%
we find that%
\begin{eqnarray}
\gamma _{1}\left( \mathbf{q,k},\epsilon ,\epsilon +\omega \right) &\equiv
&\gamma \left( \mathbf{q,k},\epsilon -i\eta ,\epsilon +\omega +i\eta \right)
=\frac{1}{1+s_{0}\left( a\right) /a}, \\
\gamma _{2}\left( \mathbf{q,k},\epsilon ,\epsilon +\omega \right) &\equiv
&\gamma \left( \mathbf{q,k},\epsilon +i\eta ,\epsilon +\omega +i\eta \right)
=1,
\end{eqnarray}%
where $a=ql/(1+i\omega \tau )$. Hereafter we shall assume $\omega \tau =%
\frac{v_{s}}{v_{F}}ql\ll 1$ and set $a=ql$. So that the polarization
function $P$ can be evaluated as follows,%
\begin{equation}
P\left( \mathbf{q},i\omega _{n}\right) =\sum_{\mathbf{k}}\sum_{ik_{m}}%
\mathcal{G}\left( \mathbf{k+q},ik_{m}\right) \mathcal{G}\left( \mathbf{k}%
,i\omega _{n}+ik_{m}\right) \gamma \left( \mathbf{q,k},ik_{m},i\omega
_{n}+ik_{m}\right) ,
\end{equation}%
Taking analytical continuation, we have%
\begin{eqnarray}
P\left( \mathbf{q},\omega \right) &=&2i\sum_{\mathbf{k}}\int_{-\infty
}^{\infty }\frac{d\epsilon }{2\pi }n_{F}\left( \epsilon \right) \gamma
_{2}\left( \mathbf{q,k},\epsilon ,\epsilon +\omega \right) \notag \\
&&\times \left[ \mathcal{G}_{\text{ret}}\left( \mathbf{k},\epsilon +\omega
\right) \mathcal{G}_{\text{ret}}\left( \mathbf{k+q},\epsilon \right) -%
\mathcal{G}_{\text{adv}}\left( \mathbf{k+q},\epsilon -\omega \right)
\mathcal{G}_{\text{adv}}\left( \mathbf{k},\epsilon \right) \right] \notag \\
&&+2i\sum_{\mathbf{k}}\int_{-\infty }^{\infty }\frac{d\epsilon }{2\pi }%
n_{F}\left( \epsilon \right) \gamma _{1}\left( \mathbf{q,k},\epsilon
,\epsilon +\omega \right) \notag \\
&&\times \left[ -\mathcal{G}_{\text{ret}}\left( \mathbf{k},\epsilon +\omega
\right) \mathcal{G}_{\text{adv}}\left( \mathbf{k+q},\epsilon \right) +%
\mathcal{G}_{\text{adv}}\left( \mathbf{k+q},\epsilon -\omega \right)
\mathcal{G}_{\text{ret}}\left( \mathbf{k},\epsilon \right) \right] \notag \\
&=&-N\left( 0\right) \left[ 1-i\omega \tau \frac{s_{0}\left( a\right) /a}{%
1+s_{0}\left( a\right) /a}\right] ,
\end{eqnarray}%
When the Thomas Fermi screening length $k_{\text{TF}}^{-1}\ll q^{-1}$, $%
N\left( 0\right) U^{\left( 0\right) }\left( \mathbf{q},\omega \right) \gg 1$%
, $U\left( \mathbf{q},\omega \right) $ can be reduced to%
\begin{equation}
U\left( \mathbf{q},\omega \right) =\frac{1}{N\left( 0\right) \left[
1-i\omega \tau \frac{s_{0}\left( a\right) /a}{1+s_{0}\left( a\right) /a}%
\right] }.
\end{equation}%
Then we are ready to calculate $M_{\mathbf{k}\lambda }^{(1)}\left( \mathbf{q}%
\right) $,%
\begin{eqnarray}
M_{\mathbf{k}\lambda }^{(1)}\left( \mathbf{q},\omega \right) &=&\frac{2}{%
\beta }\sum_{\mathbf{k}}M_{\mathbf{k}\lambda }\left( \mathbf{q}\right)
\sum_{ik_{m}}\mathcal{G}\left( \mathbf{k+q},ik_{m}\right) \mathcal{G}\left(
\mathbf{k},i\omega _{n}+ik_{m}\right) \gamma U\left( \mathbf{q},i\omega
_{n}\right) \notag \\
&=&\frac{1}{3}f\left( k,q\right) P\left( \mathbf{q},\omega \right) U\left(
\mathbf{q},\omega \right) -2i\omega f\left( k,q\right) \sum_{\mathbf{k}%
}\left( \cos ^{2}\theta -\frac{1}{3}\right) \notag \\
&&\times \int_{-\infty }^{\infty }\frac{d\epsilon }{2\pi }\left[ -\frac{%
\partial n_{F}\left( \epsilon \right) }{\partial \epsilon }\right] \mathcal{G%
}_{\text{ret}}\left( \mathbf{k},\epsilon +\omega \right) \mathcal{G}_{\text{%
adv}}\left( \mathbf{k+q},\epsilon \right) \gamma _{1}U\left( \mathbf{q}%
,\omega \right) \notag \\
&=&f\left( k,q\right) \left[ -\frac{1}{3}+i\frac{\omega \tau }{a}\frac{%
s_{2}\left( a\right) -s_{0}\left( a\right) /3}{1+\left( 1-i\omega \tau
\right) s_{0}\left( a\right) /a}\right]
\end{eqnarray}%
Therefore%
\begin{equation*}
\tilde{M}_{\mathbf{k}\lambda }\left( \mathbf{q}\right) =\frac{k^{2}q}{m\sqrt{%
2\rho _{ion}\omega _{\mathbf{q}\lambda }}}\left[ \cos ^{2}\theta -\frac{1}{3}%
+i\frac{v_{s}}{v_{F}}\frac{s_{2}\left( a\right) -s_{0}\left( a\right) /3}{%
1+\left( 1-i\omega \tau \right) s_{0}\left( a\right) /a}\right] .
\end{equation*}%
Thus we can calculate the sound attenuation constant through the unscreened
bubble [Fig1.(a)] with the traceless coupling matrix,%
\begin{equation}
\tilde{M}_{\mathbf{k}\lambda }\left( \mathbf{q}\right) =\frac{\left( \mathbf{%
k}\cdot \mathbf{q}\right) \left( \mathbf{k}\cdot \hat{\varepsilon}_{\mathbf{q%
}\lambda }\right) -\frac{1}{3}k^{2}\left( \mathbf{q}\cdot \hat{\varepsilon}_{%
\mathbf{q}\lambda }\right) }{m\sqrt{2\rho _{ion}\omega _{\mathbf{q}\lambda }}%
}+O\left( \frac{v_{s}}{v_{F}}\right) ,
\end{equation}%
for longitudinal mode.
\subsection{Longitudinal sound attenuation}
Then we calculate longitudinal sound attenuation constant using the above
spinon phonon coupling. In this case, we can express $\Pi \left( \mathbf{q}%
,i\omega _{n}\right) $ in terms of a vertex function $\Gamma \left( \mathbf{%
q,k},ik_{m},i\omega _{n}+ik_{m}\right) $,
\begin{equation}
\Pi \left( \mathbf{q},i\omega _{n}\right) =\frac{2}{\beta }\sum_{\mathbf{k}}%
\tilde{M}_{\mathbf{k}\lambda }\left( \mathbf{q}\right) \sum_{ik_{m}}\mathcal{%
G}\left( \mathbf{k+q},ik_{m}\right) \mathcal{G}\left( \mathbf{k},i\omega
_{n}+ik_{m}\right) \Gamma \left( \mathbf{q,k},ik_{m},i\omega
_{n}+ik_{m}\right) , \label{PiL1}
\end{equation}%
where the vertex function $\Gamma $ obeys%
\begin{eqnarray}
\Gamma \left( \mathbf{q,k},ik_{m},i\omega _{n}+ik_{m}\right) &=&\tilde{M}_{%
\mathbf{k}\lambda }\left( \mathbf{q}\right) +n_{imp}\sum_{\mathbf{k}^{\prime
}}\mathcal{G}\left( \mathbf{k}^{\prime }\mathbf{+q},ik_{m}\right) \mathcal{G}%
\left( \mathbf{k}^{\prime },i\omega _{n}+ik_{m}\right) \notag \\
&&\times T_{\mathbf{k+q,k}^{\prime }\mathbf{+q}}\left( ik_{m}\right) T_{%
\mathbf{k}^{\prime }\mathbf{k}}\left( i\omega _{n}+ik_{m}\right) \Gamma
\left( \mathbf{q,k}^{\prime },ik_{m},i\omega _{n}+ik_{m}\right) ,
\end{eqnarray}%
and is shown in Fig.4 diagramatically.
\begin{figure}[tbph]
\includegraphics[width=7.5cm]{fig4.eps}
\caption{Vertex correction in longitudinal sound, the dash line across the
vertex denotes impurity scattering.}
\label{fig4}
\end{figure}
It is more convenient to write the analytical continuations of $\Gamma $ as
follows,
\begin{eqnarray}
\Gamma _{1}\left( \mathbf{q,k},\epsilon ,\epsilon +\omega \right) &\equiv
&\Gamma \left( \mathbf{q,k},\epsilon -i\eta ,\epsilon +\omega +i\eta \right)
, \\
\Gamma _{2}\left( \mathbf{q,k},\epsilon ,\epsilon +\omega \right) &\equiv
&\Gamma \left( \mathbf{q,k},\epsilon +i\eta ,\epsilon +\omega +i\eta \right)
.
\end{eqnarray}%
We find out the following two solutions,%
\begin{eqnarray}
\Gamma _{1}\left( \mathbf{q,k},\epsilon ,\epsilon +\omega \right) &=&\tilde{M%
}_{\mathbf{k}\lambda }\left( \mathbf{q}\right) -\frac{qk_{F}^{2}}{m\sqrt{%
2\rho _{ion}\omega _{\mathbf{q}\lambda }}}\frac{\left[ s_{2}\left( a\right) -%
\frac{1}{3}s_{0}\left( a\right) \right] /a}{1+s_{0}\left( a\right) /a}, \\
\Gamma _{2}\left( \mathbf{q,k},\epsilon ,\epsilon +\omega \right) &=&\tilde{M%
}_{\mathbf{k}\lambda }\left( \mathbf{q}\right) .
\end{eqnarray}%
Thus the retarded phonon polarization function can be calculated as%
\begin{eqnarray*}
\Pi _{\text{ret}}\left( \mathbf{q},\omega \right) &=&2i\sum_{\mathbf{k}}%
\tilde{M}_{\mathbf{k}\lambda }\left( \mathbf{q}\right) \int_{-\infty
}^{\infty }\frac{d\epsilon }{2\pi }n_{F}\left( \epsilon \right) \left[
\mathcal{G}_{\text{ret}}\left( \mathbf{k},\epsilon +\omega \right) \mathcal{G%
}_{\text{ret}}\left( \mathbf{k+q},\epsilon \right) \Gamma _{2}\left( \mathbf{%
q,k},\epsilon ,\epsilon +\omega \right) \right. \\
&&\left. -\mathcal{G}_{\text{adv}}\left( \mathbf{k+q},\epsilon -\omega
\right) \mathcal{G}_{\text{adv}}\left( \mathbf{k},\epsilon \right) \Gamma
_{2}^{\ast }\left( \mathbf{q,k},\epsilon ,\epsilon +\omega \right) \right] \\
&&+2i\sum_{\mathbf{k}}\tilde{M}_{\mathbf{k}\lambda }\left( \mathbf{q}\right)
\int_{-\infty }^{\infty }\frac{d\epsilon }{2\pi }n_{F}\left( \epsilon
\right) \Gamma _{1}\left( \mathbf{q,k},\epsilon ,\epsilon +\omega \right) \\
&&\times \left[ -\mathcal{G}_{\text{ret}}\left( \mathbf{k},\epsilon +\omega
\right) \mathcal{G}_{\text{adv}}\left( \mathbf{k+q},\epsilon \right) +%
\mathcal{G}_{\text{adv}}\left( \mathbf{k+q},\epsilon -\omega \right)
\mathcal{G}_{\text{ret}}\left( \mathbf{k},\epsilon \right) \right] .
\end{eqnarray*}%
The imaginary part of the terms with $\Gamma _{2}$ and $\Gamma _{2}^{\ast }$
will vanish, resulting in%
\begin{eqnarray}
\text{Im}\Pi _{\text{ret}}\left( \mathbf{q},\omega \right) &=&-2\omega \text{%
Re}\sum_{\mathbf{k}}\tilde{M}_{\mathbf{k}\lambda }\left( \mathbf{q}\right)
\int_{-\infty }^{\infty }\frac{d\epsilon }{2\pi }\left[ -\frac{\partial
n_{F}\left( \epsilon \right) }{\partial \epsilon }\right] \mathcal{G}_{\text{%
ret}}\left( \mathbf{k},\epsilon +\omega \right) \mathcal{G}_{\text{adv}%
}\left( \mathbf{k+q},\epsilon \right) \Gamma _{1}\left( \mathbf{q,k}%
,\epsilon ,\epsilon +\omega \right) \notag \\
&=&\frac{\omega N\left( 0\right) k_{F}^{3}}{2m\rho _{ion}v_{s}}\text{Re}%
\left\{ s_{4}\left( a\right) -\frac{2}{3}s_{2}\left( a\right) +\frac{1}{9}%
s_{0}\left( a\right) -\frac{\left[ s_{2}\left( a\right) -\frac{1}{3}%
s_{0}\left( a\right) \right] ^{2}}{a+s_{0}\left( a\right) }\right\} ,
\end{eqnarray}
Using the expressions of $s_{n}\left( a\right) $,%
\begin{eqnarray*}
s_{0}\left( a\right) &=&-\tan ^{-1}a, \\
s_{2}\left( a\right) &=&-\frac{a-\tan ^{-1}a}{a^{2}}, \\
s_{4}\left( a\right) &=&-\frac{-3a+a^{3}+3\tan ^{-1}a}{3a^{4}},
\end{eqnarray*}%
we obtain the longitudinal sound attenuation constant,%
\begin{eqnarray}
\alpha &=&\frac{\omega N\left( 0\right) k_{F}^{3}}{m\rho _{ion}v_{s}^{2}}%
\frac{1}{3ql}\left[ \frac{q^{2}l^{2}\tan ^{-1}\left( ql\right) }{ql-\tan
^{-1}\left( ql\right) }-\frac{1}{3}\right] \notag \\
&=&\frac{nm}{\rho _{ion}v_{s}\tau }\left[ \frac{q^{2}l^{2}\tan ^{-1}\left(
ql\right) }{ql-\tan ^{-1}\left( ql\right) }-\frac{1}{3}\right] , \label{aL}
\end{eqnarray}%
where the density of spinons $n=\frac{N\left( 0\right) k_{F}^{2}}{3m}$ is
used. Eq.(\ref{aL}) coincides with Pippard's longitudinal sound attenuation
constant.
Similarly, we obtain the longitudinal sound attenuation constant in 2D by
replacing $s_{n}\left( a\right) $ by $t_{n}\left( a\right) $ so on and so
forth,%
\begin{eqnarray}
\alpha &=&-\frac{\omega N\left( 0\right) k_{F}^{3}}{m\rho _{ion}v_{s}^{2}}%
\text{Re}\left\{ t_{4}\left( a\right) -t_{2}\left( a\right) +\frac{1}{4}%
t_{0}\left( a\right) -\frac{\left[ t_{2}\left( a\right) -\frac{1}{2}%
t_{0}\left( a\right) \right] ^{2}}{a+t_{0}\left( a\right) }\right\} \notag
\\
&=&\frac{nm}{\rho _{ion}v_{s}\tau }\left[ \frac{q^{2}l^{2}}{1-\sqrt{%
1+q^{2}l^{2}}}-\frac{1}{2}\right] . \label{aL2D}
\end{eqnarray}
\subsection{Transverse sound attenuation in an electron gas}
We proceed with transverse sound, where there is no vertex correction
(impurity line across the bubbles) because the vertex is odd in the $\mathbf{%
k}$ component along $\mathbf{q}$. The single bubble diagram $\Pi ^{(0)}$ can
be evaluated as follows,%
\begin{eqnarray}
\Pi _{\text{ret}}^{\left( 0\right) }\left( \mathbf{q},\omega \right)
&=&-2i\sum_{\mathbf{k}}[M_{\mathbf{k}\lambda }\left( \mathbf{q}\right)
]^{2}\int_{-\infty }^{\infty }\frac{d\epsilon }{2\pi }\left\{ \left[
n_{F}\left( \epsilon \right) -n_{F}\left( \epsilon +\omega \right) \right]
\mathcal{G}_{\text{ret}}\left( \mathbf{k},\epsilon +\omega \right) \mathcal{G%
}_{\text{adv}}\left( \mathbf{k+q},\epsilon \right) \right. \notag \\
&&\left. -n_{F}\left( \epsilon \right) [\mathcal{G}_{\text{ret}}\left(
\mathbf{k},\epsilon +\omega \right) \mathcal{G}_{\text{ret}}\left( \mathbf{%
k+q},\epsilon \right) -\mathcal{G}_{\text{adv}}\left( \mathbf{k+q},\epsilon
-\omega \right) \mathcal{G}_{\text{adv}}\left( \mathbf{k},\epsilon \right)
]\right\} . \label{PiT01}
\end{eqnarray}%
Similarly to longitudinal mode, the imaginary part of $\mathcal{G}_{\text{ret%
}}\mathcal{G}_{\text{ret}}$ and $\mathcal{G}_{\text{adv}}\mathcal{G}_{\text{%
adv}}$ terms vanishes. So that%
\begin{eqnarray}
\text{Im}\Pi _{\text{ret}}^{\left( 0\right) }\left( \mathbf{q},\omega
\right) &=&-2\omega \text{Re}\sum_{\mathbf{k}}[M_{\mathbf{k}\lambda }\left(
\mathbf{q}\right) ]^{2}\int_{-\infty }^{\infty }\frac{d\epsilon }{2\pi }%
\left[ -\frac{\partial n_{F}\left( \epsilon \right) }{\partial \epsilon }%
\right] \mathcal{G}_{\text{ret}}\left( \mathbf{k},\epsilon +\omega \right)
\mathcal{G}_{\text{adv}}\left( \mathbf{k+q},\epsilon \right) \notag \\
&=&\frac{\omega N\left( 0\right) k_{F}^{3}}{4\rho _{ion}mv_{s}}\text{Re}%
\left[ s_{2}\left( a\right) -s_{4}\left( a\right) \right] \notag \\
&=&\frac{\omega N\left( 0\right) k_{F}^{3}}{4\rho _{ion}mv_{s}}\frac{%
s_{1}\left( ql\right) -s_{3}\left( ql\right) }{iql}, \label{PiT02}
\end{eqnarray}%
where the relation%
\begin{equation}
s_{n}\left( a\right) =-\frac{i\left[ 1-\left( -\right) ^{n}\right] }{2n}-%
\frac{i}{a}s_{n-1}\left( a\right) \label{itsn}
\end{equation}%
is used to derive the last line in Eq.(\ref{PiT02}) and we keep all the
terms up to the leading order of $v_{s}/v_{F}$.
Now we go on calculating $\Pi ^{(1)}$. Since the gauge field propagator is
of the form%
\begin{equation}
D_{\alpha \beta }\left( \mathbf{q},i\omega _{n}\right) =\left( \delta
_{\alpha \beta }-q_{\alpha }q_{\beta }/q^{2}\right) D^{T}\left( \mathbf{q}%
,i\omega _{n}\right) ,
\end{equation}%
$\Pi ^{\left( 1\right) }\left( \mathbf{q},i\omega _{n}\right) $ can be
written as,
\begin{eqnarray}
\Pi ^{\left( 1\right) }\left( \mathbf{q},i\omega _{n}\right) &=&\frac{e^{2}}{%
\beta ^{2}m^{2}}\sum_{\alpha \beta }\sum_{\mathbf{k}}M_{\mathbf{k}\lambda
}\left( \mathbf{q}\right) \sum_{ik_{m}}\mathcal{G}\left( \mathbf{k+q}%
,ik_{m}\right) \mathcal{G}\left( \mathbf{k},i\omega _{n}+ik_{m}\right)
\notag \\
&&\times \sum_{\mathbf{k}^{\prime }}M_{\mathbf{k}^{\prime }\lambda }\left(
\mathbf{q}\right) \left( 2k_{\alpha }+q_{\alpha }\right) \left( 2k_{\beta
}^{\prime }+q_{\beta }\right) \left( \delta _{\alpha \beta }-q_{\alpha
}q_{\beta }/q^{2}\right) D^{T}\left( \mathbf{q},i\omega _{n}\right) \notag
\\
&&\times \sum_{ik_{m}^{\prime }}\mathcal{G}\left( \mathbf{k}^{\prime }%
\mathbf{+q},ik_{m}^{\prime }\right) \mathcal{G}\left( \mathbf{k}^{\prime
},i\omega _{n}+ik_{m}^{\prime }\right) \notag \\
&=&\frac{4e^{2}}{\beta ^{2}m^{2}}D^{T}\left( \mathbf{q},i\omega _{n}\right)
\sum_{\mathbf{kk}^{\prime }}M_{\mathbf{k}\lambda }\left( \mathbf{q}\right)
M_{\mathbf{k}^{\prime }\lambda }\left( \mathbf{q}\right) \left[ \mathbf{k}%
\cdot \mathbf{k}^{\prime }-\left( \mathbf{k}\cdot \mathbf{\hat{q}}\right)
\left( \mathbf{k}^{\prime }\cdot \mathbf{\hat{q}}\right) \right] \notag \\
&&\times \sum_{ik_{m},ik_{m}^{\prime }}\mathcal{G}\left( \mathbf{k+q}%
,ik_{m}\right) \mathcal{G}\left( \mathbf{k},i\omega _{n}+ik_{m}\right)
\mathcal{G}\left( \mathbf{k}^{\prime }\mathbf{+q},ik_{m}^{\prime }\right)
\mathcal{G}\left( \mathbf{k}^{\prime },i\omega _{n}+ik_{m}^{\prime }\right) ,
\end{eqnarray}%
Summation over $ik_{m}$ and $ik_{m}^{\prime }$ leads to%
\begin{eqnarray}
\Pi ^{\left( 1\right) }\left( \mathbf{q},i\omega _{n}\right) &=&\frac{e^{2}}{%
m^{2}}D^{T}\left( \mathbf{q},i\omega _{n}\right) \sum_{\mathbf{kk}^{\prime
}}M_{\mathbf{k}\lambda }\left( \mathbf{q}\right) M_{\mathbf{k}^{\prime
}\lambda }\left( \mathbf{q}\right) \left[ \mathbf{k}\cdot \mathbf{k}^{\prime
}-\left( \mathbf{k}\cdot \mathbf{\hat{q}}\right) \left( \mathbf{k}^{\prime
}\cdot \mathbf{\hat{q}}\right) \right] \notag \\
&&\times \int_{-\infty }^{\infty }\frac{d\epsilon }{\pi }n_{F}\left(
\epsilon \right) \left[ \mathcal{G}\left( \mathbf{k},\epsilon +i\omega
_{n}\right) A\left( \mathbf{k+q},\epsilon \right) +\mathcal{G}\left( \mathbf{%
k+q},\epsilon -i\omega _{n}\right) A\left( \mathbf{k},\epsilon \right) %
\right] \notag \\
&&\times \int_{-\infty }^{\infty }\frac{d\epsilon ^{\prime }}{\pi }%
n_{F}\left( \epsilon ^{\prime }\right) \left[ \mathcal{G}\left( \mathbf{k}%
^{\prime },\epsilon ^{\prime }+i\omega _{n}\right) A\left( \mathbf{k}%
^{\prime }\mathbf{+q},\epsilon ^{\prime }\right) +\mathcal{G}\left( \mathbf{k%
}^{\prime }\mathbf{+q},\epsilon ^{\prime }-i\omega _{n}\right) A\left(
\mathbf{k}^{\prime },\epsilon ^{\prime }\right) \right] ,
\end{eqnarray}%
where the spectral function $A\left( \mathbf{k},\epsilon \right) $ is given
by%
\begin{equation}
\mathcal{G}_{\text{ret}}\left( \mathbf{k},\epsilon \right) -\mathcal{G}_{%
\text{adv}}\left( \mathbf{k},\epsilon \right) =2i\text{Im}\mathcal{G}_{\text{%
ret}}\left( \mathbf{k},\epsilon \right) =-iA\left( \mathbf{k},\epsilon
\right) .
\end{equation}%
Analytically continue $i\omega _{n}\rightarrow \omega +i\eta $, we have%
\begin{eqnarray*}
\Pi _{\text{ret}}^{\left( 1\right) }\left( \mathbf{q},\omega \right) &=&%
\frac{e^{2}}{m^{2}}D^{T}\left( \mathbf{q},\omega \right) \sum_{\mathbf{kk}%
^{\prime }}M_{\mathbf{k}\lambda }\left( \mathbf{q}\right) M_{\mathbf{k}%
^{\prime }\lambda }\left( \mathbf{q}\right) \left[ \mathbf{k}\cdot \mathbf{k}%
^{\prime }-\left( \mathbf{k}\cdot \mathbf{\hat{q}}\right) \left( \mathbf{k}%
^{\prime }\cdot \mathbf{\hat{q}}\right) \right] \\
&&\times \int_{-\infty }^{\infty }\frac{d\epsilon }{\pi }n_{F}\left(
\epsilon \right) \left[ \mathcal{G}_{\text{ret}}\left( \mathbf{k},\epsilon
+\omega \right) A\left( \mathbf{k+q},\epsilon \right) +\mathcal{G}_{\text{adv%
}}\left( \mathbf{k+q},\epsilon -\omega \right) A\left( \mathbf{k},\epsilon
\right) \right] \\
&&\times \int_{-\infty }^{\infty }\frac{d\epsilon ^{\prime }}{\pi }%
n_{F}\left( \epsilon ^{\prime }\right) \left[ \mathcal{G}_{\text{ret}}\left(
\mathbf{k}^{\prime },\epsilon ^{\prime }+\omega \right) A\left( \mathbf{k}%
^{\prime }\mathbf{+q},\epsilon ^{\prime }\right) +\mathcal{G}_{\text{adv}%
}\left( \mathbf{k}^{\prime }\mathbf{+q},\epsilon ^{\prime }-\omega \right)
A\left( \mathbf{k}^{\prime },\epsilon ^{\prime }\right) \right] .
\end{eqnarray*}%
After integrating over $\mathbf{k}$ and $\mathbf{k}^{\prime }$, $\mathcal{G}%
_{\text{ret}}\mathcal{G}_{\text{ret}}$ and $\mathcal{G}_{\text{adv}}\mathcal{%
G}_{\text{adv}}$ terms vanish, we obtain%
\begin{eqnarray}
\Pi _{\text{ret}}^{\left( 1\right) }\left( \mathbf{q},\omega \right) &=&-%
\frac{e^{2}}{m^{2}}D_{\text{ret}}^{T}\left( \mathbf{q},\omega \right) \sum_{%
\mathbf{kk}^{\prime }}M_{\mathbf{k}\lambda }\left( \mathbf{q}\right) M_{%
\mathbf{k}^{\prime }\lambda }\left( \mathbf{q}\right) \left[ \mathbf{k}\cdot
\mathbf{k}^{\prime }-\left( \mathbf{k}\cdot \mathbf{\hat{q}}\right) \left(
\mathbf{k}^{\prime }\cdot \mathbf{\hat{q}}\right) \right] \notag \\
&&\times \int_{-\infty }^{\infty }\frac{d\epsilon }{\pi }n_{F}\left(
\epsilon \right) \left[ -\mathcal{G}_{\text{ret}}\left( \mathbf{k},\epsilon
+\omega \right) \mathcal{G}_{\text{adv}}\left( \mathbf{k+q},\epsilon \right)
+\mathcal{G}_{\text{adv}}\left( \mathbf{k+q},\epsilon -\omega \right)
\mathcal{G}_{\text{ret}}\left( \mathbf{k},\epsilon \right) \right] \notag \\
&&\times \int_{-\infty }^{\infty }\frac{d\epsilon ^{\prime }}{\pi }%
n_{F}\left( \epsilon ^{\prime }\right) \left[ -\mathcal{G}_{\text{ret}%
}\left( \mathbf{k}^{\prime },\epsilon ^{\prime }+\omega \right) \mathcal{G}_{%
\text{adv}}\left( \mathbf{k}^{\prime }\mathbf{+q},\epsilon ^{\prime }\right)
+\mathcal{G}_{\text{adv}}\left( \mathbf{k}^{\prime }\mathbf{+q},\epsilon
^{\prime }-\omega \right) \mathcal{G}_{\text{ret}}\left( \mathbf{k}^{\prime
},\epsilon ^{\prime }\right) \right] \notag \\
&=&-\frac{e^{2}\omega ^{2}}{m^{2}}D_{\text{ret}}^{T}\left( \mathbf{q},\omega
\right) \sum_{\mathbf{kk}^{\prime }}M_{\mathbf{k}\lambda }\left( \mathbf{q}%
\right) M_{\mathbf{k}^{\prime }\lambda }\left( \mathbf{q}\right) \left[
\mathbf{k}\cdot \mathbf{k}^{\prime }-\left( \mathbf{k}\cdot \mathbf{\hat{q}}%
\right) \left( \mathbf{k}^{\prime }\cdot \mathbf{\hat{q}}\right) \right]
\notag \\
&&\times \int_{-\infty }^{\infty }\frac{d\epsilon }{\pi }\left[ -\frac{%
\partial n_{F}\left( \epsilon \right) }{\partial \epsilon }\right] \mathcal{G%
}_{\text{ret}}\left( \mathbf{k},\epsilon +\omega \right) \mathcal{G}_{\text{%
adv}}\left( \mathbf{k+q},\epsilon \right) \notag \\
&&\times \int_{-\infty }^{\infty }\frac{d\epsilon ^{\prime }}{\pi }\left[ -%
\frac{\partial n_{F}\left( \epsilon ^{\prime }\right) }{\partial \epsilon
^{\prime }}\right] \mathcal{G}_{\text{ret}}\left( \mathbf{k}^{\prime
},\epsilon ^{\prime }+\omega \right) \mathcal{G}_{\text{adv}}\left( \mathbf{k%
}^{\prime }\mathbf{+q},\epsilon ^{\prime }\right) .
\end{eqnarray}%
Therefore%
\begin{eqnarray}
\Pi _{\text{ret}}^{\left( 1\right) }\left( \mathbf{q},\omega \right) &=&-%
\frac{e^{2}k_{F}^{2}\omega }{2m^{2}}D_{\text{ret}}^{T}\left( \mathbf{q}%
,\omega \right) \frac{\omega ^{2}N\left( 0\right) k_{F}^{3}}{4\rho
_{ion}mv_{s}} \notag \\
&&\times \frac{N\left( 0\right) }{qv_{F}}\left[ s_{1}\left( ql\right)
-s_{3}\left( ql\right) \right] ^{2} \notag \\
&=&iF\left( \mathbf{q},\omega \right) \text{Im}\Pi _{\text{ret}}^{\left(
0\right) }\left( \mathbf{q},\omega \right) ,
\end{eqnarray}%
where%
\begin{equation}
F\left( \mathbf{q},\omega \right) =-\frac{e^{2}k_{F}^{2}\omega }{2m^{2}}%
\frac{N\left( 0\right) }{qv_{F}}D_{\text{ret}}^{T}\left( \mathbf{q},\omega
\right) ql\left[ s_{1}\left( ql\right) -s_{3}\left( ql\right) \right] .
\end{equation}
For EM field the propagator $D_{\text{ret}}^{T}$ is given by $D_{\text{ret}%
}^{\text{EM}}\left( \mathbf{q},\omega \right) $%
\begin{equation}
D_{\text{ret}}^{\text{EM}}=\frac{1}{i\omega \sigma _{\perp }\left( q,\omega
\right) +\omega ^{2}-c^{2}q^{2}}.
\end{equation}%
Following Pippard's notation, we write $\sigma _{\perp }\left( q,\omega
\right) =g\sigma _{0}$, where $\sigma _{0}=e^{2}n\tau /m$ is the DC
conductivity. To determine the factor $g$, we shall calculate $\sigma
_{\perp }\left( q,\omega \right) $ using the relation,%
\begin{equation}
\sigma _{\perp }\left( q,\omega \right) =-\frac{1}{\omega }\text{Im}\Pi
_{j\bot }\left( \mathbf{q},\omega \right) ,
\end{equation}%
where $\Pi _{j\bot }\left( \mathbf{q},i\omega _{n}\right) =\int_{0}^{\beta
}d\tau e^{i\omega _{n}\tau }\Pi _{j\bot }\left( \mathbf{q},\tau \right) $
and $\Pi _{j\bot }\left( \mathbf{q},\tau \right) =-\left\langle T_{\tau }%
\mathbf{j}_{\perp }\left( \mathbf{q},\tau \right) \cdot \mathbf{j}_{\perp
}\left( -\mathbf{q},0\right) \right\rangle $ the retarded correlation
function. To be simple, we shall further count $\Pi _{\bot }\left( \mathbf{q}%
,\omega \right) $ as the single bubble contribution. So that
\begin{equation}
\Pi _{j\bot }\left( \mathbf{q},i\omega _{n}\right) =\frac{2e^{2}}{\beta m^{2}%
}\sum_{\mathbf{k}}\frac{1}{2}\left[ \mathbf{k-}\left( \mathbf{k\cdot \hat{q}}%
\right) \mathbf{\hat{q}}\right] ^{2}\sum_{ik_{m}}\mathcal{G}\left( \mathbf{%
k+q},ik_{m}\right) \mathcal{G}\left( \mathbf{k},i\omega _{n}+ik_{m}\right) .
\end{equation}%
Taking analytical continuation and then we have the imaginary part of $\Pi
_{j\bot }\left( \mathbf{q},\omega \right) $%
\begin{eqnarray}
\text{Im}\Pi _{j\bot }\left( \mathbf{q},\omega \right) &=&-\frac{\omega e^{2}%
}{m^{2}}\text{Re}\sum_{\mathbf{k}}[k^{2}\mathbf{-}\left( \mathbf{k\cdot \hat{%
q}}\right) ^{2}]\int_{-\infty }^{\infty }\frac{d\epsilon }{2\pi }\left[ -%
\frac{\partial n_{F}\left( \epsilon \right) }{\partial \epsilon }\right]
\mathcal{G}_{\text{ret}}\left( \mathbf{k},\epsilon +\omega \right) \mathcal{G%
}_{\text{adv}}\left( \mathbf{k+q},\epsilon \right) \notag \\
&=&\frac{\omega e^{2}k_{F}^{2}}{2\pi m^{2}}\frac{N\left( 0\right) \pi }{%
qv_{F}}\text{Re}\left[ s_{0}\left( a\right) -s_{2}\left( a\right) \right] .
\end{eqnarray}
Then we obtain%
\begin{eqnarray}
\sigma _{\perp }\left( q,\omega \right) &=&-\frac{e^{2}k_{F}^{2}}{2m^{2}}%
\frac{N\left( 0\right) }{qv_{F}}\text{Re}\left[ s_{0}\left( a\right)
-s_{2}\left( a\right) \right] \notag \\
&=&\frac{3\sigma _{0}}{2ql}\left[ s_{2}\left( ql\right) -s_{0}\left(
ql\right) \right] ,
\end{eqnarray}%
where $\sigma _{0}=\frac{N\left( 0\right) e^{2}k_{F}^{2}\tau }{3m^{2}}$ is
used. So that the factor $g$ reads%
\begin{equation}
g=\frac{3}{2ql}\left[ s_{2}\left( ql\right) -s_{0}\left( ql\right) \right] .
\end{equation}%
We find that $g\rightarrow 1-\frac{2\left( ql\right) ^{2}}{15}$ when $ql\ll
1 $ and $g\rightarrow \frac{3\pi }{4ql}$ when $ql\gg 1$. We are interested
in the case when $c^{2}q^{2}\ll \omega \sigma _{\perp }\left( q,\omega
\right) $, say, $q\ll g^{-1/2}k_{0}$, where $k_{0}^{-1}$ is the classical
skin depth. This holds under the condition $q\ll k_{0}$ if $ql\ll 1$ and $%
q^{2}\ll k_{0}^{2}/\left( ql\right) $ if $ql\gg 1$. In this case,%
\begin{equation}
D_{\text{ret}}^{\text{EM}}=\frac{1}{i\omega \sigma _{\perp }\left( q,\omega
\right) },
\end{equation}%
and%
\begin{eqnarray}
F\left( \mathbf{q},\omega \right) &=&-\frac{e^{2}k_{F}^{2}\omega }{2m^{2}}%
\frac{N\left( 0\right) }{qv_{F}}\frac{ql\left[ s_{1}\left( ql\right)
-s_{3}\left( ql\right) \right] }{i\omega \sigma _{\perp }\left( q,\omega
\right) } \notag \\
&=&\frac{3i}{2g}\left[ s_{1}\left( ql\right) -s_{3}\left( ql\right) \right] .
\end{eqnarray}%
Using the relation (\ref{itsn}), we have%
\begin{eqnarray*}
s_{1}\left( a\right) &=&-i-\frac{is_{0}\left( a\right) }{a}, \\
s_{3}\left( a\right) &=&-\frac{i}{3}-\frac{is_{2}\left( a\right) }{a}.
\end{eqnarray*}%
So that%
\begin{eqnarray}
s_{1}\left( ql\right) -s_{3}\left( ql\right) &=&-\frac{2i}{3}-i\frac{%
s_{0}\left( ql\right) -s_{2}\left( ql\right) }{ql}+O\left( \frac{v_{s}}{v_{F}%
}\right) \notag \\
&=&-\frac{2i}{3}\left( 1-g\right) +O\left( \frac{v_{s}}{v_{F}}\right) ,
\end{eqnarray}%
and%
\begin{equation}
F=\frac{1-g}{g}+O\left( \frac{v_{s}}{v_{F}}\right) .
\end{equation}%
So that we obtain
\begin{equation}
\Pi _{\text{ret}}^{\left( 1\right) }\left( \mathbf{q},\omega \right) =\frac{%
1-g}{g}\text{Im}\Pi _{\text{ret}}^{\left( 0\right) }\left( \mathbf{q},\omega
\right) +O\left( \frac{v_{s}}{v_{F}}\right) .
\end{equation}%
Thus the ultrasound attenuation coeffecient reads%
\begin{equation}
\alpha =-\frac{2}{v_{s}}\text{Im}(\Pi _{\text{ret}}^{(0)}+\Pi _{\text{ret}%
}^{(1)})=\frac{nm}{\rho _{ion}v_{s}\tau }\frac{1-g}{g}.
\end{equation}
\section{Transverse sound attenuation in a spin liquid}
For a spin liquid, the spinons and gauge fields are treated in 2D. The gauge
field propagator $D^{T} $ is replaced by%
\begin{equation}
D_{\text{ret}}^{T}=\frac{1}{i\omega \tilde{\sigma}_{\perp }\left( q,\omega
\right) -\chi q^{2}},
\end{equation}%
where $\tilde{\sigma}_{\perp }=\tilde{g}\tilde{\sigma}_{0}$, $\tilde{\sigma}%
_{0}=n\tau /m$, $n$ is the spinon density and $\chi =1/(24\pi m)$ is the
Landau diagramnetism. Note that the coupling constant to the gauge field has
been set to unity instead of $e$.
Similary, we have%
\begin{equation}
\text{Im}\tilde{\Pi}_{j\perp }\left( \mathbf{q},\omega \right) =\frac{\omega
e^{2}k_{F}^{2}}{\pi m^{2}}\frac{N\left( 0\right) \pi }{qv_{F}}\text{Re}\left[
t_{0}\left( ql\right) -t_{2}\left( ql\right) \right] ,
\end{equation}%
and%
\begin{eqnarray}
\tilde{\sigma}_{\perp }\left( q,\omega \right) &=&-\frac{1}{\omega }\text{Im}%
\tilde{\Pi}_{j\bot }\left( \mathbf{q},\omega \right) \notag \\
&=&-\frac{e^{2}k_{F}^{2}}{m^{2}}\frac{N\left( 0\right) }{qv_{F}}\text{Re}%
\left[ t_{0}\left( ql\right) -t_{2}\left( ql\right) \right] \notag \\
&=&-\frac{2\tilde{\sigma}_{0}}{ql}\text{Re}\left[ t_{0}\left( ql\right)
-t_{2}\left( ql\right) \right] .
\end{eqnarray}%
So that the factor $\tilde{g}$ reads%
\begin{equation}
\tilde{g}=-\frac{2}{ql}\text{Re}\left[ t_{0}\left( ql\right) -t_{2}\left(
ql\right) \right] .
\end{equation}%
We also find that $\tilde{g}\rightarrow 1-\frac{\left( ql\right) ^{2}}{4}$
when $ql\ll 1$ and $\tilde{g}\rightarrow \frac{2}{ql}$ when $ql\gg 1$.
The imaginary part of $\tilde{\Pi}_{\text{ret}}^{(0)}$ is given by%
\begin{equation}
\text{Im}\tilde{\Pi}_{\text{ret}}^{\left( 0\right) }\left( \mathbf{q},\omega
\right) =\frac{\omega N\left( 0\right) k_{F}^{3}}{2\rho _{ion}mv_{s}}\frac{%
t_{1}\left( ql\right) -t_{3}\left( ql\right) }{iql},
\end{equation}%
and $\tilde{\Pi}_{\text{ret}}^{(1)}$ is given by%
\begin{eqnarray}
\tilde{\Pi}_{\text{ret}}^{\left( 1\right) }\left( \mathbf{q},\omega \right)
&=&(1+\tilde{F})\text{Im}\tilde{\Pi}_{\text{ret}}^{\left( 0\right) }\left(
\mathbf{q},\omega \right) , \\
\tilde{F} &=&\frac{2i}{\tilde{g}}\left[ t_{1}\left( ql\right) -t_{3}\left(
ql\right) \right] .
\end{eqnarray}%
So that we still can write $\tilde{\Pi}_{\text{ret}}^{\left( 1\right) }$ as%
\begin{equation}
\tilde{\Pi}_{\text{ret}}^{\left( 1\right) }=\frac{1-\tilde{g}}{\tilde{g}}%
\text{Im}\tilde{\Pi}_{\text{ret}}^{\left( 0\right) }+O(\frac{v_{s}}{v_{F}})%
\text{.}
\end{equation}
\subsection{Onset of superconductivity}
For transeverse ultrasound, a rapid fall of the ratio $\alpha /\alpha _{N}$
below $T_{c}$ due to $\Pi ^{\left( 1\right) }$ has been discussed in the
paper in the clean limit $ql\gg 1$. We shall focus on $\Pi ^{\left( 0\right)
}$ term, which gives rise to the ratio $\alpha ^{(0)}/\alpha _{N}^{(0)}$ and
$\alpha ^{(0)}$ is given by%
\begin{equation}
\alpha ^{(0)}=-\frac{2}{v_{s}}\text{Im}\Pi _{\text{ret}}^{(0)}.
\end{equation}%
$\Pi ^{\left( 0\right) }$ will decrease below $T_{c}$ because of the opening
of the energy gap.
During the process of the attenuation of a sound wave in such a fermionic
system, the sound wave passes its energy to fermions by fermion phonon
coupling and fermions dissipate this extra energy due to disorder to
complete the attenuation. Therefore the fermion life time $\tau $ should be
finite to relax the sound wave. On the other hand $v_{s}\ll v_{F}$, it is
different from many other relaxation mechanisms. So that despite $ql\gtrsim 1
$, the physically relevant situation is reached by $\omega \tau \ll 1$. It
means we can not take $\tau \rightarrow \infty $ at first even in the clean
limit because finite $\tau $ is still seen for $\omega \tau \ll 1$.
Otherwise, we would obtain a $\Pi ^{\left( 0\right) }$ which does not depend
on $ql$ and conflicts with Eq.(\ref{PiT02}). It is interesting that when
screening is included by $\Pi ^{\left( 0\right) }+\Pi ^{\left( 1\right) }$,
the result does not depend on $\tau $ and appears to agree with the infinite
$\tau $ calculation (see Eq.(\ref{ImPi0})). It is only when screening is suppressed by
Meissner effect that we can see this distinction. Below we shall discuss in
the limit $\omega \tau \ll 1\ll \Delta \tau $, which is most interesting for
us. Note that our results differ from those in early literatures
(e.g., see J. R. Cullen and R. A. Ferrell, Phys. Rev. \textbf{146}, 282 (1966).),
since they worked in the clean limit by setting $\tau
\rightarrow \infty $ which is not valid for $\omega \tau \ll 1$.
To study the pairing state with finite $\tau $, we shall adopt the following
impurity avaraged Green's function,%
\begin{eqnarray*}
\mathcal{G}\left( \mathbf{k},i\omega _{n}\right) &=&\frac{i\tilde{\omega}%
_{n}+\xi _{\mathbf{k}}}{\left( i\tilde{\omega}_{n}\right) ^{2}-\xi _{\mathbf{%
k}}^{2}-\left[ \tilde{\Delta}_{\mathbf{k}}\left( \omega _{n}\right) \right]
^{2}}, \\
\mathcal{F}\left( \mathbf{k},i\omega _{n}\right) &=&-\frac{\tilde{\Delta}_{%
\mathbf{k}}\left( \omega _{n}\right) }{\left( i\tilde{\omega}_{n}\right)
^{2}-\xi _{\mathbf{k}}^{2}-\left[ \tilde{\Delta}_{\mathbf{k}}\left( \omega
_{n}\right) \right] ^{2}}, \\
\tilde{\omega}_{n} &=&\omega _{n}(1+\frac{1}{2\tau \sqrt{\omega
_{n}^{2}+\Delta _{\mathbf{k}}^{2}}}), \\
\tilde{\Delta}_{\mathbf{k}}\left( \omega _{n}\right) &=&\Delta _{\mathbf{k}%
}(1+\frac{1}{2\tau \sqrt{\omega _{n}^{2}+\Delta _{\mathbf{k}}^{2}}}),
\end{eqnarray*}%
for superconducting states and replace the terms with $\mathcal{GG}$ by $%
\mathcal{GG}-\mathcal{FF}$. The results should coincide to Eq.(\ref{PiT02})
when $\Delta _{\mathbf{k}}\rightarrow 0$. We do frequency summation firstly.%
\begin{eqnarray}
S &=&\frac{1}{\beta }\sum_{ik_{m}}\mathcal{G}\left( \mathbf{k}%
,ik_{m}+i\omega _{n}\right) \mathcal{G}\left( \mathbf{k+q},ik_{m}\right) -%
\mathcal{F}\left( \mathbf{k},ik_{m}+i\omega _{n}\right) \mathcal{F}\left(
\mathbf{k+q},ik_{m}\right) \notag \\
&=&-\int_{C}\frac{dz}{2\pi i}n_{F}\left( z\right) \left[ \mathcal{G}\left(
\mathbf{k},\epsilon +i\omega _{n}\right) \mathcal{G}\left( \mathbf{k+q}%
,z\right) -\mathcal{F}\left( \mathbf{k},\epsilon +i\omega _{n}\right)
\mathcal{F}\left( \mathbf{k+q},\epsilon \right) \right] \notag \\
&=&-\int_{-\infty }^{\infty }\frac{d\epsilon }{2\pi i}n_{F}\left( \epsilon
\right) \left\{ \mathcal{G}\left( \mathbf{k},\epsilon +i\omega _{n}\right) %
\left[ \mathcal{G}\left( \mathbf{k+q},\epsilon +i\eta \right) -\mathcal{G}%
\left( \mathbf{k+q},\epsilon -i\eta \right) \right] \right. \notag \\
&&+\mathcal{G}\left( \mathbf{k+q},\epsilon -i\omega _{n}\right) \left[
\mathcal{G}\left( \mathbf{k},\epsilon +i\eta \right) -\mathcal{G}\left(
\mathbf{k},\epsilon -i\eta \right) \right] \notag \\
&&-\mathcal{F}\left( \mathbf{k},\epsilon +i\omega _{n}\right) \left[
\mathcal{F}\left( \mathbf{k+q},\epsilon +i\eta \right) -\mathcal{F}\left(
\mathbf{k+q},\epsilon -i\eta \right) \right] \notag \\
&&\left. -\mathcal{F}\left( \mathbf{k+q},\epsilon -i\omega _{n}\right) \left[
\mathcal{F}\left( \mathbf{k},\epsilon +i\eta \right) -\mathcal{F}\left(
\mathbf{k},\epsilon -i\eta \right) \right] \right\} .
\end{eqnarray}%
The interval $\left( -\Delta ,\Delta \right) $, for which the Green's
functions are continuous across the real $\epsilon $ axis, can be excluded
from the $\epsilon $ integral. Taking $i\omega _{n}\rightarrow \omega +i\eta
$, we have%
\begin{eqnarray}
S &=&-\int_{-\infty }^{\infty }\frac{d\epsilon }{2\pi i}n_{F}\left( \epsilon
\right) \left\{ \mathcal{G}_{\text{ret}}\left( \mathbf{k},\epsilon +\omega
\right) \left[ \mathcal{G}_{\text{ret}}\left( \mathbf{k+q},\epsilon \right) -%
\mathcal{G}_{\text{adv}}\left( \mathbf{k+q},\epsilon \right) \right] \right.
\notag \\
&&+\mathcal{G}_{\text{adv}}\left( \mathbf{k+q},\epsilon -\omega \right) %
\left[ \mathcal{G}_{\text{ret}}\left( \mathbf{k},\epsilon \right) -\mathcal{G%
}_{\text{adv}}\left( \mathbf{k},\epsilon \right) \right] \notag \\
&&-\mathcal{F}_{\text{ret}}\left( \mathbf{k},\epsilon +\omega \right) \left[
\mathcal{F}_{\text{ret}}\left( \mathbf{k+q},\epsilon \right) -\mathcal{F}_{%
\text{adv}}\left( \mathbf{k+q},\epsilon \right) \right] \notag \\
&&\left. -\mathcal{F}_{\text{adv}}\left( \mathbf{k+q},\epsilon -\omega
\right) \left[ \mathcal{F}_{\text{ret}}\left( \mathbf{k},\epsilon \right) -%
\mathcal{F}_{\text{adv}}\left( \mathbf{k},\epsilon \right) \right] \right\} ,
\end{eqnarray}%
where%
\begin{eqnarray*}
\mathcal{G}_{\text{ret(adv)}}\left( \mathbf{k},\epsilon \right) &=&\frac{%
\epsilon _{\mathbf{k}\pm }^{\prime }+\xi _{\mathbf{k}}}{\epsilon _{\mathbf{k}%
\pm }^{\prime 2}-\xi _{\mathbf{k}}^{2}-\Delta _{\mathbf{k}\pm }^{\prime 2}},
\\
\mathcal{F}_{\text{ret(adv)}}\left( \mathbf{k},\epsilon \right) &=&-\frac{%
\Delta _{\mathbf{k}\pm }^{\prime }}{\epsilon _{\mathbf{k}\pm }^{\prime
2}-\xi _{\mathbf{k}}^{2}-\Delta _{\mathbf{k}\pm }^{\prime 2}}, \\
\mathcal{G}_{\text{ret(adv)}}\left( \mathbf{k},\epsilon +\omega \right) &=&%
\frac{\epsilon _{\mathbf{k}\pm }^{\prime \prime }+\xi _{\mathbf{k}}}{%
\epsilon _{\mathbf{k}\pm }^{\prime \prime 2}-\xi _{\mathbf{k}}^{2}-\Delta _{%
\mathbf{k}\pm }^{\prime \prime 2}}, \\
\mathcal{F}_{\text{ret(adv)}}\left( \mathbf{k},\epsilon +\omega \right) &=&-%
\frac{\Delta _{\mathbf{k}\pm }^{\prime \prime }}{\epsilon _{\mathbf{k}\pm
}^{\prime \prime 2}-\xi _{\mathbf{k}}^{2}-\Delta _{\mathbf{k}\pm }^{\prime
\prime 2}}
\end{eqnarray*}%
with%
\begin{eqnarray*}
\epsilon _{\mathbf{k}\pm }^{\prime } &=&\epsilon \left( 1\pm \frac{i}{2\tau
\sqrt{\epsilon ^{2}-\Delta _{\mathbf{k}}^{2}}}\right) , \\
\Delta _{\mathbf{k}\pm }^{\prime } &=&\Delta _{\mathbf{k}}\left( 1\pm \frac{i%
}{2\tau \sqrt{\epsilon ^{2}-\Delta _{\mathbf{k}}^{2}}}\right) , \\
\epsilon _{\mathbf{k}\pm }^{\prime \prime } &=&\left( \epsilon +\omega
\right) \left( 1\pm \frac{i}{2\tau \sqrt{\left( \epsilon +\omega \right)
^{2}-\Delta _{\mathbf{k}}^{2}}}\right) , \\
\Delta _{\mathbf{k}\pm }^{\prime \prime } &=&\Delta _{\mathbf{k}}\left( 1\pm
\frac{i}{2\tau \sqrt{\left( \epsilon +\omega \right) ^{2}-\Delta _{\mathbf{k}%
}^{2}}}\right) .
\end{eqnarray*}%
Then we perform integation over $\mathbf{k}$ in $\Pi ^{(0)}$ which can
reduced to an integral over $\nu =\cos \theta $ and $\xi _{\mathbf{k}}$. To
do this, we write $\mathcal{G}_{\text{ret(adv)}}\left( \mathbf{k},\epsilon
\right) $ and $\mathcal{F}_{\text{ret(adv)}}\left( \mathbf{k},\epsilon
\right) $ in terms of the poles of $\xi _{\mathbf{k}}$,
\begin{eqnarray*}
\mathcal{G}_{\text{ret(adv)}}\left( \mathbf{k},\epsilon \right) &=&\frac{%
\epsilon _{\mathbf{k}\pm }^{\prime }+\xi _{\mathbf{k}}}{\epsilon _{\mathbf{k}%
\pm }^{\prime 2}-\xi _{\mathbf{k}}^{2}-\Delta _{\mathbf{k}\pm }^{\prime 2}}=%
\frac{\epsilon _{\mathbf{k}\pm }^{\prime }+\xi _{\mathbf{k}}}{2\zeta _{%
\mathbf{k\pm }}^{\prime }}\left[ \frac{1}{\zeta _{\mathbf{k\pm }}^{\prime
}-\xi _{\mathbf{k}}}+\frac{1}{\zeta _{\mathbf{k\pm }}^{\prime }+\xi _{%
\mathbf{k}}}\right] , \\
\mathcal{F}_{\text{ret(adv)}}\left( \mathbf{k},\epsilon \right) &=&-\frac{%
\Delta _{\mathbf{k}\pm }^{\prime }}{\epsilon _{\mathbf{k}\pm }^{\prime
2}-\xi _{\mathbf{k}}^{2}-\Delta _{\mathbf{k}\pm }^{\prime 2}}=-\frac{\Delta
_{\mathbf{k}\pm }^{\prime }}{2\zeta _{\mathbf{k\pm }}}\left[ \frac{1}{\zeta
_{\mathbf{k\pm }}^{\prime }-\xi _{\mathbf{k}}}+\frac{1}{\zeta _{\mathbf{k\pm
}}^{\prime }+\xi _{\mathbf{k}}}\right] , \\
\mathcal{G}_{\text{ret(adv)}}\left( \mathbf{k},\epsilon +\omega \right) &=&%
\frac{\epsilon _{\mathbf{k}\pm }^{\prime \prime }+\xi _{\mathbf{k}}}{%
\epsilon _{\mathbf{k}\pm }^{\prime \prime 2}-\xi _{\mathbf{k}}^{2}-\Delta _{%
\mathbf{k}\pm }^{\prime \prime 2}}=\frac{\epsilon _{\mathbf{k}\pm }^{\prime
\prime }+\xi _{\mathbf{k}}}{2\zeta _{\mathbf{k\pm }}^{\prime \prime }}\left[
\frac{1}{\zeta _{\mathbf{k\pm }}^{\prime \prime }-\xi _{\mathbf{k}}}+\frac{1%
}{\zeta _{\mathbf{k\pm }}^{\prime \prime }+\xi _{\mathbf{k}}}\right] , \\
\mathcal{F}_{\text{ret(adv)}}\left( \mathbf{k},\epsilon +\omega \right) &=&-%
\frac{\Delta _{\mathbf{k}\pm }^{\prime \prime }}{\epsilon _{\mathbf{k}\pm
}^{\prime \prime 2}-\xi _{\mathbf{k}}^{2}-\Delta _{\mathbf{k}\pm }^{\prime
\prime 2}}=-\frac{\Delta _{\mathbf{k}\pm }^{\prime \prime }}{2\zeta _{%
\mathbf{k\pm }}}\left[ \frac{1}{\zeta _{\mathbf{k\pm }}^{\prime \prime }-\xi
_{\mathbf{k}}}+\frac{1}{\zeta _{\mathbf{k\pm }}^{\prime \prime }+\xi _{%
\mathbf{k}}}\right] ,
\end{eqnarray*}%
where%
\begin{eqnarray*}
\zeta _{\mathbf{k\pm }}^{\prime } &=&\sqrt{\epsilon _{\mathbf{k}\pm
}^{\prime 2}-\Delta _{\mathbf{k}\pm }^{\prime 2}}=\zeta _{\mathbf{k}%
}^{\prime }\pm \frac{i}{2\tau }, \\
\zeta _{\mathbf{k\pm }}^{\prime \prime } &=&\sqrt{\epsilon _{\mathbf{k}\pm
}^{\prime \prime 2}-\Delta _{\mathbf{k}\pm }^{\prime \prime 2}}=\zeta _{%
\mathbf{k}}^{\prime \prime }\pm \frac{i}{2\tau }, \\
\zeta _{\mathbf{k}}^{\prime } &=&\sqrt{\epsilon ^{2}-\Delta _{\mathbf{k}}^{2}%
}, \\
\zeta _{\mathbf{k}}^{\prime \prime } &=&\sqrt{\left( \epsilon +\omega
\right) ^{2}-\Delta _{\mathbf{k}}^{2}}.
\end{eqnarray*}%
We find that the following relations will be useful in determing the
imaginary part of $\Pi ^{(0)}$,%
\begin{eqnarray*}
\frac{\epsilon _{\mathbf{k}\pm }^{\prime }}{\zeta _{\mathbf{k\pm }}^{\prime }%
} &=&\frac{\epsilon }{\sqrt{\epsilon ^{2}-\Delta _{\mathbf{k}}^{2}}}, \\
\frac{\Delta _{\mathbf{k}\pm }^{\prime }}{\zeta _{\mathbf{k\pm }}^{\prime }}
&=&\frac{\Delta _{\mathbf{k}}}{\sqrt{\epsilon ^{2}-\Delta _{\mathbf{k}}^{2}}}%
, \\
\frac{\epsilon _{\mathbf{k}\pm }^{\prime \prime }}{\zeta _{\mathbf{k\pm }%
}^{\prime \prime }} &=&\frac{\epsilon +\omega }{\sqrt{\epsilon ^{2}-\Delta _{%
\mathbf{k}}^{2}}}, \\
\frac{\Delta _{\mathbf{k}\pm }^{\prime \prime }}{\zeta _{\mathbf{k\pm }%
}^{\prime \prime }} &=&\frac{\Delta _{\mathbf{k}}}{\sqrt{\left( \epsilon
+\omega \right) ^{2}-\Delta _{\mathbf{k}}^{2}}}.
\end{eqnarray*}%
Integrating with respect to $\xi _{\mathbf{k}}$ leads to%
\begin{eqnarray*}
&&\int \frac{d\xi _{\mathbf{k}}}{\pi i}\mathcal{G}_{\text{adv}}\left(
\mathbf{k+q},\epsilon \right) \mathcal{G}_{\text{ret}}\left( \mathbf{k}%
,\epsilon +\omega \right) \\
&=&\int \frac{d\xi _{\mathbf{k}}}{\pi i}\frac{\epsilon _{\mathbf{k+q}%
-}^{\prime }+\xi _{\mathbf{k}}+qv_{F}\nu }{2\zeta _{\mathbf{k+q-}}^{\prime }}%
\frac{\epsilon _{\mathbf{k}+}^{\prime \prime }+\xi _{\mathbf{k}}}{2\zeta _{%
\mathbf{k+}}^{\prime \prime }} \\
&&\times \left[ \frac{1}{\zeta _{\mathbf{k+q-}}^{\prime }-\xi _{\mathbf{k}%
}-qv_{F}\nu }+\frac{1}{\zeta _{\mathbf{k+q-}}^{\prime }+\xi _{\mathbf{k}%
}+qv_{F}\nu }\right] \left[ \frac{1}{\zeta _{\mathbf{k+}}^{\prime \prime
}-\xi _{\mathbf{k}}}+\frac{1}{\zeta _{\mathbf{k+}}^{\prime \prime }+\xi _{%
\mathbf{k}}}\right] \\
&=&\frac{1}{2\zeta _{\mathbf{k+q-}}^{\prime }\zeta _{\mathbf{k+}}^{\prime
\prime }}\frac{\left( \epsilon _{\mathbf{k+q}-}^{\prime }+\zeta _{\mathbf{%
k+q-}}^{\prime }\right) \left( \epsilon _{\mathbf{k}+}^{\prime \prime
}+\zeta _{\mathbf{k+}}^{\prime \prime }\right) }{\zeta _{\mathbf{k+}%
}^{\prime \prime }-\zeta _{\mathbf{k+q-}}^{\prime }+qv_{F}\nu }+\frac{1}{%
2\zeta _{\mathbf{k+q-}}^{\prime }\zeta _{\mathbf{k+}}^{\prime \prime }}\frac{%
-\left( \epsilon _{\mathbf{k+q}-}^{\prime }-\zeta _{\mathbf{k+q-}}^{\prime
}\right) \left( \epsilon _{\mathbf{k}+}^{\prime \prime }-\zeta _{\mathbf{k+}%
}^{\prime \prime }\right) }{\zeta _{\mathbf{k+}}^{\prime \prime }-\zeta _{%
\mathbf{k+q-}}^{\prime }-qv_{F}\nu } \\
&&+\frac{1}{2\zeta _{\mathbf{k+q-}}^{\prime }\zeta _{\mathbf{k+}}^{\prime
\prime }}\frac{-\left( \epsilon _{\mathbf{k+q}-}^{\prime }-\zeta _{\mathbf{%
k+q-}}^{\prime }\right) \left( \epsilon _{\mathbf{k}+}^{\prime \prime
}+\zeta _{\mathbf{k+}}^{\prime \prime }\right) }{\zeta _{\mathbf{k+}%
}^{\prime \prime }+\zeta _{\mathbf{k+q-}}^{\prime }+qv_{F}\nu }+\frac{1}{%
2\zeta _{\mathbf{k+q-}}^{\prime }\zeta _{\mathbf{k+}}^{\prime \prime }}\frac{%
\left( \epsilon _{\mathbf{k+q}-}^{\prime }+\zeta _{\mathbf{k+q-}}^{\prime
}\right) \left( \epsilon _{\mathbf{k}+}^{\prime \prime }-\zeta _{\mathbf{k+}%
}^{\prime \prime }\right) }{\zeta _{\mathbf{k+}}^{\prime \prime }+\zeta _{%
\mathbf{k+q-}}^{\prime }-qv_{F}\nu }
\end{eqnarray*}%
where%
\begin{equation*}
\int \frac{d\xi _{\mathbf{k}}}{\pi i}F\left( \xi _{\mathbf{k}}\right) \frac{1%
}{\zeta _{\mathbf{k\pm }}^{\prime }-\xi _{\mathbf{k}}}=\mp F\left( \zeta _{%
\mathbf{k\pm }}^{\prime }\right)
\end{equation*}%
etc. is used. Similarly, we have
\begin{eqnarray*}
&&\int \frac{d\xi _{\mathbf{k}}}{\pi i}\mathcal{F}_{\text{adv}}\left(
\mathbf{k+q},\epsilon \right) \mathcal{F}_{\text{ret}}\left( \mathbf{k}%
,\epsilon +\omega \right) \\
&=&\frac{1}{2\zeta _{\mathbf{k+q-}}^{\prime }\zeta _{\mathbf{k+}}^{\prime
\prime }}\frac{\Delta _{\mathbf{k+q}-}^{\prime }\Delta _{\mathbf{k}%
+}^{\prime \prime }}{\zeta _{\mathbf{k+}}^{\prime \prime }-\zeta _{\mathbf{%
k+q-}}^{\prime }+qv_{F}\nu }-\frac{1}{2\zeta _{\mathbf{k+q-}}^{\prime }\zeta
_{\mathbf{k+}}^{\prime \prime }}\frac{\Delta _{\mathbf{k+q}-}^{\prime
}\Delta _{\mathbf{k}+}^{\prime \prime }}{\zeta _{\mathbf{k+}}^{\prime \prime
}-\zeta _{\mathbf{k+q-}}^{\prime }-qv_{F}\nu } \\
&&-\frac{1}{2\zeta _{\mathbf{k+q-}}^{\prime }\zeta _{\mathbf{k+}}^{\prime
\prime }}\frac{\Delta _{\mathbf{k+q}-}^{\prime }\Delta _{\mathbf{k}%
+}^{\prime \prime }}{\zeta _{\mathbf{k+}}^{\prime \prime }+\zeta _{\mathbf{%
k+q-}}^{\prime }+qv_{F}\nu }+\frac{1}{2\zeta _{\mathbf{k+q-}}^{\prime }\zeta
_{\mathbf{k+}}^{\prime \prime }}\frac{\Delta _{\mathbf{k+q}-}^{\prime
}\Delta _{\mathbf{k}+}^{\prime \prime }}{\zeta _{\mathbf{k+}}^{\prime \prime
}+\zeta _{\mathbf{k+q-}}^{\prime }-qv_{F}\nu }.
\end{eqnarray*}%
So that%
\begin{eqnarray}
&&\int \frac{d\xi _{\mathbf{k}}}{\pi i}\left[ \mathcal{G}_{\text{adv}}\left(
\mathbf{k+q},\epsilon \right) \mathcal{G}_{\text{ret}}\left( \mathbf{k}%
,\epsilon +\omega \right) -\mathcal{F}_{\text{adv}}\left( \mathbf{k+q}%
,\epsilon \right) \mathcal{F}_{\text{ret}}\left( \mathbf{k},\epsilon +\omega
\right) \right] \notag \\
&=&\frac{1}{2\zeta _{\mathbf{k+q-}}^{\prime }\zeta _{\mathbf{k+}}^{\prime
\prime }}\frac{\left( \epsilon _{\mathbf{k+q}-}^{\prime }+\zeta _{\mathbf{%
k+q-}}^{\prime }\right) \left( \epsilon _{\mathbf{k}+}^{\prime \prime
}+\zeta _{\mathbf{k+}}^{\prime \prime }\right) -\Delta _{\mathbf{k+q}%
-}^{\prime }\Delta _{\mathbf{k}+}^{\prime \prime }}{\zeta _{\mathbf{k+}%
}^{\prime \prime }-\zeta _{\mathbf{k+q-}}^{\prime }+qv_{F}\nu } \notag \\
&&-\frac{1}{2\zeta _{\mathbf{k+q-}}^{\prime }\zeta _{\mathbf{k+}}^{\prime
\prime }}\frac{\left( \epsilon _{\mathbf{k+q}-}^{\prime }-\zeta _{\mathbf{%
k+q-}}^{\prime }\right) \left( \epsilon _{\mathbf{k}+}^{\prime \prime
}-\zeta _{\mathbf{k+}}^{\prime \prime }\right) -\Delta _{\mathbf{k+q}%
-}^{\prime }\Delta _{\mathbf{k}+}^{\prime \prime }}{\zeta _{\mathbf{k+}%
}^{\prime \prime }-\zeta _{\mathbf{k+q-}}^{\prime }-qv_{F}\nu } \notag \\
&&-\frac{1}{2\zeta _{\mathbf{k+q-}}^{\prime }\zeta _{\mathbf{k+}}^{\prime
\prime }}\frac{\left( \epsilon _{\mathbf{k+q}-}^{\prime }-\zeta _{\mathbf{%
k+q-}}^{\prime }\right) \left( \epsilon _{\mathbf{k}+}^{\prime \prime
}+\zeta _{\mathbf{k+}}^{\prime \prime }\right) -\Delta _{\mathbf{k+q}%
-}^{\prime }\Delta _{\mathbf{k}+}^{\prime \prime }}{\zeta _{\mathbf{k+}%
}^{\prime \prime }+\zeta _{\mathbf{k+q-}}^{\prime }+qv_{F}\nu } \notag \\
&&+\frac{1}{2\zeta _{\mathbf{k+q-}}^{\prime }\zeta _{\mathbf{k+}}^{\prime
\prime }}\frac{\left( \epsilon _{\mathbf{k+q}-}^{\prime }+\zeta _{\mathbf{%
k+q-}}^{\prime }\right) \left( \epsilon _{\mathbf{k}+}^{\prime \prime
}-\zeta _{\mathbf{k+}}^{\prime \prime }\right) -\Delta _{\mathbf{k+q}%
-}^{\prime }\Delta _{\mathbf{k}+}^{\prime \prime }}{\zeta _{\mathbf{k+}%
}^{\prime \prime }+\zeta _{\mathbf{k+q-}}^{\prime }-qv_{F}\nu }.
\end{eqnarray}%
For the terms of $\mathcal{G}_{\text{ret}}\mathcal{G}_{\text{ret}}-\mathcal{F%
}_{\text{ret}}\mathcal{F}_{\text{ret}}$ and $\mathcal{G}_{\text{adv}}%
\mathcal{G}_{\text{adv}}-\mathcal{F}_{\text{adv}}\mathcal{F}_{\text{adv}}$,
we need only to replace $\epsilon _{-}^{\prime }$ and $\zeta _{\mathbf{-}%
}^{\prime }$ by $\epsilon _{+}^{\prime }$ and $\zeta _{\mathbf{+}}^{\prime }$
in the above, so on and so forth. Then we find that only the terms of $%
\mathcal{G}_{\text{adv}}\mathcal{G}_{\text{ret}}-\mathcal{F}_{\text{adv}}%
\mathcal{F}_{\text{ret}}$ contribute to the imaginary part of $\Pi _{\text{%
ret}}^{(0)}$. Considering $\left[ M_{\mathbf{k}\lambda }\left( \mathbf{q}%
\right) \right] ^{2}$ is an even function of $\nu $, we have%
\begin{eqnarray}
\text{Im}\Pi _{\text{ret}}^{(0)} &=&2\omega \pi N\left( 0\right) \text{Re}%
\int_{-1}^{1}d\nu \int_{\left\vert \Delta _{\mathbf{k}}\right\vert }^{\infty
}\frac{d\epsilon }{2\pi }\frac{[M_{\mathbf{k}\lambda }\left( \mathbf{q}%
\right) ]^{2}\left[ 1+\frac{\epsilon \left( \epsilon +\omega \right) -\Delta
_{\mathbf{k}}\Delta _{\mathbf{k+q}}}{\sqrt{\epsilon ^{2}-\Delta _{\mathbf{k+q%
}}^{2}}\sqrt{\left( \epsilon +\omega \right) ^{2}-\Delta _{\mathbf{k}}^{2}}}%
\right] }{\sqrt{\left( \epsilon +\omega \right) ^{2}-\Delta _{\mathbf{k}}^{2}%
}-\sqrt{\epsilon ^{2}-\Delta _{\mathbf{k+q}}^{2}}+i/\tau +qv_{F}\nu }\left[ -%
\frac{\partial n_{F}\left( \epsilon \right) }{\partial \epsilon }\right]
\notag \\
&\simeq &2\omega \pi N\left( 0\right) \text{Re}\int_{-1}^{1}d\nu
\int_{\left\vert \Delta _{\mathbf{k}}\right\vert }^{\infty }\frac{d\epsilon
}{2\pi }\left[ -\frac{\partial n_{F}\left( \epsilon \right) }{\partial
\epsilon }\right] \frac{[M_{\mathbf{k}\lambda }\left( \mathbf{q}\right) ]^{2}%
\left[ 1+\frac{\epsilon ^{2}-\Delta _{\mathbf{k}}\Delta _{\mathbf{k+q}}}{%
\sqrt{\epsilon ^{2}-\Delta _{\mathbf{k+q}}^{2}}\sqrt{\epsilon ^{2}-\Delta _{%
\mathbf{k}}^{2}}}\right] }{\sqrt{\epsilon ^{2}-\Delta _{\mathbf{k}}^{2}}-%
\sqrt{\epsilon ^{2}-\Delta _{\mathbf{k+q}}^{2}}+i/\tau +qv_{F}\nu }.
\end{eqnarray}%
For a $s$-wave pairing state, Im$\Pi _{\text{ret}}^{(0)}$ can be evaluated
explicitly,%
\begin{eqnarray}
\text{Im}\Pi _{\text{ret}}^{(0)} &\simeq &2\omega \pi N\left( 0\right) \text{%
Re}\int_{\Delta }^{\infty }\frac{d\epsilon }{2\pi }\left[ -\frac{\partial
n_{F}\left( \epsilon \right) }{\partial \epsilon }\right] \int_{-1}^{1}d\nu
\frac{\lbrack M_{\mathbf{k}\lambda }\left( \mathbf{q}\right) ]^{2}}{%
qv_{F}\nu +i/\tau } \notag \\
&=&2n_{F}\left( \Delta \right) \text{Im}\Pi _{N}^{(0)}.
\end{eqnarray}%
The ratio $\alpha ^{(0)}/\alpha _{N}^{(0)}$ is given by%
\begin{equation}
\frac{\alpha ^{(0)}}{\alpha _{N}^{(0)}}=2n_{F}\left( \Delta \right) ,
\end{equation}%
in the limit $\omega \tau \ll 1\ll \Delta \tau .$
\end{widetext}
\end{document}
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 3,118
|
Produced by Jonathan Ingram, Dave Maddock, Charles Franks
and the Online Distributed Proofreading Team.
[Illustration: SIR ISAAC NEWTON (From the bust by Roubiliac In Trinity
College, Cambridge.)]
HISTORY OF ASTRONOMY
BY
GEORGE FORBES,
M.A., F.R.S., M. INST. C. E.,
(FORMERLY PROFESSOR OF NATURAL PHILOSOPHY, ANDERSON'S COLLEGE, GLASGOW)
AUTHOR OF "THE TRANSIT OF VENUS," RENDU'S "THEORY OF THE GLACIERS OF
SAVOY," ETC., ETC.
CONTENTS
PREFACE
BOOK I. THE GEOMETRICAL PERIOD
1. PRIMITIVE ASTRONOMY AND ASTROLOGY
2. ANCIENT ASTRONOMY--CHINESE AND CHALDAEANS
3. ANCIENT GREEK ASTRONOMY
4. THE REIGN OF EPICYCLES--FROM PTOLEMY TO COPERNICUS
BOOK II. THE DYNAMICAL PERIOD
5. DISCOVERY OF THE TRUE SOLAR SYSTEM--TYCHO BRAHE--KEPLER
6. GALILEO AND THE TELESCOPE--NOTIONS OF GRAVITY BY HORROCKS, ETC.
7. SIR ISAAC NEWTON--LAW OF UNIVERSAL GRAVITATION
8. NEWTON'S SUCCESSORS--HALLEY, EULER, LAGRANGE, LAPLACE, ETC.
9. DISCOVERY OF NEW PLANETS--HERSCHEL, PIAZZI, ADAMS, AND LE
VERRIER
BOOK III. OBSERVATION
10. INSTRUMENTS OF PRECISION--SIZE OF THE SOLAR SYSTEM
11. HISTORY OF THE TELESCOPE--SPECTROSCOPE
BOOK IV. THE PHYSICAL PERIOD
12. THE SUN
13. THE MOON AND PLANETS
14. COMETS AND METEORS
15. THE STARS AND NEBULAE
INDEX
PREFACE
An attempt has been made in these pages to trace the evolution of
intellectual thought in the progress of astronomical discovery, and,
by recognising the different points of view of the different ages, to
give due credit even to the ancients. No one can expect, in a history
of astronomy of limited size, to find a treatise on "practical" or on
"theoretical astronomy," nor a complete "descriptive astronomy," and
still less a book on "speculative astronomy." Something of each of
these is essential, however, for tracing the progress of thought and
knowledge which it is the object of this History to describe.
The progress of human knowledge is measured by the increased habit of
looking at facts from new points of view, as much as by the
accumulation of facts. The mental capacity of one age does not seem to
differ from that of other ages; but it is the imagination of new
points of view that gives a wider scope to that capacity. And this is
cumulative, and therefore progressive. Aristotle viewed the solar
system as a geometrical problem; Kepler and Newton converted the point
of view into a dynamical one. Aristotle's mental capacity to
understand the meaning of facts or to criticise a train of reasoning
may have been equal to that of Kepler or Newton, but the point of view
was different.
Then, again, new points of view are provided by the invention of new
methods in that system of logic which we call mathematics. All that
mathematics can do is to assure us that a statement A is equivalent to
statements B, C, D, or is one of the facts expressed by the statements
B, C, D; so that we may know, if B, C, and D are true, then A is true.
To many people our inability to understand all that is contained in
statements B, C, and D, without the cumbrous process of a mathematical
demonstration, proves the feebleness of the human mind as a logical
machine. For it required the new point of view imagined by Newton's
analysis to enable people to see that, so far as planetary orbits are
concerned, Kepler's three laws (B, C, D) were identical with Newton's
law of gravitation (A). No one recognises more than the mathematical
astronomer this feebleness of the human intellect, and no one is more
conscious of the limitations of the logical process called
mathematics, which even now has not solved directly the problem of
only three bodies.
These reflections, arising from the writing of this History, go to
explain the invariable humility of the great mathematical astronomers.
Newton's comparison of himself to the child on the seashore applies to
them all. As each new discovery opens up, it may be, boundless oceans
for investigation, for wonder, and for admiration, the great
astronomers, refusing to accept mere hypotheses as true, have founded
upon these discoveries a science as exact in its observation of facts
as in theories. So it is that these men, who have built up the most
sure and most solid of all the sciences, refuse to invite others to
join them in vain speculation. The writer has, therefore, in this
short History, tried to follow that great master, Airy, whose pupil he
was, and the key to whose character was exactness and accuracy; and he
recognises that Science is impotent except in her own limited sphere.
It has been necessary to curtail many parts of the History in the
attempt--perhaps a hopeless one--to lay before the reader in a limited
space enough about each age to illustrate its tone and spirit, the
ideals of the workers, the gradual addition of new points of view and
of new means of investigation.
It would, indeed, be a pleasure to entertain the hope that these pages
might, among new recruits, arouse an interest in the greatest of all
the sciences, or that those who have handled the theoretical or
practical side might be led by them to read in the original some of
the classics of astronomy. Many students have much compassion for the
schoolboy of to-day, who is not allowed the luxury of learning the art
of reasoning from him who still remains pre-eminently its greatest
exponent, Euclid. These students pity also the man of to-morrow, who
is not to be allowed to read, in the original Latin of the brilliant
Kepler, how he was able--by observations taken from a moving platform,
the earth, of the directions of a moving object, Mars--to deduce the
exact shape of the path of each of these planets, and their actual
positions on these paths at any time. Kepler's masterpiece is one of
the most interesting books that was ever written, combining wit,
imagination, ingenuity, and certainty.
Lastly, it must be noted that, as a History of England cannot deal
with the present Parliament, so also the unfinished researches and
untested hypotheses of many well-known astronomers of to-day cannot be
included among the records of the History of Astronomy. The writer
regrets the necessity that thus arises of leaving without mention the
names of many who are now making history in astronomical work.
G. F.
_August 1st, 1909._
BOOK I. THE GEOMETRICAL PERIOD
1. PRIMITIVE ASTRONOMY AND ASTROLOGY.
The growth of intelligence in the human race has its counterpart in
that of the individual, especially in the earliest stages.
Intellectual activity and the development of reasoning powers are in
both cases based upon the accumulation of experiences, and on the
comparison, classification, arrangement, and nomenclature of these
experiences. During the infancy of each the succession of events can
be watched, but there can be no _a priori_ anticipations.
Experience alone, in both cases, leads to the idea of cause and effect
as a principle that seems to dominate our present universe, as a rule
for predicting the course of events, and as a guide to the choice of a
course of action. This idea of cause and effect is the most potent
factor in developing the history of the human race, as of the
individual.
In no realm of nature is the principle of cause and effect more
conspicuous than in astronomy; and we fall into the habit of thinking
of its laws as not only being unchangeable in our universe, but
necessary to the conception of any universe that might have been
substituted in its place. The first inhabitants of the world were
compelled to accommodate their acts to the daily and annual
alternations of light and darkness and of heat and cold, as much as to
the irregular changes of weather, attacks of disease, and the fortune
of war. They soon came to regard the influence of the sun, in
connection with light and heat, as a cause. This led to a search for
other signs in the heavens. If the appearance of a comet was sometimes
noted simultaneously with the death of a great ruler, or an eclipse
with a scourge of plague, these might well be looked upon as causes in
the same sense that the veering or backing of the wind is regarded as
a cause of fine or foul weather.
For these reasons we find that the earnest men of all ages have
recorded the occurrence of comets, eclipses, new stars, meteor
showers, and remarkable conjunctions of the planets, as well as
plagues and famines, floods and droughts, wars and the deaths of great
rulers. Sometimes they thought they could trace connections which
might lead them to say that a comet presaged famine, or an eclipse
war.
Even if these men were sometimes led to evolve laws of cause and
effect which now seem to us absurd, let us be tolerant, and gratefully
acknowledge that these astrologers, when they suggested such "working
hypotheses," were laying the foundations of observation and deduction.
If the ancient Chaldaeans gave to the planetary conjunctions an
influence over terrestrial events, let us remember that in our own
time people have searched for connection between terrestrial
conditions and periods of unusual prevalence of sun spots; while De la
Rue, Loewy, and Balfour Stewart[1] thought they found a connection
between sun-spot displays and the planetary positions. Thus we find
scientific men, even in our own time, responsible for the belief that
storms in the Indian Ocean, the fertility of German vines, famines in
India, and high or low Nile-floods in Egypt follow the planetary
positions.
And, again, the desire to foretell the weather is so laudable that we
cannot blame the ancient Greeks for announcing the influence of the
moon with as much confidence as it is affirmed in Lord Wolseley's
_Soldier's Pocket Book_.
Even if the scientific spirit of observation and deduction (astronomy)
has sometimes led to erroneous systems for predicting terrestrial
events (astrology), we owe to the old astronomer and astrologer alike
the deepest gratitude for their diligence in recording astronomical
events. For, out of the scanty records which have survived the
destructive acts of fire and flood, of monarchs and mobs, we have
found much that has helped to a fuller knowledge of the heavenly
motions than was possible without these records.
So Hipparchus, about 150 B.C., and Ptolemy a little later, were able
to use the observations of Chaldaean astrologers, as well as those of
Alexandrian astronomers, and to make some discoveries which have
helped the progress of astronomy in all ages. So, also, Mr. Cowell[2]
has examined the marks made on the baked bricks used by the Chaldaeans
for recording the eclipses of 1062 B.C. and 762 B.C.; and has thereby
been enabled, in the last few years, to correct the lunar tables of
Hansen, and to find a more accurate value for the secular acceleration
of the moon's longitude and the node of her orbit than any that could
be obtained from modern observations made with instruments of the
highest precision.
So again, Mr. Hind [3] was enabled to trace back the period during
which Halley's comet has been a member of the solar system, and to
identify it in the Chinese observations of comets as far back as 12
B.C. Cowell and Cromellin extended the date to 240 B.C. In the same
way the comet 1861.i. has been traced back in the Chinese records to
617 A.D. [4]
The theoretical views founded on Newton's great law of universal
gravitation led to the conclusion that the inclination of the earth's
equator to the plane of her orbit (the obliquity of the ecliptic) has
been diminishing slowly since prehistoric times; and this fact has
been confirmed by Egyptian and Chinese observations on the length of
the shadow of a vertical pillar, made thousands of years before the
Christian era, in summer and winter.
There are other reasons why we must be tolerant of the crude notions
of the ancients. The historian, wishing to give credit wherever it may
be due, is met by two difficulties. Firstly, only a few records of
very ancient astronomy are extant, and the authenticity of many of
these is open to doubt. Secondly, it is very difficult to divest
ourselves of present knowledge, and to appreciate the originality of
thought required to make the first beginnings.
With regard to the first point, we are generally dependent upon
histories written long after the events. The astronomy of Egyptians,
Babylonians, and Assyrians is known to us mainly through the Greek
historians, and for information about the Chinese we rely upon the
researches of travellers and missionaries in comparatively recent
times. The testimony of the Greek writers has fortunately been
confirmed, and we now have in addition a mass of facts translated from
the original sculptures, papyri, and inscribed bricks, dating back
thousands of years.
In attempting to appraise the efforts of the beginners we must
remember that it was natural to look upon the earth (as all the first
astronomers did) as a circular plane, surrounded and bounded by the
heaven, which was a solid vault, or hemisphere, with its concavity
turned downwards. The stars seemed to be fixed on this vault; the
moon, and later the planets, were seen to crawl over it. It was a
great step to look on the vault as a hollow sphere carrying the sun
too. It must have been difficult to believe that at midday the stars
are shining as brightly in the blue sky as they do at night. It must
have been difficult to explain how the sun, having set in the west,
could get back to rise in the east without being seen _if_ it was
always the same sun. It was a great step to suppose the earth to be
spherical, and to ascribe the diurnal motions to its rotation.
Probably the greatest step ever made in astronomical theory was the
placing of the sun, moon, and planets at different distances from the
earth instead of having them stuck on the vault of heaven. It was a
transition from "flatland" to a space of three dimensions.
Great progress was made when systematic observations began, such as
following the motion of the moon and planets among the stars, and the
inferred motion of the sun among the stars, by observing their
_heliacal risings_--i.e., the times of year when a star
would first be seen to rise at sunrise, and when it could last be seen
to rise at sunset. The grouping of the stars into constellations and
recording their places was a useful observation. The theoretical
prediction of eclipses of the sun and moon, and of the motions of the
planets among the stars, became later the highest goal in astronomy.
To not one of the above important steps in the progress of astronomy
can we assign the author with certainty. Probably many of them were
independently taken by Chinese, Indian, Persian, Tartar, Egyptian,
Babylonian, Assyrian, Phoenician, and Greek astronomers. And we have
not a particle of information about the discoveries, which may have
been great, by other peoples--by the Druids, the Mexicans, and the
Peruvians, for example.
We do know this, that all nations required to have a calendar. The
solar year, the lunar month, and the day were the units, and it is
owing to their incommensurability that we find so many calendars
proposed and in use at different times. The only object to be attained
by comparing the chronologies of ancient races is to fix the actual
dates of observations recorded, and this is not a part of a history of
astronomy.
In conclusion, let us bear in mind the limited point of view of the
ancients when we try to estimate their merit. Let us remember that the
first astronomy was of two dimensions; the second astronomy was of
three dimensions, but still purely geometrical. Since Kepler's day we
have had a dynamical astronomy.
FOOTNOTES:
[1] Trans. R. S. E., xxiii. 1864, p. 499, _On Sun Spots_, etc., by
B. Stewart. Also Trans. R. S. 1860-70. Also Prof. Ernest Brown, in
_R. A. S. Monthly Notices_, 1900.
[2] _R. A. S. Monthly Notices_, Sup.; 1905.
[Illustration: CHALDAEAN BAKED BRICK OR TABLET, _Obverse and reverse
sides_, Containing record of solar eclipse, 1062 B.C., used lately by
Cowell for rendering the lunar theory more accurate than was possible
by finest modern observations. (British Museum collection,
No. 35908.)]
[3] _R. A. S. Monthly Notices_, vol. x., p. 65.
[4] R. S. E. Proc., vol. x., 1880.
2. ANCIENT ASTRONOMY--THE CHINESE AND CHALDAEANS.
The last section must have made clear the difficulties the way of
assigning to the ancient nations their proper place in the development
of primitive notions about astronomy. The fact that some alleged
observations date back to a period before the Chinese had invented the
art of writing leads immediately to the question how far tradition can
be trusted.
Our first detailed knowledge was gathered in the far East by
travellers, and by the Jesuit priests, and was published in the
eighteenth century. The Asiatic Society of Bengal contributed
translations of Brahmin literature. The two principal sources of
knowledge about Chinese astronomy were supplied, first by Father
Souciet, who in 1729 published _Observations Astronomical,
Geographical, Chronological, and Physical_, drawn from ancient
Chinese books; and later by Father Moyriac-de-Mailla, who in 1777-1785
published _Annals of the Chinese Empire, translated from
Tong-Kien-Kang-Mou_.
Bailly, in his _Astronomie Ancienne_ (1781), drew, from these and
other sources, the conclusion that all we know of the astronomical
learning of the Chinese, Indians, Chaldaeans, Assyrians, and Egyptians
is but the remnant of a far more complete astronomy of which no trace
can be found.
Delambre, in his _Histoire de l'Astronomie Ancienne_ (1817),
ridicules the opinion of Bailly, and considers that the progress made
by all of these nations is insignificant.
It will be well now to give an idea of some of the astronomy of the
ancients not yet entirely discredited. China and Babylon may be taken
as typical examples.
_China_.--It would appear that Fohi, the first emperor, reigned
about 2952 B.C., and shortly afterwards Yu-Chi made a sphere to
represent the motions of the celestial bodies. It is also mentioned,
in the book called Chu-King, supposed to have been written in 2205
B.C., that a similar sphere was made in the time of Yao (2357
B.C.).[1] It is said that the Emperor Chueni (2513 B.C.) saw five
planets in conjunction the same day that the sun and moon were in
conjunction. This is discussed by Father Martin (MSS. of De Lisle);
also by M. Desvignolles (Mem. Acad. Berlin, vol. iii., p. 193), and by
M. Kirsch (ditto, vol. v., p. 19), who both found that Mars, Jupiter,
Saturn, and Mercury were all between the eleventh and eighteenth
degrees of Pisces, all visible together in the evening on February
28th 2446 B.C., while on the same day the sun and moon were in
conjunction at 9 a.m., and that on March 1st the moon was in
conjunction with the other four planets. But this needs confirmation.
Yao, referred to above, gave instructions to his astronomers to
determine the positions of the solstices and equinoxes, and they
reported the names of the stars in the places occupied by the sun at
these seasons, and in 2285 B.C. he gave them further orders. If this
account be true, it shows a knowledge that the vault of heaven is a
complete sphere, and that stars are shining at mid-day, although
eclipsed by the sun's brightness.
It is also asserted, in the book called _Chu-King_, that in the
time of Yao the year was known to have 3651/4 days, and that he
adopted 365 days and added an intercalary day every four years (as in
the Julian Calendar). This may be true or not, but the ancient Chinese
certainly seem to have divided the circle into 365 degrees. To learn
the length of the year needed only patient observation--a
characteristic of the Chinese; but many younger nations got into a
terrible mess with their calendar from ignorance of the year's length.
It is stated that in 2159 B.C. the royal astronomers Hi and Ho failed
to predict an eclipse. It probably created great terror, for they were
executed in punishment for their neglect. If this account be true, it
means that in the twenty-second century B.C. some rule for calculating
eclipses was in use. Here, again, patient observation would easily
lead to the detection of the eighteen-year cycle known to the
Chaldeans as the _Saros_. It consists of 235 lunations, and in
that time the pole of the moon's orbit revolves just once round the
pole of the ecliptic, and for this reason the eclipses in one cycle
are repeated with very slight modification in the next cycle, and so
on for many centuries.
It may be that the neglect of their duties by Hi and Ho, and their
punishment, influenced Chinese astronomy; or that the succeeding
records have not been available to later scholars; but the fact
remains that--although at long intervals observations were made of
eclipses, comets, and falling stars, and of the position of the
solstices, and of the obliquity of the ecliptic--records become rare,
until 776 B.C., when eclipses began to be recorded once more with some
approach to continuity. Shortly afterwards notices of comets were
added. Biot gave a list of these, and Mr. John Williams, in 1871,
published _Observations of Comets from 611 B.C. to 1640 A.D.,
Extracted from the Chinese Annals_.
With regard to those centuries concerning which we have no
astronomical Chinese records, it is fair to state that it is recorded
that some centuries before the Christian era, in the reign of
Tsin-Chi-Hoang, all the classical and scientific books that could be
found were ordered to be destroyed. If true, our loss therefrom is as
great as from the burning of the Alexandrian library by the Caliph
Omar. He burnt all the books because he held that they must be either
consistent or inconsistent with the Koran, and in the one case they
were superfluous, in the other case objectionable.
_Chaldaeans_.--Until the last half century historians were
accustomed to look back upon the Greeks, who led the world from the
fifth to the third century B.C., as the pioneers of art, literature,
and science. But the excavations and researches of later years make us
more ready to grant that in science as in art the Greeks only
developed what they derived from the Egyptians, Babylonians, and
Assyrians. The Greek historians said as much, in fact; and modern
commentators used to attribute the assertion to undue modesty. Since,
however, the records of the libraries have been unearthed it has been
recognised that the Babylonians were in no way inferior in the matter
of original scientific investigation to other races of the same era.
The Chaldaeans, being the most ancient Babylonians, held the same
station and dignity in the State as did the priests in Egypt, and
spent all their time in the study of philosophy and astronomy, and the
arts of divination and astrology. They held that the world of which we
have a conception is an eternal world without any beginning or ending,
in which all things are ordered by rules supported by a divine
providence, and that the heavenly bodies do not move by chance, nor by
their own will, but by the determinate will and appointment of the
gods. They recorded these movements, but mainly in the hope of tracing
the will of the gods in mundane affairs. Ptolemy (about 130 A.D.)
made use of Babylonian eclipses in the eighth century B.C. for
improving his solar and lunar tables.
Fragments of a library at Agade have been preserved at Nineveh, from
which we learn that the star-charts were even then divided into
constellations, which were known by the names which they bear to this
day, and that the signs of the zodiac were used for determining the
courses of the sun, moon, and of the five planets Mercury, Venus,
Mars, Jupiter, and Saturn.
We have records of observations carried on under Asshurbanapal, who
sent astronomers to different parts to study celestial phenomena. Here
is one:--
To the Director of Observations,--My Lord, his humble servant
Nabushum-iddin, Great Astronomer of Nineveh, writes thus: "May Nabu
and Marduk be propitious to the Director of these Observations, my
Lord. The fifteenth day we observed the Node of the moon, and the moon
was eclipsed."
The Phoenicians are supposed to have used the stars for navigation,
but there are no records. The Egyptian priests tried to keep such
astronomical knowledge as they possessed to themselves. It is probable
that they had arbitrary rules for predicting eclipses. All that was
known to the Greeks about Egyptian science is to be found in the
writings of Diodorus Siculus. But confirmatory and more authentic
facts have been derived from late explorations. Thus we learn from
E. B. Knobel[2] about the Jewish calendar dates, on records of land
sales in Aramaic papyri at Assuan, translated by Professor A. H. Sayce
and A. E. Cowley, (1) that the lunar cycle of nineteen years was used
by the Jews in the fifth century B.C. [the present reformed Jewish
calendar dating from the fourth century A.D.], a date a "little more
than a century after the grandfathers and great-grandfathers of those
whose business is recorded had fled into Egypt with Jeremiah" (Sayce);
and (2) that the order of intercalation at that time was not
dissimilar to that in use at the present day.
Then again, Knobel reminds us of "the most interesting discovery a few
years ago by Father Strassmeier of a Babylonian tablet recording a
partial lunar eclipse at Babylon in the seventh year of Cambyses, on
the fourteenth day of the Jewish month Tammuz." Ptolemy, in the
Almagest (Suntaxis), says it occurred in the seventh year of Cambyses,
on the night of the seventeenth and eighteenth of the Egyptian month
Phamenoth. Pingre and Oppolzer fix the date July 16th, 533 B.C. Thus
are the relations of the chronologies of Jews and Egyptians
established by these explorations.
FOOTNOTES:
[1] These ancient dates are uncertain.
[2] _R. A. S. Monthly Notices_, vol. lxviii., No. 5, March, 1908.
3. ANCIENT GREEK ASTRONOMY.
We have our information about the earliest Greek astronomy from
Herodotus (born 480 B.C.). He put the traditions into writing. Thales
(639-546 B.C.) is said to have predicted an eclipse, which caused much
alarm, and ended the battle between the Medes and Lydians. Airy fixed
the date May 28th, 585 B.C. But other modern astronomers give
different dates. Thales went to Egypt to study science, and learnt
from its priests the length of the year (which was kept a profound
secret!), and the signs of the zodiac, and the positions of the
solstices. He held that the sun, moon, and stars are not mere spots on
the heavenly vault, but solids; that the moon derives her light from
the sun, and that this fact explains her phases; that an eclipse of
the moon happens when the earth cuts off the sun's light from her. He
supposed the earth to be flat, and to float upon water. He determined
the ratio of the sun's diameter to its orbit, and apparently made out
the diameter correctly as half a degree. He left nothing in writing.
His successors, Anaximander (610-547 B.C.) and Anaximenes (550-475
B.C.), held absurd notions about the sun, moon, and stars, while
Heraclitus (540-500 B.C.) supposed that the stars were lighted each
night like lamps, and the sun each morning. Parmenides supposed the
earth to be a sphere.
Pythagoras (569-470 B.C.) visited Egypt to study science. He deduced
his system, in which the earth revolves in an orbit, from fantastic
first principles, of which the following are examples: "The circular
motion is the most perfect motion," "Fire is more worthy than earth,"
"Ten is the perfect number." He wrote nothing, but is supposed to have
said that the earth, moon, five planets, and fixed stars all revolve
round the sun, which itself revolves round an imaginary central fire
called the Antichthon. Copernicus in the sixteenth century claimed
Pythagoras as the founder of the system which he, Copernicus, revived.
Anaxagoras (born 499 B.C.) studied astronomy in Egypt. He explained
the return of the sun to the east each morning by its going under the
flat earth in the night. He held that in a solar eclipse the moon
hides the sun, and in a lunar eclipse the moon enters the earth's
shadow--both excellent opinions. But he entertained absurd ideas of
the vortical motion of the heavens whisking stones into the sky, there
to be ignited by the fiery firmament to form stars. He was prosecuted
for this unsettling opinion, and for maintaining that the moon is an
inhabited earth. He was defended by Pericles (432 B.C.).
Solon dabbled, like many others, in reforms of the calendar. The
common year of the Greeks originally had 360 days--twelve months of
thirty days. Solon's year was 354 days. It is obvious that these
erroneous years would, before long, remove the summer to January and
the winter to July. To prevent this it was customary at regular
intervals to intercalate days or months. Meton (432 B.C.) introduced a
reform based on the nineteen-year cycle. This is not the same as the
Egyptian and Chaldean eclipse cycle called _Saros_ of 223
lunations, or a little over eighteen years. The Metonic cycle is 235
lunations or nineteen years, after which period the sun and moon
occupy the same position relative to the stars. It is still used for
fixing the date of Easter, the number of the year in Melon's cycle
being the golden number of our prayer-books. Melon's system divided
the 235 lunations into months of thirty days and omitted every
sixty-third day. Of the nineteen years, twelve had twelve months and
seven had thirteen months.
Callippus (330 B.C.) used a cycle four times as long, 940 lunations,
but one day short of Melon's seventy-six years. This was more correct.
Eudoxus (406-350 B.C.) is said to have travelled with Plato in
Egypt. He made astronomical observations in Asia Minor, Sicily, and
Italy, and described the starry heavens divided into constellations.
His name is connected with a planetary theory which as generally
stated sounds most fanciful. He imagined the fixed stars to be on a
vault of heaven; and the sun, moon, and planets to be upon similar
vaults or spheres, twenty-six revolving spheres in all, the motion of
each planet being resolved into its components, and a separate sphere
being assigned for each component motion. Callippus (330 B.C.)
increased the number to thirty-three. It is now generally accepted
that the real existence of these spheres was not suggested, but the
idea was only a mathematical conception to facilitate the construction
of tables for predicting the places of the heavenly bodies.
Aristotle (384-322 B.C.) summed up the state of astronomical knowledge
in his time, and held the earth to be fixed in the centre of the
world.
Nicetas, Heraclides, and Ecphantes supposed the earth to revolve on
its axis, but to have no orbital motion.
The short epitome so far given illustrates the extraordinary deductive
methods adopted by the ancient Greeks. But they went much farther in
the same direction. They seem to have been in great difficulty to
explain how the earth is supported, just as were those who invented
the myth of Atlas, or the Indians with the tortoise. Thales thought
that the flat earth floated on water. Anaxagoras thought that, being
flat, it would be buoyed up and supported on the air like a kite.
Democritus thought it remained fixed, like the donkey between two
bundles of hay, because it was equidistant from all parts of the
containing sphere, and there was no reason why it should incline one
way rather than another. Empedocles attributed its state of rest to
centrifugal force by the rapid circular movement of the heavens, as
water is stationary in a pail when whirled round by a string.
Democritus further supposed that the inclination of the flat earth to
the ecliptic was due to the greater weight of the southern parts owing
to the exuberant vegetation.
For further references to similar efforts of imagination the reader is
referred to Sir George Cornwall Lewis's _Historical Survey of the
Astronomy of the Ancients_; London, 1862. His list of authorities
is very complete, but some of his conclusions are doubtful. At p. 113
of that work he records the real opinions of Socrates as set forth by
Xenophon; and the reader will, perhaps, sympathise with Socrates in
his views on contemporary astronomy:--
With regard to astronomy he [Socrates] considered a knowledge of it
desirable to the extent of determining the day of the year or month,
and the hour of the night, ... but as to learning the courses of the
stars, to be occupied with the planets, and to inquire about their
distances from the earth, and their orbits, and the causes of their
motions, he strongly objected to such a waste of valuable time. He
dwelt on the contradictions and conflicting opinions of the physical
philosophers, ... and, in fine, he held that the speculators on the
universe and on the laws of the heavenly bodies were no better than
madmen (_Xen. Mem_, i. 1, 11-15).
Plato (born 429 B.C.), the pupil of Socrates, the fellow-student of
Euclid, and a follower of Pythagoras, studied science in his travels
in Egypt and elsewhere. He was held in so great reverence by all
learned men that a problem which he set to the astronomers was the
keynote to all astronomical investigation from this date till the time
of Kepler in the sixteenth century. He proposed to astronomers _the
problem of representing the courses of the planets by circular and
uniform motions_.
Systematic observation among the Greeks began with the rise of the
Alexandrian school. Aristillus and Timocharis set up instruments and
fixed the positions of the zodiacal stars, near to which all the
planets in their orbits pass, thus facilitating the determination of
planetary motions. Aristarchus (320-250 B.C.) showed that the sun must
be at least nineteen times as far off as the moon, which is far short
of the mark. He also found the sun's diameter, correctly, to be half a
degree. Eratosthenes (276-196 B.C.) measured the inclination to the
equator of the sun's apparent path in the heavens--i.e., he
measured the obliquity of the ecliptic, making it 23 deg. 51', confirming
our knowledge of its continuous diminution during historical times. He
measured an arc of meridian, from Alexandria to Syene (Assuan), and
found the difference of latitude by the length of a shadow at noon,
summer solstice. He deduced the diameter of the earth, 250,000
stadia. Unfortunately, we do not know the length of the stadium he
used.
Hipparchus (190-120 B.C.) may be regarded as the founder of
observational astronomy. He measured the obliquity of the ecliptic,
and agreed with Eratosthenes. He altered the length of the tropical
year from 365 days, 6 hours to 365 days, 5 hours, 53 minutes--still
four minutes too much. He measured the equation of time and the
irregular motion of the sun; and allowed for this in his calculations
by supposing that the centre, about which the sun moves uniformly, is
situated a little distance from the fixed earth. He called this point
the _excentric_. The line from the earth to the "excentric" was
called the _line of apses_. A circle having this centre was
called the _equant_, and he supposed that a radius drawn to the
sun from the excentric passes over equal arcs on the equant in equal
times. He then computed tables for predicting the place of the sun.
He proceeded in the same way to compute Lunar tables. Making use of
Chaldaean eclipses, he was able to get an accurate value of the moon's
mean motion. [Halley, in 1693, compared this value with his own
measurements, and so discovered the acceleration of the moon's mean
motion. This was conclusively established, but could not be explained
by the Newtonian theory for quite a long time.] He determined the
plane of the moon's orbit and its inclination to the ecliptic. The
motion of this plane round the pole of the ecliptic once in eighteen
years complicated the problem. He located the moon's excentric as he
had done the sun's. He also discovered some of the minor
irregularities of the moon's motion, due, as Newton's theory proves,
to the disturbing action of the sun's attraction.
In the year 134 B.C. Hipparchus observed a new star. This upset every
notion about the permanence of the fixed stars. He then set to work to
catalogue all the principal stars so as to know if any others appeared
or disappeared. Here his experiences resembled those of several later
astronomers, who, when in search of some special object, have been
rewarded by a discovery in a totally different direction. On comparing
his star positions with those of Timocharis and Aristillus he found no
stars that had appeared or disappeared in the interval of 150 years;
but he found that all the stars seemed to have changed their places
with reference to that point in the heavens where the ecliptic is 90 deg.
from the poles of the earth--i.e., the equinox. He found that this
could be explained by a motion of the equinox in the direction of the
apparent diurnal motion of the stars. This discovery of _precession of
the equinoxes_, which takes place at the rate of 52".1 every year, was
necessary for the progress of accurate astronomical observations. It
is due to a steady revolution of the earth's pole round the pole of
the ecliptic once in 26,000 years in the opposite direction to the
planetary revolutions.
Hipparchus was also the inventor of trigonometry, both plane and
spherical. He explained the method of using eclipses for determining
the longitude.
In connection with Hipparchus' great discovery it may be mentioned
that modern astronomers have often attempted to fix dates in history
by the effects of precession of the equinoxes. (1) At about the date
when the Great Pyramid may have been built gamma Draconis was near to the
pole, and must have been used as the pole-star. In the north face of
the Great Pyramid is the entrance to an inclined passage, and six of
the nine pyramids at Gizeh possess the same feature; all the passages
being inclined at an angle between 26 deg. and 27 deg. to the horizon and in
the plane of the meridian. It also appears that 4,000 years
ago--i.e., about 2100 B.C.--an observer at the lower end of the
passage would be able to see gamma Draconis, the then pole-star, at its
lower culmination.[1] It has been suggested that the passage was made
for this purpose. On other grounds the date assigned to the Great
Pyramid is 2123 B.C.
(2) The Chaldaeans gave names to constellations now invisible from
Babylon which would have been visible in 2000 B.C., at which date it
is claimed that these people were studying astronomy.
(3) In the Odyssey, Calypso directs Odysseus, in accordance with
Phoenician rules for navigating the Mediterranean, to keep the Great
Bear "ever on the left as he traversed the deep" when sailing from the
pillars of Hercules (Gibraltar) to Corfu. Yet such a course taken now
would land the traveller in Africa. Odysseus is said in his voyage in
springtime to have seen the Pleiades and Arcturus setting late, which
seemed to early commentators a proof of Homer's inaccuracy. Likewise
Homer, both in the _Odyssey_ [2] (v. 272-5) and in the _Iliad_
(xviii. 489), asserts that the Great Bear never set in those
latitudes. Now it has been found that the precession of the equinoxes
explains all these puzzles; shows that in springtime on the
Mediterranean the Bear was just above the horizon, near the sea but
not touching it, between 750 B.C. and 1000 B.C.; and fixes the date of
the poems, thus confirming other evidence, and establishing Homer's
character for accuracy. [3]
(4) The orientation of Egyptian temples and Druidical stones is such
that possibly they were so placed as to assist in the observation of
the heliacal risings [4] of certain stars. If the star were known,
this would give an approximate date. Up to the present the results of
these investigations are far from being conclusive.
Ptolemy (130 A.D.) wrote the Suntaxis, or Almagest, which includes a
cyclopedia of astronomy, containing a summary of knowledge at that
date. We have no evidence beyond his own statement that he was a
practical observer. He theorised on the planetary motions, and held
that the earth is fixed in the centre of the universe. He adopted the
excentric and equant of Hipparchus to explain the unequal motions of
the sun and moon. He adopted the epicycles and deferents which had
been used by Apollonius and others to explain the retrograde motions
of the planets. We, who know that the earth revolves round the sun
once in a year, can understand that the apparent motion of a planet is
only its motion relative to the earth. If, then, we suppose the earth
fixed and the sun to revolve round it once a year, and the planets
each in its own period, it is only necessary to impose upon each of
these an additional _annual_ motion to enable us to represent truly
the apparent motions. This way of looking at the apparent motions
shows why each planet, when nearest to the earth, seems to move for a
time in a retrograde direction. The attempts of Ptolemy and others of
his time to explain the retrograde motion in this way were only
approximate. Let us suppose each planet to have a bar with one end
centred at the earth. If at the other end of the bar one end of a
shorter bar is pivotted, having the planet at its other end, then the
planet is given an annual motion in the secondary circle (the
epicycle), whose centre revolves round the earth on the primary circle
(the _deferent_), at a uniform rate round the excentric. Ptolemy
supposed the centres of the epicycles of Mercury and Venus to be on a
bar passing through the sun, and to be between the earth and the
sun. The centres of the epicycles of Mars, Jupiter, and Saturn were
supposed to be further away than the sun. Mercury and Venus were
supposed to revolve in their epicycles in their own periodic times and
in the deferent round the earth in a year. The major planets were
supposed to revolve in the deferent round the earth in their own
periodic times, and in their epicycles once in a year.
It did not occur to Ptolemy to place the centres of the epicycles of
Mercury and Venus at the sun, and to extend the same system to the
major planets. Something of this sort had been proposed by the
Egyptians (we are told by Cicero and others), and was accepted by
Tycho Brahe; and was as true a representation of the relative motions
in the solar system as when we suppose the sun to be fixed and the
earth to revolve.
The cumbrous system advocated by Ptolemy answered its purpose,
enabling him to predict astronomical events approximately. He improved
the lunar theory considerably, and discovered minor inequalities which
could be allowed for by the addition of new epicycles. We may look
upon these epicycles of Apollonius, and the excentric of Hipparchus,
as the responses of these astronomers to the demand of Plato for
uniform circular motions. Their use became more and more confirmed,
until the seventeenth century, when the accurate observations of Tycho
Brahe enabled Kepler to abolish these purely geometrical makeshifts,
and to substitute a system in which the sun became physically its
controller.
FOOTNOTES:
[1] _Phil. Mag_., vol. xxiv., pp. 481-4.
[2]
Plaeiadas t' esoronte kai opse duonta bootaen
'Arkton th' aen kai amaxan epiklaesin kaleousin,
'Ae t' autou strephetai kai t' Oriona dokeuei,
Oin d'ammoros esti loetron Okeanoio.
"The Pleiades and Booetes that setteth late, and the Bear,
which they likewise call the Wain, which turneth ever in one
place, and keepeth watch upon Orion, and alone hath no part in
the baths of the ocean."
[3] See Pearson in the Camb. Phil. Soc. Proc., vol. iv., pt. ii., p.
93, on whose authority the above statements are made.
[4] See p. 6 for definition.
4. THE REIGN OF EPICYCLES--FROM PTOLEMY TO COPERNICUS.
After Ptolemy had published his book there seemed to be nothing more
to do for the solar system except to go on observing and finding more
and more accurate values for the constants involved--viz., the periods
of revolution, the diameter of the deferent,[1] and its ratio to that
of the epicycle,[2] the distance of the excentric[3] from the centre
of the deferent, and the position of the line of apses,[4] besides the
inclination and position of the plane of the planet's orbit. The only
object ever aimed at in those days was to prepare tables for
predicting the places of the planets. It was not a mechanical problem;
there was no notion of a governing law of forces.
From this time onwards all interest in astronomy seemed, in Europe at
least, to sink to a low ebb. When the Caliph Omar, in the middle of
the seventh century, burnt the library of Alexandria, which had been
the centre of intellectual progress, that centre migrated to Baghdad,
and the Arabs became the leaders of science and philosophy. In
astronomy they made careful observations. In the middle of the ninth
century Albategnius, a Syrian prince, improved the value of
excentricity of the sun's orbit, observed the motion of the moon's
apse, and thought he detected a smaller progression of the sun's
apse. His tables were much more accurate than Ptolemy's. Abul Wefa, in
the tenth century, seems to have discovered the moon's "variation."
Meanwhile the Moors were leaders of science in the west, and Arzachel
of Toledo improved the solar tables very much. Ulugh Begh, grandson of
the great Tamerlane the Tartar, built a fine observatory at Samarcand
in the fifteenth century, and made a great catalogue of stars, the
first since the time of Hipparchus.
At the close of the fifteenth century King Alphonso of Spain employed
computers to produce the Alphonsine Tables (1488 A.D.), Purbach
translated Ptolemy's book, and observations were carried out in
Germany by Mueller, known as Regiomontanus, and Waltherus.
Nicolai Copernicus, a Sclav, was born in 1473 at Thorn, in Polish
Prussia. He studied at Cracow and in Italy. He was a priest, and
settled at Frauenberg. He did not undertake continuous observations,
but devoted himself to simplifying the planetary systems and devising
means for more accurately predicting the positions of the sun, moon,
and planets. He had no idea of framing a solar system on a dynamical
basis. His great object was to increase the accuracy of the
calculations and the tables. The results of his cogitations were
printed just before his death in an interesting book, _De
Revolutionibus Orbium Celestium_. It is only by careful reading of
this book that the true position of Copernicus can be realised. He
noticed that Nicetas and others had ascribed the apparent diurnal
rotation of the heavens to a real daily rotation of the earth about
its axis, in the opposite direction to the apparent motion of the
stars. Also in the writings of Martianus Capella he learnt that the
Egyptians had supposed Mercury and Venus to revolve round the sun, and
to be carried with him in his annual motion round the earth. He
noticed that the same supposition, if extended to Mars, Jupiter, and
Saturn, would explain easily why they, and especially Mars, seem so
much brighter in opposition. For Mars would then be a great deal
nearer to the earth than at other times. It would also explain the
retrograde motion of planets when in opposition.
We must here notice that at this stage Copernicus was actually
confronted with the system accepted later by Tycho Brahe, with the
earth fixed. But he now recalled and accepted the views of Pythagoras
and others, according to which the sun is fixed and the earth
revolves; and it must be noted that, geometrically, there is no
difference of any sort between the Egyptian or Tychonic system and
that of Pythagoras as revived by Copernicus, except that on the latter
theory the stars ought to seem to move when the earth changes its
position--a test which failed completely with the rough means of
observation then available. The radical defect of all solar systems
previous to the time of Kepler (1609 A.D.) was the slavish yielding to
Plato's dictum demanding uniform circular motion for the planets, and
the consequent evolution of the epicycle, which was fatal to any
conception of a dynamical theory.
Copernicus could not sever himself from this obnoxious tradition.[5]
It is true that neither the Pythagorean nor the Egypto-Tychonic system
required epicycles for explaining retrograde motion, as the Ptolemaic
theory did. Furthermore, either system could use the excentric of
Hipparchus to explain the irregular motion known as the equation of
the centre. But Copernicus remarked that he could also use an
epicycle for this purpose, or that he could use both an excentric and
an epicycle for each planet, and so bring theory still closer into
accord with observation. And this he proceeded to do.[6] Moreover,
observers had found irregularities in the moon's motion, due, as we
now know, to the disturbing attraction of the sun. To correct for
these irregularities Copernicus introduced epicycle on epicycle in the
lunar orbit.
This is in its main features the system propounded by Copernicus. But
attention must, to state the case fully, be drawn to two points to be
found in his first and sixth books respectively. The first point
relates to the seasons, and it shows a strange ignorance of the laws
of rotating bodies. To use the words of Delambre,[7] in drawing
attention to the strange conception,
he imagined that the earth, revolving round the sun, ought always to
show to it the same face; the contrary phenomena surprised him: to
explain them he invented a third motion, and added it to the two
real motions (rotation and orbital revolution). By this third motion
the earth, he held, made a revolution on itself and on the poles of
the ecliptic once a year ... Copernicus did not know that motion in
a straight line is the natural motion, and that motion in a curve is
the resultant of several movements. He believed, with Aristotle,
that circular motion was the natural one.
Copernicus made this rotation of the earth's axis about the pole of
the ecliptic retrograde (i.e., opposite to the orbital revolution),
and by making it perform more than one complete revolution in a year,
the added part being 1/26000 of the whole, he was able to include the
precession of the equinoxes in his explanation of the seasons. His
explanation of the seasons is given on leaf 10 of his book (the pages
of this book are not all numbered, only alternate pages, or leaves).
In his sixth book he discusses the inclination of the planetary orbits
to the ecliptic. In regard to this the theory of Copernicus is unique;
and it will be best to explain this in the words of Grant in his great
work.[8] He says:--
Copernicus, as we have already remarked, did not attack the
principle of the epicyclical theory: he merely sought to make it
more simple by placing the centre of the earth's orbit in the centre
of the universe. This was the point to which the motions of the
planets were referred, for the planes of their orbits were made to
pass through it, and their points of least and greatest velocities
were also determined with reference to it. By this arrangement the
sun was situate mathematically near the centre of the planetary
system, but he did not appear to have any physical connexion with
the planets as the centre of their motions.
According to Copernicus' sixth book, the planes of the planetary
orbits do not pass through the sun, and the lines of apses do not pass
through to the sun.
Such was the theory advanced by Copernicus: The earth moves in an
epicycle, on a deferent whose centre is a little distance from the
sun. The planets move in a similar way on epicycles, but their
deferents have no geometrical or physical relation to the sun. The
moon moves on an epicycle centred on a second epicycle, itself centred
on a deferent, excentric to the earth. The earth's axis rotates about
the pole of the ecliptic, making one revolution and a twenty-six
thousandth part of a revolution in the sidereal year, in the opposite
direction to its orbital motion.
In view of this fanciful structure it must be noted, in fairness to
Copernicus, that he repeatedly states that the reader is not obliged
to accept his system as showing the real motions; that it does not
matter whether they be true, even approximately, or not, so long as
they enable us to compute tables from which the places of the planets
among the stars can be predicted.[9] He says that whoever is not
satisfied with this explanation must be contented by being told that
"mathematics are for mathematicians" (Mathematicis mathematica
scribuntur).
At the same time he expresses his conviction over and over again that
the earth is in motion. It is with him a pious belief, just as it was
with Pythagoras and his school and with Aristarchus. "But" (as Dreyer
says in his most interesting book, _Tycho Brahe_) "proofs of the
physical truth of his system Copernicus had given none, and could give
none," any more than Pythagoras or Aristarchus.
There was nothing so startlingly simple in his system as to lead the
cautious astronomer to accept it, as there was in the later Keplerian
system; and the absence of parallax in the stars seemed to condemn his
system, which had no physical basis to recommend it, and no
simplification at all over the Egypto-Tychonic system, to which
Copernicus himself drew attention. It has been necessary to devote
perhaps undue space to the interesting work of Copernicus, because by
a curious chance his name has become so widely known. He has been
spoken of very generally as the founder of the solar system that is
now accepted. This seems unfair, and on reading over what has been
written about him at different times it will be noticed that the
astronomers--those who have evidently read his great book--are very
cautious in the words with which they eulogise him, and refrain from
attributing to him the foundation of our solar system, which is
entirely due to Kepler. It is only the more popular writers who give
the idea that a revolution had been effected when Pythagoras' system
was revived, and when Copernicus supported his view that the earth
moves and is not fixed.
It may be easy to explain the association of the name of Copernicus
with the Keplerian system. But the time has long passed when the
historian can support in any way this popular error, which was started
not by astronomers acquainted with Kepler's work, but by those who
desired to put the Church in the wrong by extolling Copernicus.
Copernicus dreaded much the abuse he expected to receive from
philosophers for opposing the authority of Aristotle, who had declared
that the earth was fixed. So he sought and obtained the support of
the Church, dedicating his great work to Pope Paul III. in a lengthy
explanatory epistle. The Bishop of Cracow set up a memorial tablet in
his honour.
Copernicus was the most refined exponent, and almost the last
representative, of the Epicyclical School. As has been already
stated, his successor, Tycho Brahe, supported the same use of
epicycles and excentrics as Copernicus, though he held the earth to be
fixed. But Tycho Brahe was eminently a practical observer, and took
little part in theory; and his observations formed so essential a
portion of the system of Kepler that it is only fair to include his
name among these who laid the foundations of the solar system which we
accept to-day.
In now taking leave of the system of epicycles let it be remarked that
it has been held up to ridicule more than it deserves. On reading
Airy's account of epicycles, in the beautifully clear language of his
_Six Lectures on Astronomy_, the impression is made that the
jointed bars there spoken of for describing the circles were supposed
to be real. This is no more the case than that the spheres of Eudoxus
and Callippus were supposed to be real. Both were introduced only to
illustrate the mathematical conception upon which the solar,
planetary, and lunar tables were constructed. The epicycles
represented nothing more nor less than the first terms in the Fourier
series, which in the last century has become a basis of such
calculations, both in astronomy and physics generally.
[Illustration: "QUADRANS MURALIS SIVE TICHONICUS." With portrait of
Tycho Brahe, instruments, etc., painted on the wall; showing
assistants using the sight, watching the clock, and recording. (From
the author's copy of the _Astronomiae Instauratae Mechanica._)]
FOOTNOTES:
[1] For definition see p. 22.
[2] _Ibid_.
[3] For definition see p. 18.
[4] For definition see p. 18.
[5] In his great book Copernicus says: "The movement of the heavenly
bodies is uniform, circular, perpetual, or else composed of circular
movements." In this he proclaimed himself a follower of Pythagoras
(see p. 14), as also when he says: "The world is spherical because the
sphere is, of all figures, the most perfect" (Delambre,
_Ast. Mod. Hist_., pp. 86, 87).
[6] Kepler tells us that Tycho Brahe was pleased with this
device, and adapted it to his own system.
[7] _Hist. Ast._, vol. i., p. 354.
[8] _Hist. of Phys. Ast._, p. vii.
[9] "Est enim Astronomi proprium, historiam motuum coelestium
diligenti et artificiosa observatione colligere. Deinde causas
earundem, seu hypotheses, cum veras assequi nulla ratione possit
... Neque enim necesse est, eas hypotheses esse veras, imo ne
verisimiles quidem, sed sufficit hoc usum, si calculum observationibus
congruentem exhibeant."
BOOK II. THE DYNAMICAL PERIOD
5. DISCOVERY OF THE TRUE SOLAR SYSTEM--TYCHO BRAHE--KEPLER.
During the period of the intellectual and aesthetic revival, at the
beginning of the sixteenth century, the "spirit of the age" was
fostered by the invention of printing, by the downfall of the
Byzantine Empire, and the scattering of Greek fugitives, carrying the
treasures of literature through Western Europe, by the works of
Raphael and Michael Angelo, by the Reformation, and by the extension
of the known world through the voyages of Spaniards and Portuguese.
During that period there came to the front the founder of accurate
observational astronomy. Tycho Brahe, a Dane, born in 1546 of noble
parents, was the most distinguished, diligent, and accurate observer
of the heavens since the days of Hipparchus, 1,700 years before.
Tycho was devoted entirely to his science from childhood, and the
opposition of his parents only stimulated him in his efforts to
overcome difficulties. He soon grasped the hopelessness of the old
deductive methods of reasoning, and decided that no theories ought to
be indulged in until preparations had been made by the accumulation of
accurate observations. We may claim for him the title of founder of
the inductive method.
For a complete life of this great man the reader is referred to
Dreyer's _Tycho Brahe_, Edinburgh, 1890, containing a complete
bibliography. The present notice must be limited to noting the work
done, and the qualities of character which enabled him to attain his
scientific aims, and which have been conspicuous in many of his
successors.
He studied in Germany, but King Frederick of Denmark, appreciating his
great talents, invited him to carry out his life's work in that
country. He granted to him the island of Hveen, gave him a pension,
and made him a canon of the Cathedral of Roskilde. On that island
Tycho Brahe built the splendid observatory which he called Uraniborg,
and, later, a second one for his assistants and students, called
Stjerneborg. These he fitted up with the most perfect instruments, and
never lost a chance of adding to his stock of careful observations.[1]
The account of all these instruments and observations, printed at his
own press on the island, was published by Tycho Brahe himself, and the
admirable and numerous engravings bear witness to the excellence of
design and the stability of his instruments.
His mechanical skill was very great, and in his workmanship he was
satisfied with nothing but the best. He recognised the importance of
rigidity in the instruments, and, whereas these had generally been
made of wood, he designed them in metal. His instruments included
armillae like those which had been used in Alexandria, and other
armillae designed by himself--sextants, mural quadrants, large
celestial globes and various instruments for special purposes. He
lived before the days of telescopes and accurate clocks. He invented
the method of sub-dividing the degrees on the arc of an instrument by
transversals somewhat in the way that Pedro Nunez had proposed.
He originated the true system of observation and reduction of
observations, recognising the fact that the best instrument in the
world is not perfect; and with each of his instruments he set to work
to find out the errors of graduation and the errors of mounting, the
necessary correction being applied to each observation.
When he wanted to point his instrument exactly to a star he was
confronted with precisely the same difficulty as is met in gunnery and
rifle-shooting. The sights and the object aimed at cannot be in focus
together, and a great deal depends on the form of sight. Tycho Brahe
invented, and applied to the pointers of his instruments, an
aperture-sight of variable area, like the iris diaphragm used now in
photography. This enabled him to get the best result with stars of
different brightness. The telescope not having been invented, he
could not use a telescopic-sight as we now do in gunnery. This not
only removes the difficulty of focussing, but makes the minimum
visible angle smaller. Helmholtz has defined the minimum angle
measurable with the naked eye as being one minute of arc. In view of
this it is simply marvellous that, when the positions of Tycho's
standard stars are compared with the best modern catalogues, his
probable error in right ascension is only +- 24", 1, and in declination
only +- 25", 9.
Clocks of a sort had been made, but Tycho Brahe found them so
unreliable that he seldom used them, and many of his position-measurements
were made by measuring the angular distances from known stars.
Taking into consideration the absence of either a telescope or a
clock, and reading his account of the labour he bestowed upon each
observation, we must all agree that Kepler, who inherited these
observations in MS., was justified, under the conditions then
existing, in declaring that there was no hope of anyone ever improving
upon them.
In the year 1572, on November 11th, Tycho discovered in Cassiopeia a
new star of great brilliance, and continued to observe it until the
end of January, 1573. So incredible to him was such an event that he
refused to believe his own eyes until he got others to confirm what he
saw. He made accurate observations of its distance from the nine
principal stars in Casseiopeia, and proved that it had no measurable
parallax. Later he employed the same method with the comets of 1577,
1580, 1582, 1585, 1590, 1593, and 1596, and proved that they too had
no measurable parallax and must be very distant.
The startling discovery that stars are not necessarily permanent, that
new stars may appear, and possibly that old ones may disappear, had
upon him exactly the same effect that a similar occurrence had upon
Hipparchus 1,700 years before. He felt it his duty to catalogue all
the principal stars, so that there should be no mistake in the
future. During the construction of his catalogue of 1,000 stars he
prepared and used accurate tables of refraction deduced from his own
observations. Thus he eliminated (so far as naked eye observations
required) the effect of atmospheric refraction which makes the
altitude of a star seem greater than it really is.
Tycho Brahe was able to correct the lunar theory by his observations.
Copernicus had introduced two epicycles on the lunar orbit in the hope
of obtaining a better accordance between theory and observation; and
he was not too ambitious, as his desire was to get the tables accurate
to ten minutes. Tycho Brahe found that the tables of Copernicus were
in error as much as two degrees. He re-discovered the inequality
called "variation" by observing the moon in all phases--a thing which
had not been attended to. [It is remarkable that in the nineteenth
century Sir George Airy established an altazimuth at Greenwich
Observatory with this special object, to get observations of the moon
in all phases.] He also discovered other lunar equalities, and wanted
to add another epicycle to the moon's orbit, but he feared that these
would soon become unmanageable if further observations showed more new
inequalities.
But, as it turned out, the most fruitful work of Tycho Brahe was on
the motions of the planets, and especially of the planet Mars, for it
was by an examination of these results that Kepler was led to the
discovery of his immortal laws.
After the death of King Frederick the observatories of Tycho Brahe
were not supported. The gigantic power and industry displayed by this
determined man were accompanied, as often happens, by an overbearing
manner, intolerant of obstacles. This led to friction, and eventually
the observatories were dismantled, and Tycho Brahe was received by the
Emperor Rudolph II., who placed a house in Prague at his disposal.
Here he worked for a few years, with Kepler as one of his assistants,
and he died in the year 1601.
It is an interesting fact that Tycho Brahe had a firm conviction that
mundane events could be predicted by astrology, and that this belief
was supported by his own predictions.
It has already been stated that Tycho Brahe maintained that
observation must precede theory. He did not accept the Copernican
theory that the earth moves, but for a working hypothesis he used a
modification of an old Egyptian theory, mathematically identical with
that of Copernicus, but not involving a stellar parallax. He says
(_De Mundi_, etc.) that
the Ptolemean system was too complicated, and the new one which that
great man Copernicus had proposed, following in the footsteps of
Aristarchus of Samos, though there was nothing in it contrary to
mathematical principles, was in opposition to those of physics, as
the heavy and sluggish earth is unfit to move, and the system is
even opposed to the authority of Scripture. The absence of annual
parallax further involves an incredible distance between the
outermost planet and the fixed stars.
We are bound to admit that in the circumstances of the case, so long
as there was no question of dynamical forces connecting the members of
the solar system, his reasoning, as we should expect from such a man,
is practical and sound. It is not surprising, then, that astronomers
generally did not readily accept the views of Copernicus, that Luther
(Luther's _Tischreden_, pp. 22, 60) derided him in his usual pithy
manner, that Melancthon (_Initia doctrinae physicae_) said that
Scripture, and also science, are against the earth's motion; and that
the men of science whose opinion was asked for by the cardinals (who
wished to know whether Galileo was right or wrong) looked upon
Copernicus as a weaver of fanciful theories.
Johann Kepler is the name of the man whose place, as is generally
agreed, would have been the most difficult to fill among all those who
have contributed to the advance of astronomical knowledge. He was born
at Wiel, in the Duchy of Wurtemberg, in 1571. He held an appointment
at Gratz, in Styria, and went to join Tycho Brahe in Prague, and to
assist in reducing his observations. These came into his possession
when Tycho Brahe died, the Emperor Rudolph entrusting to him the
preparation of new tables (called the Rudolphine tables) founded on
the new and accurate observations. He had the most profound respect
for the knowledge, skill, determination, and perseverance of the man
who had reaped such a harvest of most accurate data; and though Tycho
hardly recognised the transcendent genius of the man who was working
as his assistant, and although there were disagreements between them,
Kepler held to his post, sustained by the conviction that, with these
observations to test any theory, he would be in a position to settle
for ever the problem of the solar system.
[Illustration: PORTRAIT OF JOHANNES KEPLER. By F. Wanderer, from
Reitlinger's "Johannes Kepler" (original in Strassburg).]
It has seemed to many that Plato's demand for uniform circular motion
(linear or angular) was responsible for a loss to astronomy of good
work during fifteen hundred years, for a hundred ill-considered
speculative cosmogonies, for dissatisfaction, amounting to disgust,
with these _a priori_ guesses, and for the relegation of the
science to less intellectual races than Greeks and other Europeans.
Nobody seemed to dare to depart from this fetish of uniform angular
motion and circular orbits until the insight, boldness, and
independence of Johann Kepler opened up a new world of thought and of
intellectual delight.
While at work on the Rudolphine tables he used the old epicycles and
deferents and excentrics, but he could not make theory agree with
observation. His instincts told him that these apologists for uniform
motion were a fraud; and he proved it to himself by trying every
possible variation of the elements and finding them fail. The number
of hypotheses which he examined and rejected was almost incredible
(for example, that the planets turn round centres at a little distance
from the sun, that the epicycles have centres at a little distance
from the deferent, and so on). He says that, after using all these
devices to make theory agree with Tycho's observations, he still found
errors amounting to eight minutes of a degree. Then he said boldly
that it was impossible that so good an observer as Tycho could have
made a mistake of eight minutes, and added: "Out of these eight
minutes we will construct a new theory that will explain the motions
of all the planets." And he did it, with elliptic orbits having the
sun in a focus of each.[2]
It is often difficult to define the boundaries between fancies,
imagination, hypothesis, and sound theory. This extraordinary genius
was a master in all these modes of attacking a problem. His analogy
between the spaces occupied by the five regular solids and the
distances of the planets from the sun, which filled him with so much
delight, was a display of pure fancy. His demonstration of the three
fundamental laws of planetary motion was the most strict and complete
theory that had ever been attempted.
It has been often suggested that the revival by Copernicus of the
notion of a moving earth was a help to Kepler. No one who reads
Kepler's great book could hold such an opinion for a moment. In fact,
the excellence of Copernicus's book helped to prolong the life of the
epicyclical theories in opposition to Kepler's teaching.
All of the best theories were compared by him with observation. These
were the Ptolemaic, the Copernican, and the Tychonic. The two latter
placed all of the planetary orbits concentric with one another, the
sun being placed a little away from their common centre, and having no
apparent relation to them, and being actually outside the planes in
which they move. Kepler's first great discovery was that the planes
of all the orbits pass through the sun; his second was that the line
of apses of each planet passes through the sun; both were
contradictory to the Copernican theory.
He proceeds cautiously with his propositions until he arrives at his
great laws, and he concludes his book by comparing observations of
Mars, of all dates, with his theory.
His first law states that the planets describe ellipses with the sun
at a focus of each ellipse.
His second law (a far more difficult one to prove) states that a line
drawn from a planet to the sun sweeps over equal areas in equal
times. These two laws were published in his great work, _Astronomia
Nova, sen. Physica Coelestis tradita commentariis de Motibus Stelloe;
Martis_, Prague, 1609.
It took him nine years more[3] to discover his third law, that the
squares of the periodic times are proportional to the cubes of the
mean distances from the sun.
These three laws contain implicitly the law of universal
gravitation. They are simply an alternative way of expressing that law
in dealing with planets, not particles. Only, the power of the
greatest human intellect is so utterly feeble that the meaning of the
words in Kepler's three laws could not be understood until expounded
by the logic of Newton's dynamics.
The joy with which Kepler contemplated the final demonstration of
these laws, the evolution of which had occupied twenty years, can
hardly be imagined by us. He has given some idea of it in a passage
in his work on _Harmonics_, which is not now quoted, only lest
someone might say it was egotistical--a term which is simply grotesque
when applied to such a man with such a life's work accomplished.
The whole book, _Astronomia Nova_, is a pleasure to read; the
mass of observations that are used, and the ingenuity of the
propositions, contrast strongly with the loose and imperfectly
supported explanations of all his predecessors; and the indulgent
reader will excuse the devotion of a few lines to an example of the
ingenuity and beauty of his methods.
It may seem a hopeless task to find out the true paths of Mars and the
earth (at that time when their shape even was not known) from the
observations giving only the relative direction from night to
night. Now, Kepler had twenty years of observations of Mars to deal
with. This enabled him to use a new method, to find the earth's
orbit. Observe the date at any time when Mars is in opposition. The
earth's position E at that date gives the longitude of Mars M. His
period is 687 days. Now choose dates before and after the principal
date at intervals of 687 days and its multiples. Mars is in each case
in the same position. Now for any date when Mars is at M and the earth
at E3 the date of the year gives the angle E3SM. And the
observation of Tycho gives the direction of Mars compared with the
sun, SE3M. So all the angles of the triangle SEM in any of these
positions of E are known, and also the ratios of SE1, SE2, SE3,
SE4 to SM and to each other.
For the orbit of Mars observations were chosen at intervals of a year,
when the earth was always in the same place.
[Illustration]
But Kepler saw much farther than the geometrical facts. He realised
that the orbits are followed owing to a force directed to the sun; and
he guessed that this is the same force as the gravity that makes a
stone fall. He saw the difficulty of gravitation acting through the
void space. He compared universal gravitation to magnetism, and
speaks of the work of Gilbert of Colchester. (Gilbert's book, _De
Mundo Nostro Sublunari, Philosophia Nova_, Amstelodami, 1651,
containing similar views, was published forty-eight years after
Gilbert's death, and forty-two years after Kepler's book and
reference. His book _De Magnete_ was published in 1600.)
A few of Kepler's views on gravitation, extracted from the
Introduction to his _Astronomia Nova_, may now be mentioned:--
1. Every body at rest remains at rest if outside the attractive power
of other bodies.
2. Gravity is a property of masses mutually attracting in such manner
that the earth attracts a stone much more than a stone attracts the
earth.
3. Bodies are attracted to the earth's centre, not because it is the
centre of the universe, but because it is the centre of the attracting
particles of the earth.
4. If the earth be not round (but spheroidal?), then bodies at
different latitudes will not be attracted to its centre, but to
different points in the neighbourhood of that centre.
5. If the earth and moon were not retained in their orbits by vital
force (_aut alia aligua aequipollenti_), the earth and moon would come
together.
6. If the earth were to cease to attract its waters, the oceans would
all rise and flow to the moon.
7. He attributes the tides to lunar attraction. Kepler had been
appointed Imperial Astronomer with a handsome salary (on paper), a
fraction of which was doled out to him very irregularly. He was led to
miserable makeshifts to earn enough to keep his family from
starvation; and proceeded to Ratisbon in 1630 to represent his claims
to the Diet. He arrived worn out and debilitated; he failed in his
appeal, and died from fever, contracted under, and fed upon,
disappointment and exhaustion. Those were not the days when men could
adopt as a profession the "research of endowment."
Before taking leave of Kepler, who was by no means a man of one idea,
it ought to be here recorded that he was the first to suggest that a
telescope made with both lenses convex (not a Galilean telescope) can
have cross wires in the focus, for use as a pointer to fix accurately
the positions of stars. An Englishman, Gascoigne, was the first to use
this in practice.
From the all too brief epitome here given of Kepler's greatest book,
it must be obvious that he had at that time some inkling of the
meaning of his laws--universal gravitation. From that moment the idea
of universal gravitation was in the air, and hints and guesses were
thrown out by many; and in time the law of gravitation would doubtless
have been discovered, though probably not by the work of one man, even
if Newton had not lived. But, if Kepler had not lived, who else could
have discovered his laws?
FOOTNOTES:
[1] When the writer visited M. D'Arrest, the astronomer, at
Copenhagen, in 1872, he was presented by D'Arrest with one of several
bricks collected from the ruins of Uraniborg. This was one of his most
cherished possessions until, on returning home after a prolonged
absence on astronomical work, he found that his treasure had been
tidied away from his study.
[2] An ellipse is one of the plane, sections of a cone. It is an oval
curve, which may be drawn by fixing two pins in a sheet of paper at S
and H, fastening a string, SPH, to the two pins, and stretching it
with a pencil point at P, and moving the pencil point, while the
string is kept taut, to trace the oval ellipse, APB. S and H are the
_foci_. Kepler found the sun to be in one focus, say S. AB is the
_major axis_. DE is the _minor axis_. C is the _centre_. The direction
of AB is the _line of apses_. The ratio of CS to CA is the
_excentricity_. The position of the planet at A is the _perihelion_
(nearest to the sun). The position of the planet at B is the
_aphelion_ (farthest from the sun). The angle ASP is the _anomaly_
when the planet is at P. CA or a line drawn from S to D is the _mean
distance_ of the planet from the sun.
[Illustration]
[3] The ruled logarithmic paper we now use was not then to be had by
going into a stationer's shop. Else he would have accomplished this in
five minutes.
6. GALILEO AND THE TELESCOPE--NOTIONS OF GRAVITY BY HORROCKS, ETC.
It is now necessary to leave the subject of dynamical astronomy for a
short time in order to give some account of work in a different
direction originated by a contemporary of Kepler's, his senior in fact
by seven years. Galileo Galilei was born at Pisa in 1564. The most
scientific part of his work dealt with terrestrial dynamics; but one
of those fortunate chances which happen only to really great men put
him in the way of originating a new branch of astronomy.
The laws of motion had not been correctly defined. The only man of
Galileo's time who seems to have worked successfully in the same
direction as himself was that Admirable Crichton of the Italians,
Leonardo da Vinci. Galileo cleared the ground. It had always been
noticed that things tend to come to rest; a ball rolled on the ground,
a boat moved on the water, a shot fired in the air. Galileo realised
that in all of these cases a resisting force acts to stop the motion,
and he was the first to arrive at the not very obvious law that the
motion of a body will never stop, nor vary its speed, nor change its
direction, except by the action of some force.
It is not very obvious that a light body and a heavy one fall at the
same speed (except for the resistance of the air). Galileo proved this
on paper, but to convince the world he had to experiment from the
leaning tower of Pisa.
At an early age he discovered the principle of isochronism of the
pendulum, which, in the hands of Huyghens in the middle of the
seventeenth century, led to the invention of the pendulum clock,
perhaps the most valuable astronomical instrument ever produced.
These and other discoveries in dynamics may seem very obvious now; but
it is often the most every-day matters which have been found to elude
the inquiries of ordinary minds, and it required a high order of
intellect to unravel the truth and discard the stupid maxims scattered
through the works of Aristotle and accepted on his authority. A blind
worship of scientific authorities has often delayed the progress of
human knowledge, just as too much "instruction" of a youth often ruins
his "education." Grant, in his history of Physical Astronomy, has well
said that "the sagacity and skill which Galileo displays in resolving
the phenomena of motion into their constituent elements, and hence
deriving the original principles involved in them, will ever assure to
him a distinguished place among those who have extended the domains of
science."
But it was work of a different kind that established Galileo's popular
reputation. In 1609 Galileo heard that a Dutch spectacle-maker had
combined a pair of lenses so as to magnify distant objects. Working on
this hint, he solved the same problem, first on paper and then in
practice. So he came to make one of the first telescopes ever used in
astronomy. No sooner had he turned it on the heavenly bodies than he
was rewarded by such a shower of startling discoveries as forthwith
made his name the best known in Europe. He found curious irregular
black spots on the sun, revolving round it in twenty-seven days; hills
and valleys on the moon; the planets showing discs of sensible size,
not points like the fixed stars; Venus showing phases according to her
position in relation to the sun; Jupiter accompanied by four moons;
Saturn with appendages that he could not explain, but unlike the other
planets; the Milky Way composed of a multitude of separate stars.
His fame flew over Europe like magic, and his discoveries were much
discussed--and there were many who refused to believe. Cosmo de Medici
induced him to migrate to Florence to carry on his observations. He
was received by Paul V., the Pope, at Rome, to whom he explained his
discoveries.
He thought that these discoveries proved the truth of the Copernican
theory of the Earth's motion; and he urged this view on friends and
foes alike. Although in frequent correspondence with Kepler, he never
alluded to the New Astronomy, and wrote to him extolling the virtue of
epicycles. He loved to argue, never shirked an encounter with any
number of disputants, and laughed as he broke down their arguments.
Through some strange course of events, not easy to follow, the
Copernican theory, whose birth was welcomed by the Church, had now
been taken up by certain anti-clerical agitators, and was opposed by
the cardinals as well as by the dignitaries of the Reformed
Church. Galileo--a good Catholic--got mixed up in these discussions,
although on excellent terms with the Pope and his entourage. At last
it came about that Galileo was summoned to appear at Rome, where he
was charged with holding and teaching heretical opinions about the
movement of the earth; and he then solemnly abjured these
opinions. There has been much exaggeration and misstatement about his
trial and punishment, and for a long time there was a great deal of
bitterness shown on both sides. But the general verdict of the present
day seems to be that, although Galileo himself was treated with
consideration, the hostility of the Church to the views of Copernicus
placed it in opposition also to the true Keplerian system, and this
led to unprofitable controversies. From the time of Galileo onwards,
for some time, opponents of religion included the theory of the
Earth's motion in their disputations, not so much for the love, or
knowledge, of astronomy, as for the pleasure of putting the Church in
the wrong. This created a great deal of bitterness and intolerance on
both sides. Among the sufferers was Giordano Bruno, a learned
speculative philosopher, who was condemned to be burnt at the stake.
Galileo died on Christmas Day, 1642--the day of Newton's birth. The
further consideration of the grand field of discovery opened out by
Galileo with his telescopes must be now postponed, to avoid
discontinuity in the history of the intellectual development of this
period, which lay in the direction of dynamical, or physical,
astronomy.
Until the time of Kepler no one seems to have conceived the idea of
universal physical forces controlling terrestrial phenomena, and
equally applicable to the heavenly bodies. The grand discovery by
Kepler of the true relationship of the Sun to the Planets, and the
telescopic discoveries of Galileo and of those who followed him,
spread a spirit of inquiry and philosophic thought throughout Europe,
and once more did astronomy rise in estimation; and the irresistible
logic of its mathematical process of reasoning soon placed it in the
position it has ever since occupied as the foremost of the exact
sciences.
The practical application of this process of reasoning was enormously
facilitated by the invention of logarithms by Napier. He was born at
Merchistoun, near Edinburgh, in 1550, and died in 1617. By this system
the tedious arithmetical operations necessary in astronomical
calculations, especially those dealing with the trigonometrical
functions of angles, were so much simplified that Laplace declared
that by this invention the life-work of an astronomer was doubled.
Jeremiah Horrocks (born 1619, died 1641) was an ardent admirer of
Tycho Brahe and Kepler, and was able to improve the Rudolphine tables
so much that he foretold a transit of Venus, in 1639, which these
tables failed to indicate, and was the only observer of it. His life
was short, but he accomplished a great deal, and rightly ascribed the
lunar inequality called _evection_ to variations in the value of
the eccentricity and in the direction of the line of apses, at the
same time correctly assigning _the disturbing force of the Sun_
as the cause. He discovered the errors in Jupiter's calculated place,
due to what we now know as the long inequality of Jupiter and Saturn,
and measured with considerable accuracy the acceleration at that date
of Jupiter's mean motion, and indicated the retardation of Saturn's
mean motion.
Horrocks' investigations, so far as they could be collected, were
published posthumously in 1672, and seldom, if ever, has a man who
lived only twenty-two years originated so much scientific knowledge.
At this period British science received a lasting impetus by the wise
initiation of a much-abused man, Charles II., who founded the Royal
Society of London, and also the Royal Observatory of Greeenwich, where
he established Flamsteed as first Astronomer Royal, especially for
lunar and stellar observations likely to be useful for navigation. At
the same time the French Academy and the Paris Observatory were
founded. All this within fourteen years, 1662-1675.
Meanwhile gravitation in general terms was being discussed by Hooke,
Wren, Halley, and many others. All of these men felt a repugnance to
accept the idea of a force acting across the empty void of space.
Descartes (1596-1650) proposed an ethereal medium whirling round the
sun with the planets, and having local whirls revolving with the
satellites. As Delambre and Grant have said, this fiction only
retarded the progress of pure science. It had no sort of relation to
the more modern, but equally misleading, "nebular hypothesis." While
many were talking and guessing, a giant mind was needed at this stage
to make things clear.
7. SIR ISAAC NEWTON--LAW OF UNIVERSAL GRAVITATION.
We now reach the period which is the culminating point of interest in
the history of dynamical astronomy. Isaac Newton was born in
1642. Pemberton states that Newton, having quitted Cambridge to avoid
the plague, was residing at Wolsthorpe, in Lincolnshire, where he had
been born; that he was sitting one day in the garden, reflecting upon
the force which prevents a planet from flying off at a tangent and
which draws it to the sun, and upon the force which draws the moon to
the earth; and that he saw in the case of the planets that the sun's
force must clearly be unequal at different distances, for the pull out
of the tangential line in a minute is less for Jupiter than for
Mars. He then saw that the pull of the earth on the moon would be less
than for a nearer object. It is said that while thus meditating he saw
an apple fall from a tree to the ground, and that this fact suggested
the questions: Is the force that pulled that apple from the tree the
same as the force which draws the moon to the earth? Does the
attraction for both of them follow the same law as to distance as is
given by the planetary motions round the sun? It has been stated that
in this way the first conception of universal gravitation arose.[1]
Quite the most important event in the whole history of physical
astronomy was the publication, in 1687, of Newton's _Principia
(Philosophiae Naturalis Principia Mathematica)_. In this great work
Newton started from the beginning of things, the laws of motion, and
carried his argument, step by step, into every branch of physical
astronomy; giving the physical meaning of Kepler's three laws, and
explaining, or indicating the explanation of, all the known heavenly
motions and their irregularities; showing that all of these were
included in his simple statement about the law of universal
gravitation; and proceeding to deduce from that law new irregularities
in the motions of the moon which had never been noticed, and to
discover the oblate figure of the earth and the cause of the
tides. These investigations occupied the best part of his life; but he
wrote the whole of his great book in fifteen months.
Having developed and enunciated the true laws of motion, he was able
to show that Kepler's second law (that equal areas are described by
the line from the planet to the sun in equal times) was only another
way of saying that the centripetal force on a planet is always
directed to the sun. Also that Kepler's first law (elliptic orbits
with the sun in one focus) was only another way of saying that the
force urging a planet to the sun varies inversely as the square of the
distance. Also (if these two be granted) it follows that Kepler's
third law is only another way of saying that the sun's force on
different planets (besides depending as above on distance) is
proportional to their masses.
Having further proved the, for that day, wonderful proposition that,
with the law of inverse squares, the attraction by the separate
particles of a sphere of uniform density (or one composed of
concentric spherical shells, each of uniform density) acts as if the
whole mass were collected at the centre, he was able to express the
meaning of Kepler's laws in propositions which have been summarised as
follows:--
The law of universal gravitation.--_Every particle of matter in the
universe attracts every other particle with a force varying inversely
as the square of the distance between them, and directly as the
product of the masses of the two particles_.[2]
But Newton did not commit himself to the law until he had answered
that question about the apple; and the above proposition now enabled
him to deal with the Moon and the apple. Gravity makes a stone fall
16.1 feet in a second. The moon is 60 times farther from the earth's
centre than the stone, so it ought to be drawn out of a straight
course through 16.1 feet in a minute. Newton found the distance
through which she is actually drawn as a fraction of the earth's
diameter. But when he first examined this matter he proceeded to use
a wrong diameter for the earth, and he found a serious discrepancy.
This, for a time, seemed to condemn his theory, and regretfully he
laid that part of his work aside. Fortunately, before Newton wrote the
_Principia_ the French astronomer Picard made a new and correct
measure of an arc of the meridian, from which he obtained an accurate
value of the earth's diameter. Newton applied this value, and found,
to his great joy, that when the distance of the moon is 60 times the
radius of the earth she is attracted out of the straight course 16.1
feet per minute, and that the force acting on a stone or an apple
follows the same law as the force acting upon the heavenly bodies.[3]
The universality claimed for the law--if not by Newton, at least by
his commentators--was bold, and warranted only by the large number of
cases in which Newton had found it to apply. Its universality has been
under test ever since, and so far it has stood the test. There has
often been a suspicion of a doubt, when some inequality of motion in
the heavenly bodies has, for a time, foiled the astronomers in their
attempts to explain it. But improved mathematical methods have always
succeeded in the end, and so the seeming doubt has been converted into
a surer conviction of the universality of the law.
Having once established the law, Newton proceeded to trace some of its
consequences. He saw that the figure of the earth depends partly on
the mutual gravitation of its parts, and partly on the centrifugal
tendency due to the earth's rotation, and that these should cause a
flattening of the poles. He invented a mathematical method which he
used for computing the ratio of the polar to the equatorial diameter.
He then noticed that the consequent bulging of matter at the equator
would be attracted by the moon unequally, the nearest parts being most
attracted; and so the moon would tend to tilt the earth when in some
parts of her orbit; and the sun would do this to a less extent,
because of its great distance. Then he proved that the effect ought to
be a rotation of the earth's axis over a conical surface in space,
exactly as the axis of a top describes a cone, if the top has a sharp
point, and is set spinning and displaced from the vertical. He
actually calculated the amount; and so he explained the cause of the
precession of the equinoxes discovered by Hipparchus about 150 B.C.
One of his grandest discoveries was a method of weighing the heavenly
bodies by their action on each other. By means of this principle he
was able to compare the mass of the sun with the masses of those
planets that have moons, and also to compare the mass of our moon with
the mass of the earth.
Thus Newton, after having established his great principle, devoted his
splendid intellect to the calculation of its consequences. He proved
that if a body be projected with any velocity in free space, subject
only to a central force, varying inversely as the square of the
distance, the body must revolve in a curve which may be any one of the
sections of a cone--a circle, ellipse, parabola, or hyperbola; and he
found that those comets of which he had observations move in parabolae
round the Sun, and are thus subject to the universal law.
Newton realised that, while planets and satellites are chiefly
controlled by the central body about which they revolve, the new law
must involve irregularities, due to their mutual action--such, in
fact, as Horrocks had indicated. He determined to put this to a test
in the case of the moon, and to calculate the sun's effect, from its
mass compared with that of the earth, and from its distance. He proved
that the average effect upon the plane of the orbit would be to cause
the line in which it cuts the plane of the ecliptic (i.e., the line of
nodes) to revolve in the ecliptic once in about nineteen years. This
had been a known fact from the earliest ages. He also concluded that
the line of apses would revolve in the plane of the lunar orbit also
in about nineteen years; but the observed period is only ten
years. For a long time this was the one weak point in the Newtonian
theory. It was not till 1747 that Clairaut reconciled this with the
theory, and showed why Newton's calculation was not exact.
Newton proceeded to explain the other inequalities recognised by Tycho
Brahe and older observers, and to calculate their maximum amounts as
indicated by his theory. He further discovered from his calculations
two new inequalities, one of the apogee, the other of the nodes, and
assigned the maximum value. Grant has shown the values of some of
these as given by observation in the tables of Meyer and more modern
tables, and has compared them with the values assigned by Newton from
his theory; and the comparison is very remarkable.
Newton. Modern Tables.
deg. ' " deg. ' "
Mean monthly motion of Apses 1.31.28 3.4.0
Mean annual motion of nodes 19.18.1,23 19.21.22,50
Mean value of "variation" 36.10 35.47
Annual equation 11.51 11.14
Inequality of mean motion of apogee 19.43 22.17
Inequality of mean motion of nodes 9.24 9.0
The only serious discrepancy is the first, which has been already
mentioned. Considering that some of these perturbations had never been
discovered, that the cause of none of them had ever been known, and
that he exhibited his results, if he did not also make the
discoveries, by the synthetic methods of geometry, it is simply
marvellous that he reached to such a degree of accuracy. He invented
the infinitesimal calculus which is more suited for such calculations,
but had he expressed his results in that language he would have been
unintelligible to many.
Newton's method of calculating the precession of the equinoxes,
already referred to, is as beautiful as anything in the _Principia_.
He had already proved the regression of the nodes of a satellite
moving in an orbit inclined to the ecliptic. He now said that the
nodes of a ring of satellites revolving round the earth's equator
would consequently all regress. And if joined into a solid ring its
node would regress; and it would do so, only more slowly, if
encumbered by the spherical part of the earth's mass. Therefore the
axis of the equatorial belt of the earth must revolve round the pole
of the ecliptic. Then he set to work and found the amount due to the
moon and that due to the sun, and so he solved the mystery of 2,000
years.
When Newton applied his law of gravitation to an explanation of the
tides he started a new field for the application of mathematics to
physical problems; and there can be little doubt that, if he could
have been furnished with complete tidal observations from different
parts of the world, his extraordinary powers of analysis would have
enabled him to reach a satisfactory theory. He certainly opened up
many mines full of intellectual gems; and his successors have never
ceased in their explorations. This has led to improved mathematical
methods, which, combined with the greater accuracy of observation,
have rendered physical astronomy of to-day the most exact of the
sciences.
Laplace only expressed the universal opinion of posterity when he said
that to the _Principia_ is assured "a pre-eminence above all the
other productions of the human intellect."
The name of Flamsteed, First Astronomer Royal, must here be mentioned
as having supplied Newton with the accurate data required for
completing the theory.
The name of Edmund Halley, Second Astronomer Royal, must ever be held
in repute, not only for his own discoveries, but for the part he
played in urging Newton to commit to writing, and present to the Royal
Society, the results of his investigations. But for his friendly
insistence it is possible that the _Principia_ would never have
been written; and but for his generosity in supplying the means the
Royal Society could not have published the book.
[Illustration: DEATH MASK OF SIR ISAAC NEWTON.
Photographed specially for this work from the original, by kind
permission of the Royal Society, London.]
Sir Isaac Newton died in 1727, at the age of eighty-five. His body
lay in state in the Jerusalem Chamber, and was buried in Westminster
Abbey.
FOOTNOTES:
[1] The writer inherited from his father (Professor J. D. Forbes) a
small box containing a bit of wood and a slip of paper, which had been
presented to him by Sir David Brewster. On the paper Sir David had
written these words: "If there be any truth in the story that Newton
was led to the theory of gravitation by the fall of an apple, this bit
of wood is probably a piece of the apple tree from which Newton saw
the apple fall. When I was on a pilgrimage to the house in which
Newton was born, I cut it off an ancient apple tree growing in his
garden." When lecturing in Glasgow, about 1875, the writer showed it
to his audience. The next morning, when removing his property from the
lecture table, he found that his precious relic had been stolen. It
would be interesting to know who has got it now!
[2] It must be noted that these words, in which the laws of
gravitation are always summarised in histories and text-books, do not
appear in the _Principia_; but, though they must have been composed by
some early commentator, it does not appear that their origin has been
traced. Nor does it appear that Newton ever extended the law beyond
the Solar System, and probably his caution would have led him to avoid
any statement of the kind until it should be proved.
With this exception the above statement of the law of universal
gravitation contains nothing that is not to be found in the
_Principia_; and the nearest approach to that statement occurs in the
Seventh Proposition of Book III.:--
Prop.: That gravitation occurs in all bodies, and that it is
proportional to the quantity of matter in each.
Cor. I.: The total attraction of gravitation on a planet arises, and
is composed, out of the attraction on the separate parts.
Cor. II.: The attraction on separate equal particles of a body is
reciprocally as the square of the distance from the particles.
[3] It is said that, when working out this final result, the
probability of its confirming that part of his theory which he had
reluctantly abandoned years before excited him so keenly that he was
forced to hand over his calculations to a friend, to be completed by
him.
8. NEWTON'S SUCCESSORS--HALLEY, EULER, LAGRANGE, LAPLACE, ETC.
Edmund Halley succeeded Flamsteed as Second Astronomer Royal in
1721. Although he did not contribute directly to the mathematical
proofs of Newton's theory, yet his name is closely associated with
some of its greatest successes.
He was the first to detect the acceleration of the moon's mean
motion. Hipparchus, having compared his own observations with those of
more ancient astronomers, supplied an accurate value of the moon's
mean motion in his time. Halley similarly deduced a value for modern
times, and found it sensibly greater. He announced this in 1693, but
it was not until 1749 that Dunthorne used modern lunar tables to
compute a lunar eclipse observed in Babylon 721 B.C., another at
Alexandria 201 B.C., a solar eclipse observed by Theon 360 A.D., and
two later ones up to the tenth century. He found that to explain
these eclipses Halley's suggestion must be adopted, the acceleration
being 10" in one century. In 1757 Lalande again fixed it at 10."
The Paris Academy, in 1770, offered their prize for an investigation
to see if this could be explained by the theory of gravitation. Euler
won the prize, but failed to explain the effect, and said: "It appears
to be established by indisputable evidence that the secular inequality
of the moon's mean motion cannot be produced by the forces of
gravitation."
The same subject was again proposed for a prize which was shared by
Lagrange [1] and Euler, neither finding a solution, while the latter
asserted the existence of a resisting medium in space.
Again, in 1774, the Academy submitted the same subject, a third time,
for the prize; and again Lagrange failed to detect a cause in
gravitation.
Laplace [2] now took the matter in hand. He tried the effect of a
non-instantaneous action of gravity, to no purpose. But in 1787 he
gave the true explanation. The principal effect of the sun on the
moon's orbit is to diminish the earth's influence, thus lengthening
the period to a new value generally taken as constant. But Laplace's
calculations showed the new value to depend upon the excentricity of
the earth's orbit, which, according; to theory, has a periodical
variation of enormous period, and has been continually diminishing for
thousands of years. Thus the solar influence has been diminishing, and
the moon's mean motion increased. Laplace computed the amount at 10"
in one century, agreeing with observation. (Later on Adams showed that
Laplace's calculation was wrong, and that the value he found was too
large; so, part of the acceleration is now attributed by some
astronomers to a lengthening of the day by tidal friction.)
Another contribution by Halley to the verification of Newton's law was
made when he went to St. Helena to catalogue the southern stars. He
measured the change in length of the second's pendulum in different
latitudes due to the changes in gravity foretold by Newton.
Furthermore, he discovered the long inequality of Jupiter and Saturn,
whose period is 929 years. For an investigation of this also the
Academy of Sciences offered their prize. This led Euler to write a
valuable essay disclosing a new method of computing perturbations,
called the instantaneous ellipse with variable elements. The method
was much developed by Lagrange.
But again it was Laplace who solved the problem of the inequalities of
Jupiter and Saturn by the theory of gravitation, reducing the errors
of the tables from 20' down to 12", thus abolishing the use of
empirical corrections to the planetary tables, and providing another
glorious triumph for the law of gravitation. As Laplace justly said:
"These inequalities appeared formerly to be inexplicable by the law of
gravitation--they now form one of its most striking proofs."
Let us take one more discovery of Halley, furnishing directly a new
triumph for the theory. He noticed that Newton ascribed parabolic
orbits to the comets which he studied, so that they come from
infinity, sweep round the sun, and go off to infinity for ever, after
having been visible a few weeks or months. He collected all the
reliable observations of comets he could find, to the number of
twenty-four, and computed their parabolic orbits by the rules laid
down by Newton. His object was to find out if any of them really
travelled in elongated ellipses, practically undistinguishable, in the
visible part of their paths, from parabolae, in which case they would
be seen more than once. He found two old comets whose orbits, in shape
and position, resembled the orbit of a comet observed by himself in
1682. Apian observed one in 1531; Kepler the other in 1607. The
intervals between these appearances is seventy-five or seventy-six
years. He then examined and found old records of similar appearance in
1456, 1380, and 1305. It is true, he noticed, that the intervals
varied by a year and a-half, and the inclination of the orbit to the
ecliptic diminished with successive apparitions. But he knew from
previous calculations that this might easily be due to planetary
perturbations. Finally, he arrived at the conclusion that all of these
comets were identical, travelling in an ellipse so elongated that the
part where the comet was seen seemed to be part of a parabolic
orbit. He then predicted its return at the end of 1758 or beginning of
1759, when he should be dead; but, as he said, "if it should return,
according to our prediction, about the year 1758, impartial posterity
will not refuse to acknowledge that this was first discovered by an
Englishman."[3] [_Synopsis Astronomiae Cometicae_, 1749.]
Once again Halley's suggestion became an inspiration for the
mathematical astronomer. Clairaut, assisted by Lalande, found that
Saturn would <DW44> the comet 100 days, Jupiter 518 days, and
predicted its return to perihelion on April 13th, 1759. In his
communication to the French Academy, he said that a comet travelling
into such distant regions might be exposed to the influence of forces
totally unknown, and "even of some planet too far removed from the sun
to be ever perceived."
The excitement of astronomers towards the end of 1758 became intense;
and the honour of first catching sight of the traveller fell to an
amateur in Saxony, George Palitsch, on Christmas Day, 1758. It reached
perihelion on March 13th, 1759.
This fact was a startling confirmation of the Newtonian theory,
because it was a new kind of calculation of perturbations, and also it
added a new member to the solar system, and gave a prospect of adding
many more.
When Halley's comet reappeared in 1835, Pontecoulant's computations
for the date of perihelion passage were very exact, and afterwards he
showed that, with more exact values of the masses of Jupiter and
Saturn, his prediction was correct within two days, after an invisible
voyage of seventy-five years!
Hind afterwards searched out many old appearances of this comet, going
back to 11 B.C., and most of these have been identified as being
really Halley's comet by the calculations of Cowell and Cromellin[4]
(of Greenwich Observatory), who have also predicted its next
perihelion passage for April 8th to 16th, 1910, and have traced back
its history still farther, to 240 B.C.
Already, in November, 1907, the Astronomer Royal was trying to catch
it by the aid of photography.
FOOTNOTES:
[1] Born 1736; died 1813.
[2] Born 1749; died 1827.
[3] This sentence does not appear in the original memoir communicated
to the Royal Society, but was first published in a posthumous reprint.
[4] _R. A. S. Monthly Notices_, 1907-8.
9. DISCOVERY OF NEW PLANETS--HERSCHEL, PIAZZI, ADAMS, AND LE VERRIER.
It would be very interesting, but quite impossible in these pages, to
discuss all the exquisite researches of the mathematical astronomers,
and to inspire a reverence for the names connected with these
researches, which for two hundred years have been establishing the
universality of Newton's law. The lunar and planetary theories, the
beautiful theory of Jupiter's satellites, the figure of the earth, and
the tides, were mathematically treated by Maclaurin, D'Alembert,
Legendre, Clairaut, Euler, Lagrange, Laplace, Walmsley, Bailly,
Lalande, Delambre, Mayer, Hansen, Burchardt, Binet, Damoiseau, Plana,
Poisson, Gauss, Bessel, Bouvard, Airy, Ivory, Delaunay, Le Verrier,
Adams, and others of later date.
By passing over these important developments it is possible to trace
some of the steps in the crowning triumph of the Newtonian theory, by
which the planet Neptune was added to the known members of the solar
system by the independent researches of Professor J.C. Adams and of
M. Le Verrier, in 1846.
It will be best to introduce this subject by relating how the
eighteenth century increased the number of known planets, which was
then only six, including the earth.
On March 13th, 1781, Sir William Herschel was, as usual, engaged on
examining some small stars, and, noticing that one of them appeared to
be larger than the fixed stars, suspected that it might be a comet.
To test this he increased his magnifying power from 227 to 460 and
932, finding that, unlike the fixed stars near it, its definition was
impaired and its size increased. This convinced him that the object
was a comet, and he was not surprised to find on succeeding nights
that the position was changed, the motion being in the ecliptic. He
gave the observations of five weeks to the Royal Society without a
suspicion that the object was a new planet.
For a long time people could not compute a satisfactory orbit for the
supposed comet, because it seemed to be near the perihelion, and no
comet had ever been observed with a perihelion distance from the sun
greater than four times the earth's distance. Lexell was the first to
suspect that this was a new planet eighteen times as far from the sun
as the earth is. In January, 1783, Laplace published the elliptic
elements. The discoverer of a planet has a right to name it, so
Herschel called it Georgium Sidus, after the king. But Lalande urged
the adoption of the name Herschel. Bode suggested Uranus, and this
was adopted. The new planet was found to rank in size next to Jupiter
and Saturn, being 4.3 times the diameter of the earth.
In 1787 Herschel discovered two satellites, both revolving in nearly
the same plane, inclined 80 deg. to the ecliptic, and the motion of both
was retrograde.
In 1772, before Herschel's discovery, Bode[1] had discovered a curious
arbitrary law of planetary distances. Opposite each planet's name
write the figure 4; and, in succession, add the numbers 0, 3, 6, 12,
24, 48, 96, etc., to the 4, always doubling the last numbers. You
then get the planetary distances.
Mercury, dist.-- 4 4 + 0 = 4
Venus " 7 4 + 3 = 7
Earth " 10 4 + 6 = 10
Mars " 15 4 + 12 = 16
-- 4 + 24 = 28
Jupiter dist. 52 4 + 48 = 52
Saturn " 95 4 + 96 = 100
(Uranus) " 192 4 + 192 = 196
-- 4 + 384 = 388
All the five planets, and the earth, fitted this rule, except that
there was a blank between Mars and Jupiter. When Uranus was
discovered, also fitting the rule, the conclusion was irresistible
that there is probably a planet between Mars and Jupiter. An
association of twenty-four astronomers was now formed in Germany to
search for the planet. Almost immediately afterwards the planet was
discovered, not by any member of the association, but by Piazzi, when
engaged upon his great catalogue of stars. On January 1st, 1801, he
observed a star which had changed its place the next night. Its motion
was retrograde till January 11th, direct after the 13th. Piazzi fell
ill before he had enough observations for computing the orbit with
certainty, and the planet disappeared in the sun's rays. Gauss
published an approximate ephemeris of probable positions when the
planet should emerge from the sun's light. There was an exciting hunt,
and on December 31st (the day before its birthday) De Zach captured
the truant, and Piazzi christened it Ceres.
The mean distance from the sun was found to be 2.767, agreeing with
the 2.8 given by Bode's law. Its orbit was found to be inclined over
10 deg. to the ecliptic, and its diameter was only 161 miles.
On March 28th, 1802, Olbers discovered a new seventh magnitude star,
which turned out to be a planet resembling Ceres. It was called
Pallas. Gauss found its orbit to be inclined 35 deg. to the ecliptic, and
to cut the orbit of Ceres; whence Olbers considered that these might
be fragments of a broken-up planet. He then commenced a search for
other fragments. In 1804 Harding discovered Juno, and in 1807 Olbers
found Vesta. The next one was not discovered until 1845, from which
date asteroids, or minor planets (as these small planets are called),
have been found almost every year. They now number about 700.
It is impossible to give any idea of the interest with which the first
additions since prehistoric times to the planetary system were
received. All of those who showered congratulations upon the
discoverers regarded these discoveries in the light of rewards for
patient and continuous labours, the very highest rewards that could be
desired. And yet there remained still the most brilliant triumph of
all, the addition of another planet like Uranus, before it had ever
been seen, when the analysis of Adams and Le Verrier gave a final
proof of the powers of Newton's great law to explain any planetary
irregularity.
After Sir William Herschel discovered Uranus, in 1781, it was found
that astronomers had observed it on many previous occasions, mistaking
it for a fixed star of the sixth or seventh magnitude. Altogether,
nineteen observations of Uranus's position, from the time of
Flamsteed, in 1690, had been recorded.
In 1790 Delambre, using all these observations, prepared tables for
computing its position. These worked well enough for a time, but at
last the differences between the calculated and observed longitudes of
the planet became serious. In 1821 Bouvard undertook a revision of the
tables, but found it impossible to reconcile all the observations of
130 years (the period of revolution of Uranus is eighty-four years).
So he deliberately rejected the old ones, expressing the opinion that
the discrepancies might depend upon "some foreign and unperceived
cause which may have been acting upon the planet." In a few years the
errors even of these tables became intolerable. In 1835 the error of
longitude was 30"; in 1838, 50"; in 1841, 70"; and, by comparing the
errors derived from observations made before and after opposition, a
serious error of the distance (radius vector) became apparent.
In 1843 John Couch Adams came out Senior Wrangler at Cambridge, and
was free to undertake the research which as an undergraduate he had
set himself--to see whether the disturbances of Uranus could be
explained by assuming a certain orbit, and position in that orbit, of
a hypothetical planet even more distant than Uranus. Such an
explanation had been suggested, but until 1843 no one had the boldness
to attack the problem. Bessel had intended to try, but a fatal
illness overtook him.
Adams first recalculated all known causes of disturbance, using the
latest determinations of the planetary masses. Still the errors were
nearly as great as ever. He could now, however, use these errors as
being actually due to the perturbations produced by the unknown
planet.
In 1844, assuming a circular orbit, and a mean distance agreeing with
Bode's law, he obtained a first approximation to the position of the
supposed planet. He then asked Professor Challis, of Cambridge, to
procure the latest observations of Uranus from Greenwich, which Airy
immediately supplied. Then the whole work was recalculated from the
beginning, with more exactness, and assuming a smaller mean distance.
In September, 1845, he handed to Challis the elements of the
hypothetical planet, its mass, and its apparent position for September
30th, 1845. On September 22nd Challis wrote to Airy explaining the
matter, and declaring his belief in Adams's capabilities. When Adams
called on him Airy was away from home, but at the end of October,
1845, he called again, and left a paper with full particulars of his
results, which had, for the most part, reduced the discrepancies to
about 1". As a matter of fact, it has since been found that the
heliocentric place of the new planet then given was correct within
about 2 deg.
Airy wrote expressing his interest, and asked for particulars about
the radius vector. Adams did not then reply, as the answer to this
question could be seen to be satisfactory by looking at the data
already supplied. He was a most unassuming man, and would not push
himself forward. He may have felt, after all the work he had done,
that Airy's very natural inquiry showed no proportionate desire to
search for the planet. Anyway, the matter lay in embryo for nine
months.
Meanwhile, one of the ablest French astronomers, Le Verrier,
experienced in computing perturbations, was independently at work,
knowing nothing about Adams. He applied to his calculations every
possible refinement, and, considering the novelty of the problem, his
calculation was one of the most brilliant in the records of
astronomy. In criticism it has been said that these were exhibitions
of skill rather than helps to a solution of the particular problem,
and that, in claiming to find the elements of the orbit within certain
limits, he was claiming what was, under the circumstances, impossible,
as the result proved.
In June, 1846, Le Verrier announced, in the _Comptes Rendus de
l'Academie des Sciences_, that the longitude of the disturbing planet,
for January 1st, 1847, was 325, and that the probable error did not
exceed 10 deg.
This result agreed so well with Adams's (within 1 deg.) that Airy urged
Challis to apply the splendid Northumberland equatoreal, at Cambridge,
to the search. Challis, however, had already prepared an exhaustive
plan of attack which must in time settle the point. His first work
was to observe, and make a catalogue, or chart, of all stars near
Adams's position.
On August 31st, 1846, Le Verrier published the concluding
part of his labours.
On September 18th, 1846, Le Verrier communicated his results to the
Astronomers at Berlin, and asked them to assist in searching for the
planet. By good luck Dr. Bremiker had just completed a star-chart of
the very part of the heavens including Le Verrier's position; thus
eliminating all of Challis's preliminary work. The letter was received
in Berlin on September 23rd; and the same evening Galle found the new
planet, of the eighth magnitude, the size of its disc agreeing with Le
Verrier's prediction, and the heliocentric longitude agreeing within
57'. By this time Challis had recorded, without reduction, the
observations of 3,150 stars, as a commencement for his search. On
reducing these, he found a star, observed on August 12th, which was
not in the same place on July 30th. This was the planet, and he had
also observed it on August 4th.
The feeling of wonder, admiration, and enthusiasm aroused by this
intellectual triumph was overwhelming. In the world of astronomy
reminders are met every day of the terrible limitations of human
reasoning powers; and every success that enables the mind's eye to see
a little more clearly the meaning of things has always been heartily
welcomed by those who have themselves been engaged in like
researches. But, since the publication of the _Principia_, in 1687,
there is probably no analytical success which has raised among
astronomers such a feeling of admiration and gratitude as when Adams
and Le Verrier showed the inequalities in Uranus's motion to mean that
an unknown planet was in a certain place in the heavens, where it was
found.
At the time there was an unpleasant display of international jealousy.
The British people thought that the earlier date of Adams's work, and
of the observation by Challis, entitled him to at least an equal share
of credit with Le Verrier. The French, on the other hand, who, on the
announcement of the discovery by Galle, glowed with pride in the new
proof of the great powers of their astronomer, Le Verrier, whose life
had a long record of successes in calculation, were incredulous on
being told that it had all been already done by a young man whom they
had never heard of.
These displays of jealousy have long since passed away, and there is
now universally an _entente cordiale_ that to each of these great men
belongs equally the merit of having so thoroughly calculated this
inverse problem of perturbations as to lead to the immediate discovery
of the unknown planet, since called Neptune.
It was soon found that the planet had been observed, and its position
recorded as a fixed star by Lalande, on May 8th and 10th, 1795.
Mr. Lassel, in the same year, 1846, with his two-feet reflector,
discovered a satellite, with retrograde motion, which gave the mass of
the planet about a twentieth of that of Jupiter.
FOOTNOTES:
[1] Bode's law, or something like it, had already been fore-shadowed
by Kepler and others, especially Titius (see _Monatliche
Correspondenz_, vol. vii., p. 72).
BOOK III. OBSERVATION
10. INSTRUMENTS OF PRECISION--STATE OF THE SOLAR SYSTEM.
Having now traced the progress of physical astronomy up to the time
when very striking proofs of the universality of the law of
gravitation convinced the most sceptical, it must still be borne in
mind that, while gravitation is certainly the principal force
governing the motions of the heavenly bodies, there may yet be a
resisting medium in space, and there may be electric and magnetic
forces to deal with. There may, further, be cases where the effects of
luminous radiative repulsion become apparent, and also Crookes'
vacuum-effects described as "radiant matter." Nor is it quite certain
that Laplace's proofs of the instantaneous propagation of gravity are
final.
And in the future, as in the past, Tycho Brahe's dictum must be
maintained, that all theory shall be preceded by accurate
observations. It is the pride of astronomers that their science stands
above all others in the accuracy of the facts observed, as well as in
the rigid logic of the mathematics used for interpreting these facts.
It is interesting to trace historically the invention of those
instruments of precision which have led to this result, and, without
entering on the details required in a practical handbook, to note the
guiding principles of construction in different ages.
It is very probable that the Chaldeans may have made spheres, like the
armillary sphere, for representing the poles of the heavens; and with
rings to show the ecliptic and zodiac, as well as the equinoctial and
solstitial colures; but we have no record. We only know that the tower
of Belus, on an eminence, was their observatory. We have, however,
distinct records of two such spheres used by the Chinese about 2500
B.C. Gnomons, or some kind of sundial, were used by the Egyptians and
others; and many of the ancient nations measured the obliquity of the
ecliptic by the shadows of a vertical column in summer and winter. The
natural horizon was the only instrument of precision used by those who
determined star positions by the directions of their risings and
settings; while in those days the clepsydra, or waterclock, was the
best instrument for comparing their times of rising and setting.
About 300 B.C. an observatory fitted with circular instruments for
star positions was set up at Alexandria, the then centre of
civilisation. We know almost nothing about the instruments used by
Hipparchus in preparing his star catalogues and his lunar and solar
tables; but the invention of the astrolabe is attributed to him.[1]
In more modern times Nuremberg became a centre of astronomical
culture. Waltherus, of that town, made really accurate observations of
star altitudes, and of the distances between stars; and in 1484
A.D. he used a kind of clock. Tycho Brahe tried these, but discarded
them as being inaccurate.
Tycho Brahe (1546-1601 A.D.) made great improvements in armillary
spheres, quadrants, sextants, and large celestial globes. With these
he measured the positions of stars, or the distance of a comet from
several known stars. He has left us full descriptions of them,
illustrated by excellent engravings. Previous to his time such
instruments were made of wood. Tycho always used metal. He paid the
greatest attention to the stability of mounting, to the orientation of
his instruments, to the graduation of the arcs by the then new method
of transversals, and to the aperture sight used upon his
pointer. There were no telescopes in his day, and no pendulum
clocks. He recognised the fact that there must be instrumental
errors. He made these as small as was possible, measured their amount,
and corrected his observations. His table of refractions enabled him
to abolish the error due to our atmosphere so far as it could affect
naked-eye observations. The azimuth circle of Tycho's largest quadrant
had a diameter of nine feet, and the quadrant a radius of six feet. He
introduced the mural quadrant for meridian observations.[2]
[Illustration: ANCIENT CHINESE INSTRUMENTS, Including quadrant, celestial
globe, and two armillae, in the Observatory at Peking. Photographed in
Peking by the author in 1875, and stolen by the Germans when the
Embassies were relieved by the allies in 1900.]
The French Jesuits at Peking, in the seventeenth century, helped the
Chinese in their astronomy. In 1875 the writer saw and photographed,
on that part of the wall of Peking used by the Mandarins as an
observatory, the six instruments handsomely designed by Father
Verbiest, copied from the instruments of Tycho Brahe, and embellished
with Chinese dragons and emblems cast on the supports. He also saw
there two old instruments (which he was told were Arabic) of date
1279, by Ko Show-King, astronomer to Koblai Khan, the grandson of
Chenghis Khan. One of these last is nearly identical with the armillae
of Tycho; and the other with his "armillae aequatoriae maximae," with
which he observed the comet of 1585, besides fixed stars and
planets.[3]
The discovery by Galileo of the isochronism of the pendulum, followed
by Huyghens's adaptation of that principle to clocks, has been one of
the greatest aids to accurate observation. About the same time an
equally beneficial step was the employment of the telescope as a
pointer; not the Galilean with concave eye-piece, but with a
magnifying glass to examine the focal image, at which also a fixed
mark could be placed. Kepler was the first to suggest this. Gascoigne
was the first to use it. Huyghens used a metal strip of variable width
in the focus, as a micrometer to cover a planetary disc, and so to
measure the width covered by the planet. The Marquis Malvasia, in
1662, described the network of fine silver threads at right angles,
which he used in the focus, much as we do now.
In the hands of such a skilful man as Tycho Brahe, the old open
sights, even without clocks, served their purpose sufficiently well to
enable Kepler to discover the true theory of the solar system. But
telescopic sights and clocks were required for proving some of
Newton's theories of planetary perturbations. Picard's observations at
Paris from 1667 onwards seem to embody the first use of the telescope
as a pointer. He was also the first to introduce the use of Huyghens's
clocks for observing the right ascension of stars. Olaus Romer was
born at Copenhagen in 1644. In 1675, by careful study of the times of
eclipses of Jupiter's satellites, he discovered that light took time
to traverse space. Its velocity is 186,000 miles per second. In 1681
he took up his duties as astronomer at Copenhagen, and built the first
transit circle on a window-sill of his house. The iron axis was five
feet long and one and a-half inches thick, and the telescope was fixed
near one end with a counterpoise. The telescope-tube was a double
cone, to prevent flexure. Three horizontal and three vertical wires
were used in the focus. These were illuminated by a speculum, near the
object-glass, reflecting the light from a lantern placed over the
axis, the upper part of the telescope-tube being partly cut away to
admit the light. A divided circle, with pointer and reading
microscope, was provided for reading the declination. He realised the
superiority of a circle with graduations over a much larger
quadrant. The collimation error was found by reversing the instrument
and using a terrestrial mark, the azimuth error by star observations.
The time was expressed in fractions of a second. He also constructed a
telescope with equatoreal mounting, to follow a star by one axial
motion. In 1728 his instruments and observation records were destroyed
by fire.
Hevelius had introduced the vernier and tangent screw in his
measurement of arc graduations. His observatory and records were burnt
to the ground in 1679. Though an old man, he started afresh, and left
behind him a catalogue of 1,500 stars.
Flamsteed began his duties at Greenwich Observatory, as first
Astronomer Royal, in 1676, with very poor instruments. In 1683 he put
up a mural arc of 140 deg., and in 1689 a better one, seventy-nine inches
radius. He conducted his measurements with great skill, and
introduced new methods to attain accuracy, using certain stars for
determining the errors of his instruments; and he always reduced his
observations to a form in which they could be readily used. He
introduced new methods for determining the position of the equinox and
the right ascension of a fundamental star. He produced a catalogue of
2,935 stars. He supplied Sir Isaac Newton with results of observation
required in his theoretical calculations. He died in 1719.
Halley succeeded Flamsteed to find that the whole place had been
gutted by the latter's executors. In 1721 he got a transit instrument,
and in 1726 a mural quadrant by Graham. His successor in 1742,
Bradley, replaced this by a fine brass quadrant, eight feet radius, by
Bird; and Bradley's zenith sector was purchased for the observatory.
An instrument like this, specially designed for zenith stars, is
capable of greater rigidity than a more universal instrument; and
there is no trouble with refraction in the zenith. For these reasons
Bradley had set up this instrument at Kew, to attempt the proof of the
earth's motion by observing the annual parallax of stars. He certainly
found an annual variation of zenith distance, but not at the times of
year required by the parallax. This led him to the discovery of the
"aberration" of light and of nutation. Bradley has been described as
the founder of the modern system of accurate observation. He died in
1762, leaving behind him thirteen folio volumes of valuable but
unreduced observations. Those relating to the stars were reduced by
Bessel and published in 1818, at Koenigsberg, in his well-known
standard work, _Fundamenta Astronomiae_. In it are results showing the
laws of refraction, with tables of its amount, the maximum value of
aberration, and other constants.
Bradley was succeeded by Bliss, and he by Maskelyne (1765), who
carried on excellent work, and laid the foundations of the Nautical
Almanac (1767). Just before his death he induced the Government to
replace Bird's quadrant by a fine new mural _circle_, six feet in
diameter, by Troughton, the divisions being read off by microscopes
fixed on piers opposite to the divided circle. In this instrument the
micrometer screw, with a divided circle for turning it, was applied
for bringing the micrometer wire actually in line with a division on
the circle--a plan which is still always adopted.
Pond succeeded Maskelyne in 1811, and was the first to use this
instrument. From now onwards the places of stars were referred to the
pole, not to the zenith; the zero being obtained from measures on
circumpolar stars. Standard stars were used for giving the clock
error. In 1816 a new transit instrument, by Troughton, was added, and
from this date the Greenwich star places have maintained the very
highest accuracy.
George Biddell Airy, Seventh Astronomer Royal,[4] commenced his
Greenwich labours in 1835. His first and greatest reformation in the
work of the observatory was one he had already established at
Cambridge, and is now universally adopted. He held that an observation
is not completed until it has been reduced to a useful form; and in
the case of the sun, moon, and planets these results were, in every
case, compared with the tables, and the tabular error printed.
Airy was firmly impressed with the object for which Charles II. had
wisely founded the observatory in connection with navigation, and for
observations of the moon. Whenever a meridian transit of the moon
could be observed this was done. But, even so, there are periods in
the month when the moon is too near the sun for a transit to be well
observed. Also weather interferes with many meridian observations. To
render the lunar observations more continuous, Airy employed
Troughton's successor, James Simms, in conjunction with the engineers,
Ransome and May, to construct an altazimuth with three-foot circles,
and a five-foot telescope, in 1847. The result was that the number of
lunar observations was immediately increased threefold, many of them
being in a part of the moon's orbit which had previously been bare of
observations. From that date the Greenwich lunar observations have
been a model and a standard for the whole world.
Airy also undertook to superintend the reduction of all Greenwich
lunar observations from 1750 to 1830. The value of this laborious
work, which was completed in 1848, cannot be over-estimated.
The demands of astronomy, especially in regard to small minor planets,
required a transit instrument and mural circle with a more powerful
telescope. Airy combined the functions of both, and employed the same
constructors as before to make a _transit-circle_ with a telescope of
eleven and a-half feet focus and a circle of six-feet diameter, the
object-glass being eight inches in diameter.
Airy, like Bradley, was impressed with the advantage of employing
stars in the zenith for determining the fundamental constants of
astronomy. He devised a _reflex zenith tube_, in which the zenith
point was determined by reflection from a surface of mercury. The
design was so simple, and seemed so perfect, that great expectations
were entertained. But unaccountable variations comparable with those
of the transit circle appeared, and the instrument was put out of use
until 1903, when the present Astronomer Royal noticed that the
irregularities could be allowed for, being due to that remarkable
variation in the position of the earth's axis included in circles of
about six yards diameter at the north and south poles, discovered at
the end of the nineteenth century. The instrument is now being used
for investigating these variations; and in the year 1907 as many as
1,545 observations of stars were made with the reflex zenith tube.
In connection with zenith telescopes it must be stated that Respighi,
at the Capitol Observatory at Rome, made use of a deep well with a
level mercury surface at the bottom and a telescope at the top
pointing downwards, which the writer saw in 1871. The reflection of
the micrometer wires and of a star very near the zenith (but not quite
in the zenith) can be observed together. His mercury trough was a
circular plane surface with a shallow edge to retain the mercury. The
surface quickly came to rest after disturbance by street traffic.
Sir W. M. H. Christie, Eighth Astronomer Royal, took up his duties in
that capacity in 1881. Besides a larger altazimuth that he erected in
1898, he has widened the field of operations at Greenwich by the
extensive use of photography and the establishment of large
equatoreals. From the point of view of instruments of precision, one
of the most important new features is the astrographic equatoreal, set
up in 1892 and used for the Greenwich section of the great
astrographic chart just completed. Photography has come to be of use,
not only for depicting the sun and moon, comets and nebulae, but also
to obtain accurate relative positions of neighbouring stars; to pick
up objects that are invisible in any telescope; and, most of all
perhaps, in fixing the positions of faint satellites. Thus Saturn's
distant satellite, Phoebe, and the sixth and seventh satellites of
Jupiter, have been followed regularly in their courses at Greenwich
ever since their discovery with the thirty-inch reflector (erected in
1897); and while doing so Mr. Melotte made, in 1908, the splendid
discovery on some of the photographic plates of an eighth satellite of
Jupiter, at an enormous distance from the planet. From observations in
the early part of 1908, over a limited arc of its orbit, before
Jupiter approached the sun, Mr. Cowell computed a retrograde orbit and
calculated the future positions of this satellite, which enabled
Mr. Melotte to find it again in the autumn--a great triumph both of
calculation and of photographic observation. This satellite has never
been seen, and has been photographed only at Greenwich, Heidelberg,
and the Lick Observatory.
Greenwich Observatory has been here selected for tracing the progress
of accurate measurement. But there is one instrument of great value,
the heliometer, which is not used at Greenwich. This serves the
purpose of a double image micrometer, and is made by dividing the
object-glass of a telescope along a diameter. Each half is mounted so
as to slide a distance of several inches each way on an arc whose
centre is the focus. The amount of the movement can be accurately
read. Thus two fields of view overlap, and the adjustment is made to
bring an image of one star over that of another star, and then to do
the same by a displacement in the opposite direction. The total
movement of the half-object glass is double the distance between the
star images in the focal plane. Such an instrument has long been
established at Oxford, and German astronomers have made great use of
it. But in the hands of Sir David Gill (late His Majesty's Astronomer
at the Cape of Good Hope), and especially in his great researches on
Solar and on Stellar parallax, it has been recognised as an instrument
of the very highest accuracy, measuring the distance between stars
correctly to less than a tenth of a second of arc.
The superiority of the heliometer over all other devices (except
photography) for measuring small angles has been specially brought
into prominence by Sir David Gill's researches on the distance of the
sun--_i.e.,_ the scale of the solar system. A measurement of the
distance of any planet fixes the scale, and, as Venus approaches the
earth most nearly of all the planets, it used to be supposed that a
Transit of Venus offered the best opportunity for such measurement,
especially as it was thought that, as Venus entered on the solar disc,
the sweep of light round the dark disc of Venus would enable a very
precise observation to be made. The Transit of Venus in 1874, in
which the present writer assisted, overthrew this delusion.
In 1877 Sir David Gill used Lord Crawford's heliometer at the Island
of Ascension to measure the parallax of Mars in opposition, and found
the sun's distance 93,080,000 miles. He considered that, while the
superiority of the heliometer had been proved, the results would be
still better with the points of light shown by minor planets rather
than with the disc of Mars.
In 1888-9, at the Cape, he observed the minor planets Iris, Victoria,
and Sappho, and secured the co-operation of four other heliometers.
His final result was 92,870,000 miles, the parallax being 8",802
(_Cape Obs_., Vol. VI.).
So delicate were these measures that Gill detected a minute periodic
error of theory of twenty-seven days, owing to a periodically
erroneous position of the centre of gravity of the earth and moon to
which the position of the observer was referred. This led him to
correct the mass of the moon, and to fix its ratio to the earth's mass
= 0.012240.
Another method of getting the distance from the sun is to measure the
velocity of the earth's orbital motion, giving the circumference
traversed in a year, and so the radius of the orbit. This has been
done by comparing observation and experiment. The aberration of light
is an angle 20" 48, giving the ratio of the earth's velocity to the
velocity of light. The velocity of light is 186,000 miles a second;
whence the distance to the sun is 92,780,000 miles. There seems,
however, to be some uncertainty about the true value of the
aberration, any determination of which is subject to irregularities
due to the "seasonal errors." The velocity of light was experimentally
found, in 1862, by Fizeau and Foucault, each using an independent
method. These methods have been developed, and new values found, by
Cornu, Michaelson, Newcomb, and the present writer.
Quite lately Halm, at the Cape of Good Hope, measured
spectroscopically the velocity of the earth to and from a star by
observations taken six months apart. Thence he obtained an accurate
value of the sun's distance.[5]
But the remarkably erratic minor planet, Eros, discovered by Witte in
1898, approaches the earth within 15,000,000 miles at rare intervals,
and, with the aid of photography, will certainly give us the best
result. A large number of observatories combined to observe the
opposition of 1900. Their results are not yet completely reduced, but
the best value deduced so far for the parallax[6] is 8".807 +-
0".0028.[7]
FOOTNOTES:
[1] In 1480 Martin Behaim, of Nuremberg, produced his _astrolabe_ for
measuring the latitude, by observation of the sun, at sea. It
consisted of a graduated metal circle, suspended by a ring which was
passed over the thumb, and hung vertically. A pointer was fixed to a
pin at the centre. This arm, called the _alhidada_, worked round the
graduated circle, and was pointed to the sun. The altitude of the sun
was thus determined, and, by help of solar tables, the latitude could
be found from observations made at apparent noon.
[2] See illustration on p. 76.
[3] See Dreyer's article on these instruments in _Copernicus_,
Vol. I. They were stolen by the Germans after the relief of the
Embassies, in 1900. The best description of these instruments is
probably that contained in an interesting volume, which may be seen in
the library of the R. A. S., entitled _Chinese Researches_, by
Alexander Wyllie (Shanghai, 1897).
[4] Sir George Airy was very jealous of this honourable title. He
rightly held that there is only one Astronomer Royal at a time, as
there is only one Mikado, one Dalai Lama. He said that His Majesty's
Astronomer at the Cape of Good Hope, His Majesty's Astronomer for
Scotland, and His Majesty's Astronomer for Ireland are not called
Astronomers Royal.
[5] _Annals of the Cape Observatory_, vol. x., part 3.
[6] The parallax of the sun is the angle subtended by the earth's
radius at the sun's distance.
[7] A. R. Hinks, R.A.S.; _Monthly Notices_, June, 1909.
11. HISTORY OF THE TELESCOPE
Accounts of wonderful optical experiments by Roger Bacon (who died in
1292), and in the sixteenth century by Digges, Baptista Porta, and
Antonio de Dominis (Grant, _Hist. Ph. Ast_.), have led some to
suppose that they invented the telescope. The writer considers that it
is more likely that these notes refer to a kind of _camera
obscura_, in which a lens throws an inverted image of a landscape
on the wall.
The first telescopes were made in Holland, the originator being either
Henry Lipperhey,[1] Zacharias Jansen, or James Metius, and the date
1608 or earlier.
In 1609 Galileo, being in Venice, heard of the invention, went home
and worked out the theory, and made a similar telescope. These
telescopes were all made with a convex object-glass and a concave
eye-lens, and this type is spoken of as the Galilean telescope. Its
defects are that it has no real focus where cross-wires can be placed,
and that the field of view is very small. Kepler suggested the convex
eye-lens in 1611, and Scheiner claimed to have used one in 1617. But
it was Huyghens who really introduced them. In the seventeenth century
telescopes were made of great length, going up to 300 feet. Huyghens
also invented the compound eye-piece that bears his name, made of two
convex lenses to diminish spherical aberration.
But the defects of colour remained, although their cause was unknown
until Newton carried out his experiments on dispersion and the solar
spectrum. To overcome the spherical aberration James Gregory,[2] of
Aberdeen and Edinburgh, in 1663, in his _Optica Promota_,
proposed a reflecting speculum of parabolic form. But it was Newton,
about 1666, who first made a reflecting telescope; and he did it with
the object of avoiding colour dispersion.
Some time elapsed before reflectors were much used. Pound and Bradley
used one presented to the Royal Society by Hadley in 1723. Hawksbee,
Bradley, and Molyneaux made some. But James Short, of Edinburgh, made
many excellent Gregorian reflectors from 1732 till his death in 1768.
Newton's trouble with refractors, chromatic aberration, remained
insurmountable until John Dollond (born 1706, died 1761), after many
experiments, found out how to make an achromatic lens out of two
lenses--one of crown glass, the other of flint glass--to destroy the
colour, in a way originally suggested by Euler. He soon acquired a
great reputation for his telescopes of moderate size; but there was a
difficulty in making flint-glass lenses of large size. The first
actual inventor and constructor of an achromatic telescope was Chester
Moor Hall, who was not in trade, and did not patent it. Towards the
close of the eighteenth century a Swiss named Guinand at last
succeeded in producing larger flint-glass discs free from
striae. Frauenhofer, of Munich, took him up in 1805, and soon
produced, among others, Struve's Dorpat refractor of 9.9 inches
diameter and 13.5 feet focal length, and another, of 12 inches
diameter and 18 feet focal length, for Lamont, of Munich.
In the nineteenth century gigantic _reflectors_ have been
made. Lassel's 2-foot reflector, made by himself, did much good work,
and discovered four new satellites. But Lord Rosse's 6-foot
reflector, 54 feet focal length, constructed in 1845, is still the
largest ever made. The imperfections of our atmosphere are against
the use of such large apertures, unless it be on high mountains.
During the last half century excellent specula have been made of
silvered glass, and Dr. Common's 5-foot speculum (removed, since his
death, to Harvard) has done excellent work. Then there are the 5-foot
Yerkes reflector at Chicago, and the 4-foot by Grubb at Melbourne.
Passing now from these large reflectors to refractors, further
improvements have been made in the manufacture of glass by Chance, of
Birmingham, Feil and Mantois, of Paris, and Schott, of Jena; while
specialists in grinding lenses, like Alvan Clark, of the U.S.A., and
others, have produced many large refractors.
Cooke, of York, made an object-glass, 25-inch diameter, for Newall, of
Gateshead, which has done splendid work at Cambridge. We have the
Washington 26-inch by Clark, the Vienna 27-inch by Grubb, the Nice
291/2-inch by Gautier, the Pulkowa 30-inch by Clark. Then there was
the sensation of Clark's 36-inch for the Lick Observatory in
California, and finally his _tour de force_, the Yerkes 40-inch
refractor, for Chicago.
At Greenwich there is the 28-inch photographic refractor, and the
Thompson equatoreal by Grubb, carrying both the 26-inch photographic
refractor and the 30-inch reflector. At the Cape of Good Hope we find
Mr. Frank McClean's 24-inch refractor, with an object-glass prism for
spectroscopic work.
It would be out of place to describe here the practical adjuncts of a
modern equatoreal--the adjustments for pointing it, the clock for
driving it, the position-micrometer and various eye-pieces, the
photographic and spectroscopic attachments, the revolving domes,
observing seats, and rising floors and different forms of mounting,
the siderostats and coelostats, and other convenient adjuncts, besides
the registering chronograph and numerous facilities for aiding
observation. On each of these a chapter might be written; but the
most important part of the whole outfit is the man behind the
telescope, and it is with him that a history is more especially
concerned.
SPECTROSCOPE.
Since the invention of the telescope no discovery has given so great
an impetus to astronomical physics as the spectroscope; and in giving
us information about the systems of stars and their proper motions it
rivals the telescope.
Frauenhofer, at the beginning of the nineteenth century, while
applying Dollond's discovery to make large achromatic telescopes,
studied the dispersion of light by a prism. Admitting the light of the
sun through a narrow slit in a window-shutter, an inverted image of
the slit can be thrown, by a lens of suitable focal length, on the
wall opposite. If a wedge or prism of glass be interposed, the image
is deflected to one side; but, as Newton had shown, the images formed
by the different colours of which white light is composed are
deflected to different extents--the violet most, the red least. The
number of colours forming images is so numerous as to form a
continuous spectrum on the wall with all the colours--red, orange,
yellow, green, blue, indigo, and violet. But Frauenhofer found with a
narrow slit, well focussed by the lens, that some colours were missing
in the white light of the sun, and these were shown by dark lines
across the spectrum. These are the Frauenhofer lines, some of which
he named by the letters of the alphabet. The D line is a very marked
one in the yellow. These dark lines in the solar spectrum had already
been observed by Wollaston. [3]
On examining artificial lights it was found that incandescent solids
and liquids (including the carbon glowing in a white gas flame) give
continuous spectra; gases, except under enormous pressure, give bright
lines. If sodium or common salt be thrown on the colourless flame of a
spirit lamp, it gives it a yellow colour, and its spectrum is a bright
yellow line agreeing in position with line D of the solar spectrum.
In 1832 Sir David Brewster found some of the solar black lines
increased in strength towards sunset, and attributed them to
absorption in the earth's atmosphere. He suggested that the others
were due to absorption in the sun's atmosphere. Thereupon Professor
J. D. Forbes pointed out that during a nearly total eclipse the lines
ought to be strengthened in the same way; as that part of the sun's
light, coming from its edge, passes through a great distance in the
sun's atmosphere. He tried this with the annular eclipse of 1836,
with a negative result which has never been accounted for, and which
seemed to condemn Brewster's view.
In 1859 Kirchoff, on repeating Frauenhofer's experiment, found that,
if a spirit lamp with salt in the flame were placed in the path of the
light, the black D line is intensified. He also found that, if he used
a limelight instead of the sunlight and passed it through the flame
with salt, the spectrum showed the D line black; or the vapour of
sodium absorbs the same light that it radiates. This proved to him the
existence of sodium in the sun's atmosphere.[4] Iron, calcium, and
other elements were soon detected in the same way.
Extensive laboratory researches (still incomplete) have been carried
out to catalogue (according to their wave-length on the undulatory
theory of light) all the lines of each chemical element, under all
conditions of temperature and pressure. At the same time, all the
lines have been catalogued in the light of the sun and the brighter of
the stars.
Another method of obtaining spectra had long been known, by
transmission through, or reflection from, a grating of equidistant
lines ruled upon glass or metal. H. A. Rowland developed the art of
constructing these gratings, which requires great technical skill, and
for this astronomers owe him a debt of gratitude.
In 1842 Doppler[5] proved that the colour of a luminous body, like the
pitch or note of a sounding body, must be changed by velocity of
approach or recession. Everyone has noticed on a railway that, on
meeting a locomotive whistling, the note is lowered after the engine
has passed. The pitch of a sound or the colour of a light depends on
the number of waves striking the ear or eye in a second. This number
is increased by approach and lowered by recession.
Thus, by comparing the spectrum of a star alongside a spectrum of
hydrogen, we may see all the lines, and be sure that there is hydrogen
in the star; yet the lines in the star-spectrum may be all slightly
displaced to one side of the lines of the comparison spectrum. If
towards the violet end, it means mutual approach of the star and
earth; if to the red end, it means recession. The displacement of
lines does not tell us whether the motion is in the star, the earth,
or both. The displacement of the lines being measured, we can
calculate the rate of approach or recession in miles per second.
In 1868 Huggins[6] succeeded in thus measuring the velocities of stars
in the direction of the line of sight.
In 1873 Vogel[7] compared the spectra of the sun's East (approaching)
limb and West (receding) limb, and the displacement of lines endorsed
the theory. This last observation was suggested by Zoellner.
FOOTNOTES:
[1] In the _Encyclopaedia Britannica_, article "Telescope," and in
Grant's _Physical Astronomy_, good reasons are given for awarding the
honour to Lipperhey.
[2] Will the indulgent reader excuse an anecdote which may encourage
some workers who may have found their mathematics defective through
want of use? James Gregory's nephew David had a heap of MS. notes by
Newton. These descended to a Miss Gregory, of Edinburgh, who handed
them to the present writer, when an undergraduate at Cambridge, to
examine. After perusal, he lent them to his kindest of friends,
J. C. Adams (the discoverer of Neptune), for his opinion. Adams's
final verdict was: "I fear they are of no value. It is pretty evident
that, when he wrote these notes, _Newton's mathematics were a little
rusty_."
[3] _R. S. Phil. Trans_.
[4] The experiment had been made before by one who did not understand
its meaning;. But Sir George G. Stokes had already given verbally the
true explanation of Frauenhofer lines.
[5] _Abh. d. Koen. Boehm. d. Wiss_., Bd. ii., 1841-42, p. 467. See
also Fizeau in the _Ann. de Chem. et de Phys_., 1870, p. 211.
[6] _R. S. Phil. Trans_., 1868.
[7] _Ast. Nach_., No. 1, 864.
BOOK IV. THE PHYSICAL PERIOD
We have seen how the theory of the solar system was slowly developed
by the constant efforts of the human mind to find out what are the
rules of cause and effect by which our conception of the present
universe and its development seems to be bound. In the primitive ages
a mere record of events in the heavens and on the earth gave the only
hope of detecting those uniform sequences from which to derive rules
or laws of cause and effect upon which to rely. Then came the
geometrical age, in which rules were sought by which to predict the
movements of heavenly bodies. Later, when the relation of the sun to
the courses of the planets was established, the sun came to be looked
upon as a cause; and finally, early in the seventeenth century, for
the first time in history, it began to be recognised that the laws of
dynamics, exactly as they had been established for our own terrestrial
world, hold good, with the same rigid invariability, at least as far
as the limits of the solar system.
Throughout this evolution of thought and conjecture there were two
types of astronomers--those who supplied the facts, and those who
supplied the interpretation through the logic of mathematics. So
Ptolemy was dependent upon Hipparchus, Kepler on Tycho Brahe, and
Newton in much of his work upon Flamsteed.
When Galileo directed his telescope to the heavens, when Secchi and
Huggins studied the chemistry of the stars by means of the
spectroscope, and when Warren De la Rue set up a photoheliograph at
Kew, we see that a progress in the same direction as before, in the
evolution of our conception of the universe, was being made. Without
definite expression at any particular date, it came to be an accepted
fact that not only do earthly dynamics apply to the heavenly bodies,
but that the laws we find established here, in geology, in chemistry,
and in the laws of heat, may be extended with confidence to the
heavenly bodies. Hence arose the branch of astronomy called
astronomical physics, a science which claims a large portion of the
work of the telescope, spectroscope, and photography. In this new
development it is more than ever essential to follow the dictum of
Tycho Brahe--not to make theories until all the necessary facts are
obtained. The great astronomers of to-day still hold to Sir Isaac
Newton's declaration, "Hypotheses non fingo." Each one may have his
suspicions of a theory to guide him in a course of observation, and
may call it a working hypothesis. But the cautious astronomer does
not proclaim these to the world; and the historian is certainly not
justified in including in his record those vague speculations founded
on incomplete data which may be demolished to-morrow, and which,
however attractive they may be, often do more harm than good to the
progress of true science. Meanwhile the accumulation of facts has
been prodigious, and the revelations of the telescope and spectroscope
entrancing.
12. THE SUN.
One of Galileo's most striking discoveries, when he pointed his
telescope to the heavenly bodies, was that of the irregularly shaped
spots on the sun, with the dark central _umbra_ and the less
dark, but more extensive, _penumbra_ surrounding it, sometimes
with several umbrae in one penumbra. He has left us many drawings of
these spots, and he fixed their period of rotation as a lunar month.
[Illustration: SOLAR SURFACE, As Photographed at the Royal
Observatory, Greenwich, showing sun-spots with umbrae, penumbrae, and
faculae.]
It is not certain whether Galileo, Fabricius, or Schemer was the first
to see the spots. They all did good work. The spots were found to be
ever varying in size and shape. Sometimes, when a spot disappears at
the western limb of the sun, it is never seen again. In other cases,
after a fortnight, it reappears at the eastern limb. The faculae, or
bright areas, which are seen all over the sun's surface, but specially
in the neighbourhood of spots, and most distinctly near the sun's
edge, were discovered by Galileo. A high telescopic power resolves
their structure into an appearance like willow-leaves, or rice-grains,
fairly uniform in size, and more marked than on other parts of the
sun's surface.
Speculations as to the cause of sun-spots have never ceased from
Galileo's time to ours. He supposed them to be clouds. Scheiner[1]
said they were the indications of tumultuous movements occasionally
agitating the ocean of liquid fire of which he supposed the sun to be
composed.
A. Wilson, of Glasgow, in 1769,[2] noticed a movement of the umbra
relative to the penumbra in the transit of the spot over the sun's
surface; exactly as if the spot were a hollow, with a black base and
grey shelving sides. This was generally accepted, but later
investigations have contradicted its universality. Regarding the cause
of these hollows, Wilson said:--
Whether their first production and subsequent numberless changes
depend upon the eructation of elastic vapours from below, or upon
eddies or whirlpools commencing at the surface, or upon the
dissolving of the luminous matter in the solar atmosphere, as clouds
are melted and again given out by our air; or, if the reader
pleases, upon the annihilation and reproduction of parts of this
resplendent covering, is left for theory to guess at.[3]
Ever since that date theory has been guessing at it. The solar
astronomer is still applying all the instruments of modern research to
find out which of these suppositions, or what modification of any of
them, is nearest the truth. The obstacle--one that is perhaps fatal to
a real theory--lies in the impossibility of reproducing comparative
experiments in our laboratories or in our atmosphere.
Sir William Herschel propounded an explanation of Wilson's observation
which received much notice, but which, out of respect for his memory,
is not now described, as it violated the elementary laws of heat.
Sir John Herschel noticed that the spots are mostly confined to two
zones extending to about 35 deg. on each side of the equator, and that a
zone of equatoreal calms is free from spots. But it was
R. C. Carrington[4] who, by his continuous observations at Redhill, in
Surrey, established the remarkable fact that, while the rotation
period in the highest latitudes, 50 deg., where spots are seen, is
twenty-seven-and-a-half days, near the equator the period is only
twenty-five days. His splendid volume of observations of the sun led
to much new information about the average distribution of spots at
different epochs.
Schwabe, of Dessau, began in 1826 to study the solar surface, and,
after many years of work, arrived at a law of frequency which has been
more fruitful of results than any discovery in solar physics.[5] In
1843 he announced a decennial period of maxima and minima of sun-spot
displays. In 1851 it was generally accepted, and, although a period of
eleven years has been found to be more exact, all later observations,
besides the earlier ones which have been hunted up for the purpose, go
to establish a true periodicity in the number of sun-spots. But quite
lately Schuster[6] has given reasons for admitting a number of
co-existent periods, of which the eleven-year period was predominant
in the nineteenth century.
In 1851 Lament, a Scotchman at Munich, found a decennial period in the
daily range of magnetic declination. In 1852 Sir Edward Sabine
announced a similar period in the number of "magnetic storms"
affecting all of the three magnetic elements--declination, dip, and
intensity. Australian and Canadian observations both showed the
decennial period in all three elements. Wolf, of Zurich, and Gauthier,
of Geneva, each independently arrived at the same conclusion.
It took many years before this coincidence was accepted as certainly
more than an accident by the old-fashioned astronomers, who want rigid
proof for every new theory. But the last doubts have long vanished,
and a connection has been further traced between violent outbursts of
solar activity and simultaneous magnetic storms.
The frequency of the Aurora Borealis was found by Wolf to follow the
same period. In fact, it is closely allied in its cause to terrestrial
magnetism. Wolf also collected old observations tracing the
periodicity of sun-spots back to about 1700 A.D.
Spoerer deduced a law of dependence of the average latitude of
sun-spots on the phase of the sun-spot period.
All modern total solar eclipse observations seem to show that the
shape of the luminous corona surrounding the moon at the moment of
totality has a special distinct character during the time of a
sun-spot maximum, and another, totally different, during a sun-spot
minimum.
A suspicion is entertained that the total quantity of heat received by
the earth from the sun is subject to the same period. This would have
far-reaching effects on storms, harvests, vintages, floods, and
droughts; but it is not safe to draw conclusions of this kind except
from a very long period of observations.
Solar photography has deprived astronomers of the type of Carrington
of the delight in devoting a life's work to collecting data. It has
now become part of the routine work of an observatory.
In 1845 Foucault and Fizeau took a daguerreotype photograph of the
sun. In 1850 Bond produced one of the moon of great beauty, Draper
having made some attempts at an even earlier date. But astronomical
photography really owes its beginning to De la Rue, who used the
collodion process for the moon in 1853, and constructed the Kew
photoheliograph in 1857, from which date these instruments have been
multiplied, and have given us an accurate record of the sun's surface.
Gelatine dry plates were first used by Huggins in 1876.
It is noteworthy that from the outset De la Rue recognised the value
of stereoscopic vision, which is now known to be of supreme
accuracy. In 1853 he combined pairs of photographs of the moon in the
same phase, but under different conditions regarding libration,
showing the moon from slightly different points of view. These in the
stereoscope exhibited all the relief resulting from binocular vision,
and looked like a solid globe. In 1860 he used successive photographs
of the total solar eclipse stereoscopically, to prove that the red
prominences belong to the sun, and not to the moon. In 1861 he
similarly combined two photographs of a sun-spot, the perspective
effect showing the umbra like a floor at the bottom of a hollow
penumbra; and in one case the faculae were discovered to be sailing
over a spot apparently at some considerable height. These appearances
may be partly due to a proper motion; but, so far as it went, this was
a beautiful confirmation of Wilson's discovery. Hewlett, however, in
1894, after thirty years of work, showed that the spots are not always
depressions, being very subject to disturbance.
The Kew photographs [7] contributed a vast amount of information about
sun-spots, and they showed that the faculae generally follow the spots
in their rotation round the sun.
The constitution of the sun's photosphere, the layer which is the
principal light-source on the sun, has always been a subject of great
interest; and much was done by men with exceptionally keen eyesight,
like Mr. Dawes. But it was a difficult subject, owing to the rapidity
of the changes in appearance of the so-called rice-grains, about 1" in
diameter. The rapid transformations and circulations of these
rice-grains, if thoroughly studied, might lead to a much better
knowledge of solar physics. This seemed almost hopeless, as it was
found impossible to identify any "rice-grain" in the turmoil after a
few minutes. But M. Hansky, of Pulkowa (whose recent death is
deplored), introduced successfully a scheme of photography, which
might almost be called a solar cinematograph. He took photographs of
the sun at intervals of fifteen or thirty seconds, and then enlarged
selected portions of these two hundred times, giving a picture
corresponding to a solar disc of six metres diameter. In these
enlarged pictures he was able to trace the movements, and changes of
shape and brightness, of individual rice-grains. Some granules become
larger or smaller. Some seem to rise out of a mist, as it were, and to
become clearer. Others grow feebler. Some are split in two. Some are
rotated through a right angle in a minute or less, although each of
the grains may be the size of Great Britain. Generally they move
together in groups of very various velocities, up to forty kilometres
a second. These movements seem to have definite relation to any
sun-spots in the neighbourhood. From the results already obtained it
seems certain that, if this method of observation be continued, it
cannot fail to supply facts of the greatest importance.
It is quite impossible to do justice here to the work of all those who
are engaged on astronomical physics. The utmost that can be attempted
is to give a fair idea of the directions of human thought and
endeavour. During the last half-century America has made splendid
progress, and an entirely new process of studying the photosphere has
been independently perfected by Professor Hale at Chicago, and
Deslandres at Paris.[8] They have succeeded in photographing the sun's
surface in monochromatic light, such as the light given off as one of
the bright lines of hydrogen or of calcium, by means of the
"Spectroheliograph." The spectroscope is placed with its slit in the
focus of an equatoreal telescope, pointed to the sun, so that the
circular image of the sun falls on the slit. At the other end of the
spectroscope is the photographic plate. Just in front of this plate
there is another slit parallel to the first, in the position where the
image of the first slit formed by the K line of calcium falls. Thus is
obtained a photograph of the section of the sun, made by the first
slit, only in K light. As the image of the sun passes over the first
slit the photographic plate is moved at the same rate and in the same
direction behind the second slit; and as successive sections of the
sun's image in the equatoreal enter the apparatus, so are these
sections successively thrown in their proper place on the photographic
plate, always in K light. By using a high dispersion the faculae which
give off K light can be correctly photographed, not only at the sun's
edge, but all over his surface. The actual mechanical method of
carrying out the observation is not quite so simple as what is here
described.
By choosing another line of the spectrum instead of calcium K--for
example, the hydrogen line H(3)--we obtain two photographs, one
showing the appearance of the calcium floculi, and the other of the
hydrogen floculi, on the same part of the solar surface; and nothing
is more astonishing than to note the total want of resemblance in the
forms shown on the two. This mode of research promises to afford many
new and useful data.
The spectroscope has revealed the fact that, broadly speaking, the sun
is composed of the same materials as the earth. Angstrom was the first
to map out all of the lines to be found in the solar spectrum. But
Rowland, of Baltimore, after having perfected the art of making true
gratings with equidistant lines ruled on metal for producing spectra,
then proceeded to make a map of the solar spectrum on a large scale.
In 1866 Lockyer[9] threw an image of the sun upon the slit of a
spectroscope, and was thus enabled to compare the spectrum of a spot
with that of the general solar surface. The observation proved the
darkness of a spot to be caused by increased absorption of light, not
only in the dark lines, which are widened, but over the entire
spectrum. In 1883 Young resolved this continuous obscurity into an
infinite number of fine lines, which have all been traced in a shadowy
way on to the general solar surface. Lockyer also detected
displacements of the spectrum lines in the spots, such as would be
produced by a rapid motion in the line of sight. It has been found
that both uprushes and downrushes occur, but there is no marked
predominance of either in a sun-spot. The velocity of motion thus
indicated in the line of sight sometimes appears to amount to 320
miles a second. But it must be remembered that pressure of a gas has
some effect in displacing the spectral lines. So we must go on,
collecting data, until a time comes when the meaning of all the facts
can be made clear.
_Total Solar Eclipses_.--During total solar eclipses the time is so
short, and the circumstances so impressive, that drawings of the
appearance could not always be trusted. The red prominences of jagged
form that are seen round the moon's edge, and the corona with its
streamers radiating or interlacing, have much detail that can hardly
be recorded in a sketch. By the aid of photography a number of records
can be taken during the progress of totality. From a study of these
the extent of the corona is demonstrated in one case to extend to at
least six diameters of the moon, though the eye has traced it
farther. This corona is still one of the wonders of astronomy, and
leads to many questions. What is its consistency, if it extends many
million miles from the sun's surface? How is it that it opposed no
resistance to the motion of comets which have almost grazed the sun's
surface? Is this the origin of the zodiacal light? The character of
the corona in photographic records has been shown to depend upon the
phase of the sun-spot period. During the sun-spot maximum the corona
seems most developed over the spot-zones--i.e., neither at the
equator nor the poles. The four great sheaves of light give it a
square appearance, and are made up of rays or plumes, delicate like
the petals of a flower. During a minimum the nebulous ring seems to
be made of tufts of fine hairs with aigrettes or radiations from both
poles, and streamers from the equator.
[Illustration: SOLAR ECLIPSE, 1882. From drawing by W. H. Wesley,
Secretary R.A.S.; showing the prominences, the corona, and an unknown
comet.]
On September 19th, 1868, eclipse spectroscopy began with the Indian
eclipse, in which all observers found that the red prominences showed
a bright line spectrum, indicating the presence of hydrogen and other
gases. So bright was it that Jansen exclaimed: "_Je verrai ces
lignes-la en dehors des eclipses_." And the next day he observed the
lines at the edge of the uneclipsed sun. Huggins had suggested this
observation in February, 1868, his idea being to use prisms of such
great dispersive power that the continuous spectrum reflected by our
atmosphere should be greatly weakened, while a bright line would
suffer no diminution by the high dispersion. On October 20th
Lockyer,[10] having news of the eclipse, but not of Jansen's
observations the day after, was able to see these lines. This was a
splendid performance, for it enabled the prominences to be observed,
not only during eclipses, but every day. Moreover, the next year
Huggins was able, by using a wide slit, to see the whole of a
prominence and note its shape. Prominences are classified, according
to their form, into "flame" and "cloud" prominences, the spectrum of
the latter showing calcium, hydrogen, and helium; that of the former
including a number of metals.
The D line of sodium is a double line, and in the same eclipse (1868)
an orange line was noticed which was afterwards found to lie close to
the two components of the D line. It did not correspond with any known
terrestrial element, and the unknown element was called "helium." It
was not until 1895 that Sir William Ramsay found this element as a gas
in the mineral cleavite.
The spectrum of the corona is partly continuous, indicating light
reflected from the sun's body. But it also shows a green line
corresponding with no known terrestrial element, and the name
"coronium" has been given to the substance causing it.
A vast number of facts have been added to our knowledge about the sun
by photography and the spectroscope. Speculations and hypotheses in
plenty have been offered, but it may be long before we have a complete
theory evolved to explain all the phenomena of the storm-swept
metallic atmosphere of the sun.
The proceedings of scientific societies teem with such facts and
"working hypotheses," and the best of them have been collected by Miss
Clerke in her _History of Astronomy during the Nineteenth Century_. As
to established facts, we learn from the spectroscopic researches (1)
that the continuous spectrum is derived from the _photosphere_ or
solar gaseous material compressed almost to liquid consistency; (2)
that the _reversing layer_ surrounds it and gives rise to black
lines in the spectrum; that the _chromosphere_ surrounds this, is
composed mainly of hydrogen, and is the cause of the red prominences
in eclipses; and that the gaseous _corona_ surrounds all of
these, and extends to vast distances outside the sun's visible
surface.
FOOTNOTES:
[1] _Rosa Ursina_, by C. Scheiner, _fol_.; Bracciani, 1630.
[2] _R. S. Phil. Trans_., 1774.
[3] _Ibid_, 1783.
[4] _Observations on the Spots on the Sun, etc.,_ 4 deg.; London and
Edinburgh, 1863.
[5] _Periodicitaet der Sonnenflecken. Astron. Nach. XXI._, 1844,
P. 234.
[6] _R.S. Phil. Trans._ (ser. A), 1906, p. 69-100.
[7] "Researches on Solar Physics," by De la Rue, Stewart and Loewy;
_R. S. Phil. Trans_., 1869, 1870.
[8] "The Sun as Photographed on the K line"; _Knowledge_, London,
1903, p. 229.
[9] _R. S. Proc._, xv., 1867, p. 256.
[10] _Acad. des Sc._, Paris; _C. R._, lxvii., 1868, p. 121.
13. THE MOON AND PLANETS.
_The Moon_.--Telescopic discoveries about the moon commence with
Galileo's discovery that her surface has mountains and valleys, like
the earth. He also found that, while she always turns the same face to
us, there is periodically a slight twist to let us see a little round
the eastern or western edge. This was called _libration_, and the
explanation was clear when it was understood that in showing always
the same face to us she makes one revolution a month on her axis
_uniformly_, and that her revolution round the earth is not
uniform.
Galileo said that the mountains on the moon showed greater differences
of level than those on the earth. Shroeter supported this
opinion. W. Herschel opposed it. But Beer and Maedler measured the
heights of lunar mountains by their shadows, and found four of them
over 20,000 feet above the surrounding plains.
Langrenus [1] was the first to do serious work on selenography, and
named the lunar features after eminent men. Riccioli also made lunar
charts. In 1692 Cassini made a chart of the full moon. Since then we
have the charts of Schroeter, Beer and Maedler (1837), and of Schmidt,
of Athens (1878); and, above all, the photographic atlas by Loewy and
Puiseux.
The details of the moon's surface require for their discussion a whole
book, like that of Neison or the one by Nasmyth and Carpenter. Here a
few words must suffice. Mountain ranges like our Andes or Himalayas
are rare. Instead of that, we see an immense number of circular
cavities, with rugged edges and flat interior, often with a cone in
the centre, reminding one of instantaneous photographs of the splash
of a drop of water falling into a pool. Many of these are fifty or
sixty miles across, some more. They are generally spoken of as
resembling craters of volcanoes, active or extinct, on the earth. But
some of those who have most fully studied the shapes of craters deny
altogether their resemblance to the circular objects on the moon.
These so-called craters, in many parts, are seen to be closely
grouped, especially in the snow-white parts of the moon. But there are
great smooth dark spaces, like the clear black ice on a pond, more
free from craters, to which the equally inappropriate name of seas has
been given. The most conspicuous crater, _Tycho_, is near the south
pole. At full moon there are seen to radiate from Tycho numerous
streaks of light, or "rays," cutting through all the mountain
formations, and extending over fully half the lunar disc, like the
star-shaped cracks made on a sheet of ice by a blow. Similar cracks
radiate from other large craters. It must be mentioned that these
white rays are well seen only in full light of the sun at full moon,
just as the white snow in the crevasses of a glacier is seen bright
from a distance only when the sun is high, and disappears at
sunset. Then there are deep, narrow, crooked "rills" which may have
been water-courses; also "clefts" about half a mile wide, and often
hundreds of miles long, like deep cracks in the surface going straight
through mountain and valley.
The moon shares with the sun the advantage of being a good subject for
photography, though the planets are not. This is owing to her larger
apparent size, and the abundance of illumination. The consequence is
that the finest details of the moon, as seen in the largest telescope
in the world, may be reproduced at a cost within the reach of all.
No certain changes have ever been observed; but several suspicions
have been expressed, especially as to the small crater _Linne_, in the
_Mare Serenitatis_. It is now generally agreed that no certainty can
be expected from drawings, and that for real evidence we must await
the verdict of photography.
No trace of water or of an atmosphere has been found on the moon. It
is possible that the temperature is too low. In any case, no
displacement of a star by atmospheric refraction at occultation has
been surely recorded. The moon seems to be dead.
The distance of the moon from the earth is just now the subject of
re-measurement. The base line is from Greenwich to Cape of Good Hope,
and the new feature introduced is the selection of a definite point on
a crater (Moesting A), instead of the moon's edge, as the point whose
distance is to be measured.
_The Inferior Planets_.--When the telescope was invented, the phases
of Venus attracted much attention; but the brightness of this planet,
and her proximity to the sun, as with Mercury also, seemed to be a bar
to the discovery of markings by which the axis and period of rotation
could be fixed. Cassini gave the rotation as twenty-three hours, by
observing a bright spot on her surface. Shroeter made it 23h. 21m. 19s.
This value was supported by others. In 1890 Schiaparelli[2] announced
that Venus rotates, like our moon, once in one of her revolutions, and
always directs the same face to the sun. This property has also been
ascribed to Mercury; but in neither case has the evidence been
generally accepted. Twenty-four hours is probably about the period of
rotation for each of these planets.
Several observers have claimed to have seen a planet within the orbit
of Mercury, either in transit over the sun's surface or during an
eclipse. It has even been named _Vulcan_. These announcements would
have received little attention but for the fact that the motion of
Mercury has irregularities which have not been accounted for by known
planets; and Le Verrier[3] has stated that an intra-Mercurial planet
or ring of asteroids would account for the unexplained part of the
motion of the line of apses of Mercury's orbit amounting to 38" per
century.
_Mars_.--The first study of the appearance of Mars by Miraldi led him
to believe that there were changes proceeding in the two white caps
which are seen at the planet's poles. W. Herschel attributed these
caps to ice and snow, and the dates of his observations indicated a
melting of these ice-caps in the Martian summer.
Schroter attributed the other markings on Mars to drifting clouds. But
Beer and Maedler, in 1830-39, identified the same dark spots as being
always in the same place, though sometimes blurred by mist in the
local winter. A spot sketched by Huyghens in 1672, one frequently seen
by W. Herschel in 1783, another by Arago in 1813, and nearly all the
markings recorded by Beer and Maedler in 1830, were seen and drawn by
F. Kaiser in Leyden during seventeen nights of the opposition of 1862
(_Ast. Nacht._, No. 1,468), whence he deduced the period of rotation
to be 24h. 37m. 22s.,62--or one-tenth of a second less than the period
deduced by R. A. Proctor from a drawing by Hooke in 1666.
It must be noted that, if the periods of rotation both of Mercury and
Venus be about twenty-four hours, as seems probable, all the four
planets nearest to the sun rotate in the same period, while the great
planets rotate in about ten hours (Uranus and Neptune being still
indeterminate).
The general surface of Mars is a deep yellow; but there are dark grey
or greenish patches. Sir John Herschel was the first to attribute the
ruddy colour of Mars to its soil rather than to its atmosphere.
The observations of that keen-sighted observer Dawes led to the first
good map of Mars, in 1869. In the 1877 opposition Schiaparelli revived
interest in the planet by the discovery of canals, uniformly about
sixty miles wide, running generally on great circles, some of them
being three or four thousand miles long. During the opposition of
1881-2 the same observer re-observed the canals, and in twenty of them
he found the canals duplicated,[4] the second canal being always 200
to 400 miles distant from its fellow.
The existence of these canals has been doubted. Mr. Lowell has now
devoted years to the subject, has drawn them over and over again, and
has photographed them; and accepts the explanation that they are
artificial, and that vegetation grows on their banks. Thus is revived
the old controversy between Whewell and Brewster as to the
habitability of the planets. The new arguments are not yet generally
accepted. Lowell believes he has, with the spectroscope, proved the
existence of water on Mars.
One of the most unexpected and interesting of all telescopic
discoveries took place in the opposition of 1877, when Mars was
unusually near to the earth. The Washington Observatory had acquired
the fine 26-inch refractor, and Asaph Hall searched for satellites,
concealing the planet's disc to avoid the glare. On August 11th he had
a suspicion of a satellite. This was confirmed on the 16th, and on the
following night a second one was added. They are exceedingly faint,
and can be seen only by the most powerful telescopes, and only at the
times of opposition. Their diameters are estimated at six or seven
miles. It was soon found that the first, Deimos, completes its orbit
in 30h. 18m. But the other, Phobos, at first was a puzzle, owing to
its incredible velocity being unsuspected. Later it was found that the
period of revolution was only 7h. 39m. 22s. Since the Martian day is
twenty-four and a half hours, this leads to remarkable results.
Obviously the easterly motion of the satellite overwhelms the diurnal
rotation of the planet, and Phobos must appear to the inhabitants, if
they exist, to rise in the west and set in the east, showing two or
even three full moons in a day, so that, sufficiently well for the
ordinary purposes of life, the hour of the day can be told by its
phases.
The discovery of these two satellites is, perhaps, the most
interesting telescopic visual discovery made with the large telescopes
of the last half century; photography having been the means of
discovering all the other new satellites except Jupiter's fifth (in
order of discovery).
[Illustration: JUPITER. From a drawing by E. M. Antoniadi, showing
transit of a satellite's shadow, the belts, and the "great red spot"
(_Monthly Notices_, R. A. S., vol. lix., pl. x.).]
_Jupiter._--Galileo's discovery of Jupiter's satellites was followed
by the discovery of his belts. Zucchi and Torricelli seem to have seen
them. Fontana, in 1633, reported three belts. In 1648 Grimaldi saw but
two, and noticed that they lay parallel to the ecliptic. Dusky spots
were also noticed as transient. Hooke[5] measured the motion of one in
1664. In 1665 Cassini, with a fine telescope, 35-feet focal length,
observed many spots moving from east to west, whence he concluded that
Jupiter rotates on an axis like the earth. He watched an unusually
permanent spot during twenty-nine rotations, and fixed the period at
9h. 56m. Later he inferred that spots near the equator rotate quicker
than those in higher latitudes (the same as Carrington found for the
sun); and W. Herschel confirmed this in 1778-9.
Jupiter's rapid rotation ought, according to Newton's theory, to be
accompanied by a great flattening at the poles. Cassini had noted an
oval form in 1691. This was confirmed by La Hire, Roemer, and
Picard. Pound measured the ellipticity = 1/(13.25).
W. Herschel supposed the spots to be masses of cloud in the
atmosphere--an opinion still accepted. Many of them were very
permanent. Cassini's great spot vanished and reappeared nine times
between 1665 and 1713. It was close to the northern margin of the
southern belt. Herschel supposed the belts to be the body of the
planet, and the lighter parts to be clouds confined to certain
latitudes.
In 1665 Cassini observed transits of the four satellites, and also saw
their shadows on the planet, and worked out a lunar theory for
Jupiter. Mathematical astronomers have taken great interest in the
perturbations of the satellites, because their relative periods
introduce peculiar effects. Airy, in his delightful book,
_Gravitation_, has reduced these investigations to simple
geometrical explanations.
In 1707 and 1713 Miraldi noticed that the fourth satellite varies much
in brightness. W. Herschel found this variation to depend upon its
position in its orbit, and concluded that in the positions of
feebleness it is always presenting to us a portion of its surface,
which does not well reflect the sun's light; proving that it always
turns the same face to Jupiter, as is the case with our moon. This
fact had also been established for Saturn's fifth satellite, and may
be true for all satellites.
In 1826 Struve measured the diameters of the four satellites, and
found them to be 2,429, 2,180, 3,561, and 3,046 miles.
In modern times much interest has been taken in watching a rival to
Cassini's famous spot. The "great red spot" was first observed by
Niesten, Pritchett, and Tempel, in 1878, as a rosy cloud attached to a
whitish zone beneath the dark southern equatorial band, shaped like
the new war balloons, 30,000 miles long and 7,000 miles across. The
next year it was brick-red. A white spot beside it completed a
rotation in less time by 51/2 minutes than the red spot--a difference
of 260 miles an hour. Thus they came together again every six weeks,
but the motions did not continue uniform. The spot was feeble in
1882-4, brightened in 1886, and, after many changes, is still visible.
Galileo's great discovery of Jupiter's four moons was the last word in
this connection until September 9th, 1892, when Barnard, using the
36-inch refractor of the Lick Observatory, detected a tiny spot of
light closely following the planet. This proved to be a new satellite
(fifth), nearer to the planet than any other, and revolving round it
in 11h. 57m. 23s. Between its rising and setting there must be an
interval of 21/2 Jovian days, and two or three full moons. The sixth
and seventh satellites were found by the examination of photographic
plates at the Lick Observatory in 1905, since which time they have
been continuously photographed, and their orbits traced, at Greenwich.
On examining these plates in 1908 Mr. Melotte detected the eighth
satellite, which seems to be revolving in a retrograde orbit three
times as far from its planet as the next one (seventh), in these two
points agreeing with the outermost of Saturn's satellites (Phoebe).
_Saturn._--This planet, with its marvellous ring, was perhaps the most
wonderful object of those first examined by Galileo's telescope. He
was followed by Dominique Cassini, who detected bands like Jupiter's
belts. Herschel established the rotation of the planet in 1775-94.
From observations during one hundred rotations he found the period to
be 10h. 16m. 0s., 44. Herschel also measured the ratio of the polar to
the equatoreal diameter as 10:11.
The ring was a complete puzzle to Galileo, most of all when the planet
reached a position where the plane of the ring was in line with the
earth, and the ring disappeared (December 4th, 1612). It was not until
1656 that Huyghens, in his small pamphlet _De Saturni Luna Observatio
Nova_, was able to suggest in a cypher the ring form; and in 1659, in
his Systema Saturnium, he gave his reasons and translated the cypher:
"The planet is surrounded by a slender flat ring, everywhere distinct
from its surface, and inclined to the ecliptic." This theory explained
all the phases of the ring which had puzzled others. This ring was
then, and has remained ever since, a unique structure. We in this age
have got accustomed to it. But Huyghens's discovery was received with
amazement.
In 1675 Cassini found the ring to be double, the concentric rings
being separated by a black band--a fact which was placed beyond
dispute by Herschel, who also found that the thickness of the ring
subtends an angle less than 0".3. Shroeter estimated its thickness at
500 miles.
Many speculations have been advanced to explain the origin and
constitution of the ring. De Sejour said [6] that it was thrown off
from Saturn's equator as a liquid ring, and afterwards solidified. He
noticed that the outside would have a greater velocity, and be less
attracted to the planet, than the inner parts, and that equilibrium
would be impossible; so he supposed it to have solidified into a
number of concentric rings, the exterior ones having the least
velocity.
Clerk Maxwell, in the Adams prize essay, gave a physico-mathematical
demonstration that the rings must be composed of meteoritic matter
like gravel. Even so, there must be collisions absorbing the energy of
rotation, and tending to make the rings eventually fall into the
planet. The slower motion of the external parts has been proved by the
spectroscope in Keeler's hands, 1895.
Saturn has perhaps received more than its share of attention owing to
these rings. This led to other discoveries. Huyghens in 1655, and
J. D. Cassini in 1671, discovered the sixth and eighth satellites
(Titan and Japetus). Cassini lost his satellite, and in searching for
it found Rhea (the fifth) in 1672, besides his old friend, whom he
lost again. He added the third and fourth in 1684 (Tethys and
Dione). The first and second (Mimas and Encelades) were added by
Herschel in 1789, and the seventh (Hyperion) simultaneously by Lassel
and Bond in 1848. The ninth (Phoebe) was found on photographs, by
Pickering in 1898, with retrograde motion; and he has lately added a
tenth.
The occasional disappearance of Cassini's Japetus was found on
investigation to be due to the same causes as that of Jupiter's fourth
satellite, and proves that it always turns the same face to the
planet.
_Uranus and Neptune_.--The splendid discoveries of Uranus and two
satellites by Sir William Herschel in 1787, and of Neptune by Adams
and Le Verrier in 1846, have been already described. Lassel added two
more satellites to Uranus in 1851, and found Neptune's satellite in
1846. All of the satellites of Uranus have retrograde motion, and
their orbits are inclined about 80 deg. to the ecliptic.
The spectroscope has shown the existence of an absorbing atmosphere on
Jupiter and Saturn, and there are suspicions that they partake
something of the character of the sun, and emit some light besides
reflecting solar light. On both planets some absorption lines seem to
agree with the aqueous vapour lines of our own atmosphere; while one,
which is a strong band in the red common to both planets, seems to
agree with a line in the spectrum of some reddish stars.
Uranus and Neptune are difficult to observe spectroscopically, but
appear to have peculiar spectra agreeing together. Sometimes Uranus
shows Frauenhofer lines, indicating reflected solar light. But
generally these are not seen, and six broad bands of absorption
appear. One is the F. of hydrogen; another is the red-star line of
Jupiter and Saturn. Neptune is a very difficult object for the
spectroscope.
Quite lately [7] P. Lowell has announced that V. M. Slipher, at
Flagstaff Observatory, succeeded in 1907 in rendering some plates
sensitive far into the red. A reproduction is given of photographed
spectra of the four outermost planets, showing (1) a great number of
new lines and bands; (2) intensification of hydrogen F. and C. lines;
(3) a steady increase of effects (1) and (2) as we pass from Jupiter
and Saturn to Uranus, and a still greater increase in Neptune.
_Asteroids_.--The discovery of these new planets has been
described. At the beginning of the last century it was an immense
triumph to catch a new one. Since photography was called into the
service by Wolf, they have been caught every year in shoals. It is
like the difference between sea fishing with the line and using a
steam trawler. In the 1908 almanacs nearly seven hundred asteroids are
included. The computation of their perturbations and ephemerides by
Euler's and Lagrange's method of variable elements became so laborious
that Encke devised a special process for these, which can be applied
to many other disturbed orbits. [8]
When a photograph is taken of a region of the heavens including an
asteroid, the stars are photographed as points because the telescope
is made to follow their motion; but the asteroids, by their proper
motion, appear as short lines.
The discovery of Eros and the photographic attack upon its path have
been described in their relation to finding the sun's distance.
A group of four asteroids has lately been found, with a mean distance
and period equal to that of Jupiter. To three of these masculine names
have been given--Hector, Patroclus, Achilles; the other has not yet
been named.
FOOTNOTES:
[1] Langrenus (van Langren), F. Selenographia sive lumina austriae
philippica; Bruxelles, 1645.
[2] _Astr. Nach._, 2,944.
[3] _Acad. des Sc._, Paris; _C.R._, lxxxiii., 1876.
[4] _Mem. Spettr. Ital._, xi., p. 28.
[5] _R. S. Phil. Trans_., No. 1.
[6] Grant's _Hist. Ph. Ast_., p. 267.
[7] _Nature_, November 12th, 1908.
[8] _Ast. Nach_., Nos. 791, 792, 814, translated by G. B. Airy.
_Naut. Alm_., Appendix, 1856.
14. COMETS AND METEORS.
Ever since Halley discovered that the comet of 1682 was a member of
the solar system, these wonderful objects have had a new interest for
astronomers; and a comparison of orbits has often identified the
return of a comet, and led to the detection of an elliptic orbit where
the difference from a parabola was imperceptible in the small portion
of the orbit visible to us. A remarkable case in point was the comet
of 1556, of whose identity with the comet of 1264 there could be
little doubt. Hind wanted to compute the orbit more exactly than
Halley had done. He knew that observations had been made, but they
were lost. Having expressed his desire for a search, all the
observations of Fabricius and of Heller, and also a map of the comet's
path among the stars, were eventually unearthed in the most unlikely
manner, after being lost nearly three hundred years. Hind and others
were certain that this comet would return between 1844 and 1848, but
it never appeared.
When the spectroscope was first applied to finding the composition of
the heavenly bodies, there was a great desire to find out what comets
are made of. The first opportunity came in 1864, when Donati observed
the spectrum of a comet, and saw three bright bands, thus proving that
it was a gas and at least partly self-luminous. In 1868 Huggins
compared the spectrum of Winnecke's comet with that of a Geissler tube
containing olefiant gas, and found exact agreement. Nearly all comets
have shown the same spectrum.[1] A very few comets have given bright
band spectra differing from the normal type. Also a certain kind of
continuous spectrum, as well as reflected solar light showing
Frauenhofer lines, have been seen.
[Illustration: COPY OF THE DRAWING MADE BY PAUL FABRICIUS. To define
the path of comet 1556. After being lost for 300 years, this drawing
was recovered by the prolonged efforts of Mr. Hind and Professor
Littrow in 1856.]
When Wells's comet, in 1882, approached very close indeed to the sun,
the spectrum changed to a mono-chromatic yellow colour, due to sodium.
For a full account of the wonders of the cometary world the reader is
referred to books on descriptive astronomy, or to monographs on
comets.[2] Nor can the very uncertain speculations about the structure
of comets' tails be given here. A new explanation has been proposed
almost every time that a great discovery has been made in the theory
of light, heat, chemistry, or electricity.
Halley's comet remained the only one of which a prediction of the
return had been confirmed, until the orbit of the small, ill-defined
comet found by Pons in 1819 was computed by Encke, and found to have a
period of 3 1/3 years. It was predicted to return in 1822, and was
recognised by him as identical with many previous comets. This comet,
called after Encke, has showed in each of its returns an inexplicable
reduction of mean distance, which led to the assertion of a resisting
medium in space until a better explanation could be found.[3]
Since that date fourteen comets have been found with elliptic orbits,
whose aphelion distances are all about the same as Jupiter's mean
distance; and six have an aphelion distance about ten per cent,
greater than Neptune's mean distance. Other comets are similarly
associated with the planets Saturn and Uranus.
The physical transformations of comets are among the most wonderful of
unexplained phenomena in the heavens. But, for physical astronomers,
the greatest interest attaches to the reduction of radius vector of
Encke's comet, the splitting of Biela's comet into two comets in 1846,
and the somewhat similar behaviour of other comets. It must be noted,
however, that comets have a sensible size, that all their parts cannot
travel in exactly the same orbit under the sun's gravitation, and that
their mass is not sufficient to retain the parts together very
forcibly; also that the inevitable collision of particles, or else
fluid friction, is absorbing energy, and so reducing the comet's
velocity.
In 1770 Lexell discovered a comet which, as was afterwards proved by
investigations of Lexell, Burchardt, and Laplace, had in 1767 been
deflected by Jupiter out of an orbit in which it was invisible from
the earth into an orbit with a period of 51/2 years, enabling it to be
seen. In 1779 it again approached Jupiter closer than some of his
satellites, and was sent off in another orbit, never to be again
recognised.
But our interest in cometary orbits has been added to by the discovery
that, owing to the causes just cited, a comet, if it does not separate
into discrete parts like Biela's, must in time have its parts spread
out so as to cover a sensible part of the orbit, and that, when the
earth passes through such part of a comet's orbit, a meteor shower is
the result.
A magnificent meteor shower was seen in America on November 12th-13th,
1833, when the paths of the meteors all seemed to radiate from a point
in the constellation Leo. A similar display had been witnessed in
Mexico by Humboldt and Bonpland on November 12th, 1799. H. A. Newton
traced such records back to October 13th, A.D. 902. The orbital motion
of a cloud or stream of small particles was indicated. The period
favoured by H. A. Newton was 3541/2 days; another suggestion was 3751/2
days, and another 331/4 years. He noticed that the advance of the date
of the shower between 902 and 1833, at the rate of one day in seventy
years, meant a progression of the node of the orbit. Adams undertook
to calculate what the amount would be on all the five suppositions
that had been made about the period. After a laborious work, he found
that none gave one day in seventy years except the 331/4-year period,
which did so exactly. H. A. Newton predicted a return of the shower on
the night of November 13th-14th, 1866. He is now dead; but many of us
are alive to recall the wonder and enthusiasm with which we saw this
prediction being fulfilled by the grandest display of meteors ever
seen by anyone now alive.
The _progression_ of the nodes proved the path of the meteor
stream to be retrograde. The _radiant_ had almost the exact
longitude of the point towards which the earth was moving. This proved
that the meteor cluster was at perihelion. The period being known, the
eccentricity of the orbit was obtainable, also the orbital velocity of
the meteors in perihelion; and, by comparing this with the earth's
velocity, the latitude of the radiant enabled the inclination to be
determined, while the longitude of the earth that night was the
longitude of the node. In such a way Schiaparelli was able to find
first the elements of the orbit of the August meteor shower
(Perseids), and to show its identity with the orbit of Tuttle's comet
1862.iii. Then, in January 1867, Le Verrier gave the elements of the
November meteor shower (Leonids); and Peters, of Altona, identified
these with Oppolzer's elements for Tempel's comet 1866--Schiaparelli
having independently attained both of these results. Subsequently
Weiss, of Vienna, identified the meteor shower of April 20th (Lyrids)
with comet 1861. Finally, that indefatigable worker on meteors,
A. S. Herschel, added to the number, and in 1878 gave a list of
seventy-six coincidences between cometary and meteoric orbits.
Cometary astronomy is now largely indebted to photography, not merely
for accurate delineations of shape, but actually for the discovery of
most of them. The art has also been applied to the observation of
comets at distances from their perihelia so great as to prevent their
visual observation. Thus has Wolf, of Heidelburg, found upon old
plates the position of comet 1905.v., as a star of the 15.5 magnitude,
783 days before the date of its discovery. From the point of view of
the importance of finding out the divergence of a cometary orbit from
a parabola, its period, and its aphelion distance, this increase of
range attains the very highest value.
The present Astronomer Royal, appreciating this possibility, has been
searching by photography for Halley's comet since November, 1907,
although its perihelion passage will not take place until April, 1910.
FOOTNOTES:
[1] In 1874, when the writer was crossing the Pacific Ocean in
H.M.S. "Scout," Coggia's comet unexpectedly appeared, and (while
Colonel Tupman got its positions with the sextant) he tried to use the
prism out of a portable direct-vision spectroscope, without success
until it was put in front of the object-glass of a binocular, when, to
his great joy, the three band images were clearly seen.
[2] Such as _The World of Comets_, by A. Guillemin; _History of
Comets_, by G. R. Hind, London, 1859; _Theatrum Cometicum_, by S. de
Lubienietz, 1667; _Cometographie_, by Pingre, Paris, 1783; _Donati's
Comet_, by Bond.
[3] The investigations by Von Asten (of St. Petersburg) seem to
support, and later ones, especially those by Backlund (also of
St. Petersburg), seem to discredit, the idea of a resisting medium.
15. THE FIXED STARS AND NEBULAE.
Passing now from our solar system, which appears to be subject to the
action of the same forces as those we experience on our globe, there
remains an innumerable host of fixed stars, nebulas, and nebulous
clusters of stars. To these the attention of astronomers has been more
earnestly directed since telescopes have been so much enlarged.
Photography also has enabled a vast amount of work to be covered in a
comparatively short period, and the spectroscope has given them the
means, not only of studying the chemistry of the heavens, but also of
detecting any motion in the line of sight from less than a mile a
second and upwards in any star, however distant, provided it be bright
enough.
[Illustration: SIR WILLIAM HERSCHEL, F.R.S.--1738-1822. Painted by
Lemuel F. Abbott; National Portrait Gallery, Room XX.]
In the field of telescopic discovery beyond our solar system there is
no one who has enlarged our knowledge so much as Sir William Herschel,
to whom we owe the greatest discovery in dynamical astronomy among the
stars--viz., that the law of gravitation extends to the most distant
stars, and that many of them describe elliptic orbits about each
other. W. Herschel was born at Hanover in 1738, came to England in
1758 as a trained musician, and died in 1822. He studied science when
he could, and hired a telescope, until he learnt to make his own
specula and telescopes. He made 430 parabolic specula in twenty-one
years. He discovered 2,500 nebulae and 806 double stars, counted the
stars in 3,400 guage-fields, and compared the principal stars
photometrically.
Some of the things for which he is best known were results of those
accidents that happen only to the indefatigable enthusiast. Such was
the discovery of Uranus, which led to funds being provided for
constructing his 40-feet telescope, after which, in 1786, he settled
at Slough. In the same way, while trying to detect the annual parallax
of the stars, he failed in that quest, but discovered binary systems
of stars revolving in ellipses round each other; just as Bradley's
attack on stellar parallax failed, but led to the discovery of
aberration, nutation, and the true velocity of light.
_Parallax_.--The absence of stellar parallax was the great
objection to any theory of the earth's motion prior to Kepler's
time. It is true that Kepler's theory itself could have been
geometrically expressed equally well with the earth or any other point
fixed. But in Kepler's case the obviously implied physical theory of
the planetary motions, even before Newton explained the simplicity of
conception involved, made astronomers quite ready to waive the claim
for a rigid proof of the earth's motion by measurement of an annual
parallax of stars, which they had insisted on in respect of
Copernicus's revival of the idea of the earth's orbital motion.
Still, the desire to measure this parallax was only intensified by the
practical certainty of its existence, and by repeated failures. The
attempts of Bradley failed. The attempts of Piazzi and Brinkley,[1]
early in the nineteenth century, also failed. The first successes,
afterwards confirmed, were by Bessel and Henderson. Both used stars
whose proper motion had been found to be large, as this argued
proximity. Henderson, at the Cape of Good Hope, observed alpha
Centauri, whose annual proper motion he found to amount to 3".6, in
1832-3; and a few years later deduced its parallax 1".16. His
successor at the Cape, Maclear, reduced this to 0".92.
In 1835 Struve assigned a doubtful parallax of 0".261 to Vega (alpha
Lyrae). But Bessel's observations, between 1837 and 1840, of 61 Cygni,
a star with the large proper motion of over 5", established its annual
parallax to be 0".3483; and this was confirmed by Peters, who found
the value 0".349.
Later determinations for alpha2 Centauri, by Gill,[2] make its parallax
0".75--This is the nearest known fixed star; and its light takes 4 1/3
years to reach us. The light year is taken as the unit of measurement
in the starry heavens, as the earth's mean distance is "the
astronomical unit" for the solar system.[3] The proper motions and
parallaxes combined tell us the velocity of the motion of these stars
across the line of sight: alpha Centauri 14.4 miles a second=4.2
astronomical units a year; 61 Cygni 37.9 miles a second=11.2
astronomical units a year. These successes led to renewed zeal, and
now the distances of many stars are known more or less accurately.
Several of the brightest stars, which might be expected to be the
nearest, have not shown a parallax amounting to a twentieth of a
second of arc. Among these are Canopus, alpha Orionis, alpha Cygni, beta
Centauri, and gamma Cassiopeia. Oudemans has published a list of
parallaxes observed.[4]
_Proper Motion._--In 1718 Halley[5] detected the proper motions
of Arcturus and Sirius. In 1738 J. Cassinis[6] showed that the former
had moved five minutes of arc since Tycho Brahe fixed its position. In
1792 Piazzi noted the motion of 61 Cygni as given above. For a long
time the greatest observed proper motion was that of a small star 1830
Groombridge, nearly 7" a year; but others have since been found
reaching as much as 10".
Now the spectroscope enables the motion of stars to be detected at a
single observation, but only that part of the motion that is in the
line of sight. For a complete knowledge of a star's motion the proper
motion and parallax must also be known.
When Huggins first applied the Doppler principle to measure velocities
in the line of sight,[7] the faintness of star spectra diminished the
accuracy; but Voegel, in 1888, overcame this to a great extent by long
exposures of photographic plates.
It has often been noticed that stars which seem to belong to a group
of nearly uniform magnitude have the same proper motion. The
spectroscope has shown that these have also often the same velocity in
the line of sight. Thus in the Great Bear, beta, gamma, delta,
epsilon, zeta, all agree as to angular proper motion. delta was too
faint for a spectroscopic measurement, but all the others have been
shown to be approaching us at a rate of twelve to twenty miles a
second. The same has been proved for proper motion, and line of sight
motion, in the case of Pleiades and other groups.
Maskelyne measured many proper motions of stars, from which W.
Herschel[8] came to the conclusion that these apparent motions are for
the most part due to a motion of the solar system in space towards a
point in the constellation Hercules, R.A. 257 deg.; N. Decl. 25 deg. This
grand discovery has been amply confirmed, and, though opinions differ
as to the exact direction, it happens that the point first indicated
by Herschel, from totally insufficient data, agrees well with modern
estimates.
Comparing the proper motions and parallaxes to get the actual velocity
of each star relative to our system, C.L. Struve found the probable
velocity of the solar system in space to be fifteen miles a second, or
five astronomical units a year.
The work of Herschel in this matter has been checked by comparing
spectroscopic velocities in the line of sight which, so far as the
sun's motion is concerned, would give a maximum rate of approach for
stars near Hercules, a maximum rate of recession for stars in the
opposite part of the heavens, and no effect for stars half-way
between. In this way the spectroscope has confirmed generally
Herschel's view of the direction, and makes the velocity eleven miles
a second, or nearly four astronomical units a year.
The average proper motion of a first magnitude star has been found to
be 0".25 annually, and of a sixth magnitude star 0".04. But that all
bright stars are nearer than all small stars, or that they show
greater proper motion for that reason, is found to be far from the
truth. Many statistical studies have been made in this connection, and
interesting results may be expected from this treatment in the hands
of Kapteyn of Groningen, and others.[9]
On analysis of the directions of proper motions of stars in all parts
of the heavens, Kapteyn has shown[10] that these indicate, besides the
solar motion towards Hercules, two general drifts of stars in nearly
opposite directions, which can be detected in any part of the
heavens. This result has been confirmed from independent data by
Eddington (_R.A.S., M.N._) and Dyson (_R.S.E. Proc._).
Photography promises to assist in the measurement of parallax and
proper motions. Herr Pulfrich, of the firm of Carl Zeiss, has vastly
extended the applications of stereoscopic vision to astronomy--a
subject which De la Rue took up in the early days of photography. He
has made a stereo-comparator of great beauty and convenience for
comparing stereoscopically two star photographs taken at different
dates. Wolf of Heidelberg has used this for many purposes. His
investigations depending on the solar motion in space are remarkable.
He photographs stars in a direction at right angles to the line of the
sun's motion. He has taken photographs of the same region fourteen
years apart, the two positions of his camera being at the two ends of
a base-line over 5,000,000,000 miles apart, or fifty-six astronomical
units. On examining these stereoscopically, some of the stars rise out
of the general plane of the stars, and seem to be much nearer. Many of
the stars are thus seen to be suspended in space at different
distances corresponding exactly to their real distances from our solar
system, except when their proper motion interferes. The effect is most
striking; the accuracy of measurement exceeds that of any other method
of measuring such displacements, and it seems that with a long
interval of time the advantage of the method increases.
_Double Stars._--The large class of double stars has always been much
studied by amateurs, partly for their beauty and colour, and partly as
a test for telescopic definition. Among the many unexplained stellar
problems there is one noticed in double stars that is thought by some
to be likely to throw light on stellar evolution. It is this: There
are many instances where one star of the pair is comparatively faint,
and the two stars are contrasted in colour; and in every single case
the general colour of the faint companion is invariably to be classed
with colours more near to the blue end of the spectrum than that of
the principal star.
_Binary Stars._--Sir William Herschel began his observations of double
stars in the hope of discovering an annual parallax of the stars. In
this he was following a suggestion of Galileo's. The presumption is
that, if there be no physical connection between the stars of a pair,
the largest is the nearest, and has the greatest parallax. So, by
noting the distance between the pair at different times of the year, a
delicate test of parallax is provided, unaffected by major
instrumental errors.
Herschel did, indeed, discover changes of distance, but not of the
character to indicate parallax. Following this by further observation,
he found that the motions were not uniform nor rectilinear, and by a
clear analysis of the movements he established the remarkable and
wholly unexpected fact that in all these cases the motion is due to a
revolution about their common centre of gravity.[11] He gave the
approximate period of revolution of some of these: Castor, 342 years;
delta Serpentis, 375 years; gamma Leonis, 1,200 years; epsilon Bootis,
1,681 years.
Twenty years later Sir John Herschel and Sir James South, after
re-examination of these stars, confirmed[12] and extended the results,
one pair of Coronae having in the interval completed more than a whole
revolution.
It is, then, to Sir William Herschel that we owe the extension of the
law of gravitation, beyond the limits of the solar system, to the
whole universe. His observations were confirmed by F.G.W. Struve (born
1793, died 1864), who carried on the work at Dorpat. But it was first
to Savary,[13] and later to Encke and Sir John Herschel, that we owe
the computation of the elliptic elements of these stars; also the
resulting identification of their law of force with Newton's force of
gravitation applied to the solar system, and the force that makes an
apple fall to the ground. As Grant well says in his _History_:
"This may be justly asserted to be one of the most sublime truths
which astronomical science has hitherto disclosed to the researches of
the human mind."
Latterly the best work on double stars has been done by
S. W. Burnham,[14] at the Lick Observatory. The shortest period he
found was eleven years (kappa Pegasi). In the case of some of
these binaries the parallax has been measured, from which it appears
that in four of the surest cases the orbits are about the size of the
orbit of Uranus, these being probably among the smallest stellar
orbits.
The law of gravitation having been proved to extend to the stars, a
discovery (like that of Neptune in its origin, though unlike it in the
labour and originality involved in the calculation) that entrances the
imagination became possible, and was realised by Bessel--the discovery
of an unknown body by its gravitational disturbance on one that was
visible. In 1834 and 1840 he began to suspect a want of uniformity in
the proper motion of Sirius and Procyon respectively. In 1844, in a
letter to Sir John Herschel,[15] he attributed these irregularities in
each case to the attraction of an invisible companion, the period of
revolution of Sirius being about half a century. Later he said: "I
adhere to the conviction that Procyon and Sirius form real binary
systems, consisting of a visible and an invisible star. There is no
reason to suppose luminosity an essential quality of cosmical
bodies. The visibility of countless stars is no argument against the
invisibility of countless others." This grand conception led Peters to
compute more accurately the orbit, and to assign the place of the
invisible companion of Sirius. In 1862 Alvan G. Clark was testing a
new 18-inch object-glass (now at Chicago) upon Sirius, and, knowing
nothing of these predictions, actually found the companion in the very
place assigned to it. In 1896 the companion of Procyon was discovered
by Professor Schaeberle at the Lick Observatory.
Now, by the refined parallax determinations of Gill at the Cape, we
know that of Sirius to be 0".38. From this it has been calculated that
the mass of Sirius equals two of our suns, and its intrinsic
brightness equals twenty suns; but the companion, having a mass equal
to our sun, has only a five-hundredth part of the sun's brightness.
_Spectroscopic Binaries_.--On measuring the velocity of a star in the
line of sight at frequent intervals, periodic variations have been
found, leading to a belief in motion round an invisible
companion. Vogel, in 1889, discovered this in the case of Spica (alpha
Virginis), whose period is 4d. 0h. 19m., and the diameter of whose
orbit is six million miles. Great numbers of binaries of this type
have since then been discovered, all of short period.
Also, in 1889, Pickering found that at regular intervals of fifty-two
days the lines in the spectrum of zeta of the Great Bear are
duplicated, indicating a relative velocity, equal to one hundred miles
a second, of two components revolving round each other, of which that
apparently single star must be composed.
It would be interesting, no doubt, to follow in detail the
accumulating knowledge about the distances, proper motions, and orbits
of the stars; but this must be done elsewhere. Enough has been said to
show how results are accumulating which must in time unfold to us the
various stellar systems and their mutual relationships.
_Variable Stars._--It has often happened in the history of different
branches of physical science that observation and experiment were so
far ahead of theory that hopeless confusion appeared to reign; and
then one chance result has given a clue, and from that time all
differences and difficulties in the previous researches have stood
forth as natural consequences, explaining one another in a rational
sequence. So we find parallax, proper motion, double stars, binary
systems, variable stars, and new stars all bound together.
The logical and necessary explanation given of the cause of ordinary
spectroscopic binaries, and of irregular proper motions of Sirius and
Procyon, leads to the inference that if ever the plane of such a
binary orbit were edge-on to us there ought to be an eclipse of the
luminous partner whenever the non-luminous one is interposed between
us. This should give rise either to intermittence in the star's light
or else to variability. It was by supposing the existence of a dark
companion to Algol that its discoverer, Goodricke of York,[16] in
1783, explained variable stars of this type. Algol (beta Persei)
completes the period of variable brightness in 68.8 hours. It loses
three-fifths of its light, and regains it in twelve hours. In 1889
Vogel,[17] with the Potsdam spectrograph, actually found that the
luminous star is receding before each eclipse, and approaching us
after each eclipse; thus entirely supporting Goodricke's opinion.
There are many variables of the Algol type, and information is
steadily accumulating. But all variable stars do not suffer the sudden
variations of Algol. There are many types, and the explanations of
others have not proved so easy.
The Harvard College photographs have disclosed the very great
prevalence of variability, and this is certainly one of the lines in
which modern discovery must progress.
Roberts, in South Africa, has done splendid work on the periods of
variables of the Algol type.
_New Stars_.--Extreme instances of variable stars are the new stars
such as those detected by Hipparchus, Tycho Brahe, and Kepler, of
which many have been found in the last half-century. One of the latest
great "Novae" was discovered in Auriga by a Scotsman, Dr. Anderson, on
February 1st, 1892, and, with the modesty of his race, he communicated
the fact to His Majesty's Astronomer for Scotland on an unsigned
post-card.[18] Its spectrum was observed and photographed by Huggins
and many others. It was full of bright lines of hydrogen, calcium,
helium, and others not identified. The astounding fact was that lines
were shown in pairs, bright and dark, on a faint continuous spectrum,
indicating apparently that a dark body approaching us at the rate of
550 miles a second[19] was traversing a cold nebulous atmosphere, and
was heated to incandescence by friction, like a meteor in our
atmosphere, leaving a luminous train behind it. It almost disappeared,
and on April 26th it was of the sixteenth magnitude; but on August
17th it brightened to the tenth, showing the principal nebular band in
its spectrum, and no sign of approach or recession. It was as if it
emerged from one part of the nebula, cooled down, and rushed through
another part of the nebula, rendering the nebular gas more luminous
than itself.[20]
Since 1892 one Nova after another has shown a spectrum as described
above, like a meteor rushing towards us and leaving a train behind,
for this seems to be the obvious meaning of the spectra.
The same may be said of the brilliant Nova Persei, brighter at its
best than Capella, and discovered also by Dr. Anderson on February
22nd, 1901. It increased in brightness as it reached the densest part
of the nebula, then it varied for some weeks by a couple of
magnitudes, up and down, as if passing through separate nebular
condensations. In February, 1902, it could still be seen with an
opera-glass. As with the other Novae, when it first dashed into the
nebula it was vaporised and gave a continuous spectrum with dark lines
of hydrogen and helium. It showed no bright lines paired with the dark
ones to indicate a train left behind; but in the end its own
luminosity died out, and the nebular spectrum predominated.
The nebular illumination as seen in photographs, taken from August to
November, seemed to spread out slowly in a gradually increasing circle
at the rate of 90" in forty-eight days. Kapteyn put this down to the
velocity of light, the original outburst sending its illumination to
the nebulous gas and illuminating a spherical shell whose radius
increased at the velocity of light. This supposition seems correct, in
which case it can easily be shown from the above figures that the
distance of this Nova was 300 light years.
_Star Catalogues._--Since the days of very accurate observations
numerous star-catalogues have been produced by individuals or by
observatories. Bradley's monumental work may be said to head the list.
Lacaille's, in the Southern hemisphere, was complementary. Then
Piazzi, Lalande, Groombridge, and Bessel were followed by Argelander
with his 324,000 stars, Rumker's Paramatta catalogue of the southern
hemisphere, and the frequent catalogues of national observatories.
Later the Astronomische Gesellschaft started their great catalogue,
the combined work of many observatories. Other southern ones were
Gould's at Cordova and Stone's at the Cape.
After this we have a new departure. Gill at the Cape, having the comet
1882.ii. all to himself in those latitudes, wished his friends in
Europe to see it, and employed a local photographer to strap his
camera to the observatory equatoreal, driven by clockwork, and
adjusted on the comet by the eye. The result with half-an-hour's
exposure was good, so he tried three hours. The result was such a
display of sharp star images that he resolved on the Cape Photographic
Durchmusterung, which after fourteen years, with Kapteyn's aid in
reducing, was completed. Meanwhile the brothers Henry, of Paris, were
engaged in going over Chacornac's zodiacal stars, and were about to
catalogue the Milky Way portion, a serious labour, when they saw
Gill's Comet photograph and conceived the idea of doing the rest of
their work by photography. Gill had previously written to Admiral
Mouchez, of the Paris Observatory, and explained to him his project
for charting the heavens photographically, by combining the work of
many observatories. This led Admiral Mouchez to support the brothers
Henry in their scheme.[21] Gill, having got his own photographic work
underway, suggested an international astrographic chart, the materials
for different zones to be supplied by observatories of all nations,
each equipped with similar photographic telescopes. At a conference in
Paris, 1887, this was decided on, the stars on the charts going down
to the fourteenth magnitude, and the catalogues to the eleventh.
[Illustration: GREAT COMET, Nov. 14TH, 1882. (Exposure 2hrs. 20m.) By
kind permission of Sir David Gill. From this photograph originated all
stellar chart-photography.]
This monumental work is nearing completion. The labour involved was
immense, and the highest skill was required for devising instruments
and methods to read off the star positions from the plates.
Then we have the Harvard College collection of photographic plates,
always being automatically added to; and their annex at Arequipa in
Peru.
Such catalogues vary in their degree of accuracy; and fundamental
catalogues of standard stars have been compiled. These require
extension, because the differential methods of the heliometer and the
camera cannot otherwise be made absolute.
The number of stars down to the fourteenth magnitude may be taken at
about 30,000,000; and that of all the stars visible in the greatest
modern telescopes is probably about 100,000,000.
_Nebulae and Star-clusters._--Our knowledge of nebulae really dates from
the time of W. Herschel. In his great sweeps of the heavens with his
giant telescopes he opened in this direction a new branch of
astronomy. At one time he held that all nebulae might be clusters of
innumerable minute stars at a great distance. Then he recognised the
different classes of nebulae, and became convinced that there is a
widely-diffused "shining fluid" in space, though many so-called nebulae
could be resolved by large telescopes into stars. He considered that
the Milky Way is a great star cluster, whose form may be conjectured
from numerous star-gaugings. He supposed that the compact "planetary
nebulae" might show a stage of evolution from the diffuse nebulae, and
that his classifications actually indicate various stages of
development. Such speculations, like those of the ancients about the
solar system, are apt to be harmful to true progress of knowledge
unless in the hands of the ablest mathematical physicists; and
Herschel violated their principles in other directions. But here his
speculations have attracted a great deal of attention, and, with
modifications, are accepted, at least as a working hypothesis, by a
fair number of people.
When Sir John Herschel had extended his father's researches into the
Southern Hemisphere he was also led to the belief that some nebulae
were a phosphorescent material spread through space like fog or mist.
Then his views were changed by the revelations due to the great
discoveries of Lord Rosse with his gigantic refractor,[22] when one
nebula after another was resolved into a cluster of minute stars. At
that time the opinion gained ground that with increase of telescopic
power this would prove to be the case with all nebulae.
In 1864 all doubt was dispelled by Huggins[23] in his first examination
of the spectrum of a nebula, and the subsequent extension of this
observation to other nebulae; thus providing a certain test which
increase in the size of telescopes could never have given. In 1864
Huggins found that all true nebulae give a spectrum of bright
lines. Three are due to hydrogen; two (discovered by Copeland) are
helium lines; others are unknown. Fifty-five lines have been
photographed in the spectrum of the Orion nebula. It seems to be
pretty certain that all true nebulae are gaseous, and show almost
exactly the same spectrum.
Other nebulae, and especially the white ones like that in Andromeda,
which have not yet been resolved into stars, show a continuous
spectrum; others are greenish and give no lines.
A great deal has to be done by the chemist before the astronomer can
be on sure ground in drawing conclusions from certain portions of his
spectroscopic evidence.
The light of the nebulas is remarkably actinic, so that photography
has a specially fine field in revealing details imperceptible in the
telescope. In 1885 the brothers Henry photographed, round the star
Maia in the Pleiades, a spiral nebula 3' long, as bright on the plate
as that star itself, but quite invisible in the telescope; and an
exposure of four hours revealed other new nebula in the same
district. That painstaking and most careful observer, Barnard, with
101/4 hours' exposure, extended this nebulosity for several degrees,
and discovered to the north of the Pleiades a huge diffuse nebulosity,
in a region almost destitute of stars. By establishing a 10-inch
instrument at an altitude of 6,000 feet, Barnard has revealed the wide
distribution of nebular matter in the constellation Scorpio over a
space of 4 deg. or 5 deg. square. Barnard asserts that the "nebular
hypothesis" would have been killed at its birth by a knowledge of
these photographs. Later he has used still more powerful instruments,
and extended his discoveries.
The association of stars with planetary nebulae, and the distribution
of nebulae in the heavens, especially in relation to the Milky Way, are
striking facts, which will certainly bear fruit when the time arrives
for discarding vague speculations, and learning to read the true
physical structure and history of the starry universe.
_Stellar Spectra._--When the spectroscope was first available for
stellar research, the leaders in this branch of astronomy were Huggins
and Father Secchi,[24] of Rome. The former began by devoting years of
work principally to the most accurate study of a few stars. The
latter devoted the years from 1863 to 1867 to a general survey of the
whole heavens, including 4,000 stars. He divided these into four
principal classes, which have been of the greatest service. Half of
his stars belonged to the first class, including Sirius, Vega,
Regulus, Altair. The characteristic feature of their spectra is the
strength and breadth of the hydrogen lines and the extreme faintness
of the metallic lines. This class of star is white to the eye, and
rich in ultra violet light.
The second class includes about three-eighths of his stars, including
Capella, Pollux, and Arcturus. These stars give a spectrum like that
of our sun, and appear yellowish to the eye.
The third class includes alpha Herculis, alpha Orionis (Betelgeux), Mira
Ceti, and about 500 red and variable stars. The spectrum has fluted
bands shaded from blue to red, and sharply defined at the more
refrangible edge.
The fourth class is a small one, containing no stars over fifth
magnitude, of which 152 Schjellerup, in Canes Venatici, is a good
example. This spectrum also has bands, but these are shaded on the
violet side and sharp on the red side. They are due to carbon in some
form. These stars are ruby red in the telescope.
It would appear, then, that all stars are suns with continuous
spectra, and the classes are differentiated by the character of the
absorbent vapours of their atmospheres.
It is very likely that, after the chemists have taught us how to
interpret all the varieties of spectrum, it will be possible to
ascribe the different spectrum-classes to different stages in the
life-history of every star. Already there are plenty of people ready
to lay down arbitrary assumptions about the lessons to be drawn from
stellar spectra. Some say that they know with certainty that each star
begins by being a nebula, and is condensed and heated by condensation
until it begins to shine as a star; that it attains a climax of
temperature, then cools down, and eventually becomes extinct. They go
so far as to declare that they know what class of spectrum belongs to
each stage of a star's life, and how to distinguish between one that
is increasing and another that is decreasing in temperature.
The more cautious astronomers believe that chemistry is not
sufficiently advanced to justify all of these deductions; that, until
chemists have settled the lately raised question of the transmutation
of elements, no theory can be sure. It is also held that until they
have explained, without room for doubt, the reasons for the presence
of some lines, and the absence of others, of any element in a stellar
spectrum; why the arc-spectrum of each element differs from its spark
spectrum; what are all the various changes produced in the spectrum of
a gas by all possible concomitant variations of pressure and
temperature; also the meanings of all the flutings in the spectra of
metalloids and compounds; and other equally pertinent matters--until
that time arrives the part to be played by the astronomer is one of
observation. By all means, they say, make use of "working hypotheses"
to add an interest to years of laborious research, and to serve as a
guide to the direction of further labours; but be sure not to fall
into the error of calling any mere hypothesis a theory.
_Nebular Hypothesis._--The Nebular Hypothesis, which was first, as it
were, tentatively put forward by Laplace as a note in his _Systeme du
Monde_, supposes the solar system to have been a flat, disk-shaped
nebula at a high temperature in rapid rotation. In cooling it
condensed, leaving revolving rings at different distances from the
centre. These themselves were supposed to condense into the nucleus
for a rotating planet, which might, in contracting, again throw off
rings to form satellites. The speculation can be put in a really
attractive form, but is in direct opposition to many of the actual
facts; and so long as it is not favoured by those who wish to maintain
the position of astronomy as the most exact of the sciences--exact in
its facts, exact in its logic--this speculation must be recorded by
the historian, only as he records the guesses of the ancient Greeks--as
an interesting phase in the history of human thought.
Other hypotheses, having the same end in view, are the meteoritic
hypothesis of Lockyer and the planetesimal hypothesis that has been
largely developed in the United States. These can best be read in the
original papers to various journals, references to which may be found
in the footnotes of Miss Clerke's _History of Astronomy during the
Nineteenth Century_. The same can be said of Bredichin's hypothesis of
comets' tails, Arrhenius's book on the applications of the theory of
light repulsion, the speculations on radium, the origin of the sun's
heat and the age of the earth, the electron hypothesis of terrestrial
magnetism, and a host of similar speculations, all combining to throw
an interesting light on the evolution of a modern train of thought
that seems to delight in conjecture, while rebelling against that
strict mathematical logic which has crowned astronomy as the queen of
the sciences.
FOOTNOTES:
[1] _R. S. Phil Trans_., 1810 and 1817-24.
[2] One of the most valuable contributions to our knowledge of stellar
parallaxes is the result of Gill's work (_Cape Results_, vol. iii.,
part ii., 1900).
[3] Taking the velocity of light at 186,000 miles a second, and the
earth's mean distance at 93,000,000 miles, 1 light year=5,865,696,000,000
miles or 63,072 astronomical units; 1 astronomical unit a year=2.94
miles a second; and the earth's orbital velocity=18.5 miles a second.
[4] Ast. Nacht., 1889.
[5] R. S. Phil. Trans., 1718.
[6] Mem. Acad. des Sciences, 1738, p. 337.
[7] R. S Phil. Trans., 1868.
[8] _R.S. Phil Trans._, 1783.
[9] See Kapteyn's address to the Royal Institution, 1908. Also Gill's
presidential address to the British Association, 1907.
[10] _Brit. Assoc. Rep._, 1905.
[11] R. S. Phil. Trans., 1803, 1804.
[12] Ibid, 1824.
[13] Connaisance des Temps, 1830.
[14] _R. A. S. Mem._, vol. xlvii., p. 178; _Ast. Nach._, No. 3,142;
Catalogue published by Lick Observatory, 1901.
[15] _R. A. S., M. N._, vol. vi.
[16] _R. S. Phil. Trans._, vol. lxxiii., p. 484.
[17] _Astr. Nach._, No. 2,947.
[18] _R. S. E. Trans_., vol. xxvii. In 1901 Dr. Anderson discovered
Nova Persei.
[19] _Astr. Nach_., No. 3,079.
[20] For a different explanation see Sir W. Huggins's lecture, Royal
Institution, May 13th, 1892.
[21] For the early history of the proposals for photographic
cataloguing of stars, see the _Cape Photographic Durchmusterung_, 3
vols. (_Ann. of the Cape Observatory_, vols. in., iv., and v.,
Introduction.)
[22] _R. S. Phil. Trans._, 1850, p. 499 _et seq._
[23] _Ibid_, vol. cliv., p. 437.
[24] _Brit. Assoc. Rep._, 1868, p. 165.
INDEX
Abul Wefa, 24
Acceleration of moon's mean motion, 60
Achromatic lens invented, 88
Adams, J. C., 61, 65, 68, 69, 70, 87, 118, 124
Airy, G. B., 13, 30, 37, 65, 69, 70, 80, 81, 114, 119
Albetegnius, 24
Alphonso, 24
Altazimuth, 81
Anaxagoras, 14, 16
Anaximander, 14
Anaximenes, 14
Anderson, T. D., 137, 138
Angstrom, A. J., 102
Antoniadi, 113
Apian, P., 63
Apollonius, 22, 23
Arago, 111
Argelander, F. W. A., 139
Aristarchus, 18, 29
Aristillus, 17, 19
Aristotle, 16, 30, 47
Arrhenius, 146
Arzachel, 24
Asshurbanapal, 12
Asteroids, discovery of, 67, 119
Astrology, ancient and modern, 1-7, 38
Backlund, 122
Bacon, R., 86
Bailly, 8, 65
Barnard, E. E., 115, 143
Beer and Maedler, 107, 110, 111
Behaim, 74
Bessel, F.W., 65, 79, 128, 134, 139
Biela, 123
Binet, 65
Biot, 10
Bird, 79, 80
Bliss, 80
Bode, 66, 69
Bond, G. P., 99, 117, 122
Bouvard, A., 65, 68
Bradley, J., 79, 80, 81, 87, 127, 128, 139
Bredechin, 146
Bremiker, 71
Brewster, D., 52, 91, 112
Brinkley, 128
Bruno, G., 49
Burchardt, 65, 123
Burnham, S. W., 134
Callippus, 15, 16, 31
Carrington, R. C., 97, 99, 114
Cassini, G. D., 107, 114, 115, 116, 117, 118
Cassini, J., 109, 129
Chacornac, 139
Chaldaean astronomy, 11-13
Challis, J., 69, 70, 71, 72
Chance, 88
Charles, II., 50, 81
Chinese astronomy, 8-11
Christie, W. M. H. (Ast. Roy.), 64, 82, 125
Chueni, 9
Clairaut, A. C., 56, 63, 65
Clark, A. G., 89, 135
Clerke, Miss, 106, 146
Comets, 120
Common, A. A., 88
Cooke, 89
Copeland, R., 142
Copernicus, N., 14, 24-31, 37, 38, 41, 42, 49, 128
Cornu, 85
Cowell, P. H., 3, 5, 64, 83
Crawford, Earl of, 84
Cromellin, A. C., 5, 64
D'Alembert, 65
Damoiseau, 65
D'Arrest, H. L., 34
Dawes, W. R., 100, 111
Delambre, J. B. J., 8, 27, 51, 65, 68
De la Rue, W., 2, 94, 99, 100, 131
Delaunay, 65
Democritus, 16
Descartes, 51
De Sejour, 117
Deslandres, II., 101
Desvignolles, 9
De Zach, 67
Digges, L., 86
Dollond, J., 87, 90
Dominis, A. di., 86
Donati, 120
Doppler, 92, 129
Draper, 99
Dreyer, J. L. E., 29,77
Dunthorne, 60
Dyson, 131
Eclipses, total solar, 103
Ecphantes, 16
Eddington, 131
Ellipse, 41
Empedocles, 16
Encke, J. F., 119, 122, 123, 133
Epicycles, 22
Eratosthenes, 18
Euclid, 17
Eudoxus, 15, 31
Euler, L., 60, 61, 62, 65, 88, 119
Fabricius, D.,95, 120, 121
Feil and Mantois, 88
Fizeau, H. L., 85, 92, 99
Flamsteed, J., 50, 58, 68, 78, 79, 93
Fohi, 8
Forbes, J. D., 52, 91
Foucault, L., 85, 99
Frauenhofer, J., 88, 90, 91
Galilei, G., 38, 46-49, 77, 93, 94, 95, 96, 107, 113, 115, 116, 133
Galle, 71, 72
Gascoigne, W., 45, 77
Gauss, C. F., 65, 67
Gauthier, 98
Gautier, 89
Gilbert, 44
Gill, D., 84, 85, 128, 135, 139, 140
Goodricke, J., 136
Gould, B. A., 139
Grant, R., 27, 47, 51, 86, 134
Graham, 79
Greek astronomy, 8-11
Gregory, J. and D., 87
Grimaldi, 113
Groombridge, S., 139
Grubb, 88, 89
Guillemin, 122
Guinand, 88
Hale, G. E., 101
Hall, A., 112
Hall, C. M., 88
Halley, E., 19, 51, 58, 60, 61, 62, 63, 64, 79, 120, 122, 125, 129
Halley's comet, 62-64
Halm, 85
Hansen, P. A., 3, 65
Hansky, A. P., 100
Harding, C. L., 67
Heliometer, 83
Heller, 120
Helmholtz, H. L. F., 35
Henderson, T., 128
Henry, P. and P., 139, 140, 143
Heraclides, 16
Heraclitus, 14
Herodotus, 13
Herschel, W., 65, 68, 97, 107, 110, 114, 115, 116, 117, 118, 126, 127,
130, 131, 132, 141, 142
Herschel, J., 97, 111, 133, 134, 142
Herschel, A. S., 125
Hevelius, J., 178
Hind, J. R., 5, 64, 120, 121, 122
Hipparchus, 3, 18, 19, 20, 22, 23, 24, 26, 36, 55, 60, 74, 93, 137
Hooke, R., 51, 111, 114
Horrocks, J., 50, 56
Howlett, 100
Huggins, W., 92, 93, 99, 106, 120, 129, 137, 138, 142, 144
Humboldt and Bonpland, 124
Huyghens, C., 47, 77, 87, 110, 116, 117
Ivory, 65
Jansen, P. J. C., 105, 106
Jansen, Z., 86
Kaiser, F., 111
Kapteyn, J. C., 131, 138, 139
Keeler, 117
Kepler, J., 17, 23, 26, 29, 30, 36, 37, 38-46, 48, 49, 50, 52, 53, 63,
66, 77, 87, 93, 127, 137
Kepler's laws, 42
Kirchoff, G.R., 91
Kirsch, 9
Knobel, E.B., 12, 13
Ko-Show-King, 76
Lacaile, N.L., 139
Lagrange, J.L., 61, 62, 65, 119
La Hire, 114
Lalande, J.J.L., 60, 63, 65, 66, 72, 139
Lamont, J., 98
Langrenus, 107
Laplace, P.S. de, 50, 58, 61, 62, 65,66, 123, 146
Lassel, 72, 88, 117, 118
Law of universal gravitation, 53
Legendre, 65
Leonardo da Vinci, 46
Lewis, G.C., 17
Le Verrier, U.J.J., 65, 68, 70, 71,72, 110, 118, 125
Lexell, 66, 123
Light year, 128
Lipperhey, H., 86
Littrow, 121
Lockyer, J.N., 103, 105, 146
Logarithms invented, 50
Loewy, 2, 100
Long inequality of Jupiter and Saturn, 50, 62
Lowell, P., 111, 112, 118
Lubienietz, S. de, 122
Luther, M., 38
Lunar theory, 37, 50, 56, 64
Maclaurin, 65
Maclear, T., 128
Malvasia, 77
Martin, 9
Maxwell, J. Clerk, 117
Maskelyne, N., 80, 130
McLean, F., 89
Medici, Cosmo di, 48
Melancthon, 38
Melotte, 83, 116
Meteors, 123
Meton, 15
Meyer, 57, 65
Michaelson, 85
Miraldi, 110, 114
Molyneux, 87
Moon, physical observations, 107
Mouchez, 139
Moyriac de Mailla, 8
Napier, Lord, 50
Nasmyth and Carpenter, 108
Nebulae, 141, 146
Neison, E., 108
Neptune, discovery of, 68-72
Newall, 89
Newcomb, 85
Newton, H.A., 124
Newton, I., 5, 19, 43, 49, 51-60, 62, 64, 68, 77, 79, 87, 90, 93, 94,
114, 127, 133
Nicetas, 16, 25
Niesten, 115
Nunez, P., 35
Olbers, H.W.M., 67
Omar, 11, 24
Oppolzer, 13, 125
Oudemans, 129
Palitsch, G., 64
Parallax, solar, 85, 86
Parmenides, 14
Paul III., 30
Paul V., 48
Pemberton, 51
Peters, C.A.F., 125, 128, 135
Photography, 99
Piazzi, G., 67, 128, 129, 139
Picard, 54, 77, 114
Pickering, E.C., 118, 135
Pingre, 13, 122
Plana, 65
Planets and satellites, physical observations, 109-119
Plato, 17, 23, 26, 40
Poisson, 65
Pond, J., 80
Pons, 122
Porta, B., 86
Pound, 87, 114
Pontecoulant, 64
Precession of the equinoxes, 19-21, 55, 57
Proctor, R.A., 111
Pritchett, 115
Ptolemy, 11, 13, 21, 22, 23, 24, 93
Puiseux and Loewy, 108
Pulfrich, 131
Purbach, G., 24
Pythagoras, 14, 17, 25, 29
Ramsay, W., 106
Ransome and May, 81
Reflecting telescopes invented, 87
Regiomontanus (Mueller), 24
Respighi, 82
Retrograde motion of planets, 22
Riccioli, 107
Roberts, 137
Roemer, O.,78, 114
Rosse, Earl of, 88, 142
Rowland, H. A., 92, 102
Rudolph H.,37, 39
Rumker, C., 139
Sabine, E., 98
Savary, 133
Schaeberle, J. M., 135
Schiaparelli, G. V., 110, 111, 124, 125
Scheiner, C., 87, 95, 96
Schmidt, 108
Schott, 88
Schroeter, J. H., 107, 110, 111, 124, 125
Schuster, 98
Schwabe, G. H., 97
Secchi, A., 93, 144
Short, 87
Simms, J., 81
Slipher, V. M., 119
Socrates, 17
Solon, 15
Souciet, 8
South, J., 133
Spectroscope, 89-92
Spectroheliograph, 101
Spoerer, G. F. W., 98
Spots on the sun, 84;
periodicity of, 97
Stars, Parallax, 127;
proper motion, 129;
double, 132;
binaries, 132, 135;
new, 19, 36, 137;
catalogues of, 19, 36, 139;
spectra of, 143
Stewart, B., 2, 100
Stokes, G. G., 91
Stone, E. J., 139
Struve, C. L., 130
Struve, F. G. W,, 88, 115, 128, 133
Telescopes invented, 47, 86;
large, 88
Temple, 115, 125
Thales, 13, 16
Theon, 60
Transit circle of Roemer, 78
Timocharis, 17, 19
Titius, 66
Torricelli, 113
Troughton, E., 80
Tupman, G. L., 120
Tuttle, 125
Tycho Brahe, 23, 25, 30, 33-38, 39, 40, 44, 50, 75, 77, 93, 94, 129, 137
Ulugh Begh, 24
Uranus, discovery of, 65
Velocity of light, 86, 128;
of earth in orbit, 128
Verbiest, 75
Vogel, H. C., 92, 129, 135, 136
Von Asten, 122
Walmsley, 65
Walterus, B., 24, 74
Weiss, E., 125
Wells, 122
Wesley, 104
Whewell, 112
Williams, 10
Wilson, A., 96, 100
Winnecke, 120
Witte, 86
Wollaston, 90
Wolf, M., 119, 125, 132
Wolf, R., 98
Wren, C., 51
Wyllie, A., 77
Yao, 9
Young, C. A., 103
Yu-Chi, 8
Zenith telescopes, 79, 82
Zoellner, 92
Zucchi, 113
End of the Project Gutenberg EBook of History of Astronomy, by George Forbes
***
|
{
"redpajama_set_name": "RedPajamaBook"
}
| 14
|
package org.glassfish.jaxb.runtime.v2.runtime.reflect;
import org.glassfish.jaxb.runtime.api.AccessorException;
import org.glassfish.jaxb.runtime.v2.runtime.XMLSerializer;
/**
* {@link Lister} for primitive type arrays.
*
* <p>
* B y t e ArrayLister is used as the master to generate the rest of the
* lister classes. Do not modify the generated copies.
*/
final class PrimitiveArrayListerByte<BeanT> extends Lister<BeanT,byte[],Byte,PrimitiveArrayListerByte.ByteArrayPack> {
private PrimitiveArrayListerByte() {
}
/*package*/ static void register() {
primitiveArrayListers.put(Byte.TYPE,new PrimitiveArrayListerByte());
}
@Override
public ListIterator<Byte> iterator(final byte[] objects, XMLSerializer context) {
return new ListIterator<>() {
int idx = 0;
@Override
public boolean hasNext() {
return idx < objects.length;
}
@Override
public Byte next() {
return objects[idx++];
}
};
}
@Override
public ByteArrayPack startPacking(BeanT current, Accessor<BeanT, byte[]> acc) {
return new ByteArrayPack();
}
@Override
public void addToPack(ByteArrayPack objects, Byte o) {
objects.add(o);
}
@Override
public void endPacking( ByteArrayPack pack, BeanT bean, Accessor<BeanT,byte[]> acc ) throws AccessorException {
acc.set(bean,pack.build());
}
@Override
public void reset(BeanT o,Accessor<BeanT,byte[]> acc) throws AccessorException {
acc.set(o,new byte[0]);
}
static final class ByteArrayPack {
byte[] buf = new byte[16];
int size;
void add(Byte b) {
if(buf.length==size) {
// realloc
byte[] nb = new byte[buf.length*2];
System.arraycopy(buf,0,nb,0,buf.length);
buf = nb;
}
if(b!=null)
buf[size++] = b;
}
byte[] build() {
if(buf.length==size)
// if we are lucky enough
return buf;
byte[] r = new byte[size];
System.arraycopy(buf,0,r,0,size);
return r;
}
}
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 8,671
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Downtown Records LLC é uma gravadora estadunidense. Downtown foi fundada em Janeiro de 2006 por Josh Deutsch, ex-Vice-Presidente de A&R na Virgin Records. A música no selo Downtown é distribuída pela Alternative Distribution Alliance da Warner Music e através da América do Norte em uma joint venture com a Atlantic Records.
Artistas Atualmente no Selo
Art Brut
Cyndi Lauper
Cold War Kids
Eagles of Death Metal
Gnarls Barkley
Kevin Michael
Wax On Radio
Mos Def
Ligações externas
Página Oficial da Downtown Records
Gravadoras dos Estados Unidos
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 6,487
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Alt-J at Benedum Center Pittsburgh
Mathematically speaking, Alt-J means 'to change'. And they've been doing just that in the realm of music. Alt-J continually blazes new and experimental trails that only a selected few or maybe no one has dared to tread before. From the confines of their college dorms and garage studios, they crafted a potent mixture of electro pop, dance, and indie rock sensibilities, which they unleashed through albums that earned a new generation of fans among indie aficionados. Now they're taking their innovative sound on the road and on to the live stage. Check out Alt-J as they hit the stage of the Benedum Center on Thursday 2nd April 2015. Fans from all over will definitely storm the gates. The easy way to get in is to get hold of those precious tickets, now, before it's too late!
From the confines of their college dorms in 2007, bassist Gwil Sainsbury, vocalist and guitarist Joe Newman, percussionist Thom Green and keyboardist Gus Unger-Hailton formed a band of what they're now known today, Alt-J. After graduating from college, they released their debut album "An Awesome Wave", released in May 2012 in Europe and September 2012 in the United States. Much to their surprise, this album also brought home the award 2012 British Mercury Prize. In 2014, their sophomore album "This Is All Yours", was released on the 22nd of September and went straight to number 1 in the UK charts.
Touring and festivals contributed much to the band's success. They quickly built a cult following, following them around festival stages all across Great Britain and Ireland. And soon enough, their fan base swelled into massive proportions, reaching beyond the transatlantic ocean. The inevitable next stop were the shores of North America. They spent almost all of 2013 touring around the American continent, which included milestone performances at legendary festivals such as Chicago's Lollapalooza, California's Coachella Music and Arts Festival, San Diego's Wrex the Hall, and Washington state's Sasquatch! festival. And in-between, they managed to gain critical acclaim and bagged several prestigious awards such as numerous Brit Awards, Album of the Year from BBC Radio 6, and another Album of the year win from the Ivor Novello Awards.
Alt-J truly lives up to it's name, or rather its Mathematical symbolism. Their sound is continuously evolving, their concerts are consistently jam-packed due to their growing fan-base. There are no signs of them slowing down. Well, that's your cue. Tickets to their Benedum Center show on Thursday 2nd April 2015 are definitely moving fast. So get on the move and buy your tickets now!
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 9,588
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\section{Introduction}\label{sec1}
In the recent two decades, the study of cosmology has entered the era of precision cosmology. A standard model of cosmology has been established, usually called the $\Lambda$ cold dark matter ($\Lambda$CDM) model. The measurements of cosmic microwave background (CMB) anisotropies from the Planck satellite mission have constrained the six primary parameters of the $\Lambda$CDM model with unprecedented precision. However, with the measurement precisions of the cosmological parameters improved, some puzzling issues appeared. For example, the inferred values of the Hubble constant from the Planck observation of the CMB anisotropies (based on the $\Lambda$CDM model) \cite{Planck:2018vyg} and from the Cepheid-supernova distance ladder measurement \cite{Riess:2019cxk} are inconsistent, with the tension between them more than 4$\sigma$ significance \cite{Riess:2019cxk}.
Namely, there is an inconsistency of measurements between the early and late universe, which is the so-called ``Hubble tension'' problem. The Hubble tension recently has been widely discussed in the literature (see, e.g., Refs.~\cite{Riess:2019qba,Verde:2019ivm,Li:2013dha,Zhang:2014dxk,Gao:2021xnk,cai:2020,Cai:2021wgv,Zhao:2017urm,Guo:2018ans,Guo:2019dui,Yang:2018euj,Vagnozzi:2019ezj,DiValentino:2019jae,DiValentino:2019ffd,Liu:2019awo,Zhang:2019cww,Ding:2019mmw,Feng:2019jqa,Lin:2020jcb,Xu:2020uws,Li:2020tds,Hryczuk:2020jhi,Wang:2021kxc,Vagnozzi:2021tjv,Vagnozzi:2021gjh,DiValentino:2021izs}).
Furthermore, theoretically, for the $\Lambda$CDM model, the cosmological constant $\Lambda$, which is equivalent to the density of vacuum energy, has always been suffering from serious theoretical challenges, such as the ``fine-tuning'' and ``cosmic coincidence'' problems \cite{Sahni:1999gb,Bean:2005ru}. Thus, it is hard to say that the $\Lambda$CDM model with only six base parameters is the eventual model of cosmology. All of these facts actually imply that the $\Lambda$CDM model needs to be further extended and some extra parameters concerning new physics need to be introduced into the new models. Of course, some novel cosmological probes should also be further developed.
To extend the $\Lambda$CDM cosmology, the primary idea is to consider the dynamical dark energy with the dark-energy density no longer a constant. In this class of models,
the simplest one is the model with a dark energy having a constant equation-of-state (EoS) parameter, $w=p_{\rm de} / \rho_{\rm de}=$ constant, which is usually called the $w$CDM model.
For some popular dark energy models, see, e.g., Refs.~\cite{Chevallier:2000qy,Linder:2002et,Huterer:2000mj,Wetterich:2004pv,Jassal:2004ej,Upadhye:2004hh,Xia:2004rw,Zhang:2005yz,Zhang:2005hs,Zhang:2006qu,Linder:2006sv,Zhang:2007sh,Lazkoz:2010gz,Ma:2011nc,Li:2011dr,Li:2012vn,Li:2012via}. There is also a class of models known as the interacting dark energy (IDE) models in which some direct, non-gravitational interaction between dark energy and dark matter is considered.
The interaction between dark sectors could help resolve (or alleviate) the coincidence problem of dark energy, and also can help alleviate the Hubble tension. The IDE models have been widely studied and deeply explored till now (see, e.g., Refs.~\cite{Amendola:1999er,Amendola:1999qq,Tocchini-Valentini:2001wmi,Amendola:2001rc,Comelli:2003cv,Chimento:2003iea,Cai:2004dk,Zhang:2004gc,Ferrer:2004nv,Zhang:2005rj,Sadjadi:2006qp,Barrow:2006hia,Sasaki:2006kq,Abdalla:2007rd,Bean:2007ny,Guo:2007zk,Zhang:2009un,Caldera-Cabral:2009hoy,Valiviita:2009nu,He:2009mz,Koyama:2009gd,Li:2009zs,Xia:2009zzb,Cai:2009ht,Li:2011ga,Zhang:2012uu,Xu:2013jma,Zhang:2013zyn,Wang:2013qy,Salvatelli:2013wra,Yang:2014okp,Wang:2014oga,Faraoni:2014vra,Fan:2015rha,Yang:2015tzc,Duniya:2015nva,Murgia:2016ccp,Costa:2016tpb,Xia:2016vnp,Guo:2017hea,Zhang:2017ize,Feng:2018yew,Yang:2018euj,Guo:2018ans,Zhao:2018fjj,Feng:2019mym,Li:2019loh,Li:2020gtk}).
Currently, the mainstream cosmological probes mainly include, e.g., the CMB anisotropies, baryon acoustic oscillations (BAO), type Ia supernovae (SN), direct determination of the Hubble constant ($H_{0}$), weak gravitational lensing, redshift space distortions, and clusters of galaxies. The combinations of these cosmological data based on the electromagnetic (EM) observations have provided precise measurements for the base cosmological parameters. But for some extended parameters beyond the standard $\Lambda$CDM model, e.g., the EoS parameter of dark energy, the tensor-to-scalar ratio, and the total mass of neutrinos, they still cannot be precisely measured. Therefore, on one hand, the EM observations should be further greatly developed, and on the other hand, some novel cosmological probes are also needed to be developed in the future. In the next few decades, the gravitational-wave (GW) standard siren observation is one of the most promising cosmological probes.
The detection of the GW event GW170817 \cite{LIGOScientific:2017vwq} from the binary neutron star (BNS) merger initiated the multi-messenger astronomy era. Because in this event, not only GWs but also the EM signals in various bands were detected for the same transient source \cite{LIGOScientific:2017zic,LIGOScientific:2017ync}. From the analysis of the waveform of GW, one can obtain the absolute luminosity distance to the source. Furthermore, the redshift of the source can also be determined by identifying the EM counterpart of the GW source. With the known distance and redshift of a celestial source, a distance--redshift relation can be established, which can be used to explore the expansion history of the universe \cite{Schutz:1986gp}. Such a tool of exploring the evolution of the universe provided by GWs is called ``standard sirens'' (note here that the case having EM counterparts is usually referred to as bright sirens, to be differentiated with the case of dark sirens without EM counterparts) \cite{Holz:2005df}.
The main advantage of the GW standard siren method is that the absolute luminosity distances can be measured. This is obviously superior to the SN observation, in that the latter can only measure the ratio of luminosity distances at different redshifts. In addition, the GW observation can observe much higher redshift events, compared to the SN observation.
It is indisputable that the GW standard siren will be developed into a powerful cosmological probe in the future. The third-generation (3G) ground-based GW detectors, such as the Einstein Telescope (ET) \cite{ET-web,Punturo:2010zz} in Europe and the Cosmic Explorer (CE) \cite{CE-web,Evans:2016mbw} in the United States, have been proposed. In the 2030s, ET will be brought into operation. CE will start its observation in the mid-2030s. The 3G ground-based GW detectors have a much wider detection-frequency range and a much better detection sensitivity, which can observe much more BNS events at much deeper redshifts. Recently, the GW standard sirens have been widely discussed in the literature \cite{Cai:2016sby,Cai:2017aea,Cai:2017plb,Zhang:2019ylr,Zhao:2018gwk,Du:2018tia,Yang:2019bpr,Yang:2019vni,Bachega:2019fki,Chang:2019xcb,He:2019dhl,Liu:2017xef,Berti:2018cxi,Liu:2018sia,Will:1994fb,Zhao:2019gyk,Wang:2021srv,Qi:2021iic,Jin:2021pcv,Buchmuller:2019gfy,Borhanian:2022czq,Colgain:2022xcz,Zhu:2021bpp,deSouza:2021xtg,Wang:2022oou,Jin:2022qnj,Wu:2022dgy} {(see Ref.~\cite{Bian:2021ini} for a recent review)}. It is found that the GW standard siren observations from ET and CE would play an important role in the cosmological parameter estimation \cite{Zhang:2019ple,Zhang:2018byx,Wang:2018lun,Zhang:2019loq,Li:2019ajo,Jin:2020hmc}.
In cosmology, neutrinos plays a crucial role in helping shape the large-scale structure and the expansion history of the universe.
The phenomenon of neutrino oscillation indicates that neutrinos have masses and there are mass splttings between different neutrino species. However, it is extremely difficult to measure the absolute masses of neutrinos. Neutrino oscillation experiments cannot measure the absolute neutrino masses, but can only give the squared
mass differences between the different mass eigenstates of neutrinos. The solar and reactor experiments give $\Delta m_{21}^{2} \simeq 7.5 \times 10^{-5}$ $\rm eV^{2}$ and the atmospheric and accelerator beam experiments give $|\Delta m_{31}^{2}| \simeq 2.5 \times 10^{-3}$ $\rm eV^{2}$ \cite{ParticleDataGroup:2014cgo,Xing:2020ijf}. Thus, there are two possible mass hierarchies of the neutrino mass spectrum, namely, the normal hierarchy (NH) with $m_{1} < m_{2} \ll m_{3}$ and the inverted hierarchy (IH) with $m_{3} \ll m_{1} < m_{2}$.
In addition, in some cases one also considers the cosmological models of neglecting the neutrino mass splittings, namely $m_1=m_2=m_3$, which is usually called the degenerate hierarchy (DH).
Although the neutrino masses can hardly be measured by particle physics experiments, they can be effectively constrained by the cosmological observations. This is because massive neutrinos can exert some impacts on the evolution of the universe. Using the current cosmological observations, an upper limit on the total neutrino mass $\sum m_\nu$ can be obtained. So far, the most stringent limit on the total neutrino mass comes from the Planck 2018 CMB observation, and the combination CMB+BAO+SN gives the $95\%$ CL upper limit $\sum m_\nu<0.12$ eV, for the DH case in the $\Lambda$CDM model. See e.g. Refs.~\cite{Hu:1997mj,Reid:2009nq,Thomas:2009ae,Carbone:2010ik,Huo:2011ve,Wang:2012vh,Li:2012spm,Audren:2012vy,Riemer-Sorensen:2013jsa,Font-Ribera:2013rwa,Zhang:2014nta,Zhang:2014ifa,Zhou:2014fva,Planck:2015fie,Zhang:2015rha,Geng:2015haa,Lu:2016hsd,Kumar:2016zpg,Xu:2016ddc,Vagnozzi:2017ovm,Zhang:2017rbg,Zhao:2017jma,Vagnozzi:2018jhn,Li:2017iur,Wang:2017htc,Feng:2017usu,Zhao:2016ecj,Zhang:2015uhk,Huang:2015wrx, Wang:2016tsz,Giusarma:2016phn,Allahverdi:2016fvl,Gariazzo:2018pei,RoyChoudhury:2018gay,Han:2017wnk,Zhang:2019ipd,DiazRivero:2019ukx,Zhang:2020mox} for studies on neutrino mass in cosmology.
In a recent forecast \cite{Wang:2018lun}, it was shown that the standard sirens observed by the ET can be used to improve the constraints on the total neutrino mass in the $\Lambda$CDM model. Using 1000 GW standard siren data points of the BNS merger events, it is found that the upper limits on $\sum m_\nu$ can be tightened by about $10\%$ \cite{Wang:2018lun}. However, weighing neutrinos in cosmology depends on the cosmological model considered, and thus one would be curious about whether the role the GW data play in helping measure the neutrino mass will change if an extension to the $\Lambda$CDM model is considered. In this work, we consider the IDE models, and we wish to see what will happen on measuring neutrino mass when the IDE models are considered.
In an IDE model, the energy conservation equations for dark energy and CDM satisfy
\begin{align}
&\dot{\rho}_{\mathrm{de}}=-3 H(1+w) \rho_{\mathrm{de}}+Q, \\
&\dot{\rho}_{\mathrm{c}}=-3 H \rho_{\mathrm{c}}-Q,
\end{align}
where $Q$ is the energy transfer rate, $\rho_{\rm de}$ and $\rho_c$ represent the energy densities of dark energy and CDM, respectively, $H$ is the Hubble parameter, and a dot represents the derivative with respect to the cosmic time $t$. In this work, we consider the interaction form of $Q=\beta H \rho_{\mathrm{c}}$, where $\beta$ is a dimensionless coupling parameter. Here, $\beta>0$ and $\beta<0$ means CDM decaying into dark energy and dark energy decaying into CDM, respectively.
In this work, we consider the IDE versions of the $\Lambda$CDM and $w$CDM models, which are called the I$\Lambda$CDM and I$w$CDM models. We will discuss the cosmological parameter estimation in the I$\Lambda$CDM+$\sum m_{\nu}$ and I$w$CDM+$\sum m_{\nu}$ models. Moreover, we will consider the three neutrino mass hierarchy cases, i.e., the NH, IH, DH cases. To avoid the perturbation divergence problem in the IDE models, in this work we employ the extended parameterized post-Friedmann (ePPF) framework \cite{Li:2014eha,Li:2014cee} to calculate the perturbations of dark energy.
We simulate the GW standard siren data observed by ET and CE, and we use these simulated GW data to investigate how well they can be used to improve the constraints on the neutrino mass as well as other cosmological parameters on the basis of the current CMB+BAO+SN constraints.
{The rest of this paper is organized as follows. In Sec.~\ref{sec2.1}, we introduce the methods of simulating the GW standard siren data. In Sec.~\ref{sec2.2} we describe the EM cosmological observations used in this work. In Sec.~\ref{sec2.3}, we briefly describe the methods of constraining cosmological parameters. In Sec.~\ref{sec3}, we give the constraint results and make some relevant discussions. The conclusion is given in Sec.~\ref{sec4}.}
\section{Method and data}\label{sec2}
In this section, we first introduce the method of simulating the GW standard siren data from ET and CE. Then, we describe the current mainstream EM cosmological observations used in this work. Finally, we briefly introduce the method of constraining cosmological parameters.
\subsection{Simulation of the GW standard sirens}\label{sec2.1}
{The primary GW sources in the detection frequency band of the ground-based GW detectors are the mergers of BNS, binary stellar-mass black hole (BBH), and so on. The BNS mergers could produce rich EM signals \cite{Li:1998bw} that can be detected by the EM observatories, thus enabling precise redshift measurements. Owing to the fact that there are no EM signals produced in the process of the BBH mergers, their redshifts could not be precisely measured through the detection of the EM counterparts. Hence, in this work, we only simulate the GW standard sirens from the BNS mergers.}
Following Refs.~\cite{Zhao:2010sz,Cai:2016sby}, the redshift distribution of the BNS mergers takes the form
\begin{equation}
P(z)\propto \frac{4\pi d_{\rm C}^2(z)R(z)}{H(z)(1+z)},
\label{equa:pz}
\end{equation}
where $d_{\rm C}(z)$ is the comoving distance at the redshift $z$, and $R(z)$ represents the redshift evolution of the burst rate, which takes the form \cite{Schneider:2000sg,Cutler:2009qv,Cai:2016sby}
\begin{equation}
R(z)=\begin{cases}
1+2z, & z\leq 1, \\
\frac{3}{4}(5-z), & 1<z<5, \\
0, & z\geq 5.
\end{cases}
\label{equa:rz}
\end{equation}
In Fig.~\ref{fig1}, we show the redshift distribution of BNS mergers.
\begin{figure}[!htp]
\includegraphics[width=8.6cm]{fig1.pdf}\ \hspace{1cm}
\centering \caption{\label{fig1} The redshift distribution of BNS mergers.}
\end{figure}
Considering the transverse-traceless gauge, the strain $h(t)$ in the GW interferometers can be described by two independent polarization amplitudes, $h_+(t)$ and $h_\times(t)$,
\begin{equation}
h(t)=F_+(\theta, \phi, \psi)h_+(t)+F_\times(\theta, \phi, \psi)h_\times(t),
\end{equation}
where $F_{+}$ and $F_{\times}$ are the antenna response functions, $\theta$ and $\phi$ describe the location of the GW source relative to the GW detector, and $\psi$ is the polarization angle.
The antenna response functions of ET are \cite{Zhao:2010sz}
\begin{align}
F_+^{(1)}(\theta, \phi, \psi)=&~~\frac{{\sqrt 3 }}{2}\bigg[\frac{1}{2}\big(1 + {\cos ^2}(\theta )\big)\cos (2\phi )\cos (2\psi ) \nonumber\\
&~~- \cos (\theta )\sin (2\phi )\sin (2\psi )\bigg],\nonumber\\
F_\times^{(1)}(\theta, \phi, \psi)=&~~\frac{{\sqrt 3 }}{2}\bigg[\frac{1}{2}\big(1 + {\cos ^2}(\theta )\big)\cos (2\phi )\sin (2\psi ) \nonumber\\
&~~+ \cos (\theta )\sin (2\phi )\cos (2\psi )\bigg].
\label{equa:F1}
\end{align}
Since ET has three interferometers with $60^\circ$ inclined angles between each other, the other two response functions are $F_{+,\times}^{(2)}(\theta, \phi, \psi)=F_{+,\times}^{(1)}(\theta, \phi+2\pi/3, \psi)$ and $F_{+,\times}^{(3)}(\theta, \phi, \psi)=F_{+,\times}^{(1)}(\theta, \phi+4\pi/3, \psi)$.
For CE, the antenna response functions are
\begin{align}
F_+(\theta, \phi, \psi)=&~~\frac{1}{2}\big(1 + {\cos ^2}(\theta )\big)\cos (2\phi )\cos (2\psi ) \nonumber\\
&~~- \cos (\theta )\sin (2\phi )\sin (2\psi ),\nonumber\\
F_\times(\theta, \phi, \psi)=&~~\frac{1}{2}\big(1 + {\cos ^2}(\theta )\big)\cos (2\phi )\sin (2\psi ) \nonumber\\
&~~+ \cos (\theta )\sin (2\phi )\cos (2\psi ).
\label{equa:F2}
\end{align}
{We consider the waveform in the inspiralling stage for a non-spinning BNS system. Here we adopt the restricted post-Newtonian (PN) approximation and calculate the waveform to the 3.5 PN order \cite{Sathyaprakash:2009xs,Blanchet:2004bb},}
\begin{equation}
\tilde{h}(f)=\mathcal{A}f^{-7/6}\exp[i(2\pi ft_{\rm c}-\pi/4-2\psi_{\rm c}+2{\Psi}(f/2)-\varphi_{(2.0)})],
\label{equa:hf}
\end{equation}
where the Fourier amplitude $\mathcal{A}$ is given by
\begin{align}
\mathcal{A}=&~~\frac{1}{d_{\rm L}}\sqrt{F_+^2\big(1+\cos^2(\iota)\big)^2+4F_\times^2\cos^2(\iota)}\nonumber\\
&~~\times \sqrt{5\pi/96}\pi^{-7/6}\mathcal{M}_{\rm c}^{5/6},
\label{equa:A}
\end{align}
where $\mathcal{M}_{\rm c}=(1+z)M \eta^{3/5}$ is the observed chirp mass, $M=m_1+m_2$ is the total mass of the coalescing binary system with $m_1$ and $m_2$ being the component masses, $\eta=m_1 m_2/M^2$ is the symmetric mass ratio, $d_{\rm L}$ is the luminosity distance to the GW source, $\iota$ is the inclination angle between the binary's orbital angular momentum and the line of sight, $t_{\rm c}$ is the coalescence time, and $\psi_{\rm c}$ is the coalescence phase. The definitions of the functions $\Psi$ and $\varphi_{(2.0)}$ can refer to Refs.~\cite{Sathyaprakash:2009xs,Blanchet:2004bb}.
The signal-to-noise ratio (SNR) for the network of $N$ (i.e., $N$ = 3 for ET and $N$ = 1 for CE) independent interferometers can be calculated by
\begin{equation}
\rho=\sqrt{\sum\limits_{i=1}^{N}(\rho^{(i)})^2},
\label{euqa:rho}
\end{equation}
where $\rho^{(i)}=\sqrt{\langle \tilde{h}^{(i)},\tilde{h}^{(i)}\rangle}$. The inner product is defined as
\begin{equation}
\left\langle{a,b}\right\rangle=4\int_{f_{\rm lower}}^{f_{\rm upper}}\frac{ a(f) b^\ast(f)+ a^\ast(f) b(f)}{2}\frac{df}{S_{\rm n}(f)},
\label{euqa:product}
\end{equation}
where $f_{\rm lower}$ is the lower cutoff frequency ($f_{\rm lower}=1$ Hz for ET and $f_{\rm lower}=5$ Hz for CE), $f_{\rm upper}=2/(6^{3/2}2\pi M_{\rm obs})$ is the frequency at the last stable orbit
with $M_{\rm obs}=(m_1+m_2)(1+z)$ \cite{Zhao:2010sz}, and $S_{\rm n}(f)$ is the one-side noise power spectral density (PSD). We adopt PSD of ET from Ref.~\cite{ETcurve-web} and that of CE from Ref.~\cite{CEcurve-web}. In this work, we choose the threshold of SNR to be 8 in our simulation.
{For the 3G ground-based GW detectors, a few $\times 10^5$ BNS merger events per year could be detected, but only about 0.1\% of them may have $\gamma$-ray bursts toward us \cite{Yu:2021nvx}. Recently, in Ref.~\cite{Chen:2020zoq} Chen \emph{et al.} made a forecast and showed that 910 GW standard siren events could be observed by a 10-year observation of CE and Swift++. Therefore, in our forecast in the present work, for ET and CE, we simulate 1000 GW standard sirens from BNS mergers based on the 10-year observation. }
We consider three measurement errors of $d_{\rm L}$, consisting of the instrumental error $\sigma_{d_{\rm L}}^{\rm inst}$, the weak-lensing error $\sigma_{d_{\rm L}}^{\rm lens}$, and the peculiar velocity error $\sigma_{d_{\rm L}}^{\rm pv}$. Therefore, the total error of $d_{\rm L}$ is
\begin{align}
\sigma_{d_{\rm L}}&~~=\sqrt{(\sigma_{d_{\rm L}}^{\rm inst})^2+(\sigma_{d_{\rm L}}^{\rm lens})^2+(\sigma_{d_{\rm L}}^{\rm pv})^2}.\label{total}
\end{align}
We first use the Fisher information matrix to calculate $\sigma_{d_{\rm L}}^{\rm inst}$. For a network of $N$ independent interferometers, the Fisher information matrix can be written as
\begin{equation}
\boldsymbol{F}_{ij}=\left\langle\frac{\partial \boldsymbol{h}(f)}{\partial \theta_i}, \frac{\partial \boldsymbol{h}(f)}{\partial \theta_j}\right\rangle,
\end{equation}
with $\boldsymbol{h}$ given by
\begin{equation}
\boldsymbol{h}(f)=\left[\tilde{h}_1 (f),\tilde{h}_2 (f),\cdots,\tilde{h}_N (f)\right],
\end{equation}
where $\theta_i$ denotes nine parameters ($d_{\rm L}$, $\mathcal{M}_{\rm c}$, $\eta$, $\theta$, $\phi$, $\iota$, $t_{\rm c}$, $\psi_{\rm c}$, $\psi$) for a GW event. Then we have
\begin{equation}
\Delta \theta_i =\sqrt{(F^{-1})_{ii}},
\end{equation}
where $F_{ij}$ is the total Fisher information matrix for the network of $N$ interferometers. Note that here $\sigma_{d_{\rm L}}^{\rm inst}=\Delta \theta_1$.
{The error caused by weak lensing is adopted from Refs.~\cite{Hirata:2010ba,Speri:2020hwc},
\begin{equation}
\sigma_{d_{\rm L}}^{\rm lens}(z)=F_{\rm {delens}}(z)\times d_{\rm L}(z)\times 0.066\bigg[\frac{1-(1+z)^{-0.25}}{0.25}\bigg]^{1.8}.\label{lens}
\end{equation}
Here, we consider a delensing factor $F_{\rm {delens}}$. We use dedicated matter surveys along the line of sight of the GW event in order to estimate the lensing magnification distribution, which can remove part of the uncertainty due to weak lensing. This reduces the weak lensing uncertainty. The delensing factor is given by
\begin{equation}
F_{\rm {delens}}(z)=1-\frac{0.3}{\pi / 2} \arctan \left(z / 0.073\right).
\end{equation}}
{The error caused by the peculiar velocity of the GW source is given by \cite{Kocsis:2005vv}
\begin{equation}
\sigma_{d_{\rm L}}^{\rm pv}(z)=d_{\rm L}(z)\times \bigg[ 1+ \frac{c(1+z)^2}{H(z)d_{\rm L}(z)}\bigg]\frac{\sqrt{\langle v^2\rangle}}{c},\label{pv}
\end{equation}
where $H(z)$ is the Hubble parameter. $\sqrt{\langle v^2\rangle}$ is the peculiar velocity of the GW source and we roughly set $\sqrt{\langle v^2\rangle}=500\ {\rm km\ s^{-1}}$.}
{For each simulated GW source, the sky location ($\theta$, $\phi$), the masses of NSs ($m_1$, $m_2$), the binary inclination $\iota$, the coalescence phase $\psi_{\rm c}$, and the polarization angle $\psi$ are evenly sampled in the ranges of [0, $\pi$], [0, $2\pi$], $[1, 2]\ M_{\odot}$, $[1, 2]\ M_{\odot}$, [0, $\pi/9$], [0, $2\pi$], and [0, $2\pi$], respectively, where $M_{\odot}$ is the solar mass. The merger time is chosen to $t_{\rm c}=0$ for simplicity. In this work, we assume that the EM counterparts could be detected through the detections of short $\gamma$-ray bursts to determine sources' redshifts. The maximal inclination angle that could be detected is about $\iota=20^\circ$ \cite{li2015extracting}, so we set the inclination angle to be in the range of [0, $\pi/9$].}
\begin{figure}[!htp]
\includegraphics[width=0.9\linewidth,angle=0]{fig2a.pdf}\ \hspace{1cm}
\includegraphics[width=0.9\linewidth,angle=0]{fig2b.pdf}\ \hspace{1cm}
\centering \caption{\label{fig2} {Distribution of $\sigma_{d_{\rm L}}/d_{\rm L}$ as a function of redshift. The color indicates SNR of the simulated GW standard sirens. {\it Upper}: 1000 GW standard sirens from a 10-year observation of ET. {\it Lower}: 1000 GW standard sirens from a 10-year observation of CE.}}
\end{figure}
{In Fig.~\ref{fig2}, we show the $\sigma_{d_{\rm L}}/d_{\rm L}$ scatter plot of the simulated standard siren data from ET (upper panel) and CE (lower panel). We can see that: (i) the total errors of $d_{\rm L}$ from CE are smaller than those from ET; (ii) SNR of CE is higher than that of ET at the same redshift.}
\begin{figure*}[!htp]
\includegraphics[scale=0.5]{fig3a.pdf}\ \hspace{1cm}
\includegraphics[scale=0.5]{fig3b.pdf}\ \hspace{1cm}
\centering \caption{\label{fig3} {The simulated GW standard siren data points observed by ET and CE. The blue data points represent the 1000 standard sirens from the 10-year observation of ET and the orange data points represent the 1000 standard sirens from the 10-year observation of CE. {\it Left}: the standard siren data points without Gaussian randomness, where the central values of the luminosity distances are calculated by the fiducial cosmological model, and the solid green line represents the $d_{\rm L}(z)$ curve predicted by the fiducial model. {\it Right}: the standard siren data points with Gaussian randomization, reflecting the fluctuations in measured values resulted from actual observations.}}
\end{figure*}
{In Fig.~\ref{fig3}, we show the simulated GW standard sirens from ET and CE. In the left panel, we show the standard siren data points without Gaussian randomness, where the central value of the luminosity distance is calculated by the fiducial cosmological model. In the right panel, in order to reflect the fluctuations in measured values resulting from actual observations, we show the standard siren data points with Gaussian randomization (the central values are randomly chosen in the range of [$d_{\rm L}-\sigma_{d_{\rm L}}$, $d_{\rm L}+\sigma_{d_{\rm L}}$]). Note that we use the left-panel standard siren data to perform cosmological parameter estimation. We can clearly see that the measurement errors of $d_{\rm L}$ from CE are smaller than those from ET, because CE has a better sensitivity than ET.}
\subsection{Other cosmological observations}\label{sec2.2}
In this work, we consider three current mainstream EM cosmological observations, including CMB, BAO, and SN.
For the CMB data, we consider the Planck TT, TE, EE spectra at $\ell \geq 30$, the low-$\ell$ temperature Commander likelihood, and the low-$\ell$ SimAll EE likelihood from the Planck 2018 release \cite{Planck:2018vyg}. For the BAO data, we consider the measurements from 6dFGS ($z_{\rm eff}=0.106$) \cite{Beutler:2011hx}, SDSS-MGS ($z_{\rm eff}=0.15$) \cite{Ross:2014qpa}, and BOSS DR12 ($z_{\rm eff}=0.38$, 0.51, and 0.61) \cite{BOSS:2016wmc}. For the SN data, we use the latest Pantheon sample, which is comprised of 1048 data points from the Pantheon compilation \cite{Scolnic:2017caz}.
\subsection{Method of constraining cosmological parameters}\label{sec2.3}
To resolve the large-scale instability problem in the IDE cosmology \cite{Valiviita:2008iv}, we apply the ePPF approach \cite{Li:2014eha,Li:2014cee} for the IDE scenario so that the whole parameter space of IDE models can be explored without any divergence of the dark-energy perturbation. In this work, we employ the modified version of the available Markov-Chain Monte Carlo package {\tt CosmoMC} \cite{Lewis:2002ah}, with the ePPF code \cite{Li:2014eha,Li:2014cee} inserted, to constrain the neutrino mass and other cosmological parameters. In order to show the impacts of GW data from CE and ET on constraining cosmological parameters, we use CMB+BAO+SN, CMB+BAO+SN+ET, and CMB+BAO+SN+CE to make our analysis. For convenience, we use CBS to standard for CMB+BAO+SN in the following.
For the GW standard siren observation with $N$ data points, the $\chi^2$ function can be written as
\begin{align}
\chi_{\rm GW}^2=\sum\limits_{i=1}^{N}\left[\frac{{d}_L^i-d_{\rm L}({z}_i;\vec{\Omega})}{{\sigma}_{d_{\rm L}}^i}\right]^2,
\label{equa:chi2}
\end{align}
where ${z}_i$, ${d}_L^i$, and ${\sigma}_{d_{\rm L}}^i$ are the $i$th GW event's redshift, luminosity distance, and the measurement error of the luminosity distance, respectively. $\vec{\Omega}$ represents the set of cosmological parameters.
When considering the combination of the current EM observations and the GW standard siren observations, the total $\chi^{2}_{\rm tot}$ function is
\begin{equation}
\chi^{2}_{\rm tot}=\chi^{2}_{\rm CMB}+\chi^{2}_{\rm BAO}+\chi^{2}_{\rm SN}+\chi^{2}_{\rm GW}.
\end{equation}
\begin{figure*}[!htp]
\includegraphics[width=0.45\textwidth]{fig4a.pdf} \ \hspace{1cm}
\includegraphics[width=0.45\textwidth]{fig4b.pdf}\ \hspace{1cm}
\centering \caption{\label{fig4} {Two-dimensional marginalized contours (68.3\% and 95.4\% confidence level) in the $\sum m_\nu$--$H_0$ and $\Omega_{\rm m}$--$H_0$ planes using the CBS, CBS+ET, and CBS+CE data. Here CBS stands for CMB+BAO+SN.}}
\end{figure*}
\begin{figure*}[!htp]
\includegraphics[width=0.45\textwidth]{fig5a.pdf}\ \hspace{1cm}
\includegraphics[width=0.45\textwidth]{fig5b.pdf}\ \hspace{1cm}
\centering \caption{\label{fig5} {Two-dimensional marginalized contours (68.3\% and 95.4\% confidence level) in the $\sum m_\nu$--$\beta$ and $\Omega_{\rm m}$--$H_0$ planes using the CBS, CBS+ET, and CBS+CE data. Here CBS stands for CMB+BAO+SN.}}
\end{figure*}
\begin{figure*}[!htp]
\includegraphics[width=0.45\textwidth]{fig6a.pdf}\ \hspace{1cm}
\includegraphics[width=0.45\textwidth]{fig6b.pdf}\ \hspace{1cm}
\centering \caption{\label{fig6} {Two-dimensional marginalized contours (68.3\% and 95.4\% confidence level) in the $\sum m_\nu$--$w$ and $w$--$\beta$ planes using the CBS, CBS+ET, and CBS+CE data. Here CBS stands for CMB+BAO+SN.}}
\end{figure*}
\begin{table*}[htbp]
\caption{\label{tab1}{The absolute and relative errors of cosmological parameters in the $\Lambda$CDM+$\sum m_\nu$ model using the CBS, CBS+ET, and CBS+CE data. Note that $H_0$ is in units of km s$^{-1}$ Mpc$^{-1}$ and CBS stands for CMB+BAO+SN. Here, $2\sigma$ upper limits on $\sum m_\nu$ are given.}}
\setlength\tabcolsep{0.5pt}
\renewcommand{\arraystretch}{1.5}
\centering
{
\begin{tabular}{cccccccccccccc}\\
\hline
\multicolumn{1}{c}{$\Lambda$CDM}&&\multicolumn{3}{c}{CMB+BAO+SN}&&\multicolumn{3}{c}{CMB+BAO+SN+ET}&&\multicolumn{3}{c}{CMB+BAO+SN+CE}\cr
\cline{1-1}\cline{3-5}\cline{7-9}\cline{11-13}
Parameter&&NH&IH&DH&&NH&IH&DH&&NH&IH&DH\cr
\hline
$\sigma(\Omega_{\rm m})$&&$0.0062$&$0.0062$&$0.0064$&&$
0.0044$&$0.0044$&$0.0043$&&$0.0036$&$0.0037$&$0.0036$\cr
$\sigma(H_0)$&&$0.47$&$0.46$&$0.49$&&$0.32$&$0.32$&$
0.32$&&$0.26$&$0.26$&$0.26$\cr
$\varepsilon(\Omega_{\rm m})$&&$1.98\%$&$1.97\%$&$2.07\%$
&&$1.41\%$&$1.40\%$&$1.39\%$
&&$1.15\%$&$1.18\%$&$1.16\%$\cr
$\varepsilon(H_0)$&&$0.70\%$&$0.68\%$&$0.72\%$
&&$0.47\%$&$0.48\%$&$0.47\%$
&&$0.39\%$&$0.39\%$&$0.38\%$\cr
$\sum m_\nu$ [eV]&&$\ <0.156$&$\ <0.184$&$\ <0.121$&&$\ <0.146$&$\ <0.179$&$\ <0.106$&&$\ <0.144$&$\ <0.176$&$\ <0.104$\cr
\hline
\end{tabular}
}
\end{table*}
\begin{table*}[htbp]
\caption{\label{tab2} {The absolute and relative errors of cosmological parameters in the I$\Lambda$CDM+$\sum m_\nu$ model using the CBS, CBS+ET, and CBS+CE data. Note that $H_0$ is in units of km s$^{-1}$ Mpc$^{-1}$ and CBS stands for CMB+BAO+SN. Here, $2\sigma$ upper limits on $\sum m_\nu$ are given.}}
\setlength\tabcolsep{0.5pt}
\renewcommand{\arraystretch}{1.5}
\centering
{
\begin{tabular}{cccccccccccccc}\\
\hline
\multicolumn{1}{c}{I$\Lambda$CDM}&&\multicolumn{3}{c}{CMB+BAO+SN}&&\multicolumn{3}{c}{CMB+BAO+SN+ET}&&\multicolumn{3}{c}{CMB+BAO+SN+CE}\cr
\cline{1-1}\cline{3-5}\cline{7-9}\cline{11-13}
Parameter&&NH&IH&DH&&NH&IH&DH&&NH&IH&DH\cr
\hline
$\sigma(\Omega_{\rm m})$&&$0.0081$&$0.0082$&$0.0081$
&&$0.0046$&$0.0045$&$0.0046$
&&$0.0037$&$0.0037$&$0.0037$
\cr
$\sigma(H_0)$&&$0.65$&$0.65$&$0.65$
&&$0.35$&$0.35$&$0.36$
&&$0.27$&$0.27$&$0.27$
\cr
$\sigma(\beta)$&&$ 0.0013$&$0.0013$&$0.0013$
&&$0.00104$&$0.00103$&$0.00105$
&&$0.00096$&$ 0.00096$&$0.00101$
\cr
$\varepsilon(\Omega_{\rm m})$
&&$2.62\%$&$2.65\%$&$2.65\%$
&&$1.49\%$&$1.46\%$&$1.50\%$
&&$1.20\%$&$1.20\%$&$1.20\%$
\cr
$\varepsilon(H_0)$
&&$0.96\%$&$0.96\%$&$0.96\%$
&&$0.52\%$&$0.52\%$&$0.53\%$
&&$0.40\%$&$0.40\%$&$0.40\%$
\cr
$\sum m_\nu$ [eV]
&&$< 0.191$&$\ < 0.224$&$\ < 0.148$
&&$\ < 0.188$&$\ < 0.220$&$\ < 0.147$
&&$\ < 0.187$&$\ < 0.220$&$\ < 0.142$\cr
\hline
\end{tabular}
}
\end{table*}
\begin{table*}[htbp]
\caption{\label{tab3}{The absolute and relative errors of cosmological parameters in the I$w$CDM+$\sum m_\nu$ model using the CBS, CBS+ET, and CBS+CE data. Note that $H_0$ is in units of km s$^{-1}$ Mpc$^{-1}$ and CBS stands for CMB+BAO+SN. Here, $2\sigma$ upper limits on $\sum m_\nu$ are given.}}
\setlength\tabcolsep{0.5pt}
\renewcommand{\arraystretch}{1.5}
\centering
{
\begin{tabular}{cccccccccccccc}\\
\hline
\multicolumn{1}{c}{I$w$CDM}&&\multicolumn{3}{c}{CMB+BAO+SN}&&\multicolumn{3}{c}{CMB+BAO+SN+ET}&&\multicolumn{3}{c}{CMB+BAO+SN+CE}\cr
\cline{1-1}\cline{3-5}\cline{7-9}\cline{11-13}
Parameter&&NH&IH&DH&&NH&IH&DH&&NH&IH&DH\cr
\hline
$\sigma(\Omega_{\rm m})$&&$0.0079$&$0.0079$&$0.0081$&&$
0.0049$&$0.0049$&$0.0047$
&&$0.0040$&$0.0041$&$0.0039$\cr
$\sigma(H_0)$&&$0.82$&$0.82$&$0.84$
&&$0.55$&$0.54$&$0.53$
&&$0.46$&$0.47$&$0.46$\cr
$\sigma(w)$&&$0.037$&$0.037$&$0.038$
&&$0.033$&$0.033$&$0.032$
&&$0.030$&$0.030$&$0.030$\cr
$\sigma(\beta)$&&$0.00088$&$0.00086$&$0.00087$
&&$0.00080$&$0.00080$&$0.00080$
&&$0.00079$&$0.00080$&$0.00079$\cr
$\varepsilon(\Omega_{\rm m})$
&&$2.56\%$&$2.55\%$&$2.64\%$
&&$1.59\%$&$1.59\%$&$1.53\%$
&&$1.30\%$&$1.33\%$&$1.27\%$\cr
$\varepsilon(H_0)$
&&$1.20\%$&$1.20\%$&$1.23\%$
&&$0.81\%$&$0.79\%$&$0.78\%$
&&$0.67\%$&$0.69\%$&$0.67\%$\cr
$\varepsilon(w)$
&&$3.53\%$&$3.50\%$&$3.66\%$
&&$3.15\%$&$3.12\%$&$3.09\%$
&&$2.86\%$&$2.84\%$&$2.89\%$\cr
$\sum m_\nu$ [eV]&&$< 0.192$&$\ < 0.221$&$\ < 0.154$
&&$\ < 0.185$&$\ < 0.215$&$\ < 0.138$
&&$\ < 0.176$&$\ < 0.213$&$
<0.133$\cr
\hline
\end{tabular}
}
\end{table*}
\section{Results and discussion}\label{sec3}
In this section, we report the constraint results of cosmological parameters in the $\Lambda$CDM+$\sum m_{\nu}$, I$\Lambda$CDM+$\sum m_{\nu}$, and I$w$CDM+$\sum m_{\nu}$ models. In these models, the three mass hierarchy cases of neutrinos, i.e., the NH, IH, and DH cases, have been considered. The constraint results of the NH case are shown as a representative in Figs.~\ref{fig4}--\ref{fig6} and the constraint results are summarized in Tables \ref{tab1}--\ref{tab3}. Note that for the constraints on the total neutrino mass, the $2\sigma$ upper limits are given. Note also that using the squared mass differences derived from the neutrino oscillation experiments, one can obtain the lower limits for the total neutrino mass, i.e., 0.05 eV for NH and 0.1 eV for IH; in the case of DH, the smallest value of the total neutrino mass is zero.
For a parameter $\xi$, we use $\sigma(\xi)$ and $\varepsilon(\xi)$ to represent its absolute and relative errors, respectively, with $\varepsilon(\xi)$ defined as $\varepsilon(\xi)=\sigma(\xi)/\xi$.
We first take a look at the results in the $\Lambda$CDM+$\sum m_{\nu}$ model. In Fig.~\ref{fig4}, we show the constraints on the $\Lambda$CDM+$\sum m_{\nu}$ model in the $\sum m_{\nu}$--$H_0$ and $\Omega_{\rm m}$--$H_0$ planes from the CBS, CBS+ET, and CBS+CE data. We find that the addition of the GW data to the CBS data could lead to the reduction of the upper limits of $\sum m_{\nu}$ to some extent. The CBS+CE data give slightly smaller upper limits on $\sum m_{\nu}$ than those from the CBS+ET data. Concretely, when adding the ET data to the CBS data, the upper limits on $\sum m_{\nu}$ could be reduced by 2.7\%--12.4\% in the three hierarchy cases. While for CE, the upper limits on $\sum m_{\nu}$ could be reduced by 4.3\%--14.0\% in the three hierarchy cases. Here the results of ET are consistent with the previous results in Ref.~\cite{Wang:2018lun}.
Although using the GW data could only slightly improve the limits on the neutrino mass, they can significantly help improve the constraints on other cosmological parameters.
We find that the constraints on $\Omega_{\rm m}$ and $H_0$ could be improved by 29.0\%--32.8\% and 30.4\%--34.7\%, respectively, when adding the ET data to the CBS data, and by 40.3\%--43.8\% and 43.5\%--46.9\%, respectively, for the case of CE.
In Fig.~\ref{fig5}, we show the constraints on the I$\Lambda$CDM+$\sum m_{\nu}$ model in the $\sum m_{\nu}$--$\beta$ and $\Omega_{\rm m}$--$H_0$ planes from the CBS, CBS+ET, and CBS+CE data. We can clearly see that, when considering the interaction between vacuum energy and dark matter, the improvement of the limits on $\sum m_\nu$ by adding GW data is rather not evident. In the case of ET, the improvement of the limit on $\sum m_\nu$ is only 0.7\%--1.8\%, and in the case of CE, the improvement is 1.8\%--4.1\%. Therefore, we find that compared with the standard $\Lambda$CDM model, in its interaction version, the I$\Lambda$CDM model, the improvement of the limits on $\sum m_\nu$ by GW data from ET and CE becomes weaker.
We also find that the constraints on the coupling parameter $\beta$ can be improved by using the GW data to a certain extent. In the I$\Lambda$CDM+$\sum m_{\nu}$ model, the constraints on $\beta$ are improved by 19.2\%--20.8\% and 22.3\%--26.2\%, respectively, when the GW data of ET and CE are added on the basis of the CBS case.
In Fig.~\ref{fig6}, we show the constraints on the I$w$CDM+$\sum m_{\nu}$ model in the $\sum m_{\nu}$--$w$ and $w$--$\beta$ planes from the CBS, CBS+ET, and CBS+CE data. We find that in this case the improvement of the limits on the neutrino mass is better than in the previous case. For ET, the improvement of the limit on $\sum m_\nu$ is 2.7\%--10.4\%, and for CE, the improvement is 3.6\%--13.6\%.
We find that in this case the constraints on the coupling parameter $\beta$ and the EoS parameter of dark energy $w$ can both be significantly improved by considering the addition of GW data. The constraints on $\beta$ and $w$ are improved by 7.0\%--9.1\% and 10.8\%--15.8\% when considering the ET data, and by 7.0\%--10.2\% and 18.9\%--21.1\% with considering the CE data.
In this work, we discuss the cosmological constraints on the IDE models in the cases of considering the GW standard siren observations from 3G ground-based GW detectors ET and CE. The results show that the limits on the neutrino mass can only be slightly improved with the help of the GW data, on the basis of the CBS constraint. Since the GW data can precisely constrain the Hubble constant $H_0$, the addition of them in the cosmological fit can help break the cosmological parameter degeneracies formed by other cosmological observations. Therefore, the consideration of GW standard siren data can help significantly improve the constraints on the most cosmological parameters. However, the effect of massive neutrinos in the late universe and on the large scales cannot be distinctively distinguished from that of the cold dark matter, leading to the improvement of the limits on the neutrino mass by considering GW data is not obvious. Anyway, even though the impact on constraining the neutrino mass is not apparent, the GW standard sirens are rather useful in helping improve the constraints on the most cosmological parameters including the EoS of dark energy and the coupling between dark energy and dark matter.
\section{Conclusion}\label{sec4}
In the era of 3G ground-based GW detectors, a lot of GW standard siren data with the know redshifts could be obtained by the multi-messenger observation for BNS merger events. Obviously, these standard sirens would exert great impacts on the cosmological parameter estimation. Since the GW standard sirens can tightly constrain the Hubble constant, the consideration of them in a joint cosmological fit can lead to the cosmological parameter degeneracies formed by other cosmological observations being well broken. The GW standard sirens can thus be used to help significantly improve the constraints on cosmological parameters in the future.
It is of great interest to investigate whether the limits on the total neutrino mass can also be effectively improved by considering the GW standard siren data. In particular, the cosmological constraints on the neutrino mass are strongly model-dependent, and so the cases in different cosmological scenarios are needed to be detailedly discussed. In this work, we discuss the issue of weighing neutrinos in the IDE models by using the GW standard siren observations by ET and CE.
We consider the simplest IDE models, namely the I$\Lambda$CDM and I$w$CDM models with $Q=\beta H \rho_{\mathrm{c}}$. We simulate the GW standard siren data of the BNS mergers observed by ET and CE (in a way of multi-messenger detection). We investigate whether the GW standard sirens observed by ET and CE could help improve the constraint on the neutrino mass in the IDE models.
It is found that the GW standard siren observations from ET and CE can only slightly improve the constraint on the neutrino mass in the IDE models, compared to the current limit given by CMB+BAO+SN.
This is mainly because the effect of massive neutrinos in the late universe and on the large scales cannot be distinctively distinguished from that of the CDM, leading to the improvement of the limits on the neutrino mass by considering GW data is not obvious.
Although the limit on neutrino mass can only be slightly updated by considering the GW standard sirens, they are fairly useful in helping improve the constraints on the most cosmological parameters including the EoS of dark energy and the coupling between dark energy and dark matter.
\begin{acknowledgments}
This work was supported by the National Natural Science Foundation of China (Grants Nos. 11975072, 11835009, 11875102, and 11690021), the Liaoning Revitalization Talents Program (Grant No. XLYC1905011), the Fundamental Research Funds for the Central Universities (Grant No. N2005030), the National 111 Project of China (Grant No. B16009), and the Science Research Grants from the China Manned Space Project (Grant No. CMS-CSST-2021-B01).
\end{acknowledgments}
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 1,277
|
package org.seleniumhq.selenium.fluent;
import org.openqa.selenium.By;
import org.openqa.selenium.SearchContext;
import org.openqa.selenium.WebDriver;
import org.openqa.selenium.WebElement;
import org.openqa.selenium.support.ui.Select;
import org.seleniumhq.selenium.fluent.internal.Context;
import org.seleniumhq.selenium.fluent.internal.Execution;
import java.util.List;
import java.util.concurrent.TimeUnit;
public class FluentSelect extends FluentWebElement {
private Select currentSelect;
protected FluentSelect(WebDriver delegate, WebElement currentElement, Context context, Monitor monitor, boolean booleanInsteadOfNoSuchElement) {
super(delegate, new Internal.WebElementHolder(null, currentElement, null), context, monitor, booleanInsteadOfNoSuchElement);
}
protected FluentSelect(WebDriver delegate, Select currentSelect, WebElement currentElement, Context context, Monitor monitor, boolean booleanInsteadOfNoSuchElement) {
super(delegate, new Internal.WebElementHolder(null, currentElement, null), context, monitor, booleanInsteadOfNoSuchElement);
this.currentSelect = currentSelect;
}
@Override
public FluentSelect ifInvisibleWaitUpTo(Period period) {
Context ifInvisibleWaitUpTo = Context.singular(context, "ifInvisibleWaitUpTo", period);
executeAndWrapReThrowIfNeeded(new IfInvisibleWait(period), ifInvisibleWaitUpTo, true);
return new FluentSelect(delegate, currentElement.getFound(), ifInvisibleWaitUpTo, monitor, booleanInsteadOfNotFoundException);
}
/**
* @return Whether this select element support selecting multiple options at the same time? This
* is done by checking the value of the "multiple" attribute.
*/
public boolean isMultiple() {
return executeAndWrapReThrowIfNeeded(new IsMultiple(), Context.singular(context, "isMultiple"), true);
}
/**
* @return All options belonging to this select tag
*/
public List<WebElement> getOptions() {
return executeAndWrapReThrowIfNeeded(new GetOptions(), Context.singular(context, "getOptions"), true);
}
/**
* @return All selected options belonging to this select tag
*/
public List<WebElement> getAllSelectedOptions() {
return executeAndWrapReThrowIfNeeded(new GetAllSelectedOptions(), Context.singular(context, "getAllSelectedOptions"), true);
}
/**
* @return The first selected option in this select tag (or the currently selected option in a
* normal select)
*/
public WebElement getFirstSelectedOption() {
return executeAndWrapReThrowIfNeeded(new GetFirstSelectedOption(), Context.singular(context, "getFirstSelectedOption"), true);
}
/**
* Select all options that display text matching the argument. That is, when given "Bar" this
* would select an option like:
* <p/>
* <option value="foo">Bar</option>
*
* @param text The visible text to match against
*/
public FluentSelect selectByVisibleText(final String text) {
executeAndWrapReThrowIfNeeded(new SelectByVisibleText(text), Context.singular(context, "selectByVisibleText", null, text), true);
return new FluentSelect(super.delegate, currentElement.getFound(), this.context, monitor, booleanInsteadOfNotFoundException);
}
/**
* Select the option at the given index. This is done by examing the "index" attribute of an
* element, and not merely by counting.
*
* @param index The option at this index will be selected
*/
public FluentSelect selectByIndex(final int index) {
executeAndWrapReThrowIfNeeded(new SelectByIndex(index), Context.singular(context, "selectByIndex", null, index), true);
return new FluentSelect(super.delegate, currentElement.getFound(), this.context, monitor, booleanInsteadOfNotFoundException);
}
/**
* Select all options that have a value matching the argument. That is, when given "foo" this
* would select an option like:
* <p/>
* <option value="foo">Bar</option>
*
* @param value The value to match against
*/
public FluentSelect selectByValue(final String value) {
executeAndWrapReThrowIfNeeded(new SelectByValue(value), Context.singular(context, "selectByValue", null, value), true);
return new FluentSelect(super.delegate, currentElement.getFound(), this.context, monitor, booleanInsteadOfNotFoundException);
}
/**
* Clear all selected entries. This is only valid when the SELECT supports multiple selections.
*
* @throws UnsupportedOperationException If the SELECT does not support multiple selections
*/
public FluentSelect deselectAll() {
executeAndWrapReThrowIfNeeded(new DeselectAll(), Context.singular(context, "deselectAll"), true);
return new FluentSelect(super.delegate, currentElement.getFound(), this.context, monitor, booleanInsteadOfNotFoundException);
}
/**
* Deselect all options that have a value matching the argument. That is, when given "foo" this
* would deselect an option like:
* <p/>
* <option value="foo">Bar</option>
*
* @param value The value to match against
*/
public FluentSelect deselectByValue(final String value) {
executeAndWrapReThrowIfNeeded(new DeselectByValue(value), Context.singular(context, "deselectByValue", null, value), true);
return new FluentSelect(super.delegate, currentElement.getFound(), this.context, monitor, booleanInsteadOfNotFoundException);
}
private <T> T executeAndWrapReThrowIfNeeded(Execution<T> execution, Context ctx, boolean expectedToBeThere) {
return executeAndWrapReThrowIfNeeded(execution, currentElement, ctx, expectedToBeThere);
}
/**
* Deselect the option at the given index. This is done by examining the "index" attribute of an
* element, and not merely by counting.
*
* @param index The option at this index will be deselected
*/
public FluentSelect deselectByIndex(final int index) {
executeAndWrapReThrowIfNeeded(new DeselectByIndex(index), Context.singular(context, "deselectByIndex", null, index), true);
return new FluentSelect(super.delegate, currentElement.getFound(), this.context, monitor, booleanInsteadOfNotFoundException);
}
/**
* Deselect all options that display text matching the argument. That is, when given "Bar" this
* would deselect an option like:
* <p/>
* <option value="foo">Bar</option>
*
* @param text The visible text to match against
*/
public FluentSelect deselectByVisibleText(final String text) {
executeAndWrapReThrowIfNeeded(new DeselectByVisibleText(text), Context.singular(context, "deselectByVisibleText", null, text), true);
return new FluentSelect(super.delegate, currentElement.getFound(), this.context, monitor, booleanInsteadOfNotFoundException);
}
protected synchronized Select getSelect() {
if (currentSelect == null) {
currentSelect = new Select(currentElement.getFound());
}
return currentSelect;
}
public FluentSelect within(Period period) {
return new RetryingFluentSelect(delegate, Context.singular(context, "within", null, period), currentSelect, currentElement.getFound(), period, monitor, booleanInsteadOfNotFoundException);
}
private class RetryingFluentSelect extends FluentSelect {
private final Period period;
public RetryingFluentSelect(WebDriver webDriver, Context context, Select currentSelect, WebElement currentElement, Period period, Monitor monitor, boolean booleanInsteadOfNoSuchElement) {
super(webDriver, currentSelect, currentElement, context, monitor, booleanInsteadOfNoSuchElement);
this.period = period;
}
@Override
protected WebElement findElement(By by, Context ctx, SearchContext searchContext) {
return retryingFindIt(by, searchContext);
}
@Override
protected List<WebElement> findElements(By by, Context ctx) {
return retryingFindThem(by);
}
@Override
protected Period getPeriod() {
return period;
}
@Override
protected void changeTimeout() {
delegate.manage().timeouts().implicitlyWait(period.howLong(), period.timeUnit());
}
@Override
protected void resetTimeout() {
delegate.manage().timeouts().implicitlyWait(0, TimeUnit.SECONDS);
}
}
private class DeselectAll extends Execution<Boolean> {
public Boolean execute() {
getSelect().deselectAll();
return true;
}
}
private class SelectByValue extends Execution<Boolean> {
private final String value;
public SelectByValue(String value) {
this.value = value;
}
public Boolean execute() {
Select select = getSelect();
select.selectByValue(value);
return true;
}
}
private class SelectByIndex extends Execution<Boolean> {
private final int index;
public SelectByIndex(int index) {
this.index = index;
}
public Boolean execute() {
getSelect().selectByIndex(index);
return true;
}
}
private class SelectByVisibleText extends Execution<Boolean> {
private final String text;
public SelectByVisibleText(String text) {
this.text = text;
}
public Boolean execute() {
getSelect().selectByVisibleText(text);
return true;
}
}
private class GetFirstSelectedOption extends Execution<WebElement> {
public WebElement execute() {
return getSelect().getFirstSelectedOption();
}
}
private class GetAllSelectedOptions extends Execution<List<WebElement>> {
public List<WebElement> execute() {
return getSelect().getAllSelectedOptions();
}
}
private class GetOptions extends Execution<List<WebElement>> {
public List<WebElement> execute() {
return getSelect().getOptions();
}
}
private class IsMultiple extends Execution<Boolean> {
public Boolean execute() {
return getSelect().isMultiple();
}
}
private class DeselectByValue extends Execution<Boolean> {
private final String value;
public DeselectByValue(String value) {
this.value = value;
}
public Boolean execute() {
getSelect().deselectByValue(value);
return true;
}
}
private class DeselectByIndex extends Execution<Boolean> {
private final int index;
public DeselectByIndex(int index) {
this.index = index;
}
public Boolean execute() {
getSelect().deselectByIndex(index);
return true;
}
}
private class DeselectByVisibleText extends Execution<Boolean> {
private final String text;
public DeselectByVisibleText(String text) {
this.text = text;
}
public Boolean execute() {
getSelect().deselectByVisibleText(text);
return true;
}
}
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 8,791
|
\section{Introduction}
\section{Introduction and Related Work}
\label{sec:sample1}
Machine Learning (ML) is an Artificial Intelligence (AI) method that allows computers to act without requiring definitive programming. ML assists in improving the accuracy of prediction for outcomes in various applications these days. Predictions are made by models using sample data referred to as training data. With the advent of machine learning, the field of VLSI design and testing has the prospect of achieving high levels of automation, speed, and efficiency. In the past, many AI/ML approaches have been introduced to achieve noteable results in the VLSI design domain \cite{b12,b25,b26,b27,b28,b29}.
Most of these approaches are highly dependent on a large amount of training data, which is a challenge for many applications. Other fields, such as sound classification, medical image analysis, disease diagnosis, face recognition, etc., employing AI/ML techniques also face the issue of data scarcity. Data scarcity can be defined as the lack of sufficient quantity or diversity in training data that can increase the learning ability of a machine learning model. As discussed by A. Munappy et al. \cite{b13}, in real-world industrial applications of deep learning in different domains, the shortage of diverse data is one of the challenges that can significantly impact the overall performance of deep learning systems. Various studies have been done to overcome this challenge. Data augmentation and synthetic data generation have been used to overcome this challenge and build large-scale training datasets in these fields. Data augmentation with synthetically created samples has been proven beneficial for several machine learning models \cite{b14}.
\begin{figure}[t!]
\centering
\includegraphics[scale=0.23]{Tuning_using_GAN_drawiov3_drawio.png}
\caption{\label{figure:1b}An example of machine learning based data augmentation method using GANs for tuning AIMDs}
\end{figure}
A. Mikołajczyk and M. Grochowski \cite{b15} compared and analyzed multiple data augmentation methods in image classification and improved the training process efficiency for image classification. To solve the problem of class imbalance due to the lack of fraudulent electricity consumers, M. Asif et al. \cite{b16} proposed employing an evolutionary bidirectional Wasserstein Generative Adversarial Network (Bi-WGAN). They \cite{b16} use Bi-WGAN to synthesize the most plausible fraudulent electricity consumer samples to detect non-technical losses (NTL) in smart meters. W. Tan and H. Guo \cite{b17} also utilized a data augmentation method in their automatic COVID-19 diagnosis framework from lung CT images and improved the generalization capability of the 2D CNN classification models. Their data augmentation method uses multiple Hounsfield Unit (HU) normalization windows. HU window determines the variety of tissue densities visible in the CT images. Kortylewski et al. \cite{b19} used synthetically generated data to reduce the number of real-world images needed for training deep face recognition systems and simultaneously achieved an increased performance.
Synthetic data has also been used for facial expression analysis \cite{b20}, signal generation \cite{b21}, industrial data generation \cite{b22}, etc.
For image augmentation, various algorithms such as geometric transformations, color space augmentations, kernel filters, mixing images, random erasing, feature space augmentation, adversarial training, generative adversarial networks, neural style transfer, meta-learning, etc. are used \cite{b18}. Existing work regarding data augmentation and synthetic data generation deals with image data. It uses image-based evaluation measures such as inception score, Frechet inception distance (FID), average log-likelihood, Parzen window estimates, visual fidelity, etc. Generative adversarial networks and variational autoencoders have been used for many image data augmentation tasks \cite{b21,b22,b23}. GAN has also shown promising results for synthesizing artificial data for Intrusion Detection Systems (IDS), medical records, educational records etc \cite{b41,b42}. Generative models are known to produce large and diverse synthetic data for image datasets. Data augmentation has improved ML models for image-related tasks; data augmentation or artificial data generation can potentially enhance the ML models working on circuit data. For electronic circuits, circuit data refers to data regarding component values, temperature, process, output variations, node voltages, branch currents, delays, power, etc. Hence, a synthetic data generation method for augmenting circuit data using generative adversarial networks (GAN) is proposed for the first time in this work. Our contribution is summarized below:
\begin{enumerate}
\item Data augmentation for electronic circuit data.
\item Prevention of mode collapse. Mode collapse is observed when the generated artificial data is repetitive and covers only few recurring samples.
\item Reduction in prediction error of a previously trained ML model using the generated artificial data for delay prediction in complex circuits. Additionally, the artificial data for basic circuits is scalable to complex and larger circuits.
\end{enumerate}
This paper is organized as follows. Section 2 presents a detailed description of the used circuit data. This section also answers why data augmentation is needed for circuit data and various applications where data augmentation for circuit data can prove beneficial are discussed. Section 3 briefly introduces GAN architecture, working, and issues such as mode collapse. Section 3 further presents ways to prevent mode collapse. Section 4 offers the setup of experiments and performance evaluation methodology followed by the obtained experimental results. Finally, in Section 5, the conclusions are drawn.
\begin{table*}
\centering
\begin{tabular}{|p{5cm}|p{10cm}|p{1.3cm}|}
\hline
Dataset & Applications & \#Features \\ \hline
Current Reference Circuit & Building block for oscillators, amplifiers, and phase-locked loops. Used in AIMDs such as pacemakers, communication devices, etc. \cite{b33} & 9 \\ \hline
Low Dropout regulator (LDO) & In wired and wireless communications for portable battery-powered equipment, implanted biomedical devices, automotive applications, digital Core supply, and consumer electronics. \cite{b34,b35,b36} & 12 \\ \hline
Operational Trans-conductance Amplifier & For designing basic voltage amplifiers, active filters, etc. For example, it finds applications in biomedical instruments. \cite{b33} & 7 \\ \hline
Comparator Circuit & For interfacing with digital logic in electronic devices \cite{b37,b38} & 5 \\ \hline
Voltage Reference & For designing power supplies, measurement and control systems, DACs, and ADCs. These are used in high-precision applications like medical and scientific equipment. \cite{b33} & 6 \\ \hline
Temperature Sensor & In medical devices, handling chemicals, food processing, etc. \cite{b39,b40} & 6 \\ \hline
\end{tabular}
\caption{\label{table:data}Different analog circuits with their practical applications which we have used in this work.}
\end{table*}
\section{Description of Circuit Data and Need for Data Augmentation}
The hardware for all the applications in healthcare, mobility, the internet of things, wearable and implantable devices, etc., consists of analog and digital electronic circuitry. Data extracted from these circuits is helpful if used to train a machine learning model. For example, we can predict the working condition of the device from data, find the faulty component within the device, use this data for tuning purposes and correct any minor faults, or use data for designing circuits with the help of a proper machine learning model \cite{b27,b28}. The necessary circuit data for these purposes will mainly consist of important circuit parameters and the actual output of the circuit.
Getting sufficient circuit data is an important issue, especially when the circuit is deployed already or is unreachable or extracting the data is limited by expense, resources, and privacy issues. For example, once implanted within a patient's body, biomedical devices such as active implantable medical devices (AIMDs) cannot be tuned manually, but can be fine tuned by programming with new operational parameters \cite{b43}. ML can aid this tuning process. But the data required is limited by patient privacy and other issues. Data augmentation solves this insufficient data issue and helps train and develop a good ML model for such tasks (refer Figure \ref{figure:1b}). Another example where data augmentation can be helpful is when it is computationally expensive to obtain a large amount of training data for tasks such as design automation, optimization, testing, etc.
\subsection{Description of Circuit Data}
We have used six datasets from six widely used analog electronic circuits and fourteen delay datasets from fourteen basic digital circuits for this work. Datasets were collected using EDA tools Cadence Virtuoso \cite{b30}, Micro-Cap \cite{b31}, and HSpice \cite{b32}. The training data was generated by varying process variables (process, temperature, and supply) and design variables (transistors widths/lengths, capacitor and resistor values, etc) for a given circuit topology.
The practical applications of the analog circuits are summarized in Table \ref{table:data}. For digital circuits, refer Table \ref{table:digitaldata}. The data for each analog circuit consists of parameters such as output current, MOSFET process corners, temperature, supply voltage, resistance, etc. Similarly for digital circuits, it consists of parameters such as temperature, supply voltage, MOSFET width, MOSFET length, oxide thickness, delay for output nodes wrt. different input nodes etc.
We take the circuit parameters, which are most likely to vary while the device is working, or the parameters that can affect the functionality of the circuit; for example, leakage currents and corner variations. This data can be helpful for many tuning and troubleshooting purposes \cite{b12}.
\tiny
\normalsize
\begin{table}
\centering
\begin{tabular}{|p{6.0cm}|p{1.2cm}|}
\hline
Dataset & \#Features \\ \hline
NOT gate delay & 17 \\ \hline
Two input NAND gate delay & 19 \\ \hline
Two input AND gate delay & 19 \\ \hline
Two input NOR gate delay & 19 \\ \hline
Two input OR gate delay & 19 \\ \hline
Two input XOR gate delay & 19 \\ \hline
Three input AND-OR circuit delay & 21 \\ \hline
Full adder delay & 21 \\ \hline
2:1 Multiplexer delay & 21 \\ \hline
Three input NAND gate delay & 21 \\ \hline
Three input AND gate delay & 21 \\ \hline
Three input NOR gate delay & 21 \\ \hline
Four input AND-OR circuit (AO22) delay & 23 \\ \hline
Four input AND-OR circuit (AO31) delay & 23 \\ \hline
\end{tabular}
\caption{\label{table:digitaldata}List of digital circuit datasets used in this work.}
\end{table}
\subsection{Need of Data Augmentation for Circuit Data}
These days various devices are being heavily used in applications where they are expected to stay and function for an extended period of time. It may be possible that these devices are inconvenient to reach once they are in use. In case of any malfunction, the electronic components in these devices must be tuned to achieve proper functioning. A machine learning model can carry out this tuning process externally, but massive data is needed to train the ML model to achieve perfect functioning. An example of such device is AIMDs. Still, AIMDs include pacemakers, ventricular assist devices, deep brain stimulators, implantable hearing aids, etc. Once implanted inside a user's body, these devices are inconvenient to reach.
Gathering this massive data from its electronic components and circuits is a tremendous challenge. This data collection process is currently limited by concerns such as:
\begin{enumerate}
\item Data may have privacy issues or data may be proprietary.
\item It may be computationally expensive or power consuming to obtain data.
\item Data may be practically difficult to obtain.
\end{enumerate}
Moreover, many ML applications in VLSI design deal with automation in designing and testing circuits. ML is also proposed for design optimization tasks. Data is the primary requirement for training good and accurate machine learning models for the above-mentioned tasks. Data augmentation can be helpful when it is computationally expensive or time-consuming to obtain a large amount of training data.
Hence, data augmentation and synthetic data generation can prove helpful for training accurate ML models for such applications.
\section{Data Augmentation Using Generative Adversarial Networks(GANs)}
\subsection{Description of GAN Architecture}
GANs are a type of generative machine learning model that tries to learn the data distribution and create synthetic data.
GAN architecture consists of two deep neural networks, one of which we call a generator, and the other is called a discriminator. The training data, which is the actual existing data, is referred to as real data, and the data generated by GAN is referred to as artificial data here.
The generator has the task of creating the samples intended to come from the same distribution as the real data. The generator takes a random noise vector as input. This vector represents the latent features of the data generated. For example, this vector represents features like shape and color for image data. The generator gives artificial samples at the output.
\begin{figure}[t!]
\centering
\includegraphics[scale=0.32]{data_validationv2.png}
\caption{\label{figure:56}Validation process for artificially generated data.}
\end{figure}
\begin{figure*}[t!]
\centering
\includegraphics[scale=0.32]{complete_pipelinev2.png}
\caption{\label{figure:57}Complete training process.}
\end{figure*}
The discriminator examines the samples from the generator and the real samples and tells if they are real or artificial. Thus, we can say that discriminator is just a conventional classifier that classifies input data into two classes: real or artificial. Discriminator, in this way, learns the features of the real data.
Conceptually discriminator then provides feedback to the generator, which helps the generator create data resembling real data. Technically the generator is trained to develop data towards what the discriminator thinks is real. Both networks are trained alternatively, and they compete to improve themselves. Eventually, the discriminator identifies the tiny difference between the real and the generated, and the generator creates data such that the discriminator cannot differentiate anymore. The GAN is then said to have reached convergence and now can produce data resembling natural data.
\textbf{Loss Function for GAN:} GAN training process can be written as the following optimization objective:
\begin{equation}
\min_{G} \max_{D} E_{x\sim X} \log(D(x)) + E_{z\sim Z} \log(1 - D(G(z))). \label{eqn:minmax}
\end{equation}
Here $X$ is the original real data, and $Z$ is the latent variable distribution. The above optimization objective translates to $D$, the discriminator wanting to maximize the classification performance between real and artificial samples and G, the generator wanting to minimize the same. The above Equation \eqref{eqn:minmax} is the binary cross entropy loss between real and artificial samples.
Practically, we would want to optimize both $G$ and $D$ separately at each iteration:
\begin{itemize}
\item Optimization objective for discriminator:
\begin{equation*}
\max_{D} E_{x\sim X} \log(D(x)) + E_{z\sim Z} \log(1 - D(G(z))).
\end{equation*}
\item Optimization objective for generator:
\begin{equation*}
\min_{G} E_{z\sim Z} \log(1 - D(G(z))).
\end{equation*}
\end{itemize}
But such a minimax game does not perform well in practice because when the discriminator rejects the generator sample with high confidence then \(D(G(z)) = 0\). Thus, the optimization objective for generator
vanishes and the gradient for generator vanishes with it. Due to this the generator is now stuck at poor performance.
\subsection{Preventing Mode collapse in GANs}
Other deep learning models are trained to achieve a single minima, whereas GANs are trained to achieve equilibrium between two networks working as adversaries. The model parameters may oscillate, destabilize, and never converge, making the training unstable. Due to this instability, a common issue faced in GANs is mode collapse \cite{b1,b2,b3}.
Different approaches have been proposed to address the problem of mode collapse in GANs. Martin Arjovsky et al. proposed WGAN \cite{b2}, where the objective function for training was changed to Wasserstein distance. Ishaan Gulrajani et al. proposed adding the gradient penalties in the objective function to enforce the Lipschitz constraint to improve the training of WGAN \cite{b3}. Various approaches used multiple generators \cite{b4,b6,b7}. Unrolled GANs \cite{b5} were proposed to prevent the generator from overfitting for a particular discriminator.
Input-based regularizations \cite{b3} had drawbacks while imposing regularization on the space outside of the supports of the generator and data distributions.
The standard form for GAN is given by Equation \eqref{eqn:minmax}, which can be further written as
\begin{align*}
\min_{G} \max_{D} F(G,D),
\end{align*}
Spectral normalization proposed by Takeru Miyato et al. \cite{b9} has presented more promising results while tackling mode collapse in GANs. They target to find the discriminator $D$ from a set of $K$ Lipschitz continuous functions to stabilize the training of the discriminator
\begin{equation*}
\arg \max_{||f||_{lip}<K} F(G,D),
\end{equation*}
where $||f||_{lip}$ is the Lipschitz constant of the discriminator function $f.$
Their approach constrains the spectral norm of each discriminator layer to control the Lipschitz constant of the overall discriminator function.
Spectral normalization as given by Takeru Miyato et al. \cite{b9} is as follows
\begin{align*}
W_{SN}(W):= W/\sigma(W),
\end{align*}
where $W$ is the weight matrix of a layer, $\sigma(W)$ is the spectral norm of the matrix $W$, which is equivalent to the largest singular value of $W$. They make sure that the Lipschitz constant of the discriminator function is bounded by normalizing weights of each layer such that $\sigma(W_{SN}(W))=1$.
Kanglin Liu et al. \cite{b8} proposed spectral regularization to solve the continuing mode collapse issue even in the Spectral Normalized GANs(SN-GANs) \cite{b9}. Spectral regularization is based on the observation that mode collapse and spectral collapse in discriminator's weight matrices go hand in hand; moreover, they demonstrated that spectral collapse is the cause of mode collapse. They define spectral collapse as the vanishing of many singular values of a matrix. Spectral collapse for a discriminator with spectral normalization can be explained as a considerable decrease of singular values of $W_{SN}(W)$ in the discriminator. The weight matrix after applying singular value decomposition can be represented as
\begin{equation*}
W = U \cdot \Sigma \cdot V^{T},
\end{equation*}
where $U$ and $V$ are orthogonal matrix, and $\Sigma$ is given as
\begin{equation*}
\Sigma = \begin{bmatrix}
D & 0 \\
0 & 0
\end{bmatrix},
\end{equation*}
where $D$ represents spectral distribution of $W$ as follows
\begin{equation*}
D = \begin{bmatrix}
\sigma_{1} & & &\\
& \sigma_2 & &\\
& & \ddots & \\
& & & \sigma_{r}
\end{bmatrix}.
\end{equation*}
To avoid spectral collapse, the following steps are followed to obtain spectral regularized weights:
\begin{enumerate}
\item To compensate $D$, $\Delta D$ is found, where $\Delta D$ is given by
\begin{equation*}
\Delta D = \begin{bmatrix}
{\sigma_{1}-\sigma_{1}} & \hdots & \hdots & \hdots & \hdots & 0\\
0 & \ddots & \hdots & \hdots & \hdots & \vdots \\
\vdots & \hdots & {\sigma_{1}-\sigma_{i}} & \hdots & \hdots & \vdots\\
\vdots & \hdots & \hdots & 0 & \hdots & \vdots \\
\vdots & \hdots & \hdots & \hdots & \ddots & \vdots \\
0 & \hdots & \hdots & \hdots &\hdots & 0 \\
\end{bmatrix}.
\end{equation*}
Here $i$ is a hyper-parameter such that
\begin{equation*}
1 \le i \le r.
\end{equation*}
\item $D'$ is formed from $D$ and $\Delta D$
\small
\begin{equation*}
D' = D + \Delta D =\begin{bmatrix}
\sigma_{1} & \hdots & \hdots & \hdots & \hdots & 0\\
0 & \ddots & \hdots & \hdots & \hdots & \vdots\\
\vdots & \hdots & \sigma_{1} & \hdots & \hdots & \vdots\\
\vdots & \hdots & \hdots & \sigma_{i+1} & \hdots & \vdots\\
\vdots & \hdots & \hdots & \hdots & \ddots & \vdots\\
0 & \hdots & \hdots & \hdots & \hdots & \sigma_{r} \\
\end{bmatrix}.
\end{equation*}
\item $W$ turns to $W'=W +\Delta W$ such that
\begin{equation*}
W'= U \cdot \begin{bmatrix}
D & 0 \\
0 & 0
\end{bmatrix} \cdot V^{T} + U \cdot \begin{bmatrix}
{\Delta D} & 0 \\
0 & 0
\end{bmatrix} \cdot V^{T},
\end{equation*}
where $\Delta W = U \cdot \begin{bmatrix}
{\Delta D} & 0 \\
0 & 0
\end{bmatrix} \cdot V^{T}.$
\item To maintain Lipschitz continuity, spectral normalization is applied. Spectral regularized weights $(W_{SR}(W))$ are obtained as follows
\begin{equation*}
W_{SR}(W) = W'/\sigma(W) = {(W + \Delta W)}/\sigma(W).
\end{equation*}
\end{enumerate}
\begin{figure*}[h!]
\centering
\includegraphics[scale=0.35]{Current_ref_layersV3.png}
\caption{\label{figure:2b}Performance of GAN model with different hidden layers w.r.t. Cadence for current reference circuit data.}
\end{figure*}
\begin{figure*}[t!]
\centering
\begin{subfigure}[b]{0.30\textwidth}
\centering
\includegraphics[width=\textwidth]{currentref_3l_00025_3v6}
\caption{$\alpha=0.00025$}
\label{figure:8}
\end{subfigure}
\begin{subfigure}[b]{0.30\textwidth}
\centering
\includegraphics[width=\textwidth]{currentref_3l_0005_3v6.png}
\caption{$\alpha=0.0005$}
\label{figure:7}
\end{subfigure}
\begin{subfigure}[b]{0.30\textwidth}
\centering
\includegraphics[width=\textwidth]{currentref_3l_001_3v6.png}
\caption{$\alpha=0.001$}
\label{figure:6}
\end{subfigure}
\caption{Here, $\alpha$ represents the learning rate for ADAM optimizer. Performance of GAN model with three layers for Current reference dataset (see Table \ref{table:data}) for different learning rates.}
\label{figure:58}
\end{figure*}
We compared the performance of our GAN with spectral normalization and spectral regularization. To obtain quality data augmentation we use density distribution plots and calculate KL divergence between the distributions of generated data and training data to understand and compare the performance. Here, KL divergence is a measure of how one probability distribution differs from another. We found spectral regularization indeed delivers better results. The results are summarized in the next section.
\section{Numerical Experiments}
\subsection{Setup of Experiments}
We use {\tt Python-3.8.16} and Google Colab for the training of GAN models. Moreover, our implementation uses {\tt Keras-2.9.0} and {\tt Tensorflow-2.9.2}.
\subsubsection{GAN Architecture}
For each dataset, a GAN model consisting of a discriminator model and a
generator model was formed. The discriminator and generator models are neural networks with the same number of layers. The generator network has input dimensions the same as the latent dimensions. Input to the generator is randomly generated latent points. Generator network has output dimensions the same as the dimensions of real data points. Discriminator network has input dimensions the same as the dimensions of
real data points. Discriminator network has output dimension of 1 for the output as classification into artificial or real. For the hidden layers, we have used the leaky ReLU activation function. The output layer for the generator model uses a hyperbolic tangent activation function, whereas, the output layer for the discriminator model uses sigmoid activation. Both these networks in sequential form create the GAN architecture.
\subsubsection{Performance Evaluation of GAN}
Assessing the performance of different GAN models is necessary to compare the quality of synthetic data generated. Numerous quantitative and qualitative measures have been suggested relating to the evaluation and interpretation of generative models \cite{b10}, for example, inception score, Frechet inception distance, average log-likelihood, Parzen window estimates, and visual fidelity. These measures have been proposed to focus on image data generation; moreover, a single standard cannot cover all facets of image generation. Thus, there is no concurrence regarding the best measure \cite{b10}.
Theis et al. \cite{b11} also pointed out that a model may perform well concerning a measure and not perform well concerning others. They \cite{b11} also suggested that evaluation for generative models needs to be done directly in the context of the intended application.
Thus keeping the above points in mind, the performance analysis of the GAN models was first done with respect to a trained Artificial Neural Network(ANN) model. GAN was used to generate data comprising input features and output features for ANN, then gave the generated input features (generated by GAN generator) to ANN as input. The ANN predicted the value of the output feature for these input feature values. Then both the output values were compared. Despite the small overall percentage error, the generated synthetic datasets had a high percentage error for many individual samples. To get a proper idea of the artificial dataset quality, we changed our approach for evaluation.
We finally evaluated the GAN models for circuit data directly with respect to the simulator, which was the source of our data itself. We select a few features from the generated synthetic dataset and
give them as input to the simulator. Let us call these features as input features and the remaining features as output features. Now we compare the output feature
values from the simulator and the generator. Our metric for comparison
is the average percentage error. Figure \ref{figure:56} shows the complete evaluation process for artificially generated data.
Very few real data samples are used for our experiments to train the GAN. Then artificial data samples are generated using only the generator. Next, we evaluate the GAN performance using these artificial samples, as shown in Figure \ref{figure:56}. If we observe a reduction in error with increasing epochs, we keep training the GAN for more epochs and then save the model with satisfactory performance. If the error does not reduce or keeps increasing, we tune the hyperparameters and try to obtain satisfactory performance. Figure \ref{figure:57} explains the complete experimental process for training the GAN on circuit data.
\subsection{Results}
We evaluated our GAN with respect to a pre-trained ANN model which was trained on the current reference circuit data.
The performance specifications of this ANN model are listed in Table \ref{table:2}.
\begin{table}
\centering
\begin{tabular}{|p{4cm}|p{2.5cm}|}
\hline
Mean squared error & 1.92e-05\\ \hline
Root mean squared error & 0.004\\ \hline
Mean absolute error & 0.003\\ \hline
R2 Score & 0.991 \\ \hline
Mean Percentage error & 0.88 \\ \hline
\end{tabular}
\caption{\label{table:2}Performance of trained ANN w.r.t. Cadence.
}
\end{table}
\begin{table}
\centering
\begin{tabular}{|p{0.8cm}|p{1.2cm}|p{1.2cm}|p{1.2cm}|p{1.2cm}|}
\hline
\textbf{ } & \textbf{Model 1} & \textbf{Model 2} & \textbf{Model 3} & \textbf{Model 4} \\ \hline
MSE & 4.6e-13 & 3.7e-13 & 1.2e-13 & 3.2e-13\\
RMSE & 6.8e-07 & 6.1e-07 & 3.5e-07 & 5.6e-07\\
MAE & 5.9e-07 & 4.8e-07 & 2.6e-07 & 4.3e-07\\\hline
\end{tabular}
\caption{\label{table:3}Performance of GAN w.r.t. ANN for current reference circuit data. Here MSE stands for mean square error, RMSE stands for root mean square error, and MAE stands for mean average error.}
\end{table}
The artificial data generated using generator network was then given to ANN and the error was calculated for the predicted output as shown in Table \ref{table:3}.
However, this evaluation method had drawbacks. Despite the small mean squared error, we observed that the synthetic data-sets generated had high absolute percentage error for many individual samples.
Therefore, we compared the output feature values from the generator and the simulator to get the right idea of performance (see Figures \ref{figure:58},\ref{figure:2b},\ref{figure:59}).
\subsubsection{Hyperparameter Search} We began our hyper-parameter search by looking for the optimum number of layers. We observed the performance of the GAN model with varying numbers of hidden layers (refer to Figure~\ref{figure:2b}).
We observed that the increasing number of hidden layers seemed too complex for our data sets, and this benefited very little in decreasing the percentage error. Moreover, more layers will lead to more computation time for calculating spectral values while using spectral regularization or normalization. Hence, we reduced the number of layers.
From Figure~\ref{figure:2b}, we find that there is no clear choice for the number of hidden layers as two and three hidden layers both perform well for all input features simultaneously. We used three hidden layers for the current reference dataset as a tradeoff between model complexity and performance. For some datasets, we used two hidden layers with comparable performance.
We next experiment with different learning rates. Figure~\ref{figure:58} shows that a learning rate of around 0.0005 provides a low percentage error.
\begin{figure*}
\centering
\begin{subfigure}[b]{0.445\textwidth}
\centering
\includegraphics[width=0.75\textwidth]{SR_currentref_3l_0005_3v4}
\caption{Performance of GAN model with 3 hidden layers and learning rate 0.0005 with spectral regularization w.r.t. Cadence Virtuoso\ for current reference circuit data.}
\label{figure:11}
\end{subfigure}
\begin{subfigure}[b]{0.38\textwidth}
\centering
\includegraphics[width=\textwidth]{SN_currentref_3l_0005_3v5.png}
\caption{Performance of GAN model with 3 hidden layers learning rate 0.0005 and spectral normalization w.r.t. Cadence Virtuoso for current reference circuit data.}
\label{figure:10}
\end{subfigure}
\caption{Performance of GAN model with 3 layers for Current reference dataset after applying spectral methods.}
\label{figure:59}
\end{figure*}
On further investigation, we find that the GAN suffers from mode collapse, i.e., the model becomes good at generating only a few points from the entire training data distribution. Thus, the generator generates only these points and successfully fools the discriminator. This is evident in Figure \ref{figure:12}, where the density distribution of generated data without spectral regularization or normalization has peaked in some areas of training data only. This shows the generated data is less diverse. Also, the KL divergence is high for the generated data distribution (refer Figure \ref{figure:12}).
\begin{table*}[h!]
\centering
\begin{tabular}{|p{3.2cm}|p{1.6cm}|p{1.8cm}|p{2.3cm}|p{3cm}|p{3.1cm}|}
\hline
\textbf{Complex digital circuit} & \textbf{Simulated delay(ps)} & \textbf{Predicted delay with real data(ps) } & \textbf{Predicted delay with real + artificial data(ps)} & \textbf{Error in predicted delay with real data(\%) } & \textbf{Error in predicted delay with real + artificial data(\%) } \\ \hline
ISCAS C17 & 10.7 & 11 & 10.6 & 3.08 & 0.65\\ \hline
4-bit ripple carry adder & 41 & 43.1 & 42 & 5 & 2.4\\ \hline
\end{tabular}
\caption{\label{table:complexcircuits}Comparison of percentage error w.r.t. simulated delay for the predicted delay in complex digital circuits.}
\end{table*}
\begin{table*}[h!]
\centering
\begin{tabular}{|p{4.8cm}|p{1.05cm}|p{1.05cm}|p{1.05cm}|p{1.05cm}|p{1.05cm}|p{1.05cm}|p{1.05cm}|p{1.05cm}|}
\hline
Delay dataset & \multicolumn{8}{|c|}{Average percentage error} \\
\cline{2-9}
{} & delay lh node a & delay hl node a & delay lh node b & delay hl node b &
delay lh node c & delay hl node c & delay lh node d & delay hl node d\\ \hline
NOT gate & 7.00 & 5.81 & - & - & - & - & - & - \\ \hline
Two input NAND gate & 5.43 & 6.01 & 6.06 & 6.52 & - & - & - & - \\ \hline
Two input AND gate & 5.75 & 5.26 & 6.42 & 5.81 & - & - & - & - \\ \hline
Two input NOR gate & 7.30 & 4.87 & 7.34 & 5.36 & - & - & - & - \\ \hline
Two input OR gate & 6.05 & 5.77 & 5.49 & 6.37 & - & - & - & - \\ \hline
Two input XOR gate & 5.83 & 5.90 & 5.25 & 4.63 & - & - & - & - \\ \hline
Three input AND-OR circuit & 8.85 & 7.25 & 6.80 & 8.05 & 5.9 & 8.74 & - & - \\ \hline
Full adder & 4.50 & 4.54 & 4.24 & 3.57 & 3.80 & 3.30 & - & - \\ \hline
2:1 Multiplexer & 5.37 & 4.38 & 5.45 & 4.78 & 5.84 & 5.58 & - & -\\ \hline
Three input NAND gate & 9.15 & 4.44 & 8.71 & 4.27 & 8.37 & 6.19 & - & -\\ \hline
Three input AND gate & 5.41 & 5.10 & 4.64 & 4.64 & 5.41 & 4.19 & - & -\\ \hline
Three input NOR gate & 7.09 & 4.32 & 6.62 & 4.25 & 7.41 & 4.37 & - & -\\ \hline
Four input AND-OR circuit (AO22) & 5.13 & 3.71 & 4.60 & 4.13 & 5.50 & 4.15 & 5.01 & 4.77 \\ \hline
Four input AND-OR circuit (AO31) & 5.40 & 4.91 & 5.50 & 6.11 & 5.15 & 5.42 & 5.48 & 6.04 \\ \hline
\end{tabular}
\caption{\label{table:errordigitaldata}Percentage error obtained for different digital circuit datasets used in this work.}
\end{table*}
\subsubsection{Effect of Spectral Normalization and Spectral Regularization for Avoiding Mode Collapse}
To deal with the issue of mode collapse, we experimented with the spectral normalization proposed by Takeru Miyato et al. \cite{b9} and spectral regularization proposed by Kanglin Liu et al. \cite{b8}. We observe that both of these methods successfully avoid mode collapse in our models, as seen in the distribution plot in Figure \ref{figure:12}. The plots show that although the error percentage is slightly more, the generated data has a diverse distribution. The increase in error can be attributed to the absence of mode collapse.
On comparing spectral regularization and spectral normalization, we found spectral regularization to be performing better with respect to distribution plots (Figure \ref{figure:12}) as well as average percentage error, refer to
Figure \ref{figure:11} and Figure \ref{figure:10}. Moreover, Figure \ref{figure:12} also confirms that the Kl divergence for the data distribution generated using spectral regularization is lower than the KL divergence for the data distribution generated using spectral normalization.
We train the GAN model with spectral regularization on various other similar datasets from different analog circuits (Refer Table \ref{table:data}) and digital circuits (Refer Table \ref{table:digitaldata}). Figure \ref{figure:60} shows a reduction in error with increasing epochs for data from other analog circuits, Figure \ref{figure:61}
shows the same for delay datasets from various digital circuits. Table \ref{table:errordigitaldata} shows the low percentage error obtained for various digital circuits. Figure
\ref{figure:23},\ref{figure:25},\ref{figure:26} and \ref{figure:27} show the distribution density plots fitting towards the training data distribution with increasing epochs for few circuits. These figures also ensure that the GAN is free from mode collapse. Hence, we can infer that the generated artificial data is high quality and can be applied to other applications.
\subsubsection{Experiments on Complex Circuits}
As proposed earlier, data augmentation and synthetic data generation can prove helpful for training good ML models for different electronic designs. We experimented with training ML models for some complex digital circuits. We compared the performance of the same model by training with very few real data samples and then training after adding the synthetic data to increase the training data size. We find that the model performs better when we add artificial data samples. The above digital circuits(Refer Table \ref{table:digitaldata}) are the building blocks for various complex digital circuits. Thus, we used the data generated for these basic circuits for training ML models for complex digital circuits.
We used ISCAS benchmark C17 circuit and a 4-bit ripple carry adder for our experiments. We tested a gradient-boosting regression model to predict the delays for the complex circuits. After training on data, the model predicted the delay for individual digital blocks/gates in the circuit, which we used to find the overall delay in the circuit. As shown in Table \ref{table:complexcircuits}, we find a decrease in percentage error for predicted delay when we use the artificial data in addition to actual data for training the ML model for the circuits. Table \ref{table:complexcircuits} shows the decrease is more than 50\% of the original error.
\begin{figure*}[h]
\centering
\includegraphics[max size={\textwidth}{\textheight}]{Current_ref1v5.png}
\caption{\label{figure:12}Comparison of the distribution of training dataset for current reference circuit and various generated datasets. KL divergence between data distributions from different generators with respect to training data is also shown in the lower left. (KL divergence measures how one probability distribution differs from another.)}
\end{figure*}
\begin{figure*}
\centering
\begin{subfigure}[b]{0.325\textwidth}
\centering
\includegraphics[width=\textwidth]{SR_LDO_combinedv5.png}
\caption{$GAN\ models\ wrt\ Microcap\ for\ LDO\\ circuit.\ (Best\ performance\ with\ 2\ hidden\\ layers\ and\ learning\ rate\ of\ 0.001)$}
\label{figure:15}
\end{subfigure}
\begin{subfigure}[b]{0.325\textwidth}
\centering
\includegraphics[width=\textwidth]{SR_OTA_3l_0005_3v3.png}
\caption{$GAN\ model\ with\ 3\ hidden\ layers\ and\\ learning\ rate\ of\ 0.0005\ wrt\ Cadence\\ Virtuoso\ for\ OTA\ circuit.$}
\label{figure:16}
\end{subfigure}
\begin{subfigure}[b]{0.325\textwidth}
\centering
\includegraphics[width=\textwidth]{SR_COMP_3l_0005_3v3.png}
\caption{$GAN\ model\ with\ 3\ hidden\ layers\ and\\ learning\ rate\ of\ 0.0005\ wrt\ Cadence\\ Virtuoso\ for\ Comparator\ circuit.$}
\label{figure:18}
\end{subfigure}
\caption{Performance of GAN models with spectral regularization for different analog circuit datasets.}
\label{figure:60}
\end{figure*}
\begin{figure*}
\centering
\begin{subfigure}[b]{0.325\textwidth}
\centering
\includegraphics[width=\textwidth]{NAND2_delayCv3.png}
\caption{$Model\ with\ 3\ hidden\ layers\ for\\ delay\ in\ two\ input\ NAND\ gate.$}
\label{figure:31}
\end{subfigure}
\begin{subfigure}[b]{0.325\textwidth}
\centering
\includegraphics[width=\textwidth]{NOR2_delayCv3.png}
\caption{$Model\ with\ 2\ hidden\ layers\ for\\ delay\ in\ two\ input\ NOR\ gate.$}
\label{figure:33}
\end{subfigure}
\begin{subfigure}[b]{0.325\textwidth}
\centering
\includegraphics[width=\textwidth]{AO12_delayJv3.png}
\caption{$Model\ with\ 3\ hidden\ layers\ for\ delay\\ in\ three\ input\ AND-OR\ (AO12)\ gate.$}
\label{figure:42}
\end{subfigure}
\vspace{-0.16cm}
\begin{subfigure}[b]{0.325\textwidth}
\centering
\includegraphics[width=\textwidth]{FA_delayCv3.png}
\caption{$Model\ with\ 3\ hidden\ layers\ for\\ delay\ in\ Full\ adder.$}
\label{figure:43}
\end{subfigure}
\begin{subfigure}[b]{0.325\textwidth}
\centering
\includegraphics[width=\textwidth]{MUX21_delayCv3.png}
\caption{$Model\ with\ 3\ hidden\ layers\ for\\ delay\ in\ $2:1$\ Multiplexer.$}
\label{figure:44}
\end{subfigure}
\begin{subfigure}[b]{0.325\textwidth}
\centering
\includegraphics[width=\textwidth]{NAND3_delayBv3.png}
\caption{$Model\ with\ 3\ hidden\ layers\ for\ delay\\ in\ three\ input\ NAND\ gate.$}
\label{figure:45}
\end{subfigure}
\begin{subfigure}[b]{0.325\textwidth}
\centering
\includegraphics[width=\textwidth]{AND2_delayCv3.png}
\caption{$Model\ with\ 3\ hidden\ layers\ for\\ delay\ in\ two\ input\ AND\ gate.$}
\label{figure:29}
\end{subfigure}
\begin{subfigure}[b]{0.325\textwidth}
\centering
\includegraphics[width=\textwidth]{OR2_delayCv3.png}
\caption{$Model\ with\ 3\ hidden\ layers\ for\\ delay\ in\ two\ input\ OR\ gate.$}
\label{figure:48}
\end{subfigure}
\begin{subfigure}[b]{0.325\textwidth}
\centering
\includegraphics[width=\textwidth]{AO22_delayCv3.png}
\caption{$Model\ with\ 2\ hidden\ layers\ for\ delay\\ in\ four\ input\ AND-OR22\ gate.$}
\label{figure:49}
\end{subfigure}
\begin{subfigure}[b]{0.325\textwidth}
\centering
\includegraphics[width=\textwidth]{AND3_delayCv3.png}
\caption{$Model\ with\ 4\ hidden\ layers\ for\\ delay\ in\ three\ input\ AND\ gate.$}
\label{figure:50}
\end{subfigure}
\begin{subfigure}[b]{0.325\textwidth}
\centering
\includegraphics[width=\textwidth]{NOR3_delayCv3.png}
\caption{$Model\ with\ 4\ hidden\ layers\ for\\ delay\ in\ three\ input\ NOR\ gate.$}
\label{figure:51}
\end{subfigure}
\begin{subfigure}[b]{0.325\textwidth}
\centering
\includegraphics[width=\textwidth]{AO31_delayCv3.png}
\caption{$Model\ with\ 4\ hidden\ layers\ for\ delay\\ in\ four\ input\ AND-OR31\ gate.$}
\label{figure:52}
\end{subfigure}
\caption{Performance of GAN models with learning rate=0.0005 and spectral regularization, for delay datasets of different digital circuits wrt HSPICE.}
\label{figure:61}
\end{figure*}
\begin{figure*}[h]
\centering
\includegraphics[max size={\textwidth}{\textheight}]{OTABv5.png}
\caption{\label{figure:23}Comparison of distribution of training dataset for OTA circuit and various generated datasets using a generator with three hidden layers and learning rate 0.0005 at different epochs. (Epoch with lowest percentage error highlighted in red.)}
\end{figure*}
\begin{figure*}[h]
\centering
\includegraphics[max size={\textwidth}{\textheight}]{COMPBv5.png}
\caption{\label{figure:25}Comparison of distribution of training dataset for comparator circuit and various generated datasets using a generator with three hidden layers and learning rate 0.0005 at different epochs. (Epoch with lowest percentage error highlighted in red.)}
\end{figure*}
\begin{figure*}[h]
\centering
\includegraphics[max size={\textwidth}{\textheight}]{AND2C_delay_distributionv7.png}
\caption{\label{figure:26}Comparison of distribution of training dataset for delay in two input AND gate circuit and various generated datasets using a generator with three hidden layers and learning rate 0.0005 at different epochs. (Epoch with lowest percentage error highlighted in red.)}
\end{figure*}
\begin{figure*}[h]
\centering
\includegraphics[max size={\textwidth}{\textheight}]{NAND2C_delay_distributionv7.png}
\caption{\label{figure:27}Comparison of distribution of training dataset for delay in NAND gate circuit and various generated datasets using a generator with three hidden layers and learning rate 0.0005 at different epochs. (Epoch with lowest percentage error highlighted in red.)}
\end{figure*}
\section{Conclusion}
This paper presents an artificial data generation method for circuits to aid the training of ML models for design automation, tuning, optimization, etc. Model accuracy is heavily dependent on the quantity and quality of training data, but large amounts of training data for electronic circuits can be computationally expensive or practically difficult to obtain. The generated synthetic data is beneficial for training the models when the training data is scarce.
GANs have been used in image and audio data modality and have provided promising results in terms of quality and speed. This work adapts GAN to create artificial data for various electronic circuits.
The training data are obtained by various simulations in the Cadence Virtuoso, HSPICE, and Microcap design environment with TSMC 180nm and 22nm CMOS technology nodes. An evaluation methodology using the simulators is proposed to evaluate the quality of generated data. Spectral regularization has been used to avoid mode collapse in GAN. Artificial data has been generated and tested for six analog and fourteen basic digital circuit designs. The experimental results confirm a low average percentage error for the generated data. The proposed artificial data has finally been applied to gradient-boosting regression models for predicting delays in the ISCAS benchmark C17 circuit and a four-bit ripple carry adder. The simulation results show a reduction in model percentage error by more than 50\% of the previous percentage error when additional artificial data is used for training.
The proposed methodology for generating artificial data has the potential to be applied to many other circuit designs and provide greater accuracy to ML models, especially when the training data is scarce and is challenging to obtain.
\clearpage
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{
"redpajama_set_name": "RedPajamaArXiv"
}
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Home > INSTRUCTION > State Standards and Frameworks > disciplinary_literacy
Teaching And Learning: Disciplinary Literacy
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Welcome, Maryland Educators!
This section of the site was developed to support educators in the teaching of disciplinary literacy in Science and Technical Subjects as well as Social Studies and History. The site contains resources to support you in the classroom when implementing the Disciplinary Literacy Frameworks (Standards). You may want to bookmark this page as your mdk12.org homepage.
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Disciplinary Literacy Education
WHAT IS DISCIPLINARY LITERACY?
DISCIPLINARY LITERACY STANDARDS
TEXT COMPLEXITY IN THE DISCIPLINARY LITERACY CLASSROOM
TEXT DEPENDENT QUESTIONS IN THE DISCIPLINARY LITERACY CLASSROOM
PLANNING PROCESS FOR DISCIPLINARY LITERACY
Disciplinary Literacy in Maryland — A Shared Responsibility for Students' Literacy Development
Literacy skills are an important part of every academic discipline. However, each discipline relies on different types of texts, writing styles, and language to convey ideas and learning. For students to be fully prepared for the challenges and expectations of college and career, it is critical that they develop literacy skills in all content areas. As Maryland transitions into the Common Core State Curriculum, educators in all science, technical subjects, and history/social studies classrooms will be expected to incorporate content-specific literacy into their instruction.
Definition of Disciplinary Literacy:
Disciplinary Literacy is the use of discipline-specific practices to access, apply, and communicate content knowledge.
Maryland Common Core State Curriculum Frameworks
In June, 2010, the Maryland State Board of Education adopted the Common Core State Standards for English Language Arts K-12 and Literacy in History/Social Studies, Science, and Technical Subjects 6-12. These Standards represent a shift in reading to explicitly identify and include reading and writing standards in the content areas of Science /Technical Subjects and History/Social Studies as companions to the English Language Arts Standards. Collectively, these standards represent a shared responsibility for reading and writing across content areas. The Common Core Standards for Disciplinary Literacy are organized by content: Science, Technical Subjects, and History/Social Studies. Each set of standards is further organized into strands for reading and writing. It is important to view the draft frameworks in color. The Common Core State Standards appear in black. The Standards specify the literacy skills and understandings required for college and career readiness in each discipline. The Essential Skills and Knowledge added by Maryland Educators appear in red and support the understanding of each Standard. Standards for K-5 reading in History/Social Studies, Science, and Technical Subjects are integrated into the K-5 Reading Standards.
LITERACY FOR HISTORY/SOCIAL STUDIES, SCIENCE & TECHNOLOGY FRAMEWORKS: (PDF)
DISCIPLINARY LITERACY FRAMEWORKS
READING IN HISTORY/SOCIAL STUDIES
WRITING IN HISTORY/SOCIAL STUDIES
READING IN SCIENCE & TECHNOLOGY
WRITING IN SCIENCE & TECHNOLOGY
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{"url":"https:\/\/www.man.com\/maninstitute\/ri-podcast-elizabeth-mrema","text":"# A Sustainable Future: Why Biodiversity Is a Financial Risk\n\n### Elizabeth Mrema, United Nations Assistant Secretary-General and Executive Secretary of the Convention on Biological Diversity (CBD), discusses COP-15 and the new biodiversity framework.\n\nIt is well established that climate change poses significant risks to businesses and future investments but these concerns are often intricately connected to biodiversity and nature-related issues. Elizabeth Mrema, Executive Secretary of the United Nations Convention on Biological Diversity, and co-chair of the Taskforce on Nature-related Financial Disclosures joins the podcast to discuss how firms can report and act on evolving nature-related risks.\n\nIn this far-reaching conversation, Elizabeth Mrema and Jason Mitchell, co-Head of Responsible Investment at Man Group, talk about the upcoming UN Biodiversity Conference COP-15, the legacy of the 2010 governmental Aichi Biodiversity Targets and what the new expectations may be for a post-pandemic global biodiversity framework.\n\nRecording date: 05 August 2021\n\nElizabeth Mrema, UN Convention on Biological Diversity, on Why Biodiversity Loss is a Business Risk.\n\nElizabeth Maruma Mrema is United Nations Assistant Secretary-General and Executive Secretary of the Convention on Biological Diversity (CBD), a multilateral treaty addressing the loss of biodiversity and climate change, and co-chair of the Taskforce on Nature-related Financial Disclosures (TNFD).\n\nElizabeth has two decades of experience working in the development and environment sectors. She is biodiversity leader and lawyer, from Tanzania, with a track record of negotiating next-generation policies and enabling instruments for planet, people, and prosperity. Elizabeth\u2019s work as Deputy Director of the Ecosystems Division at the UN Environment Programme (UNEP) focused on the development, implementation, and enforcement of environmental laws both at the national, regional, and international level.\n\nHer previous work includes being the Executive Secretary of the UNEP\/Secretariat of the Convention on the Conservation of Migratory Species of Wild Animals (CMS) in which she oversaw the conservation of migratory animals globally.\n\n## Episode Transcript\n\n##### Note: This transcription was generated using a combination of speech recognition software and human transcribers and may contain errors. As a part of this process, this transcript has also been edited for clarity.\n\nJason Mitchell:\n\nWelcome to the podcast, Executive Secretary Elizabeth Mrema. It's great to have you here, and thanks so much for taking the time today.\n\nElizabeth Mrema:\n\nThank you. Thank you very much.\n\nJason Mitchell:\n\nI appreciate it. So, Elizabeth, we have a lot of great stuff to talk about. I'd like to start out doing some scene setting. It seems like a reflection of the 2010 Aichi Convention is, in some ways the natural starting point for our discussion, given the lessons on how to structure new biodiversity targets in the upcoming, UN Biodiversity Conference or COP-15 that's planned to be held in Kunming, China this October. So how is the fact that no nation met the 20 original Aichi Biodiversity Targets from 2010, shaped negotiations and expectations around new commitments and targets going this year into COP-15?\n\nElizabeth Mrema:\n\nThank you. Thank you very much for the question I just want to add, which is very important, but I would like to make a bit of correction. You see, at times when we say none of the 20 Aichi Targets were met, I'm sure governments might be disappointed. Because there are some targets not fully achieved or fully met, but a lot of progress had been made to about six of them, without which the situation would have been even more terrible than where we are today. So I think we need to give credit to where a little progress has been made, and if that is scaled up in the future we might be in a better position.\n\nElizabeth Mrema:\n\nNonetheless, yes. None of the targets was fully met, although as we speak now, one target is about to be reached or already reached and this is Target 11 on protected areas. 17% of the terrestrial land has been reached with a few decimal points remaining for the 10% required for the marine environment. So why we fail to achieve all the 20 targets fully as expected a decade ago? There are several reasons, and I will try just to highlight some key ones. One, there was an expectation I think, that the responsibility for the implementation or reaching out the Aichi Biodiversity Targets, squarely laid on governments.\n\nElizabeth Mrema:\n\nWhile we know very well, biodiversity affects every aspect of the society and everybody, and therefore it needed everybody, all stakeholders to be part and parcel for its implementation. But the problem that could not have been part and parcel of its implementation because not all of them were engaged in its development. So it did not engage all stakeholders in its development, and that paid off negatively when it came to implementation. Even at government level, with that expectation that was the responsibility of the government. And because the Aichi Biodiversity Targets, most of our focal points are ministries or departments of environment.\n\nElizabeth Mrema:\n\nAgain, a national level there was that lack of whole of government, whole of society, integrated mainstreamed approach for its implementation, and it became then the responsibility of ministries of environment and not all government departments. We know very well for many countries to-date, ministries of environment at national level, for a number of countries are \"The weak,\" ministries comparing to other ministries, which are considered more of a priority at national level finance, planning, agriculture, fisheries, and water view.\n\nElizabeth Mrema:\n\nWhile environment brings all of them together and a whole society, whole of government approach. Also the Aichi Targets were adopted without a review monitoring mechanisms. So over the period, we are not able to assess progress of its implementation and be able to adjust as we went along. And then furthermore, the Aichi Biodiversity Targets were expected to be implemented for 10 years, 2011 to 2020. Many countries took a step back, began developing National Biodiversity Action Plan and Strategies. And it's a consultative process, rightly so, but that process took three or four years before it was completed.\n\nElizabeth Mrema:\n\nSo actually for many countries, the actual implementation began after three or four years. So practically, the decade ended up being half way decade, and therefore probably the six partly achieved targets could have been fully achieved, who knows if that time lag had not been lost. And then of course issues of clarity, understanding the targets was also an issue. As negotiators and when we look at biodiversity issues, actually those mostly affected are people on the ground and these are the ones that need the scientific documents to be translated into simpler language, which they can understand.\n\nElizabeth Mrema:\n\nAnd in many cases, probably even to their local languages. So, that kind of clarity also had an impact in the status of implementation. And then of course, major aspect of it was lack of financial resources, matches Aichi Target I think 19, had expected international financial flows to double, much as international financial flows increased tremendously, but was not adequate to support fully implementation of the Aichi Biodiversity Targets. So there was that lack of financial resources, which then compromised the achievement.\n\nElizabeth Mrema:\n\nInadequate political will also could have been another factor into the equation, and all of this put together resulted into the state of affairs we found ourselves 2020, the end of the Aichi Biodiversity Target ended. What have we learned from that, especially as we are now in the current process for the development of the new post 2020 global biodiversity framework? So that we don't repeat the mistakes of the past, but at the same time, we take the positive lessons from that and build into the new framework which is being led by the two co-chairs from Canada and Uganda.\n\nElizabeth Mrema:\n\nSo one, the development now of the new framework is ensuring an effective, participative, consultative process with literary, all stakeholders. In particular, indigenous peoples, local communities, the youth, the women, the private sector, and when I talk private sector, I mean the banks, the insurance, the industry, the business. And through this engagement, we have seen for instance, particularly with the private sector, where we initiatives now like business for nature, finance for nature, and a whole lot of work currently going on under the world economic forum linking nature, finance and economics.\n\nElizabeth Mrema:\n\nAgain, this came is the result of that. Furthermore, when the party set up the process for the development of the framework, they categorically asked for a simpler, smart targets of the framework. And what did they mean by smart? The targets have to be specific, measurable, achievable, realistic, and time-bound, so is to be able to pave the way to a more comprehensive and successful, hopefully this year framework. The first draft of the framework has already been issued since 12th of July. It will be now negotiated between 23rd August to September 3rd this year.\n\nElizabeth Mrema:\n\nAnd the framework again, will be accompanied with a glossary, with an indicator plus a component of means of implementation. And under the means of implementation, we'll have resource mobilization strategic, capacity building technology, framework component, review and monitoring mechanism. And we hope with the new framework when it is adopted, there will be no, again, delay of three, four years as we did for the Aichi Targets, because all our parties now have the National Biodiversity Strategy and Action Plans already in place.\n\nElizabeth Mrema:\n\nAnd because the framework is building on the Aichi Biodiversity Targets, so there are tools to begin implementation and if update will be needed, we'll then be done in tandem as opposed to taking a pause and do the update first. So if that happens, then we will have a full decade, which is now already less by two years or a year, but I hope the party governments will be able to catch up.\n\nJason Mitchell:\n\nSo, it sounds actually quite positive. It sounds like your efforts are explicitly correcting some of those problems from Aichi 2010. I'm wondering, to what degree can you help us out in understanding the tone of some of the pre-negotiation technical committees going into COP-15 over the last couple of months? And more specifically, how are you balancing a more pragmatic agreement that reflects the disappointment and learnings of Aichi with calls by let's say the CBD Alliance for a much more ambitious action plan?\n\nElizabeth Mrema:\n\nYou see all stakeholders have agreed, including governments have agreed that the framework need to be innovative, transformative, ambitious, and all sorts of buzzwords. The question is, what is ambitious? What do we mean when we say ambitious? And if it's ambitious, is up what limit or what measurement? And I think this is where probably one who will say is a gray word or language that creates that disappointment of Aichi made by the parties and stakeholders. But that disappointment actually makes both the parties and stakeholders probably more committed to really develop a new set of targets and a more ambitious action plan.\n\nElizabeth Mrema:\n\nOf course, CBD Alliance are saying the current draft is not ambitious, but remember the draft has tried to include into it all the views which had been compiled from all stakeholders. It's a formidable task, and I don't think it's easy to really please one stakeholder and not offending the other. So that balancing act we need to realize, one. Two, the negotiations now are about to begin end of this month. We will see how the negotiations go, maybe they will further increase the ambition expected. So I think we need to give that a chance and we hope that the ambition could be increased to the level that CBD Alliance is looking for.\n\nElizabeth Mrema:\n\nBut if I go to the technical committees which we have referred, the tone was actually definitely one of cooperation among the parties. And then of course, they were able to lay the path to a participative process, in this process of development of the framework. And of course the process which was adopted by the parties to develop the framework, also has set out a set of principles to guide not just the development, but also in future its implementation. And it cannot get the implementation if the development does not take into account these principle. And those principles are participatory, inclusiveness, gender responsiveness, transformative, comprehensive, catalytic, visible, knowledge, scientifically-based, transparent, efficient, results oriented, interactive, flexible. So you see all those words are the principles guiding the framework.\n\nJason Mitchell:\n\nI see. Considering the COP-15 has been postponed twice because of COVID-19. How would you say the pandemic has influenced and shaped the policy agenda around biodiversity over the last year and a half? And it's actually worth asking because we've started to see some talk about a third delay to COP-15, the conference into next year. How likely do you think that is?\n\nElizabeth Mrema:\n\nTrue. The pandemic has resulted into the postponement of the conference of the parties twice. We are looking at meeting in October, but well the pandemic situation has been unfortunate. And we're really in solidarity with all countries globally for the loss of the people, for people getting sick, for the impacts on their social economic development as fear, but for our process in rated comments, it has given us an opportunity in terms of more time to develop the framework, more time to prepare for the conference of the parties.\n\nElizabeth Mrema:\n\nBecause I don't think, I tend to be corrected, if we had the COP last year in May, probably the first draft framework we have today, will not have been in the content we are seeing because it would have been rushed in its development. We will not have had such a wide consultative process as we have had in the last two years plus. So, all these time has given us that opportunity and this fact of working from home, it has even made it easier and cheaper to reach out to different stakeholders. Cheaper in terms of, people did not need to travel, needed to ensure they have good connectivity. It has been a challenge for a number of countries, but at least we've been able to reach out.\n\nElizabeth Mrema:\n\nThe co-chairs have been able to reach out to many stakeholders and get them engaged in this process. So that has been a major plus for our purposes. The other major plus is the better understanding, now globally. I stand to be corrected, that people know probably are more aware of the impact of biodiversity loss in the society and the impacts of human activities on nature causing biodiversity loss, causing climate change, causing the degradation, impacting on our health better than probably any other time in the history. That again has enabled to propel the focus on the content of the global biodiversity framework. What that means for the next COP, our technical committee meetings, we call them Subsidiary Bodies of Science and Implementation, which met in May and June for six weeks, virtually.\n\nElizabeth Mrema:\n\nThese meetings were to contribute to the COP-15, as well as contribute elements for the post 2020 framework. The parties agreed to postpone those meetings as opposed to closing them until when they are able to meet face to face. So if they're able to meet face to face, then it means that's when they will finalize those contributions and negotiations needed into the post 2020 and the framework. Likewise, the working group which will meet at the end of August, on that 3rd September, it will also suspend its meeting until when negotiators are able to meet face to face.\n\nJason Mitchell:\n\nI see.\n\nElizabeth Mrema:\n\nCurrently, again keeping the situation under strict review, particularly now when it comes to not just the pandemic, but also the status of vaccination, particularly for many countries, which are not as privileged as well as some of us are, so their vaccination status. Then we are looking at having the face to face probably in January.\n\nJason Mitchell:\n\nI see. I see. Let me ask you one final point around the negotiations. One of the traditional points of tension between developed and developing economies during the climate COPs was always the socioeconomic development. In fact, I remember when I was in COP-15 in Copenhagen in 2009, when this dialogue infamously broke down. To what degree has the biodiversity conventions article 20 specifically, which relates to financial resources and obligations of developed and developing countries diffuse this? I guess I'm wondering, to what degree is biodiversity in a way being used as a bargaining chip during these negotiations? How do you find the right balance between national biodiversity commitments and socioeconomic growth?\n\nElizabeth Mrema:\n\nAs we move through the negotiations, we will have a better picture. But for now, we are looking at one hand, the sustainable use of biodiversity being supported by enabling conditions, such as sustainable social economic development, and adequate means of implementation, which I'd mentioned earlier, issues of financial resources, capacities, and technology. And then of course, such aspects are one pillar of the fear of change underlining also the draft framework. And of course, these are those I mentioned the components of the framework, which in other words, the framework will be adopted with the means of implementation.\n\nElizabeth Mrema:\n\nAnd the means of implementation without financial resources, there can be no implementation. Without enhancing the capacity, transpiring appropriate technology, then there will be weakness in the implementation. Developing a holistic resource mobilization strategy to mobilize resources from all sources was noted as among the key issues to be discussed at our next scope. Currently, the draft framework already proposes the need to raise $200 billion per year of financial resources, which will be required for the implementation of the framework. And out of that 10 billion per year is the movement of resources from developed to developing world. Elizabeth Mrema: So clearly the recent statistics have already given us that figure and the framework has taken cognizance of that. So for many countries, how we'll get these resources will be key. But by saying so, we are also saying, it doesn't mean that the financial resources 100% have to come from international financial flows, but from all sources, international, domestic but also disincentivizing nature, negative finances. Currently, statistics show that$500 billion are spent from nature, negative outcomes and we need this to to be repurposed, redirected into nature, positive outcomes.\n\nElizabeth Mrema:\n\n$100,000 billion US alone, incentivizes harmful agriculture. So you see, if these resources are redirected, we'll already be able hopefully to get half, if not more of the required resources per year for the implementation of the framework. Not only that, the world economic forum has given us statistics which show that, almost half of the worlds total GDP specifically$44 trillion being moderately or highly dependent on nature and its benefits or services. And all we are saying there is money there, and this shows why even the private sector has an interest because these expose to risk from nature loss.\n\nElizabeth Mrema:\n\nAnd we're basically, also saying that, if we're able to transition from nature, negative economy to nature, positive economy, that will be able to generate $10 trillion in business opportunities and being able to create almost 400 million jobs by 2030, in fact, specifically 395 million jobs by 2030. So you see, there's a lot of money which he needs to be repurposed, redirected into nature positive. Jason Mitchell: How do you talk to that in terms of whether it's statistics or a message? And I guess, I want to draw out climate change as a parallel. climate change has benefited significantly from a very reductionist approach. By that I mean, by describing its arc, by say the atmosphere can increase in CO2 purports million or galvanizing governments in the private sector under the rates to net zero, which we've seen into the climate COP-26 later this month. Jason Mitchell: Critics and I fully recognize this, critics would say it's overly simplistic, but it has been incredibly effective at galvanizing climate action. What's the analog for biodiversity in your perspective? How do you condense the vast complexity and biological breadth of nature into definable targets that aren't overly general? And by that I mean, for instance, the 30% protection by 2030 target. Elizabeth Mrema: Biodiversity loss and climate change intrinsically connected. And biodiversity plays a big positive role in climate change adaptation and mitigation because biodiversity contributes about 30% of the greenhouse gas emissions. So for example, conservation of habitats can reduce the amount of carbon dioxide released into the atmosphere, and this is what the forest does. Not surprising that major subject of climate change now, and even as it prepares to COP-26, nature based solution comes out more and more. So if climate change sees nature being part of the solution for climate change clearly then for biodiversity, loss equally nature is critical. Elizabeth Mrema: If nature is degraded, it affects biodiversity. It affects climate. Although of course, for biodiversity, we'll also add ecosystem based solutions. So both nature based solutions, but also ecosystems based solution. So you can see each depends on the other, in terms of solutions. The scientific research of course still needs to identify for us all the complex interaction between biodiversity and ecosystem functioning globally. And in this context, a simple target just rates to net zero is rather challenging to conceptualize for biodiversity, because such complexity of course is considered in the context of global biodiversity. Elizabeth Mrema: And to this effect, we see the framework coming with different targets for different things, which are comprehensive enough to reflect that complexity of biodiversity and its various ecosystems. But to say, we'll be able to get the 1.5 degrees like climate in their complexity, mosaic biodiversity, which can compose many things it's still a challenge. Elizabeth Mrema: But who knows when we get into the negotiations, we might get to magic figures. Jason Mitchell: Let's switch lanes a little bit and go into the TNFD or the Taskforce on Nature-related Financial Disclosures, which congratulations, you are a recently appointed co-chair which is a fantastic role. I guess, sort of looking at TNFD, one thing that is clear is that it borrows a lot from the TCFD or the Taskforce on Climate-related Financial Disclosures, that framework which makes complete sense. One area though, where it gives much more breadth where it diverges from TCFD is in the interpretation of nature related risks and opportunities. Jason Mitchell: Yeah. Again, speaking to that vast complexity of what nature represents, is that a necessary compromise, given the lack of historical nature related data and data metrics that we have? TCFD at least had the benefit of starting with 15 years of carbon disclosure project data, as well as scope one and two, and even to some degree three GHG reporting protocol. Elizabeth Mrema: You are right. When we look at climate change issues, and the world looking at climate change or action as the case may be, it started many years ago before biodiversity became the center of discussions as it is today. And that's why I'm saying, probably pandemic has also provided that awareness opportunity, which probably would not have been where it has reached today. But you are also correct that TNFD really borrows and we rely heavily on TCFD because we don't want to reinvent the wheel. And the actors, in most cases, if we are talking to the financial sector, we are still talking to the same stakeholder. Elizabeth Mrema: So you want this stakeholder when they look at climate related risk and nature related risks, they should see that the two speak to each other, and especially if we say climate change and biodiversity loss are connected. So TCFD provides us the framework for financial institutions and corporates to be able to identify and report, not just on climate related risks, but TNFD we learn from that, build upon that to be able to now, to deliver as a framework for financial institutions and corporates to report and act on evolving nature related risks. Elizabeth Mrema: So basically is how their operations or investments will impact or impact all depends on nature. And therefore, to what extent are they exposed to nature related financial risks. TNFD of course, hopefully we'll also call on financial sector to integrate financial related risks in their decision-making, financial and corporates need decision data. And recently under the secretariat, we actually had a workshop or with financial sector in June, and basically looking aware, looking at the importance of biodiversity data is a key issue for TNFD. And because TNFD only came recently, but of course, remember the last two years we had an informal working group working on these issues with the financial sector. Elizabeth Mrema: So a lot of groundwork has already been done and would want the financial sector, not just to look, data is one, but not just only financial, I mean, in nature related risks, but also opportunities. Because if for the$4 trillion depends are highly dependent on nature, \\$10 billion per year comes from nature, there are opportunities there, clearly. So the risks and opportunities need to be looked together, but you need the data and the data then will be key. And in this workshop, of course, they underlined the importance of data collection and management of that data is still a challenge.\n\nElizabeth Mrema:\n\nAnd the express they need, the participants have relevant data being translated into a meaningful information, which they can use. And currently, of course, for a number of NGO, they were saying data is scattered across just too many data basis, and they counted about 300. So there's need to consolidate all this data and make it more easily accessible, not just to individuals, but also public and private organization.\n\nJason Mitchell:\n\nThere's another divergence between the TNFD and TCFD, which I personally welcome. I think it's fantastic to see. I do think I recognize that it is a bit contentious or controversial depending on where you're looking jurisdictionally at this. And that's around this issue of double materiality or outside in, inside out. And TNFD specifically includes it within its text, where TCFD solely looks at the financial materiality of climate impacts on the company itself so it actually doesn't address double materiality. Can you give us some context for how this came about? Also, how does this choice in some respects complicate an already complex effort?\n\nElizabeth Mrema:\n\nNot being an expert on TCFD matter, but don't try to relate that into TNFD. I think first, we need to realize just as with climate, nature related risks can affect the operations of companies, as well as financial institutions, and that's leading to financial risks. But of course these companies and financial institutions can also affect biodiversity through their activities in financing and therefore contributing to biodiversity loss. So actually many businesses are dependent on the proper sourcing of biodiversity in their supply chain.\n\nElizabeth Mrema:\n\nFurthermore, of course, for TNFD we are, as I said, is basically to recommend the use of both nature related risks, but also opportunities and take this broader perspective to refer to the risks because we know the opportunities with an organization posed by the linkages between those activities and nature. And of course, when we say opportunities, that then brings in the incentive to really see what TNFD wants to come about with, and get the financial institutions to engage into it. But in the short term, financial risks, which includes unfortunately longer term risks represented by the impacts and dependencies on nature.\n\nElizabeth Mrema:\n\nThat means that organization will need to disclose not just how nature may impact the organization's immediate financial performance in terms of looking from outside in, but also how the organizations will be impacted by nature and looking from inside out, either positively or negatively. So it will be fundamental, to consider both aspects related to nature related risks, even if this does not make our work of future business of reporting easy and will make it more complex, I think is the best way to address them better beginning it now, rather than doing it later.\n\nJason Mitchell:\n\nI agree with that. We talked a little bit about the lack of biodiversity data and at the same time, the high number of existing frameworks. And I'm wondering, in your mind, how does the TNFD avoid clashes with other initiatives? Initiatives like the OECD, Multi-Stakeholder Group, the emergence of national biodiversity policies, like the EU 2030 Biodiversity Strategy. I guess more importantly, how do you see the TNFD framework co-existing with national policy efforts?\n\nElizabeth Mrema:\n\nYes. Important question. And it's not the intention of TNFD to overlap or conflict, so it will be important to really also take stock of existing relevant initiatives. So that then TNFD either fills the gap or uses the existing information in its own to create that harmony and synergy among different initiatives, because otherwise then it will be a total confusion to the financial sector. And if we can't have them on board now, then we will lose them in the longer term causing more biodiversity loss, including climate change.\n\nElizabeth Mrema:\n\nSo what TNFD intends, we hope that the TNFD will define the framework that we'll be able to serve as a mechanism to help organizations understand, disclose and manage their financial risks and opportunities associated with a deteriorating state of nature. While of course, transitioning to an economy, consistent with meeting the future, nature related, international agreements, like our own Convention on Biological Diversity, as well as the ambition being set out in the post 2020 global biodiversity framework. We hope also there will be a need to align with and draw from the existing framework, initiative standards and avoid any duplication or conflict when we develop standards either for disclosure or broader activities themselves.\n\nElizabeth Mrema:\n\nAnd we hope that then by doing so then TNFD, intend for each outputs to be integrated into existing frameworks and standards in the space that has already been developed or published in these other different initiatives. For instance, to be able to engage and draw from the work of key bodies is like Financial Stability Board or Network of Central Banks for Greening the Financial System and the like. And we also hope that the reporting mechanism will be based on standards and national, international regulations that already exist, all being developed by governments and others stakeholders.\n\nElizabeth Mrema:\n\nFor instance, we know recently the French financial institution are required by a new law in France from their French financial regulator to disclose both biodiversity and climate related risks and impacts of their work. In the same way, the EU 2030 Biodiversity Strategy, as well as ongoing being discussed UK environment bill seek to use disclosure to understand what impacts and dependencies offer in organizational sector or nature. So all these initiatives are actually in favor of biodiversity, complimenting each other, contributing to the Aichi Biodiversity Targets. But, of course, obliging now the financial sector to report on the impacts on the dependence of their operations or nature or biodiversity.\n\nJason Mitchell:\n\nYeah. It's such an ambitious effort. How do you see the TNFD managing to be broad enough to be a common framework, yet still able to address challenges around geolocation in geo specificities? Many people sort of point to the fact that, a gallon of water in Montreal, for instance, isn't the same as a gallon of water in Chennai India?\n\nElizabeth Mrema:\n\nTNFD's approach is meant to be inclusive. It's meant to work with existing standard bodies to be able to develop that hopefully, a global framework, which draws from existing initiatives and standards that are relevant. So it is in these discussions that then we'll be able to understand, yes, we are dealing with a gallon of water, but is different from one country to the other, or different from one region to the other. And what does that mean to develop a global standard which brings align these different specificities? And of course, by doing so hopefully then the framework will undergo a lot of pile lots in order to be able to refine and ensure it's applicable in different sectors and different geographies. That's what I can see.\n\nJason Mitchell:\n\nGot it. What role do you see the private sector, particularly markets playing in biodiversity? Besides pointing to an institutional failure, I found this descriptive review out of the UK, particularly interesting in terms of it claiming that the decline in natural capital, which it seizes declining by 40% per person, between 1992 and 2014. It also represents a market failure, so it's not just an institutional failure, it's a market failure. And as we know, market prices don't reflect the true value of services and products that nature provides for free.\n\nElizabeth Mrema:\n\nYes. And indeed, that's why Dasgupta really criticize that thinking where the economic theories being used currently looking at nature as a product for free and not costing nature in its work. No wonder we've blunder it and now we are paying for it. But private sector has a key role to play in reversing nature loss. And this is what Dasgupta is reminding us in the review. Investments in nature, positive activities or companies, or transition to sustainable production practices, transformation of supply chains, assessment of impacts and dependencies on nature. Likewise, biodiversity risk identification and management all count among the initiatives, the private sector can take.\n\nElizabeth Mrema:\n\nThe public sector has on the other hand, complemental role to play also in supporting these efforts through the implementation of economic and financial sector policies and regulations that can directly then impacted the operation of companies from private sector. So among those policies that align incentives and market prices are all central in order to internalize the negative externalities. The private sector and public sector need to work together to limit and even prevent the market failures. So one cannot work against the other.\n\nJason Mitchell:\n\nI've got Elizabeth, one more question, in staying with this market's theme. Climate policy and environmental economics have, in essence, helped produce carbon markets. How do you see markets providing a price signal to protect against biodiversity the loss and nature related risks? What are the ways in which biodiversity can leverage nature based offset markets in particular?\n\nElizabeth Mrema:\n\nNumber one, of course, the climate community and biodiversity community need to work together. So as you note, ecosystem services and benefits are under-priced and therefore under provided. And hence we need the public policies institutions that may seek to address this imbalance by reforming the subsidies policies, which then compliment standards and regulations to support ecosystem conservation and restoration. We need economic instruments such as biodiversity relevant taxes, fees, and charges, tradable permits, biodiversity offsets, and payments for ecosystem services that can also be used as tools to better reflect the cost of biodiversity loss on the economy and the human wellbeing. So clearly nature can no longer be for free to plunder.\n\nJason Mitchell:\n\nSuch a great way to end this. Thank you so much, Elizabeth. So it's been fascinating to discuss how discussions are progressing into the run-up to the COP-15 UN Biodiversity Conference. What can be improved upon from the 2010 Aichi Convention Targets and why it's vital that global market led initiatives like the TNFD provide a framework to report and act on nature related risks. So I'd really like to thank you for your time and insights. I'm Jason Mitchell, Co-Head of Responsible Investment at Man Group. Here today with Executive Secretary Elizabeth Mrema, Executive Secretary of the United Nations Convention Biological Diversity and co-chair of the Taskforce on the Nature-related Financial Disclosure. Many thanks for joining us on A Sustainable Future, and I hope you'll join us on our next podcast episode. Thanks so much, Elizabeth.\n\nElizabeth Mrema:\n\nThank you very much, Jason.","date":"2021-09-28 01:33:37","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.35161659121513367, \"perplexity\": 1904.4549296525329}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-39\/segments\/1631780058589.72\/warc\/CC-MAIN-20210928002254-20210928032254-00435.warc.gz\"}"}
| null | null |
{"url":"https:\/\/northerndean.org\/2019\/04\/02\/exfat-whos-exfat\/","text":"# exFAT? Who are you calling exFAT?\n\nYeah, in the machinations around my phones and breaking them, I wanted to put a few files onto the microSD card from the phone. I put it into an adapter, put the adapter into my computer, and\u2026 filesystem exFAT not recognized?!? Hmm.\n\nI guess when I loaded up Ubuntu 18.04 onto this computer, I didn\u2019t put the exFAT utilities onto it.\n\nIt turns out that it\u2019s as simple as:\nsudo su - apt-get update apt-get install exfat-utils\n\nOf course, you need to enter the root password when you \u201csudo su\u201d.","date":"2023-02-07 11:40:36","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.4167684018611908, \"perplexity\": 5970.6444663837565}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 20, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2023-06\/segments\/1674764500456.61\/warc\/CC-MAIN-20230207102930-20230207132930-00174.warc.gz\"}"}
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There Isn't a Better Time To Join The World Tolerance Network
Some positive dialogue can go a long way….
Illustration by Brittany England via Greatist
To get through these difficult times, solidarity, respect and tolerance are extremely important. And one way to promote tolerance while supporting the "Stay Home" campaign during the COVID-19 pandemic is to register with the WorldTolerance Network.
Une publication partagée par Year of Tolerance عام التسامح (@theyearoftolerance) le 19 Févr. 2020 à 10 :35 PST
The network is inviting people to write articles about their experiences and opinions around the different topics found under the tolerance umbrella. Those who join can also participate in discussions and build a network of relationships with other members through virtually interacting with them from home.
Une publication partagée par المعهد الدولي للتسامح (@iitolerance) le 9 Janv. 2020 à 1 :42 PST
The World Tolerance Network ropes in 12 categories, including government institutions, individual, community and governmental initiatives. Youth, media platforms (including TV), social media and digital networks, human rights and charitable institutions, the private sector, research centres, as well as universities and other educational institutes are also included.
Launched last October, the World Tolerance Network is the first global digital platform that brings together tolerance enthusiasts, peace experts and academia. The aim of the network, initiated by HH Sheikh Mohammed bin Rashid Al Maktoum's The International Institute for Tolerance, is to consolidate and spread the values of tolerance. It is also working towards building global leaders and groups that contribute to providing knowledge within a sound intellectual framework away from prejudice, violence and hatred. Plus, the World Tolerance Network supports cultural exchange while respecting diversity and pluralism, in addition to accepting and respecting others' opinions in different disciplines of life.
Visit www.worldtolerancenetwork.com to get started…
By Roula Allam
World Tolerance NetworkUAEHH Sheikh Mohammed Bin Rashid Al MaktoumCOVID-19 PandemicStay Home CampaignsMental Health AdvocatesStand in SolidarityLockdownSelf-Isolation
Saudi Arabia Reintroduces Native Species Into Their Natural Habitats In AlUla
The Kingdom's Women's Football Team Makes History As They Win In International Tournament
Saudi Heritage Commission Restores The Historical Significance Of Uqair Harbor
The Mummy Of This Egyptian King Will Be Exhibited In Jeddah
Here's Saudi Arabia's Progression On Its NEOM Megaproject So Far…
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{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
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# **Orientalismo**
### **Edward W. Said**
Presentación de
Juan Goytisolo
Traducción de
M.ª Luisa Fuentes
www.megustaleerebooks.com
### Prólogo a la nueva edición española
Mi libro se publicó originalmente en Estados Unidos y poco después fue traducido a numerosas lenguas en todo el mundo, incluido el español, pero como era de esperar, en cada país se leyó de manera diferente. Aunque creí haber dejado claro que mi propósito no era examinar la historia de los «estudios orientales» en todo el mundo, sino solo en los casos especiales de Gran Bretaña y Francia, y posteriormente en Estados Unidos, ello no impidió que algunos críticos resaltaran el hecho irrelevante de que yo había desatendido el orientalismo alemán, holandés o italiano. En posteriores respuestas a mis críticos reiteré, aunque creo que sin demasiado éxito, lo que no necesitaba repetir: que mi interés se centraba en la conexión entre imperio y orientalismo, es decir, en un tipo especial de conocimiento y de poder imperial. Alguna gente estaba empeñada simplemente en resaltar mi olvido de Alemania y Holanda, por ejemplo, sin considerar en primer lugar si tal crítica era relevante o si tenía algún interés.
Había otra crítica que sí tenía más fundamento: yo había dicho muy poco sobre la extremadamente compleja y densa relación entre España y el islam, que ciertamente no se podía caracterizar simplemente como una relación imperial. Desde 1978, y debido en gran parte a mi creciente familiaridad con la obra de Américo Castro y de Juan Goytisolo, he llegado a darme cuenta no solo de cuánto hubiera deseado saber más acerca del orientalismo español mientras escribía mi libro durante los años setenta, sino de hasta qué punto España es una notable excepción en el contexto del modelo general europeo cuyas líneas generales se describen en _Orientalismo_.
Más que en cualquier otra parte de Europa, el islam formó parte de la cultura española durante varios siglos, y los ecos y pautas que perduran de tal relación siguen nutriendo la cultura española hasta nuestros días. Esto es algo que he aprendido gracias a la obra y la amistad de Juan Goytisolo, uno de los grandes pioneros en abordar esta cuestión, y por lo que le estaré eternamente agradecido. Sin embargo es crucial insistir en que lo que otorga su riqueza y complejidad a la imagen del islam en España es el hecho de ser parte sustancial de la cultura española y no una fuerza exterior y distante de la que hay que defenderse como si fuera un ejército invasor. El Oriente que describo en mi libro como creado en cierto modo por los conquistadores, administradores, académicos, viajeros, artistas, novelistas y poetas británicos y franceses es siempre algo que está «afuera», algo (como decía Schlegel a principios del siglo XIX) que representaba la forma más elevada, y en cierto modo, más inaccesible de ese romanticismo que los europeos buscan sin descanso.
En este sentido el contraste con España no podía ser mayor, puesto que el islam y la cultura española se habitan mutuamente en lugar de confrontarse con beligerancia. Ciertamente no se puede pasar por alto ni minimizar la larga y a menudo complicada relación entre la ideología de la España católica y el pasado judeomusulmán tanto tiempo suprimido, aunque me atrevería a decir que hasta en tales polémicas existe una relación de complementariedad e incluso de intimidad que raramente se ha repetido fuera de la península Ibérica.
Aunque lo que estoy señalando aquí condena en cierto modo a mi libro por ignorar un episodio verdaderamente significativo en la poco edificante historia de las relaciones entre Oriente y Occidente, me gustaría sin embargo apuntar que, de cualquier modo, el lector español encontrará en estas páginas un contraste implícito entre lo que pasé tanto tiempo investigando, por un lado, y la tan diferente experiencia española, por otro. Por encima de todo me parece que la simbiosis entre España y el islam nos proporciona un maravilloso modelo alternativo al crudo reduccionismo de lo que se ha dado en llamar «el choque de civilizaciones», una simplificación de la realidad originada en el mundo universitario norteamericano que sirve a los propósitos de dominación de Estados Unidos como superpotencia tras el 11 de septiembre, pero que no transmite la verdad de cómo las civilizaciones y culturas se solapan, confluyen y se nutren unas a otras. Es en ese modelo, en el que las culturas «comparten», en el que deberíamos concentrarnos, y es por ello por lo que, tanto para musulmanes como para españoles, Andalucía es un gran símbolo.
EDWARD W. SAID
_Nueva York, 3 de abril de 2002_
### Presentación
### Un intelectual libre
En 1978, la publicación de _Orientalismo_ , del palestino Edward Said, profesor de literatura inglesa y comparada en la Universidad de Columbia, en Nueva York —conocido hasta entonces por sus excelentes estudios de crítica literaria—, produjo el efecto de un cataclismo en el ámbito selecto, un tanto cerrado y autosuficiente, de los orientalistas anglosajones y franceses. Su examen de las relaciones Occidente-Oriente, la minuciosa exposición de la empresa de conocimiento, apropiación y definición —siempre reductiva— de lo «oriental» en todas sus formas sociales, culturales, religiosas, literarias y artísticas por parte de aquellos en provecho exclusivo, no de los pueblos estudiados, sino de los que, gracias a su superioridad técnica, económica y militar, se apercibían para su conquista y explotación, ponían no solo en tela de juicio el rigor de sus análisis, sino en bastantes casos la probidad y honradez de sus propósitos eruditos. Salvo raras excepciones, nos dice Said, el orientalismo no ha contribuido al entendimiento y progreso de los pueblos árabes, islámicos, hindúes, etcétera, objeto de su observación: los ha clasificado en unas categorías intelectuales y «esencias» inmutables destinadas a facilitar su sujeción al «civilizador» europeo. Fundándose en premisas vagas e inciertas, forjó una avasalladora masa de documentos que, copiándose unos a otros, apoyándose unos en otros, adquirieron con el tiempo un indiscutido —pero discutible— valor científico. Una cáfila de clisés etnocentristas, acumulados durante los siglos de lucha de la cristiandad contra el islam, orientaron así la labor escrita de viajeros, letrados, comerciantes y diplomáticos: su visión subjetiva, embebida de prejuicios, teñía sus observaciones de tal modo que, enfrentados a una realidad compleja e indomesticable, preferían soslayarla a favor de la «verdad» abrumadora del «testimonio» ya escrito.
Con un rigor implacable, Said exponía los mecanismos de la fabricación del Otro que, desde la Edad Media, articulan el proyecto orientalista. La dureza del ataque, como señaló en su día Maxime Rodinson, convirtió a _Orientalismo_ en el centro de una agria polémica cuyos ecos no se han desvanecido aún. Las críticas y defensas apasionadas del libro mostraban en cualquier caso que el autor había dado en el blanco: nadie puede permanecer indiferente a él. Pero mi iniciativa no dio resultado. El tema de la obra resultaba aún exótico en aquellos años y me resigné a acoger _Orientalismo_ en una discreta colección que entonces dirigía y cuya difusión era escasa, por no decir nula. Por fortuna, las cosas han cambiado.
Como sus lectores españoles bien saben, la obra de Edward Said abarca un área muy vasta de conocimientos, algo bastante insólito, como veremos, en el universo arabomusulmán, tradicionalmente endogámico, replegado sobre sí mismo y con escasa curiosidad por el mundo exterior (compárese, por ejemplo, el número de libros escritos en Occidente sobre esta civilización tan cercana, pero inasimilable a la nuestra —sin duda, varios millares de títulos— con la cincuentena escasa de obras que los viajeros y ensayistas del Oriente Próximo y el Magreb escribieron sobre Europa antes de la Primera Guerra Mundial, y mediremos el abismo que separa el Occidente avanzado de esa nebulosa de culturas, creencias religiosas y lenguas capsuladas en el término «oriental» forjado por nosotros. Quiero precisar aquí que España es un caso aparte: nuestra anorexia cognitiva y asimiladora tocante a otras culturas nos distancia también irremediablemente de Europa).
El lector de Edward Said puede escoger, según sus preferencias, entre las diferentes facetas de su obra: el excelente analista de la ficción autobiográfica de Joseph Conrad; el crítico literario de _Intención y método_ y _El mundo, el texto y la crítica_ ; el musicólogo, cuyas inolvidables conferencias en el Collège de France tuve el privilegio de escuchar; el narrador del bellísimo viaje a la tierra nativa que, al serle arrebatada en su niñez, lo convirtió para siempre en un palestino errante; el analista político, implacable observador del mal llamado proceso de paz, consecuencia de los Acuerdos de Oslo...
Pero quiero subrayar ahora un punto que me parece esencial para la comprensión de una labor tan rica y aguijadora. Como otros exiliados a lo largo de la historia, Said ha sabido sacar fuerza de la desdicha propia y la de su pueblo con miras a convertirla en la baza de un reto: el de transformar, conforme a la célebre frase de André Malraux, «el destino en conciencia» y el de servirse de esta para componer una obra cuya exigencia íntima y móvil desinteresado la sitúen por encima de los azares y circunstancias de todo compromiso político concreto. Said nunca ha sacrificado el juicio individual al prejuicio colectivo, y este rasgo de carácter, infrecuente en todas las sociedades, hace de él una _rara avis_ dentro del palomar donde zurean las palomas amaestradas al servicio del poder de turno, ya sea político, empresarial o mediático.
Su condición de exiliado, primero en Egipto y luego en Estados Unidos, le ha concedido, como compensación personal, la fructuosa marginalidad de quien, en razón de las circunstancias, acampa en una zona fronteriza, en la periferia de Occidente y del Oriente Próximo, desde la que contempla su cultura a la luz de otras culturas, y su lengua, a la luz de otras lenguas. Conocedor profundo de la literatura e historiografía anglosajonas y francesas y de las claves de la dominación imperialista de Occidente sobre el mundo arabomusulmán, ha podido examinar a este a la vez con intimidad y a distancia, con amor, pero sin indulgencia.
Ensayo tras ensayo, libro tras libro, Edward Said ha denunciado la perniciosa ausencia de autocrítica en los medios intelectuales árabes: el ensimismamiento de su cultura, su refugio suicida en el pasado, la negación y el no reconocimiento de las realidades que aborrecen y temen, el complejo de amor/odio respecto a Occidente, la falta de democracia real y la instrumentalización de las elites por los gobernantes. Un conjunto de males que le conduce a preguntarse en _Palestina. Paz sin territorios_ : «¿Estamos condenados para siempre al subdesarrollo, la dependencia y la mediocridad?... ¿Estamos escogiendo ser una reproducción del África del siglo XIX a finales del siglo XX?».
Una crítica lúcida como la de Said, dirigida a la vez a los mecanismos de dominación de Occidente y a las raíces del subdesarrollo cultural, democrático y social de los países árabes, resulta más necesaria que nunca. Todos nos hallamos hoy enfrentados al horror sin paliativos de un terrorismo fanático y ciego, y a otros horrores, como los que son el pan diario de los palestinos, interesadamente encubiertos por la hipocresía de muchos gobiernos.
JUAN GOYTISOLO
_Para Janet e Ibrahim_
No pueden representarse a sí mismos, deben ser representados.
KARL MARX,
_El dieciocho brumario de Luis Bonaparte_
Oriente es una carrera.
BENJAMIN DISRAELI, _Tancred_
### Introducción
### I
En una visita que hizo a Beirut durante la terrible guerra civil de 1975-1976, un periodista francés, profundamente entristecido, escribió refiriéndose al devastado centro de la ciudad: «Hubo una época en la que parecía formar parte [...] del Oriente descrito por Chateaubriand y Nerval». Sin duda, tenía mucha razón en lo que respecta al lugar, especialmente desde el punto de vista de un europeo. Oriente era casi una invención europea y, desde la antigüedad, había sido escenario de romances, seres exóticos, recuerdos y paisajes inolvidables y experiencias extraordinarias. Ahora estaba desapareciendo, en cierto sentido había existido, pero su momento ya había pasado. Parecía irrelevante, tal vez, el hecho de que los propios orientales se estuvieran jugando algo en el proceso, de que incluso en los tiempos de Chateaubriand y Nerval hubieran vivido allí y de que en esos momentos fueran ellos los que sufrían; lo principal para el visitante europeo era la representación que Europa tenía de Oriente y de su destino inmediato, factores ambos que tenían una trascendencia particular y nacional, para el periodista y para sus lectores franceses.
Los estadounidenses no sienten exactamente lo mismo acerca de Oriente, al que tienden a asociar, más bien, con el Extremo Oriente (China y Japón, sobre todo). Al contrario que estos, los franceses y británicos —y en menor medida los alemanes, rusos, españoles, portugueses, italianos y suizos— han tenido una larga tradición en lo que llamaré _orientalismo_ , que es un modo de relacionarse con Oriente basado en el lugar especial que este ocupa en la experiencia de Europa occidental. Oriente no es solo el vecino inmediato de Europa, es también la región en la que Europa ha creado sus colonias más grandes, ricas y antiguas, es la fuente de sus civilizaciones y sus lenguas, su contrincante cultural y una de sus imágenes más profundas y repetidas de lo Otro. Además, Oriente ha servido para que Europa (u Occidente) se defina en contraposición a su imagen, su idea, su personalidad y su experiencia. Sin embargo, Oriente no es puramente imaginario. Oriente es una parte integrante de la civilización y de la cultura _material_ europea. El orientalismo expresa y representa, desde un punto de vista cultural e incluso ideológico, esa parte como un modo de discurso que se apoya en unas instituciones, un vocabulario, unas enseñanzas, unas imágenes, unas doctrinas e incluso unas burocracias y estilos coloniales. En contraposición, el conocimiento que Estados Unidos tiene de Oriente parece considerablemente menos denso; sin embargo, las aventuras japonesa, coreana e indochina probablemente estén creando ahora una conciencia de lo «oriental» más seria y realista. Por otra parte, la creciente expansión política y económica de Estados Unidos en Oriente Próximo ha influido decisivamente en nuestro conocimiento de esta región.
Es evidente (y a lo largo de las páginas siguientes lo será aún más) que cuando hablo de orientalismo me refiero a bastantes cosas, todas ellas, en mi opinión, dependientes entre sí. En general, la acepción de orientalismo más admitida es la académica, y esta etiqueta sirve para designar un gran número de instituciones de este tipo. Alguien que enseñe, escriba o investigue sobre Oriente —y esto es válido para un antropólogo, un sociólogo, un historiador o un filólogo— tanto en sus aspectos específicos como generales, es un orientalista, y lo que él o ella hace es orientalismo. Si lo comparamos con los términos «estudios orientales» o «estudios de áreas culturales» ( _area studies_ ), el de «orientalismo» es el que actualmente menos prefieren los especialistas, porque resulta demasiado vago y recuerda la actitud autoritaria y despótica del colonialismo del siglo XIX y principios del XX. Sin embargo, se han escrito muchos libros y se han celebrado muchos congresos con «Oriente» como tema central y con el orientalismo, con su nueva o vieja apariencia, como principal autoridad. La realidad es que, aunque ya no sea lo que en otro tiempo fue, el orientalismo sigue presente en el mundo académico a través de sus doctrinas y tesis sobre Oriente y lo oriental.
En cuanto a esta tradición académica, cuyos destinos, transmigraciones, especializaciones y transmisiones son, en parte, el objeto de este estudio, existe un significado más general del término orientalismo. Es un estilo de pensamiento que se basa en la distinción ontológica y epistemológica que se establece entre Oriente y —la mayor parte de las veces— Occidente. Así pues, una gran cantidad de escritores —entre ellos, poetas, novelistas, filósofos, políticos, economistas y administradores del Imperio— han aceptado esta diferencia básica entre Oriente y Occidente como punto de partida para elaborar teorías, epopeyas, novelas, descripciones sociales e informes políticos relacionados con Oriente, sus gentes, sus costumbres, su «mentalidad», su destino, etc. Este tipo de orientalismo se puede encontrar en Esquilo, Victor Hugo, Dante y Karl Marx. Más adelante, en esta introducción, trataré de los problemas metodológicos que se plantean al estudiar un tema tan vasto como éste.
Siempre se ha producido un intercambio entre el aspecto académico y el más o menos imaginativo del orientalismo, pero desde los últimos años del siglo XVIII la comunicación entre ambos ha sido considerable y bastante sistemática, quizá incluso regulada. Con esto, llego al tercer significado de orientalismo, que se define de una manera más histórica y material que los otros dos. Si tomamos como punto de partida aproximado el final del siglo XVIII, el orientalismo se puede describir y analizar como una institución colectiva que se relaciona con Oriente, relación que consiste en hacer declaraciones sobre él, adoptar posturas con respecto a él, describirlo, enseñarlo, colonizarlo y decidir sobre él; en resumen, el orientalismo es un estilo occidental que pretende dominar, reestructurar y tener autoridad sobre Oriente. Para definir el orientalismo me parece útil emplear la noción de discurso que Michel Foucault describe en _L'Archéologie du savoir_ y en _Surveiller et punir_*. Creo que si no se examina el orientalismo como un discurso, posiblemente no se comprenda esta disciplina tan sistemática a través de la cual la cultura europea ha sido capaz de manipular e incluso dirigir Oriente desde un punto de vista político, sociológico, militar, ideológico, científico e imaginario a partir del período posterior a la Ilustración. Por otro lado, el orientalismo mantiene una posición de autoridad tal que no creo que nadie que escriba, piense o haga algo relacionado con Oriente sea capaz de hacerlo sin darse cuenta de las limitaciones de pensamiento y acción que el orientalismo impone. En pocas palabras, por el orientalismo, Oriente no fue (y no es) un tema sobre el que se tenga libertad de pensamiento o acción. Esto no significa que tenga que determinar unilateralmente lo que se puede decir sobre Oriente, pero sí que constituye una completa red de intereses que inevitablemente se aplica (y, por tanto, siempre está implicada) siempre que aparece esa particular entidad que es Oriente. ¿Cómo ocurre este proceso? Eso es lo que este libro intenta exponer. También pretende demostrar cómo la cultura europea adquirió fuerza e identidad al ensalzarse a sí misma en detrimento de Oriente, al que consideraba una forma inferior y rechazable de sí misma.
Hay una diferencia cualitativa y cuantitativa, tanto desde un punto de vista histórico como cultural, entre la presencia franco-británica en Oriente y, hasta la ascensión estadounidense después de la Segunda Guerra Mundial, la presencia de otras potencias europeas y atlánticas. Hablar de orientalismo, pues, es hablar principalmente, aunque no exclusivamente, de una empresa cultural británica y francesa, un proyecto cuyas dimensiones abarcan campos tan dispares como los de la propia imaginación: todo el territorio de la India y de los países del Mediterráneo oriental, las tierras y textos bíblicos, el comercio de las especias, los ejércitos coloniales y una larga tradición de administradores coloniales, un impresionante conjunto de textos, innumerables «expertos» en todo lo referido a Oriente, un cuerpo de profesores orientalistas, un complejo aparato de ideas «orientales» (despotismo, esplendor, crueldad, sensualidad orientales), muchas sectas orientales, filosofías y sabidurías orientales adaptadas al uso local europeo... la lista podría extenderse más o menos indefinidamente. Mi punto de vista es que el orientalismo proviene de una relación muy particular que mantuvieron Francia y Gran Bretaña con Oriente que hasta principios del siglo XIX solo se había limitado a la India y a las tierras bíblicas. Desde el comienzo del siglo XIX, y hasta el fin de la Segunda Guerra Mundial, Francia y Gran Bretaña dominaron Oriente y el orientalismo; desde la Segunda Guerra Mundial, Estados Unidos ha dominado Oriente y se relaciona con él del mismo modo en que Francia y Gran Bretaña lo hicieron en otra época. De esta relación, cuya dinámica es muy fructífera, incluso aunque siempre manifieste la fuerza hegemónica de Occidente (Gran Bretaña, Francia o Estados Unidos), proviene el enorme volumen de textos que yo denomino orientalistas.
Debo decir que, además del importante número de libros y autores que examino, existe una cantidad mucho mayor de la que simplemente he tenido que prescindir. Mis tesis, sin embargo, no se apoyan en un catálogo exhaustivo de textos que tratan de Oriente, ni en la colección de escritos, autores e ideas claramente delimitados que forman en conjunto el canon del orientalismo; en su lugar, he basado mi estudio en una alternativa metodológica diferente cuya columna vertebral, en cierto sentido, es el conjunto de generalizaciones históricas que he presentado en esta introducción y que a continuación quiero analizar con más detalle.
### II
He comenzado asumiendo que Oriente no es una realidad inerte. No está simplemente _allí_ , lo mismo que el propio Occidente tampoco está precisamente _allí_. Tenemos que admitir seriamente la gran observación de Vico acerca de que los hombres hacen su propia historia, de que lo que ellos pueden conocer es aquello que han hecho, y debemos extenderla al ámbito de la geografía: esos lugares, regiones y sectores geográficos que constituyen Oriente y Occidente, en tanto que entidades geográficas y culturales —por no decir nada de las entidades históricas—, son creación del hombre. Por consiguiente, en la misma medida en que lo es el propio Occidente, Oriente es una idea que tiene una historia, una tradición de pensamiento, unas imágenes y un vocabulario que le han dado una realidad y una presencia en y para Occidente. Las dos entidades geográficas, pues, se apoyan, y hasta cierto punto se reflejan la una en la otra.
Después de haber dicho esto, parece razonable exponer algunas puntualizaciones. En primer lugar, sería un error concluir que Oriente fue _esencialmente_ una idea o una creación sin su realidad correspondiente. Cuando Disraeli dijo en su novela _Tancred_ que Oriente era una carrera, quería decir que, para los occidentales jóvenes e inteligentes, estudiar Oriente podía llegar a ser una actividad apasionante; no se debería interpretar lo que dijo como que Oriente fuera _solo_ una carrera para los occidentales. Había —y hay— culturas y naciones, localizadas en Oriente, cuyas vidas, historias y costumbres poseen una realidad obviamente más rica que cualquier cosa que se pueda decir de ellas en Occidente. Sobre este punto, mi estudio no tiene nada que añadir; simplemente constata su existencia. Pero el fenómeno del orientalismo, tal y como yo lo trato aquí, aborda principalmente no la correspondencia entre el orientalismo y Oriente, sino la coherencia interna del orientalismo y sus ideas sobre Oriente (Oriente como una carrera), a pesar de, más allá de cualquier correspondencia o no con un Oriente «real». Creo que la afirmación de Disraeli sobre Oriente se refiere básicamente a esta coherencia creada, a esta verdadera constelación de ideas que es la cuestión esencial siempre que nos ocupamos de Oriente, y no a su mera y pura existencia, por citar a Wallace Stevens.
La segunda puntualización se refiere a que las ideas, las culturas y las historias no se pueden entender ni estudiar seriamente sin estudiar al mismo tiempo su fuerza o, para ser más precisos, sus configuraciones de poder. Creer que Oriente fue creado —o, como yo digo, «orientalizado»— y creer que tales cosas suceden simplemente como una necesidad de la imaginación, es faltar a la verdad. La relación entre Occidente y Oriente es una relación de poder, y de complicada dominación: Occidente ha ejercido diferentes grados de hegemonía sobre Oriente, como señala bastante bien el título del clásico de K. M. Panikkar, _Asia and Western Dominance_. Oriente fue orientalizado, no solo porque se descubrió que era «oriental», según los estereotipos de un europeo medio del siglo XIX, sino también porque se podía conseguir que lo fuera —es decir, se le podía obligar a serlo—. Tomemos, por ejemplo, el encuentro de Flaubert con una cortesana egipcia, encuentro que debió de crear un modelo muy influyente sobre la mujer oriental; ella nunca hablaba de sí misma, nunca mostraba sus emociones, su condición presente o pasada. Él hablaba por ella y la representaba. Él era extranjero, relativamente rico y hombre, y esos eran unos factores históricos de dominación que le permitían, no solo poseer a Kuchuk Hanem físicamente, sino hablar por ella y decir a sus lectores en qué sentido ella era típicamente oriental. Mi tesis es que la situación de fuerza de Flaubert en relación a Kuchuk Hanem no era un ejemplo aislado, y puede servir bastante bien como modelo de la relación de fuerzas entre Oriente y Occidente y del discurso acerca de Oriente que permite este modelo.
Esto nos lleva a una tercera puntualización. No hay que creer que el orientalismo es una estructura de mentiras o de mitos que se desvanecería si dijéramos la verdad sobre ella. Yo mismo creo que el orientalismo es mucho más valioso como signo del poder europeoatlántico sobre Oriente que como discurso verídico sobre Oriente (que es lo que en su forma académica o erudita pretende ser). Sin embargo, lo que tenemos que respetar e intentar comprender es la solidez del entramado del discurso orientalista, sus estrechos lazos con las instituciones socioeconómicas y políticas existentes y su extraordinaria durabilidad. Después de todo, un sistema de ideas capaz de mantenerse intacto, y que se ha enseñado como una ciencia (en academias, libros, congresos, universidades y organismos de asuntos exteriores) desde el período de Ernest Renan hacia finales de 1848 hasta el presente en Estados Unidos, debe ser algo más grandioso que una mera colección de mentiras. El orientalismo, pues, no es una fantasía que creó Europa acerca de Oriente, sino un cuerpo de teoría y práctica en el que, durante muchas generaciones, se ha realizado una inversión considerable. Debido a esta continua inversión, el orientalismo ha llegado a ser un sistema para conocer Oriente, un filtro aceptado que Oriente atraviesa para penetrar en la conciencia occidental; igualmente, esa misma inversión hizo posibles —de hecho, las hizo realmente productivas— las declaraciones que en un principio se formularon dentro de la disciplina orientalista y que más tarde proliferaron en el interior de la cultura general.
Gramsci ha efectuado una útil distinción analítica entre sociedad civil y sociedad política según la cual la primera está formada por asociaciones voluntarias (o, al menos, racionales y no coercitivas), como las escuelas, las familias y los sindicatos, y la segunda por instituciones estatales (el ejército, la policía y la burocracia central) cuya función dentro del Estado es la dominación directa. La cultura, por supuesto, funciona en el marco de la sociedad civil, donde la influencia de las ideas, las instituciones y las personas se ejerce, no a través de la dominación, sino a través de lo que Gramsci llama consenso. Así, en cualquier sociedad no totalitaria ciertas formas culturales predominan sobre otras y determinadas ideas son más influyentes que otras; la forma que adopta esta supremacía cultural es lo que Gramsci llama «hegemonía», un concepto indispensable para comprender, de un modo u otro, la vida cultural en el Occidente industrial. Es la hegemonía —o, mejor, los efectos de la hegemonía cultural— lo que da al orientalismo la durabilidad y la fuerza de la que he estado hablando hasta ahora. El orientalismo no dista mucho de lo que Denys Hay ha llamado la idea de Europa, una noción colectiva que nos define a «nosotros» europeos, contra todos «aquellos» no europeos, y se puede decir que el componente principal de la cultura europea es precisamente aquel que contribuye a que esta cultura sea hegemónica tanto dentro como fuera de Europa: la idea de una identidad europea superior a todos los pueblos y culturas no europeos. Existe, además, la hegemonía de las ideas europeas sobre Oriente, que reiteran la superioridad europea sobre un Oriente retrasado y normalmente anulan la posibilidad de que un pensador más independiente o más o menos escéptico pueda tener diferentes puntos de vista sobre la materia.
De una manera bastante constante, la estrategia del orientalismo ha dependido de esa superioridad _de posición_ flexible que sitúa a Occidente ante una serie completa de posibles relaciones con Oriente sin que Occidente pierda nunca la ventaja. ¿Por qué tenía que haber sido de otra manera, sobre todo durante el período de máxima supremacía europea, desde finales del Renacimiento hasta nuestros días? El científico, el erudito, el misionero, el comerciante o el soldado estaban o pensaban en Oriente porque podían estar allí o pensar en él sin que Oriente les ofreciera apenas resistencia. Bajo el lema general de conocer Oriente y dentro de los límites que el paraguas de la hegemonía occidental imponía, a partir de finales del siglo XVIII emergió un Oriente complejo, adaptado a los estudios académicos, a las exposiciones en los museos, a las reconstrucciones en la oficina colonial, a la ilustración teórica de tesis antropológicas, biológicas, lingüísticas, raciales e históricas sobre el género humano y el universo, y a ejemplificar teorías económicas y sociológicas de desarrollo, de revolución, de personalidad cultural y de carácter nacional o religioso. Además, el examen imaginario de las realidades de Oriente se basaba, más o menos exclusivamente, en una conciencia occidental soberana. A partir de la posición central e indiscutida de esta conciencia surgió un mundo oriental, primero de acuerdo a las ideas generales sobre quién o qué era un oriental, y después, de acuerdo a una lógica detallada y gobernada no solo por una realidad empírica, sino también por una serie de deseos, represiones, inversiones y proyecciones. Si bien podemos encontrar grandes trabajos orientalistas de auténtica erudición, como son _Chrestomathie Arabe_ , de Silvestre de Sacy, o _An Account of the Manners and Customs of the Modern Egyptians_ , de Edward William Lane, también tenemos que señalar que las ideas sobre las razas de Renan y Gobineau surgieron del mismo movimiento, al igual que muchas novelas pornográficas victorianas (véase el análisis de Steven Marcus, «The Lustful Turk»).
En este punto, debemos preguntarnos si lo que importa en materia de orientalismo es un conjunto de ideas generales al que se supedita el resto del material (ideas que, no se puede negar, transmitían doctrinas sobre la superioridad europea, modelos racistas e imperialistas y puntos de vista dogmáticos sobre «lo oriental», como si fuera una abstracción ideal e inmutable), o el trabajo mucho más variado realizado por un número casi incontable de autores a los que podríamos elegir como ejemplos concretos de escritores que se han ocupado de Oriente. En cierto sentido, las dos alternativas, la general y la particular, constituyen realmente dos perspectivas del mismo material: en ambos casos habría que ocuparse de los pioneros en la especialidad, como por ejemplo William Jones, y de los grandes artistas, como Nerval o Flaubert. ¿Y por qué no sería posible emplear las dos perspectivas a la vez, o una después de la otra? ¿No habrá algún peligro evidente de distorsión (que precisamente es a lo que los orientalistas académicos han sido muy propensos) si el nivel de descripción que sistemáticamente se mantenga es demasiado general o demasiado específico?
Mis dos temores son la distorsión y la inexactitud, o, mejor dicho, el tipo de inexactitud producido por una generalización demasiado dogmática y por una concentración demasiado positivista. Al intentar ocuparme de estos problemas, he procurado tratar tres aspectos de mi propia realidad contemporánea que me parece ofrecen la solución a estas dificultades metodológicas y de perspectiva; dificultades que pueden obligar, en el primer caso, a escribir un texto polémico basado en un nivel de descripción tan inaceptablemente general que el esfuerzo no merezca la pena; o, en el segundo caso, a escribir una serie de análisis tan detallados y atomizados que se pierda el rastro de las líneas generales que constituyen la base de la especialidad y le confieren su particular coherencia. ¿Cómo, entonces, admitir la individualidad y conciliarla con su contexto intelectual, general y hegemónico, sin que, de ningún modo, este sea un contexto pasivo o meramente dictatorial?
### III
A continuación voy a exponer y explicar brevemente los tres aspectos de mi realidad contemporánea a los que me he referido antes, para que se pueda comprender cómo me han conducido por un camino determinado a lo largo de la investigación y de la redacción de este estudio.
1. _La distinción entre conocimiento puro y conocimiento político_. Es muy fácil sostener que los conocimientos sobre Shakespeare o Wordsworth no tienen interés político, mientras que los conocimientos sobre la China o la URSS contemporáneas sí. Desde un punto de vista formal y profesional a mí se me denomina «humanista», título que indica que las humanidades son mi especialidad y que, por tanto, sería difícil encontrar algún tema de interés político en el trabajo que realizo dentro de esta especialidad. Por supuesto, todas estas etiquetas y términos, según los estoy utilizando, deberían matizarse, pero creo que la veracidad general de lo que estoy señalando es de sobra válida. Una de las razones que se esgrimen para decir que un humanista que escribe sobre Wordsworth o un autor especializado en Keats realizan un trabajo que no tiene implicaciones políticas es que su labor parece no tener ningún efecto político directo en la realidad de todos los días. Un especialista en economía soviética trabaja en un área de estudios muy espinosa y en la que están implicados muchos intereses; los estudios o propuestas que pueda presentar en el proceso de investigación serán tenidos en cuenta por los políticos, los organismos gubernamentales, los economistas de las diferentes instituciones y los expertos de los departamentos de inteligencia. La diferencia entre los «humanistas» y las personas cuyo trabajo tiene una implicación o una trascendencia política se puede ampliar diciendo que las tendencias ideológicas del primero tienen una importancia incidental en la política (aunque quizá tengan gran importancia para sus colegas, que pueden acusarle de estalinista, fascista o liberal), mientras que la ideología del segundo es parte consustancial de su material —de hecho, la economía, la política y la sociología, en el mundo académico moderno, se consideran ciencias ideológicas— y, por tanto, se da por supuesto que es «política».
Con todo, la mayoría de los conocimientos que se producen actualmente en Occidente (y ahora me refiero sobre todo a Estados Unidos) está sometida a una limitación determinante: la concepción de que todo conocimiento está constituido por ideas no políticas; esto es, ideas eruditas, académicas, imparciales y suprapartidistas. Se puede aceptar esta pretensión desde un punto de vista teórico, pero en la práctica, la realidad es mucho más problemática. Nadie ha inventado un método que sirva para aislar al erudito de las circunstancias de su vida, de sus compromisos (conscientes o inconscientes) con una clase, con un conjunto de creencias, con una posición social o con su mera condición de miembro de una sociedad. Todo esto influye en su trabajo profesional, aunque, naturalmente, sus investigaciones y los frutos de ellas intenten alcanzar un grado de relativa libertad con respecto a las restricciones y limitaciones que impone la cruda realidad de todos los días. En efecto, el conocimiento es algo menos parcial que el individuo que lo produce (con sus circunstancias vitales que le enredan y confunden); por tanto, este conocimiento no puede ser no político.
Si las discusiones sobre literatura o filología clásica están impregnadas de significación política o, por el contrario, no se dejan influir por ella es un complicado asunto del que he tratado en otra obra. Ahora me interesa señalar que el consenso general y liberal que sostiene que el conocimiento «verdadero» es fundamentalmente no político (y que, a la inversa, el conocimiento abiertamente político no es verdadero), no hace más que ocultar las condiciones políticas oscuras y muy bien organizadas que rigen la producción de cualquier conocimiento. Como hoy día se utiliza el adjetivo «político» para desacreditar cualquier trabajo que se atreva a violar el protocolo de una pretendida objetividad suprapolítica, todo esto nos resulta difícil de entender. Podemos decir que la sociedad civil admite una gradación en la importancia política de los diversos campos del conocimiento. Hasta cierto punto, la importancia política de una materia proviene de que pueda traducirse directamente a términos económicos, y la importancia política será aún mayor si su campo de estudio tiene afinidad con ciertas fuentes reconocidas de poder en la sociedad política. Como ejemplo un estudio económico sobre las fuentes de energía soviéticas a largo plazo y su efecto en la capacidad militar probablemente será subvencionado por el Departamento de Defensa de Estados Unidos y, en consecuencia, adquirirá una categoría política que no podría conseguir nunca un estudio sobre las primeras obras narrativas de Tolstoi financiado, en parte, por una fundación privada. Sin embargo, los dos trabajos pertenecen a lo que la sociedad civil considera un campo similar: los estudios rusos, aunque uno pueda estar realizado por un economista muy conservador y el otro, por un historiador radical de la literatura. Lo que quiero decir es que «Rusia», como tema general, tiene prioridad política sobre las diferencias más o menos precisas que se puedan establecer entre la «economía» y la «historia literaria», porque la sociedad política, en el sentido en que Gramsci utiliza el término, penetra dentro de los dominios de la sociedad civil, en este caso representada por el mundo académico, y los satura de significaciones que le conciernen directamente a ella.
No quiero extenderme más en el aspecto teórico de este problema; me parece que el valor y la credibilidad de mi propuesta se pueden demostrar de una manera más concreta: siguiendo, por ejemplo, el camino de Noam Chomsky, quien ha estudiado la conexión instrumental que existió entre la guerra del Vietnam y el concepto de erudición objetiva que se utilizó para encubrir algunas investigaciones militares subvencionadas por el Estado. Ahora bien, como Gran Bretaña, Francia y, recientemente, Estados Unidos son potencias imperiales, siempre que algún asunto relacionado con sus intereses en el extranjero está en juego, sus sociedades políticas transmiten a sus sociedades civiles una sensación de urgencia y una fuerte dosis de política, por expresarlo de algún modo. Creo que se puede decir, por ejemplo, que un inglés que a finales del siglo XIX se interesaba por países como la India o Egipto, lo hacía sin olvidar nunca el hecho de que eran colonias británicas. Puede parecer, a simple vista, que decir esto no tiene nada que ver con decir que todo el conocimiento académico sobre la India y Egipto está, de alguna manera, matizado, condicionado y violado por la densa realidad política; no obstante, esto es _lo que estoy tratando de decir_ en este estudio. Porque si es cierto que ninguna obra humanística puede permanecer ajena a las implicaciones que su autor tiene en tanto que sujeto humano, determinado por sus propias circunstancias, debe ser cierto también que ningún europeo o estadounidense que estudie Oriente puede renunciar a las circunstancias principales de _su_ realidad: que él se enfrenta a Oriente, primero como europeo o estadounidense y después como individuo. Y ser europeo o estadounidense en esta situación no es sin duda una realidad intrascendente; ha significado y significa ser consciente, aunque sea vagamente, de pertenecer a una potencia con unos intereses muy definidos en Oriente, y, más importante aún, de pertenecer a una parte de la Tierra que ha mantenido una serie de relaciones históricas con Oriente desde prácticamente los tiempos de Homero.
Expuestas de este modo, estas realidades políticas son todavía demasiado indefinidas y generales como para resultar realmente interesantes. Cualquiera estaría de acuerdo con ellas, sin aceptar por ello necesariamente que le importaran mucho a Flaubert, por ejemplo, cuando escribió _Salammbo_ ,* o a H. A. R. Gibb cuando escribió _Modern Trends in Islam_. El problema reside en que existe una diferencia demasiado grande entre la gran realidad dominante, como la he descrito yo, y los detalles de la vida cotidiana que rigen el minucioso ejercicio de escribir una novela o un texto especializado. Pero si, de entrada, descartamos la idea de que esas «grandes» realidades, como la dominación imperial, puedan aplicarse de una manera mecánica y determinista a asuntos tan complejos como la cultura y las ideas, estaremos a punto de iniciar un estudio muy interesante. Pienso que el interés que Europa y Estados Unidos han mostrado hacia Oriente ha sido, sin duda, de orden político, como lo demuestran ciertos hechos históricos que ya he expuesto aquí; pero también considero que la cultura creó ese interés, que contribuyó vigorosamente, junto con razones puramente políticas, económicas y militares, a convertir Oriente en un lugar variado y complejo dentro del campo que yo denomino orientalismo.
Por tanto, el orientalismo no es una simple disciplina o tema político que se refleja pasivamente en la cultura, en la erudición o en las instituciones, ni una larga y difusa colección de textos que tratan de Oriente; tampoco es la representación o manifestación de alguna vil conspiración «occidental» e imperialista, que pretende oprimir al mundo «oriental». Por el contrario, es la _distribución_ de una cierta conciencia geopolítica en unos textos estéticos, eruditos, económicos, sociológicos, históricos y filológicos; es la _elaboración_ de una distinción geográfica básica (el mundo está formado por dos mitades diferentes, Oriente y Occidente) y también, de una serie completa de «intereses» que no solo crea el propio orientalismo, sino que también mantiene a través de sus descubrimientos eruditos, sus reconstrucciones filológicas, sus análisis psicológicos y sus descripciones geográficas y sociológicas; es una cierta _voluntad o intención_ de comprender —y en algunos casos, de controlar, manipular e incluso incorporar— lo que manifiestamente es un mundo diferente (alternativo o nuevo); es, sobre todo, un discurso que de ningún modo se puede hacer corresponder directamente con el poder político, pero que se produce y existe en virtud de un intercambio desigual con varios tipos de poder: se conforma a través de un intercambio con el poder político (como el estado colonial o imperial), con el poder intelectual (como las ciencias predominantes: la lingüística comparada, la anatomía o cualquiera de las ciencias de la política moderna), con el poder cultural (como las ortodoxias y los cánones que rigen los gustos, los valores y los textos); con el poder moral (como las ideas sobre lo que «nosotros» hacemos y «ellos» no pueden hacer o comprender del mismo modo que «nosotros»). De hecho, mi tesis consiste en que el orientalismo es —y no solo representa— una dimensión considerable de la cultura, política e intelectual moderna, y, como tal, tiene menos que ver con Oriente que con «nuestro» mundo.
El orientalismo es una realidad cultural y política, lo que significa que no existe en un espacio vacío carente de archivos; muy al contrario, pienso que es posible demostrar que lo que se piensa, se dice o incluso se hace en relación a Oriente sigue unas líneas muy determinadas que se pueden aprehender intelectualmente. Creo también que al estudiar la manera en que la superestructura ejerce presiones sobre los detalles de la composición, se pueden encontrar ciertos matices, los cuales constituyen las realidades de la intertextualidad. La mayoría de los eruditos humanistas, creo, están perfectamente de acuerdo con la idea de que los textos existen dentro de los contextos, de que existe un concepto que es la intertextualidad y de que la presión ejercida por las convenciones, las generaciones precedentes y los estilos retóricos limitan lo que Walter Benjamin llamó una vez la «sobrevaloración del individuo productivo en nombre del ...] principio de "creatividad"», principio según el cual se supone que el poeta ha creado su obra por sí mismo, a partir de su propia inspiración. Sin embargo, actualmente existe una especial aversión a reconocer que las fuerzas políticas, institucionales e ideológicas actúan también en el autor, como individuo. Cualquier humanista que haga una interpretación de Balzac, tendrá en consideración la influencia que se aprecia en la _Comédie humaine_[ * del conflicto entre Geoffroy Saint-Hilaire y Cuvier; pero, sin embargo, no concederá importancia a la influencia de las teorías monárquicas y reaccionarias que hay en la obra porque considerará que disminuyen su «genio» literario. Del mismo modo —como Harry Bracken ha demostrado sin lugar a dudas—, los filósofos suelen discutir sobre Locke, Hume y el empirismo sin tener nunca en cuenta que hay una conexión explícita entre las doctrinas filosóficas de estos autores clásicos y la teoría racial, la justificación de la esclavitud o los argumentos en favor de la explotación colonial. Éstos son los procedimientos más comunes que permiten a la erudición contemporánea conservar su pureza.
Quizá sea cierto que casi siempre que la cultura ha intentado meter las narices en el fango de la política, los resultados han sido enormemente iconoclastas; quizá también, la interpretación social de la literatura en mi propio campo de estudio no ha ido paralela a los enormes avances técnicos del análisis textual detallado. Pero no se puede eludir el hecho de que los estudios literarios, en general, y los teóricos marxistas estadounidenses, en particular, no han realizado grandes esfuerzos por salvar el abismo existente entre los niveles de la superestructura y de la base en la erudición histórica textual; en alguna otra ocasión he llegado a decir que el estamento literario y cultural en su conjunto se ha dejado en el tintero el estudio serio del imperialismo y la cultura. Por consiguiente, el orientalismo nos sitúa cara a cara con este asunto; es decir, con el hecho de reconocer que el imperialismo político orienta todo un campo de estudios, de imaginación y de instituciones académicas, de modo que es imposible eludirlo desde un punto de vista intelectual e histórico. Pero siempre quedará la eterna excusa de decir que un erudito literario y un filósofo, por ejemplo, están preparados para hacer literatura y filosofía, respectivamente, y no política ni análisis ideológicos. En otras palabras, que el argumento del especialista puede bloquear con bastante eficacia la perspectiva intelectual, que, en mi opinión, es más extensa y seria.
Me parece que al problema del estudio del imperialismo y la cultura (u orientalismo) se le puede dar una simple respuesta compuesta de dos partes. En primer lugar, casi todos los escritores del siglo XIX (y esto mismo sería válido para los de períodos anteriores) eran extraordinariamente conscientes de la realidad del imperio; este es un tema que no se ha estudiado muy bien, pero un especialista moderno en la época victoriana tendrá que admitir que los héroes de la cultura liberal, como John Stuart Mill, Thomas Arnold, Carlyle, Newman, Macaulay, Ruskin, George Eliot, e incluso Dickens, tenían unas opiniones muy concretas sobre la raza y el imperialismo, que podemos encontrar fácilmente en sus escritos. De igual modo, un especialista debe acabar admitiendo que Mill, por ejemplo, dejó claro en _On liberty_ y en _Representative Government_ * que sus puntos de vista no podían ser aplicados a la India (al fin y al cabo fue funcionario en la India Office durante una gran parte de su vida) porque los indios eran inferiores tanto por su civilización como por su raza. El mismo tipo de paradoja podremos encontrar en Marx; más adelante lo demostraré. En segundo lugar, creer que la política, en forma de imperialismo, tiene un efecto en la producción literaria, en la erudición, en las teorías sociales y en la escritura de la historia no equivale, en modo alguno, a afirmar que, por tanto, la cultura es algo degradado o denigrado; muy al contrario, toda mi tesis consiste en que podremos comprender mejor la persistencia y la durabilidad de un sistema hegemónico, como la propia cultura, cuando reconozcamos que las coacciones internas que estos imponen en los escritores y pensadores son _productivas_ y no unilateralmente inhibidoras. Esta es la idea que, indudablemente, Gramsci, Foucault y Raymond Williams, cada uno a su manera, han intentado exponer. Solamente, una o dos páginas de Williams sobre «Los usos del Imperio», en _The Long Revolution_ , nos dicen mucho más acerca de la riqueza cultural del siglo XIX que la mayoría de los volúmenes de análisis textual hermético.
Por tanto, yo estudio el orientalismo como un intercambio dinámico entre los autores individuales y las grandes iniciativas políticas que generaron los tres grandes imperios —británico, francés y estadounidense— en cuyo territorio intelectual e imaginario se produjeron los escritos. Lo que, como erudito, me interesa más, no es la gran realidad política, sino el detalle, del mismo modo que, lo que nos interesa en personas como Lane, Flaubert o Renan no es la verdad (para ellos, indiscutible) de que los occidentales son superiores a los orientales, sino el testimonio preparado y modulado que ofrecen los detalles de su obra dentro del enorme espacio abierto por esa verdad. Solo hay que recordar, para que entendamos lo que digo, que _Manners and_ _Customs of Modern Egyptians_ , de Lane, es un clásico de la observación histórica y antropológica por su estilo y sus detalles inteligentes y brillantes y no porque refleje la superioridad racial.
El tipo de cuestiones que el orientalismo plantea, por tanto, son las siguientes: ¿qué tipo de energías intelectuales, estéticas y culturales participaron en la elaboración de una tradición imperialista como la orientalista? ¿Cómo la filología, la lexicografía, la historia, la biología, las teorías políticas y económicas, la narrativa y la poesía lírica se pusieron al servicio de una visión del mundo tan imperialista como la orientalista? ¿Qué cambios, modulaciones, refinamientos e incluso revoluciones sufrió el orientalismo? ¿Qué significado adquieren en este contexto la originalidad, la continuidad y la individualidad? ¿Cómo se transmite o reproduce el orientalismo de una época a otra? En fin, ¿cómo podemos estudiar el fenómeno cultural e histórico del orientalismo considerándolo como una _obra humana voluntaria_ —y no como una especie de razonamiento en el vacío—, con toda su complejidad histórica y con todo su detalle y valor, sin, al mismo tiempo, perder de vista la alianza entre la acción cultural, las tendencias políticas, el Estado y las realidades específicas de dominación? Un estudio guiado por estas preocupaciones puede abordar, de modo responsable, cuestiones políticas y culturales. Pero esto no significa que este estudio establezca una regla inmutable sobre las relaciones entre conocimiento y política. Mi tesis es que toda investigación humanística debe establecer la naturaleza de esta relación en el contexto específico de su estudio, de su tema y de sus circunstancias históricas.
2. _La cuestión metodológica_. He dedicado una de mis obras a analizar y exponer la importancia que, para trabajar en el campo de las ciencias humanas, tiene el hecho de encontrar y formular un primer paso, un punto de partida, un principio inicial. Lo que aprendí entonces e intenté exponer fue que no existe algo dado o fácil de encontrar que pueda ser considerado como un punto de partida: los principios tienen que establecerse de acuerdo a cada proyecto, de tal manera que _posibiliten_ la realización de lo que viene a continuación. Jamás había comprobado, de una manera tan consciente, la dificultad que entraña esta regla, como en mi estudio de orientalismo (si la he resuelto con o sin éxito, no lo puedo decir). La idea de un comienzo, el acto de comenzar implica necesariamente un acto de delimitación, un acto por el que algo se separa de una gran masa de material y se extrae de ella para que represente y sea un punto de partida, un comienzo. Para alguien que se dedique al estudio de los textos, esta noción de delimitación inicial es lo que Louis Althusser llamó la _problemática_ , una unidad determinada y específica de un texto o de un grupo de textos que ha surgido a través del análisis. Pero, en el caso del orientalismo (al contrario que en el de los textos de Marx, que es el que Althusser estudia), no solo existe el problema de encontrar un punto de partida o problemática, sino también el de designar qué textos, autores y períodos son los que más convienen al estudio.
En mi opinión, no tenía sentido intentar escribir una historia del orientalismo narrativa y enciclopédica, en primer lugar porque, si el principio directriz de mi estudio era «la idea europea de Oriente», el material del que me hubiera tenido que ocupar no habría tenido límites, en segundo lugar porque el modelo narrativo no se ajustaba a mis intereses descriptivos y políticos, y en tercer lugar porque obras como _La Renaissance orientale_ , de Raymond Schwab; _Die Arabischen Studien in Europa bis in den Anfang des 20. Jahrhunderts_ , de Johann Fück, y más recientemente _The Matter af Araby in Medieval England_ , de Dorothee Metlitzki, ya incluyen trabajos enciclopédicos acerca de ciertos aspectos de los contactos entre Europa y Oriente, y sus objetivos se diferencian de la labor crítica que yo he esbozado en un contexto general, político e intelectual.
Se me planteaba también el problema de reducir un archivo muy denso a dimensiones manejables y, lo que es más importante, el de destacar dentro, de ese grupo de textos algún concepto de naturaleza intelectual sin por ello descuidar el orden cronológico. Mi punto de partida, por tanto, ha sido la experiencia británica, francesa y estadounidense en Oriente, en un sentido global, las bases históricas e intelectuales que la hicieron posible y sus cualidades y características. Por razones que explicaré a continuación, he limitado el ya de por sí limitado (pero todavía excesivamente vasto) conjunto de cuestiones a la experiencia que británicos, franceses y estadounidenses han tenido en el mundo árabe y en el mundo islámico, los cuales, durante casi un milenio han representado Oriente. Al hacer esto, parece que de entrada he eliminado una gran parte de Oriente —India, Japón, China y otras zonas del Extremo Oriente—, no porque estas regiones carezcan de importancia (que, evidentemente la tienen), sino porque es posible estudiar la experiencia que Europa tuvo en Oriente Próximo y en los países islámicos independientemente de su experiencia en el Extremo Oriente. Sin embargo, en ciertos períodos de esta historia general de intereses europeos en Oriente, determinadas regiones, como Egipto, Siria o Arabia, no se pueden abordar sin estudiar también la implicación que Europa tuvo en lugares más remotos como son Persia y la India: un ejemplo importante a este respecto es la conexión que tuvieron Egipto y la India para la Gran Bretaña de los siglos XVIII y XIX. Otros ejemplos importantes son el papel desempeñado por Francia descifrando el _Zend Avesta_ , la preeminencia de París como centro de estudios de sánscrito durante la primera década del siglo XIX, y el hecho de que el interés que mostró Napoleón por Oriente estuviera determinado por su conocimiento del papel británico en la India; toda esta preocupación por el Extremo Oriente influyó directamente en el interés que Francia manifestó por el Oriente Próximo, el islam y los árabes.
Gran Bretaña y Francia dominaron el Mediterráneo oriental desde finales del siglo XVII. Pero al estudiar esta dominación sistemática, no he hecho justicia a las importantes contribuciones que Alemania, Italia, Rusia, España y Portugal hicieron al orientalismo ni al gran impulso que la revolución en los estudios bíblicos —estimulada por sus pioneros, el obispo Lowth, Eichhorn, Herder y Michaelis— dio, en el siglo XVIII, al estudio de Oriente. En primer lugar, tenía que centrarme rigurosamente en el material británico y francés, y, después, en el estadounidense porque me parecía indiscutible, no solo que Gran Bretaña y Francia fueron las naciones pioneras en Oriente y en los estudios orientales, sino también que mantuvieron estas posiciones de vanguardia gracias a los dos entramados coloniales más grandes que la historia anterior al siglo XX ha conocido. En lo que se refiere a Oriente, Estados Unidos, desde la Segunda Guerra Mundial, ha seguido, creo que bastante conscientemente, las sendas trazadas por las dos potencias europeas. En consecuencia, considero que por su calidad, coherencia y cantidad, los escritos británicos, franceses y estadounidenses sobre Oriente superan a los trabajos, indudablemente cruciales, hechos en Alemania, Italia, Rusia y cualquier otro lugar. Pero también pienso que es verdad que los avances más decisivos que se hicieron en la erudición oriental fueron realizados primero por Gran Bretaña y Francia, y, después, por los alemanes. Silvestre de Sacy, por ejemplo, no fue solo el primer orientalista europeo moderno y profesional que se ocupó del islam, de la literatura árabe, de la religión drusa y de la Persia sasánida, sino que también fue el profesor de Champollion y de Franz Bopp, fundador de la lingüística comparada alemana. El mismo derecho a recibir este trato prioritario y preeminente tienen William Jones y Edward William Lane.
En segundo lugar —y esto que voy a decir compensa ampliamente las lagunas que pueda presentar este estudio del orientalismo—, recientemente se han publicado importantes trabajos sobre la tradición de los estudios bíblicos que se realizaron hasta el comienzo de lo que llamo el orientalismo moderno. El mejor, el más relevante y claro es el impresionante _«Kubla Khan» and The Fail of Jerusalem_ , de E. S. Shaffer, un estudio indispensable sobre los orígenes del romanticismo y sobre la actividad intelectual que subyace en gran parte de la obra de Coleridge, Browning y George Eliot. Hasta cierto punto, la obra de Shaffer desarrolla las ideas proporcionadas por Schwab, articulando los materiales relevantes que se pueden encontrar en los especialistas alemanes de textos bíblicos, y utilizándolos para leer, de una manera inteligente y siempre interesante, las obras de tres grandes escritores británicos. Pero el libro carece del sentido político e ideológico que los escritores británicos y franceses de los que yo me ocupo dieron al orientalismo; además, al contrario que Shaffer, yo intento aclarar las evoluciones posteriores del orientalismo académico y literario: por un lado, las conexiones entre el orientalismo británico y el francés, y por otro, la ascensión de un imperialismo de inspiración puramente colonial. También quiero demostrar que todos estos temas se reproducen con más o menos exactitud en el orientalismo americano posterior a la Segunda Guerra Mundial.
Sin embargo, hay un aspecto en el que mi estudio no es acertado: aparte de alguna referencia ocasional, no analizo de manera exhaustiva los progresos de los eruditos alemanes después del período inicial dominado por Silvestre de Sacy. Cualquier estudio que pretenda ofrecer unos conocimientos sobre el orientalismo académico y preste poca atención a eruditos como Steinthal, Müller, Becker, Goldziher, Brockelmann, Nöldeke —por mencionar solo a unos pocos—, se merece algunos reproches que, en mi caso, yo mismo me hago. Siento particularmente no prestar más atención a la erudición alemana cuyo prestigio científico creció a mediados del siglo XIX. George Eliot denunció a los eruditos británicos que la ignoraban; estoy pensando en el retrato inolvidable que ella hace del señor Casaubon en _Middlemarch_.* Una de las razones por las que Casaubon no puede terminar su _Key to All Mythologies_ es, de acuerdo con su joven primo Will Ladislaw, su desconocimiento de la erudición alemana. Y es que Casaubon no solo ha elegido un tema «que cambia con tanta rapidez como la química, un tema en el que constantemente se producen nuevos descubrimientos que dan lugar a nuevos puntos de vista»; también está llevando a cabo una labor parecida a la refutación de Paracelso, «porque no es un orientalista, ya sabes».
George Eliot no estaba equivocada cuando daba a entender que, más o menos hacia 1830, que es la época en la que _Middlemarch_ se sitúa, la erudición alemana había alcanzado preeminencia europea. Pero durante los dos primeros tercios del siglo XIX jamás pudo desarrollarse en el contexto de la erudición alemana una estrecha colaboración entre los orientalistas y un interés _nacional_ prolongado y constante por Oriente. No había nada en Alemania que se correspondiera con la presencia británica y francesa en la India, el Mediterráneo oriental y África del Norte. Es más, el Oriente alemán era casi exclusivamente un Oriente erudito o, al menos, clásico: sirvió de tema para poemas, obras de imaginación e incluso novelas, pero nunca fue real como Egipto y Siria lo fueron para Chateaubriand, Lane, Lamartine, Burton, Disraeli o Nerval. Es significativo el hecho de que dos de los trabajos alemanes sobre Oriente más renombrados, _Westöstlicher Diwan_ , de Goethe, y _Über die Sprache und Weisheit der Indier_ , de Friedrich Schlegel, se basaran, respectivamente, en un viaje por el Rin y en unas horas pasadas en las bibliotecas de París. La labor que llevó a cabo la erudición alemana consistió en refinar y perfeccionar las técnicas que se aplicaban a los textos, los mitos, las ideas y las lenguas que la Gran Bretaña y la Francia imperiales recogían literalmente de Oriente.
No obstante, lo que el orientalismo alemán tenía en común con el británico y el francés y, más tarde, con el estadounidense, era una especie de _autoridad_ intelectual sobre Oriente dentro de la cultura occidental. Esta autoridad debe ser, en gran medida, uno de los temas de estudio de cualquier descripción del orientalismo, y así lo es en esta obra. Incluso el nombre _orientalismo_ sugiere el estilo serio, quizá ponderado, de un experto; cuando lo aplico a las ciencias sociales estadounidenses modernas (aunque los investigadores de este campo no se autodenominan orientalistas, y por tanto, mi uso del término es anómalo), es para destacar el hecho de que los expertos en Oriente Próximo siguen inspirándose en los vestigios de las posiciones intelectuales del orientalismo europeo del siglo XIX.
La autoridad no tiene nada de misterioso o natural; se forma, se irradia y se difunde; es instrumental y persuasiva; tiene categoría, establece los cánones del gusto y los valores; apenas se puede distinguir de ciertas ideas que dignifica como verdades, y de las tradiciones, percepciones y juicios que forma, transmite y reproduce. Sobre todo, la autoridad se puede —de hecho se debe— analizar. Todos estos atributos que tiene la autoridad se pueden aplicar al orientalismo, y en gran medida mi trabajo en este estudio consiste en describir, por un lado, la autoridad histórica del orientalismo y, por otro, a las personas que son una autoridad en materia de orientalismo.
Para realizar este estudio sobre la autoridad, mis principales recursos metodológicos son lo que puede llamarse la _localización estratégica_ , que es una manera de describir la posición que el autor de un texto adopta con respecto al material oriental sobre el que escribe, y la _formación estratégica_ , que es una forma de analizar la relación entre los textos y el modo en que los grupos, los tipos e incluso los géneros de textos adquieren entidad, densidad y poder referencial entre ellos mismos y, más tarde, dentro de toda la cultura. Utilizo la noción de estrategia simplemente para definir el problema al que todo escritor sobre Oriente tiene que enfrentarse: cómo abarcarlo, cómo aproximarse a él, cómo evitar ser vencido o aplastado por su sublimidad, su extensión y sus terribles dimensiones. Todo el que escribe sobre Oriente debe definir su posición con respecto a él; trasladada al texto, esta posición presupone el tipo de tono narrativo que él adopta, la clase de estructura que construye y el género de imágenes, temas y motivos que utiliza en su texto; a esto se le añaden las maneras deliberadas de dirigirse al lector, de abarcar Oriente y, finalmente, de representarlo o de hablar en su nombre. Sin embargo, nada de esto sucede en la esfera de lo abstracto. Cualquier escritor que trate de Oriente (y esto es válido incluso para Homero) asume algún precedente oriental, algunos conocimientos previos de Oriente, conocimientos a los que hace referencia y en los que se apoya. Además, toda obra sobre Oriente se asocia a otras obras, a determinados públicos e instituciones y al propio Oriente. El conjunto de relaciones entre las obras, los públicos y algunos aspectos particulares de Oriente constituye, por tanto, una formación que se puede analizar —por ejemplo, la relación entre los estudios filológicos, las antologías de literatura oriental, los relatos de viajes y los libros de fantasías orientales— y cuya presencia en el tiempo, en el discurso y en las instituciones (escuelas, bibliotecas y organismos de asuntos exteriores) le da fuerza y autoridad.
Espero haber dejado claro que mi preocupación por la autoridad no presupone un análisis de lo que subyace en el texto orientalista, sino, por el contrario, un análisis de su superficie, de la exterioridad con relación a lo que describe. Creo que nunca se insistirá demasiado en esta idea. El orientalismo se fundamenta en la exterioridad, es decir en el hecho de que el orientalista, poeta o erudito, hace hablar a Oriente, lo describe, y ofrece abiertamente sus misterios a Occidente, porque Oriente solo le preocupa en tanto que causa primera de lo que expone. Lo que dice o escribe, en virtud de que está dicho o escrito, pretende indicar que el orientalista está fuera de Oriente tanto desde un punto de vista existencial como moral. El producto principal de esta exterioridad es, por supuesto, la representación: ya en la obra de Esquilo _Los persas_ , Oriente deja de tener la categoría de un Otro lejano y a veces amenazante, para encarnarse en figuras relativamente familiares (en el caso de Esquilo, las mujeres asiáticas oprimidas). La inmediatez dramática de la representación en _Los persas_ encubre el hecho de que el público observa una representación muy artificiosa de lo que un no oriental ha convertido en símbolo de todo Oriente. Mi análisis del texto orientalista, por tanto, hace hincapié en la evidencia —que de ningún modo es invisible— de que estas representaciones son _representaciones_ , y no retratos «naturales» de Oriente. Esta evidencia se puede encontrar de manera destacada en los textos que podríamos llamar verídicos (historias, análisis filológicos, tratados políticos) y en los textos reconocidos como abiertamente artísticos (por ejemplo, los imaginarios). Los aspectos que se deben considerar son el estilo, las figuras del discurso, las escenas, los recursos narrativos y las circunstancias históricas y sociales, pero no la exactitud de la representación ni su fidelidad a algún gran original. La exterioridad de la representación está siempre gobernada por alguna versión de la perogrullada que dice que si Oriente pudiera representarse a sí mismo, lo haría; pero como no puede, la representación hace el trabajo para Occidente y, _faute de mieux_ , para el pobre Oriente. «No pueden representarse a sí mismos, deben ser representados», como escribió Marx en _El dieciocho brumario de Luis Bonaparte_.*
Otra de las razones que me llevan a insistir en la idea de la exterioridad es mi necesidad de aclarar, al referirnos al discurso cultural y al intercambio dentro de una cultura, que lo que comúnmente circula por ella no es «la verdad», sino sus representaciones. No hace falta demostrar de nuevo que el propio lenguaje es un sistema muy organizado y codificado que emplea muchos recursos para expresar, indicar, intercambiar mensajes e información, representar, etc. Al menos en cualquier ejemplo de lenguaje escrito, no hay nada que sea una presencia dada, sino una _represencia_ o representación. El valor, la eficacia, la fuerza y la veracidad aparente de una afirmación escrita acerca de Oriente dependen, por tanto, muy poco de Oriente como tal e instrumentalmente no pueden depender de él. Por el contrario, para el lector, la afirmación escrita es una presencia porque ha excluido y desplazado a «Oriente» como _realidad_ y lo ha convertido en algo superfluo. Así, todo el orientalismo pretende reemplazar a Oriente, pero se mantiene distante con respecto a él: que el orientalismo tenga sentido es una cuestión que depende más de Occidente que de Oriente, y este sentido le debe mucho a las técnicas occidentales de representación que hacen que Oriente sea algo visible y claro, que esté «allí» en el discurso que se elabora sobre él. Y estas representaciones, para lograr sus efectos, se apoyan en instituciones, tradiciones, convenciones y códigos de inteligibilidad, y no en un Oriente distante y amorfo.
La diferencia entre las representaciones de Oriente que se hacían antes del último tercio del siglo XVIII y las posteriores a esta época (esto es, las que pertenecen a lo que llamo orientalismo moderno) estriba en que, en el último período, el horizonte de las representaciones se amplió mucho más. Es cierto que, después de William Jones y de Anquetil-Duperron, y tras la expedición de Napoleón a Egipto, Europa llegó a conocer Oriente de una manera más científica, a vivir en él con una autoridad y una disciplina que nunca antes había tenido. Pero lo que le importaba a Europa era la mayor capacidad y el mayor perfeccionamiento que adquirían sus técnicas para recibir Oriente. Cuando, a finales del siglo XVIII, Oriente reveló definitivamente la edad de sus lenguas —que se remontaban en el tiempo más allá de la genealogía divina del hebreo—, fue un grupo de europeos el que hizo el descubrimiento y lo transmitió a otros eruditos; finalmente, este descubrimiento se preservó en la ciencia de la filología indoeuropea, una nueva y poderosa ciencia que nacía para examinar el Oriente lingüístico y, con ella, como muestra Foucault en _Les mots et les choses_ ,* nacía también una completa red de intereses científicos afines. Del mismo modo, William Beckford, Byron, Goethe y Victor Hugo reestructuraron Oriente por medio de su arte y lograron que sus colores, sus luces y sus gentes fueran visibles a través de las imágenes, los ritmos y los motivos que ellos utilizaron para describirlos. El Oriente «real», a lo sumo, provocaba la visión de un escritor, pero raramente la guiaba.
El orientalismo respondió más a la cultura que lo produjo que a su supuesto objetivo, que también estaba producido por Occidente. Así, la historia del orientalismo presenta una gran coherencia interna y un conjunto muy articulado de relaciones con la cultura dominante que lo envuelve. Mi análisis, en consecuencia, intenta demostrar cómo es la forma de esta disciplina, cuál es su organización interna, quiénes son sus pioneros y sus autoridades patriarcales, cuáles son sus textos canónicos, sus ideas doxológicas y quiénes son sus figuras ejemplares, sus seguidores, comentadores y nuevas autoridades; intento también explicar cómo el orientalismo adoptó unas ideas «sólidas», unas doctrinas y tendencias que imperaban en la cultura, y cómo, frecuentemente, se inspiró en ellas. Así, había y hay un Oriente lingüístico, un Oriente freudiano, un Oriente spengleriano, un Oriente darwiniano, un Oriente racista, etc., y por ello, todavía no ha habido un Oriente puro o no condicionado; nunca ha existido una forma no material de orientalismo y mucho menos algo tan inocente como una «idea» de Oriente. En este punto, en esta firme convicción y en sus consecuencias metodológicas subsecuentes, difiero de los eruditos que estudian la historia de las ideas. En efecto, el énfasis, la forma ejecutiva y, sobre todo, la efectividad material de las afirmaciones del discurso orientalista son posibles en unas circunstancias que cualquier historia hermética de las ideas tiende a ignorar completamente. Sin esos énfasis y sin esa efectividad material, el orientalismo sería, simplemente, una idea como cualquier otra, mientras que, por el contrario, es y ha sido mucho más que eso. Por esto, me propongo examinar no solo trabajos eruditos, sino también obras literarias y políticas, artículos periodísticos, libros de viajes, y estudios religiosos y filológicos. En otras palabras, adopto una perspectiva híbrida que, en líneas generales, es histórica y «antropológica», dado que creo que todos los textos tienen vínculos con el mundo y con sus circunstancias de acuerdo a unas condiciones que, por supuesto, varían de un género a otro y de un período histórico a otro.
Todavía creo, al contrario que Michel Foucault, a cuya obra debo mucho, que los escritores individuales influyen de manera determinante en ese cuerpo de textos colectivo y anónimo que constituye una formación discursiva como la orientalista. La unidad que presenta el enorme conjunto de textos que analizo se debe, en parte, al hecho de que con frecuencia se refieren unos a otros: el orientalismo es, después de todo, un sistema constituido por citas de obras y autores. El libro _Manners and Customs of the Modern Egyptians_ , de William Lane, fue leído y citado por hombres tan diferentes como Nerval, Flaubert y Richard Burton. Esta obra era una autoridad que cualquiera que escribiera o pensara sobre Oriente, y no solo sobre Egipto, debía utilizar: cuando Nerval reprodujo párrafos literales de _Modern Egyptians_ , recurrió a la autoridad de Lane para describir escenas campesinas de Siria, pero no de Egipto. La autoridad de Lane y las oportunidades que ofrecía citarlo discriminada o indiscriminadamente estaban allí porque el orientalismo había sido capaz de convertirlo en un texto de referencia. Sin embargo, no se puede comprender esta característica de Lane sin entender las peculiaridades de _su_ texto; esto es válido también para Renan, Sacy, Lamartine, Schlegel y otros escritores influyentes. Foucault cree que, en general, el texto o el autor individual cuentan poco; la experiencia me demuestra que esto no es así en el caso del orientalismo (quizá en ningún otro caso sea así). De acuerdo con esto, utilizo en mis análisis explicaciones de textos con el fin de revelar la dialéctica entre el texto o el autor individual y la formación colectiva compleja a la que la obra contribuye.
Pero este libro, aunque incluye una amplia selección de escritores, dista mucho de ser una historia completa o una relación general del orientalismo, y soy muy consciente de esta carencia. El discurso orientalista ha podido sobrevivir y funcionar en la sociedad occidental gracias a la riqueza de la red que lo forma: todo lo que yo he hecho es describir algunas partes de esta red en determinados momentos y sugerir la existencia de un todo mucho mayor, detallado, interesante y dotado de personajes, textos y sucesos fascinantes. Me justifico pensando que este libro no es más que el principio, y espero que haya eruditos y críticos que quizá quieran escribir otros. Aún queda por realizar un ensayo general que trate el tema del imperialismo y la cultura; habría que profundizar en el asunto de las conexiones entre el orientalismo y la pedagogía, en el del orientalismo italiano, alemán y suizo, en el de la dinámica que se crea entre los escritos eruditos y los imaginarios y en el de la relación entre los conceptos administrativos y las disciplinas intelectuales. Quizá el objetivo más importante de todos sería estudiar alguna posible alternativa contemporánea al orientalismo, preguntarse cómo se pueden estudiar otras culturas y pueblos desde una perspectiva libertaria, y no represiva o manipulativa. Pero entonces habría que replantearse el complejo problema del conocimiento y el poder. Todos estos son objetivos que he dejado sin completar en este estudio, lo cual no deja de ser embarazoso.
La última observación acerca del método que quiero hacer aquí —aunque quizá resulte algo pretenciosa por mi parte— es que he escrito este estudio pensando en bastantes tipos de lectores. A los que estudian literatura y crítica literaria, el orientalismo les ofrece un ejemplo magnífico de las relaciones entre la sociedad, la historia y la textualidad; además, el papel que Oriente ha desempeñado en la cultura occidental relaciona el orientalismo con la ideología, la política y la lógica del poder, que son materias, en mi opinión, de trascendencia para la comunidad literaria. Pensando en los que hoy día estudian Oriente, desde los eruditos universitarios hasta los artífices de la política, he escrito este libro con dos objetivos: en primer lugar, presentarles su genealogía intelectual de una manera que nunca se había hecho antes; y en segundo, criticar —esperando suscitar nuevas discusiones— las asunciones normalmente incuestionables en las que la mayoría de sus trabajos se fundamenta. El lector que no sea un especialista encontrará en este estudio temas que siempre llaman la atención, todos ellos relacionados no solo con la manera en que Occidente concibe y trata lo Otro, sino también con el papel singularmente importante que ha desempeñado la cultura occidental en lo que Vico llama el mundo de naciones. Finalmente, para los lectores del llamado Tercer Mundo, este estudio pretende ser un paso hacia la comprensión no tanto de la política occidental hacia el mundo no occidental, como de la _fuerza_ del discurso cultural occidental, un discurso que, con demasiada frecuencia, ha sido erróneo, meramente decorativo o «superestructural». Espero haber descrito la formidable estructura de la dominación cultural y haber mostrado, particularmente a los pueblos que fueron colonizados, los peligros y las tentaciones de emplear esa estructura sobre ellos mismos o sobre otros.
Las tres grandes partes y los capítulos más breves en los que está dividido este libro intentan facilitar la exposición lo más posible. La primera parte «El ámbito del orientalismo», perfila a grandes rasgos todos los aspectos del tema, y los analiza en términos de experiencias y tiempo históricos, y en términos de motivos filosóficos y políticos. La segunda parte, «Estructuras y reestructuras del orientalismo», intenta describir el desarrollo del orientalismo moderno de manera cronológica y también a través de la descripción de un conjunto de recursos comunes a las obras de poetas, artistas y eruditos importantes. La tercera parte, «El orientalismo en nuestros días», empieza donde acaba el anterior, más o menos hacia 1870. Este es el período de la gran expansión colonial en Oriente que culmina con la Segunda Guerra Mundial. La última sección de la tercera parte muestra cómo la hegemonía pasó de manos británicas y francesas a manos estadounidenses; en él intento, finalmente, resumir las realidades sociales e intelectuales del orientalismo estadounidense de nuestros días.
3. _La dimensión personal_. En su libro _Quaderni dal carcere_ ,* Gramsci dice: «El punto de partida de cualquier elaboración crítica es la toma de conciencia de lo que uno realmente es; es decir, la premisa "conócete a ti mismo" en tanto que producto de un proceso histórico concreto que ha dejado en ti infinidad de huellas sin, a la vez, dejar un inventario de ellas». La única traducción inglesa existente termina así, inexplicablemente, el comentario de Gramsci, mientras que, de hecho, el texto en italiano concluye añadiendo: «Por tanto, es un imperativo comenzar por recopilar ese inventario».
La inversión personal que he hecho en este estudio deriva en gran parte de mi conciencia de ser «oriental» y de haber sido un chico que creció en dos colonias británicas. Toda mi educación en esas colonias (Palestina y Egipto) y en Estados Unidos ha sido occidental y, sin embargo, esa profunda y temprana conciencia ha persistido en mí de muchas formas. Al estudiar el orientalismo he pretendido hacer el inventario de las huellas que ha dejado en mí la cultura cuya dominación ha sido un factor muy poderoso en la vida de todos los orientales. Por eso, me he concentrado en el estudio del Oriente islámico. Si lo que he logrado ha sido el inventario prescrito por Gramsci, no soy yo quien debe juzgarlo, aunque soy consciente de lo importante que es intentar hacerlo. A lo largo de mi trabajo, de la manera más rigurosa y racional que me ha sido posible, he intentado mantener un espíritu crítico y emplear los instrumentos de investigación histórica, humanista y cultural de los cuales mi educación me ha hecho un afortunado beneficiario. Nada de esto, a pesar de todo, me ha hecho perder contacto con mi realidad cultural ni con la implicación personal de ser «un oriental».
Las circunstancias históricas que han hecho posible un estudio como este son bastante complejas, y aquí solo puedo mencionarlas de una manera esquemática. Todo aquel que haya residido en Occidente desde los años cincuenta, y en particular en Estados Unidos, habrá vivido una época de extraordinaria turbulencia en las relaciones EsteOeste. A nadie se le habrá escapado el hecho de que, durante este período, el «Este» siempre ha supuesto un peligro y una amenaza, tanto si se refería al Oriente tradicional como a Rusia. En las universidades, la creación de institutos y programas de estudios de áreas culturales ( _area studies_ ) ha convertido el estudio erudito de Oriente en una rama de la política nacional. En Estados Unidos, los organismos públicos demuestran un sano interés por Oriente debido a su importancia estratégica y económica y a su tradicional exotismo. El mundo, de pronto, se ha convertido en un lugar muy accesible para el ciudadano occidental que vive en la era de la electrónica y, en consecuencia, también Oriente se ha aproximado a él, y ahora quizá sea menos un mito que una encrucijada de intereses occidentales, especialmente estadounidenses.
Uno de los aspectos que el mundo electrónico posmoderno ha traído consigo es el reforzamiento de los estereotipos a través de los cuales se observa Oriente; la televisión, las películas y todos los recursos de los medios de comunicación han contribuido a que la información utilice moldes cada vez más estandarizados. En lo que se refiere a Oriente, la estandarización y la formación de estereotipos culturales han reforzado el mantenimiento de la demonología del «misterioso Oriente» que en el siglo XIX era dominio del mundo académico y del de la imaginación. Todo esto resulta mucho más evidente si analizamos el modo en que se intenta comprender el Oriente Próximo. Tres factores han contribuido a que cualquier percepción —incluso la más simple— de los árabes y del islam se convierta en un asunto muy politizado y casi desagradable: _a_ ) la historia de prejuicios populares antiárabes y antiislámicos en Occidente que se refleja de una manera inmediata en la historia del orientalismo; _b_ ) la lucha entre los árabes y el sionismo israelí y sus efectos en los judíos estadounidenses, en la cultura liberal y en la mayoría de la población; _c_ ) la ausencia casi total de una predisposición cultural que posibilite una identificación con los árabes y el islam y una discusión desapasionada sobre ellos. No es necesario decir que, como Oriente Próximo se identifica con la política de las grandes potencias, la economía del petróleo y la dicotomía simplista que califica a Israel de libre y democrático y a los árabes de diabólicos, totalitarios y terroristas, las oportunidades de saber claramente de qué se habla cuando se habla de Oriente Próximo son muy pequeñas, lo que no deja de ser deprimente. Una de las razones que me ha empujado a escribir este libro es mi propia experiencia personal. La vida de un palestino árabe en Occidente, particularmente en Estados Unidos, es descorazonadora. Existe en este país el consenso casi unánime de que políticamente no existe y si se le permite existir es como un estorbo o como un oriental. La red de racismo, de estereotipos culturales, de imperialismo político y de ideología deshumanizada que se cierne sobre el árabe o el musulmán es realmente sólida, y todo palestino ha llegado a sentirla como un castigo que le ha reservado el destino; pero todavía le resulta más duro constatar que en Estados Unidos ninguna persona académicamente comprometida con Oriente Próximo —es decir, ningún orientalista— se ha identificado jamás, desde un punto de vista cultural y político, sinceramente con los árabes; es verdad que ha habido identificaciones en determinadas áreas, pero nunca han adoptado la forma «aceptable» de la identificación progresista con el sionismo, y todas, también con demasiada frecuencia, han tenido el defecto de estar asociadas a intereses políticos y económicos desacreditados (por ejemplo, los arabistas de las compañías de petróleo y del Departamento de Estado) o a la religión.
El nexo entre conocimiento y poder que crea «al oriental» y que en cierto sentido lo elimina como ser humano para mí no es una cuestión exclusivamente académica, es una cuestión _intelectual_ de una importancia evidente. He podido valerme de mis preocupaciones humanísticas y políticas para analizar y describir una materia muy concreta, el nacimiento, desarrollo y consolidación del orientalismo. Con demasiada frecuencia, se presupone que la literatura y la cultura son inocentes política e históricamente. Yo siempre he creído lo contrario, y este estudio me ha convencido (y espero que les suceda lo mismo a mis colegas literarios) de que la sociedad y la cultura literaria solo se pueden comprender y analizar juntas. Además, y por una lógica casi ineludible, he acabado escribiendo una historia vinculada de manera secreta y misteriosa al antisemitismo occidental. Este antisemitismo y el orientalismo en su rama islámica se parecen mucho; esto es una verdad histórica, cultural y política con una ironía implícita que cualquier palestino captará inmediatamente. Pero también me gustaría haber contribuido a mejorar el conocimiento del modo en que la dominación cultural ha actuado. Si esto fomenta un nuevo tipo de relación con Oriente —de hecho, si elimina «Oriente» y «Occidente» totalmente—, habremos avanzado algo en el proceso de lo que Raymond Williams ha llamado el «desaprehendimiento del espíritu inherente de dominación».
# PRIMERA PARTE
### El ámbito del orientalismo
[...] el genio inquieto y ambicioso de los europeos... impaciente por emplear los nuevos instrumentos de su poder...
JEAN-BAPTISTE-JOSEPH FOURIER,
_Préface historique (1809)_ ,
_Description de l'Égypte_
### I
### Conocer lo oriental
El 13 de junio de 1910, Arthur James Balfour pronunció un discurso ante la Cámara de los Comunes sobre «Los problemas a los que tenemos que enfrentarnos en Egipto»: «Estos —dijo— pertenecen a una categoría que difiere completamente de la de los problemas que afectan a la isla de Wight y a la parte de West Riding de Yorkshire». Hablaba con la autoridad que le daba haber sido durante muchos años miembro del Parlamento, ex secretario particular de lord Salisbury, ex secretario de Estado para Irlanda, ex secretario de Estado para Escocia, ex primer ministro y testigo de numerosas crisis, éxitos y cambios en la política exterior. Durante su participación en los asuntos del imperio, Balfour sirvió a una reina que en 1876 había sido proclamada emperatriz de la India; estuvo muy bien situado en puestos de gran influencia que le permitieron seguir de cerca las guerras contra los afganos y zulúes, la ocupación británica de Egipto en 1882, la muerte del general Gordon en Sudán, el incidente de Fashoda, la batalla de Omdurman, la guerra de los Bóers y la guerra ruso-japonesa. Además, su notoria posición social, la amplitud de sus conocimientos —podía escribir de temas tan variados como Bergson, Haendel, teísmo y golf—, su inteligencia, su educación en Eton y en el Trinity College de Cambridge y su aparente dominio de los temas relacionados con los asuntos imperiales conferían a lo que decía ante la Cámara de los Comunes en junio de 1910 una considerable autoridad. Pero todavía había algo más en el discurso de Balfour o, por lo menos, en su necesidad de pronunciarlo de una manera didáctica y moralista. En efecto, algunos miembros del Parlamento estaban poniendo en duda la necesidad de «Inglaterra en Egipto», tema de un libro de tono entusiasta escrito por Alfred Milner en 1892, y con ello hacían referencia a que, aunque la ocupación de Egipto había sido en algún momento beneficiosa, ahora que el nacionalismo egipcio estaba en alza se había convertido en una fuente de problemas, y la continua presencia británica en Egipto no era ya fácil de mantener. Balfour, pues, debía informar y dar explicaciones.
Recordando el desafío de J. M. Robertson, diputado por Tyneside, el propio Balfour retomó la cuestión planteada por aquel: «¿Qué derecho tienen ustedes a adoptar esos aires de superioridad respecto a la gente a la que deciden llamar oriental?». La elección del término «oriental» era canónica, lo habían empleado Chaucer, Mandeville, Shakespeare, Dryden, Pope y Byron. Designaba Asia o el Este desde un punto de vista geográfico, moral y cultural; se podía hablar en Europa de una personalidad oriental, de un ambiente oriental, de un cuento oriental, de un despotismo oriental o de un modo de producción oriental y ser comprendido. Marx había utilizado el término, y ahora lo hacía Balfour; su decisión era comprensible y no suscitó el menor comentario.
No quiero adoptar ninguna actitud de superioridad, pero les pido [a Robertson y a todos aquellos] [...] que tengan algún conocimiento de la historia, por superficial que sea, que se enfrenten cara a cara con los problemas que se le plantean a un estadista británico cuando está en una posición de supremacía sobre grandes razas como la de Egipto y las de los países de Oriente. Nosotros conocemos la civilización egipcia mejor que la de cualquier otro país. La conocemos desde sus inicios, de una manera más íntima, sabemos mucho sobre ella. Sabemos que rebasa los pequeños confines de la historia de nuestra raza que se pierde en el período prehistórico, cuando la civilización egipcia había pasado ya su época de esplendor. Miren a todos los países orientales. No hablen de superioridad o inferioridad.
Dos grandes temas dominan sus puntualizaciones en estas y en las siguientes líneas: el conocimiento y el poder, los temas de Bacon. A medida que Balfour va justificando la necesidad que Gran Bretaña tiene de ocupar Egipto, la supremacía se asocia en su mente con «nuestro» conocimiento de Egipto y no principalmente con el poder militar y económico. Conocimiento, para Balfour, significa estudiar una civilización desde sus orígenes hasta su época de esplendor y su declive, y, por supuesto, significa _tener los medios para hacerlo_. Conocimiento significa elevarse por encima de las contingencias inmediatas, salir de uno mismo y alcanzar lo extraño y lo distante. El objeto de un conocimiento así está expuesto por naturaleza a que se proceda a su verificación; es «una realidad» que, aunque se desarrolle, cambie o se transforme de la misma manera en que frecuentemente lo hacen las civilizaciones, es, fundamental e incluso ontológicamente, estable. Conocer así un objeto es dominarlo, tener autoridad sobre él, y autoridad aquí significa, para «nosotros», negarle autonomía —al país oriental—, porque nosotros lo conocemos, y, en cierto sentido, existe tal y como nosotros lo conocemos. Para Balfour, el conocimiento que Gran Bretaña tiene de Egipto es Egipto, y la carga que este conocimiento supone hace que preguntas acerca de la inferioridad o superioridad parezcan mezquinas. En ningún momento Balfour niega la superioridad británica ni la inferioridad egipcia; las da por supuestas a medida que describe las consecuencias del conocimiento.
En primer lugar, examinemos las realidades del caso. Las naciones occidentales desde el momento en que aparecen en la historia dan testimonio de su capacidad de autogobierno [...], que tienen por méritos propios. Pueden ustedes revisar la historia completa de los orientales, de las regiones que de una manera general denominamos Este y nunca encontrarán rastros de autogobierno. Todas sus grandes épocas (que realmente fueron grandiosas) surgieron bajo el despotismo, bajo un gobierno absoluto; todas sus grandes contribuciones a la civilización (que fueron muy importantes) se realizaron bajo este sistema de gobierno. Un conquistador sucedió a otro, una dominación a otra, pero nunca, en ninguna de las revoluciones que han cambiado su destino y su fortuna, habrán ustedes visto que alguna de estas naciones haya establecido por sus propios medios lo que nosotros, desde un punto de vista occidental, llamamos autogobierno. Esta es la realidad; no es una cuestión de superioridad o inferioridad. Supongo que un verdadero sabio oriental diría que la labor de gobernar que nos hemos propuesto en Egipto, y en cualquier otro lugar, no es digna de un filósofo, es la tarea sucia e inferior de hacer lo que es necesario hacer.
Como estas realidades son realidades, Balfour debe entonces pasar al siguiente punto de su argumentación.
¿Es beneficioso para estas grandes naciones (admito su grandiosidad) que ese gobierno absoluto lo ejerzamos nosotros? Creo que sí. Creo que la experiencia demuestra que con este gobierno ellos han conseguido el mejor gobierno de todos los que han tenido a lo largo de la historia del mundo, lo cual no es solo un beneficio para ellos, sino que, indudablemente, lo es para todo el Occidente civilizado. Estamos en Egipto no simplemente por el bien de los egipcios, aunque estemos allí por su bien; estamos allí también por el bien de toda Europa.
Balfour no presenta ninguna prueba de que los egipcios o «las razas con las que mantenemos relaciones» aprecien o incluso entiendan el bien que la ocupación colonial les está haciendo. Pero tampoco se le ocurre permitir hablar al egipcio por sí mismo, ya que presumiblemente cualquier egipcio que esté dispuesto a hablar será probablemente «el agitador que quiere causar dificultades», y no el buen indígena que cierra los ojos ante «las dificultades» de la dominación extranjera. Por tanto, después de haber presentado los problemas éticos, Balfour, por fin, pasa a los prácticos:
Si nuestra misión es gobernarlos, tanto si nos lo agradecen como si no, tanto si recuerdan auténtica y verdaderamente todas las pérdidas de las que les hemos librado como si no [Balfour, sin duda, incluye dentro de estas pérdidas, la pérdida o, al menos, el aplazamiento indefinido de la independencia egipcia], y aunque no se imaginen todos los beneficios que les hemos proporcionado; si ese es nuestro deber, ¿cómo debemos llevarlo a cabo?
Inglaterra exporta «lo mejor que tiene a estos países»; nuestros desinteresados administradores cumplen con su trabajo «en medio de decenas de miles de personas que pertenecen a un credo y a una raza diferentes, que tienen distintas disciplinas y condiciones de vida». Lo que hace que su tarea de gobierno sea posible es que se sienten apoyados en su país por un gobierno que respalda sus acciones. Sin embargo,
las poblaciones indígenas tienen el sentimiento instintivo de que esas personas con las que deben tratar no están respaldadas por la fuerza, la autoridad, la comprensión y el apoyo completo y total del país que los mandó allí; esas poblaciones pierden el sentido del orden que es el verdadero fundamento de su civilización; del mismo modo, nuestros oficiales pierden el sentido del poder y de la autoridad que es el fundamento principal de todo lo que pueden hacer en beneficio de aquellos entre los que se les ha enviado.
La lógica de Balfour es interesante, sobre todo porque es totalmente coherente con las premisas de su discurso. Inglaterra conoce Egipto, Egipto es lo que Inglaterra conoce; Inglaterra sabe que Egipto no es capaz de tener un autogobierno, Inglaterra confirma que, al ocupar Egipto, Egipto es para los egipcios lo que Inglaterra ha ocupado y ahora gobierna; la ocupación extranjera se convierte, pues, en «el fundamento principal» de la civilización egipcia contemporánea; Egipto necesita —de hecho, exige— la ocupación británica. Pero si la particular intimidad que existe entre gobernador y gobernado en Egipto se ve turbada por las dudas del Parlamento, entonces «la autoridad de lo que [...] es la raza dominante —y que, según pienso, debe seguir siendo la raza dominante— ha sido minada». Y no solo sufre el prestigio inglés: «En vano puede un puñado de funcionarios británicos (por muy buenas cualidades de carácter y talento que ustedes piensen que tienen) llevar a cabo en Egipto la gran misión que no solo nosotros, sino el mundo civilizado, les ha encomendado».
Si lo consideramos como un ejercicio de retórica, el discurso de Balfour es significativo porque en él desempeña y representa el papel de varios personajes. Está, por supuesto, «el del inglés», al que se refiere con el pronombre «nosotros», que destaca su condición de hombre distinguido y poderoso que se siente representante de lo mejor que ha dado la historia de su nación. Balfour también puede hablar en nombre del mundo civilizado occidental y del relativamente pequeño cuerpo de funcionarios coloniales que está en Egipto. Si no habla directamente en nombre de los orientales es porque, después de todo, ellos hablan otra lengua; sin embargo, él sabe lo que sienten porque conoce su historia, la confianza que tienen en hombres como él y sus expectativas. No obstante, Balfour habla por ellos, porque, quizá, lo que ellos dirían si se les preguntara y fueran capaces de contestar, confirmaría de manera superflua lo que ya es evidente: que son una raza sometida, dominada por una raza que los conoce y que sabe mejor que ellos lo que les conviene. Tuvieron sus grandes momentos en el pasado, pero su utilidad en el mundo moderno se debe a que los imperios poderosos y modernos les han sacado de la miseria y del declive y les han convertido en habitantes readaptados de colonias productivas.
Egipto, en particular, ofrecía un excelente argumento, y Balfour, como miembro del Parlamento de su país, era perfectamente consciente de que tenía derecho a hablar del Egipto moderno en nombre de Inglaterra, de Occidente y de la civilización occidental. Porque Egipto no era una colonia como las otras: era la justificación del imperialismo occidental; había sido, hasta su anexión por parte de Inglaterra, un ejemplo casi clásico del retraso oriental e iba a significar el triunfo del conocimiento y del poder inglés. Entre 1882, año en que Inglaterra ocupó Egipto y puso fin a la rebelión nacionalista del coronel al-Urabi, y 1907, el representante inglés en Egipto, el dueño de Egipto, fue Eveling Baring, lord Cromer (también conocido por «Over-baring»). El 30 de julio de 1907, Balfour apoyó en la Cámara de los Comunes el proyecto de conceder 50.000 libras a Cromer en el momento de su jubilación como recompensa por los servicios prestados en Egipto. Cromer _ha hecho Egipto_ , dijo Balfour:
Todo lo que ha tocado ha sido un éxito [...]. Los servicios prestados por lord Cromer durante el pasado cuarto de siglo han contribuido a sacar a Egipto de la profunda degradación social y económica en la que se encontraba y a llevarlo a la posición que, creo, ahora mantiene entre las naciones orientales, posición absolutamente única en cuanto a prosperidad financiera y moral.
Balfour no se aventuró a explicar cómo se medía la prosperidad moral de Egipto. Las exportaciones británicas a Egipto equivalían a las que Gran Bretaña realizaba a toda África; eso verdaderamente indicaba una cierta prosperidad económica para Egipto e Inglaterra (aunque desigualmente repartida). Pero lo que en realidad importaba era la tutela ininterrumpida y total que ejercía Occidente sobre un país oriental, empezando por los eruditos, los misioneros, los hombres de negocios, los soldados y los maestros que prepararon y después llevaron a cabo la ocupación, y acabando por los altos funcionarios como Cromer y Balfour, que pensaban que estaban creando, dirigiendo e incluso a veces impulsando el resurgir de Egipto desde su estado de abandono oriental hasta la preeminencia que entonces tenía.
Si el éxito británico en Egipto fue excepcional, como dijo Balfour, no fue, sin embargo, algo inexplicable o irracional. Los asuntos egipcios habían sido dirigidos de acuerdo a una teoría general contenida en las nociones generales que Balfour tenía sobre la civilización oriental y en la gestión de los asuntos diarios que Cromer llevó a cabo en Egipto. Lo más importante de esta teoría durante la primera década del siglo XX fue que funcionó y, además, asombrosamente bien. El razonamiento reducido a su forma más simple era claro, preciso y fácil de comprender: hay occidentales y hay orientales. Los primeros dominan, los segundos deben ser dominados. Y esto normalmente significa que su territorio debe ser ocupado, que sus asuntos internos deben estar férreamente controlados y que su sangre y sus riquezas deben ponerse a disposición de un poder occidental. El hecho de que Balfour y Cromer hubieran sido capaces, como veremos, de despellejar tan brutalmente a la humanidad hasta reducirla a esencias culturales y raciales, no era, en absoluto, una muestra de su particular maldad; por el contrario, indicaba con qué facilidad esa teoría general, una vez puesta en práctica, pasó a formar parte de la corriente general de pensamiento y hasta qué punto fue eficaz.
A diferencia de Balfour, cuyas tesis sobre los orientales pretendían ser universales, Cromer habló sobre los orientales de una manera específica, de acuerdo con su experiencia de gobernador y administrador primero en la India y después, durante veinticinco años, en Egipto, período en el que llegó a ser cónsul general supremo del Imperio británico. Los «orientales» de Balfour son las «razas sometidas» de Cromer, sobre las que escribió un largo ensayo publicado en la _Edinburgh Review_ de enero de 1908. Una vez más, el conocimiento que tiene Gran Bretaña de las razas sometidas o de los orientales es lo que hace que su administración sea fácil y provechosa; el conocimiento da poder, un mayor poder requiere un mayor conocimiento, etc., en una dialéctica de información y control cada vez más beneficiosa. La idea de Cromer es que el Imperio británico no se disolverá mientras se mantengan a raya el militarismo y el egoísmo comercial en la metrópoli y se haga lo mismo con las «instituciones libres» en la colonia (en tanto que opuestas al gobierno británico «de acuerdo al código de moralidad cristiana»). Porque si, según Cromer, la lógica es algo «cuya existencia el oriental está totalmente dispuesto a ignorar», el método adecuado para gobernarlo no es imponerle medidas ultracientíficas u obligarle a aceptar la lógica a la fuerza; el método adecuado consiste en comprender sus limitaciones y en «procurar encontrar, en la satisfacción de la raza sometida, un vínculo de unión más valioso y, si se puede, más fuerte entre los dirigentes y los dirigidos». Disimulada tras la idea de la pacificación de la raza sometida, se esconde la potencia imperial; su eficacia es el resultado de su refinada aptitud para comprender y de sus escasas manifestaciones de poder; no es producto de sus soldados, de sus brutales recaudaciones de impuestos ni de su fuerza sin límites. En una palabra, el Imperio debe ser prudente, debe templar su codicia con generosidad, y su impaciencia con disciplina flexible.
Para ser más explícito, lo que se quiere decir cuando se dice que el espíritu comercial debería estar bajo cierto tipo de control es que, tratando con los indios, los egipcios, los silluks o los zulúes, la primera cuestión es considerar lo que estos pueblos (que, desde un punto de vista nacional, están todos _in statu pupillari_ ) piensan que es mejor para sus propios intereses; sin embargo, este es un punto que merece una reflexión más seria, pues es esencial que en cada caso particular se tomen las decisiones de acuerdo, principalmente, a lo que nosotros, según el conocimiento y la experiencia occidentales atemperados por algunas consideraciones locales, consideremos que es mejor para la raza sometida, sin pensar en las ventajas reales o supuestas que Inglaterra pueda obtener como nación o —como frecuentemente sucede— en los intereses particulares representados por una o más clases influyentes de ingleses. Si la nación británica, en su conjunto, conserva el espíritu de este principio y exige que se aplique rigurosamente, aunque nunca podamos crear un patriotismo semejante al que se basa en la afinidad de raza o en la comunidad lingüística, quizá podamos fomentar algún tipo de fidelidad cosmopolita fundamentada en el respeto que siempre se otorga a los talentos superiores y a las conductas desinteresadas y en la gratitud derivada de favores concedidos y de los que se concederán. Entonces, podremos esperar que el egipcio dude antes de confiar su destino a algún futuro al-Urabi ...]. Incluso el salvaje centroafricano puede a fin de cuentas aprender el poema «Astrea Redux»,[* representada por el oficial británico que le niega la ginebra pero le da justicia. Y además, ganará el comercio.
La medida en que un dirigente debe «considerar seriamente» las propuestas de la raza sometida queda muy bien reflejada en la oposición de Cromer al nacionalismo egipcio. Las instituciones indígenas libres, la supresión de la ocupación extranjera y la plena soberanía nacional fueron exigencias constantemente rechazadas por Cromer, que afirmó sin ambigüedad que «el futuro real de Egipto [...] no puede seguir las directrices de un nacionalismo estrecho, que solo contaría con los nativos de Egipto [...], sino más bien las de un cosmopolitismo más extenso». Las razas sometidas no podían saber lo que era bueno para ellas. La inmensa mayoría eran orientales y Cromer conocía muy bien sus caracteres ya que había tenido con ellos experiencias en la India y en Egipto. Para él, lo más cómodo respecto a los orientales consistía en que, aunque las circunstancias pudieran diferir levemente aquí y allí, gobernarlos era en todas partes más o menos lo mismo. Porque, naturalmente, los orientales eran en todas partes más o menos iguales.
Ahora, después de una serie de aproximaciones, por fin llegamos al núcleo del conocimiento esencial, académico y práctico que tanto Cromer como Balfour heredaron de un siglo de orientalismo occidental moderno: el conocimiento acerca de los orientales, su raza, su carácter, su cultura, su historia, sus tradiciones, su sociedad y sus posibilidades. Este conocimiento era real y Cromer creía que lo había utilizado cuando gobernó en Egipto; además se trataba de un conocimiento que se había llevado a la práctica y que era inmutable ya que los «orientales», para cualquier propósito práctico, eran una esencia platónica que todo orientalista (o dirigente de orientales) podía examinar, entender y exponer. Así, en el capítulo 34 de su obra de dos volúmenes _Modern Egypt_ , relato magistral de su experiencia y de sus realizaciones, Cromer expuso sus normas personales extraídas de la sabiduría orientalista:
Sir Alfred Lyall me dijo una vez: «La precisión es incompatible con la mente oriental. Todo angloindio debería recordar siempre esta máxima». La falta de exactitud, que fácilmente degenera en falsedad, es en realidad la principal característica de la mente oriental. El europeo hace razonamientos concienzudos, y sus afirmaciones acerca de la realidad están exentas de cualquier ambigüedad; es, por naturaleza, lógico, aunque no haya estudiado lógica y es, también por naturaleza, escéptico; exige pruebas antes de aceptar la verdad de cualquier proposición y su diestra inteligencia funciona como el engranaje de una máquina. La mente del oriental, por otro lado, igual que sus pintorescas calles, carece por completo de simetría, y su manera de razonar está llena de descripciones desordenadas. A pesar de que los antiguos árabes desarrollaron considerablemente la ciencia de la dialéctica, sus descendientes tienen deficiencias en sus facultades lógicas. Con frecuencia, son incapaces de sacar conclusiones obvias de unas simples premisas de las que pueden admitir la verdad. Trate de sonsacarle a cualquier egipcio una afirmación clara sobre los hechos; su explicación, en general, será larga y carente de lucidez; con toda probabilidad se contradirá media docena de veces antes de terminar su historia y normalmente se derrumbará si se le somete al más mínimo interrogatorio.
Después de esto, califica a los orientales y a los árabes de crédulos, «faltos de energía e iniciativa», muy propensos a la «adulación servil», a la intriga, a los ardides y a la crueldad con los animales; los orientales no son capaces de andar por un camino o una acera (sus mentes desordenadas se confunden cuando intentan comprender lo que el europeo lúcido entiende inmediatamente: que los caminos y las aceras están hechos para andar); los orientales son unos mentirosos empedernidos, unos «letárgicos y desconfiados» y son en todo opuestos a la caridad, a la rectitud y a la nobleza de la raza anglosajona.
Cromer no hace ningún esfuerzo por disimular que para él los orientales no son más que el material humano que él gobierna en las colonias británicas: «Como simplemente soy un diplomático y un administrador que también estudia al ser humano, aunque siempre desde la perspectiva de gobernarlo —dice Cromer— [...] me contento con observar el hecho de que el oriental, de un modo u otro, normalmente actúa, habla y piensa de una manera completamente opuesta a la de un europeo». Las descripciones de Cromer, por supuesto, se basan parcialmente en la observación directa, aunque en diversos lugares alude a las autoridades orientalistas ortodoxas (en particular a Ernest Renan y a Constantin de Volney) para reforzar sus puntos de vista. También se remite a estas autoridades cuando explica por qué los orientales son como son. No tiene ninguna duda acerca de que _cualquier_ conocimiento que se tenga sobre el oriental, confirmará sus puntos de vista que, a juzgar por su descripción del egipcio que se derrumba ante el interrogatorio, consideran al oriental culpable; su crimen consiste en que el oriental es oriental, y esta tautología debía de ser entonces muy aceptada, como lo indica el hecho de que se pudiera escribir esto sin ni siquiera apelar a la lógica o a la simetría de la mente europea. Así, cualquier desviación de lo que se consideraban las normas de comportamiento oriental era antinatural. El último informe anual que envió Cromer desde Egipto proclamaba, por consiguiente, que el nacionalismo egipcio era una «idea totalmente nueva y una planta que procedía del exterior y que no era indígena».
Creo que nos equivocaríamos si menospreciáramos el cúmulo de conocimientos recibidos y los códigos de ortodoxia orientalista a los que Cromer y Balfour se refieren en todo momento en sus escritos y en su quehacer político. Decir que el orientalismo era una racionalización del principio colonial es ignorar hasta qué punto el principio colonial estaba ya justificado de antemano por el orientalismo. Los hombres siempre han dividido el mundo en regiones que tienen diferencias reales o imaginarias; la demarcación absoluta entre Oriente y Occidente que Balfour y Cromer aceptaron con tanta complacencia había estado formándose durante años, incluso siglos. Hubo, por supuesto, numerosos viajes, descubrimientos, contactos comerciales y bélicos, pero, además, a partir de mediados del siglo XVIII, hubo dos elementos principales en las relaciones Este-Oeste: uno fue que Europa adquirió unos conocimientos sistemáticos y crecientes acerca de Oriente que fueron reforzados por el choque colonial y por el interés general ante todo lo extraño e inusual que explotaban las nuevas ciencias, como eran la etnología, la anatomía comparada, la filosofía y la historia; además, a este conocimiento sistemático se le añadió una considerable cantidad de obras literarias producidas por novelistas, poetas, traductores y viajeros de talento. El otro elemento que marcó estas relaciones fue que Europa mantuvo siempre una posición de fuerza, por no decir de dominio; y no se puede encontrar ningún eufemismo para explicar esto. Es verdad que la relación entre el fuerte y el débil podía disimularse o mitigarse —como cuando Balfour reconoció la «grandeza» de las civilizaciones orientales—, pero la relación esencial en el terreno político, cultural e incluso religioso se consideraba —en Occidente, que es lo que nos preocupa aquí— una relación entre un socio fuerte y otro débil.
Se han utilizado muchos términos para describir esta relación; Balfour y Cromer en concreto usaron algunos. El oriental es irracional, depravado (perdido), infantil, «diferente»; mientras que el europeo es racional, virtuoso, maduro, «normal». La manera de fomentar esta relación consistía en acentuar el hecho de que el oriental había vivido en un mundo propio, diferente, pero completamente organizado, un mundo con sus propias fronteras nacionales, culturales y epistemológicas, y con sus propios principios de coherencia interna. Pero lo que le daba al mundo oriental su inteligibilidad e identidad, no era el resultado de sus propios esfuerzos, sino más bien la compleja serie de manipulaciones inteligentes que permitían a Occidente caracterizar a Oriente. Así, los dos elementos de la relación cultural de los que he hablado se dan a la vez. El conocimiento de Oriente, porque nació de la fuerza, _crea_ en cierto sentido a Oriente, al oriental y a su mundo. En el discurso de Cromer y Balfour, el oriental es descrito como algo que se juzga (como en un tribunal), que se estudia y examina (como en un currículo), que se corrige (como en una escuela o una prisión), y que se ilustra (como en un manual de zoología). En cada uno de estos casos, el oriental es _contenido_ y _representado_ por las estructuras dominantes, pero ¿de dónde provienen estas?
La fuerza cultural no es un concepto del que podamos tratar fácilmente, pero uno de los propósitos de este libro es enfocar y analizar el orientalismo como un ejercicio de fuerza cultural y reflexionar sobre ello. En otras palabras, es mejor no aventurar generalizaciones sobre una noción tan vaga, aunque tan importante, como la de fuerza cultural, mientras no se haya analizado primero una gran cantidad de material. Para empezar, puede decirse que Occidente, durante los siglos XIX y XX, asumió que Oriente —y todo lo que en él había—, si bien no era manifiestamente inferior a Occidente, sí necesitaba ser estudiado y rectificado por él. Oriente se examinaba enmarcado en un aula, un tribunal, una prisión o un manual ilustrado, y el orientalismo era, por tanto, una ciencia sobre Oriente que situaba los asuntos orientales en una clase, un tribunal, una prisión o un manual para analizarlos, estudiarlos, juzgarlos, corregirlos y gobernarlos.
Durante los primeros años del siglo XX, hombres como Balfour y Cromer pudieron decir lo que dijeron y de la manera en que lo dijeron porque una tradición de orientalismo que se remontaba a un período anterior al siglo XIX les había proporcionado un vocabulario, unas imágenes, una retórica y unas figuras con las que decirlo. Pero el orientalismo reforzó la certidumbre de que Europa, u Occidente, dominaba literalmente la mayor parte de la superficie de la Tierra, y a su vez fue reforzado por ella. El período en el que se produjo el gran progreso de las instituciones y del contenido del orientalismo coincidió exactamente con el período de mayor expansión europea; desde 1815 a 1914 el dominio colonial europeo directo se amplió desde más o menos un 35 por ciento de la superficie de la Tierra hasta un 85 por ciento. Todos los continentes resultaron afectados, pero, sobre todo, África y Asia. Los dos grandes imperios eran el británico y el francés, aliados y socios en algunos momentos y hostiles rivales en otros. En Oriente, desde las costas orientales del Mediterráneo hasta Indochina y Malasia, sus posesiones coloniales y sus esferas de influencia imperial eran colindantes, frecuentemente rozaban entre sí, y, a menudo, habían sido objeto de sus disputas. Pero fue en Oriente Próximo, en las tierras del Oriente Próximo árabe en las que se supone que el islam define las características culturales y étnicas, donde británicos y franceses se enfrentaron entre sí y con «Oriente» de una manera más intensa, familiar y compleja. Durante la mayor parte del siglo XIX, como lord Salisbury señaló en 1881, sus perspectivas comunes sobre Oriente crearon complicados problemas: «Cuando cuentas con un fiel aliado, resuelto a entrometerse en un país en el que tú estás profundamente interesado, tienes tres caminos abiertos ante ti: puedes renunciar a él, monopolizarlo, o compartirlo. Renunciar a él habría supuesto permitir que los franceses se interpusieran en nuestra ruta hacia la India, monopolizarlo habría significado un riesgo importante de guerra; por tanto, resolvimos compartirlo».
Y, en efecto, lo compartieron; cómo lo hicieron es lo que vamos a ver ahora. Lo que compartieron no fue solo la tierra, los beneficios y la soberanía; fue también esa especie de poder intelectual que yo he denominado orientalismo, y que, en cierto sentido, constituyó la biblioteca o el archivo de las informaciones que fueron en común e incluso al unísono adquiridas. Lo que mantuvo el archivo unido fue un parentesco ideológico y un conjunto unificador de valores que habían demostrado su eficacia de diferentes maneras. Estas ideas explicaban el comportamiento de los orientales, les proporcionaban una mentalidad, una genealogía, una atmósfera y, lo más importante, permitían a los europeos tratarlos e incluso considerarlos como un fenómeno con unas características regulares. Pero, como cualquier conjunto de ideas duraderas, las nociones orientalistas influyeron en aquellos a los que se denominaba orientales, así como en los llamados occidentales o europeos. En resumen, el orientalismo se puede comprender mejor si se analiza como un conjunto de represiones y limitaciones mentales más que como una simple doctrina positiva. Si la esencia del orientalismo es la distinción incuestionable entre la superioridad occidental y la inferioridad oriental, debemos estar dispuestos a observar cómo el orientalismo, a través de su evolución y de su historia subsecuente, profundizó e incluso agudizó la distinción. Cuando durante el siglo XIX se hizo práctica común que Gran Bretaña retirara a sus administradores de la India y de cualquier otro lugar una vez que hubieran llegado a los cincuenta y cinco años de edad, el orientalismo alcanzó un refinamiento complementario: ningún oriental tendría la posibilidad de ver a un occidental envejecer y degenerarse, y de igual modo, ningún occidental necesitaría reflejarse en los ojos de la raza sometida, a no ser que fuera para verse como un joven representante del Raj,* vigoroso, racional y siempre alerta.
Las ideas orientalistas adoptaron diferentes formas durante los siglos XIX y XX. En primer lugar, en Europa existía una gran cantidad de literatura sobre Oriente que se había heredado del pasado. Lo que distinguió el final del siglo XVIII y los principios del XIX, cuando según nuestro planteamiento empezó el orientalismo moderno, es que se produjo un resurgir de lo oriental, como expresó Edgar Quinet. De pronto, una amplia y variada gama de pensadores, políticos y artistas adquirió una nueva conciencia de Oriente, desde China al Mediterráneo, debido, en parte, al descubrimiento y a la traducción de unos textos orientales del sánscrito, del farsi y del árabe, y también a una percepción nueva de la relación Oriente-Occidente. Para mis propósitos, el tono de esta relación entre el Oriente Próximo y Europa lo dio la invasión napoleónica de Egipto en 1798, invasión que fue, por muchas razones, un modelo perfecto de lo que es una verdadera apropiación científica de una cultura por otra aparentemente más fuerte. En efecto, con la ocupación napoleónica de Egipto, se pusieron en marcha muchos procesos entre Oriente y Occidente, procesos que todavía hoy dominan nuestras perspectivas culturales y políticas. Y la expedición napoleónica, con su gran monumento colectivo de erudición, la _Description de l'Égypte_ , proporcionó al orientalismo su escenario o su decorado, ya que Egipto y, a continuación, las demás tierras islámicas se convirtieron en marco de estudios experimentales, un laboratorio, un teatro para el conocimiento efectivo de Oriente. Volveré a la aventura napoleónica algo más adelante.
Con experiencias como la de Napoleón, Oriente, en tanto que objeto de conocimientos para Occidente, se puso al día; esta nueva forma que adoptó fue el orientalismo de los siglos XIX y XX. Desde el principio del período que estoy examinando, los orientalistas tenían la ambición de formular sus descubrimientos, sus experiencias y sus intuiciones de manera correcta, en términos modernos, querían poner en contacto las ideas sobre Oriente con las realidades modernas. Las investigaciones de Renan sobre las lenguas semíticas en 1848, por ejemplo, fueron expresadas en un estilo que pretendía demostrar su autoridad en gramática y anatomía comparadas y en teorías raciales; todo esto concedía prestigio a su orientalismo, pero la otra cara de la moneda consistía en que el orientalismo se hacía más vulnerable que nunca a las modas y a las corrientes de pensamiento que tenían considerable influencia en Occidente. Así, el orientalismo estuvo sometido al imperialismo, al positivismo, a la utopía, al historicismo, al darwinismo, al racismo, al psicoanálisis, al marxismo, a las teorías de Spengler, etc. Pero, como muchas otras ciencias naturales y sociales, también tuvo sus «paradigmas» de investigación, sus propias sociedades culturales y su propia organización interna. Durante el siglo XIX, el prestigio de su actuación creció enormemente, aumentó su reputación y la influencia de instituciones como la Société Asiatique, la Royal Asiatic Society, la Deutsche Morgenländische Gesellschaft y la American Oriental Society. Con el auge de estas sociedades, aumentó también en toda Europa el número de cátedras de estudios orientales y, en consecuencia, hubo una expansión de los medios de difusión del orientalismo. Las publicaciones orientalistas que empezaron con _Fundgraben des Orients_ (1809) contribuyeron a incrementar la masa de conocimientos y el número de sus especialidades.
No obstante, solo una pequeña parte de esta actividad y muy pocas de estas instituciones existieron y florecieron libremente, ya que el orientalismo, en su tercera forma, impuso sus límites a todo pensamiento que se refiriera a Oriente. Incluso los escritores más imaginativos de la época, hombres como Flaubert, Nerval o Scott, estaban coaccionados a la hora de sentir o decir algo sobre Oriente porque el orientalismo era, en última instancia, una visión política de la realidad cuya estructura acentuaba la diferencia entre lo familiar (Europa, Occidente, «nosotros») y lo extraño (Oriente, el Este, «ellos»). Esta visión, en cierto sentido, creó y luego sirvió a los dos mundos así concebidos. Los orientales vivían en su mundo, «nosotros» vivíamos en el nuestro. Esta visión y la realidad material se apoyaban y se estimulaban mutuamente. Tener una cierta libertad para relacionarse con el otro era siempre un privilegio del occidental, porque la suya era la cultura más fuerte; él podía penetrar, abarcar, dar forma y significado al gran misterio asiático, como Disraeli lo expresó una vez. Sin embargo, hasta ahora, no hemos señalado el restringido vocabulario de este privilegio ni las limitaciones relativas de esta visión. Lo que quiero demostrar es que la realidad orientalista es antihumana y persistente y que su campo de acción así como sus instituciones y su influencia universal se han mantenido hasta nuestros días.
Pero ¿cómo ha funcionado y funciona el orientalismo? ¿Cómo describirlo en tanto que fenómeno histórico, modo de pensamiento, problema contemporáneo y realidad material? Tengamos en cuenta de nuevo a Cromer, un hábil técnico del Imperio, pero también un político que se benefició del orientalismo. Él puede proporcionarnos los rudimentos de la respuesta. En _The Government of Subject Races_ se enfrenta al siguiente problema: ¿cómo Gran Bretaña, una nación de individuos, va a poder administrar un imperio tan vasto de acuerdo a una serie de principios rectores? Compara al «administrador local», que por un lado conoce el mundo indígena como un especialista y, por otro, posee la individualidad anglosajona, con la autoridad central en la metrópoli. El primero puede «tratar temas de interés local de una manera que tienda a dañar o incluso a poner en peligro los intereses imperiales; la autoridad central está en una posición que le permite evitar cualquier peligro que surja por esta causa». ¿Por qué? Porque esta autoridad puede «asegurar el funcionamiento armonioso de las diferentes partes de la máquina» y debe intentar, en la medida de lo posible, «realizar las circunstancias que puedan surgir en el gobierno de la posesión». El lenguaje es vago y poco atractivo, pero el argumento no es difícil de entender; Cromer imagina un centro de poder en Occidente desde el cual sale una gran máquina que se extiende hacia Oriente y que, aunque sostiene a la autoridad central, recibe órdenes de ella. Lo que los brazos de la máquina le ofrecen en Oriente de alimento —material humano, riqueza, conocimientos, etc.—, esta lo procesa y lo convierte en más poder. El especialista transforma de una manera inmediata lo que es una simple materia oriental en una sustancia útil; por ejemplo, el oriental se convierte en una raza sometida, en un modelo de mentalidad «oriental» para reforzar la «autoridad» en la metrópoli. Los «intereses locales» son los intereses especiales del orientalista, la «autoridad central» es el interés general del conjunto de la sociedad imperial. Lo que Cromer ve con bastante exactitud es la administración del conocimiento por parte de la sociedad, el hecho de que el conocimiento —incluso el más especializado— está regulado primero por los intereses locales de un especialista y después por los intereses generales de un sistema social de autoridad. La interacción entre los intereses locales y los centrales es compleja, pero de ninguna manera se debe al azar.
El propio Cromer, administrador colonial, dice que «el tema apropiado de su estudio es también el hombre». Cuando Pope reclamaba que el tema apropiado para estudiar la humanidad era el hombre, quería decir todos los hombres, incluyendo «al pobre indio», mientras que cuando Cromer utiliza la palabra «también», nos recuerda que ciertos hombres, por ejemplo los orientales, pueden ser escogidos como tema de estudio _apropiado_. El estudio apropiado de los orientales, en este sentido, es el orientalismo, separado de forma adecuada de otras formas de conocimiento, pero, al fin y al cabo, útil (porque es finito) para la realidad material y social, que contiene todo el saber, lo apoya y le proporciona su utilidad. Así, un orden de soberanía se establece entre Oriente y Occidente, una cadena irrisoria de seres, a la que Kipling dio una vez su forma más clara:
Una mula, un caballo, un elefante o un novillo obedecen a su conductor, el conductor a su sargento, el sargento a su teniente, el teniente a su capitán, el capitán a su comandante, el comandante a su coronel, el coronel a su brigada, que dirige tres regimientos, y el brigada a su general que obedece al virrey, que es servidor de la Emperatriz.
Esta monstruosa cadena de subordinación ha sido sólidamente forjada; del mismo modo, el «funcionamiento armonioso» de Cromer ha sido manejado con gran vigor; con esta misma solidez y vigor el orientalismo puede expresar la fuerza de Occidente y la debilidad de Oriente desde la perspectiva del primero. Esta fuerza y esta debilidad son tan intrínsecas al orientalismo como lo son a cualquier concepción que divida el mundo en grandes regiones generales, en entidades que coexisten en un estado de tensión producido por lo que se cree que es una diferencia radical.
Así que este es el principal tema intelectual suscitado por el orientalismo: ¿se puede dividir la realidad humana, como de hecho la realidad humana parece estar auténticamente dividida, en culturas, historias, tradiciones, sociedades e incluso razas claramente diferentes entre sí y continuar viviendo asumiendo humanamente las consecuencias? Al decir esto último me refiero a si hay alguna manera de evitar la hostilidad expresada por la división de los hombres entre, por ejemplo, «nosotros» (occidentales) y «ellos» (orientales). Pues estas divisiones son unas ideas generales que se han utilizado a lo largo de la historia y se utilizan en el presente para insistir en la importancia de la distinción entre unos hombres y otros con fines que, en general, no han sido ni son especialmente admirables. Cuando se utilizan las categorías de oriental y occidental como punto de partida y de llegada de un análisis, una investigación o un asunto político (como Balfour y Cromer las usaron), los resultados que se obtienen normalmente son, por un lado, la polarización de la distinción: el oriental se vuelve más oriental y el occidental más occidental y, por otro, la limitación de las relaciones humanas entre las diferentes culturas, tradiciones y sociedades. En resumen, que desde los comienzos de la historia moderna hasta el momento, el orientalismo, como forma de pensamiento que se relaciona con el exterior, ha demostrado de manera característica la tendencia deplorable de toda ciencia que se basa en distinciones tan rigurosas como son las de «Este» y «Oeste», tendencia que consiste en canalizar el pensamiento hacia un compartimiento, el «Oeste», o hacia otro, el «Este». Como esta tendencia ocupa justo el centro de la teoría, la práctica y los valores orientalistas que se encuentran en Occidente, el sentido del poder occidental sobre Oriente se acepta sin discusión, como si de una verdad científica se tratara.
Uno o dos ejemplos actuales bastarían para clarificar esta observación. Es natural que los hombres que están en el poder pasen revista de vez en cuando al mundo del que se tienen que ocupar; Balfour lo hacía frecuentemente; nuestro coetáneo Henry Kissinger también lo hace y rara vez con más franqueza explícita que en su ensayo «Domestic Structure and Foreign Policy». El drama que describe es real y consiste en que Estados Unidos debe ordenar su comportamiento en el mundo ante la presión que recibe, por un lado, de fuerzas interiores y, por otro, de realidades exteriores. El discurso de Kissinger debe establecer, por esta razón, una polaridad entre Estados Unidos y el mundo; además, por supuesto, él habla siendo consciente de que es una voz autorizada por la gran potencia occidental cuya historia reciente y realidad actual la han situado ante un mundo que no acepta fácilmente su poder ni su dominación. Kissinger constata que Estados Unidos puede tratar con el Occidente industrial desarrollado de una manera menos problemática que con el mundo en vías de desarrollo. Además, las relaciones actuales entre Estados Unidos y el llamado Tercer Mundo (que incluye China, Indochina, Oriente Próximo, África y Latinoamérica) son claramente un conjunto de problemas espinosos que ni siquiera Kissinger puede ocultar.
El método que Kissinger utiliza en su ensayo sigue lo que los lingüistas llaman la oposición binaria; es decir, expone que hay dos estilos en política exterior (el profético y el político), dos tipos de técnicas, dos períodos, etc. Cuando, al final de la parte histórica de su argumento, se encuentra cara a cara con el mundo contemporáneo, lo divide, por consiguiente, en dos mitades: los países desarrollados y los países en vías de desarrollo. La primera mitad, constituida por Occidente, «está profundamente impregnada de la noción de que el mundo real es exterior al observador, de que el conocimiento consiste en registrar y clasificar los datos con toda la precisión posible». La prueba que Kissinger presenta de esto es la revolución newtoniana, que, según él, no ha tenido lugar en el mundo en vías de desarrollo: «Las culturas que escaparon al primer impacto del pensamiento newtoniano han conservado de modo esencial la perspectiva prenewtoniana de que el mundo real es casi completamente _interior_ al observador»; en consecuencia, añade, «la realidad empírica tiene para muchas de las nuevas naciones una trascendencia diferente de la que tiene para Occidente porque, en cierto sentido, nunca han experimentado el proceso de descubrirla».
Al contrario que Cromer, Kissinger no necesita citar a sir Alfred Lyall al hablar de la poca habilidad del oriental para ser exacto; su argumento es lo suficientemente indiscutible como para no exigir ninguna validación particular. Nosotros tuvimos nuestra revolución newtoniana, ellos, no; como pensadores, nosotros somos mejores que ellos. Bien, las líneas de demarcación son trazadas en su mayor parte del mismo modo en que Balfour y Cromer lo hicieron; pero entre Kissinger y los imperialistas británicos hay por lo menos sesenta años de diferencia. Numerosas guerras y revoluciones han demostrado de manera concluyente que el estilo profético prenewtoniano que Kissinger asocia con los países «inexactos» y en vías de desarrollo y con la Europa anterior al Congreso de Viena no ha dejado de tener sus éxitos. De nuevo, al contrario que Balfour y Cromer, Kissinger se siente obligado a respetar esta perspectiva prenewtoniana ya que «ofrece una gran flexibilidad de cara al desorden revolucionario contemporáneo». Así, el deber de los hombres en el mundo posnewtoniano (real) es «construir un orden internacional _antes_ de que una crisis lo imponga como necesidad»: en otras palabras, todavía debemos encontrar el medio de dominar al mundo en vías de desarrollo. ¿No es esto similar a la visión que tenía Cromer de una máquina que funcionaba armoniosamente y que estaba destinada, en última instancia, a beneficiar a alguna autoridad central opuesta al mundo en vías de desarrollo?
Kissinger quizá no conocía la genealogía del saber en el que estaba buceando cuando dividió el mundo en concepciones de la realidad prenewtonianas y posnewtonianas; pero su distinción es idéntica a la ortodoxa que realizaron los orientalistas y que consistía en separar a los orientales de los occidentales. Al igual que la distinción orientalista, la de Kissinger presupone una valoración, a pesar de la aparente neutralidad de su tono. Así, expresiones como «profético», «exactitud», «interior», «realidad empírica» y «orden» están diseminadas a lo largo de toda su descripción y designan virtudes atractivas, familiares y deseables o defectos amenazantes, extraños y desordenados. Los orientalistas tradicionales, como veremos, y Kissinger conciben las diferencias entre las culturas como una realidad que primero crea un muro que las separa, y segundo invita a Occidente a controlar, dominar y gobernar a lo Otro (gracias a su conocimiento superior y a su poder de acomodación). No hace falta recordar ahora con qué resultados y a qué precio se han mantenido estas divisiones militantes.
Hay otro ejemplo que enlaza claramente (quizá demasiado claramente) con el análisis de Kissinger. En su número de febrero de 1972, el _American Journal of Psychiatry_ publicó un artículo de Harold W. Glidden, miembro retirado del Bureau of Intelligence and Research del Departamento de Estado de Estados Unidos; el título del artículo («The Arab World»), su tono y su contenido denotan el espíritu característico de un orientalista. Así, en sus cuatro páginas a doble columna, Glidden, para hacer un retrato psicológico de unos cien millones de personas durante un período de mil trescientos años, cita exactamente cuatro fuentes: un libro reciente sobre Trípoli, un número del periódico egipcio _Al-Ahram_ , la revista _Modern Orient_ y un libro del conocido orientalista Majid Khadduri. El artículo pretende descubrir «el funcionamiento interno del comportamiento árabe» que desde _nuestro_ punto de vista es «aberrante», pero que para los árabes es «normal». Tras este afortunado comienzo, nos dice que los árabes fomentan el conformismo, que viven en una cultura de la deshonra cuyo «sistema de prestigio» implica la posibilidad de atraer seguidores y clientes (además nos ha dicho que la «sociedad árabe se basa y siempre se ha basado en un sistema de relaciones cliente-patrón»), que los árabes solo funcionan en situaciones conflictivas, que el prestigio se fundamenta únicamente en la habilidad de dominar a otros, que una cultura de la deshonra, y por tanto el propio islam, convierte la venganza en una virtud (en este punto Glidden cita triunfalmente _Al-Ahram_ del 29 de junio de 1970 para demostrar que «en 1969 en Egipto, de 1.070 casos de asesinato en los que los autores habían sido arrestados, se descubrió que la causa del 20 por ciento de los mismos había sido el deseo de borrar la deshonra, del 30 por ciento el deseo de reparar algún error real o imaginario y del 31 por ciento el deseo de una venganza de sangre») y que si desde un punto de vista occidental «lo único racional que podrían hacer los árabes sería acordar la paz [...], para ellos, la situación no está gobernada por una lógica de este tipo, ya que la objetividad no es un valor en el sistema árabe».
Glidden continúa aún con mayor entusiasmo: «Es importante señalar que, mientras el sistema de valores árabe exige una solidaridad absoluta dentro del grupo, al mismo tiempo incita a sus miembros a un tipo de rivalidad que destruye esta solidaridad»; en la sociedad árabe solo «cuenta el éxito», y «el fin justifica los medios»; los árabes viven «naturalmente» en un mundo «caracterizado por una ansiedad que se expresa a través de un recelo y una desconfianza generalizados y a través de lo que ha sido calificado como hostilidad sin límites»; «el arte del subterfugio está muy desarrollado en la vida árabe y en el propio islam»; la necesidad de venganza que tienen los árabes predomina sobre cualquier otra porque sin ella, el árabe sentiría una vergüenza que lo destruiría. Por tanto, si «los occidentales sitúan la paz en un lugar preferente dentro de su escala de valores» y si «tenemos una conciencia muy desarrollada del valor del tiempo», esto no es aplicable a los árabes. «De hecho —nos dice— en la sociedad tribal árabe (donde nacieron los valores árabes) la lucha, más que la paz, era la situación normal, porque las incursiones guerreras eran uno de los dos principales soportes de la economía.» El propósito de esta sabia disquisición es simplemente demostrar que en la escala de valores occidental y oriental «la disposición relativa de los elementos es bastante diferente».
En este tipo de planteamientos se manifiesta la culminación de la confianza del orientalismo en sí mismo. A cualquier idea general meramente enunciada se le reconoce la dignidad de la verdad; cualquier lista teórica de atributos orientales se aplica al comportamiento de los orientales en el mundo real. Por un lado están los occidentales y por otro los arabo-orientales; los primeros son (citamos sin seguir ningún orden especial) racionales, pacíficos, liberales, lógicos, capaces de mantener valores reales y no son desconfiados por naturaleza; los segundos no tienen ninguna de estas características. ¿De qué perspectiva colectiva, y sin embargo detallada, de Oriente se derivan estas afirmaciones? ¿Qué técnicas especializadas, qué presiones de la imaginación, qué instituciones, qué tradiciones y qué fuerzas culturales produjeron una similitud tan grande entre las descripciones de Oriente que encontramos en Cromer y Balfour, y las de los hombres de Estado contemporáneos?
### II
### La geografía imaginaria y sus representaciones:
### orientalizar lo oriental
Estrictamente hablando, el orientalismo es un campo de estudio erudito. Se considera que su existencia formal comenzó en el Occidente cristiano con la decisión que adoptó en 1312 el Concilio de Vienne de establecer una serie de cátedras de «árabe, griego, hebreo y siríaco en París, Oxford, Bolonia, Aviñón y Salamanca». Pero para dar cuenta de lo que es el orientalismo no solo hay que considerar al orientalista profesional y su trabajo, sino que también es necesario analizar la propia noción de este campo de estudio, campo que tiene como base una unidad geográfica, cultural, lingüística y étnica llamada Oriente. Es evidente que los campos de estudio se crean y que, con el tiempo, adquieren coherencia e integridad porque los eruditos se consagran con devoción a lo que parece ser una disciplina comúnmente aceptada. Pero esto es válido siempre y cuando no planteemos la posibilidad de que, quizá, la definición del campo no sea tan simple como pretenden sus partidarios más convencidos, normalmente eruditos, profesores, expertos, etc. Además, un campo de estudio puede cambiar tan radicalmente —incluso en las disciplinas más tradicionales como la filología, la historia y la teología— que se haga imposible dar una definición que abarque toda su materia. Esto se puede aplicar perfectamente bien al campo del orientalismo por algunas razones importantes.
Hablar de una especialidad científica que se restringe a un «campo» geográfico es, en el caso del orientalismo, bastante revelador ya que, probablemente, nadie pueda imaginar un campo simétrico llamado occidentalismo. La actitud particular, quizá incluso excéntrica, del orientalismo se hace patente enseguida ya que, aunque muchas disciplinas eruditas supongan la adopción de una postura determinada con respecto a un material _humano_ (un historiador se ocupa del pasado de los hombres desde la perspectiva privilegiada del presente), no existe ningún campo análogo a este en el que se adopte una postura inmutable y con una base casi totalmente geográfica para abordar una gran variedad de realidades sociales, lingüísticas, políticas e históricas. El clasicista, el especialista en lenguas romances e incluso el especialista en América concentran su interés en una porción relativamente modesta del mundo, y no en la mitad completa de él. El orientalismo, pues, es un campo que tiene una considerable ambición geográfica; y, como los orientalistas tradicionalmente se han ocupado de los asuntos orientales (tanto un especialista en derecho islámico como un experto en los dialectos chinos o en las religiones indias es considerado un orientalista por las personas que se consideran a sí mismas orientalistas), debemos acostumbrarnos a la idea de que una de las características más importantes del orientalismo es su enorme y heterogéneo tamaño, además de una capacidad casi infinita para la subdivisión, como resultado de la confusa amalgama de vaguedad imperial y de detalles precisos.
Todo esto define al orientalismo como disciplina académica. El «ismo» sirve para subrayar la especificidad de la disciplina. Su evolución histórica ha tendido, por regla general, a incrementar sus dimensiones y no a desarrollar una mayor selectividad como disciplina. Orientalistas del Renacimiento como Erpenio y Guillaume Postel fueron, en primer lugar, especialistas en las lenguas de las regiones bíblicas, aunque Postel se jactara de poder atravesar Asia hasta llegar a China sin necesidad de un intérprete. Por regla general, hasta la mitad del siglo XVIII los orientalistas fueron eruditos bíblicos, estudiantes de lenguas semíticas, islamólogos o, cuando los jesuitas abrieron el camino hacia los nuevos estudios sobre China, sinólogos. La extensión completa del Asia Central no fue académicamente conquistada por el orientalismo hasta que, a finales del siglo XVIII, Anquetil-Duperron y sir William Jones fueron capaces de comprender y dar a conocer la extraordinaria riqueza del persa avéstico y del sánscrito. Hacia la mitad del siglo XIX, el orientalismo se había convertido en el tesoro de conocimientos más vasto que se podía imaginar. Hay dos excelentes muestras de este nuevo eclecticismo triunfante. Una de ellas es la descripción enciclopédica del orientalismo desde aproximadamente 1765 hasta 1850, realizada por Raymond Schwab en su obra _La Renaissance orientale_. Además de los descubrimientos científicos sobre lo oriental que realizaron los eruditos profesionales, en esta época hubo una verdadera epidemia de _Orientalia_ en Europa que afectó a todos los grandes poetas, ensayistas y filósofos del momento. Schwab opinaba que la palabra «oriental» describía un entusiasmo de aficionado o de profesional por todo lo asiático, y que era un maravilloso sinónimo de lo exótico, lo misterioso, lo profundo y lo seminal. Todo esto constituye una transposición, más reciente y hacia el Este, del entusiasmo similar que a principios del Renacimiento sintió Europa por la antigüedad griega y latina. En 1829, Victor Hugo subrayó este cambio de dirección de la siguiente manera: _«Au siècle de Louis XIV on était helléniste, maintenant on est orientaliste»_. El orientalista del siglo XIX era, por tanto, un erudito (sinólogo, islamólogo, especialista en indoeuropeo), un entusiasta con talento (Hugo en _Les Orientales_ o Goethe en _Westöstlicher Diwan_ ), o ambas cosas a la vez (Richard Burton, Edward Lane, Friedrich Schlegel).
La segunda prueba que demuestra hasta qué punto el orientalismo a partir del Concilio de Vienne había empezado a abarcar un número cada vez mayor de materias se puede encontrar en las crónicas del siglo XIX que describen la propia disciplina. La más completa de todas es _Vingt-sept ans d'histoire des études orientales_ , de Jules Mohl, un diario de dos volúmenes que registra todo lo que el orientalismo produjo entre 1840 y 1867. Mohl era el secretario de la Société Asiatique en París, y, durante algo más de la primera mitad del siglo XIX, París fue la capital del mundo orientalista (y según Walter Benjamin, la del siglo XIX). El puesto de Mohl en la Société no podía haber sido más crucial para el campo del orientalismo. Mohl consiguió que todo lo que los eruditos europeos escribieron sobre Asia durante esos veintisiete años se considerara dentro del campo de los «estudios orientales». Esta consideración consistía, por supuesto, en publicar los trabajos en cuestión, de modo que la cantidad de material de interés para los eruditos orientalistas que se publicó es impresionante. El árabe, numerosos dialectos indios, el hebreo, el pahleví, el asirio, el babilonio, el mongol, el chino, el birmano, el mesopotámico, el javanés... la lista de trabajos filológicos considerados como orientalistas es casi infinita. Además, los estudios orientalistas aparentemente englobaban todo, desde la edición y traducción de textos, hasta estudios de numismática, antropología, arqueología, sociología, economía, historia, literatura y cultura de cualquiera de las civilizaciones asiáticas o norteafricanas conocidas, antiguas o modernas. La _Histoire des orientalistes de l'Europe du XII e au XIXe siècle_ (18681870), de Gustave Dugat, es una historia selectiva de las grandes personalidades, pero la variedad de temas presentada no es menor que la de Mohl.
Sin embargo, este eclecticismo tenía sus puntos débiles. Los orientalistas académicos, en su mayoría, estaban interesados en el período clásico de la lengua o de la sociedad que estudiaban. Hasta más avanzado el siglo, con la gran y única excepción del Institut d'Égypte de Napoleón, no se prestó atención al estudio académico del Oriente moderno o contemporáneo. Además, Oriente se estudiaba a través de los libros y de los manuscritos y no, como en el caso de la influencia griega en el Renacimiento, a través de obras plásticas, como esculturas y cerámicas. Incluso la relación entre los orientalistas y Oriente era textual; esto fue así hasta el punto de que se dice que algunos orientalistas alemanes de principios del siglo XIX perdieron el gusto por lo oriental al contemplar una estatua india de ocho brazos. Cuando un orientalista viajaba al país en el que estaba especializado, lo hacía llevando consigo sentencias abstractas e inmutables sobre la «civilización» que había estudiado; pocas veces se interesaron los orientalistas por algo que no fuera probar la validez de sus «verdades» mohosas y aplicarlas, sin mucho éxito, a los indígenas incomprensibles y, por tanto, degenerados. A fin de cuentas, el gran poder y el enorme ámbito del orientalismo produjeron no solo una gran cantidad de conocimientos exactos y positivos sobre Oriente, sino también unos conocimientos de segundo orden (que se ocultan en lugares tales como el cuento «oriental», la mitología del misterioso Oriente, la idea de que los asiáticos son impenetrables) que tenían su propia vida, y que constituyen lo que V. G. Kiernan ha llamado con gran acierto «el sueño colectivo de Europa con respecto a Oriente». Esto produjo un resultado positivo: un buen número de escritores importantes del siglo XIX se apasionó por Oriente. Creo que es perfectamente legítimo hablar del orientalismo como de un género literario representado por las obras de Hugo, Goethe, Nerval, Flaubert, Fitzgerald y otros. Sin embargo, en este género de obras inevitablemente aparece siempre una mitología fluctuante de Oriente, un Oriente que no se deriva solo de actitudes contemporáneas y de prejuicios populares, sino también de lo que Vico llamó la presunción de las naciones y de los eruditos. Ya he mencionado el uso político que se ha hecho de este material en el siglo XX.
Hoy día es poco probable, menos probable que antes de la Segunda Guerra Mundial, que un orientalista se autodenomine orientalista; sin embargo, la denominación sigue siendo útil, por ejemplo, cuando las universidades mantienen programas o departamentos de lenguas y civilizaciones orientales. Hay una «facultad» oriental en Oxford y un Departamento de Estudios Orientales en Princeton. En 1959, el gobierno británico encargó a una comisión que «revisara los progresos que se habían hecho en las universidades dentro de los campos de estudios orientales, eslavos, de Europa del Este y africanos [...] y que considerara e hiciera propuestas para un mejor desarrollo futuro». Parece que el amplio significado de la palabra _oriental_ no fue un obstáculo para el Informe Hayter (así se llamó cuando apareció en 1961), significado que también las universidades americanas encontraron válido. Pero incluso la figura más importante de los estudios islámicos modernos angloamericanos, H. A. R. Gibb, prefirió llamarse orientalista antes que arabista. El propio Gibb, clasicista como era, podía utilizar el horrible neologismo «estudios de áreas culturales» para designar al orientalismo como una manera de mostrar que los estudios de áreas culturales y el orientalismo, después de todo, no eran más que títulos geográficos intercambiables. Pero creo que esto era un modo ingenuo de encubrir las relaciones mucho más interesantes que se establecían entre el conocimiento y la geografía, relaciones que voy a estudiar brevemente.
A pesar de la confusión que le producen ciertos deseos, impulsos e imágenes vagas, parece que la mente tiende a formular con persistencia lo que Claude Lévi-Strauss ha llamado una ciencia de lo concreto. Una tribu primitiva, por ejemplo, tiende a asignar un lugar, una función y una significación concreta a cualquier especie de hoja que se encuentre en su entorno. Muchas de estas hierbas y flores no tienen ninguna utilidad práctica, pero el argumento de Lévi-Strauss consiste en que la mente exige un orden y el orden se logra haciendo distinciones, tomando nota de todo y situando cada realidad de la que la mente es consciente en un lugar seguro y preciso, dando, por tanto, a las cosas algún papel que desempeñar en la economía de los objetos y de las identidades que crean el medio ambiente. Este tipo de clasificación rudimentaria tiene una lógica para la tribu; pero las reglas lógicas según las cuales un helecho verde en una sociedad es símbolo de gracia y en otra es un elemento maléfico no son ni racionales ni universales. Siempre, cuando se hacen distinciones entre las cosas, se manejan valores puramente arbitrarios, valores cuya historia, si se pudiera descifrar completamente, mostraría, con toda probabilidad, la misma arbitrariedad. Esto es evidente en el caso de la moda: ¿por qué las pelucas, los cuellos de encaje y los zapatos altos con hebillas aparecen y desaparecen en cuestión de años? La respuesta, por un lado, tiene que ver con la utilidad y, por otro, con la estética inherente a la moda. Pero si estamos de acuerdo en que todas las cosas en la historia, como la historia misma, están hechas por el hombre, debemos ser conscientes de hasta qué punto es posible que a muchos objetos, lugares y épocas se les asignen papeles y se les den significados que adquieren una validez objetiva solo _después_ de que se hayan realizado las asignaciones. Este proceso se lleva a cabo de manera más frecuente cuando se trata de realidades relativamente inusuales, extrañas y cambiantes o de comportamientos anormales.
Podemos mantener que la mente crea algunos objetos distintivos que, aunque parecen existir objetivamente, solo tienen una realidad ficticia. Un grupo de personas que viva en unas cuantas hectáreas establecerá las fronteras entre su territorio, los inmediatamente colindantes y el territorio más alejado, al que llamará «el territorio de los bárbaros». En otras palabras, la práctica universal de establecer en la mente un espacio familiar que es «nuestro» y un espacio no familiar que es el «suyo» es una manera de hacer distinciones geográficas que _pueden ser_ totalmente arbitrarias. Utilizo la palabra «arbitrario» porque la geografía imaginaria que distingue entre «nuestro territorio y el territorio de los bárbaros» no requiere que los bárbaros reconozcan esta distinción. A «nosotros» nos basta con establecer esas fronteras en nuestras mentes; así pues, «ellos» pasan a ser «ellos» y tanto su territorio como su mentalidad son calificados como diferentes de los «nuestros». Hasta cierto punto, las sociedades modernas y primitivas parecen obtener negativamente el sentido de su identidad de ese modo. Probablemente, un ateniense del siglo V se sentía no bárbaro en el mismo grado en que se sentía ateniense. A las fronteras geográficas le siguen las sociales, étnicas y culturales de manera previsible. Pero lo que ocurre con frecuencia es que nos sentimos no extranjeros porque tenemos una idea poco rigurosa de lo que hay en el exterior, «más allá» de nuestro propio territorio. Todo tipo de suposiciones, asociaciones y ficciones parecen confluir en el espacio no familiar que está fuera del nuestro.
El filósofo francés Gaston Bachelard realizó un análisis sobre lo que él llamó la poética del espacio. El interior de una casa, decía, adquiere un sentido real o imaginario de intimidad, de secreto o de seguridad a causa de las experiencias que parecen apropiadas para ese interior. El espacio objetivo de una casa (sus esquinas, sus pasillos, su sótano, sus habitaciones) es mucho menos importante que la cualidad con la que está dotado poéticamente y que, en general, es una cualidad con un valor imaginario o visual que podemos nombrar y sentir: así, una casa podrá estar embrujada, podrá sentirse como un hogar o como una prisión, o podrá ser mágica. El espacio adquiere un sentido emocional e incluso racional por una especie de proceso poético a través del cual las extensiones lejanas, vagas y anónimas se llenan de significaciones para nosotros, aquí. El mismo proceso sucede cuando nos ocupamos del tiempo. La mayor parte de lo que asociamos o incluso de lo que sabemos acerca de «hace mucho tiempo», «al principio» o «al final de los tiempos» es poético, creado. Para un historiador del Egipto del Imperio Medio «hace mucho tiempo» tendrá un significado muy claro, pero incluso ese significado no disipará totalmente las cualidades imaginarias y casi ficticias que se sienten cuando se trata de un tiempo muy diferente y distante del nuestro propio. No hay duda de que la geografía y la historia imaginarias ayudan a que la mente intensifique el sentimiento íntimo que tiene de sí misma, dramatizando la distancia y la diferencia entre lo que está cerca de ella y lo que está lejos. Todo esto es semejante a la impresión que a veces tenemos de que nos habríamos sentido más «en casa» en el siglo XVI o en Tahití.
Pero no sirve de nada pretender que todos nuestros conocimientos acerca del tiempo y del espacio o, mejor dicho, sobre la historia y la geografía, son imaginarios. Existe una historia y una geografía positivas que en Europa y en Estados Unidos han conseguido logros importantes. En estos momentos, los eruditos saben más acerca del mundo, de su pasado y de su presente de lo que sabían antes, en la época de Gibbon, por ejemplo. Pero esto no significa que conozcan todo lo que hay que conocer ni, lo que es más importante, que lo que conocen haya disipado efectivamente el conocimiento geográfico e histórico imaginario del que he estado hablando. No necesitamos decidir ahora si la historia y la geografía están impregnadas de este tipo de conocimiento imaginario o si, de alguna manera, este no influye sobre ellas. De momento, digamos simplemente que está ahí como algo _más_ que se añade a lo que aparece como un conocimiento meramente positivo.
En Europa, casi desde los primeros momentos, Oriente fue una idea que rebasaba los límites del conocimiento empírico que se tenía sobre él. Por lo menos hasta principios del siglo XVIII, como R. W. Southern ha demostrado de manera tan elegante, la comprensión que Europa tenía de una de las formas de la cultura oriental, la islámica, se basaba en una ignorancia compleja, ya que la noción de Oriente parecía siempre haber atraído asociaciones de ideas que no estaban determinadas por una ignorancia total ni por una información completa. Consideremos en primer lugar la demarcación entre Oriente y Occidente que ya parece clara en la época de la _Ilíada_. Dos de las cualidades más influyentes que se han asociado a Oriente aparecen ya en _Los persas_ de Esquilo, la obra de teatro ateniense más antigua que se conoce, y en _Las bacantes_ de Eurípides, la última existente. Esquilo describe el sentimiento de desastre que invade a los persas cuando conocen que sus ejércitos guiados por el rey Jerjes han sido derrotados por los griegos. El coro canta la siguiente oda:
_Ahora está gimiendo toda la tierra de Asia_
_al haberse quedado vacía_.
_Jerjes se lo llevó —¡ay, ay!—_ ,
_Jerjes hizo que perecieran —¡ay, ay!—_ ,
_Jerjes lo organizó todo de modo insensato_
_con sus barcos_.
¿ _Por qué Darío, jefe de arqueros_
_que nunca hizo daño_ ,
_no estuvo entonces también al mando de los ciudadanos_ ,
_el amado caudillo de Susa_?
Lo que importa aquí es que Asia habla a través de la imaginación de Europa y gracias a ella; una Europa que, según se la describe, ha vencido a ese «otro» mundo hostil de más allá de los mares que es Asia. Se le atribuyen a Asia sentimientos de vacío, de pérdida y de desastre; son el precio que ha de pagar por haber desafiado a Europa. También se la representa lamentándose de que en un glorioso pasado tuvo mejor suerte y salió victoriosa de sus contiendas contra Europa.
En _Las bacantes_ , quizá el drama más asiático de todos los dramas atenienses, a Dionisos se le relaciona de manera explícita con sus orígenes asiáticos y con los excesos extrañamente amenazadores de los misterios orientales. Penteo, rey de Tebas, es asesinado por su madre, Ágave, y por las otras bacantes. Por haber desafiado a Dionisos al no reconocer su poder ni su divinidad, Penteo es horriblemente castigado y la obra termina con el reconocimiento general del terrible poder de ese dios excéntrico. Los comentaristas modernos de _Las bacantes_ han observado los extraordinarios efectos intelectuales y estéticos que tiene la obra; no han pasado por alto el detalle histórico de que Eurípides «seguramente estuvo influido por el nuevo aspecto que debieron adoptar los cultos dionisíacos a la luz de las religiones extranjeras de Bendis, Cibeles, Sabazios, Adonis e Isis, que fueron introducidas desde Asia Menor y el Mediterráneo oriental y se extendieron por El Pireo y Atenas durante los años de frustración e irracionalidad de la guerra del Peloponeso».
Los dos aspectos de Oriente que lo oponen a Occidente en este par de obras seguirán siendo los motivos esenciales de la geografía imaginaria europea. Una línea de separación se dibuja entre los dos continentes; Europa es poderosa y capaz de expresarse, Asia está derrotada y distante. Esquilo _representa_ a Asia, la hace hablar en boca de la anciana reina de Persia, la madre de Jerjes. Europa articula Oriente; esta articulación es la prerrogativa, no ya de un titiritero, sino de un auténtico creador cuyo poder de dar vida representa, fomenta y constituye un espacio que, de otro modo, sería silencioso y peligroso, que estaría más allá de las fronteras familiares. Hay una analogía entre la _orchestra_ de Esquilo que contiene al mundo asiático tal y como lo concibe el dramaturgo y la instruida envoltura de la erudición orientalista que también se mantendrá firme en la vasta y amorfa extensión asiática para someterla a un examen a veces favorable, pero siempre dominante. En segundo lugar, está el motivo de un Oriente que se insinúa peligroso. La racionalidad se ve minada por los excesos orientales cuyo misterioso atractivo se opone a los valores que parecen ser normales. La diferencia que separa al Este del Oeste se simboliza a través de la severidad con la que, al principio, Penteo rechaza a las histéricas bacantes; pero cuando más tarde él mismo se hace bacante, es asesinado por no haber sabido valorar las primeras amenazas de Dionisos, más que por haber sucumbido ante él. La lección que Eurípides intenta darnos se hace más dramática por la presencia en la obra de Cadmo y Tiresias, dos ancianos prudentes que se dan cuenta de que «la soberanía» sola no dirige a los hombres; estos personajes explican que el juicio existe para aprehender correctamente la fuerza de los poderes extraños y para acomodarse a ellos con habilidad. A partir de aquí los misterios orientales se tomarán en serio, sobre todo porque suponen un desafío para la mente racional occidental, que deberá ejercer de otra manera su ambición y su poder permanentes.
Pero una gran división como la existente entre Occidente y Oriente desemboca en otras más pequeñas, sobre todo cuando una civilización tiende a llevar a cabo empresas y actividades en el exterior, como por ejemplo viajes, conquistas y nuevas experiencias. En la Grecia y la Roma clásicas, los geógrafos, los historiadores, los personajes públicos como César, los oradores y los poetas contribuyeron a los fondos de la ciencia taxonómica tradicional, que hacía distinciones entre las diferentes razas, regiones, naciones y mentes; en gran medida este proceso se llevó a cabo para su utilización interna y sirvió para demostrar que los romanos y los griegos eran superiores a otros pueblos. Pero el interés por Oriente tenía su propia tradición de clasificación y jerarquización. Desde por lo menos el siglo II a.C., ningún viajero, ningún potentado occidental ambicioso que dirigiera su mirada hacia el Este podía ignorar que Heródoto —historiador, viajero y cronista de curiosidad inagotable— y Alejandro —rey guerrero, conquistador y científico— habían estado allí. Oriente se subdividía, por tanto, en regiones ya conocidas, visitadas, y conquistadas por Heródoto, Alejandro y sus epígonos, y en regiones que todavía no habían sido conocidas, visitadas, ni conquistadas. El cristianismo completó el establecimiento de las principales esferas existentes dentro de Oriente: había un Oriente Próximo y un Extremo Oriente, un Oriente familiar, que René Grousset llama _«l'empire du levant»_ , y un Oriente extraño. En la geografía de la mente, por tanto, se producía una oscilación con respecto a Oriente, a veces era un mundo antiguo al que se volvía, como al Edén o al Paraíso, para establecer allí una nueva versión de lo antiguo, y otras era un lugar completamente nuevo al que se llegaba, como Colón a América, para establecer un Nuevo Mundo (aunque irónicamente, el propio Colón creyó que había descubierto una parte nueva del mundo antiguo). Ciertamente ninguno de estos orientes era en sentido estricto una cosa o la otra; lo que es interesante es la oscilación entre los dos, su poder de sugestión y su capacidad para entretener y confundir la mente.
Consideremos ahora cómo Oriente y en particular Oriente Próximo, desde la antigüedad se conocía en Occidente como su gran opositor complementario. Se conocía la Biblia y la ascensión del cristianismo; se sabía de algunos viajeros que habían trazado las rutas del comercio y construido un sistema regulado de intercambios comerciales, como Marco Polo y después de él Lodovico di Varthema y Pietro della Valle; se conocía a ciertos fabulistas, como Mandeville; se conocían los terribles movimientos orientales de conquista, principalmente el islam, y las peregrinaciones militantes, sobre todo las Cruzadas. Todo junto dio lugar a un archivo con una estructura interna que se construyó a partir de la literatura relacionada con estas experiencias y de la que proviene un número restringido de géneros típicos: el viaje, la historia, la fábula, el estereotipo y la confrontación polémica. Estas lentes a través de las cuales se observa Oriente modelan el lenguaje, la percepción y la forma del contacto entre el Este y el Oeste. Lo que da una cierta unidad a estos contactos tan numerosos es la oscilación de la que he hablado antes. Lo que es evidentemente extraño y lejano adquiere, por una u otra razón, la categoría de algo más familiar. Se tiende a dejar de juzgar las cosas porque sean completamente extrañas o completamente conocidas; surge una nueva categoría intermedia, una categoría que permite ver realidades nuevas, realidades que se ven por primera vez como versiones de una realidad previamente conocida. En esencia, una categoría de este tipo no es una manera de recibir nueva información, sino un método para controlar lo que parece ser una amenaza para la perspectiva tradicional del mundo. Si la mente debe tratar de pronto con lo que considera una forma de vida radicalmente nueva (como el islam apareció en Europa en la alta Edad Media), la respuesta, por regla general, es conservadora y defensiva. Se considera que el islam es una versión nueva y fraudulenta de alguna experiencia previa, en este caso, del cristianismo. La amenaza es sofocada, los valores familiares se imponen y al final la mente reduce la presión que se ejerce sobre ella adaptando las cosas a su medida, considerándolas «originales» o «repetitivas». El islam, por tanto, es «manejado»: se controla su novedad y su sugestividad de manera que sea posible hacer discriminaciones relativamente matizadas que habrían sido imposibles si la cruda novedad del islam no hubiera sido tratada. La idea de Oriente en toda su extensión, por tanto, oscila en la mente occidental entre el menosprecio hacia lo que es familiar y el estremecimiento de placer —o temor— hacia la novedad.
Pero desde el punto de vista del islam, aunque Europa no le respetara, era normal que le temiera. Tras la muerte de Mahoma en el año 632, la hegemonía militar y después la cultural y religiosa del islam creció enormemente. Primero Persia, Siria y Egipto, luego Turquía, después el norte de África; todas estas regiones fueron cayendo ante los ejércitos musulmanes; en los siglos VIII y IX se conquistó España, Sicilia y partes de Francia; en los siglos XIII y XIV el islam llegó al poder en la India, Indonesia y China. Y ante este asalto extraordinario, Europa solo pudo responder con miedo e incluso con una especie de terror. Los autores cristianos que fueron testigos de las conquistas islámicas tenían escaso interés en aprender la elevada cultura y la magnificencia de los musulmanes, que eran, como dijo Gibbon, «contemporáneos al período más oscuro e indolente de los anales europeos» (aunque con algo de satisfacción añadió: «Desde que ha aumentado la producción de ciencia en Occidente, parece que el estudio en Oriente ha languidecido y declinado»). La opinión cristiana característica sobre los ejércitos orientales era que tenían «todo el aspecto de un enjambre de abejas, pero que con mano dura [...] devastaban todo»; así los describía Erchembert, un clérigo de Monte Cassino del siglo XI.
No sin razón el islam pasó a ser un símbolo de terror, de devastación, de lo demoníaco y de hordas de odiados bárbaros. Para Europa el islam fue un trauma que perduró hasta el final del siglo XVII, el «peligro otomano» latente en toda Europa representaba para toda la civilización cristiana una constante amenaza y, con el tiempo, la civilización europea incorporó al tejido de su vida esa amenaza y su tradición, sus grandes acontecimientos, sus figuras, virtudes y vicios. En la Inglaterra renacentista, como cuenta Samuel Chew en su clásico estudio _The Crescent and the Rose_ , «un hombre de educación e inteligencia medias» podía observar y tenía al alcance de la mano en la escena londinense un número relativamente grande de acontecimientos detallados de la historia del islam otomano y de sus incursiones en la Europa cristiana. Quiero decir con esto que las ideas sobre el islam que circulaban eran necesariamente una versión devaluada del sólido peligro que simbolizaba para Europa. Como los sarracenos de Walter Scott, la representación que hacía Europa de los musulmanes, otomanos o árabes, era siempre una manera de controlar a un Oriente temible, y lo mismo se puede decir hasta cierto punto de los métodos de los orientalistas eruditos contemporáneos, cuyo tema de estudio no es el propio Oriente, sino Oriente convertido en algo conocido y, por tanto, menos temible para los lectores occidentales.
No hay nada especialmente controvertido o reprensible en esta domesticación de lo exótico; en realidad se produce entre todas las culturas y entre todos los hombres. Pero lo que a mí me interesa es insistir en el hecho de que el orientalista, igual que cualquier persona que reflexionara en el Occidente europeo sobre Oriente o que tuviera alguna experiencia de él, realizó este tipo de operación mental. No obstante, lo que es todavía más importante es el vocabulario y las imágenes limitadas que, como consecuencia de esto, se impusieron a sí mismos. La manera en que el islam fue recibido por Occidente es un ejemplo perfecto de ello y ha sido admirablemente estudiado por Norman Daniel. Una de las fuerzas que actuaban en los pensadores cristianos cuando intentaban comprender el islam era la analogía: como Cristo era la base de la fe cristiana, se suponía —bastante incorrectamente— que Mahoma era para el islam lo que Cristo para el cristianismo. De ahí, el polémico nombre «mahometismo» dado al islam, y el epíteto de «impostor» que se aplicaba automáticamente a Mahoma. A partir de este y otros muchos malentendidos, «se formó un círculo cerrado que nunca fue roto por una exteriorización de la imaginación [...]. El concepto cristiano del islam era integral y autosuficiente». El islam se convirtió en una imagen —la expresión es de Daniel, pero me parece que tiene implicaciones importantes para el orientalismo en general— cuya función no era tanto representar al islam en sí mismo, como representarlo para el cristiano de la Edad Media.
La invariable tendencia a despreciar lo que el Corán significaba o lo que los musulmanes pensaban o decían en determinadas circunstancias implica necesariamente que la doctrina coránica y las otras doctrinas islámicas se presentaban bajo una forma convincente para los cristianos; y que las formas más extravagantes podrían llegar a ser aceptadas si contribuían a aumentar la distancia que separaba a los escritores y a su público de las fronteras del islam. Con muchas reticencias, se aceptó que lo que los musulmanes decían que creían era lo que realmente creían. Había una imagen cristiana en la que los detalles (incluso bajo la presión de los hechos) se reducían a su mínima expresión, mientras que las líneas generales nunca se abandonaban. Había diferencias de matices, pero solo dentro de un esquema común. Todas las correcciones realizadas para aumentar la precisión solo servían para defender lo que acababa de constatarse como vulnerable y para sostener una estructura debilitada. La opinión cristiana era un monumento que no se podía demoler, ni siquiera reconstruir.
Esta imagen rigurosa que el cristianismo tenía del islam se reforzó de muchas maneras; entre ellas se encuentran —durante la Edad Media y el principio del Renacimiento— las diferentes formas de poesía, de controversias eruditas y de supersticiones populares. En esa época Oriente Próximo no estaba en absoluto integrado en la imagen corriente que del mundo se tenía en la cristiandad latina: la _Chanson de Roland_ , por ejemplo, muestra a los sarracenos adorando a Mahoma y a Apolo. Hacia la mitad del siglo XV, como R. W. Southern ha demostrado brillantemente, los pensadores europeos serios veían cada vez con mayor claridad «que había que hacer algo a propósito del islam», el cual había invertido la situación al haber conseguido sus tropas entrar en Europa oriental. Southern cuenta un episodio espectacular que se produjo entre 1450 y 1460, cuando cuatro hombres instruidos, Juan de Segovia, Nicolás de Cusa, Jean Germain y Eneas Silvio (Pío II), intentaron ocuparse del problema del islam a través de una _contraferentia_ o «conferencia». La idea fue de Juan de Segovia, y consistía en celebrar una conferencia conjuntamente con el islam en la que los cristianos intentarían que los musulmanes se convirtieran en masa. Él consideraba que esta conferencia era un instrumento con una función política y estrictamente religiosa, y, con palabras que estremecerían la sensibilidad moderna, exclamó que «incluso aunque tuviera que durar diez años, sería menos costosa y menos perjudicial que una guerra». No hubo ningún acuerdo entre los cuatro hombres, pero el episodio es crucial porque fue un intento bastante sutil —que formaba parte de una tentativa general europea, desde Beda el Venerable a Lutero— de colocar a un Oriente representativo frente a Europa, de poner _en el escenario_ a Europa y a Oriente juntos, y porque fue un intento coherente con la idea de los cristianos de hacer comprender a los musulmanes que el islam no era más que una versión malinterpretada del cristianismo. Southern concluye de la siguiente manera:
Para nosotros, es evidente que ninguno de estos sistemas cristianos europeos de pensamiento era capaz de dar una explicación totalmente satisfactoria del fenómeno que pretendían explicar, el islam, y aún eran menos capaces de influir en el desarrollo de los acontecimientos de una manera decisiva. En la práctica, el curso de los acontecimientos nunca se desarrolló ni tan bien ni tan mal como los observadores inteligentes habían predicho, y quizá valga la pena señalar que nunca evolucionó de manera más favorable porque los mejores jueces esperaran en secreto un final feliz. ¿Hubo algún progreso [en el conocimiento que el cristiano tenía del islam]? Debo expresar mi convicción de que lo hubo. Incluso si la solución del problema continuaba estando oculta, la manera de exponerlo se volvió más compleja y racional y tuvo mayor relación con la experiencia [...]. Los eruditos que trabajaron en el problema del islam en la Edad Media fracasaron en su intento de encontrar la solución que buscaban y deseaban, pero desarrollaron unos hábitos de pensamiento y un poder de comprensión que, si se hubiera tratado de otras personas y de otros campos de estudio, habrían merecido conseguir buenos resultados.
La mejor parte del análisis de Southern en estas líneas y en las siguientes es su breve historia de los puntos de vista occidentales sobre el islam y su demostración de que finalmente es la ignorancia occidental la que se vuelve más refinada y compleja y no el conocimiento occidental positivo el que adquiere más importancia y precisión. En efecto, las ficciones tienen su propia lógica y su propia dialéctica de crecimiento y declive. En la Edad Media, al carácter de Mahoma se le asignaban gran cantidad de atributos que se correspondían con el «carácter de Hermanos del Libre Espíritu (del siglo XII) que, efectivamente, habían surgido en Europa reclamando que se creyera en ellos y buscando adeptos». Del mismo modo, como Mahoma era considerado un propagador de una revelación falsa, se convirtió también en un compendio de lascivia, libertinaje, sodomía y una completa gama de perfidias que «lógicamente» se derivaban todas de sus fraudes doctrinales. Así, Oriente adquirió, por decirlo de algún modo, representantes y representaciones cada vez más concretas, y coherentes con alguna exigencia occidental. Es como si, después de haber decidido que Oriente era un lugar apropiado para encarnar lo infinito en forma finita, Europa no pudiera dejar de poner en práctica esta teoría; Oriente y el oriental, árabe, musulmán, indio, chino, etc., se convirtieron en seudoencarnaciones repetitivas de algún gran original (Cristo, Europa, Occidente) al que se suponía que estaban imitando. La fuente de estas ideas occidentales más bien narcisistas cambió con el tiempo, pero no su carácter. Así, encontraremos que en los siglos XII y XIII se creía que Arabia era «un asilo natural para los herejes proscritos situado al borde del mundo cristiano», y que Mahoma era un apóstata astuto; mientras que en el siglo XX un instruido orientalista, un especialista erudito señalará que el islam realmente no es más que una herejía arriana de segundo orden.
Nuestra descripción inicial del orientalismo como disciplina erudita adopta ahora un carácter nuevo y concreto. Normalmente un campo de estudio es un espacio cerrado. La idea de la representación es una idea teatral: Oriente constituye el escenario en el que todo el Este está encerrado; sobre este escenario aparecerán figuras cuyo papel consiste en representar el todo del que emanan. Parece ser entonces que Oriente es más un campo cerrado, un escenario teatral próximo a Europa que una extensión ilimitada más allá del mundo familiar, del mundo europeo. Un orientalista no es más que un especialista particular de un saber del que toda Europa es responsable, igual que un determinado público es histórica y culturalmente responsable de los dramas que el dramaturgo ha compuesto de manera técnica (y a los que el público responde). En las profundidades de este escenario oriental se alza un repertorio cultural prodigioso cuyas obras individuales evocan un mundo de una riqueza fabulosa: las esfinges, Cleopatra, el Edén, Troya, Sodoma y Gomorra, Astarté, Isis, Osiris, Saba, Babilonia, los genios, los magos, Nínive, el Preste Juan, Mahoma y mucho más; se realizan puestas en escena, en algunos casos, de nombres mitad imaginados, mitad conocidos, de monstruos, demonios, héroes, terrores, placeres y deseos. La imaginación europea se alimentó copiosamente de este repertorio; desde la Edad Media hasta el siglo XVIII grandes escritores como Ariosto, Milton, Marlowe, Tasso, Shakespeare, Cervantes y los autores de la _Chanson de Roland_ y del _Cantar de Mio Cid_ se inspiraron en la riqueza de Oriente para escribir sus obras de tal forma que contribuyeron a perfilar con mayor nitidez los contornos de las imágenes, las ideas y las figuras que lo poblaban. Además, una gran parte de lo que se consideraba erudición orientalista en Europa utilizó estos mitos ideológicos incluso cuando el conocimiento parecía progresar auténticamente.
La _Bibliothèque orientale_ , de Barthélemy d'Herbelot, publicada en 1697 después de su muerte con un prefacio de Antoine Galland, es un ejemplo célebre que nos permite observar cómo confluían en el teatro orientalista la forma dramática y las imágenes eruditas. La introducción de la reciente _Cambridge History of Islam_ considera que la _Bibliothèque_ , el discurso preliminar de George Sale en su traducción del Corán (1734) y la _History of Saracens_ (1708-1718), de Simon Ockley, fueron «muy importantes» para extender «la nueva comprensión del islam» y para transmitirla a «un público menos académico». Esto es una descripción imperfecta de la obra de D'Herbelot, ya que esta no se limitaba exclusivamente al islam, como ocurre con las de Sale y Ockley. Con la excepción de la _Historia orientalis_ , de Johann H. Hottinger, que apareció en 1651, la _Bibliothèque_ siguió siendo la única obra de referencia en Europa hasta principios del siglo XVI. Fue una obra que realmente hizo época debido al enorme campo que abarcaba; Galland, que fue el primer traductor europeo de _Las mil y una noches_ y un arabista importante, comparó la obra de D'Herbelot con todas las anteriores a ella haciendo hincapié en la prodigiosa ambición de esta empresa. D'Herbelot, dijo Galland, leyó muchos libros en árabe, persa y turco que le permitieron descubrir materias que hasta entonces habían permanecido ocultas a los europeos. Después de escribir un diccionario de estas tres lenguas orientales, D'Herbelot estudió la historia, la teología, la geografía, la ciencia y el arte orientales tanto en sus aspectos fabulosos como reales. Más tarde decidió componer dos obras: la primera de ellas, una _bibliothèque_ o «biblioteca», un diccionario dispuesto alfabéticamente, y la segunda, un _florilège_ o antología. Solo completó la primera.
Refiriéndose a la _Bibliothèque_ , Galland afirmó que el adjetivo « _orientale_ » pretendía incluir principalmente a los países del Mediterráneo oriental, sin embargo —Galland dice con admiración— el período de tiempo abarcado no comenzaba con la creación de Adán y terminaba en los _«temps où nous sommes»_ : D'Herbelot se remontó aún más atrás, hasta un período _«plus haut»_ si consideramos las historias fabulosas que cuenta acerca del reino de los solimanes antes de la creación de Adán. Según avanza la descripción de Galland, nos vamos dando cuenta de que la _Bibliothèque_ , al pretender ser un compendio completo de los conocimientos existentes sobre materias como la Creación, el Diluvio, la destrucción de Babel, etc., es como «cualquier otra» historia con la diferencia de que las fuentes de D'Herbelot eran orientales. Dividió la historia en dos tipos: la historia sagrada y la historia profana (los judíos y cristianos entraban en el primer apartado y los musulmanes en el segundo), y en dos períodos: antes y después del Diluvio. Así, D'Herbelot pudo estudiar historias tan diversas como la historia de los mongoles, la de los tártaros, la de los turcos, y la de los eslavos; también incluyó todas las provincias del imperio musulmán, desde el Extremo Oriente hasta las Columnas de Hércules con sus costumbres, sus ritos, sus tradiciones, sus comentarios, sus dinastías, sus palacios, sus ríos y su flora. Esta obra, aunque también prestaba cierta atención a _«la doctrine perverse de Mahomet, qui a causé si grands dommages au Christianisme»_ , se detenía en el tema más que cualquier otro trabajo anterior. Galland concluyó su _«Discours»_ asegurando al lector que la _Bibliothèque_ de D'Herbelot era _«utile et agréable»_. Otros orientalistas como Postel, Escalígero, Golio, Pockoke y Erpenio escribieron estudios orientalistas que resultaron ser demasiado gramaticales, lexicográficos, geográficos, etc. Solo D'Herbelot pudo escribir una obra capaz de convencer a los lectores europeos de que el estudio de la cultura oriental no era solamente algo ingrato e infructuoso; solo D'Herbelot, según Galland, intentó formar en la mente de sus lectores una idea suficientemente amplia de lo que significaba conocer y estudiar Oriente, una idea que pudiera a la vez llenar la mente y satisfacer las grandes esperanzas previamente concebidas.
Con esfuerzos como los de D'Herbelot, Europa descubrió que era capaz de abarcar Oriente y de orientalizarlo. Se puede encontrar un cierto aire de superioridad en algunas partes de lo que Galland decía sobre su _materia orientalia_ y la de D'Herbelot; del mismo modo que, en la obra de los geógrafos del siglo XVII, como Raphael du Mans, los europeos podían percibir que Oriente se estaba distanciando de la ciencia occidental y estaba siendo superado por ella. Pero lo que parece evidente no es solo la ventaja de la perspectiva occidental, sino también la existencia de una técnica triunfante que permite abarcar la inmensa fecundidad de Oriente y hacerla accesible sistemática e incluso alfabéticamente al público occidental. Cuando Galland dijo que D'Herbelot respondió a lo que se esperaba de él, creo que se refería a que la _Bibliothèque_ no intentó modificar las ideas recibidas sobre Oriente. La labor de cualquier orientalista es _confirmar_ Oriente ante los ojos de sus lectores, jamás pretende ni intenta perturbar las sólidas convicciones que ya tienen. Todo lo que la _Bibliothèque orientale_ hizo fue representar Oriente de una manera más completa y clara; lo que podía haber sido una colección de hechos desconectados entre sí y tomados al azar, hechos referidos a la historia del Mediterráneo oriental, a la imaginería bíblica, a la cultura islámica, a unos nombres de lugares, etc., se transformó en un panorama racional de Oriente de la A a la Z. En la entrada «Mahoma», D'Herbelot primero dio todos los nombres que se le atribuían al profeta y luego confirmó sus valores ideológicos y doctrinales de la siguiente manera:
_C'est le fameux imposteur Mahomet, Auteur et Fondateur d'une hérésie, qui a pris le nom de religion, que nous apellons Mahometane_. Voyez _le titre d'Eslam_.
_Le Interprètes de l'Alcoran et autres docteurs de la Loy Musulmane ou Mahometane ont appliqué à ce faux prophète tous les éloges, que les Ariens, Paulitiens ou Paulianistes & autres Hérétiques ont attribué à Jésus-Christ, en lui ôtant sa Divinité_ ...].[*
«Religión mahometana» es la designación europea apropiada (e insultante); «islam», que precisamente es el nombre musulmán correcto, es relegado a otra entrada. La «herejía [...] que nosotros llamamos mahometana» está «tomada» como la imitación de una imitación cristiana de la verdadera religión. Así, en el largo relato histórico de la vida de Mahoma, D'Herbelot puede dedicarse a hacer una narración más o menos directa. Pero lo que cuenta en la _Bibliothèque_ es el puesto que se le asigna a Mahoma. El peligro que supone una herejía que circula libremente desaparece cuando se la transforma en la materia ideológicamente explícita de una entrada alfabética. Mahoma ya no se pasea por el mundo occidental como un libertino inmoral y amenazante, permanece tranquilamente situado en su parte (que se admite que es importante) del escenario orientalista. Se le dan una genealogía, una explicación e incluso una evolución y todo eso se clasifica en simples afirmaciones que le impiden seguir vagando por otros lugares.
Unas «imágenes» de Oriente como estas son imágenes porque representan o hacen las veces de una gran entidad que, de otra manera, sería demasiado difusa, y porque permiten abarcarla o verla; son también _caracteres_ , como el del fanfarrón, el avaro o el glotón que produjeron Teofrasto, La Bruyère o Selden. Quizá no sea correcto decir que unos caracteres como los de _miles gloriosus_ o Mahoma el impostor se pueden ver, ya que se supone que el confinamiento discursivo de un carácter permite aprehender un tipo genérico sin dificultad ni ambigüedad. El carácter de Mahoma que ofrece D'Herbelot es, con todo, una _imagen_ porque el falso profeta forma parte de una representación teatral general llamada _orientale_ cuya totalidad está contenida en la _Bibliothèque_.
La calidad didáctica de la representación orientalista no se puede separar del resto del espectáculo. En una obra erudita como la _Bibliothèque orientale_ , que fue el resultado de estudios e investigaciones sistemáticos, el autor impone un orden estricto al material con el que ha trabajado; además quiere que el lector comprenda bien que lo que la página impresa transmite es un juicio ordenado y sistematizado del material. Lo que la _Bibliothèque_ ofrece es una idea del poder y la efectividad del orientalismo que le recuerda al lector que, en lo sucesivo, para llegar a Oriente, deberá atravesar las redes y los códigos que ofrece el orientalismo. Oriente no solo es adaptado a las exigencias morales del cristianismo occidental, sino que también es limitado por una serie de actitudes y juicios que la mente occidental remite a otros trabajos orientalistas y no a las fuentes orientales para su verificación y corrección. El escenario orientalista, como lo he llamado, se convierte en un sistema de rigor moral y epistemológico. De ese modo, como disciplina que representa el conocimiento institucionalizado que Occidente tiene de Oriente, el orientalismo llega a ejercer una influencia que se extiende en tres direcciones: hacia Oriente, hacia el orientalismo y hacia el «consumidor» occidental de orientalismo. Sería incorrecto, en mi opinión, subestimar la fuerza de esta triple acción. En efecto, Oriente («allí», hacia el Este) es corregido e incluso penalizado por encontrarse fuera de las fronteras de la sociedad europea, de «nuestro» mundo; Oriente así se _orientaliza_ , proceso que no solo afecta a Oriente en tanto que provincia del orientalismo, sino que obliga al lector occidental no iniciado a aceptar las codificaciones orientalistas (por ejemplo, la clasificación alfabética de la _Bibliothèque_ de D'Herbelot) como si fueran el _verdadero_ Oriente. En resumen, la realidad está en función del juicio erudito y no del material en sí mismo, que con el tiempo parece deberle al orientalismo incluso la existencia.
Todo este proceso didáctico tiene una explicación fácil y comprensible. Hay que recordar que todas las culturas imponen ciertas correcciones sobre la cruda realidad, transformando una suma de objetos mal delimitados en unidades de conocimiento. El problema no reside en que se realice esta conversión, es perfectamente natural que la mente humana se resista al asalto que le produce lo extraño; por esta razón, ciertas culturas han tendido a imponer transformaciones completas sobre otras culturas, recibiéndolas no como son, sino como deberían ser para beneficiar al receptor. Para el occidental, sin embargo, lo oriental siempre _se parecía_ a algún aspecto de Occidente; para los románticos alemanes, por ejemplo, la religión india era esencialmente una versión oriental del panteísmo germano-cristiano. Pero la labor del orientalista consiste siempre en convertir Oriente en algo diferente de lo que es, en otra cosa: lo hace en su beneficio, en el de su cultura y, en algunos casos, por lo que cree que es el bien del oriental. Este proceso de conversión es un proceso sistemático: se enseña, tiene sus propias sociedades, sus publicaciones, sus tradiciones, su vocabulario y su retórica, todo lo cual se relaciona de modo fundamental con las normas culturales y políticas que prevalecen en Occidente. Y, como demostraré, tiende a volverse más totalizador en sus tentativas, de tal modo que cuando uno pasa revista al orientalismo de los siglos XIX y XX, la impresión que predomina es la de una fría esquematización.
Esta esquematización comenzó muy pronto y los ejemplos que he dado sobre la representación que Occidente hacía de Oriente en la Grecia clásica lo demuestran. La construcción de las representaciones más recientes está fuertemente articulada sobre las antiguas, su esquematización ha estado extraordinariamente cuidada y su colocación en la geografía imaginaria de Occidente ha tenido una eficacia espectacular. Todo esto se puede ilustrar muy bien a través de un análisis del _Inferno_ de Dante. Los logros de Dante en _La Divina Comedia_ consistieron en combinar, sin una relación aparente, la pintura realista de la vida mundana y un sistema universal y eterno de valores cristianos. Lo que Dante, el peregrino, ve cuando atraviesa el Infierno, el Purgatorio y el Paraíso es una visión única del Juicio. Paolo y Francesca, por ejemplo, son considerados prisioneros eternos del Infierno por sus pecados, pero los vemos representando, de hecho viviendo, los personajes y las acciones que les han llevado allí, donde permanecerán eternamente. Así, cada una de las figuras de la visión de Dante no solo se representa a sí misma, sino también es una re-presentación típica de su personaje y del destino que se le asigna.
_«Maometto»_ —Mahoma— aparece en el canto 28 del _Inferno_. Está situado en el octavo de los nueve círculos del Infierno, en la novena de las diez Fosas de Malebolge, un círculo de fosas tenebrosas que rodean la fortaleza de Satán en el Infierno. Así, Dante, antes de llegar hasta Mahoma, atraviesa círculos en los que hay gente cuyos pecados son menores: los lujuriosos, los avaros, los gulosos, los heréticos, los coléricos, los suicidas y los blasfemos. Después de Mahoma solo están los farsantes y los traidores (entre los que están Judas, Bruto y Casio) antes de llegar al fondo del Infierno que es donde se encuentra Satán. Mahoma, pues, pertenece, dentro de la rígida jerarquía de malvados, a la categoría de lo que Dante llama _seminator di scandalo e di scisma_. El castigo de Mahoma, que es también su destino eterno, es particularmente repugnante: ser eternamente partido en dos, desde la barbilla hasta el ano, como si fuera, dice Dante, un barril cuyas duelas se abriesen. Los versos de Dante no escatiman aquí ninguno de los detalles escatológicos que un castigo tan violento supone. Las entrañas y los excrementos de Mahoma se describen con una precisión absoluta. Mahoma explica a Dante su castigo, el mismo que se le ha asignado a Ali, que le precede en la línea de pecadores a los que el diablo ayudante está dividiendo en dos; le pide a Dante que advierta a un tal fra Dolcino, cura renegado cuya secta predicaba la comunidad de mujeres y de bienes y que fue acusado de tener una querida, del destino que le espera. El lector habrá podido darse cuenta de que Dante vio un paralelismo entre la sensualidad indignante de fra Dolcino y la de Mahoma y entre las pretensiones de lograr una supremacía teológica de ambos.
Pero esto no es todo lo que Dante tiene que decir sobre el islam. Antes de esto, en el _Inferno_ aparece un pequeño grupo de musulmanes. Avicena, Averroes y Saladino están entre esos virtuosos paganos que, junto a Héctor, Eneas, Abraham, Sócrates, Platón y Aristóteles, están encerrados en el primer círculo para sufrir un castigo mínimo (e incluso honorable) por no haber podido beneficiarse de la revelación cristiana. Dante, naturalmente, admira sus grandes virtudes y sus talentos, pero como no fueron cristianos debe condenarlos, aunque sea levemente, al Infierno. Es verdad que la eternidad puede nivelar las diferencias, pero en cualquier caso, el anacronismo y la anomalía tan particular que supone poner a las grandes figuras precristianas en la misma categoría de condenación «pagana» que a los musulmanes poscristianos no le crea ningún problema a Dante. Aunque el Corán especifica que Jesús es un profeta, Dante prefiere considerar a Saladino y a los grandes filósofos musulmanes como fundamentalmente ignorantes del cristianismo. El hecho de que también ellos puedan ocupar el nivel distinguido junto a los héroes y sabios de la antigüedad es un punto de vista histórico comparable al que adoptó Rafael en el fresco _La escuela de Atenas_ en el que Averroes aparece en la Academia al lado de Sócrates y Platón (y comparable también a los _Dialogues des morts_ , de Fénelon, escritos entre 1700 y 1718, donde Sócrates y Confucio discuten entre ellos).
La discriminación y los refinamientos de la comprensión poética del islam por parte de Dante son un ejemplo de esa determinación esquemática, casi cosmológica, con la que el islam y sus representantes son creados por la aprehensión geográfica, histórica y sobre todo moral de Occidente. Los datos empíricos sobre Oriente o sobre alguna de sus partes tienen poca importancia, lo que cuenta y es decisivo es lo que he llamado la visión orientalista, visión que en ningún caso está reservada solo al erudito profesional, sino que más bien pertenece a todos los que en Occidente han pensado sobre Oriente. El poder poético de Dante acentúa y hace más representativas estas perspectivas sobre Oriente. Mahoma, Saladino, Averroes y Avicena han sido fijados en una cosmología visionaria —fijados, dispuestos, encajonados y aprisionados—, después de haber tenido en cuenta solamente su «función» y los personajes que representan en el escenario sobre el que aparecen. Isaiah Berlin ha descrito el efecto de estas actitudes de la siguiente manera:
En una cosmología de este tipo [...], el mundo de los hombres (y en algunas versiones, el universo entero) es una jerarquía simple y total; de tal forma que para explicar por qué cada objeto es como es, está donde está en el momento en el que está y hace lo que hace se dice _eo ipso_ cuál es su objetivo, hasta qué punto lo cumple satisfactoriamente y cuáles son las relaciones de coordinación y subordinación entre los objetivos de las diferentes entidades teleológicas de la pirámide armoniosa que forman colectivamente. Si esta imagen de la realidad es verdadera, la explicación histórica, como cualquier otra forma de explicación, debe consistir sobre todo en asignar a los individuos, los grupos, las naciones y las especies su propio lugar en el esquema universal. Conocer el lugar «cósmico» de un objeto o de una persona es decir lo que es y lo que hace y al mismo tiempo, por qué debe ser lo que es y hacer lo que hace. Por lo tanto, es una sola y misma cosa ser y tener un valor, existir y tener una función (y cumplirla más o menos bien). El esquema y solo él da la vida o la quita y confiere un designio, es decir un valor y un sentido, a todo lo que existe. Comprender es percibir los esquemas [...]. Cuanto más inevitable podamos mostrar que es un suceso, una acción o un carácter, mejor lo entenderemos, más profunda será la intuición del investigador y más cerca estaremos de la verdad última. Esta actitud es profundamente antiempírica.
Así es la actitud orientalista en general. Comparte con la magia y la mitología el carácter de sistema cerrado que se contiene y refuerza a sí mismo y en el que los objetos son lo que son porque son lo que son de una vez y para siempre, por razones ontológicas que ningún material empírico puede expulsar o alterar. El contacto europeo con Oriente y específicamente con el islam fortaleció este sistema de representación de Oriente y, como Henry Pirenne ha sugerido, hizo del islam la esencia misma de un ser exterior contra el cual se cimentó la civilización europea a partir de la Edad Media. El declive del Imperio romano, como resultado de la invasión de los bárbaros, tuvo el efecto paradójico de incorporar modos bárbaros a la cultura romana y mediterránea: la Romania; mientras que, dice Pirenne, como consecuencia de las invasiones islámicas, que comenzaron en el siglo VII, el centro de la cultura europea se alejó del Mediterráneo que era entonces una provincia árabe, y se situó en el norte: «El germanismo comienza su papel. Hasta entonces se había prolongado la tradición romana. Ahora va a desarrollarse una civilización romano-germánica original». Europa estaba encerrada en sí misma: Oriente, cuando no era simplemente un lugar de comercio, estaba cultural, intelectual y espiritualmente _fuera_ de Europa y de la civilización europea que, en palabras de Pirenne, se convirtió en «una gran comunidad cristiana tan amplia como la _ecclesia_ [...]. Occidente estaba entonces viviendo su propia vida». En el poema de Dante, en las obras de Pedro el Venerable y de otros orientalistas cluniacenses, en los escritos de polemistas cristianos contra el islam, desde Guibert de Nogent y Beda a Roger Bacon, Guillermo de Trípoli, Burchard de Mont-Sion y Lutero, en el _Cantar de Mio Cid_ , en la _Chanson de Roland_ y en el _Otelo_ de Shakespeare (ese «engañador del mundo») Oriente y el islam siempre se representaban como intrusos que tenían un papel especial que desempeñar _en el interior_ de Europa.
La geografía imaginaria que se extiende desde los vivos retratos que se encuentran en el _Inferno_ hasta los prosaicos casilleros de la _Bibliothèque orientale_ , de D'Herbelot, legitima un vocabulario y un universo de discurso peculiar y representativo de la discusión y comprensión del islam y de Oriente. Lo que este discurso considera que es un hecho —por ejemplo, que Mahoma es un impostor— es un componente del discurso, una afirmación que el discurso obliga a hacer siempre que el nombre de Mahoma aparece. Subyaciendo en todas las diferentes unidades del discurso orientalista —con esto me refiero simplemente al vocabulario que se emplea cuando se habla o escribe de Oriente— hay un conjunto de figuras representativas o tropos. Estas figuras son para el Oriente real —o para el islam que es de lo que principalmente estoy tratando— lo que los disfraces estilizados son para los personajes de una obra; son algo parecido a, por ejemplo, la cruz que Cualquier Hombre lleva o el disfraz de abigarrados colores que viste el arlequín en la _commedia dell'arte_. En otras palabras, no necesitamos buscar una correspondencia entre el lenguaje utilizado para describir Oriente y el propio Oriente no solamente porque el lenguaje sea impreciso, sino porque ni siquiera pretende ser preciso. Lo que intenta hacer, como Dante lo intentó en el _Inferno_ , es describir Oriente como algo extraño e incorporarlo esquemáticamente a un escenario teatral cuyo público, director y actores son _para_ Europa y solo para Europa. De aquí la oscilación entre lo familiar y lo extraño. Mahoma siempre es el impostor (familiar porque pretende ser como el Jesús que nosotros conocemos) y siempre el oriental (extraño, porque aunque de alguna manera sea como Jesús, después de todo, es muy diferente).
Mejor que hacer una lista de todas las figuras del discurso que se asocian a Oriente —su extrañeza, su diferencia, su sensualidad exótica...— podemos generalizar sobre ellas viendo cómo se transmitieron a través del Renacimiento. Son declarativas y evidentes, el tiempo que emplean es el eterno intemporal, transmiten una impresión de repetición y de firmeza, son siempre simétricas y, sin embargo, radicalmente inferiores a su equivalente europeo que a veces se especifica y a veces no. Para todas estas funciones, frecuentemente es suficiente con emplear la palabra _es_. Así, Mahoma _es_ un impostor; la frase fue canonizada en la _Bibliothèque_ de D'Herbelot y dramatizada, de alguna manera, por Dante. No se necesita ninguna justificación, la prueba necesaria para culpar a Mahoma está contenida en la palabra «es». No es necesario precisar la frase, ni tampoco decir que Mahoma _era_ un impostor, ni hace falta considerar por un momento que quizá no sea necesario repetir la afirmación; esta se repite, él _es_ un impostor, y cada vez que se dice, se vuelve poco a poco más impostor, mientras que el autor de la declaración gana un poco más de autoridad simplemente por haberla hecho. Así, la famosa biografía de Mahoma del siglo XVII escrita por Humphrey Prideaux tiene como subtítulo _The True Nature of Imposture_. En fin, es evidente que una categoría como la de impostor (u oriental en este caso) implica —de hecho exige— la existencia de un contrario que no sea otra cosa de manera fraudulenta ni tenga necesidad de una identificación explícita constante. Y ese contrario es el «occidental» o, en el caso de Mahoma, Jesús.
Desde un punto de vista filosófico, el tipo de lenguaje, de pensamiento y de visión que yo he llamado de manera general orientalismo es una forma extrema de realismo; es una manera habitual de tratar cuestiones, objetos, cualidades y regiones supuestamente orientales; los que lo emplean quieren designar, nombrar, indicar y fijar aquello de lo que están hablando con una palabra o una frase. Se considera entonces que esa palabra, o esa frase, ha adquirido una cierta realidad o que simplemente es la realidad. Desde un punto de vista retórico, el orientalismo es absolutamente anatómico y enumerativo: utilizar su vocabulario es comprometerse a particularizar y dividir las realidades de Oriente en partes manejables. Desde un punto de vista psicológico, el orientalismo es una forma de paranoia, un saber que no es del mismo tipo que el saber histórico ordinario, por ejemplo. Estas son algunas consecuencias de la geografía imaginaria y de las espectaculares fronteras que traza. A continuación voy a estudiar algunas de las transmutaciones específicamente modernas de estas consecuencias orientalistas.
### III
### Proyectos
Es necesario examinar las conquistas más llamativas del orientalismo, aunque solo sea para juzgar hasta qué punto Michelet estaba equivocado (y se alejaba de la verdad) cuando enunció la idea de esa grandiosa amenaza: «Oriente avanza invencible y fatal hacia los dioses de la luz a causa del encanto de sus sueños, de la magia de su _chiaroscuro_ ». Las relaciones culturales, materiales e intelectuales entre Europa y Oriente han pasado por numerosas fases, aunque la línea de demarcación entre Este y Oeste siempre ha causado cierta impresión en Europa. Pero, en general, fue el Oeste el que avanzó hacia el Este, y no a la inversa. El orientalismo es el término genérico que empleo para describir la aproximación occidental hacia Oriente, es una disciplina a través de la cual Oriente fue (y es) abordado sistemáticamente como tema de estudio, de descubrimiento y de práctica. Pero además utilizo la palabra para designar ese conjunto de sueños, imágenes y vocabularios que están a disposición de cualquiera que intente hablar de lo que queda al este de la línea divisoria. Estos dos aspectos del orientalismo no son incompatibles, ya que utilizándolos Europa pudo avanzar hacia Oriente con seguridad y no de una manera metafórica. Llegados a este punto me gustaría examinar las huellas materiales de este avance.
Hasta el siglo XIX, con la excepción del islam, Oriente fue para Europa un dominio con una historia continua de dominación occidental que nadie había puesto en cuestión. Esto resulta evidente si consideramos la experiencia británica en la India, la experiencia portuguesa en las Indias Orientales, China y Japón y las experiencias francesa e italiana en diferentes regiones de Oriente. Hubo casos ocasionales en los que la intransigencia indígena quiso perturbar el idilio, como cuando en 1638-1639 un grupo de cristianos japoneses expulsó a los portugueses de la región; sin embargo, por regla general, solo el Oriente árabe e islámico presentó ante Europa un desafío permanente desde un punto de vista político e intelectual y, durante algún tiempo, económico. Por tanto, a lo largo de casi toda su historia el orientalismo ha estado marcado por el sello de la turbia actitud de Europa con respecto al islam. Es este aspecto tan delicado del orientalismo el que me interesa estudiar.
Sin duda, el islam, por muchas razones, fue una provocación real; estaba inquietantemente cerca de la cristiandad, tanto desde un punto de vista geográfico como cultural. Se inspiraba en las tradiciones judeohelénicas, había legado algunos de sus elementos creativos al cristianismo; podía enorgullecerse de sus numerosos éxitos militares y políticos; y esto no era todo, los países islámicos estaban justo al lado de las tierras bíblicas, y las dominaban; además, el corazón de los dominios islámicos siempre ha sido la región más cercana a Europa, la que se ha llamado Oriente Próximo. El árabe y el hebreo eran lenguas semíticas y juntas disponían de un material enormemente importante para el cristianismo. Desde el final del siglo VII hasta la batalla de Lepanto en 1571, el islam, en cualquiera de sus formas árabe, otomana, norteafricana o española, dominó y amenazó de modo efectivo a la cristiandad europea. El islam superó y eclipsó a Roma, y esto es algo que ningún europeo de ayer o de hoy puede olvidar. Y Gibbon tampoco fue una excepción como se evidencia en el párrafo siguiente de su _Decline and Fall_ :*
En los días victoriosos de la República romana, el senado tenía como objetivos limitar sus consejos y legiones a una sola guerra y destruir completamente a un primer enemigo antes de provocar las hostilidades de un segundo. Estas dos tímidas máximas políticas fueron desdeñadas por la magnanimidad y el entusiasmo de los califas árabes que con el mismo éxito y vigor invadieron las tierras de los sucesores de Augusto y de Artajerjes; y así, estas monarquías rivales se convirtieron a la vez en presa de un enemigo al que durante mucho tiempo habían despreciado. Durante los diez años que duró la administración de Omar, los sarracenos redujeron y pusieron bajo su obediencia treinta y seis mil ciudades y castillos, destruyeron cuatro mil iglesias o templos de infieles y edificaron mil cuatrocientas mezquitas para practicar la religión de Mahoma. Cien años después de que el profeta hubiera huido de La Meca, las armas y el reino de sus sucesores se extendían desde la India al océano Atlántico sobre provincias diversas y distantes [...].
Cuando el término _Oriente_ no era simplemente sinónimo de todo el Oriente asiático, ni designaba de manera general lo lejano y exótico, se entendía que se refería rigurosamente al Oriente islámico. Este Oriente «militante» llegaba a representar lo que Henri Baudet ha llamado «el maremoto asiático». Ciertamente esto sucedió en Europa hasta que a mediados del siglo XVIII, ciertos compendios de saber «oriental», como era el caso de la _Bibliothèque orientale_ de D'Herbelot, cesaron de referirse únicamente al islam, a los árabes y a los otomanos. Hasta ese momento, la memoria cultural había dado una preeminencia comprensible a los sucesos relativamente lejanos, como la caída de Constantinopla, las Cruzadas y las conquistas de Sicilia y España. Pero si todo esto significó la amenaza de Oriente, al mismo tiempo, no logró que desapareciera el resto de Asia.
En efecto, estaba la India, donde Portugal había instalado las primeras bases de la presencia europea a principios del siglo XVI, después fue Europa, principalmente Inglaterra, la que, tras un largo período (desde 1600 hasta 1758) de actividad esencialmente comercial, dominó políticamente la India y la ocupó. Pero la India, por sí misma, nunca supuso una amenaza indígena para Europa. Por el contrario, fue la disgregación de la autoridad local que dejó el país abierto a la rivalidad y al control político europeo, lo que ocasionó que Europa pudiera tratar al Oriente indio con esa arrogancia de propietario y jamás con el sentimiento de peligro reservado al islam. Sin embargo, entre esta arrogancia y lo que parecía ser un conocimiento positivo preciso existió una gran disparidad. En la _Bibliothèque_ de D'Herbelot las entradas de los temas indopersas estaban todas fundamentadas en fuentes islámicas, y es cierto que hasta principios del siglo XIX, cuando se hablaba de «lenguas orientales», se entendía únicamente «lenguas semíticas». El resurgir oriental del que hablaba Quinet tuvo la función de ensanchar los límites bastante estrechos dentro de los cuales el islam era el ejemplo oriental que servía para todo. El sánscrito, la religión y la historia de la India no alcanzaron la categoría de conocimientos científicos hasta finales del siglo XVIII, después de los esfuerzos realizados por sir William Jones, pero incluso el interés que Jones tuvo por la India le vino a través de su previo interés por el islam.
No es sorprendente, pues, que el primer gran trabajo de erudición oriental después de la _Bibliothèque_ de D'Herbelot fuera la _History of Saracens_ , de Simon Ockley, cuyo primer volumen apareció en 1708. Un reciente historiador del orientalismo opina que la actitud que Ockley adopta con los musulmanes —a saber, que los cristianos europeos les debían sus primeros conocimientos filosóficos— «fue un impacto doloroso» para su público europeo. En efecto, Ockley no se contentó con exponer esta clara superioridad islámica; también «dio a Europa su primera muestra auténtica y sustancial del punto de vista árabe en las guerras con Bizancio y Persia». Sin embargo, Ockley tuvo buen cuidado de disociarse de la influencia contagiosa del islam, y, al contrario que su colega William Whiston (sucesor de Newton en Cambridge), siempre dejó bien claro que el islam era una indignante herejía. Por otra parte, Whiston fue expulsado de Cambridge en 1709 debido al entusiasmo que manifestó por todo lo islámico.
Para acceder a las riquezas (orientales) de la India siempre había sido necesario atravesar las provincias islámicas y resistir los peligrosos efectos del islam, sistema de creencias cuasi arriano. Y al menos durante la gran parte del siglo XVIII, Gran Bretaña y Francia lo consiguieron. El Imperio otomano permanecía desde hacía tiempo inmerso en una situación de senectud confortable (para Europa), hasta ser inscrito en el siglo XIX como «la cuestión oriental». Gran Bretaña y Francia se enfrentaron en la India entre 1744 y 1748 y de nuevo entre 1756 y 1763, hasta que en 1769 Gran Bretaña se hizo con el control económico y político del subcontinente. ¿Hasta qué punto, pues, fue inevitable la decisión que tomó Napoleón de acosar al Imperio oriental británico, interceptando en primer lugar su paso por territorio islámico en Egipto?
Aunque fue inmediatamente precedida por al menos dos grandes proyectos orientalistas, la invasión napoleónica de Egipto en 1798 y su incursión en Siria tuvieron enormes consecuencias para la historia moderna del orientalismo. Antes de Napoleón, solo se habían llevado a cabo dos intentos (ambos realizados por eruditos) de invadir Oriente, desvelarlo e ir más allá del refugio relativo del Oriente bíblico. El primero fue el de Abraham-Hyacinthe Anquetil-Duperron (1731-1805), un teórico excéntrico del igualitarismo, un hombre que trataba de conciliar en su mente el jansenismo con el catolicismo ortodoxo y el brahmanismo, y que quiso viajar a Asia para probar que la existencia primitiva del pueblo elegido y de las genealogías bíblicas era verdadera. En lugar de esto, rebasó los límites de su primer objetivo y viajó hasta Surat donde encontró un depósito de textos avésticos y los tradujo. Raymond Schwab ha dicho a propósito del misterioso fragmento avéstico que impulsó a Anquetil a hacer ese viaje que mientras «los eruditos observaban el famoso fragmento de Oxford y después volvían a sus estudios, Anquetil lo vio y se fue a la India». Schwab también señala que Anquetil y Voltaire, aunque temperamental e ideológicamente opuestos entre sí, tenían un interés similar por Oriente y por la Biblia, «el uno para hacer que la Biblia fuera más incuestionable, el otro para hacerla más increíble». La traducción que Anquetil hizo del _Zend Avesta_ sirvió irónicamente a los propósitos de Voltaire, ya que los descubrimientos de Anquetil «condujeron rápidamente a la crítica de los textos (bíblicos) que hasta entonces se habían considerado textos revelados». El efecto de la expedición de Anquetil está muy bien descrito por Schwab:
En 1759, Anquetil terminó en Surat su traducción del _Avesta_ ; en 1786 en París, el de los _Upanisads_ : había abierto un canal entre los hemisferios del genio humano al desbloquear y extender el viejo humanismo de la cuenca del Mediterráneo. Hacía menos de cincuenta años, sus compatriotas se preguntaban cómo era lo persa cuando él les enseñaba a comparar los monumentos persas con los griegos. Antes de sus investigaciones, la información sobre el pasado remoto de nuestro planeta solo se buscaba entre los grandes escritores latinos, griegos, judíos y árabes; la Biblia se consideraba un bloque aislado, un aerolito. El universo de la escritura estaba al alcance de la mano, pero apenas nadie parecía sospechar la inmensidad de aquellas tierras desconocidas. Con su traducción del _Avesta_ empezaron a conseguirse los primeros logros que llegaron a sus cotas más altas debido a las investigaciones en Asia Central sobre las lenguas que se multiplicaron después de Babel. En nuestras escuelas, hasta entonces limitadas a la estrecha herencia grecolatina del Renacimiento (gran parte de la cual había sido transmitida a Europa por el islam), él introdujo la visión de numerosas civilizaciones inmemoriales y de una infinidad de literaturas. Desde entonces ya no eran solo algunas provincias europeas las que habían dejado su marca en la historia.
Por primera vez Oriente se revelaba ante Europa en la materialidad de sus textos, de sus lenguas y de sus civilizaciones. También por primera vez, Asia adquiría unas dimensiones intelectuales e históricas precisas que permitían consolidar los mitos de su distancia y su inmensidad geográfica. Por ese sentido inevitable que siempre tiende a compensar la repentina expansión cultural, a las labores orientales de Anquetil le sucedieron las de William Jones, segundo de los proyectos prenapoleónicos que he mencionado antes. Si Anquetil abrió grandes perspectivas, Jones las cerró, codificando, haciendo tablas y comparando. Antes de abandonar Inglaterra para marchar a la India en 1783, Jones ya dominaba el árabe, el hebreo y el persa. Estos eran quizá sus méritos menos importantes; también era poeta, jurista, tenía una mente enciclopédica, era un clasicista, un erudito infatigable cuyas capacidades valdrían como carta de recomendación para Benjamin Franklin, Edmund Burke, William Pitt y Samuel Johnson. Con el tiempo fue nombrado para «un puesto honorable y provechoso en las Indias», y nada más llegar allí para tomar posesión de su cargo en la Compañía de las Indias Orientales, comenzó sus investigaciones personales, que consistieron en reunir, delimitar y domesticar Oriente y de ese modo convertirlo en una provincia del conocimiento europeo. En su obra personal titulada _Objects of Enquiry During My Residence in Asia_ enumeró entre sus temas de investigación: «Las leyes de los hindúes y de los mahometanos, la política y la geografía modernas del Indostán, el mejor modo de gobernar Bengala, la aritmética, la geometría y diversas ciencias de los asiáticos, la medicina, la química, la cirugía y la anatomía de los indios, la producción natural de la India, la poesía, la retórica y la moralidad en Asia, la música de las naciones orientales, los negocios, la industria, la agricultura, y el comercio de la India». El 17 de agosto de 1787 escribió modestamente a lord Althorp: «Mi ambición es conocer la _India_ mejor de lo que cualquier otro europeo la haya conocido jamás». Aquí es donde Balfour en 1910 pudo encontrar el primer modelo de su pretensión de conocer Oriente, como inglés, más y mejor que cualquier otra persona.
Oficialmente Jones se ocupaba de los asuntos legales, una actividad con una significación simbólica en la historia del orientalismo. Siete años antes de que Jones llegara a la India, Warren Hastings había decidido que los indios debían gobernarse según sus propias leyes, proyecto más ambicioso de lo que parece, si tenemos en cuenta que el código de leyes sánscrito solo existía entonces para uso corriente en una traducción al persa, y ningún inglés en esa época sabía sánscrito lo suficientemente bien como para consultar los textos originales. Un funcionario oficial de la Compañía, Charles Wilkins, primero aprendió bien sánscrito y después comenzó a traducir las _leyes_ de Manu; en esta tarea la ayuda de Jones fue muy importante (Wilkins fue el primer traductor del _Bhagavadgita_ ). En enero de 1784, Jones convocó la asamblea inaugural de la Asiatic Society of Bengal que iba a ser para la India lo que la Royal Society era para Inglaterra. Como primer presidente de la sociedad y magistrado, Jones adquirió un conocimiento efectivo de Oriente y de los orientales, que más tarde le llevaría a ser el fundador indiscutible del orientalismo (la frase es de A. J. Arberry). Los objetivos de Jones fueron gobernar, aprender y después comparar Oriente con Occidente, objetivos que realizó con su irresistible tendencia a codificar y a reducir la infinita variedad de Oriente a «un resumen completo» de leyes, figuras, costumbres y obras. Su declaración más famosa indica hasta qué punto el orientalismo moderno, incluso en sus comienzos filosóficos, fue una disciplina comparativa cuyo principal objetivo era encontrar una fuente oriental lejana e inofensiva para las lenguas europeas:
El _sánscrito_ , sin tener en cuenta su antigüedad, es una lengua con una estructura maravillosa, más perfecta que la del _griego_ , más rica que la del _latín_ y de un refinamiento más exquisito que la de cualquiera de las dos aunque mantenga con ambas una gran afinidad tanto en las raíces de los verbos como en las formas gramaticales, una afinidad tan fuerte que no la ha podido producir el azar; de hecho tan fuerte que ningún filólogo podría examinarlas sin concluir que las tres proceden de un tronco común.
Muchos de los primeros orientalistas ingleses que estuvieron en la India fueron, como Jones, juristas eruditos y otros eran médicos con fuertes tendencias misioneras, lo que no deja de ser interesante. Según lo que conocemos de ellos, la mayoría estaban obsesionados con el doble propósito de estudiar «las ciencias y las artes de Asia, con la esperanza de lograr mejoras allí y de perfeccionar el conocimiento de las artes en Europa»: así se presentó el objetivo común de los orientalistas en el _Centenary Volume_ de la Royal Asiatic Society fundada en 1823 por Henry Thomas Colebrooke. En su trato con los orientales de su tiempo, los primeros orientalistas profesionales, como Jones, tenían solo dos funciones que desempeñar, pero no podemos reprocharles hoy la estrechez que el carácter occidental oficial de su presencia en Oriente imponía a su humanidad. Eran o bien jueces o bien médicos. Incluso Edgar Quinet, que escribió desde un punto de vista más metafísico que realista, fue vagamente consciente de esta relación terapéutica. _«L'Asie a les prophétes —dijo en Le Génie des religions—_ , _l'Europe a les docteurs»_. El conocimiento apropiado de Oriente pasaba por un estudio concienzudo de los textos clásicos y solo después de eso, por la aplicación de esos textos al Oriente moderno. Enfrentado a la decrepitud evidente del oriental moderno y a su impotencia política, el orientalista europeo estimó que su deber era rescatar una parte del grandioso pasado clásico de Oriente que se había perdido, para así «facilitar las mejoras» en el Oriente actual. Lo que el europeo tomó del pasado oriental clásico fue una visión (y miles de hechos y objetos) que solo él podía utilizar en las mejores condiciones; al oriental moderno, le facilitó las cosas y le hizo beneficiarse de su opinión sobre lo que era mejor para el Oriente moderno.
Una de las características que tenían todos los proyectos orientalistas anteriores al de Napoleón era que su éxito no se podía preparar con antelación. Anquetil y Jones, por ejemplo, aprendieron lo que aprendieron sobre Oriente una vez que estuvieron allí. Se enfrentaron a todo Oriente y solo después de algún tiempo y de una dosis considerable de improvisación pudieron reducirlo a una provincia más pequeña. Por otro lado, Napoleón quería nada menos que apoderarse de todo Egipto, y sus preparativos antes de la expedición fueron de una magnitud y meticulosidad sin precedentes. Aun así, estos preparativos fueron fanáticamente esquemáticos y —si se me permite usar la palabra— librescos, características que voy a analizar a continuación. Parece ser que, sobre todo, eran tres cosas las que Napoleón tenía en mente cuando en 1797 se preparaba en Italia para su siguiente golpe militar. Primero, y dejando aparte el poder siempre amenazante de Inglaterra, después de sus éxitos militares que habían culminado con el Tratado de Campo Formio ya solo le quedaba el Este para conseguir una gloria adicional. Además, Talleyrand había hecho recientemente unas observaciones sobre _«les avantages à retirer de colonies nouvelles dans les circonstances présentes»_ , y esta idea, junto a la agradable posibilidad de perjudicar a Gran Bretaña, le empujó hacia Oriente. Segundo, a Napoleón siempre, desde su adolescencia, le había atraído Oriente; sus manuscritos de juventud, por ejemplo, contienen un resumen que hizo de la _Histoire des arabes_ , de Marigny, y de todos sus escritos y conversaciones se deduce que estaba impregnado, como Jean Thiry ha dicho, de las memorias y las glorias que formaban parte del Oriente de Alejandro en general y de Egipto en particular. Así, la idea de reconquistar Egipto como un nuevo Alejandro se le ocurrió por sí misma, combinada con el beneficio adicional de conseguir una nueva colonia islámica a costa de Inglaterra. En tercer lugar Napoleón consideró que Egipto era un proyecto viable precisamente porque lo conocía desde un punto de vista táctico, estratégico, histórico y —no lo subestimemos— textual, a través de la lectura de los textos de las autoridades europeas clásicas y recientes. Todo esto indica que, para Napoleón, Egipto era un proyecto que fue adquiriendo realidad primero en su mente y después a través de sus preparativos de la conquista, gracias a unas experiencias que pertenecen más al ámbito de las ideas y de los mitos reunidos en los textos que al de la realidad empírica. Por tanto, sus planes para Egipto se convirtieron en el primero de una serie de contactos entre Europa y Oriente en los que la especialidad del orientalista se ponía directamente al servicio de la conquista colonial; en efecto, a partir de los tiempos de Napoleón, cuando un orientalista tenía que decidir si su lealtad y sus simpatías estaban del lado de Oriente o del Occidente conquistador, siempre elegía este último. Lo mismo podríamos decir del propio emperador, que veía Oriente solo como lo habían codificado primero los textos clásicos y después los expertos orientalistas, cuya visión, basada en los textos clásicos, parecía un útil sustituto de cualquier contacto verdadero con el Oriente real.
Es bastante conocido el hecho de que Napoleón implicó a docenas de «sabios» en su expedición egipcia; por eso no es necesario que nos extendamos más en este asunto. Su intención era conformar una especie de archivo viviente de la expedición, compuesto por estudios de todos los temas y dirigidos por los miembros del Institut d'Égypte que él había fundado. Lo que quizá sea menos conocido es que Napoleón se apoyó en la obra de un viajero francés, el conde de Volney, cuyo _Voyage en Égypte et en Syrie_ apareció en dos volúmenes en 1787. Salvo un corto prefacio personal que informa al lector de que al haber recibido una repentina cantidad de dinero (de una herencia), pudo hacer un viaje al Este en 1783, el _Voyage_ de Volney es un documento de una impersonalidad casi opresiva. Volney, evidentemente, se consideraba un hombre de ciencia cuya labor era siempre registrar el « _état_ » de lo que veía. El punto culminante del _Voyage_ se encuentra en el segundo volumen y consiste en una exposición sobre el islam como religión. Las opiniones de Volney eran canónicamente hostiles al islam, como religión y como sistema de instituciones políticas. Sin embargo, Napoleón consideró que esta obra y las _Considérations sur la guerre actuel des turcs_ (1788), de Volney, tenían una particular importancia. Volney, después de todo, era un astuto francés y —como Chateaubriand y Lamartine un cuarto de siglo después— consideraba Oriente Próximo el lugar propicio para realizar las ambiciones coloniales francesas. Lo que Napoleón encontró útil en Volney fue la enumeración por orden creciente de dificultad de los obstáculos a los que cualquier fuerza expedicionaria francesa debería enfrentarse en Oriente.
Napoleón se refiere explícitamente a Volney en sus reflexiones sobre la expedición egipcia, las _Campagnes d'Égypte et de Syrie 1798-1799_ , que dictó al general Bertrand en Santa Elena. Volney, dijo él, consideraba que había tres barreras que se oponían a la hegemonía francesa en Oriente, y que cualquier fuerza expedicionaria francesa, por tanto, tendría que librar tres batallas: una contra Inglaterra, la segunda contra la Sublime Puerta y la tercera y más difícil contra los musulmanes. Los juicios de Volney eran sagaces y difíciles de refutar, ya que para Napoleón era evidente, como lo hubiera sido para cualquiera que leyera a Volney, que el _Voyage_ y las _Considérations_ eran textos que debían determinar las acciones de todo europeo que deseara vencer en Oriente. En otras palabras, que la obra de Volney constituyó un manual destinado a atenuar el impacto humano que un europeo podía sentir al entrar en contacto directo con Oriente: leed los libros, parece haber sido la tesis de Volney, y lejos de sentiros desorientados por Oriente, lo someteréis.
Napoleón tomó las palabras de Volney casi al pie de la letra, pero con una sutilidad característica. Desde el momento en que la Armée d'Égypte apareció en el horizonte egipcio, todos los esfuerzos que se hicieron iban dirigidos a convencer a los musulmanes de que _«nous sommes les vrais musulmans»_ , como proclamó Bonaparte el 2 de julio de 1798 ante el pueblo de Alejandría. Equipado con un grupo de orientalistas (y sentado a bordo de un buque llamado _Orient_ ), Napoleón utilizó la enemistad de los egipcios hacia los mamelucos, así como llamamientos a la idea revolucionaria de la igualdad de oportunidades para todos, para hacer una guerra benigna y selectiva contra el islam. Lo que más impresionó al primer cronista árabe de la expedición, Abd-al-Rahman al-Jabarti, fue la manera en la que Napoleón utilizó a los eruditos para cuidar sus contactos con los nativos; también quedó sorprendido al observar de cerca al estamento intelectual europeo moderno. Napoleón intentó por todos los medios demostrar que combatía por el islam; todo lo que decía se traducía al árabe literario, y recomendaba al ejército francés que jamás olvidara la sensibilidad islámica. (Desde este punto de vista compárense las tácticas de Napoleón en Egipto, con las del _Requerimiento_ , un documento español redactado en 1513 que debía ser leído en voz alta a los indios.)* Cuando Napoleón consideró que su fuerza era insuficiente para imponerse a los egipcios, intentó hacer que los imames, cadíes, muftíes y ulemas interpretaran el Corán en favor de la Grande Armée. Con este propósito, invitó a los sesenta ulemas que enseñaban en al-Azhar a su cuartel general, les brindó honores militares completos y después les cumplimentó con su admiración por el islam y por Mahoma y con su veneración evidente hacia el Corán con el que parecía perfectamente familiarizado. Esto funcionó, y pronto la población de El Cairo pareció haber perdido su desconfianza hacia los ocupantes. Después, Napoleón le dio a su representante Kleber rigurosas instrucciones para que, cuando él se fuera, administrara Egipto valiéndose de los orientalistas y de los dirigentes religiosos que pudiera ganar para su causa; cualquier otra política sería demasiado costosa y poco razonable. Hugo creyó haber plasmado la gloria diplomática de la expedición oriental de Napoleón en su poema «Lui»:
_Au Nil je le retrouve encore_
_L'Égypte resplendit des feux de son aurore;_
_Son astre impérial se lève a l'Oriente_.
_Vainqueur, enthousiaste, éclatant de prestiges_ ,
_Prodige, il étonna la terre des prodiges_.
_Les vieux scheiks vénéraient l'émir jeune et prudent;_
_Le peuple redoutait ses armes inouïes_ ;
_Sublime, il apparut aux tribes éblouies_
_Comme un Mahomet d'Occident_.*
Un triunfo así solo podía haber sido preparado antes de la expedición militar y lo tenía que haber organizado alguien que solamente conociera Oriente a través de lo que había leído en los libros o de lo que le habían transmitido los eruditos. La idea de llevarse consigo una academia entera es una muestra de esa actitud textual hacia Oriente, actitud que, a su debido tiempo, fue reforzada por unos decretos revolucionarios específicos (particularmente el del 10 de germinal del año III —30 de marzo de 1793—, que establecía una _école publique_ en la Bibliothèque Nationale para enseñar árabe, turco y persa) cuyo objetivo racionalista era disipar los misterios e institucionalizar todo el conocimiento, incluso el más recóndito. Así, muchos de los traductores orientalistas de Napoleón fueron discípulos de Silvestre de Sacy que, a partir de junio de 1796, fue el único profesor de árabe de la École Publique des Langues Orientales. Sus discípulos fueron los grandes orientalistas que dominaron el campo durante más o menos tres cuartos de siglo. Muchos de ellos resultaron ser muy útiles desde un punto de vista político, del mismo modo que algunos lo habían sido para Napoleón en Egipto.
Pero los contactos que Napoleón mantuvo con los musulmanes constituían solo una parte de su proyecto de dominar Egipto. La otra parte consistía en dejarlo completamente abierto, hacerlo totalmente accesible al investigador europeo. Egipto, ese país que hasta entonces había estado inmerso en la oscuridad, esa parte de Oriente hasta aquel momento conocida solo por medios indirectos, por las expediciones de los primeros viajeros, de los eruditos y de los conquistadores, se iba a convertir en un departamento del saber francés. En este punto también son evidentes las actitudes textuales y esquemáticas. El Instituto, con sus equipos de químicos, historiadores, biólogos, arqueólogos, cirujanos y especialistas en la antigüedad, constituía la división instruida del ejército, si bien su labor era menos agresiva: traducir Egipto al francés moderno. A diferencia de la _Description de l'Égypte_ , del abad Le Mascrier de 1735, la de Napoleón iba a ser una empresa universal. Casi desde el principio de la ocupación, Napoleón se encargó de que el Instituto comenzara sus reuniones, sus experimentos y su misión de recopilar material, como diríamos hoy. Lo más importante era que todo lo que se decía, se veía y se estudiaba, se registrara y, de hecho, se registró en esa gran apropiación colectiva de un país por otro que es la _Description de l'Égypte_ , publicada en veintitrés enormes volúmenes entre 1809 y 1828.
Lo singular de la _Description_ no es solo su tamaño, ni siquiera la inteligencia de sus autores, sino su actitud hacia el tema del que se ocupa; y es esta actitud la que hace que sea una obra de gran interés para el estudio de los proyectos orientalistas modernos. Las primeras páginas de su _Préface historique_ escrito por Jean-Baptiste-Joseph Fourier, secretario del Instituto, dejan claro que al «hacer» Egipto, los eruditos estaban también abordando directamente un tema con una especie de significación cultural e histórica no adulterada. Egipto era el centro de atención de las relaciones entre África y Asia, entre Europa y el Este, entre la memoria y la actualidad.
Situado entre África y Asia y de fácil comunicación con Europa, Egipto ocupa el centro del antiguo continente. Este país solo muestra grandes recuerdos, es la patria de las artes y conserva innumerables monumentos; sus principales templos y los palacios que habitaron sus reyes todavía subsisten a pesar de que sus edificios menos antiguos ya se habían construido antes de la guerra de Troya. Homero, Licurgo, Solón, Pitágoras y Platón fueron a Egipto para estudiar ciencias, religión y leyes. Alejandro fundó allí una ciudad opulenta que durante mucho tiempo dominó el comercio y fue testigo de las decisiones que Pompeyo, César, Marco Aurelio y Augusto tomaron sobre el destino de Roma y del mundo entero. Es, por tanto, normal que este país atraiga la atención de los ilustres príncipes que dirigen el destino de las naciones.
No ha habido ningún país medianamente poderoso en Occidente o en Asia que no haya vuelto sus ojos hacia Egipto y no lo haya visto, de alguna manera, como un terreno naturalmente suyo.
Como Egipto estaba cargado de significado para las artes, las ciencias y el gobierno, su papel consistía en ser el escenario en el que sucederían acciones de una importancia histórica y mundial. Así, al apoderarse de Egipto, una potencia moderna demostraría de modo natural su fuerza, y justificaría la historia; el propio destino de Egipto era ser anexionado preferiblemente por Europa. Además esta potencia entraría también a formar parte de una historia cuyo factor común lo definían personajes de la talla de Homero, Alejandro, César, Platón, Solón y Pitágoras que en otro tiempo habían honrado a Oriente con su presencia. Oriente, en resumen, existió como un conjunto de valores que se relacionaban no con sus realidades modernas, sino con una serie de contactos que había tenido con un pasado europeo remoto. Esto es un ejemplo puro de la actitud esquemática y textual a la que me he referido.
Fourier continúa en el mismo tono durante más de cien páginas (a propósito, cada página tiene un metro cuadrado de superficie, parece como si se hubiera pensado que el proyecto y el tamaño de las páginas debían tener las mismas dimensiones). A partir de un pasado impreciso y mal delimitado, sin embargo, debe justificar la expedición napoleónica como un hecho necesario cuando sucedió. Fourier nunca abandona la perspectiva teatral; conocedor de su público europeo y de los personajes orientales que manipulaba escribió:
Uno recuerda la impresión que produjeron en toda Europa las asombrosas noticias de que Francia estaba en Oriente [...]. Este gran proyecto se meditó en silencio y fue preparado con tanta actividad y secreto que consiguió esquivar la inquieta vigilancia de nuestros enemigos; solo en el momento en que ocurrió, supieron que se había concebido, emprendido y llevado a cabo con éxito [...].
Un _coup de théâtre_ tan dramático tenía ventajas también para Oriente:
Esta región que ha transmitido sus conocimientos a tantas naciones, está hoy inmersa en la barbarie.
Solo un héroe podía reunir todos estos factores, y esto es lo que Fourier describe ahora:
Napoleón valoró la influencia que este suceso tendría en las relaciones entre Europa, Oriente y África en lo referente a la navegación por el Mediterráneo y al destino de Asia [...]. Quería ofrecer a Oriente el útil ejemplo de Europa, y, finalmente, también pretendía hacer la vida de los habitantes más agradable, y procurarles las ventajas de una civilización perfeccionada.
Nada de esto podía conseguirse sin aplicar las artes y las ciencias al proyecto.
Restaurar una región en estado de barbarie para devolverla a su antigua grandeza clásica, y enseñar (en su beneficio) a Oriente los métodos del Occidente moderno; subordinar o moderar el poder militar para ampliar el proyecto de obtener un conocimiento glorioso en el proceso de la dominación política de Oriente; formular Oriente, darle una forma, una identidad y una definición; reconocer su lugar en la memoria, su importancia para la estrategia imperial y su papel «natural» como apéndice de Europa; dignificar todos los conocimientos almacenados durante la ocupación colonial con el título de «Contribución a la ciencia moderna», cuando los nativos no habían sido consultados y solo habían sido tenidos en cuenta como pretextos para un texto que ni siquiera les era útil a ellos; tener el sentimiento como europeo de disponer, casi a voluntad, de la historia, el tiempo y la geografía de Oriente; instituir nuevas áreas de especialización; establecer nuevas disciplinas; dividir, organizar, esquematizar, poner en cuadros, hacer índices y registrar todo lo que era visible (o invisible); hacer generalizaciones de cada detalle observable y de cada generalización una ley inmutable sobre la naturaleza, el temperamento, la mentalidad, las costumbres o el tipo de los orientales y, sobre todo, transmutar la realidad viviente en una sustancia textual; poseer (o pensar que se posee) la realidad, esencialmente porque no hay nada en Oriente que parezca resistirse a su poder: estas son las características de la proyección orientalista que se realizó en la _Description de l'Égypte_ y que permitió y reforzó la absorción totalmente orientalista de Egipto por parte de Napoleón a través de los instrumentos del conocimiento y del poder occidentales. Así, Fourier concluye su prefacio anunciando que la historia recordará cómo _«Égypte fut le théâtre de sa gloire [de Napoleón], et préserve de l'oubli toutes les circonstances de cet évènement extraordinaire»_.
La _Description_ , de este modo, desplaza a la historia egipcia u oriental en tanto que historia que posee su propia coherencia, identidad y sentido. En su lugar, la historia relatada en la _Description_ sustituye a la historia egipcia u oriental identificándola directa e indirectamente con la historia del mundo, por no decir con la de Europa. Preservar un suceso del olvido es equivalente, en la mente orientalista, a transformar Oriente en un teatro para sus representaciones de Oriente: esto es lo que casi exactamente dice Fourier. Además el poder puro y simple de haber descrito Oriente en términos occidentales modernos consigue que Oriente salga del reino de las tinieblas silenciosas donde ha permanecido ignorado (con la excepción de algún murmullo producido por el sentimiento vasto pero indefinido de su propio pasado) y alcance la claridad de la ciencia europea moderna. Allí, este nuevo Oriente figura —por ejemplo, en las tesis biológicas expuestas por Geoffroy Saint-Hilaire en la _Description_ — como una confirmación de las leyes de especialización zoológica formuladas por Buffon, o sirve de _«contraste frappante avec les habitudes des nations Européennes»_. Las _«bizarres jouissances»_ de los orientales sirven para iluminar la sobriedad y la racionalidad de los hábitos occidentales, o, por citar una utilidad adicional de Oriente, se buscan para los cuerpos de los europeos equivalentes de esas características fisiológicas de los orientales que les han permitido embalsamar sus cuerpos, de tal forma que los caballeros caídos en el campo del honor puedan ser conservados como reliquias vivas de la gran campaña oriental de Napoleón.
Pero, aunque la ocupación militar napoleónica de Egipto fue un fracaso, no supuso la destrucción de la fertilidad de su proyección completa sobre Egipto y el resto de Oriente. De la ocupación nació, literalmente, la experiencia totalmente moderna de Oriente tal y como se interpretaba desde el interior del universo discursivo que Napoleón había cimentado en Egipto, y cuyos agentes de dominación y diseminación incluían el Instituto y la _Description_. La idea, como ha explicado Charles-Roux, era que Egipto, «devuelto a la prosperidad, regenerado por una administración inteligente e iluminada [...] alumbraría a todos sus vecinos orientales». Sin duda, las otras potencias europeas iban a competir en esta misión y Gran Bretaña más que ninguna otra. Pero lo que iba a ser la perdurable herencia legada a Oriente por esta misión común de Occidente —a pesar de las querellas, de la rivalidad o de la guerra abierta entre los europeos— serían los nuevos proyectos, las nuevas visiones y nuevas empresas que combinaban otras partes más del Viejo Continente con el espíritu europeo de conquista. Después de Napoleón, por tanto, el lenguaje del orientalismo cambió radicalmente; superó el realismo descriptivo y pasó a ser no solo un estilo de representación, sino un lenguaje y un medio de creación. Al mismo tiempo que las _langues mères_ , nombre que Antoine Fabre d'Olivet dio a las fuentes latentes y olvidadas de las lenguas populares de la Europa moderna, Oriente fue reconstruido, ensamblado de nuevo y fabricado con habilidad; en resumen, fue devuelto a la vida por los esfuerzos orientalistas. La _Description_ pasó a ser el patrón de todos los esfuerzos que posteriormente se hicieron con el fin de aproximar Oriente a Europa, de absorberlo enteramente y —lo que es más importante— de aniquilarlo o, al menos, dominar y reducir su extrañeza y, en el caso del islam, su hostilidad. Así, el Oriente islámico en lo sucesivo iba a aparecer como una categoría que denotaba el poder orientalista y no al pueblo islámico como grupo de seres humanos ni su historia como historia.
Así, a partir de la expedición napoleónica se publicó toda una serie de productos textuales, desde el _Itinéraire_ de Chateaubriand al _Voyage en Oriente_ , de Lamartine, _Salambó_ , de Flaubert, y, en la misma tradición, _Manners and Customs of Modern Egyptians_ , de Lane, y _Personal Narrative of Pilgrimage to al-Madinah and Meccah_ ,* de Richard Burton. Lo que unía a estos autores no era solo el fondo de leyendas y experiencias que tenían en común, sino también el hecho de que sabían bien que Oriente era una especie de seno del que habían salido. Si, paradójicamente, estas creaciones llegaron a ser simulacros muy estilizados e imitaciones muy elaboradas de lo que se creía que era un Oriente vivo, esto no disminuye en modo alguno la fuerza de su concepción imaginaria ni la del magisterio europeo sobre Oriente, cuyos prototipos fueron, respectivamente, Cagliostro, la gran personificación europea de Oriente, y Napoleón, su primer conquistador moderno.
La obra artística o textual no fue lo único que produjo la expedición napoleónica. Hubo además, lo cual ciertamente fue más influyente, un proyecto científico, cuya manifestación principal es el _Système comparé et histoire générale des langues sémitiques_ , de Ernest Renan, acabado en 1848 para obtener —con claridad— el Prix Volney; y un proyecto geopolítico, cuyas mayores manifestaciones son el canal de Suez de Ferdinand de Lesseps y la ocupación británica de Egipto en 1882. La diferencia entre los dos tipos de proyectos no reside solo en sus diferentes dimensiones, sino también en la calidad de su convicción orientalista. Renan creyó de verdad que, en su obra, había creado de nuevo Oriente tal y como era realmente. Lesseps, por otro lado, siempre estuvo un poco asustado por la novedad que suponía su proyecto en el viejo Oriente y este sentimiento se transmitió a todos para los que la apertura del canal en 1869 no fue un hecho ordinario. En su _Excursionist and Tourist Advertiser_ del 1 de julio de 1869, el entusiasmo de Thomas Cook relevaba al de Lesseps:
El 17 de noviembre se va a celebrar el éxito de la hazaña técnica más grande del presente siglo con una fiesta de inauguración magnífica a la que casi todas las familias reales europeas mandarán un representante. La ocasión será verdaderamente excepcional. La construcción de una vía de comunicación por agua entre Europa y el Este es una idea de hace muchos siglos que ha estado en la mente de los griegos, los romanos, los sajones y los galos; pero hasta hace pocos años la civilización moderna no ha empezado a prepararse seriamente para emular el trabajo de los antiguos faraones que hace muchos siglos construyeron un canal entre los dos mares, del cual todavía quedan algunas huellas [...]. Todo lo referente a los trabajos [modernos], se hace a escala gigantesca, y la lectura de un pequeño folleto que describe esta empresa, y que debemos a la pluma del caballero de St. Stoess, nos da una fuerte impresión del genio del gran Maestro —Ferdinand de Lesseps—, a cuya perseverancia, calma, osadía y previsión se debe el que, por fin, se haya convertido en una realidad verdadera y tangible [...] el proyecto de acercar los países del Oeste a los del Este y de unir, así, las civilizaciones de diferentes épocas.
La combinación de viejas ideas con nuevos métodos, la unión de culturas cuyas relaciones hasta el siglo XIX habían sido diferentes, la auténtica imposición del poder de la tecnología moderna y de la voluntad intelectual sobre entidades hasta entonces estables y separadas geográficamente, como Oriente y Occidente, es lo que Thomas Cook percibe y lo que en sus publicaciones, discursos, proyectos y cartas Ferdinand de Lesseps propaga.
Desde un punto de vista genealógico, Ferdinand de Lesseps había tenido un comienzo afortunado; Mathieu de Lesseps, su padre, había llegado a Egipto con Napoleón y, después de la evacuación de los franceses en 1801, se quedó allí (como «representante no oficial francés», dice Marlowe) durante cuatro años. En muchos de sus escritos posteriores, Ferdinand se refiere al hecho de que el propio Napoleón estaba interesado en abrir un canal, pero que nunca pensó que fuera un objetivo realizable porque sus expertos le informaron mal. Contagiado por la irregular historia de los proyectos del canal, que incluía unos planes franceses concebidos por Richelieu y por los saint-simonianos, Ferdinand de Lesseps volvió a Egipto en 1854 para embarcarse en la empresa que se completaría quince años más tarde. No tenía una base de conocimientos de ingeniería; solo una tremenda fe en sus habilidades casi divinas como arquitecto, promotor y creador le mantuvieron firme en su propósito, y su talento diplomático y financiero le hizo ganar apoyo en Egipto y en Europa; parecía haber adquirido los conocimientos necesarios para llevar las cosas a buen puerto. Lo que quizá le resultó más útil fue que supo cómo colocar a sus colaboradores potenciales en el teatro de la historia mundial y hacerles ver lo que su « _pensée morale_ », como él llamó a su proyecto, significaba realmente.
Ustedes perciben —les dijo en 1860— los inmensos servicios que el acercamiento de Occidente y Oriente pueden rendir a la civilización y a la riqueza común. El mundo espera de ustedes el progreso y ustedes deben responder a las esperanzas del mundo.
De acuerdo con estas ideas, el nombre de la compañía inversora formada por Lesseps en 1858 era muy significativo y reflejaba los grandiosos planes que abrigaba: la Compagnie Universalle. En 1862, la Académie Française ofreció un premio al mejor poema que se escribiera sobre el canal. Bournier, el ganador, se expresó con varias hipérboles que no contradecían en lo fundamental la imagen que Lesseps tenía de su empresa; veamos algunas de ellas:
_Vos pères, les héros, son venus jusqu'ici_ ;
_Soyez ferme comme aux intrepides_ ,
_Comme eux vous combattez aux pieds des pyramides_ ,
_Et leurs quatre mille ans vous contemplent aussi_!
_Oui, c'est pour l'univers! Pour l'Asie et l'Europe_ ,
_Pour ces climats lointain que la nuit enveloppe_ ,
_Pour le Chinois perfide et l'Indien demi-nu_ ;
_Pour les peuples heureux, libres, humains et braves_ ,
_Pour les peuples méchants, pour les peuples esclaves_ ,
_Pour ceux à qui le Christ est encore inconnu_.*
Nunca Lesseps fue tan elocuente e ingenioso como cuando le convocaron para que justificara el enorme gasto de dinero y de hombres que requería el canal. Fascinó a todos los oyentes con sus estadísticas. Con la misma facilidad podía citar a Heródoto o hablar de estadísticas marítimas. En sus artículos de periódicos de 1864 citó, aprobándola, una observación de Casimir Laconte que decía que una vida excéntrica debería desarrollar en los hombres una originalidad significativa, y a partir de esa originalidad habrían de surgir grandes e inusuales hazañas. Esas hazañas eran su propia justificación. A pesar de su historia inmemorial de fracasos, a pesar de su costo desorbitado, a pesar de su desmesurada ambición por alterar la manera en la que Europa trataba a Oriente, el canal merecía la pena. Se trataba de un proyecto capaz de anular las objeciones de los que fueron consultados y, al mejorar Oriente de manera global, era capaz también de hacer lo que los astutos egipcios, los pérfidos chinos y los indios semidesnudos nunca habrían podido hacer por sí mismos.
La ceremonia de inauguración en noviembre de 1869 fue una ocasión que encarnaba perfectamente las ideas de Ferdinand de Lesseps, así como la historia de sus maquinaciones. Durante años, sus discursos, sus cartas y sus panfletos estuvieron repletos de un vocabulario muy enérgico y teatral. En su búsqueda del éxito, llegó a decir de sí mismo (y siempre en primera persona del plural), nosotros hemos creado, luchado, dispuesto, logrado, actuado, reconocido, perseverado y avanzado; nada —repitió muchas veces— podía habernos parado, nada era imposible; y, al final, nada importaba excepto la consecución de _«le résultat final, le grand but»_ , que él había concebido, definido, y finalmente ejecutado. Cuando el enviado papal a las ceremonias habló el 16 de noviembre ante los dignatarios reunidos, se esforzaba en su discurso por igualar el espectáculo intelectual e imaginativo que el canal de Ferdinand de Lesseps ofrecía:
[...] Es factible afirmar que ha sonado la hora, no solamente una de las más solemnes de este siglo, sino también una de las más grandes y decisivas que haya visto la humanidad desde que tiene historia en la tierra. Este lugar en el que confluyen, sin tocarse, África y Asia, esta gran fiesta del género humano, esta asistencia augusta y cosmopolita, todas las razas del globo, todas las banderas, todos los pabellones flotando alegremente en este cielo radiante e inmenso, debajo del cual está la cruz respetada por todos frente a la media luna, ¡cuánta maravilla, cuántos sorprendentes contrastes, cuántos sueños supuestamente quiméricos convertidos en realidades palpables! Y, en esta reunión de tantos prodigios, ¡cuántos temas y perspectivas del porvenir, cuántas gloriosas esperanzas!
[...] Los dos extremos del globo se aproximan; aproximándose se reconocen; reconociéndose todos los hombres, hijos de un único y mismo Dios, experimentan los estremecimientos alegres de su mutua fraternidad. ¡Oh Occidente! ¡Oh Oriente! ¡Acercaos, mirad, reconoced, saludad, abrazaos!
[...] Pero tras el fenómeno material, la mirada del penador descubre horizontes más vastos que los espacios mensurables; horizontes sin límites en los que se proyectan los más altos destinos, las más gloriosas conquistas, las más inmortales certidumbres del género humano.
¡Oh Dios! ¡Que vuestro soplo divino planee sobre las aguas! ¡Que pase y vuelva a pasar, de Occidente a Oriente, de Oriente a Occidente! ¡Oh Dios! ¡Sírvete de esta vía para acercar los hombres unos a otros
El mundo entero parecía congregarse para rendir homenaje a un plan que Dios solo podía bendecir y aprovechar. Se disolvieron las viejas distinciones e inhibiciones. La cruz miraba desde lo alto hacia la media luna, Occidente había llegado a Oriente para no abandonarlo jamás (hasta que en julio de 1956, Gamal Abdel Nasser, recuperó para Egipto el canal pronunciando el nombre de Ferdinand de Lesseps).
En la idea del canal de Suez vemos la conclusión lógica del pensamiento orientalista y, lo que es más interesante, del esfuerzo orientalista. Para Occidente, en otros tiempos Asia había representado el silencio, la distancia y lo extraño; el islam constituía una hostilidad militante para la cristiandad europea. Para superar esas temibles constantes, Oriente requería primero ser conocido, después invadido y conquistado, y luego ser creado de nuevo por los eruditos, los soldados y los jueces que habían desenterrado unas lenguas, unas historias, unas razas y unas culturas olvidadas, para proponerlas —en medio de la incomprensión del Oriente moderno— como el verdadero Oriente clásico que podía ser utilizado para juzgar y gobernar al Oriente moderno. Aparecía un Oriente de inventario; Oriente era una palabra erudita que designaba lo que la Europa moderna acababa de hacer con un Este todavía original. Ferdinand de Lesseps y su canal, finalmente, acabaron con el distanciamiento de Oriente, con su intimidad monástica _lejos de_ Occidente y con su exotismo constante. Igual que una barrera de tierra pudo ser transmutada en una arteria líquida, así también Oriente sufrió un cambio sustancial, dejó de ser una presencia resistente y hostil, para convertirse en un socio servicial y sumiso. Después de Ferdinand de Lesseps ya nadie podía hablar de Oriente como si se tratara de otro mundo; solo existía «nuestro» mundo, «un» mundo que navegaba unido porque el canal de Suez había demostrado lo equivocados que estaban esos últimos provincianos que creían todavía en la diferencia entre los mundos. Por tanto, la noción de «oriental» es una noción administrativa o ejecutiva y está subordinada a factores demográficos, económicos y sociológicos. Para los imperialistas, como Balfour, o para los antiimperialistas, como J. A. Hobson, el oriental, como el africano, es miembro de una raza sometida, y no exclusivamente un habitante de una cierta zona geográfica. Ferdinand de Lesseps había hecho desaparecer la identidad geográfica de Oriente al arrastrar (casi literalmente) Oriente hacia Occidente y, finalmente, al disipar la amenaza del islam. Después de esto, surgirán nuevas categorías y experiencias, incluyendo las imperialistas, y, en su momento, el orientalismo se adaptará a ellas, pero no sin algunas dificultades.
### IV
### Crisis
Puede parecer extraño hablar de una actitud _textual_ , pero un estudioso de la literatura entenderá más fácilmente lo que significa esta expresión si recuerda el tipo de perspectiva adoptada por Voltaire en _Candide_ * o incluso los comportamientos ante la realidad satirizados por Cervantes en _Don Quijote_. Según ambos escritores, el sentido común enseña que es un error suponer que los libros y los textos pueden ayudar a comprender el desorden impredecible y problemático en el que los seres humanos viven. Aplicar literalmente a la realidad lo que se ha aprendido en los libros es correr el riesgo de volverse loco o de arruinarse. A nadie se le ocurriría utilizar el _Amadís de Gaula_ para comprender la España del siglo XVI (o la actual), igual que nadie usaría la Biblia para comprender, por ejemplo, la Cámara de los Comunes. Pero ciertas personas han intentado e intentan todavía usar los textos de esta manera simplista, por eso _Cándido_ y _Don Quijote_ siguen teniendo actualmente un gran atractivo para los lectores. Parece que un error frecuente es preferir la autoridad esquemática de un texto a los contactos humanos que entrañan el riesgo de resultar desconcertantes; este error ¿está constantemente presente o hay ciertas circunstancias que hacen prevalecer estas actitudes textuales más que otras?
Hay dos situaciones que favorecen la actitud textual. Una es la que se presenta cuando un ser humano entra en contacto con algo relativamente desconocido y amenazante que, hasta entonces, había estado lejos de él. En tal caso no solo recurre a las experiencias que ha tenido y que se pueden aproximar a esa novedad, sino también a lo que ha leído sobre el tema. Los libros y las guías de viajes son un tipo de textos de alguna manera «naturales», tan lógicos en su composición y en su utilización como cualquier otro libro, precisamente a causa de esta tendencia humana de recurrir a un texto cuando las incertidumbres de un viaje a un país extranjero parecen amenazar su tranquilidad. Muchos viajeros dicen que no han encontrado en determinado país lo que esperaban, y con esto quieren decir que ese país no era lo que cierto libro decía que sería. Y, por supuesto, muchos escritores de libros o guías de viajes componen este tipo de obras para decir que un país es así o que es pintoresco, caro, interesante, etc. En ambos casos la idea que subyace es que los hombres, los lugares y las experiencias se pueden describir siempre en un libro, de tal modo que el libro (o el texto) adquiere una autoridad y un uso mayor incluso que la realidad que describe. Lo que resulta cómico en Fabrizio del Dongo, cuando busca la batalla de Waterloo, no es que no llegue a encontrarla, sino que la busca como algo de lo que los textos le han contado muchas cosas.
La segunda circunstancia que favorece la actitud textual es su éxito aparente. Si alguien lee un libro que afirma que los leones son fieros y se encuentra con un león fiero (naturalmente, estoy simplificando), lo más probable es que se anime a leer más libros del mismo autor y los crea. Pero si, además, el libro del león le instruye sobre cómo tratar a un león fiero y las instrucciones funcionan perfectamente, entonces el autor no solo adquirirá una gran credibilidad, sino que se verá impulsado a escribir otras obras. Existe una compleja dialéctica de reforzamiento por la cual las experiencias de los lectores con la realidad se determinan según lo que han leído, y esto a su vez influye en que los escritores traten temas definidos previamente por las experiencias de los lectores. Un libro que explique cómo manejar a un fiero león puede, así, dar lugar a una serie de libros que traten de temas tales como la fiereza de los leones, los orígenes de la fiereza, etc. De modo similar, a medida que el centro de atención del texto se va concretando más —ya no son los leones, sino su fiereza— podremos esperar que los modos recomendados para manejar la fiereza de un león, de hecho, _incrementarán_ su fiereza y le forzarán a ser fiero, ya que eso es lo que es, y ya que eso es lo que, en esencia, sabemos nosotros o _solo_ podemos saber sobre él.
Un texto que pretenda incluir conocimientos sobre la realidad y que surja de circunstancias similares a las que acabo de describir no es fácil de desechar pues se valora por su competencia. La autoridad de los eruditos, de las instituciones y de los gobiernos puede añadírsele y rodearlo con una aureola de prestigio todavía mayor que su garantía de éxito práctico; y, lo que es más grave, este género de textos puede _crear_ no solo un conocimiento, sino también la realidad que parece describir. Con el tiempo, este conocimiento y esta realidad dan lugar a una tradición, o a lo que Michel Foucault llama un discurso; la presencia y el peso específico de esta tradición, más que la originalidad de su autor, son realmente los responsables de los textos producidos a partir de ella. Los textos de este tipo se componen de esas unidades de información preexistentes que Flaubert depositó en el catálogo de _idées reçues_.
Consideremos ahora, según todo esto, a Napoleón y a Ferdinand de Lesseps. Todo lo que más o menos sabían sobre Oriente procedía de los libros que se habían escrito dentro de la tradición del orientalismo y que estaban situados en la biblioteca orientalista de las _idées reçues_. Para ellos, Oriente, como el fiero león, era algo que encontrar y con lo que tratar, _porque_ hasta cierto punto los textos hacían que ese Oriente fuera posible. Era un Oriente silencioso, que estaba a disposición de Europa, para que Europa realizara allí proyectos que implicaban a los nativos, aunque ellos nunca fueran responsables directos, y era un Oriente incapaz de resistirse a los proyectos, las imágenes y las descripciones inventadas para él. En la primera parte he considerado que esta relación entre los escritos occidentales (con sus consecuencias) y el mutismo oriental es el resultado y la muestra de la gran fuerza cultural occidental, y de su voluntad de poder sobre Oriente. Pero esta fuerza tiene otro aspecto, un aspecto cuya existencia depende de las presiones que la tradición orientalista y su actitud textual ejercían sobre Oriente, un aspecto que vive su propia vida al igual que la vivirán los libros sobre los fieros leones hasta que los leones puedan hablar. Pocas veces se ha considerado a Napoleón y a Ferdinand de Lesseps —por citar a dos personas de entre las muchas que hicieron proyectos para Oriente— desde una perspectiva que los muestre actuando en el silencio continuo y en la indeterminación de Oriente, porque precisamente el discurso orientalista, además de la impotencia de Oriente para hacer algo a propósito de ellos, llenó su actividad de sentido, de inteligibilidad y de realidad. El discurso orientalista y lo que lo hizo posible —en el caso de Napoleón, el hecho de tener una potencia militar mucho mayor que la de Oriente— les proporcionaron unos orientales que podían ser descritos en obras como la _Description de l'Égypte_ y un Oriente que podía ser horadado, como hizo Ferdinand de Lesseps en Suez. Además, el orientalismo les ofreció el éxito, al menos desde su punto de vista que no tiene nada que ver con el de los orientales.
Una vez que empezamos a pensar en el orientalismo como en una especie de proyección de Occidente sobre Oriente y de voluntad de gobernarlo, nos encontramos con algunas sorpresas. Porque si es cierto que historiadores como Michelet, Ranke, Tocqueville y Burckhardt manejan sus narraciones «como si fueran una historia de una clase particular», lo mismo se puede decir de los orientalistas que conspiraron contra la historia, el carácter y el destino orientales durante cientos de años. Durante los siglos XIX y XX el número de orientalistas empezó a aumentar porque, por entonces, el territorio de la geografía imaginaria y real había disminuido, porque los contactos entre orientales y europeos eran determinados por la imparable expansión europea en busca de mercados, recursos y colonias y, finalmente, porque el orientalismo había llevado a cabo su propia metamorfosis dejando de ser un discurso erudito, para convertirse en una institución imperial. La prueba de esta metamorfosis aparece ya en lo que he dicho sobre Napoleón, Lesseps, Balfour y Cromer. Sus proyectos sobre Oriente solo pueden ser concebidos como los esfuerzos de visionarios, genios y héroes, en el sentido de Carlyle, desde un punto de vista muy rudimentario. En realidad, Napoleón, Ferdinand de Lesseps, Cromer y Balfour son mucho más _normales_ y mucho menos excepcionales, si recordamos los esquemas de D'Herbelot y de Dante y si les añadimos una máquina modernizada y eficaz (como el imperio europeo de mediados del siglo XIX) y un giro positivo: ya que no se puede eliminar Oriente ontológicamente (como quizá hicieron D'Herbelot y Dante), se tienen los medios para capturarlo, tratarlo, describirlo, mejorarlo y alterarlo radicalmente.
Lo que intento exponer aquí es que la transición desde una aprehensión, una formulación o una definición meramente textual de Oriente, hasta su puesta en práctica en Oriente se llevó a cabo, y que el orientalismo desempeñó una función importante en esta transición —si se me permite utilizar la palabra en sentido literal— _absurda_. En lo que se refiere a su trabajo estrictamente erudito (y creo que la idea de un trabajo estrictamente erudito, desinteresado y abstracto es difícil de entender, aunque sin embargo, la podemos admitir intelectualmente), el orientalismo tuvo muchos logros. Durante su época de esplendor, en el siglo XIX, produjo eruditos, incrementó el número de lenguas que se enseñaban en Occidente y la cantidad de manuscritos editados, traducidos y comentados; en muchos casos proporcionó a Oriente estudiantes europeos llenos de sensibilidad e interés real hacia temas como la gramática del sánscrito, la numismática fenicia y la poesía árabe. Sin embargo —y aquí debemos hablar con claridad—, el orientalismo dominó Oriente. Como sistema de pensamiento sobre Oriente siempre trascendió el detalle específicamente humano para pasar al detalle general «transhumano»; una observación sobre un poeta árabe del siglo X se extendía para convertirse en una política hacia (y acerca de) la mentalidad oriental en Egipto, Irak o Arabia. De igual modo, una aleya del Corán podía ser considerada la mejor muestra de la arraigada sensualidad musulmana. El orientalismo presuponía un Oriente inmutable, absolutamente diferente de Occidente (las razones de esto cambian de una época a otra). Y el orientalismo, en la forma que adoptó después del siglo XVIII, nunca pudo revisarse ni corregirse. Todo esto es la causa de que Cromer y Balfour, como observadores y administradores de Oriente, fueran inevitables.
La proximidad entre política y orientalismo o, dicho de modo más prudente, la enorme probabilidad de que las ideas que el orientalismo proporcionaba sobre Oriente pudieran utilizarse en la práctica política es una verdad importante pero extremadamente delicada. Plantea cuestiones sobre la predisposición hacia la inocencia o culpabilidad, hacia la indiferencia o la complicidad de los grupos de presión cuando se trata de campos como los estudios sobre los negros o las mujeres, provoca necesariamente inquietudes en las conciencias a propósito de las generalizaciones culturales, raciales o históricas, de sus usos, de su valor, de su grado de objetividad y de sus últimos propósitos. Sobre todo, las circunstancias políticas y culturales en las que el orientalismo occidental floreció llaman la atención por la posición rebajada de Oriente o del oriental como objeto de estudio. El Oriente orientalizado que ha definido Anuar Abdel Malek perfectamente, ¿pudo haber sido creado por alguna otra relación que no fuera la relación política amo-esclavo?
_a_ ) En el terreno del _planteamiento del problema y de la problemática_ [...] [el orientalismo] considera a Oriente y a los orientales como un «objeto» de estudio marcado con el sello de lo Otro —como todo lo que es diferente, bien sea «sujeto» u «objeto»— pero con un carácter de lo Otro constitutivo y esencialista [...], este «objeto» de estudio será, como es costumbre, pasivo, no participativo, dotado de una subjetividad «histórica» y, sobre todo, no activo, no autónomo y no soberano con respecto a sí mismo: el único Oriente u oriental o «sujeto» que podría ser, a lo sumo, admitido es el ser alienado filosóficamente, es decir, otro que él mismo en relación a sí mismo, poseído, comprendido, definido y tratado por otros.
_b_ ) En el terreno de la _temática_ [los orientalistas] adoptan una concepción esencialista de los países, naciones y pueblos del Oriente que estudian, una concepción que se expresa a través de una tipología étnica característica [...] y que desembocará en el racismo.
Según los orientalistas tradicionales existiría una esencia —a veces incluso descrita claramente en términos metafísicos— que constituiría el fondo inalienable y común de todos los seres considerados; esta esencia sería a la vez «histórica», ya que entronca con las profundidades de la historia, y fundamentalmente ahistórica, ya que congela al ser, «al objeto» de estudio dentro de su especificidad inalienable y no evolutiva en lugar de definirlo, como a todos los seres, estados, naciones, pueblos y culturas, como un producto, un resultado del vector de fuerzas que actúa en el campo de la evolución histórica.
Así se llega a una tipología —basada en una especificidad real, pero separada de la historia y, consecuentemente, concebida como algo intangible y esencial— que convierte al «objeto» estudiado en otro ser con respecto al cual el sujeto que estudia es trascendente; tendremos un _homo sinicus_ , un _homo arabicus_ (y por qué no un _homo_ _aegypticus_ , etc.), un _homo africanus_ y el hombre el «hombre normal», se entiende —será— el hombre europeo del período histórico, es decir, desde la antigüedad griega. Podemos observar hasta qué punto en los siglos XVIII y XIX a la hegemonía de las minorías poseedoras desvelado por Marx y Engels y al antropocentrismo desmantelado por Freud se les añade un eurocentrismo en el campo de las ciencias humanas y sociales, y más particularmente en el de aquellas en relación directa con los pueblos no europeos.
Abdel Malek considera que el orientalismo es un campo de estudio con una historia que, según el «oriental» de finales del siglo XX, le ha conducido a la parálisis antes descrita. Indiquemos brevemente las grandes líneas de esta historia según avanzaba el siglo XIX y «la hegemonía de las minorías poseedoras» y el antropocentrismo, aliados con el eurocentrismo, acumulaban peso y poder. Desde las últimas décadas del siglo XVIII y durante al menos un siglo y medio, Gran Bretaña y Francia dominaron la disciplina del orientalismo. Los grandes descubrimientos filológicos hechos en gramática comparada por Jones, Franz Bopp, Jakob Grimm y otros se debieron a unos manuscritos llevados de Oriente a París y Londres. Casi sin excepción, todo orientalista comenzó su carrera como filólogo, y la revolución en la filología que produjeron los estudios de Bopp, Sacy, Burnouf y sus discípulos creó una ciencia comparada basada en la hipótesis de que las lenguas pertenecen a familias, entre las cuales la indoeuropea y la semítica destacan como dos ejemplos importantes. Por tanto, desde sus comienzos el orientalismo presentó dos características: primero, una conciencia científica de reciente invención basada en la importancia lingüística de Oriente para Europa y segundo, una propensión a dividir, subdividir y volver a dividir sus temas sin cambiar nunca de opinión sobre Oriente, que siempre era el mismo objeto invariable, uniforme y radicalmente específico.
Friedrich Schlegel, que aprendió sánscrito en París, ilustra estas dos características. Aunque en el momento en que publicó su _Über die Sprache und Weisheit der Indier_ en 1808, Schlegel había renunciado prácticamente al orientalismo, todavía mantenía que el sánscrito y el persa por un lado y el griego y el alemán por otro tenían más afinidades entre sí que con las lenguas semíticas, chinas, americanas o africanas; además, la familia indoeuropea, desde un punto de vista estético, era simple y satisfactoria, características que no tenía la semítica. Este tipo de abstracciones no generó problemas para Schlegel, quien a lo largo de su vida estuvo fascinado por las naciones, las razas, las mentalidades y los pueblos como temas de los cuales se podía hablar con pasión (dentro de la perspectiva estrecha de miras del populismo esbozado por Herder). Pero Schlegel no habló nunca del Oriente vivo y contemporáneo. Cuando dijo en 1800: «En Oriente es donde debemos buscar el romanticismo más elevado», se refería al Oriente de Sakuntala, del _Zend Avesta_ y de los _Upanisads_. En cuanto a los semitas, como su lengua era aglutinante, no estética y mecánica, eran diferentes, inferiores y retrasados. Las conferencias de Schlegel sobre lengua, vida, historia y literatura están llenas de estas discriminaciones que hizo sin la menor restricción. El hebreo, dijo, fue creado para servir de vehículo a la expresión profética y a la adivinación; los musulmanes, sin embargo, se han adherido a un «teísmo muerto y vacío, a una fe unitaria puramente negativa».
En gran medida, el racismo contenido en las críticas de Schlegel sobre los semitas y los demás orientales «inferiores» fue muy corriente en la cultura europea. Pero nunca, excepto quizá más tarde en el siglo XIX entre los antropólogos darwinistas y los frenólogos, había sido la base de una materia científica como fue el caso de la lingüística comparada o la filología. La lengua y la raza parecían intrínsecamente aliadas, y el «buen» Oriente se situaba invariablemente en un período clásico, en algún lugar de la India de hacía tiempo, mientras que el «mal» Oriente se relegaba al Asia de hoy, a algunas partes del norte de África y al islam dondequiera que estuviera presente. Los «arios» estaban encerrados en Europa y en el Oriente antiguo, como ha demostrado Léon Poliakov (sin señalar, sin embargo, que los «semitas» no eran solo los judíos sino también los musulmanes); el mito ario dominó la antropología histórica y cultural a costa de los pueblos «inferiores».
Si quisiéramos hacer la genealogía intelectual oficial del orientalismo, esta comprendería ciertamente a Gobineau, Renan, Humboldt, Steinthal, Burnouf, Remusat, Palmer, Weil, Dozy y Muir por mencionar solo unos pocos nombres célebres del siglo XIX. También habría que incluir la capacidad de difusión de sociedades culturales como la Société Asiatique, fundada en 1822, la Royal Asiatic Society, fundada en 1823, The American Oriental Society, fundada en 1842, etc. Pero quizá tenderíamos a ignorar la importante contribución de las obras de ficción y de los libros de viajes, que reforzaron las divisiones establecidas por los orientalistas entre los diferentes contextos geográficos, temporales y raciales de Oriente. Esto sería un error ya que, en lo que respecta al Oriente islámico, esta literatura es especialmente rica y contribuye de manera significativa a la formación del discurso orientalista; comprende obras de Goethe, Hugo, Lamartine, Chateaubriand, Kinglake, Nerval, Flaubert, Lane, Burton, Scott, Byron, Vigny, Disraeli, George Eliot y Gautier. Más tarde, a finales del siglo XIX y principios del XX, podríamos añadir en la lista a Doughty, Barrès, Loti, T. E. Lawrence y Forster, escritores todos que contribuyeron a configurar de una manera más marcada el «gran misterio asiático» de Disraeli. Estas iniciativas fueron fomentadas considerablemente, no solo por la exhumación de las civilizaciones orientales muertas (por parte de los arqueólogos europeos) en Mesopotamia, Egipto, Siria y Turquía, sino también por las inspecciones geográficas hechas a lo largo de todo Oriente.
La ocupación europea de todo Oriente Próximo (con la excepción de partes del Imperio otomano, que fueron ocupadas después de 1918) supuso, a finales del siglo XIX, una ayuda para estas realizaciones. Las principales potencias coloniales fueron de nuevo Gran Bretaña y Francia, aunque Rusia y Alemania desempeñaron también un papel de cierta importancia. Colonizar significaba primero reconocer —en realidad crear— intereses; estos podían ser comerciales, concernientes a las comunicaciones, religiosos, militares o culturales. Por lo que se refiere al islam y a los territorios islámicos, Gran Bretaña, por ejemplo, como potencia cristiana, estimaba que tenía intereses legítimos que preservar. Se desarrolló un complejo aparato destinado a atender estos intereses. Las antiguas organizaciones, como la Society for Promoting Christian Knowledge (1698) y la Society for the Propagation of the Gospel in Foreign Parts (1701) vieron cómo su obra se continuaba y más tarde era fomentada por la Baptist Missionary Society (1792), la Church Missionary Society (1799), la British and Foreign Bible Society (1804) y la London Society for Promoting Christianity Among the Jews (1808). Estas misiones «se adhirieron abiertamente a la expansión de Europa». Añadamos a todo esto sociedades comerciales, sociedades eruditas, fundaciones para la exploración geográfica, fundaciones para realizar traducciones, la implantación en Oriente de escuelas, misiones, oficinas consulares, fábricas y a veces importantes comunidades europeas, y la noción de «interés» adquirirá un gran sentido. Después, estos intereses serán defendidos con mucho celo y costo.
Hasta aquí he trazado un esquema a grandes rasgos. Pero ¿qué ocurre con las experiencias y las emociones típicas que acompañan tanto a los avances eruditos del orientalismo como a las conquistas políticas realizadas con su ayuda? Primero hay una decepción ante la evidencia de que el Oriente moderno no es en absoluto como el de los textos. Gérard de Nerval escribe a Théophile Gautier a finales de agosto de 1843 lo siguiente:
Ya he perdido un reino tras otro, una provincia tras otra, la mitad más bonita del universo, y pronto no conoceré ningún lugar en el que poder refugiar mis sueños, pero es Egipto lo que más siento haber excluido de mi imaginación y haber alojado tristemente en la memoria.
Esto es lo que escribe el autor de un gran _Voyage en Orient_. El lamento de Nerval es un tópico del romanticismo (el sueño traicionado que describió Albert Béguin en _L'Âme romantique et le rêve_ )* y de los que viajaban al Oriente bíblico desde Chateaubriand a Mark Twain. Cualquier experiencia directa que se tenía con el Oriente real conllevaba comentarios irónicos sobre sus valorizaciones; comentarios que se pueden encontrar en el «Mahometsgesang» de Goethe o en el «Adieux de l'hôtesse arabe» de Hugo. El recuerdo del Oriente moderno entra en conflicto con la imaginación, hace que se vuelva a la imaginación, que es un lugar más propicio para la sensibilidad europea que el Oriente real. Para una persona que nunca ha visto Oriente, dijo Nerval una vez a Gautier, un loto siempre será un loto, para mí es solo una especie de cebolla. Escribir sobre el Oriente moderno es revelar una inquietante desmitificación de las imágenes recogidas en los textos o encerrarse en el Oriente del que Hugo habló en su prefacio a _Les Orientales_ ; Oriente como una _image_ o un _pensée_ , símbolos de _«une sorte de préoccupation générale»_.
Si el desencanto personal y la preocupación general encarnan bastante bien la sensibilidad orientalista, también conllevan otros hábitos de pensamiento, sentimiento y percepción más familiares. La mente aprende a distinguir entre una aprehensión general de Oriente y una experiencia específica de él, cada una va por su lado, por decirlo de algún modo. En la novela de Scott, _The Talisman_ * (1825), sir Kenneth (del Leopardo Rampante) lucha en algún lugar del desierto palestino contra un solo sarraceno y quedan en tablas; a medida que el cruzado y su oponente, que es Saladino disfrazado, se enzarzan en una conversación, el cristiano va descubriendo que, después de todo, su antagonista musulmán no es un tipo tan malo. Pero subraya:
Yo pensaba [...] que vuestra cegada raza descendía del temible demonio, sin cuya ayuda nunca hubierais sido capaces de mantener esa tierra bendita de Palestina contra tantos valientes soldados de Dios. Hablo así no de ti en particular, sarraceno, sino de tu gente y de tu religión en general. Lo que me parece extraño, sin embargo, no es que descendáis del espíritu del Diablo, sino que os enorgullezcáis de ello.
En efecto, los sarracenos se jactan de remontar su linaje a Eblis, el Lucifer musulmán. Pero lo que es verdaderamente curioso no es el débil historicismo por medio del que Scott hace que la escena sea «medieval», dejando que los cristianos ataquen teológicamente a los musulmanes de una manera que los europeos del siglo XIX no compartirían, sino más bien la condescendencia desenvuelta con la que condena a un pueblo entero «en general», mientras mitiga la ofensa con un frío «no me refiero a ti en particular».
Scott, sin embargo, no era un especialista en el islam (aunque H. A. R. Gibb, que sí lo era, elogiara la perspectiva penetrante que sobre el islam y sobre la personalidad de Saladino expone en _El talismán_ ) y se tomaba enormes libertades con el papel de Eblis, convirtiéndolo en un héroe para los creyentes. Los conocimientos de Scott probablemente procedían de Byron y de Beckford, pero lo que nos interesa destacar es que el carácter general atribuido a las realidades orientales podía mantenerse a pesar de la fuerza retórica y existencial de las excepciones evidentes. Es como si, por un lado, existiese un baúl llamado «oriental» en el que se metían sin reflexionar todas las actitudes autoritarias, anónimas y tradicionales de los occidentales hacia los orientales, mientras que, sin embargo, por otro lado y siguiendo la tradición anecdótica de los narradores de cuentos, era posible relatar lo que se había experimentado en Oriente, experiencias que tenían poco que ver con el baúl de utilidad general. La propia estructura de la prosa de Scott muestra estos dos puntos de vista muy entrelazados, ya que la categoría general le asigna por adelantado al ejemplo específico el terreno limitado sobre el que se actúa: aunque la excepción específica sea muy profunda y aunque un oriental individual pueda escapar a las barreras que se han colocado a su alrededor, él es _primero_ un oriental, _segundo_ un ser humano y _por último_ , de nuevo, un oriental.
Una categoría tan general como la de «oriental» es susceptible de bastantes variaciones interesantes. El entusiasmo de Disraeli por Oriente apareció primero durante un viaje que realizó en 1831. En El Cairo escribió: «Sin embargo mis ojos y mi mente sufren con una grandeza tan pequeña en armonía con nuestra propia apariencia». La grandeza y la pasión generales inspiraban un sentido trascendente de las cosas y muy poca paciencia ante la realidad verdadera. Su novela _Tancred_ está llena de tópicos raciales y geográficos; todo es cuestión de raza, declara Sidonia, de tal forma que la salvación solo se puede encontrar en Oriente, entre sus razas. Allí, en el ejemplo que nos ocupa, los drusos, los cristianos, los musulmanes y los judíos se codean sin dificultad porque —alguien dice con humor— los árabes son simplemente judíos a caballo y todos, en el fondo de su corazón, son orientales. La armonía se establece entre categorías generales, pero no entre las categorías y su contenido. Un oriental vive en Oriente, vive una vida de holgura oriental, en un estado de despotismo y sensualidad orientales, imbuido en un sentimiento de fatalismo oriental. Escritores tan diferentes como Marx, Disraeli, Burton y Nerval podían mantener entre ellos una larga conversación utilizando, por decirlo de algún modo, todas estas generalizaciones sin necesidad de hacerse preguntas y sabiendo que todo era perfectamente comprensible para todos.
A este desencanto y a esta idea general —por no decir esquizofrénica— de Oriente, con frecuencia se le añade otra peculiaridad. Como se convierte en un objeto general, Oriente puede servir para ilustrar una forma particular de excentricidad. Aunque el individuo oriental no pueda trastornar o alterar las categorías generales que dan sentido a su extravagancia, esta, sin embargo, puede ser apreciada por sí misma. Aquí, por ejemplo, Flaubert describe el espectáculo de Oriente:
Para divertir a la muchedumbre, un día el bufón de Mohammed Ali cogió a una mujer en un bazar de El Cairo, la puso encima del mostrador de la tienda y copuló con ella públicamente, mientras el tendero seguía fumándose tranquilamente una pipa.
En la carretera desde El Cairo a Shubra, hace algún tiempo, un joven se hacía sodomizar públicamente por un gran mono, como en la historia anterior, para dar una buena opinión de sí mismo y hacer reír a la gente.
Hace poco tiempo murió un morabito. Era un idiota que había pasado durante mucho tiempo por un santo iluminado por Dios; todas las mujeres musulmanas iban a verle y a masturbarle y, al final, murió de agotamiento, ya que desde la mañana a la noche aquello era un meneo continuo.
_Quid dicis_ del siguiente hecho: hace algún tiempo un _santón_ (un cura asceta) solía caminar por las calles de El Cairo totalmente desnudo, excepto una gorra que llevaba en la cabeza y otra en la verga. Para mear se quitaba la gorra de la verga y las mujeres estériles que querían tener niños corrían, se situaban debajo de la parábola de orina y se frotaban con el líquido.
Flaubert reconoce con franqueza que todo esto es especialmente grotesco. «Todos los viejos temas cómicos» —con lo que Flaubert se refería a «el esclavo apaleado [...], el grosero traficante de mujeres [...], el mercader ratero»— adquieren un nuevo significado «fresco [...], verdadero y encantador» en Oriente. Estos significados no se pueden reproducir, solamente se pueden disfrutar sobre el terreno y «relatar» de manera aproximada. Oriente es _observado_ , ya que su comportamiento casi agresivo (aunque nunca demasiado) proviene de una reserva de excentricidad infinita; el europeo cuya sensibilidad visita Oriente es un observador que nunca se implica, permanece distante, siempre dispuesto a recibir nuevos ejemplos de lo que la _Description de l'Égypte_ llamó _«bizarres jouissances»_. Oriente se vuelve un cuadro vivo de singularidad.
Este cuadro se convierte de una manera bastante lógica en un tema particular en los textos. De ese modo se cierra el círculo expuesto al principio; Oriente es algo para lo que los textos no preparan, regresa para ser algo sobre lo que se escribe de manera disciplinada. Se puede traducir su extrañeza, descifrar sus significados, domesticar su hostilidad, pero la _generalidad_ asignada a Oriente, el desencanto que se siente tras haberlo visitado, la excentricidad sin solución que exhibe, todo queda redistribuido en lo que se dice o se escribe sobre él. El islam, por ejemplo, era típicamente oriental para los orientalistas de finales del siglo XIX y principios del XX. Carl Becker argumentaba que, a pesar de que el «islam» (nótese la gran generalización) heredó la tradición helénica, no pudo abarcar ni utilizar la tradición humanística griega; además, para comprender el islam era necesario, sobre todo, considerarlo más que como una religión «original», como una tentativa oriental frustrada de aplicar la filosofía griega sin la inspiración creativa que encontramos en el Renacimiento europeo. Para Louis Massignon, quizá el orientalista francés más conocido e influyente, el islam era la negación sistemática de la encarnación cristiana y su mayor héroe no era Mahoma ni Averroes sino al-Hallay, un santo musulmán que fue crucificado por los musulmanes ortodoxos por haberse atrevido a personificar el islam. Lo que Becker y Massignon explícitamente apartaron de su estudio fue la excentricidad de Oriente que de algún modo reconocieron indirectamente al hacer grandes esfuerzos por regularla en lenguaje occidental. Mahoma fue expulsado, pero al-Hallay fue una figura de primera fila porque se consideró a sí mismo una representación de Cristo.
Como jueces de Oriente, los orientalistas modernos no adoptan la posición objetiva que creen e incluso dicen adoptar. Su distanciamiento humano, cuyo máximo distintivo es una falta de solidaridad encubierta por los conocimientos profesionales, se ve acompañado del peso de todas las actitudes, las perspectivas y los humores ortodoxos del orientalismo que he descrito. Su Oriente no es Oriente tal y como es, es Oriente tal y como ha sido orientalizado. Un arco ininterrumpido de conocimiento y poder conecta a los hombres de Estado europeos u occidentales con los orientalistas occidentales y conforma el perfil del escenario que contiene a Oriente. Al final de la Primera Guerra Mundial, África y Oriente constituían para Occidente no ya un espectáculo intelectual, sino un terreno privilegiado. El ámbito del orientalismo coincidía exactamente con el del imperio y fue esta unanimidad absoluta entre los dos la que provocó la única crisis en la historia del pensamiento occidental referente a Oriente. Y esta crisis todavía continúa.
A partir de los años veinte, desde un extremo a otro del Tercer Mundo, la reacción al imperio y al imperialismo ha sido dialéctica. En la época de la Conferencia de Bandung en 1955, Oriente entero había conseguido la independencia política de los imperios occidentales y se enfrentaba a una nueva configuración de las potencias imperiales, Estados Unidos y la Unión Soviética. Incapaz de reconocer a «su» Oriente en el nuevo Tercer Mundo, el orientalista entonces hace frente a un Oriente desafiante y políticamente armado ante el cual tiene dos posibilidades. Una, seguir como si nada hubiera pasado y la otra, adaptar los modos antiguos a la nueva situación. Pero para el orientalista que cree que Oriente nunca cambia, lo nuevo es simplemente lo viejo traicionado por los nuevos «des-orientales» (si nos podemos permitir el neologismo) que lo interpretan incorrectamente. Una tercera posibilidad revisionista que consistiría en prescindir del orientalismo solo es tenida en consideración por una pequeña minoría.
Una muestra de esta crisis, según Abdel Malek, no fue simplemente que «los movimientos de liberación nacional en el Oriente ex colonial» hicieron estragos en las concepciones orientalistas de «las razas sometidas», pasivas y fatalistas; sino también el hecho de que «los especialistas y el público en general tomaron conciencia del desfase existente no solo entre la ciencia orientalista y el material que se estudiaba, sino también —y esto debía ser determinante— entre las concepciones, los métodos y los instrumentos de trabajo de las ciencias humanas y sociales y los del orientalismo». Los orientalistas —desde Renan a Goldziher, Macdonald, Von Grunebaum, Gibb y Bernard Lewis— concebían el islam, por ejemplo, como una «síntesis cultural» (según lo expresó P. M. Holt) que podía estudiarse independientemente de la economía, la sociología y la política de los pueblos islámicos. Para el orientalismo, el islam tenía un significado que se podía encontrar, si se buscaba la formulación más simple, en el primer tratado de Renan: para comprenderlo mejor, había que reducir el islam a la «tienda y la tribu». El impacto del colonialismo, de las circunstancias mundiales y de la evolución histórica significó para los orientalistas lo mismo que las moscas para los niños traviesos, que las matan —o las desdeñan— para divertirse; es decir, nunca fue tomado lo suficientemente en serio como para complicar al islam esencial.
La propia carrera de H. A. R. Gibb es un ejemplo de las dos aproximaciones posibles con las que el orientalismo ha respondido al Oriente moderno. En 1945, Gibb pronunció en la Universidad de Chicago las Haskell Lectures. El mundo que analizaba no era el mismo que Balfour y Cromer habían conocido antes de la Primera Guerra Mundial. Bastantes revoluciones, dos guerras mundiales, numerosos cambios económicos, políticos y sociales habían convertido la realidad de 1945 en un objeto nuevo, de una novedad indiscutible e incluso catastrófica. Sin embargo, vemos que Gibb abre las conferencias que él llamó _Modern Trends in Islam_ del siguiente modo:
El estudioso de la civilización árabe se detiene ante el contraste sorprendente entre la fuerza imaginativa que presentan, por ejemplo, ciertas ramas de la literatura árabe y la literalidad y la pedantería que manifiestan el razonamiento y en la explicación, incluso cuando se aplican a esas mismas producciones. Es verdad que ha habido grandes filósofos en los pueblos musulmanes y que muchos de ellos eran árabes, pero fueron raras excepciones. La mente árabe, bien sea en relación al mundo exterior o en relación a los procesos de pensamiento, no puede deshacerse del profundo sentimiento de que los sucesos concretos están separados y son individuales. Creo que este es uno de los principales factores que hay detrás de la «ausencia de sentido de la ley» que el profesor Macdonald vio como una diferencia característica del oriental.
Esto es también lo que explica —y que es tan difícil de entender para el estudioso occidental [hasta que se le explica a través del orientalismo]— la aversión que tienen los musulmanes a los procesos intelectuales de racionalismo [...]. La negación de los modos de pensamiento racionalistas y de la ética utilitaria que es inseparable de ellos tiene sus raíces, por tanto, no en lo que se llama el «oscurantismo» de los teólogos musulmanes, sino en el atomismo y la discontinuidad de la imaginación árabe.
Henos aquí ante un orientalismo puro; pero incluso si se reconoce el extraordinario conocimiento del islam institucional que caracteriza el resto del libro, los prejuicios iniciales de Gibb siguen siendo un obstáculo formidable para alguien que espera comprender el islam moderno. ¿Qué significa «diferencia» cuando la preposición «de» ha desaparecido totalmente? ¿No se nos pide de nuevo que inspeccionemos al musulmán oriental como si su mundo, «a diferencia del nuestro», nunca hubiera superado el siglo VII? En cuanto al propio islam moderno, a pesar de que lo conoce de manera compleja y magistral, ¿por qué Gibb lo debe considerar con esa hostilidad implacable? Si, de entrada, el islam es defectuoso por sus imperfecciones permanentes, el orientalista se opondrá a cualquier intento islámico de reformar el islam porque, de acuerdo a sus puntos de vista, la reforma es una traición al islam: esta es exactamente la tesis de Gibb. ¿Cómo puede un oriental librarse de estas cadenas en el mundo moderno si no es repitiendo las palabras del Tonto de _El rey Lear_ : «Me quieren azotar por decir la verdad, tú quieres azotarme si miento, y a veces soy azotado por guardar silencio»?
Dieciocho años después, Gibb se dirigió a sus compatriotas ingleses; entonces hablaba como director del Center for Middle Eastern Studies de Harvard. El tema de su conferencia era «Area Studies Reconsidered»; entre otros _aperçus_ afirmó que «Oriente es demasiado importante como para dejarlo en manos de los orientalistas». Esto suponía el anuncio de la nueva o segunda aproximación orientalista, así como _Modern Trends_ había sido un ejemplo de la primera, la tradicional. La fórmula de Gibb en «Area Studies Reconsidered» tenía buenas intenciones, al menos en lo que se refería a los especialistas occidentales cuyo trabajo consistía en preparar a los estudiantes para las carreras de «la vida pública y los negocios». Lo que ahora necesitamos, dijo Gibb, es que trabajen juntos el orientalista tradicional y un buen especialista en ciencias humanas: entre los dos harán un trabajo «interdisciplinario». Pero el orientalista tradicional no aportará un conocimiento anticuado de Oriente, no: sus conocimientos de especialista le servirán para recordar a sus colegas no iniciados en los estudios de «áreas culturales» que «aplicar la psicología y los mecanismos de las instituciones políticas occidentales a situaciones asiáticas y a situaciones árabes es puro Walt Disney».
En la práctica, esta noción significa que cuando los orientales combaten la ocupación colonial, usted debe afirmar (para no arriesgarse a decir un «disneyismo») que los orientales nunca han entendido el significado del autogobierno de la manera en la que «nosotros» lo hacemos. Cuando algunos orientales se oponen a la discriminación racial, mientras otros la practican, usted dirá «en el fondo son orientales» y los intereses de clase, las circunstancias políticas y los factores económicos son totalmente irrelevantes. O con Bernard Lewis, usted podrá decir que cuando los palestinos árabes se oponen al asentamiento y a la ocupación de sus tierras por parte de los israelíes, eso no es más que el «retorno del islam» o, como escribe un conocido orientalista contemporáneo, la oposición islámica a los pueblos no islámicos, un principio del islam que se remonta al siglo VII. La historia, la política y la economía no importan. El islam es el islam, Oriente es Oriente y por favor remita todas sus ideas sobre la izquierda o la derecha, las revoluciones y los cambios a Disneylandia.
Si estas tautologías, afirmaciones y rechazos solo les son familiares a los historiadores, sociólogos, economistas y humanistas del campo del orientalismo y no a los de otros, la razón es del todo obvia, ya que, al igual que su tema supuesto, el orientalismo no ha permitido que las ideas violaran su profunda serenidad. Pero los orientalistas modernos —o los expertos en áreas culturales, para darles su nuevo nombre— no se han recluido en los departamentos de lenguas; por el contrario, han sacado provecho de los consejos de Gibb y la mayoría de ellos hoy no se distinguen de otros «especialistas» y «asesores» de lo que Harold Lasswell ha llamado las ciencias políticas. Así, se han reconocido rápidamente las posibilidades militares y de seguridad nacional que ofrece la alianza entre un especialista en «análisis del carácter nacional» y un experto en instituciones islámicas por razones de conveniencia, si no es por otras razones. Después de todo, «Occidente» desde la Segunda Guerra Mundial se ha encontrado ante un enemigo totalitario y astuto que ha encontrado aliados entre las crédulas naciones orientales (africanas, asiáticas y subdesarrolladas). ¿Qué mejor manera de burlar a ese enemigo que jugando con la mente ilógica del oriental de una manera que solo el orientalista puede concebir? Así, se crearon unas tácticas magistrales, como la técnica del palo y la zanahoria, la Alianza para el Progreso, la OTASE,* etc., todas fundamentadas en el «conocimiento» tradicional, tratado de una forma que permitiera manipular mejor su supuesto objetivo.
Así, mientras una confusión revolucionaria agita el Oriente islámico, los sociólogos nos recuerdan que los árabes se entregan a las «funciones orales», y los economistas —orientalistas reciclados— señalan que ni el capitalismo ni el socialismo son etiquetas adecuadas para el islam moderno. Mientras el anticolonialismo se extiende y, de hecho, unifica todo el mundo oriental, el orientalista condena todo esto no solo porque es algo nocivo, sino porque es un insulto para las democracias occidentales. Mientras que el mundo se enfrenta a graves problemas de gran importancia general, entre ellos el peligro nuclear, la catastrófica escasez de recursos y la exigencia sin precedentes de igualdad, justicia y equidad económica entre los hombres, los políticos explotan unas caricaturas de Oriente cuya fuente ideológica no es solo la tecnócrata medianamente instruida, sino también la orientalista muy instruida. Los arabistas legendarios del Departamento de Estado previenen contra los planes árabes de apoderarse del mundo. Los pérfidos chinos, los indios semidesnudos y los musulmanes pasivos son descritos como buitres que se alimentan de «nuestra» generosidad y cuando «los perdemos» se ven condenados al comunismo o a sus instintos orientales persistentes: la diferencia apenas es significativa.
Estas actitudes orientalistas contemporáneas inundan la prensa y el espíritu popular. La imagen que se tiene de los árabes es la de camelleros, terroristas, gentes con nariz ganchuda o libertinos cuya inmerecida riqueza es una afrenta para la verdadera civilización. Se supone, siempre de manera oculta, que aunque el consumidor occidental pertenece a una minoría numérica, tiene el derecho de poseer o de gastar (o las dos cosas) la mayor parte de los recursos de la Tierra. ¿Por qué?, porque él, al contrario que el oriental, es un ser humano verdadero. Este es el mejor ejemplo que hoy puede ilustrar lo que Anuar Abdel Malek llama «la hegemonía de las minorías poseedoras» y el antropocentrismo, aliados con el eurocentrismo: un occidental blanco de clase media cree en su prerrogativa humana, no solo para manipular el mundo no blanco, sino también para poseerlo simplemente porque por definición «él» no es tan humano como «nosotros» lo somos. No existe ningún otro ejemplo tan puro como este de lo que es un pensamiento deshumanizado.
En cierto sentido, las limitaciones del orientalismo son, como he dicho antes, las que se derivan de reconocer, reducir a la esencia y despojar de humanidad a otra cultura, a otro pueblo y a otra región geográfica. Pero el orientalismo dio un paso más: consideró que Oriente era algo cuya existencia no solo se mostraba a Occidente, sino que también se fijaba para él en el tiempo y en el espacio. Los éxitos descriptivos y textuales del orientalismo han sido tan impresionantes que algunos períodos enteros de la historia cultural, política y social de Oriente se han considerado meras reacciones a Occidente. Occidente es el agente, Oriente el paciente, Occidente es el espectador, el juez y el jurado de todas las facetas del comportamiento oriental. Pero si la historia del siglo XX ha provocado cambios intrínsecos en Oriente y para Oriente, el orientalismo se ha quedado estupefacto: ha sido incapaz de darse cuenta de que hasta cierto punto
los nuevos líderes, los nuevos intelectuales y los nuevos responsables políticos [orientales], han aprendido muchas lecciones del trabajo de sus predecesores. También les han ayudado las transformaciones estructurales e institucionales llevadas a cabo durante el período transcurrido y el hecho de que, en gran medida, tienen más confianza en sí mismos y quizá son algo más agresivos. Ya no tienen que actuar esperando obtener un veredicto favorable del jurado invisible de Occidente. No dialogan con Occidente, dialogan con sus compatriotas.
Además el orientalista asume que para lo que no le han preparado sus textos es para el resultado de una agitación externa en Oriente, o de la inanidad mal dirigida de este. Ninguno de los innumerables textos orientalistas que tratan sobre el islam, incluyendo su máximo exponente, _The Cambridge History of Islam_ , han sido capaces de preparar a sus lectores para lo que ha sucedido a partir de 1948 en Egipto, Palestina, Irak, Siria, Líbano o en Yemen antes de la unificación. Cuando los dogmas sobre el islam no pueden ni siquiera ser útiles para los doctores panglosianos* del orientalismo, se recurre a la jerga de las ciencias humanas orientalizadas, a unas abstracciones que se venden bien: elites, estabilidad política, modernización y desarrollo institucional; todas marcadas con el sello de la sabiduría orientalista. Mientras tanto, una grieta cada vez más grande y más peligrosa va separando Oriente de Occidente.
La crisis actual representa, de modo dramático, la disparidad entre los textos y la realidad. Pero en este estudio de orientalismo no quiero solo exponer las fuentes de las concepciones del orientalismo, sino también reflexionar sobre su importancia, ya que el intelectual de nuestros días estima con razón que dar la espalda a una parte del mundo que le interesa de un modo tan directo es evitar la realidad. Con demasiada frecuencia, los humanistas han concentrado su atención en temas de investigación compartimentados. Nunca han observado ni aprendido de disciplinas tales como el orientalismo, cuya ambición constante era controlar la _totalidad_ de un mundo y no una parte fácil de delimitar, como sería por ejemplo un autor o una colección de textos. Sin embargo, junto a estos compartimientos académicos de seguridad como son los de la «historia», la «literatura» o las «humanidades» y a pesar de sus aspiraciones desbordantes, el orientalismo está comprometido con las circunstancias mundiales e históricas que ha tratado de disimular tras un conformismo a menudo pomposo y tras las llamadas al racionalismo. El intelectual contemporáneo puede aprender del orientalismo, por un lado, a limitar o ampliar de una manera realista la extensión de las pretensiones de su disciplina y, por otro, a ver el fundamento humano (lo que Yeats llamó la trapería infecta del corazón) en el que los textos, los puntos de vista, los métodos y las disciplinas nacen, crecen, se desarrollan y degeneran. Estudiar el orientalismo es también proponer maneras intelectuales de tratar los problemas metodológicos que la historia ha ido planteando con respecto al tema de Oriente. Pero antes, debemos ver cuáles son los valores humanísticos que el orientalismo, por su extensión, sus experiencias y sus estructuras, ha llegado casi a eliminar.
# SEGUNDA PARTE
### Estructuras y reestructuras del orientalismo
Cuando el Sayyid 'Omar, el Nakib el Ashraf (o jefe de los descendientes del profeta) casó a una de sus hijas, hace unos cuarenta y cinco años, delante de la procesión caminaba un hombre joven que se había hecho una incisión en el abdomen y se había sacado gran parte de los intestinos, los cuales llevaba delante sobre una bandeja de plata. Después de que la procesión concluyera, los devolvió a su lugar y permaneció en la cama durante muchos días antes de recobrarse de los efectos de este acto absurdo y repugnante.
EDWARD WILLIAM LANE,
_An Account of the Manners and Customs of the Modern Egyptians_
[...] en el caso de caída de este imperio, sea por una revolución en Constantinopla, sea por desmembramiento progresivo, las potencias tomarán cada una, a título de protectorado, la parte del imperio que les sea asignada por las estipulaciones del congreso; que estos protectorados, definidos y limitados territorialmente según vecinajes, seguridad de las fronteras, analogía de religiones, costumbres e intereses [...] no aceptarán otra soberanía que la de las potencias. Esta especie de soberanía así definida y consagrada como derecho europeo consistirá principalmente en el derecho de ocupar determinada parte del territorio o de la costa para fundar en ellos, o bien ciudades libres o bien emporios comerciales. Cada potencia ejercerá sobre su territorio no solo una tutela armada y civilizadora; también garantizará su existencia y sus signos de identidad, bajo la bandera de una nacionalidad más fuerte [...]
ALPHONSE DE LAMARTINE,
_Voyage en Orient_
### I
### Fronteras trazadas de nuevo, temas redefinidos,
### religión secularizada
Gustave Flaubert murió en 1880 sin haber concluido _Bouvard et Pécuchet_ ,* su novela enciclopédica cómica sobre la degeneración del conocimiento y la inanidad del esfuerzo humano. Sin embargo, las líneas esenciales de su proyecto son nítidas y están claramente apoyadas por los abundantes detalles de la novela. Los dos protagonistas pertenecen a la burguesía y cuando uno de ellos recibe una inesperada herencia, deciden abandonar la ciudad y retirarse a vivir al campo, donde harán lo que les plazca ( _«nous ferons tout ce que nous plaira!»_ ). Según Flaubert retrata sus experiencias, hacer lo que les place conduce a Bouvard y a Pécuchet a realizar un recorrido teórico y práctico por la agricultura, la historia, la química, la educación, la arqueología y la literatura, siempre con resultados menos brillantes de los esperados. Recorren diversos campos del conocimiento como viajeros en el tiempo y en el saber, experimentando las desilusiones, desastres y decepciones que esperan a los aficionados mediocres. Lo que en realidad atraviesan es toda la experiencia de desilusión del siglo XIX, a través de la cual —según dijo Charles Morazé— _«les bourgeois conquerants»_ se convierten en víctimas de su propia incompetencia y mediocridad. Cualquier entusiasmo se transforma en una fórmula aburrida y cualquier disciplina o tipo de conocimiento pasa de la esperanza y del poder al desorden, la ruina y la tristeza.
Entre los borradores escritos por Flaubert para la conclusión de este panorama de desesperación, hay dos elementos de especial interés para nosotros. Los dos hombres discuten sobre el futuro de la especie humana. Pécuchet ve «el futuro de la humanidad oscuro», mientras que Bouvard lo ve «¡brillante!»:
El hombre moderno está en continuo progreso. Europa será regenerada por Asia. Siendo ley histórica que la civilización vaya de Oriente a Occidente [...] las dos formas de humanidad finalmente se fundirán en una sola.
Este eco obvio de Quinet representa el inicio de otro de los ciclos de entusiasmo y de desilusión por los que pasarán los dos hombres. Las notas de Flaubert indican que, como todos los demás proyectos, esta anticipación de Bouvard es interrumpida bruscamente por la realidad, esta vez por la repentina aparición de unos gendarmes que le acusan de corrupción. Algunas líneas después, sin embargo, aparece el segundo tema que nos interesa. Los dos hombres se confiesan mutuamente su deseo secreto de volver a ser copistas. Se construyen un escritorio doble, se compran libros, lápices, borradores y —según concluye la escena Flaubert— _«ils s'y mettent»_ : se ponen a trabajar. Bouvard y Pécuchet han intentado vivir y aplicar más o menos directamente el conocimiento y, finalmente, quedan reducidos a copiarlo, sin criticarlo, de un texto a otro.
Aunque no esté totalmente desarrollada, la visión que Bouvard tiene de una Europa regenerada por Asia (y lo que llegará a ser en el pupitre del copista) se puede comentar de diversas maneras. Como muchas de las otras visiones de los dos hombres, esta es _global_ y es _reconstructiva_ ; representa lo que Flaubert sintió que era la idea predilecta del siglo XIX: reconstruir el mundo de acuerdo con un proyecto imaginario que a veces se acompaña de una técnica científica particular. Entre las visiones que Flaubert tiene en mente, están las utopías de Saint-Simon y de Fourier, la regeneración científica como la concibió Auguste Compte y todas las religiones técnicas o seculares promovidas por ideólogos, positivistas, eclécticos, ocultistas, tradicionalistas e idealistas como Destutt de Tracy, Cabanis, Michelet, Cousin, Proudhon, Cournot, Cabet, Janet y Lamennais. A lo largo de la novela, Bouvard y Pécuchet abrazan las diversas causas defendidas por estos personajes y, una vez que las han estropeado, emprenden la búsqueda de otras nuevas, aunque sin obtener mejores resultados.
Las raíces de estas ambiciones revisionistas son románticas de una manera muy específica. Debemos recordar hasta qué punto una gran parte de los proyectos espirituales e intelectuales de finales del siglo XVIII fueron, en su mayor parte, una teología reconstruida; un supernaturalismo natural, como M. H. Abrams lo ha denominado. Este tipo de pensamiento se puede encontrar en las actitudes típicas del siglo XIX que Flaubert satiriza en _Bouvard y Pécuchet_. La noción de regeneración, por tanto, representa una vuelta
a una notable tendencia romántica, después del racionalismo y el _decorum_ de la Ilustración [...], [un retorno] al drama puro, a los misterios supranacionales de la historia y doctrinas cristianas, a los violentos conflictos y a los abruptos cambios de la vida interior cristiana, fomentando los extremos de destrucción y creación, de infierno y cielo, de exilio y reunión, de muerte y resurrección, de desesperación y alegría, de paraíso perdido y paraíso reencontrado. [...] Pero como vivieron inexorablemente después de la Ilustración, los escritores románticos revivieron estos viejos temas con una diferencia: su empresa consistía en mantener una perspectiva panorámica de la historia y del destino humano, de los paradigmas existenciales y de los valores cardinales de su herencia religiosa, reconstruyéndolos de una manera que los hiciera intelectualmente aceptables, así como emocionalmente pertinentes para su época.
Lo que Bouvard tenía en mente —la regeneración de Europa por Asia— era una idea romántica muy influyente. Friedrich Schlegel y Novalis, por ejemplo, exhortaban a sus compatriotas y a los europeos en general a que estudiaran de modo detallado la India porque, decían, eran la cultura y la religión indias las que podían derrotar el materialismo y el mecanicismo (y el republicanismo) de la cultura occidental. Y de esta derrota surgiría una nueva, revitalizada Europa: la metáfora bíblica de la muerte, de la resurrección y de la redención es evidente en esta prescripción. Además, el proyecto orientalista de los románticos no era simplemente un ejemplo específico de una tendencia general; era una poderosa configuración de la tendencia misma, como ha expuesto Raymond Schwab, con argumentos muy convincentes, en _La Renaissance orientale_. Lo que importaba no era tanto Asia en sí como su _utilidad para_ la Europa moderna. De esta manera cualquiera que, como Schlegel o Franz Bopp, dominara una lengua oriental era un héroe espiritual, un caballero errante que devolvía a Europa el sentido, entonces perdido, de su misión sagrada. Es precisamente este sentido lo que las religiones seculares más recientes, retratadas por Flaubert, perpetuaron en el siglo XIX. No menos que Schlegel, Wordsworth y Chateaubriand, Auguste Compte —como Bouvard— era partidario y defensor de un mito secular posterior a la Ilustración cuyos grandes rasgos eran, sin duda, cristianos.
Al permitir de manera regular a Bouvard y Pécuchet partir de unas ideas revisionistas que les llevan a un final cómicamente degradado, Flaubert ponía de relieve la imperfección humana común a todos los proyectos. Observó perfectamente que bajo la _idée reçue_ de «Europa-regenerada-por-Asia» se escondía una arrogancia insidiosa. «Europa» y «Asia» no eran nada sin la técnica de los visionarios que transformaba los vastos dominios geográficos en entidades susceptibles de ser manejadas y dirigidas. En el fondo, Europa y Asia eran, pues, nuestra Europa y nuestra Asia —nuestra _voluntad_ y _representación_ como dijo Schopenhauer—. Las leyes históricas eran en realidad las leyes de los _historiadores_ , igual que «las dos formas de humanidad» destacaban menos la realidad que la capacidad europea de hacer pasar por inevitables las distinciones que había hecho el hombre. En cuanto a la frase —«finalmente se fundirán en una sola»—, Flaubert ridiculizaba la alegre indiferencia de la ciencia hacia la realidad, una ciencia que diseccionaba y fundía entidades humanas como si fueran materiales inertes. No obstante, la ciencia de la que se burlaba Flaubert no era cualquier ciencia: era la ciencia europea exultante y llena de un entusiasmo a veces mesiánico, cuyas victorias incluían revoluciones fallidas, guerras, opresión y un incorregible apetito de poner en práctica, de manera inmediata y quijotesca, las grandes ideas librescas. Lo que esta ciencia o este conocimiento nunca tuvo en cuenta fue su propia inocencia malvada e interesada profundamente arraigada ni la resistencia que le oponía la realidad. Cuando Bouvard juega a ser científico asume inocentemente que la ciencia simplemente es, que la realidad es como el científico dice que es, que no importa si el científico es un loco o un visionario; él (o cualquiera que piense como él) no puede percibir que Oriente quizá no quiera regenerar Europa o que Europa no esté dispuesta a fundirse democráticamente con los asiáticos, ya sean amarillos o morenos. En resumen, un científico así no reconoce en su ciencia la voluntad de poder egoísta que alimenta sus empresas y corrompe sus ambiciones.
Flaubert, por supuesto, cree que sus pobres locos están hechos para enfrentarse a estas dificultades. Bouvard y Pécuchet han aprendido que es mejor no traficar al mismo tiempo con las ideas y la realidad. La novela concluye con una imagen de los dos hombres satisfechos de copiar fielmente sus ideas favoritas de un libro en su papel. El saber ya no requiere ser aplicado a la realidad; es lo que se transmite en silencio y sin comentarios de un texto a otro. Las ideas se propagan y se diseminan anónimamente, se repiten sin atribución, se vuelven literalmente _idées reçues_ : lo que importa es que están _allí_ para ser repetidas, imitadas y de nuevo vueltas a imitar sin ser criticadas.
De una forma muy resumida, este breve episodio sacado de las notas tomadas por Flaubert para _Bouvard y Pécuchet_ enmarca las estructuras específicamente modernas del orientalismo que, después de todo, es una disciplina que se sitúa entre las creencias seculares (y cuasi religiosas) del pensamiento europeo del siglo XIX. Hemos descrito ya el ámbito general del pensamiento sobre Oriente que fue transmitido a través de la Edad Media y del Renacimiento, períodos en los que el islam era lo esencial de Oriente. Durante el siglo XVIII, sin embargo, hubo un número de elementos nuevos que se añadieron y entrecruzaron, elementos que dejaban entrever la fase evangélica que se avecinaba y cuyos grandes rasgos Flaubert recrearía más tarde.
Primer elemento, Oriente se estaba abriendo considerablemente más allá de los países islámicos. Este cambio cuantitativo se debía, en gran medida, a la continua, y expansiva, exploración europea del resto del mundo. La influencia creciente de los libros de viajes, de las utopías imaginarias, de los viajes morales y de los relatos científicos contribuyó a que Oriente se considerara dentro de un marco más definido y a la vez extenso. Si el orientalismo debe principalmente sus progresos a los fructíferos descubrimientos que Anquetil y Jones hicieron sobre Oriente durante el último tercio del siglo, estos deben enmarcarse en el contexto más amplio que crearon Cook y Bougainville, los viajes de Tournefort y Adanson, la _Histoire des navigations aux terres australes_ , del presidente De Brosses, los comerciantes franceses en el Pacífico, los misioneros jesuitas en China y en las Américas, las exploraciones y relatos de William Dampier y las innumerables especulaciones sobre los gigantes, los patagones, los salvajes, los nativos y los monstruos que supuestamente residían en Extremo Oriente y en el Oeste, norte o sur de Europa. Todos estos horizontes que se iban ensanchando mantenían firmemente a Europa en el centro privilegiado, y con el papel de observador principal (o el de principalmente observado, como en _Citizen of the World_ , de Goldsmith). Incluso cuando Europa avanzaba hacia el exterior, la conciencia que tenía de su fuerza cultural se reforzaba. No solo a partir de las grandes instituciones, como las diferentes compañías de las Indias, sino también a partir de los relatos de los viajeros se crearon las colonias y se aseguraron las perspectivas etnocentristas.
Segundo elemento, una actitud más informada hacia lo extraño y lo exótico instigada no solo por los viajeros y exploradores, sino también por los historiadores, para quienes la experiencia europea podía ser comparada, en su propio beneficio, con la de otras civilizaciones diferentes y más antiguas. Esta fuerte corriente de la antropología histórica del siglo XVIII, descrita por los eruditos como la confrontación de los dioses, significaba que Gibbon podía leer las lecciones del declive de Roma en el auge del islam, y que Vico podía comprender la civilización moderna a través del esplendor poético bárbaro de sus primeros comienzos. Mientras que los historiadores del Renacimiento habían juzgado y considerado de modo inflexible que Oriente era un enemigo, los del siglo XVIII afrontaron sus peculiaridades con cierta imparcialidad, intentando trabajar, si estaba a su alcance, directamente con materiales surgidos de fuentes orientales, quizá porque esta técnica ayudaba al europeo a conocerse mejor a sí mismo. La traducción de George Sale del Corán y su discurso preliminar ilustran el cambio. Al contrario que sus predecesores, Sale intentaba ocuparse de la historia árabe a través de fuentes árabes; además dejaba a los comentaristas musulmanes del texto sagrado hablar por sí mismos. En la obra de Sale, como a lo largo de todo el siglo XVIII, la simple comparación fue la fase inicial de estas disciplinas comparativas (filología, anatomía, jurisprudencia y religión) que el siglo XIX glorificaría.
Sin embargo, había entre algunos pensadores una tendencia a rebasar los límites del estudio comparativo y sus revisiones juiciosas sobre la humanidad desde «la China a Perú» a través de una identificación por simpatía. Este es el tercer elemento que se dio en el siglo XVIII y que preparó el camino para el orientalismo moderno. Lo que hoy llamamos historicismo es una idea que se desarrolló ya en el siglo XVIII; Vico, Herder y Hamman, entre otros, creyeron que todas las culturas tenían una coherencia interna y orgánica, y que sus elementos se mantenían unidos por un espíritu, un genio, un _klima_ o una idea nacional que una persona del exterior solo podía penetrar a través de un acto de simpatía histórica. Así, el libro _Ideen zur Philosophie der Geschichte de Menschheit_ (1784-1791), de Herder, era una presentación panorámica de diversas culturas, cada una de las cuales estaba impregnada de un espíritu creador hostil y solo era accesible para el observador que sacrificaba sus prejuicios al _Einfühlung_. Imbuido por el sentimiento populista y pluralista de la historia, que reclamaron Herder y muchos otros, una mente del siglo XVIII podía abrir una brecha en los muros doctrinales que se levantaban entre Occidente y el islam, y descubrir elementos de afinidad entre él y Oriente que estaban escondidos. Napoleón es un ejemplo famoso de esta identificación (normalmente selectiva) por simpatía. Mozart es otro; _La flauta mágica_ (en la que los códigos masónicos se entremezclan con visiones de un Oriente benévolo) y _El rapto del serrallo_ sitúan en Oriente una forma de humanidad particularmente magnánima. Y es esto, mucho más que los modos elegantes de la música «turca», lo que constituye la simpatía de Mozart por el Este.
Es muy difícil, sin embargo, separar estas intuiciones que se tienen de Oriente, como las de Mozart, de todo el abanico de representaciones prerrománticas y románticas que dibujan Oriente como un lugar exótico. El orientalismo popular de finales del siglo XVIII y principios del XIX tuvo un éxito considerable. Pero esta moda, muy fácil de identificar en William Beckford, Byron, Thomas Moore y Goethe, no se puede separar del gusto por los cuentos góticos, los idilios seudomedievales y las visiones del esplendor y de la crueldad bárbaras. Por consiguiente, en algunos casos la representación de Oriente se puede asociar con las prisiones de Piranesi, en otros, con los lujosos ambientes de Tiépolo, e incluso en otros, con la exótica sublimidad de las pinturas de finales del siglo XVIII. Ya en el siglo XIX, en las obras de Delacroix y literalmente de decenas de pintores franceses y británicos, el cuadro de género oriental dio a esta representación una expresión visual y una vida propia (que este libro desgraciadamente debe dejar de lado). Sensualidad, promesa, terror, sublimidad, placer idílico, intensa energía: Oriente como motivo de las imágenes orientalistas prerrománicas y pretécnicas de la Europa de finales del siglo XVIII era realmente una cualidad camaleónica que designaba el adjetivo «oriental». No obstante, este Oriente indeterminado iba a ser severamente empequeñecido con el advenimiento del orientalismo académico.
El cuarto elemento que preparó el camino a las estructuras del orientalismo moderno fue el impulso que se dio a las clasificaciones de la naturaleza y del hombre en tipos. Los nombres más destacados son, por supuesto, Linneo y Buffon; pero el proceso intelectual por el cual la extensión corporal (e inmediatamente después moral, intelectual y espiritual) —la materialidad típica de un objeto— dejaría de ser un mero espectáculo y se transformaría en una medida precisa de elementos característicos estuvo muy difundido. Linneo dijo que toda nota tomada sobre un tipo natural «debería derivarse del número, de la forma, de la proporción y de la situación», y, en efecto, si se examinan las obras de Kant, Diderot o Johnson se ve que hay en todas ellas una inclinación similar a resaltar características generales y a reducir un gran número de objetos a una cantidad menor de tipos, los cuales se pueden ordenar y describir. Según la historia natural, la antropología y la generalización cultural, un tipo tenía un _carácter_ particular que proporcionaba al observador una designación y, como dice Foucault, «una derivación controlada». Estos tipos y caracteres pertenecían a un sistema o red de generalizaciones. Así,
toda designación debe hacerse a través de una cierta relación con todas las otras designaciones posibles. Conocer lo que pertenece propiamente a un individuo es tener ante sí la clasificación de todos los otros —o la posibilidad de clasificarlos.
En los escritos de filósofos, historiadores, enciclopedistas y ensayistas encontramos el «carácter como designación» presentándose como clasificación fisiológico-moral: hay, por ejemplo, hombres salvajes, europeos, asiáticos, etc. Por supuesto, esto aparece en Linneo, pero también en Montesquieu, en Johnson, en Blumenbach, en Soemmerring y en Kant. Las características fisiológicas y morales se distribuyen más o menos igualmente: el americano es «rojo, colérico, erguido», el asiático es «amarillo, melancólico y rígido», y el africano es «negro, flemático, laxo». Pero estas designaciones adquirieron fuerza cuando más adelante, en el siglo XIX, se unieron al carácter como derivación, como tipo genético. En la obra de Vico y de Rousseau, por ejemplo, la fuerza de la generalización moral aumenta por la precisión con la que se muestran las figuras dramáticas, casi arquetípicas —hombre primitivo, gigantes, héroes—, que son la génesis de los temas de la moral corriente, de la filosofía e incluso de la lingüística. De este modo, cuando se refería a un oriental, lo hacía en términos universales genéticos como su estado «primitivo», sus características primarias y su fondo espiritual particular.
Los cuatro elementos que he descrito —expansión, confrontación histórica, simpatía y clasificación— son las corrientes de pensamiento del siglo XVIII cuya presencia condicionó las estructuras específicas, intelectuales e institucionales del orientalismo moderno. Sin ellas, el orientalismo, como veremos a continuación, no hubiera podido existir. Además estos elementos tuvieron el efecto de liberar Oriente en general y el islam en particular del examen estrictamente religioso por el cual habían sido estudiados hasta entonces (y juzgados) por el Occidente cristiano. En otras palabras, el orientalismo moderno deriva de los elementos secularizantes de la cultura europea del siglo XVIII.
1. La extensión de Oriente más hacia el Este, desde un punto de vista geográfico, y más lejos en el tiempo, desde un punto de vista temporal, suavizó e incluso hizo desaparecer el marco bíblico. Los puntos de referencia ya no eran el cristianismo y el judaísmo, con sus calendarios y sus mapas bastante modestos, sino India, China, Japón y Sumer, el budismo, el sánscrito, el zoroastrismo o mazdeísmo y los seguidores de Manu.
2. La capacidad de tratar históricamente (y no reductivamente, como un tópico de política eclesiástica) las culturas no europeas y no judeocristianas fue consolidándose a medida que la propia historia era concebida de una manera más radical que antes; comprender bien Europa significaba también entender las relaciones objetivas entre Europa y sus propias fronteras temporales y culturales hasta entonces inaccesibles. En cierto sentido, la idea de Juan de Segovia de la _contraferentia_ entre Oriente y Europa se llevó a cabo, pero de una manera totalmente laica; Gibbon podía tratar a Mahoma como una figura histórica que influyó en Europa y no como un sinvergüenza diabólico que deambulaba por algún lugar entre la magia y la falsa profecía.
3. Una identificación selectiva con las regiones y las culturas diferentes de la nuestra corroía la resistencia del yo y de la identidad, los cuales anteriormente habían estado distinguiendo entre una comunidad de creyentes dispuestos en línea de batalla frente a las hordas de bárbaros. Las fronteras de la Europa cristiana ya no eran una especie de aduana; y las nociones de asociación humana y de posibilidad humana adquirieron una legitimidad extensa general en lugar de una legitimidad restringida.
4. Las clasificaciones de la humanidad se multiplicaron sistemáticamente al mismo tiempo que las posibilidades de designación y de derivación se refinaron para llegar más allá de las categorías denominadas por Vico naciones gentiles y sagradas; la raza, el color, el origen, el temperamento, el carácter y los tipos encubrían la distinción entre cristianos y todos los demás.
Sin embargo, si estos elementos conectados entre sí representaban una tendencia a la secularización, esto no quiere decir que los antiguos modelos religiosos de la historia, del destino humano y de los «paradigmas existenciales» de los hombres fueran simplemente desplazados; muy al contrario, fueron reconstituidos, reorganizados, y redistribuidos en los marcos seculares que acabamos de enumerar. Cualquiera que estudiara Oriente debía disponer de un vocabulario secular acorde con estos marcos. Pero si bien el orientalismo proporcionó el vocabulario, el repertorio de conceptos y las técnicas —ya que, desde el final del siglo XVIII, eso fue lo que el orientalismo _hizo_ y lo que el orientalismo _fue_ —, también conservó, como corriente permanente en su discurso, un impulso religioso reconstruido y un supernaturalismo naturalizado. Lo que voy a intentar demostrar es que este impulso del orientalismo residía en la concepción que el orientalista tenía de sí mismo, de Oriente y de su disciplina.
El orientalista moderno era, desde su punto de vista, un héroe que rescataba Oriente de la oscuridad, de la alienación y de la extrañeza con las que él mismo se había distinguido convenientemente. Sus investigaciones reconstruían las lenguas perdidas de Oriente, sus costumbres e incluso sus mentalidades, como Champollion reconstruyó los jeroglíficos egipcios a partir de la Piedra de Rosetta. Las técnicas específicas del orientalismo —la lexicografía, la gramática, la traducción y la descodificación de culturas— restauraron, encarnaron y reafirmaron los valores tanto de un Oriente antiguo clásico como de las disciplinas tradicionales (filología, historia, retórica y polémica doctrinal). Pero durante este proceso, Oriente y las disciplinas orientalistas cambiaron dialécticamente, ya que no podían sobrevivir en su forma original. Oriente, incluso en la forma «clásica» que los orientalistas normalmente estudiaron, fue modernizado y devuelto al presente; las disciplinas tradicionales también fueron introducidas en la cultura contemporánea. Pero ambos presentaban las huellas del _poder_ : el poder de haber resucitado, incluso creado, Oriente, poder que residía en las nuevas técnicas científicamente avanzadas de la filología y de la generalización antropológica. En resumen, al haber llevado Oriente a la modernidad, el orientalista podía celebrar su método y su posición como si fueran los de un creador secular, un hombre que creaba nuevos mundos como una vez Dios había creado el antiguo. Para asegurar la continuación de estos métodos y de estas posiciones, más allá de la duración de la vida de cualquier orientalista individual, debería ser una tradición secular de continuidad, un orden laico de metodologistas disciplinados, cuya hermandad estaría basada no en un linaje de sangre, sino en un discurso común, una práctica, una biblioteca y un conjunto de ideas recibidas, en resumen, una doxología, común a todos los que entraran en sus filas. Flaubert fue lo suficientemente presciente como para ver que, con el tiempo, el orientalista moderno se iba a convertir en un copista, como Bouvard y Pécuchet; pero al principio, en los tiempos de Silvestre de Sacy y Ernest Renan, ese peligro no se vislumbraba.
Mi tesis consiste en que los aspectos esenciales del orientalismo moderno, teoría y praxis (de las que se deriva el orientalismo de nuestros días), se pueden entender no como un repentino acceso de conocimiento objetivo sobre Oriente, sino como un conjunto de estructuras heredadas del pasado, secularizadas, redispuestas y reformadas por ciertas disciplinas, como la filología, las cuales en su momento se constituyeron como sustitutos (o versiones) naturalizados, modernizados y laicos de un supernaturalismo cristiano. En la forma de nuevos textos y de ideas, Oriente se fue acomodando a estas estructuras. Los lingüistas y exploradores como Jones y Anquetil contribuyeron a la formación del orientalismo moderno, ciertamente, pero lo que en realidad distingue a este, como un campo, un grupo de ideas, un discurso, es la obra de la generación siguiente. Si tomamos la expedición de Napoleón (1798-1801) como una especie de primera experiencia de habilitación para el orientalismo moderno, podemos considerar a sus héroes primigenios —que en los estudios islámicos son Silvestre de Sacy, Renan y Lane— como los constructores del campo, los creadores de una tradición y los padres fundadores de la hermandad orientalista. Lo que Silvestre de Sacy, Renan y Lane hicieron fue colocar al orientalismo sobre una base científica y racional. Esto les llevó no solo a realizar su propia obra ejemplar, sino también a crear un vocabulario y unas ideas que podían ser utilizadas de modo impersonal por cualquiera que quisiera llegar a ser orientalista. Su fundamentación del orientalismo fue una hazaña considerable. Se hizo posible una terminología científica; se desterró la oscuridad e instauró una forma especial de esclarecer Oriente; se estableció la figura del orientalista como autoridad central _para_ Oriente; se legitimó un tipo especial de trabajo orientalista especialmente coherente; se puso en circulación en el mundo de la cultura una forma de texto de referencia que en lo sucesivo _hablaría por Oriente_. Y, sobre todo, la obra de los fundamentadores labró un campo de estudio y una familia de ideas que, en su momento, pudieron formar a una comunidad de eruditos cuyo linaje, tradiciones y ambiciones eran a la vez interiores al campo y lo suficientemente exteriores como para tener el prestigio del público. Durante el siglo XIX, a medida que Europa iba invadiendo Oriente, el orientalismo ganaba más confianza pública, pero el que esta ganancia coincidiera con una pérdida de originalidad no nos debería sorprender, ya que sus métodos desde el principio fueron la reconstrucción y la repetición.
Una observación final: las ideas, las instituciones y las personas de finales del siglo XVIII y del siglo XIX, de las cuales me voy a ocupar a continuación, constituyen una parte importante y una elaboración crucial de la primera fase de la época más grande de apropiación territorial jamás conocida. En vísperas de la Primera Guerra Mundial, Europa había colonizado el 85 por ciento de la Tierra. Decir simplemente que el orientalismo moderno ha sido uno de los aspectos del imperialismo y del colonialismo es decir algo irrefutable. Pero no basta decirlo, hay que estudiarlo analítica e históricamente. Me interesa mostrar cómo el orientalismo moderno, a diferencia de la conciencia precolonial de Dante y D'Herbelot, incorpora una disciplina sistemática de _acumulación_ ; y esto, lejos de ser una peculiaridad exclusivamente intelectual o teórica, ha llevado al orientalismo a tender fatalmente hacia la acumulación sistemática de seres humanos y de territorios. Reconstruir una lengua oriental muerta o perdida significaba, en última instancia, reconstruir un Oriente muerto o ignorado; también significaba que la precisión, la ciencia e incluso la imaginación de la reconstrucción podían preparar el camino para lo que los ejércitos, las administraciones y las burocracias harían después sobre el terreno, en Oriente. En cierta medida, la justificación del orientalismo no estaba solo en sus éxitos artísticos o intelectuales, sino en su eficacia, su utilidad y su autoridad posterior. Esto, ciertamente, merece que se le preste una especial atención.
### II
### Silvestre de Sacy y Ernest Renan:
### la antropología racional y el laboratorio filológico
La vida de Silvestre de Sacy estuvo dominada por dos grandes temas: el esfuerzo heroico y la devoción por la utilidad pedagógica y racional. Nacido en 1757 dentro de una familia jansenista que ejercía tradicionalmente la _notaría_ , Antoine-Isaac-Silvestre recibió, en una abadía benedictina, clases particulares, primero de árabe, caldeo, siríaco y más tarde de hebreo. El árabe en particular fue la lengua que le abrió las puertas de Oriente, ya que era en árabe, según Joseph Reinaud, en lo que estaban escritas las obras orientales más antiguas e instructivas, fueran sagradas o profanas. Aunque era legitimista, en 1769 fue nombrado primer profesor de árabe de la recientemente creada École de Langues Orientales Vivantes, de la que fue director en 1824. En 1806 fue profesor del Collège de France, aunque desde 1805 ya era orientalista residente en el Ministerio de Asuntos Exteriores francés. Su trabajo (por el que no cobró nada hasta 1811) consistió primero en traducir los boletines de la Grande Armée y el _Manifiesto_ de 1806 con el que Napoleón esperaba excitar el «fanatismo musulmán» contra los rusos ortodoxos. Pero durante muchos años Sacy preparó a un grupo de intérpretes para la trujamanía francooriental, así como a futuros eruditos. Cuando los franceses ocuparon Argelia en 1830, fue Sacy quien tradujo la proclama a los argelinos. El ministro de Asuntos Exteriores y, en ocasiones, el ministro de la Guerra le consultaban sobre los asuntos diplomáticos relativos a Oriente. A los setenta y cinco años sucedió a Dacier como secretario de la Académie des Inscriptions, y también fue conservador de los manuscritos orientales en la Bibliothèque Royale. A lo largo de su larga y distinguida carrera, su nombre se asociaba correctamente a la reestructuración y la reforma de la enseñanza (particularmente de los estudios orientales) en la Francia posrevolucionaria. En 1832, al mismo tiempo que Cuvier, fue nombrado par de Francia.
No es solo porque Sacy fuera el primer presidente de la Société Asiatique (fundada en 1822) por lo que su nombre se asocia al comienzo del orientalismo moderno; es porque su trabajo proporcionó a esta profesión todo un cuerpo sistemático de textos, una práctica pedagógica, una tradición erudita y un importante nexo de unión entre la erudición oriental y el interés público. En la obra de Sacy, por primera vez en Europa desde el Congreso de Viena, actúa junto a la disciplina erudita un principio metodológico consciente. Y lo que no es menos importante, Sacy siempre se consideró a sí mismo un hombre situado al frente de un proyecto de renovación de la ciencia. Fue un impulsor consciente de serlo y, lo que concierne más a nuestra tesis general, se comportaba en sus escritos como un eclesiástico secularizado para el que Oriente y sus estudiantes eran la doctrina y los feligreses, respectivamente. El duque de Broglie, contemporáneo y admirador suyo, dijo a propósito de su obra que unía las maneras de un científico con las de un profesor de historia sagrada, y que Silvestre de Sacy era el único hombre capaz de conciliar «los objetivos de Leibniz con los esfuerzos de Bossuet». En consecuencia, todo lo que escribió iba dirigido de manera específica a sus estudiantes (en el caso de su primera obra, sus _Principes de grammaire générale_ de 1799, el estudiante era su propio hijo) y lo exponía no como algo nuevo, sino como un extracto revisado de lo mejor que ya se había hecho, dicho o escrito.
Estas dos características —la presentación didáctica para los estudiantes y la manifiesta intención de recapitular a través de la revisión y del extracto— son cruciales. Los escritos de Sacy siempre tienen el tono de un discurso hablado; su prosa está salpicada de pronombres en primera persona, con reservas personales y un estilo retórico. Incluso en sus escritos más abstrusos —como una nota erudita sobre la numismática sasánida del siglo III— lo que se siente, más que una pluma que escribe, es una voz que habla. Las primeras líneas de la dedicatoria a su hijo de _Principes de grammaire générale_ dan el tono de la obra: _«C'est à toi, mon cher fils, que ce petit ouvrage a été entrepris»_ , lo que quiere decir, yo te escribo (o te hablo) porque necesitas saber estas cosas y, como no existen de forma asequible, yo mismo he hecho este trabajo para ti. Discurso directo, utilidad, racionalidad inmediata y benéfica. Sacy creía que cualquier cosa podía aclararse y racionalizarse sin importar la dificultad de la tarea ni la oscuridad del tema. He aquí la severidad de Bossuet, el humanismo abstracto de Leibniz y el _tono_ de Rousseau, todo junto dentro del mismo estilo.
El tono de Silvestre de Sacy contribuye a formar un círculo que los separa, a él y a su público, del resto del mundo, igual que un profesor y sus alumnos en un aula cerrada también forman un espacio aislado. El tema de los estudios orientales no es como el de la física, la filosofía o la literatura clásica. Es un tema secreto, esotérico, que tiene importancia para la gente que ya se interesa por Oriente y quiere conocerlo mejor y de una manera más metódica. En este sentido, la disciplina pedagógica busca más la efectividad que la atracción. El orador, por tanto, _despliega_ su material ante sus discípulos, cuyo papel es recibir lo que se les da en forma de temas cuidadosamente seleccionados y preparados. Como Oriente es una realidad antigua y lejana, se trata de restaurar y de revisar lo que ha desaparecido del ámbito más amplio de los conocimientos. Y como la enorme riqueza de Oriente (en espacio, tiempo y cultura) no puede exponerse en su totalidad, basta con presentar sus partes más representativas. Así, los intereses de Sacy se inclinan hacia la antología, la crestomatía, el cuadro y la exposición de principios generales, en los que un conjunto relativamente pequeño de ejemplos poderosos lleva Oriente hasta el estudiante. Estos ejemplos son poderosos por dos razones: porque reflejan la autoridad que tiene Sacy, como occidental, para seleccionar de Oriente lo que su distancia y excentricidad habían mantenido hasta entonces escondido, y porque contienen en sí mismos (o han recibido del orientalismo) el poder semiótico de significar Oriente.
Toda la obra de Sacy es, en esencia, una recopilación y una laboriosa revisión; es ceremoniosamente didáctica. Además de los _Principes de grammaire générale_ , escribió una _Chrestomathie arabe_ en tres volúmenes (1806 y 1827), una antología de textos gramaticales árabes (1825), una gramática árabe en 1810 ( _à l'usage des élèves de l'École Spéciale_ ), algunos tratados sobre la prosodia árabe y la religión drusa y numerosos ensayos cortos sobre numismática, onomástica, epigrafía, historia y pesos y medidas orientales. Hizo un buen número de traducciones y de comentarios detallados sobre el _Calila e Dimna_ y las _Maqamat_ de al-Hariri. Silvestre de Sacy empleó la misma energía como editor de textos que como memorialista e historiador de la ciencia moderna. Hay pocas cosas dignas de mención en otras disciplinas afines con las que no estaba _au courant_ , salvo que sus propios escritos eran simplistas y, en lo que no concernía al orientalismo, de un positivismo estrecho.
Sin embargo, cuando en 1802 Napoleón encargó al Institut de France que formara un _tableau générale_ sobre el estado y los progresos de las artes y las ciencias desde 1789, Sacy fue elegido miembro del equipo de redactores. Entre los especialistas era el más riguroso y, entre los que trataban cuestiones generales, el de pensamiento más histórico. El informe Dacier, como se conoció oficiosamente, presentaba muchas de las predilecciones de Sacy y contenía sus contribuciones al estado de la ciencia oriental. Su título — _Tableau historique de l'érudition française_ — anuncia la nueva conciencia histórica (en oposición a la conciencia religiosa); conciencia que es teatral porque permite situar la ciencia sobre un escenario en el que se la puede observar fácilmente en su totalidad. El prefacio de Dacier, dirigido al emperador, expone este tema perfectamente. Esta visión de conjunto le permitía hacer algo que ningún otro soberano había intentado hacer, a saber, abarcar de un solo _coup d'oeil_ la universalidad de los conocimientos humanos. Si este _Tableau historique_ hubiera sido acometido en otros tiempos, continuaba Dacier, quizá hoy habríamos conservado muchas obras maestras que ahora están perdidas o destruidas; el interés y la utilidad del _Tableau_ residían en que preservaba el conocimiento y lo hacía inmediatamente accesible. Dacier dio a entender que la expedición a Egipto había facilitado el trabajo y había contribuido a elevar el grado de nuestros conocimientos geográficos modernos. (En el _discours_ de Dacier, mejor que en cualquier otro lugar, puede verse claramente cómo la forma teatral del _Tableau historique_ tiene su equivalente moderno en las galerías y mostradores de los grandes almacenes.)
La importancia que tiene el _Tableau historique_ para comprender la fase inaugural del orientalismo reside en que exterioriza la forma del conocimiento orientalista y sus características y describe la relación del orientalismo con su materia de estudio. En las páginas de Sacy sobre el orientalismo —como en todos sus escritos— habla de su propio trabajo diciendo que _ha descubierto, ha traído a la luz, ha rescatado_ una gran cantidad de material oscuro. ¿Por qué? Para _situarlo ante_ el estudiante. Por eso, como todos los eruditos de su tiempo, Sacy consideraba que un trabajo de erudición era una adición positiva a un edificio que todos los eruditos levantaban juntos. Conocer era esencialmente _hacer visible_ un material, y el objetivo de un _tableau_ era la construcción de una especie de panóptico a la manera de Jeremy Bentham. La disciplina erudita era, por tanto, una técnica específica de poder: hacía que el que la usara ganara (y sus estudiantes también) instrumentos y conocimientos que (si era un historiador) hasta entonces habían estado perdidos. Y es verdad que el vocabulario de poder y de adquisición especializados se asocia particularmente a la reputación de Sacy como pionero del orientalismo. Su heroísmo como erudito consistió en haberse enfrentado con éxito a unas dificultades insuperables; consiguió los medios para ofrecer a sus estudiantes un campo donde no había nada. _Compuso_ libros, preceptos, ejemplos, dijo el duque de Broglie sobre Sacy. El resultado fue la producción de materiales sobre Oriente, de métodos para estudiarlo y de ejemplos con los que ni siquiera los orientales contaban.
Comparada con la labor de cualquier helenista o latinista que trabajara en el equipo del Institut, la de Sacy fue algo fabuloso. Ellos tenían los textos, las convenciones, las escuelas; él no tenía nada de esto y, en consecuencia, debía ponerse a hacerlo. La dinámica de la pérdida primera y la ganancia posterior es, en los escritos de Sacy, una obsesión, y su inversión en ella fue realmente pesada. Como sus colegas de otros campos, creía que conocer era ver —panópticamente, por decirlo de algún modo— pero, contrariamente a ellos, no solo tenía que identificar el conocimiento, también debía descifrarlo, interpretarlo y, lo que era más difícil, hacerlo accesible. Sacy consiguió producir un campo de estudio completo. Como europeo escudriñó en los archivos orientales y pudo hacerlo sin abandonar Francia. Los textos que aisló, los trajo, los mejoró y luego los anotó, codificó, arregló y comentó. Con el tiempo, Oriente se volvió menos importante de lo que los orientalistas hacían de él, pues, después de haber sido relegado por Sacy al interior del discurso cerrado del _tableau_ pedagógico, el Oriente del orientalista rechazaba salir a la realidad.
Sacy era demasiado inteligente como para dejar que sus opiniones y su práctica se quedaran sin un soporte teórico. En primer lugar, siempre dejó claro por qué «Oriente» no podía sobrevivir al contacto con el gusto, la inteligencia o la paciencia de un europeo. Sacy defendía la utilidad y el interés de cosas como la poesía árabe, pero lo que realmente decía era que la poesía árabe tenía que ser transformada convenientemente por el orientalista antes de que pudiera comenzar a ser apreciada. Esto se debía a razones enormemente epistemológicas, pero también suponía una autojustificación del orientalista. La poesía árabe la produjo un pueblo completamente extraño (al europeo), bajo unas condiciones climáticas, sociales e históricas muy diferentes de las que conocía un europeo; además, esta poesía se alimentaba de «opiniones, prejuicios, creencias y supersticiones que solo podemos precisar después de un estudio doloroso y largo». Incluso si se han experimentado los rigores de una formación especializada, gran parte de la descripción que hay en la poesía no será accesible para los europeos «que han alcanzado un alto grado de civilización». Sin embargo, lo que podamos dominar tendrá un gran valor para nosotros como europeos acostumbrados a disfrazar nuestros atributos exteriores, nuestra actividad física y nuestra relación con la naturaleza. Por tanto, el orientalista es útil para poner a disposición de sus compatriotas un gran abanico de experiencias inusuales y, lo que todavía es más valioso, un tipo de literatura capaz de ayudarnos a comprender la poesía «realmente divina» de los hebreos.
Por tanto, si bien es cierto que el orientalista es necesario porque pesca algunas joyas útiles en las profundidades del lejano Oriente, y porque no podemos conocer Oriente sin su mediación, también es verdad que no es necesario considerar todos los escritos orientales. Esta es la introducción de Silvestre de Sacy a su teoría de los fragmentos, una preocupación romántica muy frecuente. Las producciones literarias orientales no solo son esencialmente extrañas al europeo, tampoco presentan un interés continuo, ni están escritas con suficiente «gusto y espíritu crítico» como para merecer ser publicadas de otra manera que no sea en extractos ( _pour mériter d'être publiés autrement que par extrait_ ). Así, se le pide al orientalista que presente Oriente a través de una serie de fragmentos representativos, fragmentos reeditados, explicados, anotados y rodeados de más fragmentos todavía. Para hacer este tipo de presentación se necesita un género determinado: la crestomatía, que es donde, en el caso de Sacy, se manifiestan de manera más directa y provechosa el interés y la utilidad del orientalismo. Su obra más famosa fue la _Chrestomathie arabe_ , compuesta en tres volúmenes, que estaba sellada al principio, por decirlo de algún modo, con un pareado árabe de rima interna: _Kitab al-anis al-mufid lil-Talib al-mustafid; / wa yami'i al shadur min manzum wa manthur_.*
Las antologías de Sacy se usaron mucho en Europa durante bastantes generaciones de estudiantes. Aunque su contenido pretendía ser característico, las antologías ocultaban y encubrían la censura que los orientalistas ejercían sobre Oriente. Además, el orden interno de sus contenidos, los arreglos que se hacían a sus partes y la elección de sus fragmentos nunca revelaban su secreto; tenemos la impresión de que si los fragmentos no han sido escogidos por su importancia, ni por su evolución cronológica, ni por su belleza estética (lo que no es el caso de los fragmentos de Sacy), deberían al menos incluir cierta naturalidad oriental, o cierta necesidad representativa. Pero esto tampoco se dice nunca. Lo que Sacy simplemente pretende es esforzarse en beneficio de sus estudiantes, para que no tengan la necesidad de comprar o (leer) una biblioteca enorme de material oriental. Con el tiempo, el lector olvida los esfuerzos del orientalista y piensa que la reestructuración de Oriente que supone una crestomatía es Oriente _tout court_. La estructura objetiva (la designación de Oriente) y la reestructura subjetiva (la representación de Oriente hecha por un orientalista) se vuelven intercambiables. La racionalidad del orientalista invade Oriente; los principios de Oriente pasan a ser los mismos que los del orientalista. De ser distante, se vuelve algo accesible; no tenía cómo mantener su interés y adquiere una utilidad pedagógica; estaba perdido y ha sido encontrado, incluso aunque se hayan eliminado algunos fragmentos perdidos. Las antologías de Silvestre de Sacy no solo complementan Oriente, lo suplen con una presencia de Oriente para Occidente. La obra de Sacy canoniza Oriente; engendra un canon de objetos textuales que pasa de una generación de estudiantes a la siguiente.
Y la herencia viva de los discípulos de Sacy fue asombrosa. Los principales arabistas europeos del siglo XIX remontaban su autoridad intelectual hasta él. Las universidades y las academias de Francia, España, Noruega, Suecia, Dinamarca y, especialmente, Alemania estaban saturadas de estudiantes formados a su sombra, gracias a los cuadros antológicos que proporcionaban sus obras. Sin embargo, como normalmente sucede con todos los patrimonios intelectuales, junto con las riquezas se transmitían también las restricciones. La originalidad genealógica de Silvestre de Sacy consistió en haberse ocupado de Oriente como de una realidad que tenía que ser restaurada no solo a causa de la presencia desordenada y elusiva del Oriente moderno, sino también a pesar de ella. Sacy _situó_ a los árabes en Oriente, el cual a su vez estaba situado en el marco general de la ciencia moderna. El orientalismo, por tanto, formaba parte de la erudición europea, pero su material tenía que ser creado de nuevo por el orientalista antes de que pudiera entrar en las galerías al lado del latinismo y del helenismo. Cada orientalista volvió a crear su propio Oriente de acuerdo con las reglas epistemológicas fundamentales de la pérdida y la ganancia que Sacy había proporcionado y promulgado. Fue el padre del orientalismo y la primera víctima de la disciplina, ya que los orientalistas posteriores, con sus traducciones de textos, fragmentos y extractos nuevos, desplazaron totalmente la obra de Sacy y aportaron su propio Oriente restaurado. A pesar de todo, el proceso que Sacy puso en marcha continuó, especialmente cuando la filología adquirió un poder sistemático e institucional que Sacy nunca había explotado. Esa fue la conquista de Renan: haber asociado Oriente con las disciplinas comparativas más recientes, de las cuales la filología era una de las más eminentes.
La diferencia entre Sacy y Renan es la diferencia que existe entre la inauguración y la continuidad. Sacy es el creador cuya obra representa la aparición del campo y su categoría de disciplina científica del siglo XIX enraizada en el romanticismo revolucionario. Renan procede de la segunda generación del orientalismo. Su objetivo fue consolidar el discurso oficial del orientalismo, sistematizar sus intuiciones y establecer y administrar sus instituciones intelectuales. En lo que respecta a Sacy, fueron sus esfuerzos personales los que desbrozaron y abonaron el campo y sus estructuras; en cuanto a Renan, fue el hecho de haber adaptado el orientalismo a la filología y ambas disciplinas a la cultura intelectual de su época lo que perpetuó las estructuras del orientalismo desde un punto de vista intelectual y las hizo más visibles.
Renan no fue en sí mismo totalmente original, pero tampoco un mero seguidor. Se le considera, por tanto, una figura cultural, un orientalista importante al que no se puede reducir simplemente a su propia personalidad ni al conjunto de ideas esquemáticas en las que creía. Se comprenderá mejor a Renan si se le concibe como una fuerza dinámica cuyos componentes fueron ya preparados por pioneros como Silvestre de Sacy, pero que transformó las realizaciones de estos en un conjunto de textos de referencia que puso en circulación una y otra vez (por forzar un poco más la imagen) en el mundo cultural al referirse continuamente a ellos. En resumen, Renan es una figura que debemos abordar como representante de un tipo de praxis cultural e intelectual, como un estilo de hacer afirmaciones orientalistas dentro de lo que Michel Foucault llamaría el archivo de su tiempo. Lo que importa no es solo lo que dijo Renan, sino la manera en que lo dijo, lo que, teniendo en cuenta su cultura y formación, eligió como tema de estudio, lo que combinó y con qué lo combinó, etc. Las relaciones de Renan con el tema oriental, con su época, con sus lectores e incluso con su propio trabajo se pueden describir sin recurrir a fórmulas que reconozcan tácitamente la estabilidad ontológica (por ejemplo, el _zeitgeist_ , la historia de las ideas, un autor y su época). En su lugar podemos leer a Renan como a un escritor que realiza un trabajo descriptible en un lugar definido temporal, espacial y culturalmente (por tanto, desde el punto de vista del archivo) para unos lectores y, lo que no es menos importante, para perpetuar su propia posición en el orientalismo de su época.
Renan llegó al orientalismo a través de la filología, y es la extraordinaria riqueza y la posición cultural de esta disciplina lo que dio al orientalismo sus características técnicas más importantes. Quien considere que la _filología_ es el estudio ingrato e infructuoso de las palabras se sorprenderá al saber que Nietzsche se proclamó filólogo junto con las mentes más grandes del siglo XIX, pero no se sorprenderá al recordar a _Louis Lambert_ de Balzac:
¡Qué libro tan maravilloso podría escribirse narrando la vida y las aventuras de una palabra! Sin duda, ha recibido diversas impresiones de los sucesos a los que ha servido; dependiendo de los lugares en los que haya sido utilizada, una palabra habrá despertado en diferentes personas, diferentes tipos de ideas; pero ¿no es todavía mejor considerar a una palabra en su triple vertiente de alma, cuerpo y movimiento?
¿Cuál es esta categoría —Nietzsche preguntará más tarde—, que los incluye a él, a Wagner, a Schopenhauer y a Leopardi, como filólogos? Este término parece implicar tanto que se posee un don y una intuición excepcional para el lenguaje, como que uno es capaz de crear una obra cuya articulación tiene una fuerza estética e histórica. Aunque la profesión de filólogo nació el día de 1777 «cuando F. A. Wolf inventó para sí mismo el nombre de _stud. philol_.», a Nietzsche, sin embargo, le cuesta exponer que los que estudian de modo profesional la Grecia y la Roma clásicas son comúnmente incapaces de entender su propia disciplina: «ellos nunca llegan a las _raíces del tema_ : nunca presentan la filología como un problema». Ya que si se considera solo como «un conocimiento del mundo antiguo, la filología no puede, por naturaleza, durar eternamente; su material es combustible». Esto es lo que la mayoría de los filólogos no puede entender. Pero lo que distingue a los pocos espíritus excepcionales, a los que Nietzsche considera dignos de elogio —no sin ambigüedad, ni de la manera tan rápida y sencilla en la que lo estoy describiendo yo— es su relación profunda con la modernidad, una relación que les ofrece la práctica de la filología.
La filología contribuye a que todo sea problemático —ella misma, los que la practican y el presente—. Encarna la peculiar condición del hombre moderno y del europeo, ya que ninguna de estas dos categorías tiene un significado verdadero si no se pone en relación con otra cultura y otra época más antiguas. Nietzsche también considera que la filología _ha nacido y ha sido creada_ , en el sentido de Vico, como símbolo de una iniciativa humana, elaborado de acuerdo con unas categorías de descubrimiento humano, de descubrimiento de sí mismo y de originalidad. La filología es una manera de separarse históricamente, como lo hacen los grandes artistas, del propio tiempo y del propio pasado inmediato, incluso aunque, paradójica y antinómicamente, al hacer esto se esté caracterizando en realidad la propia modernidad.
Entre el Friedrich August Wolf de 1777 y el Friedrich Nietzsche de 1875 está Ernest Renan, un filólogo orientalista, y también un hombre con una idea compleja e interesante de la manera en que la filología y la cultura moderna están comprometidas mutuamente. En _L'Avenir de la science_ * (escrito en 1848 y publicado en 1890) escribió que «los fundadores del espíritu moderno son los filólogos». Y ¿qué es el espíritu moderno, decía en una frase anterior, si no «racionalismo, crítica y liberalismo, [todo lo cual] se fundó el mismo día que la filología»? La filología, sigue diciendo, es una disciplina comparativa que solo pertenece a la modernidad y es un símbolo de la superioridad moderna (y europea); todos los avances que la humanidad ha conseguido desde el siglo XV se deben a mentes que deberíamos llamar filológicas. La labor de la filología en la cultura moderna (una cultura que Renan llama filológica) es continuar observando la realidad y la naturaleza con claridad, hacer surgir el supernaturalismo y seguir los pasos de los descubrimientos de las ciencias físicas. Pero más importante que todo esto, la filología posibilita una visión general de la vida humana y del sistema de las cosas: «Yo, al estar allí, en el centro, inhalando el perfume de todo, juzgando, comparando, combinando e induciendo, llegaré al verdadero sistema de las cosas». Hay una inconfundible aureola de poder alrededor del filólogo. Renan expone su punto de vista sobre ella y las ciencias naturales del siguiente modo:
Hacer filosofía es conocer las cosas; siguiendo la acertada frase de Cuvier, la filosofía es _instruir al mundo en la teoría_. Como Kant, yo creo que cualquier demostración puramente especulativa no tiene más validez que una demostración matemática, y no puede enseñarnos nada sobre la realidad existente. La filología es la _ciencia exacta_ de los objetos mentales [ _la philologie est la science exacte des choses de_ _l'esprit_ ]. Es para las ciencias humanas lo que la física y la química son para las ciencias filosóficas de los cuerpos.
Volveré más tarde a esta cita de Cuvier que Renan menciona, así como a las constantes referencias de Renan a las ciencias naturales. De momento, debemos señalar que toda la parte central de _El porvenir de la ciencia_ se consagra a definir con admiración la filología, una ciencia que Renan describe como la disciplina más difícil de abarcar y más precisa de todas. Al aspirar a hacer de la filología una verdadera ciencia de la humanidad, Renan se une explícitamente a Vico, Herder, Wolf y Montesquieu, así como a los filólogos casi contemporáneos a él como Wilhelm von Humboldt, Bopp y el gran orientalista Eugène Burnouf (a quien dedica el volumen). Renan sitúa la filología en el centro de lo que él siempre llama la marcha de la ciencia y, de hecho, el propio libro es un manifiesto del progreso humano, lo que no deja de ser irónico si consideramos su subtítulo («Pensées de 1848») y otros libros de 1848 como son _Bouvard y Pécuchet_ y _El dieciocho brumario de Luis Bonaparte_. En cierto sentido, el manifiesto generalmente y sus exposiciones sobre la filología particularmente —por esa época ya había escrito el grueso del tratado de filología de las lenguas semíticas que le había valido el Prix Volney— señalaban a Renan como un intelectual con una relación claramente perceptible con los grandes problemas sociales que se planteaban hacia 1848. Estableció esta relación a través de la disciplina _menos_ inmediata de todas (la filología), la única que aparentemente tenía el menor grado de interés para el _público_ , la más conservadora y la más tradicional; esto nos lleva a pensar que la posición de Renan era extremadamente deliberada. Por eso no hablaba realmente como un hombre a todos los hombres, sino como una voz reflexiva, especializada, que, como él mismo escribió en su prefacio de 1890, daba por supuestas la desigualdad de las razas y la dominación necesaria de la mayoría por la minoría, como si se tratara de una ley antidemocrática de la naturaleza y de la sociedad.
Pero ¿cómo pudo Renan mantenerse y mantener esta posición tan paradójica? Porque, por un lado, ¿qué era la filología, sino una ciencia de toda la humanidad, una ciencia que partía de la unidad de los grupos humanos y del valor de todos los detalles humanos?, y por otra parte, ¿qué era el filólogo —como el propio Renan demostró por sus notorios prejuicios racistas hacia los semitas orientales, cuyo estudio le había proporcionado su renombre profesional—, sino un hombre que dividía duramente a los hombres en razas superiores e inferiores, un crítico liberal cuya obra albergaba las nociones más esotéricas sobre la temporalidad, el origen, el desarrollo, las relaciones y los valores humanos? En parte, la respuesta está en que Renan, como muestran sus primeras cartas filológicas dirigidas a Victor Cousin, Michelet y Alexander von Humboldt, tenía un fuerte sentimiento corporativista como erudito y orientalista profesional, un sentimiento que, de hecho, le distanciaba de las masas. No obstante, lo que es más importante, en mi opinión, es la idea que tenía Renan de su papel como filólogo orientalista dentro de la gran historia general del desarrollo y de los objetivos de la filología, tal y como él los concibió. En otras palabras, lo que quizá nos parezca paradójico es el resultado esperado que obtuvo por la manera en que percibía su posición dinástica dentro de la filología, dentro de su historia y de sus descubrimientos inaugurales, y por lo que hizo en el interior de todo ello. Por tanto, Renan no debería ser caracterizado como alguien que habla _sobre_ filología, sino más bien como alguien que _habla filológicamente_ con toda la fuerza de un iniciado que utiliza el lenguaje codificado de una ciencia nueva y prestigiosa cuyas afirmaciones sobre el propio lenguaje no pueden construirse de un modo directo o inocente.
La filología, tal y como Renan la entendió, la recibió y le fue enseñada, le imponía un conjunto de reglas doxológicas. Ser filólogo significaba que las actividades realizadas eran guiadas, ante todo, por una serie de descubrimientos recientes, por una nueva valoración que había dado lugar al comienzo efectivo de la ciencia filológica y que le había proporcionado una epistemología propia; estoy hablando del período que va desde 1780 hasta más o menos 1835, y cuya última parte coincide con el momento en que Renan comenzó sus estudios. Sus memorias recogen la crisis religiosa que culminó con su pérdida de la fe y que le llevó en 1845 a dedicar su vida a la erudición. Así fueron sus inicios en la filología, su concepción del mundo, su crisis y su estilo. Creía que en el terreno personal su vida reflejaba la vida institucional de la filología. Sin embargo, decidió ser también en la vida el cristiano que en otro tiempo había sido, pero en ese momento sin cristianismo y con lo que él llamaba _«la science laïque»_ (la ciencia laica).
Algunos años más tarde Renan dio el mejor ejemplo de lo que una ciencia laica podía y no podía hacer en una conferencia pronunciada en la Sorbona en 1878 «sobre los servicios que la filología proporciona a las ciencias históricas». Lo que este texto revela es que Renan tenía en mente la religión mientras hablaba de filología —por ejemplo, lo que la filología, como religión, nos enseña acerca del origen de la humanidad, de la civilización y del lenguaje—, para que su audiencia viera con claridad que la filología elaboraba un mensaje mucho menos coherente, menos ensamblado y positivo que la religión. Como la perspectiva de Renan era irremediablemente histórica y, como él mismo dijo, morfológica, se hacía evidente que la única manera que tenía, como hombre joven, de salir de la religión y entrar en la erudición filológica era conservar en esa nueva ciencia laica la concepción del mundo histórico que le había dado la religión. Por eso, «me parecía que solo había una ocupación digna de llenar y dar sentido a mi vida; y esta era la de proseguir mis investigaciones críticas sobre el cristianismo [alusión a un gran proyecto erudito de Renan sobre la historia y los orígenes del cristianismo], utilizando los recursos mucho más extensos que me ofrecía la ciencia laica». Renan se asimiló a la filología según su propio estilo poscristiano.
La diferencia entre la historia interna que proponía el cristianismo y la historia que proponía la filología, disciplina relativamente nueva, era precisamente lo que hacía que la filología moderna fuera posible, y eso Renan lo sabía perfectamente. En efecto, siempre que se habla de «filología» a finales del siglo XVIII y principios del XIX, debemos entender la _nueva_ filología, cuyos éxitos principales incluían la gramática comparada, la nueva clasificación o agrupación de las lenguas en familias y el rechazo de los orígenes divinos del lenguaje. No es exagerado decir que estos logros fueron la consecuencia más o menos directa de la idea de que el lenguaje era un fenómeno enteramente humano, idea que llegó a ser corriente cuando se descubrió empíricamente que las lenguas llamadas sagradas (principalmente el hebreo) no eran de una antigüedad primordial ni de procedencia divina. Lo que Foucault llamó el descubrimiento del lenguaje fue, por tanto, un acontecimiento secular que reemplazó a la concepción religiosa según la cual Dios habría dado el lenguaje al hombre en el Edén. En efecto, una de las consecuencias de este cambio, por el cual una concepción de la filiación lingüística etimológica y dinástica se abandonó por una visión del lenguaje como un dominio autónomo que se apoya en una estructura y coherencia interna, es la dramática subsistencia del interés en las tesis de los orígenes del lenguaje. Mientras discutir sobre dichos orígenes estaba de moda en la época en que el ensayo de Herder sobre los orígenes del lenguaje recibió la medalla de la Academia de Berlín (1772), a partir de la primera década del nuevo siglo fue prácticamente excluido de la discusión erudita en Europa.
Lo que, de diferentes maneras, William Jones afirmó en sus _Anniversary Discourses_ (1785-1792) y Franz Bopp adelantó en su _Vergleichende Grammatik_ (1832) era que la idea de la dinastía divina del lenguaje quedaba definitivamente interrumpida y desacreditada como concepto. En resumen, se necesitaba una nueva concepción histórica, ya que el cristianismo parecía incapaz de resistir las pruebas empíricas que reducían la categoría divina de su principal texto. Para algunos, como dijo Chateaubriand, la fe era inquebrantable, a pesar de que sabían que el sánscrito era anterior al hebreo:
¡Ay! Lo que ha ocurrido es que un conocimiento más profundo de la lengua culta de la India ha hecho que numerosos siglos vuelvan al estrecho círculo de la Biblia. Qué bien que volví a hacerme creyente antes de tener que experimentar esta mortificación.
Para otros, especialmente para los filólogos, como el pionero Bopp, el estudio del lenguaje entrañaba su propia historia, su propia filosofía y su propio saber, lo cual eliminaba cualquier noción sobre una lengua primera dada por Dios al hombre en el Edén. Como el estudio del sánscrito y la tendencia expansiva de finales del siglo XVIII parecían haber desplazado los primeros comienzos de la civilización más hacia el este de los países bíblicos, así también el lenguaje dejó de manifestar la continuidad entre un poder exterior y el locutor humano, y se convirtió en un campo interno creado y realizado por aquellos que lo utilizaban. No hubo una lengua primitiva, igual que —salvo por un método que a continuación voy a exponer— no hubo una lengua simple.
El legado de esta primera generación de filólogos fue para Renan muy importante, más incluso que la obra de Sacy. Siempre que hablaba de la lengua y la filología, ya fuera al inicio, en el intermedio o al final de su larga carrera, repetía las lecciones de la nueva filología, cuyo mayor pilar lo constituyeron los dogmas antidinásticos y anticontinuos de la práctica de la lingüística técnica (opuesta a la divina). Para la lingüística, el lenguaje no podía ser descrito como el resultado de una fuerza que emanaba unilateralmente de Dios. Como Coleridge dijo, «el lenguaje es el arsenal de la mente humana; contiene los trofeos de su pasado y las armas de sus conquistas futuras». La idea de un primer lenguaje edénico fue desplazada por la noción heurística de una protolengua (el indoeuropeo, el semítico) cuya existencia nunca se debatía porque se reconocía que una lengua de este género no podía ser restablecida, sino solamente reconstruida a través de un proceso filológico. Si consideramos que una lengua sirve, de nuevo heurísticamente, como piedra de toque para todas las demás, el sánscrito es la forma más antigua del indoeuropeo. La propia terminología ha cambiado: ahora hay _familias_ de lenguas (la analogía con las clasificaciones de las especies y las clasificaciones anatómicas es notoria), hay una forma lingüística _perfecta_ , la cual no necesita corresponderse con ninguna lengua «real», y hay lenguas originales solo como una función del discurso filológico y no de la naturaleza.
Sin embargo, algunos escritores han comentado acertadamente el hecho de que el sánscrito y las realidades de la India en general simplemente estaban ocupando el lugar del hebreo y de la ilusión edénica. Ya en 1804, Benjamin Constant señaló en su _Journal Intime_ que no iba a hablar de la India en su _De la Religion_ porque entre los ingleses que la dominaban y los alemanes que la estudiaban infatigablemente ese país se había convertido en la _fons et origo_ de todo; luego vinieron los franceses que, después de Napoleón y Champollion, decidieron que todo se había originado en Egipto y en el nuevo Oriente. Estos entusiasmos teleológicos se alimentaron, después de 1808, de la célebre obra de Friedrich Schlegel, _Über die Sprache und Weisheit der Indier_ , que parecía confirmar su propia afirmación de 1800, según la cual Oriente era la forma más pura de romanticismo.
Lo que la generación de Renan —educada entre 1835 y 1848— retuvo de todo este entusiasmo por Oriente era la necesidad intelectual de Oriente para todo erudito occidental especializado en lenguas, culturas y religiones. El texto clave en este punto fue _Le Génie des religions_ (1832), de Edgar Quinet, una obra que anunciaba el resurgir oriental y ponía en contacto a Oriente y Occidente a través de una mutua relación funcional. Ya he mencionado la gran significación de esta relación tal y como la analiza comprensible y profundamente Raymond Schwab en _La Renaissance orientale_ ; por lo que me concierne, lo único que quiero es señalar los aspectos específicos de la obra que pesaron en la vocación de Renan por la filología y el orientalismo. La asociación de Quinet con Michelet y su interés por Herder y Vico, respectivamente, inculcaron a estas nuevas generaciones la necesidad, como historiadores eruditos que eran, de afrontar, casi a la manera de un público que ve cómo se desenvuelve un suceso teatral o de un creyente testigo de una revelación, lo diferente, lo extraño y lo distante. La formulación de Quinet es que Oriente propone y Occidente dispone: Asia tiene sus profetas, Europa tiene sus doctores (esto es, sus intelectuales, sus científicos: el juego de palabras es intencionado). De este encuentro nace un nuevo dogma o un nuevo dios; pero lo que quiere decir Quinet es que el Este y el Oeste cumplen con sus destinos y confirman sus identidades en este encuentro. La actitud erudita, la del erudito occidental que examina desde un lugar particularmente bien elegido el Oriente pasivo, seminal, femenino, e incluso silencioso y débil, y que luego lo _articula_ para hacerle revelar sus secretos a través de su autoridad erudita de filólogo, capaz de descodificar las lenguas secretas y esotéricas, persistirá en Renan. Lo que, sin embargo, no mantuvo Renan en la década de 1840, durante su aprendizaje como filólogo, fue la actitud teatral, que reemplazó por la actitud científica.
Para Quinet y Michelet, la historia era una obra de teatro. Quinet describe de modo significativo el mundo como un templo, y la historia humana como una especie de rito religioso. Michelet y Quinet _veían_ el mundo del que trataban. El origen de la historia de la humanidad era algo que podían describir en los mismos términos espléndidos, apasionados y dramáticos que Vico y Rousseau emplearon para retratar la vida en la tierra en épocas primitivas. Para Michelet y Quinet no cabía la menor duda de que ellos pertenecían a la comunidad romántica europea que pretendía «ya fuera en la epopeya o en cualquier otro género mayor —el drama, la prosa romance o la "gran oda" visionaria— reestructurar radicalmente, en un lenguaje adecuado a las circunstancias históricas e intelectuales de su propio tiempo, el esquema cristiano de la caída, la redención y la aparición de una tierra nueva que constituiría un paraíso restaurado». Creo que para Quinet la idea de un nuevo dios naciente ocupaba, en suma, el lugar que la desaparición del antiguo dios había dejado vacante; pero para Renan ser filólogo significaba privarse de cualquier relación con el viejo dios de los cristianos, de tal forma que, en su lugar, una nueva doctrina —probablemente la ciencia— ocuparía, libremente un espacio nuevo. Renan iba a consagrar toda su carrera a dar cuerpo a este progreso.
Él mismo lo dice muy claramente al final de su mediocre ensayo sobre los orígenes del lenguaje: el hombre ya no es un inventor y la era de la creación definitivamente ha pasado. Hubo un período, sobre el cual solo podemos hacer suposiciones, en el que el hombre fue literalmente _transportado_ del silencio a las palabras. Después de esto, existió el lenguaje, y para el verdadero hombre de ciencia el objetivo es examinar cómo es el lenguaje, no cómo ha llegado. Sin embargo, si Renan descarta la creación apasionada de los tiempos primitivos (que había fascinado a Herder, Vico, Rousseau e incluso a Quinet y Michelet), instituye en su lugar un tipo nuevo y deliberado de creación artificial, una creación que se lleva a cabo como producto de un análisis científico. En su _leçon inaugurale_ en el Collège de France (el 21 de febrero de 1862), proclamó que sus cursos estaban abiertos al público para que este pudiera ver sin intermediarios « _le laboratoire même de la science filologique_ ». Cualquiera que hubiera leído a Renan habría comprendido que una afirmación así solo era una ironía típica, aunque débil, que pretendía deleitar pasivamente antes que sorprender. Cuando Renan accedió a la cátedra de hebreo, su primera lección versó sobre la contribución de los pueblos semíticos a la historia de la civilización. ¿Qué mayor afrenta se le podía hacer sutilmente a la historia «sagrada» que la de sustituir la intervención divina en la historia por un laboratorio filológico, y la de declarar que, en consecuencia, el interés de Oriente simplemente residía en la utilidad de su material para las investigaciones europeas? Los fragmentos sin vida que Silvestre de Sacy había dispuesto en tablas estaban siendo reemplazados por algo nuevo.
La conmovedora peroración con la que Renan concluye su _leçon_ tenía otra función además de la de conectar la filología semítica y oriental con el futuro y con la ciencia. Étienne Quatremère, quien había precedido a Renan en la cátedra de hebreo, había personificado la caricatura popular de lo que era un erudito. Dotado de una gran capacidad de trabajo y prodigiosamente pedante en sus maneras, llevó a cabo su trabajo —escribió Renan en un artículo bastante frío dedicado a su memoria en el _Journal des débats_ en octubre de 1857— como un trabajador laborioso que, aunque prestó numerosos servicios con su esfuerzo, no fue capaz de ver el conjunto del edificio que se estaba construyendo. El edificio no era ni más ni menos que _«la science historique de l'esprit humain»_ que estaba en proceso de construcción piedra sobre piedra. Quatremère no era de nuestra época, y Renan en su trabajo estaba decidido a serlo. Además, si Oriente hasta entonces se había identificado exclusiva e indiscriminadamente con la India y China, la ambición de Renan era labrarse una provincia oriental para sí mismo: el Oriente semítico. No dudaba en destacar la confusión fortuita y seguramente bastante corriente que existía entre el árabe y el sánscrito (como ocurría en _La Peau de Chagrin_ ,* de Balzac, donde la inscripción árabe del talismán fatídico es descrita como sánscrito) y se dedicó, pues, a realizar con las lenguas semíticas lo que Bopp había hecho con el indoeuropeo, según dijo en 1855 en el prefacio de su tratado comparativo de las lenguas semíticas. Por tanto, los planes de Renan consistían en iluminar las lenguas semíticas con una luz viva y fascinante, _à la_ Bopp, y en elevar el estudio de esas lenguas inferiores e ignoradas a la categoría de una nueva ciencia apasionante del espíritu, _à la_ Louis Lambert.
En más de una ocasión Renan afirmó de modo bastante explícito que los semitas y el semítico eran _créations_ del estudio filológico orientalista. Como él era quien realizaba el estudio, esto quería decir que la importancia de su papel en esta creación nueva y artificial no ofrecía dudas. Sin embargo, ¿cómo entendía Renan la palabra _création_ en estas circunstancias? ¿Cómo estaba relacionada esta _création_ con la creación natural o con la creación que Renan y otros atribuían a un laboratorio y a unas ciencias clasificatorias y naturales, principalmente a la que se denominaba anatomía filosófica? En este punto no nos queda más remedio que especular un poco. A lo largo de su carrera parece que Renan imaginaba que el papel de la ciencia en la vida humana (y cito, traduciendo de la manera más literal que puedo) consistía en: «decir (hablar o articular) definitivamente al hombre el nombre [¿logos?] de las cosas». La ciencia otorga el discurso a las cosas; más aún, la ciencia saca a relucir (razón para ser pronunciado) el discurso potencial intrínseco a las cosas. El especial valor de la lingüística (como se ha denominado con frecuencia a la mueva filología) no viene determinado porque se parezca a las ciencias naturales, sino más bien porque se ocupa de las palabras como si fueran objetos naturales y silenciosos a los que se obliga a revelar sus secretos. Es necesario recordar que el mayor paso dado en el estudio de las inscripciones y de los jeroglíficos se produjo cuando Champollion descubrió que los símbolos trazados en la Piedra de Rosetta tenían un componente _fonético_ , así como semántico. Hacer que los objetos hablaran era como hacer que las palabras hablaran, era darles valor de circunstancia y un lugar preciso en un orden de regularidad regido por una ley. En su primera acepción, la palabra _création_ , tal y como la empleaba Renan, significaba la articulación por la cual un objeto como el _semítico_ podía ser considerado en cierto modo una criatura. En la segunda, _création_ también se refería al decorado —en el caso del semítico significaba historia, cultura, raza y espíritu orientales— que el hombre de ciencia había esclarecido y rescatado de su mutismo. Finalmente, _création_ era la formulación de un sistema de clasificación por el cual era posible observar el objeto en cuestión comparativamente con otros objetos semejantes; y al decir «comparativamente» Renan se refería a una completa red de relaciones paradigmáticas que funcionaba entre las lenguas semíticas y las indoeuropeas.
Si hasta ahora he insistido tanto en este estudio relativamente olvidado que Renan escribió acerca de las lenguas semíticas es por muchas razones. El semítico fue el estudio científico hacia el cual se inclinó después de haber perdido su fe cristiana; ya he expuesto antes cómo llegó a concebir el estudio del semítico como un sustituto de su fe que le permitía relacionarse de modo crítico con ella. El estudio del semítico fue el primer trabajo orientalista y científico de verdadero valor realizado por Renan (terminado en 1847, se publicó por primera vez en 1855), y formó parte de sus principales trabajos posteriores sobre los orígenes del cristianismo y sobre la historia de los judíos como si fuera una propedéutica de ellos. Por su intención, por no decir por sus logros —es interesante señalar que fueron pocas las obras clásicas o contemporáneas sobre la historia del orientalismo o sobre la historia de la lingüística que hicieron algo más que citar de pasada a Renan—, su trabajo sobre el semítico se proponía como una ruptura filológica, en el que años después él siempre apoyó sus posturas (con frecuencia malas) sobre religión, raza y nacionalismo. Siempre que Renan quería hacer una afirmación a propósito de los judíos o de los musulmanes, por ejemplo, lo hacía conservando sus críticas manifiestamente duras hacia los semitas (críticas sin fundamento, excepto según la ciencia que él practicaba). Además, el semítico de Renan pretendió ser una contribución tanto al desarrollo de la lingüística indoeuropea como a la diferenciación de los orientalismos. Para el primero, a la forma semítica le correspondía una forma degradada, tanto en un sentido moral como biológico; para el segundo, era una —por no decir la— forma estable de decadencia cultural. Para terminar, el semítico era la primera creación de Renan, una ficción que él había inventado en el laboratorio filológico para satisfacer el sentido que tenía sobre su lugar y su misión públicos. No debemos perder de vista ni un instante que el semítico era para el ego de Renan el símbolo de la dominación europea (y, en consecuencia, de la suya) sobre Oriente y sobre su propia época.
Por tanto, como rama de Oriente, el semítico no era enteramente un objeto natural —como, por ejemplo, una especie de mono— ni era completamente un objeto no natural o divino, como había sido considerado una vez. Más bien el semítico ocupaba una posición intermedia, legitimada en sus irregularidades (la regularidad la definía el indoeuropeo) por una relación inversa con las lenguas regulares, comprendido como un fenómeno excéntrico y cuasi monstruoso en parte porque las bibliotecas, los laboratorios y los museos podían servir para exponerlo y analizarlo. En su tratado Renan adoptó un tono de voz y un método de exposición que se derivaban, en gran medida, del conocimiento libresco y de la observación de la naturaleza que habían practicado hombres como Cuvier y los Geoffroy Saint-Hilaire, _père et fils_. Esto suponía un logro estilístico importante, ya que le permitía utilizar de una manera coherente la _biblioteca_ —en lugar del primitivismo o el _fiat_ divino—, como marco conceptual en el que comprender la lengua, y servirse al mismo tiempo del _museo_ , que era el lugar al que se llevaban los resultados de las observaciones del laboratorio para exhibirlos, estudiarlos y enseñarlos. Renan siempre trata de realidades humanas concretas —la literatura, la historia, la cultura, la inteligencia y la imaginación— como si se hubieran transformado en otra realidad particularmente desviada, porque son semíticas y orientales y porque terminan en el laboratorio para ser analizadas. Por eso, los semitas son monoteístas fanáticos que no han producido mitología, arte, comercio, ni civilización; tienen una conciencia estrecha y rígida; en conjunto representan « _une combinaison inférieure de la nature humaine_ ». Al mismo tiempo Renan quiere dejar claro que él habla de un prototipo, pero no de un verdadero tipo semita con una existencia real (aunque no mantiene tampoco esta posición en muchos de sus escritos cuando habla de los judíos y musulmanes de hoy con muy poca objetividad científica). Así, por un lado tenemos la transformación del humano en un espécimen y, por otro, el juicio comparativo por el que el espécimen permanece como espécimen y como tema de estudio filológico y científico.
Diseminadas a lo largo de su _Histoire générale et système comparé des langues sémitiques_ hay algunas reflexiones sobre los vínculos entre la lingüística y la anatomía —para Renan son igualmente importantes—; son notas acerca de cómo estos vínculos podrían ser empleados para hacer la historia humana ( _les sciences historiques_ ). Pero primero debemos considerar los vínculos implícitos. No creo que sea erróneo o exagerado decir que una página típica de la _Histoire générale_ orientalista de Renan se construía tipográfica y estructuralmente pensando en una página de anatomía filosófica comparada al estilo de Cuvier o Geoffroy Saint-Hilaire. Los lingüistas y los anatomistas pretenden hablar de temas que no son directamente accesibles ni observables en la naturaleza; un esqueleto o el dibujo detallado de un músculo y los paradigmas constituidos por los lingüistas a partir de un protosemítico o de un protoindoeuropeo puramente hipotéticos son del mismo modo productos de laboratorio y de biblioteca. El texto de una obra de lingüística o de anatomía tiene la misma relación general con la naturaleza (o con la realidad) que la vitrina de un museo que muestra un espécimen de mamífero o un órgano. Lo que se ofrece en el caso de la página y en el del museo es una exageración trucada, como muchos de los fragmentos orientales de Sacy, cuyo propósito es exhibir una relación entre la ciencia (o el científico) y el objeto, pero no una relación entre el objeto y la naturaleza. Léase una página cualquiera de Renan sobre el árabe, el hebreo, el arameo o el protosemítico y se leerá un acto de poder, por el cual la autoridad del filólogo orientalista selecciona a voluntad de la biblioteca ejemplos del discurso humano, y los remite a ella rodeados por una suave prosa europea que destaca los defectos, las virtudes, los barbarismos y las imperfecciones de la lengua, el pueblo y la civilización. El tono y el tiempo de la exposición se expresan casi de modo uniforme en el presente actual, y esto produce la impresión de una demostración pedagógica durante la cual el erudito-científico se coloca ante nosotros en la plataforma de una clase-laboratorio para crear, encerrar y juzgar la materia que estudia.
El deseo de Renan de transmitir la idea de que se está llevando a cabo una demostración se intensifica cuando explícitamente señala que mientras la anatomía emplea signos estables y visibles con los que asignar objetos a tipos generales, la lingüística no lo hace. El filólogo debe, por tanto, hacer corresponder de una manera u otra un hecho lingüístico dado con un período histórico: de ahí la posibilidad de una clasificación. Sin embargo, como Renan decía con frecuencia, la temporalidad lingüística y la historia están llenas de lagunas, de enormes discontinuidades y de períodos hipotéticos. Así, los sucesos lingüísticos ocurren en una dimensión temporal no lineal y esencialmente discontinua que la lingüística controla de una manera muy particular. Esta manera es comparativa, como todo el tratado de Renan sobre la rama semítica de las lenguas orientales se empeña en demostrar: el indoeuropeo se toma como la norma viva y _orgánica_ y, por comparación, se observa que las lenguas orientales semíticas son _inorgánicas_. El tiempo se transforma en el espacio de una clasificación comparativa que, en el fondo, se fundamenta en una oposición binaria rígida entre las lenguas orgánicas e inorgánicas. Por tanto, por un lado está el proceso orgánico y biológicamente generativo representado por el indoeuropeo, mientras que por otro está el proceso inorgánico esencialmente no regenerativo, osificado en el semítico. Y lo que es más importante, Renan afirma de una manera muy clara que un juicio tan imperioso como este lo ha emitido el filólogo orientalista en su laboratorio, ya que las distinciones como las que él ha hecho solo son posibles y accesibles para un especialista preparado:
Por tanto, nos negamos a admitir que las lenguas semíticas tengan la facultad de regenerarse, aunque reconozcamos que no escapan, más que otras obras de la conciencia humana, a la necesidad del cambio y de las modificaciones sucesivas.
Pero tras esta oposición radical existe otra que actúa en la mente de Renan y en algunas páginas del primer capítulo del libro V expone su posición de un modo cándido al lector. Esto sucede cuando presenta las opiniones de Geoffroy Saint-Hilaire sobre la «degradación de los tipos». Aunque Renan no especifica de qué Geoffroy Saint-Hilaire se trata, la referencia es bastante clara ya que tanto Étienne como su hijo Isidore fueron muy conocidos y extraordinariamente influyentes, sobre todo entre los literatos franceses de la primera mitad del siglo XIX, por sus reflexiones como biólogos. Recordemos que Étienne fue miembro de la expedición napoleónica y que Balzac le dedicó una parte importante del prefacio de _La comedia humana_ ; muchas evidencias indican que también Flaubert leyó a ambos, al padre y al hijo, y usó sus puntos de vista en su obra. Étienne e Isidore no solo fueron herederos de la tradición de la biología «romántica», que incluía a Goethe y Cuvier, interesados por la analogía, la homología y por la _ur-form_ * en las especies, sino que también fueron especialistas en la filosofía y la anatomía de la monstruosidad —la teratología, como Isidore la llamó—, según la cual las aberraciones fisiológicas más horrendas se consideraban el resultado de una degradación interna dentro de la vida de la especie. No puedo aquí entrar en las complejidades (y en la fascinación macabra) de la teratología; es suficiente con mencionar que Étienne e Isidore Geoffroy Saint-Hilaire explotaron el poder teórico del paradigma lingüístico para explicar las desviaciones posibles dentro del sistema biológico. Así, Étienne pensaba que un monstruo era una _anomalía_ , en el mismo sentido en que en una lengua las palabras existen en relaciones analógicas y anómalas entre sí: en lingüística esta idea se remonta al menos a _De lingua latina_ de Varrón. Ninguna anomalía puede considerarse simplemente como una excepción gratuita, sino que, por el contrario, las anomalías confirman la estructura regular que conecta a todos los miembros de la misma clase. En anatomía esta opinión era muy audaz. Étienne Geoffroy Saint-Hilaire dice en cierto momento del «Préliminaire» a su _Philosophie anatomique_ :
Y, en efecto, el carácter de nuestra época es tal que hoy es imposible encerrarse estrictamente en el marco de una simple monografía. Estudie un objeto aislado y solo será capaz de devolverlo a sí mismo; en consecuencia, solo podrá tener un conocimiento imperfecto. Pero obsérvelo en medio de seres que están vinculados entre sí de diferentes maneras y que se apartan de otros de maneras diferentes, y descubrirá relaciones más extensas. Primero lo conocerá mejor, incluso en su especificidad: pero lo que es más importante, al considerarlo en el centro de su propia esfera de actividad, conocerá con precisión cómo se comporta en su propio mundo exterior y cómo sus propias características se construyen por reacción a su medio ambiente.
Geoffroy Saint-Hilaire no solo dice que el carácter específico de la investigación de su época (escribe en 1822) es el examen comparativo de los fenómenos; también declara que para un hombre de ciencia no existe ningún fenómeno que, por muy aberrante y excepcional que sea, no pueda explicarse haciendo referencia a otros fenómenos. Señalemos también cómo Geoffroy Saint-Hilaire emplea la metáfora del centro ( _le centre de sa sphère d'activité_ ) que después utilizará Renan en _El porvenir de la ciencia_ para describir la posición que ocupa todo objeto en la naturaleza —incluido el filólogo— una vez que el objeto es científicamente _situado_ allí por el científico que lo examina. Después, entre el objeto y el científico se establece un vínculo solidario. Naturalmente, esto solo puede ocurrir durante la experiencia realizada en el laboratorio y no en cualquier lugar. Lo que se quiere demostrar es que un científico dispone de una cierta ventaja que le permite ver naturalmente y conocer científicamente incluso un suceso totalmente inusual; esto significa que puede hacerlo sin el concurso de lo sobrenatural, recurriendo solamente a un medio ambiente constituido por el científico. En consecuencia la propia naturaleza puede ser percibida de nuevo como continua, armoniosamente coherente y fundamentalmente inteligible.
Así, para Renan el semítico es un fenómeno con un desarrollo interrumpido si lo comparamos con las lenguas y las culturas maduras del grupo indoeuropeo e incluso con las demás lenguas semíticas orientales. Sin embargo, la paradoja que sostiene Renan es que, aunque a veces nos hace ver que las lenguas se corresponden de alguna manera con _«êtres vivants de la nature»_ , en otros momentos demuestra que sus lenguas orientales, las lenguas semíticas, son inorgánicas, detenidas, totalmente osificadas e incapaces de regenerarse; en otras palabras, prueba que el semítico no es una lengua viva y, por tanto, los semitas tampoco son seres vivos. Además, la lengua y la cultura indoeuropeas están vivas y son orgánicas a causa del laboratorio y no a pesar de él. Lejos de ser un asunto marginal en Renan, esta paradoja constituye, en mi opinión, el centro de su obra, de su estilo y de su existencia en el archivo de la cultura de su tiempo; cultura a la que hizo importantes contribuciones igual que otros hombres tan diferentes entre sí como Matthew Arnold, Oscar Wilde, James Frazer y Marcel Proust. Ser capaz de sustentar una visión que incorpora y mantiene la vida y a las criaturas cuasi vivientes (el indoeuropeo y la cultura europea) junto con los fenómenos inorgánicos paralelos cuasi monstruosos (el semítico, la cultura oriental) es precisamente el éxito del científico europeo en su laboratorio. Él _construye_ , y el acto mismo de construir es un signo del poder imperial sobre los fenómenos recalcitrantes, al tiempo que una confirmación de la cultura dominante y su «naturalización». En realidad, no es decir mucho que el laboratorio filológico de Renan es el verdadero local de su etnocentrismo europeo; lo que hay que destacar es que el laboratorio filológico no existe fuera del discurso o de los escritos a través de los cuales se produce y se experimenta constantemente. De este modo, incluso la cultura que él llama orgánica y viva —la europea— es también una _criatura en proceso de creación_ en el laboratorio y por la filología.
La última parte de la carrera de Renan fue totalmente europea y cultural y estuvo jalonada de algunas realizaciones que le hicieron célebre. Si su estilo consiguió alguna autoridad, creo que se debió a la técnica que poseía para construir lo inorgánico (o lo perdido) y para darle la apariencia de vida. Lo que le hizo más famoso, naturalmente, fue su _Vie de Jésus_ ,* la obra que inauguró su historia monumental sobre el cristianismo y el pueblo judío. No obstante, tenemos que tener en cuenta que la _Vida de Jesús_ fue exactamente una obra del mismo tipo de hazaña que la _Histoire générale_ , la construcción de un historiador capaz de fabricar hábilmente —la paradoja se verá enseguida— una biografía oriental muerta (para Renan muerta en el doble sentido de una fe muerta y de un período histórico perdido y luego muerto), _como si fuera_ la narración verídica de una vida natural. Todo lo que Renan decía había pasado primero por el laboratorio filológico; cuando aparecía en el tejido impreso del texto, tenía la fuerza creadora de vida de una marca cultural contemporánea que extraía de la modernidad todo su poder científico y su autosatisfacción. Para este tipo de cultura, las entidades históricas, como la dinastía, la tradición, la religión y las comunidades étnicas, existían todas simplemente en función de una teoría cuya labor era instruir al mundo. Al adoptar esta última frase de Cuvier, Renan estaba situando con circunspección la demostración científica por encima de la experiencia; la temporalidad era relegada al mundo de la experiencia cotidiana, sin utilidad científica, mientras que a la periodicidad particular de la cultura y al comparativismo cultural (que engendró el etnocentrismo, la teoría racial y la opresión económica) se les concedían por adelantado los poderes de una visión moral.
El estilo de Renan, su carrera de orientalista y de hombre de letras, el contexto del sentimiento que comunica y su relación especialmente íntima con la cultura general y erudita de la Europa de su época —liberal, exclusivista, imperiosa y antihumana, en un sentido muy particular— yo los calificaría de _célibes_ y científicos. Para él, la creación era algo encerrado en el reino de _l'avenir_ , que asoció con la ciencia en su célebre manifiesto. Aunque como historiador de la cultura pertenece a la escuela de hombres como Turgot, Condorcet, Guizot, Cousin, Jouffroy y Ballanche, y como erudito a la escuela de Silvestre de Sacy, Caussin de Perceval, Ozanam, Fauriel y Burnouf, el mundo de Renan es un mundo de historia y de ciencia particularmente devastado y furiosamente masculino; en realidad no es el mundo de padres, madres y niños, sino el de hombres como su Jesús, su Marco Aurelio, su Caliban* y su dios solar (este último, tal y como lo describe en «Rêves» en los _Dialogues philosophiques_ ). Apreció de modo peculiar el poder de la ciencia y de la filología orientalista; buscó sus visiones penetrantes y sus técnicas y las utilizó para intervenir, normalmente con una eficacia considerable, en la vida de su época. Y, sin embargo, para él el papel ideal era el de espectador.
Según Renan, un filólogo debía preferir el _bonheur_ a la _jouissance_ ; es decir, elegir la felicidad elevada, aunque fuera estéril, en lugar del placer sexual. Las palabras pertenecen al ámbito del _bonheur_ , al igual que el estudio de las palabras, si hablamos de un modo ideal. Según mis conocimientos, en los escritos públicos de Renan hay muy pocos lugares en los que asigne un papel beneficioso y activo a las mujeres. En una ocasión considera que las mujeres extranjeras (nodrizas y sirvientes) debieron de instruir a los niños de los conquistadores normandos, y que eso pudo ser una de las causas de los cambios que se produjeron en la lengua; pero hay que señalar que no dice que esto favoreciera la productividad y la diseminación, sino el cambio interno y, con él, un cambio subsidiario. «El hombre —dice al final del mismo ensayo— no pertenece ni a su lengua ni a su raza; se pertenece a sí mismo antes que nada, ya que antes que nada es un ser libre y moral.» El hombre era libre y moral, pero encadenado por la raza, la historia y las ciencias que, según las concebía Renan, eran condiciones que el erudito imponía al hombre.
El estudio de las lenguas orientales le llevó hasta el corazón de estas condiciones, y la filología en concreto puso de manifiesto que el conocimiento del hombre no era poéticamente transfigurante —parafraseando a Ernst Cassirer—, a no ser que previamente hubiera sido separado de la realidad (igual que Sacy había separado necesariamente sus fragmentos de árabe de su realidad) y, por tanto, atrapado en una camisa de fuerza doxológica. Al convertirse en _filología_ , el estudio de las palabras que antes habían realizado Vico, Herder, Rousseau, Michelet y Quinet perdió su trama y su calidad de presentación dramática, como dijo Schelling. En su lugar la filología se convirtió en algo complejo desde un punto de vista epistemológico; el _Sprachgefühl_ ya no era suficiente, ya que las propias palabras se relacionaban menos con los sentidos o el cuerpo (como Vico había creído) que con un mundo ciego, sin imágenes y abstracto regido por formulaciones de invernadero como la raza, la mente, la cultura y la nación. En este mundo que estaba construido en forma de discurso y que era llamado Oriente, se podían hacer cierta clase de afirmaciones que poseían todas el mismo grado de generalidad poderosa y de validez cultural. Todo el esfuerzo de Renan fue negarle a la cultura oriental el derecho a ser creada, excepto artificialmente en el laboratorio filológico. Un hombre no era hijo de la cultura; esa concepción dinástica había sido puesta en duda con bastante eficacia por la filología. La filología enseñaba que la cultura era una construcción, una _articulación_ (en el mismo sentido en que Dickens usó la palabra para la profesión de Mr. Venus en _Our Mutual Friend_ ), incluso una creación, pero nada más que una estructura cuasi orgánica.
Lo que me interesa de manera particular en Renan es conocer hasta qué punto él sabía que era una criatura de su tiempo y de su cultura etnocéntrica. Respondiendo a un discurso académico pronunciado por Ferdinand de Lesseps en 1885, Renan afirmó: «Era tan triste ser más sabio que la propia nación [...]. No se puede sentir amargura hacia la patria. Mejor es equivocarse con ella que tener demasiada razón con aquellos que dicen duras verdades». La economía de esta declaración es casi demasiado perfecta para ser verdad. En efecto, ¿no dice el viejo Renan que la mejor relación es la de paridad con la propia cultura, su moralidad y su _ethos_ durante la vida y no una relación dinástica según la cual se es o un hijo de la propia época o su progenitor? Y, en este punto, volvemos al laboratorio, ya que es ahí, según pensaba Renan, donde cesan las responsabilidades filiales y, en última instancia, sociales y donde las responsabilidades científicas y orientalistas toman el relevo. Su laboratorio era la plataforma desde la que, como orientalista, Renan se dirigía al mundo; mediatizaba sus declaraciones, les daba confianza, precisión general así como continuidad. De este modo, el laboratorio filológico tal y como Renan lo entendía no solo redefinió su época y su cultura dotándolas y dándoles forma a través de nuevas maneras, sino que dio a la materia oriental una coherencia erudita y, más aún, le convirtió a él (y más tarde a los orientalistas que siguieron su tradición) en la figura de la _cultura_ occidental que ha llegado a ser. Nosotros quizá debamos preguntarnos si esta nueva autonomía dentro de la cultura era la libertad que, según esperaba Renan, iba a traer consigo su ciencia orientalista filológica o si, según entendería un historiador crítico del orientalismo, establecía una afiliación compleja entre el orientalismo y su supuesta materia humana subjetiva, afiliación que se basaba finalmente en el poder y no en la objetividad desinteresada.
### III
### El estudio y la experiencia de Oriente: los requisitos de la lexicografía y la imaginación
Las opiniones de Renan sobre los semitas orientales obedecen menos al ámbito de los prejuicios populares y del antisemitismo corriente que al de la filología oriental científica. Cuando leemos a Renan y a Sacy podemos observar fácilmente cómo las generalizaciones culturales habían empezado a adquirir la estructura de enunciados científicos y la atmósfera del estudio correctivo. Como muchas especialidades académicas en sus comienzos, el orientalismo moderno mantenía su material de estudio, que él mismo definía, apresado en una especie de torno que le impedía evolucionar. Por esta razón desarrolló un vocabulario erudito cuyas funciones, al igual que su estilo, situaban a Oriente en una estructura _comparativa_ de la misma clase que la que Renan empleaba y manipulaba. Este tipo de comparación apenas es descriptivo y, con frecuencia, sirve tanto para evaluar como para exponer. A continuación podemos apreciar el modo comparativo típico de Renan:
Podemos observar cómo en todos los aspectos de la vida la raza semítica parece incompleta debido a su simplicidad. Esta raza —si me atrevo a usar la analogía— es para la familia indoeuropea lo que el carboncillo para la pintura; carece de esa variedad, de esa amplitud y de esa abundancia de vida que es condición de lo perfecto. Igual que esos seres tan poco fecundos que, tras una infancia agradable, solo alcanzan una mediocre virilidad, las naciones semíticas experimentaron su mayor florecimiento en su primera edad, pero nunca fueron capaces de alcanzar la verdadera madurez.
Los indoeuropeos son aquí la piedra de toque, igual que lo son cuando Renan dice que la sensibilidad de los orientales semitas nunca alcanzó los niveles logrados por las razas indogermánicas.
No podemos saber con absoluta certeza si esta actitud comparativa es principalmente una necesidad erudita o si esconde un prejuicio racista etnocéntrico; lo que sí podemos afirmar es que ambas nociones funcionan juntas y se apoyan mutuamente. Lo que Renan y Sacy intentaron hacer fue reducir a dos dimensiones el carácter humano de Oriente, reducción que facilitaba el estudio de sus características pero le despojaba de su humanidad, fuente de posibles complicaciones. En el caso de Renan, la legitimidad de estos esfuerzos se la daba la filología, cuyos dogmas ideológicos fomentaban la reducción de una lengua a sus raíces; hecho esto, el filólogo encuentra la posibilidad de conectar estas raíces lingüísticas, como Renan y otros hicieron con las de la raza, la mente, el carácter y el temperamento. Renan reconoció, por ejemplo, que su afinidad con Gobineau se debía a una perspectiva filológica y orientalista común; y en posteriores ediciones de la _Histoire générale_ incorporó a su propia obra parte del trabajo de Gobineau. Así fue como la comparación en el estudio de Oriente y los orientales llegó a ser sinónimo de la aparente desigualdad ontológica entre Occidente y Oriente.
Vale la pena recapitular brevemente las principales características de esta desigualdad. Ya me he referido al entusiasmo que Schlegel sentía por la India y a su posterior repulsión hacia ella y, naturalmente, hacia el islam. Muchos de los primeros aficionados a Oriente comenzaron acogiendo Oriente como un _dérangement_ saludable de sus hábitos de pensamiento y de espíritu europeos. Sobrevaloraban Oriente a causa de su panteísmo, su espiritualidad, su estabilidad, su longevidad, su primitivismo, etc. Schelling, por ejemplo, pensaba que el politeísmo oriental había preparado el camino para el monoteísmo judeocristiano: Abraham había estado prefigurado por Brahma. Pero casi sin excepción a esta sobreestimación de este tipo le siguió la reacción contraria: de repente Oriente aparecía lamentablemente deshumanizado, antidemocrático, atrasado, bárbaro, etc. Una oscilación del péndulo en una dirección causaba una oscilación igual hacia el lado opuesto: Oriente era minusvalorado. El orientalismo como profesión creció a partir de estas oposiciones, de estas compensaciones y de estas correcciones fundadas en la desigualdad; ideas que eran a la vez resultado y causa de ideas similares existentes en el conjunto de la cultura. En realidad, podemos remontar este proyecto de restricción y de reestructuración asociado con el orientalismo a la desigualdad por la cual la relativa pobreza (o riqueza) de Oriente requería un tratamiento erudito y científico del mismo tipo de los que se llevaban a cabo en disciplinas como la filología, la biología, la historia, la antropología, la filosofía o la economía.
Y de este modo la verdadera profesión del orientalista incluía esta desigualdad y las particulares paradojas que engendraba. Lo más frecuente era que un individuo entrara en esta profesión como una manera de reconocer los derechos de Oriente sobre él; pero lo más habitual era también que su formación de orientalista le abriera los ojos, por decirlo de algún modo, y le dejara simplemente una clase de proyecto demoledor a través del cual lo que antes había sido un Oriente grandioso era reducido considerablemente a dimensiones más pequeñas que nada tenían que ver con las que en otro momento se le habían atribuido. ¿Cómo explicar de otro modo la labor que representa la obra de William Muir (1819-1905), por ejemplo, o la de Reinhart Dozy (1820-1883) y la impresionante antipatía hacia Oriente, el islam y los árabes que encontramos en ambos? Un hecho significativo es que Renan fue uno de los seguidores de Dozy, y en la obra de cuatro volúmenes de Dozy, _Histoire des Mussulmans d'Espagne_ , _jusqu'au la conquête de l'Andalousie par les Almoravides_ (1861),* encontramos muchas de las críticas antisemitas de Renan, que serían compensadas en 1864 por un volumen que demostraba que el dios primitivo de los judíos no era Yavéh sino Baal, y la prueba de esto estaba en La Meca. Los libros de Muir, _Life of Mahomet_ (1858-1861) y _The Caliphate_ , _Its Rise_ , _Decline and Fall_ (1891), todavía se consideran auténticos monumentos de erudición, pero la actitud hacia su materia de estudio lo expresa claramente cuando dijo: «La espada de Mahoma y el Corán son los enemigos más tenaces de la Civilización, de la Libertad y de la Verdad que el mundo jamás ha conocido». Ideas parecidas a estas las podemos encontrar en las obras de Alfred Lyall, uno de los autores que Cromer citaba con aprobación.
Aunque el orientalista no emite juicios sobre su material de la misma forma en que lo hicieron Dozy y Muir, sin embargo se ve influido por el principio de desigualdad expresado por estos. La labor del orientalista profesional sigue siendo juntar los fragmentos de un retrato, como si se tratara de un cuadro restaurado, de Oriente o de lo oriental; fragmentos que, como los desenterrados por Silvestre de Sacy, suministran el material, pero la forma narrativa, la continuidad y las figuras las construye el erudito, para quien la erudición consiste en burlar la no historia irregular (no occidental) de Oriente por medio de una crónica bien ordenada de retratos y tramas. El _Essai sur l'histoire des arabes avant l'islamisme_ , _pendant l'époque de Mahomet_ (obra en tres volúmenes, 1847-1848), de Caussin de Perceval, es un estudio totalmente especializado cuyas fuentes son bien los documentos con los que otros orientalistas (principalmente, claro, Sacy) habían contribuido a su campo de estudios o bien documentos —como los textos de Ibn Jaldún, en los que Caussin confiaba mucho— que se guardaban en las bibliotecas orientalistas de Europa. La tesis de Caussin es que Mahoma hizo de los árabes un pueblo y que el islam fue esencialmente un instrumento político, pero de ningún modo un instrumento espiritual. Caussin se esfuerza en aclarar una enorme cantidad de detalles confusos. De este modo, lo que resulta de su estudio del islam es literalmente un retrato unidimensional de Mahoma, de quien construye, al parecer al final de la obra (después de la descripción de su muerte), una fotografía muy meticulosa y detallada. El Mahoma de Caussin no es un demonio ni un prototipo de Cagliostro, es un hombre que se adapta a una historia del islam (la versión que más se ajusta a sus intenciones) como movimiento exclusivamente político, y que es materializado a través de numerosas citas que están sacadas del texto y del contexto. La intención de Caussin era no omitir nada en lo referente al tema de Mahoma; de ahí que el Profeta sea visto con una luz fría, despojado de su inmensa fuerza religiosa y de toda su capacidad residual de atemorizar a los europeos. Lo importante, lo que resalta en este punto es que el personaje de Mahoma y lo que significó en su propia época y en su propia región está desdibujado de tal forma que solo queda de él una imagen muy reducida, una miniatura.
Un Mahoma análogo al de Caussin y no especializado es el de Carlyle, un Mahoma obligado a servir a una tesis que ignora totalmente las circunstancias históricas y culturales de la época y de la región del propio Profeta. Aunque Carlyle cita a Sacy, su ensayo es claramente una argumentación y una defensa de una serie de ideas generales sobre la sinceridad, el heroísmo y el hecho de ser un profeta. Su actitud es saludable: Mahoma no es un ser de leyenda, un sensualista vergonzoso ni un pequeño hechicero que entrena pichones para que picoteen los guisantes de su oreja. Por el contrario, es un hombre con una verdadera visión y una profunda convicción, a pesar de ser el autor de un libro, el Corán, que es «un revoltijo confuso y fastidioso, indigesto, repetitivo, de una amplitud que hace perder el aliento, embrollado; muy indigesto, informe, en fin, de una estupidez insoportable». Sin ser él mismo un dechado de lucidez y gracia estilística, Carlyle afama estas cosas como una manera de rescatar a Mahoma de los modelos benthamianos, según los cuales tanto Mahoma como él serían condenados juntos. Sin embargo, Mahoma es un héroe trasplantado a Europa desde ese mismo Oriente bárbaro que lord Macaulay encontró deficiente en su famoso «Minute» de 1835, en el que afirmaba que «nuestros nativos sometidos» tenían más que aprender de nosotros que nosotros de ellos.
En otras palabras, tanto Caussin como Carlyle nos mostraron que no debemos temer a Oriente, puesto que las realizaciones orientales están muy lejos de las europeas. Las perspectivas de los orientalistas y de los no orientalistas coinciden en este punto. En efecto, dentro del campo comparativo que llegó a ser el orientalismo después de la revolución filológica de principios del siglo XIX, y fuera de él, en los estereotipos populares o en las imágenes que los filósofos como Carlyle formaron de Oriente y en los estereotipos como los de Macaulay, Oriente en sí mismo fue subordinado intelectualmente a Occidente. Como materia de estudio y de reflexión, Oriente adquirió todas las marcas de una debilidad intrínseca. Se convirtió en el tema de los caprichos de diversas teorías que lo usaban como ilustración. El cardenal Newman, que no era un orientalista, utilizó el islam oriental como punto de partida de sus conferencias de 1853 que pretendían justificar la intervención británica en la guerra de Crimea. Cuvier encontró que Oriente era útil para su obra _Le Régne animal_ (1816). Oriente fue un cómodo tema de conversación que se sacaba en los diversos salones de París. La lista de referencias, préstamos y transformaciones que se asociaba con la idea de Oriente es inmensa, pero en el fondo, lo que realmente realizaron los primeros orientalistas y lo que los no orientalistas de Occidente explotaron fue un modelo reducido de Oriente adaptado a la cultura reinante y dominante y a sus exigencias teóricas (e inmediatamente después, a sus exigencias prácticas).
En determinadas ocasiones podemos encontrar algunas excepciones o, si no excepciones, al menos ciertas complicaciones interesantes de esta asociación desigual entre el Este y el Oeste. Karl Marx definió la noción de sistema económico asiático en su análisis sobre la dominación británica de la India escrito en 1853 e inmediatamente después le añadió la depredación humana introducida dentro de este sistema por la interferencia colonial de Inglaterra, su rapacidad y su completa crueldad. Artículo tras artículo volvía cada vez con mayor convicción a la idea de que incluso destruyendo Asia, Gran Bretaña estaba posibilitando allí una verdadera revolución. El estilo de Marx nos obliga a afrontar, como criaturas individuales que somos, la dificultad que supone intentar reconciliar nuestra repugnancia natural hacia los sufrimientos que padecen los orientales mientras su sociedad se transforma violentamente, con la necesidad histórica de esas transformaciones:
En este momento, por muy triste que sea desde un punto de vista humano ver a esas numerosas organizaciones sociales patriarcales, inofensivas y laboriosas desorganizarse y disolverse en sus elementos constitutivos y lanzarse a un mar de dolor, y observar cómo sus individuos pierden al mismo tiempo su antigua forma de civilización y sus medios de subsistencia tradicionales, no debemos olvidar que esas idílicas comunidades campesinas, a pesar de su aspecto inofensivo, siempre han constituido el sólido fundamento del despotismo oriental, y han mantenido la razón humana constreñida dentro de un marco extremadamente estrecho, convirtiéndola en un instrumento dócil de superstición y en esclava de las reglas admitidas, privándola de toda grandeza y de toda fuerza histórica [...].
Es verdad que Inglaterra, al provocar una revolución social en Indostán, solo actuaba guiada por los más viles intereses, y se comportaba de un modo estúpido para conseguir sus objetivos. Pero la cuestión no es esa. La pregunta es la siguiente: ¿puede la humanidad cumplir con su destino sin una revolución fundamental en el estado social asiático? Si no es así, cualesquiera que hayan sido sus crímenes, al provocar esta revolución, Inglaterra estaba siendo un instrumento inconsciente de la historia. En ese caso, por mucha tristeza que podamos sentir ante el espectáculo del desmoronamiento de un mundo antiguo, tenemos el derecho de exclamar con Goethe:
_Sollte diese Qual uns quälen_
_Da sie unsere Lust vermehrt_
_Hat nicht Myriaden Seelen_
_Timurs Herrschaft aufgeziehrt_?*
La cita con la que Marx apoya su argumento sobre el tormento que produce placer está sacada del _Westöstlicher Diwan_ y nos descubre la fuente de las concepciones que Marx tiene sobre Oriente. Son ideas románticas e incluso mesiánicas: Oriente como material humano es menos importante que como elemento de un proyecto romántico de redención. Los análisis económicos de Marx encajan perfectamente en una típica empresa orientalista, aunque sus sentimientos de humanidad y su simpatía hacia la miseria del pueblo estén claramente comprometidas. Pero, al final, es la visión orientalista y romántica la que gana, mientras que las perspectivas teóricas socioeconómicas de Marx se sumergen en esta imagen clásica:
Inglaterra tiene que cumplir una doble misión en la India, una destructiva y la otra regeneradora: aniquilar la sociedad asiática y establecer los fundamentos de la sociedad occidental en Asia.
La idea de regenerar un Asia fundamentalmente sin vida es puro orientalismo romántico, pero, claro, viniendo del mismo autor que no podía olvidar fácilmente el sufrimiento que implicaba, esta afirmación es inquietante. Nos obliga a plantearnos dos preguntas: primero, ¿cómo la ecuación moral que plantea Marx entre la pérdida de Asia y el gobierno colonial británico que condena, se desvía hacia la antigua desigualdad entre Este y Oeste que hemos estado subrayando? Y segundo, ¿dónde está la solidaridad humana, en qué mundo de pensamiento ha desaparecido mientras la visión orientalista ocupaba su lugar?
Inmediatamente volvemos a comprender que los orientalistas, como muchos otros pensadores de principios del siglo XIX, conciben la humanidad en términos de grandes colectividades o en generalidades abstractas. Los orientalistas no están interesados en los individuos ni son capaces de hablar sobre ellos; en lugar de eso se ocupan de las entidades artificiales que quizá tengan sus raíces en el populismo de Herder. Hay orientales, asiáticos, semitas, musulmanes, árabes, judíos, razas, mentalidades, naciones y otras realidades del mismo tipo, algunas de las cuales son producto de operaciones eruditas del mismo estilo que las que se encuentran en la obra de Renan. De igual modo, la antigua distinción entre «Europa» y «Asia» o entre «Occidente» y «Oriente» reagrupa, tras estas grandes etiquetas, todas las variedades posibles de la pluralidad humana, y las reduce en este proceso a una o dos abstracciones colectivas finales. Marx no es una excepción. Para ilustrar una teoría le era más fácil utilizar el Oriente colectivo que las identidades humanas existenciales, ya que entre Oriente y Occidente, como en una declaración profética, solo importaba o existía la vasta colectividad anónima. Ningún otro tipo de relación estaba disponible, ni siquiera aunque fuera una relación muy limitada.
Marx todavía era capaz de sentir algún tipo de solidaridad, de identificarse, aunque solo fuera un poco, con la pobre Asia: esto nos sugiere que algo ocurrió antes de que las etiquetas vencieran, antes de que Marx se volviera hacia Goethe como fuente de sabiduría sobre Oriente. Es como si la mente individual (Marx en este caso) solo pudiera encontrar una individualidad precolectiva y preoficial en Asia —encontrarla y ceder a las presiones que ejercía sobre sus emociones, sentimientos y sentidos— para abandonarla cuando se enfrentaba a un censor más formidable en el mismo vocabulario que se veía forzado a utilizar. Lo que ese censor hacía era parar y después espantar la solidaridad con una definición: esa gente, decía, no sufre; son orientales y de ahí que deban ser tratados de manera distinta a la que acabas de emplear. La capa de sentimientos, por tanto, desaparecía cuando se encontraba con las definiciones inmutables construidas por la ciencia orientalista y apoyadas por el saber «oriental» (por ejemplo, el _Diwan_ ) supuestamente apropiado para ella. El vocabulario emocionado se disipaba a medida que se sometía a la acción policíaca lexicográfica de la ciencia orientalista e incluso del arte orientalista. Una experiencia era desplazada por una definición de diccionario: esto se advierte claramente en los ensayos de Marx sobre la India, donde lo que al final sucede es que algo le obliga a volver a Goethe y a permanecer en su Oriente orientalizado y protector.
Por una parte, naturalmente, Marx se preocupaba de defender sus propias tesis sobre la revolución socioeconómica; pero, por otra, también parecía haber recurrido a un cuerpo masivo de textos que había sido consolidado internamente por el orientalismo y llevado también por este más allá de los límites de su campo, textos que gobernaban y presidían cualquier afirmación que se hiciera sobre Oriente. En la primera parte de este libro he intentado mostrar cómo este control había tenido una historia cultural general en Europa desde la antigüedad; en esta parte, mi intención ha sido mostrar cómo en el siglo XIX se crearon una terminología y una práctica modernas cuya existencia dominaba el discurso que sobre Oriente realizaban tanto los orientalistas como los no orientalistas. Sacy y Renan eran ejemplos de la manera en que el orientalismo fabricaba, respectivamente, un cuerpo de textos o un proceso enraizado en la filología, por los cuales Oriente adquirió una identidad discursiva que lo ha situado en un nivel inferior con respecto a Occidente. Tomando a Marx como ejemplo de un no orientalista cuyos compromisos primero se disuelven y luego son usurpados por las generalizaciones orientalistas, vemos que debemos tener en cuenta el particular proceso de consolidación lexicográfica e institucional del orientalismo. ¿Qué operación era esta, por la cual siempre que se hablaba de Oriente un mecanismo formidable de definiciones omnicompetentes se presentaba como el único elemento válido para la discusión? Y, desde el momento que debemos exponer cómo actuaba este mecanismo de manera específica (y efectiva) sobre las experiencias humanas que con frecuencia lo contradecían, tenemos también que mostrar dónde fueron _estas_ y qué forma adoptaron _estas_ mientras duraron.
Todo esto es una operación difícil y compleja de describir, al menos tan difícil y tan compleja como ha de explicar la manera en que una disciplina en expansión expulsa a sus rivales y consigue que sus tradiciones, sus métodos y sus instituciones ganen autoridad y que sus afirmaciones, personalidades y organismos adquieran una legitimidad cultural general. Podemos simplificar sensiblemente la complejidad puramente narrativa del proceso especificando los tipos de experiencias características que el orientalismo empleó para sus propios fines y representó para su amplio público de no especialistas. En lo esencial, estas experiencias son la continuación de las que, según he descrito, tenían lugar en Sacy y Renan. Pero mientras estos dos eruditos representan un orientalismo totalmente libresco, ya que ninguno de los dos pretendía tener una competencia particular _in situ_ en lo que a Oriente se refiere, hay otra tradición que reclama su legitimidad por el hecho, particularmente apremiante, de residir en Oriente y de tener con él un contacto existencial verdadero. Anquetil, Jones y la expedición napoleónica definen, por supuesto, los primeros contornos de esta tradición, y serán los que, más tarde, mantengan una influencia inmutable sobre todos los orientalistas residentes en Oriente. Estos contornos son los del poder europeo: residir en Oriente es vivir una vida privilegiada, no la de un ciudadano normal, sino la de un representante europeo cuyo imperio (francés o británico) _contiene_ a Oriente por sus armas militares, económicas y, sobre todo, culturales. La estancia en Oriente y sus frutos eruditos van así a alimentar la tradición libresca de actividades textuales que hemos encontrado en Renan y Sacy. Las dos experiencias juntas constituirán la formidable biblioteca contra la cual nadie, ni siquiera Marx, se podía rebelar y que nadie podía evitar.
Residir en Oriente implica, hasta cierto punto, una experiencia y un testimonio personal. La contribución a la biblioteca del orientalismo y a su consolidación dependen de la manera en que la experiencia y el testimonio cesen de ser documentos puramente personales y lleguen a formar parte de los códigos fundadores de la ciencia orientalista. En otras palabras, dentro de un texto debe tener lugar una metamorfosis que transforme una afirmación personal en una afirmación oficial. Por tanto, el relato de una estancia y una experiencia oriental realizado por un europeo debe despojarse de las descripciones puramente autobiográficas e indulgentes, o al menos reducirlas al mínimo, en favor de descripciones que permitan al orientalismo en general y a posteriores orientalistas en particular sacar, construir y fundar otras observaciones y descripciones científicas. De esta manera una de las cosas que podemos esperar es que los sentimientos personales se conviertan, de modo más explícito que en Marx, en afirmaciones orientales oficiales.
Ahora nos encontramos con una situación más rica y más complicada por el hecho de que durante todo el siglo XIX, Oriente, y especialmente Oriente Próximo, fue uno de los lugares preferidos por los europeos tanto para viajar como para escribir sobre él. Además vemos desarrollarse una literatura europea de estilo oriental basada frecuentemente en las experiencias personales vividas en Oriente. Flaubert nos viene enseguida a la mente como uno de los grandes modelos de esta literatura; Disraeli, Mark Twain y Kinglake son otros ejemplos evidentes. Sin embargo, lo verdaderamente interesante es la diferencia existente entre los textos que pasaron del orientalismo personal al profesional y los que, también basados en la estancia y testimonio personales, siguieron siendo «literatura» sin convertirse en ciencia. Y es esta diferencia la que a continuación voy a explorar.
El hecho de ser europeo en Oriente _siempre_ implica que se tiene conciencia de ser distinto del entorno y de estar en una situación de desigualdad con respecto a él. Pero lo importante es destacar cuál es la intención de esta conciencia. ¿Para qué ir a Oriente? ¿Por qué llegar hasta allí si, como en el caso de algunos escritores, por ejemplo Scott, Hugo y Goethe, se viaja a Oriente para un tipo de experiencia muy concreta sin abandonar realmente Europa? Un número reducido de categorías de intenciones se presentan esquemáticamente. Una: el escritor utiliza su estancia con el objetivo específico de proporcionar al orientalismo profesional material científico. Dos: el escritor que tiene el mismo propósito pero que es menos propenso a sacrificar la originalidad y el estilo propios de su conciencia individual a las definiciones orientalistas impersonales. Estas últimas aparecen en su obra, pero no se distinguen fácilmente de sus caprichos estilísticos personales. Tres: el escritor para el que el viaje a Oriente, real o metafórico, supone la realización de un proyecto profundamente sentido y acuciante; su texto se construye sobre una estética personal y es alimentado e informado por el proyecto. En las categorías dos y tres hay bastante más espacio que en la uno para la participación de una conciencia personal —o al menos no orientalista—. Si escogemos _Manners and Customs of the Modern Egyptians_ , de Edward William Lane, como ejemplo excepcional de la categoría uno; _Mi peregrinación a Medina y La Meca_ , de Burton, como perteneciente a la categoría dos, y _Voyage en Orient_ , de Nerval, como representante de la tres, advertiremos claramente cuál es el espacio relativo dejado en el texto a la presencia e identidad del autor.
Sin embargo, y a pesar de sus diferencias, estas tres categorías no están tan distanciadas entre sí como en principio se podría imaginar. Ninguna categoría contiene tampoco tipos representativos «puros». Por ejemplo, las obras de las tres categorías se apoyan en los poderes puramente egoístas de la conciencia europea que es su centro. En todos los casos, Oriente está _para_ el observador europeo y, lo que es más importante, en la categoría que contiene _Modern Egyptians_ , de Lane, el ego orientalista es mucho más evidente, aunque su estilo se esfuerce por conseguir una impersonalidad imparcial. Además, ciertos motivos se repiten constantemente en los tres tipos. Uno de estos es el que presenta a Oriente como un lugar de peregrinación y, por tanto, la imagen que se da de él es la de un espectáculo o un _tableau vivant_. Cualquier obra sobre Oriente que esté en alguna de estas categorías trata de caracterizar el lugar, por supuesto, pero lo que ofrece más interés es saber en qué medida la estructura interna de la obra es de alguna manera sinónimo de una _interpretación_ global de Oriente (o un intento de ello). La mayoría de las veces, lo cual no es sorprendente, esta interpretación es una forma de reestructuración romántica de Oriente, una revisión de él que lo restituye redentoramente al presente. Toda interpretación y toda estructura creada para Oriente, entonces, es una reinterpretación y una reconstrucción de este.
Una vez dicho esto, volvamos directamente a las diferencias entre las categorías. El libro de Lane sobre los egipcios tuvo una gran difusión y consolidó la reputación de su autor como figura eminente de la erudición orientalista. En otras palabras, Lane adquirió autoridad no solo por lo que dijo, sino porque la manera en que lo dijo podía adaptarse al orientalismo. Se le citó como fuente de conocimientos sobre Egipto o Arabia, mientras que Burton y Flaubert se leían, y se leen, por lo que relatan Burton y Flaubert, esto es, sin tener en cuenta sus conocimientos sobre Oriente. La función del autor en _Modern Egyptians_ , de Lane, es menos fuerte que en las otras categorías, porque su obra se difundía dentro de la profesión, era consolidada por ella e institucionalizada con ella. En una obra catalogada dentro de una disciplina profesional como esta, la identidad del autor está subordinada a las exigencias tanto del campo como del tema. Pero esto no se lleva a cabo de un modo simple o de una manera que no conlleve problemas.
La obra clásica de Lane, _An Account of Manners and Customs of the Modern Egyptians_ (1836), fue el resultado consciente de una serie de trabajos y de dos períodos de estancia en Egipto (1825-1828 y 1833-1835). Hacemos hincapié en el término «consciente», porque la impresión que Lane quería dar era la de que su estudio era un trabajo de descripción inmediato y directo, sin ornamentos y neutro, cuando, en realidad, fue el producto de una considerable labor de redacción (la obra que él escribió no fue la misma que finalmente se publicó) y también de toda una variedad de esfuerzos muy particulares. Nada, ni su nacimiento ni su formación parecían destinar a Lane hacia Oriente, solamente quizá su metódica aplicación y su facilidad para los estudios clásicos y las matemáticas, lo que explica la nitidez interna y evidente de su libro. Su prefacio ofrece una serie de claves interesantes sobre cómo se preparó para redactar el libro. Fue a Egipto en un principio para estudiar árabe. Entonces, después de haber tomado algunas notas sobre el Egipto moderno, la Society for the Diffusion of Useful Knowledge le animó a escribir una obra sistemática sobre el país y sus habitantes. Su obra pasó de ser un conjunto de observaciones escritas al azar, a constituir un documento lleno de informaciones útiles, informaciones preparadas para que fueran accesibles a cualquiera que quisiera conocer lo esencial sobre una sociedad extranjera. El prefacio deja bien claro que un conocimiento así debe disponer de alguna manera del saber preexistente y debe tener un carácter particularmente eficaz: en este punto Lane se revela como un polemista sutil. Debe demostrar, en principio, que ha hecho lo que otros antes que él no pudieron hacer o no hicieron y luego, que ha sido capaz de conseguir información auténtica y realmente correcta. Y, de este modo, comienza a aparecer su particular autoridad.
Aunque Lane se entretiene en su prefacio hablando del _Account of the people of Aleppo_ del doctor Russell (una obra olvidada), es evidente que el antecedente que aparece como su principal competidor es la _Description de l'Égypte_ , pero esta obra, que Lane relega a una larga nota a pie de página, se menciona despectivamente entre comillas como «la gran obra francesa» sobre Egipto. _Esta_ obra era de una generalidad demasiado filosófica y demasiado descuidada, dice Lane; y el famoso estudio de Jacob Burckhardt no era más que una simple colección de sabiduría proverbial egipcia, «un mal análisis sobre la moralidad de un pueblo». A diferencia del francés y de Burckhardt, Lane fue capaz de sumergirse en la vida de los nativos, de vivir como vivían ellos, de adaptarse a sus hábitos y «de evitar provocar en terreno extranjero cualquier sospecha de que él [...] era una persona que no tenía derecho a mezclarse con ellos». Por temor a que eso implicara que Lane había perdido la objetividad, continúa diciendo que se limitó solamente a las _palabras_ (la cursiva es suya) del Corán y que siempre fue consciente de sus diferencias con respecto a una cultura esencialmente extraña. De esta manera, mientras una parte de la identidad de Lane flota fácilmente sobre la superficie del mar musulmán sin sospecha, otra parte sumergida conserva su poder secreto europeo para comentar, conseguir y poseer todo lo que le rodea.
El orientalista puede imitar a Oriente sin que Oriente pueda imitar al orientalista. Lo que él dice sobre Oriente, por tanto, debe comprenderse como una descripción obtenida a través de un intercambio unilateral: mientras _ellos_ hablaban y actuaban _él_ observaba y escribía. Su poder consistía en existir entre ellos como un interlocutor indígena y también como un escritor secreto. Lo que escribía estaba destinado a ser un conocimiento útil, no para ellos, sino para Europa y para sus diferentes instituciones de difusión. Así, hay algo que la prosa de Lane nunca nos permite olvidar: el ego, el pronombre de primera persona que se desplaza por Egipto, a través de sus costumbres, rituales, festivales, infancia, madurez y ritos funerarios, y que es a la vez un disfraz oriental y un procedimiento orientalista destinado a captar y transmitir las valiosas informaciones que, de otra manera, serían inaccesibles. Como narrador, Lane es tanto un objeto de exhibición como un exhibidor, ganándose así la confianza de los dos lados de un solo golpe, mostrando dos tipos de apetito: un apetito oriental que le lleva a entablar relaciones de camaradería (o, al menos, eso parece) y un apetito occidental para adquirir conocimientos útiles que le dan autoridad.
El último episodio de su prefacio es la mejor muestra de todo esto. Allí Lane describe a su principal informador y amigo, el _sheij_ Ahmad, como un compañero y como una curiosidad. Los dos juntos hicieron que Lane pasara por musulmán; pero solo después de vencer el miedo que le inspiraban los audaces gestos de Lane, Ahmad pudo realizar el ritual de la oración a su lado en una mezquita. Antes de esto, hay dos escenas en las que Ahmad es retratado como un extraño tragón de vidrio y como un polígamo. En las tres partes de que consta el episodio del _sheij_ Ahmad, la distancia entre el musulmán y Lane aumenta, incluso aunque en lo que es la propia acción decrezca. Como intermediario y traductor del comportamiento musulmán, por decirlo de algún modo, Lane irónicamente entra en el esquema musulmán, pero solo lo suficiente como para poder describirlo en una discreta prosa inglesa. Su identidad de falso creyente y de europeo privilegiado es la esencia misma de la mala fe, ya que, sin ninguna duda, el segundo destruye al primero. Así, lo que parece ser el relato objetivo de las acciones y los gestos de _un_ musulmán más bien raro, Lane lo muestra como el centro inocentemente expuesto de la fe de _todos_ los musulmanes. Lane no le da mucha importancia al hecho de traicionar su amistad con Ahmad o con otros que le suministran información. Lo que le importa es que el relato parezca preciso, general y desapasionado, que el lector inglés esté convencido de que Lane nunca estuvo contaminado por la herejía o la apostasía y que, finalmente, el texto de Lane elimine el contenido humano de su tema, en favor de su validez científica.
Para conseguir todos estos fines, el libro se organiza no solo como la narración de la estancia de Lane en Egipto, sino también como una estructura narrativa envuelta en la reestructuración y en el análisis detallado orientalistas. Pienso realmente que esto es lo más importante que Lane consiguió con su obra. Por lo demás, como dijo Fielding, el perfil y la forma de _Modern Egyptians_ están en la línea de cualquier novela del siglo XVIII. El libro comienza con una descripción del país y del paisaje, para seguir tratando, en diferentes capítulos, las «Características personales» y «La infancia y la primera educación». Veinticinco capítulos sobre temas tales como las fiestas, las leyes, el carácter, la industria, la magia y la vida doméstica preceden a la última parte, «Muerte y ritos funerarios». A primera vista, su exposición es cronológica y sigue el desarrollo de la propia vida. Habla de sí mismo como de un observador de escenas que sigue las grandes etapas de la vida humana: su modelo es el esquema narrativo de _Tom Jones_ ,* con el nacimiento del héroe, sus aventuras, su matrimonio e implícitamente su muerte. En el texto de Lane la voz narrativa es atemporal; sin embargo, su tema de estudio, el egipcio moderno, pasa por un ciclo de vida individual. Esta inversión, por la cual un individuo solitario se otorga a sí mismo facultades atemporales e impone a una sociedad y a un pueblo una duración de vida personal, no es más que la primera de una serie de operaciones que regulan lo que habría podido ser la simple narración de unos viajeros a países extranjeros, y que transforman un texto sin artificios en una enciclopedia de exotismo y en un campo de pruebas para la investigación orientalista.
Lane domina el material no solo a través de su doble presencia en la escena (como falso musulmán y como auténtico occidental) y de su manipulación de la voz y del objeto narrativos, sino también a través de su utilización del detalle. Cada una de las grandes secciones de cada capítulo está introducida invariablemente por una observación general nada sorprendente. Por ejemplo, «se observa generalmente que muchas de las peculiaridades más relevantes de las maneras, las costumbres y el carácter de una nación se pueden atribuir a las peculiaridades físicas del país». Lo que sigue lo confirma fácilmente: el Nilo, el clima «notablemente saludable» de Egipto y el trabajo «preciso» del campesino. Pero, en lugar de que esto desemboque en el episodio siguiente según el orden narrativo, se añaden detalles y, en consecuencia, la realización narrativa que se espera —por razones puramente formales— no se da. Dicho de otro modo, aunque las grandes líneas del texto de Lane se adapten a la secuencia narrativa y casual, nacimiento-vida-muerte, los detalles particulares que se introducen a lo largo de la secuencia desvían el movimiento narrativo. Se pasa de una observación general al esbozo de un cierto aspecto del carácter egipcio, a una descripción de la infancia, adolescencia, madurez y senectud de un egipcio, y Lane está siempre presente, con gran cantidad de detalles para _impedir las transiciones suaves_. Tras haber oído que el clima de Egipto es saludable, por ejemplo, nos informa de que pocos egipcios viven algo más de unos cuarenta años debido a las enfermedades mortales, a la falta de asistencia médica y a los veranos asfixiantes. Después nos dice que el calor «provoca en los egipcios [generalización que no se prueba] una intemperancia por los placeres sexuales» y, de pronto, nos enredamos en unas descripciones, completadas con diagramas y dibujos lineales, sobre la arquitectura, la decoración, las fuentes y las cerraduras de El Cairo. Cuando el hilo narrativo reaparece es solamente como una mera formalidad.
Lo que perturba el orden narrativo, en el mismo instante en que este es la ficción dominante del texto de Lane, es la pura, simple e irresistible descripción monumental. Lane tiene como objetivo hacer que Egipto y los egipcios sean totalmente visibles, que nada se oculte a su lector; quiere entregarle a los egipcios sin demasiada profundidad, pero con multitud de detalles superfluos. Como narrador de historias, muestra una fuerte propensión por los brutales pasajes sadomasoquistas y picantes: la automutilación de los derviches, la crueldad de los jueces, la mezcla de religión y permisividad de los musulmanes, el exceso de pasiones libidinosas, etc. Sin embargo, poco importa hasta qué punto el suceso puede ser extraño y perverso, ni hasta qué punto nos podemos desorientar ante este torbellino de detalles, Lane está en todas partes a la vez, su labor consiste en reunir las piezas y en permitirnos avanzar, aunque sea a trompicones. En cierta medida, lo único que hace es comportarse como un europeo que puede controlar de manera discursiva las pasiones y las excitaciones a las que los musulmanes están, desgraciadamente, sometidos. No obstante, en mayor medida, la capacidad de Lane para detenerse en un tema tan profuso dentro de las inflexibles riendas de la disciplina y del distanciamiento proviene de su fría distanciación de la vida de los egipcios y de la fecundidad egipcia.
El principal momento simbólico llega al principio del capítulo VI, «Vida doméstica. Continuación». Lane, en ese momento, adopta la convención de narrar su paso por la vida egipcia y después de haber terminado su recorrido por las habitaciones y los hábitos públicos de un hogar egipcio (mezcla el mundo de la sociedad y del espacio), comienza a hablar del lado íntimo de la vida en el hogar. Enseguida «debe ofrecer una descripción del matrimonio y de las ceremonias matrimoniales». Como es habitual, la descripción empieza con una observación general acerca del hecho de no casarse: «cuando un hombre ha alcanzado la edad suficiente y cuando no hay ningún impedimento justificado, los egipcios estiman que es impropio e incluso vergonzoso». Sin transición, Lane aplica esta observación a su propia persona y se encuentra culpable. A lo largo de un extenso párrafo cuenta las presiones que se han ejercido sobre él para que se case, lo cual ha rehusado con firmeza. Al final, después de que un amigo nativo le ofrece arreglar _un matrimonio de conveniencia_ , Lane también lo rechaza; el pasaje entero termina bruscamente con un punto y guión. Resume sus consideraciones generales con otra observación general.
Lo que vemos aquí no es solo la típica manera con la que Lane interrumpe la narración principal con detalles que no tienen nada que ver con ella, sino también su desvinculación firme y literal de los procesos productivos de la sociedad oriental. La mininarración de su negativa a entrar en la sociedad que describe termina con un hiato dramático: _su_ historia, parece decir él, no puede continuar por más tiempo, porque no ha entrado en la intimidad de la vida doméstica y así se le pierde de vista como candidato a ella. Él se anula literalmente a sí mismo como sujeto humano al negarse a casarse en la sociedad de los hombres. Conserva así su identidad autorizada de participante fingido y refuerza la objetividad de su narración. Si ya sabíamos que Lane no era musulmán, ahora también sabemos que para llegar a ser un orientalista —en lugar de un oriental— ha tenido que rehusar a los placeres sexuales de la vida doméstica. Además, también ha evitado datarse a sí mismo entrando en el ciclo de la vida humana. Solo así, de esta manera negativa, ha podido mantener su autoridad de observador atemporal.
Lane tenía que elegir entre vivir sin «inconvenientes ni incomodidades» o llevar a buen puerto su estudio de los egipcios modernos. Eligió, y esto le permitió definir a los egipcios, ya que si se hubiera convertido en uno de ellos, su perspectiva ya no habría sido lexicográfica de manera aséptica y asexual. De dos formas importantes y apremiantes, por tanto, Lane gana credibilidad y legitimidad eruditas. Lo logra, en primer lugar, al interferir en el curso narrativo de la vida humana a través de sus detalles colosales en los que la inteligencia observadora de un extranjero puede introducir y después recomponer una gran cantidad de información. Lane destripa a los egipcios para exponer sus entrañas, por decirlo de algún modo, y después, amonestándolos, los cose; y en segundo lugar, al rehusar participar en la creación de la vida egipcio-oriental, domina sus apetitos animales en aras de la difusión y la información no en y para Egipto, sino en y para la ciencia europea en general. Al haber conseguido imponer una voluntad erudita sobre una realidad desordenada, y desplazarse intencionadamente desde su residencia al _escenario_ de su reputación erudita, Lane adquirió una gran fama en los anales del orientalismo. Un saber útil como el suyo solo pudo llevarse a cabo, formularse y difundirse gracias a las negaciones de este tipo.
Las otras dos grandes obras de Lane, su _Arabic Lexicon_ , que nunca terminó, y su mediocre traducción de _Las mil y una noches_ , consolidaron el sistema de conocimiento que _Modern Egyptians_ había inaugurado. En ambos trabajos, su individualidad ha desaparecido totalmente en tanto que presencia creativa, aunque siga manteniéndose, por supuesto, la idea de una obra narrativa. Lane, el hombre, aparece solo como la persona oficial del anotador y del traductor (en _Las mil y una noches_ ) y el lexicógrafo impersonal. De ser un autor contemporáneo a su materia, Lane pasó a ser —como orientalista erudito del árabe y del islam clásicos— su superviviente. Pero lo interesante es la forma de esa supervivencia. El legado de Lane no le importaba a Oriente, por supuesto, sino a las instituciones y agencias de la sociedad europea. Y estas, ya fueran académicas —sociedades, instituciones y agencias orientalistas oficiales— o extraacadémicas de diferentes tipos, figuraban en la obra de los posteriores residentes europeos en Oriente.
Si leemos _Modern Egyptians_ , no como una fuente de tradición oriental, sino como una obra dirigida hacia la expansiva organización del orientalismo académico, nos resultará esclarecedora. La subordinación del ego genético a la autoridad erudita en Lane corresponde exactamente a la creciente especialización e institucionalización del conocimiento sobre Oriente representado por varias sociedades orientales. La Royal Asiatic Society fue fundada diez años antes de que el libro de Lane apareciera, pero su comité de lectura —cuyo «objetivo era recibir las informaciones y los estudios relativos a las artes, las ciencias, la literatura, la historia y las antigüedades» de Oriente»— era, por su estructura, el destinatario de los fondos de información de Lane tal y como eran procesados y formulados. En cuanto a la difusión de obras como la de Lane, no solo había varias sociedades de conocimientos útiles, sino que en esa época, en la que el programa orientalista original de apoyar el comercio y los intercambios con Oriente se estaba agotando, había también sociedades eruditas especializadas cuyos productos eran trabajos que mostraban los valores potenciales (si no reales) de la erudición. Así, un programa de la Société Asiatique establece:
Componer o imprimir gramáticas, diccionarios y otros libros elementales reconocidos como útiles o indispensables para el estudio de aquellas lenguas enseñadas por los profesores designados [de lenguas orientales]; contribuir, a través de suscripciones o de otros medios, a la publicación de obras del mismo género realizadas en Francia o en el extranjero; adquirir manuscritos asiáticos o copiar total o parcialmente los que existen en Europa; traducir o sacar extractos de ellos, multiplicar su número reproduciéndolos mediante el grabado, la impresión o la litografía; proporcionar a los autores de obras útiles sobre geografía, historia, arte y ciencias los medios para hacer disfrutar al público del fruto de sus desvelos; atraer la atención del público, a través de una colección periódica dedicada a la literatura asiática, hacia las producciones científicas, literarias y poéticas de Oriente, hacia las del mismo tipo que se producen regularmente en Europa, hacia los hechos orientales que puedan ser relevantes para Europa, hacia sus descubrimientos y obras de cualquier tipo en las que los pueblos orientales puedan ser el tema principal: estos son los objetivos que se propone la Société Asiatique.
El orientalismo, como saber especializado, se organiza sistemáticamente adquiriendo material oriental y difundiéndolo de forma regulada. Por un lado están las obras de gramática copiadas e impresas y los textos originales adquiridos, y por otro, la extensa difusión y el incremento numérico de todas estas obras o incluso el hecho de dar una forma periódica a este conocimiento. Lane escribió su obra y sacrificó su ego dentro de este sistema y por él. El modo en el que su obra persiste en el archivo del orientalismo está previsto para eso. Tenía que haber un «museo» dijo Sacy,
un enorme almacén de objetos de todo tipo, de dibujos, libros originales y relatos de viajes; todo ello ofrecido a los que quieran dedicarse al estudio de [Oriente], de tal forma que cualquier estudiante pueda ser capaz de trasladarse, como por encanto, al centro de una tribu mongola, por ejemplo, o al de la raza china que ha sido el objeto de sus estudios [...]. Se puede decir [...] que tras la publicación de libros elementales sobre [...] las lenguas orientales, no hay nada más importante que establecer la piedra angular de este museo, al cual considero como el comentario y la interpretación [trujamanía], viva de los diccionarios.
La palabra «trujamanía» se deriva exactamente del árabe _turjaman_ , que significa «intérprete», «intermediario» o «portavoz». Por un lado, el orientalismo tomó posesión de Oriente tan literal y extensamente como le fue posible; por otro, domesticó este conocimiento para Occidente filtrándolo a través de sus códigos reguladores, sus clasificaciones, sus casos de especies, sus revisiones periódicas, diccionarios, gramáticas, comentarios, ediciones y traducciones, todo lo cual junto forma un simulacro de Oriente y lo reproduce materialmente en y para Occidente. Oriente, en resumen, iba a dejar de ser el testimonio personal y a veces engañoso de viajeros y residentes intrépidos para transformarse en definiciones impersonales dadas por un ejército de trabajadores científicos, iba a dejar de ser la experiencia consecutiva de la investigación individual para convertirse en un tipo de museo imaginario sin muros, donde todo lo que había sido recogido a partir de los espacios enormes y de las enormes variedades de la cultura oriental se volvía categóricamente _oriental_. Iba a ser reconvertido y reestructurado a partir de un puñado de fragmentos traídos pieza a pieza por exploradores, expediciones, comisiones, ejércitos y mercaderes en una entidad con un significado orientalista lexicográfico, bibliográfico, departamentado y _textualizado_. Hacia mediados del siglo XIX, Oriente se había convertido en una carrera, como Disraeli dijo, en la que uno podía rehacer y restituir no solo a Oriente, sino también a sí mismo.
### IV
### Peregrinos y peregrinaciones:
### británicos y franceses
Todo europeo que haya viajado a Oriente o vivido allí durante algún tiempo habrá tenido que protegerse de sus inquietantes influencias. Lane, por ejemplo, cuando se puso a escribir sobre Oriente, lo programó y situó de nuevo. Las excentricidades de la vida oriental, con sus viejos calendarios, sus exóticas configuraciones espaciales, sus lenguas desesperadamente extrañas y su moralidad aparentemente perversa, se reducían de manera considerable cuando aparecían como una serie de detalles presentados en el estilo normativo de la prosa europea. Es correcto decir que al orientalizar Oriente, Lane no solo lo definía, sino que lo editaba; en suma, suprimía lo que podía perturbar la sensibilidad europea y sus propios sentimientos humanos. En la mayoría de los casos, Oriente parecía ofender el decoro sexual; todo en Oriente —o al menos en el Oriente egipcio de Lane— rezumaba peligro sexual y suponía una amenaza para la higiene y la decencia domésticas debido a una excesiva «libertad para el contacto sexual», como dijo Lane reprimiéndose menos de lo que era habitual en él.
Pero había otro tipo de amenazas, además de las sexuales. Todas ellas ponían a prueba el sentido que tenían los europeos de la discontinuidad y la racionalidad del tiempo, el espacio y la identidad personal. En Oriente uno se veía, de pronto, frente a una antigüedad inimaginable, una belleza inhumana y unas distancias ilimitadas. Estas podían experimentarse de una manera más inocente, diríamos, si fueran temas de reflexión y de escritura y no sensaciones vividas directamente. En el «Giaour», de Byron, en el _Westöstlicher Diwan_ , de Goethe; y en _Les Orientales_ , de Hugo, Oriente es una forma de liberación y un lugar de oportunidades originales cuyas claves principales fueron captadas por Goethe en «Hégira»:
_Nord und West Süd zersplittern_
_Throne bersten, Reiche zittern,_
_Fluchte du, in reinen Osten_
_Patriarchenluft zu Kosten_
Siempre se _volvía_ a Oriente —«Dort, im Reinen und in Rechten / will ich menschlichen Geschlechten / In des Ursprungs Tiefe dringen».* Y se concebía como la realización y la confirmación de todo lo que habíamos imaginado:
_Gottes ist der Oriente_!
_Gottes ist der Okzident_!
_Nord und südliches Gelände_
_Ruht im Frieden seiner Hände_. _*_
Oriente, con su poesía, su atmósfera y sus posibilidades estaba representado por poetas como Hafiz; _unbegrenzt_ , ilimitado, dijo Goethe, más viejo y más joven que nosotros europeos. Y para Hugo en «Cri de guerre du mutfi» y en «La douleur du pacha», la ferocidad y la desordenada melancolía de los orientales estaban mediatizadas, más que por el temor real por sus vidas o por un sentimiento de pérdida desorientada, por Volney y George Sale, cuyas obras eruditas tradujeron el esplendor de los bárbaros en útiles informaciones para el talento sublime del poeta.
Todo lo que algunos orientalistas como Lane, Sacy, Renan, Volney, Jones (por no mencionar la _Description de l'Égypte_ ) y otros pioneros convirtieron en material accesible, fue explotado por la mayor parte de los literatos. Recordemos ahora nuestra anterior exposición sobre los tres tipos de obras que tratan de Oriente y que se basan en una estancia allí. Las rigurosas exigencias de la ciencia despojaban los escritos orientalistas de la sensibilidad del autor: de ahí la autocensura de Lane y de ahí también el primer tipo de obras que enumeramos. En los tipos dos y tres, el «yo» está presente de manera mucho más clara, sirviendo a una voz cuya tarea es dispensar un conocimiento real (segundo tipo) o dominando y mediatizando todo lo que se nos dice sobre Oriente (tercer tipo). Sin embargo, desde el principio hasta el final del siglo XIX —después de Napoleón— Oriente fue un lugar de peregrinación, y cualquier obra importante que perteneciera a un orientalismo auténtico, por no decir académico, tomó su forma, estilo e intención de la idea de la peregrinación a Oriente. La fuente principal de esta idea, así como de tantas otras formas de escritos orientalistas de las que ya hemos tratado, es la idea romántica de una reconstrucción restauradora (el supernaturalismo natural).
Todo peregrino ve las cosas a su manera, pero la utilidad de la peregrinación, la figura y la forma que puede adoptar o las verdades que revela no son ilimitadas. Todas las peregrinaciones a Oriente cruzaban o tenían que cruzar las tierras bíblicas; la mayoría de ellas, de hecho, eran intentos de revivir o de liberar de un Oriente inmenso e increíblemente fecundo una parte de la realidad judeocristiana/ grecorromana. Para estos peregrinos, el Oriente orientalizado, el Oriente de los eruditos orientalistas, era un guante que recoger, al igual que la Biblia, las Cruzadas, el islam, Napoleón y Alejandro eran predecesores imponentes con los que había que contar. No es solo que un Oriente instruido inhiba los ensueños y las fantasías personales, sino que incluso su existencia pone barreras entre el viajero de hoy y lo que escribe, a menos que, como fue el caso de Nerval y Flaubert en su manera de utilizar a Lane, el trabajo orientalista se separe de la biblioteca y se tome como un proyecto estético. Otro tipo de inhibición se debe al hecho de que la obra orientalista está demasiado circunscrita a las exigencias oficiales de la ciencia orientalista. Un peregrino como Chateaubriand exclamaba de modo insolente que emprendía su viaje exclusivamente por propio interés: « _J'allais chercher des images: voilà tout_ ». Flaubert, Vigny, Nerval, Kinglake, Disraeli y Burton, todos realizaron sus peregrinaciones para disipar el moho del archivo orientalista preexistente. Sus escritos debían ser un receptáculo nuevo para la experiencia oriental; sin embargo, como veremos más adelante, incluso este proyecto se resolvió normalmente (aunque no siempre) limitándose al reduccionismo orientalista. Las razones son complejas y tienen mucho que ver con la naturaleza del peregrino, su manera de escribir y la forma intencional de su obra.
¿Qué era Oriente para el viajero del siglo XIX? Veamos primero las diferencias entre el viajero de habla inglesa y el de lengua francesa. Para el primero, Oriente era la India, por supuesto, una posesión británica real; atravesar Oriente Próximo era, por tanto, ir de paso hacia una de las colonias más importantes. Por esta razón el espacio disponible para el juego imaginario estaba ya limitado por las realidades de la administración, de la legalidad territorial y del poder ejecutivo. Scott, Kinglake, Disraeli, Warburton, Burton e incluso George Eliot (en cuyo _Daniel Deronda_ hace planes para Oriente) son escritores, como habían sido el propio Lane y Jones, para los que Oriente se define por la posesión material, por una imaginación material, por decirlo de algún modo. Inglaterra había derrotado a Napoleón, había desposeído a Francia: lo que un espíritu inglés examinaba era un dominio imperial que hacia 1880 se había convertido en un territorio continuo, desde el Mediterráneo hasta la India, ocupado por los británicos. Escribir sobre Egipto, Siria o Turquía, así como viajar por estos países, consistía en visitar el reino de la voluntad política. El imperativo territorial era extremadamente compulsivo incluso para un escritor tan liberado como Disraeli, cuyo _Tancred_ no es simplemente una fantasía oriental, sino un ejercicio de astuta organización política de fuerzas reales en territorios reales.
Por el contrario, el peregrino francés estaba henchido de un agudo sentimiento de pérdida en Oriente. Llegaba allí, a un lugar en el que Francia, a diferencia de Gran Bretaña, no tenía ninguna presencia soberana. En el Mediterráneo resonaban los ecos de las derrotas francesas, desde las Cruzadas a Napoleón. Lo que iba a ser conocido como la « _mission civilisatrice_ » empezó en el siglo XIX siendo simplemente una presencia política de segunda fila, después de Gran Bretaña. En consecuencia, los peregrinos franceses desde Volney hacían planes, proyectos, imaginaban y reflexionaban sobre lugares que estaban principalmente _en su mente_ ; inventaban composiciones para un concierto típicamente francés, quizá incluso europeo, en Oriente, que naturalmente se suponía que ellos dirigirían. Su Oriente era el de las memorias, el de las ruinas sugestivas, el de los secretos olvidados, el de las correspondencias escondidas y el de un estilo de vida casi virtuoso; un Oriente cuya forma literaria más elevada se encontraría en Nerval y Flaubert, cuyas obras estaban sólidamente enraizadas en una dimensión imaginaria irrealizable (excepto desde un punto de vista estético).
Esto mismo se puede decir también de un cierto número de viajeros eruditos franceses que, en su mayoría, se interesaban por el pasado bíblico o por las Cruzadas, como Henri Bordeaux explica en su libro _Voyageurs d'Orient_. A los nombres que él cita, debemos añadir (sugerencia de Hassan al-Nouty) los de los orientalistas semitistas, incluyendo a Quatremère; Saulcy, el explorador del mar Muerto; Renan, en su dimensión de arqueólogo fenicio; Judas, el especialista en lenguas fenicias; Catafago y Défrémery, que estudiaron a los asirios, a los ismailíes y a los selyúcidas; el conde de Clermont-Ganneau, que exploró Judea, y el marqués de Vogüé, cuyo trabajo se centró en la epigrafía de Palmira. Además, estaba toda la escuela de egiptólogos descendientes de Champollion y Mariette, una escuela que más tarde incluiría a Maspero y Legrain. Como muestra de la diferencia entre las realidades británicas y las fantasías francesas vale la pena recordar las palabras del pintor Ludovic Lepic que, en 1884 (dos años después del comienzo de la ocupación británica), comentó en El Cairo con tristeza: _«L'Orient est mort au Caire»_. Solo Renan, con su realismo racista, excusó la represión británica de la rebelión nacionalista de al-Urabi, la cual, dijo con su inmensa sabiduría, era «una desgracia para la civilización».
A diferencia de Volney y de Napoleón, los peregrinos franceses del siglo XIX no buscaban una realidad científica, sino una realidad exótica y, sobre todo, atractiva. Ciertamente esto fue así en el caso de los peregrinos literatos, empezando por Chateaubriand, que encontró en Oriente un escenario acorde con sus mitos, obsesiones y exigencias personales. En este punto observamos cómo todos los peregrinos y especialmente los franceses explotaron Oriente en sus obras con el fin de justificar su vocación existencial. Solo cuando existía un proyecto cognitivo adicional en el hecho de escribir sobre Oriente, la efusión del «yo» parecía mejor controlada. Lamartine, por ejemplo, escribió sobre sí mismo y sobre Francia como potencia en Oriente; este segundo tema acalló y finalmente controló los imperativos que _su_ espíritu, _su_ memoria y _su_ imaginación habían acumulado en su estilo. Ningún peregrino francés o inglés podía dominar tan despiadadamente como Lane su propia persona o su propio tema. Incluso Burton y T. E. Lawrence —el primero hizo una peregrinación deliberadamente musulmana y el segundo lo que llamó una peregrinación a la inversa, es decir, saliendo desde La Meca—, que proporcionaron masivamente un orientalismo histórico, político y social, nunca fueron tan libres de sus propios egos, como Lane lo fue del suyo. Por eso, Burton, Lawrence y Charles Doughty ocupan una posición media entre Lane y Chateaubriand.
El _Itinéraire de Paris à Jérusalem, et de Jérusalem à Paris 1810-1811_ ,* de Chateaubriand, relata los detalles de un viaje emprendido entre 1805 y 1806, después de haber viajado a Norteamérica. Sus cientos de páginas son la prueba de lo que admite su autor: _«je parle éternellement de moi»_ , hasta tal punto que Stendhal, que no es un escritor propenso a la abnegación, encontró que los defectos de Chateaubriand como viajero erudito eran fruto de su «terrible egotismo». Chateaubriand llevó a Oriente una gran cantidad de objetivos y suposiciones personales que allí descargó, y después se dedicó a tomar el pulso de los lugares, las ideas y la gente de Oriente como si nada pudiera resistirse a su imperiosa imaginación. Chateaubriand llegó a Oriente como un _personaje_ construido, y no como él mismo era en verdad. Para él Bonaparte era el último cruzado; él, por su parte, era «el último francés que abandonaba su país para viajar por Tierra Santa con las ideas, los objetivos y los sentimientos de un peregrino de los tiempos antiguos». No obstante, su viaje tenía otras razones. La primera de ellas era la simetría. Después de haber estado en el Nuevo Mundo y de haber visto los monumentos de la naturaleza, necesitaba completar sus estudios visitando Oriente y los monumentos de los hombres. Había estudiado ya la antigüedad romana y celta; solo le quedaban las ruinas de Atenas, Menfis y Cartago. La segunda de estas razones era la realización personal. Necesitaba reponer su provisión de imágenes; y la tercera, autorrealización. La confirmación de la importancia del espíritu religioso, puesto que «la religión es una clase de lenguaje universal que entienden todos los hombres». ¿Dónde mejor que en Oriente para observarlo, incluso en tierras donde reina una religión relativamente inferior como el islam? Sobre todo se imponía la necesidad de ver las cosas no como eran, sino como Chateaubriand suponía que eran. El Corán era _«le livre de Mahomet»_ ; no contenía _«ni principe de civilisation, ni précepte qui puisse élever le caractère»_. Y continuaba, más o menos inventándoselo a medida que avanzaba: «Este libro no predica el odio, ni la tiranía, ni el amor a la libertad».
Para un ser tan preciado como Chateaubriand, Oriente era un lienzo estropeado que estaba esperando que él lo restaurara. El árabe oriental era «un hombre civilizado que había vuelto a caer en un estado salvaje». No es de extrañar entonces que cuando veía a los árabes intentando hablar francés, Chateaubriand sintiera la misma emoción que invadió a Robinson Crusoe el día que oyó hablar a su loro por primera vez. Sí, había lugares como Belén (con cuyo significado etimológico Chateaubriand se equivocó completamente) en los que se podía encontrar algún parecido con la civilización real —es decir, con la europea—, pero eran pocos y estaban muy alejados unos de otros. En todas partes había orientales, árabes cuya civilización, religión y maneras eran tan inferiores, bárbaras y antiestéticas que merecían ser reconquistados. Las Cruzadas, decía él, no fueron una agresión, solo fueron la contrapartida a la entrada de Omar en Europa. Además, añadía, incluso si las Cruzadas en su forma moderna o en su forma original eran una agresión, los problemas que planteaban trascendían los del hombre mortal:
Las Cruzadas no se llevaron a cabo solamente para liberar el Santo Sepulcro, sino también para saber quién triunfaría sobre la Tierra, un culto enemigo de la civilización, un culto sistemáticamente favorable a la ignorancia, al despotismo y a la esclavitud [este era el islam, por supuesto] o un culto que había hecho revivir en los pueblos modernos el genio de la sabiduría antigua y había abolido la esclavitud.
Esta es la primera vez que se menciona una idea que adquirirá una autoridad casi insoportable y automática en los escritos europeos: el tema de una Europa que enseña a Oriente lo que es la libertad, concepto que Chateaubriand —y todos después de él— creía que los orientales y los musulmanes en particular ignoraban totalmente.
La libertad, la ignoran; propiedades no tienen; la fuerza es su Dios. Cuando pasan mucho tiempo sin ver a ningún conquistador de los que imparten justicia celestial, tienen el aspecto de soldados sin jefe, de ciudadanos sin legisladores y de una familia sin padre.
Ya en 1810 nos encontramos con una Europa que habla como Cromer en 1910, que sostiene que los orientales necesitan ser conquistados y que no encuentra paradójico que la conquista occidental de Oriente no constituya, después de todo, una conquista, sino la libertad. Chateaubriand expresó la idea en los términos románticos de una misión cristiana destinada a hacer revivir un mundo muerto y a reavivar en él el sentimiento de sus propias potencialidades, que solo un europeo podía discernir bajo una superficie sin vida y degenerada. Para el viajero esto significaba que debía usar el Antiguo Testamento y los Evangelios como guía de Palestina; solo de esta forma podría ir más allá de la degeneración aparente del Oriente moderno. Pero a Chateaubriand no le parece irónico que su visita y su visión no le revelen nada sobre el oriental moderno ni sobre su destino. Lo que importa de Oriente son los sucesos que produce en la vida de Chateaubriand, las sensaciones que provoca en su espíritu y los nuevos sentimientos que le revela sobre sí mismo y sobre sus ideas y esperanzas. La libertad que tanto le interesa no es más que su propia liberación de los desiertos hostiles de Oriente.
Esta liberación le permite volver directamente al reino de la imaginación y de la interpretación imaginaria. La descripción de Oriente resulta anulada por los dibujos y los modelos que le ha impuesto el ego imperial, el cual no esconde sus poderes. Si en la prosa de Lane vemos que el ego desaparece de tal forma que Oriente puede surgir con todos sus detalles realistas, en Chateaubriand el ego se disuelve en la contemplación que él mismo crea y entonces renace más fuerte que nunca, más capaz de saborear sus poderes y de disfrutar de sus interpretaciones.
Cuando alguien viaja a Judea, primero un gran tedio se apodera de su corazón; pero cuando, al pasar de un lugar solitario a otro, el espacio se extiende sin límites ante sus ojos, poco a poco el tedio se disipa y se siente un terror secreto que, lejos de abatir el espíritu, le da coraje y eleva el ánimo. Por todas partes se van descubriendo los aspectos extraordinarios de una tierra que ha sido labrada por los milagros: el sol ardiente, el águila impetuosa, la higuera estéril, la poesía y las escenas de las Escrituras están ahí presentes. Todo nombre encierra un misterio, toda gruta declara el futuro y toda cima retiene los acentos de un profeta. El mismo Dios habló desde estas costas: los torrentes áridos, las rocas agrietadas, las tumbas entreabiertas atestiguan el prodigio; el desierto todavía permanece mudo de terror y se diría que, desde que escuchó la voz del Eterno, aún no ha sido capaz de romper el silencio.
El proceso de pensamiento en este párrafo es revelador. Una experiencia de terror pascaliano en lugar de reducir la confianza en sí mismo milagrosamente la estimula. El árido paisaje se despliega como un texto iluminado que se presenta al examen de un ego muy fuerte y reforzado. Chateaubriand ha trascendido la vil y aterradora realidad del Oriente contemporáneo de tal forma que puede establecer con él una relación original y creativa. Hacia el final del párrafo ya no es un hombre moderno, sino un profeta visionario más o menos contemporáneo de Dios; si el desierto de Judea ha estado en silencio desde que Dios habló allí, Chateaubriand es quien puede escuchar el silencio, entender su significado y hacerle hablar de nuevo para su lector.
Las grandes dotes intuitivas de Chateaubriand, que le habían permitido representar e interpretar los misterios de América del Norte en _René_ y _Atala_ , así como el cristianismo en _Le Génie du Christianisme_ ,* alcanzan nuevos niveles de interpretación durante el _Itinéraire_. El autor ya no trata del carácter primitivo natural ni del sentimiento romántico: trata ahora de la creatividad eterna y de la originalidad divina, ya que fue en el Oriente bíblico donde estas fueron depositadas primero, y allí han permanecido en forma no mediatizada y latente. Por supuesto, no pueden ser simplemente aprendidas, deben ser deseadas y realizadas por Chateaubriand. Y el _Itinéraire_ está destinado a servir a este ambicioso propósito, igual que el ego de Chateaubriand en el texto debe ser reconstruido a fondo, lo suficiente como para llevar a cabo la labor. Al contrario que Lane, Chateaubriand intenta _consumir_ Oriente. No solo se apropia de él, sino que además lo representa y habla por él, no en la historia, sino más allá de la historia en una dimensión atemporal de un mundo totalmente sano en el que los hombres y las tierras, Dios y los hombres, son uno. En Jerusalén, en el centro de su visión y en el último confín de su peregrinación, se concede una especie de reconciliación total con Oriente, con un Oriente judío, cristiano, musulmán, griego, persa, romano y finalmente francés. Se sorprende por la fe de los judíos, pero juzga que también ellos sirven para iluminar su visión general, y además le dan el patetismo necesario a su espíritu cristiano de venganza. Dios, dice, ha elegido un nuevo pueblo y no es el de los judíos.
Sin embargo, hace algunas otras concesiones a la realidad terrestre. Si Jerusalén está inscrito en su itinerario como el objeto final extraterrestre, Egipto le proporciona el material para una digresión política. Sus ideas sobre Egipto suponen un agradable suplemento a su peregrinación. El magnífico delta del Nilo le lleva a decir:
Solo los recuerdos de mi gloriosa patria me parecían dignas de esas magníficas planicies; veía los restos de los monumentos de una nueva civilización llevada a orillas del Nilo por el genio de Francia.
No obstante, estas ideas se exponen de una manera nostálgica, porque Chateaubriand cree que en Egipto puede equiparar la ausencia de Francia con la ausencia de un gobierno libre al frente de un pueblo feliz. Además, después de Jerusalén, Egipto solo parece ser una especie de anticlímax espiritual. Tras haber comentado el estado lamentable en el que se encuentra este país, Chateaubriand se plantea la rutinaria pregunta sobre la «diferencia» que resulta del desarrollo histórico: ¿cómo es posible que esta pandilla de degenerados y estúpidos «musulmanes» habite la misma tierra cuyos propietarios totalmente diferentes tanto impresionaron a Heródoto y Diodoro?
Este es su discurso de despedida de Egipto, que abandona para ir a Tunicia, a las ruinas de Cartago, y finalmente a casa. Pero antes, hace una última acción destacable en Egipto: como solo puede mirar las pirámides desde lejos, se toma la molestia de mandar allí a un emisario para que inscriba su nombre (Chateaubriand) en la piedra; y a nosotros nos dice que «uno tiene que cumplir con todas las pequeñas obligaciones de un viajero piadoso». Normalmente solo concederíamos a este rasgo encantador de banalidad turística la categoría de algo divertido, pero como preparación de la última página del _Itinéraire_ es más importante de lo que parece a primera vista. Al reflexionar sobre su proyecto, que dura ya veinte años, de estudiar _«tous les hasards et tous les chagrins»_ como si se tratara de un exilio, Chateaubriand señala de manera elegíaca que cada uno de sus libros ha sido una especie de prolongación de su existencia. Ahora que ha pasado su juventud, se encuentra como un hombre sin casa y sin la posibilidad de conseguir una. Si el cielo le concede el descanso eterno, dice, promete dedicarse en silencio a erigir un _«monument à ma patrie»_. Lo que deja en la Tierra, sin embargo, son sus obras, las cuales, si su nombre está llamado a pervivir, habrán sido suficientes, pero si no, habrán sido demasiadas.
Estas líneas finales nos remiten al interés de Chateaubriand por inscribir su nombre en las pirámides. Hemos comprendido que sus memorias orientales egoístas nos proporcionan una experiencia de su yo que exhibía constante e infatigablemente. Escribir era un acto vital para Chateaubriand, que creía que, si él estaba destinado a pervivir, su escritura debía tocarlo todo, incluso un trozo lejano de piedra. Si el orden narrativo de Lane era violado por la autoridad científica y los abundantes detalles, el de Chateaubriand se transformaba en la voluntad afirmada de un individuo egoísta y muy inconstante. Mientras que Lane sacrificaba su ego al canon orientalista, Chateaubriand hacía que todo lo que decía sobre Oriente dependiera totalmente de su ego. Sin embargo, ninguno de los dos escritores podía imaginar que pasaría a la posteridad por hacer algo provechoso. Lane entraría a formar parte de una disciplina técnica impersonal; su trabajo sería utilizado, pero no como un documento humano. Chateaubriand, por otro lado, comprendió que sus escritos, como la inscripción simbólica de su nombre en una pirámide, se confundirían con su propia persona; de lo contrario, si no consiguiera prolongar su vida a través de sus escritos, estos serían simplemente excesivos o superfluos.
Si bien todos los que viajaron a Oriente después de Chateaubriand y Lane tuvieron en cuenta sus obras (en ciertos casos, hasta el punto de copiarlas palabra por palabra), su herencia representa el destino del orientalismo y las opciones a las que estaba limitado. O se escribía ciencia, como Lane, o expresión personal, como Chateaubriand. El problema de la primera opción residía tanto en la confianza impersonal que tenía el occidental para poder realizar esas descripciones de fenómenos generales y colectivos como en que tendía a crear realidades no a partir de Oriente sino a partir de sus propias observaciones. El problema de la expresión personal era que quedaba reducida inevitablemente a una posición que equiparaba Oriente con las fantasías privadas, incluso si estas fantasías eran, desde un punto de vista estético, de un nivel muy elevado. En ambos casos, por supuesto, el orientalismo ejerció una poderosa influencia en la manera en que se describía y caracterizaba Oriente. Pero lo que esta influencia siempre impidió, incluso en nuestros días, ha sido la existencia de un cierto sentimiento de Oriente que no sea ni de una generalidad imposible ni imperturbablemente privado. Es inútil buscar en el orientalismo algún sentimiento vivo sobre la realidad humana, o incluso social, del oriental como habitante contemporáneo del mundo moderno.
Esta omisión se debe, en gran parte, a la influencia de las dos opciones que he descrito, la de Lane y la de Chateaubriand, la británica y la francesa. El desarrollo del conocimiento, particularmente del conocimiento especializado, es un proceso muy lento. Lejos de ser meramente aditivo o especulativo, es un proceso de acumulación, de abandono, de destrucción, de redisposición y de recuperación selectivos en el marco de lo que podría llamarse el consenso de la investigación. La legitimidad de un saber como el orientalismo a lo largo del siglo XIX procedía no de una autoridad religiosa, como antes de la Ilustración, sino de lo que podríamos llamar la cita restauradora de la autoridad precedente. Empezando por Sacy, la actitud del orientalista erudito era la de un científico que revisaba una serie de fragmentos textuales, los cuales editaba y organizaba después como si fuera un restaurador de dibujos antiguos que juntaba algunos de ellos para dar una imagen acumulativa de lo que representaban implícitamente. En consecuencia, los orientalistas tratan las obras de sus colegas citándolas de una manera continua. Burton, por ejemplo, se ocupó de _Las mil y una noches_ o de Egipto indirectamente _a través de_ la obra de Lane, citando a su predecesor e incluso desafiándole, aunque le estaba proporcionando una gran autoridad. El propio viaje de Nerval a Oriente siguió los pasos del de Lamartine, este los del de Chateaubriand. Para resumir, el orientalismo como forma de conocimiento en vías de desarrollo recurrió para alimentarse principalmente a las citas de los eruditos precedentes. Incluso cuando encontraba nuevos materiales, el orientalismo los juzgaba valiéndose (como hacen tan frecuentemente los eruditos) de las perspectivas, las ideologías y las tesis directrices de sus predecesores. De una manera bastante estricta, pues, los orientalistas después de Sacy y Lane reescribieron a Sacy y a Lane; y después de Chateaubriand, los peregrinos le reescribieron. Las realidades del Oriente moderno estaban sistemáticamente excluidas de estas complejas reescrituras, especialmente cuando peregrinos de talento, como Nerval y Flaubert, preferían las descripciones de Lane a lo que sus ojos y sus mentes les mostraban de manera inmediata.
En el sistema de conocimientos sobre Oriente, este es menos un lugar que un _topos_ , un conjunto de referencias, un cúmulo de características que parecen tener su origen en una cita, en el fragmento de un texto, en un párrafo de la obra de otro autor que ha escrito sobre el tema, en algún aspecto de una imagen previa o en una amalgama de todo esto. La observación directa o la descripción circunstancial de Oriente son las ficciones que presentan las obras sobre Oriente, aunque invariablemente sean totalmente secundarias con respecto a otro tipo de labores sistemáticas. En Lamartine, Nerval y Flaubert, Oriente es la representación de un material canónico orientado por una voluntad estética y activa capaz de producir interés en el lector. Sin embargo, en los tres escritores se impone el orientalismo o algún aspecto de él, aunque, como dije antes, la conciencia narrativa desempeñe un gran papel. Lo que hemos de observar es que, a pesar de toda su individualidad excéntrica, esta conciencia narrativa terminará dándose cuenta, como Bouvard y Pécuchet, de que la peregrinación, después de todo, es una forma de copiar.
Cuando Lamartine comenzó su viaje a Oriente en 1833, lo hizo, dijo él, como algo en lo que siempre había soñado: _«un voyage en Orient [était] comme un grand acte de ma vie intérieure»_. Lamartine es un cúmulo de ideas preconcebidas, de simpatías y de prevenciones: odia a los romanos y a Cartago, y ama a los judíos, a los egipcios y a los hindúes, de quienes pretende llegar a ser el Dante. Armado con un poema formal de «Adieu» a Francia en el que enumera todo lo que piensa hacer en Oriente, se embarca. En un principio encuentra que todo confirma sus predicciones poéticas o que se ajusta a su tendencia a la analogía. Lady Hester Stanhope es la Circe del desierto; Oriente es la _«patrie de mon imagination»_ ; los árabes son un pueblo primitivo; la poesía bíblica está grabada en la tierra del Líbano, y Oriente es el testimonio de la atractiva grandeza de Asia y de la comparativa pequeñez de Grecia. Poco después de su llegada a Palestina, sin embargo, se convierte en el incorregible creador de un Oriente imaginario. Afirma que las planicies de Canaán están representadas con mejor aspecto en las obras de Poussin y de Claudio de Lorena. Su viaje, que hasta entonces había sido una «traducción», como él decía, se transformó entonces en una oración que ejercitaba su memoria, su alma y su corazón más que sus ojos, su pensamiento o su espíritu.
El celo analógico (e indisciplinado) de Lamartine se desata completamente a través de esta cándida proclamación. Para él, el cristianismo es la religión de la imaginación y de los recuerdos, y como Lamartine considera que tipifica al creyente pío, se permite utilizarlos. El catálogo de sus «observaciones» sería interminable: una mujer le recuerda a la Haidée del _Don Juan_ [de Byron]; la relación entre Jesús y Palestina es como la de Rousseau y Ginebra; el verdadero río Jordán es menos importante que los «misterios» que produce en las almas; los orientales y, en particular, los musulmanes son perezosos, su política es caprichosa, apasionada y sin futuro; otra mujer le recuerda un párrafo de _Atala_ ; ni Tasso ni Chateaubriand (cuyos viajes, anteriores al suyo parecen con frecuencia molestar el egoísmo, por otra parte indiferente, de Lamartine) comprendieron bien la Tierra Santa, etc. Cuando habla sobre la poesía árabe con gran confianza, no manifiesta ningún malestar por su absoluta ignorancia de la lengua árabe. Todo lo que le importa es que sus viajes por Oriente le revelen que es _«la terre des cultes, des prodiges»_ y que él sea su poeta designado en Occidente. Sin el menor rasgo de ironía anuncia:
Esta tierra árabe es la tierra de los prodigios, aquí todo brota, y todo hombre, crédulo o fanático, puede llegar a ser un profeta en su momento.
Él ha llegado a ser un profeta por el simple hecho de vivir en Oriente.
Hacía el final de su relato, Lamartine ha cumplido su propósito de peregrinar al Santo Sepulcro, ese punto de partida y de llegada del tiempo y del espacio. Ha interiorizado la realidad lo suficiente como para desear retirarse de ella y volver a la pura contemplación, a la soledad, a la filosofía y a la poesía.
Elevándose por encima del Oriente puramente geográfico, se transforma en un Chateaubriand tardío que examina Oriente como si fuera una provincia personal (o al menos francesa) a disposición de las potencias europeas. Lamartine era un viajero y un peregrino en el tiempo y en el espacio verdaderos, pero se convirtió en un ego transpersonal que se identificaba en potencia y en conciencia con el conjunto de Europa. Lo que tiene ante sus ojos es un Oriente que comienza el proceso de su futuro e inevitable desmembramiento, conquistado y consagrado por la soberanía europea. Así, la visión de Lamartine muestra en el momento de máximo apogeo un Oriente que renace por segunda vez en forma de una voluntad europea de gobernarlo:
[...] Esta especie de soberanía así definida y consagrada como derecho europeo constará principalmente en el derecho de ocupar determinada parte del territorio o de la costa para fundar en ellos, o bien ciudades libres o bien emporios comerciales [...].
Lamartine no se para ahí, escala todavía más alto hasta un punto en el que Oriente (lo que acaba de visitar, donde acaba de estar), se reduce a «naciones sin territorio, sin _patrie_ , sin derechos, sin leyes o seguridad [...] que esperan ansiosamente protección», protección que les ofrece la ocupación europea.
En ninguna de las visiones de Oriente que fabrica el orientalismo hay literalmente una asimilación tan absoluta como esta. Para Lamartine peregrinar a Oriente ha implicado no solo penetrar en Oriente a través de una conciencia imperiosa, sino también eliminar virtualmente esa conciencia como resultado de su adhesión a un tipo de control impersonal y continental sobre Oriente. La verdadera identidad de Oriente se descompone en una serie de fragmentos consecutivos, que son esas observaciones de Lamartine, llenas de reminiscencias, que después serán recogidas y reunidas como un sueño napoleónico repetido. Mientras que la identidad humana de Lane desaparecía en la estructura científica de las clasificaciones de Egipto, la conciencia de Lamartine transgredió completamente sus fronteras normales. Haciendo esto, repite el viaje y las visiones de Chateaubriand simplemente para desplazarse más allá de la esfera de la abstracción de Shelley y de Napoleón, según la cual los mundos y las poblaciones se agitan como cartas sobre una mesa. Lo que queda de Oriente en la prosa de Lamartine no es muy sustancial. La realidad geopolítica ha sido recubierta por los planes que él ha hecho para ella; los lugares que ha visitado, la gente que ha encontrado y las experiencias que ha vivido no tienen apenas eco en sus generalizaciones pomposas. Las últimas huellas de particularidad se han eliminado del « _résumé politique_ » con el que concluye _Voyage en Orient_.
Contrastando con el egoísmo trascendente y cuasi nacional de Lamartine, debemos situar a Nerval y a Flaubert. Sus obras orientales desempeñan un papel sustancial en el conjunto de su _oeuvre_ mucho mayor que el del _Voyage_ imperialista de Lamartine en la suya. Tanto uno como otro llegaron a Oriente preparados por voluminosas lecturas de literatura clásica y moderna y de orientalismo académico. Flaubert reconoció esta preparación con mayor candor que Nerval, quien en _Les Filles du feu *_ dice, con bastante falta de franqueza, que todo lo que sabía de Oriente era un recuerdo medio olvidado de lo que había aprendido en el colegio. La evidencia de su _Voyage en Orient_ * contradice esto, aunque muestre un conocimiento mucho menos sistemático y disciplinado que el de Flaubert. Lo que importa, sin embargo, es el hecho de que los dos escritores (Nerval en 1842-1843 y Flaubert en 1849-1850) sacaron más provecho personal y estético de sus visitas a Oriente que todos los demás viajeros del siglo XIX. Hay que decir que ambos eran escritores de talento y que habían estado sumergidos en un medio cultural europeo que fomentaba la visión solidaria, aunque pervertida, de Oriente. Nerval y Flaubert pertenecían a esa comunidad de pensamiento y sentimiento que Mario Praz describió en _The Romantic Agony_ ,* una comunidad dentro de la cual las imágenes de los lugares exóticos, el cultivo de gustos sadomasoquistas (lo que Praz llama _algolagnia_ ), la fascinación por lo macabro, la noción de mujer fatal, el secreto y el ocultismo iban a permitir la forma literaria que produjeron Gautier (que estaba fascinado por Oriente), Swinburne, Baudelaire y Huysmans. Para Nerval y Flaubert figuras como las de Cleopatra, Salomé e Isis tenían una significación especial, y no era en absoluto accidental que en sus trabajos sobre Oriente y en sus visitas a él valoraran preeminentemente y realzaran el tipo femenino legendario, rico, sugestivo y asociativo.
Además de sus actitudes culturales generales, Nerval y Flaubert llevaron a Oriente una mitología personal cuyos intereses e incluso estructuras necesitaban a Oriente. Ambos hombres estaban impresionados por el resurgir oriental tal y como Quinet y otros lo habían definido: buscaban el vigor que produce todo lo que es fabulosamente antiguo y exótico. Para ambos, sin embargo, peregrinar a Oriente era buscar algo relativamente personal. Flaubert buscaba una «patria», como la llamó Jean Bruneau, en el lugar del origen de las religiones, de las visiones y de la antigüedad clásica; Nerval buscaba —o seguía— las huellas de sus sentimientos y de sus sueños personales como había hecho antes el Yorick del _Voyage sentimental_ ,* de Sterne. Para ambos escritores Oriente era, por tanto, un lugar de _déjà vu_ , y para los dos, con la economía artística característica de todas las grandes imaginaciones estéticas, era un lugar al que frecuentemente se volvía después de que el verdadero viaje hubiera concluido. Para ninguno de ellos Oriente estaba agotado por el uso que habían hecho de él, aunque sus escritos orientales evocaran a veces cierta decepción, desencanto o desmitificación.
La importancia excepcional de Nerval y Flaubert para un estudio del pensamiento orientalista del siglo XIX reside en que produjeron una obra conectada con el tipo de orientalismo del que hemos estado hablando hasta ahora, aunque permaneciera independiente de él. Primero, hay que estudiar el asunto del ámbito de sus obras. Nerval escribió _Viaje a Oriente_ como una colección de notas de viaje, de estampas, de historias y de fragmentos; su preocupación por Oriente se puede encontrar también en _Les Chimères_ ,* en sus cartas y en otros escritos en prosa. Los escritos de Flaubert, tanto anteriores como posteriores a su visita, están impregnados de Oriente. Oriente aparece en _Carnets de voyage_ y en la primera versión de _La temptation de Saint Antoine_ (y en las dos versiones siguientes), así como en _Hérodias_ ,* _Salambó_ y en numerosas notas de lectura, escenarios e historias indefinidas a los que podemos tener acceso y que han sido estudiados con mucha inteligencia por Bruneau. Hay también resonancias orientalistas en las grandes novelas de Flaubert. En resumen, tanto Nerval como Flaubert elaboraron continuamente su material oriental e incorporaron formas variadas en las estructuras particulares de sus propios proyectos estéticos. Sin embargo, esto no quiere decir que Oriente tenga un papel fortuito en sus obras, sino más bien —al contrario que en escritores como Lane (de quien sin ninguna vergüenza adoptaron algunas cosas), Chateaubriand, Lamartine, Renan y Sacy— que su Oriente no estaba delimitado, apropiado, reducido o codificado, sino habitado y explotado, desde un punto de vista estético e imaginativo, como un lugar espacioso y rico en posibilidades. Lo que contaba para ellos era la estructura de su obra como un hecho independiente, estético y personal, y no la manera en la que, si se quería, se podía dominar efectivamente Oriente o consignarlo geográficamente. Sus egos nunca absorbieron Oriente ni lo identificaron con el conocimiento documental y textual que existía sobre él (o sea con el orientalismo oficial).
Sin embargo, aunque por un lado la envergadura de su obra oriental exceda las limitaciones impuestas por el orientalismo ortodoxo, por otro, el tema de sus obras es más que oriental u orientalista (incluso a pesar de que hacen su propia orientalización de Oriente). Ellos juegan constantemente con los límites y los desafíos que Oriente y el conocimiento sobre él les presentan. Nerval, por ejemplo, cree que tiene que infundir vitalidad a lo que ve, cuando dice:
El cielo y el mar están siempre allí; el cielo de Oriente, el mar Jonio cada mañana se dan el beso sagrado del amor; pero la tierra está muerta, muerta porque el hombre la ha matado, y los dioses han huido.
Si Oriente ha de vivir verdaderamente, ahora que sus dioses han huido, debe de ser por sus esfuerzos fructíferos. En el _Viaje al Oriente_ , la conciencia del narrador es una voz siempre llena de energía que se mueve dentro de los laberintos de la existencia oriental armada —nos dice Nerval— con dos términos árabes: _tayyeb_ , la palabra para asentir, y _mafish_ , la palabra para negar. Estas dos palabras le permiten enfrentarse selectivamente al mundo oriental antitético, afrontarlo y extraer de él sus principios secretos. Está predispuesto a reconocer que Oriente es _«le pays des rêves et de l'illusion»_ , que, como los velos que ve por todas partes en El Cairo, esconde un fondo profundo y rico de sexualidad femenina. Nerval repite la experiencia de Lane al descubrir la necesidad del matrimonio en la sociedad islámica, pero, al contrario que Lane, se liga a una mujer. Su vínculo con Zaynab es más que una obligación social:
Tenía que unirme con alguna chica ingenua que fuera de esta tierra sagrada, que es nuestra primera patria, tenía que bañarme en las fuentes vivificantes de la humanidad de las cuales la poesía y la fe de nuestros padres manaron [...]. Me gustaría guiar mi vida como una novela y ponerme voluntariamente en el lugar de uno de esos héroes activos y resolutos que quieren a cualquier precio crear alrededor de ellos un drama, un nudo de complejidad, en una palabra, acción.
Nerval se sitúa en Oriente para conseguir más que un relato novelístico, una intención duradera —sin que nunca llegue a realizarse esta peregrinación completamente— de fundir la mente con la acción física. Este antirrelato, esta paraperegrinación, es una manera de apartarse de la finalidad discursiva percibida como una visión por los escritores anteriores que trataban de Oriente.
Manteniendo una relación física y de simpatía con Oriente, Nerval vaga informalmente a través de sus ricos ambientes y de su atmósfera cultural (sobre todo femenina), localizando especialmente en Egipto ese «centro maternal a la vez misterioso y accesible», a partir del cual se deriva toda la sabiduría. Sus impresiones, sueños y memorias alternan con fragmentos narrativos ordenados, amanerados y escritos al estilo oriental; las duras realidades del viaje —a Egipto, al Líbano o a Turquía— se mezclan con el dibujo de una digresión deliberada, como si Nerval estuviera repitiendo el _De París a Jerusalén_ de Chateaubriand, utilizando una ruta subterránea, mucho menos imperial y evidente. Michel Butor lo explica muy bien:
A ojos de Nerval, el viaje de Chateaubriand sigue siendo superficial, mientras que el suyo está calculado utilizando centros anexos, grupos de elipses que engloban los principales centros; esto le permite poner de relieve, por paralaje, todas las dimensiones del espesor de la trampa que ocultan los centros normales. Recorriendo las calles y los ambientes de El Cairo, Beirut o Constantinopla, Nerval está al acecho de todo lo que le permite percibir una gruta que se extiende por debajo de Roma, Atenas y Jerusalén [las principales ciudades del _De París a_ _Jerusalén_ de Chateaubriand. [...].
Como las tres ciudades de Chateaubriand están comunicadas entre sí —Roma con sus embajadores y papas reunifica la herencia y el testamento de Atenas y Jerusalén— las grutas de Nerval [...] se comunican unas con otras.
Incluso los dos largos episodios con sus respectivas tramas, «El cuento del califa al-Hakim» y «El cuento de la reina de la mañana», que se supone poseen un discurso narrativo sólido, parecen distanciar a Nerval de las finalidades «terrenales», introduciéndole cada vez más en un mundo interior y obsesivo de paradojas y sueños. Ambos cuentos manejan una identidad múltiple, uno de cuyos motivos —expuesto explícitamente— es el incesto, y ambos nos llevan al mundo oriental quintaesencial de Nerval, un mundo de sueños inciertos y fluidos, que se multiplican indefinidamente más allá de la resolución, de la precisión y de la materialidad. Cuando el viaje acaba y Nerval llega a Malta en su camino de vuelta al continente europeo, se da cuenta de que está ahora en _«le pays du froid et des oranges, et déjà l'Orient n'est plus pour moi qu'un de ses rêves du matin auxquels viennent bientôt succéder les ennuis du jour»_. Su _Viaje_ incorpora numerosas páginas copiadas de _Modern Egyptians_ , de Lane, pero incluso su clara confianza parece disolverse en el elemento cavernoso y eternamente en descomposición que es el Oriente de Nerval.
Sus _carnets_ del _voyage_ nos ofrecen, pienso, dos textos perfectos para entender cómo su Oriente se desliga de cualquier parecido con una concepción orientalista de Oriente, aunque su obra, hasta cierto punto, dependa del orientalismo. En el primero, sus apetitos se esfuerzan por recoger experiencias y recuerdos indiscriminadamente: _«Je sens le besoin de m'assimiler toute la nature (femmes étrangères). Souvenirs d'y avoir vécu»_. El segundo elabora un poco al primero: _«Les rêves et la folie_ [...] _Le désir de l'Orient. L'Europe s'élève. Le rêve se réalise_ [...] _Elle. Je l'avais fuie, je l'avais perdue_ [...] _Vaisseau d'Orient»_. Oriente es el símbolo de la búsqueda onírica de Nerval y de la mujer fugitiva y esquiva que está en el centro de aquella como un deseo y como una pérdida. _«Vaisseau d'Orient»_ —nave de Oriente— se refiere enigmáticamente a cualquiera de los dos, tanto a una mujer como a una nave que contiene Oriente o quizá a la propia nave de Nerval para Oriente, su _Viaje_ en prosa. En ambos casos Oriente se identifica con una _ausencia_ conmemorativa.
¿Cómo podemos explicar si no que en el _Viaje_ , una obra de un espíritu tan original e individual, Nerval utilice sin reparo algunos largos pasajes de Lane, que incorpora sin más como si fueran _su_ propia descripción de Oriente? Es como si, habiendo fracasado en su búsqueda de una realidad oriental estable y en su intento de dar orden sistemático a su representación de Oriente, Nerval empleara la autoridad prestada de un texto orientalista canónico. Después de su viaje, la tierra se quedó muerta y, al margen de sus encarnaciones del _Viaje_ brillantemente labradas aunque fragmentadas, su yo no estaba menos drogado y desgastado que antes. Por tanto, Oriente parecía pertenecer retrospectivamente a un reino negativo, en el cual los relatos fallidos de crónicas desordenadas y la pura y simple transcripción de textos eran sus únicas naves posibles. Por lo menos, Nerval no hizo ningún intento de salvar su proyecto entregándose de lleno a los designios de Francia sobre Oriente, aunque recurriera al orientalismo para decir lo que dijo.
En contraste con la visión negativa de un Oriente vaciado que tenía Nerval, el de Flaubert es un Oriente eminentemente corpóreo. Sus notas de viaje y sus cartas revelan a un hombre que registra escrupulosamente todos los sucesos, las personas y los paisajes, que se deleita en las _bizarreries_ y que nunca intenta reducir las incongruencias que ve ante él. En lo que escribe (o quizá porque lo escribe) destaca lo que le llama la atención y lo traduce a frases conscientemente elaboradas, por ejemplo: «las inscripciones y las cagaditas de los pájaros son los únicos elementos que, en Egipto, dan alguna sensación de vida». Sus gustos se inclinan hacia lo perverso, que adquiere forma normalmente a través de la combinación de una animalidad extrema, incluso de una obscenidad grotesca, y de un agudo refinamiento intelectual. Sin embargo, este tipo particular de perversidad no era algo simplemente observado, sino también estudiado, y llegó a representar un elemento esencial en la ficción de Flaubert. Las oposiciones familiares o las ambivalencias, como Harry Levin las llamó, que aparecen en sus escritos —la carne frente al espíritu, Salomé frente a san Juan, Salambó frente a san Antonio— son confirmadas poderosamente por lo que él, teniendo en cuenta su saber ecléctico, vio en Oriente y por la asociación que podía observar entre conocimiento y grosería carnal. En el alto Egipto estaba encantado con el arte egipcio antiguo, con su preciosidad y su lubricidad deliberada: «¿Así que las imágenes sucias existían ya en la antigüedad?». Oriente respondía realmente a más preguntas de las que planteaba, como muestra este párrafo:
Tú [la madre de Flaubert] me preguntas si Oriente está a la altura de lo que yo imaginaba que iba a ser. Sí, lo está; más que eso, se extiende más allá de la estrecha idea que tenía de él. He encontrado, claramente delimitado, todo lo que tenía brumoso en la mente. Las realidades han reemplazado a las suposiciones tan bien que con frecuencia es como si reencontrara de repente los viejos sueños olvidados.
La obra de Flaubert es tan completa y tan vasta que si intentáramos solamente dar cuenta de sus escritos orientales, lo único que podríamos hacer es un resumen desgraciadamente incompleto. Sin embargo, algunas de sus características principales se pueden describir bastante bien dentro del contexto creado por otros autores que trataron de Oriente. Permitiéndonos hacer diferencias entre sus escritos cándidamente personales (cartas, notas de viajes y apuntes diarios) y sus escritos formalmente estéticos (novelas y cuentos), podemos seguir señalando que la perspectiva oriental de Flaubert tiene sus raíces en la búsqueda en el Este y en el Sur de una «alternativa visionaria» que «significaba colores brillantes en contraste con la tonalidad gris del paisaje de las provincias francesas; significaba espectáculo apasionante en vez de rutina monótona, el misterio permanente en lugar de la familiaridad excesiva». Cuando lo visitó, sin embargo, Oriente le dio a simple vista impresión de decrepitud y de senectud. Como cualquier otro orientalismo, el de Flaubert es revitalista: _él_ debe devolverle la vida a Oriente, él debe llevarlo hasta sí mismo y hasta sus lectores, y está la experiencia que tiene de Oriente por los libros y por los lugares que ha visitado, y está su lenguaje, que se encargarán de realizar el engaño. Componía sus novelas sobre Oriente como si fueran reconstrucciones históricas y eruditas. Cartago en _Salambó_ y los productos de la febril imaginación de san Antonio fueron los frutos auténticos de lo que Flaubert leyó en las fuentes (principalmente occidentales) sobre la religión, el arte de la guerra, los rituales y las sociedades orientales.
Lo que las obras estéticas contienen, aparte de bastantes muestras de las lecturas voraces y las recensiones de Flaubert, son los recuerdos de su viaje oriental. El _Dictionnaire des idées reçues_ * dice que un orientalista es un _«homme qui a beaucoup voyagé»_. Solamente Flaubert, a diferencia de la mayoría de los viajeros, da un uso ingenioso a sus viajes. La mayor parte de sus experiencias se transmiten en forma teatral. Lo que le interesa no es solo el contenido de lo que ve, sino, como en Renan, _cómo_ ve, la manera, a veces horrible, pero siempre atractiva, en la que Oriente se presenta ante él. Flaubert es su mejor público.
[...] Hospital de Qasr al-Aini. Bien mantenido. Obra de Clot Bey —su impronta todavía se deja ver—. Bonitos casos de sífilis; en la sala de los Mamelucos de Abbas algunos la tienen en el culo. A una señal del doctor, todos se ponen de pie sobre sus camas, desabrochándose los cinturones de los pantalones (es como una maniobra militar) y abren los anos con sus dedos para mostrar sus chancros. Enormes infundíbulos: uno tiene un tumor peludo dentro del ano. La verga de un viejo completamente privada de piel; retrocedí por causa del hedor. Un raquítico: las manos retorcidas hacia atrás, las uñas largas como garfios; se veía la estructura ósea de su torso tan claramente como en un esqueleto; también el resto de su cuerpo era fantásticamente delgado, y su cabeza estaba rodeada de una lepra blanquecina.
Sala de disección: [...] sobre la mesa un cadáver árabe totalmente abierto; un pelo negro precioso [...].
Los sórdidos detalles de esta escena se pueden relacionar con muchas otras de las novelas de Flaubert en las que la enfermedad se nos presenta como un teatro clínico. Su fascinación por la disección y la belleza recuerda, por ejemplo, la escena final de _Salambó_ que culmina con la muerte ceremonial de Mâtho. En estas escenas, los sentimientos de repulsión o de simpatía están totalmente reprimidos; lo que importa es la expresión correcta del detalle exacto.
Los momentos más conocidos del viaje de Flaubert a Oriente tienen que ver con Kuchuk Hanem, una célebre bailarina y cortesana egipcia con la que se encontró en Wadi Halfa. Flaubert había leído en Lane lo que concierne a las _almeh_ y los _jawal_ , bailarinas y bailarines respectivamente, pero fue su imaginación, y no la de Lane, la que inmediatamente pudo comprender y disfrutar de la paradoja casi metafísica de la profesión de _almeh_ y del significado de su nombre. (En _Victory_ ,* Joseph Conrad repetirá la observación de Flaubert haciendo a su heroína música —Alma— irresistiblemente atractiva y peligrosa para Axel Heyst.) _Almeh_ en árabe significa «mujer instruida». Era el nombre que, en la conservadora sociedad egipcia del siglo XVIII, recibían las mujeres que eran consumadas recitadoras de poesía. Hacia la mitad del siglo XIX este título se utilizaba como una especie de nombre de oficio para las bailarinas que también eran prostitutas, y eso era Kuchuk Hanem, a la que Flaubert, antes de dormir con ella, vio bailar la danza «L'Abeille». Seguramente ella era el prototipo de la mayoría de los caracteres femeninos de sus novelas, con su sensualidad instruida, su delicadeza y (según Flaubert) su grosería no inteligente. Lo que le gustaba especialmente de ella era que parecía no exigirle nada, mientras que el «nauseabundo hedor» de sus chinches se mezclaba encantadamente con «la fragancia de su piel rociada de sándalo». Después de su viaje a Oriente, escribió una carta a Louise Colet en la que decía que «la mujer oriental no es más que una máquina; no distingue entre un hombre y otro». La sexualidad muda e insaciable de Kuchuk permitía al espíritu de Flaubert vagar a través de una serie de reflexiones cuyo poder de fascinación nos recuerda un poco a Declauriers y a Frédéric Moreau al final de _L'Éducation sentimentale_ :*
En cuanto a mí, apenas he pegado ojo. He pasado la noche contemplando a esa bella criatura dormida (ella roncaba, su cabeza se apoyaba contra mi brazo y yo había deslizado mi dedo índice bajo su collar). Mi noche ha sido un ensueño largo e infinitamente intenso; por eso he permanecido. Estuve recordando mis noches en los burdeles de París —los viejos recuerdos volvían a mí— y pensé en ella, en su danza, en su voz cuando cantaba canciones que para mí no tenían significado y de las que ni siquiera podía distinguir las palabras.
La mujer oriental es una excusa y una oportunidad para los ensueños de Flaubert. Él está embelesado por la autosuficiencia de ella, por su descuido emocional y también porque, cuando yace a su lado, le permite pensar. Kuchuk es menos una mujer que un despliegue de feminidad emocionante, aunque inexpresivo verbalmente, es el prototipo de la Salambó y de la Salomé de Flaubert, así como de todas las versiones de la tentación carnal femenina de su san Antonio. Como la reina de Saba (que bailaba también «la abeja»), ella podía decir —si pudiera hablar— _«Je ne suis pas une femme, je suis un monde»_. Vista desde otra perspectiva, Kuchuk es un símbolo inquietante de fecundidad; peculiarmente oriental en su sexualidad lujuriosa y en apariencia sin límites. Su casa cerca del alto Nilo ocupa una posición estructuralmente similar al lugar donde se oculta el velo de Tanit —la diosa descrita como _omnifécunde_ — en _Salambó_. Sin embargo, como Tanit, Salomé y la propia Salambó, Kuchuk Hanem estaba condenada a permanecer estéril, corrupta y sin descendencia. Ella y su mundo oriental iban a intensificar en Flaubert su propio sentimiento de esterilidad. Esto se advierte en el párrafo siguiente:
Tenemos una gran orquesta, una paleta rica, una gran variedad de recursos, probablemente sabemos muchos más trucos y maniobras que nunca. No, lo que nos falta es un principio intrínseco, el alma de la cosa, la idea misma de un tema. Tomamos notas, hacemos viajes; ¡minucias! Nos hacemos eruditos, arqueólogos, historiadores, doctores, gentes refinadas. ¿Adónde nos lleva todo esto? ¿Dónde está el corazón, la inspiración, la savia? ¿Por dónde empezar? ¿Adónde llegar? Chupamos muy bien, jugamos mucho con la lengua, nos besuqueamos lentamente: pero ¡lo real! Eyacular, engendrar el niño.
En el tejido que forman todas las experiencias orientales de Flaubert, las fascinantes y las desagradables, hay una asociación casi uniforme entre Oriente y el sexo. Flaubert no fue el primero en hacer esta asociación, ni el que exageró más un motivo que persistía notablemente en las actitudes occidentales hacia Oriente. De hecho, este motivo, por sí mismo, es singularmente invariable, aunque el talento de Flaubert hiciera más que el de ningún otro por darle dignidad artística. ¿Por qué parece que Oriente todavía sugiere no solamente la fecundidad, sino también la promesa (y la amenaza) sexual, una sensualidad infatigable, un deseo ilimitado y unas profundas energías generatrices? Sobre este punto solo podemos especular, ya que, a pesar de que aparece frecuentemente, no forma parte de mi análisis presente. Sin embargo, hay que reconocer su importancia como algo que suscita en los orientalistas respuestas complejas y, a veces, incluso un descubrimiento de sí mismos que les asusta, y en esto Flaubert es un caso interesante.
Oriente le ha obligado a replegarse sobre sus propios recursos humanos y técnicos. No respondió, como tampoco, lo hizo Kuchuk, a su presencia. Ante la vida que sigue su curso, Flaubert, como Lane antes que él, sintió su impotencia objetiva, y quizá también su repugnancia interior a mostrar y a participar en lo que veía. Este fue el eterno problema de Flaubert. Oriente había existido antes de que él fuera allí, y siguió haciéndolo después de su visita. Flaubert admitió la dificultad, y encontró el antídoto en su trabajo (en particular en una obra oriental como _La tentación de san Antonio_ ), que consistía en acentuar la forma enciclopédica de su material a expensas de su implicación humana en la vida. De hecho, san Antonio no es más que un hombre para quien la realidad la componen una serie de libros, espectáculos y reconstrucciones históricas que se despliegan ante sus ojos como tentaciones. Los inmensos conocimientos de Flaubert están estructurados —como Michel Foucault ha señalado bien— como una biblioteca teatral y fantástica que desfila ante la mirada del anacoreta como un residuo; el desfile lleva en su forma los recuerdos que Flaubert tiene de Qasr al-Aini (la parada militar de sifilíticos) y la danza de Kuchuk. Lo que es más pertinente, sin embargo, es que san Antonio es un célibe para quien las tentaciones son esencialmente sexuales. Después de salir bien parado de todo tipo de encantos peligrosos, decide echar un vistazo al proceso biológico de la vida; eso le produce el delirio de poder ver la vida en el momento de nacer, una escena para la cual Flaubert se sintió incompetente durante su estancia en Oriente. Sin embargo, porque san Antonio delira se supone que vamos a leer la escena irónicamente. Lo que se le concede al final es el deseo de _convertirse_ en sustancia, de convertirse en vida, es, al menos, un deseo que no sabemos si puede realizarse o cumplirse.
A pesar de su capacidad y enorme poder de absorción intelectual, Flaubert sintió en Oriente, primero, que «cuanto más te concentras en él [en detalle] menos abarcas el todo» y, segundo, que «las piezas ocupan un lugar por sí mismas». En el mejor de los casos, esto produce una forma _espectacular_ , pero Oriente permanece cerrado a la participación total del occidental. En cierta medida, esto supuso una dificultad personal para Flaubert, que inventó algunos medios —de algunos de los cuales ya hemos hablado— para tratarla. En un plano más general esto suponía una dificultad _epistemológica_ , y para resolverla existía, por supuesto, la disciplina orientalista. En cierto momento de su viaje oriental, Flaubert tuvo en cuenta lo que el desafío epistemológico podía dar de sí. Sin lo que él llamaba espíritu y estilo, la mente podía «perderse en la arqueología»; con esto hacía alusión a un tipo de incorporación arqueológica por la cual lo exótico y lo extraño sería formulado en forma de léxicos, de códigos y finalmente de modelos del mismo tipo de los que él iba a ridiculizar en el _Diccionario de lugares comunes_. Bajo la influencia de una actitud así, el mundo estaría «regido como un colegio. Los profesores serán la ley. Todo será uniforme». Él pensaba sin ninguna duda que, comparados con una disciplina impuesta como esa, su propio método y su manera de tratar el material exótico y especialmente el material oriental que había acumulado a través de su propia experiencia y de las lecturas que le habían llevado largos años, eran infinitamente preferibles. En este método al menos había espacio para un sentido de inmediatez, para la imaginación y el olfato, mientras que en las filas de los volúmenes arqueológicos todo lo que no era «ciencia» quedaba eliminado. Flaubert sabía mejor que la mayoría de los novelistas lo que era un saber organizado, sus productos y sus resultados. Esos resultados son evidentes en las desventuras de Bouvard y Pécuchet, pero habrían sido igualmente cómicos en campos como el del orientalismo, donde las actitudes textuales pertenecen al mundo de las _idées reçues_. Por tanto, se puede construir el mundo con inspiración y estilo o copiarlo incansablemente de acuerdo con unas reglas académicas impersonales. En ambos casos, en lo que concierne a Oriente se reconoce con franqueza que es un mundo situado en un lugar fuera de los apegos sentimentales y de los valores ordinarios de _nuestro_ mundo occidental.
En todas sus novelas Flaubert asocia Oriente al escapismo en su vertiente de fantasía sexual. Emma Bovary y Frédéric Moreau languidecen por lo que no tienen en sus vidas burguesas apagadas (o atormentadas) y lo que desean conscientemente les llega fácilmente en sus ensueños envuelto en clichés o modelos orientales: harenes, princesas, esclavos, velos, bailarinas y bailarines, sorbetes, ungüentos, etc. Este repertorio es familiar, no tanto porque nos recuerda los propios viajes de Flaubert y sus obsesiones con respecto a Oriente, sino porque una vez más se hace una clara asociación entre Oriente y la licencia sexual. Podemos reconocer también que en la Europa del siglo XIX, con su creciente _embourgeoisement_ , la sexualidad estaba institucionalizada hasta un grado considerable. Por un lado, no existía nada parecido a la sexualidad libre y, por otro, la sexualidad en la sociedad implicaba un tejido de obligaciones legales, morales, políticas e incluso económicas que eran bastante meticulosas y ciertamente molestas. Del mismo modo que las diferentes posesiones coloniales eran útiles —además de por sus beneficios económicos para la Europa metropolitana— para enviar allí a los hijos rebeldes, a la población excedente de delincuentes, a los pobres y a otros indeseables, Oriente era un lugar donde se podía buscar una experiencia sexual que resultaba inaccesible en Europa. Ningún escritor europeo que escribiera sobre, o viajara a Oriente después de 1800, estuvo dispensado de esta búsqueda: Flaubert, Nerval, «Dirty Dick» Burton y Lane son los más notables. Ya en el siglo XX, uno piensa en Gide, Conrad, Maugham y muchos más. Lo que buscaban con frecuencia —correctamente, creo— era una sexualidad de diferente clase, quizá más libertina y menos cargada de pecado; pero incluso esta búsqueda, si era repetida por mucha gente, podía llegar a ser tan regulada y uniforme como el mismo saber (y eso es lo que pasó). Con el tiempo, «la sexualidad oriental» se convirtió en una mercancía tan normalizada como cualquier otra en la cultura de masas, con el resultado de que los lectores y escritores podían obtenerla si lo deseaban sin necesidad de ir a Oriente.
Es cierto que hacia mediados del siglo XIX, Francia, no menos que Inglaterra y que el resto de Europa, disponía de una floreciente industria de conocimientos del tipo que Flaubert temía. Se compuso un gran número de textos y, lo que es más importante, por todas partes se encontraban organismos e instituciones encargadas de difundirlos y propagarlos. Como los historiadores de las ciencias y del conocimiento han observado, la organización del campo de la ciencia y de la erudición que se llevó a cabo durante el siglo XIX fue rigurosa y totalmente englobante. La investigación se convirtió en una actividad regular, hubo un considerable intercambio de informaciones, un acuerdo sobre cuáles eran los problemas y un consenso sobre los paradigmas apropiados para la investigación y sobre sus resultados. El aparato que servía a los estudios orientales formaba parte de la escena y esto era algo que seguramente Flaubert tenía en mente cuando afirmó que «todo será uniforme». Un orientalista no sería ya nunca más un aficionado lleno de entusiasmo y bien dotado o, si lo era, tendría problemas para que le tomaran en serio como erudito. Ser un orientalista iba a significar tener una preparación universitaria en el campo de los estudios orientales (hacia 1850, todas las grandes universidades europeas tenían cursos completos de alguna de las disciplinas orientalistas), obtener una subvención para hacer viajes (quizá de las sociedades asiáticas o de los fondos para la exploración geográfica o de una beca del gobierno) y publicar de una forma autorizada (quizá bajo los auspicios de una sociedad erudita o de una fundación para la traducción de textos orientales). Y a la vez, en el interior de la cofradía de eruditos orientalistas y para el público en general, la ciencia era esa autorización uniforme que revestía el trabajo de la erudición orientalista, y no el testimonio personal o el impresionismo subjetivo.
A esta regulación opresiva de los temas orientales se añadía la atención cada vez mayor que las potencias (como se llamaba a los imperios europeos) prestaban a Oriente y, en particular, a los países del Mediterráneo oriental. Desde el Tratado de Chanak, firmado en 1806 por el Imperio otomano y Gran Bretaña, el problema de Oriente planeaba cada vez más sobre el horizonte mediterráneo de Europa. Los intereses británicos eran más sustanciales en Oriente que los franceses, pero no debemos olvidar los avances de Rusia (Samarcanda y Bujará se tomaron en 1868 y el ferrocarril transcaspiano se prolongaba constantemente), ni los de Alemania y el Imperio austrohúngaro. Las intervenciones de Francia en el norte de África, sin embargo, no eran los únicos componentes de su política islámica. En 1860, durante los enfrentamientos entre maronitas y drusos en el Líbano (que Lamartine y Nerval ya habían predicho), Francia apoyó a los cristianos e Inglaterra a los drusos. El tema crucial de cualquier política europea en Oriente residía en el problema de las minorías cuyos «intereses» las potencias pretendían proteger y representar cada una a su manera. Los judíos, los griegos, los rusos ortodoxos, los drusos, los circasianos, los armenios, los kurdos y las pequeñas sectas cristianas eran el objetivo de los planes y proyectos que las potencias extranjeras hacían y estudiaban, y de la política oriental que improvisaban y construían para ellos.
Menciono todo esto para que se comprenda hasta qué punto, durante la segunda mitad del siglo XIX, seguía vigente la confluencia de intereses, de saber oficial y de presión institucional en Oriente, y hasta qué punto lo invadía como tema de estudio y como territorio. Incluso los relatos de viajes más inocentes —había literalmente cientos de ellos después de 1850— contribuyeron, a dar mayor densidad a la conciencia que el público tenía de Oriente; una línea de demarcación muy clara separaba las delicias, las variadas hazañas y los testimonios solemnes de los peregrinos a Oriente (entre los que estaban algunos viajeros estadounidenses como Mark Twain y Herman Melville), de los relatos de autoridad escritos por viajeros, eruditos, misioneros, funcionarios gubernamentales y otros testigos expertos. Esta línea de demarcación estuvo claramente presente en la mente de Flaubert, como debió de estarlo también en la conciencia de cualquier individuo que no se contentara con observar Oriente de modo inocente como terreno de explotación literaria.
Los escritores ingleses tuvieron en conjunto un sentimiento más pronunciado que los franceses sobre lo que suponían las peregrinaciones. En este sentido, la India fue una constante real y de gran valor y, en consecuencia, todo el territorio que se extendía entre el Mediterráneo y la India adquirió un peso muy importante. Escritores románticos como Byron y Scott tuvieron, por tanto, una visión política de Oriente Próximo y una conciencia muy combativa acerca de la manera en que debían conducirse las relaciones entre esta región y Europa. El sentido histórico de Scott en _El talismán_ y en _Count Robert of Paris_ le permitió situar estas novelas en la Palestina de las Cruzadas y en el Bizancio del siglo XI, respectivamente, sin al mismo tiempo abandonar la aguda apreciación política sobre el modo de actuar de las potencias en el extranjero. Podemos atribuir sin dificultad el fracaso del _Tancred_ de Disraeli al conocimiento quizá demasiado desarrollado que tenía su autor de la política oriental y de la red de intereses del Estado británico. El deseo ingenuo de Tancredo es ir a Jerusalén, pero enseguida Disraeli se enreda en descripciones de una complicación absurda sobre cómo un jefe tribal libanés intenta manipular a los drusos, a los musulmanes, a los judíos y a los europeos para su propio beneficio político. Al final de la novela, la búsqueda oriental de Tancredo más o menos ha desaparecido porque no hay nada en la visión material que Disraeli tiene de las realidades orientales que alimente los impulsos algo caprichosos del peregrino. Ni siquiera George Eliot, que jamás había visitado Oriente, pudo sostener el equivalente judío de la peregrinación oriental en _Daniel Deronda_ (1876) sin extraviarse en la complejidad de las realidades británicas tal y como afectaban de manera decisiva al proyecto oriental.
Así, siempre que el motivo oriental no era principalmente una materia estilística (como en las _Rubaiyat_ de Fitzgerald, o en las _Adventures of Hajji Baba of Ispahan_ , de Morier) el escritor inglés se veía forzado a confrontar su fantasía individual con una serie de resistencias imponentes. No hay ninguna obra inglesa equivalente a las de Chateaubriand, Lamartine, Nerval y Flaubert, del mismo modo que los primeros orientalistas compañeros de Lane —Silvestre de Sacy y Renan— eran bastante más conscientes que él de que en cierto modo estaban creando lo que escribían. La forma de obras como _Eothen_ (1844), de Kinglake, y _Mi peregrinación a Medina y La Meca_ (18551856), de Burton, es rígidamente cronológica y debidamente lineal, como si los autores estuvieran describiendo una tarde de compras en un bazar oriental en vez de una aventura. La obra de Kinglake, que no se merece la celebridad y el éxito popular que obtuvo, es un catálogo patético de etnocentrismos pomposos y de pesados relatos sin pies ni cabeza sobre el Oriente de los ingleses. El propósito ostensible del libro es probar que viajar a Oriente es importante para «modelar vuestro carácter; es decir, vuestra propia identidad»; pero, en realidad, este no tiende más que a solidificar «vuestro» antisemitismo, xenofobia y prejuicios raciales generales. Se nos dice, por ejemplo, que _Las mil y una noches_ es una obra demasiado viva e imaginativa para haber sido creada por «un simple oriental, que en lo que se refiere a la creación es un ser muerto y seco: una momia intelectual». Aunque Kinglake confiesa alegremente que no sabe ninguna lengua oriental, su ignorancia no le impide hacer generalizaciones sobre Oriente, su cultura, su mentalidad y su sociedad. Muchas de las actitudes que reproduce son canónicas, por supuesto, pero es interesante constatar que la experiencia de haber visto Oriente influye muy poco en sus opiniones. Como muchos otros viajeros, se interesa más por rehacerse a sí mismo, y rehacer Oriente (muerto y seco, una momia mental) que por ver lo que hay que ver. Cualquier ser de los que se encuentra no hace más que corroborar su creencia de que la mejor manera de tratar a los orientales es intimidándolos y ¿qué mejor instrumento de intimidación que un ego occidental soberano? De camino a Suez, a través del desierto, solo, se glorifica de su autosuficiencia y de su poder: «Yo estaba allí, en el desierto africano y yo mismo, _no otros, estaba a cargo de mi vida_ ». Oriente le sirve para el propósito relativamente inútil de abarcarse a sí mismo.
Como antes lo había hecho Lamartine, Kinglake identificaba confortablemente la conciencia de su superioridad con la de su país, con la diferencia de que en el caso del inglés, su gobierno estaba más próximo a instalarse en el resto de Oriente que en el del francés, por el momento. Flaubert vio esto con una precisión perfecta:
Me parece casi imposible que dentro de un breve período de tiempo Inglaterra no se convierta en la dueña de Egipto. Ya tiene Adén lleno de tropas y el paso de Suez facilitará que una buena mañana lleguen los uniformes rojos a El Cairo. Las noticias se sabrán en Francia dos semanas después y todo el mundo se sorprenderá. Recuerden mi predicción: al primer síntoma de perturbación en Europa, Inglaterra ocupará Egipto, y Rusia ocupará Constantinopla, y nosotros, en represalia, iremos a que nos masacren en las montañas de Siria.
A pesar de toda su individualidad fanfarrona, los puntos de vista de Kinglake expresan una voluntad pública y nacional sobre Oriente; su ego es el instrumento de la expresión de esta voluntad, él no la controla en absoluto. No hay ninguna evidencia, en sus escritos, que pruebe que haya luchado por crear una nueva opinión de Oriente; ni sus conocimientos ni su personalidad son adecuados para ello, y esa es la gran diferencia que hay entre él y Richard Burton. Como viajero, Burton era un auténtico aventurero, y como erudito podía equipararse en importancia a cualquier orientalista académico europeo. Su carácter le hizo concienciarse de la necesidad de batirse con los profesores uniformados que dirigían la ciencia europea con gran precisión anónima y rigor científico. Todo lo que Burton escribió testimonia esta combatividad; en pocas ocasiones muestra un desdén más cándido hacia sus adversarios que en el prefacio de su traducción de _Las mil y una noches_. Parece que, de manera infantil, intenta demostrar que sabe más que cualquier otro erudito profesional, que ha conseguido muchos más detalles que ellos y que puede manejar los materiales con más tacto y frescura que ellos.
Como he dicho antes, la obra de Burton, basada en su experiencia personal, ocupa una posición intermedia dentro de los géneros orientalistas que, por un lado, representa Lane y, por otro, los escritores franceses de los que he hablado. Sus narraciones orientales tienen la estructura de las peregrinaciones, y en el caso de _The Land of Midian Revisited_ , son peregrinaciones que vuelven a lugares que unas veces tienen una significación religiosa y otras política y económica. Se presenta en las obras como el personaje principal, como el centro de la aventura fantástica e, incluso imaginaria (como los escritores franceses) o como el comentador occidental de la sociedad y de las costumbres orientales autorizado y objetivo (como Lane). Thomas Assad le ha considerado con razón el primero de una serie de viajeros victorianos a Oriente dotados de un individualismo salvaje (los otros fueron Blunt y Doughty). El trabajo de Assad se basa en las diferencias en el tono y la inteligencia que existen entre las obras de estos escritores y obras como _Discoveries in the Ruins of Nineveh and Babylon_ , de Austen Layard (1851), el famoso libro de Eliot Warburton, _The Crescent and the Cross_ (1844), _Visit to the Monasteries of Levant_ , de Robert Curzon (1849), y _Notes of a Journey from Cornhill to Grand Cairo_ (1845), de Thackeray, libro que no cita y que no es muy divertido. Sin embargo, la herencia de Burton es más compleja que individualista precisamente porque podemos encontrar en sus escritos ejemplos de la lucha entre el individualismo y un fuerte sentimiento de identificación nacional con Europa (con Inglaterra de manera específica) como potencia imperial en Oriente. Assad señala con gran precisión que Burton era un imperialista, a pesar de toda su asociación benévola con los árabes; pero lo que es más relevante es que Burton se consideraba tanto un rebelde contra la autoridad (y de ahí su identificación con el Este como lugar de libertad frente a la autoridad moral victoriana) como un agente potencial de las autoridades en Oriente. La _manera_ en que coexisten en él estos dos papeles antagonistas es muy interesante.
La cuestión, a fin de cuentas, se reduce a un problema de conocimiento de Oriente; por eso nuestro estudio acerca de cómo el orientalismo fue estructurado y reestructurado en la mayor parte del siglo XIX, debe concluir con unas consideraciones sobre el orientalismo de Burton. Como viajero en busca de aventuras, Burton se sentía partícipe de la vida de la gente en cuyas tierras vivía. Con mucho más éxito que T. E. Lawrence, fue capaz de convertirse en un oriental; no solo hablaba perfectamente la lengua, sino que pudo penetrar en el corazón del islam y, disfrazado de médico musulmán indio, hacer la peregrinación a La Meca. No obstante, creo que la característica más extraordinaria de Burton fue su comprensión verdaderamente excepcional del grado en que la vida de los hombres en sociedad se regía por reglas y códigos. Todos sus vastos conocimientos sobre Oriente, presentes en cada una de las páginas de sus escritos, revelan que sabía que Oriente en general y el islam en particular eran sistemas de información, de comportamiento y de creencias; que ser oriental o musulmán consistía en saber ciertas cosas de una cierta manera, y que esas cosas evidentemente estaban sometidas a la historia, a la geografía y al desarrollo de la sociedad en unas condiciones específicas. Así, en los relatos que escribió sobre sus viajes a Oriente se muestra consciente de todo esto y capaz de dirigir el curso de su narración a través de ello. Solo alguien que conociera el árabe y el islam tan bien como Burton podía llegar tan lejos como llegó él al convertirse efectivamente en un peregrino a La Meca y a Medina. Por eso, lo que leemos en su prosa es la historia de una conciencia que se abre camino a través de una cultura extranjera porque ha conseguido absorber sus sistemas de información y de comportamiento. La libertad de Burton residía en que se sacudió suficientemente sus orígenes europeos para poder vivir como un oriental. En muchas de las escenas de _Mi peregrinación_ aparece superando los obstáculos que se le presentan a él, un extranjero en un país desconocido. Y pudo hacerlo porque tenía suficientes conocimientos sobre esa sociedad extraña.
Más que en ningún otro escritor, en Burton sentimos que las generalizaciones sobre lo oriental —por ejemplo, cuando habla de la noción de _kayf_ para el árabe o de cómo la educación se adapta a la mente oriental (páginas que están claramente escritas para refutar la afirmación simplista de Macaulay)— son el resultado de un conocimiento sobre Oriente adquirido viviendo allí, de hecho viéndolo con sus propios ojos, intentando honestamente observar la vida oriental desde el punto de vista de una persona inmersa en ella. Sin embargo, hay otro sentimiento que emana de la prosa de Burton, un sentimiento de afirmación y de dominación sobre todas las complejidades de la vida oriental. Todas sus notas a pie de página tanto en _Mi peregrinación_ como en su traducción de _Las mil y una noches_ (e igualmente en el ensayo final de esta traducción) pretenden ser testimonios de su victoria sobre el a veces escandaloso sistema de conocimiento oriental, un sistema del que él mismo consiguió ser un maestro. Ya que incluso en la prosa de Burton no se nos _da_ Oriente directamente, todo lo concerniente a él se nos presenta por medio de las intervenciones inteligentes (y a veces irritantes) de Burton, que nos recuerdan con insistencia cómo se las ha arreglado para organizar la vida oriental de acuerdo con las necesidades de su narración. Y es este hecho —porque en _Mi peregrinación_ es un hecho— lo que eleva la conciencia de Burton hasta una posición de supremacía sobre Oriente. En esta posición, su individualidad se encuentra por fuerza, y de hecho se confunde con ella, con la voz del imperio, la cual es por sí misma un sistema de reglas, de códigos y de usos epistemológicos concretos. Así, cuando Burton nos dice en _Mi peregrinación_ que «Egipto es un tesoro que hay que ganar», que «es el premio más tentador que ofrece el Este a la ambición europea, sin exceptuar ni siquiera el Cuerno de Oro», debemos reconocer cómo la voz de ese maestro extremadamente idiosincrásico del conocimiento oriental da forma y alimenta a la voz europea que ambiciona Oriente.
Las dos voces de Burton que se funden en una son el preludio de la obra de los orientalistas-agentes imperiales, como T. E. Lawrence, Edward Henry Palmer, D. G. Hogarth, Gertrude Bell, Ronald Storrs, St. John Philby y William Gifford Palgrave, por nombrar solo a algunos escritores ingleses. La doble intención de la obra de Burton pretende al mismo tiempo utilizar su estancia en Oriente para hacer ciertas observaciones científicas y sacrificar, no de manera fácil, su individualidad con este fin. La segunda de estas intenciones le lleva inevitablemente a someterse a la primera porque, como cada vez se hará más obvio, él es un europeo que se da cuenta de que su conocimiento de la sociedad oriental solo es posible para un europeo que conciba la sociedad como una colección de reglas y prácticas. Dicho de otra forma, para ser europeo en Oriente y para serlo de manera inteligente, se debe ver y conocer Oriente como un dominio gobernado por Europa. El orientalismo, que es el sistema de conocimiento europeo u occidental de Oriente, pasa a ser así sinónimo de la dominación europea sobre Oriente, y esta dominación efectivamente es más fuerte incluso que las excentricidades del estilo personal de Burton.
Burton llevó la afirmación de un conocimiento personal, auténtico, solidario y humanista de Oriente tan lejos que podía combatir contra el archivo del conocimiento europeo oficial sobre el tema. En la historia de las tentativas hechas en el siglo XIX por restaurar, reestructurar y redimir las diferentes provincias del conocimiento y de la vida, el orientalismo —como todas las demás disciplinas eruditas de inspiración romántica— desempeñó un papel importante, ya que era un sistema de observación inspirada, que no solo evolucionó hasta llegar a estar «regida como un colegio», según la expresión de Flaubert, sino que también redujo al papel de mero escriba imperial la personalidad de los orientalistas, incluso la del individualista más temible, como era Burton. Oriente era un lugar, y se convirtió en un dominio de la regla erudita real y de la dominación imperial potencial. El papel de los primeros orientalistas, como Renan, Sacy y Lane, consistió en proporcionar tanto a su obra como a Oriente una _mise en scène_ ; los orientalistas posteriores, eruditos o imaginativos, se apoderaron firmemente de esa escena. Más tarde, cuando el escenario necesitó una dirección, era evidente que las instituciones y los gobiernos eran mejores para los asuntos de la gestión que los individuos. Este es el legado del orientalismo del siglo XIX, del que el del siglo XX ha sido heredero. Hay que examinar ahora con toda precisión la manera en que el orientalismo del siglo XX —inaugurado por el largo proceso de la ocupación occidental de Oriente a partir de 1880— consiguió con éxito controlar la libertad y el conocimiento; en resumen, la manera en que el orientalismo se formalizó en una copia repetida de sí mismo.
# TERCERA PARTE
### El orientalismo en nuestros días
Se les veía con sus ídolos en los brazos como grandes niños paralíticos.
GUSTAVE FLAUBERT,
_La tentación de san Antonio_
La conquista de la tierra, que principalmente consiste en quitársela a aquellos cuyo color es diferente al nuestro o cuya nariz es un poco más plana, no es un asunto muy agradable si se observa de cerca. Solo la idea puede redimir todo esto. Una idea que lo respalde, no un pretexto sentimental, sino una idea y una fe desinteresada en ella; algo que se pueda exaltar y admirar, algo por lo que ofrecer un sacrificio.
JOSEPH CONRAD,
_El corazón de las tinieblas_
### I
### Orientalismo latente y orientalismo manifiesto
En la primera parte, he intentado delimitar el ámbito de pensamiento y acción que abarca el término _orientalismo_ , utilizando para realizar dicha delimitación como modelos privilegiados las experiencias británica y francesa de y con Oriente Próximo, el islam y los árabes. A través de estas experiencias he podido distinguir una íntima, quizá incluso la más íntima, y rica relación entre Oriente y Occidente. Sin embargo, debo puntualizar que estas experiencias constituyeron solo una parte de las relaciones mucho más amplias europeas u occidentales con Oriente. No obstante, lo que más parece haber influido en el orientalismo ha sido el sentimiento constante de confrontación que han experimentado los occidentales que han tratado con el Este. La noción fronteriza de Este y Oeste, los grados variables de inferioridad y fuerza proyectados, el alcance del trabajo realizado y los tipos de características peculiares adscritos a Oriente: todos estos elementos dan cuenta de una decidida división imaginaria y geográfica entre el Este y el Oeste, división que ha perdurado durante muchos siglos. En la segunda parte mi atención se ha concentrado de manera más precisa en un objetivo. Estaba interesado en las primeras fases de lo que he denominado orientalismo moderno, que empezó a finales del siglo XVIII y en los primeros años del XIX. Como no pretendía que mi estudio fuera una crónica narrativa sobre el desarrollo de los estudios orientales en el Occidente moderno, me propuse a cambio hacer una descripción del surgimiento, desarrollo e instituciones del orientalismo tal y como se fueron formando en contraposición a unos antecedentes determinados por la historia intelectual, cultural y política hasta más o menos 1870 o 1880. Aunque mi interés por el orientalismo incluía en esos momentos una amplia variedad de eruditos y de escritores de ficción, mi intención no podía ser más que la de presentar un retrato de las estructuras típicas (y sus tendencias ideológicas) que conforman el campo, sus asociaciones con otros campos y el trabajo de algunos de sus eruditos más influyentes. Mis principales supuestos de trabajo han sido —y siguen siendo— que los campos de aprendizaje, así como las obras de incluso el artista más excéntrico están limitados y condicionados por la sociedad, por las tradiciones culturales, por las circunstancias mundiales y por influencias estabilizadoras, como son las escuelas, las bibliotecas y los gobiernos; también que los escritos eruditos y los de ficción no son jamás libres, sino que están limitados en sus imágenes, supuestos e intenciones; y, finalmente, que los avances realizados por una «ciencia» como el orientalismo en su forma académica son menos verdad de lo que a menudo nos gusta pensar. En pocas palabras, mi estudio hasta aquí ha intentado describir la _economía_ que hace que el orientalismo sea un tema coherente, incluso aunque admitamos que como idea, concepto o imagen, la palabra _Oriente_ tiene una considerable e interesante resonancia cultural en Occidente.
Soy muy consciente de que estas hipótesis pueden ser discutibles en determinados aspectos. La mayoría de nosotros asume de modo general que la ciencia y la erudición avanzan; tenemos la impresión de mejorar a medida que pasa el tiempo y se acumula más información, se perfeccionan los métodos y las generaciones más recientes de intelectuales mejoran respecto a las anteriores. Además, cultivamos una mitología de la creación según la cual creemos que el genio artístico, un talento original, o el intelecto poderoso pueden traspasar los límites de su propio tiempo y de su propio espacio para proponer al mundo una nueva obra. No tendría sentido negar que estas ideas tienen algo de verdad. Sin embargo, las posibilidades de trabajo que se le presentan a un genio original en la cultura no son nunca ilimitadas. Asimismo, también es verdad que un gran talento tiene un respeto muy sano por lo que otros han hecho antes que él y por lo que su campo de estudio ya contiene. El trabajo de los predecesores, la vida institucional de un campo de estudio y la naturaleza colectiva de cualquier experiencia erudita, por no mencionar las circunstancias sociales y económicas, tienden a limitar los efectos de la producción individual del erudito. Un campo como el orientalismo tiene una identidad acumulada y corporativa particularmente fuerte dadas sus asociaciones con la ciencia tradicional (los clásicos, la Biblia, la filología), con las instituciones públicas (gobiernos, compañías comerciales, sociedades geográficas, universidades) y con obras determinadas por su género (libros de viajes, libros de exploraciones, de fantasía o descripciones exóticas). Como resultado de todo esto, el orientalismo se ha constituido como un tipo de consenso: ciertos asuntos, ciertos tipos de enunciados, ciertos tipos de trabajos han sido correctos para el orientalista. Este ha construido su trabajo y su investigación apoyándose en ellos y, a su vez, ellos, cada uno en un momento determinado, han ejercido su influencia sobre los nuevos escritores e intelectuales. El orientalismo, en consecuencia, se puede considerar una forma regularizada (u «orientalizada») de escribir, de ver y de estudiar dominada por imperativos, perspectivas y prejuicios ideológicos claramente adaptados a Oriente. Oriente es una entidad que se enseña, se investiga, se administra y de la que se opina siguiendo determinados modos.
Oriente tal y como aparece en el orientalismo es, por tanto, un sistema de representaciones delimitado por toda una serie de fuerzas que sitúan a Oriente dentro de la ciencia y de la conciencia occidentales y, más tarde, dentro del imperio occidental. Si esta definición de orientalismo parece sobre todo política, es simplemente porque considero que el orientalismo es en sí mismo el producto de ciertas fuerzas y actividades de carácter político. El orientalismo es una escuela de interpretación cuyo material es Oriente, sus civilizaciones, sus pueblos y sus regiones. Sus descubrimientos objetivos —la obra de numerosos eruditos consagrados que editaron y tradujeron textos, codificaron gramáticas, escribieron diccionarios, reconstruyeron épocas pasadas y produjeron un saber verificable en un sentido positivista— están, y siempre han estado, condicionados por el hecho de que sus verdades, como cualquier otra verdad transmitida por medio del lenguaje, están materializadas en el lenguaje, y que la esencia del lenguaje —como dijo Nietzsche— es ser:
un ejército móvil de metáforas, metonimias, antropomorfismos; en pocas palabras, una suma de relaciones humanas que han sido aumentadas, traspuestas y embellecidas por la poética y la retórica y que, después de ser usadas durante un largo tiempo, parecen firmes, canónicas y obligatorias para la gente: las verdades son ilusiones de las que se ha olvidado que lo son.
Tal vez una visión como la de Nietzsche nos sorprende por ser demasiado nihilista, pero al menos llama la atención sobre el hecho de que, desde que ha existido en la conciencia de Occidente, Oriente ha sido una palabra que poco a poco se ha hecho corresponder con un vasto campo de significados, asociaciones y connotaciones que no se referían necesariamente al oriente real, sino más bien al campo que rodeaba a la palabra.
El orientalismo no es, pues, solamente una doctrina positiva sobre el Oriente que existe en un momento dado en Occidente. Es también una tradición académica muy influyente (cuando se refiere a un especialista académico al que se denomina orientalista), así como una zona de interés definida por viajeros, empresas comerciales, gobiernos, expediciones militares, lectores de novelas y de relatos de aventuras exóticas, historiadores naturales y peregrinos para los que Oriente es un tipo específico de conocimiento sobre lugares, gentes y civilizaciones específicas. En efecto, el estilo oriental se convirtió en algo frecuente y se afianzó firmemente en el discurso europeo. Bajo este tipo de lenguaje o estilo subyacía una base doctrinal sobre Oriente; estas doctrinas se habían forjado a partir de las experiencias de muchos europeos, experiencias que coincidían todas en aspectos esenciales de Oriente como el carácter, el despotismo, la sensualidad y el gusto orientales. Para cualquier europeo del siglo XIX —y creo que se puede decir casi sin excepciones— el orientalismo era este sistema de verdades, verdades en el sentido que Nietzsche da a la palabra. Es por tanto exacto que todo europeo en todo lo que podía decir sobre Oriente era, en consecuencia, racista, imperialista y casi totalmente etnocéntrico. Parte de la mordaz acusación que está contenida en estos calificativos quedará atenuada si recordamos que las sociedades humanas, al menos las culturas más avanzadas, raramente han ofrecido al individuo algo diferente que imperialismo, racismo y etnocentrismo a la hora de tratar con las «otras» culturas. De este modo, el orientalismo sostuvo ciertas presiones culturales de carácter general que tendían a resaltar y a hacer más rígido el sentimiento de diferenciación entre la parte europea y la parte asiática del mundo. Mi argumento es que el orientalismo constituye fundamentalmente una doctrina política que se impuso sobre Oriente porque era más débil que Occidente; y que Occidente malogró la diferencia de Oriente con su debilidad.
Ya expliqué esta proposición en la primera parte y prácticamente todo lo incluido en las páginas siguientes fue un intento en parte de corroborarlo. La presencia misma de un «campo» como el del orientalismo sin su correspondiente en Oriente sugiere la fuerza relativa de Oriente y Occidente. Existe una gran cantidad de páginas escritas sobre Oriente que suponen un grado y un volumen de interacción con el mismo bastante impresionante; sin embargo, lo que indica de modo decisivo la fuerza occidental es que no se puede comparar el movimiento de occidentales hacia el Este (desde finales del siglo XVIII), con el de orientales hacia el Oeste. Dejando a un lado el hecho de que los ejércitos occidentales, los cuerpos consulares, los mercaderes, las expediciones científicas y arqueológicas siempre iban hacia el Este, el número de personas que viajó desde el Oriente islámico a Europa entre 1800 y 1900 es minúsculo si se compara con el de viajeros en la otra dirección. Más aún, los viajeros orientales en Occidente estaban allí para aprender y admirar una cultura más avanzada, mientras que los propósitos de los viajeros occidentales en Oriente eran, como ya hemos visto, de carácter bastante diferente. Además, se ha cifrado en cerca de 60.000 el número de libros escritos entre 1800 y 1950 que trataban sobre Oriente Próximo. No hay ninguna cifra de libros que se escribieran en Oriente y trataran sobre Occidente que pueda remotamente compararse con esta. Como entramado cultural, el orientalismo es todo agresión, actividad, juicios, deseo hecho realidad y conocimiento. Oriente existía para Occidente o al menos eso creían los innumerables orientalistas cuya actitud era paternalista o cándidamente condescendiente —a no ser, por supuesto, que fueran anticuarios, en cuyo caso el Oriente «clásico» les honraba a ellos y no al «lamentable» Oriente moderno—. Y, por último, había numerosas agencias e instituciones que costeaban el trabajo de los eruditos occidentales y que, por supuesto, no tenían paralelo en la sociedad oriental.
Este desequilibrio entre Este y Oeste evidentemente está en función de esquemas históricos cambiantes. Durante su apogeo militar y político, del siglo VIII al XVI, el islam dominó tanto el Este como el Oeste. Después, el centro de poder se trasladó hacia el Oeste y ahora, a finales del siglo XX, parece que se dirige de nuevo hacia el Este. La exposición del orientalismo del siglo XIX que he hecho en la segunda parte la he dejado en un momento particularmente intenso, la última parte del siglo, cuando los aspectos dilatorios, abstractos y descriptivos del orientalismo estaban a punto de adquirir un nuevo sentido de misión universal al servicio del colonialismo tradicional. Es precisamente este proyecto lo que quiero describir a continuación, sobre todo porque nos proporcionará una perspectiva importante para entender la crisis del orientalismo en el siglo XX y el resurgimiento de fuerzas políticas y culturales en Oriente.
En repetidas ocasiones he hecho alusión a las conexiones entre el orientalismo como cuerpo de ideas, creencias, esquemas y saber sobre Oriente y otras escuelas de pensamiento generales dentro de la cultura. Una de las evoluciones importantes del orientalismo del siglo XIX y XX fue la producción de algunas ideas, esenciales sobre Oriente —tales como su sensualidad, su tendencia al despotismo, su mentalidad aberrante, sus hábitos de imprecisión y su retraso— y su concreción dentro de una coherencia individualizada e indiscutida. De este modo, el que un escritor utilizara la palabra _oriental_ constituía una referencia suficiente para que el lector identificara un cuerpo específico de información sobre Oriente. Esta información parecía ser neutra desde un punto de vista moral y objetivamente válida; parecía gozar de una categoría epistemológica semejante a la de la cronología histórica y a la de la localización geográfica. Por tanto, en su forma más básica, el material oriental no podía ser violado por los descubrimientos de nadie, ni tampoco podía ser revalorizado completamente. Por el contrario, la obra de varios eruditos y escritores de ficción del siglo XIX hizo que esta área de conocimientos fuera más clara, más detallada, más sustancial y más diferenciada del «occidentalismo». Más aún, las ideas del orientalismo podían ponerse en relación con teorías filosóficas de carácter general (como las que hacen referencia a la historia del hombre y de la civilización) y difundir hipótesis globales, como a veces las denominan los filósofos; en muchos sentidos, los profesionales que contribuían al conocimiento de Oriente estaban ansiosos por expresar sus formulaciones e ideas, su obra erudita, sus observaciones consideradas contemporáneas en un lenguaje y en una terminología cuya validez cultural se derivaba de otras ciencias y de otros sistemas de pensamiento.
La distinción que estoy haciendo se establece realmente entre un positivismo casi inconsciente y en cualquier caso impalpable que denominaré orientalismo _latente_ , y los diferentes criterios establecidos sobre la sociedad, las lenguas, las literaturas, la historia y la sociología orientales que denominaré orientalismo _manifiesto_. Cualquier cambio que se produzca en el conocimiento de Oriente está basado de modo casi exclusivo en el orientalismo manifiesto; la unanimidad, la estabilidad y la perdurabilidad del orientalismo latente son más o menos constantes. Las diferencias en lo que a Oriente se refiere entre las ideas de los escritores del siglo XIX que analicé en la segunda parte se pueden caracterizar de forma exclusiva como diferencias manifiestas, diferencias en la forma y en el estilo personal, raramente de contenido básico. Todos ellos mantuvieron intacto el distanciamiento de Oriente, su excentricidad, su retraso, su silenciosa indiferencia, su femenina impenetrabilidad y su maleabilidad supina. Esto es por lo que todo escritor que trata de Oriente, desde Renan a Marx (ideológicamente hablando), o desde los eruditos más rigurosos (Lane y Sacy) a los escritores de imaginación más prodigiosa (Flaubert y Nerval) concibieron Oriente como un escenario que requería la atención, la reconstrucción e incluso la redención occidental. Oriente existía como un lugar aislado de la corriente de progreso científico, artístico y comercial europeo. Por lo tanto, cualesquiera que fueran los valores, buenos o malos, imputados a Oriente, parecían ser funciones de algún interés occidental altamente especializado en Oriente. Esta era la situación desde aproximadamente 1870 hasta la primera parte del siglo XX. Permítaseme ofrecer algunos ejemplos que ilustran lo que quiero decir.
Las tesis sobre el retraso oriental, la degeneración, y su desequilibrio con respecto a Occidente se asociaban bastante fácilmente en el siglo XIX con las ideas sobre las bases biológicas de la desigualdad entre las razas. De este modo, las clasificaciones de las razas que encontramos en _Le Règne animal_ , de Cuvier, en el _Essai sur l'inégalité des races humaines_ ,* de Gobineau, y en _The Dark Races of Man_ , de Robert Knox, encontraron un socio interesado en el orientalismo latente. A estas ideas se añadía un darwinismo de segundo orden que parecía acentuar la validez «científica» de la división de las razas entre avanzadas y atrasadas o, de otro modo, entre europea-aria y oriental-africana. De esta forma toda la cuestión del imperialismo, tal y como se debatía a finales del siglo XIX entre los proimperialistas y los antiimperialistas, evidenciaba la tipología binaria de las razas, culturas y sociedades avanzadas y atrasadas (o sometidas). La obra _Chapters on the Principles of International Law_ (1894), de John Westlake, sostiene, por ejemplo, que las regiones de la tierra designadas como «incivilizadas» (una palabra cargada de presupuestos orientalistas, entre otros muchos) deberían ser anexionadas y ocupadas por las potencias avanzadas. De modo similar, las ideas de escritores tales como Carl Peters, Leopold de Saussure y Charles Temple recurren a la dicotomía avanzado/atrasado, preconizada con insistencia por el orientalismo de finales del siglo XIX.
Junto con todos los demás pueblos calificados de atrasados, degenerados y bárbaros, se veía a los orientales dentro de un marco delimitado por el determinismo biológico y la represión políticomoral. De este modo, lo oriental se asociaba a ciertos elementos de la sociedad occidental (como los delincuentes, los locos, las mujeres y los pobres) que tenían una identidad que podríamos definir como de lamentablemente ajena. A los orientales raramente se les miraba directamente; se les contemplaba a través de un filtro, se les analizaba no como a ciudadanos o simplemente como a gente, sino como a problemas que hay que resolver, aislar o —como las potencias coloniales abiertamente hicieron con su territorio— dominar. La clave es que la designación misma de oriental llevaba asociado un marcado juicio evaluativo y, en el caso de los pueblos que habitaban el decadente Imperio otomano, un programa de acción implícito. Desde el momento en que el oriental era miembro de una raza sometida, tenía que ser sometido; era así de simple. El _locus classicus_ de un juicio y una acción así se encuentra en la obra _Les Lois psychologiques de l'évolution des peuples_ (1894), de Gustave Le Bon.
Sin embargo, existen otros usos del orientalismo latente. Si ese grupo de ideas nos permitía separar a los orientales de las potencias avanzadas y civilizadas y si el Oriente «clásico» servía para justificar tanto al orientalista como su indiferencia por los orientales modernos, el orientalismo latente propiciaba también una concepción del mundo particularmente (por no decir odiosamente) masculina. Ya he mencionado esto de pasada en la exposición sobre Renan. Se consideraba al hombre oriental aislado de la comunidad en la que vivía y se le observaba, como muchos orientalistas siguiendo a Lane lo contemplaron, con algo de desprecio y de temor. El orientalismo en sí mismo, además, era un dominio exclusivo del hombre; como muchos grupos profesionales durante la época moderna, se concebía a sí mismo y a su tema de estudio con ojos sexistas. Todo esto es particularmente evidente en los escritos de los viajeros y novelistas, en los que las mujeres son habitualmente creaciones del poder-fantasía del hombre. Ellas expresan una sensualidad sin límites, son más bien estúpidas y, sobre todo, son complacientes y serviciales. El personaje de Kuchuk Hanem, de Flaubert, es el prototipo de esta caricatura que, por otra parte, era bastante común en las novelas pornográficas (como _Aphrodite_ , de Pierre Louÿs). Además, la concepción masculina del mundo, cuando se trata de la actividad práctica del orientalista, tiende a ser eternamente estática, congelada y fija. Se le niega a Oriente y al oriental incluso la más mínima posibilidad de desarrollo, de transformación, de movimiento humano —en el sentido más profundo de la palabra—. Como un conocimiento y últimamente poseedores de una cualidad inmóvil e improductiva, Oriente y el oriental llegan a ser identificados con un tipo mal entendido de eternidad: de ahí que, cuando Oriente merece cierta aprobación, se recurre a frases tales como «la sabiduría de Oriente».
Habiendo sido transportado desde una evaluación social implícita a una valoración cultural general, este estático orientalismo masculino adoptó toda una variedad de formas a finales del siglo XIX, especialmente cuando se empezó a hablar del islam. Historiadores de la cultura tan reputados como Leopold von Ranke y Jacob Burckhardt atacaron al islam como si estuvieran tratando no tanto con una abstracción antropomórfica, sino con una cultura político-religiosa sobre la cual eran posibles y estaban justificadas las grandes generalizaciones. En su obra _Weltgeschichte_ (1881-1888), Ranke hablaba de un islam vencido por los pueblos germánicos y en «Historische Fragmente» (notas inéditas, 1893), Burckhardt hablaba del islam en términos de miserable, vacío y trivial. Oswald Spengler, sin embargo, acometió este proyecto intelectual con bastante más talento y entusiasmo. Sus ideas sobre una personalidad de mago (tipificada en el oriental musulmán) inspiraron _Der Untergand des Abendlandes_ (1918-1922)* y la «morfología» de culturas por la que abogaba.
Estas nociones sobre Oriente tan ampliamente difundidas se apoyaban en la ausencia casi absoluta en la cultura occidental de una visión de Oriente como realidad auténticamente sentida y experimentada. Por una serie de razones evidentes, Oriente siempre ocupaba la posición de un intruso y de un socio débil de Occidente. Esto ocurrió hasta el punto de que los eruditos occidentales estaban al tanto de los movimientos culturales y de pensamiento que había en Oriente, pero los entendían simplemente como sombras silenciosas que debían ser iluminadas por un orientalista y traídas a la realidad por él, o como un tipo de proletariado cultural e intelectual útil para la gran actividad interpretativa del orientalista y necesario para su papel de juez superior, hombre instruido y poderosa voluntad cultural. Lo que quiero decir es que cuando se discute sobre Oriente, Oriente es el elemento ausente, mientras que se tiene la impresión de que el orientalista y lo que este dice son el elemento presente. No debemos olvidar que es la ausencia de Oriente la que propicia y posibilita la «presencia» del orientalista. El hecho de que existieran estas sustituciones y estos desplazamientos, como debemos llamarlos, claramente presiona al orientalista para que reduzca la presencia de Oriente en su obra, a pesar de que ha dedicado una buena parte de su tiempo a aclararlo y exponerlo. ¿Cómo, si no, se podrían explicar el tipo de trabajos eruditos que asociamos con Julius Wellhausen y Theodor Nöldeke e, incluso pasándolos por alto, todas esas afirmaciones simplistas y demoledoras que prácticamente ridiculizan al propio tema que han escogido? Nöldeke podía así declarar en 1887 que el conjunto total de su obra terminaba por confirmar su «lamentable opinión» sobre los pueblos orientales. Y, al igual que Carl Becker, Nöldeke era un filohelénico que curiosamente mostraba su amor por Grecia haciendo gala de su desprecio evidente por Oriente que, después de todo, era lo que había estudiado como erudito.
Jacques Waardenburg, en un estudio inteligente y rico sobre el orientalismo, _L'Islam dans le miroir de l'Occident_ , analiza cómo cinco importantes especialistas dieron una imagen determinada del islam. La metáfora de la imagen en el espejo para definir el orientalismo de finales del siglo XIX y principios del XX resulta adecuada. En la obra de cada uno de estos eminentes orientalistas hay una visión del islam sumamente tendenciosa que llega a la hostilidad en cuatro de ellos, como si cada hombre viera el islam como un reflejo de la debilidad elegida por él mismo. Cada estudioso poseía profundos conocimientos y el estilo de su contribución resultaba único. Entre los cinco orientalistas proporcionaban ejemplos de lo mejor y más valioso de la tradición desde aproximadamente 1880 hasta el período de entreguerras. Así, la apreciación de Ignaz Goldziher acerca de la tolerancia del islam hacia otras religiones se veía socavada por su propio desagrado ante el antropomorfismo de Mahoma y el concepto de teología y jurisprudencia demasiado exterior del islam; el interés de Duncan Black Macdonald en la piedad y la ortodoxia islámicas estaba viciado por su percepción de lo que él consideraba cristiandad herética del islam; la percepción de la civilización islámica por parte de Carl Becker le hacía concebirla como «tristemente subdesarrollada»; los sofisticados estudios sobre el misticismo islámico de C. Snouck Hurgronje (aspecto este que él consideraba parte esencial del islam) le condujeron a un juicio muy duro acerca de las restrictivas limitaciones de tal misticismo y, por último, la extraordinaria identificación de Louis Massignon con la teología islámica, la pasión mística y el arte poético le mantuvieron curiosamente alejado del islam y le llevaron a perdonarlo por lo que él calificaba de revuelta persistente contra la idea de encarnación. Las diferencias manifiestas en sus métodos parecen menos importantes que su consenso de orientalistas sobre el islam, a saber, su inferioridad latente.
El estudio de Waardenburg tiene la virtud adicional de mostrar el modo en que estos cinco estudiosos compartían una tradición intelectual y metodológica común de auténtica dimensión internacional. Incluso desde el primer congreso de orientalistas en 1873, los eruditos de este campo conocían los trabajos de los demás y sentían la presencia de sus colegas de un modo muy directo. Lo que Waardenburg no subraya suficientemente es el hecho de que la mayoría de los orientalistas del siglo XIX mantenía relaciones con el estamento político. Snouck Hurgronje pasó directamente de sus estudios sobre el islam a ser consejero del gobierno holandés para la administración de las colonias musulmanas en Indonesia; Macdonald y Massignon eran frecuentemente solicitados como expertos en los asuntos islámicos por los administradores coloniales desde el norte de África a Pakistán; y, como Waardenburg dice (demasiado brevemente), en cierto momento los cinco intelectuales conformaron una visión coherente del islam que tuvo una fuerte influencia en los círculos de gobierno de todo el mundo occidental. Debemos añadir a la observación de Waardenburg que estos cinco eruditos completaron y perfeccionaron en extremo la tendencia existente desde los siglos XVI y XVII de tratar a Oriente no solo como un vago problema literario, sino —de acuerdo con Masson-Oursel— como «un firme propósito de asimilar adecuadamente el valor de las lenguas para penetrar en las costumbres y los pensamientos, para forzar incluso los secretos de la historia».
Ya me referí anteriormente a la incorporación y asimilación de Oriente cuando estas actividades las practicaron escritores tan distintos como Dante o D'Herbelot. Existe claramente una diferencia entre aquellos intentos y los que, a finales del siglo XIX, se habían convertido en una formidable empresa europea de dimensión cultural, política y material. El proceso colonial del siglo XIX conocido como «la lucha por África» no se limitó a África, por supuesto, del mismo modo que la penetración en Oriente no se realizó de forma repentina y dramática después de unos años de estudios eruditos sobre Asia. Muy al contrario, debemos considerar el largo y lento proceso de apropiación por el cual Europa, o la conciencia europea de Oriente, se transformó y pasó de ser literaria y contemplativa a ser una entidad administrativa, económica e incluso militar. El cambio fundamental fue espacial y geográfico, o mejor, fue un cambio de calidad en el modo de comprensión geográfico y espacial de todo lo referido a Oriente. La antigua designación por la que el espacio geográfico que quedaba al este de Europa se llamaba «Oriente» y que se había utilizado durante siglos era en parte política, en parte doctrinal y en parte imaginativa; no llevaba implícita o aparejada necesariamente ninguna conexión entre la experiencia real de Oriente y el conocimiento de lo que es lo oriental, y de hecho Dante y D'Herbelot no pretendían probar nada con sus ideas sobre Oriente, tan solo que se veían corroboradas por una larga tradición _aprendida_ (y no existencial). Sin embargo, cuando Lane, Renan, Burton, así como los cientos de viajeros y estudiosos europeos del siglo XIX, tratan sobre Oriente, podemos percibir enseguida en ellos una actitud mucho más íntima y un sentimiento de propiedad respecto a Oriente y las realidades orientales. Tanto en la forma clásica y a menudo casi remota en la que fue construido por el orientalista como en la forma real en la que el Oriente moderno se ha vivido, estudiado o imaginado, su _espacio geográfico_ ha sido penetrado, poseído y moldeado de nuevo. Los efectos acumulados durante décadas de soberanía y control occidentales hicieron que Oriente dejara de ser una entidad ajena y extraña para transformarse en una entendida como espacio colonial. Lo que se consideraba importante a finales del siglo XIX no era _que_ Occidente hubiera irrumpido en Oriente y hubiera tomado posesión de él, sino, más bien, _cómo_ percibían los británicos y franceses el modo en que habían llevado a cabo esta empresa.
El escritor británico en Oriente y, más aún el administrador colonial británico trataba con el territorio en el cual vivía y no tenía la menor duda de que el poder británico estaba en una fase ascendente, incluso aunque los nativos se sintieran más atraídos por Francia y por los modos de pensar y las costumbres francesas. Sin embargo, en lo que se refiere al espacio colonial efectivamente ocupado, hay que destacar que Inglaterra estaba realmente allí, mientras que Francia no, puesto que limitaba su papel al de frívola seductora de patanes orientales. No hay mejor indicación de esta diferencia cualitativa en cuanto a actitudes geográficas que lo que lord Cromer tenía que decir al respecto, un tema especialmente importante para él:
Las razones por las que la civilización francesa presenta un grado especial de atracción para los asiáticos y los orientales son bien simples. Resulta de hecho más atractiva que las civilizaciones de Inglaterra y Alemania y, más aún, es más fácil de imitar. Compárese al británico inexpresivo y vergonzoso con el francés vivaz y hombre de mundo que no sabe lo que significa la palabra vergüenza y que en diez minutos actúa como si fuera amigo íntimo de cualquiera a quien haya podido conocer. El oriental poco educado no reconoce que el primero tiene en todo momento el mérito de la sinceridad, mientras que el segundo está representando un papel. Tiende a mirar con frialdad al inglés y se arroja en los brazos del francés.
Las insinuaciones sexuales aparecen más o menos de modo natural en el texto de Cromer. El francés es todo sonrisas, agudeza, gracia, moda. El inglés, por el contrario, es laborioso, trabajador, preciso, un seguidor típico del modelo de Bacon. No hay que perder de vista que la perspectiva de Cromer se basa en la solidez británica opuesta a la seducción francesa, que no tiene ninguna presencia efectiva en la realidad de Egipto.
¿Puede causar algún tipo de sorpresa [continúa Cromer] que el egipcio, con su limitado bagaje intelectual, no alcance a ver que el razonamiento de los franceses se asienta sobre algún tipo de falacia, o que prefiera la superficialidad brillante típica de los franceses a la actividad laboriosa, aunque poco atractiva, de los ingleses o alemanes? Fijémonos también en la perfección teórica de los sistemas administrativos franceses, en su cuidado del detalle y la previsión con la que aparentemente cuenta para poder afrontar cualquier posible contingencia que se presente. Compárense ahora estas circunstancias con las de los sistemas prácticos ingleses que limitan las reglas a unos pocos aspectos básicos y dejan otros muchos detalles a la libre opción del individuo. El egipcio semieducado naturalmente prefiere el sistema francés, ya que externamente es de una apariencia más perfecta y resulta más fácil de aplicar. Sin embargo, no observa que los ingleses desean elaborar un sistema que se adapte a los hechos con los que se ha de enfrentar, mientras que la objeción principal que existe para aplicar las medidas administrativas francesas en Egipto es que son los hechos los que con frecuencia tienen que ajustarse a un sistema ya perfilado.
Desde el momento en que existe una presencia británica en Egipto, y tal presencia —de acuerdo con Cromer— está allí no tanto para aleccionar al egipcio, sino para «formar su carácter», se deduce de ello que la efímera atracción por lo francés es como la que ejerce una damisela con «cierto encanto artificial», mientras que la atracción por lo británico es la de «una matrona sobria de cierta edad, de mayor valor moral, pero de una apariencia exterior menos apetecible».
Tras el contraste utilizado por Cromer entre la sobria matrona británica y la francesa presumida, se encuentra la situación auténticamente privilegiada de los asentamientos británicos en Oriente. «Los hechos con los que los ingleses tenían que enfrentarse» eran en su conjunto más complejos y más interesantes, en virtud de las posesiones británicas, que cualquiera que un francés espabilado pudiera tratar. Dos años después de la publicación de su obra _Modern Egypt_ (1908), Cromer continuaba sus razonamientos filosóficos en _Ancient and Modern Imperialism_. Comparado con el imperialismo romano, con una política claramente asimilacionista, explotadora y represiva, a Cromer le parecía preferible el imperialismo británico, aunque lo tachaba de ser algo más desdibujado que aquel. En ciertos aspectos, sin embargo, los británicos eran muy claros incluso aunque lo fueran «de una manera débil y descuidada, pero característicamente anglosajona». Su imperio parecía no decidirse entre «una de las dos opciones: la ocupación militar total o el principio de la nacionalidad [para las razas sometidas]». Esta indecisión resultó ser simplemente una cuestión de forma, ya que en la práctica tanto Cromer como los británicos se habían opuesto al «principio de nacionalidad». Había que considerar además otros aspectos. El primero de ellos era que Gran Bretaña nunca iba a renunciar al imperio. El segundo consistía en que había que tener en cuenta que el matrimonio en el que uno de los cónyuges fuese británico y el otro nativo se consideraba como algo indeseable. El tercero —y más importante en mi opinión— era que Cromer concebía la presencia del Imperio británico en las colonias orientales como una realidad con un efecto duradero, por no decir casi eterno, en las mentes y sociedades orientales. Su metáfora para expresar ese efecto resulta casi teológica y se corresponde con la rotundidad de su concepción de la penetración occidental en el espacio oriental. «El país —afirma— sobre el que haya pasado el aliento de Occidente intensamente cargado de pensamiento científico, y sobre el que a su paso haya dejado una marca duradera, nunca podrá ser el mismo que antes.»
Sin embargo, al mencionar estos aspectos, Cromer no estaba siendo original en sus formulaciones. Tanto lo que observó como el modo en que lo expresó eran algo común entre sus colegas de la clase dirigente imperial y de la comunidad intelectual. Este consenso al que nos referimos es evidente sobre todo en el caso de otros colegas de Cromer en el vicerreinato, como Curzon, Swelttenham y Lugard. Lord Curzon, en particular, siempre hablaba de la _lingua franca_ imperial y, de un modo incluso más radical que Cromer, concebía la relación entre Gran Bretaña y Oriente en términos de posesión, en términos de un gran espacio geográfico totalmente poseído por un administrador colonial eficiente. Para él, como afirmó en una ocasión, el imperio no era un «objeto de ambición», sino «primeramente y de modo fundamental, un gran acontecimiento histórico, político y sociológico». En 1909, dirigiéndose a los delegados de la Imperial Press Conference reunidos en Oxford, les recordó que «nosotros los preparamos aquí, y después les enviamos a ustedes sus gobernadores, administradores y jueces, sus maestros, predicadores y abogados». Esta concepción casi pedagógica del imperio tenía para Curzon una especial validez en Asia, tierra que, como él mismo dijo una vez, «le hace a uno pararse y pensar».
A veces me gusta imaginarme este gran entramado imperial en forma de una enorme estructura, como la de algún «Palacio de Arte» tennysoniano, cuyos cimientos están en este país, en el que han sido posados y deben ser mantenidos por manos británicas, pero cuyos pilares son las colonias, y por encima de todo, muy alto, se extiende el esplendor de una cúpula asiática.
Con la idea del «Palacio de Arte» en mente, Curzon y Cromer formaron parte de un comité creado en 1909 para propiciar la creación de una escuela de estudios orientales. Aparte de comentar con melancolía que había aprendido la lengua vernácula cuando contribuyó personalmente al desarrollo de la «campaña contra el hambre» en la India, Curzon defendió la necesidad de los estudios orientales como una parte de la responsabilidad que Gran Bretaña había contraído con Oriente. El 27 de septiembre de 1909 se dirigió a la Cámara de los Lores afirmando que:
[...] nuestra familiaridad, no simplemente con las lenguas de los pueblos del Este, sino también con sus costumbres, sus sentimientos, sus tradiciones, su historia y su religión, nuestra capacidad para comprender lo que podríamos llamar el «genio de Oriente» es la única base sobre la que en el futuro seremos capaces de mantener, con ciertas garantías de éxito, la posición que hasta ahora hemos ganado. Ningún paso que se tome para fortalecer esta posición debe carecer de la merecida atención del gobierno de Su Majestad o de un debate en esta Cámara de los Lores.
En una conferencia sobre el tema celebrada cinco años después en Mansion House, Curzon puso de forma definitiva los puntos sobre las íes. Los estudios orientales, afirmaba, no son un simple lujo intelectual; son:
una obligación imperial. Desde mi punto de vista, la creación de una escuela [de estudios orientales; más tarde se convirtió en la London University School of Oriental and African Studies] como esta en Londres es parte del mobiliario necesario para el imperio. Aquellos de nosotros que, de un modo u otro, hemos pasado algunos años en Oriente, que lo consideramos como la parte más feliz de nuestras vidas, y que pensamos que el trabajo que hicimos allí, fuera grande o pequeño, fue la más alta responsabilidad que jamás haya descansado en los hombros de un británico, sentimos que hay una carencia en nuestro equipamiento como nación que hay que solucionar con decisión. Y consideramos también que aquellos que en Londres, por medio de ayuda económica o por cualquier otro de ayuda activa y práctica, contribuyen a solucionar esta carencia, están cumpliendo con un deber patriótico para con el imperio y promoviendo la causa de la buena voluntad entre los hombres.
En gran medida las ideas de Curzon sobre los estudios orientales tienen su origen, lógicamente, en todo un siglo de administración británica utilitaria y filosófica sobre las colonias orientales. La influencia de Bentham y de Mills en el modo británico de gobernar Oriente (y en el de la India particularmente) fue considerable, y consiguió eliminar muchas reglamentaciones e innovaciones superfluas; además, como Eric Stokes ha mostrado de manera convincente, el utilitarismo combinado con la herencia del liberalismo y de las doctrinas evangélicas, como filosofías británicas de gobierno en Oriente, acentuaron la importancia racional de un ejecutivo fuerte y armado de diferentes códigos legales y penales, de un sistema doctrinal que versara sobre temas tales como las fronteras y las rentas territoriales, y de una irreductible autoridad imperial supervisora. La piedra angular de todo el sistema era un conocimiento de Oriente perfeccionado de tal forma que, cuando las sociedades tradicionales fueran a convertirse en sociedades comerciales modernas, los británicos no perderían nada de su control paternal ni de sus ingresos. Sin embargo, cuando Curzon se refería de una manera poco elegante a los estudios orientales como «el mobiliario necesario del imperio» estaba dando una imagen estática de las transacciones con las que ingleses y nativos llevaban sus negocios y permanecían cada uno en su sitio. Desde la época de sir William Jones, Oriente había sido tanto lo que Gran Bretaña gobernaba como lo que Gran Bretaña conocía sobre él: la coincidencia entre geografía, conocimiento y poder, con Gran Bretaña siempre en el lugar del maestro, era completa. Decir, como dijo Curzon, que «Oriente es una universidad en la que el erudito no consigue licenciarse nunca» era una manera de decir que Oriente necesitaba nuestra presencia allí más o menos para siempre.
Sin embargo, estaban las otras potencias europeas, Francia y Rusia entre ellas, que siempre amenazaban la presencia británica (quizá de modo marginal). Curzon, ciertamente, era consciente de que las grandes potencias occidentales consideraban el mundo como Gran Bretaña lo hacía. La transformación de la geografía «aburrida y pedante» —expresión de Curzon para referirse a las materias geográficas que habían dejado de estudiarse como tema académico—, en «la más cosmopolita de todas las ciencias», indicaba exactamente esta nueva predilección occidental. No sin razón, Curzon declaraba, en 1912, a la Geographical Society que él mismo presidía que:
Se produjo una absoluta revolución no solamente en la manera y en los métodos de enseñar la geografía, sino en la estimación que la opinión pública tiene de ella. En nuestros días consideramos el conocimiento geográfico como una parte esencial del conocimiento general. Con la ayuda de la geografía, y no de otra manera, entendemos la acción de las grandes faenas naturales, la distribución de la población, el crecimiento del comercio, la expansión de las fronteras, la evolución de los estados y los espléndidos logros de la energía humana en todas sus manifestaciones.
Reconocemos que la geografía sirve a la historia. [...] La geografía también es una ciencia hermana de la economía y de la política; y todos aquellos de entre nosotros que hayan intentado estudiar geografía, se habrán dado cuenta de que en el momento en que se distancian un poco del campo geográfico se encuentran rozando las fronteras de la geología, la zoología, la etnología, la química, la física y casi todas las ciencias semejantes. Por tanto, podemos decir, con razón, que la geografía es una de las primeras ciencias, que es parte del equipo que se necesita para comprender bien la concepción de civismo, y es un auxiliar indispensable en la formación de un hombre público.
La geografía era esencialmente la materia que sostenía el conocimiento sobre Oriente. Todas las características latentes e inmutables de Oriente descansaban sobre su geografía y estaban enraizadas en ella. Así, por un lado, el Oriente geográfico alimentaba a sus habitantes, les garantizaba sus características y definía su especificidad; por otro, el Oriente geográfico solicitaba la atención de Occidente, incluso cuando —por una de esas paradojas que revela frecuentemente el conocimiento organizado— el Este era el Este y el Oeste era el Oeste. El carácter cosmopolita de la geografía residía, en opinión de Curzon, en su importancia universal para todo Occidente, cuya relación con el resto del mundo era una relación de franca codicia. No obstante, el apetito geográfico podía también adoptar la neutralidad moral del impulso epistemológico de descubrir, de establecer y de desvelar, como cuando en _Heart of Darkness_ ,* Marlow confiesa sentir pasión por los mapas:
Me pasaría horas y horas mirando Sudamérica, África o Australia, y me perdería en todas las glorias de la exploración. En esa época había muchos espacios blancos sobre la tierra y cuando veía uno particularmente atrayente en el mapa (aunque todos lo son) lo señalaba con el dedo y decía: cuando sea mayor, iré allí.
Setenta años antes de que Marlow dijera esto, no le perturbaba lo más mínimo a Lamartine que lo que en el mapa eran espacios blancos estuviera habitado por nativos; ni Emer de Vattel (la gran autoridad suizo-prusiana en derecho internacional) tuvo en teoría la menor reserva cuando invitó en 1758 a los estados europeos a tomar posesión de los territorios habitados únicamente por tribus nómadas. Lo importante era dignificar la simple conquista con una idea, transformar el apetito de más espacio geográfico en una teoría sobre la relación particular que existía entre la geografía, por un lado, y los pueblos civilizados o incivilizados por otro. Francia también contribuyó a esas racionalizaciones de una manera particular.
Al final del siglo XIX, las circunstancias políticas e intelectuales que confluían en Francia hacían de la geografía y de la especulación geográfica (en los dos sentidos de la palabra) un pasatiempo nacional. El clima general de opinión en Europa era propicio; ciertamente el éxito del imperialismo británico hablaba con bastante autoridad por sí mismo. Sin embargo, para Francia y para los que en Francia pensaban sobre esta cuestión, Gran Bretaña siempre parecía un obstáculo para la realización del papel imperial que Francia podría desempeñar en Oriente, y para su relativo éxito. Antes de la guerra franco-prusiana existía una gran cantidad de espejismos políticos sobre Oriente, los cuales no eran exclusivos de los poetas y novelistas. Veamos, por ejemplo, lo que dice Saint-Marc Girardin en la _Revue des Deux Mondes_ , del 15 de marzo de 1862:
Francia tiene mucho que hacer en Oriente porque Oriente espera mucho de ella. Le pide incluso más de lo que puede hacer; le entregaría de buena gana el cuidado total de su porvenir, lo que para Francia y para Oriente sería un gran peligro: para Francia porque, dispuesta como está a hacer suya la causa de poblaciones sufrientes, se carga a menudo de más obligaciones de las que puede asumir; para Oriente porque todo pueblo que espera su destino del extranjero solo puede tener una salud precaria, y no hay salvación para las naciones que no se hacen a sí mismas.
Esto, sin duda, habría hecho exclamar a Disraeli, como con frecuencia lo hizo, que Francia tenía solo «intereses sentimentales» en Siria (que es el Oriente del que Girardin escribía). La ficción de las _«populations souffrantes»_ la había usado Napoleón cuando exhortaba a los egipcios contra los turcos y en favor del islam. Durante los años treinta, cuarenta, cincuenta y sesenta, las poblaciones de Oriente que sufrían eran las minorías cristianas de Siria. Y no había ninguna muestra de que _«l'Orient»_ esperara que Francia lo salvara. Habría sido más justo decir que Gran Bretaña interceptaba el camino de Francia en Oriente ya que, incluso si Francia tenía un sentimiento de obligación hacia Oriente (y había algunos franceses que lo tenían), muy poco era lo que Francia podía hacer deslizándose entre Gran Bretaña y la enorme masa de territorios que dominaba desde la India al Mediterráneo.
Algunas de las consecuencias más importantes que tuvo en Francia la guerra de 1870 fueron el florecimiento tremendo de las sociedades geográficas y la exigencia, reiterada con insistencia, de adquisición territorial. A finales de 1871, la Société de Géographie de París declaraba que ya no se limitaría a la «especulación científica». Exhortaba a los ciudadanos a no «olvidar que nuestra antigua preponderancia fue puesta en cuestión el día que cesamos de competir [...] por las conquistas de la civilización sobre la barbarie». Guillaume Depping, un líder de lo que se ha llamado el movimiento geográfico, aseguraba en 1881 que durante la guerra de 1870 «el maestro de escuela era quien había triunfado», queriendo decir que los verdaderos triunfos eran los de la geografía científica prusiana sobre la incompetencia estratégica francesa. El _Journal officiel_ del gobierno publicó muchos números que hablaban de las virtudes (y beneficios) de la exploración geográfica y de la aventura colonial; un ciudadano podía leer en un número, a través de Ferdinand de Lesseps, acerca de «las oportunidades en África» y, a través de Garnier, sobre «la exploración del río azul». La geografía científica enseguida dio paso a la «geografía comercial», al tiempo que se fomentaba la conexión del orgullo nacional por los resultados científicos y culturales con unos motivos beneficiosos bastante rudimentarios, con el fin de canalizarla hacia el apoyo a la adquisición colonial. En palabras de un entusiasta, «las sociedades geográficas se formaron para romper el encanto fatal que nos mantiene encadenados a nuestras costas». Para contribuir a esta liberación se trababan toda suerte de combinaciones, incluyendo el alistamiento de Julio Verne —cuyo «suceso increíble», como se decía, enlazaba ostensiblemente el espíritu científico con un nivel muy alto de racionalismo—, para dirigir «una campaña de exploración científica alrededor del mundo», y un plan para crear un enorme mar nuevo al sur de la costa de África del norte, así como un proyecto para «unir» Argelia y Senegal por ferrocarril, una verdadera «cinta de acero», como los autores del proyecto decían.
Una gran parte del fervor expansionista de Francia durante el último tercio del siglo XIX lo engendraron el deseo explícito de compensación por la victoria prusiana de 1870-1871, y el de igualar las conquistas imperiales británicas. Este deseo era tan fuerte y provenía de una tradición de rivalidad anglo-francesa en Oriente tan antigua que Francia parecía literalmente obsesionada con Gran Bretaña, ansiosa por alcanzar y emularla en todo lo relacionado con Oriente. Cuando al final de los años 1870, la Société Académique Indochinoise reformuló sus objetivos, encontró importante «incluir Indochina en el dominio del orientalismo». ¿Por qué? Para convertir a Cochinchina en la «India francesa». La ausencia de posesiones coloniales sustanciales era, según el estamento militar, la causa de la debilidad bélica y comercial en la guerra con Prusia, por no decir nada de la amplia y clara inferioridad colonial si se comparaba con Gran Bretaña. El «poder de expansión de las razas occidentales —decía La Roncière Le Noury, un distinguido geógrafo—, sus causas superiores, sus elementos y sus influencias en los destinos humanos serán un bonito estudio para historiadores futuros». Sin embargo, solo si las razas blancas satisfacen su gusto por viajar —índice de su supremacía intelectual— podrá producirse la expansión colonial.
De este tipo de tesis procede la idea corriente de que Oriente es un espacio geográfico para cultivar, cosechar y guardar. De acuerdo con esto, proliferaron las imágenes relacionadas con el cuidado agrícola y con la atención sexual franca. Aquí vemos una efusión típica, escrita por Gabriel Charmes en 1880:
El día en que ya no estemos en Oriente y que estén otras grandes potencias europeas, todo habrá terminado para nuestro comercio en el Mediterráneo, para nuestro futuro en Asia, para el tráfico de nuestros puertos del sur. _Una de las fuentes más fértiles de nuestra nación se_ _habrá secado_. (La cursiva es mía).
Otro pensador, Leroy-Beaulieu, llevó esta filosofía todavía más lejos:
Una sociedad coloniza cuando, habiendo alcanzado un alto grado de madurez y fuerza, procrea, protege, se sitúa en buenas condiciones de desarrollo y lleva la virilidad a una nueva sociedad que ha salido de sus entrañas. La colonización es uno de los fenómenos más complejos y delicados de la fisiología social.
Esta ecuación de autorreproducción y de colonización le llevan a Leroy-Beaulieu a expresar la idea, algo siniestra, de que todo lo que está vivo en la sociedad moderna es «magnificado por el derrame de su actividad exuberante en el exterior». Por tanto, dijo:
La colonización es la fuerza expansiva de un pueblo; es su poder de reproducción; _es su crecimiento y su multiplicación a través del espacio_ ; es la sujeción del universo o una gran parte de él, a la lengua, a las costumbres, a las ideas y a las leyes de ese pueblo.
El aspecto más destacado de estas líneas es que el espacio de las regiones más débiles o subdesarrolladas, como Oriente, era visto como algo que invitaba al interés, a la penetración y a la inseminación de Francia; en una palabra, a la colonización. Las concepciones geográficas abolían de modo literal y figurativo las entidades concretas contenidas por las fronteras. Igual que los empresarios visionarios, como Ferdinand de Lesseps, cuyo plan era liberar Oriente y Occidente de sus vínculos geográficos, los eruditos, administradores, geógrafos y agentes comerciales franceses derramaron su exuberante actividad sobre el lánguido y femenino Oriente. Había sociedades geográficas dos veces más importantes por su número y por el de sus miembros que las de toda Europa; había poderosos organismos como el Comité de l'Asie Française y el Comité d'Orient; había sociedades eruditas, la más importante de ellas la Société Asiatique, que contaba con una organización y unos miembros muy introducidos en las universidades, en los institutos y en el gobierno. Cada uno a su manera hacía que los intereses franceses en Oriente fueran más reales, más sustanciales. Casi un siglo de lo que entonces parecía un estudio pasivo de Oriente había tenido que terminar cuando Francia afrontaba sus responsabilidades transnacionales durante las últimas dos décadas del siglo XIX.
En la única parte de Oriente en la que los intereses franceses y británicos literalmente se sobreponían, los territorios del entonces agonizante Imperio otomano, los dos antagonistas manejaban su conflicto con una característica y casi perfecta coherencia. Gran Bretaña estaba en Egipto y en Mesopotamia; en virtud de una serie de tratados cuasi imaginarios con los jefes locales, despojados de todo poder, controlaba el mar Rojo, el golfo Pérsico, el canal de Suez y la mayor parte de la masa territorial intermedia entre el Mediterráneo y la India. El destino de Francia, por otro lado, parecía ser planear sobre Oriente descendiendo de vez en cuando para ejecutar ciertos proyectos que repetían el éxito de los de Ferdinand de Lesseps con el canal; la mayor parte de estos esquemas eran proyectos de ferrocarriles, como el que se planeó sobre un territorio más o menos británico, la línea Siria-Mesopotamia. Además, Francia se consideraba la protectora de las minorías cristianas de Oriente Próximo: maronitas, caldeas y nestorianas. Francia y Gran Bretaña, sin embargo, se pusieron de acuerdo en principio sobre la necesidad de repartir la Turquía asiática cuando llegara el momento. Antes y durante la Primera Guerra Mundial, la diplomacia secreta se dedicó a dividir Oriente Próximo en esferas de influencia primero y en territorios bajo su mandato (u ocupados) después. En Francia, una buena parte del sentimiento expansionista que se formó durante el apogeo del movimiento geográfico se concentraba en la partición de la Turquía asiática, y para promover este fin «se lanzó una espectacular campaña de prensa» en París en 1914. En Inglaterra numerosos comités estaban autorizados a estudiar y recomendar la mejor política para dividir Oriente. Comisiones como el Bunsen Committee darían lugar a los equipos anglofranceses, de los cuales el más famoso fue el dirigido por Mark Sykes y Georges Picot. Estos planes tenían como misión la división equitativa del espacio geográfico, los cuales se esforzaban deliberadamente en calmar la rivalidad anglo-francesa. Ya que, como Sykes dijo en un memorando:
Estaba claro [...] que tarde o temprano iba a producirse una sublevación árabe y hacía falta que tanto los franceses como nosotros estuviéramos en los mejores términos si queríamos que esta sublevación no fuera una maldición, sino una bendición.
La animosidad persistía, sin embargo. Y se le añadía, además, la irritación causada por el programa de autodeterminación nacional de Wilson, que, como el mismo Sykes debió de decirle, parecía invalidar todo el esqueleto de los planes coloniales y de partición que las potencias habían acordado juntas. Rebasaría nuestros propósitos examinar toda la historia controvertida y laberíntica de Oriente Próximo a principios del siglo XX, cuando su suerte la decidían las potencias, las dinastías nativas, varios partidos y movimientos nacionalistas y los sionistas. Lo que nos atañe más inmediatamente es la estructura epistemológica a través de la cual se veía Oriente y a partir de la cual actuaron las potencias. En efecto, a pesar de sus diferencias, británicos y franceses veían Oriente como una entidad geográfica —y cultural, política, demográfica, sociológica e histórica— sobre cuyo destino creían tener títulos tradicionales. Oriente para ellos no era un descubrimiento súbito, ni un mero accidente histórico, sino una zona situada al este de Europa cuyo valor se definía siempre en función de Europa, y de modo particular, en términos que reclamaban para Europa —para su ciencia, su erudición, su inteligencia y su administración— el honor de haber hecho de Oriente lo que entonces era. Y esa había sido la conquista —inadvertida o no— del orientalismo moderno.
A principios del siglo XIX había dos métodos principales por los cuales el orientalismo traía Oriente a Occidente. Uno era utilizando las posibilidades que tenía la ciencia moderna de propagarse: su aparato de difusión en las profesiones eruditas, en las universidades, en las sociedades profesionales, en las organizaciones consagradas a la exploración y a la geografía y en la industria editorial. Todo eso, como hemos visto, reposaba sobre la autoridad prestigiosa de los pioneros, eruditos, viajeros y poetas cuya visión acumulativa había conformado un Oriente quintaesencial. La manifestación doctrinal —doxológica— de este Oriente es lo que he llamado aquí orientalismo latente. A quien quería hacer una declaración de cierto peso sobre Oriente, el orientalismo latente le proporcionaba una capacidad enunciativa que podía ser utilizada, o más bien movilizada y transformada en un discurso razonable, en cada ocasión concreta que se presentaba. Así, cuando Balfour habló del oriental ante la Cámara de los Comunes en 1910, seguramente tenía en mente estas capacidades enunciativas del lenguaje corriente y bastante racional de su tiempo que permitían nombrar y hablar de lo que se llamaba un «oriental» sin riesgo de resultar demasiado oscuro. Sin embargo, como todas las capacidades enunciativas y los discursos que ellas permitían, el orientalismo latente era profundamente conservador —es decir, consagrado a preservarse—. Transmitido de generación en generación formaba parte de la cultura en la misma medida en que lo hacía también el lenguaje sobre una parte de la realidad como la geometría o la física. El orientalismo fundamentaba su existencia más que en su apertura y en su receptividad hacia Oriente, en su coherencia interna, en su repetitiva consistencia acerca de su poder constitutivo sobre Oriente. De esta manera, el orientalismo pudo sobrevivir a tantas revoluciones, a las dos guerras mundiales y al desmembramiento literal de los imperios.
El segundo método a través del cual el orientalismo traía Oriente a Occidente era el resultado de una convergencia importante. Durante décadas, los orientalistas habían hablado de Oriente, habían traducido sus textos y habían explicado sus civilizaciones, religiones, dinastías, culturas y mentalidades como temas académicos ocultos a la vista de Europa debido a su extrañeza inimitable. El orientalista era un experto, como Renan o Lane, cuyo trabajo en la sociedad consistía en interpretar Oriente para sus compatriotas. La relación entre el orientalista y Oriente era esencialmente hermenéutica: ante una civilización o un monumento cultural distante y apenas inteligible, el erudito orientalista reducía la oscuridad traduciendo y describiendo con cierta benevolencia, y abarcando, desde el interior, el objeto difícil de alcanzar. El orientalista permanecía, sin embargo, fuera de Oriente, y este, a pesar de los esfuerzos que se hacían para que pareciera inteligible, permanecía más allá de Occidente. Esta distancia cultural, temporal y geográfica se expresaba en metáforas sobre la profundidad, el secreto y la promesa sexual: frases como «los velos de una novia oriental» o «el Oriente impenetrable» pasaron al lenguaje común.
Sin embargo, la distancia entre Oriente y Occidente estaba casi paradójicamente en proceso de reducción a lo largo del siglo XIX. A medida que los contactos comerciales, políticos y existenciales entre el Este y el Oeste crecían (según las formas que hemos estado estudiando), se desarrollaba una tensión entre los dogmas del orientalismo latente que se apoyaba en los estudios del Oriente «clásico», y las descripciones de un Oriente presente, moderno, manifiesto, articulado por los viajeros, peregrinos, estadistas, etc. En algún momento imposible de precisar, la tensión causó una convergencia de los dos tipos de orientalismo. Probablemente —y esto solo es una especulación— la convergencia se produjo cuando los orientalistas, empezando por Sacy, se pusieron a aconsejar a los gobiernos sobre lo que el Oriente moderno era. En este punto el papel del especialista, con su particular formación y bagaje, tomó otra dimensión: el orientalista podía considerarse el agente secreto de la potencia occidental cuando esta intentaba establecer una política hacia Oriente. Todo europeo instruido (y no tan instruido) que viajara a Oriente, se sentiría como un testigo occidental que había logrado traspasar los velos de la oscuridad. Esto se hace patente en Burton, Lane, Doughty, Flaubert y en otras grandes figuras de las que he estado hablando.
Los descubrimientos occidentales sobre el Oriente manifiesto y moderno adquirían una urgencia apremiante a medida que las adquisiciones territoriales en Oriente aumentaban. Así, lo que el orientalista erudito definía como el Oriente «esencial», a veces se contradijo, pero en muchos casos se confirmó cuando Oriente se convirtió en una obligación administrativa real. Ciertamente, las teorías de Cromer sobre el oriental —teorías sacadas del archivo orientalista tradicional— estaban totalmente justificadas porque él estaba gobernando de hecho a millones de orientales. Esto no fue menos cierto en el caso de la experiencia francesa en Siria, en el norte de África y en cualquier otro lugar donde tuviera colonias. Pero esta convergencia entre la doctrina del orientalismo latente y la experiencia del orientalismo manifiesto nunca se produjo de manera más espectacular que cuando, como resultado de la Primera Guerra Mundial, Gran Bretaña y Francia examinaron el Imperio otomano para desmembrarlo. Ahí, tumbado en la mesa de operaciones, estaba el enfermo de Europa, revelándose con toda su debilidad, sus características y sus líneas topográficas.
El orientalista, con sus conocimientos especiales, desempeñaba en esta operación un papel de estimable importancia. Ese papel crucial de agente secreto en Oriente había sido ya perfilado cuando el erudito británico Edward Henry Palmer fue enviado al Sinaí en 1882 para valorar el sentimiento antibritánico y la posibilidad de que fuera utilizado en favor de la revolución de al-Urabi. A Palmer lo mataron en el proceso, pero él fue el más desafortunado de los muchos que llevaron a cabo tareas similares para el imperio, tareas que entonces suponían un trabajo difícil y serio, confiado en parte al «experto» regional. No sin razón, otro orientalista, D. G. Hogarth, autor del famoso relato sobre la exploración de Arabia titulado acertadamente _The Penetration of Arabia_ (1904), fue puesto al frente del Arab Bureau en El Cairo durante la Primera Guerra Mundial. Y no fue por casualidad que hombres y mujeres como Gertrude Bell, T. E. Lawrence y St. John Philby, todos expertos en Oriente, tuvieran puestos en la región —como agentes del imperio, como amigos y como formuladores de alternativas políticas—, a causa de su conocimiento íntimo y experto de Oriente y los orientales. Ellos formaban una «banda» —como Lawrence lo llamó una vez— unida por conceptos contradictorios y similitudes personales: una fuerte individualidad, una identificación y una simpatía intuitiva hacia Oriente, un sentido celosamente guardado de su misión personal en Oriente, una excentricidad cultivada y finalmente una desaprobación hacia Oriente. Para todos ellos Oriente era su experiencia directa y particular que habían tenido allí. En ellos el orientalismo y una praxis efectiva para manipular Oriente recibieron su última forma europea, antes de que el imperio desapareciera y pasara su herencia a otros candidatos al papel de potencia dominante.
Estos individualistas no eran académicos. Se habían beneficiado, como veremos, del estudio académico de Oriente, pero sin pertenecer en modo alguno a la comunidad oficial y profesional de orientalistas eruditos. Su papel, sin embargo, no consistía en menospreciar el orientalismo académico ni trastornarlo, sino más bien en hacerlo eficaz. Sus antecesores fueron gente como Lane y Burton, tanto por su autodidactismo enciclopédico como por el conocimiento preciso y cuasi erudito de Oriente que habían mostrado en sus contactos con los orientales y en sus escritos sobre ellos. Sustituyeron el estudio de Oriente por un tipo de elaboración del orientalismo latente al que tenían fácil acceso, porque formaba parte de la cultura imperial de su época. Su estructura de referencias eruditas estaba formada por gente como William Muir, Anthony Bevan, D. S. Margoliouth, Charles Lyall, E. G. Browne, R. A. Nicholson, Guy Le Strange, E. D. Ross y Thomas Arnold, quien era descendiente directo de Lane. Sus perspectivas imaginarias se las proporcionó principalmente su ilustre contemporáneo Rudyard Kipling, quien había cantado tan memorablemente la «dominación sobre la palmera y el pino».
La diferencia entre Gran Bretaña y Francia en estas materias era asimismo coherente con la historia de cada una de las potencias en Oriente: los británicos estaban allí; los franceses lamentaban la pérdida de la India y de los territorios intermedios. Hacia finales de siglo, Siria se convirtió en el principal foco de atención de la actividad francesa, pero incluso allí era de sentido común que Francia no podía igualar a Gran Bretaña ni en la calidad de su personal ni en el grado de influencia política. La competencia anglo-francesa por los despojos otomanos se sentía hasta en el campo de batalla en el Hiyaz, en Siria, y en Mesopotamia; pero en todos estos lugares, como señaló un hombre tan astuto como Edmond Bremond, los orientalistas y los expertos locales franceses eran dominados por la brillantez y la habilidad táctica de sus homólogos británicos. A excepción de algún genio ocasional, como Louis Massignon, no hubo ningún Lawrence, ningún Sykes, ni ninguna Bells, aunque hubo determinados imperialistas como Étienne Flandin y Franklin-Bouillon. En una conferencia que dio en la Alliance Française, en París en 1913, el conde de Cressaty, un vociferante imperialista, proclamó que Siria era el Oriente particular de Francia, el lugar de los intereses franceses políticos, morales y económicos; intereses, añadió, que deben ser defendidos durante esta _«âge des envahissants impérialistes»_ ; es más, Cressaty destacó que, a pesar de la presencia de firmas comerciales e industriales en Oriente y a pesar del gran número de estudiantes nativos matriculados en colegios franceses, Francia estaba siendo atropellada, en Oriente, amenazada no solo por Gran Bretaña, sino también por Austria, Alemania y Rusia. Si Francia debía continuar previendo _«le retour de l'islam»_ haría mejor en tomar posesión de Oriente: este era el argumento propuesto por Cressaty y secundado por el senador Paul Doumer. Estas posiciones se retomaron en numerosas ocasiones y de hecho Francia se las apañó muy bien en el norte de África y en Siria después de la Primera Guerra Mundial. Pero los franceses tuvieron siempre la sensación de que la administración particular y concreta de las poblaciones orientales que surgían de nuevo en la historia y de los territorios teóricamente independientes era algo que se les había escapado, mientras que los británicos siempre habían podido mantenerlas. En última instancia, quizá, la diferencia que siempre se siente entre el orientalismo moderno británico y el francés es estilística; la aportación de generalizaciones sobre Oriente y los orientales, el sentido de distinción preservado entre Oriente y Occidente, y el deseo de una dominación occidental sobre Oriente son iguales en las dos tradiciones. En efecto, entre los numerosos elementos que caracterizan al «experto», uno de los más evidentes es el estilo, que es el resultado de las circunstancias mundiales específicas, amoldado por las tradiciones, las instituciones, la voluntad y la inteligencia con el fin de que adquiera una forma articulada. Es de este determinante, de este perceptible y modernizado refinamiento que se percibe en el orientalismo de principios del siglo XX en Gran Bretaña y Francia de lo que a continuación vamos a tratar.
### II
### El estilo, la competencia y la visión del experto:
### el orientalismo en el mundo
Tal y como aparece en numerosos poemas, en novelas como _Kim_ ,* en fórmulas y en tópicos, el hombre blanco de Kipling no es más que un personaje de ficción, pero como idea, persona y estilo de vida parece haber sido muy útil para muchos ingleses a lo largo de sus estancias en el extranjero. El color de su piel les distinguía de modo espectacular y tranquilizador del mar de indígenas, pero para el británico que circulaba en medio de los indios, de los africanos o de los árabes existía también el conocimiento certero de que formaba parte de una larga tradición de responsabilidad hacia las razas de color, y que podía recurrir a las reservas empíricas y espirituales de esa tradición. Y es de esa tradición, de sus glorias y de sus dificultades de lo que escribía Kipling cuando celebraba la «ruta» escogida por el hombre blanco en las colonias.
_Esta es la ruta que pisan los hombres blancos_ ,
_cuando van a limpiar un territorio_ :
_bajo sus pies, el hierro; sobre sus cabezas, las hojas,_
_a izquierda y derecha, el abismo_.
_Hemos pisado esta ruta, con lluvia y viento_ ,
_y nuestra estrella nos guía_.
¡ _Ah! ¡Es tan bueno para el mundo que los hombres blancos avancen_
_sobre su gran ruta, codo con codo_
«Limpiar un territorio» es lo que mejor hacen los hombres blancos en delicado concierto los unos con los otros. Esto es una alusión a los peligros que entrañaba la rivalidad europea en las colonias; ya que si no llegaban a coordinar sus políticas, los hombres blancos de Kipling estarían bastante bien dispuestos a ir a la guerra: «Libertad para nosotros y libertad para nuestros hijos / y a falta de libertad, la guerra». Detrás de la máscara de líder benévolo que utiliza el hombre blanco, se esconde siempre la voluntad expresa de usar la fuerza, de matar y de ser matado. Lo que dignifica su misión es un cierto sentido de dedicación intelectual: él es un hombre blanco, pero no busca simplemente obtener beneficios, pues su «estrella» se sitúa probablemente mucho más allá de los bienes terrenales. Muchos hombres blancos, seguramente se preguntaron con frecuencia por qué combatían en esa «ruta con lluvia y viento». Estaban perturbados al ver que el color de su piel les daba una categoría ontológica superior, además de un gran poder sobre buena parte del mundo habitado. A fin de cuentas, ser un hombre blanco, para Kipling y para los que estaban influidos por sus percepciones y su retórica, era una cuestión de autoconfirmación. Se llegaba a ser un hombre blanco porque se _era_ un hombre blanco; y, más importante aún, «al beber de esa copa», al vivir ese destino inalterable en «los días del hombre blanco» quedaba poco tiempo para hacer especulaciones ociosas sobre los orígenes, las causas y la lógica de la historia.
Ser un hombre blanco, por tanto, era una idea y una realidad. Suponía una posición razonada ante los mundos blanco y no blanco. Significaba —en las colonias— hablar de una manera determinada, comportarse de acuerdo con unos códigos y reglamentos e incluso tener ciertos sentimientos y no otros. Significaba hacer ciertos juicios, evaluaciones y gestos. Era una forma de autoridad ante la cual los no blancos e incluso los propios blancos debían inclinarse. En su forma institucional (gobiernos coloniales, cuerpos consulares y asentamientos comerciales), era una agencia de expresión, difusión y realización de una política hacia el mundo, y dentro de esa agencia, aunque estaban permitidas ciertas libertades personales, lo que imperaba era la idea impersonal y comunal de ser un hombre blanco. Ser un hombre blanco, en resumen, era una manera concreta de estar en el mundo, una manera de apoderarse de la realidad, del lenguaje y del pensamiento. Hacía que un estilo específico fuera posible. Y que el propio Kipling, así como su hombre blanco, hubieran podido hacer algo más que simplemente existir.
Estas ideas y sus autores surgen a partir de unas complejas circunstancias históricas y culturales de las cuales al menos dos tienen mucho en común con la historia del orientalismo del siglo XIX. Una de ellas es el hábito aprobado culturalmente de desplegar grandes generalizaciones por las cuales la realidad se divide en varios colectivos: lenguas, razas, tipos, colores y mentalidades; cada categoría no es tanto una designación neutral como una interpretación evaluativa. Subrayando estas categorías está la rígida oposición binómica de «nuestro» y «suyo», con el primero invadiendo siempre al segundo (incluso hasta el punto de hacer «suyo» exclusivamente una función de «nuestro»). Esta oposición fue reforzada no solo por la antropología, la lingüística y la historia, sino también, por supuesto, por las tesis darwinianas sobre la supervivencia y la selección natural, y —no menos decisivo— por la retórica del gran humanismo cultural. Lo que les dio a escritores como Renan y Arnold el derecho de generalizar sobre la raza fue el carácter oficial de su formación cultural literaria. «Nuestros» valores eran liberales, humanos y correctos; se apoyaban en la tradición de las _belles-lettres_ , en la erudición informada y en la investigación racional; como europeos (y hombres blancos), «nosotros», hemos participado en ellos cada vez que sus virtudes eran ensalzadas. Sin embargo, las asociaciones humanas formadas por valores culturales reiterados tendían a la exclusión en la misma medida que a la inclusión. Por cada idea sobre «nuestro» arte promulgada por Arnold, Ruskin, Mill, Newman, Carlyle, Renan, Gobineau o Compte, se formaba otro eslabón en la cadena que «nos» mantenía unidos, mientras que otro intruso era desterrado. Incluso si este era siempre el resultado de esta retórica, sin tener en cuenta dónde o cuándo ocurría, debemos recordar que en la Europa del siglo XIX un edificio imponente de erudición y cultura se estaba construyendo, por decirlo de algún modo, frente a los intrusos (las colonias, los pobres, los delincuentes), edificio cuyo papel en la cultura era definir todo para lo que _ellos_ eran constitucionalmente inaptos.
La otra circunstancia común a la creación del hombre blanco y del orientalismo reside en el «campo» dispuesto por cada uno de ellos, así como en la imposición que este campo hace de ciertos modos, incluso ciertos ritos, de comportamiento, de aprendizaje y de posesión. Solo un occidental podía hablar de los orientales, por ejemplo, igual que había sido el hombre blanco el que había podido designar y dar nombre a las gentes de color o no blancas. Toda afirmación hecha por los orientalistas o por los hombres blancos (términos normalmente intercambiables) transmitía la idea de la distancia irreductible que separaba al blanco del de color, o al occidental del oriental. Además, detrás de cada afirmación resonaba la tradición de la experiencia, del saber y de la educación que mantenía al oriental-de color en su posición de _objeto estudiado por el occidental blanco_ , en vez de lo contrario. Desde una posición de poder —como la de Cromer— el oriental pertenecía al sistema de autoridad cuyo principio era simplemente asegurar que no pudiera nunca ser independiente ni gobernarse por sí mismo. La premisa era que, como los orientales desconocían lo que era el autogobierno, había que mantenerlos así por su bien.
Ya que el hombre blanco, como el orientalista, vivía muy cerca de la línea de tensión que contenía a los hombres de color, sentía que su deber era definir y redefinir el dominio que examinaba. Párrafos de descripción narrativa alternados regularmente con párrafos de definición y de juicios reformulados que interrumpen la narración; este es el estilo característico de las obras de los expertos orientalistas que actuaban utilizando al hombre blanco de Kipling como una máscara. Así T. E. Lawrence escribió a V. W. Richards en 1918:
[...] los árabes seducían mi imaginación. Es la vieja civilización que se ha refinado a sí misma despejándose de los dioses domésticos y de la mitad de los ornamentos que la nuestra se apresura a asumir. El evangelio de la desnudez con respecto a las cosas materiales es bueno, y aparentemente implica también un tipo de desnudez moral. Estas gentes solo piensan en el momento y se esfuerzan por atravesar holgadamente la vida sin tener que doblar esquinas ni escalar colinas. Es, en parte, una fatiga mental y moral, una raza agotada, y para evitar las dificultades tienen que reducir muchas cosas que nosotros consideramos honorables e importantes; sin embargo, a pesar de no compartir su punto de vista, creo que puedo entenderlo lo suficiente como para verme a mí y a otros extranjeros desde su perspectiva y no condenarla. Sé que soy un extraño para ellos y siempre lo seré; pero no puedo creer que sean inferiores como tampoco podría hacerme a su manera de vivir.
Encontramos una perspectiva similar, aunque el tema tratado parezca diferente en estas observaciones de Gertrude Bell:
¿Cuántos miles de años ha durado este estado de cosas [a saber, que los árabes viven en «estado de guerra»]? Los que estudian los antecedentes más antiguos del desierto interior nos lo dirán, porque este estado se remonta a sus orígenes; pero a lo largo de todos estos siglos, el árabe no ha adquirido ninguna experiencia. Nunca está a salvo, y, no obstante, se comporta como si la seguridad fuera su pan de cada día.
A lo que, como una glosa, podríamos añadir otra observación que hace, esta vez sobre la vida en Damasco:
Comienzo viendo vagamente lo que significa la civilización de una gran ciudad oriental; cómo viven y lo que piensan; y me he acostumbrado a ellos. Creo que el hecho de que sea inglesa es una gran ayuda [...]. Nosotros desde hace cinco años estamos ascendiendo en el mundo. La diferencia es muy marcada. Creo que, en gran medida, se debe al éxito de nuestro gobierno en Egipto [...]. La derrota de Rusia cuenta mucho y mi impresión es que la vigorosa política de lord Curzon en el golfo Pérsico y en la frontera india cuenta todavía mucho más. Solo quien conozca muy bien Oriente podrá comprender cómo todo esto se relaciona. No es exagerado decir que si la misión inglesa hubiera retrocedido ante las puertas de Kabul, se le habrían puesto muy malas caras al turista inglés en las calles de Damasco.
En afirmaciones como estas nos damos cuenta enseguida de que las expresiones «el árabe» o «los árabes» tienen una aureola que los aparta, los define y les da una coherencia colectiva que los anula como personas individuales con una historia personal que contar. Lo que seducía la imaginación de Lawrence era la claridad del árabe, como una imagen o como una supuesta filosofía (o actitud) ante la vida: en ambos casos Lawrence se vincula al árabe desde la perspectiva purificadora de alguien que no es árabe, de alguien para quien esa simplicidad ingenua y primitiva que posee el árabe es algo definido por el observador que en este caso es el hombre blanco. Pero el refinamiento árabe, el cual se corresponde en lo esencial con la visión que Yeats tiene de Bizancio donde
_las llamas no se alimentan de astillas, ni de sílex o acero_ ,
_no las agita ningún viento, son llamas engendradas de una llama_ ,
_donde vienen los espíritus concebidos por la sangre_ ,
_y dejan sus furores y sus complejidad..._
se asocia con la permanencia árabe como si el árabe no hubiera estado sometido al proceso ordinario de la historia. Paradójicamente, le parece a Lawrence que el árabe se ha agotado en su persistencia temporal. La gran edad de la civilización árabe ha servido así para refinar al árabe hasta sus atributos esenciales y para cansarlo moralmente en el proceso. Lo que nos queda son los árabes de Gertrude Bell: siglos de experiencia y ninguna sabiduría. En tanto que entidad colectiva, entonces, el árabe no acumula ninguna densidad existencial, ni siquiera semántica. Permanece lo mismo, con la excepción de los refinamientos exhaustivos mencionados por Lawrence, de un extremo a otro de «los antecedentes del desierto interior». Debemos asumir que si _un_ árabe siente alegría, si está triste por la muerte de su hijo o de su padre o si percibe las injusticias de la tiranía política, estas percepciones están necesariamente subordinadas al puro, simple y persistente hecho de que es un árabe.
El carácter primitivo de este estado existe simultáneamente en dos niveles, por lo menos: uno, en _el de la definición_ , que es reductor; y dos (según Lawrence y Gertrude Bell), en _el de la realidad_. Esta coincidencia absoluta no era una simple coincidencia. Primero, solo se podía haber realizado desde el exterior, gracias a un vocabulario y a unos instrumentos epistemológicos destinados a llegar al corazón de las realidades y a evitar las distracciones de las circunstancias accidentales o de la experiencia. Después, la coincidencia era un hecho que, sobre todo, resultaba de la actuación conjunta del método, de la tradición y de la política. Cada uno anulaba de alguna manera las diferencias entre el tipo — _el_ oriental, _el_ semita, _el_ árabe, _el_ Oriente— y la realidad humana ordinaria («el misterio incontrolable sobre el terreno bestial» de Yeats), en la que todos los seres humanos viven. Para el investigador erudito, un tipo marcado con el sello de lo «oriental» era lo mismo que cualquier otro individuo oriental que pudiera encontrar. Años de tradición habían dado cierta legitimidad al discurso sobre cuestiones tales como el espíritu semítico u oriental. Y el buen sentido político había enseñado, según la maravillosa frase de Gertrude Bell, que en Oriente «todo es consistente». El carácter primitivo, por tanto, era algo inherente a Oriente, _era_ Oriente y una idea a la que todo el que trataba con Oriente o escribía sobre él tenía que volver como a una piedra de toque más duradera que el tiempo o la experiencia.
Todo esto se entiende muy bien cuando se aplica a los agentes, expertos y consejeros blancos en Oriente. Lo que les importaba a Lawrence y a Gertrude Bell era que sus referencias a los árabes o a los orientales pertenecieran a una convención reconocible y autorizada de la formulación; una convención a la que todo detalle se podía subordinar. Pero, más particularmente, ¿de dónde venían «el árabe», «el semita» o «el oriental»?
Hemos señalado cómo, durante el siglo XIX, en escritores como Renan, Lane, Flaubert, Caussin de Perceval, Marx y Lamartine, las generalizaciones sobre «Oriente» adquirieron poder a partir de la presumida representatividad de todo lo oriental. Cada átomo de Oriente manifestaba su orientalidad en la misma medida que el atributo de ser oriental anulaba cualquier otra circunstancia. Un hombre oriental, primero era un oriental y solo después era un hombre. Esta tipificación tan radical se veía reforzada, de forma natural, por las ciencias (o discursos, como yo prefiero llamarlos) que adoptaban una postura regresiva y descendente con respecto a la categoría de las especies, la cual se suponía que era una explicación ontogenética de cualquier miembro de una especie. Así, dentro de estas extensas y semipopulares denominaciones, como la de «oriental», se estaban realizando algunas distinciones científicamente válidas, muchas de las cuales se fundamentaban principalmente en los tipos de lenguas —por ejemplo, el semítico, el dravídico, el hamítico—, pero enseguida pudieron encontrarse indicios antropológicos, psicológicos, biológicos y culturales para apoyarlas. El «semítico» de Renan, por ejemplo, era una generalización lingüística que, en sus manos, podía añadirse así misma todo tipo de ideas paralelas de anatomía, de historia, de antropología e incluso de geología. El «semítico», pues, se podía emplear no solo como una descripción o designación simple; se podía aplicar a cualquier complejo de sucesos históricos y políticos para reducirlos a un núcleo antecedente e inherente a ellos. El «semítico», por tanto, era una categoría transtemporal y transindividual que pretendía predecir cualquier acto individual del comportamiento «semítico» apoyándose en alguna esencia «semítica» preexistente y que, igualmente, fomentaba la interpretación de todos los aspectos de la vida y de la actividad humanas en términos de algún elemento común «semítico».
Podría parecer que el dominio particular de estas ideas relativamente punitivas de la cultura liberal europea del final del siglo XIX pertenecía al ámbito de lo misterioso, a menos que recordemos que lo que reclamaban las ciencias como la lingüística, la antropología y la biología era su categoría de ciencias empíricas y, de ningún modo, especulativas o idealistas. Es cierto que el semítico de Renan, como el indoeuropeo de Bopp, era un objeto construido, pero se consideraba lógico e inevitable como protoforma que tenía en cuenta los datos específicamente aprehendibles y empíricamente analizables de las lenguas semíticas específicas. Por tanto, al intentar formular un tipo lingüístico prototípico y primitivo (así como uno cultural, psicológico e histórico) también se «intentaba definir un potencial humano primario» a partir del cual se derivarían los ejemplos completamente específicos de comportamiento. Ahora bien, ese intento habría sido imposible si no se hubiera creído también —en términos clásicos empíricos— que la mente y el cuerpo eran realidades dependientes entre sí, determinadas originalmente por un conjunto dado de condiciones geográficas, biológicas y cuasi históricas. Nadie podía salir de esta estructura establecida que ningún nativo podía descubrir o examinar. Los antiguos prejuicios de los orientalistas se apoyaban en estas ideas empíricas. En todos sus estudios sobre el islam «clásico», el budismo o el zoroastrismo, se sentían, como confiesa el doctor Casaubon de George Eliot, actuando «como el fantasma de algún antepasado que vaga por el mundo y trata mentalmente de reconstruirlo como era antes, a pesar de los cambios monstruosos y confusos».
Si estas tesis sobre las características lingüísticas de la civilización, que luego se convirtieron en tesis raciales, fueron solo una parte del antiguo debate entre los científicos y los eruditos europeos, debemos descartarlas porque el material que proporcionaban solo serviría para un drama insignificante. Lo importante, sin embargo, es que tanto los términos del debate como el debate en sí estaban muy extendidos. En la cultura de finales del siglo XIX, como Lionel Trilling ha dicho, «la teoría racial, alentada por el nacionalismo y el imperialismo crecientes y apoyada por una ciencia incompleta y mal asimilada, era casi indiscutible». La teoría racial, las ideas sobre los orígenes y las primitivas clasificaciones, la decadencia moderna, el progreso de la civilización, el destino de la raza blanca (o aria) y la necesidad de territorios coloniales: todos estos eran elementos que formaban parte de la peculiar amalgama de ciencia, política y cultura cuyo propósito, casi sin excepción, era siempre llevar a Europa, o a la raza europea, al dominio sobre las partes de la humanidad no europea. También existía una unanimidad general, según la versión transformada y extraña del darwinismo que el propio Darwin había aprobado, acerca de que los modernos orientales eran residuos degradados de una grandeza anterior; las civilizaciones antiguas o «clásicas» de Oriente se podían percibir a través de los desórdenes de la decadencia presente, pero solo _a_ ) porque un especialista blanco con unas técnicas científicas muy refinadas podía hacer el examen y la reconstrucción, y _b_ ) porque un vocabulario de generalidades dramáticas (los semitas, los arios, los orientales) hacía referencia más que a un conjunto de ficciones a una serie completa de distinciones aparentemente objetivas y acordadas. Así, cualquier consideración sobre lo que los orientales eran capaces o no de hacer se apoyaba en «verdades» biológicas como las que se explican detalladamente en «A Biological View of Our Foreign Policy» (1896), de P. Charles Michel, de la obra _The Struggle for Existence in Human Society_ (1888) de Thomas Henry Huxley, así como en _Social Evolution_ (1894) de Benjamin Kidd, _History of Intellectual Development on the Lines of Modern Evolution_ (1897-1901) de John B. Crozier, y en _The Biology of British Politics_ (1904), de Charles Harvey. Se asumía que si las lenguas eran tan distintas entre sí como los lingüistas decían que eran, también, de modo similar, los usuarios del lenguaje —sus mentes, culturas, potenciales e incluso sus cuerpos— eran diferentes. Y estas distinciones estaban respaldadas por la fuerza de una verdad ontológica y empírica y por la demostración convincente de esa verdad en ciertos estudios sobre los orígenes, los desarrollos, el carácter y el destino.
El punto sobre el que hay que insistir es que esa verdad sobre las diferencias distintivas entre las razas, las civilizaciones y las lenguas era (o pretendía ser) radical e indiscutible. Llegaba hasta el fondo de las realidades, se aseguraba de que no pudiera salirse de los orígenes y de los tipos que esos orígenes permitían; establecía fronteras reales entre seres humanos, fronteras a partir de las cuales se construían las razas, las naciones y las civilizaciones; forzaba la visión hasta llevarla lejos de las realidades humanas comunes y plurales, como son la alegría, el sufrimiento o la organización política, y en vez de esto destacaba las cuestiones descendentes y regresivas de los orígenes inmutables. Ningún científico podía ya salirse de estos orígenes en su investigación, igual que ningún oriental podía escapar a las categorías de «los semitas», «los árabes» o «los indios», de los cuales su realidad presente —devastada, colonizada y atrasada— le excluía a no ser que fuera por la presentación didáctica del investigador blanco.
La profesión de investigador especializado confería ciertos privilegios únicos. Recordemos que Lane podía aparecer como un oriental y, sin embargo, conservar su objetividad erudita. Los orientales que él estudió se convirtieron, de hecho, en _sus_ orientales, ya que en el relato que escribió sobre ellos los concibió no solo como gente normal, sino como objetos monumentalizados. Esta doble perspectiva fomentaba un tipo de ironía estructurada. Por un lado, había una colección de pueblos que vivían en el presente; por otro, estos pueblos —como tema de estudio— pasaban a ser «los egipcios», «los musulmanes» o «los orientales». Solo el erudito podía ver, y manipular, la discrepancia que existía entre los dos niveles. La tendencia del primero era siempre hacia una mayor variedad, aunque esa variedad siempre se restringía y comprimía de manera descendente y regresiva hacia la terminal _radical_ de la generalidad. Cualquier ejemplo sobre el comportamiento de los nativos modernos se convertía en una efusión que había que remitir a la terminal original, la cual se iba fortaleciendo en el proceso. Este tipo de «remisión» era precisamente la _disciplina_ del orientalismo.
La habilidad que tenía Lane para tratar a los egipcios como seres presentes y como validaciones de etiquetas _sui generis_ era una función de la disciplina orientalista y de los puntos de vista que se mantenían en general sobre el musulmán o el semita de Oriente Próximo. Solo en los semitas orientales se podía observar el presente y el origen juntos. Los judíos y los musulmanes, como temas de estudio orientalista, se comprendían enseguida a la vista de sus orígenes primitivos: esto era (y hasta cierto punto sigue siendo) la piedra angular del orientalismo moderno. Renan había afirmado que los semitas eran un ejemplo de desarrollo detenido y, hablando desde un punto de vista funcional, esto llegó a significar que para el orientalismo ningún semita moderno, por muy moderno que se considerara, podía separarse de sus orígenes. Esta regla funcional actuaba en los niveles temporal y espacial. Ningún semita llegó más allá del desarrollo del período «clásico», ningún semita pudo nunca deshacerse del ambiente pastoral y desértico de su tienda y de su tribu. Cualquier manifestación de la vida real del «semita» podía y debía ser remitida al pasado, a la categoría primitiva explicativa de «el semítico».
La eficacia de un sistema de referencia así, según el cual todo ejemplo individual de comportamiento real podía reducirse a un pequeño número de categorías explicativas «originales» fue considerable hacia finales del siglo XIX. Para el orientalismo era el equivalente de lo que la burocracia era para la administración pública. El departamento era más útil que el archivo individual y, en realidad, el ser humano era significativo principalmente en tanto que ofrecía la oportunidad de abrir un archivo. Debemos imaginarnos al orientalista en el papel de un empleado que amontona una gran cantidad de archivos en un armario con la etiqueta de «los semitas». Con la ayuda de los recientes descubrimientos realizados en la antropología comparada y primitiva, un erudito, como William Robertson Smith, podía reunir en un solo grupo a los habitantes de Oriente Próximo y escribir sobre su sistema de parentesco, sobre sus costumbres matrimoniales y la forma y el contenido de sus prácticas religiosas. La autoridad del trabajo de Smith reside en la desmitificación franca y brutal que hace de los semitas. Las barreras nominales que el islam y el judaísmo presentaban al mundo se anulan. Smith utiliza la filología semítica, la mitología y la erudición «para construir [...] una imagen hipotética del desarrollo de los sistemas sociales, coherente con todas las realidades árabes». Si esta imagen llega a revelar que las raíces del monoteísmo, las cuales pertenecen al pasado pero que todavía conservan su influencia, se encuentran en el totemismo o en el culto a los animales, el erudito habrá tenido éxito. Y esto, dice Smith, a pesar de que «nuestras fuentes mahometanas cubren con un velo, en la medida de sus posibilidades, los detalles del antiguo paganismo».
En su obra sobre los semitas, Smith abarca áreas como la teología, la literatura y la historia. La escribió con un conocimiento pleno del trabajo de los orientalistas (véase, por ejemplo, el sabio ataque de Smith en 1887 a la _Histoire du peuple d'Israël_ , de Renan) y, lo que es más importante, la concibió como ayuda para comprender a los semitas modernos. Smith, en mi opinión, fue un eslabón crucial en la cadena intelectual que relacionaba al hombre blanco como experto con el Oriente moderno. La ciencia compartimentada que proporcionaron Lawrence, Hogarth, Bell y otros, en tanto que expertos en cuestiones orientales, no habría sido posible sin Smith. E incluso Smith, el sabio arqueólogo, no habría tenido ni la mitad de autoridad de la que tuvo si no hubiera contado con esa experiencia adicional y directa con las «realidades árabes». Smith combinó la «comprensión» de las categorías primitivas con la habilidad de observar verdades generales detrás de las irregularidades empíricas del comportamiento oriental contemporáneo, y esta combinación hizo que sus escritos tuvieran mucho peso. Además fue esta especial combinación la que anunció el estilo del experto sobre el que Lawrence, Bell y Philby construyeron su reputación.
Como Burton y Charles Doughty habían hecho antes que él, Smith viajó al Hiyaz entre 1880 y 1881. Arabia había sido un lugar especialmente privilegiado para el orientalismo no solo porque los musulmanes trataban el islam como el _genius loci_ de Arabia, sino también porque el Hiyaz aparecía históricamente tan desnudo y retrasado como de hecho era geográficamente; el desierto de Arabia era, de este modo, considerado un decorado sobre el que se podían hacer afirmaciones acerca del pasado con la misma forma exactamente (y con el mismo contenido) que las que se hacían sobre el presente. En el Hiyaz se podía hablar de musulmanes, de islam moderno e islam primitivo sin molestarse en hacer distinciones. A este vocabulario desnudo de fundamento histórico, Smith aportó el distintivo de la autoridad suplementaria que le proporcionaban sus estudios semíticos. Sus comentarios constituyen el punto de vista de un erudito que tiene a su disposición _todos_ los antecedentes del islam, de los árabes y de Arabia:
Es una característica del mahometismo que todo sentimiento nacional adopte un aspecto religioso, puesto que toda la política y las formas sociales de un país musulmán están recubiertas de una vestimenta religiosa. Pero sería un error suponer que el auténtico sentimiento religioso está en el fondo de todo lo que se justifica adoptando una forma religiosa. Los prejuicios del árabe tienen sus raíces en un conservadurismo que es más profundo que su creencia en el islam. En efecto, entre los grandes defectos de la religión del Profeta se encuentran el hecho de que se preste muy fácilmente a los prejuicios de la raza entre la cual fue promulgada y el hecho de que haya adoptado tantas ideas bárbaras y obsoletas, las cuales incluso Mahoma debía de haber visto que no tenían ningún valor religioso, pero las mantuvo dentro de su sistema para facilitar la propagación de sus doctrinas reformadas. Sin embargo, muchos de los prejuicios que nos parecen más puramente mahometanos no tienen su fundamento en el Corán.
El «nos» de la última frase de este sorprendente fragmento de lógica define de manera explícita el punto de vista aventajado del hombre blanco. Este «nos» permite decir en la primera frase que toda la vida política y social está «recubierta» de una vestimenta religiosa (el islam, entonces, se puede caracterizar como totalitario); luego, decir en la segunda que la religión solo es una tapadera utilizada por los musulmanes (en otras palabras, todos los musulmanes son esencialmente hipócritas). En la tercera frase se sostiene que el islam —entonces incluso se adueña de la fe del árabe— en realidad no reformó la base conservadora del árabe preislámico. Y esto no es todo. Puesto que si el islam tuvo éxito como religión, fue porque permitió irreflexivamente que esos prejuicios árabes «auténticos» se deslizaran dentro de él; por esta táctica (ahora vemos que era una táctica del islam) debemos culpar a Mahoma, quien era, después de todo, un cripto-jesuita sin escrúpulos. Pero todo esto es más o menos madurado en la última frase, en la que Smith «nos» dice que todo lo que ha dicho sobre el islam no es válido porque, después de todo, los aspectos quintaesenciales del islam que Occidente conoce no son «mahometanos».
Los principios de identidad y de no contradicción no van ligados claramente al orientalista. Lo que los invalida es la competencia del experto orientalista, la cual se basa en una verdad colectiva e irrefutable que está totalmente dentro de la comprensión filosófica y retórica del orientalista. Smith es capaz de hablar sin la menor duda del «carácter árido, práctico [...] constitutivamente irreligioso de la mente árabe», del islam como de un sistema de «hipocresía organizada», de la imposibilidad de «sentir ningún respeto hacia la devoción musulmana en la cual el formalismo y la vana repetición son reducidos a un sistema». Sus ataques contra el islam no tienen un carácter relativo, ya que para él está claro que la superioridad de Europa y de la cristiandad es real y no imaginaria. En el fondo, la visión que Smith tiene del mundo es binaria, y esto se evidencia en párrafos como el siguiente:
El viajero árabe es totalmente diferente a nosotros. Para él moverse de un sitio a otro es una tarea muy fastidiosa, no disfruta con el esfuerzo [como «nosotros»], y se queja de hambre y de fatiga con todas sus fuerzas [lo que «nosotros» no hacemos]. Nunca podrás persuadir al oriental de que, al bajar del camello, te pueda apetecer otra cosa que no sea tumbarte inmediatamente sobre el tapiz para reposar ( _isterih_ ), mientras fumas y bebes. Además, el árabe no se impresiona por el paisaje [y «nosotros» sí].
«Nosotros» somos esto y «ellos» son aquello. ¿Qué árabe, qué islam, cuándo, cómo, de acuerdo a qué criterios? Estas parecen ser distinciones irrelevantes en el estudio meticuloso que hace Smith de su experiencia en el Hiyaz. El punto crucial es que todo lo que se puede saber o aprender sobre los «semitas» y los «orientales» se puede corroborar inmediatamente no solo en los archivos, sino directamente sobre el terreno.
La obra de los grandes expertos franceses e ingleses del siglo XX sobre temas orientales se deriva de esta estructura coercitiva que encadena a todo hombre moderno «de color» a unas verdades generales que el erudito blanco europeo formula acerca de sus prototípicos ancestros lingüísticos, antropológicos o doctrinales. Estos expertos también aportaron a esta estructura su mitología y sus obsesiones personales que, en escritores como Doughty y Lawrence, se han estudiado con considerable energía. Cada uno de ellos —Wilfrid Scawen Blunt, Doughty, Lawrence, Bell, Hogarth, Philby, Sykes, Storrs— creía que su visión de los asuntos orientales era individual, creada por él mismo a partir de algún encuentro intenso y personal con Oriente, el islam o los árabes; cada uno de ellos expresaba su desprecio general por el conocimiento oficial sobre Oriente. «El sol hace de mí un árabe —escribió Doughty en _Arabia Deserta_ —, pero nunca me ha afectado el orientalismo.» Sin embargo, en el análisis final todos ellos (excepto Blunt) expresaron la tradicional hostilidad occidental y su temor a Oriente. Sus puntos de vista depuraron y dieron un giro personal con respecto al estilo académico del orientalismo moderno con su repertorio de grandiosas generalizaciones, de «ciencia» tendenciosa contra la que no había ninguna posibilidad de apelación ni de fórmulas reductivas. (Doughty de nuevo dice en la misma página en la que se burla del orientalismo: «los semitas se pueden comparar con un hombre sentado en una cloaca que le cubre hasta los ojos y cuyas cejas tocan el cielo»). Ellos actuaban, hacían promesas, recomendaban la política que había que seguir de acuerdo con estas generalizaciones y, lo que no deja de ser una ironía notable, adquirieron la identidad de orientales blancos en la cultura de sus países, incluso cuando, como en el caso de Doughty, Lawrence, Hogarth y Bell, su compromiso profesional con Oriente (como el de Smith) no les impedía despreciarlo totalmente. Se trataba para ellos de conservar el control del hombre blanco sobre Oriente y el islam.
Una nueva dialéctica surge a partir de este proyecto. Lo que se le exige al experto oriental ya no es simplemente «comprender», ahora hace falta lograr que Oriente entre en acción, su poder debe ser alistado en el lado de «nuestros» valores, de «nuestra» civilización, de «nuestros» intereses y de «nuestros» objetivos. El conocimiento de Oriente se traduce directamente en una actividad cuyos resultados dan lugar a nuevas corrientes de pensamiento y acción en Oriente. No obstante, en su momento estas exigirán al hombre blanco que reafirme de nuevo su control, y esta vez no como autor de un trabajo erudito sobre Oriente, sino como creador de la historia contemporánea de Oriente como actualidad brutal (ya que, puesto que él la ha comenzado, solo el experto puede comprenderla adecuadamente). El orientalista ahora se ha convertido en una figura de la historia de Oriente que no se puede distinguir de ella, es quien le da forma, y es su signo característico para Occidente. Veamos esta dialéctica brevemente expuesta:
Algunos ingleses, entre los cuales Kitchener era el principal, creían que una rebelión árabe contra los turcos permitiría que Inglaterra, mientras luchaba contra Alemania, derrotara a su aliado turco. Su conocimiento de la naturaleza y del poder de los pueblos árabes les hacía pensar que esa rebelión podría tener éxito, y les indicaba el carácter y el método que debían seguir. Así, habiendo obtenido del gobierno británico la seguridad formal de ayuda, permitieron que comenzara. Pero la revuelta del Jerife de La Meca fue una sorpresa para muchos y encontró a los aliados desprevenidos. Suscitó sentimientos confusos, creó fuertes amistades y enemistades y, entre ese choque de celos, sus asuntos empezaron a desviarse.
Esta es la propia sinopsis de Lawrence, que realiza en el capítulo 1 de su _The Seven Pillars of Wisdom_.* El «conocimiento» de «algunos ingleses» crea un movimiento en Oriente cuyos «acontecimientos» producen consecuencias mixtas; las ambigüedades, los resultados medio imaginados, tragicómicos, de este nuevo resucitado Oriente pasan a ser el tema de lo que escriben los expertos, una nueva forma de discurso orientalista que presenta una visión del Oriente contemporáneo no como narración, sino con toda su complejidad, su problemática y su esperanza traicionada; con el autor blanco orientalista como su definición articulada y profética.
La derrota de la narración en favor de la visión —que constatamos incluso en _The Seven Pillars_ — es algo que ya encontrábamos en _Modern Egyptians_ , de Lane. El conflicto entre una visión holística (descripción, relato monumental) de Oriente y una narración de los sucesos de Oriente se produce en diferentes planos que conllevan diferentes desenlaces. Ya que este conflicto es algo que se renueva con frecuencia en el discurso orientalista, conviene que lo analicemos brevemente. El orientalista observa Oriente desde arriba con la intención de abarcar el panorama total que se extiende ante sus ojos: cultura, religión, mentalidad, historia y sociedad. Para hacer esto debe observar cada detalle a través del dispositivo de un conjunto de categorías reduccionistas (los semitas, la mente musulmana, Oriente, etc.). Como estas categorías son ante todo esquemáticas y eficaces, y como está más o menos asumido que ningún oriental puede conocerse a sí mismo como lo conoce un orientalista, la coherencia y la fuerza de cualquier visión de Oriente, en última instancia, viene a depender de la persona, institución o discurso que la sustenta. Cualquier visión global es fundamentalmente conservadora, y ya hemos subrayado hasta qué punto en la historia de las ideas de Occidente sobre Oriente Próximo, estas ideas se han mantenido sin tener en cuenta ningún testimonio que las contradijera. (De hecho, podemos decir que estas ideas producen testimonios que prueban su validez.)
El orientalista, principalmente, es el tipo de agente de esta visión global. Lane es un ejemplo típico del modo en que un individuo cree que ha subordinado sus ideas, o incluso lo que ve, a las exigencias de una perspectiva «científica» del fenómeno global conocido colectivamente como Oriente o la nación oriental. Una visión es, por tanto, estática, igual que las categorías científicas que inspiraron al orientalismo de finales del siglo XIX son también estáticas: no hay recursos más allá de «los semitas» o de «la mente oriental». Estos son los límites extremos que mantienen a todas las variedades del comportamiento oriental dentro de la perspectiva general de un campo entero. Como disciplina, como profesión, como lenguaje o discurso especializado, el orientalismo apuesta por la permanencia de todo Oriente, ya que sin «Oriente» no puede haber ningún conocimiento consistente, inteligible y articulado llamado «orientalismo». Así, Oriente pertenece al orientalismo del mismo modo que se asume que hay cierta información que pertenece a (o se relaciona con) Oriente.
Hay una constante presión contra este sistema estático de «esencialismo sincrónico». Lo he denominado visión, porque presupone que todo Oriente puede verse panópticamente, hay una presión constante. La fuente de esta presión es narrativa, en el sentido de que si se puede mostrar que un detalle oriental cualquiera se modifica, o se desarrolla, se introduce la diacronía en el sistema. Lo que parecía estable —y Oriente es sinónimo de estabilidad y de eternidad inmutables— ahora aparece inestable. La inestabilidad sugiere que la historia, con sus detalles destructivos, sus corrientes de cambio, su tendencia hacia el crecimiento, el declive o el movimiento dramático es posible en Oriente y para Oriente. La historia y la narración a través de la cual se presenta la historia demuestran que esa visión es insuficiente y que «Oriente» como una categoría ontológica incondicionada no hace justicia al potencial de la realidad para el cambio.
Además, la narrativa es la forma específica que adopta la historia escrita para contrarrestar la permanencia de su visión. Lane percibió los peligros de la narración cuando rehusó dar una forma lineal a sus informaciones, prefiriendo en su lugar la forma monumental de la visión enciclopédica o lexicográfica. La narración afirma que los hombres nacen, se desarrollan y mueren, que las instituciones y las condiciones de la vida real tienden a cambiar, que es bastante probable que la modernidad y la contemporaneidad finalmente sobrepasen a las civilizaciones «clásicas» y, sobre todo, afirma que la dominación de la realidad por la visión no es más que una voluntad de poder, una voluntad de verdad y de interpretación y no una condición objetiva de la historia. En resumen, la narración introduce un punto de vista, una perspectiva y una conciencia que se oponen al tejido unitario de la visión; la narración viola las ficciones apolíneas y serenas que propone la visión.
Cuando, como resultado de la Primera Guerra Mundial, Oriente entró en la historia, el orientalista como agente fue quien llevó a cabo el trabajo. Hannah Arendt hizo la brillante observación de que el equivalente a la burocracia era el agente imperial, lo que en nuestro caso quiere decir que si la empresa académica colectiva llamada orientalismo era una institución burocrática que se basaba en una cierta visión conservadora del mundo, los que servían a esa visión en Oriente eran los agentes imperiales, como T. E. Lawrence. En su obra podemos ver más claramente el conflicto entre la historia narrativa y la visión, cuando —en sus propias palabras— el «nuevo imperialismo» intentaba provocar «una vaga actividad, haciendo recaer la responsabilidad en las gentes locales [de Oriente]». Como existía una gran competición entre las potencias europeas, estas presionaban a Oriente para que entrara en la vida activa, para que fuera útil, para que cambiara desde su pasividad «oriental» inmutable a su moderna vida militante. No obstante, era importante no dejar nunca que Oriente siguiera su propio camino o se emancipara: la perspectiva canónica era que los orientales no tenían una tradición de libertad.
El gran drama de la obra de Lawrence reside en que simboliza la batalla que se libra en primer lugar para estimular a Oriente (sin vida, sin tiempo, sin fuerza) al movimiento; en segundo lugar, para imponer sobre ese movimiento una forma esencialmente occidental, y en tercer lugar, para mantener a ese Oriente nuevo y resurgido dentro de una visión personal cuyo modo retrospectivo incluye un poderoso sentimiento de fracaso y traición:
Tenía la intención de hacer una nueva nación, de restaurar una influencia perdida, de dar a veinte millones de semitas los fundamentos sobre los que construir el palacio soñado de sus pensamientos nacionales [...]. Todas las provincias sometidas del imperio no valían para mí la muerte de un niño inglés. Si he restituido en Oriente un poco de amor propio, un objetivo, un ideal; si he hecho más exigente el modelo de autoridad del blanco sobre el rojo, he preparado hasta cierto punto a esos pueblos para el nuevo tipo de gobierno en el que las razas dominantes olvidarán sus brutales realizaciones y los blancos, los rojos, los amarillos, los marrones y los negros se mantendrán unidos y sin miradas de desconfianza al servicio del mundo.
Nada de esto, ya fuera como intención, como experiencia real, o como proyecto fallido habría sido remotamente posible sin la perspectiva del orientalista blanco como punto de partida:
El judío en la metrópoli, en Brighton, el avaro, el adorar de Adonis, el libidinoso de Damasco revelaban toda la capacidad semita para la alegría, y expresaba la misma energía que nos ofrecía, en el polo opuesto, la ardiente renuncia de los esenios, o de los cristianos primitivos, o de los primeros califas que juzgaban que el camino del cielo era más fácil para los pobres de espíritu. El semita siempre ha oscilado entre la lujuria y la mortificación.
Lawrence en estas afirmaciones está respaldado por una tradición respetable que atraviesa, como el rayo de un faro, todo el siglo XIX. Su fuente lumínica es, por supuesto, «Oriente», y es lo suficientemente fuerte como para alumbrar tanto la topografía gruesa como la fina, que queda dentro de su alcance. El judío, el adorador de Adonis, el libidinoso de Damasco son signos no tanto de humanidad como de, podríamos decir, un campo semiótico llamado semítico y que la rama semítica del orientalismo ha convertido en un campo coherente. Dentro de este campo ciertas cosas son posibles:
Se podía atar a los árabes a una idea como a un cordel; la libre lealtad de sus espíritus les convertía en servidores fieles y sumisos. Ninguno de ellos intentaría escapar antes de que llegara el éxito y con él las responsabilidades, los deberes y los compromisos. Entonces, la idea moría y la obra terminaba en ruina [...]. Sin un credo, podrían ser llevados a las cuatro esquinas del mundo (aunque no al cielo) mostrándoles las riquezas y los placeres de la tierra; pero si en el camino [...] se encontraran al profeta de una idea sin techo bajo el que abrigar la cabeza y sin otro medio de subsistencia que la caza o la caridad, entonces ellos abandonarían toda su riqueza por su inspiración [...]. Eran tan inestables como el agua, y como el agua, quizá, al final prevalecerían. Desde la aurora de la vida, en sucesivas olas, habían estado precipitándose sobre las falacias de la carne. Todas las olas se rompieron [...]. Fue una de esas olas (y no la menor) la que yo pude levantar y enrollar antes del soplo de una idea, hasta que alcanzó su cresta y después cayó sobre Damasco. El reflujo de esta ola, retenido por la resistencia de los fuertes materiales, proporcionará el cuerpo de la siguiente ola cuando llegue el momento en que el mar se levante de nuevo.
Lawrence se introduce a sí mismo en el cuadro bajo la forma de condicional. Así, prepara la posibilidad de la penúltima frase, en la que, como manipulador de los árabes, se sitúa al frente de ellos. Como el Kurtz de Conrad, Lawrence se ha distanciado de la tierra para ser identificado con una nueva realidad, con el fin de ser capaz —dirá después— «de forzar a Asia [...] a adoptar la nueva forma que inexorablemente los tiempos nos traen».
La revuelta árabe adquiere significado únicamente cuando Lawrence se lo da; este significado, así comunicado a Asia, era un triunfo, «una expansión triunfal [...] en la que sentíamos que habíamos asumido el dolor, la experiencia de un otro y su personalidad». El orientalista se ha convertido ahora en el oriental representativo, a diferencia de otros observadores anteriores que habían participado en la vida del país, como Lane, y para quienes Oriente era algo que se mantenía cuidadosamente a distancia. Sin embargo, en Lawrence hay un conflicto irresoluble entre el hombre blanco y el oriental y, aunque no lo diga explícitamente, ese conflicto restablece en su mente el conflicto histórico entre Este y Oeste. Consciente de su poder sobre Oriente, consciente de su duplicidad, pero inconsciente de todo lo que en Oriente le sugiere que la historia, después de todo, es la historia y que incluso sin él los árabes resolverán sus querellas con los turcos, Lawrence reduce la narración completa de la revuelta (sus éxitos pasajeros y su amarga derrota) a la visión que él tiene _de sí mismo_ como una «guerra civil permanente» y sin solución.
En realidad, hemos soportado por amor hacia nosotros mismos los sufrimientos de otros o, al menos, por un beneficio futuro: y no podemos evitar saberlo a no ser que nos engañemos a nosotros mismos sobre nuestros sentimientos y nuestros motivos [...].
Parecía que no había ningún camino recto para nosotros, líderes en las tortuosidades de este laberinto moral, en la sucesión de estos círculos desconocidos o de estos motivos tumultuosos que siempre anulan o acentúan sus precedentes.
A este sentimiento íntimo de derrota, Lawrence iba a añadirle enseguida una teoría sobre «los viejos» que le robaron el triunfo. En cualquier caso, todo lo que le importa a Lawrence es que, como experto blanco, como heredero de años de sabiduría académica y popular sobre Oriente, es capaz de subordinar su estilo existencial al de los orientales, y después asumir el papel de profeta oriental que da forma a un movimiento en la «nueva Asia». Y cuando, por cualquier razón, el movimiento fracasa (es retomado por otros, sus objetivos son traicionados o sus sueños de independencia invalidados) es la desilusión de _Lawrence_ lo que cuenta. Lejos de ser simplemente un hombre perdido en el curso confuso de los acontecimientos, Lawrence se identifica completamente con la lucha de la nueva Asia naciente.
Mientras Esquilo había representado Asia lamentándose por sus pérdidas y Nerval había expresado su desilusión ante Oriente por no ser más fantástico de lo que él había querido, Lawrence _se convierte_ tanto en el continente de luto como en la conciencia subjetiva que expresa un desencanto casi cósmico. Lawrence y su visión, al final —y no solo gracias a Lowell Thomas y a Robert Graves—, se convierten en el símbolo mismo del problema oriental: Lawrence, en resumen, había asumido la responsabilidad de Oriente intercalando su experiencia instruida entre el lector y la historia. En realidad, lo que Lawrence presenta a su lector es el poder de un experto no mediatizado, el poder de ser, por un corto período de tiempo, Oriente. Todos los acontecimientos que se atribuyen a la revuelta árabe histórica se reducen, finalmente, a las experiencias de Lawrence en lo que a ella se refiere.
En este caso, por tanto, el estilo no es solo el poder de simbolizar esas enormes generalidades como Asia, Oriente o los árabes; es también una forma de desplazamiento e incorporación, por la cual una voz pasa a ser una historia completa y —para el occidental blanco, como lector o escritor— el único tipo de Oriente que es posible conocer. Igual que Renan había trazado el mapa del campo de posibilidades que se abría para los semitas en la cultura, el pensamiento y la lengua, también Lawrence traza el mapa del campo del espacio (y de hecho, se apropia de ese espacio) y del tiempo del Asia moderna. El efecto de este estilo es que pone a Asia al alcance de la mano de Occidente, para tocarla, pero solo durante un breve instante. Al final nos queda la sensación de una patética distancia que todavía «nos» separa de un Oriente destinado a sufrir su extrañeza como marca de su permanente enajenación con respecto a Occidente. Esta conclusión decepcionante se corrobora en el final de _A Passage to India_ ,* de E. M. Forster, donde Aziz y Fielding intentan reconciliarse y fracasan:
—¿Por qué ahora no podemos ser amigos? —dijo el otro, sujetándolo afectuosamente—. Es lo que yo quiero. Es lo que tú quieres.
Sin embargo, los caballos no lo querían: se apartaron bruscamente; la tierra no lo quería, y enviaba rocas junto a las cuales los jinetes tenían que pasar en fila india; los templos, el estanque, la cárcel, el palacio, los pájaros, los animales muertos y el Pabellón de los Huéspedes, que aparecieron al salir ellos del desfiladero y ver Mau a sus pies: ellos tampoco lo querían, y lo dijeron con sus cien voces: «No, todavía no»; y el cielo dijo: «No, ahí, no».
Este estilo, esta sólida definición es con la que Oriente siempre, lamentablemente, va a tropezar.
A pesar de su pesimismo, hay un mensaje político positivo detrás de estas frases. Como Cromer y Balfour sabían muy bien, el conocimiento y el poder superiores de Occidente podían ayudar a salvar el abismo existente entre el Este y el Oeste. La visión de Cromer tiene como complemento en Francia _Une enquête aux pays du Levant_ , de Maurice Barrès, donde se relata un viaje por Oriente Próximo en 1914. Como muchas otras obras anteriores, la _Enquête_ es una recapitulación en la que el autor no solo busca las fuentes y los orígenes de la cultura occidental en Oriente, sino que también reproduce a Nerval, Flaubert y Lamartine en sus viajes al Oriente. Para Barrès, sin embargo, hay una dimensión política adicional en este viaje: busca probar, a través de evidencias concluyentes, el papel constructivo de Francia en Oriente. Sin embargo, la diferencia entre los expertos franceses y los británicos sigue existiendo: los primeros se ocupan de una conjunción real de gentes y territorios, mientras que los segundos tratan de un dominio de posibilidades espirituales. En opinión de Barrès, donde mejor se ve la presencia de Francia es en las escuelas francesas de Alejandría: «Es encantador ver a esas pequeñas niñas orientales acoger y reproducir tan vivamente la _fantaisie_ y la melodía [en su francés hablado] de la Île-de-France». Aunque Francia no posea realmente colonias allí, eso no significa que no tenga posesiones:
Hay allí, en Oriente, un sentimiento hacia Francia tan religioso y fuerte que es capaz de absorber y conciliar todas nuestras aspiraciones más diversas. En Oriente, nosotros representamos espiritualmente la justicia y la categoría del ideal. Inglaterra es poderosa allí; Alemania, todopoderosa; pero nosotros poseemos las almas de los orientales.
Discutiéndolo estruendosamente con Jaurés, este célebre doctor europeo propone vacunar a Asia contra sus propios defectos, occidentalizar a los orientales, ponerles en saludable contacto con Francia. Sin embargo, incluso en estos proyectos, la visión de Barrès preserva la distinción entre Este y Oeste que pretende atenuar:
¿Cómo podremos formar una elite intelectual, con la que poder trabajar, de orientales que no estén desarraigados, que continúen evolucionando de acuerdo con sus propias normas, que sigan llenos de sus tradiciones familiares y que así formulen un vínculo entre nosotros y la masa de nativos? ¿Cómo estableceremos relaciones con vistas a preparar el camino para llegar a acuerdos y tratados que serían la forma deseada de nuestro futuro político [en Oriente]? Todas estas cosas son, finalmente, tratar de suscitar en estos pueblos extraños el gusto por mantener contacto con nuestra inteligencia, _aunque este_ _gusto pueda, de hecho, provenir de sus destinos nacionales_. (La cursiva es del propio Barrès.)
Como, a diferencia de Lawrence y Hogarth (cuyo libro _The Wandering Scholar_ es un relato totalmente informativo en el que no hay rastro de romanticismo alguno de dos viajes a los países del Mediterráneo oriental en 1896 y 1910), Barrès habla de un nuevo mundo de probabilidades lejanas, está más preparado para imaginar un Oriente que sigue su propia vida. Sin embargo, el lazo (o la correa) entre Este y Oeste por el que aboga, está concebido para permitir una variedad constante de presión intelectual que va desde el Oeste hasta el Este. Barrès ve las cosas no en términos de batallas o de aventuras espirituales, sino en los de un imperialismo intelectual tan enraizado como sutil. La visión británica, encarnada por Lawrence, es la de la gran corriente de Oriente, de los pueblos, de las organizaciones políticas y de los movimientos guiados y mantenidos a raya por la experta tutela del hombre blanco; Oriente es «nuestro» Oriente, «nuestra» gente, «nuestros» dominios. Los británicos hacían menos discriminaciones entre las elites y las masas que los franceses, cuyas percepciones se basaban siempre en las minorías y en las presiones insidiosas ejercidas por la comunión espiritual entre Francia y sus retoños coloniales. El agente orientalista británico —Lawrence, Bell, Philby, Storrs, Hogarth— retomó, durante y después de la Primera Guerra Mundial, el papel de experto y aventurero excéntrico (creado y personificado en el siglo XIX por Lane, Burton, Hester, Stanhope), así como el de autoridad colonial que ocupaba una posición privilegiada al lado del mandatario nativo: Lawrence con los hashimíes y Philby con la dinastía saudí son los dos ejemplos más conocidos. La doctrina de los expertos británicos sobre las cuestiones orientales se formó en torno al consenso de la ortodoxia y de la autoridad soberana; los expertos orientales franceses se ocuparon entre las dos guerras de la heterodoxia y de los lazos espirituales y excéntricos. No es casualidad que las dos personalidades eruditas más importantes de este período, una inglesa y otra francesa, fueran H. A. R. Gibb y Louis Massignon; el primero centraba su interés en la noción de _sunna_ (u ortodoxia) del islam, mientras que el segundo lo hacía en el personaje sufí teosófico y casi cristiano Mansur al-Hallay. Volveré a hablar de estos dos grandes orientalistas un poco más adelante.
Si me he ocupado en este capítulo de los agentes imperiales y de los políticos más que de los eruditos ha sido para acentuar el gran giro que se produjo en el orientalismo, en el conocimiento de Oriente y en los contactos con él. Acentuamos el hecho de que el orientalismo pasó de ser una actitud académica a ser una actitud _instrumental_. Lo que supone este giro es tanto un cambio en la actitud como en el orientalista individual, el cual no necesita ya considerarse a sí mismo —como Lane, Sacy, Renan, Caussin, Müller y otros— miembro de una especie de comunidad gremial que tiene sus propias tradiciones y rituales internos. Ahora el orientalista se ha convertido en el representante de su cultura occidental; ahora es un hombre que concentra en su propia obra una dualidad importante de la que esa obra (sin tener en cuenta su forma específica) es una expresión simbólica: conciencia occidental, conocimiento, ciencia así como los más mínimos detalles orientales. Formalmente, el orientalista se ve a sí mismo llevando a cabo la unión entre Oriente y Occidente, pero principalmente lo hace reafirmando la supremacía tecnológica, política y cultural de Occidente. En una unión de este tipo la historia está totalmente atenuada, por no decir eliminada. Considerada como una corriente de desarrollo, como el hilo conductor de una narración o como una fuerza que se despliega sistemática y materialmente en el tiempo y en el espacio, la historia humana —sea del Este o del Oeste— se subordina a una concepción esencialista e idealista de Occidente y Oriente. Porque se siente situado en el mismo borde de la línea divisoria entre Oriente y Occidente, el orientalista no solo habla de vastas generalidades, sino que también busca convertir cada uno de los aspectos de la vida oriental u occidental en un signo no mediatizado de una u otra mitad geográfica.
Esta alternancia en las obras del orientalista entre su personalidad de experto y su personalidad de testigo y de espectador en tanto que representante de Occidente está elaborada de manera preeminente en términos visuales. Aquí tenemos un párrafo típico (citado por Gibb) de la obra clásica de Duncan Macdonald _The Religious Attitude and Life in Islam_ (1909):
Los árabes no se muestran como especialmente fáciles de convencer, sino más bien como hombres positivos y materialistas que plantean preguntas, que se ríen de sus propias supersticiones y usos y que gustan de poner a prueba lo sobrenatural; y todo esto de una manera curiosamente atolondrada y casi infantil.
El verbo principal de esta oración es _mostrar_ , que nos da a entender que los árabes se exponen a sí mismos (voluntaria o involuntariamente) para que se les haga un examen de experto. El número de atributos que se les asignan por su calidad de simples aposiciones hace que «los árabes» adquieran una especie de ingravidez existencial; «los árabes», de esta manera, son reincorporados a la muy extensa designación, corriente en el pensamiento antropológico moderno, de «infantes primitivos». Macdonald sugiere también que para hacer este tipo de descripciones hay una posición particularmente privilegiada ocupada por el orientalista occidental, cuya función representativa es precisamente _mostrar_ lo que necesita ser visto. Cualquier historia específica puede verse en el límite, o en la frontera sensible, de Oriente y Occidente juntos. La dinámica compleja de la vida humana —lo que yo he llamado historia como narración— se convierte en algo irrelevante o trivial en comparación con la visión circular según la cual los detalles de la vida oriental sirven simplemente para reafirmar la orientalidad del tema y la occidentalidad del observador.
Si esta visión recuerda de alguna manera a la de Dante, es porque no hemos percibido las enormes diferencias que hay entre este Oriente y el de Dante. La evidencia aquí pretende ser (y probablemente es considerada como tal) científica; su antecedente, hablando desde un punto de vista genealógico, es la ciencia europea intelectual y humana del siglo XIX. Además, Oriente no es solo una maravilla, un enemigo o una rama del exotismo; es una realidad política llena de grandes y significativas consecuencias. Como Lawrence, Macdonald no puede realmente separar sus características de representante occidental de su papel de erudito. Así, su visión del islam, en la misma medida que la visión que Lawrence tenía de los árabes, entremezcla la _definición_ del objeto con la _identidad_ de la persona que lo define. Todos los orientales árabes deben estar acomodados para que se les pueda observar a través de la visión de un tipo oriental tal y como la construye el erudito occidental, y deben también estar acomodados para figurar en un encuentro específico con Oriente en el que el occidental abarca de nuevo la esencia de Oriente como una consecuencia de su extrañamiento íntimo. Para Lawrence, como para Forster, esta sensación anterior provoca tanto el desánimo como el fracaso personal; para eruditos como Macdonald, su extrañamiento da más fuerza al discurso orientalista.
Y extiende ampliamente este discurso por el mundo de la cultura, de la política y de la actualidad. En el período de entreguerras, como podemos juzgar fácilmente a partir de las novelas de Malraux, por ejemplo, las relaciones entre Este y Oeste adquirieron una difusión a la vez extensa e inquieta. Los signos de las reivindicaciones orientales de independencia política estaban en todas partes. Es cierto que los aliados fomentaron estas reivindicaciones en el Imperio otomano desmembrado y, como es evidente por la revuelta árabe y sus repercusiones, estas enseguida se convirtieron en un problema. Oriente, entonces, parecía constituir un desafío no solo para Occidente en general, sino para el espíritu, el conocimiento y la dominación de Occidente. Después de todo un siglo de intervención constante en Oriente (y de su estudio), el papel de Occidente en un Oriente afectado por la crisis de la modernidad parecía bastante más delicado. Estaban las cuestiones de la ocupación total, estaban las cuestiones de los territorios bajo mandato; estaban las cuestiones de la competición europea en Oriente; estaban las cuestiones de las relaciones con las elites nativas y los movimientos populares nativos, y de las reivindicaciones de autogobierno e independencia; estaba también el asunto de los contactos culturales entre Oriente y Occidente. Cada uno de estos problemas forzaban a una reconsideración del conocimiento occidental sobre Oriente. Un erudito de tanto valor como Sylvain Lévi, presidente de la Société Asiatique entre 1928 y 1935, profesor de sánscrito en el Collège de France, reflexionó seriamente en 1925 sobre la urgencia del problema Este-Oeste:
Nuestro deber es comprender la civilización oriental. El problema humanístico, que consiste, en el plano intelectual, en hacer un esfuerzo benévolo e inteligente para comprender las civilizaciones extranjeras tanto en sus formas pasada como futuras, se nos plantea, a nosotros franceses [aunque sentimientos similares podían haber sido expresados por un inglés: el problema era un problema _europeo_ ] en la práctica, en lo que respecta a nuestras grandes colonias asiáticas.
[...] Estas poblaciones son las herederas de una larga tradición histórica, artística y religiosa, de la cual no han perdido del todo la conciencia y la cual están ansiosos de prolongar. Hemos asumido la responsabilidad de intervenir en su desarrollo, a veces sin consultarles, a veces en respuesta a sus peticiones. [...] Nosotros pretendemos, con o sin razón, representar una civilización superior y por el derecho que dicha superioridad nos confiere, superioridad que hemos afirmado con mucha seguridad y que los indígenas no han podido contestar, hemos puesto en duda todas sus tradiciones.
[...] De una manera general, por tanto, dondequiera que el europeo haya intervenido, el indígena ha percibido, con una desesperación verdaderamente desgarradora, que su buena suerte en el terreno moral más todavía que en el material, lejos de aumentar, disminuía. Todo lo que era la base de su vida social vacilaba y se tambaleaba bajo sus pies y los pilares de oro sobre los que creía reconstruir de nuevo su vida no le parecían más que cartón dorado.
Esta decepción se traduce en un rencor que se extiende de un extremo al otro de Oriente, y el rencor está muy cerca de convertirse en odio, y el odio solo espera el momento para pasar a la acción.
Si Europa, por pereza o incomprensión, no hace el esfuerzo que solo sus intereses requieren de ella, _el drama asiático estará cerca de_ _convertirse en una crisis_.
Es aquí donde la ciencia, que es una forma de vida y un instrumento de política —es decir, en lo que nos concierne— debe hacer un esfuerzo para penetrar en la civilización y en la vida indígenas y en su espíritu íntimo para descubrir sus valores fundamentales y sus características, duraderas, mejor que asfixiar la vida nativa con la amenaza incoherente de las importaciones europeas. Debemos ofrecernos a nosotros mismos a estas civilizaciones como hacemos con otros de nuestros productos en el mercado de intercambio local. [La cursiva es del original.]
Lévi no tiene ninguna dificultad en conectar el orientalismo con la política, ya que la larga (o más bien prolongada) intervención de Occidente en Oriente no puede ser negada ni en sus consecuencias para el conocimiento ni en sus efectos sobre el desgraciado indígena; ambos se suman para formar lo que podrá ser un futuro amenazante. A pesar de todo el humanismo que expresa, de toda la solicitud admirable que tiene por los otros, Lévi concibe el momento presente en términos desagradablemente estrechos. Imagina que los orientales sienten que su mundo está amenazado por una civilización superior, pero lo que les hace moverse no son los deseos positivos de libertad, independencia política o conquistas culturales _según sus propios criterios_ , sino el rencor o la maldad celosa. La panacea que Lévi ofrece ante este giro de los acontecimientos de tan mal aspecto es poner a la venta Oriente para el consumidor occidental, ponerlo ante él como una de entre tantas mercancías que llaman su atención. De un solo tiro desintegrarás Oriente (al hacerle pensar que está a la altura en el mercado europeo de las ideas) y apaciguarás el miedo occidental ante el maremoto oriental. En el fondo, naturalmente, el principal punto de Lévi —y su confesión más significativa— es que, a menos que se haga algo con Oriente, «el drama asiático se aproximará a un punto de crisis».
Asia sufre, pero con su sufrimiento amenaza a Europa: la eterna frontera erizada entre Este y Oeste se mantiene casi sin cambios desde la antigüedad clásica. Lo que Lévi dice como el más augusto de los orientalistas modernos encuentra un eco menos sutil en los humanistas de la cultura. Por ejemplo, en 1925 la revista francesa _Le cahiers du mois_ realizaba una encuesta entre notables personalidades intelectuales; entre los escritores encuestados había tanto orientalistas (Lévi, Émile Senart), como hombres de letras (André Gide, Paul Valéry y Edmond Jaloux). Las preguntas trataban sobre las relaciones entre Oriente y Occidente, con un propósito e incluso con una cierta imprudencia provocativa, lo cual era un indicativo del ambiente cultural del período. Reconoceremos inmediatamente cómo el tipo de ideas promulgadas por la erudición orientalista había alcanzado entonces el nivel de verdades aceptadas y casi indiscutibles. Una de las preguntas era si Oriente y Occidente eran mutuamente impenetrables (la idea procedía de Maeterlinck) o no; otra consistía en si la influencia oriental representaba _«un peril grave»_ —en palabras de Henri Massis— para el pensamiento francés, y la tercera versaba sobre aquellos valores en la cultura occidental a los que se podía adscribir una superioridad sobre Oriente. La respuesta de Valéry me parece digna de ser citada tanto por lo claras que son las líneas de su argumentación como por lo consagradas que estaban, al menos a principios de siglo:
Desde un punto de vista cultural, no creo que tengamos mucho que temer _actualmente_ de la influencia oriental. No nos es desconocida. Debemos a Oriente todos los principios de nuestras artes y la mayor parte de nuestros conocimientos. Podríamos acoger muy bien todo lo que nos viniera de Oriente si algo nuevo pudiera venir de allí, lo cual dudo mucho. Esta duda es precisamente nuestra garantía y nuestra arma europea.
Además, de lo que se trata realmente en estos temas es de _digerir_. Pero eso ha sido siempre la gran especialidad de la mente europea a lo largo de las diferentes épocas. Nuestro papel, por tanto, es mantener este poder de elección, de comprensión universal y de transformación de todo en sustancia nuestra, capacidades que nos han hecho lo que somos. Los griegos y los romanos nos mostraron cómo actuar con los monstruos de Asia, cómo tratarlos a través del análisis, cómo extraer de ellos su quintaesencia. [...] La cuenca del Mediterráneo me parece como un vaso cerrado, donde las esencias del vasto Oriente siempre han llegado para ser condensadas. [La cursiva y la omisión son del original.]
Si la cultura europea, de manera general, ha digerido Oriente, Valéry era consciente de que una de las agencias específicas que había ejecutado esta labor había sido el orientalismo. En el mundo de los principios de autodeterminación nacional de Wilson, Valéry se apoya confiadamente en los análisis para descartar la amenaza oriental. «El poder de elección» consiste, esencialmente para Europa, primero en reconocer que Oriente es el origen de la ciencia europea y luego en tratarlo como un origen caduco. Así, en otro contexto, Balfour podía considerar que los habitantes de Palestina tenían un derecho prioritario sobre la tierra, pero estaban lejos de tener la autoridad subsiguiente para mantenerla; los simples deseos de 700.000 árabes, dijo, en ningún momento se podían comparar con el destino de un movimiento colonial esencialmente europeo.
Asia representaba así la desagradable probabilidad de una repentina erupción que iba a destruir «nuestro» mundo, como John Buchan dijo en 1922:
La Tierra está bullendo de poder incoherente y de inteligencia desorganizada. ¿Han pensado alguna vez en el caso de China? Allí tienen millones de mentes rápidas que revientan fabricando nimiedades. No tienen ninguna dirección, ni poder que los conduzca y así todos sus esfuerzos son vanos y el mundo se ríe de China.
Sin embargo, si China se organizara (como lo haría) ya no sería una cuestión de risa. El esfuerzo de Europa, por tanto, debía consistir en mantenerse como lo que Valéry llamó « _une machine puissante_ » que absorbía lo que podía de fuera de Europa y lo reconvertía todo de tal forma que le fuera útil desde un punto de vista intelectual y material, y que mantenía Oriente selectivamente organizado (o desorganizado). Esto solo se podía hacer a través de una visión clara y del análisis. A menos que Oriente no se observara como lo que era, su poder —militar, material y espiritual— tarde o temprano sumergiría a Europa. Los grandes imperios coloniales, los grandes sistemas de represión sistemáticos existieron para parar esta temida eventualidad. Los sujetos coloniales, como George Orwell los observó en Marrakesh en 1939, solo debían ser concebidos como un tipo de emanación continental, africana, asiática u oriental:
Cuando caminas por una ciudad como esta —200.000 habitantes, de los cuales al menos 20.000 no poseen literalmente nada excepto los andrajos que los envuelven—, cuando ves cómo vive la gente y, más aún, lo fácilmente que muere, siempre es difícil creer que caminas entre seres humanos. En realidad, todos los imperios coloniales se fundamentan en este hecho. La gente tiene caras morenas, y además ¡tienen tantas! ¿Son ellos realmente de la misma carne que tú? ¿Tienen siquiera nombre? ¿O son simplemente una especie de materia morena indiferenciada, tan individualizados más o menos como las abejas o los insectos coralinos? Ellos salen de la tierra, sudan y pasan hambre durante unos cuantos años, y después se hunden en los montículos sin nombre del cementerio y nadie se da cuenta de que se han ido. E incluso las tumbas son absorbidas pronto por la tierra.
Aparte de los caracteres pintorescos propuestos a los lectores europeos por algunas novelas exóticas de escritores menores (Pierre Loti, Marmaduke Pickthall, etc.), el no europeo que conocen los europeos es precisamente el que describe Orwell. Es un personaje cómico o un átomo en una vasta colectividad, designado, ya sea en el discurso ordinario o en el discurso cultivado, como un tipo indiferenciado llamado oriental, africano, amarillo, moreno o musulmán. El orientalismo ha contribuido a crear este tipo de abstracciones por su poder de generalización, que convierte a los ejemplares de una civilización en portadores de los valores, las ideas y las posiciones que los orientalistas, por su parte, habían encontrado en «Oriente» y habían transformado en una corriente cultural común.
Si pensamos que en 1934, Raymond Schwab publicó su brillante biografía de Anquetil-Duperron —y comenzó ciertos estudios que debían situar al orientalismo en su propio contexto cultural—, debemos señalar también que lo que hizo contrastaba y se oponía totalmente a lo que pensaban y sentían sus colegas artistas e intelectuales, para los que Oriente y Occidente seguían siendo las mismas abstracciones de segunda mano que habían sido para Valéry. No se puede decir en puridad que Pound, Eliot, Yeats, Arthur Waley, Fenollosa, Paul Claudel (en su _Connaisance de l'est_ ), Victor Ségalen y otros hubieran ignorado la «sabiduría de Oriente», como Max Müller la llamó unas cuantas generaciones antes. Más bien que el mundo de la cultura consideró Oriente y el islam en particular con esa desconfianza que siempre ha pesado sobre su actitud erudita con respecto a Oriente. Podemos encontrar un bueno y muy explícito ejemplo de esta actitud en las diversas conferencias sobre «Oriente y Occidente» que, en 1924, dio en la Universidad de Chicago Valentine Chirol, famoso periodista europeo que tenía una gran experiencia en Oriente. Su claro propósito era demostrar a los estadounidenses cultivados que Oriente no estaba tan lejos como quizá ellos creían o sentían. Su línea de pensamiento es sencillo: Oriente y Occidente son opuestos el uno al otro de una manera irreductible, y Oriente —en particular el «mahometismo»— es una de «las grandes fuerzas mundiales» responsables de «las líneas de discrepancia más profundas del mundo». Me parece que los títulos de sus seis conferencias dan una buena idea de las generalizaciones majestuosas de Chirol: «Su antiguo campo de batalla», «La desaparición del Imperio otomano: el caso particular de Egipto», «La gran experiencia británica en Egipto», «Protectorados y mandatos», «Un nuevo factor: el bolchevismo», y, por último, «Algunas conclusiones generales».
A las exposiciones sobre Oriente destinadas a un público relativamente amplio, como las de Chirol, podemos añadir el testimonio de Élie Faure, que en sus reflexiones apela, como Chirol, a la historia, a sus conocimientos particulares sobre la cultura y a la ya familiar oposición entre el occidentalismo blanco y el orientalismo de color. En sus reflexiones encontramos algunas paradojas, como cuando dice « _le carnage permanent de l'indifférence orientale_ » (ya que, al contrario que «nosotros», «ellos» no tienen ninguna concepción de la paz), Faure continúa mostrando que los cuerpos de los orientales son perezosos, afirma que Oriente no tiene ninguna concepción de la historia, de la nación o de la _patrie_ , y que Oriente es esencialmente místico, etc. Faure argumenta asimismo que, a menos que el oriental no aprenda a ser racional, a desarrollar técnicas de conocimiento y de positividad, no podrá haber ninguna _aproximación_ entre Este y Oeste. En el ensayo de Fernand Baldensperger _«où s'affrontent l'Orient et l'Occident intellectuels»_ , expone lo que es ya un lugar común, esto es, el dilema Este-Oeste, aunque habla también de que existe y se constata un desdén oriental inherente hacia la idea, la disciplina mental y la interpretación racional.
Dichos como si provinieran de las profundidades de la cultura europea, por escritores que, de hecho, creen hablar en nombre de esta cultura, estos tópicos (ya que son perfectas _idées reçues_ ) no se pueden comprender simplemente como manifestaciones de una arrogancia provinciana. No lo son; por ello —como debe ser evidente para quien conozca un poco alguna obra de Faure o de Baldensperger— son todavía algo más paradójico. Dichas manifestaciones tienen como base la transformación de la ciencia profesional y exigente que es el orientalismo, cuya función en la cultura del siglo XIX había sido restablecer para Europa una porción perdida de humanidad, pero que en el siglo XX se había convertido en un instrumento político y, lo que es más importante, en un código por el cual Europa podía interpretar en su beneficio a Oriente y a sí misma. Por razones que ya he expuesto anteriormente, el orientalismo moderno llevaba ya la impronta del gran miedo europeo hacia el islam, miedo que aumentó con los desafíos políticos de la época de _entre-deux-guerres_. Lo que quiero decir con esto es que lo que era la especialidad relativamente inocente de la filología, se convirtió en una disciplina capaz de dirigir movimientos políticos, de administrar colonias y de hacer declaraciones casi apocalípticas, presentando la difícil misión civilizadora del hombre blanco; esta metamorfosis actuó dentro de una cultura que se pretendía liberal, preocupada por unos criterios que presumían de catolicidad, pluralidad y apertura mental. En realidad, a lo que dio lugar fue a todo lo opuesto a lo liberal: el endurecimiento de la doctrina y del significado de lo que la «ciencia» impartía como «verdad». Ya que, si esta verdad se reservaba el derecho de juzgar que Oriente era inalterablemente oriental, como ya he indicado anteriormente, entonces el liberalismo no era más que una forma de opresión y de prejuicios.
Normalmente, desde el interior de la cultura, nunca se ha reconocido —y no se reconoce— la extensión de este no liberalismo, y esto es debido a razones que este libro está intentando explorar. Sin embargo, en alguna ocasión ha sido puesto en tela de juicio, lo que no deja de ser reconfortante. Veamos un ejemplo del libro de I. A. Richards, _Mencius on the Mind_ (1923); en las líneas que siguen podemos fácilmente sustituir la palabra «chinos» por «orientales»:
En lo que se refiere al efecto producido en Occidente por el mayor conocimiento del pensamiento chino, es interesante señalar que un escritor al que no es posible calificar de ignorante o descuidado, como M. Étienne Gilson, puede, sin embargo, hablar, en el prefacio inglés de _The philosophy of St. Thomas Aquinus_ , de la filosofía tomista, diciendo que esta «acepta y reúne toda la tradición humana». Así es como todos nosotros razonamos; para nosotros, el mundo occidental es siempre el Mundo (o la parte del mismo que cuenta); pero un observador imparcial quizá diría que este tipo de provincianismo es peligroso. Y en Occidente todavía no somos lo suficientemente felices como para estar seguros de que no estamos sufriendo sus efectos.
Richards exige en su libro que se ejerza lo que él llama la definición múltiple, esto es, un tipo auténtico de pluralismo que elimine la rigidez de los sistemas de definición. Aceptemos o no su ataque contra el provincianismo de Gilson, podemos abrazar su proposición de que el humanismo liberal, del que el orientalismo ha sido históricamente uno de sus departamentos, _retarda_ la aparición de una significación general, que va ampliándose y que permite llegar a una comprensión verdadera. Lo que sustituyó a la significación general en el orientalismo del siglo XX —es decir, en el interior del dominio técnico— es el tema del que nos va a ocupar inmediatamente.
### III
### El orientalismo anglo-francés moderno
### en plena expansión
Nos hemos acostumbrado a la idea de que cualquier experto contemporáneo en algún aspecto de Oriente es un especialista en «estudios de áreas culturales» ( _area studies_ ), y, por ello, hemos perdido la noción de que, hasta más o menos la Segunda Guerra Mundial, el orientalista se consideraba un experto en materias generales (con grandes conocimientos específicos) que había desarrollado un gran talento para hacer afirmaciones totalizadoras. Con esto quiero decir que cuando formulaba una idea no muy complicada sobre, por ejemplo, gramática árabe o religión hindú, se entendía que el orientalista (y él mismo lo entendía así) hacía una afirmación sobre Oriente en su totalidad y, de este modo, lo totalizaba. Así, cualquier estudio concreto de algún aspecto del material oriental también confirmaba, de manera resumida, la profunda orientalidad de ese material. Y como, de modo general, se creía que todo Oriente presentaba una profunda cohesión orgánica, para el erudito orientalista era perfectamente correcto desde un punto de vista hermenéutico considerar que la evidencia material de la que se ocupaba le debía llevar, en última instancia, a una mejor comprensión de aspectos tales como el carácter, la mente, el _ethos_ o la concepción del mundo oriental.
En las dos primeras partes de este libro he presentado argumentos similares a estos a propósito de períodos más antiguos de la historia del pensamiento orientalista. En su historia reciente lo que nos interesa, sin embargo, es la diferencia entre los períodos inmediatamente anterior y posterior a la Primera Guerra Mundial. En ambos períodos, como en los más antiguos, Oriente es oriental cualquiera que sea el estilo o la técnica que se emplee para describirlo; la diferencia entre los dos períodos en cuestión viene determinada por la _razón_ que daba el orientalista para ver la orientalidad esencial de Oriente. Un buen ejemplo de la razón fundamental anterior a la guerra, la podemos encontrar en el párrafo siguiente de Snouck Hurgronje, extraído de la reseña que hizo en 1899 del libro de Eduard Sachau _Muhammedanisches Recht_ :
[...] el derecho que, en la práctica, debía hacer todavía mayores concesiones a los usos y costumbres del pueblo y a la arbitrariedad de sus dirigentes, conservaba, sin embargo, una considerable influencia sobre la vida intelectual de los musulmanes. Por eso, siempre ha sido —y todavía lo es para nosotros— un importante tema de estudio no solo por razones abstractas ligadas a la historia del derecho, la civilización y la religión, sino también por cuestiones prácticas. A medida que las relaciones de Europa con el Oriente musulmán se vayan haciendo más íntimas y a medida que los países musulmanes vayan cayendo bajo la soberanía europea, será más importante para nosotros, europeos, conocer bien la vida intelectual, la ley religiosa y el sustrato conceptual del islam.
Aunque Hurgronje acepta que algo tan abstracto como el derecho islámico se sometió ocasionalmente a la presión de la historia y de la sociedad, le interesa mucho más conservar la abstracción para utilizarla intelectualmente, porque en las grandes líneas de su pensamiento, «el derecho islámico» confirma la disparidad entre Este y Oeste. La distinción entre Oriente y Occidente no era para él un estereotipo puramente académico o popular; muy al contrario dicha distinción significaba la relación de poder histórico y esencial entre los dos. El conocimiento de Oriente prueba, amplía o profundiza la diferencia por la cual la soberanía europea (la frase tiene sus venerables orígenes en el siglo XIX) se extiende de manera efectiva sobre Asia. Conocer Oriente como un todo es, pues, conocerlo porque se te confía a ti, si eres un occidental.
Encontramos un fragmento casi simétrico al de Snouck Hurgronje en el párrafo con el que Gibb concluye su artículo «Literature» en _The Legacy of Islam_ , publicado en 1931. Después de haber descrito los tres contactos casuales entre el Este y el Oeste que se remontan al siglo XVIII, Gibb pasa al siglo XIX:
Después de estos tres momentos de contacto casual, los románticos alemanes se volvieron de nuevo hacia el Este y, por primera vez, tenían el propósito de abrir una vía para que la verdadera herencia de la poesía oriental penetrase en la poesía europea. Parecía que el siglo XIX, con su nuevo sentimiento de poder y de superioridad, les cerraba la puerta en las narices. Hoy, por otro lado, hay signos de cambio. La literatura oriental se ha empezado a estudiar por sí misma y se está adquiriendo una nueva comprensión del Este. A medida que Oriente vaya recobrando su lugar legítimo en la vida de la humanidad, la literatura oriental podrá, una vez más, desempeñar su función histórica y ayudarnos a liberarnos de las concepciones opresivas que limitan todo lo que, en la literatura, en el pensamiento y en la historia, es importante para nuestro propio segmento del globo.
La expresión de Gibb, «por sí misma», es diametralmente opuesta a la cadena de razones subordinadas a la declaración de Hurgronje acerca de la soberanía europea sobre Oriente. Lo que persiste, no obstante, es esa identidad global, inviolable de una cosa llamada «el Este» y de otra llamada «el Oeste». Estas entidades tienen utilidad la una para la otra, y Gibb evidentemente tiene la loable intención de demostrar que la influencia de la literatura oriental en la occidental no es necesariamente (por sus resultados) lo que Brunetière ha llamado «una desgracia nacional». Por el contrario, Gibb quiere decir que se puede afrontar Oriente como una especie de desafío humanista para los confines locales del etnocentrismo occidental.
Aunque Gibb haya abordado por adelantado la idea de _Weltliteratur_ , de Goethe, su llamamiento al estímulo humanístico recíproco entre el Este y el Oeste refleja el cambio en las realidades políticas y culturales de después de la guerra. La soberanía que ejercía Europa sobre Oriente no había terminado, pero con todo había evolucionado. En el Egipto británico, por ejemplo, se había pasado de una aceptación más o menos tranquila por parte de los nativos, a una situación política cada vez más contestada por las reivindicaciones displicentes de independencia. Estos fueron unos años de constantes problemas para los británicos con Zaghlul, el partido Wafd, etc. Además, desde 1925 se había producido una recesión económica mundial, y esto había incrementado la tensión que refleja la prosa de Gibb. Sin embargo, el mensaje específicamente cultural que subyace en lo que dice es el más fuerte; parece decir a sus lectores: prestad atención a Oriente, porque puede serle útil a la mente occidental que lucha por vencer la estrechez de espíritu, la especialización opresiva y las perspectivas limitadas.
De Hurgronje a Gibb, el terreno ha cambiado considerablemente, como lo han hecho las prioridades; ya no se admite sin apenas controversia que la dominación europea sobre Oriente sea un hecho casi natural, ni se asume que Oriente necesite la iluminación occidental. Lo que importa, durante estos años de entreguerras, es una autodefinición cultural que trascienda lo provinciano y lo xenófobo. Para Gibb, Occidente necesita, pues, a Oriente como algo para ser estudiado, porque libera el espíritu de una especialización estéril, porque calma la aflicción causada por un egocentrismo estrecho, excesivo y nacionalista, y porque ayuda a comprender las cuestiones realmente centrales en el estudio de la cultura. Si Oriente, en esta nueva e incipiente dialéctica de la conciencia cultural, aparece como un socio es, en primer lugar, porque ahora supone un desafío mayor del que constituía antes, y en segundo, porque Occidente está entrando en una fase de crisis cultural relativamente nueva, causada, en parte, por el debilitamiento de la soberanía occidental sobre el resto del mundo.
Por tanto, durante la época de entreguerras vamos a encontrar elementos comunes entre las mejores obras orientalistas —representadas por las impresionantes carreras de Massignon y el propio Gibb— y la mejor erudición humanista del período. Así, la actitud totalizadora de la que he hablado antes puede ser considerada el equivalente orientalista de los intentos llevados a cabo por las humanidades puramente occidentales para entender la cultura _como un todo_ de manera antipositiva, intuitiva y comprensiva. Tanto el orientalista como el no orientalista comienzan a sentir que la cultura occidental atraviesa una importante etapa de crisis que ha sido impuesta por amenazas tales como la barbarie, la estrechez de los intereses técnicos, la aridez moral, los nacionalismos estridentes, etc. La idea de utilizar textos específicos, por ejemplo, para trabajar desde lo específico a lo general (para comprender la vida completa de un período y, en consecuencia, de una cultura) es común en los humanistas occidentales que se inspiran en la obra de Wilhelm Dilthey, y en los más encumbrados eruditos orientalistas, como Massignon y Gibb. El proyecto de revitalizar la filología —que encontramos en la obra de Curtis, Vossler, Auerbach, Spitzer, Gundolf y Hofmannsthal— tiene así su contrapartida en el nuevo vigor que infunden a la filología orientalista estrictamente técnica los estudios de Massignon sobre lo que él ha denominado el léxico místico, el vocabulario de la devoción islámica, etc.
No obstante, hay otra conjunción más interesante entre el orientalismo en esta fase de su historia y las ciencias del hombre europeas ( _sciences de l'homme_ ), el _Geisteswissenschaften_ contemporáneo a él. Debemos señalar en primer lugar que los estudios culturales no orientalistas eran forzosamente los más inmediatamente sensibles a las amenazas hechas a la cultura humanística por la especialización técnica amoral y tendente a exagerar su importancia, las cuales estaban representadas, al menos en parte, por el auge del fascismo en Europa. Esta sensibilidad hizo que las preocupaciones del período de entreguerras se extendieran al período que siguió a la Segunda Guerra Mundial. Podemos encontrar un testimonio elocuente, erudito y personal de esta sensibilidad en la magistral obra de Erich Auerbach, _Mimesis_ ,* y en sus posteriores reflexiones metodológicas, como en _Philology_. Nos dice que escribió _Mimesis_ durante su exilio en Turquía y que la obra, en gran medida, pretendía ser un intento de _ver_ la evolución de la cultura occidental casi en el último momento en el que esta todavía conservaba su integridad y su coherencia como civilización; por tanto, se proponía escribir una obra general basada en unos análisis textuales específicos que pusieran de manifiesto los principios de las realizaciones literarias occidentales en toda su variedad, su riqueza y su fertilidad. Su objetivo fundamental era, por tanto, hacer una síntesis de la cultura occidental en la que la propia síntesis tuviera la misma importancia que el gesto mismo de hacerla. Gesto que era posible, según Auerbach, gracias a lo que él llamaba «el humanismo burgués tardío». El detalle concreto se convertía así en un símbolo muy mediatizado del proceso de la historia mundial.
No menos importante para Auerbach —y esto se puede aplicar al orientalismo— era la tradición humanística de compromiso con una cultura o literatura nacional que no fuera la suya. Auerbach ponía como ejemplo de este compromiso a Curtis, cuya prodigiosa producción le mostraba que este, como alemán, había elegido de modo deliberado dedicarse profesionalmente a las literaturas romances y no a la germánica. No por casualidad Auerbach terminó sus reflexiones otoñales con una cita significativa del _Didascalicon_ , de Hugo de Saint-Victor: «El hombre que encuentra su patria dulce es todavía un tierno principiante; aquel para el que cualquier tierra es su tierra natal es ya fuerte; pero quien es perfecto es aquel para quien el mundo entero es como un país extranjero». Esto es, cuanto más capaces seamos de abandonar nuestra patria cultural, más capaces seremos de juzgarla a ella y al mundo entero con el distanciamiento espiritual y la generosidad necesaria para verlos como son verdaderamente. Y estaremos también más capacitados para juzgarnos a nosotros mismos y a otras culturas con la misma combinación de intimidad y distancia.
Una fuerza cultural no menos importante ni menos formativa desde un punto de vista metodológico, fue el uso que las ciencias sociales hicieron de los «tipos» como procedimiento analítico y como modo de observar las realidades familiares de una manera nueva. La historia del «tipo» tal y como se encuentra en los pensadores de principios del siglo XX, como Weber, Durkheim, Lukács, Mannheim y otros sociólogos del conocimiento, ha sido examinada en numerosas ocasiones. Sin embargo, creo que no se ha señalado que los estudios de Weber sobre el protestantismo, el judaísmo y el budismo le llevaron (quizá inconscientemente) al terreno que los orientalistas originariamente habían descifrado y conquistado. Allí encontró estímulo en todos los pensadores del siglo XIX que creían en la existencia de un tipo de diferencia ontológica entre las «mentalidades» económicas (y también religiosas) orientales y occidentales. A pesar de que Weber nunca estudió concienzudamente el islam, sin embargo, tuvo una considerable influencia en el campo de los estudios islámicos, principalmente porque su noción de tipo era una confirmación «desde fuera» de muchas de las tesis canónicas sostenidas por los orientalistas, en las que las ideas sobre la economía nunca sobrepasaban la afirmación de la incapacidad fundamental oriental para la industria, el comercio y la racionalidad económica. En el campo islámico, esos tópicos se aceptaron durante, literalmente, cientos de años hasta que en 1966 apareció el importante estudio de Maxime Rodinson _Islam and Capitalism_.* La noción de tipo —oriental, islámico, árabe, etc.— todavía persiste y se alimenta de las mismas abstracciones, paradigmas o tipos que aparecen en las ciencias humanas modernas.
A lo largo de este libro he hablado con frecuencia de la desorientación que sentían los orientalistas cuando trataban con o vivían en una cultura profundamente diferente a la suya. En ese momento, una de las diferencias más sorprendentes entre el orientalismo en su versión islámica y todas las demás disciplinas humanistas en las que se aplicaban las nociones de Auerbach sobre la necesidad de la desorientación, era que los orientalistas islamistas nunca consideraron su desorientación con respecto al islam como algo saludable o como una actitud que implicara una mejor comprensión de su propia cultura. Por el contrario, su desorientación frente al islam solo sirvió para intensificar el sentimiento que tenían de la superioridad de la cultura europea, y su antipatía se extendió a todo Oriente, del cual el islam se consideraba un representante degradado (y normalmente muy peligroso). También he demostrado que estas tendencias entraron a formar parte del edificio de la tradición de los estudios orientalistas a lo largo del siglo XIX, y con el tiempo acabaron siendo un elemento clásico de la formación orientalista que se transmitía de generación en generación. Además, creo que había grandes probabilidades de que los eruditos europeos siguieran concibiendo Oriente Próximo a través de la perspectiva de sus «orígenes» bíblicos, es decir, como un lugar en el que primaba el aspecto religioso inmutable. Dada su especial relación con el cristianismo y el judaísmo, el islam siguió siendo por siempre para el orientalista, la idea (o el tipo) del descaro cultural original, agravado, naturalmente, por el miedo a que la civilización islámica permaneciera, de alguna manera, opuesta al Occidente cristiano.
Por todo esto, el orientalismo islamológico en la época de entreguerras también participó del sentimiento general de crisis cultural que habían anunciado Auerbach y los demás autores que hemos citado brevemente, aunque sin evolucionar en la misma línea que las demás ciencias humanas. Como el orientalismo islamológico conservó la polémica actitud _religiosa_ que había desarrollado desde sus orígenes, permaneció, por decirlo de algún modo, anclado en determinadas vías metodológicas. Su alienación cultural debía en principio preservarse de la historia moderna, de las circunstancias sociopolíticas del momento y de las revisiones necesarias que los nuevos datos imponían a cualquier «tipo» teórico o histórico. Y después, las abstracciones que ofrecía el orientalismo (o más bien las ocasiones que ofrecía para hacer abstracciones) en el caso de la civilización islámica adquirieron una nueva validez, ya que se asumió que el islam funcionaba como decían los orientalistas que lo hacía (sin hacer ninguna referencia a la realidad, sino solo a un conjunto de principios clásicos), y también que el islam moderno no era más que una versión repetida del antiguo, sobre todo porque se suponía que la modernidad para el islam era más un insulto que un desafío. (La enorme cantidad de asunciones y suposiciones que contiene esta descripción tiene por objeto dar una imagen de las vueltas y los giros tan excéntricos que el orientalismo necesitaba dar para mantener su peculiar manera de observar la realidad humana.) A fin de cuentas, si la ambición sintetizadora de la filología (tal y como la concebían Auerbach o Curtis) debía conducir a que el erudito ampliara su conciencia y su sentido de la fraternidad humana y de la universalidad de ciertos principios de comportamiento humano, en el caso del orientalismo la síntesis llevó a que se intensificara aún más el sentimiento de las diferencias entre Oriente y Occidente que reflejaba el islam.
Lo que estoy describiendo, pues, son los aspectos que han caracterizado al orientalismo islamológico hasta nuestros días: su posición retrógrada comparada con la de las demás ciencias humanas (e incluso con otras ramas del orientalismo), su retraso general desde el punto de vista metodológico e ideológico y su relativo aislamiento con respecto al desarrollo que se produjo en las demás ciencias humanas y en el mundo real condicionado por factores históricos, económicos, sociales y políticos. Hacia finales del siglo XIX ya se percibía este retraso en el orientalismo islamológico (o semítico), quizá porque algunos observadores empezaron a darse cuenta de que dicho orientalismo conservaba el sustrato religioso a partir del cual se había originado. El primer congreso orientalista se celebró en París en 1873, y casi desde el principio los eruditos de otras ramas vieron con claridad que los semitistas e islamólogos tenían un cierto retraso intelectual desde un punto de vista general. En un informe acerca de los congresos que se habían celebrado entre 1873 y 1897, el erudito inglés R. N. Cust dijo sobre la especialidad semítico-islámica:
Estas reuniones [las del campo semítico antiguo] contribuyeron al progreso de la ciencia oriental.
No se puede decir lo mismo de la sección del semítico moderno que, aunque estuvo muy concurrida, los temas que se discutieron en ella no tenían, desde el punto de vista literario, el más mínimo interés; eran temas que quizá pudieran llenar el espíritu de eruditos aficionados de la vieja escuela, pero no los de la gran clase de « _indicatores_ » del siglo XX. Tengo que remontarme a Plinio para encontrar un término. En esta sección faltó el espíritu filológico y antropológico moderno, y las informaciones dadas se parecen mucho a las de un congreso de profesores de universidad del siglo pasado, que se celebraba para discutir cómo interpretar un párrafo de una obra de teatro griega o cómo acentuar una vocal, antes de que el nacimiento de la filología comparada hubiera disipado las telarañas de los escoliastas. ¿Merecía, en verdad, la pena discutir sobre si Mahoma podía sujetar una pluma o si podía escribir?
Hasta cierto punto esta cualidad arqueológica polémica que describió Cust era la versión erudita del antisemitismo europeo. Incluso la denominación «semítico moderno» que quería englobar tanto a musulmanes como a judíos (y que tenía su origen en el campo llamado «semítico antiguo» del que Renan fue el pionero) portaba su bandera racista de un modo que, sin duda, pretendía ser ostentosamente decente. Unas líneas después en su informe, Cust comenta el hecho de que en la misma reunión «los arios» proporcionaron mucha materia de reflexión. El «ario» es claramente una abstracción que se opone al «semita», pero por alguna de las razones que he dicho antes se tenía la sensación de que estas etiquetas atávicas parecían ser especialmente pertinentes para los semitas, con las costosas consecuencias humanas y morales para el conjunto de las personas que la historia del siglo XX se ha encargado de mostrar. Sin embargo, en lo que no hemos insistido bastante al hablar del antisemitismo moderno ha sido en la legitimación que el orientalismo daba a estas denominaciones atávicas y, lo que es más importante para mis argumentos, en la manera en que esta legitimación académica e intelectual ha persistido en nuestra época cuando se habla del islam, de los árabes o de Oriente Próximo. En efecto, mientras que ya nadie puede escribir disquisiciones eruditas (y ni tan siquiera populares) sobre «la mentalidad de los negros» o «la personalidad de los judíos», sigue siendo posible realizar estudios sobre temas tales como «la mentalidad islámica» o «el carácter árabe». Volveré a este tema más adelante.
De este modo, para comprender apropiadamente la genealogía intelectual del orientalismo islámico de la época de entreguerras —según se puede apreciar de manera intensa y satisfactoria (digo esto sin ninguna ironía) en Massignon y Gibb—, debemos comprender las diferencias entre la actitud totalizadora que el orientalista adoptaba hacia su material y el tipo de actitud con la que guardaba un gran parecido cultural y que aparece en la obra de filólogos como Auerbach y Curtis. La crisis intelectual del orientalismo islámico era un aspecto más de la crisis espiritual del «humanismo burgués tardío», pero en su forma y en su estilo, este orientalismo _islamológico_ presentaba los problemas de la humanidad separados en dos categorías: «oriental» y «occidental». Se creía que la liberación, la autoexpresión y la autorrealización no representaban para el oriental lo mismo que para el occidental. El orientalista islamológico expresaba sus ideas sobre el islam de tal manera que subrayaba su propia _resistencia_ (así como la que se atribuía a los musulmanes) al cambio y a la comprensión mutua entre el Este y el Oeste, y al desarrollo de hombres y mujeres que los sacara de las instituciones arcaicas, primitivas y clásicas y los introdujera de lleno en la modernidad. De hecho, esta resistencia al cambio era un sentimiento tan fuerte y el poder que se le asignaba era tan universal que, al leer a los orientalistas, se entiende que el apocalipsis que hay que temer no es la destrucción de la civilización occidental, sino la de las barreras que mantienen separado al Este del Oeste. Cuando Gibb se opuso al nacionalismo en los estados islámicos modernos, lo hizo porque tenía la impresión de que corroería las estructuras internas que mantenían el carácter oriental del islam; el resultado neto del nacionalismo secular sería que Oriente no se diferenciaría de Occidente. Con todo, hace falta rendir tributo a los extraordinarios poderes de identificación comprensiva que Gibb mostraba hacia una religión extraña, puesto que explicó su desacuerdo de modo que parecía _hablar por_ la comunidad islámica ortodoxa. ¿Hasta qué punto este alegato era un retorno al viejo hábito orientalista de hablar por los nativos, o era un intento serio de hablar en defensa de los intereses del islam? Cualquiera de las dos podría ser la respuesta.
Evidentemente ningún erudito o pensador es el representante perfecto de algún tipo ideal o de alguna escuela a los que pertenece en virtud de su origen, de su nacionalidad o de los accidentes de la historia. Sin embargo, en una tradición que está relativamente muy aislada y muy especializada, como la orientalista, creo que todo erudito tiene muy presente, en parte conscientemente y en parte inconscientemente, su tradición nacional, por no decir su ideología nacional. Esto es particularmente cierto en el orientalismo, porque las naciones europeas están políticamente comprometidas en los asuntos de uno u otro país oriental. Inmediatamente pensamos en Snouck Hurgronje, por citar un ejemplo que no es ni británico ni francés, erudito con un sentimiento de identidad nacional muy simple y claro. Sin embargo, incluso después de haber hecho todas las reservas convenientes sobre la diferencia entre un individuo y un tipo (o entre un individuo y una tradición), es sorprendente ver hasta qué punto Gibb y Massignon _eran_ tipos representativos. Quizá sería mejor decir que Gibb y Massignon respondieron a todas las expectativas que les crearon las tradiciones nacionales, la política de sus países y la historia interna de sus «escuelas» nacionales de orientalismo.
Sylvain Lévi realizó una distinción muy mordaz entre estos dos eruditos:
El interés político que vincula a Inglaterra con la India mantiene el trabajo británico en contacto con las realidades concretas, y la cohesión entre las representaciones del pasado y el espectáculo del presente.
Francia, alimentada por la tradición clásica, busca el espíritu humano y se interesa por la India del mismo modo que lo hace por China.
Sería muy fácil decir que esta polaridad produce por un lado un trabajo sobrio, eficaz y concreto y, por otro, un trabajo universalista, especulativo y brillante. Pero la polaridad puede servir también para esclarecer dos carreras largas y extremadamente distinguidas que dominaron entre las dos el orientalismo islamista francés y angloestadounidense hasta los años sesenta; si podemos hablar de dominación es porque cada uno de estos dos eruditos procedía de una tradición consciente y continuó trabajando en ella; una tradición cuyas coacciones (o limitaciones desde un punto de vista político e intelectual) pueden describirse como lo ha hecho Sylvain Lévi.
Gibb nació en Egipto, Massignon en Francia. Los dos iban a convertirse en hombres profundamente religiosos y estudiosos no tanto de la sociedad como de la vida religiosa en la sociedad. Ambos eran también profundos conocedores del mundo. Una de sus mayores conquistas fue hacer que la erudición tradicional fuera algo útil para el mundo político moderno. Sin embargo, sus obras tienen un alcance —casi una textura— muy diferente, incluso si aceptamos las disparidades obvias derivadas de su formación y de su educación religiosa. Massignon consagró toda su vida a estudiar la obra de al-Hallay «cuyas huellas —dijo Gibb en 1962 en un artículo necrológico en memoria de Massignon— nunca dejó de buscar en la literatura y la devoción islámicas tardías»; la extensión casi ilimitada de sus trabajos le llevaría prácticamente a todas partes, encontrando testimonios de _«l'esprit humain à travers l'espace et le temps»_. Con una _oeuvre_ que englobaba «todos los aspectos y regiones de la vida y del pensamiento musulmán contemporáneo», la presencia de Massignon en el orientalismo era un desafío constante para sus colegas. Ciertamente Gibb, en principio, admiró —aunque al final se distanció de ella— la manera en la que Massignon se dedicaba a:
temas que, en cierta manera, ligaban la vida espiritual de los musulmanes y de los católicos [y le permitían encontrar] un elemento familiar en el culto a Fátima y, en consecuencia, un campo particular de interés en el estudio del pensamiento shií en muchas de sus manifestaciones o en la comunidad de orígenes abrahámicos y en temas como el de los Siete Durmientes. Sus escritos sobre estos temas adquirieron, gracias a las cualidades que él les confirió, una significación permanente para los estudios islámicos. Sin embargo, precisamente a causa de estas cualidades, se puede decir que están compuestos en dos registros. Uno, el nivel ordinario de la erudición objetiva que buscaba elucidar la naturaleza del fenómeno dado a través del uso magistral de los instrumentos clásicos de la investigación académica. El otro, un nivel en el que los datos objetivos y la comprensión son absorbidos y transformados por una intuición individual de dimensiones espirituales. No ha sido siempre fácil trazar una línea de división entre este último y la transfiguración que provenía de la efusión de las riquezas de su propia personalidad.
Gibb da a entender aquí que es más probable que los católicos se vean atraídos por el estudio del «culto a Fátima» que los protestantes, pero muestra claramente sus reticencias con respecto a alguien que difumina la distinción entre la erudición «objetiva» y la erudición (e incluso elaboración) fundamentada en la «intuición individual de las dimensiones espirituales». Gibb, sin embargo, tenía razón en el siguiente párrafo de su necrológica al reconocer la «fecundidad» del espíritu de Massignon en campos tan diversos como «el simbolismo del arte musulmán, la estructura de la lógica musulmana, las complejidades de las finanzas de la Edad Media y la organización de corporaciones artesanales». Y tenía también razón al definir el interés precoz de Massignon por las lenguas semíticas en tanto que precursoras de los «estudios elípticos que para el no iniciado casi rivalizaban con los misterios de la hermética antigua». Sin embargo, Gibb concluye con una nota generosa en la que señala que:
para nosotros, la lección que, con su ejemplo, dio a los orientalistas de su generación es que el orientalismo clásico ya no es adecuado si no va acompañado de cierto grado de compromiso con las fuerzas vitales que han dado sentido y valor a los diversos aspectos de las culturas orientales.
Esa fue, por supuesto, la mayor contribución de Massignon, y es cierto que en la islamología francesa contemporánea (como a veces se llama) se ha desarrollado una tradición de identificación con las «fuerzas vitales» que inspiran «la cultura oriental». Es suficiente mencionar los extraordinarios trabajos de eruditos, como Jacques Berque, Maxime Rodinson, Yves Lacoste y Roger Arnaldez —muy diferentes unos de otros por sus maneras e intenciones a la hora de abordar el tema—, para quedar sorprendidos por el efecto fecundo del ejemplo de Massignon cuya huella intelectual en ellos es innegable.
Al centrar sus comentarios de una manera algo anecdótica en los diferentes puntos fuertes y débiles de la obra de Massignon, Gibb ignora ciertos aspectos evidentes que les diferencian entre sí y que, sin embargo, si se toman como un todo, convierten a Massignon en el símbolo perfecto del desarrollo crucial del orientalismo francés. Una de ellas es el bagaje cultural personal de Massignon que ilustra muy bien la descripción del orientalismo francés que hace Sylvain Lévi. La misma idea de «un espíritu humano» era algo más o menos ajeno a la formación intelectual y religiosa de Gibb y de tantos otros orientalistas británicos modernos, mientras que en el caso de Massignon, la noción de «espíritu» como realidad estética, religiosa, moral e histórica era algo de lo que parecía haberse alimentado desde su infancia. Su familia mantenía relaciones amistosas con gente como J. K. Huysmans, y el clima intelectual de su primera educación y las ideas del simbolismo tardío aparecen de manera clara en todo lo que escribió e incluso en la variedad particular de catolicismo (y de misticismo sufí) que le interesó. No hay señales de austeridad en la obra de Massignon, está escrita en uno de los mejores estilos del siglo. Sus ideas sobre la experiencia humana bebieron de las obras de pensadores y artistas contemporáneos, y esta amplitud cultural y estilística le sitúan en una categoría muy diferente de la de Gibb. Sus primeras ideas se formaron durante el período llamado de decadencia estética, pero también recibieron la influencia de Bergson, Durkheim y Mauss. Su primer contacto con el orientalismo fue a través de Renan, a cuyas clases asistió de joven. También fue alumno de Sylvain Lévi y entre sus amigos estuvieron Paul Claudel, Gabriel Bounoure, Jacques y Raïssa Maritain y Charles de Foucauld. Más tarde fue capaz de asimilar los trabajos hechos en los campos relativamente recientes de la sociología urbana, la lingüística estructural, el psicoanálisis, la antropología contemporánea y la nueva historia. Sus ensayos, por no hablar de su estudio monumental sobre al-Hallay, beben sin esfuerzo del corpus entero de la literatura islámica. Su erudición asombrosa y su personalidad casi familiar le hacen a veces parecer un sabio inventado por Jorge Luis Borges. Estuvo muy interesado por los temas «orientales» en la literatura europea que también interesaron a Gibb, pero, al contrario que este, Massignon no se vio atraído ni por los escritores europeos que «comprendieron» Oriente ni por los textos europeos que fueron corroboraciones artísticas independientes de lo que los eruditos orientalistas revelarían después (por ejemplo, el interés de Gibb por Scott como fuente para el estudio de Saladino). El «Oriente» de Massignon estaba totalmente en consonancia con el mundo de los Siete Durmientes o de las oraciones abrahámicas (los dos temas revelados por Gibb como signos distintivos de las opiniones no ortodoxas de Massignon sobre el islam): excéntrico, un poco extraño, y respondía totalmente al brillante talento de interpretación de Massignon (que en cierto sentido lo fabricó como tema). Si a Gibb le gustaba el Saladino de Walter Scott, la predilección de Massignon se inclinaba hacia Nerval, el suicida, el _poète maudit_ de una gran curiosidad psicológica. Esto no significa que Massignon fuera esencialmente un estudioso del pasado; al contrario, tuvo una gran presencia en las relaciones franco-islámicas y en la vida política y cultural. Era un hombre apasionado que creía que el mundo del islam podía ser penetrado no solo exclusivamente por la erudición, sino por la devoción a todas sus actividades. Así fomentó fervientemente la cofradía Badaliyya, uno de los subgrupos de la cristiandad oriental subsumido dentro del islam.
Las grandes dotes literarias de Massignon a veces dan a su trabajo erudito la apariencia de una especulación caprichosa demasiado cosmopolita y con frecuencia reservada a los iniciados. Esta apariencia es engañosa y, de hecho, se ajustan bastante poco a lo que debería ser una descripción de sus obras. Lo que intentaba evitar era lo que él llamaba _«l'analyse analytique et statique de l'orientalisme»_ , un tipo de acumulación inerte sobre textos o problemas islámicos supuestos, de fuentes, de orígenes, de pruebas, de demostraciones, etc. Siempre incluía todo lo que consideraba imprescindible del contexto de un escrito o de un problema, para animarlos, para sorprender a su lector con las visiones penetrantes que tiene alguien que, como Massignon, ama atravesar las barreras de las disciplinas o de la tradición para penetrar en el corazón humano de cualquier texto. Ningún orientalista moderno —ciertamente tampoco Gibb, que casi le igualó en influencia y talento— podía referirse en un ensayo tan fácilmente (y con tanta precisión) a una multitud de místicos islámicos y a Jung, Heisenberg, Mallarmé y Kierkegaard; y ciertamente muy pocos orientalistas tenían esa amplitud de miras combinada con la experiencia política concreta de la que él podía hablar en 1952 en su ensayo «L'Occident devant l'Orient: Primauté d'une solution culturelle». Su universo cultural estaba, sin embargo, bien definido, tenía una estructura precisa que permaneció intacta desde el principio hasta el final de su carrera y estuvo encorsetada, a pesar de la inigualable riqueza de sus intereses y de sus referencias, en un conjunto de ideas básicamente inmutables. Describamos rápidamente esta estructura y enumeremos resumidamente estas ideas.
Massignon toma como punto de partida la existencia de tres religiones abrahámicas, de las cuales el islam es la religión de Israel, es el monoteísmo de un pueblo excluido de la promesa hecha por Dios a Isaac. El islam es, por tanto, una religión de resistencia (contra Dios Padre y contra Cristo, su encarnación) que conserva dentro de sí la tristeza que comenzó con las lágrimas de Agar. Esto hace que el árabe sea la lengua de las lágrimas, igual que toda la noción de _yihad_ en el islam (de la cual Massignon dice explícitamente que es la forma épica del islam que Renan fue incapaz de ver o de comprender) tiene una dimensión intelectual importante cuya misión es la guerra contra el cristianismo y el judaísmo, enemigos exteriores, y contra la herejía, enemigo interior. Sin embargo, en el interior del islam Massignon creía que podía distinguir una serie de contracorrientes que se convirtieron en su principal interés intelectual de estudio y estaban encarnadas en el misticismo, un camino hacia la gracia divina. La principal característica del misticismo era, por supuesto, su carácter subjetivo, en el que las tendencias irracionales e incluso inexplicables se inclinaban hacia la experiencia singular, individual y momentánea de la participación en lo Divino. Todo el extraordinario trabajo de Massignon sobre el misticismo fue así un intento de describir el itinerario de las almas, para salir del consenso limitativo que les imponía la comunidad islámica ortodoxa o _sunna_. Un místico iraní era más intrépido que un místico árabe, en parte porque era ario (las viejas etiquetas del siglo XIX «ario» y «semita» son coacciones para Massignon, como también lo es la oposición binaria hecha por Schlegel entre las dos familias de lenguas) y en parte porque era un hombre que buscaba la perfección. Según Massignon, la mística árabe se inclinaba hacia lo que Waardenburg llama un monismo testimonial. La figura ejemplar y modélica para Massignon era al-Hallay, quien buscaba su liberación fuera de la comunidad ortodoxa pidiendo, y obteniendo al final, la crucifixión que el islam rechazaba y rehusaba totalmente; Mahoma, según Massignon, había rechazado deliberadamente la ocasión que se le había ofrecido de llenar el vacío que le separaba de Dios. La conquista era, por tanto, haber logrado una unión mística con Dios a contracorriente del islam.
El resto de la comunidad ortodoxa vive en lo que Massignon llama una condición de _«soif ontologique»_ , sed ontológica. Dios se presenta al hombre como una especie de ausencia, de negación de estar presente y, sin embargo, la conciencia que tiene un musulmán devoto de su sumisión ( _islam_ ) a la voluntad de Dios da lugar a un celoso sentido de la trascendencia de Dios y a una intolerancia ante la idolatría de cualquier tipo. El sitio de estas ideas está en el «corazón circunciso», que mientras que es abarcado por su fervor musulmán testimonial, puede también, como en el caso de místicos como al-Hallay, inflamarse de una pasión divina o de amor de Dios. Tanto en un caso como en otro, la unidad trascendental de Dios ( _tawhid_ ) es algo que debe ser realizado y comprendido cada vez más por el devoto musulmán, ya sea llevando su testimonio, ya sea a través del amor místico de Dios: esto es, según escribe Massignon en un complicado ensayo, lo que define la «intención» del islam. Está claro que las simpatías de Massignon se inclinan hacia la vocación mística del islam tanto por su proximidad a su propio temperamento de católico devoto, como por su influencia continua dentro del cuerpo ortodoxo de creencias. La imagen que Massignon tiene del islam es la de una religión comprometida sin cesar en sus negaciones, en su llegada tardía (con respecto a otras religiones abrahámicas), en su sentido relativamente desnudo de las realidades del mundo, en sus numerosas estructuras de defensa contra las «conmociones psíquicas» del género de las practicadas por al-Hallay y otros místicos sufíes y en su soledad al ser la única religión que sigue siendo «oriental» dentro de los tres grandes monoteísmos existentes.
Pero esta perspectiva tan obviamente severa sobre el islam con sus «invariantes simples» (sobre todo para un pensamiento tan exuberante cono el de Massignon) no conlleva, por su parte, ninguna hostilidad profunda hacia él. Al leer a Massignon uno se siente sorprendido por su reiterada insistencia en la necesidad de una lectura compleja: es imposible dudar de la sinceridad de sus consejos. En 1951 escribió que su humanismo no era «ni un prurito de exotismo ni un rechazo de Europa, sino una equiparación de nuestros métodos de investigación y las tradiciones vivas de civilizaciones antiguas». Cuando se ha llevado a la práctica este tipo de orientalismo en la lectura de un texto árabe o islámico, se producen interpretaciones de una inteligencia casi abrumadora; uno sería estúpido si no respetara el genio auténtico y la grandeza del espíritu de Massignon. Pero lo que debe llamarnos la atención en su definición de orientalismo son dos frases: «nuestros métodos de investigación» y «las tradiciones vivas de antiguas civilizaciones». Massignon concebía lo que hacía como la síntesis de dos cantidades que se oponían brutalmente, pero es esta asimetría particular entre ellas lo que es inquietante y no simplemente el hecho de la oposición entre Europa y Oriente. La implicación de Massignon consiste en que para él la esencia de la diferencia entre el Este y el Oeste es la esencia entre la modernidad y la tradición antigua. Y de hecho en sus escritos sobre problemas políticos y contemporáneos, que es donde más directamente se pueden apreciar los límites de su método, la oposición Este-Oeste aparece de una manera muy particular.
La visión de Massignon del encuentro entre el Este y el Oeste atribuye una gran responsabilidad al Oeste por su invasión del Este, su colonialismo y sus ataques contra el islam. Massignon combatió infatigablemente a favor de la civilización musulmana y, como prueban sus numerosos ensayos y cartas escritos después de 1948, en apoyo de los refugiados palestinos y en defensa de los derechos de los árabes musulmanes y cristianos de Palestina contra el sionismo, contra lo que, en referencia a lo que había dicho Abba Eban, él mordazmente llamó el _«burgeois colonialism»_ de los israelíes. Sin embargo, la estructura en la que la visión de Massignon se apoya también sitúa al Oriente islámico esencialmente en la antigüedad y a Occidente en la modernidad. Como Robertson Smith, Massignon considera que el oriental no es un hombre moderno, sino un semita; esta categoría reduccionista tuvo una poderosa influencia en su pensamiento. Cuando, por ejemplo, en 1960, Jacques Berque, su colega en el Collège de France, y él publicaron su diálogo sobre «los árabes» en _Esprit_ , la mayor parte del tiempo la pasaron conversando sobre si la mejor manera de estudiar los problemas de los árabes de hoy no sería simplemente decir que, en lo esencial, el conflicto árabe-israelí era en realidad un problema _semita_. Berque intentó gentilmente demorar la cuestión y hacer admitir a Massignon que, como el resto del mundo, los árabes habían sufrido lo que él llamó una «variación antropológica». Massignon rechazó la idea al instante. Sus repetidos esfuerzos por comprender y registrar el conflicto palestino, a pesar de su profundo humanismo, realmente nunca llegaron a ir más allá de la querella entre Isaac e Ismael o, en lo que se refería a su propia querella contra Israel, la tensión entre el judaísmo y el cristianismo. Cuando los sionistas invadían ciudades y pueblos árabes era la sensibilidad religiosa de Massignon la que se ofendía.
Europa, y Francia en particular, se consideraban realidades _contemporáneas_. En parte por sus primeros contactos políticos con Gran Bretaña durante la Primera Guerra Mundial, Massignon siempre detestó a Inglaterra y la política inglesa. Lawrence y las personas como él representaban una política demasiado compleja a la que él, Massignon, se oponía en sus tratos con Faisal. _«Je cherchais avec Faysal_ [...] _à pénétrer dans le sens même de sa tradition à lui.»_ Los británicos parecían representar «la expansión» en Oriente, una política económica amoral y una filosofía desfasada de influencia política. El francés era un hombre más moderno, que se había visto obligado a tomar de Oriente la espiritualidad, los valores tradicionales, etc., que él había perdido. La inversión de Massignon en esta perspectiva vino, creo, por vía de la tradición, de todo el siglo XIX, que consideraba que Oriente era una terapia para Occidente, una tradición que se dibujaba ya en Quinet. En Massignon, se le añadió un sentimiento de compasión cristiana.
En cuanto a los musulmanes, debemos recurrir a la ciencia de la compasión y a la «participación» incluso en la construcción de su lengua y de su estructura mental en la que debemos participar porque en última instancia esta ciencia es el testimonio de unas verdades que son también las nuestras o son verdades que hemos perdido y debemos ganar. En fin, porque en el fondo, todo lo que existe de alguna manera es bueno y porque esos pobres pueblos colonizados no son solamente buenos para nuestros propósitos, sino en sí mismos [ _en soi_ ].
Sin embargo, el oriental _«en soi»_ era incapaz de apreciarse o de comprenderse a sí mismo. Debido en parte a lo que Europa le había hecho, había perdido su religión y su _philosophie_ ; los musulmanes tenían _«un vide immense»_ dentro de ellos; estaban encerrados en la anarquía o el suicidio. Se había convertido en una obligación de Francia asociarse con el deseo musulmán de defender su cultura tradicional, de regir su vida dinástica y el patrimonio de los creyentes.
Ningún erudito, ni siquiera Massignon, puede resistir las presiones que se ejercen sobre él y su nación o sobre la tradición erudita en la que trabaja. En gran parte de las afirmaciones que Massignon hizo sobre Oriente y sobre su relación con Occidente parecía que retomaba y repetía las ideas de otros orientalistas franceses. Sin embargo, debemos admitir que la sutileza, el estilo personal y el genio individual pueden, al final, suplantar las limitaciones políticas que actúan de manera impersonal a través de la tradición y del ambiente nacional. Incluso así, en el caso de Massignon también tenemos que reconocer que, en cierto sentido, sus ideas sobre Oriente siguieron siendo totalmente tradicionales y orientalistas a pesar de su personalidad y de su notable originalidad. Según él, el Oriente islámico era espiritual, semítico, tribal, radicalmente monoteísta y no ario. Estos adjetivos se parecen a un catálogo de descripciones antropológicas de finales del siglo XIX. Las experiencias relativamente prosaicas de la guerra, del colonialismo, del imperialismo, de la opresión económica, del amor, de la muerte y del intercambio cultural parecen siempre a ojos de Massignon haber sido filtradas a través de unas lentes metafísicas y, en última instancia, deshumanizadas: estas lentes son semíticas, europeas, orientales, occidentales, arias, etc. Las categorías estructuraban su mundo y le daban lo que él llamó una especie de sentido profundo —al menos para él—. Por otro lado, en medio de las ideas individuales y muy detalladas del mundo erudito, Massignon adquirió una posición. Reconstruyó y defendió el islam contra Europa por un lado y contra su propia ortodoxia por otro. Esta intervención —porque de eso se trataba— en Oriente, como animador y como campeón, simbolizaba su propia aceptación de la diferencia de Oriente, así como sus esfuerzos por transformarlo en lo que él quería. Ambas cosas entrelazadas, la voluntad de conocimiento sobre Oriente y la voluntad de conocimiento en su beneficio, son muy fuertes en Massignon. La desproporcionada importancia que Massignon concede a al-Hallay se debe, en primer lugar, a la decisión del erudito de promocionar una figura sobre la cultura que la sustente y en segundo lugar al hecho de que al-Hallay había llegado a representar un desafío constante e incluso irritante para el cristiano occidental para el cual la fe no era (y quizá, no podía ser) un autosacrificio llevado al extremo al que lo llevaba el sufí. En ambos casos el al-Hallay de Massignon pretendía esencialmente personificar y encarnar los valores que estaban fuera de la ley en el sistema doctrinal principal del islam, un sistema que el propio Massignon describe sobre todo para derrotarlo con al-Hallay.
Sin embargo, no deberíamos decir inmediatamente que la obra de Massignon era perversa o que su debilidad más grande consistía en que el islam que representaba no era la religión a la que un musulmán «medio» o «común» podría adherirse. Un erudito musulmán distinguido ha abogado precisamente por esta última posición pero sin citar el nombre de Massignon como el de un ofensor. Por mucho que uno se incline a aprobar estas tesis —ya que, como este libro ha intentado demostrar, el islam ha estado fundamentalmente mal representado en Occidente— la verdadera cuestión es saber si, de hecho, puede haber una verdadera representación de algo, o si todas y cada una de las representaciones, porque _son_ representaciones, están incrustadas primero en la lengua y después en la cultura, las instituciones y el ambiente político del que las hace. Si la última alternativa es la correcta (como yo creo), tenemos que estar dispuestos a aceptar el hecho de que una representación está _eo ipso_ comprometida, entrelazada, incrustada y entretejida con muchas otras realidades, además de con la «verdad» de la que ella misma es una representación. Todo esto nos debe llevar a considerar desde un punto de vista metodológico, que las representaciones (representaciones buenas o malas, la distinción es a lo sumo una cuestión de grado) ocupan un campo común definido más que por algún único material común inherente, por una historia, tradición o universo común de discurso. Dentro de este campo, que ningún erudito solitario y aislado puede crear, pero del que todo erudito recibe y en el que encuentra un lugar para él, el investigador individual hace su contribución. Estas contribuciones, incluso para un genio excepcional, son estrategias que sirven para redistribuir el material dentro del campo. Incluso el erudito que desentierra un manuscrito perdido produce el texto «encontrado» en un contexto ya preparado para él, ya que ese es el verdadero significado de _encontrar_ un texto nuevo. Así, cada contribución individual, primero causa unos cambios dentro del campo y después promueve una nueva estabilidad, del mismo modo que en una superficie cubierta con veinte compases, la introducción del número veintiuno hará que todos los otros tiemblen y luego se asienten en una nueva configuración acomodada.
Las representaciones del orientalismo en la cultura europea acumulan lo que podríamos llamar una consistencia discursiva que no solo tiene una historia sino también una presencia material (e institucional) que mostrar. Como he dicho con respecto a Renan, una consistencia así era una forma de praxis cultural, un sistema de oportunidades para hacer afirmaciones sobre Oriente. Lo que quiero decir sobre este sistema no es que sea una mala representación de alguna esencia oriental —en la que de momento no creo—, sino que actúa, como normalmente lo hacen las representaciones, con un propósito, de acuerdo a una tendencia y en un ambiente histórico, intelectual e incluso económico específico. En otras palabras, las representaciones tienen sus fines, son efectivas la mayoría de las veces y consiguen uno o más de sus objetivos. Las representaciones son formaciones o, como Roland Barthes ha dicho a propósito de todas las operaciones del lenguaje, son deformaciones. Oriente, en tanto que representación en Europa, es formado —o deformado— a partir de una sensibilidad cada vez más específica hacia una región geográfica llamada «Este». Los especialistas en esta región hacen su trabajo, por decirlo de algún modo, porque en cierto momento su profesión de orientalista les exige que presenten a la sociedad imágenes de Oriente, conocimiento e ideas sobre él. Y, en gran medida, el orientalista proporciona a su propia sociedad representaciones de Oriente que: _a_ ) llevan su impronta distintiva; _b_ ) ilustran su concepción de lo que Oriente puede o debe ser; _c_ ) rebaten conscientemente las opiniones sobre Oriente; _d_ ) ofrecen al discurso orientalista lo que en ese momento parece que más necesita, y _e_ ) responden a ciertas exigencias culturales, profesionales, nacionales, políticas y económicas de la época. Es evidente que, aunque jamás esté ausente, el papel del conocimiento positivo está lejos de ser absoluto. Al contrario, el «conocimiento» —que nunca es bruto, inmediato o simplemente objetivo— es lo que los cinco atributos de la representación orientalista que acabo de enumerar _distribuyen_ y vuelven a distribuir.
Viéndolo desde este punto de vista, Massignon es menos un «genio» mítico que un tipo de sistema de producir cierta clase de afirmaciones, diseminadas en la gran masa de formaciones discursivas que juntas constituyen el archivo o el material cultural de su época. No creo que deshumanicemos a Massignon si reconocemos esto ni que le reduzcamos a ser el sujeto de un determinismo vulgar. Por el contrario, veremos, en cierta medida, cómo un ser humano ha tenido y ha podido conseguir una capacidad cultural y productiva dotada de una dimensión institucional o extrahumana, y seguramente a esto es a lo que debe aspirar el ser humano finito, si no debe contentarse con su presencia meramente mortal en el tiempo y el espacio. Cuando Massignon dijo: _«Nous sommes tous des sémites»_ , indicaba el alcance de sus ideas sobre su sociedad, mostrando hasta qué punto sus ideas sobre Oriente podían trascender las circunstancias locales y anecdóticas de un francés o de la sociedad francesa. La categoría de semita extraía su sustancia del orientalismo de Massignon, pero su fuerza se derivaba de su tendencia a salir de los límites de la disciplina para extenderse por una historia y una antropología más vastas, en las que parecía tener cierta validez y poder.
Las formulaciones de Massignon y sus representaciones al menos tuvieron una influencia directa, por no decir una validez indiscutible, entre el gremio de los orientalistas profesionales. Como he dicho antes, el reconocimiento que Gibb hace de los logros de Massignon constituye la asunción (implícita) de que Massignon debe ser considerado como una alternativa al trabajo de Gibb. Por supuesto, estoy atribuyendo al artículo necrológico escrito por Gibb, afirmaciones que se encuentran solo en forma de indicios que no llegan a ser explícitos, pero que son de una importancia evidente si tenemos en cuenta la propia carrera de Gibb en contraste con la de Massignon. El artículo conmemorativo que escribió Albert Hourani sobre Gibb para la British Academy (al que me he referido en bastantes ocasiones) resume admirablemente su carrera, sus ideas principales y la importancia de su trabajo. Estoy de acuerdo con la exposición de Hourani y con sus grandes líneas, pero hay algo que falta, aunque esta ausencia esté parcialmente subsanada en un texto muy breve que William Polk escribió sobre Gibb, «Sir Hamilton Gibb Between Orientalism and History». Hourani tiende a ver en Gibb el producto de encuentros e influencias personales, etc., mientras que Polk, que es bastante menos sutil que Hourani en su manera de comprender a Gibb, concibe a este como la culminación de una tradición académica específica que —por utilizar una expresión que no aparece en la prosa de Polk— podemos llamar paradigma o consenso de investigación académica.
Esta idea, tomada un poco impertinentemente de Thomas Kuhn, se aplica muy bien a Gibb que, como nos recuerda Hourani, era en muchos aspectos una figura profundamente institucional. Todo lo que Gibb dijo o hizo desde el principio de su carrera en Londres, pasando por sus años en Oxford, hasta sus años influyentes como director del Center for Middle Eastern Studies de Harvard, tiene el sello inconfundible de una mente que opera con facilidad dentro de las instituciones establecidas. Mientras Massignon era irremediablemente el hombre de fuera, Gibb es el de dentro. En cualquier caso, ambos alcanzaron la cima del prestigio en el orientalismo francés y anglo-estadounidense, respectivamente. Oriente era para Gibb un lugar con el que tenía un contacto directo; era una entidad sobre la que se leía, se estudiaba, se escribía dentro de los límites de las sociedades culturales, la universidad y las conferencias eruditas. Como Massignon, Gibb presumía de tener amigos musulmanes, pero daba la sensación de que —como las de Lane— eran más amistades útiles que determinantes. En consecuencia, Gibb era una figura dinástica en el interior de la estructura académica del orientalismo británico (y más tarde del estadounidense), un erudito cuya obra demostraba de una manera bastante consciente las tendencias nacionales de una tradición académica establecida dentro de las universidades, de los gobiernos y de las fundaciones para la investigación.
Una muestra de todo esto es que Gibb, ya en su madurez, hablaba y escribía para organismos que determinaban las líneas políticas. En 1951, por ejemplo, escribió un artículo para un libro conjunto que llevaba el significativo título de _The Near East and the Great Powers_ , en el que intentaba explicar la necesidad de desarrollar los programas anglo-estadounidenses de estudios orientales:
[...] en conjunto, la situación de los países occidentales con respecto a los países de Asia y África ha cambiado. Ya no podemos apoyarnos mucho más en ese factor de prestigio que parece haber desempeñado un gran papel en el pensamiento de antes de la guerra, ni podemos esperar más a que los pueblos de Asia y África o los de Europa oriental vengan a nosotros y aprendan de nosotros mientras nosotros descansamos tranquilamente. Tenemos que aprender de ellos, de tal forma que podamos trabajar con ellos y tener una relación más cercana que se aproxime a una relación que esté basada en términos de reciprocidad.
Los términos de esta nueva relación los explicó después en «Area Studies Reconsidered». No había que considerar que los estudios orientales eran actividades eruditas, sino instrumentos de la política nacional hacia los estados del mundo poscolonial, que acababan de conseguir su independencia y que quizá fueran intratables. El orientalista, consciente de su importancia para la comunidad atlántica, debía ser el guía de los políticos, de los hombres de negocios y de los eruditos de las nuevas generaciones.
Lo que más contaba en la última visión de Gibb no era el trabajo positivo del orientalista como erudito (por ejemplo, el tipo de erudito que Gibb había sido en su juventud cuando estudiaba las invasiones musulmanas de Asia Central) sino su poder de adaptación para su utilidad en el mundo público. Hourani lo explica muy bien:
[...] le resultaba claro [a Gibb] que los gobiernos modernos y las elites actuaban ignorando o rehusando sus propias tradiciones de vida social y de moralidad, y que esta era la causa de sus errores. Por eso sus principales esfuerzos iban dirigidos a esclarecer, a través de un estudio cuidadoso del pasado, la naturaleza específica de la sociedad musulmana y de las creencias y la cultura que constituían su núcleo. Incluso este problema tendía a concebirlo primero principalmente en términos políticos.
No obstante, esta última visión no habría sido posible si no hubiera sido preparada bastante rigurosamente por las obras más antiguas de Gibb, y es ahí donde en primer lugar debemos buscar para entender sus ideas. Una de las primeras influencias que se advierten en la obra de Gibb fue la de Duncan Macdonald, de cuyo trabajo claramente tomó la idea de que el islam era un sistema de vida coherente, un sistema cuya coherencia se debía no tanto a la gente que llevaba esa vida como a un cierto tipo de doctrina, un cierto método para practicar la religión y una cierta idea de orden, en la cual todos los pueblos musulmanes participaban. Entre el pueblo y el «islam» había obviamente un tipo de contacto dinámico, pero lo que importaba para el occidental que lo estudiaba era el poder que poseía el islam para hacer inteligibles las experiencias de los pueblos islámicos y no al contrario.
Macdonald y, más tarde, Gibb no abordaron jamás las dificultades epistemológicas y metodológicas del «islam» como un objeto (sobre el que se pueden hacer extensas afirmaciones extremadamente generales). Macdonald creía, por su parte, que se podían percibir ciertos aspectos en el islam de una abstracción todavía más grande y portentosa: la mentalidad oriental. Todo el primer capítulo de su libro más influyente (cuya importancia Gibb no pudo minimizar o subestimar), _The Religious Attitude and Life in Islam_ , es una antología de algunas declaraciones indiscutibles sobre la mente oriental. Empieza diciendo que «es evidente, creo, y está admitido que la concepción de lo invisible es mucho más inmediata y real para los orientales que para los occidentales». Los «grandes elementos de modificación que parecen de vez en cuando casi trastornar la ley general» no la trastornan ni tampoco trastornan otras leyes generales que gobiernan la mente de los orientales. «La diferencia esencial en la mente oriental no es una credulidad que se testimonie en relación con las cosas invisibles, sino la impotencia de construir un sistema en lo que concierne a las cosas visibles.» Otro aspecto de esta dificultad —a la que Gibb, más tarde, iba a achacar la ausencia de forma en la literatura árabe y la visión esencialmente atomista de la realidad que tienen los musulmanes— es «que la diferencia en el oriental no es esencialmente la religiosidad, sino la ausencia de sentimiento de la ley. Para él no hay un orden inamovible de la naturaleza». Si un «hecho» así parece no dar cuenta de los extraordinarios logros de la ciencia islámica, sobre la que se fundó en gran medida la ciencia occidental, entonces Macdonald permanece en silencio. Continúa su catálogo: «Es evidente que todo es posible para el oriental. Lo sobrenatural está tan cerca que quizá lo pueda tocar en algún momento». Que una _ocasión_ —a saber, que el nacimiento histórico y geográfico del monoteísmo fue en Oriente— se convierte, en el argumento de Macdonald, en una completa teoría sobre la diferencia entre el Este y el Oeste; esto indica hasta qué punto Macdonald está comprometido con el «orientalismo». Veamos su resumen:
_Incapacidad_ , por tanto, para ver la vida con firmeza y para verla como un todo, para entender que una teoría de la vida debe cubrir todos los hechos, y _aptitud_ para ser marcado por una sola idea y ser ciego para todo lo demás: ahí reside, creo, la diferencia, entre Oriente y Occidente.
Nada de esto, por supuesto, es particularmente nuevo. Desde Schlegel a Renan, desde Robertson Smith a T. E. Lawrence, estas ideas han sido repetidas y reiteradas. Representan una decisión sobre Oriente, pero de ningún modo un hecho de la naturaleza. Cualquiera que, como Macdonald y Gibb, entre conscientemente a formar parte de una profesión llamada orientalismo, lo hace después de haber tomado una decisión: que Oriente es Oriente, que es diferente, etc. Las elaboraciones, refinamientos y consecuentes articulaciones del campo mantienen y, por tanto, prolongan la decisión de confinar o encerrar Oriente. No se puede apreciar ninguna ironía en las opiniones de Macdonald (o de Gibb) sobre la aptitud del oriental para estar marcado por una sola idea; ninguno de los dos parece capaz de reconocer en qué medida la aptitud del _orientalismo_ puede estar marcado por la sola idea de la diferencia oriental. Y ninguno de los dos se preocupa por utilizar las denominaciones de «islam» u «Oriente» sin hacer distinciones, usándolas como nombres propios con adjetivos atributivos y verbos que se derivan de ellos como si se refirieran a personas y no a ideas platónicas.
No por casualidad el dominio de casi todas las obras de Gibb sobre el islam y los árabes, era la tensión entre el «islam» como realidad oriental trascendente y coaccionante, y las realidades de la experiencia cotidiana. Como erudito y como cristiano devoto, su interés se centraba en el «islam», pero las complicaciones introducidas en esta religión por el nacionalismo, la lucha de clases, las experiencias individualizantes del amor, la cólera o el trabajo eran relativamente triviales para él. El carácter empobrecedor de esta inversión es particularmente evidente en _Whither Islam_?, de 1933, un volumen del cual Gibb fue el editor y al que contribuyó con un ensayo que da título a la obra (este libro también incluye un notorio artículo de Massignon sobre el islam norteafricano). La tarea de Gibb, según la comprendía él, era enjuiciar el islam, su situación presente y su posible porvenir. En esta tarea, las regiones individuales y manifiestamente diferentes del mundo islámico iban a ser más que refutaciones de la unidad del islam, ejemplos de ella. El propio Gibb propuso, a manera de introducción, una definición del islam; luego, en el artículo que sirve de conclusión al ensayo pretende pronunciarse sobre su realidad actual y su futuro real. Como Macdonald, Gibb parece totalmente a gusto con la idea de un Oriente monolítico cuyas circunstancias existenciales no se pueden reducir fácilmente a la raza o a la teoría racial; al negarle resolutamente todo valor a la generalización racial, Gibb se sentía por encima de todo aquello que había sido más reprensible a las generaciones de orientalistas precedentes. Gibb tiene, por tanto, una visión generosa y comprensiva del universalismo del islam y de su tolerancia, las cuales permitieron a diferentes comunidades étnicas y religiosas coexistir en paz y democráticamente dentro de su imperio. Hay una nota de profetismo amenazante en Gibb cuando distingue a los sionistas y a los cristianos maronitas como las únicas comunidades étnicas del mundo islámico que son incapaces de aceptar la coexistencia.
Sin embargo, el núcleo del argumento de Gibb es que el islam, quizá porque representa finalmente la preocupación exclusiva del oriental más que por la naturaleza, por lo invisible, el cual tiene una prioridad y un dominio últimos sobre la vida entera del Oriente islámico. Para Gibb, el islam _es_ ortodoxia islámica, _es_ también comunidad de creyentes, _es_ vida, unidad, inteligibilidad y valores. _Es_ también ley y orden, a pesar de las interrupciones de mal gusto de los yihadíes y de los agitadores comunistas. Al leer una página tras otra de la prosa de Gibb en _Whither Islam_? aprendemos que los nuevos bancos comerciales de Egipto y Siria son hechos islámicos o de iniciativa islámica; que las escuelas y el nivel creciente de alfabetización son realidades islámicas, también, como el periodismo, la occidentalización y las sociedades intelectuales. En ningún momento Gibb habla del colonialismo europeo cuando estudia el auge del nacionalismo y sus «toxinas». Nunca se le ocurre pensar que la historia del islam moderno podía ser más inteligible si se tuviera en cuenta su resistencia, política o no, al colonialismo, y le parece irrelevante indicar si los gobiernos «islámicos» de los que habla son republicanos, feudales o monárquicos.
El «islam», para Gibb, es una especie de superestructura puesta en peligro por la política (el nacionalismo, la agitación comunista, la occidentalización) y por los peligrosos intentos musulmanes de interferir en su soberanía intelectual. En el párrafo siguiente, nótese cómo el término _religión_ y sus cognados o afines dan el tono de la prosa de Gibb, a la vez que lo da también una cierta irritación decorosa a propósito de las presiones mundanas ejercidas sobre el «islam»:
El islam, como religión, apenas ha perdido su fuerza, pero islam como árbitro de la vida social [en el mundo moderno] está siendo destronado; al lado de esto, o encima, nuevas fuerzas ejercen una autoridad que a veces está en contradicción con sus tradiciones y sus prescripciones sociales, pero que, sin embargo, son fuerzas que se labran su camino. Por decirlo en los términos más simples posible, lo que ha ocurrido es esto. Hasta hace poco, el musulmán corriente, ciudadano y campesino, no tenía ningún interés ni función políticos, no tenía un fácil acceso a ninguna literatura, excepto a la literatura religiosa, no tenía festivales ni vida comunitaria excepto la que se vinculaba con la religión, lo poco o nada que veía del mundo exterior, lo hacía a través de las lentes de la religión. _En consecuencia, para él la religión lo_ _significaba todo_. Ahora, sin embargo, sobre todo en los países más avanzados, sus intereses se han extendido y sus actividades no están ya limitadas por la religión. Tiene inquietudes políticas; lee, o hace que le lean, una gran cantidad de artículos sobre temas de todo tipo que no tienen nada que ver con la religión, y en los que el punto de vista religioso no se menciona en absoluto y el veredicto depende de principios totalmente diferentes [...]». [La cursiva está añadida.]
Hay que admitir que esta imagen es un poco difícil de concebir, ya que, a diferencia de cualquier otra religión el _islam es o significa todo_. Como descripción de un fenómeno humano, la hipérbole, creo, solo aparece en el orientalismo. La propia vida —la política, la literatura, la energía, la actividad, el crecimiento— es una intrusión (para un occidental) en esta totalidad oriental inimaginable. Pero en tanto que «complemento y contrapunto de la civilización europea», el islam en su forma moderna es, no obstante, un objeto útil: este es el núcleo de la declaración o proposición de Gibb sobre el islam moderno. En efecto, «según la perspectiva más amplia de la historia, lo que ahora está sucediendo entre Europa y el islam es la reintegración de la civilización occidental, que fue artificialmente quebrantada por el Renacimiento y que reafirma ahora su unidad con una fuerza superior».
A diferencia de Massignon, que no hace ningún esfuerzo por ocultar sus especulaciones metafísicas, Gibb enuncia las suyas como si se tratara de conocimientos objetivos (una categoría que él echa de menos en Massignon). Sin embargo, según casi todos los criterios, la mayor parte de las obras generales de Gibb sobre el islam _son_ metafísicas, no solo porque usa abstracciones, como la de «islam», como si tuvieran un significado claro y distintivo, sino también porque nunca se ve con nitidez dónde, en el tiempo y en el espacio, se sitúa el «islam» de Gibb. Si, por un lado y siguiendo a Macdonald, sitúa al islam definitivamente fuera de Occidente, por otro, en gran parte de su obra, lo «reintegra» a Occidente. En 1955 hizo algunas aclaraciones sobre esta cuestión de interior-exterior: Occidente solo tomó del islam aquellos elementos no científicos que se habían derivado originariamente de Occidente, mientras que, al adoptar la ciencia islámica, Occidente simplemente seguía la ley según la dual «la ciencia natural y la tecnología [...] son indefinidamente transmisibles». El resultado neto es que el islam en «el arte, la estética, la filosofía y el pensamiento religioso» es un fenómeno de segundo orden (ya que estos proceden de Occidente), y en lo que se refiere a la ciencia y a la técnica, un simple canal para los elementos que no son islámicos _sui generis_.
Cualquier claridad sobre lo que el islam es en el pensamiento de Gibb deberá encontrarse en el interior de estas limitaciones metafísicas y, de hecho, sus dos importantes obras de los años cuarenta _Modern Trends in Islam_ , y _Mahommedanism: An Historical Survey_ proporcionan bastante material sobre todo esto. En ambos libros, a Gibb le cuesta estudiar la crisis presente del islam, oponiendo su ser inherente y esencial a las tentativas modernas que se han realizado para modificarlo. Ya he mencionado antes la hostilidad de Gibb con respecto a las corrientes modernizadoras del islam y su obstinado compromiso con la ortodoxia islámica. Es momento ahora de mencionar la preferencia de Gibb por la palabra _mahometanismo_ en vez de _islam_ (ya que, dice él, el islam realmente se basa en una idea de sucesión apostólica que culminó con Mahoma) y su afirmación de que la ciencia por excelencia del islam es el derecho, que muy pronto reemplazó a la teología. Lo que es verdaderamente curioso acerca de estas afirmaciones es que son enunciados sobre el islam hechos no sobre la base de la evidencia interna al islam, sino, más bien, sobre la de una lógica deliberadamente externa al islam. Ningún musulmán se llamará a sí mismo mahometano ni, como se sabe, sentirá necesariamente que el derecho sea más importante que la teología. Lo que hace Gibb es situarse, como erudito, dentro de las contradicciones que él mismo discierne en ese punto del «islam» en el que «hay una cierta dislocación no expresada entre el proceso formal exterior y las realidades interiores».
El orientalista, por tanto, considera que su misión es explicar esta dislocación y, en consecuencia, decir la verdad sobre el islam que, por definición —ya que sus contradicciones inhiben su poder de autodiscernimiento—, el islam no puede explicar ni expresar. La mayor parte de las afirmaciones generales de Gibb sobre el islam proporcionan al islam unos conceptos que la religión o la cultura, de nuevo por _su_ definición, no pueden abarcar. «La filosofía oriental nunca valoró la idea fundamental de justicia de la filosofía griega.» En cuanto a las sociedades orientales «a diferencia de las sociedades occidentales, [ellas] generalmente se han consagrado a sí mismas a construir organizaciones sociales estables [más que a] conformar sistemas ideales de pensamiento filosófico». La principal debilidad interna del islam es que «rompió la asociación entre las órdenes religiosas y las clases superiores y medias musulmanas». No obstante, Gibb también es consciente de que el islam nunca se ha quedado aislado del resto del mundo y, por tanto, debe de estar sujeto a una serie de dislocaciones exteriores, de insuficiencias y de disyunciones entre él y el mundo. Así, dice que el islam moderno es el resultado de una religión clásica que entra en contacto asincrónico con las ideas occidentales románticas. Por reacción a este asalto, el islam desarrolla una escuela de modernistas cuyas ideas revelan desesperación, ideas adoptadas al mundo moderno: el mahdismo, el nacionalismo, el califato revivido. Pero la reacción conservadora a este modernismo no está menos inadaptada a la modernidad, ya que ha generado una especie de ludismo estricto. Entonces nos preguntamos, ¿qué es el islam, a fin de cuentas, si no puede dominar sus dislocaciones internas ni tratar satisfactoriamente con su entorno? La respuesta se puede encontrar en el siguiente párrafo de _Modern Trends_ :
El islam es una religión viva y vital, que apela a los corazones, mentes y conciencias de cientos de miles de seres, les proporciona una norma según la cual vivir con honestidad, con sobriedad y con temor de Dios. No es el islam lo que está petrificado, sino sus formulaciones ortodoxas, su teología sistemática y su apología social. Aquí es verdaderamente donde se encuentran las dislocaciones, donde se siente el descontento de muchos de sus fieles más instruidos e inteligentes y donde el peligro para el futuro es más evidente. Ninguna religión puede, en última instancia, resistir la desintegración si una brecha perpetua separa las exigencias de su voluntad y el recurso al intelecto de sus fieles. El hecho de que el problema de la dislocación no haya sido todavía planteado por la gran mayoría de los musulmanes justifica la negación de los ulemas a dejarse presionar para tomar las medidas apresuradas que prescriben los modernistas; pero la extensión del modernismo es un aviso de que no podemos aplazar indefinidamente la reformulación.
Al intentar determinar los orígenes y las causas de la petrificación de las fórmulas del islam, podemos, quizá, encontrar algunas claves que nos ayuden a responder a la cuestión que los modernistas plantean, y que hasta ahora no han sido capaces de contestar; la cuestión de la manera en que se pueden reformular los principios fundamentales del islam sin que sus elementos esenciales se vean afectados.
La última parte de este fragmento es bastante familiar: hace pensar en la capacidad tradicional que ya tiene el orientalista para reconstruir y reformular Oriente dada la incapacidad de Oriente para hacerlo por sí mismo. En parte, pues, el islam de Gibb existe _antes que_ el islam tal y como se practica, se estudia y se predica en Oriente. Pero este islam prospectivo no es una mera ficción orientalista derivada de sus ideas: se fundamenta en un «islam» que —como no puede existir realmente— _apela_ a toda una comunidad de creyentes. La razón de que el «islam» puede existir en la formulación más o menos futura que el orientalista hace de él es que en Oriente el islam es usurpado y traducido por el lenguaje de su clero, el cual hace un llamamiento al espíritu de la comunidad. Mientras la llamada sea silenciosa, el islam estará a salvo; cuando el clero reformador retoma su papel (legítimo) de reformular el islam para hacerlo capaz de entrar en la modernidad, comienza el problema. Y este problema es, naturalmente, la dislocación.
En la obra de Gibb, la dislocación designa algo más significativo que una supuesta dificultad intelectual interior al islam. Esta palabra denota, creo, el propio privilegio del orientalista y la propia posición en la que se sitúa para escribir, legislar y reformular el islam. Lejos de ser un discernimiento casual de Gibb, la dislocación es la vía epistemológica que le lleva hacia su tema y, en consecuencia, la plataforma de observación desde la cual podía tener una visión de conjunto del islam en todos sus escritos y en todos los puestos importantes e influyentes que ocupó. Entre el llamamiento silencioso del islam a una comunidad monolítica de creyentes ortodoxos y una articulación totalmente verbal del islam realizada por un cuerpo de activistas políticos engañado, burócratas desesperados y reformadores oportunistas, estaba Gibb y desde ahí escribió y reformuló. Escribió lo que el islam no podía decir y lo que el clero no quería decir. Lo que Gibb escribió iba de alguna manera por delante del islam; en ese sentido reconoció que en algún momento del futuro el islam podría decir lo que no podía decir entonces. En otro sentido importante, sin embargo, los escritos de Gibb sobre el islam se adelantaron a la religión en tanto que cuerpo coherente de creyentes «vivos», ya que sus obras podían abarcar el «islam» como un llamamiento silencioso hecho a los musulmanes _antes_ de que su fe se convirtiera en un tema de discusión, de práctica o de debate en el mundo.
La contradicción en la obra de Gibb —ya que es una contradicción hablar del «islam» diciendo lo que no quiere decir su clero y lo que sus fieles laicos, si pudieran hablar, dirían— es atenuada de algún modo por la actitud metafísica que predomina en su obra y que de hecho predomina en toda la historia del orientalismo moderno que él heredó a través de mentores como Macdonald. Oriente y el islam tienen una especie de categoría extra-real y reducida desde un punto de vista fenomenológico que los sitúa fuera del alcance de cualquiera que no sea un experto occidental. Desde el comienzo de la especulación occidental sobre Oriente, una de las cosas que Oriente no podía hacer era representarse a sí mismo. El testimonio de Oriente solo era creíble después de pasar a través del trabajo orientalista y refinado por él. La obra de Gibb pretende ser el islam (o el mahometanismo) _como es_ y _como podría ser_. Desde un punto de vista metafísico —y solo metafísico—, él hace de la esencia y la potencialidad un solo hecho. Solo una actitud metafísica pudo producir los famosos ensayos de Gibb «The Structure of Religious Thought in Islam» o «An Interpretation of Islamic History» sin dejarse inquietar por la distinción entre conocimiento objetivo y subjetivo de la crítica de Gibb a Massignon. Las afirmaciones sobre el «islam» se enuncian con una confianza y una serenidad verdaderamente olímpicas. No hay ninguna dislocación ni discontinuidad sentida entre las páginas de Gibb y el fenómeno que describe, ya que cada uno de ellos, según el propio Gibb, puede reducirse al otro. Así, el «islam» y la descripción que Gibb hace de él tienen una tranquilidad, una simplicidad discursiva cuyo factor común es la página bien ordenada del erudito inglés.
Concedo mucha importancia a la apariencia y al modelo elegido de la página orientalista como objeto impreso. En este libro he hablado de la enciclopedia alfabética de D'Herbelot, de las gigantescas hojas de la _Description de l'Égypte_ , del cuaderno de laboratoriomuseo de Renan, de las elipses y pequeños episodios de _Modern Egyptians_ , de Lane, de los extractos antológicos de Sacy, etc. Estas páginas son signos de un cierto Oriente y de un cierto orientalista presentados al lector. Hay un orden en estas páginas por el cual el lector no solo aprehende «Oriente» sino también al orientalista como intérprete, exhibidor, personalidad, mediador y experto representativo (y representante). De una manera notoria Gibb y Massignon produjeron páginas que recapitulaban la historia de los escritos orientalistas en Occidente como si esta historia estuviera encarnada en diversos estilos genéricos y topográficos y reducida finalmente a la uniformidad de las monografías eruditas. El espécimen oriental, el exceso oriental, la unidad lexicográfica oriental, la serie oriental y el ejemplo oriental: todos estos han sido subordinados en Gibb y Massignon a la autoridad lineal y prosaica del análisis discursivo presentado en ensayos, en artículos cortos y en libros eruditos universitarios. En su época, desde el final de la Primera Guerra Mundial hasta el principio de los años sesenta, tres formas principales de obras orientalistas se transformaron radicalmente: la enciclopedia, la antología y el relato personal. Su autoridad se redistribuyó, o se dispersó o se disipó para pasar a un comité de expertos ( _The Encyclopaedia of Islam_ , _The Cambridge History of Islam_ ) a un servicio de nivel menos elevado (enseñanza elemental de lenguas que no solo prepara para la diplomacia, como era el caso de la _Chrestomathie_ de Sacy, sino para el estudio de la sociología, la economía o la historia) o a un dominio de revelaciones sensacionales (que tienen más que ver con personalidades o gobiernos —Lawrence es el ejemplo más evidente— que con la ciencia). Gibb, con su prosa tranquila y descuidada pero profundamente secuencial, y Massignon, con el instinto de un artista para quien ninguna referencia es demasiado extravagante mientras esté dominada por un talento interpretativo excéntrico, llevaron la autoridad esencialmente _ecuménica_ del orientalismo europeo tan lejos como podía llegar. Después de ellos la nueva realidad —el nuevo estilo especializado— fue de manera general anglo-estadounidense y, hablando más estrictamente, el de las ciencias sociales estadounidenses. El viejo orientalismo se rompió en mil pedazos; sin embargo, cada uno de ellos todavía sirvió a los dogmas orientalistas tradicionales.
### IV
### La fase reciente
Desde la Segunda Guerra Mundial, y más exactamente a partir de las guerras arabo-israelíes, el árabe musulmán se ha convertido en una figura de la cultura popular estadounidense; del mismo modo, en el mundo académico, en el de la política y en el de los negocios se ha prestado mucha atención a los árabes. Esto simboliza el gran cambio que se produjo en la configuración internacional de fuerzas. Francia y Gran Bretaña ya no ocupan el centro de la escena política mundial; el Imperio estadounidense los ha desplazado. Todas las partes del mundo que antes estuvieron colonizadas están ahora vinculadas a Estados Unidos a través de una compleja red de intereses, y la proliferación de especialidades universitarias separa (y, sin embargo, conecta) todas las antiguas disciplinas filológicas creadas en Europa, como es el caso del orientalismo. El especialista en áreas culturales, como se llama hoy día, reivindica la competencia de un experto regional, que se pone al servicio del gobierno, del mundo de los negocios o de ambos. El conjunto de conocimientos cuasi materiales almacenados en los anales del orientalismo europeo moderno —tal y como consta, por ejemplo, en el registro que Jules Mohl hizo en el siglo XIX— se disolvió y se ha puesto de nuevo en circulación con nuevas formas. Toda una serie de representaciones híbridas de Oriente habitan la cultura. Japón, Indochina, India, Pakistán: sus representaciones han tenido y siguen teniendo grandes repercusiones, y han sido estudiadas y discutidas en muchos lugares por razones evidentes. El islam y los árabes tienen su propia representación también, y nos ocuparemos de ella aquí tratándolos como aparecen, con esa persistencia fragmentaria —aunque de una poderosa coherencia ideológica— que ha sido poco discutida y dentro de la cual el orientalismo europeo tradicional, en Estados Unidos, se ha readaptado.
1. _Imágenes populares y representaciones científicas_
A continuación voy a exponer algunos ejemplos sobre cómo se representa al árabe hoy día. Nótese hasta qué punto «el árabe» parece dispuesto a acoplarse a las transformaciones y reducciones —todas de una clase especialmente tendenciosa— a las que de modo constante se le fuerza. El disfraz que se había pensado para la décima reunión de alumnos de la Universidad de Princeton se tenía preparado antes de la guerra árabe-israelí en junio de 1967. El disfraz elegido —sería un error describirlo como algo más que una cruda sugerencia— era el de árabe: una túnica, el tocado y las sandalias. Justo después de la guerra, cuando se empezó a percibir que el tema árabe era embarazoso, se decidió hacer un cambio en el programa de la reunión. El plan original había sido llevar el disfraz a la reunión; el cambio suponía que la clase debía marchar en procesión con las manos sobre la cabeza en un gesto abyecto de derrota. En esto era en lo que se habían convertido los árabes. Habían dejado de ser el vago estereotipo de unos nómadas camelleros para pasar a ser una caricatura aceptada que los mostraba como la imagen misma de la incompetencia y de la derrota; este era todo el margen que se les daba.
Sin embargo, después de la guerra de 1973 los árabes empezaron a perfilarse como una gran amenaza. Aparecían constantemente dibujos que mostraban a un _sheij_ árabe de pie al lado de un surtidor de gasolina. Estos árabes, no obstante, eran claramente «semitas»: sus agudas narices de gancho y su malvada sonrisa bajo el bigote recordaban a una población no semita que los «semitas» estaban detrás de «todos» nuestros problemas. En este caso, el problema era principalmente la escasez de petróleo. El ánimo popular antisemita se transfirió suavemente del judío al árabe, ya que la figura era más o menos la misma.
Así, si alguna vez se presta atención al árabe es siempre como un valor negativo. Se le considera un elemento perturbador de la existencia de Israel y de Occidente o, desde otra perspectiva, un obstáculo insalvable para la creación del Estado de Israel en 1948. En la medida en que este árabe tenga cualquier historia, esta es una parte de la historia que le ha dado (o que le ha quitado, la diferencia es mínima) la tradición orientalista y después la tradición sionista. Palestina era considerada —por Lamartine y los primeros sionistas— un desierto vacío que esperaba que le llegara el momento de florecer; se suponía que los habitantes que podía haber allí eran nómadas sin importancia que no tenían ningún derecho sobre la tierra y, por tanto, ninguna realidad cultural o nacional. Así, el árabe se concibió a partir de entonces como una sombra que seguía los pasos de los judíos. En esta sombra —porque los árabes y los judíos eran orientales semitas— se podía situar cualquier tipo de desconfianza tradicional y latente que el occidental pudiera sentir hacia Oriente. En efecto, el judío de la Europa prenazi se ha bifurcado: lo que ahora nos encontramos es un héroe judío conformado a partir de un culto reconstruido del orientalista-aventurero-pionero (Burton, Lane, Renan), y su sombra rastrera, misteriosamente temible, que es el árabe oriental. Aislado de todo salvo del pasado que la polémica orientalista creó para él, el árabe está encadenado a un destino que le fija y le condena a una serie de reacciones periódicamente castigadas por lo que Barbara Tuchman llama con un nombre teológico «la terrible y rápida espada de Israel».
Además de su antisionismo, el árabe es un abastecedor de petróleo. Esta es otra característica negativa, ya que en la mayor parte de las disertaciones sobre el petróleo árabe, se hace corresponder el boicot de 1973-1974 (que principalmente benefició a las compañías petrolíferas occidentales y a una pequeña elite de gobernantes árabes), con la ausencia de cualquier cualificación moral árabe para poseer esa vasta reserva de petróleo. Sin los eufemismos habituales, la cuestión que normalmente se plantea es si gente como los árabes tienen el derecho de mantener al mundo desarrollado (libre, democrático y moral) amenazado. De este tipo de cuestiones se pasa con frecuencia a la sugerencia de que los marines podrían invadir los campos petrolíferos árabes.
En el cine y en la televisión, el árabe se asocia con la lascivia o con una deshonestidad sanguinaria. Aparece como un degenerado hipersexual, bastante capaz, es cierto, de tramar intrigas tortuosas, pero esencialmente sádico, traidor y vil. Comerciante de esclavos, camellero, traficante, canalla subido de tono: estos son algunos de los papeles tradicionales que los árabes desempeñan en el cine. El líder árabe (líder de indeseables, piratas e «indígenas» insurgentes) se puede ver con frecuencia chillando al héroe y a la rubia occidentales capturados (y llenos de santidad): «Mis hombres os van a matar, pero antes se quieren divertir un poco». Mientras habla, echa una mirada maliciosa a la rubia: esta es una imagen degradada del _sheij_ de Valentino que está en circulación. En los resúmenes de actualidad y en las fotografías de prensa, los árabes aparecen siempre en multitudes, sin ninguna individualidad, ninguna característica o experiencia personal. La mayoría de las imágenes representan el alcance y la miseria de la masa o sus gestos irracionales (y de ahí desesperadamente excéntricos). Detrás de todas estas imágenes está la amenaza del _yihad_ ; su consecuencia inmediata es el temor a que los musulmanes (o árabes) invadan el mundo.
Los libros y artículos sobre el islam y los árabes que se publican regularmente no se diferencian en absoluto de las virulentas polémicas antiislámicas de la Edad Media y del Renacimiento. No existe ningún otro grupo étnico o religioso sobre el que se pueda decir o escribir cualquier cosa sin tropezar con ninguna objeción o protesta. La guía del curso 1975 publicada por los estudiantes no graduados del Columbia College decía, a propósito de los cursos de árabe, que una de cada dos palabras en esta lengua tenía que ver con la violencia, y que el espíritu árabe, según lo «refleja» la lengua, está siempre lleno de afectación. En un reciente artículo escrito por Emmett Tyrrell en _Harper's Magazine_ , la calumnia racista está todavía más marcada. Dice que los árabes son básicamente asesinos y que la violencia y el fraude se los transmiten unos a otros a través de los genes. Un estudio titulado _The Arabs in American Textbooks_ revela una serie de errores sorprendentes y unas representaciones de un grupo étnico-religioso que hacen gala de una gran dureza e insensibilidad. Un manual afirma que «poca gente de esta zona [árabe] sabe siquiera que hay una mejor forma de vida» y luego sigue preguntando de manera desarmante: «¿Qué mantiene a los pueblos de Oriente Próximo juntos?». La respuesta que da sin dudar ni un momento es: «El lazo más fuerte es la hostilidad de los árabes —su odio— hacia los judíos y hacia el Estado de Israel». En otro libro encontramos esta materia sobre el islam: «La religión musulmana, llamada islam, empezó en el siglo VII. La empezó un rico negociante de Arabia llamado Mahoma. Se decía profeta. Encontró seguidores entre otros árabes; les dijo que ellos habían sido elegidos para gobernar el mundo». A este trozo de ciencia le sigue otro igualmente preciso: «Poco después de la muerte de Mahoma, sus enseñanzas se anotaron en un libro llamado Corán. Se convirtió en el libro sagrado del islam».
Estas crudas, y a veces simplistas, ideas se veían apoyadas y no contradichas por el universitario cuyo trabajo era estudiar el Oriente Próximo árabe. (Merece la pena señalar de pasada que la ceremonia de Princeton a la que me he referido antes tuvo lugar en una universidad que se enorgullece de su departamento de estudios sobre Oriente Próximo, departamento que se fundó en 1927 y que es el más antiguo de Estados Unidos.) Tomemos como ejemplo el informe escrito en 1967 por Morroe Berger, profesor de sociología y estudios de Oriente Próximo en Princeton, a petición del Departamento de Salud, Educación y Asistencia Social; era entonces presidente de la Middle East Studies Association (MESA), una asociación profesional de eruditos que se ocupaba de todos los aspectos de Oriente Próximo «en primer lugar desde el nacimiento del islam y desde el punto de vista de la ciencia social y de las disciplinas humanísticas», y fundada en 1967. Él tituló su artículo «Middle Eastern and North African Studies: Developments and Needs», que fue publicado en el segundo número de _MESA Bulletin_. Después de examinar la importancia estratégica, económica y política de la región para Estados Unidos y de aprobar los diferentes proyectos del gobierno de Estados Unidos y de las fundaciones privadas para apoyar los programas en las universidades —el National Defense Education Act de 1958 (una iniciativa directamente inspirada por el _Sputnik_ ), el estado de relaciones entre el Social Sciences Research Council y los estudios sobre Oriente Próximo, etc.—, Berger llega a las siguientes conclusiones:
El Oriente Próximo y el África del norte modernos no son el centro de grandes logros culturales y no es probable que lo lleguen a ser en un futuro inmediato. El estudio de la región o de sus lenguas, por tanto, no recompensa al investigador en lo que se refiere a la cultura moderna.
[...] Nuestra región no es un centro de poder político ni tiene la posibilidad de serlo [...]. Oriente Próximo (en menor medida que África del norte) ha visto reducida su importancia política (e incluso sus «titulares» y «problemas») en favor de Estados Unidos, África, América Latina y Extremo Oriente.
[...] Así, el Oriente Próximo de hoy cumple muy escasamente los requisitos que parecen importantes para llamar la atención de los eruditos. Esto no disminuye la validez o el valor intelectual de los estudios sobre esta región ni afecta a la calidad del trabajo que hacen los eruditos. Sin embargo, limita, y de esto deberíamos ser conscientes, la capacidad del campo para crecer en número de estudiantes y de profesores.
Como profecía, este texto es lamentable; lo que lo hace todavía más desafortunado es que Berger había sido elegido no solo porque era un experto en el Oriente Próximo moderno, sino también —como se indica claramente en la conclusión de su informe— porque se suponía que estaba en una buena posición para predecir su futuro y el de la política futura. Creo que su incapacidad para ver que Oriente Próximo tenía una gran significación política y, potencialmente, un gran poder político no es una aberración fortuita. Sus dos principales errores, en el primer párrafo y en el último, se derivan genealógicamente de la historia del orientalismo tal y como la hemos expuesto. En lo que Berger dice acerca de la ausencia de grandes logros culturales y en lo que concluye sobre el estudio futuro —que Oriente Próximo no llama la atención de los eruditos por su debilidad intrínseca— tenemos una duplicación exacta de la opinión orientalista canónica de que los semitas nunca crearon una gran cultura y de que, como Renan dijo con frecuencia, el mundo semítico estaba demasiado empobrecido como para atraer la atención universal. Además, al hacer estos juicios consagrados por el uso y al estar totalmente ciego ante lo que tenía delante —después de todo Berger no escribía hace cincuenta años, sino durante el período en el que Estados Unidos importaba ya el 10 por ciento de su petróleo de Oriente Próximo y cuando sus inversiones estratégicas y económicas en la zona eran enormes— Berger estaba asegurando su propia posición central como orientalista. En efecto, lo que dice es que sin su mediación, sin su papel interpretativo, la región no se podría comprender y esto se debía, en parte, a que solo un orientalista era capaz de interpretar Oriente ya que Oriente era radicalmente incapaz de interpretarse a sí mismo.
El hecho de que Berger no fuera un orientalista clásico (no lo era y no lo es) cuando escribió esto, sino un sociólogo profesional, no disminuye la magnitud de su deuda con el orientalismo y sus ideas. Entre estas ideas se encuentra una antipatía especialmente legitimada hacia la materia de su estudio que se ve degradada por ella. Este sentimiento es tan fuerte que oscurece las realidades que tiene ante sus ojos y, lo que todavía es más sorprendente, le lleva a preguntarse por qué, si Oriente Próximo «no es un centro de grandes logros culturales», debe recomendar a alguien que dedique su vida, como él ha hecho, a estudiar esa cultura. Los eruditos —en mayor medida que, por ejemplo, los doctores— estudian lo que les gusta y lo que les interesa; solo un exagerado sentido del deber cultural puede llevar a un erudito a estudiar algo de lo que no tiene una buena opinión. Pero es justamente este sentido del deber lo que el orientalismo ha fomentado, porque durante generaciones la cultura en su conjunto ha situado al orientalista sobre unas barricadas, desde donde, a través de su trabajo profesional, se enfrentaba a Oriente —a su barbarie, sus excentricidades y su desorden— y lo mantenía a raya en beneficio de Occidente.
Menciono a Berger como ejemplo de la actitud académica hacia el Oriente islámico y como ejemplo de cómo una perspectiva erudita puede apoyar las caricaturas que propaga la cultura popular. No obstante, Berger representa también las transformaciones más corrientes que sufre el orientalismo; su conversión de una disciplina fundamentalmente filológica y desde una aprehensión vaga y general de Oriente, a una ciencia social y especializada. Ningún orientalista trata ya en sus inicios de conocer las lenguas esotéricas de Oriente, sino que comienza por adquirir una formación en ciencias sociales para luego «aplicar» su ciencia a Oriente o a cualquier otro lugar. Esta es la contribución específica de Estados Unidos a la historia del orientalismo y puede fecharse, _grosso modo_ , a partir del período inmediatamente posterior a la Segunda Guerra Mundial, cuando Estados Unidos ocupa la posición que acaban de dejar Gran Bretaña y Francia. Con anterioridad a este momento excepcional, la experiencia americana en Oriente se limitaba a algunos ejemplos aislados en la cultura, como Melville, quien se interesó por él, algunos cínicos, como Mark Twain, que lo visitaron y escribieron sobre él, los trascendentalistas, que vieron afinidades entre el pensamiento indio y el suyo propio y unos cuantos estudiantes de teología y de estudios bíblicos, que estudiaron las lenguas orientales bíblicas. Hubo también algunos encuentros diplomáticos y militares ocasionales con los piratas de la barbarie y gentes de su calaña y también se llevó a cabo una rara expedición naval al Extremo Oriente; naturalmente, también estaban allí, como en todas partes, los misioneros. Sin embargo, no había una tradición profundamente sentida de orientalismo y, en consecuencia, en Estados Unidos el conocimiento sobre Oriente nunca pasó, como hizo en Europa, por los procesos de refinamiento, división y reconstrucción que empezaron con el estudio filológico. Además, tampoco existió una inversión imaginaria, quizá porque la frontera estadounidense que contaba era la que tenía con el Oeste. Inmediatamente después de la Segunda Guerra Mundial, Oriente se convirtió, más que en la cuestión religiosa que había sido durante siglos para Europa, en una cuestión administrativa y política. Entraron en escena el nuevo científico social y el nuevo experto sobre cuyos hombros iba a recaer el peso del orientalismo. En su momento, como veremos, realizaron tales cambios que el orientalismo se transformó en algo difícil de reconocer. En cualquier caso, el nuevo orientalista retomó las actitudes culturales hostiles y las mantuvo.
Un aspecto sorprendente de la atención que las nuevas ciencias sociales estadounidenses prestan a Oriente es que evita la literatura. Podemos leer páginas y páginas escritas por expertos en el Oriente Próximo moderno sin encontrar nunca ni la más mínima referencia a la literatura. Lo que parece ser mucho más importante para el experto regional son los «hechos» que un texto literario quizá puede distorsionar. El efecto que tiene esta importante omisión de la conciencia estadounidense moderna sobre el Oriente árabe o islámico es mantener a esta región y a sus gentes conceptualmente mutiladas y reducidas a «actitudes», a «tendencias» y a estadísticas; en resumen, mantenerlas deshumanizadas. Cualquier poeta o escritor árabe —que son muy numerosos— escribe sobre sus experiencias, sus valores y su humanidad (por muy extraño que pueda parecer), y de esta manera perturba de modo eficaz los diversos esquemas (imágenes, estereotipos y abstracciones) por los que se representa a Oriente. Un texto literario habla más o menos de la realidad viva. Su fuerza no reside en que sea árabe, francés o inglés; su fuerza está en el poder y en la vitalidad de las palabras que, por introducir una metáfora de Flaubert extraída de _La tentación de san Antonio_ , arrancan a los ídolos de los brazos de los orientalistas y les hacen abandonar esas abominables criaturas —que son sus ideas sobre Oriente— que intentan hacer pasar por Oriente.
El hecho de que la literatura esté ausente en los estudios estadounidenses contemporáneos sobre Oriente Próximo y de que la filología ocupe una posición bastante precaria ilustra una nueva excentricidad del orientalismo; y, en realidad, el uso que hago de este último término es anómalo, pues lo que hacen hoy los expertos académicos en Oriente Próximo se parece muy poco al orientalismo tradicional que terminó con Gibb y Massignon. Los principales aspectos que se reproducen son una cierta hostilidad cultural y un sentimiento que se fundamenta más en la competencia del «experto» que en la de la filología. Desde un punto de vista genealógico, el orientalismo estadounidense moderno se deriva de varias jerarquías como las escuelas de lenguas del ejército establecidas durante y después de la guerra, un repentino interés gubernamental y empresarial en el mundo no occidental durante el período de posguerra, la guerra fría con la Unión Soviética y una actitud misionera residual hacia los orientales a quienes consideraban listos para reeducarlos. El estudio no filológico de lenguajes esotéricos orientales era útil por obvias razones estratégicas rudimentarias; pero también era provechoso para dar un estatus de autoridad, casi místico, al experto, quien en demasiadas ocasiones debía tratar, con mucha pericia, con un material excesivamente oscuro.
En la jerarquía de las ciencias sociales, el estudio del lenguaje no es más que un mero instrumento para conseguir objetivos mayores, pero ciertamente no para leer textos literarios. En 1958, por ejemplo, el Middle East Institute —organismo cuasi gubernamental creado para fomentar y supervisar las investigaciones sobre Oriente Próximo— publicó un _Report on Current Research_. La contribución al «estado actual de los estudios árabes en Estados Unidos» (realizado, curiosamente, por un profesor de hebreo) tiene como prólogo un epígrafe que anuncia que «el conocimiento de lenguas extranjeras no es solo del dominio de los estudios literarios; es una útil herramienta de trabajo para ingenieros, economistas, científicos sociales y muchos otros especialistas». El informe completo destaca la importancia del árabe para los ejecutivos de compañías petrolíferas, los técnicos y el personal militar. Sin embargo, el punto más importante que trata el informe se resume en estas tres frases: «Las universidades rusas ahora están formando muchas personas que hablan árabe con fluidez. Rusia se ha dado cuenta de lo importante que es dirigirse al espíritu de los hombres utilizando su propia lengua. Estados Unidos no debe esperar más para desarrollar sus programas de lenguas modernas». Así, las lenguas orientales pasan a ser parte de algún objetivo político —como, hasta cierto punto, siempre han sido— o parte de algún esfuerzo continuo de propaganda. En ambos casos, el estudio de las lenguas orientales se convierte en un instrumento de las tesis de Harold Lasswell sobre la propaganda, en las que lo que cuenta no es lo que la gente es, o piensa, sino lo que se le puede hacer ser o pensar:
El punto de vista del propagandista combina, en realidad, el respeto por la individualidad con la indiferencia por la democracia formal. El respeto por la individualidad proviene de la dependencia que se establece entre las operaciones a gran escala y el apoyo que reciben de la masa y de la experiencia de las diversas preferencias humanas. [...] Este interés por los hombres en masa no responde a ningún dogmatismo democrático basado en la creencia de que los hombres son los mejores jueces de sus propios intereses. El propagandista moderno, como el psicólogo moderno, reconoce que los hombres a menudo son malos jueces de sus propios intereses, que van revoloteando de una opción a otra sin una razón sólida o que se reenganchan tímidamente a los fragmentos de alguna rosa fosilizada del pasado. Calcular la posibilidad de transformar de manera duradera los hábitos y los valores implica mucho más que evaluar cuáles son las preferencias de los hombres en general. Significa tener en cuenta la red de relaciones en la que los hombres están atrapados, buscar signos de preferencia que puedan no reflejar ninguna deliberación y dirigir un programa hacia una solución que en realidad sea apropiada. [...] Con respecto a los ajustes que necesita una acción de masas, la labor del propagandista es inventar símbolos objetivos que tengan el doble papel de facilitar la adopción y la adaptación. Estos símbolos deben inducir espontáneamente a la aceptación. [...] Continúa con que la dirección ideal es controlar la situación no de manera impositiva, sino por adivinación. [...] El propagandista da por supuesto que el mundo es totalmente causal, pero que solo parcialmente es predecible [...].
La adquisición de una lengua extranjera es, pues, un elemento que forma parte de un asalto sutil contra las poblaciones, igual que el estudio de una región extranjera se convierte en un programa de control por adivinación.
Este programa, sin embargo, debe conservar siempre un barniz liberal que normalmente se deja en manos de los eruditos, hombres de buena voluntad o entusiastas. La idea es que, al estudiar a los orientales, a los musulmanes o a los árabes, «nosotros» podemos llegar a conocer otro pueblo, su forma de vida y pensamiento, etc. Con este objetivo, siempre es mejor dejarles hablar por sí mismos, representarse (aunque tras esta ficción esté la frase de Marx —con la que Lasswell está de acuerdo— a través de Luis Napoleón: «No pueden representarse a sí mismos, deben ser representados»), pero solamente hasta cierto punto y de manera particular. En 1973, durante los angustiosos días de la guerra árabe-israelí, el _New York Times Magazine_ había solicitado dos artículos, uno que representara el lado israelí del conflicto y otro el árabe. El primero se lo encargó a un jurista israelí, el segundo a un ex embajador estadounidense en un país árabe que no tenía ninguna formación en estudios orientales. Para no pasar inmediatamente a la simple conclusión de que se creía que los árabes eran incapaces de representarse a sí mismos, haríamos bien recordando que tanto árabes como judíos, en este caso, eran semitas (en el amplio sentido cultural del que he hablado) y que ambos _estaban siendo representados_ para un público occidental. Vale la pena ahora recordar el episodio de Proust en el que describe la entrada de un judío a un salón de la aristocracia:
Los romanos, los egipcios y los turcos pueden odiar a los judíos. Pero en un salón francés las diferencias entre estos pueblos apenas son perceptibles, y un israelita haciendo su entrada como si saliera de las profundidades del desierto, con el cuerpo doblado como el de una hiena, la nuca inclinada oblicuamente y esparciendo con orgullo _salams_ satisface completamente el gusto por lo oriental [ _un goût pour_ _l'orientalisme_ ].
2. _La política de relaciones culturales_
Es verdad que Estados Unidos no ha llegado a ser un imperio mundial hasta el siglo XX, pero también es verdad que el modo en que se interesó por Oriente durante el siglo XIX supuso una preparación para su posterior interés imperial. Dejemos aparte las campañas contra los piratas de Berbería de 1801 y 1815, y consideremos la fundación de la American Oriental Society en 1842. En su primera reunión anual de 1845, su presidente, John Pickering, expuso claramente que Estados Unidos se proponía estudiar Oriente, para seguir el ejemplo de las potencias imperiales europeas. El mensaje de Pickering decía que la estructura de los estudios orientales —entonces y ahora— era política y no simplemente erudita. Podemos observar en el siguiente resumen cómo sus argumentos en favor del orientalismo no ofrecen ninguna duda con respecto a sus intenciones:
En la primera reunión anual de la American Oriental Society en 1843, el presidente Pickering comenzó su notorio resumen del campo que se proponía cultivar llamando la atención sobre las circunstancias particularmente favorables del momento, la paz que reinaba en todas partes, el libre acceso a los países orientales y las grandes facilidades de comunicación. La Tierra parecía tranquila en los tiempos de Metternich y Luis Felipe. El Tratado de Nankín había abierto las puertas de China. Los buques que navegaban sobre el océano habían adoptado la propulsión a hélice. Morse había terminado su telégrafo y ya había propuesto la colocación de un cable transatlántico. Los objetivos de la sociedad eran cultivar el aprendizaje de las lenguas asiáticas, africanas y polinesias y en todo lo referente a Oriente, crear en el país un gusto por los estudios orientales, publicar textos, traducciones y ponencias y reunir una biblioteca y un gabinete. La mayor parte de este trabajo se ha realizado en el campo asiático, y particularmente en el sánscrito y las lenguas semíticas.
Metternich, Luis Felipe, el Tratado de Nankín y la propulsión a hélice dan una idea de la constelación imperial que facilitaba la penetración euro-americana en Oriente, y que de hecho nunca ha cesado. Incluso los legendarios misioneros estadounidenses que fueron a Oriente Próximo durante los siglos XIX y XX consideraron que su papel había sido determinado no tanto por Dios como por _su_ Dios, _su_ cultura y _su_ destino. Las primeras instituciones misioneras —imprentas, escuelas, universidades, hospitales, etc.— contribuyeron, naturalmente, al bienestar de la región, pero debido a su carácter específicamente imperial y al apoyo que recibían del gobierno de Estados Unidos, estas instituciones no fueron diferentes de sus simétricas francesas y británicas. Durante la Primera Guerra Mundial, entre las razones que pesaron para que Estados Unidos entrara en la guerra figuraba su interés político por el sionismo y Palestina (interés que con el tiempo cada vez sería mayor). Las discusiones con los británicos antes y después de la Declaración Balfour (noviembre de 1917) reflejan la seriedad con que Estados Unidos se tomó la declaración. Durante la Segunda Guerra Mundial y después de ella, los intereses de Estados Unidos en Oriente Próximo crecieron con bastante rapidez. El Cairo, Teherán y África del norte eran importantes escenarios de la guerra, y en ese decorado, con la explotación de sus recursos petrolíferos, estratégicos y humanos que habían comenzado Gran Bretaña y Francia, Estados Unidos se preparaba para ejercer su nuevo papel imperial después de la guerra.
Uno de los aspectos de este papel, y no el menos importante, era «la política de relaciones culturales», según lo definió Mortimer Graves en 1950. En su opinión, parte de esta política consistía en procurarse «todas las publicaciones interesantes escritas en alguna de las lenguas importantes de Oriente Próximo a partir de 1900», tentativa que «nuestro Congreso debería reconocer como una de las medidas que hay que adoptar para afianzar la seguridad de nuestro país». Lo que claramente estaba en juego, dijo Graves (hablando, a oídos muy receptivos, por cierto), era la necesidad de que «los estadounidenses comprendan mucho mejor las fuerzas que están compitiendo con nuestras ideas en Oriente Próximo. Las principales, evidentemente, son el comunismo y el islam». A partir de esta preocupación, y como una adición contemporánea a la American Oriental Society, que se inclinaba más hacia el pasado, nació un enorme aparato de investigación sobre Oriente Próximo. El modelo, tanto por su actitud francamente estratégica como por su sensibilidad para los asuntos políticos y de seguridad (y no por su pura erudición, como con frecuencia se pretende) fue el Middle East Institute, fundado en Washington en 1946 bajo los auspicios del gobierno federal, por no decir en su seno o por él. A partir de estas organizaciones fueron apareciendo la Middle East Studies Association, el poderoso apoyo de la Fundación Ford y de otras fundaciones, los diversos programas federales de ayuda a las universidades, varios proyectos federales de investigación, proyectos de investigación establecidos por entidades tales como el Departamento de Defensa, la RAND Corporation y el Hudson Institute y los esfuerzos hechos por los bancos, las compañías petroleras, las multinacionales, etc. No creo que sea minimizar las cosas decir que todo esto conserva, tanto por su funcionamiento general como por sus detalles, el punto de vista orientalista tradicional que se había desarrollado en Europa.
El paralelismo entre el proyecto imperialista europeo y el estadounidense en Oriente (tanto en Oriente Próximo como en el Extremo Oriente) es muy claro. Lo que tal vez sea menos obvio es, primero, hasta qué punto la tradición europea de erudición orientalista fue si no retomada, al menos acomodada, normalizada, domesticada, popularizada y mantenida dentro del florecimiento que durante la época de posguerra tuvieron los estudios sobre Oriente Próximo en Estados Unidos; y segundo, hasta qué punto la tradición europea ha dado lugar en Estados Unidos a una actitud coherente en la mayor parte de los eruditos, de las instituciones, de los estilos de discurso y de las orientaciones, aun a pesar de la aparición y el uso en ese mismo momento en las ciencias sociales de unos refinamientos y unas técnicas de apariencia (de nuevo) extraordinariamente sutiles. Ya he expuesto las ideas de Gibb. Sin embargo, debo señalar que a mediados de los cincuenta Gibb fue nombrado director del Harvard Center for Middle East Studies, puesto desde el cual sus ideas y su estilo ejercieron una influencia importante. La presencia de Gibb en Estados Unidos no tuvo la misma repercusión que la de Philip Hitti en Princeton desde finales de los años veinte. El Departamento de Princeton produjo un numeroso grupo de eruditos importantes, y la particular calidad de sus estudios orientales fomentó el interés erudito por el tema. Por otro lado, Gibb tuvo un contacto más real con los aspectos políticos del orientalismo; su posición en Harvard, mucho más que la de Hitti en Princeton, enfocó el orientalismo hacia una aproximación a la guerra fría a través de los estudios de áreas culturales.
La obra personal de Gibb, sin embargo, no empleaba abiertamente el lenguaje del discurso cultural de la tradición de Renan, Becker y Massignon. Pero encontramos que dicho discurso, su aparato intelectual y sus dogmas están muy presentes principalmente (aunque no exclusivamente) en el trabajo y la autoridad institucional de Gustave von Grunebaum en Chicago y después en UCLA. Gustave von Grunebaum llegó a Estados Unidos con la corriente inmigratoria intelectual de eruditos europeos que huían del fascismo. Desde entonces produjo una _oeuvre_ orientalista sólida que se concentró en el islam como cultura holística, y sobre la cual continuó haciendo, a lo largo de su carrera, generalizaciones esencialmente reduccionistas y negativas. Su estilo, en el que a menudo encontramos indicios caóticos de su polimatía austrogermana y de los prejuicios canónicos seudocientíficos del orientalismo francés, inglés e italiano, que él absorbió, y un esfuerzo casi desesperado por seguir siendo el erudito-observador imparcial, es de muy difícil comprensión. En una página típica suya, en la que trata la imagen que el islam tiene de sí mismo, reúne media docena de referencias a textos islámicos de tantos períodos como puede y también referencias a Husserl, a los presocráticos, a Lévi-Strauss y a diferentes investigadores estadounidenses de ciencias sociales. No le supone ningún problema pensar que el islam es un fenómeno unitario, a diferencia de todas las demás religiones y civilizaciones; a partir de ahí, expone que no es humano, que es incapaz de desarrollarse, de conocerse a sí mismo, de ser objetivo y que no es creativo ni científico, pero sí autoritario. Veamos dos fragmentos característicos de su obra. Debemos recordar que Von Grunebaum escribía con la especial autoridad con la que contaba un erudito europeo en Estados Unidos, que enseñaba, administraba y concedía becas a un gran número de eruditos de la disciplina:
Es esencial darse cuenta de que la civilización musulmana es una entidad cultural que no comparte nuestras aspiraciones básicas. No tiene ningún interés vital hacer un estudio estructurado de otras culturas, como fin o como medio, para comprender con mayor claridad su carácter y su historia. Si esta observación fuera válida solamente para el islam contemporáneo, nos inclinaríamos a vincularla con el estado profundamente perturbador del islam que no le permite ver más allá de sí mismo a no ser que se vea obligado a ello. Pero como también es válida para el pasado, quizá podamos intentar vincularla con el antihumanismo fundamental de esta civilización [islámica], es decir, con el rechazo resuelto a aceptar que el hombre, no importa hasta qué punto, es el árbitro o la medida de las cosas, y la tendencia a quedarse satisfechos con la verdad considerada como la descripción de las estructuras mentales o, en otras palabras, con la verdad psicológica.
[El nacionalismo árabe o islámico] carece, a pesar de que ocasionalmente lo utiliza como un tópico, del concepto de derecho divino de una nación, carece de una ética formativa y, también, carece de la creencia en el progreso mecanicista de finales del siglo XIX; y, sobre todo, carece del vigor intelectual que posee todo fenómeno primario. Tanto el poder como la voluntad de poder son fines en sí mismos [parece que esta frase no es útil para su razonamiento, pero le da a Von Grunebaum, sin duda, la seguridad de que habla del islam con sabiduría y no con maldad]. El resentimiento con respecto a las afrentas políticas [que siente el islam] engendra impaciencia e impide que las esferas intelectuales hagan planes y análisis a largo plazo.
En cualquier otro contexto, este tipo de escritos sería calificado de polémico. En el contexto orientalista, por supuesto, es relativamente ortodoxo, y pasa por ser la sabiduría canónica dentro de los estudios estadounidenses sobre Oriente de después de la Segunda Guerra Mundial, debido en parte al prestigio cultural que se atribuía a los eruditos europeos. No obstante, hay que señalar que la obra de Von Grunebaum es aceptada en la disciplina sin la menor crítica, a pesar de que la propia disciplina ya no es capaz hoy de producir hombres como él. Solo un erudito ha hecho una crítica seria a las ideas de Von Grunebaum: Abdallah Laroui, un intelectual marroquí teórico, político e historiador.
Laroui se sirve del motivo de la repetición reduccionista que Von Grunebaum utiliza en su obra como instrumento práctico para hacer un estudio crítico antiorientalista y, en conjunto, hace un trabajo impresionante. Se pregunta por qué la obra de Von Grunebaum es reduccionista a pesar de la enorme cantidad de detalles que presenta y de su aparente alcance. Laroui dice: «Los calificativos que Von Grunebaum atribuye a la palabra islam (medieval, clásico, moderno) son neutros o incluso superficiales. No hay ninguna diferencia entre el islam clásico y el islam medieval o el islam normal y corriente [...]. Solo hay, por tanto, [según Von Grunebaum] un islam que se transforma [...]». El islam moderno, de acuerdo con Von Grunebaum, rechaza Occidente porque sigue siendo fiel a su aspiración fundamental, pero solo se puede modernizar reinterpretándose a partir del punto de vista occidental, lo que naturalmente es imposible, como lo muestra Von Grunebaum. Al exponer las conclusiones de Von Grunebaum que se acumulan para formar un retrato del islam en el que este aparece como una cultura incapaz de innovar, Laroui no menciona el hecho de que la necesidad que tiene el islam de emplear métodos occidentales para progresar se ha convertido, como idea y quizá debido a la gran influencia de Von Grunebaum, casi en una perogrullada dentro del campo de los estudios de Oriente Próximo. (Por ejemplo, David Gorden, en su libro _Self Determination and History in the Third World_ , incita a los árabes, africanos y asiáticos a la «madurez», y sostiene que solo podrán conseguirla aprendiendo de la objetividad occidental.)
El análisis de Laroui expone también cómo Von Grunebaum ha utilizado la teoría culturalista de A. L. Kroeber para entender el islam y cómo este utensilio ha supuesto necesariamente una serie de reducciones y eliminaciones que hacen que el islam pueda ser representado como un sistema cerrado de exclusiones. Así, cualquiera de los numerosos aspectos de la cultura islámica podía ser considerado por Von Grunebaum como un reflejo directo de una matriz invariable, como una teoría particular de Dios que los constreñía a todos dentro de un sentido del orden. El desarrollo, la historia, la tradición y la realidad en el islam son, por tanto, intercambiables. Laroui sostiene con razón que la historia en tanto que orden complicado de sucesos, de temporalidades y de significaciones no puede reducirse a esa noción de cultura, del mismo modo que no puede reducirse a la ideología, ni la ideología a la teología. Von Grunebaum se ha convertido en la presa de los dogmas orientalistas que había heredado y de una peculiaridad particular del islam que había elegido interpretar como un defecto: que hay en el islam una teoría de la religión, pero muy pocos testimonios de experiencias religiosas; hay una teoría política, pero pocos documentos políticos precisos; hay una teoría de la estructura social, pero pocas acciones individualizadas; hay una teoría de la historia, pero pocos sucesos fechados; hay una teoría económica, pero pocas series cuantificadas, etc.» Lo que se obtiene como resultado de todo esto es una visión histórica del islam totalmente obstaculizada por la teoría de una cultura incapaz de hacer justicia a su realidad existencial en la experiencia de sus miembros, e incluso incapaz de examinarla. El islam de Von Grunebaum, después de todo, es el islam de los primeros orientalistas europeos, es decir, un islam monolítico que desprecia la experiencia humana ordinaria, masivo, reduccionista e inmutable.
En el fondo, esta idea del islam es política, y ni siquiera podemos decir, de modo eufemístico, que sea imparcial. Su enorme influencia sobre los nuevos orientalistas (es decir, los que son más jóvenes que Von Grunebaum) se debe en parte a su autoridad tradicional y en parte a su utilidad para abarcar una vasta región del mundo y proclamar que es un fenómeno totalmente coherente. Como Occidente siempre ha tenido dificultades para contener políticamente al islam —y es cierto que, a partir de la Segunda Guerra Mundial, el nacionalismo árabe ha sido un movimiento que ha declarado abiertamente su hostilidad al imperialismo occidental—, su deseo de hacer, en represalia, afirmaciones sobre el islam que le satisfagan intelectualmente se acrecienta. Una persona que es una autoridad en el campo ha dicho del islam (sin especificar a qué islam o aspecto del islam se refiere) que es «un prototipo de sociedad tradicional cerrada». Nótese aquí el uso edificante que se hace de la palabra «islam» para significar a la vez una sociedad, una religión, un prototipo y una realidad. Pero este mismo erudito va a subordinar todo esto a la idea de que, a diferencia de las sociedades normales («las nuestras»), el islam y las sociedades de Oriente Próximo son totalmente «políticas»; adjetivo destinado a reprochar al islam que no es «liberal», y que no es capaz de separar (como «nosotros» hacemos) la política de la cultura. El resultado que se obtiene es un retrato injustamente ideológico de «nosotros» y de «ellos»:
Nuestro objetivo principal debe seguir siendo comprender la sociedad de Oriente Próximo como un todo. Solo una sociedad [como la «nuestra»] que ha adquirido una estabilidad dinámica, puede permitirse pensar en la política, la economía o la cultura como dominios auténticamente independientes de la existencia y no como simples divisiones útiles para el estudio. En una sociedad tradicional que no separa los asuntos del César de los de Dios o que está en continuo proceso de cambio, la relación entre la política y los demás aspectos de la vida, diremos, es una fuente de problemas. Por ejemplo, los asuntos de si un hombre tiene cuatro mujeres o una, de si ayuna o come, de si gana o pierde tierra, de si cree en la revelación o en la razón, se han convertido en problemas políticos en Oriente Próximo [...]. En la misma medida en que lo hace el propio musulmán, el nuevo orientalista debe preguntarse otra vez cuáles pueden ser las estructuras y las relaciones significativas de la sociedad islámica.
La trivialidad de la mayoría de los ejemplos (tener cuatro mujeres, ayunar o comer, etc.) se utiliza para mostrar cómo el islam lo abarca todo, y con qué tiranía. No se nos dice _dónde_ se supone que ocurre eso, pero se nos recuerda el factor, que sin duda no es político, de que los orientalistas «son, en gran medida, responsables de haber proporcionado a Oriente Próximo una apreciación exacta de su pasado» por si acaso habíamos olvidado que, por definición, los orientalistas saben cosas que los orientales no pueden saber por sí mismos.
Si esto resume la escuela «dura» del nuevo orientalismo estadounidense, la escuela «blanda» subraya el hecho de que los orientalistas tradicionales nos han dado las bases fundamentales de la historia, la religión y la sociedad islámicas, pero se han «contentado con demasiada frecuencia con resumir el significado de una civilización a partir de algún manuscrito». El nuevo especialista en áreas culturales expone sus argumentos contra el orientalista tradicional de modo filosófico:
La metodología de la investigación y de los paradigmas de la disciplina no está ahí para determinar lo que se elige estudiar ni para limitar la observación. Los estudios de áreas culturales, desde esta perspectiva, sostienen que el conocimiento verdadero solo es posible a partir de las cosas que existen, mientras que los métodos y las teorías son abstracciones que ordenan las observaciones y ofrecen explicaciones según unos criterios que no son empíricos.
Bien, pero ¿ _cómo_ se conocen «las cosas que existen» y en qué medida «las cosas que existen» están _constituidas_ por el que las conoce? Todavía queda esto por discutir, mientras que la nueva aprehensión (que no apela a los valores) de Oriente como algo que existe se institucionaliza en los programas de estudios de áreas culturales. Sin teorización tendenciosa, el islam _raramente_ se estudia, _raramente_ se investiga, y _raramente_ se conoce. La ingenuidad de esta idea no oculta lo que ideológicamente significa, a saber, las absurdas tesis que dicen que el hombre no desempeña ningún papel en la definición del material y del proceso de conocimiento, que la realidad oriental es estática, que «existe» y que solo un revolucionario mesiánico (según la terminología de Henry Kissinger) se negará a admitir la diferencia entre la realidad exterior y la que tiene en mente.
Entre la escuela dura y la blanda, sin embargo, florecen versiones más o menos diluidas del antiguo orientalismo, en algunos casos con una nueva jerga académica, en otros con la antigua. No obstante, los principales dogmas del orientalismo existen hoy en su forma más pura en los estudios sobre los árabes y el islam. Recapitulémoslos aquí: uno es la diferencia absoluta y sistemática entre Occidente, que es racional, desarrollado, humano y superior, y Oriente, que es aberrante, subdesarrollado e inferior. Otro consiste en que las abstracciones sobre Oriente, y particularmente las que se basan en textos que representan a una civilización oriental «clásica», son siempre preferibles al testimonio directo de las realidades orientales modernas. Un tercer dogma es que Oriente es eterno, uniforme e incapaz de definirse a sí mismo. Por tanto, se asume como inevitable y como científicamente «objetivo» un vocabulario generalizado y sistemático para describir Oriente desde un punto de vista occidental. El cuarto dogma se refiere a que Oriente es, en el fondo, una entidad que hay que temer (el peligro amarillo, las hordas mongoles, los dominios morenos) o que hay que controlar (por medio de la pacificación, de la investigación y el desarrollo y de la ocupación abierta siempre que sea posible).
Lo extraordinario es que estas nociones persistan sin que se produzca un desafío significativo en el estudio académico y gubernamental del Oriente Próximo moderno. Lamentablemente el trabajo de los eruditos islámicos o árabes que rebaten los dogmas orientalistas no ha tenido ningún efecto demostrable —si es que ha llegado a haber algún gesto desafiante—; algún artículo aislado aquí y allí, aunque importante en su momento y en su región, no ha podido afectar al curso de un consenso investigador que se impone y al que mantienen todo tipo de agencias, instituciones y tradiciones. Lo más importante de todo esto es que el orientalismo islámico en la época contemporánea ha llevado una vida bastante diferente de la de otras subdisciplinas orientalistas. El Comittee of Concerned Asia Scholars (que está compuesto por estadounidenses) encabezó una revolución durante los años sesenta en las filas de los especialistas en Asia oriental. Los especialistas en estudios africanos también fueron puestos en custodia por algunos revisionistas y lo mismo ocurrió con especialistas en otras zonas del Tercer Mundo. Solo los arabistas y los islamólogos han permanecido al margen de cualquier tipo de revisión. Para ellos, todavía existen cosas como _una_ sociedad islámica, _un_ espíritu árabe y _una_ psique oriental. Incluso aquellos cuya especialidad es el mundo islámico moderno utilizan anacrónicamente textos como el Corán para interpretar cualquier faceta de la sociedad egipcia o argelina contemporáneas. El islam, o su ideal del siglo VII que compone el orientalista, se supone que posee una total unidad, que elude las influencias más recientes e importantes del colonialismo, el imperialismo e incluso la vida política normal. Estereotipos sobre cómo los musulmanes (o mahometanos, como todavía se les sigue llamando) se comportan, se siguen difundiendo con una sangre fría que nadie se atrevería a mostrar al hablar de los negros o de los judíos. En el mejor de los casos, el musulmán es un «informante nativo» para el orientalista. Secretamente, sin embargo, sigue siendo un hereje despreciable que por sus pecados debe, además, soportar la posición totalmente ingrata de ser conocido —negativamente— como un antisionista.
Hay, naturalmente, un sistema organizado sobre estudios de Oriente Próximo, un pozo de intereses, unas redes de «antiguos alumnos» o de «expertos» que vinculan los negocios multinacionales, las fundaciones, las compañías petrolíferas, las misiones, los servicios militares, los departamentos de exteriores y las centrales de inteligencia con el mundo académico. Hay becas y premios, organizaciones, jerarquías, institutos, centros, facultades y departamentos dedicados a legitimar y mantener la autoridad de un puñado de ideas básicas y básicamente inmutables sobre el islam, Oriente y los árabes. Un análisis crítico hecho recientemente sobre el funcionamiento de los estudios sobre Oriente Próximo en Estados Unidos revela no ya que el campo sea «monolítico», sino que es complejo, que contiene orientalistas del viejo estilo, especialistas deliberadamente marginales, especialistas contra la insurgencia, artífices de la política y «una pequeña minoría [...] de poderosos agentes académicos». En cualquier caso, la esencia del dogma orientalista persiste.
Como ejemplo de lo más brillante y prestigioso que el campo produce, consideremos ahora brevemente la _Cambridge History of Islam_ , en dos volúmenes, que se publicó por primera vez en Inglaterra en 1970 y que es un compendio regular de ortodoxia orientalista. Decir, como muchas lumbreras han dicho sobre esta obra, que es un fracaso intelectual si se valora desde cualquier perspectiva que no sea la orientalista viene a ser lo mismo que decir que podía haber sido una historia del islam diferente y mejor. De hecho, como muchos lúcidos eruditos han señalado, esta historia estaba ya condenada desde el momento en que se planeó por primera vez y no podía haber sido diferente o mejor en su ejecución. Sus editores habían aceptado demasiadas ideas sin apenas ninguna crítica, había demasiados conceptos vagos, se ponía poco acento en los aspectos metodológicos (que seguían siendo iguales a como habían sido en el discurso orientalista durante, al menos, dos siglos) y no se hacía ningún esfuerzo para que la idea del islam resultara interesante. Además, el problema no es solo que _The Cambridge History of Islam_ conciba y represente erróneamente el islam como religión sino que no ofrece ninguna idea colectiva del islam como historia. La total ausencia de ideas y de inteligencia metodológica es, en esta obra más que en ninguna otra, una realidad absoluta.
El capítulo de Erfan Shahid sobre la Arabia preislámica que abre la _History_ perfila la fructífera consonancia entre topografía y economía humana a partir de la cual el islam apareció en el siglo VII. Pero ¿qué se puede decir con justicia sobre una historia del islam, a la que P. M. Holt define muy a la ligera en la introducción como una «síntesis cultural», que pasa directamente de la Arabia preislámica a Mahoma, de este a los califas ortodoxos y al califato omeya sin hacer ni la más mínima referencia al islam como creencia, fe o doctrina? Durante cientos de páginas, en el primer volumen, se expone el islam a través de una aburrida lista cronológica de batallas, reinos, muertes, ascensiones y apogeos, idas y venidas, todo ello escrito en su mayor parte en un estilo monótono y pesado.
Tomemos como ejemplo el período abbasí que se extiende desde el siglo VIII hasta el XI. Cualquiera que tenga el más mínimo conocimiento de la historia árabe o islámica sabrá que este fue un momento cumbre en la civilización islámica, tan brillante desde el punto de vista de la historia de la cultura como el Renacimiento en Italia. Sin embargo, en ninguna de las cuarenta páginas de esta descripción se deja entrever algún indicio de riqueza. Por el contrario, lo que podemos encontrar son frases como esta: «Una vez conseguido el control del califato, [al-Ma'mun] parecía querer reducir su contacto con la sociedad de Bagdad y se estableció en Merv, dejando el gobierno de Irak al cuidado de uno de sus hombres de confianza, al-Hasan ben Sahl, hermano de al-Fadl, que se había enfrentado casi en solitario a una revuelta shií, la de Abdul-Saraya, que el II de Jumada de 199/enero del 815 hizo un llamamiento a las armas desde Kufa en apoyo del hasaní Ibn Tabataba». Llegado este punto, una persona que no sea especialista en el islam no sabrá lo que es un shií o un hasaní, ni tendrá la menor idea de lo que significa II de Jumada de 199, excepto que se refiere a algún tipo de fecha. Y, por supuesto, creerá que los abbasíes, incluido Harun al-Rashid, fueron un grupo incorregiblemente aburrido y sanguinario.
Las tierras islámicas centrales se definen excluyendo el norte de África y al-Andalus, y _su_ historia es una marcha ordenada desde el pasado hasta los tiempos modernos. En el primer volumen, por tanto, el islam es una denominación geográfica que se emplea cronológica y selectivamente según conviene a los expertos. En ningún momento, a lo largo de los capítulos sobre el islam clásico, hay una adecuada preparación para las decepciones que nos esperan cuando lleguemos a los «tiempos recientes», como se los llama. El capítulo sobre los territorios árabes modernos está escrito sin el más mínimo conocimiento de los procesos revolucionarios de la zona. El autor adopta una actitud hacia los árabes de maestro de escuela totalmente reaccionario («es preciso señalar que durante este período la juventud educada y no educada de los países árabes, con su entusiasmo e idealismo, era un terreno abonado para la explotación política y a veces, quizá inconscientemente, se convirtió en instrumento de agitadores y extremistas sin escrúpulos»), atemperada por algún elogio que otro al nacionalismo libanés (aunque nunca se nos dice que el atractivo del fascismo para un reducido número de árabes durante los años treinta afectó especialmente a los libaneses maronitas que en 1936 fundaron las Falanges libanesas a imagen y semejanza de los «camisas negras» de Mussolini). «El desorden y la agitación» se destacan como características de 1936 sin apenas mencionar el sionismo, y nunca se permite que las nociones de anticolonialismo o antiimperialismo violen la serenidad de la narración. Los siguientes capítulos, «El impacto político de Occidente» y «El cambio económico y social» —ideas que no se especifican más—, se añaden como concesiones repugnantes para el islam porque tienen algo que ver con «nuestro» mundo en general. El cambio se hace equivaler unilateralmente con la modernización, pero no se deja claro en ningún momento por qué otros tipos de cambio deben ser imperiosamente rechazados. Como se asume que las únicas relaciones valiosas del islam han sido con Occidente, la importancia de Bandung, de África o del Tercer Mundo en general se desdeña. La alegre indiferencia hacia las tres cuartas partes de la realidad de alguna manera explica la asombrosa y ligera afirmación de que «el terreno histórico ha sido clarificado [¿por quién?, ¿para qué?, ¿cómo?] para una nueva relación entre Occidente y el islam [...] basada en la igualdad y la cooperación».
Si al final del primer volumen estamos sumergidos en un mar de contradicciones y dificultades sobre lo que el islam realmente es, en el segundo volumen no encontramos nada que nos pueda ayudar. La mitad del libro está dedicado a los siglos X, XI y XII en la India, Pakistán, Indonesia, España, norte de África y Sicilia. Hay una mayor distinción en los capítulos sobre África del norte, aunque en todas partes prevalece la misma combinación de jerga orientalista profesional y detalles históricos mal dirigidos. Hasta ahí, después de aproximadamente mil doscientas páginas de densa prosa, el «islam» ya no parece una síntesis cultural sino una lista de reyes, batallas y dinastías. En la segunda mitad del volumen, la gran síntesis se completa con artículos sobre «El escenario geográfico», «Las fuentes de la civilización islámica», «La religión y la cultura» y «La guerra».
En este punto se plantean algunas preguntas y algunas objeciones que parecen bastante justificadas. ¿Por qué se dedica un capítulo a la guerra, cuando de lo que, realmente se habla (de manera interesante, por cierto) es de la sociología de los ejércitos islámicos? ¿Debemos asumir que hay un modo islámico de hacer la guerra diferente del cristiano? Guerra comunista _versus_ guerra capitalista se propone como un tema análogo conveniente. ¿Qué utilidad tienen para comprender el islam —a no ser que sea la exposición de la erudición de Gustave von Grunebaum— las citas opacas de Leopold von Ranke que, junto a otro material igualmente ponderoso e irrelevante, concluye las páginas sobre la civilización islámica? ¿No es deshonesto disfrazar la tesis real de Von Grunebaum de que la civilización islámica descansa en lo que los musulmanes tomaron de las civilizaciones judeocristiana, helénica y austrogermana? Compárese esta idea —que el islam es una cultura plagiada de otras— con la que se adelantaba en la primera parte de que la «llamada literatura árabe» había sido escrita por persas (de lo que, por supuesto, no se ofrece ninguna prueba ni se cita ningún nombre). Cuando Louis Gardet se ocupa del capítulo de «Religión y cultura» se nos dice de forma resumida que solo merece la pena estudiar los cinco primeros siglos del islam. ¿Significa esto que la religión y la cultura en «la época moderna» no se pueden «sintetizar» o significa que el islam adquirió su forma definitiva en el siglo XII? ¿Existe realmente una realidad como la «geografía islámica» que incluya la «anarquía planeada» de las ciudades musulmanas o es principalmente un tema inventado para demostrar una teoría rígida sobre el determinismo racial y geográfico? Sutilmente se nos recuerda «el ayuno del Ramadán con su actividad nocturna» a partir de lo cual se supone que vamos a sacar la conclusión de que el islam es una religión «proyectada para habitantes de las ciudades». Esto es una explicación que necesita una aclaración.
Las secciones que tratan de las instituciones económicas y sociales, del derecho, la justicia, el misticismo, el arte y la arquitectura, la ciencia y varias literaturas islámicas tienen en conjunto un nivel más alto que la mayor parte de la _History_. Sin embargo, no hay ninguna evidencia de que sus autores tengan algo en común con los humanistas modernos o los científicos sociales de otras disciplinas. Las técnicas de la historia convencional de las ideas, del análisis marxista o de la nueva historia están ausentes. En resumen, parece que los historiadores del islam piensan que este encaja mejor en las tendencias platónicas y anticuarias. Para algunos de los autores de la _History_ , el islam es política y religión; para otros es un estilo de ser; para otros «se puede diferenciar de la sociedad musulmana»; para otros es una especie misteriosamente conocida; y para todos los autores, el islam es algo remoto y sin tensión, sin mucho que enseñarnos sobre las complejidades de los musulmanes de hoy. Cerniéndose sobre toda la empresa que es _The Cambridge History of Islam_ está la vieja perogrullada orientalista de que hablar del islam es hablar sobre textos y no sobre personas.
La pregunta fundamental que se plantea en los textos contemporáneos orientalistas, como _The Cambridge History of Islam_ , es si el origen étnico y la religión son las mejores diferencias, o al menos las más útiles, básicas y claras de la experiencia humana. ¿Qué importa más a la hora de comprender la política contemporánea, saber que X e Y están en una situación de desventaja en determinadas formas o que son musulmanes o judíos? Esta, naturalmente, es una pregunta discutible y nosotros somos muy propensos, en términos racionales, a insistir tanto en las descripciones étnico-religiosas como en las socioeconómicas. Sin embargo, el orientalismo postula la categoría islámica como la dominante y esta es la principal consideración que se debe hacer acerca de sus tácticas intelectuales retrógradas.
3. _Simplemente islam_
La teoría de la simplicidad semita, tal y como la encontramos en el orientalismo moderno, está tan profundamente enraizada que apenas se diferencia de la manera en que actúa en las obras europeas antisemitas, como _The Protocols of the Elders of Zion_ ,* y en los comentarios, como los que Chaim Weizmann envió a Arthur Balfour el 30 de mayo de 1918:
Los árabes, que superficialmente son inteligentes y de espíritu vivo, respetan una cosa y solo una: el poder y el éxito [...]. Las autoridades británicas [...], conociendo como conocen la naturaleza traidora de los árabes [...], deben observar constantemente y con cuidado [...]. Cuanto más justo intenta ser el régimen inglés, más arrogantes se vuelven los árabes [...]. Las condiciones actuales tenderían necesariamente hacia la creación de una Palestina árabe si hubiera un pueblo árabe en Palestina. Pero no se llegará a este resultado porque el _fellah_ tiene al menos cuatro siglos de retraso y el _effendi_ es deshonesto, mal educado, ávido y, también, poco patriota e ineficaz.
El denominador común entre Weizmann y los antisemitas europeos es la perspectiva orientalista que considera a los semitas (o a las subdivisiones de estos) como personas privadas por naturaleza de las cualidades deseables de los occidentales. Pero la diferencia entre Renan y Weizmann reside en que este último podía apoyar su retórica en la solidez de unas instituciones, mientras que el primero no. ¿Acaso no hay en el orientalismo del siglo XX esa misma «infancia graciosa» y sin edad que Renan vio como la manera invariable de ser de los semitas, pero ahora aliada con la erudición, con el Estado y con todas sus instituciones?
La versión de este mito se ha mantenido en el siglo XX causando mucho más daño. Ha producido una imagen del árabe según la concibe una sociedad occidental «avanzada». En su resistencia a los colonialistas extranjeros, el palestino es o un salvaje estúpido o una masa despreciable desde un punto de vista moral y existencial. Según la ley israelí, solo un judío tiene plenos derechos ciudadanos y el privilegio de inmigrar sin ningún tipo de restricción. Los árabes, que son los habitantes de la tierra, tienen derechos más limitados: no pueden inmigrar, y si parece que no tienen los mismos derechos es porque están «menos desarrollados». El orientalismo gobierna la política israelí hacia los árabes, como prueba ampliamente el recientemente publicado informe Koenig. Hay árabes buenos (los que hacen lo que se les dice) y árabes malos (los que no lo hacen y, por tanto, son terroristas). Pero sobre todo hay árabes, y de ellos se espera que, una vez derrotados, se sienten obedientemente al otro lado de una línea habilitada por el menor número de hombres, en la teoría de que los árabes han de aceptar el mito de la superioridad israelí y no atacar jamás. Basta con echar una ojeada al libro del general Yehoshafat Harkabi _Arab Attitudes to Israel_ para ver cómo —como Robert Alter escribió con admiración en _Commentary—_ la mente árabe depravada, antisemita hasta el fondo del corazón, violenta y desequilibrada solo puede producir retórica y poco más. Un mito sostiene y produce otro. Se responden mutuamente tendiendo a la simetría y a los esquemas; esquemas que se espera que los árabes, en tanto que orientales, produzcan, pero que como seres humanos, ninguno de ellos puede verdaderamente admitir.
Desde él mismo, en sí mismo, como conjunto de creencias y como método de análisis, el orientalismo no se puede desarrollar. De hecho, por su doctrina, es la antítesis del desarrollo. Su argumento central es el mito del desarrollo interrumpido de los semitas. A partir de esta matriz salen otros mitos cada uno de los cuales muestra a los semitas como lo opuesto al occidental y como la víctima irremediable de sus propias debilidades. Por toda una serie de concatenaciones, de sucesos y de circunstancias, el mito semítico se bifurcó en el movimiento sionista; uno de los semitas siguió el mismo camino que el orientalismo y el otro, el árabe, se vio obligado a seguir el del oriental. Siempre que se invoca la tienda o la tribu se utiliza el mito, lo que también sucede siempre que se evoca el carácter nacional árabe. Las instituciones construidas alrededor de estos instrumentos aumentan su influencia sobre la mente. Todo orientalista se apoya literalmente en un sistema cuyo poder es vacilante, considerando que los mitos que propaga el orientalismo son efímeros. Este sistema culmina hoy en las instituciones del Estado. Escribir sobre el mundo oriental árabe es, por tanto, escribir con la autoridad de una nación y no con la confirmación de una ideología llamativa, sino con la certidumbre indiscutida de poseer la verdad apoyada por la fuerza absoluta.
En su número de 1974, _Commentary_ ofrecía a sus lectores un artículo del profesor Gil Carl Alroy, titulado «Do the Arabs Want Peace?». Alroy es profesor de ciencias políticas y autor de dos obras _Attitudes Towards Jewish Statehood in The Arab World_ e _Images of Middle East Conflict_. Es un hombre que afirma «conocer a los árabes» y es, evidentemente, un experto en el arte de fabricar imágenes. Su tesis es bastante predecible: los árabes quieren destruir Israel, los árabes dicen realmente lo que quieren decir (y Alroy se sirve, con ostentación, de sus recursos para citar testimonios de periódicos egipcios, testimonios que identifica en todas partes con los «árabes», como si los periódicos árabes y los egipcios fueran una misma cosa), y del mismo modo continúa con un celo incansable y parcial. El eje central de su artículo, que también lo es en todas las obras anteriores escritas por otros «arabistas» (sinónimo de «orientalistas») como el general Harkabi cuyo campo de estudio es «la mente árabe», es una hipótesis de trabajo acerca de cómo son los árabes en realidad si se les despoja de todos sus desatinos externos. En otras palabras, Alroy debe probar que como los árabes son en primer lugar unánimes en su propensión a la venganza de sangre, en segundo lugar psicológicamente inadaptados a la paz y en tercer lugar están ligados congénitamente a un concepto de justicia que significa justo lo contrario a ella, no hay que confiar en ellos, hay que combatirlos como se combate cualquier enfermedad mortal. El primer testimonio que exhibe Alroy es una cita del ensayo de Harold W. Glidden «The Arab World» (al que me referí en la primera parte). Alroy encuentra que Glidden ha sabido captar muy bien las diferencias culturales entre la perspectiva occidental y la árabe. La tesis de Alroy, por tanto, se confirma: los árabes son unos salvajes incorregibles. Así, de esta manera tan superflua, es como una autoridad especializada en la mente árabe expone a un enorme público de judíos, que probablemente se interesa por el tema, que deben seguir teniendo cuidado. Y lo hace de una manera académica, desapasionada, honesta, utilizando testimonios de los propios árabes —que, según dice con una seguridad pasmosa, han desechado decididamente [...] la verdadera paz— y utilizando, asimismo, el psicoanálisis.
Este tipo de afirmaciones se puede explicar si se admite una diferencia implícita y poderosa que actúa en favor del orientalista y contra el oriental: que mientras que el primero _escribe_ , el segundo es _descrito_. Al segundo se le atribuye el papel pasivo, al primero el poder de observar, estudiar, etc.; como Roland Barthes ha dicho, un mito (y los que lo perpetúan) puede inventarse a sí mismo (y ellos a ellos mismos) sin cesar. El oriental es presentado como fijo, estable, necesitado de investigación, necesitado incluso de conocerse a sí mismo. No se deja ninguna posibilidad a la dialéctica, aunque realmente no se desea. Hay una fuente de información (el oriental) y una fuente de conocimiento (el orientalista); en resumen, un escritor y su tema de estudio que sin él sería inerte. La relación entre los dos es radicalmente una cuestión de poder que se representa a través de numerosas imágenes. He aquí un ejemplo extraído de _Golden River to Golden Road_ , de Raphael Patai:
Para poder valorar correctamente lo que la cultura de Oriente Próximo _aceptará de buen grado_ de las reservas de la civilización occidental, que son de una riqueza desconcertante, _primero se debe adquirir_ una comprensión mejor y más sana de aquella cultura. El mismo requisito se necesita para _calibrar_ los efectos probables de _los rasgos_ _que se acaban de introducir_ en el contexto cultural de las poblaciones que viven de acuerdo a la tradición. También hay que estudiar, mucho más a fondo de lo que se ha hecho hasta ahora, de qué manera y por qué medios se pueden _hacer atractivas las nuevas ofertas_ _culturales_. En resumen, la única manera en que el «nudo gordiano» de la resistencia a la occidentalización en Oriente Próximo _puede ser_ _desatado_ es estudiando Oriente Próximo, _obteniendo una imagen más_ _completa_ de su cultura tradicional y un mejor conocimiento del _proceso de transformación que se lleva a cabo_ en estos momentos y _penetrando más profundamente_ en la psicología de los grupos humanos de la cultura de Oriente Próximo. Es una _tarea experimental, pero_ _la recompensa, la armonía entre Occidente_ y una región del mundo vecina de una importancia capital, merece la pena.
Las figuras metafóricas sobre las que este párrafo se apoya (y que yo he puesto en cursiva) provienen de toda una serie de actividades humanas, comerciales, hortícolas, religiosas, veterinarias e históricas, pero en todos los casos la relación entre Oriente Próximo y Occidente se define en realidad desde un punto de vista sexual. Como dije anteriormente al hablar de Flaubert, la asociación entre Oriente y el sexo persiste notablemente. Oriente Próximo se resiste, como lo haría cualquier doncella, pero el macho erudito obtiene la recompensa abriendo brutalmente y penetrando el «nudo gordiano» a pesar de que esto sea «una tarea experimental». El resultado de la conquista sobre la modestia virginal es la «armonía», pero de ningún modo la coexistencia de iguales. La relación de fuerzas que subyace entre el erudito y su tema de estudio no se ve alterada ni un instante: es siempre y de modo uniforme favorable al orientalista. El estudio, la comprensión, el conocimiento y la evaluación que se esconden tras la máscara aduladora de la «armonía» son instrumentos de conquista.
Las operaciones verbales que se hacen en escritos como el de Patai (quien ha llegado incluso a superar su trabajo anterior con su reciente _The Arab Mind_ ) aspiran a una comprensión y a una reducción muy particulares. La mayor parte de su parafernalia es antropológica —describe Oriente Próximo como un «área de cultura»— pero lo que consigue es erradicar la pluralidad de las diferencias entre los árabes (sean cuales fueran en realidad) en favor de una diferencia que separa a los árabes de los demás. Como tema de estudio y análisis se les puede controlar con mayor precisión. Además, reduciéndolos de este modo, los desatinos generales, como el que Sania Hamady tiene en su _Temperament and Character of the Arabs_ , están permitidos, legitimados y valorizados:
Hasta ahora, los árabes han manifestado una incapacidad para la unidad disciplinada y permanente, han experimentado explosiones de entusiasmo, pero no han persistido pacientemente en esfuerzos colectivos a los que, por lo general, se han adherido a medias. Muestran una carencia para la coordinación y la armonía en la organización y en la función, y tampoco han manifestado habilidad alguna para la cooperación. Cualquier acción colectiva que se haga en beneficio de todos o por interés de todos es ajena a ellos.
El estilo de esta prosa quizá diga más de lo que se propone Hamady. Verbos como «manifestar», «revelar» y «mostrar» se utilizan sin objeto indirecto. ¿A quién revelan, manifiestan y muestran los árabes? Obviamente a nadie en particular, pero a todo el mundo en general. Esta es una manera de decir que estas verdades son evidentes solo para un observador privilegiado o iniciado, ya que en ningún lugar Hamady cita ninguna prueba de sus observaciones. Además, dada la futilidad de lo que dice, ¿qué tipo de pruebas podría haber? Según avanza en su argumento, su confianza se va acrecentando: «Cualquier acción colectiva [...] es ajena a ellos». Las categorías se endurecen, las afirmaciones son más inflexibles y los árabes han sido totalmente transformados, han dejado de ser personas para convertirse en un tema supuesto del estilo de Hamady. Los árabes existen solo para ofrecerle una oportunidad al observador tirano: «El mundo es _mi_ idea».
Y así, en todos los trabajos de los orientalistas contemporáneos extrañas afirmaciones se extienden por sus páginas. Se puede tratar de un Manfred Halpern, sosteniendo que, aunque todos los procesos del pensamiento humano se pueden reducir a seis, la mente islámica solo es capaz de realizar cuatro, o de un Morroe Berger, presuponiendo que como la lengua árabe es muy adecuada para la retórica, en consecuencia los árabes son verdaderamente incapaces de pensar. Estas afirmaciones se podrían calificar de mitos por su función y su estructura, pero también hay que intentar comprender cuáles son los otros imperativos que gobiernan su utilización. En este punto, naturalmente, solo podemos especular. Las generalizaciones orientalistas sobre los árabes son muy detalladas cuando critican punto por punto sus características, pero lo son mucho menos cuando analizan los puntos fuertes de los árabes. La familia, la retórica y el carácter árabes, a pesar de las descripciones copiosas que ofrece el orientalista, aparecen desnaturalizados y sin potencia humana incluso cuando estas descripciones son capaces de abarcar con amplitud y profundidad el dominio al que se aplican. Hamady, de nuevo, dice:
Así, el árabe vive en un ambiente duro y frustrante. Tiene pocas posibilidades de desarrollar sus potencialidades y de definir su lugar en la sociedad, apenas cree en el progreso y en el cambio, y solo encuentra salvación en el más allá.
Todo lo que se escribe sobre el árabe es justamente lo que no puede conseguir por sí mismo. El orientalista está totalmente seguro de _sus_ posibilidades, no es pesimista, es capaz de definir su lugar y el de los árabes. La imagen del oriental árabe que emana de este texto es totalmente negativa. Sin embargo, nos preguntamos, ¿por qué se le consagran tantas obras? ¿Qué es lo que apasiona al orientalista, si no es —y ciertamente no lo es— el amor a la ciencia, al espíritu, a la sociedad y a las creaciones árabes? En otras palabras, ¿de qué naturaleza es la presencia árabe en el discurso mítico sobre él?
Hay dos cosas que tener en cuenta: el número y el poder reproductor. Las dos cualidades, en última instancia, se pueden reducir a una sola, pero debemos separarlas por necesidades analíticas. Casi sin excepción, toda obra contemporánea de erudición orientalista (en especial, en el campo de las ciencias sociales) tiene mucho que decir sobre la familia, su estructura patriarcal y su influencia universal en la sociedad. La obra de Patai es un ejemplo típico. Aparece inmediatamente una paradoja muda, ya que si la familia es una institución cuyos fallos generales no pueden remediarse más que con la panacea de la «modernización», debemos reconocer que la familia continúa produciéndose, siendo fecunda y siendo la fuente de la existencia árabe en el mundo. Lo que Berger denomina «el gran valor que los hombres atribuyen a sus propias proezas sexuales», nos da una idea del poder que se oculta tras la presencia árabe en el mundo. Si la sociedad árabe se representa en términos completamente negativos y normalmente pasivos como una sociedad que es usurpada y ganada por el héroe orientalista, podemos asumir que una representación así es una manera de tratar con la gran variedad y potencialidad de la diversidad árabe cuya fuente, si no es intelectual y social, es sexual y biológica. No obstante, el tabú que es absolutamente inviolable en el discurso orientalista es que esta sexualidad nunca debe tomarse en serio. Nunca se puede culpar explícitamente a la sexualidad de la ausencia de realizaciones ni del refinamiento racional «real» que el orientalista constata en todas partes entre los árabes. No obstante, creo que esto es el eslabón perdido de las tesis cuyo principal objetivo es criticar la sociedad árabe «tradicional», como las de Hamady, Berger y Lerner. Reconocen el poder de la familia, perciben la debilidad de la mente árabe, subrayan la «importancia» del mundo oriental para Occidente, pero nunca dicen lo que implica su discurso: que lo que en realidad les queda a los árabes después de todo lo que se ha dicho es un vigor sexual indiferenciado. En raras ocasiones —como en el trabajo de Leon Mugniery— encontramos lo implícito expuesto claramente: que hay un «poderoso apetito sexual [...] característico de esos meridionales de sangre caliente». Esta manera de minimizar la sociedad árabe y de reducirla a banalidades inconcebibles reservadas solo a las razas inferiores se realiza a través de una corriente subterránea de exageración sexual. El árabe se produce a sí mismo de manera indefinida, sexualmente, y no produce nada más. El orientalista no dice nada sobre esto, aunque su tesis dependa de ello: «La cooperación en Oriente Próximo es todavía, en gran medida, un asunto de familia, y apenas se puede encontrar algo fuera del grupo de parientes consanguíneos o del pueblo». Es decir, que los árabes solo cuentan en tanto que simples seres biológicos; desde un punto de vista institucional, político y cultural no son nada o casi nada. Numéricamente, y en tanto que productores de familias, los árabes son reales.
La dificultad que conlleva este punto de vista reside en que complica la pasividad de los árabes asumida por orientalistas como Patai e incluso Hamady y otros, pero pertenece a la lógica de los mitos, como la de los sueños, adherirse a las antítesis absolutas. En efecto, un mito no analiza ni resuelve problemas, los presenta como imágenes ya montadas, igual que un espantapájaros se monta a partir de todo un batiburrillo de objetos y después es vestido para tener la apariencia de un hombre. Como la imagen _utiliza_ para sus propios fines todo el material y como por definición el mito desplaza a la vida, la antítesis entre un árabe demasiado fecundo y un muñeco pasivo no es funcional. El discurso recubre la antítesis. Un oriental árabe es esa criatura imposible cuya energía libidinosa le lleva al paroxismo de la hiperestimulación. Sin embargo, a ojos del mundo es como una marioneta que mira de reojo un paisaje moderno que no puede comprender ni afrontar.
Esta imagen del árabe parece ser relevante en los recientes estudios sobre el comportamiento político de los orientales y normalmente es expuesta con ocasión de alguna discusión erudita sobre los dos nuevos temas favoritos de los expertos orientalistas: la revolución y la modernización. Bajo los auspicios de la School of Oriental and African Studies apareció en 1972 un volumen titulado _Revolution in the Middle East and Other Case Studies_ editado por P. J. Vatikiotis. El título tiene deliberadamente resonancias médicas, por lo que debemos pensar que los orientalistas disponen finalmente de lo que normalmente evitaba el orientalismo «tradicional»: atención psicoclínica. Vatikiotis da el tono de la colección con una definición cuasi médica de lo que es una revolución, pero, como él y sus lectores tienen en mente la revolución árabe, la hostilidad de la definición parece aceptable. Hay una inteligente ironía aquí acerca de lo que voy a decir más tarde. El soporte teórico de Vatikiotis es Camus —cuya mentalidad colonial no congeniaba con la revolución ni con los árabes, como Conor Cruise O'Brien ha demostrado recientemente—, pero la frase «la revolución destruye tanto a los hombres como a los principios» de Camus se acepta y se le atribuye «un sentido fundamental»:
[...] Toda ideología revolucionaria entra en conflicto directo (de hecho es un ataque frontal) con la naturaleza racional, biológica y psicológica del hombre.
Comprometida como está con una metástasis metodológica, la ideología revolucionaria requiere que sus seguidores sean fanáticos. La política para el revolucionario no es solo una cuestión de creencias o un sustituto de la creencia religiosa. Debe dejar de ser lo que siempre ha sido, a saber, una actitud adaptable a los períodos de supervivencia. La política metastática y soteriológica aborrece la adaptabilidad; por tanto, ¿de qué otra forma puede evitar las dificultades, desdeñar y superar los obstáculos de la compleja dimensión biológica y psicológica del hombre o hipnotizar su racionalidad sutil aunque limitada y vulnerable? Teme y esquiva la naturaleza concreta y particular de los problemas humanos de la vida política, se desarrolla a partir de lo abstracto y lo prometeico, subordina todos los valores tangibles a un valor supremo: el aprovechamiento del hombre y de la historia en el gran proyecto de la liberación humana. No se conforma con la política humana que tiene tantas limitaciones irritantes. En su lugar, desea crear un nuevo mundo no de un modo adaptable, precario y delicado, es decir humano, sino por un acto terrorífico de creación olímpica pseudodivina. La política al servicio del hombre es una fórmula que es inaceptable para una ideología revolucionaria. Por el contrario, el hombre existe para servir a un orden políticamente artificial y brutalmente decretado.
Además de a otros muchos conceptos —ideas exaltadas hasta un extremo increíble y fanatismo contrarrevolucionario—, este fragmento se refiere a que esa revolución es una mala clase de sexualidad (un acto de creación seudodivina), y también una enfermedad cancerígena. Todo lo que hace el «humano», según Vatikiotis, es racional, correcto, sutil, discreto y concreto; lo que un revolucionario declara es brutal, irracional, mesmeriano y cancerígeno. La procreación, el cambio y la continuidad se identifican no solo con la sexualidad y con la locura, sino de un modo un poco paradójico, con la abstracción.
Los términos de Vatikiotis están fortalecidos y coloreados emocionalmente por llamamientos (desde la derecha) a la humanidad y a la decencia y llamamientos (contra la izquierda) para salvaguardar la humanidad del sexo, del cáncer, de la locura, de la violencia racional y de la revolución. Como lo que está en tela de juicio es la revolución árabe, debemos leer el fragmento del siguiente modo: esto es lo que es una revolución, y si los árabes la quieren, podemos imaginarnos cómo son y qué tipo de raza inferior son. Solo son capaces de la incitación sexual y no de la razón olímpica (occidental, moderna). La ironía de la que hablaba antes entra en escena ahora: en algunas partes de las páginas siguientes podemos leer que los árabes son ineptos y que ni siquiera pueden aspirar a la ambición de la revolución. De ahí se deduce que la sexualidad árabe no se debe temer por sí misma, sino por sus fallos. En resumen, Vatikiotis pide a sus lectores que crean que la revolución en Oriente Próximo es una amenaza precisamente porque no puede conseguirse.
La causa más importante de los conflictos políticos y de las revoluciones potenciales en muchos países de Oriente Próximo, África y Asia hoy en día es la incapacidad de los llamados regímenes y movimientos nacionalistas radicales para manejar los problemas sociales, económicos y políticos de independencia [...]. Hasta que los estados de Oriente Próximo no puedan controlar su actividad económica y crear o producir su propia tecnología, su acceso a la experiencia revolucionaria seguirá siendo limitado. Las categorías políticas esenciales para una revolución seguirán fallando.
En cualquier caso la revolución ya está condenada. En esta serie de definiciones, las revoluciones aparecen como quimeras de mentes sexualmente dementes que en un análisis más detallado resultan ser incapaces incluso de llegar a la locura que Vatikiotis realmente respeta y que es humana, no árabe, concreta, no abstracta, asexual y no sexual.
El ensayo erudito central de la recopilación de Vatikiotis es el de Bernard Lewis «Islamic Concepts of Revolution». Nos encontramos en este artículo con una estrategia que tiene un aire muy refinado. Muchos lectores sabrán que para los arabófonos de hoy, la palabra _thawra_ —y sus cognados más inmediatos— significa revolución y si no, lo podrán leer en la introducción de Vatikiotis. Sin embargo, Lewis no describe el significado de _thawra_ hasta el final de su artículo, después de haber hablado de conceptos como _dawla_ , _fitna_ y _bugat_ en su contexto histórico y, sobre todo, religioso. Lo que quiere exponer principalmente es que «la doctrina occidental sobre el derecho a resistirse a un mal gobierno es ajena al pensamiento islámico» que conduce al «derrotismo» y al «quietismo» como actitudes políticas. Al leer el artículo no sabemos nunca con certeza dónde se supone que tienen lugar estos términos, salvo en alguna parte de la historia de las palabras. Luego, hacia el final del ensayo leemos lo siguiente:
En los países de habla árabe, se usaba una palabra diferente [para revolución], _thawra_. La raíz th-w-r en árabe clásico significa «levantarse» (por ejemplo, un camello), «estar emocionado o excitado», y de ahí, en particular en el uso magrebí, «rebelarse». Con frecuencia se usa en el contexto del establecimiento de una soberanía independiente menor. Así, por ejemplo, los llamados gobernantes de los reinos de taifas que se impusieron en la península Ibérica durante el siglo XI, tras el desmembramiento del califato de Córdoba se llaman _thuwwar_ (singular _thair_ ). El nombre _thawra_ en principio significa «agitación», como en la frase citada en el _Sihah_ , un diccionario árabe medieval clásico, _intazir hatta taskun hadihi-l-thawra_ , «espera hasta que la agitación se calme», buen consejo. El verbo también es empleado por al-Iji en la forma _thawaran_ o _itharat fitna_ (fomentar la sedición) como uno de los peligros que debe desanimar a un hombre a resistirse a un mal gobierno. _Thawra_ es el término utilizado por los escritores árabes del siglo XIX para referirse a la Revolución francesa y por sus sucesores para referirse las revoluciones de nuestra época.
El párrafo entero está lleno de condescendencia y mala fe. ¿Para qué introducir la idea de un camello levantándose al explicar la etimología de la moderna revolución árabe si no es para desacreditarla de una manera astuta? La razón de Lewis es evidentemente reducir el valor que hoy en día tiene la revolución a una imagen que no es muy noble (o muy bella) como es la de un camello que se va a levantar del suelo. La revolución es agitación, sedición, es el establecimiento de una soberanía menor y nada más; el mejor consejo (que presumiblemente un erudito o caballero occidental puede dar) es «espera hasta que la agitación se calme». De esta exposición despectiva de _thawra_ no podremos deducir que un número incalculable de hombres está activamente comprometido con ella y de formas tan complicadas que ni siquiera Lewis, con su erudición sarcástica, puede comprender. Sin embargo, este tipo de descripción esencializada es la que es natural para los estudiantes y políticos que se interesan por Oriente Próximo. La agitación revolucionaria entre «los árabes» tiene más o menos las mismas consecuencias que un camello que se levanta, y llama la atención tanto como las habladurías de los patanes. Toda la literatura orientalista canónica será incapaz, por la misma razón ideológica, de explicar la sublevación revolucionaria que se confirma en el mundo árabe del siglo XX o de prepararnos para ella.
La manera en que Lewis asocia la palabra _thawra_ con un camello que se levanta y más en general con la agitación (y no con la lucha por unas ideas) sugiere bastante más ampliamente de lo que es habitual en él que el árabe no es más que un neurótico sexual. Cada una de las palabras o frases que usa para describir la revolución está teñida de sexualidad: estar emocionado, excitado, levantarse, pero en gran medida se trata de una «mala» sexualidad la que atribuye al árabe. Al final, como los árabes no están realmente equipados para una acción seria, su excitación sexual no es más noble que un camello que se levanta. En lugar de la revolución, está la sedición, el establecimiento de una soberanía menor y más agitación, que es lo mismo que decir que en lugar de a la copulación el árabe no puede llegar más que a los juegos preliminares, a la masturbación y al _coitus interruptus_. Creo que estas son las implicaciones de Lewis, a pesar del aire inocente de su saber y del buen tono de su lenguaje. Como es tan sensible a los matices de las palabras, debe ser consciente de que _sus_ palabras también tienen matices.
Lewis es un caso interesante que se debe examinar más en profundidad porque su situación en el mundo político de la estructura anglo-americana de Oriente Próximo es la de un orientalista instruido, y todo lo que escribe está impregnado de la «autoridad» del campo. Sin embargo, durante al menos una década y media su obra ha sido, ante todo, ideológica hasta extremos que rozan la agresividad, a pesar de sus varios intentos por resultar sutil o irónico. Me voy a referir a su obra más reciente como ejemplificación perfecta de lo que es un erudito académico cuyo trabajo se propone ser liberal, objetivo y erudito, y en realidad llega a ser casi un medio de propaganda _contra_ su propio campo de estudio. Esto no le sorprenderá a nadie que esté familiarizado con la historia del orientalismo; es el último —y en Occidente el menos criticado— de los escándalos de la «erudición».
Tan resuelto estaba Lewis a demoler, rebajar y desacreditar a través de su proyecto a los árabes y el islam que incluso sus energías como erudito e historiador parecieron fallarle. Publicó, por ejemplo, un ensayo titulado «La revuelta del islam» en un libro en 1964. Doce años después reeditó la mayor parte del mismo material levemente alterado para adaptarlo al nuevo lugar en el que lo publicaba (en este caso _Commentary_ ) y le dio un nuevo título, «El retorno del islam». Entre «la revuelta» y «el retorno» hay, naturalmente, un cambio a peor, un cambio con el que Lewis pretendía explicar a su público nuevo por qué los musulmanes (o árabes) todavía no se asentaban y aceptaban la hegemonía de Israel en Oriente Próximo.
Observemos con mayor atención cómo hace esto. En ambos artículos se refiere a unos disturbios antiimperialistas que tuvieron lugar en El Cairo en 1945 y en ambos casos los describe como antijudíos. Pero en ninguno de los artículos dice en qué se basa para decir que son antijudíos; de hecho la única evidencia material de antijudaísmo que presenta es la sorprendente información de que «varias iglesias católicas, armenias y griegas ortodoxas fueron atacadas y destrozadas». Veamos la primera versión de 1964:
El 2 de noviembre de 1945, los líderes políticos de Egipto hicieron un llamamiento para que se acudiera a las manifestaciones convocadas con ocasión del aniversario de la Declaración Balfour. Estas rápidamente degeneraron en disturbios antijudíos en el curso de los cuales una iglesia católica, otra armenia y otra griega ortodoxa fueron atacadas y destrozadas. Y ¿qué tienen que ver, si se puede preguntar, los católicos, los armenios y los griegos con la Declaración Balfour?
La versión de _Commentary_ de 1976 dice:
En cuanto al movimiento nacionalista, se había vuelto genuinamente popular, es decir menos nacional y más religioso —en otras palabras, menos árabe y más islámico—. En momentos de crisis —de los que ha habido muchos en las últimas décadas— la lealtad instintiva hacia la comunidad pesa más que cualquier otra. Algunos ejemplos son suficientes. El 2 de noviembre de 1945, se llevaron a cabo en Egipto manifestaciones [nótese aquí cómo esta última frase intenta demostrar las lealtades instintivas, mientras que en la versión anterior eran «los líderes políticos» los responsables del acto] con ocasión del aniversario de la promulgación por parte del gobierno británico de la Declaración Balfour. Aunque, ciertamente, no era esa la intención de los líderes políticos que la apoyaban, la manifestación enseguida degeneró en disturbios antijudíos y estos en un estallido más general en el curso del cual varias iglesias católicas, armenias y griegas ortodoxas [otro cambio instructivo: la impresión que se saca aquí es que muchas iglesias de las tres confesiones fueron atacadas, mientras que en la primera versión se especifica que fueron tres iglesias] fueron atacadas y destrozadas.
El propósito polémico, no erudito, es mostrar en estas líneas y en cualquier otro sitio que el islam es una ideología antisemita y no simplemente una religión. Su lógica no encuentra dificultades a la hora de afirmar que el islam es un temible fenómeno de masas y al mismo tiempo «no genuinamente popular», pero este problema no le detiene. Como la segunda versión de su tendenciosa anécdota muestra, sigue proclamando que el islam es una multitud irracional o un fenómeno de masas que lleva a los musulmanes por el camino de las pasiones, los instintos y los odios irreflexivos. El propósito principal de su exposición es atemorizar a sus lectores y convencerles de que no deben ceder ni un palmo ante el islam. Según Lewis, el islam no evoluciona, ni tampoco lo hacen los musulmanes, ellos simplemente «están» y «están» para ser observados debido a esa esencia suya (según Lewis) que incluye un odio imperecedero hacia cristianos y judíos. Lewis, en todas partes, se reprime de hacer tales afirmaciones difamatorias de modo directo; siempre se cuida de decir que, por supuesto, los musulmanes no son antisemitas del mismo modo en que lo eran los nazis, pero su religión se puede amoldar muy fácilmente al antisemitismo, como de hecho ha ocurrido. De igual manera, se refiere al racismo, la esclavitud y otros demonios «occidentales». La esencia de la ideología de Lewis sobre el islam consiste en que este nunca cambia, y la misión que él tiene ahora es informar a las facciones conservadoras de sus lectores judíos, y a cualquiera que le escuche, que cualquier consideración sobre los musulmanes debe comenzar y terminar por el hecho de que los musulmanes son musulmanes.
Admitir que toda una civilización pueda ser fiel en primer lugar a su religión es demasiado. Incluso sugerir tal cosa es considerado ofensivo por parte de la opinión liberal, siempre dispuesta a ofenderse en nombre de lo que acoge bajo su tutela. Esto se refleja en la actual incapacidad política, periodística y erudita para reconocer la importancia del factor religioso en los asuntos diarios del mundo musulmán; y también es patente en los recursos del lenguaje de izquierdas o de derechas, progresista o conservador, y en el resto de la terminología occidental que se utiliza para explicar los fenómenos de la política musulmana y que resulta tan precisa y esclarecedora como podrían ser los comentarios de un experto en béisbol sobre un partido de críquet. [Lewis le ha tomado tanto cariño a este último símil que lo cita literalmente de su polémica de 1964.]
En un trabajo posterior, Lewis nos explica qué lenguaje es el más adecuado y útil, aunque la terminología no parece ser menos «occidental» (sea cual sea el significado de «occidental»). Los musulmanes, como la mayoría de los pueblos que han sido colonizados, son incapaces de decir la verdad o incluso de verla. Según Lewis, son adictos a la mitología, como «la llamada Escuela Revisionista de Estados Unidos que vuelve la mirada a una época dorada estadounidense de virtud, y achaca virtualmente todos los pecados y crímenes del mundo a la presente situación de su país». Además de ser una consideración maliciosa y totalmente inexacta de la historia revisionista, este tipo de comentario pretende situar a Lewis, como gran historiador, por encima del insignificante subdesarrollo de los musulmanes y de los revisionistas.
Sin embargo, en lo que se refiere a la exactitud y a la adecuación a su norma de que «el erudito, no obstante, no se dejará llevar por sus prejuicios», Lewis es arrogante consigo mismo y con su causa. Se referirá, por ejemplo, al caso árabe contra el sionismo (utilizando el lenguaje del nacionalista árabe) sin, al mismo tiempo, mencionar —en ninguno de sus escritos— que existe una realidad que es la invasión sionista y la colonización de Palestina a pesar de los habitantes árabes nativos y en conflicto con ellos. Ningún israelí podría negar esto, pero Lewis, el historiador orientalista, simplemente lo pasa por alto. Hablará de que no hay democracia en Oriente Próximo, salvo en Israel, sin mencionar las medidas de defensa utilizadas por este Estado para dominar a los árabes, y sin decir nada sobre las «detenciones preventivas» de árabes en Israel, ni sobre las docenas de asentamientos ilegales en la Cisjordania y Gaza ocupadas militarmente, ni sobre la ausencia de derechos humanos para los árabes, entre ellos el principal derecho de inmigrar a la antigua Palestina. En lugar de esto, Lewis se permite la libertad erudita de decir que «el imperialismo y el sionismo [en lo que respecta a los árabes] eran lo que antes se conocía con los nombres de cristianos y judíos». Cita a T. E. Lawrence en «Los semitas» para reforzar su causa contra el islam, nunca discute el sionismo en paralelo con el islam (como si el sionismo fuera un movimiento francés y no un movimiento religioso) e intenta en todas partes demostrar que cualquier revolución en cualquier lugar es, en el mejor de los casos, una forma de «milenarismo secular».
Este tipo de procedimiento podría parecernos menos objetable si se tratara de propaganda política —que, por supuesto lo es— y si no fuera acompañado de sermones sobre la objetividad, la justicia y la imparcialidad de un verdadero historiador, así como por la idea implícita de que los musulmanes y los árabes no pueden ser objetivos, pero que los orientalistas como Lewis que escriben sobre ellos sí, por definición, por su formación y por el mero hecho de ser occidentales. Esta es la culminación del orientalismo como dogma que no solo degrada su tema de estudio, sino que también ciega a quien lo estudia. No obstante, escuchemos para terminar a Lewis diciéndonos cómo debe conducirse el historiador. Quizá deberíamos preguntarnos si son solo los orientales los que están sometidos a los prejuicios que él condena:
Las lealtades [del historiador] quizá puedan influir en la elección de su tema de investigación; pero no deberían interponerse en el tratamiento que haga de él. Si en el curso de sus investigaciones encuentra que el grupo con el que se identifica siempre tiene razón, y que los grupos con los que está en conflicto están siempre equivocados, debería aconsejársele que cuestionara sus conclusiones y que examinara de nuevo las hipótesis sobre las que seleccionó e interpretó sus evidencias, ya que no es natural que las comunidades humanas [presumiblemente también la comunidad de orientalistas] tengan siempre razón.
Al final, el historiador debe ser justo y honesto en la manera de presentar su historia. Esto no significa que deba confinarse a hacer un escueto recital de hechos definitivamente establecidos; en diversas fases de su trabajo, el historiador debe formular hipótesis y hacer juicios; lo importante es que debe hacerlos consciente y explícitamente, revisando las pruebas a favor y en contra de sus conclusiones, examinando las diversas interpretaciones posibles y estableciendo con firmeza cuál es su decisión y cómo y por qué ha llegado a ella.
Buscar algún juicio consciente, justo y explícito de Lewis sobre el islam del que se ha ocupado es buscar en vano. Prefiere trabajar, como hemos visto, a través de sugerencias e insinuaciones. Alguien podría sospechar, sin embargo, que él no es consciente de lo que está haciendo (excepto quizá en lo referente a los temas «políticos» como su prosionismo, su antinacionalismo árabe y su estridente apoyo a la guerra fría), ya que se podría decir, con razón, que toda la historia del orientalismo de la que él es heredero ha convertido estas insinuaciones e hipótesis en verdades indiscutibles.
Puede ser que la más indiscutible de todas estas «verdades» profundas y la más peculiar (ya que difícilmente se puede mantener para cualquier otra lengua) es que el árabe, como lengua, es una ideología peligrosa. El _locus classicus_ contemporáneo de esta opinión sobre el árabe es el ensayo de E. Shouby, «The Influence of the Arabic Language on the Psichology of the Arabs». Se describe al autor como «un psicólogo con una formación tanto en psicología clínica como social» y se presupone que la principal razón por la que sus opiniones tienen tanta difusión es que es árabe (nada menos que un árabe que se acusa a sí mismo). La tesis que propone es lamentablemente simplista, quizá porque no tenga la más mínima noción de lo que es una lengua ni de cómo funciona. Sin embargo, las diferentes partes de su ensayo tienen títulos que ya de por sí son muy reveladores: «La imprecisión general del pensamiento», «Insistencia exagerada en los signos lingüísticos», «Afirmación excesiva y exageración». Con frecuencia se cita a Shouby como si se tratara de una autoridad, y esto es porque él habla como tal y porque personifica a un tipo de árabe mudo que al mismo tiempo es un maestro con las palabras y realiza juegos que no son demasiado serios y no tienen demasiado interés. El mutismo desempeña un gran papel en lo que Shouby dice, ya que a lo largo de todo su artículo no introduce ninguna cita de la literatura de la que el árabe está tan orgulloso. ¿Dónde, pues, se manifiesta la influencia de la lengua árabe en la mente oriental? Exclusivamente dentro del mundo mitológico creado por el orientalismo para el árabe. El árabe es un símbolo de mutismo, y de pobreza combinados con un exceso de expresión. El hecho de que se pueda llegar a este resultado a través de la filología es una muestra del triste fin de una tradición que fue compleja y que solo existe ya en muy pocas personas. Esta manera que tiene el orientalista de apoyarse en la «filología» constituye la debilidad de una disciplina erudita completamente transformada y pasada a manos de expertos en ideología.
En todo lo que he dicho, el lenguaje del orientalismo desempeña un papel decisivo. Mete en un mismo saco contrarios como algo «natural», presenta tipos y métodos humanos con una jerga de erudito, atribuye realidad y referencia a objetos (a otras palabras) de su propia fabricación. El lenguaje mítico es un discurso, es decir, solo puede ser sistemático; un discurso no se fabrica verdaderamente a voluntad sin pertenecer —en algunos casos inconscientemente pero de cualquier forma involuntariamente— a una ideología y a unas instituciones que garantizan su existencia. Estas últimas siempre son las instituciones y la ideología de una sociedad avanzada que trata con una menos avanzada, las de una cultura fuerte que se relaciona con otra débil. La principal característica del discurso mítico es que disimula sus propios orígenes así como los de aquello que describe. «Se presenta a los árabes» con imágenes de tipos estáticos, casi ideales; no se les presenta como seres que tienen unas potencialidades en proceso de realización ni como historia en proceso de desarrollarse. El valor exagerado que se amontona sobre el árabe en tanto que lengua autoriza al orientalista a hacer de la lengua el equivalente de la mente, la sociedad, la historia y la naturaleza. Para el orientalista la lengua _habla_ el árabe oriental y no a la inversa.
4. _Orientales, orientales, orientales_
El sistema de ficciones ideológicas que se denomina orientalismo tiene serias implicaciones y no solo porque desde un punto de vista intelectual se pueda desacreditar. En efecto, Estados Unidos hoy está fuertemente implicado en Oriente Próximo, más de lo que lo está en ningún otro lugar de la Tierra. Los expertos en Oriente Próximo que asesoran a los políticos están totalmente impregnados de orientalismo. La mayor parte de esta implicación se levanta sobre cimientos de arena, ya que los expertos dan directrices basadas en abstracciones que se venden bien: elites políticas, modernización y estabilidad, la mayor parte de las cuales son simplemente los viejos estereotipos orientalistas revestidos de una jerga política, y la mayoría de ellas no han servido para describir lo que ha sucedido recientemente en el Líbano* ni antes la resistencia popular palestina contra Israel. El orientalista ahora intenta ver Oriente como una imitación de Occidente que, según Bernard Lewis, solo puede mejorarse a sí misma cuando su nacionalismo «esté preparado para entenderse con Occidente». Si mientras tanto los árabes, los musulmanes o el Tercer Mundo y el Cuarto siguen caminos inesperados, no nos sorprenderemos si encontramos a algún orientalista que nos diga que esto es una muestra de la incorregibilidad de los orientales y, por tanto, prueba de que no se puede confiar en ellos. No se puede dar cuenta de los errores del orientalismo diciendo que el verdadero Oriente es diferente de los retratos que el orientalista hace de él o diciendo que, como los orientalistas son en su mayor parte occidentales, no pueden tener un sentimiento desde dentro de lo que realmente es Oriente. Estas dos proposiciones son falsas. La tesis que yo sostengo en este libro no consiste en sugerir que existe una realidad que es el Oriente real o verdadero (islam, árabe o lo que sea) ni tampoco consiste en confirmar la situación privilegiada de toda perspectiva «interna» frente a cualquiera que sea «externa», por usar la útil distinción de Robert K. Merton. Por el contrario, lo que he pretendido decir es que «Oriente» es por sí mismo una entidad constituida y que la noción de que existen espacios geográficos con habitantes autóctonos radicalmente diferentes a los que se puede definir a partir de alguna religión, cultura o esencia racial propia de ese espacio geográfico es una idea extremadamente discutible. En realidad, yo no creo en la proposición limitada que dice que solo un negro puede escribir sobre negros o que solo un musulmán puede escribir sobre musulmanes, etcétera.
Y, sin embargo, a pesar de sus fallos, su jerga lamentable, su mal disimulado racismo y su débil aparato intelectual, el orientalismo florece hoy en las formas que he intentado describir. De hecho, hay razones para inquietarse cuando se ve que la influencia se ha extendido al propio «Oriente»: las páginas de libros y periódicos impresas en árabe (y sin duda las impresas en japonés, varios dialectos indios y en otras lenguas orientales) están llenas de análisis de segundo orden escritos por árabes acerca de la «mente árabe», del «islam» y otros mitos. El orientalismo también se ha extendido en Estados Unidos ahora que el dinero árabe y sus recursos han añadido un prestigio considerable al «interés» tradicional sentido por Oriente que siempre ha sido estratégicamente importante. El hecho es que el orientalismo se ha adaptado con éxito al nuevo imperialismo cuyas líneas directrices no solo no cuestionan, sino que confirman el proyecto imperial ininterrumpido de dominar Asia.
En lo que se refiere al aspecto de Oriente del que puedo hablar con un cierto conocimiento de causa, se puede considerar que la adaptación de la clase intelectual al nuevo imperialismo es uno de los triunfos especiales del orientalismo. El mundo árabe hoy día es un satélite intelectual, político y cultural de Estados Unidos. Esto por sí mismo no es algo lamentable; sin embargo, la forma especial que adopta esta relación de satélite sí que lo es. En primer lugar hay que tener en cuenta que las universidades en el mundo árabe están organizadas siguiendo el modelo heredado de una antigua potencia colonial, modelo que las más de las veces fue impuesto por ella. Las circunstancias actuales convierten la realidad de los programas en algo grotesco: clases abarrotadas de cientos de estudiantes, profesores mal preparados, saturados de trabajo, mal pagados y nombrados por razones políticas, una ausencia casi total de investigación y de facilidades para llevarla a cabo y, lo que es más importante, la falta de una simple biblioteca decente en toda la región. Gran Bretaña y Francia una vez dominaron el horizonte intelectual de Oriente por su preponderancia y riqueza; ahora Estados Unidos ocupa su lugar, con el resultado de que a los pocos estudiantes prometedores que realizan sus estudios en ese sistema de enseñanza se les anima a ir a Estados Unidos a continuar su trabajo. Aunque es cierto que algunos estudiantes árabes siguen yendo a Europa a estudiar, la gran mayoría, tanto los de los estados llamados progresistas como los de los conservadores, como Arabia Saudí y Kuwait, va a Estados Unidos. Además, el sistema de patrocinio de becas, negocios e investigación hace que Estados Unidos tenga la hegemonía total sobre estos asuntos. Se considera que la fuente, aunque puede que no sea una fuente real, está en Estados Unidos.
Dos factores hacen que la situación sea, de manera todavía más evidente, un triunfo del orientalismo. Siempre y cuando se pueda generalizar sobre este asunto, diremos que las tendencias de la cultura contemporánea en Oriente Próximo siguen modelos europeos y estadounidenses. Cuando Taha Husein dijo en 1936 que la cultura árabe moderna era europea y no oriental, no hacía más que reflejar el estado de la elite cultural egipcia, de la que él mismo era un miembro distinguido. Lo mismo se puede decir de la elite cultural árabe de hoy, aunque la poderosa corriente antiimperialista del Tercer Mundo que se extendió por la región a partir de los años cincuenta ha debilitado el filo occidental de la cultura dominante. Además, el mundo árabe e islámico sigue siendo un poder de segundo orden en términos de producción de cultura, de saber y de erudición. En este punto debemos ser completamente realistas al utilizar la terminología de la política de poder para describir la situación que ella crea. Ningún erudito árabe o islámico puede permitirse ignorar lo que ocurre en las publicaciones, institutos y universidades de Estados Unidos y de Europa, y lo contrario no es cierto. Por ejemplo, ninguna de las grandes publicaciones de estudios árabes se publica actualmente en el mundo árabe y, del mismo modo, ninguna de las instituciones de enseñanza del mundo árabe puede competir con centros como Oxford, Harvard o UCLA en lo que se refiere al estudio del mundo árabe y mucho menos a cualquier otra materia no oriental. El resultado predecible de todo esto es que los estudiantes (y los profesores) orientales todavía quieren venir y sentarse a los pies de los orientalistas estadounidenses para luego repetir ante su público local los estereotipos que he descrito como dogmas orientalistas. Con este sistema de reproducción es inevitable que el erudito oriental utilice su formación estadounidense para sentirse superior a sus compatriotas, porque es capaz de «dominar» el sistema orientalista. En su relación con sus superiores, los orientalistas europeos o estadounidenses, él no será más que un «informante nativo». Y, de hecho, este es el papel que le va a corresponder en Occidente si tiene la oportunidad de quedarse allí después de terminar sus estudios superiores. La mayor parte de los cursos elementales de lenguas orientales son impartidos hoy en las universidades estadounidenses por «informantes nativos», pero el poder en el sistema (universidades, fundaciones, etc.) está casi exclusivamente en manos de no orientales, aunque la proporción numérica entre profesionales orientales y no orientales no favorezca tan abrumadoramente a estos últimos.
Hay otro tipo de pruebas acerca de cómo la dominación cultural se mantiene tanto por el consentimiento de los orientales como por la presión económica brutal y directa de Estados Unidos. Por ejemplo, es posible encontrar que, mientras en Estados Unidos hay docenas de organizaciones que estudian el Oriente árabe e islámico, en el propio Oriente no hay ninguna que estudie Estados Unidos, que constituye, con diferencia, la mayor influencia económica y política de la región. Y todavía peor, no hay apenas en Oriente institutos, aunque sean modestos, que estén consagrados al estudio de Oriente. Pero esto no es nada, creo, comparado con el segundo factor que ha contribuido al triunfo del orientalismo: el consumismo en Oriente. El mundo árabe e islámico en su totalidad está sometido a la economía de mercado occidental. No hace falta recordar que el petróleo, principal recurso de la región, ha sido totalmente absorbido por la economía de Estados Unidos. No me refiero solo a que las grandes compañías petrolíferas estén bajo el control del sistema económico estadounidense, sino también a que las ganancias petrolíferas de los árabes, sin hablar de la comercialización, la investigación y la organización industrial, están establecidos en Estados Unidos. Los árabes enriquecidos por el petróleo se han convertido en clientes muy importantes de las exportaciones estadounidenses. Esto es cierto tanto a propósito de los estados del Golfo, como de los estados radicales, Libia, Irak y Argelia. Mi tesis consiste en que se trata de una relación unilateral con Estados Unidos como cliente selectivo que compra unos pocos productos (petróleo y mano de obra barata, principalmente) y los árabes consumidores de una enorme gama de productos materiales e ideológicos procedentes de Estados Unidos.
Esto ha tenido numerosas consecuencias. En la región, hay una gran uniformidad en el gusto simbolizada no solo por los transistores, los vaqueros y la Coca-Cola, sino también por las imágenes culturales del oriental que ofrecen los medios de comunicación estadounidenses y que consume sin reflexionar la gran masa de telespectadores. La paradoja del árabe que se ve a sí mismo como un «árabe» del mismo tipo del que muestra Hollywood es el resultado más simple de lo que estoy diciendo. Otro es que la economía de mercado occidental y su orientación consumista ha producido (y sigue produciendo de manera acelerada) una clase instruida cuya formación intelectual se dirige a satisfacer las demandas del mercado. Se da mucha importancia, evidentemente, a los estudios de ingeniería, negocios, económicas, pero la propia intelectualidad se convierte en auxiliar de lo que se considera que son las principales tendencias que destacan en Occidente. El papel que se le ha asignado es el de «modernizar», es decir, el de dar legitimidad y autoridad a las ideas que recibe en su mayor parte de Estados Unidos. Encontramos una prueba sorprendente de esto en las ciencias sociales y, lo que es más curioso, entre los intelectuales radicales cuyo marxismo proviene directamente de Marx, de sus ideas que hacen del Tercer Mundo un todo homogéneo y de las que ya he hablado en este libro. Así, si después de todo hay alguna exactitud intelectual en las imágenes y doctrinas del orientalismo, hay también un poderoso reforzamiento por parte de los intercambios económicos, políticos y sociales. En resumen, el Oriente moderno participa de su propia orientalización.
En conclusión, ¿cuál es la alternativa al orientalismo? ¿Es que este libro no presenta más que argumentos en _contra_ y ninguno a _favor_ de nada positivo? A lo largo de todo este libro he hablado de nuevos rumbos «descolonizadores» en lo que he llamado los estudios de áreas culturales —la obra de Anuar Abdel Malek y los estudios publicados por los miembros del Grupo Hull que estudia Oriente Próximo, los análisis y propuestas innovadoras de algunos eruditos en Europa, Estados Unidos y Oriente Próximo—, pero mi intención no ha sido más que la de mencionarlos o aludirlos de pasada. Mi proyecto era estudiar un particular sistema de ideas y, en ningún caso, reemplazarlo por otro nuevo. Además, he intentado plantear una serie de preguntas siempre relevantes cuando se tratan problemas de la experiencia humana: ¿cómo se _representan_ otras culturas? ¿Qué es _otra_ cultura? El concepto de una cultura distinta (raza, religión o civilización) ¿es útil o siempre implica una autosatisfacción (cuando se habla de la propia cultura) o una hostilidad y una agresividad (cuando se trata de la «otra»)? ¿Qué cuenta más, las diferencias culturales, religiosas y raciales o las categorías socioeconómicas y político-históricas? ¿Cómo adquieren las ideas autoridad, «normalidad» e incluso la categoría de verdades «naturales»? ¿Cuál es el papel del intelectual? ¿Será el de dar validez a la cultura y al Estado del que forma parte? ¿Qué importancia debe él dar a una conciencia crítica e independiente, a una conciencia crítica de _oposición_?
Espero haber dado implícitamente algunas respuestas a estas preguntas en lo que he dicho hasta aquí, pero quizá podría hablar un poco más explícitamente de algunas de ellas. El orientalismo, tal y como lo he descrito en este estudio, pone en tela de juicio no solo la posibilidad de que exista una erudición que no sea política, sino también la conveniencia de una relación demasiado estrecha entre el erudito y el Estado. También me parece evidente que las circunstancias que hacen que el orientalismo sea un tipo de pensamiento continuamente destinado a persuadir van a persistir. Esta es una imagen de conjunto más bien deprimente. Sin embargo, por mi parte tengo alguna esperanza racional de que, al contrario de lo que ha sucedido en el pasado, el orientalismo no va a permanecer sin ser cuestionado desde un punto de vista intelectual, ideológico y político.
Si no hubiera creído que existe una erudición que no está tan corrupta o, al menos, tan ciega ante la realidad humana como la que he estado describiendo, no habría emprendido la tarea de escribir este libro. Hoy día hay muchos eruditos que están haciendo un trabajo personal de gran valor en campos como la historia, la religión, la civilización, la sociología y la antropología islámicas. El problema comienza cuando la tradición corporativista del orientalismo se apodera del orientalista que no está vigilante, del orientalista cuya conciencia profesional no está en guardia frente a las _idées reçues_ que le transmite tan fácilmente su profesión. Así, es más probable que los trabajos más interesantes sean los de eruditos que dependen de una disciplina delimitada desde un punto de vista intelectual y no de un «campo» como el orientalismo que se define de manera canónica, imperial y geográfica. Un excelente ejemplo reciente es la antropología de Clifford Geertz, que se interesa por el islam de una manera lo suficientemente precisa y concreta como para que sean las sociedades y los problemas específicos lo que lo anima y no los rituales, las ideas preconcebidas y las doctrinas del orientalismo.
Por otro lado, eruditos y críticos que se han formado en la disciplina orientalista tradicional son perfectamente capaces de liberarse de la antigua camisa de fuerza ideológica. La formación de Jacques Berque y la de Maxime Rodinson están entre las más rigurosas, pero lo que estimula sus investigaciones, incluso las de problemas tradicionales, es su conciencia metodológica. Ya que si el orientalismo ha estado históricamente demasiado satisfecho consigo mismo, demasiado aislado, y demasiado lleno de una confianza positivista en sus métodos y en sus premisas, la única manera de abrirse a lo que se estudia en y sobre Oriente es someter de modo reflexivo el método utilizado al examen crítico. Y esto es lo que caracteriza a Berque y a Rodinson, cada uno a su manera. Lo que se puede encontrar en sus obras es, ante todo, una sensibilidad directa hacia la materia que tienen ante ellos, y, después, un continuo examen de su propia metodología y de su propia práctica, un intento constante de que su trabajo responda a la materia y no a doctrinas preconcebidas. Realmente Berque y Rodinson, así como Abdel Malek y Roger Owen también se dan cuenta de que es mejor estudiar al hombre y a la sociedad —sea oriental o no— dentro del extenso campo de las ciencias humanas. Así, estos eruditos leen y estudian con ojo crítico lo que se hace en otros campos. La atención de Berque hacia los recientes descubrimientos de la antropología estructural, la de Rodinson hacia la sociología y la teoría política, y la de Owen hacia la historia económica suponen un correctivo instructivo que las ciencias humanas actuales aportan a los problemas llamados orientales.
Sin embargo, no se puede olvidar el hecho de que incluso si no tenemos en cuenta las distinciones orientalistas entre «ellos y nosotros», una serie de realidades políticas muy poderosas y, en última instancia, ideológicas participan en la erudición de hoy. Nadie puede evitar tratar con las divisiones Este-Oeste, Norte-Sur, ricos-pobres, imperialistas-antiimperialistas o blancos-de color. No podemos esquivarlas como si no existieran; por el contrario, el orientalismo contemporáneo nos enseña mucho sobre la deshonestidad intelectual que supone disimularlas, ya que eso no consigue más que intensificar las divisiones y hacerlas más crueles y permanentes. Así, una ciencia abiertamente polémica, «progresista» y prudente puede degenerar muy fácilmente en una inercia dogmática; perspectiva que tampoco es muy edificante.
El tipo de cuestiones que he planteado muestra bastante bien mi sentimiento sobre el problema. El pensamiento y la experiencia actuales nos han enseñado a ser sensibles ante lo que implican la representación, el estudio de lo «otro», el pensamiento racista, la aceptación sin reflexión ni crítica de la autoridad y de las ideas que hacen autoridad, el papel sociopolítico de los intelectuales y el gran valor de una conciencia crítica y escéptica. Quizá, si recordamos que estudiar la experiencia humana normalmente tiene consecuencias éticas, por no decir nada de las políticas, en el mejor o peor sentido del término, no seremos indiferentes a lo que hacemos como eruditos. Y ¿qué mejores normas para el erudito que la libertad y el conocimiento humanos? Quizá debamos recordar también que el estudio del hombre en la sociedad se fundamenta en la historia y en la experiencia concreta de los hombres y no en abstracciones pedantes, en leyes oscuras o en sistemas arbitrarios. El problema entonces consiste en adaptar el estudio a la experiencia y en que esta de alguna manera le dé forma, y así la experiencia será esclarecida y quizá modificada por el estudio. Si evitamos a toda costa el objetivo de orientalizar continuamente Oriente, profundizaremos en el conocimiento y limitaremos la suficiencia de los eruditos. Sin «Oriente» habría eruditos, críticos intelectuales y seres humanos para los cuales las distinciones raciales, étnicas y nacionales serían menos importantes que la empresa común de promover la comunidad humana.
Creo positivamente —y he intentado demostrarlo en mis otras obras— que se están haciendo bastantes esfuerzos hoy en las ciencias humanas para dotar al erudito contemporáneo de intuiciones, métodos e ideas que le permitan pasar por alto los estereotipos raciales, ideológicos e imperialistas del tipo de los que el orientalismo ha proporcionado durante su ascendencia histórica. Considero que el fracaso del orientalismo ha sido humano e intelectual, ya que, al adoptar una postura de absoluta oposición a una región del mundo que considera ajena a la suya, el orientalismo no ha sido capaz de identificarse con la experiencia humana y ni siquiera de considerarla como una experiencia humana. Ahora podemos poner en duda la hegemonía mundial del orientalismo y de todo lo que representa si podemos conseguir aprovechar la concienciación política e histórica de un gran número de pueblos de la Tierra que ha tenido lugar de modo general en el siglo xx. Si este libro tiene alguna utilidad para el futuro, será la de una modesta contribución a este desafío y la de una advertencia: los sistemas de pensamiento como el orientalismo, los discursos de poder y las ficciones ideológicas —grilletes forjados por el hombre— se fabrican, se aplican y se mantienen demasiado fácilmente. Sobre todo, espero haber mostrado a mis lectores que la respuesta al orientalismo no es el occidentalismo. Ningún antiguo «oriental» se encontrará a gusto con la idea de que él es susceptible —demasiado susceptible— de estudiar a los nuevos «orientales» —u «occidentales»— que él ha fabricado. Si el conocimiento del orientalismo tiene algún sentido, es recordarnos cómo, de qué manera seductora, puede degradarse el conocimiento, no importa qué conocimiento, dónde o cuándo se produzca. Y ahora quizá más que antes.
### Epílogo de la edición de 1995
_Orientalismo_ se concluyó a finales de 1977 y se publicó un año después. Fue (y sigue siendo) el único libro que he escrito como un gesto permanente, a partir de una serie de investigaciones, realizando diversos borradores del mismo, uno tras otro, hasta llegar a su versión definitiva, sin interrupción y sin ninguna distracción seria. Excepción hecha de un año maravillosamente civilizado y de relativo poco trabajo que pasé como becario en el Center for Advanced Study in the Behavioral Sciences (1975-1976), de Stanford, tuve escasos apoyos y desperté muy poco interés en el mundo exterior. Me animaron unos pocos amigos y mis familiares más próximos, pero distaba mucho de estar claro que el estudio que estaba realizando sobre la forma en que la fuerza, la erudición y la imaginación de una tradición bicentenaria europea y estadounidense veían a Oriente Próximo, a los árabes y al islam, _pudiera_ interesar al público en general. Recuerdo, por ejemplo, que me resultó muy difícil al principio que un editor serio se interesara por el proyecto. Una editorial en concreto, que publicaba temas de humanidades, me ofreció un pequeño contrato para una breve monografía, ¡tan poco prometedor y tan pobre les debió parecer el tema inicialmente! Pero afortunadamente (que es el término que empleo para aludir a mi buena suerte en los Agradecimientos del libro) las cosas mejoraron mucho después de la conclusión de este estudio.
Tanto en Estados Unidos como en el Reino Unido (donde se publicó en 1979 una edición independiente) atrajo mucha atención. Parte de dicha atención (como podía esperarse) fue muy hostil; parte de ella, poco comprensiva, pero en su mayoría he de decir que fue positiva y entusiasta. En 1980 se publicó la edición francesa, que supuso el principio de una serie de traducciones que empezaron a publicarse y que han ido aumentando hasta el presente, muchas de las cuales provocaron controversias y discusiones en idiomas que desconozco. Se publicó una traducción al árabe, notable y controvertida, realizada por el prestigioso poeta y crítico sirio Kamal Abu Deeb, de la que comentaré algo más en las siguientes páginas. Posteriormente, _Orientalismo_ se tradujo al japonés, al alemán, al portugués, al italiano, al polaco, al español, al catalán, al turco, al serbocroata y al sueco (en 1993 fue uno de los libros que más se vendieron en Suecia, hecho que nos desconcertó tanto al editor local como a mí). Hay varias ediciones (en griego, en ruso, en noruego y en chino) que se están preparando o que están a punto de aparecer. Se habla de otras traducciones europeas, lo mismo que de una versión israelí, según varios informes. Se han realizado, asimismo, traducciones parciales piratas en Irán y en Pakistán. Muchas de las traducciones que he conocido directamente (en especial, la japonesa) han superado la primera edición: todas siguen imprimiéndose y aparecen ocasionalmente para suscitar discusiones locales que van más allá de lo que yo pensé cuando escribí el libro.
El resultado de todo esto es que _Orientalismo_ se ha convertido en varios libros diferentes, casi como si hubiese sido obra de los Borgia. Y, por lo que he podido seguir y entender de estas versiones posteriores, ese extraño, a veces inquietante y sin duda imprevisto polimorfismo es lo que quiero tratar aquí, repasando lo que otros han dicho que yo escribí, además de lo que yo escribí después de _Orientalismo_ (ocho o nueve libros y muchos artículos). Está claro que trataré de corregir las lecturas erróneas y, en algunos casos, las malas interpretaciones intencionadas.
No obstante, también citaré argumentos y posturas intelectuales que reconocen que _Orientalismo_ es un libro útil en aspectos que solo pude prever muy parcialmente en su momento. No trato de ajustar cuentas ni de acumular felicitaciones, sino de registrar una sensación más amplía de autoría que va más allá del egoísmo de la soledad que sentimos cuando iniciamos un trabajo, pues _Orientalismo_ parece hoy una obra colectiva, creo, que me supera como autor más de lo que podía esperarse cuando la escribí.
Empecemos por la forma en que se recibió el libro, que es lo que más lamento y me resulta hoy (en 1994) más difícil de superar. Me refiero al supuesto antioccidentalismo del libro, como ha sido calificado errónea pero sonoramente por sus comentaristas, tanto hostiles como simpatizantes. Este concepto consta de dos partes, que a veces se argumentan conjuntamente y a veces por separado. Se me atribuye en primer lugar que el fenómeno del orientalismo es una sinécdoque, un símbolo en miniatura, de todo Occidente y que debería tomarse como representativo del conjunto de Occidente. Siendo esto así, prosigue el argumento, todo Occidente es enemigo de los árabes y del islam, o incluso de los iraníes, de los chinos, de los hindúes y de muchos otros pueblos no europeos que sufrieron el colonialismo y los prejuicios occidentales. La segunda parte del argumento que se me atribuye no tiene tanto alcance. Afirma que un Occidente y un orientalismo depredadores han violado al islam y a los árabes (obsérvese que los términos «orientalismo» y «Occidente» se han unido). Siendo esto así, la propia existencia del orientalismo y de los orientalistas se utiliza como un pretexto para argumentar exactamente lo contrario, esto es, que el islam es perfecto, que es el único camino ( _al-hal al-wahid_ ), etc., y que para criticar el orientalismo, como yo hice en mi libro, hay que ser un defensor del islamismo o del fundamentalismo musulmán.
Apenas si sé qué hacer con todos estos cambios ridículos de un libro que para su autor y por sus argumentos es explícitamente antifundamentalista, radicalmente escéptico respecto a designaciones categóricas, tales como Oriente y Occidente, y escrupulosamente cuidadoso en cuanto a _no_ «defender», ni siquiera hablar de Oriente y del islam. Y, sin embargo, _Orientalismo_ se ha leído y de _Orientalismo_ se ha hablado en el mundo árabe como de una defensa sistemática del islam y de los árabes, pese a que digo expresamente que no tengo ningún interés y mucho menos estoy capacitado para mostrar lo que son realmente Oriente o el islam. En realidad voy mucho más allá cuando afirmo en las primeras páginas del libro que términos como «Oriente» y «Occidente» no se corresponden con una realidad estable que exista como un hecho natural. Más aún, todas esas designaciones geográficas suponen una extraña combinación de lo empírico y lo imaginativo. En el caso de Oriente, como concepto vigente en Gran Bretaña, Francia y Estados Unidos, la idea procede en gran medida del impulso no solo de describir, sino también de dominar y, en cierto modo, de defenderse contra él. Como trato de demostrar, esta idea es esencialmente cierta respecto del islam como una personificación especialmente peligrosa de Oriente.
El punto fundamental de todo ello radica, no obstante, como Vico nos enseñó, en que la historia de la humanidad la escriben seres humanos. Como quiera que la lucha por el control de un territorio es parte de dicha historia, también lo es la lucha por su significado histórico y social. El trabajo de un crítico erudito no es separar una lucha de la otra, sino conectar ambas pese al contraste existente entre la todopoderosa importancia de la primera y los aparentes refinamientos fantásticos de la segunda. Yo he tratado de demostrar que el desarrollo y el mantenimiento de cualquier cultura requieren la existencia de otro _alter ego_ diferente y competitivo. La creación de una identidad (ya sea la de Oriente u Occidente, la de Francia o Gran Bretaña, si bien es claramente un depósito de distintas experiencias colectivas, es, en última instancia, una creación), implica establecer antagonistas y «otros» cuya realidad esté siempre sujeta a una interpretación y a una reinterpretación permanentes de sus diferencias con «nosotros». Toda época y toda sociedad recrea sus «otros». Lejos de ser algo estático, la identidad de uno mismo o la del «otro» es un muy elaborado proceso histórico, social, intelectual y político que tiene lugar en un certamen, en el cual intervienen personas e instituciones de todas las sociedades. Los debates actuales sobre «lo francés» y «lo inglés» que hoy se producen en Francia y en Gran Bretaña, respectivamente, o sobre el islam en países como Egipto y Pakistán forman parte de un mismo proceso interpretativo que incluye las identidades de distintos «otros», ya sean extranjeros y refugiados o apóstatas e infieles. Debe estar claro en todos los casos que estos procesos no son meros ejercicios mentales, sino problemas sociales urgentes, los cuales afectan a temas políticos tan concretos como la legislación sobre inmigración, la legislación sobre la conducta personal, la constitución de una ortodoxia, la legitimización de la violencia y/o de la insurrección, el carácter y el contenido de la educación y la dirección de la política exterior, y que poco tienen que ver con la designación de los enemigos oficiales. En resumen, la creación de una identidad depende de la disposición de poder o de la indefensión de cada sociedad y, por tanto, es algo más que un simple pasatiempo propio de eruditos.
Lo que hace que todas estas realidades fluidas y de extraordinaria riqueza resulten difíciles de aceptar es que la mayoría de las personas rechaza el concepto subyacente: que la identidad humana no solo no es natural y estable, sino que es creada e incluso, en ocasiones, creada completamente. Parte de la resistencia y la hostilidad hacia libros como _Orientalismo_ , posteriormente, _The Invention of Tradition_ * y _Black Athena_* se debe a que parecen socavar la ingenua creencia en cierta positividad y en la historicidad inmutable de una cultura, un yo, una identidad nacional. _Orientalismo_ solo puede leerse como una defensa del islam, si se suprime la mitad de mi argumentación, en la que digo (como lo hago en mi libro posterior _Covering Islam_ ) que incluso la comunidad primitiva a la que pertenecemos por nacimiento no es inmune al debate interpretativo al que antes aludí y lo que en Occidente parece ser aparición, regreso o resurgimiento del islam es, de hecho, una lucha en las sociedades islámicas respecto de la definición de islam. Ninguna persona, ninguna autoridad ni ninguna institución controlan totalmente dicha definición, y de ahí el debate existente. El error epistemológico del fundamentalismo es creer que los «principios fundamentales» son categorías no históricas, no sujetas y, por tanto, exentas del escrutinio de los verdaderos creyentes, quienes se supone que deben aceptarlos ciegamente. Los partidarios de una versión restaurada o rediviva del primitivo islam consideran que los orientalistas (como Salman Rushdie) son peligrosos, porque manipulan dicha versión, arrojan dudas sobre ella, demuestran que es fraudulenta y que no es divina. Para ellos, por tanto, las virtudes de mi libro residían en que señalaba los maliciosos peligros de los orientalistas y que, en cierto modo, valoraba las auténticas raíces del islam.
Pese a que esto dista mucho de ser lo que yo creí que hacía, esa opinión persiste. Hay dos razones para que así sea. En primer lugar, a nadie le resulta fácil vivir tranquilo y sin temor con la tesis de que la realidad humana se hace y se deshace constantemente y de que algo parecido a una esencia estable está bajo una permanente amenaza. El patriotismo, el nacionalismo xenófobo extremo, y el absoluto y desagradable chauvinismo son las respuestas habituales a estos temores. Todos necesitamos algo en que apoyarnos; el problema radica en el carácter extremo e inmutable que demos a nuestra fórmula en la que se asienta esa base. Yo mantengo la postura de que, en el caso de un islam o de un Oriente esenciales, estas imágenes no son más que imágenes, y que las defienden tanto la comunidad de los fieles musulmanes como —la correspondencia resulta significativa— la comunidad de los orientalistas. Mi objeción a lo que he denominado orientalismo no reside en que sea solo el estudio de los idiomas, las sociedades y los pueblos del antiguo Oriente, sino en que, como sistema de pensamiento, se acerque a una realidad humana heterogénea, dinámica y compleja desde una postura esencialista y no crítica, lo que sugiere la existencia de una realidad oriental perdurable y de una esencia occidental opuesta, pero no menos perdurable, que observe Oriente desde lejos y, ¡por qué no decirlo!, desde arriba. Esta postura falsa oculta el cambio histórico. Y, más importante aún, desde mi punto de vista, oculta los _intereses_ del orientalista que, pese a las sutiles tentativas de trazar distinciones entre el orientalismo como inocente esfuerzo académico y el orientalismo como cómplice de un imperialismo, nunca puede desligarse unilateralmente del contexto imperialista general que comienza su moderna fase global con la invasión de Egipto por Napoleón en el año 1798.
Pienso en el sorprendente contraste entre la parte más débil y la parte más fuerte que es evidente en las modernas confrontaciones de Europa con lo que ha dado en denominar Oriente. La estudiada solemnidad y el tono grandioso de la _Description de l'Égypte_ de Napoleón (sus enormes hileras de volúmenes que recogen el trabajo sistemático de todo un grupo de sabios respaldado por un moderno ejército colonial conquistador) empequeñece el testimonio de personas como Abd al-Rahman al-Jabarti, quien en tres volúmenes describe la invasión francesa desde el punto de vista de los invadidos. Podría decirse que la _Description_ es una descripción científica y, por tanto, objetiva, del Egipto de principios del siglo XIX, pero la presencia de Jabarti (desconocido e ignorado por Napoleón) sugiere lo contrario. El trabajo de Napoleón es un relato «objetivo» desde el punto de vista de alguien poderoso que trata de incluir a Egipto en la órbita del Imperio francés; el de Jabarti es el de alguien que pagó el precio y fue, de forma figurada, apresado y vencido.
Dicho de otra forma, más que unos documentos inertes que certifican la eterna oposición de Occidente y Oriente, la _Description_ y las crónicas de Jabarti constituyen, conjuntamente, una experiencia histórica de la que proceden otras y antes de la cual existieron otras. Estudiar la dinámica histórica de este conjunto de experiencias es más acuciante que caer en estereotipos tales como «el conflicto de Oriente y Occidente». Por esta razón es por lo que _Orientalismo_ se lee erróneamente como una obra sospechosamente antioccidental y, por un acto de apoyo retrospectivo injustificado e incluso premeditado, ese tipo de lectura (como todas las basadas en una oposición binaria supuestamente estable) contribuye a crear la imagen de un islam inocente y agraviado.
La segunda razón por la que el antiesencialismo de mis argumentos ha resultado difícil de aceptar es política e ideológica. No había forma alguna de que yo supiera un año antes de que se publicara el libro que en Irán iba a producirse una revolución islámica de enorme alcance, ni que la batalla entre Israel y los palestinos seguiría cauces tan salvajes y tan duraderos, desde la invasión del Líbano en 1982 hasta el inicio de la _Intifada_ a finales del año 1987. El final de la guerra fría no modificó ni mucho menos puso fin al conflicto aparentemente interminable existente entre Oriente y Occidente, representados de una parte por los árabes y de otra por el Occidente cristiano. En fecha más reciente se produjeron confrontaciones no menos agudas como consecuencia de la invasión soviética de Afganistán; el reto al _statu quo_ planteado durante las décadas de los ochenta y los noventa por grupos islámicos en países tan diferentes como Argelia, Jordania, Líbano, Egipto y los Territorios Ocupados, y las distintas respuestas estadounidenses y europeas; la creación de brigadas islámicas para luchar contra los rusos desde bases situadas en Pakistán; la guerra del Golfo; el permanente apoyo occidental a Israel; y la aparición del término «islam» como un tema periodístico y académico alarmista no siempre preciso y bien informado. Todo ello dio lugar a que se produjera una sensación de persecución entre las personas que se ven obligadas, casi a diario, a declararse occidentales u orientales. Nadie parece estar libre de la oposición entre «nosotros» y «ellos», que se traduce en un sentido de identidad reforzado y profundo que no ha sido especialmente edificante.
En un contexto tan turbulento, el sino de _Orientalismo_ fue al mismo tiempo afortunado e infortunado. Ciertos miembros del mundo árabe e islámico, que sienten la intrusión occidental con ansiedad y tensión, consideraron que era el primer libro que ofrecía una respuesta seria a un Occidente que nunca había escuchado ni perdonado a los orientales que fueran orientales. Recuerdo que una de las primeras reseñas árabes del libro describía al autor como un campeón del arabismo, un defensor de los oprimidos y de los ultrajados, cuya misión consistía en entablar un épico y romántico mano-a-mano con las autoridades occidentales. Pese a la exageración, lo cierto es que logré dar cierto sentido real a la constante hostilidad de Occidente que percibían los árabes y una respuesta que muchos árabes educados consideró adecuada.
No negaré que _era_ consciente cuando escribí el libro de la verdad subjetiva que insinuaba Marx en la frase que cité como uno de los epígrafes del libro («No se pueden representar; tienen que ser representados»), esto es, que si crees que te han negado la oportunidad de hablar tratarás con todas tus fuerzas de gozar de esa oportunidad. En verdad, el subalterno _puede_ hablar, como certifica la historia de los movimientos de liberación del siglo XX. Pero nunca creí que estuviera perpetuando la hostilidad entre dos bloques monolíticos políticos y culturales rivales, cuya creación describía y cuyos terribles efectos estaba tratando de reducir. Por el contrario, la oposición Oriente-Occidente no solo era equívoca, sino que además no era deseable, y menos aún debía tenerse en cuenta para describir algo más que una fascinante historia de interpretaciones e intereses contrapuestos. Es un placer señalar que muchos lectores de Gran Bretaña y de Estados Unidos, así como otros de habla inglesa de África, Asia, Australia y del Caribe, consideraron que el libro destacaba la realidad de lo que luego se llamó multiculturalismo en vez de xenofobia y nacionalismo agresivo y racista.
No obstante, se ha considerado a _Orientalismo_ como un tipo de testimonio de una situación de sometimiento (la respuesta de los parias de la Tierra) más que como una crítica multicultural del poder que recurre a sus conocimientos para progresar. De mí, como autor, se ha dicho que desempeño un papel concreto: el de la conciencia de lo que se había suprimido y distorsionado anteriormente en los doctos textos de un discurso históricamente condicionado para que lo leyeran no los orientales, sino otros occidentales. Este es un aspecto importante y se suma al sentido de identidades fijas que luchan permanentemente divididas, las cuales mi libro rechaza expresamente, pero que, paradójicamente, presupone y de las que depende. Ninguno de los orientalistas de los que hablo parece haberse planteado el hecho de que un oriental pudiera leer sus libros. El discurso del orientalismo, su coherencia interna y sus rigurosos procedimientos se diseñaron para lectores y consumidores del Occidente metropolitano. Esto es algo que hay que reseñar a favor de personas a las que admiro auténticamente, como Edward Lane y Gustave Flaubert, ambos fascinados por Egipto, así como de arrogantes administradores coloniales como lord Cromer, intelectuales brillantes como Ernest Renan, y aristócratas como Arthur Balfour, todos los cuales se mostraron condescendientes y no gustaron de los orientales que o bien gobernaban o bien estudiaban. Debo confesar con cierto placer que he escuchado sin haber sido invitado varios pronunciamientos y discusiones entre orientalistas y que experimenté el mismo placer al dar a conocer mis hallazgos tanto a europeos como a no europeos. No albergo ninguna duda de que fue posible porque yo crucé la línea divisoria imperial entre Oriente y Occidente, hice mía la vida occidental y, pese a ello, conservé cierta conexión orgánica con el lugar del que procedía. Quiero insistir en que fue más un procedimiento de cruce que de mantenimiento de las barreras. Creo que _Orientalismo_ lo demuestra como libro, en especial cuando hablo de estudio humanístico como búsqueda ideal de la forma de superar las restricciones coercitivas impuestas al pensamiento para llegar a un tipo de erudición no dominante y no esencialista.
Todos estos aspectos se sumaron, de hecho, a las presiones que sufrió mi libro para hacerlo representar una especie de relato bíblico de heridas y sufrimientos, cuyo recital se consideraba como un golpe que tiempo atrás se debía haber devuelto a Occidente. Deploro que se defina de forma tan simple un trabajo que (aquí no seré falsamente modesto) tiene tantos matices y discrimina tanto en lo que dice sobre diferentes pueblos, diferentes períodos y diferentes estilos de occidentalismo. Cada uno de mis análisis varía el cuadro, incrementa la diferencia y las discriminaciones, separa autores y períodos, aunque todos pertenezcan al orientalismo. Leer mis análisis de Chateaubriand y de Flaubert, o los de Burton y los de Lane, con el mismo énfasis derivado del mismo mensaje reduccionista procedente de la fórmula banal de que se trata de «un ataque a la civilización occidental» es, creo, una postura simplista y errónea. Pero también estoy firmemente convencido de que es completamente correcto considerar que las recientes autoridades orientalistas, como el casi cómicamente persistente Bernard Lewis, son testigos políticamente motivados y hostiles que tratan de ocultarse tras suaves acentos y despliegues de erudición poco convincentes.
Volvamos de nuevo al contexto político e histórico del libro, que no pretendo que sea irrelevante respecto de su contenido. Una de las afirmaciones más generosamente perspicaces y más inteligentemente discriminatorias de dicha coyuntura apareció en una reseña de Basim Musallam (MERIP, 1979). Empieza por comparar mi libro con una desmitificación anterior del orientalismo que realizó el erudito libanés Michael Rustum en el año 1895 ( _Kitab al-Gharib fi alGharb_ ), pero luego afirma que la principal diferencia entre nosotros es que mi libro trata de pérdidas y el de Rustum no. Musallam dice:
Rustum escribe como hombre libre y miembro de una sociedad libre: sirio, su lengua materna es el árabe y es ciudadano de un estado otomano aún independiente [...] al contrario que Michael Rustum, Edward Said carece de una identidad aceptada de forma general, se discute cuál es su verdadero _pueblo_. Es posible que Edward Said y su generación piensen a veces que no se apoyan en nada más sólido que en los restos de la destruida sociedad de la Siria de Michael Rustum, y en su recuerdo. Otros de África y Asia han logrado éxitos en esta época de liberación nacional. Aquí, en doloroso contraste, ha existido una resistencia desesperada contra unas circunstancias agobiantes y, hasta ahora, un total fracaso. No es un árabe cualquiera el que escribió este libro, sino un árabe con unos antecedentes y una experiencia especiales (p. 22).
Musallam observa correctamente que un argelino no habría escrito el mismo tipo de libro, pesimista en general, en especial uno como el mío que se ocupa muy poco de la historia de las relaciones francesas con el norte de África, con Argelia más concretamente. Por eso estaría dispuesto a aceptar la impresión general de que _Orientalismo_ expresa una historia muy concreta de pérdida personal y desintegración nacional (solo unos años antes de que yo escribiera _Orientalismo_ , Golda Meir realizó su comentario notoria y profundamente orientalista de que no existía un pueblo palestino). Quisiera añadir también que ni en este libro ni en los dos que le siguieron inmediatamente, _The Question of Palestine_ (1980) y _Covering Islam_ (1981), quise sugerir un programa político de restauración de la identidad y de resurgimiento del nacionalismo. Hubo, claro está, en los dos últimos libros un intento de ofrecer lo que faltaba en _Orientalismo_ : un sentido de lo que, desde un punto de vista personal, podría ser una imagen alternativa de ciertas partes de Oriente (Palestina y el islam, respectivamente).
Pero en todas mis obras mantuve una postura fundamentalmente crítica de un nacionalismo perverso y sin reservas. La imagen del islam que presentaba no era una de discurso agresivo y ortodoxia dogmática, sino que se basaba en la idea de que existen comunidades de interpretación dentro y fuera del mundo islámico, que se comunican entre sí a través de un diálogo entre iguales. Mi visión de Palestina, formulada originalmente en _The Question of Palestine_ , sigue siendo hoy la misma: expresé todo tipo de reservas sobre el nativismo indiferente y el militarismo combativo del consenso nacionalista; sugerí, por el contrario, una mirada crítica del entorno árabe, la historia palestina y la realidad israelí, con la conclusión explícita de que solo un acuerdo negociado entre las dos comunidades que sufren, la árabe y la israelí, supondría un alivio a una guerra interminable. (Quisiera citar de pasada que aunque mi libro sobre Palestina fue muy bien traducido al hebreo a principios de la década de 1980 por Mifras, una pequeña editorial israelí, aún no hay traducción al árabe al día de hoy. Todas las editoriales árabes que mostraron interés por el libro quisieron que cambiara o suprimiera las secciones que son abiertamente críticas de algún régimen árabe —incluyendo la OLP—, petición que siempre me negué a cumplir.)
Lamento mucho la forma en que el mundo árabe recibió _Orientalismo_ , pese a la notable traducción de Kamal Abu Deeb. Trató de ignorar que mi libro reducía el fervor nacionalista, que algunos dedujeron de mi crítica del orientalismo, fervor que yo asociaba con impulsos de dominio y control, los cuales aparecen también en el imperialismo. El principal logro de la esmerada traducción de Abu Deeb es que trató de evitar casi totalmente el uso de expresiones occidentales «arabizadas»; términos técnicos como _discurso_ , _simulacro_ , _paradigma_ o _código_ se tradujeron usando la retórica clásica de la tradición árabe. Su idea fue situar mi trabajo dentro de una tradición totalmente consolidada, como si se dirigiera a otro desde una perspectiva de idoneidad e igualdad. De este modo, razonaba, resultaba posible que lo mismo que se podía plantear una crítica epistemológica desde la tradición occidental, también era posible hacerlo dentro de la tradición árabe.
El sentido de confrontación entre un mundo árabe, frecuentemente definido de forma emocional, y un mundo occidental, experimentada con más emoción, atenuaba el hecho de que _Orientalismo_ pretendía ser un estudio crítico y no una afirmación de identidades enfrentadas y antitéticas sin esperanza; y la actualidad que exponía en las últimas páginas de mi libro, la de un sistema muy bien razonado que mantiene una hegemonía sobre el otro, pretendía ser un pretexto para iniciar un debate que pudiera incitar a los lectores y a los críticos árabes a comprometerse de forma más decidida con el sistema del orientalismo. Sin embargo, a pesar de que estas dos intenciones presidían todo el discurso, me encontré con que o bien se me reprochaba que no hubiera prestado mayor atención a Marx (los pasajes de mi libro que más destacaban los críticos dogmáticos del mundo árabe y de la India, por ejemplo, eran los de Marx sobre el orientalismo), cuyas ideas, se alegaba, habían superado sus propios prejuicios; o bien se me criticaba que no hubiera destacado los grandes logros del orientalismo, de Occidente, etc. Pero, al igual que en la defensa del islam, el recurrir al marxismo o a «Occidente» me parece que es como usar una ortodoxia para acabar con otra.
La diferencia entre la respuesta árabe y otras respuestas a _Orientalismo_ es, creo, una indicación precisa de la forma en que décadas de pérdidas, de frustración y de ausencia de democracia han afectado a la vida intelectual y cultural del mundo árabe. Yo traté de que el libro se integrara en una corriente de pensamiento ya existente con el objetivo de liberar a los intelectuales de las trabas de sistemas como el orientalismo: quería que mis lectores se apoyaran en mi trabajo para producir nuevos estudios que iluminaran la experiencia histórica de los árabes y de otros pueblos de forma generosa y permisiva. Eso es lo que sucedió en Europa, en Estados Unidos, en Australia, en la India, en el Caribe, en Irlanda, en Hispanoamérica y en algunas partes de África. El fortalecido estudio de los discursos africanistas e hinduistas, los análisis de la historia de dependencia, la reconfiguración de la antropología, de las ciencias políticas, de la historia del arte, de la crítica literaria, de la musicología poscoloniales, además de los nuevos e importantes acontecimientos a que han dado lugar los discursos feminista y de las minorías, respecto a todo ello, me complace y me halaga que _Orientalismo_ haya marcado una diferencia. Este no parece haber sido, en mi opinión, el caso del mundo árabe, en el que, en parte gracias a que mi trabajo se percibe correctamente como eurocéntrico en sus textos y en parte porque, como dice Musallam, la batalla de la supervivencia cultural es excesivamente absorbente, libros como el mío se interpretan de forma menos útil, desde el punto de vista productivo, y más como gestos defensivos a favor o en contra de «Occidente».
No obstante, entre los estudiosos estadounidenses y británicos de carácter decididamente riguroso e inflexible, tanto _Orientalismo_ como el resto de mi obra han recibido ataques por su humanismo «residual», sus inconsistencias teóricas, su tratamiento insuficiente, tal vez sentimental, del libre albedrío. ¡Me alegro de que así sea! _Orientalismo_ es un libro parcial y no una máquina teórica. Nadie ha logrado demostrar de forma convincente que el esfuerzo individual no sea en un plano muy difícil de mostrar no solo egocéntrico, sino también, en el sentido que da a dicho término Gerard Manley Hopkins, _original_. Esto es así pese a la existencia de sistemas de pensamiento, discursos y hegemonías (aunque ninguno de ellos sea realmente inconsútil, perfecto o inevitable). El interés que he puesto en el orientalismo como fenómeno cultural (como la cultura del imperialismo a la que me refería en _Culture and Imperialism_ , su secuela, publicada en 1993)* dimana de su variabilidad y su imprevisibilidad, cualidades ambas que dan a escritores como Massignon y Burton su sorprendente fuerza e incluso su atractivo. Lo que traté de preservar en mi análisis del orientalismo fue su combinación de coherencia e incoherencia, su juego, por así decirlo, que solo puede producirse si se mantiene, como autor y como crítico, el derecho a cierta fuerza emocional, el derecho a conmoverse, irritarse, sorprenderse e incluso deleitarse. Por eso es por lo que en el debate entre Gayan Prakash, por una parte, y Rosalind O'Hanlon y David Washbrook, por otra, creo que hay que darle la razón a Prakash. Por la misma regla de tres, el trabajo de Homi Bhabha, Gayatri Spivak, Ashis Nandy, basado en las relaciones subjetivas a veces tambaleantes engendradas por el colonialismo, no puede ser rechazado por _su_ aportación a nuestra comprensión de las trampas humanistas de sistemas tales como el orientalismo.
Permítanme que finalice este examen de las transmutaciones críticas de _Orientalismo_ mencionando a un grupo de personas que fue, no inesperadamente, el que más vociferó en su respuesta a mi libro: los propios orientalistas. No fueron en modo alguno el público al que pretendí dirigirme _fundamentalmente_ , ya que yo traté de arrojar cierta luz sobre sus prácticas para que otros humanistas conocieran los procedimientos y la genealogía de un campo determinado. La misma palabra «orientalismo» se ha confinado durante un tiempo excesivamente largo a una especialidad profesional. Traté de mostrar su aplicación y su existencia en la cultura en general, en la literatura, en la ideología y en lo social, así como en las actitudes políticas. Hablar de alguien calificándolo de oriental, como hacían los orientalistas, no se limitaba a designar a dicha persona como alguien cuyo idioma, geografía e historia eran objeto de doctos tratados, pues demasiadas veces era una expresión despectiva atribuida a un ser humano de menor pureza. Por supuesto, esto no significa que niegue que para artistas como Nerval y Segalen la palabra «Oriente» estuviera maravillosa e ingeniosamente relacionada con exotismo, hechizo, misterio y promesa. Pero esto era también una vasta generalización histórica. Además de los usos citados de las palabras «Oriente», «oriental» y «orientalismo», el término «orientalista» vino, asimismo, a representar al especialista erudito, principalmente universitario, en los idiomas y en la historia de Oriente. Sin embargo, como me escribía el ya desaparecido Albert Hourani en marzo de 1992, pocos meses antes de su prematura y llorada muerte, a causa de la fuerza de mis argumentos (que decía que no podía reprocharme), mi libro produjo el desgraciado efecto de hacer casi imposible el uso del término «orientalismo» de forma neutral, ya que había pasado a ser un término del que se abusaba. Concluía diciéndome que a él le hubiera gustado que la palabra se siguiera usando para describir «una disciplina académica limitada, un tanto opaca, pero válida».
En su generalmente equilibrada reseña de _Orientalismo_ , publicada en 1979, Hourani planteó una de sus principales objeciones al libro. Decía que, aunque yo destacaba las exageraciones, el racismo y la hostilidad de los escritos de muchos orientalistas, no mencionaba sus numerosos logros académicos y humanistas. Entre los nombres que citaba se hallaban los de Marshall Hodgson, Claude Cahen, André Raymond, a quienes (junto con los autores alemanes de rigor) debe reconocerse como verdaderos contribuyentes al conocimiento humano. No obstante, esto no quiere decir que exista conflicto alguno con lo que expongo en _Orientalismo_ , puesto que yo insisto en la prevalencia en el propio discurso de una estructura de actitudes a las que no se puede renunciar y que son imprevisibles. En ningún momento sostengo que el orientalismo sea malo, ni que sea chapucero, ni que sea siempre el mismo en el trabajo de todos y cada uno de los orientalistas. Pero sí afirmo que el _gremio_ de los orientalistas cuenta con una historia específica de complicidad con el poder imperialista.
De modo que si bien acepto el argumento de Hourani, tengo serias dudas sobre si la noción de orientalismo correctamente entendida puede realmente separarse de sus circunstancias más complicadas y no siempre lisonjeras. Supongo que se puede imaginar, llegando al límite, que un especialista en archivos otomanos o fatimíes es un orientalista en el sentido que da Hourani a este término, pero aun así tendremos que preguntar dónde, cómo y con el apoyo de qué instituciones y agencias se realizan _hoy_ esos estudios. Muchos de los que escribieron después de que apareciera mi libro formularon esas mismas preguntas sobre los más recónditos y ultramundanos eruditos, a veces con resultados devastadores.
A pesar de esto, ha existido un intento sostenido de montar un argumento cuya sustancia es que una crítica del orientalismo (la mía en especial) carece de sentido y atenta contra la idea de una erudición desinteresada. Eso es lo que ha tratado de hacer Bernard Lewis, a quien he dedicado unas cuantas páginas críticas en mi libro. Quince años después de la aparición de _Orientalismo_ , Lewis publicó diversos ensayos, parte de los cuales se recogieron en un libro titulado _Islam and the West_. Una de las secciones principales de dicho libro incluye un ataque directo contra mí, que rodea de capítulos y otros ensayos que movilizan un conjunto de fórmulas laxas y característicamente orientalistas (a los musulmanes les irrita la modernidad, el islam nunca llevó a cabo la separación entre Iglesia y Estado, etc.), todas ellas con un nivel extremo de generalización y con apenas una mención de las diferencias entre las personas musulmanas, las sociedades musulmanas, las tradiciones musulmanas y las eras musulmanas. Como quiera que Lewis se ha autoproclamado portavoz del _gremio_ de los orientalistas en los que mi crítica se basó originalmente, puede que valga la pena dedicar algún tiempo más a hablar de sus procedimientos. Por otra parte, sus ideas las comparten sus escasos acólitos e imitadores, cuyo trabajo parece ser el alertar a los consumidores occidentales sobre la amenaza de un mundo islámico encolerizado, congénitamente no democrático y violento.
La verborrea de Lewis apenas oculta el soporte ideológico de su posición y su extraordinaria capacidad para equivocarse en casi todo. Claro está que todos los citados son atributos familiares a la ralea de los orientalistas, algunos de los cuales han tenido al menos el valor de ser honestos en su denigración activa de lo islámico, así como de otros pueblos no europeos. No así Lewis, que actúa distorsionando la verdad, estableciendo falsas analogías e, indirectamente, recurriendo a métodos a los que dota de esa apariencia de tranquila y omnisciente autoridad que se supone que caracteriza la forma de hablar de los eruditos. Nos servirá de ejemplo la analogía que establece entre mi crítica del orientalismo y un hipotético ataque a los estudios de la antigüedad clásica, un ataque que, dice, sería una actividad loca. Lo sería, claro está. Pero resulta que el orientalismo y el helenismo son radicalmente incomparables. El primero pretende describir toda una región del mundo como complemento de la conquista colonial de la misma; el segundo no tiene nada que ver con la conquista colonial directa de Grecia en los siglos XIX y XX. Además, el orientalismo es una expresión de antipatía hacia islam, en tanto que el helenismo expresa simpatía por la Grecia clásica.
Además, el momento político actual, con sus variados estereotipos racistas antiárabes y antimusulmanes (y sin ataques a la Grecia clásica), permite a Lewis realizar afirmaciones ahistóricas y deliberadamente políticas en forma de argumentos académicos, práctica siempre presente en los aspectos menos creíbles de un antiguo orientalismo colonialista. Por lo tanto, el trabajo de Lewis forma parte del actual entorno político, y no del puramente intelectual.
Deducir, como él hace, que la rama del orientalismo consagrada al islam y a los árabes es una docta disciplina que, por tanto, puede situarse en el mismo grupo que la filología clásica resulta descabellado, tan apropiado como sería comparar a uno de los muchos arabistas y orientalistas israelíes que trabajaron para las autoridades de ocupación de Cisjordania y Gaza con eruditos como Wilamowitz o Mommsen. Por una parte, Lewis desea reducir el orientalismo islámico a la situación de departamento inocente y entusiasta del saber. Por otra, desea insinuar que el orientalismo es demasiado complejo, demasiado diverso y demasiado técnico para existir de una forma que cualquier persona que no sea orientalista (como yo y otros muchos) pueda criticar. La táctica que sigue Lewis en este caso es suprimir una cantidad importante de experiencia histórica. Tal y como sugiero, el interés europeo por el islam no se debe a la curiosidad, sino al temor de un competidor monoteísta, cultural y militarmente formidable, del cristianismo. Los primeros eruditos europeos en temas del islam, como han demostrado numerosos historiadores, fueron polemistas medievales que escribían advirtiendo sobre la amenaza de las hordas y la apostasía musulmanas. De una u otra forma, esa mezcla de temor y hostilidad han persistido hasta nuestros días en la atención que los eruditos y quienes no lo son prestan a un islam que se considera que pertenece a una parte del mundo (Oriente) opuesta imaginaria, geográfica e históricamente a Europa y a Occidente.
Los problemas más interesantes del orientalismo islámico o árabe son, en primer lugar, las formas adoptadas por los vestigios medievales que persisten tan tenazmente y, en segundo lugar, la historia y la sociología de las conexiones entre el orientalismo y las sociedades que lo produjeron. Existen fuertes _conexiones_ , por ejemplo, entre el orientalismo y la imaginación literaria, así como con la conciencia imperial. Lo más sorprendente de muchos períodos de historia de Europa es la relación existente entre lo que escribían los eruditos y los especialistas y lo que los poetas, los novelistas, los políticos y los periodistas decían sobre el islam. Además (y este es el punto crucial que Lewis se niega a tratar), existe un notable (pero, sin embargo, inteligible) paralelismo entre el auge de la moderna erudición orientalista y la adquisición de vastos imperios orientales por Gran Bretaña y por Francia.
Aunque la relación entre la rutinaria educación clásica británica y la extensión del Imperio británico sea más compleja de lo que Lewis podría suponer, no existe un paralelismo más intenso entre poder y conocimiento en la historia moderna de la filología que el que se da en el caso del orientalismo. Gran parte de la información y los conocimientos sobre el islam y Oriente que usaron los poderes coloniales para justificar su colonialismo procedió de la erudición orientalista: un estudio reciente de muchos autores, _Orientalism and the Postcolonial Predicament_ , demuestra, con una copiosa documentación, la forma en que los conocimientos de los orientalistas se usaron por la administración colonial del sur de Asia. Persiste aún un intercambio consistente entre los eruditos en temas de la zona, como los orientalistas, y los ministerios de asuntos exteriores de determinados gobiernos. Además, muchos de los estereotipos sobre la sensualidad, la holgazanería, el fatalismo, la crueldad, la degradación y el esplendor islámicos y árabes, que se encuentran en escritores que van de John Buchan a V. S. Naipaul, han sido también presunciones que subyacen en el campo adyacente del orientalismo académico. Por el contrario, el intercambio de estereotipos entre la hindología y la sinología, por una parte, y la cultura general, por otra, no es tan floreciente, aunque haya relaciones y adopciones que destacar. Tampoco existe un gran parecido entre lo que obtienen los expertos occidentales en hindología y sinología y el hecho de que muchos eruditos profesionales europeos y estadounidenses en temas del islam dedican su vida al estudio de esta materia y, sin embargo, les resulta imposible apreciar su religión y su cultura y, menos aún, admirarlas.
Decir, como dicen Lewis y sus imitadores, que todas estas observaciones solo tratan de «abrazar causas que estén de moda» no supone en modo alguno resolver la cuestión de por qué, por ejemplo, tantos especialistas en el islam fueron y siguen siendo consultados rutinariamente y trabajan de forma activa para gobiernos cuyos únicos objetivos respecto al mundo islámico son la explotación económica, la dominación o la agresión flagrante, o por qué tantos eruditos en temas del islam (como el propio Lewis) sienten voluntariamente que parte de su deber es organizar ataques contra los pueblos árabes o islámicos modernos, señalando que la cultura «clásica» islámica puede, no obstante, ser tema que preocupe desinteresadamente al mundo académico. El espectáculo de una serie de especialistas en historia de los gremios medievales islámicos a los que se envía, formando parte de misiones del Departamento de Estado, a explicar a las embajadas de la zona los intereses de Estados Unidos en el golfo Pérsico no sugiere de forma espontánea nada que pueda compararse con el amor a Grecia que Lewis asigna al campo supuestamente análogo de la filología clásica.
No puede, por tanto, sorprendernos que el campo del orientalismo árabe e islámico, siempre dispuesto a negar su complicidad con el poder estatal, no haya planteado hasta fechas recientes una crítica interna de las relaciones que acabo de describir, y que Lewis pueda divulgar su sorprendente afirmación de que una crítica hecha al orientalismo «carezca de sentido». Tampoco resulta sorprendente que, con contadas excepciones, la mayoría de las críticas que mi trabajo ha recibido de los «especialistas» resulte ser, como en el caso de Lewis, tan solo una banal descripción de un coto cerrado en el que ha entrado un invasor inculto. Los únicos especialistas (asimismo, contadas excepciones) que trataron de ocuparse de lo que yo expongo (que no es solo el contenido del orientalismo, sino también sus relaciones, sus asociaciones, sus tendencias políticas, su visión del mundo) fueron los sinólogos y los hindólogos y la generación más joven de eruditos de Oriente Próximo, receptivos a las nuevas influencias y a los argumentos políticos que ha traído la crítica al orientalismo. Un claro exponente es Benjamin Schwarts, de la Universidad de Harvard, quien en su alocución como presidente a la Asian Studies Association en 1992, no solo no estuvo de acuerdo con parte de las críticas que se me habían hecho, sino que dio la bienvenida, intelectualmente, a los argumentos que yo exponía en mi obra.
Muchos de los principales arabistas e islamólogos han respondido con una indignación que, en su caso, reemplaza a la reflexión. La mayoría emplea palabras como «maligno», «deshonor», «libelo», como si las críticas fueran una intromisión imperdonable en su sacrosanta reserva académica. En el caso de Lewis, la defensa que plantea es un llamativo acto de mala fe, ya que él, más que la mayor parte de los orientalistas, ha sido un defensor apasionado de causas contra los árabes (y contra otros pueblos) en foros como el Congreso de los Estados Unidos, _Commentary_ y otros muchos. Por tanto, la respuesta adecuada a Lewis debe incluir un relato de lo que representa política y sociológicamente cuando pretende estar defendiendo el «honor» de su especialidad, defensa que, como resulta evidente, es un conjunto artificial de medias verdades ideológicas, que tratan de confundir a los lectores que no sean especialistas.
En resumen, las relaciones entre los orientalistas islámicos o árabes y la moderna cultura europea se pueden estudiar sin catalogar al mismo tiempo a todos los orientalistas, a toda la tradición orientalista o a todo lo escrito por los orientalistas; luego amontonarlo todo, calificándolo de imperialismo putrefacto y sin valor. Yo nunca hice eso. Decir que el orientalismo es una conspiración o sugerir que Occidente es malvado demuestra una ignorancia supina. Sin embargo, ambas afirmaciones figuran entre las necedades que Lewis y uno de sus acólitos, el publicista iraquí Kanan Makiya, han tenido la temeridad de adjudicarme. Por otra parte, resulta hipócrita prescindir del contexto cultural, político, ideológico e institucional en el que las personas escriben, piensan y hablan de Oriente, sean o no sean eruditos. Y, como dije anteriormente, es enormemente importante entender que la principal razón de la oposición al orientalismo de muchas personas sensatas no occidentales es que se percibe correctamente como un discurso de poder que se origina en una era de colonialismo, tema de un excelente y reciente simposio, «Colonialism and Culture». En este tipo de discurso, basado fundamentalmente en la presunción de que el islam es monolítico e inmutable y, por tanto, «comercializable» por «expertos» en beneficio de poderosos intereses políticos, ni los musulmanes, ni los árabes, ni ninguno de los otros pueblos deshumanizados e inferiores se reconocen como seres humanos, ni a sus observadores como simples eruditos. La mayoría de ellos detectan en el discurso del orientalismo moderno y en las copias creadas para los nativos americanos o africanos, una tendencia crónica a negar, suprimir o distorsionar el contexto cultural de dichos sistemas de pensamiento para mantener la ficción de su desinterés académico.
No quisiera, sin embargo, sugerir que el pensamiento actual, como pueden ser las opiniones de Lewis, sea el único que ha sufrido o se ha fortalecido durante los últimos quince años. No obstante, es cierto que, desde la desintegración de la Unión Soviética, ciertos eruditos y periodistas estadounidenses se han precipitado a hallar en un islam orientalizado el nuevo imperio del mal. Por consiguiente, los medios de comunicación electrónicos e impresos se han visto inundados de estereotipos degradantes, que identifican al islam con el terrorismo, a los árabes con la violencia o a Oriente con la tiranía. Y también se produjo un retorno en distintas zonas de Oriente Próximo y del Extremo Oriente a la religión nacionalista y al nacionalismo primitivo; un aspecto especialmente desgraciado de esto es la permanente _fatwa_ iraní contra Salman Rushdie. Pero esto no es todo, y lo que quiero hacer en lo que resta de este ensayo es hablar de las recientes tendencias académicas, de las críticas y de las interpretaciones que, pese a que aceptan las premisas básicas de mi libro, lo superan en modos que, creo, enriquecen nuestro sentido de la complejidad de la experiencia histórica.
Claro está que ninguna de esas tendencias ha surgido de la nada ni ha logrado su pleno reconocimiento como conocimiento y práctica plenamente establecidos. El contexto mundial sigue siendo confusamente estimulante e ideológicamente recargado, volátil, tenso, mutable e incluso violento. Aunque la Unión Soviética se haya desintegrado y los países del Este europeo hayan obtenido su independencia, las pautas de poder y dominación siguen siendo las mismas. El Sur global (al que una vez se denominó, romántica e incluso emocionalmente, el Tercer Mundo) está inmerso en la trampa de la deuda, acosado por problemas de pobreza, enfermedades y subdesarrollo, que se han incrementado durante los últimos diez o quince años. Ha desaparecido el movimiento de los países No Alineados y los líderes carismáticos que llevaron a cabo la descolonización y la independencia. Se ha hecho presente, de nuevo, una pauta alarmante de conflictos étnicos y de guerras locales, no confinada al Sur global, como demuestra el trágico caso de Bosnia. Y en lugares tales como América Central, Oriente Próximo y Asia, Estados Unidos sigue siendo el poder dominante, seguido de una Europa ansiosa y aún no unificada.
Se han dado explicaciones muy llamativas a la actual situación mundial y se ha tratado de incluir en ellas aspectos culturales y políticos. Ya he citado el fundamentalismo. Los equivalentes seculares son un regreso al nacionalismo y a las teorías que subrayan la radical distinción (una distinción falsamente exhaustiva, creo) entre las distintas culturas y civilizaciones. En fechas recientes, por ejemplo, Samuel Huntington, profesor de la Universidad de Harvard, planteó la idea, que dista mucho de ser convincente, de que la bipolaridad de la guerra fría había sido reemplazada por lo que denominó «choque de civilizaciones», tesis basada en la premisa de que las civilizaciones occidental, confucionista e islámica, entre otras, eran algo así como compartimientos impermeables cuyos miembros se hallaban en el fondo interesados fundamentalmente en mantener a raya a todos los demás.
Tal idea es ridícula, ya que uno de los grandes avances de la moderna teoría cultural es la comprensión, casi universalmente admitida, de que las culturas son híbridas y heterogéneas y de que, como señalé en _Cultura e imperialismo_ , las culturas y las civilizaciones están tan interrelacionadas y son tan interdependientes que es difícil realizar una descripción unitaria o simplemente perfilada de su individualidad. ¿Cómo hablar hoy de una «civilización occidental», salvo, en gran medida, como de una ficción ideológica que implique una especie de superioridad de un puñado de valores e ideas, ninguno de los cuales tiene mucho sentido fuera de la historia de la conquista, la inmigración, los viajes y la mezcla de pueblos que ha dado a las naciones occidentales su actual identidad mixta? Esto es especialmente cierto en el caso de Estados Unidos, que hoy solo puede describirse como un enorme palimpsesto de distintas razas y culturas que comparten una historia problemática de conquistas, exterminios y, por supuesto, importantes logros culturales y políticos. Y este era uno de los mensajes de _Orientalismo_ : que cualquier tentativa de encasillar a culturas y pueblos en castas y/o en esencias separadas y diferentes está expuesto no solo a los equívocos y las falsedades consiguientes, sino también a que nuestra comprensión se alíe con el poder para crear cosas tales como «Oriente» y «Occidente».
No quiero decir con esto que Huntington y todos los teóricos y los apologistas de una exultante tradición occidental, como Francis Fukuyama, no hayan conservado gran parte de su influencia sobre la conciencia pública. La conservan, como resulta evidente en el caso sintomático de Paul Johnson, en tiempo intelectual de izquierdas y hoy retrógrado polemista político y social. En la edición del 18 de abril de 1993 del _New York Times Magazine_ , que dista mucho de ser una publicación marginal, Johnson publicó un ensayo titulado «El colonialismo ha vuelto y no demasiado pronto», cuya idea principal era que las «naciones civilizadas» debían asumir la recolonización de los países del Tercer Mundo «en los que han desaparecido las condiciones básicas de una vida civilizada» y debían hacerlo mediante un sistema de imposición de administraciones fiduciarias. Su modelo es explícitamente el modelo colonial del siglo XIX: afirma que para que los europeos puedan comerciar de forma rentable, tendrán que imponer un orden político.
El argumento de Johnson ha tenido numerosos ecos subterráneos en las obras de quienes elaboran la política estadounidense, en los medios de comunicación y, por supuesto, en la política exterior de Estados Unidos, que sigue siendo intervencionista en Oriente Próximo, en Hispanoamérica y en Europa del Este, y francamente misionera en las restantes zonas, en especial en su política respecto a Rusia y las antiguas repúblicas soviéticas. Lo importante, sin embargo, es que se produjo una grieta, poco analizada pero seria, en la opinión pública, por un lado, entre las viejas ideas de la hegemonía occidental (de las que formaba parte el sistema del orientalismo) y, por otro, las nuevas ideas que han prendido en las comunidades subalternas y en situación de inferioridad y entre un amplio sector de intelectuales, académicos y artistas. Se produjo una revolución tan poderosa en la opinión de las mujeres, las minorías y los marginales como para afectar a la corriente principal del pensamiento mundial. Aunque tuve esa sensación cuando trabajaba en _Orientalismo_ en la década de los setenta, resulta tan aparente como para reclamar la atención de toda persona preocupada seriamente por el estudio docto y teórico de la cultura.
Pueden distinguirse dos amplias corrientes de pensamiento: el poscolonialismo y el posmodernismo. La presencia del prefijo «pos» no parece sugerir posterioridad, sino más bien, como señala Ella Shohat en un muy influyente artículo sobre lo poscolonial, «continuidades e interrupciones, pero se centra en los nuevos modos y en las nuevas formas de las antiguas prácticas colonialistas y no en nada posterior».
Tanto el poscolonialismo como el posmodernismo surgieron como movimientos relacionados con el compromiso y la investigación en la década de los ochenta y en muchos casos parecía que tenían en cuenta, como antecedentes, obras tales como _Orientalismo_. Sería imposible aquí ocuparnos de los innumerables debates terminológicos en torno a ambas palabras, algunos de ellos respecto a si deben o no incluir un guión. Por tanto, no se trata de hablar de casos aislados de exceso de jerga que produzcan risa, sino de localizar las corrientes y los esfuerzos que, desde la perspectiva de un libro publicado en 1978, parecen en cierta medida afectarlo en 1994.
Gran parte del trabajo más apremiante sobre el nuevo orden político y económico se ha centrado en lo que, en un artículo reciente, Harry Magdoff ha calificado de «globalización», un sistema por el que una reducida elite financiera amplía su poder al mundo entero, inflando los precios de las materias primas y de los servicios, redistribuyendo la riqueza desde los sectores de menor renta (habitualmente del mundo no occidental) hacia los de mayor renta. Al mismo tiempo, como exponen en términos severos Masao Miyoshi y Arif Dirlik, ha surgido un nuevo orden transnacional en el que los estados ya no tienen fronteras, el trabajo y las rentas dependen exclusivamente de unos gestores globales y el colonialismo ha reaparecido con la subordinación del Sur al Norte. Tanto Miyoshi como Dirlik prosiguen su argumento mostrando cómo el interés de los estudiosos occidentales por temas tales como el multiculturalismo y el «poscolonialismo» pueden suponer, de hecho, una retirada cultural e intelectual de las nuevas realidades del poder global. «Lo que necesitamos —dice Miyoshi— es un riguroso análisis político y económico más que un gesto de oportunidad pedagógica», del que puede servir de ejemplo la «impostura liberal» que aparece en campos nuevos como los estudios culturales y el multiculturalismo.
Pero aun en el caso de que tomemos en serio (como debemos) tales preceptos, existe una sólida base de experiencia histórica para que hoy despierten interés tanto el posmodernismo como su contrapartida, el poscolonialismo. En primer lugar, existe un sesgo eurocéntrico mucho más acentuado en el primero, una preponderancia de intensidad teórica y estética, que acentúa el pastiche entre lo local y lo contingente, la casi decorativa carencia de peso de la historia y, sobre todo, el consumismo. Los primeros estudios poscoloniales fueron realizados por distinguidos pensadores tales como Anuar Abdel Malek, Samir Amin y C. L. R. James, casi todos ellos basados en estudios del dominio y del control, y realizados bien desde el punto de vista de una independencia política ya lograda o bien desde la perspectiva de un proyecto liberador aún no completado. Sin embargo, mientras que el posmodernismo en una de sus más famosas declaraciones programáticas —la de Jean-François Lyotard— destaca la desaparición de la gran narrativa de la emancipación y de la ilustración, la argumentación que destaca en el trabajo realizado por la primera generación de artistas y eruditos poscoloniales es exactamente la contraria: la gran narrativa persiste, aunque su realización esté actualmente en suspenso, aplazada o se evite. Esta diferencia crucial entre los urgentes imperativos históricos y políticos del poscolonialismo y la relativa despreocupación del posmodernismo implica métodos y resultados diferentes, a pesar de que existe cierta superposición —en la técnica del «realismo mágico», por ejemplo— entre ambos.
Creo que sería un error el sugerir que en la mayoría de los mejores trabajos poscoloniales, que han proliferado de forma tan espectacular desde la década de los ochenta, no ha habido gran insistencia en lo local, lo regional y lo contingente. Ha existido, cierto, pero a mí me parece que está conectada de forma muy interesante en su actitud general con un conjunto universal de preocupaciones, todas ellas relacionadas con la emancipación, actitudes revisionistas frente a la historia y la cultura, y un amplio uso de la recurrencia a modelos y estilos teóricos. Uno de los aspectos destacados ha sido la crítica constante del eurocentrismo y del patriarcado. En la década de los ochenta, en todas las universidades estadounidenses y europeas, alumnos y profesores trabajaban de forma continua para ampliar el eje académico de los denominados currículos básicos, esto es, planes de estudios, en los que se incluían los escritos de mujeres, artistas y pensadores no europeos y que pertenecían a zonas sometidas al nuevo colonialismo. Todo ello acompañado por importantes cambios de método en los estudios zonales, en gran medida realizados por los orientalistas clásicos y sus equivalentes en otros campos. La antropología, las ciencias políticas, la literatura, la sociología y, sobre todo, la historia sintieron los efectos de una crítica de fuentes de gran alcance, la introducción de una teoría y la desaparición de la perspectiva eurocéntrica. El que tal vez sea el trabajo revisionista más brillante no se realizó en los estudios de Oriente Próximo, sino en el campo de la hindología con el advenimiento de los «estudios subordinados», un grupo de notables estudiosos e investigadores dirigidos por Ranajit Guha. Su objetivo era nada menos que lograr una revolución en la historiografía, siendo su meta inmediata la de rescatar los textos de la historia de la India del dominio de la elite nacionalista y devolverle el importante papel que desempeñaron los pobres urbanos y las masas rurales. Creo que sería un error el decir que tales trabajos, fundamentalmente académicos, han sido fácilmente aceptados y aliados del neocolonialismo «transnacional». Debemos registrar y reconocer el logro, aunque advirtiendo sobre los peligros latentes de este último.
Lo que me ha interesado especialmente es que los problemas poscoloniales se extiendan a la geografía. Después de todo, _Orientalismo_ es un estudio basado en una revisión de lo que durante siglos se había considerado como un abismo insalvable que separaba al Este del Oeste. Mi objetivo, como dije anteriormente, no era tanto disipar la propia diferencia (ya que no se puede negar el papel de lo nacional ni las diferencias culturales en las relaciones entre seres humanos) sino poner en tela de juicio la noción de que toda diferencia implica hostilidad, un conjunto objetivado y congelado de esencias opuestas y un completo conocimiento antagónico basado en todo ello. Lo que reclamé en _Orientalismo_ fue una forma nueva de concebir las separaciones y los conflictos que habían creado generaciones de hostilidad, guerras y control imperial. Y uno de los acontecimientos más interesantes de los estudios poscoloniales fue una nueva lectura de las obras de la cultura canónica no para denostarlas, sino para reinvestigar algunos de los principios en que se basaban, yendo más allá de la sofocante presencia en ellas de alguna versión de la dialéctica binaria amo-esclavo. Este ha sido, sin duda, el efecto comparable de novelas tan asombrosamente ingeniosas como _Midnight's Children_ ,* de Rushdie, la narrativa de C. L. R. James, la poesía de Aimé Césaire y de Derek Walcott, en cuyas obras la audacia de nuevos logros formales constituye, de hecho, una reapropiación de la experiencia histórica del colonialismo, revitalizada y convertida en nueva estética de participación y en una reformulación a veces trascendente.
Se ve una situación similar en el trabajo del grupo de distinguidos escritores irlandeses que en 1980 se constituyeron en un colectivo denominado Field Day. El prefacio a una colección de sus obras dice lo siguiente sobre ellos:
[estos escritores] creían que Field Day podría y debería contribuir a solucionar la crisis actual realizando estudios sobre la opinión, los mitos y los estereotipos vigentes, que se habían convertido en un síntoma y una causa de la situación actual (entre Irlanda y el Norte). El fracaso de los acuerdos constitucionales y políticos y el recrudecimiento de la violencia que debían reprimir o contener, hizo que esto fuera una necesidad más en el Norte que en la República [...]. La compañía decidió, por tanto, realizar varias publicaciones, empezando por una serie de folletos (además de la impresionante serie de poemas de Seamus Heaney, ensayos de Seamus Deane, comedias de Brian Friel y de Tom Paulin) en los que puede explorarse la naturaleza del problema irlandés y, por ello, hacerle frente con más éxito que anteriormente.
La idea de revisar y reformular unas experiencias históricas, que en su momento se habían basado en la separación geográfica de pueblos y culturas, es el eje de todo un torrente de obras eruditas y críticas. Hay que descubrirla en obras tales como, por citar solo tres, _Beyond Arabs and Jews: Remaking Levantine Culture_ , de Amiel Alcalay, _The Black Atlantic: Modernity and Double Consciousness_ , de Paul Gilroy, y _Subject to Others: British Women Writers and Colonial Slavery, 1670-1834_ , de Moira Ferguson. En estas obras, campos que una vez se consideraron exclusivos de un pueblo, de un sexo, de una raza o de una clase, vuelven a analizarse y se demuestra que han incluido otros. Presentado desde hace mucho tiempo como un campo de batalla entre árabes y judíos, el levante aparece en el libro de Alcalay como una cultura mediterránea común a ambos pueblos. Según Gilroy, un proceso similar altera e incluso duplica nuestra percepción del océano Atlántico, antes considerado como un paso principalmente europeo. Y al revisar la relación antagónica entre los ingleses amos-de-esclavos y los esclavos africanos, Ferguson apunta una pauta más compleja al separar a la mujer blanca del hombre blanco, nuevas degradaciones y nuevos trastornos que, por ello, aparecen en África.
Podría seguir ofreciendo más y más ejemplos. Terminaré brevemente diciendo que, aunque la animosidad y las desigualdades persisten y son la razón de mi interés por el orientalismo como fenómeno cultural y político, existe hoy al menos una aceptación general de que no representan un orden eterno, sino, más bien, una experiencia histórica cuyo final o, como mínimo, una mitigación parcial, está próxima. Mirando desde la distancia que permiten quince años intensos y teniendo en cuenta la existencia de un nuevo proyecto para reducir los efectos de las trabas imperialistas sobre el pensamiento y las relaciones humanas, _Orientalismo_ tuvo el mérito, al menos, de declararse beligerante en la lucha que persiste en el «Este» y en el «Oeste».
E. W. S.
_Nueva York, marzo de 1994_
### Agradecimientos
He estudiado el tema del orientalismo durante muchos años, pero este libro lo escribí entre 1975 y 1976, tiempo que pasé en el Center for Advanced Study in the Behavioral Sciences, en Stanford, California. En esta institución tan única como generosa tuve la gran suerte de beneficiarme de la ayuda de algunos colegas, especialmente de la de Joan Warmbrunn, Chris Hoth, Jane Kielsmeier, Preston Cutler y del director del centro, Gardner Lindzey. La lista de amigos, colegas y estudiantes que leyeron o escucharon algunas partes o el total de este manuscrito es lo suficientemente larga como para abrumarme, y, ahora que finalmente ha aparecido como libro, quizá también les abrume a ellos. En cualquier caso debo mencionar con agradecimiento el aliento, siempre tan útil, de Janet e Ibrahim Abu-Lughod, Noam Chomsky y Roger Owen, que siguieron este proyecto desde sus inicios hasta su conclusión. Asimismo, tengo que agradecer el valioso y crítico interés de los colegas, amigos y estudiantes de varios lugares cuyas preguntas y planteamientos me ayudaron considerablemente a preparar el texto. André Schiffrin y Jeanne Morton, de Pantheon Books, fueron respectivamente un editor y un redactor ideales y convirtieron la sufrida tarea (al menos, al autor así se lo parece) de preparar el manuscrito en un proceso instructivo y auténticamente inteligente. Mariam Said me ayudó mucho con sus investigaciones sobre los primeros momentos de la historia moderna de las instituciones orientalistas. Además de esto, su apoyo y afecto consiguieron que la labor de escribir este libro no fuera solo agradable, sino también posible.
E. W. S.
_Nueva York, septiembre-octubre de 1977_
### Notas
Introducción
. Véase Thierry Desjardins, _Le Martyre du Liban_ , Plon, París, 1976, p. 14.
. K. M. Panikkar, _Asia and Western Dominance_ , George Allen & Unwin, Londres, 1959.
. Véase Denys Hay, _Europe: The Emergence of an Idea_ , 2.ª ed., Edinburgh University Press, Edimburgo, 1968.
. Véase Steven Marcus, _The Other Victorians: A Study of Sexuality and Pornography in Mid-Nineteenth Century England_ , 1966; reimpr., Bantam Books, 1967, Nueva York, pp. 200-219.
. Véase mi libro _Criticism between Culture and System_ , Harvard University Press, Cambridge (Massachusetts).
. Principalmente en su _American Power and the New Mandarins: Historical and Political Essays_ , Pantheon Books, Nueva York, 1969; y _For Reasons of State_ , Pantheon Books, Nueva York, 1973.
. Véase Walter Benjamin, _Charles Baudelaire: A Lyric Poet in the Era of High Capitalism_ , trad. al inglés de Harry Zohn, New Left Books, 1973, Londres, p. 71 (original: _Charles Baudelaire_ , _Ein Lyriker im Zeitalter des Hochkapitalismus_ , Suhrkamp, Francfort del Meno, 1969, p. 76).
. Véase Harry Bracken, «Essence, Accident and Race», en _Hermathena_ , 116 (invierno, 1973), pp. 81-96.
. En una entrevista publicada en _Diacritics_ 6, n.º 3 (otoño de 1976), p. 38.
. Véase Raymond Williams, _The Long Revolution_ , Chatto & Windus, 1961, Londres, pp. 66-67.
. En mi libro _Beginnings: Intention and Method_ , Basic Books, Nueva York, 1975.
. Véase Louis Althusser, _Pour Marx_ , Maspero, París, 1965, pp. 5963. [Trad. cast., _La revolución teórica de Marx_ , Siglo XXI, México, 1969.]
. Véase Raymond Schwab, _La Renaissance orientale_ , Payot, París, 1950; Johann W. Fück, _Die Arabischen Studien in Europa bis in den Anfang des 20. Jahrhunderts_ , Otto Harrassowitz, Leipzig, 1955; Dorothee Metlitzki, _The Matter of Araby in Medieval England_ , Yale University Press, New Haven (Connecticut), 1977.
. Véase E. S. Shaffer, _«Kubla Khan» and The Fall of Jerusalem: the Mythological School in Biblical Criticism and Secular Literature_ , _17701880_ , Cambridge University Press, Cambridge, 1975.
. Véase George Eliot, _Middlemarch: A Study of Provincial Life_ , 1872; reimpr., Houghton Mifflin Co., Boston, 1956, p. 164.
. Véase Antonio Gramsci, _The Prison Notebooks: Selections_ , trad. y ed. de Quintin Hoare y Geoffrey Nowell Smith, International Publishers, 1971, Nueva York, p. 324. El párrafo completo, que no se encuentra en la traducción de Hoare y Smith, se puede encontrar en Gramsci, _Quaderni dal carcere_ , ed. Valentino Gerratana, Einaudi Editore, Turín, 1975, n.º 2, p. 1.363.
. Raymond Williams, _Culture and Society_ , _1780-1950_ , Londres, Chatto & Windus, 1958, p. 376.
PRIMERA PARTE. El ámbito del orientalismo
. Tanto esta cita como las precedentes proceden del discurso que James Balfour pronunció ante la Cámara de los Comunes que puede consultarse en Gran Bretaña, _Parliamentary Debates_ (Commons), 5.ª serie, 17 (1910): 1.140-1.146. Véase también A. P. Thornton, _The Imperial Idea and Its Enemies: A Study in British Power_ , MacMillan & Co., Londres, 1959, pp. 357-360. El discurso de Balfour era una defensa de la política de Eldon Gorst en Egipto; sobre este tema, véase Peter John Dreyfus Mellini, _Sir Eldon Gorst and British Imperial Policy in Egypt_ , Stanford University, 1971 (tesis doctoral inédita).
. Véase Denis Judd, _Balfour and The British Empire: A Study in Imperial Evolution_ , _1874-1932_ , MacMillan & Co., Londres, 1968, p. 286. Véase también la p. 292: en 1926 Balfour todavía hablaba de Egipto —sin ironía— como de una «nación independiente».
. Véase Evelyn Baring, lord Cromer, _Political and Literary Essays_ , _1908-1913_ , 1913, reimpr., Books for Libraries Press, Freeport (Nueva York), 1969, pp. 40, 53, 12-14.
. _Ibid_., p. 171.
. Véase Roger Owen, «The Influence of Lord Cromer's Indian Experience on British Policy in Egypt 1883-1907», en _Middle Eastern Affairs_ , _Number 4: St. Anthony's Papers Number 17_ , ed., Albert Hourani, Oxford University Press, Londres, 1965, pp. 109-139.
. Véase Evelyn Baring, lord Cromer, _Modern Egypt_ , MacMillan & Co., Nueva York, 1908, vol. 2, pp. 146-167. Para una opinión de la política británica en Egipto opuesta totalmente a la de Cromer, véase Wilfrid Scawen Biunt, _Secret History of the English Occupation of Egypt: Being a Personal Narrative of Events_ , Alfred A. Knopf, Nueva York, 1922. Hay una valiosa discusión sobre la oposición egipcia al gobierno británico en Mounah A. Khouri, _Poetry and the Making of Modern Egypt_ , _1882-1922_ , E. J. Brill, Leiden, 1971.
. Véase Evelyn Baring, lord Cromer, _Modern Egypt_ , _op. cit_., vol. 2, p. 164.
. Citado en John Marlowe, _Cromer in Egypt_ , Elek Books, Londres, 1970, p. 271.
. Véase Harry Magdoff, «Colonialism (1763- _c_. 1970)», en _Encyclopaedia Britannica_ , 15.ª ed., 1974, pp. 893-894. Véase también D. K. Fieldhouse, _The Colonial Empires: A Comparative Survey from the Eighteenth Century_ , Delacorte Press, Nueva York, 1967, p. 178.
. Citado en Afaf Lutfi al-Sayyid, _Egypt and Cromer: A Study in Anglo-Egyptian Relations_ , Frederik A. Praeger, Nueva York, 1969, p. 3.
. La cita se encuentra en Ian Hacking, _The Emergence of Probability: A Philosophical Study of Early Ideas About Probability_ , _Induction and Statistical Inference_ , Cambridge University Press, Londres, 1975, p. 17.
. Véase V. G. Kiernan, _The Lords of Human Kind: Black Man_ , _Yellow Man_ , _and White Man in an Age of Empire_ , Little, Brown & Co., Boston, 1969, p. 55.
. Véase Edgar Quinet, «Le Génie des religions», en _Oeuvres completes_ , Paguerre, París, 1857, pp. 55-74.
. Evelyn Baring, lord Cromer, _Political and Literary..._ , _op. cit_., p. 35.
. Véase Jonah Raskin, _The Mythology of Imperialism_ , Random House, Nueva York, 1971, p. 40.
. Véase Henry A. Kissinger, _American Foreign Policy_ , W. W. Norton & Co., Nueva York, 1974, pp. 48-49.
. Véase Harold W. Glidden, «The Arab World», en _American Journal of Psychiatry_ 128, n.º 8 (febrero de 1972), pp. 984-988.
. Véase R. W. Southern, _Western Views of Islam in the Middle Ages_ , Harvard University Press, Cambridge, 1962, p. 72. Véase también Francis Dvornik, _The Ecumenical Councils_ , Hawthorn Books, Nueva York, 1961, pp. 65-66: «De especial interés es el Canon decimoprimero, que expone que se deben crear cátedras de hebreo, griego, árabe y caldeo en las principales universidades. La sugerencia fue de Raimundo Lulio, que alegaba que aprender árabe era el mejor método para conseguir la conversión de los árabes. Aunque el Canon tuvo pocos efectos debido a la escasez de profesores de lenguas orientales, su aceptación indica el crecimiento de las ideas misioneras occidentales. Gregorio X ya había esperado la conversión de los mongoles, y los frailes franciscanos habían llegado hasta las profundidades de Asia en su celo misionero. Aunque estas esperanzas no se llegaron nunca a realizar, el espíritu misionero se siguió desarrollando. Véase también Johann W. Fück, _Die Arabischen Studien in Europa_ , _op. cit_.
. Raymond Schwab, _La Renaissance orientale_ , _op. cit_. Véase también V.-V. Balthold, _La Découverte de l'Asie: Histoire de l'orientalisme en Europe et en Russie_ , traducción de B. Nikitine, Payot, París, 1947, y las importantes páginas de Theodor Benfey, _Geschichte der Sprachwissenschaft und Orientalischen Philologie in Deutschland_ , Gottafschen, Munich, 1869. Para obtener un contraste instructivo, véase James T. Monroe, _Islam and the Arabs in Spanish Scholarship_ , E. J. Brill, Leiden, 1970.
. Victor Hugo, _Oeuvres poètiques_ , ed. Pierre Albouy, Gallimard, París, 1964, vol. 1, p. 580.
. Jules Mohl, _Ving-sept ans d'histoire des études orientales: Rapports faits à la Société Asiatique de Paris de 1840 à 1867_ , 2 vols., Reinwald, París, 1879-1880.
. Véase Gustave Dugat, _Histoire des orientalistes de l'Europe de XIIe au XIXe siècle_ , 2 vols., Adrien Maisonneuve, París, 1868-1870.
. Véase René Gérard, _L'Orient et la Pensée romantique allemande_ , Didier, París, 1963, p. 112.
. Véase V. G. Kiernan, _The Lords of Human Kind_ , _op. cit_., p. 131.
. Véase University Grants Committee, _Report of the Sub-Committee on Oriental_ , _Slavonic_ , _East European and African Studies_ , Londres, Her Majesty's Stationery Office, 1961.
. Véase H. A. R. Gibb, _Area Studies Reconsidered_ , School of Oriental and African Studies, Londres, 1964.
. Véase Claude Lévi-Strauss, _La Pensée sauvage_ , Plon, París, 1962, caps. 1-7. [Trad. cat., _El pensament salvatge_ , Edicions 62, Barcelona, 1985.]
. Véase Gaston Bachelard, _La Poétique de l'espace_ , Presses Universitaires de France, París, 1957. [Trad. cast., _La poética del espacio_ , Fondo de Cultura Económica, Madrid, 1993.]
. Véase Norman Daniel, _Western Views..._ , _op. cit_., p. 14.
. Esquilo, _Los persas_ , Gredos, Madrid.
. Eurípides, _Las bacantes_ , Madrid. Para mayor información sobre la distinción Europa-Oriente, véanse Santo Mazzarino, _Fra oriente e occidente: Ricerche di storia greca arcaica_ , La Nuova Italia, 1947, Florencia, y Denys Hay, _Europe: The Emergence of an Idea_ , Edinburgh University Press, Edimburgo, 1968.
. Véase Eurípides, _op. cit_., Madrid.
. Véase René Grousset, _L'Empire du Levant: Histoire de la question d'Orient_ , Payot, París, 1946.
. Véase Edward Gibbon, _The History of the Decline and Fall of the Roman Empire_ , Little, Brown & Co., Boston, 1855, vol. 6, p. 399.
. Véase Norman Daniel, _The Arabs and Medieval Europe_ , Longmans, Green & Co., Londres, 1975, p. 56.
. Véase Samuel C. Chew, _The Crescent and the Rose: Islam and England During the Renaissance_ , Oxford University Press, Nueva York, 1937, p. 103.
. Véase Norman Daniel, _Islam and the West: The Making of an Image_ , Edinburgh University Press, Edimburgo, 1960, p. 33. Véase también James Kritzeck, _Peter the Venerable and Islam_ , Princeton University Press, Princeton, 1964.
. Norman Daniel, _Islam and the West..._ , _op. cit_., p. 252.
. _Ibid_., pp. 259-260.
. Véase por ejemplo Williams Wistar Comfort, «The Literary Rôle of the Saracens in the French Epic», _PMLA 55_ (1940), pp. 628-659.
. Véase Norman Daniel, _Western Views_..., _op. cit_., pp. 91-92, 108109.
. Véase Norman Daniel, _Islam and the West..._ , _op. cit_., pp. 246, 296 y pássim.
. _Ibid_., p. 84.
. Véase Duncan Black Macdonald, «Whither Islam?», en _Muslim World_ , 23, enero de 1933.
. Véase P. M. Holt, «Introducción» en _The Cambridge History of Islam_ , ed. P. M. Holt, Anne K. S. Lambton y Bernard Lewis, Cambridge University Press, Cambridge, 1970, p. xvi.
. Véase Antonine Galland, «Discours» de presentación a Barthélemy d'Herbelot, _Bibliothèque orientale_ , _ou Dictionnaire universel contenant tout ce qui fait connaître les peuples de l'Orient_ , Neaulme & Van Daalen, La Haya, 1777, vol. 1, p. vii. La tesis de Galland es que D'Herbelot ha presentado un conocimiento real, y no legendario o mítico como el que se asociaba con las «maravillas de Oriente». Véase R. Wittkower, «Marvels of the East: A study in the History of Monster», _Journal of the Warburg and Courtauld Institutes_ 5 (1942), pp. 159-197.
. Véase Galland, _op. cit_., pp. xvi, xxxiii. Para el estado del conocimiento orientalista inmediatamente antes de D'Herbelot, véase V. J. Parry, «Renaissance Historical Literature in Relation to the New and Middle East (With Special Reference to Paolo Giovio)», en _Historians of the Middle East_ , ed. Bernard Lewis y P. M. Holt, Oxford University Press, Londres, 1962, pp. 277-289.
. Véase Barthold, _La Découverte..._ , _op. cit_., pp. 137-138.
. Véase D'Herbelot, _Bibliothèque..._ , _op. cit_., vol. 2; p. 648.
. Véase también Montgomery Watt, «Muhammad in the Eyes of the West», _Boston University Journal_ 22, n.º 3 (otoño de 1974), pp. 61-69.
. Véase Isaiah Berlin, _Historical Inevitability_ , Londres, Oxford University Press, 1955, pp. 13-14.
. Véase Henri Pirenne, _Mohammed et Charlemagne_ , Presses Universitaires de France, 1970, París, pp. 175 y 214. [Trad. cast., _Mahoma y Carlomagno_ , Alianza, Madrid, 1978, pp. 189 y 227.]
. Citado por Henri Baudet en _Paradise on Earth: Some Thoughts on European Images of Non-European Man_ , traducción al inglés de Elizabeth Wentholt, Yale University Press, New Haven, 1965, p. xiii.
. Véase Gibbon, _Decline and Fall of the Roman Empire_ , _op. cit_., 6, p. 289.
. Véase Baudet, _Paradise on Earth_ , _op. cit_., p. 4.
. Véase Fieldhouse, _The Colonial Empires_ , _op. cit_., pp. 138-161.
. Véase Schwab, _La Renaissance orientale_ , op. cit., p. 30.
. Véase A. J. Arberry, _Oriental Essays: Portraits of Seven Scholars_ , Macmillan Co., Nueva York, 1960, pp. 30-31.
. Véase Raymond Schwab, _Vie d'Anquetil-Duperron_ , _suivie des Usages civils et religieux des Perses par Anquetil-Duperron_ , Ernest Leroux, París, 1934, pp. 10, 96, 4, 6.
. Véase Arberry, _Oriental Essays_ , _op. cit_., pp. 62-66.
. Véase _Centenary Volume of the Royal Asiatic Society of Great Britain and Ireland 1823-1923_ , ed. Frederik Eden Pargiter, Royal Asiatic Society, Londres, 1923, p. viii.
. Véase Quinet, _Le Génie des..._ , _op. cit_., p. 47.
. Véase Jean Thiry, _Bonaparte en Égypte décembre 1797-24 août 1799_ , Berger-Levrault, París, 1973, p. 9.
. Véase Constantin-François Volney, _Voyage en Égypte et en Syrie_ , Bossange, París, 1821, 2, p. 241 y pássim.
. Véase Napoleón, _Campagnes d'Égypte et de Syrie_ , _1798-1799: Mémoires pour servir à l'histoire de Napoleón_ , Comou, 1843, París, vol. 1, p. 211.
. Véase Thiry, _Bonaparte en Égypte_ , _op. cit_., p. 126. Véase también Ibrahim Abu-Lughod, _Arab Rediscovery of Europe: A Study in Cultural Encounters_ , Princeton University Press, Princeton, 1963, pp. 12-20.
. Véase Abu-Lughod, _Arab Rediscovery of Europe_ , _op. cit_., p. 22.
. Extraído de Arthur Helps, _The Spanish Conquest of America_ , Londres, 1900, p. 196, por Stephen J. Greenblatt, «Learning to Curse: Aspect of Linguistic Colonialism in the Sixteenth Century», en _First Images of America: The Impact of the New World on the Old_ , ed. Fredi Chiapelli, University of California Press, Berkeley, 1976, p. 573.
. Véase Thiry, _Bonaparte en Égypte_ , _op. cit_., p. 200. Napoleón no estaba siendo cínico. Se sabe que habló del _Mahomet_ de Voltaire con Goethe y defendía el islam. Véase también Christian Cherfils, _Bonaparte et l'Islam d'après les documents français arabes_ , A. Pedone, París, 1914, p. 249 y pássim.
. Véase Thiry, _Bonaparte en Égypte_ , _op. cit_., p. 434.
. Véase Victor Hugo, «Les orientales», en _Oeuvres..._ , _op. cit_., vol. 1, p. 684.
. Henri Dehérain, _Silvestre de Sacy_ , _ses contemporains et ses disciples_ , Paul Geuthner, París, 1938, p. v.
. _Description de l'Égypte_ , _ou Recueil des observations et des recherches qui ont été faites in Égypte pendant l'expédition de l'armée française_ , _publié par les ordres de sa majesté l'empereur Napoléon le Grand_ , 23 vols., Imprimerie impériale, París, 1809-1828.
. Véase Fourier, _Préface historique_ , vol. 1 de la _Description de l'Égypte_ , p. 1.
. _Ibid_., p. iii.
. _Ibid_., p. xciii.
. Véase Étienne Geoffroy Saint-Hilaire, _Histoire naturelle des poissons du Nil_ , vol. 17 de la _Description de l'Égypte_ , p. 2.
. Véase M. de Chabrol, _Essai sur les moeurs des habitants modernes de l'Égypte_ , vol. 14 de la _Description de l'Égypte_ , p. 376.
. Esto es evidente en Baron Larrey, _Noice sur la conformation physique des égyptiens et des différentes races qui habitent en Égypte, suivie de quelques réflexions sur l'embaumement des momies_ , vol. 13 de la _Description de l'Égypte_.
. Citado por John Marlowe, _The Making of the Suez Canal_ , Cresset Press, 1964, Londres, p. 31.
. Citado en John Pudney, _Suez: De Lesseps' Canal_ , Frederick A. Praeger, Nueva York, 1969, pp. 141-142.
. Véase Marlowe, _The Making..., op. cit.,_ p. 62.
. Véase Ferdinand de Lesseps, _Lettres, journal et documents pour servir à l'histoire du Canal de Suez_ , Didier, París, 1881, 5, p. 310. Para una acertada caracterización de Lesseps y Cecil Rhodes como místicos, véase también Baudet, _Paradise on..., op. cit_., p. 68.
. Citado en Charles Beatty, _De Lesseps of Suez: The Man And His Times_ , Nueva York, Harpers & Brothers, 1956, p. 220.
. Véase Lesseps, _Lettres, journal et documents, op. cit.,_ 5, p. 17.
. Véase _ibid_., pp. 324-333.
. Véase Hayden White, _Metahistory: The Historical Imagination in Nineteenth Century Europe_ , Johns Hopkins University Press, Baltimore, 1973, p. 12.
. Véase Anuar Abdel Malek, «L'Orientalisme en crise», _Diogenes_ , 44 (invierno de 1963), p. 113.
. Friedrich Schlegel, _Über die Sprache und Weisheit der Indier: Ein Beitrag zur Begründung der Altertumstunde_ , Mohr & Zimmer, 1808, Heidelberg, pp. 44-59; Schlegel, _Philosophie der Geschichte: In achtzehn Vorlesungen gehalten zu Wien im Jahre 1828_ , ed. Jean-Jacques Anstett, vol. 9 de _Kritische Friedrich-Schlegel-Ausgabe_ , ed. Ernest Behler, Ferdinand Schöningh, Munich, 1971, p. 275.
. Véase Léon Poliakov, _Le Mythe aryen, Essai sur les sources du racisme et des nationalismes_ , Calman-Lévy, París, 1971.
. Véase Derk Hopwood, _The Russian Presence in Syria and Palestine, 1843-1943: Church and Politics in the Near East_ , Clarendon Press, Oxford, 1969.
. Véase A. L. Tibawi, _British Interests in Palestine, 1800-1901_ , Oxford University Press, Londres, 1961, p. 5.
. Véase Gérard de Nerval, _Oeuvres_ , ed. de Albert Béguin y Jean Richet, Gallimard, París, 1960, vol. 1, p. 933.
. Véase Victor Hugo, _Oeuvres poétiques..._ , _op. cit_., vol. 1, p. 580.
. Véase sir Walter Scott, _The Talisman_ , 1825; reimpr., J. M. Dent, Londres, 1914, pp. 38-39.
. Véase Albert Hourani, «Sir Hamilton Gibb, 1895-1971», en _Proceedings of the British Academy_ , 58 (1972), p. 495.
. Citado por B. R. Jerman, _The Young Disraeli_ , Princeton University Press, Princeton, 1960, p. 126. Véase también Robert Blake, _Disraeli_ , Eyre & Spottiswoode, Londres, 1966, pp. 59-70.
. Véase _Flaubert in Egypt: A Sensibility on Tour_ , trad. y ed. de Francis Steegrmuller, Little, Brown & Co., Boston, 1973, pp. 44-45. Véase también Gustave Flaubert, _Correspondance_ , ed. de Jean Bruneau, Gallimard, 1973, París, vol. 1, p. 542.
. Este es el argumento presentado, _Das Erbe der Antike im Orient und Okzident_ , Quelle & Meyer, Leipzig, 1931.
. Véase Louis Massignon, _La Passion d'al-Hosayn-ibn-Mansour al-Hallaj_ , Paul Geuthner, París, 1922.
. Véase Abdel Malek, «L'orientalisme en crise», en _op. cit_., p. 116.
. Véase H. A. R. Gibb, _Modern Trends in Islam_ , University of Chicago Press, Chicago, 1947, p. 7.
. Véase Gibb, _Area Studies..._ , _op. cit_., pp. 12-13.
. Véase Bernard Lewis, «The Return of Islam» en _Commentary_ , enero de 1976, pp. 39-49.
. Véase _The Policy Sciences: Recent Developments in Scope and Method_ , ed. Daniel Lerner y Harold Lasswell, Stanford University Press, Stanford, 1951.
. Véase Morroe Berger, _The Arab World Today_ , Doubleday & Co., Garden City, 1962, p. 158.
. Hay un conjunto de exposiciones críticas acerca de estas actitudes en Maxime Rodinson, _Islam et Capitalisme_ , París, Éd. du Seuil, 1966.
. Véase Ibrahim Abu-Lughod, «Retreat from the Secular Path? Islamic Dilemmas of Arab Politics», en _Review of Politics_ 28, n.º 4 (octubre de 1966), p. 475.
SEGUNDA PARTE. Estructuras y reestructuras del orientalismo
. Véase Gustave Flaubert, _Bouvard et Pécuchet_ , vol. 2 de _Oeuvres_ , ed. A. Thibaudet y R. Dumesnil, Gallimard, París, 1952, p. 985.
. Un relato esclarecedor sobre estas visiones y utopías puede encontrarse en Donald G. Charlton, _Secular Religions in France, 1815-1870_ , Oxford University Press, Londres, 1963.
. Véase M. H. Abrams, _Natural Supernaturalism: Tradition and Revolution in Romantic Literature_ , W. W. Norton & Co., Nueva York, 1971, p. 66.
. Pueden encontrarse textos aclarativos en John P. Nash, «The Connection of Oriental Studies with Commerce, Art, and Literature During the 18th-19th Centuries», _Manchester Egyptian and Oriental Society Journal_ 15 (1930), pp. 33-39; también en John F. Laffey, «Roots of French Imperialism in the Nineteenth Century: The Case of Lyon», _French Historical Studies_ 6, n.º 1 (primavera de 1969), pp. 78-92, y en R. Leportier, _L'Orient Porte des Indes_ , Éditions France-Empire, París, 1970. Hay mucha información en Henri Omont, _Missions archéologiques françaises en Orient aux XVIIe et XVIIIe siècles_ , 2 vols., Imprimerie Nationale, París, 1902, y en Margaret T. Hodgen, _Early Anthropology in the Sixteenth and Seventeenth Centuries_ , University of Pennsylvania, Filadelfia, 1964, así como en Norman Daniel, _Islam, Europe and Empire_ , University Press, Edimburgo, 1966. Dos estudios breves pero indispensables son Albert Hourani, «Islam and the Philosophers of History», _Middle Eastern Studies_ 3, n.º 3 (abril de 1967), pp. 206-268, y Maxime Rodinson, «The Western Image and Western Studies of Islam», en _The Legacy of Islam_ , ed. Joseph Schacht y C. E. Bosworth, Clarendon Press, Oxford, 1974, pp. 9-62.
. Véase P. M. Holt, «The Treatment of Arab History by Prideaux, Ockley, and Sale», en _Historians of the Middle East_ , ed. Bernard Lewis y P. M. Holt, _op. cit_., p. 302. Véase también P. M. Holt, _The Study of Modern Arab History_ , School of Oriental and African Studies, Londres, 1965.
. Isaiah Berlin da una visión de un Herder populista y pluralista en _Vico and Herder: Two Studies in the History of Ideas_ , Viking Press, Nueva York, 1976.
. Para un estudio de estos motivos y representaciones, véase Jean Starobinski, _L'Invention de la liberté_ , Skira, Ginebra-París, 1964.
. Hay un pequeño número de estudios sobre este tema todavía tan poco investigado. Entre los más conocidos se encuentran: Martha P. Conant, _The Oriental Tale in England in the Eighteenth Century_ , 1908; reimpr., Nueva York, Octagon Books, 1967; Marie E. de Meester, _Oriental Influences in the English Literature of the Nineteenth Century (Anglistische Forschungen_ , n.º 46), Heidelberg, 1915; Byron Porter Smith, _Islam in English Literature_ , American Press, Beirut, 1939. Véase también Jean-Luc Doutrelant, «L'Orient tragique au XVIIIe siècle», en _Revue des Sciences Humaines_ , 146 (abril-junio de 1972), pp. 255-282.
. Véase Michel Foucault, _Les mots et les choses. Une archéologie des sciences humaines_ , Gallimard, París, 1966, pp. 151-157. Véase también François Jacob, _La Logique du vivant. Une histoire de l'hérédité_ , Gallimard, París, 1970, p. 54 y pássim, y Georges Ganguilhem, _La Connaissance de la vie_ , Gustave-Joseph Vrin, París, 1969, pp. 44-63.
. Véase John G. Burke, «The Wild Man's Pedigree: Scientific Method and Racial Anthropology», en _The Wild Man Within: An Image in Western Thought from the Renaissance to Romanticism_ , eds. Edward Dudley y Maximillian E. Novak, University of Pittsburgh Press, Pittsburgh, Pa., pp. 262-268. Véase también Jean Biou, «Lumières et anthropophagie», en _Revue des Sciences Humaines_ , 146 (abril-junio de 1972), pp. 223-234.
. Henri Dehérain, _Silvestre de Sacy: Ses Contemporains et ses disciples_ , Paul Geuthner, París, 1938, p. 111.
. Para más detalles véase _ibid_., pp. i-xxxiiii.
. Véase duque de Broglie, «Éloge de Silvestre de Sacy», en Sacy, _Mélanges de littérature orientale_ , E. Ducrocq, París, 1833, p. xii.
. Véase Bon Joseph Dacier, _Tableau historique de l'érudition française, ou Rapport sur les progrès de l'histoire et de la littérature ancienne depuis 1789_ , Imprimerie impériale, París, 1810, pp. 23, 35, 31.
. Michel Foucault, _Surveiller et punir: Naissance de la prison_ , Gallimard, París, 1975, p. 202.
. Broglie, «Éloge de Silvestre de Sacy», _loc. cit_., p. 107.
. Sacy, _Mélanges de littérature orientale_ , _op. cit_., pp. 107, 110, 111-112.
. Silvestre de Sacy, _Chrestomathie arabe, ou Extraits de divers écrivains arabes, tant en prose qu'en vers, avec une traduction française et des notes, à l'usage des élèves de l'Ècole royale et spèciale des langues orientales vivantes_ , vol. 1, 1826, reimpr., Biblio Verlag, Osnabrück, 1973, p. viii.
. Para los conceptos de «suplementariedad», «suplir» y «súplica», véase Jacques Derrida, _De la grammatologie_ , Éditions de Minuit, París, 1967, p. 203 y pássim.
. Para una lista parcial de los estudiantes formados por Sacy y de su influencia, véase Johann W. Fück, _Die Arabischen Studien in Europa bis in den Anfang des 20. Jahrhunderts_ , Otto Harrassowitz, Leipzig, 1955, pp. 156-157.
. La definición que Foucault da de archivo se puede encontrar en _L'Archéologie du savoir_ , Gallimard, París, 1969, pp. 92-136. Gabriel Monod, que era un poco más joven que Renan, señaló que este no fue en modo alguno un revolucionario en lingüística, arqueología o exégesis, pero que, como sus conocimientos eran más vastos y precisos que los de ningún otro erudito de la época, fue su representante más eminente ( _Renan_ , _Taine_ , _Michelet_ , Calmann-Lévy, 1894, París, pp. 40-41). Véase también Jean-Louis Dumas, «La Philosophie de l'histoire de Renan», en _Revue de Métaphysique et de Morale_ 77, n.º 1 (enero-marzo de 1972), pp. 100-128.
. Véase Honoré de Balzac, _Louis Lambert_ , Calmann-Lévy, París, s.a., p. 4.
. En todas las obras de Nietzsche pueden encontrarse observaciones sobre la filología. Véanse principalmente sus notas para «Wir Philologen» extraídas de sus cuadernos de apuntes del período enero-julio de 1875, traducidas al inglés por William Arrowsmith, «Notes for "We Philologists"», _Arion_ , N.S. 1/2 (1974), pp. 279-380; véanse también los párrafos dedicados al lenguaje y al perspectivismo en _The Will to Power_ , traducción al inglés de Walter Kaufmann y R. J. Hollingdale, Vintage Books, Nueva York, 1968.
. Ernest Renan, _L'Avenir de la science: Pensées de 1848_ , 4.ª ed., Calmann-Lévy, París, 1890, pp. 141-146 y 148-149.
. _Ibid_., p. xiv y pássim.
. Todo el primer capítulo (libro 1, capítulo 1) de la _Histoire générale et systéme comparé des langues sémitiques_ en _Oeuvres complètes_ , ed. Henriette Psichari, Calmann-Lévy, París, 1947-1961, 8, pp. 143-163, es prácticamente una enciclopedia de prejuicios raciales dirigidos contra los semitas (es decir, musulmanes y judíos). El resto del tratado está generosamente salpicado de las mismas nociones, como lo están también muchas de las otras obras de Renan, incluyendo _L'Avenir de la science_.
. Véase Ernest Renan, _Correspondance: 1846-1871_ , CalmannLévy, París, 1926, vol. 1, pp. 7-12.
. Véase Ernest Renan, _Souvenirs d'enfance et de jeunesse_ en _Oeuvres complètes_ , vol. 2, p. 892. Jean Pommier trata con sumo detalle en dos de sus obras la mediación de Renan entre la religión y la filología. Véanse _Renan d'après des documents inédits_ , Perrin, París, 1923, pp. 48-68; y _La Jeunesse cléricale d'Ernest Renan_ , Les Belles Lettres, París, 1933. Véase también más recientemente J. Chaix-Ruy, _Ernest Renan_ , Emmanuel Vitte, París, 1956, pp. 89-111. La descripción clásica, concerniente más bien a la vocación religiosa de Renan, es también interesante. Véase Pierre Lasserre, _La Jeunesse d'Ernest Renan: Histoire de la crise religieuse au XIXe siècle_ , 3 vols., Garnier Frères, París, 1925. En el volumen 2, pp. 50-166 y 265-298, hay varios estudios útiles sobre las relaciones entre la filología, la filosofía y la ciencia.
. Véase Ernest Renan, «Des services rendus aux sciences historiques par la philologie», en _Oeuvres complètes_ , _op. cit_., 8, p. 1.228.
. Véase Renan, _Souvenirs_..., _op cit_., p. 892.
. Véase Foucault, _Les mots..._ , _op. cit_., pp. 262-314. Además del descrédito hacia los orígenes edénicos del lenguaje, otros acontecimientos —el Diluvio, la Torre de Babel— fueron también desacreditados como explicaciones. La historia más completa sobre la teoría acerca del origen del lenguaje está en Arno Borst, _Der Turmbau von Babel: Geschichte der Meinungen über Ursprung und Vielfalt der Sprachen un Volker_ , 6 vols., Anton Hiersemann, Stuttgart, 1957-1963.
. Citado por Raymond Schwab en _La Renaissance..._ , _op. cit_., p. 69. Sobre el peligro de dejarse llevar demasiado rápidamente por las generalizaciones en lo que se refiere a los descubrimientos orientales, véanse las reflexiones del distinguido sinólogo de la misma época Abel Rémusat, _Mélanges postumes d'histoire et littérature orientales_ , Imprimerie royale, París, 1843, p. 226 y pássim.
. Véase Samuel Taylor Coleridge, _Biographia Literaria_ , cap. 16, en _Selected Poetry and Prose of Coleridge_ , ed. Donald A. Stauffer, Random House, Nueva York, 1951, pp. 276-277.
. Véase Benjamin Constant, _Oeuvres_ , ed. Alfred Roulin, Gallimard, París, 1957, p. 78.
. Véase Abrams, _Natural..._ , _op. cit_., p. 29.
. Véase Renan, «De l'origine du langage», en _Oeuvres complètes_ , _op. cit_., 8, p. 122.
. Véase Renan, «De la part des peuples sémitiques dans l'histoire de la civilisation», en _Oeuvres complètes_ , _op. cit_., 2, p. 320.
. _Ibid_., p. 333.
. Véase Renan, «Trois Professeurs au Collège de France: Étienne Quatremère», en _Oeuvres complètes_ , _op. cit_., 1, p. 129. Renan no estaba equivocado en cuanto a Quatremère, quien tenía un especial talento para elegir temas de estudio muy interesantes y convertirlos en materias sin interés. Véanse sus ensayos «Le Goût des livres chez les orientaux» y «Des sciences chez les arabes», en sus _Mélanges d'histoire et de philologie orientales_ , E. Ducrocq, París, 1861, pp. 1-57.
. Véase Honoré de Balzac, _La Peau de chagrin_ , vol. 9 ( _Études philosophiques_ , 1), de _La Comédie humaine_ , ed. Marcel Bouteron, Gallimard, París, 1950, p. 39; y véase Renan, _Historie générale_..., _op. cit_., p. 134.
. Véanse, por ejemplo, _De l'origine du langage_ , _op. cit_., p. 102, e _Histoire générale_..., _op. cit_., p. 180.
. Véase Renan, _L'Avenir_..., _op. cit_., p. 23. El párrafo completo dice así: «En cuanto a mí, no conozco más que un solo resultado para la ciencia, que es resolver el enigma, decir definitivamente al hombre el nombre de las cosas, explicarle, darle, en nombre de la única autoridad legítima, que es la naturaleza humana en su intensidad, el símbolo que las religiones le daban de hecho y que ellos no podían aceptar».
. Véase Madeleine V. David, _Le Débat sur les écritures et l'hiéroglyphe aux XVIIe et XVIIIe siècles et l'Application de la notion de déchiffrement aux écritures mortes_ , SEVPEN, París, 1965, p. 130.
. En _La Renaissance orientale_ , de Schwab, solo se menciona a Renan de pasada; en _Les mots et les choses_ , de Foucault, no se le menciona en absoluto, y en _The Discovery of Language: Linguistic Science in the Nineteenth Century_ , de Holger Pederson, traducción de John Webster Spargo (1931, reimpr., Indiana University Press, Bloomington, 1972), se le menciona de una manera bastante despectiva; Max Müller en sus _Lectures on the Science of Language_ (1861-1864), reimpr., Armstrong & Co., Scribner, Nueva York, y Gustave Dugat en su _Histoire des orientalistes..._ , _op. cit_., no hacen ninguna mención de Renan. La obra _Essais Orientaux_ , de James Darmesteter (A. Lévy, París, 1883) —cuyo primer capítulo es de carácter histórico, «L'Orientalisme en France»—, está dedicada a Renan, pero no se hace alusión a sus contribuciones; hay media docena de notas breves sobre la producción de Renan en la enciclopedia de Jules Mohl _Vingt-sept ans d'histoire des études orientales: Rapports faits à la Société Asiatique de Paris de 1840 à 1867 (op. cit.)_.
. En las obras que tratan los temas de la raza y el racismo Renan ocupa una posición de importancia. Se habla de él en las siguientes: Ernest Seillière, _La Philosophie de l'impérialisme_ , 4 vols. (Plon, París, 1903-1908); Théophile Simar, _Étude critique sur la formation de la doctrine des races au XVIIIe siècle et son expansion au XIXe siècle_ (Hayez, Bruselas, 1922); Erich Voegelin, _Rasse und Staat_ (J. C. B. Mohn, Tubinga, 1933), y hay que citar también su _Die Rassenidee in der Geistesgeschichte von Ray bis Carus_ (Junker und Dunnhaupt, Berlín, 1933), que, aunque no trata la época de Renan, es un complemento importante de _Rasse und Staat_ ; Jacques Barzun, _Race: A Study in Modern Superstition_ (Harcourt, Nueva York, Brace & Co., 1937).
. En _La Renaissance..._ , _op. cit_., Schwab escribió algunas páginas brillantes sobre el museo, sobre el paralelismo entre la biología y la lingüística y sobre Cuvier, Balzac y otros (véase p. 323 y pássim). Sobre la biblioteca y su importancia para la cultura de mediados del siglo XIX, véase Foucault, «La Bibliothèque fantastique», prefacio de Flaubert, _La Temptation de Saint Antoine_ (Gallimard, París, 1971, pp. 7-33). El profesor Eugenio Donato contribuyó a que prestara atención a estas materias; véase su «A Mere Labyrinth of Letters: Flaubert and the Quest for Fiction», en _Modern Language Notes_ 89, n.º 6 (diciembre de 1974), pp. 885-910.
. Véase Renan, _Histoire générale_..., _op. cit_., pp. 145-146.
. Véase _L'Avenir_..., _op. cit_., p. 508 y pássim.
. Véase Renan, _Histoire générale_..., _op. cit_., p. 214.
. _Ibid_., p. 527. Esta idea se remonta a la distinción de Friedrich Schlegel entre lenguas orgánicas y aglutinantes; el semítico es un ejemplo del segundo tipo. Humboldt hace la misma distinción, al igual que la mayoría de los orientalistas a partir de Renan.
. _Ibid_., pp. 531-532.
. _Ibid_., p. 515 y pássim.
. Véase Jean Seznec, _Nouvelles Études sur «La Temptation de Saint Antoine_ », Warburg Institute, Londres, 1949, p. 80.
. Véase Étienne Geoffroy Saint-Hilaire, _Philosophie anatomique: des monstruosités humaines_ , publicado por el autor, París, 1822. El título completo de la obra de Isidore Geoffroy Saint-Hilaire es: _Histoire générale et particulière des anomalies de l'organisation chez l'homme et les animaux, l'influence phisiologique et pathologique, les rapports généraux, les lois et les causes des monstruosités, des variétés et vices de conformation, ou traité de tératologie_ , 3 vols., J.-B. Baillière, París, 1832-1836. Hay algunas páginas valiosas acerca de las ideas de Goethe sobre la biología en Erich Heller, _The Disinherited Mind_ , Meridian Books, Nueva York, 1959, pp. 3-34. Véase también François Jacob, _La Logique_..., _op. cit_., y George Canguilhem, _La Connaissance_..., _op. cit_., pp. 174-184, en las que se expone el lugar de los Saint-Hilaire en el desarrollo de las ciencias de la vida.
. Étienne Geoffroy Saint-Hilaire, _Philosophie anatomique_..., _op. cit_., pp. xxii-xxiii.
. Véase Renan, _Histoire générale_..., _op. cit_., p. 156.
. Véase Renan, _Oeuvres complètes_ , _op. cit_., 1, pp. 621-622 y pássim. Véase también H. W. Wardman, _Ernest Renan: A Critical Biography_ , Athlone Press, Londres, 1964, p. 66 y pássim, para una descripción sutil de la vida privada de Renan; aunque no sería conveniente forzar un paralelismo entre la biografía de Renan y lo que he llamado su mundo «masculino», la descripción de Wardman es muy sugestiva —al menos para mí.
. Véase Renan, «Des services rendus au sciences historiques par la philologie», _loc. cit_., pp. 1.228, 1.232.
. Véase Ernest Cassirer, _The Problem of Knowledge: Philosophy, Science, and History since Hegel_ , traducción al inglés William H. Woglom y Charles W. Hendel, Yale University Press, New Haven, 1950, p. 307. (Original: _Das Erkenntnisproblem in der Philosophie und Wissenschaft der neueren Zeit_ , vol. _Von Hegels Tod bis zum Gegenwart 1832-1932_ , Bruno Cassirer, Berlín, 1922-1957; Stuttgart, W. Kohlhammer). [Trad. cast., _El problema del conocimiento_ , Fondo de Cultura Económica, México, 1986.]
. Véase Renan, «Réponse au discours de réception de M. de Lesseps (23 avril 1885)», en _Oeuvres complètes_ , _op. cit_., 1, p. 817. Pero es en los artículos de junio de 1862 de Sainte-Beuve donde mejor se muestra, refiriéndose a Renan, lo importante que le parece pertenecer a su tiempo. Véase también Donald G. Charlton, _Positivist Thought in France During the Second Empire_ , Clarendon Press, Oxford, 1959, y su _Secular Religions in France_. Véase también Richard M. Chadbourne, «Renan and Sainte-Beuve», en _Romanic Review_ 44, n.º 2 (abril de 1953), pp. 126-135.
. Véase Renan, _Oeuvres complètes_ , _op. cit_., 8, p. 156.
. En su carta del 26 de junio de 1856 a Gobineau, _Oeuvres complètes_ , _op. cit_., 10, pp. 203-204. Las ideas de Gobineau están expuestas en su _Essai sur l'inégalité des races humaines_ (1853-1855).
. Citado por Albert Hourani en su excelente artículo «Islam and the Philosophers of History», _loc. cit_., p. 222.
. Véase Caussin de Perceval, _Essai sur l'histoire des Arabes avant l'Islamisme, pendant l'époque de Mahomet et jusqu'à la réduction de toutes les tribus sous la loi musulmane_ , 1847-1848; reimpr., Akademische Druckund Verlagsanstalt, Graz, Austria, 1967, 3, pp. 332-339.
. Véase Thomas Carlyle, _On Heroes, Hero-Worship, and the Heroic in History_ , 1841; reimpr., Longmans, Green & Co., Nueva York, 1906, p. 63. [Trad. cast., _Los héroes_ , Sarpe, Madrid, 1985.]
. Las experiencias indias de Macaulay las describe G. Otto Trevelyan en su _The Life and Letters of Lord Macaulay_ , Harper & Brothers, 1875, Nueva York, 1, pp. 344-371. El texto completo de la «Minute» de Macaulay se puede encontrar en _Imperialism: The Documentary History of Western Civilization_ , ed. Philip D. Curtin, Walker & Co., Nueva York, 1971, pp. 178-191. Algunas de las consecuencias de las opiniones de Macaulay para el orientalismo británico se estudian en A. J. Arberry, _British Orientalist_ , William Collins, Londres, 1943.
. Véase John Henry Newman, «The Turks in Their Relation to Europe», vol. 1, de su _Historical Sketches_ , 1853; reimp., Longmans, Green & Co., Londres, 1920.
. Véase Marguerite-Louise Ancelot, _Salons de Paris, foyers éteints_ , Jules Tardieu, París, 1858.
. Véase Karl Marx, _Surveys from Exile_ , ed. ing. David Fernbach, Pelican Books, Londres, 1973, pp. 306-307.
. _Ibid_., p. 320.
. Véase Edward William Lane, prefacio del autor a _An Account of the Manners and Customs of the Modern Egyptians_ , 1836; reimpr., J. M. Dent, Londres, 1936, pp. xx, xxi.
. _Ibid_., p. 1.
. _Ibid_., pp. 160-161. La biografía clásica de Lane, publicada en 1877, fue escrita por su sobrino nieto Stanley Lane-Poole. Un simpático retrato de Lane se puede encontrar en A. J. Arberry, _Oriental Essays: Portraits of Seven Scholars_ , Macmillan Co., Nueva York, 1960, pp. 87-121.
. Véase _Centenary Volume of the Royal Asiatic Society of Great Britain and Ireland, 1823-1923_ , ed. Frederick Eden Pargiter, Royal Asiatic Society, Londres, 1923, p. x.
. Véase _Société Asiatique: Livre du centenaire, 1822-1922_ , Paul Geuthner, París, 1922, pp. 5-6.
. Véase Johann Wolfgang von Goethe, _Westöstlicher Diwan_ , 1819; reimpr., Wilhelm Golmann, Munich, 1958, pp. 8-9, 12. Goethe invoca el nombre de Sacy con veneración en sus notas del _Diwan_.
. Véase Victor Hugo, «Les Orientales» en _Oeuvres_..., _op. cit_., 1, pp. 616-618.
. Véase François-René de Chateaubriand, _Oeuvres romanesques et voyages_ , ed. Maurice Regard, Gallimard, París, 1969, 2, p. 702.
. Véase Henri Bordeaux, _Voyageurs d'Orient: Des pélerins aux méharistes de Palmyre_ , Plon, París, 1926. Me han resultado útiles las ideas teóricas sobre los peregrinos y las peregrinaciones que hay en Victor Turner, _Dramas, Fields and Metaphors: Symbolic Action in Human Society_ , Cornell University Press, Ithaca, 1974, pp. 166-230.
. Véase Hassan al-Nouty, _Le Proche-Orient dans la littérature française de Nerval à Barrès_ , Nizet, París, 1958, pp. 47-48, 272, 277.
. Véase Chateaubriand, _Oeuvres..._ , _op. cit_., pp. 2, 202 y nota, 1.684, 769-770, 769, 701, 808, 908.
. _Ibid_., pp. 979, 990, 1.011, 1.052.
. _Ibid_., p. 1.069.
. _Ibid_., p. 1.031.
. _Ibid_., p. 999.
. _Ibid_., pp. 1.049, 1.126-1.127.
. _Ibid_., p. 1.137.
. _Ibid_., pp. 1.148, 1.214.
. Véase Alphonse de Lamartine, _Voyage en Orient_ , 1835; reimpr., Hachette, París, 1887, 1, pp. 10, 48-49, 118, 179, 178, 148, 189, 245-246, 251.
. _Ibid_., 1: p. 363; 2: pp. 74-75; 1: p. 475.
. _Ibid_., 2: pp. 92-93.
. _Ibid_., 2: pp. 526-527, 533. Dos obras importantes sobre escritores franceses en Oriente son Jean-Marie Carré, _Voyageurs et écrivains français en Égypte_ , 2 vols., Institut Français d'Archéologie Orientale, El Cairo, 1932, y Moënis Taha-Husein, _Le Romantisme français et l'Islam_ , Darel-Maarif, Beirut, 1962.
. Véase Gérard de Nerval, _Les Filles du feu_ , en _Oeuvres_ , _op. cit_., 1, pp. 297-298.
. Véase Mario Praz, _The Romantic Agony_ , trad. de Augus Davison, World Publishing Co., Cleveland, Ohio, 1967.
. Véase Jean Bruneau, _Le «Conte orientale» de Flaubert_ , Denoel, París, 1973, p. 79.
. Estudiados por Bruneau en la obra citada.
. Véase Nerval, _Voyage en Orient_ en _Oeuvres_ , _op. cit_., 2, pp. 68, 194, 196, 342.
. _Ibid_., p. 181.
. Véase Michel Butor, _Répertoire IV_ , Éd. de Minuit, París, 1974.
. Véase Nerval, _Voyage_..., _op. cit_., p. 628.
. _Ibid_., pp. 706, 718.
. Véase _Flaubert in Egypt: A Sensibility on Tour_ , traducido y editado por Francis Steegmuller, _op. cit_., p. 200. También he consultado los siguientes textos, en los que se puede encontrar todo el material oriental de Flaubert: _Oeuvres complètes de Gustave Flaubert_ , Club de l'Honnête homme, París, 1973, vols. 10, 11; _Les Lettres d'Égypte, de Gustave Flaubert_ , ed. A. Youssef Naaman, Gallimard, París, 1965; Flaubert, _Correspondance_ , ed. Jean Bruneau, Gallimard, París, 1973, 1, pp. 518 y ss.
. Véase Harry Levin, _The gates of Horn: A Study of Five French Realists_ , Oxford University Press, Nueva York, 1963, p. 285.
. _Flaubert in Egypt_ , _op. cit_., pp. 173, 175.
. Levin, _Gates of Horn_ , _op. cit_., p. 271.
. Véase Flaubert, _Catalogue des opinions chics_ , en _Oeuvres_ , 2, Gallimard, París, 1953, p. 1.019.
. Véase _Flaubert in Egypt..._ , _op. cit_., p. 65.
. _Ibid_., pp. 130, 220.
. Véase Flaubert, _La Temptation de Saint Antoine_ , en _Oeuvres_ , 1, Gallimard, París, 1953, p. 85.
. Véase Flaubert, «Salammbô», en _Oeuvres_ , 1, Gallimard, París, 1953, pp. 809 y ss. Véase también Maurice Z. Shroder, «On Reading Salammbô», en _L'Esprit créateur_ 10, n.º 1 (primavera de 1970), pp. 24-35.
. Véase _Flaubert in Egypt_..., _op. cit_., pp. 198-199.
. Véase Foucault, «La Bibliothèque fantastique» en Flaubert, _La Temptation de Saint Antoine_ , _op. cit_., pp. 7-33.
. Véase _Flaubert in Egypt..._ , _op. cit_., p. 79.
. _Ibid_., pp. 211-212.
. Para un estudio de este proceso, véanse Foucault, _L'Archéologie du savoir_ , _op. cit_., y Joseph Ben-David, _The Scientist's Role in Society_ , Prentice-Hall, Englewood Cliffs, 1971. Véase también Edward W. Said, «An Ethics of Language», en _Diacritics_ 4, n.º 2 (verano de 1974), pp. 28-37.
. Véase la inestimable lista dada por Richard Bevis en su _Bibliotheca Cisorientalia: An Annotated Checklist of Early English Travel Books on the Near and Milddle East_ , G. K. Hall & Co., Boston, 1973.
. Para un estudio de los viajeros americanos, véanse Dorothee Metlitski Finkelstein, _Melville's Orienda_ , Yale University Press, New Haven, 1961, y Franklin Walker, _Irreverent Pilgrims: Melville, Browne, and Mark Twain in the Holy Land_ , University of Washington Press, Seattle, 1974.
. Véase Alexander William Kinglake, _Eothen or Traces of Travel Brought Home from the East_ , ed. D. G. Hogarth, 1844; reimpr., Henry Frowde, Londres, 1906, pp. 25, 68, 220, 241.
. Véase _Flaubert in Egypt..._ , _op. cit_., p. 81.
. Véase Thomas J. Assad, _Three Victorian Travellers: Burton, Blunt and Doughty_ , Routledge & Kegan Paul, Londres, 1964, p. 5.
. Véase Richard Burton, _Personal Narrative of a Pilgrimage to alMadinah and Meccah_ , ed. Isabel Burton, Tylston & Edwards, Londres, 1893, 1, pp. 9, 108-110.
. Véase Richard Burton, «Terminal Essay», en _The Book of the Thousand and One Nights_ , Burton Club, Londres, 1886, 10, pp. 63-302.
. Véase Burton, _Pilgrimage..._ , _op. cit_., 1, pp. 112, 114.
TERCERA PARTE. El orientalismo en nuestros días
. Véase Friedrich Nietzsche, «On Truth and Lie in an Extra-Moral Sense», en _The Portable Nietzsche_ , ed. y trad. Walter Kaufmann, Viking Press, Nueva York, 1954, pp. 46-47.
. Ibrahim Abu-Lughod evalúa y estudia el número de viajeros árabes hacia Occidente en _Arab Rediscovery of Europe: A Study in Cultural Encounters_ , Princeton University Press, Princeton, 1963, pp. 75-76 y pássim.
. Véase Philip D. Curtin (ed.), _Imperialism: The Documentary..._ , _op. cit_., pp. 73-105.
. Véase Johann W. Fück, «Islam as an Historical Problem in European Historiography since 1800» en _Historians of the Middle..._ , _op. cit_., p. 307.
. _Ibid_., p. 309.
. Véase Jacques Waardenburg, _L'Islam dans le miroir de l'Occident_ , Mouton & Co., La Haya, 1963.
. _Ibid_., p. 311.
. Véase P. Masson-Oursel, «La connaissance scientifique de l'Asie en France depuis 1900 et les variétés de l'orientalisme», en _Revue Philosophique_ 143, n.os 7-9 (julio-septiembre de 1953), p. 345.
. Véase Evelyn Baring, lord Cromer, _Modern Egypt..._ , _op. cit_., 2, pp. 237-238.
. Evelyn Baring, lord Cromer, _Ancient and Modern Imperialism_ , John Murray, Londres, 1910, pp. 118, 120.
. Véase George Nathaniel Curzon, _Subjects of the Day: Being a Selection of Speeches and Writings_ , George Allen & Unwin, Londres, 1915, pp. 4-5, 10 y 28.
. _Ibid_., pp. 184, 191-192. Para la historia de la Escuela, véase C. H. Phillips, _The School of Oriental and African Studies, University of London, 1917-1967: An Introduction_ , inédito, Londres, 1967.
. Véase Eric Stokes, _The English Utilitarians and India_ , Clarendon Press, Oxford, 1959.
. Citado en Michael Edwardes, _High Noon of Empire: India Under Curzon_ , Eyre & Spottiswoode, Londres, 1965, pp. 38-39.
. Véase Curzon, _Subjets of the Day_ , _op. cit_., pp. 155-156.
. Véase Joseph Conrad, _Hearth of Darkness_ en _Youth and Two Other Stories_ , Doubleday, Page, Garden City, 1925, p. 52.
. Para extractos ilustrativos de la obra de Vattel, véase _Imperialism..._ , _op. cit_., pp. 42-45.
. Citado por M. de Caix, «La Syrie», en _Histoire des colonies françaises_ , de Gabriel Hanotaux, 6 vols., Société de l'histoire nationale, París, 1929-1933, 3, p. 481.
. Estos detalles se pueden encontrar en Vernon McKay, «Colonialism in the French Geographical Movement», en _Geographical Review_ 33, n.º 2 (abril de 1943), pp. 214-232.
. Véase Agnes Murphy, _The Ideology of French Imperialism, 1817-1881_ , Catholic University of America Press, Washington, 1948, pp. 46, 54, 36, 45.
. _Ibid_., pp. 189, 110, 136.
. Véase Jukka Nevakivi, _Britain, France and the Arab Middle East, 1914-1920_ , Athlone Press, Londres, 1969, p. 13.
. _Ibid_., p. 24.
. Véase D. G. Hogarth, _The Penetration of Arabia: A Record of the Development of Western Knowledge Concerning the Arabian Peninsula_ , Frederick A. Stokes, Nueva York, 1904. Una estupenda obra reciente sobre el mismo tema es la de Robin Bidwell, _Travellers in Arabia_ , Paul Hamlyn, Londres, 1976.
. Véase Edmond Bremond, _Le Hedjaz dans la guerre mondiale_ , Payot, París, 1931, pp. 242 y ss.
. Véase conde de Cressaty, _Les Intérêts de la France en Syrie_ , Floury, París, 1913.
. Véase Rudyard Kipling, _Verse_ , Doubleday & Co., Garden City, 1954, p. 280.
. Los temas de la exclusión y el confinamiento en la cultura del siglo XIX desempeñan un papel importante en la obra de Michel Foucault, y más concretamente en _Surveiller et Punir. Naissance de la prison_ , Gallimard, París, 1975, y en _Histoire de la Sexualité, Volume I_ , Gallimard, París, 1976. [Trad. cast., Madrid, _Historia de la sexualidad_ , Madrid, Siglo XXI, 1987.]
. _The Letters of T. E. Lawrence of Arabia_ , ed. David Garnett, 1938; reimpr., Spring Books, Londres, 1964, p. 244.
. Véase Gertrude Bell, _The Desert and the Sown_ , William Heinemann, Londres, 1907, p. 244.
. Véase Gertrude Bell, _From her Personal Papers, 1889-1914_ , ed. de Elizabeth Burgoyne, Ernest Benn, Londres, 1958, p. 204.
. Véase William Butler Yeats, «Byzantium», en _The Collected Poems_ , Macmillan Co., Nueva York, 1959, p. 244.
. Véase Stanley Diamond, _In Search of the Primitive: A Critique of Civilization_ , Transaction Books, New Brunswick, 1974, p. 119.
. Véase Harry Bracken, «Essence, Accident and Race», en _Hermathena_ 116 (invierno de 1973), pp. 81-96.
. Véase George Eliot, _Middlemarch_..., _op. cit_., p. 13.
. Véase Lionel Trilling, _Matthew Arnold_ , 1939; reimpr., Meridian, Nueva York, 1955, p. 214.
. Véase Hannah Arendt, _The Origins of Totalitarianism_ , Harcourt Brace Jovanovich, Nueva York, 1973, p. 180, nota 55. [Trad. cast., _Los orígenes del totalitarismo_ , Alianza, Madrid, 1987.]
. Véase W. Robertson Smith, _Kinship and Marriage in Early Arabia_ , ed. Stanley Cook, 1907; reimpr., Anthropological Publications, Oesterhout, 1966, pp. xiii, 241.
. Véase W. Robertson Smith, _Lectures and Essays_ , ed. de John Sutherland Black and George Chrystal, Adam & Charles Black, Londres, 1912, pp. 492-493.
. _Ibid_., pp. 492-493, 498-501.
. Véase Charles M. Doughty, _Travels in Arabia Desert_ , 2.ª ed., 2 vols., Random House, Nueva York, s.a., 1, p. 95. Véase también el excelente artículo de Richard Bevis, «Spiritual Geology: C. M. Doughty and the Land of the Arabs», en _Victorian Studies_ 16 (diciembre de 1972), pp. 163-181.
. Véase T. E. Lawrence, _The Seven Pillars of Wisdom: A Triumph_ , 1926, reimp., Doubleday, Doran & Co., Garden City, Nueva York, 1935, p. 28.
. Para una discusión sobre este punto, véase Talal Asad, «Two European Images of Non-European Rule», en _Anthropology and the Colonial Encounter_ , ed. de Talal Asad, Ithaca Press, Londres, 1975, pp. 103-118.
. Véase Hannah Arendt, _The Origins_..., _op. cit_., p. 218.
. Véase T. E. Lawrence, _Oriental Assembly_ , ed. de A. W. Lawrence, E. P. Dutton & Co., Nueva York, 1940, p. 95.
. Citado en Stephen Ely Tabachnick, «The Two Veils of T. E. Lawrence», en _Studies in the Twentieth Century_ , 16 (otoño de 1975), pp. 96-97.
. Véase Lawrence, _Seven Pillars_..., _op. cit_., pp. 42-43, 661.
. _Ibid_., pp. 549, 550-552.
. Véase E. M. Forster, _A Passage to India_ , 1924; reimpr., Harcourt, Brace & Co., Nueva York, 1952, p. 322.
. Véase Maurice Barrès, _Una Enquête aux pays du Levant_ , Plon, París, 1923, 1: p. 20; 2: pp. 181, 192, 193, 197.
. Véase D. G. Hogarth, _The Wandering Scholar_ , Oxford University Press, Londres, 1924. Hogarth describe su estilo como «el de un explorador primero y el de un erudito después», p. 4.
. Citado por H. A. R. Gibb, «Structure of Religions Thought in Islam», en _Studies on the Civilization of Islam_ , eds. de Stanford J. Shaw y William R. Polk, Beacon Press, Boston, 1962, p. 180.
. Véase Frédéric Lefèvre, «Une heure avec Sylvain Lévi» en _Memorial Sylvain Lévi_ , ed. Jacques Bacot, Paul Hartmann, París, 1937, pp. 123-124.
. Véase Paul Valéry, _Oeuvres_ , ed. Jean Hytier, Gallimard, París, 1960, 2, pp. 1.556-1.557.
. Citado en Christopher Sykes, _Crossroads to Israel_ , 1965; reimpr., Indiana University Press, Bloomington, 1973, p. 5.
. Citado en Alan Sandison, _The Wheel of Empire: A Study of the Imperial Idea in Some Late Nineteenth and Early Twentieth Century Fiction_ , St. Martin Press, Nueva York, 1967, p. 158. Un excelente estudio sobre el equivalente francés es de Martine Astier Loutfi, _Littérature et colonialisme: L'Expansion coloniale vue dans la littérature romanesque française, 18711914_ , Mouton & Co., La Haya, 1971.
. Véase Paul Valéry, _Variété_ , Gallimard, París, 1924, p. 43.
. Véase George Orwell, «Marrakech», en _A Collection of Essays_ , Doubleday Anchor Books, Nueva York, 1954, p. 187.
. Véase Valentine Chirol, _The Occident and the Orient_ , University of Chicago Press, Chicago, 1924, p. 6.
. Véase Élie Faure, «Orient et Occident», en _Mercure de France_ 229 (1 de julio-1 de agosto de 1931), pp. 263-264, 269-270, 272.
. Véase Fernand Baldensperger, «Où s'affrontent l'Orient et l'Occident intelectuels», en _Études d'histoire littéraire_ , 3.ª serie, Droz, París, 1939, p. 230.
. Véase I. A. Richards, _Mencius on the Mind: Experiments in Multiple Definitions_ , Routledge & Kegan Paul, Londres, 1932, p. xiv.
. Véase _Selected Works of C. Snouck Hurgronje_ , ed. G. H. Bousquet y J. Schacht, E. J. Brill, Leiden, 1957, p. 267.
. Véase H. A. R. Gibb, «Literature», en _The Legacy of Islam_ , ed. Thomas Arnold y Alfred Guillaume, Clarendon Press, Oxford, 1931, p. 209.
. El mejor relato de este período desde un punto de vista social, económico y cultural se puede encontrar en Jacques Berque, _L'Égypte, Imperialisme et révolution_ , Gallimard, París, 1967.
. Hay una exposición muy útil del proyecto intelectual que inspira su trabajo en _On Four Modern Humanists: Hofmannsthal, Gundolf, Curtius, Kantorowicz_ , ed. Arthur R. Evans Jr., Princeton University Press, Princeton, 1970.
. Véanse Erich Auerbach, _Mimesis: The Representation of Reality in Western Literature_ , trad. de Willard R. Trask, 1946; reimpr., Princeton University Press, Princeton, 1968 (original: _Mimesis, dargestellte Wirklichkeit in der abendländischen Literatur_ , 2.ª ed., Francke Verlag, Berna, 1959), y su _Literary Language and Its Public in Late Latin Antiquity and in the Middle Ages_ , trad. al inglés de Ralph Manheim, Bollingen Books, Nueva York, 1965.
. Véase Erich Auerbach, «Philology and _Weltliteratur_ », trad. al inglés de M. y E. W. Said, en _Centennial Review_ 13, n.º 1 (invierno de 1969), p. 11.
. _Ibid_., p. 17.
. Por ejemplo, en H. Stuart Hughes, _Consciousness and Society: The Reconstruction of European Social Thought 1890-1930_ , 1958; reimpr., Vintage Books, Nueva York, 1961.
. Véase Anuar Abdel Malek, «L'orientalisme en crise», _loc. cit_., p. 113.
. Véase R. N. Cust, «The International Congresses of Orientalist», en _Hellas_ 6, n.º 4 (1897), p. 349.
. Véase W. F. Wertheim, «Counter-insurgency Research at the Turn of the Century-Snouck Hurgronje and the Acheh War», en _Sociologische Gids_ , 19 (septiembre-diciembre de 1972).
. Véase Sylvain Lévi, «Les parts respectives des nations occidentales dans les progrès de l'indianisme», en _Mémorial Sylvain Lévi_ , _op. cit_., p. 116.
. Véase H. A. R. Gibb, «Louis Massignon (1882-1962)», en _Journal of the Royal Asiatic Society_ (1962), pp. 120, 121.
. Véase Louis Massignon, _Opera Minora_ , ed. Y. Moubarac, Dar alMaaref, Beirut, 1963, 3, p. 114. He utilizado la bibliografía completa de las obras de Massignon realizada por Moubarac, _L'Oeuvre de Louis Massignon_ , Éditions du Cénacle libanais, Beirut, 1972-1973.
. Véase Massignon, «L'Occident devant l'Orient: Primauté d'une solution culturelle», en _Opera_..., _op. cit_., 1, pp. 208-223.
. _Ibid_., p. 169.
. Véase Waardenburg, _L'Islam dans le miroir de l'Occident_ , _op. cit_., pp. 147, 183, 186, 192, 211, 213.
. Massignon, _Opera Minore_ , _op. cit_., 1, p. 227.
. _Ibid_., p. 355.
. Extracto del ensayo de Massignon sobre Biruni en Waardenburg, _L'Islam dans le miroir de l'Occident_ , _op. cit_., p. 225.
. Massignon, _Opera Minora_ , _op. cit_., 3, p. 526.
. _Ibid_., pp. 610-611.
. _Ibid_., p. 212. También en p. 211 se encuentra otro ataque contra los británicos y en pp. 423-427 su opinión sobre Lawrence.
. Citado en Waardenburg, _L'Islam dans le miroir_..., _op. cit_., p. 219.
. _Ibid_., pp. 218-219.
. Véase A. L. Tibawi, «English-Speaking Orientalists: A Critique of Their Approach to Islam and Arab Nationalism, Part I», en _Islamic Quarterly_ 8, n.os 1-2 (enero-junio de 1964), pp. 25-44; y «Part II», en _Islamic Quarterly_ 8, n.os 3-4 (julio-diciembre), pp. 73-88.
. «Une figure domine tous les genres [del trabajo orientalista], celle de Louis Massignon»: Claude Cahen y Charles Pellat. Véase «Les Études arabes et islamiques», en _Journal Asiatique_ 261, n.os 1-4 (1973), p. 104. Un panorama detallado sobre el campo orientalista islámico se puede encontrar en Jean Sauvaget, _Introduction à l'histoire de l'Orient musulman: Éléments de bibliographie_ , ed. Claude Cahen, Adrien Maisonneuve, París, 1961.
. Véase William Polk, «Sir Hamilton Gibb Between Orientalism and History», en _International Journal of Middle East Studies_ 6, n.o 2 (abril de 1975), pp. 131-139. He utilizado la bibliografía de la obra de Gibb que se encuentra en _Arabic and Islamic Studies in Honor of Hamilton A. R. Gibb_ , ed. George Makdisi, Harvard University Press, Cambridge, 1965, pp. 1-20.
. Véase H. A. R. Gibb, «Oriental Studies in the United Kingdom», en _The Near East and the Great Powers_ , ed. Richard N. Frye, Harvard University Press, Cambridge, 1951, pp. 86-87.
. Véase Albert Hourani, «Sir Hamilton Gibb, 1895-1971», en _Proceedings of the British Academy_ , 58, 1972, p. 504.
. Véase Duncan Black Macdonald, _The Religious Attitude and Life in Islam_ , 1909; reimpr., Khayats Publishers, Beirut, 1965, pp. 2-11.
. Véase H. A. R. Gibb, «Whither Islam?», en _Whither Islam? A Study Modern Movements in the Moslem World_ , ed. H. A. R. Gibb, Victor Gollancz, Londres, 1932, pp. 328-387.
. _Ibid_., p. 335.
. _Ibid_., p. 377.
. Véase H. A. R. Gibb, «The influence of Islamic Culture on Medieval Europe», en _John Rylands Library Bulletin_ 38, n.º 1 (septiembre de 1955), p. 98.
. Véase H. A. R. Gibb, _Mohammedanism: An Historical Survey_ , Oxford University Press, Londres, 1949, pp. 2, 9, 84.
. _Ibid_., pp. 11, 88, 189.
. Véase H.A. R. Gibb, _Modern Trends_..., _op. cit_., pp. 108, 113, 123.
. Los dos ensayos se encuentran en Gibb. Véase _Studies on the Civilization of Islam_ , pp. 176-208 y 3-33.
. Véase R. Emmet Tyrrell Jr., «Chimera in the Middle East», en _Harper's_ (noviembre de 1976), pp. 35-38.
. Citado en Ayad al-Qazzaz, Ruth Afiyo _et al_., _The Arabs in American Textbooks_ , State Board of Education, California, junio de 1975, pp. 10, 15.
. «Statement of Purpose», en _MESA Bulletin_ 1, n.o 1 (mayo de 1967), p. 33.
. Véase Morroe Berger, «Middle Eastern and North African Studies: Developments and Needs», en _MESA Bulletin_ 1, n.o 2 (noviembre de 1967), p. 16.
. Véase Menachem Mansoor, «Present State of Arabic Studies in the United States», en _Report on Current Research 1958_ , ed. Kathleen H. Brown, Middle East Institute, Washington, 1958, pp. 55-56.
. Véase Harold Lasswell, «Propaganda», en _Encyclopedia of the Social Sciences_ , 1934, 12, p. 527. Esta referencia se la debo a Noam Chomsky.
. Marcel Proust, _À la recherche du temps perdu_ , 2, _Le Côté de Guermantes_ , Gallimard, París, 1954, p. 190. [Trad. cast., _El mundo de Guermantes_ , Alianza, Madrid, 1998.]
. Véase Nathaniel Schmidt, «Early Oriental Studies in Europe and the Work of the American Oriental Society, 1842-1922», en _Journal of the American Oriental Society_ 43 (1923), p. 11. Véase también E. A. Speiser, «Near Eastern Studies in America, 1939-1945», en _Archiv Orientalni_ 16 (1948), pp. 76-88.
. Como ejemplo está Henry Jessup, _Fifty-Three Years in Syria_ , 2 vols., Fleming H. Revell, Nueva York, 1910.
. Para la conexión entre la Declaración Balfour y la política bélica de Estados Unidos, véase Doreen Ingrams, _Palestine Papers 1917-1922: Seeds of Conflict_ , Cox & Syman, Londres, 1972, pp. 10 y ss.
. Véase Mortimer Graves, «A Cultural Relations Policy in the Near East», en _The Near East_..., _op. cit_., pp. 76, 78.
. Véase George Camp Keiser, «The Middle East Institute: Its Inception and Its Place in American International Studies», en _The Near East_..., _op. cit_., pp. 80, 84.
. Para una exposición de esta migración, véase _The Intellectual Migration: Europe and America, 1930-1960_ , ed. Donald Fleming y Bernard Bailyn, Harvard University Press, Cambridge, 1969.
. Véase Gustave von Grunebaum, _Modern Islam: The Search for Cultural Identity_ , Vintage Books, Nueva York, 1964, pp. 55, 261.
. Véase Abdallah Laroui, «Pour une méthodologie des études islamiques: L'Islam au miroir de Gustave von Grunebaum», _Diogène_ 38 (julio-septiembre de 1973), p. 30.
. Véase David Gordon, _Self-Determination and History in the Third World_ , Princeton University Press, Princeton, 1971.
. Véase Laroui, «Pour une méthodologie des études islamiques», _loc. cit_., p. 41.
. Véase Manfred Halpern, «Middle East Studies: A Review of the State of the Field with a Few Examples», _World Politics_ 15 (octubre de 1962), pp. 121-122.
. _Ibid_., p. 117.
. Leonard Binder, «1974 Presidential Addres», _MESA Bulletin_ 9, n.o 1 (febrero de 1975), p. 2.
. _Ibid_., p. 5.
. Véase «Middle East Studies Network in the United States», _MERIP Reports_ 38 (junio de 1975), p. 5.
. Las dos mejores reseñas críticas sobre la _Cambridge History_ son la de Albert Hourani, _The English Historical Review_ 87, n.o 343 (abril de 1972), pp. 348-357, y la de Roger Owen, _Journal of Interdisciplinary History_ 4, n.o 2 (otoño de 1973), pp. 287-298.
. Véase P. M. Holt, Introduction, _The Cambridge History of Islam_ , ed. P. M. Holt, Anne K. S. Lambton y Bernard Lewis, 2 vols., Cambridge University Press, Cambridge, 1970, 1, p. xi.
. Véase D. Sourdel, «The Abbasid Caliphate», en _Cambridge History_..., _op. cit_., 1, p. 121.
. Z. N. Zeine, «The Arab Lands», en _Cambridge History_..., _op. cit_., 1, p. 575.
. Véase Dankwart A. Rustow, «The Political Impact of the West», en _Cambridge History_..., _op. cit_., 1, p. 697.
. Citado en Ingrams, _Palestine Papers, 1917-1922_ , pp. 31-32.
. Véase Robert Alter, «Rhetoric and the Arab Mind», _Commentary_ , octubre de 1968, pp. 61-85. El artículo de Alter es una exposición aduladora del general Yehoshafat Harbaki, _Arab Attitudes to Israel_ , Keter Press, Jerusalén, 1972.
. Véase Gil Carl Alroy, «Do The Arabs Want Peace?», _Commentary_ , febrero de 1974, pp. 56-61.
. Véase Roland Barthes, _Mythologies_ , Éd. du Seuil, París, 1970. [Trad. cast., _Mitologías_ , Siglo XXI, Madrid, 1980.]
. Raphael Patai, _Golden River to Golden Road: Society, Culture, and Change in the Middle East_ , University of Pennsylvania Press, Filadelfia, 1962, 3.ª ed., 1969, p. 406.
. Véase Raphael Patai, _The Arab Mind_ , Charles Scribner's Sons, Nueva York, 1973. Una obra todavía más racista es la de John Laffin, _The Arab Mind Considered: A Need for Understanding_ , Taplinger Publishing Co., Nueva York, 1976.
. Véase Sania Hamady, _Temperament and Character of the Arabs_ , Twayne Publishers, Nueva York, 1960, p. 100. Este libro ha tenido un gran éxito entre los israelíes y sus partidarios; Alroy lo cita con aprobación y también lo hace Amos Elon en _The Israelis: Founders and Sons_ , Holt, Rinehart & Winston, Nueva York, 1971. Morroe Berger ( _Arab World, op. cit_.) también lo cita frecuentemente. Su modelo es _Manners and Customs of the Modern Egyptians_ , de Lane, pero ella no tiene la familiaridad de Lane con el árabe ni sus conocimientos.
. La tesis de Manfred Halpern está expuesta en «Four Contrasting Repertories of Human Relations in Islam: Two Pre-Modern and Two Modern Ways of Dealing with Continuity and Change, Collaboration and the Conflict and the Achieving of Justice», una ponencia presentada en la vigesimosegunda Conferencia sobre Oriente Próximo, en la Universidad de Princeton, sobre psicología y estudios de Oriente Próximo el 8 de mayo de 1973. Este texto había estado preparado por el artículo de Halpern «A Redefinition of the Revolutionary Situation», _Journal of International Affairs_ , 23, n.o 1 (1969), pp. 54-75.
. Morroe Berger, _The Arab World Today_ , Doubleday Anchor Books, Nueva York, 1964, p. 140. El mismo tipo de implicaciones subyace en el torpe trabajo de cuasi arabistas como Joel Carmichael y Daniel Lerner; también se encuentra de una manera más sutil en eruditos de la historia y la política como Theodore Draper, Walter Laqueur y Élie Kedourie. Aparece de una manera muy evidente en obras que cuentan con una gran reputación como Gabriel Baer, _Population and Society in the Arab East_ , trad. Hanna Szoke, Frederik A. Praeger, Nueva York, 1964, y Alfred Bonné, _State and Economics in the Middle East: A Society in Transition_ , Routledge & Kegan Paul, Londres, 1955. El consenso parece ser que, en el caso de que piensen, los árabes piensan de diferente manera —esto es, no necesariamente con la razón y con frecuencia sin ella—. Véase también Adel Daher, RAND study, _Current Trends in Arab Intellectual Thought_ (RM5979-FF, diciembre de 1969) y su conclusión característica: «El modo de aproximación concreta para resolver los problemas está ausente de la mente árabe» (p. 29). En un estudio críptico para el _Journal of Interdisciplinary History_ (4, n.o 2, otoño de 1973, pp. 287-298), Roger Owen ataca la noción misma de «islam» como concepto que sirve para estudiar la historia. Su blanco es _The Cambridge History of Islam_ , la cual, según él, perpetúa de ciertas maneras una idea del islam (que se puede encontrar en escritores como Carl Becker y Max Weber), «definido esencialmente como un sistema religioso, feudal y antirracional, que carece de las características necesarias que han hecho el progreso europeo». Para una demostración de la inexactitud total de Weber, véase Maxime Rodinson, _Islam_..., _op. cit_.
. Véase Hamady, _Character_..., _op. cit_., p. 197.
. Véase Berger, _Arab World_..., _op. cit_., p. 102.
. Citado por Irene Gendzier en _Frantz Fanon: A Critical Study_ , Pantheon Books, Nueva York, 1973, p. 94.
. Véase Berger, _Arab World..._ , _op. cit_., p. 151.
. Véase _Revolution in the Middle East, and Other Case Studies; Proceedings of a Seminar_ , ed. P. J. Vatikiotis, George Allen & Unwin, Londres, 1972, pp. 8-9.
. _Ibid_., pp. 12, 13.
. Véase Bernard Lewis, «Islamic Concepts of Revolution», en _ibid_., pp. 33, 38-39. El estudio de Lewis _Race and Color in Islam_ , Harper & Row, Nueva York, 1971 («Raza y color en el Islam», _Al-Andalus_ , vol. XXXIII, 1968, pp. 1-51) expresa un descontento similar con un aire muy erudito; su libro _Islam in History: Ideas, Men and Events in the Middle East_ , Alcove Press, Londres, 1973, es más explícitamente político, pero no menos ácido.
. Véase Bernard Lewis, «The Revolt of Islam», en _The Middle East and The West_ , Indiana University Press, Bloomington, 1964, p. 95.
. Véase Bernard Lewis, «The Return of Islam», _Commentary_ , enero de 1976, p. 44.
. _Ibid_., p. 40.
. Véase Bernard Lewis, _History-Remembered, Recovered, Invented_ , Princeton University Press, Princeton, 1975, p. 68.
. Lewis, _Islam_..., _op. cit_., p. 65.
. Lewis, _The Middle East_..., _op. cit_., pp. 60-87.
. Lewis, _Islam_..., _op. cit_., pp. 65-66.
. Publicado originariamente en _Middle East Journal_ 5 (1951). Recogido en _Readings in Arab Middle Eastern Societies and Cultures_ , ed. Abdulla Lutfiyye y Charles W. Churchill, Mouton & Co., La Haya, 1970, pp. 688-703.
. Véase Lewis, _The Middle East_..., _op. cit_., p. 140.
. Véase Robert K. Merton, «The Perspectives of Insiders and Outsiders», en su _The Sociology of Science: Theoretical and Empirical Investigations_ , ed. Norman W. Storer, University of Chicago Press, Chicago, 1973, pp. 99-136.
. Véanse, por ejemplo, los trabajos recientes de Anuar Abdel Malek, Yves Lacoste y de los autores de los ensayos publicados en _Review of Middle East Studies 1 y 2_ , Ithaca Press, Londres, 1975, 1976, los análisis políticos sobre Oriente Próximo realizados por Noam Chomsky y el trabajo hecho por el Middle East Research and Information Project (MERIP). Una buena perspectiva se ofrece en Gabriel Ardant, Kostas Axelos, Jacques Berque _et al_., _De l'impérialisme à la décolonisation_ , Éditions de Minuit, París, 1965.
Epílogo de la edición de 1995
. Véanse Martin Bernal, _Black Athena_ , Rutgers University Press, New Brunswick, vol. I, 1987, y vol. II, 1991; y Eric J. Hobsbawm y Terence Rangers, eds., _The Invention of Tradition_ , Cambridge University Press, Cambridge, 1984.
. Véanse O'Hanlon y Washbrook, «After Orientalism: Culture, Criticism and Politics in the Third World», y Prakash, «Can the Subaltern Riude A Reply to O'Hanlon and Washbrook?», en _Comparative Studies in Society and History_ , IV, 9, enero de 1992, pp. 141-184.
. En un caso especialmente llamativo, los hábitos de generalización tendenciosa de Lewis parecen haberle ocasionado problemas legales. De acuerdo con _Libération_ (1 de marzo de 1994) y el _Guardian_ (8 de marzo de 1994), Lewis se enfrenta hoy a litigios civiles y penales planteados contra él en Francia por armenios y organizaciones de defensa de los derechos humanos. Se le acusa al amparo de la misma ley que considera delito en Francia el negar que se produjo el holocausto nazi; el cargo contra él es negar (en la prensa francesa) que se produjo un genocidio de armenios bajo el Imperio otomano.
. Véase Carol Breckenridge y Peter van der Veer, eds., _Orientalism and the Postcolonial Predicament_ , University of Pennsylvania, Filadelfia, 1993.
. Véase Nicholas B. Dirks, ed., _Colonialism and Culture_ , The University of Michigan Press, Ann Arbor, 1992.
. Véase «The Clash of Civilizations», _Foreign Affairs_ , 7, 3 (verano de 1993), pp. 22-49.
. Véase «Notes on the "Post-Colonial"», _Social Text_ , 31/32 (1992), p. 106.
. Véase Magdoff, «Globalisation-To What End?», _Socialist Register 1992: New World Order_?, eds., Ralph Milliband y Leo Panitch, Monthly Review Press, Nueva York, 1992, pp. 1-32.
. Véanse Miyoshi, «A Borderless World? From Colonialism to Transnationalism and the Decline of the Nation-State», _Critical Inquiry_ 19, 4 (verano de 1993), pp. 726-751, y Dirlik, «The Postcolonial Aura: Third World Criticism in the Age of Global Capitalism», _Critical Inquiry_ 20, 2 (invierno de 1994), pp. 328-356.
. Véase _Ireland's Field Day_ , Hutchinson, Londres, 1985, pp. vii-viii.
. Alcalay (Minneapolis, University of Minnesota Press, 1993); Gilroy (Cambridge, Harvard University Press, 1993); Ferguson (Londres, Routledge, 1992).
* Trad. cast., _Vigilar y castigar_ , Siglo XXI, Madrid, 2000.
* Trad. cast., _Salambó_ , Montesinos, Barcelona, 1984.
* Trad. cast., _La comedia humana_ , Argos-Vergara, Barcelona; obra agotada.
* Trad. cast., _Sobre la libertad_ , Alianza, Madrid, 1996; _Del gobierno representativo_ , Tecnos, Barcelona, 1982.
* Trad. cast., _Middlemarch_ , Cátedra, Madrid, 1993.
* Trad. cast., Ariel, Barcelona, 1982.
* Trad. cast., _Las palabras y las cosas_ , Siglo XXI, Madrid, 1999.
* No existe ninguna traducción íntegra de esta obra en castellano, aunque sí traducciones parciales (por ejemplo, _La política y el estado moderno_ , Península, Barcelona, 1985). Para una aproximación, _Antología_ , Siglo XXI, 1974.
* Poema de John Donne (1660), en el que compara el restablecimiento de una ley fuerte (la de la Restauración) en Inglaterra con la misma medida por parte de Julio César en Roma. _(N. del E.)_
* Palabra hindi, introducida en inglés con el sentido de «soberanía» y que hace referencia a la dominación británica en la India. _(N. del T.)_
* Este es el famoso impostor Mahoma, Autor y Fundador de una herejía, que ha adoptado el nombre de religión, a la que nosotros llamamos Mahometana. Véase la entrada de _islam_.
»Los intérpretes del Alcorán y otros Doctores de la Ley Musulmana y Mahometana atribuyeron a este falso profeta todos los elogios que los Arrianos, Paulicianos o Paulanistas y otros herejes otorgaron a Jesucristo, despojándole de su divinidad [...].»
* Trad. cast., _Historia de la decadencia y ruina del Imperio romano_ , Turner, Madrid, 1984.
* Redactado por Juan López de Palacios Rubios, dice en una de sus partes: «Y si así no lo hicieseis o en ello maliciosamente pusieseis dilación, os certifico que con la ayuda de Dios, nosotros entraremos poderosamente contra vosotros, y os haremos guerra por todas las partes y maneras que pudiéramos, y os sujetaremos al yugo y obediencia de la Iglesia y de sus Majestades, y tomaremos vuestras personas y de vuestras mujeres e hijos y los haremos esclavos, y como tales los venderemos y dispondremos de ellos como sus Majestades mandaren, y os tomaremos vuestros bienes, y os haremos todos los males y daños que pudiéramos, como a vasallos que no obedecen ni quieren recibir a su señor y le resisten y contradicen; y protestamos que las muertes y daños que de ello se siguiesen sea a vuestra culpa y no de sus Majestades, ni nuestra, ni de estos caballeros que con nosotros vienen; y de como lo decimos y requerimos pedimos al presente escribano que nos lo dé por testimonio signado, y a los presentes rogamos que de ello sean testigos». _(N. del E.)_
* «En el Nilo, lo encuentro de nuevo, / Egipto brilla con el fuego de su aurora; / su astro imperial se alza sobre Oriente.
»Vencedor, entusiasta, resplandeciente de prestigio, / prodigioso, asombró a la tierra de los prodigios. / Los viejos sheijs veneraban al emir joven y prudente; / el pueblo temía sus armas inauditas; / sublime, apareció ante las tribus maravilladas / como un Mahoma de Occidente.»
* Trad. cast., _Mi peregrinación de Medina a La Meca_ , 3 vols., Laertes, Barcelona, 1989-1993.
* «Los héroes, vuestros padres, han llegado hasta aquí, / sed firmes como aquellos intrépidos; / como ellos, combatís al pie de las pirámides, / y como a ellos, cuatro mil años os contemplan.
»¡Sí! Es por el universo. Por Asia y por Europa, / por esos paisajes lejanos que envuelve la noche, / por el chino pérfido y el indio semidesnudo; / por los pueblos dichosos, libres, humanos y bravos; / por los pueblos malvados, por los pueblos esclavos. / Por aquellos a los que Cristo les es aún desconocido.»
* Trad. cast., _Cándido_ , Edaf, Madrid, 1994.
* Trad. cast., _El alma romántica y el sueño_ , Fondo de Cultura Económica, Madrid, 1978.
* Trad. cast., _El talismán_ , Anaya, Madrid, 1996.
* Organización del Tratado del Sudeste Asiático (1954-1977), creada por Estados Unidos con sede en Bangkok, de la que formaban parte todos los estados no comunistas de la región. Sus funciones eran similares a las de la OTAN en Europa. _(N. del E.)_
* Del nombre de un personaje del _Cándido_ de Voltaire, personificación del optimismo absurdo e irracional. _(N. del E.)_
* Trad. cast., _Bouvard y Pécuchet_ , Montesinos, Barcelona, 1993.
* «Un libro agradable y beneficioso para el alumno estudioso; / reúne fragmentos de poesía y prosa.»
* Trad. cast., _El porvenir de la ciencia_ , Doncel, Madrid, 1976. Está agotado.
* Trad. cast., _La piel de zapa_ , Siruela, Madrid, 1989.
* Nombre que daba Goethe al esfuerzo fisiológico que hace todo organismo para mantener su forma original. _(N. del E.)_
* Trad. cast., _Vida de Jesús_ , Edaf, Madrid, 1987.
* Personaje de _La tempestad_ de Shakespeare, que representa al salvaje, aparentemente pérfido, pero bueno en el fondo. _(N. del E.)_
* Trad. cast., _Historia de los musulmanes en España_ , Turner, Madrid, 1984.
* «¿Debe esta tortura atormentarnos / porque aumenta nuestro placer? / ¿Acaso la ley de Timur / no ha devorado sin medida a las almas?»
* Trad. cast., _Tom Jones_ , Cátedra, Madrid, 1997.
* «Norte, Oeste y Sur desintegrados, / tronos quebrados, los imperios temblorosos. / Vuela hacia el Oriente puro, / respira el aire de los patriarcas.»
* «Allí, en la pureza y la justicia, retorno a los orígenes profundos de la raza humana.»
* «¡De Dios es Oriente! / ¡De Dios es Occidente! / Las tierras del Norte y del Sur / reposan en la paz de Sus manos.»
* Trad. cast., _De París a Jerusalén_ , Laertes, Barcelona, 1982.
* Trads. cast., _Atala_ y _René_ , Cátedra, Madrid, 1989; _El genio del cristianismo_ , Sopena, Barcelona, 1977.
* Trad. cast., _Las hijas del fuego_ , Cátedra, Madrid, 1990.
* _Viaje al oriente: relatos_ , Valdemar, Madrid, 1998.
* Trad. cast., _La carne, la muerte y el diablo en la literatura romántica_ , Acantilado, Barcelona, 1999. Obra originalmente escrita en italiano.
* Trad. cast., _Viaje sentimental_ , Bruguera, Barcelona, 1970.
* Trad. cast., _Las quimeras y otros poemas_ , Alberto Corazón, Madrid, 1974.
* Trads. cast., _Viaje a Oriente_ , Cátedra, Madrid, 1993; _La tentación de san Antonio_ , Siruela, Madrid, 1989; _Herodías_ , Valdemar, Madrid, 2000.
* Trad. cast., _Diccionario de lugares comunes_ , Canarias, Santa Cruz de Tenerife, 1997.
* Trad. cast., _Victoria_ , Ediciones B, Barcelona, 1987.
* Trad. cast., _La educación sentimental_ , Alianza, Madrid, 1995.
* Existe una trad. cast. completa y muy difícil de encontrar: _Ensayo sobre la desigualdad de las razas humanas_ , Apolo, Barcelona, 1937. _(N. del E.)_
* Trad. cast., _La decadencia de Occidente_ , 2 vols., Planeta-De Agostini, Barcelona.
* Trad. cast., _El corazón de las tinieblas_ , Alianza, Madrid, 1997. El capitán de barco Marlow es uno de sus protagonistas. _(N. del E.)_
* Trad. cast., _Kim_ , Alianza, Madrid, 1996.
* Trad. cast., _Los siete pilares de la sabiduría_ , Libertarias-Prodhufi, Barcelona, 1997.
* Trad. cast., _Pasaje a la India_ , Alianza, Madrid, 1985.
* Trad. cast., _Mimesis_ , Fondo de Cultura Económica, Madrid, 1983.
* La edición original francesa, _Islam et capitalisme_ está publicado por Le Seuil, París, 1966. Trad. cast., _Islam y capitalismo_ , Siglo XXI, México, 1973.
* Trad. cast., _Los protocolos de los sabios de Sión_ (existe una edición de fines de los años treinta, traducida por el duque de la Victoria, así como algunas posteriores, en general en editoriales de ultraderecha). El historiador Norman Cohen demostró que esta obra fue una falsificación de la policía secreta zarista de principios del siglo XX. _(N. del E.)_
* Dado que esta obra se terminó en 1977, el autor se refiere a la primera fase de la guerra civil libanesa que comenzó en 1975. _(N. del E.)_
* Trad. cat., Eric Hobsbawm y Terence Rangers, _Invent de la tradició_ , Eumo, Vic, 1989.
* Trad. cast., Martin Bernal, _Atenea negra_ , Crítica, Barcelona, 1993.
* Trad. cast., _Cultura e imperialismo_ , Anagrama, Barcelona, 1996.
* Trad. cast., _Los hijos de la medianoche_ , Alfaguara, Madrid, 1989.
**Edward W. Said** (1935-2003) nació en Jerusalén y pasó parte de su juventud en el Líbano y El Cairo. Se educó en el Victoria College de El Cairo, en el Mount Hermon School de Massachusetts y en las universidades de Princeton y Harvard. En esta última ejerció la docencia durante breves períodos, así como en las universidades de Yale y Johns Hopkins, pero fue en la Universidad de Columbia donde desarrolló casi toda su carrera investigadora como catedrático de literatura inglesa y comparada. Su actividad como pensador se extendió a la literatura, la política, la música, la filosofía y la historia. Colaboró asiduamente en las publicaciones _The Nation_ , _The Guardian_ , _London Review of Books_ , _Le Monde Diplomatique_ , _Counterpunch_ y _Al-Ahram_. En 2002 recibió, junto con Daniel Barenboim, el Premio Príncipe de Asturias a la Concordia por su aportación al acercamiento entre jóvenes talentos árabes e israelíes.
Entre su numerosa e importante producción destacan _Cultura e imperialismo_ y las siguientes tres obras, publicadas por Debolsillo: _Orientalismo_ , un clásico entre los estudios culturales y literarios, _Nuevas crónicas palestinas_ y las memorias _Fuera de lugar_ , con las que obtuvo el premio New Yorker al mejor libro de ensayo de 1999. Edward W. Said falleció en Nueva York en septiembre de 2003.
Título original: _Orientalism_
Edición en formato digital: mayo de 2013
© 1997, Edward W. Said
© 2002, Edward W. Said, por el prólogo a la nueva edición española
© 2002, Juan Goytisolo por la presentación
© 2013, Random House Mondadori, S. A.
Travessera de Gràcia, 47-49. 08021 Barcelona
© 1990, M.ª Luisa Fuentes, por la traducción
Traducción cedida por Ediciones Libertarias / Prodhufi, S. A.
© 2002, Enrique Benito, por la traducción del epílogo
© 2002, Cristóbal Pera, por la traducción del prólogo a la nueva Edición española
Diseño de portada: Penguin Random House Grupo Editorial
Ilustración de portada: _Askelon_ , Palestina (1839). Acuarela de David Roberts. © Corbis / Cover
Quedan prohibidos, dentro de los límites establecidos en la ley y bajo los apercibimientos legalmente previstos, la reproducción total o parcial de esta obra por cualquier medio o procedimiento, así como el alquiler o cualquier otra forma de cesión de la obra sin la autorización previa y por escrito de los titulares del copyright. Diríjase a CEDRO (Centro Español de Derechos Reprográficos, http://www.cedro.org) si necesita reproducir algún fragmento de esta obra.
ISBN: 978-84-9992-328-4
Conversión a formato digital: Newcomlab, S.L.
www.megustaleer.com
Índice
Orientalismo
Prólogo a la nueva edición española
Presentación: Un intelectual libre, _por Juan Goytisolo_
Introducción
PRIMERA PARTE. El ámbito del orientalismo
I. Conocer lo oriental
II. La geografía imaginaria y sus representaciones: orientalizar lo oriental
III. Proyectos
IV. Crisis
SEGUNDA PARTE. Estructuras y reestructuras del orientalismo
I. Fronteras trazadas de nuevo, temas redefinidos, religión secularizada
II. Silvestre de Sacy y Ernest Renan: la antropología racional y el laboratorio filológico
III. El estudio y la experiencia de Oriente: los requisitos de la lexicografía y la imaginación
IV. Peregrinos y peregrinaciones: británicos y franceses
TERCERA PARTE. El orientalismo en nuestros días
I. Orientalismo latente y orientalismo manifiesto
II. El estilo, la competencia y la visión del experto: el orientalismo en el mundo
III. El orientalismo anglo-francés moderno en plena expansión
IV. La fase reciente
Epílogo de la edición de 1995
Agradecimientos
Notas
Biografía
Créditos
|
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| 4,031
|
Rash of Burglaries Has Quiet San Jose Neighborhood on Edge
By Damian Trujillo • Published at 7:02 pm on August 3, 2017
People in what has long been considered one of San Jose's safest neighborhoods say they're now sleeping with one eye open.
Burglars have been descending on an area along the outskirts of Willow Glen, and in at least one case in the early morning hours, a homeowner said would-be thieves knocked on the window of his young daughter.
That family wasn't the only one victimized in the neighborhood. Others say it's been a couple of sleepless nights.
Super Bowl 13 mins ago
Super Bowl 10 hours ago
49ers Will Wear White Jerseys, Gold Pants vs. Chiefs in Super Bowl 54
"I went to sleep, and my truck wasn't there," resident Greg Baker said. "It was locked. I woke up about 4:30."
A jaguar also was stolen from the neighborhood around the same time.
Grainy surveillance video from Baker's neighbor shows what is believed to be a car driven by the suspects. Neighbors say they're looking out for each other, and the area is plastered with warning signs.
"We're on Nextdoor, so everybody is conversing with each other, and a lot of people are home and just kind of watching out for each other," neighbor Kristin Calhoun said. "Best you can do."
Baker added: "It's scary to think that this neighborhood is like this. I've lived here 22 years, and the last 4-5 years, its been crazy."
Police responded almost immediately early Wednesday morning, and neighbors said they've noticed increased patrols. They said they'll be ready in case the burglars return.
|
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"redpajama_set_name": "RedPajamaCommonCrawl"
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| 5,419
|
This rhyme is a fun way to learn names of the students in your classes.
You can also practise beat with this rhyme.
Dumplins Learn names, teach 're' and practise syncopa all with this traditional Caribbean song!
Telephone Song (Hey Charlie) A great way to learn names, this song also encourages individual singing.
|
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"redpajama_set_name": "RedPajamaC4"
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| 8,791
|
a {
color: var(--active-text-color);
}
.active-text {
color: var(--active-text-color);
cursor: pointer;
font-size: 14px;
font-weight: normal;
}
.duration {
color: var(--light-text-color);
background-color: var(--light-active-color);
display: inline-block;
padding: 0.25em 0.4em;
font-size: 75%;
font-weight: 500;
line-height: 13px;
text-align: center;
white-space: nowrap;
vertical-align: bottom;
border-radius: 0.25rem;
margin-bottom: 3px;
width: 35px;
}
.duration.ms {
background-color: var(--light-background-color-1);
}
.duration.s {
background-color: var(--light-background-color-2);
}
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background-color: var(--light-background-color-3);
}
.duration.h {
background-color: var(--light-background-color-4);
}
.duration.d {
color: white;
background-color: var(--active-color);
}
input[type='checkbox'] {
transform: translateY(1px);
}
mwc-icon {
/* The icon font can take a while to load.
* Set a default size to reduce page shifting.
*/
width: var(--mdc-icon-size, 24px);
height: var(--mdc-icon-size, 24px);
}
hr {
background-color: var(--divider-color);
border: none;
height: 1px;
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|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 9,700
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Q: NavigationService.Navigate neither navigates nor throws any exception I have a NavigationService.Navigate() call inside,
void MainPage_Loaded(object sender, RoutedEventArgs e)
{
if (!IsoStoreSettings.ContainsKey("accesstoken") || !(IsoStoreSettings.ReadKey<DateTime>("tokenexpiry") > DateTime.Now))
{
NavigationService.Navigate(new Uri("/signin.xaml", UriKind.Relative));
}
}
However, this doesn't navigate to signin.xaml. But, the OnNavigatedTo() event is getting called twice. What am I doing wrong? I also added Facebook SDK to the project.
I also have RootFrame.UriMapper = new FacebookUriMapper(); in App.xaml.cs
Update
This has something to do with the version of Facebook and Facebook.Client that I used. There are some incompatibilities between latest alpha packages.
A: Windows phone 8.1 does not support
NavigationService.Navigate(new Uri("/signin.xaml", UriKind.Relative));
instead of this you can use
Frame.Navigate(typeof(signin));
this method will navigate to signin page
A: The file FacebookUriMapper in the Facebook.Client SDK has a bug. When looking via debugger, it doesn't redirect to the target page, but switches back to the default RedirectUri in Facebook.xml. Clone the repository in your computer, open the WP8 solution, restore required Nuget packages. Now, open FacebookUriMapper.cs file, modify the last else block to return uri. Build and use this as your referenced assembly. NavigationService works absolutely fine after this.
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 3,635
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Sagay (Camiguin), une municipalité des Philippines
Sagay (Negros occidental), une municipalité des Philippines
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 7,336
|
\section{Introduction and main results}\label{intro}
Recently, there has been much progress in describing the complexity
of various relations between subspaces of a given separable Banach space.
The reader is referred to \cite{FG, FLRo, FRo} for the known results on
the relations of isomorphism, biembeddability, and more.
Isometry and local equivalence (finite representability) are handled
in \cite{Me} and \cite{GJS}, respectively.
In this paper, we consider an operator space analogue of this problem
(see Section~\ref{op_sp} for a brief introduction into operator spaces).
The Effros-Borel structure on the set
$\mathbf{S}(Z)$ of infinite-dimensional subspaces of a separable operator space $Z$
is defined in the same way as for Banach spaces, see e.g.~Chapter 12 of \cite{Ke},
or \cite{FRo}. Reasoning as in Section 2 of \cite{FRo}, we show that the
relations
of complete isomorphism, complete biembeddability, and such,
defined on $\mathbf{S}(Z)$, are analytic equivalence relations.
How ``simple'' can these relations get, without being trivial?
The main result of this paper provides a partial answer to this question.
\begin{theorem}\label{intro:Ksigma}
There exists a family $\boldsymbol{\mathfrak{F}}$ of operator spaces, such that, for any
operator space $X \in \boldsymbol{\mathfrak{F}}$, the following is true:
\begin{enumerate}
\item
$X$ is isometric to $\ell_2$.
\item
The relation of complete isomorphism and complete biembeddability
on $\mathbf{S}(X)$ are
Borel bireducible to the complete ${\mathbf{K}}_\sigma$ relation.
\end{enumerate}
The family $\boldsymbol{\mathfrak{F}}$ contains a continuum of operator spaces,
not completely isomorphic to each other.
\end{theorem}
It is possible to prove that
the relation of complete isometry on $\mathbf{S}(X)$ ($X \in \boldsymbol{\mathfrak{F}}$)
is Borel bireducible to the equality on $\mathbb R$. The proof proceeds along the
same lines as Theorem~\ref{bireducible}, but is exceedingly technical,
and not very illuminating. We therefore omit it, and present
a related Theorem~\ref{intro:banach} instead.
Each space from $\boldsymbol{\mathfrak{F}}$ has its {\it canonical basis} (defined in
Section~\ref{sequences}), which is $1$-completely unconditional.
It turns out these bases have interesting properties of their own.
\begin{theorem}\label{intro:unique_basis}
Any subspace $Y$ of an operator space $X$ from the family $\boldsymbol{\mathfrak{F}}$
has $1$-completely unconditional canonical basis.
Any $C$-completely unconditional basis in such a $Y$
is $\phi(C)$-equivalent (up to a permutation) to the
canonical basis of $Y$, with $\phi(C)$ polynomial in $C$.
\end{theorem}
For certain spaces $X$, a stronger result holds.
\begin{theorem}\label{intro:subbasis}
For any $a > 1$ there exists an operator space $X$,
belonging to the family $\boldsymbol{\mathfrak{F}}$,
such that the canonical basis in any subspace of $X$ is
$a$-equivalent to a subsequence of the canonical basis of $X$.
Consequently, every $C$-completely unconditional basic sequence in
$X$ is $\phi(C)$-equivalent (up to a permutation) to a subsequence of the
canonical basis, with $\phi(C)$ polynomial in $C$.
\end{theorem}
As part of our motivation lies in the field of Banach spaces, we mention
a few classical results related to the three theorems above.
No ``commutative'' counterpart of Theorem~\ref{intro:Ksigma}
has yet been obtained:
for a Banach space $E$, very little is known about the ``upper''
estimates on the complexity of the isomorphism relation on $\mathbf{S}(E)$.
It is possible that the relation of isomorphism on $\mathbf{S}(E)$
is complete analytic whenever $E$ is a separable Banach space,
not isomorphic to $\ell_2$.
Theorem~\ref{intro:unique_basis} shows (among other things)
that every subspace of $X$ has an unconditional basis.
One can raise a related question:
suppose every infinite dimensional subspace of a separable
Banach space $E$ has an unconditional basis.
Must $E$ be isomorphic to $\ell_2$? The answer to this question
appears to be unknown. We mention a few partial results. First,
any subspace of $E$ has the Approximation Property,
therefore, by \cite[Theorem 1.g.6]{LT2}, $E$ has to have type $2 - \varepsilon$ and
cotype $2 + \varepsilon$ for any $\varepsilon > 0$. Furthermore, by \cite[Theorem 10.13]{PiVOL},
$E$ has weak cotype $2$. By \cite{KT95}, $E$ is $\ell_2$-saturated.
Finally, if $E = \ell_2(F)$ for some Banach space $F$, then
$E$ is isomorphic to a Hilbert space \cite{KT02}.
Searching for a ``commutative'' analogues of Theorem~\ref{intro:subbasis},
we pose the following question: suppose a Banach space $E$ has
an unconditional basis $(e_i)$, such that every subspace of $E$ has
an unconditional basis, equivalent to a subsequence of $(e_i)$. Must
$E$ be isomorphic to $\ell_2$?
Finally, in the Banach space setting, we construct a space $E$
whose subspace structure is ``very simple.''
\begin{theorem}\label{intro:banach}
The following equivalence relations between infinite dimensional subspaces of
$\mathbb R \oplus_1 \ell_2$ (or, in the complex case, ${\mathbb C} \oplus_1 \ell_2$)
are Borel bireducible to $(\mathbb R,=)$: (i) isometry,
(ii) having Banach-Mazur distance $1$;
(iii) isometric bi-embeddability; (iv) almost isometric bi-embeddability.
\end{theorem}
Recall that the Banach-Mazur distance between $Y$ and $Z$ is defined as
$d(Y,Z) = \inf \{ \|u\| \|u^{-1}\| : u \in B(Y,Z) \}$.
$Y$ is called {\it almost isometrically embeddable} into $Z$
if for every $\varepsilon > 0$ there exists $Y_\varepsilon \hookrightarrow Z$ s.t. $d(Y,Y_\varepsilon) < 1+\varepsilon$
($d(\cdot , \cdot)$ denotes the Banach-Mazur distance between spaces).
The rest of the paper is organized as follows: Section~\ref{op_sp}
provides a brief introduction into operator spaces and c.b.~maps.
In Section~\ref{construct} we construct, for each contraction
$A \in B(\ell_2)$, a subspace $X(A)$ of $\mathbf{R} \oplus \mathbf{C}$,
and study the properties of the spaces $X(A)$. Further investigation is
carried out in Section~\ref{sequences}, where we concentrate on
the case when $A$ is compact. Unconditional bases
in the spaces $X(A)$ are described in Section~\ref{bases}.
In Section~\ref{classification} we show that, for the ``right''
compact contractions $A$, the relations of complete isomorphism and
complete biembeddability on $\mathbf{S}(X(A))$ are Borel bireducible
to the complete ${\mathbf{K}}_\sigma$ relation.
Having gathered all the preliminary results, we prove Theorems
\ref{intro:Ksigma}, \ref{intro:unique_basis}, and \ref{intro:subbasis} in
Section~\ref{main_proofs}.
Finally, in Section~\ref{banach} we
prove Theorem~\ref{intro:banach}.
\section{Introduction into operator spaces}\label{op_sp}
As our paper deals primarily with operator spaces, we are compelled to
recall some basic definitions and facts about the topic. An interested
reader is referred to \cite{ER, Pa, PiINTRO} for more information.
A ({\it concrete}) {\it operator space} $X$ is, for us, just a closed
subspace of $B(H)$ ($H$ is a Hilbert space). If $X$ and $Y$ are operator spaces, embedded into $B(H)$ and $B(K)$ respectively, we defined the {\it minimal tensor
product} of $X$ and $Y$ (denoted simply by $X \otimes Y$) as the
closure of the algebraic tensor product $X \odot Y$ in $B(H \otimes_2 K)$.
It is common to denote $M_n \otimes X$ by $M_n(X)$. Here, $M_n = B(\ell_2^n)$
is the space of $n \times n$ matrices. We view $M_n(X)$ as the space
of $X$-valued $n \times n$ matrices, with the norm $\| \cdot \|_n$.
It is easy to see that the sequence of {\it matricial norms} $\| \cdot \|_n$
satisfies two properties ({\it Ruan's axioms}): (i) for any $v \in M_n(X)$,
$\alpha \in M_{n,k}$, and $\beta \in M_{k,n}$,
$\|(\beta \otimes I_X) v (\alpha \otimes I_X)\|_k \leq
\|\beta\| \|x\|_n \|\alpha\|$, and (ii) for any $v \in M_n(X)$ and
$w \in M_k(X)\|$, $\|v \oplus w\|_{k+n} = \max\{\|v\|_n, \|w\|_k\}$.
It turns out that the converse is also true. Suppose $X$ is a
{\it matricially normed space} -- that is, it is a Banach space, for which
the spaces $M_n(X)$ of $n \times n$ $X$-valued matrices are equipped
with the norms $\| \cdot \|_n$, satisfying (i) and (ii) above. Then
the norms $\| \cdot \|_n$ arise from an isometric embedding of $X$ into
$B(H)$, for some Hilbert space $H$. The spaces $X$ as above are sometimes called
{\it abstract operator spaces}.
It is easy to see that a subspace of an operator space is, again, an
operator space (we use the notation $\hookrightarrow$ to denote one operator space
being a subspace of another). Moreover, a quotient and the dual of
an operator space can be again equipped with an operator space structure.
Once again, the reader is referred to \cite{ER, Pa, PiINTRO} for details.
A map $u$ from an operator space $X$ to an operator space $Y$ is called
{\it completely bounded} ({\it c.b.} for short) if its {\it c.b.~norm}
$$
\|u\|_{cb} = \sup_n \|I_{M_n} \otimes u\|_{B(M_n(X), M_n(Y))} =
\|I_{B(\ell_2)} \otimes u\|_{B(B(\ell_2) \otimes X, B(\ell_2) \otimes Y)}
$$
is finite. The set of all c.b.~maps from $X$ to $Y$ is denoted by $CB(X,Y)$. Clearly, $\|u\|_{cb} \geq \|u\|$, and $CB(X,Y) \subset B(X,Y)$
(the inclusion may be strict). The operator spaces $X$ and $Y$ are called
{\it completely isomorphic} ({\it completely isometric})
if there exists $u \in CB(X,Y)$ such that $u^{-1}$ is c.b.
(resp. $\|u\|_{cb} = \|u^{-1}\|_{cb} = 1$).
We shall use the notation $\simeq$
for complete isomorphism.
Moreover, we say that $X$ is {\it $c$-completely isomorphic to $Y$}
($X \coi{c} Y$) if there exists $u \in CB(X,Y)$ with
$\|u\|_{cb} \|u^{-1}\|_{cb} \leq c$.
Complete embeddability and biembeddability are defined in the obvious way.
Suppose the operator space s $X$ and $Y$ are embedded into $B(H)$ and $B(K)$,
respectively. We define the {\it direct sum} of operator spaces $X$ and $Y$ (denoted by $X \oplus_\infty Y$, or simply $X \oplus Y$) by viewing $X \oplus Y$
as embedded into $B(H \oplus_2 K)$. Note that any $u \in M_n(X \oplus Y)$
has a unique expansion as $v \oplus w$, with $v \in M_n(X)$ and $w \in M_n(Y)$.
Then $\|u\| = \max\{\|v\|, \|w\|\}$.
Throughout this paper, we work with the row and column spaces. Recall that
a Hilbert space $H$ can be equipped with {\it row} and {\it column}
operator space structure, denoted by $H_\mathbf{R}$ and $H_\mathbf{C}$, respectively.
The space $H_\mathbf{R}$ is defined as the linear space of operators
$\xi \otimes \xi_0$, where $\xi_0$ is a fixed unit vector, and $\xi$
runs over $H$. Here, for $\xi \in H$ and $\eta \in K$, $\xi \otimes \eta$
denotes the operator in $B(H,K)$, defined by
$(\xi \otimes \eta)\zeta = \langle \zeta, \xi \rangle \eta$.
Similarly, the space $H_\mathbf{C}$ is defined as the space of operators
$\xi_0 \otimes \xi$ ($\xi \in H$).
It is easy to see that, if $K$ is a subspace of $H$, then
$K_\mathbf{C}$ ($K_\mathbf{R}$) is a subspace of $H_\mathbf{C}$ (resp.~$H_\mathbf{R}$).
For simplicity of notation, we write denoted by $\mathbf{R}$ and $\mathbf{C}$,
instead of $(\ell_2)_\mathbf{R}$ and $(\ell_2)_\mathbf{C}$, respectively.
One can use matrix units to describe these spaces. We denote by
$E_{ij} \in B(\ell_2)$ the infinite matrix with $1$ on the intersection
of the $i$-th row and the $j$-th column, and zeroes elsewhere.
Then $\mathbf{R}$ ($\mathbf{C}$) is the closed linear span of $(E_{1j})_{j=1}^\infty$ (respectively, $(E_{i1})_{i=1}^\infty)$).
Below we list a few useful properties of row and column spaces. Here, $H$
and $K$ are Hilbert spaces.
\begin{enumerate}
\item
$H_\mathbf{R}$ and $H_\mathbf{C}$ are isometric to $H$ (as Banach spaces).
\item
For any $u \in B(H,K)$,
$\|u\| = \|u\|_{CB(H_\mathbf{R},K_\mathbf{R})} = \|u\|_{CB(H_\mathbf{C},K_\mathbf{C})}$.
\item
If $(\xi_i)$ is an orthonormal system in $H$, then,
for any finite sequence $(a_i)$ of elements of $M_n$,
$$
\begin{array}{lllll}
\|\sum_i a_i \otimes \xi_i\|_{M_n(H_\mathbf{R})} & = &
\|(\sum_i a_i a_i^*)^{1/2}\| & = & \|\sum_i a_i a_i^*\|^{1/2} ,
\cr
\|\sum_i a_j \otimes \xi_i\|_{M_n(H_\mathbf{C})} & = &
\|(\sum_i a_i^* a_i)^{1/2}\| & = & \|\sum_i a_i^* a_i\|^{1/2} .
\end{array}
$$
\item
Suppose $H^{(1)}, \ldots, H^{(n)}$ are Hilbert spaces. Then the
formal identity map $id : (H^{(1)} \oplus_2 \ldots \oplus_2 H^{(n)})_\mathbf{R}
\to H^{(1)}_\mathbf{R} \oplus \ldots \oplus H^{(n)}_\mathbf{R}$ is a complete
contraction, and $\|id^{-1}\|_{cb} \leq \sqrt{n}$.
The same is also true for column spaces.
\item
For any $u \in CB(H_\mathbf{R}, K_\mathbf{C})$ or $u \in CB(H_\mathbf{C}, K_\mathbf{R})$,
$\|u\|_2 = \|u\|_{cb}$ (here, $\| \cdot \|_2$ is the Hilbert-Schmidt norm).
\item
Duality: $H_\mathbf{R}^* = H_\mathbf{C}$, and $H_\mathbf{C}^* = H_\mathbf{R}$.
\item
For any operator space $X$
and any $u \in B(X, H_\mathbf{C})$ ($u \in B(X, H_\mathbf{R})$),
$\|u\|_{cb} = \|I_\mathbf{C} \otimes u\|_{B(\mathbf{C} \otimes X, \mathbf{C} \otimes H_\mathbf{C})}$
(resp.
$\|u\|_{cb} = \|I_\mathbf{R} \otimes u\|_{B(\mathbf{R} \otimes X, \mathbf{R} \otimes H_\mathbf{R})}$).
This result follows from the proof of Smith's lemma --
see e.g. Proposition 2.2.2 of \cite{ER}.
\item
If $H$ is separable infinite dimensional, then $H_\mathbf{R}$
($H_\mathbf{C}$) is completely isometric to $\mathbf{R}$ (resp.~$\mathbf{C}$).
\end{enumerate}
A sequence $(x_i)_{i \in I}$ in an operator space $X$ is called
{\it normalized} if $\|x_i\| = 1$ for every $i \in I$. $(x_i)$ is
said to be a {\it $c$-completely unconditional basic sequence} ($c \geq 1$)
if, for any finite sequence of matrices $(a_i)$, and any sequence of scalars
$\lambda_i \in \{ \lambda \in {\mathbb C} : |\lambda| \leq 1\}$,
we have $\|\sum_i \lambda_i a_i \otimes x_i\|_{M_n(X)} \leq
c \|\sum_i a_i \otimes x_i\|_{M_n(X)}$. It is easy to see that any
such sequence $(x_i)$ is linearly independent.
A $c$-completely unconditional basic sequence $(x_i) \subset X$
is called a {\it $c$-completely unconditional basis} in $X$
if $X = \span[x_i : i \in I]$ (here and below, $\span[{\mathcal{F}}]$
refers to the closed linear span of the family ${\mathcal{F}}$).
A convenient example of a normalized $1$-completely unconditional basis is
provided by an orthonormal basis in $\mathbf{R}$ or $\mathbf{C}$. For future reference,
we observe that any completely unconditional basis is ``similar to''
an orthogonal one. More precisely, suppose $X$ is an operator space,
which is isometric to a Hilbert space (this is the setting we are
concerned with in this paper). Suppose, furthermore, that $(x_i)$ is a
normalized $c$-completely unconditional basis in
an operator space $X$, isometric to a Hilbert space,
then $(x_i)$ is ``similar to'' an orthonormal basis:
for any finite sequence of scalars $(\alpha_i)$,
$$
c^2 \|\sum_i \alpha_i x_i\|^2 \geq
{\mathrm{Ave}}_\pm \|\sum_i \pm \alpha_i x_i\|^2 =
\sum_i |\alpha_i|^2 ,
$$
and similarly,
$c^{-2} \|\sum_i \alpha_i x_i\|^2 \leq \sum_i |\alpha_i|^2$.
Thus, there exists an $U : X \to \ell_2(I)$, s.t. $(U x_i)_{i \in I}$
is an orthonormal basis, and $\|U\|, \|U^{-1}\| \leq c$.
Families $(x_i)_{i \in I}$ and $(y_i)_{i \in I}$ in operator spaces
$X$ and $Y$, respectively, are called {\it $c$-equivalent} if there exists
a map $u : \span[x_i : i \in I] \to \span[y_i : i \in I]$, such that
$u x_i = y_i$, and $\|u\|_{cb} \|u^{-1}\|_{cb} \leq c$.
Two sequences are {\it equivalent} if they are $c$-equivalent,
for some $c$. Furthermore, $(x_i)_{i \in I}$ is $c$-equivalent
to a subfamily of $(y_j)_{j \in J}$ if there exists a subset
$I^\prime \subset J$, such that $|I| = |I^\prime|$, and
$(x_i)_{i \in I}$ is $c$-equivalent to $(y_j)_{j \in I^\prime}$.
Finally, $(x_i)_{i \in I}$ is {\it $c$-equivalent to $(y_i)_{i \in I}$
up to a permutation} if there exists a bijection $\pi : I \to I$
such that $(x_i)_{i \in I}$ is $c$-equivalent to $(y_{\pi(i)})_{i \in I}$.
A sequence $(x_i)_{i \in I}$ is called {\it completely unconditional}
if it is $c$-completely unconditional, for some $c$. A completely
unconditional basis, equivalence of sequences etc. are defined by
dropping the $c$, in a similar manner.
\section{Subspaces of $\mathbf{R} \oplus \mathbf{C}$: basic facts}\label{construct}
Suppose $H$ and $K$ are separable Hilbert spaces, and $A \in B(H,K)$
is a contraction. Denote by $X_\mathbf{R}(H,K,A)$ the subspace of
$H_\mathbf{R} \oplus K_\mathbf{C}$, spanned by $(e, Ae)$ ($e \in H$). If there is
no confusion as to the spaces $H$ and $K$, we simply write $X_\mathbf{R}(A)$. $X_\mathbf{C}(A)$ is defined in the same way.
Often, we write $X(A)$ ($X(H,K,A)$) instead of $X_\mathbf{R}(A)$ ($X_\mathbf{R}(H,K,A)$).
Note that the formal identity map
$id : H \to X(H,K,A) : \xi \mapsto \xi \oplus A \xi$ is an isometry.
Thus, we identify subspaces of $X(H,K,A)$ with those of $H$.
This identification gives meaning to the notation $A|_Y$, where
$Y \hookrightarrow X(A)$.
\begin{remark}\label{connections}
Although the spaces $\mathbf{R}$ and $\mathbf{C}$ are ``simple'', the structure of
their direct sum $\mathbf{R} \oplus C$ is rather rich.
For instance, it was shown in \cite{Xu} that the ``operator Hilbert space''
$OH$ is a subspace of a quotient of $\mathbf{R} \oplus \mathbf{C}$
(actually, the results of that paper are much more general).
It follows from \cite{Xu} that the spaces $X(A)$ ($A \in B(\ell_2)$)
defined as above are natural ``building blocks'' of subspaces of
$\mathbf{R} \oplus \mathbf{C}$.
\end{remark}
Begin by stating a simple lemma.
\begin{lemma}\label{simple_X(A)}
Suppose $H$, $K$, and $K^\prime$ are Hilbert spaces, and $A \in B(H,K)$
is a contraction.
\begin{enumerate}
\item
Suppose $U \in B(K,K^\prime)$ is such that $\|U \xi\| = \|\xi\|$ for
any $\xi \in {\mathrm{ran}} \, A$. Then $X(H,K,A)$ is completely isometric to
$X(H,K^\prime,UA)$. In particular, $X(H,K,A)$ is completely isometric to
$X(H,H,|A|)$, where $|A| = (A^* A)^{1/2}$.
\item
Suppose $P_1, \ldots, P_m$ and $Q_1, \ldots, Q_m$ are families
of orthogonal mutually orthogonal projections on $H$ and $K$,
respectively, such that $\sum_k P_k = I_H$, $\sum_k Q_k = I_K$, and
$A = \sum_{k=1}^m Q_k A P_k$. Set $H_k = P_k(H)$ and $K_k = Q_k(K)$.
Then the formal identity operator $id$ from $X(H,K,A)$ to
$X(H_1,K_1,Q_1AP_1) \oplus \ldots \oplus X(H_m,K_m,Q_mAP_m)$ is
a complete contraction, and $\|id^{-1}\|_{cb} \leq \sqrt{m}$.
\item
$X(A)$ is $|\lambda|^{-1}$-completely isomorphic to $X(\lambda A)$ whenever
$0 < |\lambda| \leq 1$.
\end{enumerate}
\end{lemma}
\begin{proof}
We only establish part (2). A Gram-Schmidt orthogonalization shows that
any element $x \in M_n(H)$ can be written as
$x = x_1 + \ldots + x_n$, with $x_k = \sum_i a_{ki} \otimes \xi_{ki}$
$a_{ki} \in M_n$, and $(\xi_{ki})$ a finite orthonormal systems
in $H_k$. Then
$$
\|x\|_{M_n(X(A))} = \max \big\{
\|\sum_k \sum_i a_{ki} \otimes \xi_{ki}\|_{M_n(H_\mathbf{R})} ,
\|\sum_k \sum_i a_{ki} \otimes A \xi_{ki}\|_{M_n(K_\mathbf{C})} \big\} .
$$
By the basic properties of row and column spaces (listed at the end
of the previous section),
$$
\eqalign{
\max_k \|\sum_i a_{ki} \otimes \xi_{ki}\|_{M_n(H_\mathbf{R})}
&
\leq
\|\sum_{k,i} a_{ki} \otimes \xi_{ki}\|_{M_n(H_\mathbf{R})}
\cr
&
\leq
\sqrt{m} \max_k \|\sum_i a_{ki} \otimes \xi_{ki}\|_{M_n(H_\mathbf{R})} .
}
$$
Furthermore, the vectors $A \xi_{ki}$ belong to the mutually
orthogonal spaces $K_k$, hence
$$
\eqalign{
\max_k \|\sum_i a_{ki} \otimes A \xi_{ki}\|_{M_n(H_\mathbf{C})}
&
\leq
\|\sum_{k,i} a_{ki} \otimes A \xi_{ki}\|_{M_n(H_\mathbf{C})}
\cr
&
\leq
\sqrt{m} \max_k \|\sum_i a_{ki} \otimes A \xi_{ki}\|_{M_n(H_\mathbf{C})} .
}
$$
Note that
$$
\eqalign{
&
\|x_k\|_{M_n(X(H_k, Q_k, Q_kAP_k))}
\cr
&
=
\max\ \{ \|\sum_i a_{ki} \otimes \xi_{ki}\|_{M_n(H_\mathbf{R})} ,
\|\sum_i a_{ki} \otimes A \xi_{ki}\|_{M_n(H_\mathbf{C})} \} .
}
$$
Therefore,
$$
\eqalign{
&
\max_k \|x_k\|_{M_n(X(H_k, Q_k, Q_kAP_k))}
\cr
&
=
\max \{ \max_k \|\sum_i a_{ki} \otimes \xi_{ki}\|_{M_n(H_\mathbf{R})} ,
\max_k \|\sum_i a_{ki} \otimes A \xi_{ki}\|_{M_n(H_\mathbf{C})} \}
\cr
&
\leq \|x\|_{M_n(X(A))}
\cr
&
\leq
\sqrt{m} \max \{ \max_k \|\sum_i a_{ki} \otimes \xi_{ki}\|_{M_n(H_\mathbf{R})} ,
\max_k \|\sum_i a_{ki} \otimes A \xi_{ki}\|_{M_n(H_\mathbf{C})} \} .
}
$$
We complete the proof by noting that
$$
\|x\|_{M_n(X(H_1,K_1,Q_1AP_1) \oplus \ldots \oplus X(H_m,K_m,Q_mAP_m))} =
\max_{1 \leq k \leq m} \|x_k\|_{M_n(X(H_k, Q_k, Q_kAP_k))} .
$$
\end{proof}
Next, we establish our key tool for computing c.b.~norms.
\begin{lemma}\label{compute_norm}
Suppose $A$ and $B$ are contractions, and $T \in B(X(A), X(B))$. Then
$$
\|T\|_{cb} = \max \big\{ \|T\|, \sup \{ \|BTu\|_2 :
u \in B(\ell_2, X(A)) , \, \|Au\|_2 \leq 1 , \, \|u\| \leq 1 \} \big\} .
$$
\end{lemma}
\begin{proof}
By definition,
$\|T\|_{cb} = \max\{\|T\|_{CB(X(A), \mathbf{R})}, \|B T\|_{CB(X(A), \mathbf{C})}\}$.
To estimate the first term, note that $id : X(A) \to \mathbf{R}$
is a complete contraction, hence
$$
\|T\|_{CB(X(A), \mathbf{R})} = \|T \circ id\|_{CB(X(A), \mathbf{R})} \leq
\|T\|_{CB(\mathbf{R}, \mathbf{R})} \|id\|_{CB(X(A), \mathbf{R})} = \|T\| .
$$
However, $\|T\| \leq \|T\|_{CB(X(A), \mathbf{R})}$, hence
$\|T\| = \|T\|_{CB(X(A), \mathbf{R})}$.
Next we estimate $\|B T\|_{CB(X(A), \mathbf{C})}$. We know that
$$
\|B T\|_{CB(X(A), \mathbf{C})} = \sup \big\{
\|(I_\mathbf{C} \otimes BT)(x)\|_{\mathbf{C} \otimes \mathbf{C}} :
x \in \mathbf{C} \otimes X(A) , \, \|x\|_{\mathbf{C} \otimes X(A)} \leq 1 \big\} .
$$
Identifying elements of $\mathbf{C} \otimes X(A)$ and $\mathbf{C} \otimes \mathbf{C}$
with operators from $\mathbf{R}$ to $X(A)$ and $\mathbf{C}$, respectively, we see
that
$$
\|B T\|_{CB(X(A), \mathbf{C})} = \sup \big\{
\|BTu\|_2 : u \in CB(\mathbf{R}, X(A)) , \, \|u\|_{cb} \leq 1 \big\} .
$$
But
$\|u\|_{cb} = \max\{ \|u\|_{CB(\mathbf{R})}, \|Au\|_{CB(\mathbf{R}, \mathbf{C})} \} =
\max\{ \|u\|, \|Au\|_2 \}$.
\end{proof}
Next we examine the exactness of $X(A)^*$.
Recall that an operator space $X$ is called {\it exact} if
there exists $c > 0$ such that, for any finite dimensional
subspace $E$ of $X$, there exists an operator $u$ from $E$ to
a subspace $F$ of $M_n$ ($n \in {\mathbb N}$), such that
$\|u\|_{cb} \|u^{-1}\|_{cb} < c$. The infimum of all the
$c$'s like this is called the {\it exactness constant} of $X$.
It is easy to see that $\mathbf{R} \oplus \mathbf{C}$ is $1$-exact, hence
so is $X(A)$. The case of the dual is different.
\begin{proposition}\label{exact}
Suppose $A \in B(H,K)$ is a contraction. Then
the exactness constant of $X(A)^*$ is at least $2^{-5/2} \|A\|_2$.
In particular, $X(A)^*$ is not exact if $A$ is not Hilbert-Schmidt.
\end{proposition}
\begin{proof}
Let $c = 2^{5/2} {\mathrm{ex}}(X(A)^*)$. By Corollary 0.7 of \cite{PiS},
there exist operators $T_1 : X(A) \to \mathbf{R}$, $T_2 : \mathbf{R} \to X(A)$,
$S_1 : X(A) \to \mathbf{C}$, and $T_2 : \mathbf{C} \to X(A)$, such that
$id = S_2 S_1 + T_2 T_1$ ($id$ is the identity on $X(A)$), and
$$
\|S_1\|_{cb} \|S_2\|_{cb} + \|T_1\|_{cb} \|T_2\|_{cb} \leq
\max \{ \|S_1\|_{cb}, \|T_1\|_{cb} \} (\|S_2\|_{cb} + \|T_2\|_{cb})
\leq c
$$
By Lemma~\ref{compute_norm},
$\|T_2\|_{cb} \geq \|A T_2\|_2$, and a simple calculation yields
$$
\|S_2\|_{cb} \geq \|S_2\|_{CB(\mathbf{C}, \mathbf{R})} = \|S_2\|_2 \geq \|A S_2\|_2 .
$$
Therefore,
$$
\eqalign{
\|S_1\|_{cb} \|S_2\|_{cb} + \|T_1\|_{cb} \|T_2\|_{cb}
&
\geq
\|S_1\| \|A S_2\|_2 + \|T_1\| \|A T_2\|_2
\cr
&
\geq
\|A (S_2 S_1 + T_2 T_1)\|_2 = \|A\|_2 ,
}
$$
which implies the desired estimate for $c$.
\end{proof}
\begin{corollary}\label{ci_to_row}
The space $X(A)$ is completely isomorphic to $\mathbf{R}$ if and only if
$A$ is Hilbert-Schmidt. Furthermore, the formal identity map
$id : \mathbf{R} \to X(A)$ is completely contractive, and
$\|id^{-1}\|_{cb} = \max\{1, \|A\|_2\}$.
\end{corollary}
\begin{proof}
The estimates on the c.b.~norm of $id$ and $id^{-1}$ follow from
Lemma~\ref{compute_norm}. Thus, $X(A) \coi{\max\{1,\|A\|_2\}} \mathbf{R}$
whenever $A$ is Hilbert-Schmidt. On the other hand, if $A$ is not Hilbert-Schmidt,
then, by Proposition~\ref{exact}, $X(A)^*$ is not exact. However,
$\mathbf{R}^* = \mathbf{C}$ is exact, thus $X(A)$ is not completely isomorphic to $\mathbf{R}$.
\end{proof}
We say that $A \in B(H,K)$ ($H$ and $K$ are Hilbert spaces) is
{\it diagonalizable} if the eigenvectors of $|A| = (A^* A)^{1/2}$
span $H$. Equivalently, there exist orthonormal systems $(\xi_i)$
and $(\eta_i)$ in $H$ and $K$, respectively, and a sequence
$(\lambda_i)$ of non-negative numbers, such that
$A = \sum_i \lambda_i \xi_i \otimes \eta_i$.
When working with $X(A)$, it is often convenient to have $A$
diagonalizable. While every compact operator is diagonalizable,
a non-compact one need not have this property. However, we have:
\begin{lemma}\label{diagonal}
Suppose $H$ and $K$ are separable Hilbert spaces, $A \in B(H,K)$ is
a contraction, and $\varepsilon > 0$. Then there exists a diagonalizable contraction
$B \in B(H,K)$ such that $\|A-B\|_2 \leq \varepsilon$, and $X(A)$ is
$(1+\varepsilon)^2$-completely isomorphic to $X(B)$.
If $A$ is non-negative, $B$ can be selected to be non-negative, too.
\end{lemma}
\begin{proof}
By Lemma~\ref{simple_X(A)}(1), it suffices to consider the case of
$A = |A|$, and $H = K$.
By \cite{Vo}, there exists a selfadjoint diagonalizable $C \in B(H)$ such
that $\|A - C\|_2 < \varepsilon/2$. Let $(c_i)$ be the eigenvalues of $C$, and
$(\xi_i)$ the corresponding norm $1$ eigenvectors. Define the operator $B$
by setting $B \xi_i = b_i \xi_i$, where
$$
b_i = \left\{ \begin{array}{ll}
c_i & 0 \leq c_i \leq 1 \cr
0 & c_i < 0 \cr
1 & c_i > 1
\end{array} \right. .
$$
We claim that $\|B - C\|_2 < \varepsilon/2$. Indeed, let
${\mathcal{I}} = \{i : b_i \neq c_i\}$. Then
$$
\|B-C\|_2^2 = \sum_{i \in \mathcal{I}} |b_i - c_i|^2 =
\sum_{i : c_i < 0} |c_i|^2 + \sum_{i : c_i > 1} |b_i|^2 .
$$
But $\langle \xi_i, A \xi_i \rangle \in [0,1]$, hence, for
$c_i < 0$, $|\langle \xi_i, A \xi_i \rangle -
\langle \xi_i, C \xi_i \rangle| \geq |c_i|$. Similarly,
for $c_i > 1$, $|\langle \xi_i, A \xi_i \rangle -
\langle \xi_i, C \xi_i \rangle| \geq |1-c_i|$. Thus,
$$
\frac{\varepsilon^2}{4} > \|A-C\|_2^2 =
\sum_{i,j} |\langle \xi_i, (A-C) \xi_j \rangle|^2 \geq
\sum_i |\langle \xi_i, (A-C) \xi_i \rangle|^2 \geq
\sum_{i \in \mathcal{I}} |b_i - c_i|^2 .
$$
By the triangle inequality, $\|A - B\|_2 < \varepsilon$.
Moreover, $B$ is a non-negative contraction.
Denote the the formal identity map from $X(A)$ to $X(B)$
by $U$. It remains to show that
$\|U\|_{cb}, \|U^{-1}\|_{cb} \leq 1+\varepsilon$.
As $U$ is an isometry, Lemma~\ref{compute_norm} implies
\begin{equation}
\|U\|_{cb} =
\sup \{ \|Bu\|_2 :
u \in B(\ell_2, X(A)) , \, \|Au\|_2 \leq 1 , \, \|u\| \leq 1 \} .
\label{norm_U}
\end{equation}
By the triangle inequality,
$$
\|Bu\|_2 \leq \|Au\|_2 + \|(B-A)u\|_2 \leq
\|Au\|_2 + \|B-A\|_2 \leq 1 + \varepsilon ,
$$
hence \eqref{norm_U} yields $\|U\|_{cb} \leq 1+\varepsilon$.
$\|U^{-1}\|_{cb}$ is estimated similarly.
\end{proof}
\begin{proposition}\label{add_row}
Suppose $H$ and $K$ are separable Hilbert spaces, $B \in B(H,K)$
is a contraction, and $0 \in \sigma_{ess}(|B|)$. Then
$X(B)$ is $4\sqrt{2}$-completely isomorphic to $X(B) \oplus \mathbf{R}$.
\end{proposition}
\begin{proof}
We can assume $B = |B|$. By Lemma~\ref{diagonal}, there exists
a non-negative diagonalizable contraction $A$ such that $A-B$ is
Hilbert-Schmidt, and $X(A) \coi{2^{1/4}} X(B)$.
As the essential spectrum is stable under compact
perturbations, $0 \in \sigma_{ess}(A)$. Write $A = {\mathrm{diag}} \, (\alpha)$,
where $\alpha = (\alpha_i)_{i \in I}$. Then $0$ is a cluster point of
the set $(\alpha_i)$. Denote the norm $1$ eigenvectors, corresponding to
$\alpha_i$, by $\xi_i$. Find $I_0 \subset I$ such that
$\sum_{i \in I_0} \alpha_i^2 < 1$. Let $I_1 = I \backslash I_0$,
and let $P_0$ and $P_1$ be the orthogonal projections onto
$H_0 = \span[\xi_i : i \in I_0]$ and
$H_1 = \span[\xi_i : i \in I_1]$, respectively.
By Lemma~\ref{simple_X(A)}, $X(A)$ is $\sqrt{2}$-completely isomorphic to
$X(H_0, H_0, P_0 A P_0) \oplus X(H_1, H_1, P_1 A P_1)$.
By Corollary~\ref{ci_to_row}, $X(H_0, H_0, P_0 A P_0)$ is
completely isometric to $\mathbf{R}$. Thus,
$$
\eqalign{
&
X(A) \coi{\sqrt{2}} X(H_0, H_0, P_0 A P_0) \oplus X(H_1, H_1, P_1 A P_1)
\cr
&
\coi{\sqrt{2}} \mathbf{R} \oplus X(H_1, H_1, P_1 A P_1)
\coi{\sqrt{2}} \mathbf{R} \oplus \mathbf{R} \oplus X(H_1, H_1, P_1 A P_1)
\cr
&
=
\mathbf{R} \oplus X(H_0, H_0, P_0 A P_0) \oplus X(H_1, H_1, P_1 A P_1)
\coi{\sqrt{2}} \mathbf{R} \oplus X(A) .
}
$$
To summarize, $X(A) \coi{4} X(A) \oplus \mathbf{R}$. As $X(A) \coi{2^{1/4}} X(B)$,
we are done.
\end{proof}
\begin{corollary}\label{inf_ker}
Suppose $H$ and $K$ are separable infinite dimensional Hilbert
spaces, and a contraction $A \in B(H,K)$ satisfies $0 \in \sigma_{ess}(|A|)$.
Consider the operator $\tilde{A} = A \oplus 0$ from
$\tilde{H} = H \oplus_2 \ell_2$ to
$\tilde{K} = K \oplus_2 \ell_2$. Then $X(A) \coi{8} X(\tilde{A})$.
\end{corollary}
\begin{proof}
Let $P$ be the orthogonal projection from $\tilde{H}$ onto $H$.
onto $H$. By Lemma~\ref{simple_X(A)}(2) and Corollary~\ref{ci_to_row},
$X(\tilde{A}) \coi{\sqrt{2}} X(A) \oplus \mathbf{R}$. However, by
Proposition~\ref{add_row}, $X(A) \coi{4\sqrt{2}} X(A) \oplus \mathbf{R}$.
\end{proof}
\section{Classification of subspaces using sequences}\label{sequences}
In this section, we study the spaces $X(A)$ when $A$ is compact, and
establish a connection between such spaces and a certain family of sequences.
We denote by $\boldsymbol{\mathfrak{C}}$ the space of compact contractions $A \in B(\ell_2)$,
which are not Hilbert-Schmidt. We denote by $\boldsymbol{\mathfrak{F}}$ the set of all spaces
$X(A)$, with $A \in \boldsymbol{\mathfrak{C}}$.
Start by defining the canonical basis in $X(A)$, where $A \in B(H,K)$
is a compact contraction. As $X(A) = X(|A|)$, we assume henceforth that
$A = |A|$, and $H = K$.
Let
$(\xi_i)_{i \in I_1}$
be the normalized eigenvectors of $A$, corresponding to the positive
eigenvalues of $A$.
Furthermore, set $H^\prime = {\mathrm{ker}} \, A$, and
let $(\xi_i)_{i \in I_0}$ be an orthonormal basis in $H^\prime$
(we assume that $I_1 \cap I_0 = \emptyset$). Let $I = I_0 \cup I_1$.
The vectors $e_i = \xi_i \oplus A \xi_i \in H_\mathbf{R} \oplus H_\mathbf{C}$
($ i \in I$) span $X(A)$. Moreover, $\|e_i\| = 1$ for each $i$, and,
for any finite sequence $(a_i) \subset M_n$,
\begin{equation}
\|\sum_i a_i \otimes e_i\|_{M_n(X(A))}^2 = \max \Big\{
\big\|\sum_i a_i a_i^*\big\|, \big\|\sum_i \|A \xi_i\|^2 a_i^* a_i\big\| \Big\} .
\label{basis_general}
\end{equation}
We say that the vectors $e_i = e_i[A]$ form the {\it canonical basis}
of $X(A)$.
Now suppose $(\alpha_i)_{i \in {\mathbb N}}$ is a sequence of numbers in $[0,1]$.
In an effort to link operator spaces with certain sequences of scalars,
we define the operator space $X^d(\alpha) = X({\mathrm{diag}} \, (\alpha))$.
To describe the operator space structure of $X^d(\alpha)$, denote by
$(\xi_i)$ the canonical orthonormal basis of $\ell_2$.
Then the vectors
$e_i(\alpha) = e_i = \xi_i \oplus \alpha_i \xi_i \in H_\mathbf{R} \oplus K_\mathbf{C}$
form a $1$-completely unconditional orthonormal basis in $X^d(\alpha)$, with
\begin{equation}
\|\sum_i a_i \otimes e_i\|^2 = \max\{ \|\sum_i a_i a_i^*\| ,
\|\sum_i \alpha_i^2 a_i^* a_i\| \}
\label{basis}
\end{equation}
for any finite sequence of matrices $(a_i)$. We call
$(e_i(\alpha))_{i \in {\mathbb N}}$ the {\it canonical basis} of $X^d(\alpha)$.
The {\it formal identity} from $X^d(\alpha)$ to $X^d(\beta)$ is the
linear operator mapping $e_i(\alpha)$ to $e_i(\beta)$.
If $\alpha = (\alpha_i)_{i=1}^n$ is a finite sequence, we define
the finite dimensional space $X^d(\alpha)$ in the same way.
To reduce ourselves to working with the spaces $X^d(\alpha)$
(and hence to sequences of scalars), define, for a compact
$A \in B(H,K)$, the sequence $\alpha = {\mathbf{D}}(A)$: if $A$ has
rank $n < \infty$, let $\alpha_1 \geq \ldots \geq \alpha_n > 0$ be
the non-zero singular values of $A$, and set $\alpha_i = 0$ for $i > n$.
If the rank of $A$ is infinite, let $(\alpha_i)$ be the singular values
of $A$, listed in the non-increasing order. We have:
\begin{proposition}\label{make_diag}
If $H$ and $K$ are separable infinite dimensional Hilbert spaces,
and $A \in B(H,K)$ is a compact contraction, then $X(A)$
is $2^6$-completely isomorphic to $X^d({\mathbf{D}}(A))$.
\end{proposition}
\begin{proof}
Let $\alpha = (\alpha_i) = {\mathbf{D}}(A)$. By Lemma~\ref{simple_X(A)}(1),
we can assume that $A = |A| = (A^* A)^{1/2}$, and $H = K$.
If $A$ has finite rank, \eqref{basis_general} shows that $X(A)$ is
completely isometric to $X^d(\alpha)$. Otherwise, write
$A = \sum_i \alpha_i \xi_i \otimes \xi_i$, for some orthonormal system
$(\xi_i)_{i=1}^\infty$ in $H$. Let $P$ be the orthogonal projection
onto $K = \span[\xi_i : i \in {\mathbb N}]$. Set $Q = I - P$, and $L = Q(H)$.
By Lemma~\ref{simple_X(A)}(2), $X(A)$ is $\sqrt{2}$-completely isomorphic to
$X(K, K, P A P) \oplus X(L, L, Q A Q)$. Furthermore, $QAQ = 0$, hence
$X(L, L, Q A Q) = L_\mathbf{R}$. It is easy to see that
$X(K, K, P A P) = X^d(\alpha)$. By Proposition~\ref{add_row}, the
latter space is $4\sqrt{2}$-completely isomorphic to
$X^d(\alpha) \oplus \mathbf{R}$. Thus,
$$
\eqalign{
X(A)
&
\coi{\sqrt{2}}
X(K, K, P A P) \oplus X(L, L, Q A Q) \coi{4\sqrt{2}}
X^d(\alpha) \oplus \mathbf{R} \oplus L_\mathbf{R}
\cr
&
\coi{\sqrt{2}}
X^d(\alpha) \oplus (\ell_2 \oplus L)_\mathbf{R} =
X^d(\alpha) \oplus \mathbf{R} \coi{4\sqrt{2}} X^d(\alpha) .
}
$$
\end{proof}
We will also use a related observation.
\begin{lemma}\label{almost_alpha}
For every compact contraction $A \in B(\ell_2)$, and every $\varepsilon > 0$,
there exists $\alpha \in c_0$ such that $X(A) \coi{1+\varepsilon} X^d(\alpha)$.
\end{lemma}
\begin{proof}
Indeed, let $\beta = {\mathbf{D}}(A)$. If $A$ is finite rank, then $X(A)$
is completely isometric to $X^d(\beta)$. If ${\mathrm{rank}} \, A = \infty$, assume
(by Lemma~\ref{simple_X(A)}) that $A = |A|$. Then
$\beta_1 \geq \beta_2 \geq > 0$ is the list of all positive eigenvalues of $A$.
Denote the corresponding norm $1$ eigenvectors by $\xi_i$. Let
$H = \span[\xi_i : i \in {\mathbb N}]$, and $K = {\mathrm{ker}} \, A$. Clearly,
$K$ and $H$ are mutually orthogonal subspaces of $\ell_2$. Let
$(\eta_j)_{j \in J}$ be the orthogonal basis of $K$. Find a
sequence $(\gamma_j)_{j \in J}$ of positive numbers, satisfying
$\sum_{j \in J} \gamma_i^2 < \varepsilon^2$. Consider the compact contraction
$\tilde{A} \in B(\ell_2)$, defined by $\tilde{A} \xi_i = \beta_i \xi_i$,
and $\tilde{A} \eta_j = \gamma_j \eta_j$. Then $\|A - \tilde{A}\|_2 < \varepsilon$.
By \eqref{basis_general}, the formal identity map
$id : X(\tilde{A}) \to X(A)$ is a complete contraction, and
$\|id^{-1}\|_{cb} < 1 + \varepsilon$. We complete the proof by identifying
$X(\tilde{A})$ with the space $X^d(\alpha)$, where the sequence
$\alpha = (\alpha_i)$ is the ``join'' of the sequences $\beta$
and $\gamma$ (that is, any number $c \in [0,1]$ occurs in
$\alpha$ as many times as it occurs in the sequences $\beta$
and $\gamma$ combined).
\end{proof}
Now denote by ${\mathcal{S}}$ the set of all sequences $(\alpha_i)_{i \in {\mathbb N}}$
satisfying $1 \geq \alpha_1 \geq \alpha_2 \geq \ldots \geq 0$, and
$\lim_i \alpha_i = 0$.
The rest of this section is devoted to the spaces $X^d(\alpha)$ ($\alpha \in {\mathcal{S}}$).
We translate the relations between sequences $\alpha, \beta \in {\mathcal{S}}$
to relations between the corresponding spaces $X^d(\alpha)$ and $X^d(\beta)$.
We say that the sequence $\alpha$ {\it dominates} $\beta$
($\alpha \succ \beta$) if there exists a set $S \subset {\mathbb N}$) and
$K > 0$ s.t. $\sum_{i \in S} \beta_i^2 < \infty$, and
$K \alpha_i \geq \beta_i$ for any $i \notin S$.
We say $\alpha$ is {\it equivalent} to $\beta$
($\alpha \sim \beta$) if $\alpha \succ \beta$, and
$\beta \succ \alpha$.
Clearly, the relation $\succ$ is reflexive and transitive.
The relation $\sim$ is, in addition to this, symmetric.
For instance, to establish the transitivity of $\succ$,
suppose $\alpha \succ \beta$, and $\beta \succ \gamma$, and
show that $\alpha \succ \gamma$. Note that there exist
sets $S_1$ and $S_2$, and constants $K_1$ and $K_2$, s.t.
$\beta_i \leq K_1 \alpha_i$ for $i \notin S_1$,
$\gamma_i \leq K_2 \beta_i$ for $i \notin S_2$,
$\sum_{i \in S_1} \beta_i^2 < \infty$, and
$\sum_{i \in S_2} \gamma_i^2 < \infty$. Let
$S = S_1 \cup S_2$, and $K = K_1 K_2$. Then
$\gamma_i \leq K \alpha_i$ for $i \notin S$.
Moreover,
$$
\sum_{i \in S} \gamma_i^2 =
\sum_{i \in S_2} \gamma_i^2 +
\sum_{i \in S_1 \backslash S_2} \gamma_i^2 \leq
\sum_{i \in S_2} \gamma_i^2 +
\sum_{i \in S_1} K_2^2 \beta_i^2 < \infty ,
$$
which is what we need. The other properties are proved in a similar fashion.
\begin{proposition}\label{equiv_seq}
For $\alpha, \beta \in {\mathcal{S}}$, $\alpha \sim \beta$ if and only if there
exists a set $S \subset {\mathbb N}$ and a constant $K$ s.t.
$\sum_{i \in S} (\alpha_i^2 + \beta_i^2) < \infty$, and
$K^{-1} \alpha_i \leq \beta_i \leq K \alpha_i$ for $i \notin S$.
\end{proposition}
\begin{proof}
If $S$ and $K$ with the properties described above exist, then
they witness the fact that $\alpha \prec \beta$ and $\alpha \succ \beta$,
hence $\alpha \sim \beta$. Conversely, suppose $\alpha \prec \beta$ and
$\alpha \succ \beta$. Then there exist a constant $K$, and sets $S_1$
and $S_2$, s.t. $\alpha_i \leq K \beta_i$ for $i \notin S_1$,
$\beta_i \leq K \alpha_i$ for $i \notin S_2$,
$\sum_{i \in S_1} \alpha_i^2 < \infty$, and
$\sum_{i \in S_2} \beta_i^2 < \infty$.
By reducing $S_1$ and $S_2$ further, we can assume that
$\alpha_i > K \beta_i$ for each $i \in S_1$, and
$\beta_i > K \alpha_i$ for each $i \in S_2$.
Then $\sum_{i \in S_1} \beta_i^2 < \infty$, and
$\sum_{i \in S_2} \alpha_i^2 < \infty$.
Therefore, $S = S_1 \cup S_2$ has the required properties.
\end{proof}
The main result of this section is:
\begin{theorem}\label{classify}
For $\alpha, \beta \in {\mathcal{S}}$, $X^d(\alpha)$ embeds completely isomorphically
into $X^d(\beta)$ if and only if $\alpha \prec \beta$.
\end{theorem}
From this we immediately obtain
\begin{corollary}\label{classify_cor}
Suppose $\alpha, \beta \in {\mathcal{S}}$.
The following three statements are equivalent.
\begin{enumerate}
\item
$X^d(\alpha)$ is completely isomorphic to $X^d(\beta)$.
\item
$X^d(\alpha)$ embeds completely isomorphically into $X^d(\beta)$,
and vice versa.
\item
$\alpha \sim \beta$.
\end{enumerate}
\end{corollary}
\begin{proof}
(1) $\Rightarrow$ (2) is trivial, while (2) $\Rightarrow$ (3) follows
from Theorem~\ref{classify} and Proposition~\ref{equiv_seq}.
To establish (3) $\Rightarrow$ (1), suppose $\alpha \sim \beta$.
By Proposition~\ref{equiv_seq}, there exists a set $\mathcal{I}$ and $K > 0$ s.t.
$\sum_{i \in \mathcal{I}} (\alpha_i^2 + \beta_i^2) < \infty$, and
$K^{-1} \alpha_i \leq \beta_i \leq K \alpha_i$ for any $i \notin \mathcal{I}$.
By Corollary~\ref{ci_to_row}, the spaces
$E_\alpha = \span[e_i : i \in \mathcal{I}] \hookrightarrow X^d(\alpha)$ and
$E_\beta = \span[e_i : i \in \mathcal{I}] \hookrightarrow X^d(\beta)$ are completely isomorphic
to $\mathbf{R}$. By \eqref{basis}, the formal identity map from
$F_\alpha = \span[e_i : i \notin \mathcal{I}] \hookrightarrow X^d(\alpha)$ to
$F_\beta = \span[e_i : i \notin \mathcal{I}] \hookrightarrow X^d(\beta)$
is a complete isomorphism.
By Lemma~\ref{simple_X(A)}(2), $X^d(\alpha) \simeq E_\alpha \oplus F_\alpha$,
and $X^d(\beta) \simeq E_\beta \oplus F_\beta$.
Therefore, the formal identity map from $X^d(\alpha)$ to $X^d(\beta)$ is
a complete isomorphism.
\end{proof}
The proof of Theorem~\ref{classify} follows from the next two lemmas.
\begin{lemma}\label{embeds}
If $\alpha, \beta \in {\mathcal{S}}$ and $\beta \prec \alpha$, then $X^d(\beta)$
embeds completely isomorphically into $X^d(\alpha)$.
\end{lemma}
\begin{proof}
By Corollary~\ref{inf_ker}, $X^d(\alpha)$ is completely isomorphic to
$X(A)$, where $A \in B(\ell_2 \oplus_2 \ell_2)$ is defined by
$A = {\mathrm{diag}} \, (\alpha) \oplus 0$.
Let $(\xi_i)$ and $(\xi_i^\prime)$ be
orthonormal bases in the first and second copies of $\ell_2$, respectively.
Then $X(A)$ is the closed linear span of the vectors
$\xi_i \oplus \alpha_i \xi_i$ and $\xi_i^\prime \oplus 0$ ($i \in {\mathbb N}$).
Find a sequence $\phi_i \in [0, \pi/2]$ s.t.
$\beta_i = \cos \phi_i \cdot \alpha_i$.
Define an orthonormal system
$\eta_i = \cos \phi_i \xi_i + \sin \phi_i \xi_i^\prime$.
For $i \in {\mathbb N}$ consider
$$
f_i = \eta_i \oplus \beta_i \xi_i =
\cos \phi_i (\xi_i \oplus \alpha_i \xi_i) +
\sin \phi_i (\xi_i^\prime \oplus 0) .
$$
Then $f_i \in X(A)$, and $\span[f_i : i \in {\mathbb N}] = X^d(\beta)$.
\end{proof}
\begin{lemma}\label{dominate}
Suppose $\alpha, \beta \in {\mathcal{S}}$, $E$ is a subspace of $X^d(\alpha)$,
and a completely bounded map $U : E \to X^d(\beta)$ has bounded
inverse (in the terminology of \cite {OiR}, $E$ is completely
semi-isomorphic to $X^d(\beta)$). Then $\beta \prec \alpha$.
\end{lemma}
\begin{proof}
We rely heavily on Wielandt's Minimax Theorem (\cite[Theorem III.6.5]{Bh}):
if $c_1 \geq c_2 \geq \ldots \geq 0$ are eigenvalues
of positive compact operator $T$, then, for any finite increasing
sequence $i_1 < \ldots < i_k$ of positive integers,
$$
\sum_{j=1}^k c_{i_j} = \sup_{E_1 \hookrightarrow \ldots \hookrightarrow E_k}
\min_{x_j \in E_j, \, (x_j) \, {\mathrm{orthonormal}}}
\langle T x_j , x_j \rangle ,
$$
where the supremum is taken over all subspaces $E_1 \hookrightarrow \ldots \hookrightarrow E_k$
of the domain of $T$, with ${\mathrm{dim}} \, E_j = i_j$ for $1 \leq j \leq k$.
Actually, the theorem is stated in \cite{Bh} for operators on finite
dimensional spaces, but a generalization to compact operators is easy
to obtain. Applying the above identity to $T = S^* S$, where $S$ is a
compact operator with singular numbers $s_1 \geq s_2 \geq \ldots \geq 0$,
we obtain:
\begin{equation}
\sum_{j=1}^k s_{i_j}^2 = \sup_{E_1 \hookrightarrow \ldots \hookrightarrow E_k, {\mathrm{dim}} \, E_j = i_j}
\min_{x_j \in E_j, \, (x_j) \, {\mathrm{orthonormal}}}
\|S x_j\|^2 .
\label{minimax}
\end{equation}
In our situation, assume $\|U\|_{cb} = 1$. Let $c = \|U^{-1}\|$,
$A = {\mathrm{diag}} \, (\alpha_i)$, $B = {\mathrm{diag}} \, (\beta_i)$, $B^\prime = B U$.
Denote the singular values of $B^\prime$ by $(\beta_i^\prime)$. Clearly,
$\beta_i^\prime \leq \beta_i \leq c \beta_i^\prime$
for every $i \in {\mathbb N}$.
Pick an orthonormal system $(x_j)_{j=1}^k$ in $E$ (the domain of $U$).
Let $u$ be the formal identity from $\mathbf{R}^k = (\ell_2^k)_\mathbf{R}$
(the $k$-dimensional row space) to $\span[x_j : 1 \leq j \leq k]$.
Then (compare with the proof of Lemma~\ref{compute_norm})
$$
\|u\|_{cb}^2 = \max\{1, \|A u\|_2^2\} \leq
1 + \sum_{j=1}^k \|A x_j\|^2 ,
$$
and (since $U$ is a complete contraction)
$$
\|u\|_{cb}^2 \geq \|U u\|_{cb}^2 \geq \|B U u\|_2^2 =
\sum_{j=1}^k \|B^\prime x_j\|^2 .
$$
Thus, $\sum_{j=1}^k \|B^\prime x_j\|^2 \leq
\sum_{j=1}^k \|A x_j\|^2 + 1$
for any orthonormal family $(x_j)_{j=1}^k$.
By \eqref{minimax},
\begin{equation}
1 + \sum_{j=1}^k \alpha_{i_j}^2 \geq
\sum_{j=1}^k \beta_{i_j}^{\prime 2}
\label{fin_sum}
\end{equation}
for any $i_1 < \ldots < i_k$ (indeed, when computing
$\sum_{j=1}^k \alpha_{i_j}^2$, we are taking the supremum over a larger
family of subspaces $(E_j)$, than when we are computing
$\sum_{j=1}^k \beta_{i_j}^{\prime 2}$).
Now let $\mathcal{I} = \{i \in {\mathbb N} : \beta_i^\prime > 2 \alpha_i\}$.
Then $\sum_{i \in \mathcal{I}} \beta_i^{\prime 2} \leq 2$.
Indeed, otherwise there exists a sequence $i_1 < \ldots < i_k$ of
elements of $\mathcal{I}$ s.t. $C = \sum_{j=1}^k \beta_{i_j}^{\prime 2} > 2$.
Then, by (\ref{fin_sum}), $\sum_{j=1}^k \alpha_{i_j}^2 \geq C - 1$.
On the other hand, $\sum_{j=1}^k \alpha_{i_j}^2 \leq C/2$,
a contradiction.
\end{proof}
Developing the ideas of this proof, we obtain:
\begin{theorem}\label{same_basis}
Suppose $\alpha, \beta \in {\mathcal{S}}$, and there exists an isomorphism
$U : X^d(\alpha) \to X^d(\beta)$ with $\|U\|_{cb}, \|U^{-1}\|_{cb} \leq C$.
Then the formal identity map $id : X^d(\alpha) \to X^d(\beta)$
satisfies $\|id\|_{cb}, \|id^{-1}\|_{cb} < 4 C^2$.
\end{theorem}
\begin{proof}
As in the proof of Lemma~\ref{dominate}, let $A = {\mathrm{diag}} \, (\alpha_i)$,
$B = {\mathrm{diag}} \, (\beta_i)$, and $B^\prime = B U$.
By Lemma~\ref{compute_norm},
$\|B^\prime u\|_2 \leq C \max\{ \|A u\|_2, \|u\|\}$
for any $u : \ell_2 \to X^d(\alpha)$.
Denote the singular numbers of $B^\prime$ by $(\beta_i^\prime)$,
and note that $\beta_i/C \leq \beta_i^\prime \leq C \beta_i$
for every $i$.
Reasoning as in the proof of Lemma~\ref{dominate}, we see that
$$
C^2(1 + \sum_{j=1}^k \alpha_{i_j}^2) \geq
\sum_{j=1}^k \beta_{i_j}^{\prime 2}
$$
Let $\mathcal{I} = \{i : \beta_i^\prime > 2C \alpha_i\}$.
As in the preceding proof,
$\sum_{i \in \mathcal{I}}\beta_i^{\prime 2} < 2 C^2$.
Therefore, $\sum_{i \in \mathcal{I}} \beta_i^2 < 2 C^4$, and
$\beta_i \leq 2 C^2 \alpha_i$ for $i \notin \mathcal{I}$.
Next we show that
$\|id : X^d(\alpha) \to X^d(\beta)\|_{cb} < 4 C^2$.
As before, denote the canonical bases in $X^d(\alpha)$ and $X^d(\beta)$
by $(e_i(\alpha))_{i \in {\mathbb N}}$ and $(e_i(\beta))_{i \in {\mathbb N}}$, respectively.
By \eqref{basis}, $Y_1 = \span[e_i(\alpha) : i \in \mathcal{I}]$ and
$Y_0 = \span[e_i(\alpha) : i \notin \mathcal{I}]$ are completely contractively
complemented subspaces of $X^d(\alpha)$. Moreover,
$$
\eqalign{
\|id|_{Y_1}\|_{cb} \leq \|V : (Y_1)_\mathbf{R} \to X^d(\beta)\|_{cb}
&
=
\max\{1, \|B V\|_{cb}\}
\cr
&
\leq
\max\big\{1, \big( \sum_{i \in \mathcal{I}} \beta_i^2 \big)^{1/2} \big\} < 2 C^2
}
$$
(here, $V$ is the formal identity from $(Y_1)_\mathbf{R}$ to
$\span[e_i(\beta) : i \in \mathcal{I}]$).
By Lemma~\ref{compute_norm} and \eqref{basis}, $\|id|_{Y_0}\|_{cb} < 2 C^2$.
Therefore,
$$
\|id : X^d(\alpha) \to X^d(\beta)\|_{cb} \leq
\|id|_{Y_1}\|_{cb} + \|id|_{Y_0}\|_{cb} < 4 C^2 .
$$
The norm of $id : X^d(\beta) \to X^d(\alpha)$ is computed the same way.
\end{proof}
\section{Completely unconditional bases}\label{bases}
In this section, we further investigate bases in spaces $X(A)$,
where $A \in B(H,K)$ is a compact contraction.
A subspace $E$ of $X(A)$ is isometric to $X(A|_E)$.
As $A|_E$ is a compact contraction,
\eqref{basis_general} implies that $E$ has a $1$-completely unconditional
basis. The key result of this section is Proposition
\ref{unique_basis},
establishing the uniqueness of a completely unconditional basis in $E$
(the existence of such a basis has been established by
Proposition \ref{make_diag}).
We also show that the canonical basis (and therefore, every completely
unconditional basis) in a completely complemented subspace of $X^d(\alpha)$
is equivalent to a subsequence of the canonical basis of $X^d(\alpha)$.
Moreover, there exists $\alpha \in {\mathcal{S}}$ such that the canonical basis
in every complemented subspace of $X^d(\alpha)$ is equivalent to a
subsequence of the canonical basis of $X^d(\alpha)$ (Theorem~\ref{subbasis}).
In general, the last statement need not be true (Remark~\ref{not_subbasis}).
First we show that any completely unconditional basic sequence in an
$X(A)$ space corresponds to a canonical basis of $X^d(\beta)$,
for some $\beta$.
\begin{proposition}\label{unconditional}
Suppose $\mathcal{I}$ is a finite or countable set, and
$(e_i^\prime)_{i \in \mathcal{I}}$ is a a $C$-completely unconditional
basic sequence in $X(A)$ ($A \in B(\ell_2)$ is a contraction,
not necessarily compact).
Let $Y = \span[e_i^\prime : i \in \mathcal{I}]$, and define the sequence
$\beta = (\beta_i)$ by setting $\beta_i = \|A e^\prime_i\|$.
Consider the operator $T : Y \to X^d(\beta) : e_i^\prime \mapsto e_i$,
where $(e_i)$ is the canonical basis of $X^d(\beta)$. Then
$\|T\|_{cb} \leq C$ and $\|T^{-1}\|_{cb} \leq C^2$.
\end{proposition}
\begin{proof}
As noted in Section~\ref{op_sp},
\begin{equation}
C^{-2} \|\sum \alpha_i e_i^\prime\|^2 \leq \sum |\alpha_i|^2 \leq
C^2 \|\sum \alpha_i e_i^\prime\|^2
\label{squares}
\end{equation}
for any finite sequence of scalars $(\alpha_i)$.
Thus, $\|T\|, \|T^{-1}\| \leq C$.
Let $B = {\mathrm{diag}} \, (\beta)$ (note that $B = B^*$).
By Lemma~\ref{compute_norm}, it suffices to show that
\begin{equation}
\|B T u\|_2 \leq C \max \{ \|A u\|_2, \|u\| \}
\label{equiv1}
\end{equation}
for any $u : \ell_2 \to Y = X(A|_Y)$, and
\begin{equation}
\|A T^{-1} u\|_2 \leq C^2 \max \{ \|B u\|_2, \|u\| \}
\label{equiv2}
\end{equation}
for any $u : \ell_2 \to X^d(\beta)$.
By Lemma~\ref{compute_norm}, the complete unconditionality of
$(e_i^\prime)$ implies:
\begin{equation}
\begin{array}{ll}
\|A \Lambda u\|_2
&
\leq C \max \{ \|A u\|_2, \|u\| \} ,
\\
\|A u\|_2
&
\leq C \max \{ \|A \Lambda u\|_2, \|u\| \}
\end{array}
\label{uncond}
\end{equation}
whenever $\Lambda = {\mathrm{diag}} \, (\lambda_i)$ (that is,
$\Lambda e_i^\prime = \lambda_i e_i^\prime$), with
$\lambda_i = \pm 1$ for each $i$, and $u \in B(\ell_2, Y)$.
Note that $\|A u\|_2^2 = \mathbf{tr} (A^* A v)$, where $v = u u^*$.
Therefore, \eqref{uncond} is equivalent to
\begin{equation}
\begin{array}{ll}
\mathbf{tr} (\Lambda^* A^* A \Lambda v)
&
\leq C^2 \max \{ \mathbf{tr}(A^* A v) , 1 \} , \\
\mathbf{tr} (A^* A v)
&
\leq C^2 \max \{ \mathbf{tr}(\Lambda^* A^* A \Lambda v) , 1 \}
\end{array}
\label{uncond_tr}
\end{equation}
whenever $v \geq 0$ and $\|v\| = 1$.
But
$\langle \Lambda^* A^* A \Lambda e_i^\prime, e_j^\prime \rangle =
\lambda_i \overline{\lambda_j}
\langle A e_i^\prime, A e_j^\prime \rangle$.
Averaging over $\lambda_i = \pm 1$ for each $i$, we see that
${\mathrm{Ave}}_\Lambda \Lambda^* A^* A \Lambda = T^* B^2 T$
(since $\langle T^* B^2 T e_i^\prime, e_j^\prime \rangle =
\delta_{ij} \langle A e_i^\prime, A e_j^\prime \rangle$,
where $\delta_{ij}$ is Kronecker's delta).
Therefore, by \eqref{uncond_tr},
$$
\eqalign{
\mathbf{tr} (T^* B^2 T v)
&
=
{\mathrm{Ave}}_\Lambda \mathbf{tr} (\Lambda^* A^* A \Lambda v)
\cr
&
\leq
\sup_\Lambda \mathbf{tr} (\Lambda^* A^* A \Lambda v) \leq
C^2 \max\{ \mathbf{tr} (A^* A v) , 1 \}
}
$$
whenever $v$ is a positive contraction. Thus, for any
contraction $u$,
$$
\eqalign{
\|B T u\|_2^2
&
=
\mathbf{tr} (T^* B^2 T u u^*)
\cr
&
\leq
C^2 \max\{ \mathbf{tr} (A^* A u u^*) , 1 \}
= C^2 \max \{ \|A u\|_2, \|u\| \}^2 ,
}
$$
which proves (\ref{equiv1}).
To establish (\ref{equiv2}), we show that,
for every $w : \ell_2 \to Y$, we have
\begin{equation}
\|A w\|_2 \leq C \max \{ \|B T w\|_2, \|w\| \}
\label{AwB}
\end{equation}
Indeed, let $w = T^{-1} u$. Then, by \eqref{AwB} and \eqref{squares},
$$
\eqalign{
\|A T^{-1} u\|_2
&
=
\|A w\|_2 \leq C \max \{ \|B T w\|_2, \|w\| \}
\cr
&
\leq
C \max \{ \|B u\|_2, C \|u\| \} \leq C^2 \max \{ \|B u\|_2, \|u\| \} .
}
$$
Moreover, \eqref{AwB} is equivalent to the following:
for any non-negative, norm one $v \in B(X^d(\alpha))$,
we have
\begin{equation}
C^2 \max\{ \mathbf{tr} (T^* B^2 T v) , 1 \} \geq \mathbf{tr} (A^* A v) .
\label{C_prime_C}
\end{equation}
As we have established before,
$\mathbf{tr} (T^* B^2 T v) =
{\mathrm{Ave}}_\Lambda \mathbf{tr} (\Lambda^* A^* A \Lambda v)$.
By the linearity and positivity of the trace,
$$
0 \leq \inf_\Lambda \mathbf{tr} (\Lambda^* A^* A \Lambda v) \leq
\mathbf{tr} (T^* B^2 T v) \leq
\sup_\Lambda \mathbf{tr} (\Lambda^* A^* A \Lambda v) .
$$
Thus, for some $\Lambda$,
$\mathbf{tr} (\Lambda^* A^* A \Lambda v) \leq \mathbf{tr} (T^* B^2 T v)$.
By (\ref{uncond_tr}),
$$
\mathbf{tr}(A^* A v) \leq C^2 \max \{ \mathbf{tr} (\Lambda^* A^* A \Lambda v) , 1 \}
\leq C^2 \max \{ \mathbf{tr} (T^* B^2 T v) , 1 \} ,
$$
which implies (\ref{C_prime_C}).
\end{proof}
\begin{proposition}\label{unique_basis}
For $\alpha \in c_0$, the completely unconditional basis in $X^d(\alpha)$
is unique (up to permutative equivalence). More precisely: if $(g_i)$
is a $C$-completely unconditional basis in $X^d(\alpha)$, then
it is $16 C^{11}$-equivalent (up to a permutation) to the
canonical basis in $X^d(\alpha)$.
\end{proposition}
\begin{proof}
Let $(e_i(\alpha))$ be the canonical basis of $X^d(\alpha)$.
Set $\beta_i = \|A g_i\|$, and let $(e_i(\beta))$ the canonical
basis of $X^d(\beta)$. By Proposition~\ref{unconditional}, the map
$T : X^d(\alpha) \to X^d(\beta) : g_i \mapsto e_i(\beta)$ satisfies
$\|T\|_{cb} \leq C$, $\|T^{-1}\|_{cb} \leq C^2$.
By Theorem~\ref{same_basis}, $id : X^d(\beta) \to X^d(\alpha)$
satisfy $\|id\|_{cb}, \|id^{-1}\|_{cb} < 4 C^4$.
Thus, the operator $U = id \circ T$ is a complete isomorphism on
$X^d(\alpha)$, with $U g_i = e_i$, $\|U\|_{cb} < 4 C^5$, and
$\|U^{-1}\|_{cb} < 4 C^6$.
\end{proof}
\begin{corollary}\label{compl_sub}
Suppose $\alpha \in {\mathcal{S}}$, and $Y$ is a $C$-completely complemented
subspace of $X^d(\alpha)$. Then $Y$ is $2^6 C^2$-completely isomorphic
to $X^d(\alpha^\prime)$, where $\alpha^\prime$ is a subsequence of $\alpha$.
\end{corollary}
\begin{proof}
Let $P$ be a projection from $X^d(\alpha)$ onto $Y$, with
$\|P\|_{cb} \leq C$. Then $X^d(\alpha)$ is $2C$-completely isomorphic
to $Y \oplus Z$, where $Z = {\mathrm{ker}} \, P$. By Lemma~\ref{almost_alpha},
$Y$ and $Z$ are $\sqrt{2}$-completely isomorphic to $X^d(\beta)$ and $X^d(\beta^\prime)$, respectively,
where $\beta$ and $\beta^\prime$ belong to ${\mathcal{S}}$.
By Lemma~\ref{simple_X(A)}(2), $X^d(\alpha)$ is $4 C$-completely isomorphic
to $X^d(\gamma)$, where $\gamma = (\gamma_i) \in {\mathcal{S}}$ is the ``join'' of
$\beta = (\beta_i)$ and $\beta^\prime = (\beta^\prime_i)$. More precisely,
the sequence $\gamma$ has the property that, for every $c \in [0,1]$,
$$
|\{ i : \gamma_i = c \}| = |\{ i : \beta_i = c \}| +
|\{ i : \beta^\prime_i = c \}| .
$$
Denoting the canonical basis of $X^d(\gamma)$ by $(e_i(\gamma))$,
we see that $X^d(\beta) = \span[e_i(\gamma) : i \in I]$, for some
infinite set $I \subset {\mathbb N}$. By Theorem~\ref{same_basis}, the formal
identity $id : X^d(\gamma) \to X^d(\alpha) : e_i(\gamma) \mapsto e_i(\alpha)$
satisfies $\|id\|_{cb}, \|id^{-1}\|_{cb} < 8 C$. In particular,
$X^d(\beta)$ $2^6 C^2$-completely isomorphic to
$\span[e_i(\alpha) : i \in I]$.
\end{proof}
\begin{remark}\label{oi_lms}
By \cite{Oi}, the completely unconditional basis in $\row \oplus \col$ is unique
up to a permutation.
\end{remark}
\begin{remark}\label{not_subbasis}
In general, the canonical basis of a subspace of $X^d(\alpha)$
($\alpha \in {\mathcal{S}}$) need not be equivalent to a subsequence of
the canonical basis of $X^d(\alpha)$. For instance,
suppose the sequence $\alpha = (\alpha_i)$ and $\beta = (\beta_i)$ are
defined by setting $\alpha_i = 2^{-n^2}$, $\beta_i = 2^{-n^2-n}$ for
$4^{n^2} \leq i < 4^{(n+1)^2}$ ($n \in \{0\} \cup {\mathbb N}$). By
Lemma~\ref{embeds}, $X^d(\beta)$ embeds completely isomorphically
into $X^d(\alpha)$. However, $(e_i(\beta))$ (the canonical basis of
$X^d(\beta)$) is not equivalent to any subsequence of
the canonical basis $(e_i(\alpha))$ of $X^d(\alpha)$.
Indeed, suppose, for the sake of achieving a contradiction, that
there exists a complete isomorphism $T$ from $X^d(\beta)$ to a subspace
of $X^d(\alpha)$, mapping $e_i(\beta)$ to $e_{k_i}(\alpha)$.
Fix $n \in {\mathbb N}$ with
$\max\{\|T\|_{cb}, \|T^{-1}\|_{cb}\} < 2^{n/2}$. Consider the sets
$$
\begin{array}{lll}
I_n & = & \{ 4^{n^2} \leq i < 4^{(n+1)^2} : k_i < 4^{(n+1)^2} \} , \cr
J_n & = & \{ 4^{n^2} \leq i < 4^{(n+1)^2} : k_i \geq 4^{(n+1)^2} \} .
\end{array}
$$
By Pigeon-Hole Principle, with $I_n$ or $J_n$ has the cardinality
grater than $4^{n^2+2n}$. If $|I_n| > 4^{n^2+2n}$, consider
$$
x = \sum_{i \in I_n} E_{i1} \otimes e_i(\beta) \in
M_{4^{(n+1)^2}}(X^d(\beta))
$$
(recall that $E_{i1}$ is the ``matrix unit'' with $1$ on the intersection of
the first column and the $i$-th row, and zeroes everywhere else).
By \eqref{basis},
$$
\|x\|^2_{M_{4^{(n+1)^2}}(X^d(\beta))} =
\max\{ 1, |I_n| \cdot 2^{-n^2-n} \} = |I_n| \cdot 2^{-n^2-n} .
$$
However, by \eqref{basis} again,
$$
\|(I_{M_{4^{(n+1)^2}}} \otimes T)x\|^2_{M_{4^{(n+1)^2}}(X^d(\alpha))} \geq
\max\{ 1, |I_n| \cdot 2^{-n^2-n} \} = |I_n| \cdot 2^{-n^2} ,
$$
yielding $\|T\|_{cb}^2 \geq 2^{-n}$. If $J_n > 4^{n^2+2n}$, consider
$$
x = \sum_{i \in J_n} E_{i1} \otimes e_i(\beta) \in
M_{4^{(n+1)^2}}(X^d(\beta)) .
$$
As before, $\|x\|^2 = |J_n| \cdot 2^{-n^2-n}$, while
$$
\|(I_{M_{4^{(n+1)^2}}} \otimes T)x\|^2_{M_{4^{(n+1)^2}}(X^d(\alpha))} \geq
\max\{ 1, |I_n| \cdot 2^{-(n+1)^2} \} = |J_n| \cdot 2^{-(n+1)^2} ,
$$
hence $\|T^{-1}\|_{cb}^2 \geq 2^{n+1}$. Thus,
$\max\{\|T\|_{cb}, \|T^{-1}\|_{cb}\} \geq 2^{n/2}$,
which yields the desired contradiction.
\end{remark}
In certain situations, the canonical basis for every subspace of
$X^d(\alpha)$ is equivalent to a subsequence of the canonical basis
of $X^d(\alpha)$.
\begin{theorem}\label{subbasis}
For any $a > 1$ there exists $\alpha \in {\mathcal{S}} \backslash \ell_2$ such that
any subspace $Y$ of $X^d(\alpha)$ (finite or infinite dimensional) has a
$1$-completely unconditional basis, $a$-equivalent to a subsequence
of the canonical basis of $X^d(\alpha)$.
\end{theorem}
Combining this result with Proposition~\ref{unique_basis}, we obtain
\begin{corollary}\label{cor_subbasis}
There exists $\alpha \in {\mathcal{S}} \backslash \ell_2$ such that
any $C$-completely unconditional basic sequence in $X^d(\alpha)$
is $A C^B$-equivalent to a subsequence of the canonical basis
of $X^d(\alpha)$ (here, $A$ and $B$ are positive).
\end{corollary}
\begin{proof}[Proof of Theorem~\ref{subbasis}]
Assume $a < 2$.
Pick a sequence of integers $1 = N_0 < N_1 < \ldots$, s.t.
$N_k > 2 N_{k-1}$ for each $k$. Define a sequence $\alpha = (\alpha_i)$
by setting $\alpha_{2i} = a^{-k}$ for $N_k \leq i < N_{k+1}$,
$\alpha_{2i-1} = 0$ for any $i \in {\mathbb N}$.
Clearly, $\alpha \in c_0 \backslash \ell_2$.
Let $A = {\mathrm{diag}} \, (\alpha)$. For a subspace $Y$ of $X(A)$, let
$\beta = (\beta_i)$ is the sequence of singular values of $A|_Y$.
Define the set $\mathcal{I}_1$ by
setting $\mathcal{I}_1 = \{1, \ldots, M\}$ if ${\mathrm{rank}} \, (A|_Y) = M < \infty$,
and $\mathcal{I}_1 = {\mathbb N}$ if ${\mathrm{rank}} \, (A|_Y) = \infty$.
We can also assume that the elements of $(\beta_i)_{i \in \mathcal{I}_1}$
are listed in the non-increasing order. Then
$\beta_i \leq \alpha_{2i}$ for each $i$.
Denote the normalized eigenvectors of $(A|_Y)^* A|_Y$, corresponding to
the eigenvalues $\beta_i$ ($i \in \mathcal{I}_1$), by $\eta_i$.
Furthermore, find the vectors $(\eta_i)_{i \in \mathcal{I}_0}$, forming
an orthonormal basis in ${\mathrm{ker}} \, (A|_Y)$. For $i \in \mathcal{I}_0$, set $\beta_i = 0$.
Let $\mathcal{I} = \mathcal{I}_1 \cup \mathcal{I}_0$ (we assume that this union is disjoint).
Then the family $(\eta_i)_{i \in \mathcal{I}}$ is the canonical basis for $Y$.
For each positive integer $k$, let $M_k$ be the smallest value of $i$
s.t. $\beta_i \leq a^{-k}$. Set $M_0 = 1$. In this notation,
$a^{1-k} \geq \beta_i > a^{-k}$ iff $M_{k-1} \leq i < M_k$.
As noted above, $\beta_i \leq \alpha_{2i}$, hence $M_k \leq N_k$.
By our choice of the sequence $(N_k)$,
$$
M_k - M_{k-1} < M_k \leq N_k \leq N_{k+1} - N_k .
$$
Thus, there exists an injective map $\pi : \mathcal{I} \to {\mathbb N}$ s.t.
$\pi(\mathcal{I}_0) \subset \{2i-1 : i \in {\mathbb N}\}$, and
$\pi([M_{k-1}, M_k)) \subset \{2i : i \in [N_k, N_{k+1})\}$
for each $k \in {\mathbb N}$. For $i \in \mathcal{I}_0$, $\alpha_{\pi(i)} = \beta_i = 0$,
while for $i \in \mathcal{I}_1$,
$a \alpha_{\pi(i)} = a^{1-k} \geq \beta_i > a^{-k} = \alpha_{\pi(i)}$.
Define the operator $T : Y \to \span[e_{\pi(i)} : i \in \mathcal{I}] \hookrightarrow X^d(\alpha)$,
defined by $T \xi_i = e_{\pi(i)}$. By \eqref{basis_general},
$T$ is a complete contraction, and $\|T^{-1}\|_{cb} \leq a$.
\end{proof}
\begin{remark}\label{complem_subsp}
The proof of Theorem~\ref{subbasis} shows that any subspace of $X^d(\alpha)$
is $a$-completely isomorphic to a completely contractively complemented subspace
of $X^d(\alpha)$. Nevertheless, $X^d(\alpha)$ contains subspaces which are not
completely complemented. To construct them, find a sequence $(\beta_i)$
such that $1 \geq \beta_1 \geq \beta_2 \geq \ldots > 0$, $\lim \beta_i = 0$,
and furthermore, $\sum_i \gamma_i^2 = \infty$, where
$\gamma_i = \alpha_i \beta_i$.
Denote the canonical basis of $X^d(\alpha)$ by $(e_i)_{i \in {\mathbb N}}$.
Then $e_{2i-1} = \xi_{2i-1} \oplus 0$, and
$e_{2i} = \xi_{2i} \oplus \alpha_i \xi_{2i}$ ($(\xi_j)$ is
an orthonormal basis in $\ell_2$).
For $k \geq 0$ and $i \in [N_k, n_{k+1})$, let
\begin{equation}
f_i = \beta_i e_{2i} + \sqrt{1 - \beta_i^2} \, e_{2i-1} =
\big(\beta_i \xi_{2i} + \sqrt{1 - \beta_i^2} \, \xi_{2i-1}\big) \oplus
\gamma_i \xi_{2i} .
\label{def_f_i}
\end{equation}
We show that $Y$ is not
completely complemented in $X^d(\alpha)$. Indeed, suppose,
for the sake of contradiction, that there exists a c.b.~projection
$P$ from $X^d(\alpha)$ onto $Y$. For $\varepsilon \in \{-1,1\}^{\mathbb N}$, define
an operator $\Lambda_\varepsilon \in B(X^d(\alpha))$ by setting
$\lambda_\varepsilon e_j = \varepsilon_{\lceil j/2 \rceil} e_j$.
For any such $\varepsilon$, \eqref{basis} implies that $\Lambda_\varepsilon$ is
a complete isometry. For any $i \in {\mathbb N}$, we have
$\Lambda_\varepsilon \xi = \varepsilon_i \xi$ whenever $\xi \in \span[e_{2i-1}, e_{2i}]$.
In particular, $\Lambda_\varepsilon f_i = \varepsilon_i f_i$.
Let $Q = {\mathrm{Ave}}_{\varepsilon \in \{-1,1\}^{\mathbb N}} \Lambda_\varepsilon P \Lambda_\varepsilon$.
Note that ${\mathrm{ran}} \, Q \subset Y$, and $Q|_Y = I_Y$, hence $Q$ is a projection
onto $Y$. Furthermore, $\|Q\|_{cb} \leq \|P\|_{cb}$.
For each $i$, we have $Q e_{2i} = a_i f_i$, and $Q e_{2i-1} = b_i f_i$.
The equations $Q f_i = f_i$ and \eqref{def_f_i} yield
$a_i \beta_i + b_i \sqrt{1 - \beta_i^2} = 1$.
Then $\sup_i \max\{|a_i|, |b_i|\} \leq \|Q\|$. As
$\lim \beta_i = 0$, there exists $K \in {\mathbb N}$ such that
$|b_i| > 1/2$ for $i > K$. Find $N \in {\mathbb N}$ s.t.
$\sum_{i = K+1}^{K + N} \gamma_i^2 > 4 \|Q\|_{cb}^2$ (this is
possible, since $\sum_i \gamma_i^2 = \infty$). Consider
$x = \sum_{i = K+1}^{K + N} E_{i1} \otimes e_{2i-1} \in M_N(X^d(\alpha))$.
Then $\|x\| = 1$, and therefore,
$$
\eqalign{
\|Q\|_{cb}
&
\geq
\|(I_{M_N} \otimes Q)x\| =
\|\sum_{i = K+1}^{K + N} E_{i1} \otimes b_i f_i\|
\cr
&
\geq
\|\sum_{i = K+1}^{K + N}
E_{i1} \otimes b_i \gamma_i \xi_{2i}\|_{M_N(\mathbf{C})} =
\Big( \sum_{i = K+1}^{K + N} |b_i|^2 \gamma_i^2 \Big)^{1/2}
\cr
&
\geq
\frac{\Big( \sum_{i = K+1}^{K + N} \gamma_i^2 \Big)^{1/2}}{2}
> \|Q\|_{cb} ,
}
$$
which is impossible.
\end{remark}
\begin{remark}\label{isom_to_complem}
Suppose a Banach space $E$ is such that every infinite dimensional subspace $E$
is isomorphic to a complemented subspace of $E$. We not not know whether $E$
is necessarily isomorphic to a Hilbert space.
\end{remark}
\section{Completely isomorphic classification of subspaces of $X(A)$}\label{classification}
The main goal of this section is to prove Theorem~\ref{bireducible}
and Corollary~\ref{biembeddable} below.
Recall that $\boldsymbol{\mathfrak{C}}$
is the set of compact contractions which are not Hilbert-Schmidt.
\begin{theorem}\label{bireducible}
If $A \in B(\ell_2)$ belongs to $\boldsymbol{\mathfrak{C}}$,
then $(\mathbf{S}(X(A)), \simeq)$ is Borel bireducible
to the complete ${\mathbf{K}}_\sigma$ relation.
\end{theorem}
Together with Corollary~\ref{classify_cor}, this theorem immediately implies
\begin{corollary}\label{biembeddable}
If $A \in B(\ell_2)$ belongs to $\boldsymbol{\mathfrak{C}}$,
then the relation of complete biembeddability on
$\mathbf{S}(X(A))$ is Borel bireducible to the complete ${\mathbf{K}}_\sigma$ relation.
\end{corollary}
The proof of Theorem~\ref{bireducible} proceeds in two steps.
First, we introduce the space $S_A$ of sequences of non-negative
generalized integers, with an equivalence
relation $\overset{*}{\sim}$, and show the latter is Borel bireducible with
$(\mathbf{S}(X(A)), \simeq)$. Then we prove that $(S_A, \overset{*}{\sim})$ is, in fact,
a complete ${\mathbf{K}}_\sigma$ relation.
Suppose $A \in B(\ell_2)$ is of class $\boldsymbol{\mathfrak{C}}$.
By Lemma~\ref{simple_X(A)}, we can assume that $\|A\| < 1$,
and $A \geq 0$. List the positive eigenvalues of $A$ in the non-increasing
order: $1 > \|A\| = s_1^o \geq s_2^o \geq \ldots > 0$.
In the terminology of Section~\ref{sequences},
$(s_i^o)_{i \in {\mathbb N}} = {\mathbf{D}}(A)$.
Clearly, $\lim_i s_i^o = 0$. Let $(\xi_i)_{i \in {\mathbb N}}$ be
the normalized eigenvectors of $A$, corresponding to the eigenvalues
$s_i^o$. We can identify $\span[\xi_i : i \in {\mathbb N}]$ with $\ell_2$.
Consider the operator
$\hat{A} = {\mathrm{diag}} \, (s_i^o) \oplus 0 \in B(\ell_2 \oplus \ell_2)$.
By Corollary~\ref{inf_ker}, $X(A) \simeq X(\hat{A})$.
For the rest of this section, we assume that $A = \hat{A}$.
Denote by $(\xi_i^\prime)_{i \in {\mathbb N}}$ the canonical orthonormal
basis in the second copy of $\ell_2$. Then the canonical basis
of $X(A)$ is the collection of vectors $e_i = \xi_i \oplus s_i^o \xi_i$
and $f_i = \xi_i^\prime \oplus 0$. As in \eqref{basis_general}, we have,
for $n \times n$ matrices $a_1, b_1, a_2, b_2, \ldots$,
\begin{equation}
\eqalign{
&
\|\sum_i a_i \otimes e_i + \sum_i b_i \otimes f_i\|_{M_n(X(A))}^2
\cr
&
=
\max \big\{ \|\sum_i a_i a_i^* + \sum_i b_i b_i^*\|,
\|\sum_i s_i^{o2} a_i^* a_i\| \big\} .
}
\label{particular_basis}
\end{equation}
For an infinite dimensional $Y \hookrightarrow X(A)$, we let
$(s_i(Y)) = \mathbf{D}(A|_Y)$. Recalling the definition of
$\mathbf{D}$ from Section~\ref{sequences}, we see that, if
${\mathrm{rank}} \, (A|_Y) = \infty$, then $s_1(Y) \geq s_2(Y) \geq \ldots$ are the
positive singular values of $A|_Y$, listed in the non-increasing order.
In the case of ${\mathrm{rank}} \, (A|_Y) = n < \infty$,
$s_1(Y) \geq s_2(Y) \geq \ldots \geq s_n(Y)$
are the $n$ positive singular values of $A|_Y$, and $s_i(Y) = 0$ for $i > n$.
In this notation, $s_k^o = s_k(X(A))$.
Clearly, $s_k(Y) \leq s^o_k$ for any $k$,
and any $Y \hookrightarrow X(A)$.
For $k \in {\mathbb N}$, set $\mathbf{n}_k(Y) = \sup\{\ell \in {\mathbb N} : 2^{1-\ell} \geq s_k(Y)\}$.
The sequence $\mathbf{n}(Y) = (\mathbf{n}_k(Y))_{k \in {\mathbb N}}$
belongs to ${\mathbb N}_*^{\mathbb N}$, where ${\mathbb N}_* = {\mathbb N} \cup \{\infty\}$ is viewed as the
$1$-point compactification of ${\mathbb N}$.
For $k \in {\mathbb N}$ let $\alpha_k = \mathbf{n}_k(X(A))$. Define $S_A$ as the set of all
elements $\beta = (\beta_i)_{i \in {\mathbb N}} \in {\mathbb N}_*^{\mathbb N}$, such that
(1) $\beta_k \geq \alpha_k$ for any $k$, and
(2) $\beta_1 \leq \beta_2 \leq \ldots$.
Equipping ${\mathbb N}_*^{\mathbb N}$ with its product topology, we see that
$S_A$ is closed.
For any infinite dimensional $Y \hookrightarrow X(A)$,
the sequence $(\mathbf{n}_k(Y))_{k \in {\mathbb N}}$ belongs
to $S_A$. Conversely, for any $\beta \in S_A$
there exists $Y \hookrightarrow X(A)$ s.t. $\beta = \mathbf{n}(Y)$.
Indeed, suppose $\beta_k \in {\mathbb N}_*$, $\beta_k \geq \alpha_k$ for any $k$,
and $\beta_1 \leq \beta_2 \leq \ldots$.
Let $g_i = \sin \phi_i e_i + \cos \phi_i f_i$, with
$s_i^o \sin \phi_i = 2^{-\beta_i}$. We denote $\span[g_i : i \in {\mathbb N}]$
by $\mathbf{Y}(\beta)$, where $\beta = (\beta_i)$. By
\eqref{particular_basis}, $\mathbf{n}(\mathbf{Y}(\beta)) = \beta$.
Define the relation $\overset{*}{\sim}$ on $S_A$ as follows: $\beta \overset{*}{\sim} \gamma$
if there exists $K \in {\mathbb N}$ and $I \subset {\mathbb N}$ s.t.
$|\beta_i - \gamma_i| \leq K$ for any
$i \notin I$, and $\sum_{i \in I} (4^{-\beta_i} + 4^{-\gamma_i}) \leq K$.
By Corollary~\ref{classify_cor}, $\beta \overset{*}{\sim} \gamma$
iff $\mathbf{Y}(\beta) \simeq \mathbf{Y}(\gamma)$, and conversely,
$Y \simeq Z$ iff $\mathbf{n}(Y) \overset{*}{\sim} \mathbf{n}(Z)$.
\begin{proposition}\label{borel1}
$\mathbf{n}$ and $\mathbf{Y}$ are Borel maps.
\end{proposition}
This immediately yields:
\begin{corollary}\label{reduction1}
$(S_A, \overset{*}{\sim})$ and $(\mathbf{S}(X(A)), \simeq)$ are Borel bireducible to each other.
\end{corollary}
\begin{proof}[Proof of Proposition~\ref{borel1}]
First we handle the map $\mathbf{Y}$.
We have to show that, for any open set $U \subset X(A)$,
$\{\beta \in S_A : \mathbf{Y}(\beta) \cap U \neq \emptyset\}$ is Borel.
But $\mathbf{Y}(\beta) \cap U \neq \emptyset$ iff there exist $m \in {\mathbb N}$ and
$\lambda_1, \ldots, \lambda_m \in \mathbb{Q} + i \mathbb{Q}$ s.t.
$\sum_{i=1}^m \lambda_i g_i \in U$. Here, the vectors $(g_i)$ come
from the definition of $\mathbf{Y}$. Note that, for each $i$, $g_i$ depends
solely (and continuously) on $\beta_i$.
Therefore, for each $m$-tuple $(\lambda_i)_{i=1}^m$,
$\sum_{i=1}^m \lambda_i g_i \in U$ is an open condition on $\beta$.
Thus, $\{\beta \in S_A : \mathbf{Y}(\beta) \cap U \neq \emptyset\}$ is Borel.
Now consider $\mathbf{n}$. Fix $m, \beta_m \in {\mathbb N}$, and show that the set
of all $Y \in \mathbf{S}(X(A))$, for which $\mathbf{n}_m(Y) > \beta_m \in {\mathbb N}$, is Borel.
To this end, find a countable set ${\mathcal{O}}_m$ of orthonormal $m$-tuples
$\xi = (\xi_1, \ldots, \xi_m)$ in $X(A)$, with the property that,
for every $\varepsilon > 0$, and any orthonormal $m$-tuple $(\eta_1, \ldots, \eta_m)$
in $X(A)$, there exists $\xi = (\xi_1, \ldots, \xi_m) \in {\mathcal{O}}_m$ s.t.
$\|\xi_i - \eta_i\| < \varepsilon$ for any $i$. Furthermore, find a set
$\Gamma_m$ of $m$-tuples
$\gamma = (\gamma_1, \ldots, \gamma_m) \in {\mathbb C}^m$, dense
in the unit sphere of $\ell_2^m$.
The Minimax Principle (see e.g. \cite[p.~75]{Bh}) states that, for an
operator $T \in B(H,K)$, we have $s_m(T) > b$ iff $H$ has an
$m$-dimensional subspace $E$ such that $\|T \eta\| > b$ for any
norm one $\eta \in E$. Therefore, $\mathbf{n}_m(Y) > \beta_m \in {\mathbb N}$
(that is, $s_m(A|_Y) \geq 2^{-\beta_m}$) iff for every $\varepsilon > 0$
there exists an $m$-tuple of orthonormal vectors
$\eta_1, \ldots, \eta_m \in Y$, s.t.
$\|\sum_{i=1}^m \gamma_i A \eta_i\| > 2^{-\beta_m} - \varepsilon$
whenever $\sum_{i=1}^m |\gamma_i|^2 = 1$. This, in turn,
is equivalent to the following statement:
for every $r \in {\mathbb N}$, there
exists $(\xi_1, \ldots, \xi_m) \in {\mathcal{O}}_m$ s.t., for $1 \leq i \leq m$,
${\mathrm{Ba}}(\xi_i, 1/r) \cap Y \neq \emptyset$ (here, ${\mathrm{Ba}}(x,c)$
denotes the open ball of radius $c$, with the center at $x$),
and $\|\sum_i \gamma^i A \xi_i\| > 2^{-\beta_m} - 1/r$
for every $(\gamma_i)_{i=1}^m \in \Gamma_m$.
This condition is Borel, hence $\mathbf{n}$ is Borel.
\end{proof}
\begin{lemma}\label{k_sigma}
$(S_A, \overset{*}{\sim})$ is a ${\mathbf{K}}_\sigma$ relation.
\end{lemma}
\begin{proof}
We have to show that the set
$F = \{ (\beta, \gamma) \in S_A \times S_A : \beta \overset{*}{\sim} \gamma\}$
is a ${\mathbf{K}}_\sigma$ set, that is, a countable union of compact sets. To this end,
define a family of subsets of $S_A \times S_A$, described below.
For $K, n \in {\mathbb N}$ and $I_n \subset \{1, \ldots, n\}$, define
$F(K,n,I_n)$ as the set of all pairs $(\beta, \gamma)$
($\beta = (\beta_i)$, $\gamma = (\gamma_i)$) with
the property that $|\beta_i - \gamma_i| \leq K$ for
$i \in \{1, \ldots, n\} \backslash I_n$, and
$\sum_{i \in I_n} (4^{-\beta_i} + 4^{-\gamma_i}) \leq K$.
Let $F(K,n) = \cup_{I_n \subset \{1, \ldots, n\}} F(K,n,I_n)$,
and $F(K) = \cap_n F(K,n)$. It suffices to show that
$F = \cup_{K \in {\mathbb N}} F(K)$.
Indeed, $F(K,n,I_n)$ is a compact subset of $S_A \times S_A$,
hence so is $F(K,n)$ (as a finite union of compact sets).
Furthermore, $F(K)$ is also compact, and $\cup_K F(K)$
is ${\mathbf{K}}_\sigma$.
Show first that $F \subset \cup_K F(K)$. By definition,
$\beta \overset{*}{\sim} \gamma$ if there exists $K \in {\mathbb N}$ and
$I \subset {\mathbb N}$ s.t. $|\beta_i - \gamma_i| \leq K$ for any $i \notin I$,
and $\sum_{i \in I} (4^{-\beta_i} + 4^{-\gamma_i}) \leq K$.
Letting $I_n = I \cap \{1, \ldots, n\}$, we see that
$(\beta, \gamma) \in F(K,n,I_n)$ for each $n$, hence
$(\beta, \gamma) \in F(K)$.
To prove the converse implication, suppose $(\beta, \gamma) \in F(K)$
for some $K$, and show that $\beta \overset{*}{\sim} \gamma$.
Construct a tree $T \subset \{0,1\}^{\mathbb N}$: for each $n$,
$T \cap \{0,1\}^n$ consists
of all the sets $I_n$ s.t. $|\beta_i - \gamma_i| \leq K$ for $i \notin I_n$,
and $\sum_{i \in I_n} (4^{-\beta_i} + 4^{-\gamma_i}) \leq K$
(we identify the set of subsets of $\{1, \ldots, n\}$ with $\{0,1\}^n$).
The set $T$ is indeed a tree: if $I_n \in T$,
then $I_n \cap \{1 \ldots, m\} \in T$ for $m < n$.
By assumption, $T$ has arbitrarily long branches. By K\"onig's Lemma
\cite[p.~20]{Ke}, $T$ has an infinite branch, which yields a set
$I \subset {\mathbb N}$ s.t. $|\beta_i - \gamma_i| \leq K$ for $i \notin I$, and
$\sum_{i \in I} (4^{-\beta_i} + 4^{-\gamma_i}) \leq K$.
\end{proof}
Next consider a space $\Xi = \prod_{k \in {\mathbb N}} \Xi_k$, where
$\Xi_k = \{0, \ldots, k-1\}$, with the equivalence relation
$c E_{\ks} b$ iff $\sup_i |c_i - b_i| < \infty$ (here, $c = (c_i)_{i \in {\mathbb N}}$,
$b = (b_i)_{i \in {\mathbb N}}$). By \cite{Ro}, $E_{\ks}$ is a complete ${\mathbf{K}}_\sigma$ relation,
hence, by Lemma~\ref{k_sigma}, it reduces $(S_A, \overset{*}{\sim})$. It remains
to prove the converse.
\begin{proposition}\label{borel2}
There exists a Borel map
$\phi : \Xi \to S_A$ s.t. $\phi(b) \overset{*}{\sim} \phi(c)$ iff $c E_{{\mathbf{K}}_\sigma} b$.
\end{proposition}
\begin{proof}
As $\sum_i 4^{-\alpha_i} = \infty$, and $\lim_i \alpha_i = \infty$, there exists
a sequence of positive integers $1 = p_0 < q_1 < p_2 < q_2 < \ldots$
s.t. $\sum_{i \in I_k} 4^{-\alpha_i} > 4^{2k}$ ($I_k = [p_k, q_k - 1)$),
and $\alpha_{p_{k+1}} > k + q_k$. Define $\phi((b_i)) = (b^\prime_j)$
by setting $b_j^\prime = \alpha_j + b_k$ if $j \in I_k$, and
$b_j^\prime = \min\{\alpha_j + k , \alpha_{p_{k+1}}\}$
if $q_k \leq j < p_{k+1}$. Clearly, $\phi$ is a Borel map.
Moreover, if $c E_{\ks} b$, then $\phi(b) \overset{*}{\sim} \phi(c)$. Suppose, on the
contrary, that $b^\prime \overset{*}{\sim} c^\prime$, where $b^\prime = \phi(b)$ and
$c^\prime = \phi(c)$. Then there exists a set $I \subset {\mathbb N}$ and $K \in {\mathbb N}$
s.t. $|b_j^\prime - c_j^\prime| \leq K$ for $j \notin I$, and
$\sum_{j \in I} (4^{-b_j^\prime} + 4^{-c_j^\prime}) \leq K$.
We shall show that $|b_k - c_k| \leq K$ for all but finitely many $k$'s.
Indeed, otherwise there exist infinitely many $k$'s s.t. $I_k \subset I$
(this follows from the fact that
$b_j^\prime - c_j^\prime = b_k - c_k$ for $j \in I_k$).
But
$$
\sum_{j \in I_k} (4^{-b_j^\prime} + 4^{-c_j^\prime}) \geq
2 \cdot 4^{-k} \sum_{j \in I_k} 4^{-\alpha_j^\prime} > 1 ,
$$
hence
$$
\sum_{j \in I} (4^{-b_j^\prime} + 4^{-c_j^\prime}) \geq
\sum_{I_k \subset I} \sum_{j \in I_k} (4^{-b_j^\prime} + 4^{-c_j^\prime}) =
\infty ,
$$
a contradiction.
\end{proof}
\begin{proof}[Conclusion of the proof of Theorem~\ref{bireducible}]
By Corollary~\ref{reduction1}, $(\mathbf{S}(X(A)), \simeq)$ and $(S_A, \overset{*}{\sim})$ are
Borel bireducible to each other. By Lemmas \ref{k_sigma} and \ref{borel2},
$(S_A, \overset{*}{\sim})$ is Borel bireducible to a complete ${\mathbf{K}}_\sigma$ relation.
\end{proof}
\begin{remark}\label{banach_classify}
For many separable Banach spaces $X$, it is known that the isomorphism
relation on $\mathbf{S}(X)$ reduces certain ``classical'' relations, such as $E_{\ks}$
(see e.g. \cite{An, FG, FLRo, FRo}).
\end{remark}
\section{Proofs of Theorems \ref{intro:Ksigma},
\ref{intro:unique_basis}, \ref{intro:subbasis}}\label{main_proofs}
Recall that the class $\boldsymbol{\mathfrak{C}}$ consists of all compact contractions,
which are not Hilbert-Schmidt, and the family $\boldsymbol{\mathfrak{F}}$ is the set of all
operator spaces $X(A)$, where $A \in B(\ell_2)$ belongs to $\boldsymbol{\mathfrak{C}}$.
Clearly, all these spaces are isometric to $\ell_2$.
\begin{proof}[Proof of Theorem \ref{intro:Ksigma}]
Suppose $X(A) \in \boldsymbol{\mathfrak{F}}$. By Theorem~\ref{bireducible} and
Corollary \ref{biembeddable}, the relations of complete
isomorphism and complete biembeddability on $\mathbf{S}(X(A))$
are complete ${\mathbf{K}}_\sigma$. To show that $\boldsymbol{\mathfrak{F}}$ contains a continuum
of spaces, not completely isomorphic to each other, pick
$A \in B(\ell_2) \cap \boldsymbol{\mathfrak{C}}$. Consider a space
$\Xi = \prod_{k \in {\mathbb N}} \Xi_k$, where $\Xi_k = \{0, \ldots, k-1\}$,
with the equivalence relation $c E_{\ks} b$ iff $\sup_i |c_i - b_i| < \infty$
(here, $c = (c_i)_{i \in {\mathbb N}}$, $b = (b_i)_{i \in {\mathbb N}}$). By the results
of Section~\ref{classification}, there exists a Borel map
$\Phi : \Xi \to \mathbf{S}(X(A))$, such that $\Phi(b) \simeq \Phi(c)$ iff
$b E_{\ks} c$. It remains to find a family
$(b_\varepsilon)_{\varepsilon \in \{0,1\}^{\mathbb N}} \subset \Xi$, such that
$b_\varepsilon E_{\ks} b_\delta$ iff $\varepsilon = \delta$. To this end, write
${\mathbb N}$ as a disjoint union of infinite sets $I_k$ ($k \in {\mathbb N}$).
For any $\varepsilon = (\varepsilon_k)_{k=1}^\infty$, define
$$
b_\varepsilon(i) = \left\{ \begin{array}{ll}
0 & i \in I_k, \, \varepsilon(k) = 0 \\
i-1 & i \in I_k, \, \varepsilon(k) = 1
\end{array} \right. .
$$
Clearly, this family $(b_\varepsilon)$ has the desired properties.
\end{proof}
\begin{proof}[Proof of Theorem \ref{intro:unique_basis}]
Consider $A \in B(\ell_2)$ of class $\boldsymbol{\mathfrak{C}}$.
The existence of the canonical basis has been established at the
beginning of Section~\ref{sequences}, while its uniqueness follows from
Proposition~\ref{unique_basis}.
\end{proof}
\begin{proof}[Proof of Theorem \ref{intro:subbasis}]
Combine Theorem~\ref{intro:unique_basis} with Theorem~\ref{subbasis}
and Corollary~\ref{cor_subbasis}.
\end{proof}
\section{Isometric classification: proof of Theorem~\ref{intro:banach}}\label{banach}
We handle the real case.
Begin by introducing a numerical invariant of
subspaces of $X = \mathbb R \oplus_1 \ell_2$. Denote by $P$ the ``natural''
projection onto $\mathbb R$. For $Y \in \mathbf{S}(X)$, define $c(Y) = \|P|_Y\|$.
\begin{lemma}\label{attains}
For $Y \in \mathbf{S}(X)$, there exists $x \in Y$ such that
$\|x\| = 1$, and $\|P x\| = c(Y)$. Moreover, if this $x$ is
written as $x = c(Y) \oplus (1 - c(Y))\xi_0$,
then $Y = \span[x, Y^\prime]$, where
$Y^\prime = \{0 \oplus \xi : \xi \in (Y \cap \ell_2) \cap \xi_0^\perp\}$.
\end{lemma}
\begin{proof}
If $c(Y) = 0$, the statement is trivial. Suppose $c(Y) = 1$. Then, for every
$n \in {\mathbb N}$, there exists $t_n \in (1-1/n, 1]$ and $\xi_n \in \ell_2$ s.t.
$\|\xi_n\| = 1$, and $t_n \oplus (1-t_n) \xi_n \in X$. As $Y$ is closed,
$1 \oplus 0 \in Y$.
Next consider $c(Y) \in (0,1)$. Suppose, for the sake of contradiction,
that there is no $x$ as in the statement of the lemma. Then for every
$n \in {\mathbb N}$ there exist $t_n \in (c(Y) - 1/n, c(Y))$, and $\xi_n \in \ell_2$
s.t. $\|\xi_n\| = 1$, and $t_n \oplus (1-t_n) \xi_n \in Y$.
Passing to a subsequence if necessary, we can assume that $(\xi_n)$ is
a Cauchy sequence in $\ell_2$. Indeed, otherwise there exist
$n_1 < n_2 < \ldots$ and $\alpha > 0$, such that, for any $i$,
$\|\xi_{n_{i+1}} - \xi_{n_i}\| > \alpha$. By the uniform convexity of
Hilbert spaces (which follows, for instance, from the parallelogram identity),
there exists $\beta > 0$ s.t.
$\|(1-t_{n_{i+1}}) \xi_{n_{i+1}} + (1-t_{n_i}) \xi_{n_i}\|/2 < 1 - c(Y) - \beta$
for any $i$. Define
$$
y_i = \frac{t_{n_{i+1}} + t_{n_i}}{2} \oplus
\frac{(1-t_{n_{i+1}}) \xi_{n_{i+1}} + (1-t_{n_i}) \xi_{n_i}}{2} \in Y .
$$
Then $\|y_i\| < 1 - \beta$, and $\lim_i \|P y_i\| = c(Y)$.
Therefore, $\|P|_Y\| > c(Y)$, which is impossible.
Thus, the sequence $(\xi_n)$ converges to some $\xi_0 \in \ell_2$. Then
$x = c(Y) \oplus (1-c(Y))\xi_0$ is the limit of the sequence
$t_n \oplus (1-t_n) \xi_n$, hence it belongs to $Y$.
Clearly, $\|P x\| = c(Y)$, and $Y = \span[x, Y \cap \ell_2]$.
Moreover, any $\xi \in Y \cap \ell_2$
is orthogonal to $\xi_0$. Indeed, otherwise there exists
$\xi \in Y \cap \ell_2$ and $z \in {\mathbb C}$ s.t. $\|\xi_0 + z \xi\| < \|\xi_0\|$.
Then $x^\prime = x + (0 \oplus \xi) = c(Y) \oplus (\xi_0 + z \xi)$
belongs to $Y$, $\|x^\prime\| < 1$, and $\|P x^\prime\| = c(Y)$,
which is impossible.
\end{proof}
For $t \in [0,1]$, define $\phi(t) = t + \sqrt{(1-t)^2 + 1}$.
Clearly, $\phi$ is continuous and increasing.
\begin{lemma}\label{weak}
For $Y \in \mathbf{S}(X)$,
$$
\phi(c(Y)) = \sup \big\{ \liminf_i \|x + y_i\| : x, y_i \in Y, \, \,
\|x\| = \|y_i\| = 1 , \, \, y_i \overset{w}{\to} 0 \big\} .
$$
Moreover, there exist a norm $1$ $x \in Y$, and a normalized
weakly null sequence $(y_i)$ in $Y$, such that
$\phi(c(Y)) = \|x + y_i\|$ for every $i$.
\end{lemma}
\begin{proof}
Assume $c(Y) \in (0,1)$ (only minimal changes are needed to
handle $c(Y) \in \{0,1\}$).
Write $x = t \oplus (1-t) \xi$ and $y_i = t_i \oplus (1-t_i) \xi_i$.
Here, $t, t_i \in [0,1]$, $\xi_i \in \ell_2$, and $\|\xi_i\| = 1$.
As $y_i \to 0$ weakly, $t_i \to 0$, and $\langle \xi, \xi_i \rangle \to 0$.
Therefore, $\lim_i \|x + y_i\| = \phi(t_i)$. Taking the supremum over all
$x \in Y$, we prove the desired equality. Furthermore, by Lemma~\ref{attains},
$Y = \span[x, Y \cap \ell_2]$, where $x = c(Y) \oplus (1-c(Y)) \xi_0$,
$\xi_0 \in \ell_2$ has norm $1$, and $Y \cap \ell_2$ is
orthogonal to $\xi_0$. Let $(\xi_i)$ be an orthonormal basis in
$Y \cap \ell_2$. Then $\phi(c(Y)) = \|x + y_i\|$ for every $i$, and
$y_i \overset{w}{\to} 0$.
\end{proof}
\begin{lemma}\label{almost_embed}
If $Y$ and $Z$ are infinite dimensional subspaces of $X$, and $Y$ is
almost isometrically embeddable into $Z$, then $c(Y) \leq c(Z)$.
\end{lemma}
\begin{proof}
By definition, for every $\lambda \in (1, 1.1)$, there exist a subspace
$W \hookrightarrow Z$ and a contraction $T : Y \to W$ with $\|T^{-1}\| < \lambda$.
It suffices to show that
\begin{equation}
\phi(c(W)) \geq \lambda^{-1} \phi(c(Y)) - 2 (\lambda - 1) .
\label{compare_phi}
\end{equation}
Indeed, then we would conclude
$$
\phi(c(Z)) \geq \phi(c(W)) \geq \lambda^{-1} \phi(c(Y)) - 2 (\lambda - 1) .
$$
As the above inequality holds for any $\lambda > 1$, we
conclude that $\phi(c(Y)) \leq \phi(c(Z))$.
By the monotonicity of $\phi$, $c(Y) \leq c(Z)$.
By Lemma~\ref{weak}, there exists a normalized weakly null sequence
$(y_i)$ in $Y$, and a norm one $x \in Y$, such that
$\phi(c(Y)) = \|x + y_i\|$. In the space $W$, consider the elements
$x^\prime = Tx/\|Tx\|$, and $y_i^\prime = T y_i/\|T y_i\|$.
Then the sequence $(y_i^\prime)$ is weakly null, and
\begin{equation}
\|x^\prime + y_i^\prime\| \geq \|T(x + y_i)\| -
\|(1-\|Tx\|^{-1}) Tx\| - \|(1-\|Ty_i\|^{-1}) Ty_i\| .
\label{triangle}
\end{equation}
But $\|T^{-1}\| \|T(x + y_i)\| \geq \|x+y_i\|$, hence
$\|T(x + y_i)\| > \lambda^{-1} \phi(c(Y))$. Furthermore,
$1 \geq \|Tx\| > \lambda^{-1}$, hence
$\|(1-\|Tx\|^{-1}) Tx\| < \lambda - 1$.
Similarly, $\|(1-\|Ty_i\|^{-1}) Ty_i\| < \lambda - 1$.
By \eqref{triangle}, $\|x^\prime + y_i^\prime\| >
\lambda^{-1} \phi(c(Y)) - 2 (\lambda - 1)$.
Applying Lemma~\ref{weak}, we obtain \eqref{compare_phi}.
\end{proof}
\begin{lemma}\label{c(Y)=c(Z)}
If $Y$ and $Z$ are infinite dimensional subspaces of $X$, and
$c(Y) = c(Z)$, then $Y$ is isometric to $Z$.
\end{lemma}
\begin{proof}
We consider the case $c(Y) = c(Z) \in (0,1)$ (the extreme
cases of $c(Y) = c(Z) \in \{0,1\}$ are handled similarly).
By Lemma~\ref{attains}, $Y$ contains a norm one
$y = c(Y) \oplus \xi_Y \in Y$ (note that $\|\xi_Y\| = 1 - c(Y)$),
s.t. $Y = \span[y, Y \cap \ell_2]$, and $Y^\prime = Y \cap \ell_2$
is orthogonal to $\xi_Y$. Thus, for any $\xi \in Y^\prime$,
$\|y + \xi\| = c(Y) + \sqrt{(1-c(Y))^2 + \|\xi\|^2}$.
Similarly, $Z = \span[z, Z^\prime]$, and
$\|z + \eta\| = c(Z) + \sqrt{(1-c(Z))^2 + \|\eta\|^2}$
for any $\eta \in Z^\prime$. As $Y^\prime$ and $Z^\prime$
are both infinite dimensional separable Hilbert spaces,
there exists an isometry $T^\prime$ from $Y^\prime$ onto $Z^\prime$.
We complete the proof by defining the isometry $T$ from $Y$ onto $Z$
by setting $T y = z$, and $T|_{Y^\prime} = T^\prime$.
\end{proof}
\begin{proof}[Proof of Theorem~\ref{intro:banach}]
By Lemmas \ref{almost_embed} and \ref{c(Y)=c(Z)}, the following statements
are equivalent for $Y, Z \in \mathbf{S}(X)$: (i) $Y$ and $Z$ are isometric,
(ii) $ d(Y,Z) = 1$, (iii) $Y$ and $Z$ are isometrically bi-embeddable,
(iv) $Y$ and $Z$ are almost isometrically bi-embeddable, (v) $c(Y) = c(Z)$.
Denote that canonical basis for $\ell_2$ by $e_0, e_1, \ldots$, and
consider a map
$$
\Phi : [0,1] \to \mathbf{S}(X) : t \to
\span[t \oplus (1-t)e_0, 0 \oplus e_1, 0 \oplus e_2, \ldots] .
$$
Then $c(\Phi(t)) = t$, hence $\Phi(t_1)$ and $\Phi(t_2)$ satisfy any
(equivalently, all) of the relations (i) -- (iv) iff $t_1 = t_2$.
It remains to prove that the maps $\Phi$ and $c$ are Borel.
To handle $\Phi$, consider an open ball $U \subset X$ with the
center at $\alpha \oplus \sum_{i=0}^N \beta_i e_i$ and radius $r$. Then
$\Phi(t) \cap U \neq \emptyset$ iff there exist
$\lambda_0, \ldots, \lambda_N \in \mathbb{Q}$ s.t.
$$
|\alpha - t \lambda_0| +
\Big( |\beta_0 - (1-t) \lambda_0|^2 +
\sum_{i=1}^N |\beta_i - \lambda_i|^2 \Big)^{1/2} < r .
$$
This inequality describes a Borel subset of $[0,1]$.
As any open subset of $X$ is a countable union of open balls,
the map $\Phi$ is Borel.
To deal with $c$, consider the sets
$$
U_t = \big\{s \oplus \xi \in \mathbb R \oplus_1 \ell_2 :
|s| > t , \, \|\xi\| < \sqrt{1 - t^2} \big\}
$$
($t \in [0,1]$). Clearly, $U_t$ is an open subset of $X$, and
$c(Y) > t$ iff $Y \cap U_t \neq \emptyset$.
\end{proof}
\begin{remark}\label{other_p}
Theorem~\ref{intro:banach} holds not only for $\mathbb R \oplus_1 \ell_2$, but
also for $\mathbb R \oplus_p \ell_2$, for $1 \leq p < 2$.
\end{remark}
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 1,758
|
Copyright ©2003 by the Cato Institute.
All rights reserved.
ISBN 1-930865-53-8
Printed in the United States of America.
Cato Institute
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Washington, D.C. 20001
www.cato.org
Copyright © 2003 by the Cato Institute.
All rights reserved.
First Paperback Printing, 2004
Library of Congress Cataloging-in-Publication Data
Bernstein, David E.
You can't say that! : the growing threat to civil liberties from antidiscrimination laws / David E. Bernstein.
p. cm.
Includes bibliographical references and index.
ISBN 1-930865-53-8 (cloth : alk. paper)
1. Civil rights--United States. 2. Discrimination--Law and legislation--United States. I. Cato Institute. II. Title.
KF4749.B47 2003
342.7308'53--dc22
2003055808
Cover design by Amanda Elliott.
Printed in the United States of America.
CATO INSTITUTE
1000 Massachusetts Ave., N.W.
Washington, D.C. 20001
To the memory of my grandparents and great-grandparents, the Bernsteins, Jozefsons, Kaplans, and Steins, who fled Europe for their lives and their freedom and found a haven of liberty for themselves and their progeny in America.
# Acknowledgments
I have been intrigued by conflicts between antidiscrimination laws and freedom of expression since 1990, when writer Sheldon Richman told me that his brother had gotten into trouble for placing a real estate advertisement in the Philadelphia Jewish Exponent stating that a house he was selling was ''walking distance to the synagogue.'' This was pertinent information for an ad in a Jewish newspaper because Orthodox Jews are forbidden to drive to synagogue on the Sabbath and on many holidays. Nevertheless, local fair housing officials thought the ad was discriminatory. They claimed that, by noting proximity to a synagogue, the ad illegally expressed an implicit preference for Jewish buyers, thereby violating laws banning housing discrimination on the basis of religion. Appalled and intrigued, I did some further research, from which I discovered that the Fair Housing Act was consistently being enforced in ways that seemed to violate the First Amendment. I also began to notice news reports suggesting that other antidiscrimination laws were increasingly impinging on civil liberties. I resolved that someday I would write a book on the subject.
An opportunity to start work on such a book came in 1998, when a fellowship grant from the John M. Olin foundation relieved me of my teaching and committee responsibilities at the George Mason University School of Law for a year. My primary project for the year was to complete Only One Place of Redress: African Americans, Labor Regulations, and the Courts from Reconstruction to the New Deal (Duke University Press, 2001), but I made substantial progress on this book as well.
One problem I confronted in starting this book was that I understood that outside of the academic press market, the market for serious nonfiction is limited, and that authors who take politically incorrect positions, as I knew I would, face a particularly difficult time finding publishers among leading trade presses. David Boaz and the Cato Institute came to the rescue. As further incentive to get going, I was invited to publish initial versions of bits and pieces of what ultimately became the book as symposium articles: ''The Right of Expressive Association and Private Universities' Racial Preferences and Speech Codes,'' William and Mary Bill of Rights Journal 9 (2001); ''Antidiscrimination Laws and the First Amendment,'' Missouri Law Review 66 (2001); and ''Sex Discrimination Laws Versus Civil Liberties,'' University of Chicago Legal Forum 1999. Michael Abramowicz, Neal Devins, Richard Epstein, Eugene Volokh, and Todd Zywicki commented on one of more of these articles. An earlier version of Chapter 12 appeared in Liberty magazine.
As the book progressed, I received assistance from a variety of sources. The Law and Economics Center at the George Mason University School of Law provided generous summer research funding. Daniel Polsby, Associate Dean for Academic Affairs at George Mason Law, arranged a reduced teaching schedule in exchange for a promise to complete a book manuscript. Walter Olson gave me helpful early advice. Lillian Bernstein read part of the book manuscript and insisted that I eliminate legal jargon. Michael Abramowicz, Stanley Bernstein, Gene Healy, Robert Levy, and Sara Pikofsky each read and commented on at least one complete draft of the book. Conversations with Eugene Volokh, both in person and via e-mail, helped clarify several important constitutional issues for me. I bounced many of the ideas in this book off my law professor colleagues on the ConLawProf listserv.
Nate Oman and James Winn provided outstanding research assistance. Nate's services were provided by the Institute for Humane Studies at George Mason University, which has been helpful to me in many ways since I was a senior in college. Olson's Overlawyered.com and Volokh's ''Freedom of Speech vs. Workplace Harassment Law'' (www.1.law.ucla.edy/~volokh/harass/) were extremely useful in providing leads on cases and other ammunition for this book. Readers who enjoy this book should be sure to visit both of those sites. John Showalter and Marni Soupcoff provided excellent editorial assistance. Micah Thorner went above and beyond the call of duty in providing amazingly prompt and efficient secretarial help while I was completing the final draft of the manuscript as a visiting professor at the Georgetown University Law Center in Spring of 2003. Finally, I would like to thank David Boaz for reading and commenting on several drafts of the book manuscript, and for otherwise shepherding this book through the publication process.
# Introduction
Intolerant activists are determined to impose their moralistic views on all Americans, regardless of the consequences for civil liberties. These zealots are politically well organized and are a dominant force in one of the two major political parties. They have already achieved many legislative victories, especially at the local level, where they often wield disproportionate power. Courts have often acquiesced to their agenda, even when it conflicts directly with constitutional provisions protecting civil liberties. Until the power of these militants is checked, the First Amendment's protection of freedom of speech and freedom of religion will be in constant danger.
To many civil libertarians, the preceding paragraph reads like a description of the Christian right. But it also describes left-wing egalitarian activists, many of whom are associated with the ''civil rights'' establishment. Their agenda of elevating antidiscrimination concerns above all others poses an acute threat to civil liberties. The First Amendment prohibits the government from interfering with freedom of expression, which includes free exercise of religion, freedom of speech, freedom of the press, and the right to petition the government for a redress of grievances. All of these civil libertarian restrictions on government power are at risk from antidiscrimination laws. For example:
* In Berkeley, the federal Department of Housing and Urban Development threatened to sanction three neighborhood activists for organizing community opposition to a plan to turn a rundown hotel into a homeless center. HUD alleged that the activists had violated the Fair Housing Act by interfering with a project that would serve a group of people who would be disproportionately mentally ill or recovering substance abusers, protected groups under the Act. HUD spokesperson John Phillips, trying to parry free speech concerns raised by the media, instead stoked them. ''To ask questions is one thing,'' Phillips told reporters. ''To write brochures and articles and go out and actively organize people to say, 'We don't want those people in those structures,' is another.''1
* In San Francisco, Krissy Keefer is using an antidiscrimination law to challenge the artistic autonomy of the San Francisco Ballet. She is suing the ballet for height and weight discrimination for refusing to accept her daughter Fredrika into its preprofessional program. Fredrika is of average height and weight, while modern ballet's aesthetic standards require that dancers be tall and lithe.2
* In Denver, the city government refused to issue a Columbus Day parade permit unless the organizers signed an agreement stating that ''there will be no references, depictions, or acknowledgment of Christopher Columbus during the parade; and no speeches or wreath laying for Christopher Columbus will be conducted.'' The city was responding to pressure from American Indian activists, who alleged that a parade celebrating Columbus would create an illegal ''hostile public environment.''3
* In New York City, Michelle Ganzy sued the Allen Christian School for firing her after she became pregnant out of wedlock. Ganzy, like all of the school's teachers, had agreed to serve as a role model for her students, in part by behaving in accordance with the school's conservative moral beliefs. Nevertheless, Ganzy sued for sex discrimination. A federal court, seemingly oblivious to the threat this lawsuit posed to the autonomy of religious institutions, ruled in her favor, holding that ''[r]estrictions on pregnancy are not permitted because they are gender discriminatory by definition.''4
* In Minneapolis, a group of librarians complained of sexual harassment because patrons using the library computers viewed images the librarians saw and found offensive. The Equal Employment Opportunity Commission found that the librarians had ''probable cause'' to pursue their claim. Because of this and similar cases, public and private libraries throughout the United States are under pressure to install filtering software on their computers, lest a librarian inadvertently view offensive material and file a sexual harassment lawsuit. Defining the issue precisely backwards, a representative of the National Organization for Women told the New York Times that she wondered ''how far First Amendment rights may go before they infringe on sexual harassment laws.''5
* In Eugene, Oregon, the state Newspaper Publishers Association published a list of 80 words and phrases that its members should ban from real estate advertisements to avoid liability under federal, state, or local fair housing laws. The forbidden words and phrases include language that signifies an obvious intent to violate fair housing laws (e.g., ''no Mexicans''), but also language that is merely descriptive, such as ''near church'' or ''walking distance to synagogue.'' Fair housing officials overzealously interpret such phrases as expressing an illicit preference for Christians and Jews, respectively. The list also includes phrases that some fair housing officials believe are used as codes to discourage minorities (''exclusive neighborhood,'' ''board approval required'') or families with children (''quiet tenants,'' ''bachelor pad'').6 There are a number of other phrases that did not make the Oregon list, but that some realtors avoid nonetheless for fear of liability, including the following: master bedroom (either sexist or purportedly evocative of slavery and therefore insulting to African Americans), great view (allegedly expresses preference for the nonblind), and walk-up (supposedly discourages the disabled).7
* Religious conservatives have also jumped on the antidiscrimination bandwagon. In Wellsville, Ohio, Dolores Stanley celebrated her new job as manager of the local Dairy Mart by removing Playboy and Penthouse from the store's shelves. ''It goes against everything I believe in as a Christian,'' Stanley said. ''There's no way I could participate in that.'' Stanley's superiors at corporate headquarters, attempting to exercise Dairy Mart's First Amendment right to sell legal magazines, told Stanley to replace the periodicals. She refused and was fired. The American Family Association, a conservative antipornography organization, represented Stanley in a lawsuit against Dairy Mart for sex and religious discrimination and for subjecting her to a ''hostile workplace environment.''8 The case settled before trial for a sum ''well into the six figures.''9
These anecdotes are just a few examples of the growing threat antidiscrimination laws pose to civil liberties. Some civil libertarians have attempted to finesse the issue by redefining civil liberties to include protection from the discriminatory behavior of private parties. Under this view, conflicts between freedom of expression and antidiscrimination laws could be construed as clashes between competing civil liberties. For purposes of this book, however, civil liberties retains its traditional definition, referring to constitutional rights protected by the First Amendment and related constitutional provisions.
The clash of civil liberties and antidiscrimination laws has emerged due to the gradual expansion of such laws to the point at which they regulate just about all aspects of American life. This expansion of antidiscrimination laws, in turn, reflects a shift in the primary justification for such laws from the practical, relatively limited goal of redressing harms visited upon previously oppressed groups, especially African Americans, to a moralistic agenda aimed at eliminating all forms of invidious discrimination. Such an extraordinarily ambitious goal cannot possibly be achieved—or even vigorously pursued—without grave consequences for civil liberties.
* * *
The civil rights movement initially focused on integrating African Americans into the nation's economic life. Civil rights activists persuasively argued that since the end of slavery, whites in the United States had used a combination of social pressure, violence, and law to exclude African Americans (and, to a lesser extent, other minorities) from certain jobs, leisure activities, and neighborhoods. In the South, especially, a web of law and custom had relegated African Americans to something akin to a lower caste than whites. Righting matters, activists argued, required federal laws banning discrimination not only by state and local governments, but also by large private employers and business proprietors.10 Other groups received protection from the 1964 Civil Rights Act by piggybacking on the moral authority of the African American freedom struggle.
The provisions of the 1964 Civil Rights Act banning racial discrimination by state and local governments were uncontroversial outside of the often overlapping racist and ''states' rights'' circles. The provisions banning discrimination by private parties, however, ran against a strong libertarian streak in American society that values freedom of association. Civil libertarians had traditionally been wary of antidiscrimination laws that applied to the private sector. In 1945, for example, a group of civil libertarians, including Nation publisher and NAACP cofounder Oswald Garrison Villard, publicly opposed a proposed New York fair employment law. They urged civil rights supporters to respect freedom of association and to ''rely on the force of slow but steadily growing public opinion,'' not legal compulsion, to combat employment discrimination.11 In 1959, liberal philosopher Hannah Arendt published an essay in which she denounced discrimination by government, especially bans on interracial marriage—a taboo subject in those days—but also made clear her opposition to antidiscrimination laws that applied to the private ''social sphere.''12 ''Discrimination,'' she wrote, ''is as indispensable a social right as equality is a political right.''
By the 1960s, however, civil rights advocates had persuaded most civil libertarians that it was impossible to defeat the quasi-caste system faced by African Americans without some interference with the private sector. In particular, civil libertarians agreed that freedom of association, which had already been effectively quashed for generations by both government and private violence in the Jim Crow South and elsewhere, could not suddenly become the governing principle of American race relations. A hands-off policy was especially unattractive in the South, where state and local government remained firmly in the hands of segregationists who could pressure businesses to retain Jim Crow. Federal antidiscrimination law instead provided business owners—of whom many had found Jim Crow to be a costly nuisance—with the wherewithal to integrate, by freeing them from the threat of retaliation by local officials.13
Civil libertarians' concerns were also assuaged because the 1964 Civil Rights Act did not drastically infringe on civil liberties. The Act did impinge on freedom of association, but it only applied to relatively large businesses—those with 15 or more employees—and to places of public accommodation. Large businesses were already subject to myriad government regulations, and public accommodations had a centuries-old common law legal duty to serve all comers.14 The Act covered educational institutions, but applied only to institutions that wished to receive federal funds, a relatively minor source of revenue for most universities at the time. Religious organizations received exemptions from some aspects of the law.
Civil rights advocates' respect for the First Amendment helped ensure that the early laws created little conflict with civil liberties. The source of this respect was that the constitutional protections afforded speech, assembly, and religion had been crucial to the success of the civil rights movement. Supreme Court decisions enforcing civil rights activists' First Amendment rights consistently checked attempts by southern states to stifle the movement. Meanwhile, the movement established a base in black churches because even racist southern governments felt compelled to provide them a large measure of autonomy. Civil rights supporters, including government officials charged with enforcing the new laws, therefore thought it both shortsighted and wrong to eviscerate civil liberties in the name of civil rights. Major civil rights groups, including the NAACP and the American Jewish Congress, even opposed hate speech laws, which enjoyed a brief wave of popularity in the late 1940s and early 1950s.15 For many years following passage of the 1964 Civil Rights Act, few if any cases brought under antidiscrimination laws impinged on freedom of expression or free exercise of religion.
Destroying the quasi-caste system that had excluded African Americans from many employment opportunities and public accommodations seemed a daunting task in 1964, but the system was dismantled surprisingly quickly and easily. Within a few years of the passage of the 1964 Civil Rights Act, racial exclusion and segregation by hotels, restaurants, theaters, and other commercial spaces virtually disappeared. Within a decade, major corporate employers not only stopped barring African Americans (and women) from many positions, but began to aggressively recruit and promote them—at times in preference to white males with better paper credentials. Universities, once notorious for exclusionary practices, engaged in particularly aggressive affirmative action policies, as did many government agencies.
Support among whites for equal opportunity continued its long-term dramatic rise. The proportion of the public telling pollsters that African Americans should have the same job opportunities as whites rose from 42 percent in 1944 to 87 percent in 1966.16 Employment discrimination persisted, especially in blue-collar redoubts such as the construction industry, and integration remained elusive in both education and housing. Nevertheless, many barriers that had seemed almost insurmountable in 1964 had ceased to exist less than a decade later.
Once the racial caste system was largely dismantled, and newly organized groups—such as older Americans, gays, and the disabled—began to use civil rights terminology in expressing their demands for government intervention on their behalf, antidiscrimi-nation activists shifted their rhetorical emphasis. They no longer focused on historical and economic arguments regarding the need to end racial discrimination in employment and places of public accommodation. Rather, they argued that discrimination—as expansively defined by organized interest groups—should be banned as a moral evil. Once private-sector discrimination was portrayed primarily as a secular sin, rather than as an economic issue, the rhetorical goal of civil rights advocates became the elimination of invidious discrimination.
Ironically, conservatives were partly responsible for this shift in emphasis. Conservatives had generally opposed the 1964 Civil Rights Act on states' rights grounds. Eventually, they became supporters of the Act and adopted the argument that antidiscrimination law's basic purpose was to eliminate the moral evil of discrimination. For example, the first President Bush, who had voted against the 1964 Civil Rights Act as a congressman from Texas, in 1990 called discrimination ''a fundamental evil that tears at the fabric of our society.''17 In part, this shift was a result of a genuine change of heart among conservatives who were embarrassed by their previous tolerance of Jim Crow. But the emphasis on the moral component of antidiscrimination law also served a tactical goal: some conservatives believed that this emphasis would advance their argument that affirmative action preferences for minorities, whether voluntary or demanded by the government, should be banned as discrimination against whites.18
As the primary justification for antidiscrimination laws shifted from aiding previously oppressed groups to an austere moralism, the laws broadly expanded at the local, state, and federal levels. Antidiscrimination laws came to protect more and more groups against more and more types of discrimination. Enforcement of the laws gradually took on authoritarian traits, encouraged by the establishment of bureaucracies at all levels of government charged solely with the enforcement of antidiscrimination laws. Indeed, many jurisdictions came to call their civil rights enforcement bureaucracies ''human rights'' agencies—the term suggesting that enforcing anti-discrimination laws against private parties is analogous to enforcing bans on other activities widely regarded as violations of human rights, such as slavery, torture, and genocide.
As the intense moralism of modern antidiscrimination ideology became entrenched in American politics and society, antidiscrimination advocates, especially those who worked for the enforcement bureaucracies, increasingly viewed civil liberties as, at best, competing rights to be balanced against efforts to wipe out bigotry. At worst, they saw civil liberties as inconvenient and unnecessary obstacles to a discrimination-free world. This had grave practical implications for the First Amendment. HUD, for example, consistently interpreted ambiguous provisions of the Fair Housing Act in ways that threatened freedom of expression. Meanwhile, many courts interpreted antidiscrimination laws broadly, at times absurdly so. For example, courts consistently broadened the definition of ''places of public accommodation'' subject to antidiscrimination law to encompass entities like membership organizations that are neither ''places'' nor ''public'' nor ''accommodations'' according to the dictionary definitions and common usages of those words.
By the mid-1980s, antidiscrimination laws had emerged as a serious threat to civil liberties. Courts found that these laws punished everything from refusing to cast a pregnant woman as a bimbo in a soap opera, to giving speeches extolling the virtues of stay-at-home mothers, to expressing politically incorrect opinions at work, to refusing to share one's house with a gay roommate, to refusing to fund heretical student organizations at a Catholic university. Defendants protested that their First Amendment rights were being trampled on, but to no avail. Through the early 1990s, courts consistently refused to enforce First Amendment rights and other constitutionally protected civil liberties when their enforcement would have limited the reach of antidiscrimination laws. The trend of recent court decisions seems more friendly to civil liberties, largely because the courts have been populated with conservatives less committed to the antidiscrimination agenda. However, the final outcome of the conflict between civil liberties and antidiscrimination laws remains unresolved. Meanwhile, the fear of litigation—fear not only of actually losing a lawsuit, but also fear of being vindicated only after a protracted, expensive legal battle—is having a profound chilling effect on the exercise of civil liberties in workplaces, universities, membership organizations, and churches throughout the United States.
* * *
This book is a broad critical overview of the growing conflict between antidiscrimination laws and civil liberties. Chapter 1, by necessity the densest and most academic chapter of the book, discusses the normative and constitutional reasons why the clash between civil liberties and antidiscrimination laws should be resolved firmly in favor of civil liberties. The next four chapters discuss the growing regulation by antidiscrimination laws of speech, including workplace speech, artistic expression, political speech, and campus speech. The sixth chapter explores the government's use of antidiscrimination laws to force individuals and businesses to engage in speech. Chapters 7 and 8 recount how the growing scope of laws banning discrimination in public accommodations threatens the autonomy of private institutions and threatens to squelch the formation of organizations established for expressive purposes. In the next two chapters, the book discusses conflicts between antidiscrimination laws and religious freedom, focusing on religious schools and religious landlords, two groups that risk discrimination lawsuits when they act in accordance with their beliefs about sexual morality. Chapter 11 raises the issue of whether there are any organizations or activities too intimate to come constitutionally within the scope of antidiscrimination laws. The final chapter discusses the American Civil Liberties Union's unwillingness to consistently defend civil liberties against antidiscrimination laws.
Given the moral authority of antidiscrimination law in a society still recovering from a viciously racist past, writing a book critical of many of antidiscrimination law's applications is necessarily perilous, the law professor's equivalent of a politician disparaging mom and apple pie. The laudable goal of the ever-broadening antidiscrimination edifice is to achieve a fairer, more just society. Yet even—or perhaps especially—well-meaning attempts to achieve a praiseworthy goal must be criticized when the means used to achieve that goal become a threat to civil liberties.
The student who callously utters a racial epithet, the business executive who excludes Jews from his club, the coworker who tells obnoxious sexist jokes, the neighbor who lobbies against housing for the mentally ill—the actions of these individuals can be infuriating, especially to those who, like the author of this book,19 have been personally victimized by bigots. But the alternative to protecting the constitutional rights of such scoundrels is much worse: the gradual evisceration of the pluralism, autonomy, and check on government power that civil liberties provide.
Students and others interested in delving into the issues discussed in You Can't Say That! in more detail should visit this book's accompanying website, http://mason.gmu.edu/~dbernste/book/, which provides links to all sources cited in the footnotes that are available online and other links to topics discussed in each chapter. The site also provides frequently updated links to reviews of You Can't Say That! , opinion editorials by the author, and videos of the author discussing the book.
# 1. Why Civil Liberties Should Be
Protected from Antidiscrimination
Laws
Almost all of the conflicts described in this book between civil liberties and antidiscrimination laws involve laws that impinge on some form of freedom of expression protected by the First Amendment and related constitutional provisions. In the normal course of things, constitutionally protected civil liberties trump conflicting statutory rules. Yet various courts, including at times the Supreme Court, have held that the government has a ''compelling interest'' in eradicating discrimination sufficient to warrant overriding civil liberties. The courts have not, however, coherently explained why they have granted antidiscrimination laws this extraordinary immunity.
Most Americans consider limiting invidious discrimination against historically disadvantaged groups to be an important governmental interest, an interest that the average citizen might find ''compelling'' in lay terms. But for an interest to be constitutionally compelling, and therefore capable of trumping civil liberties, the interest should not simply be important. Rather, that interest should be so vital that it would be virtually suicidal for society not to limit civil liberties in order to pursue it.1 Indeed, many important governmental interests, such as the government's interest in reducing violent crime, are routinely subordinated to the First Amendment because they are not, constitutionally speaking, compelling interests. For example, incendiary speech currently protected by the First Amendment can encourage violent behavior by glorifying violence against women, as much ''gangsta rap'' does. Yet courts have shown no inclination to uphold bans on such speech.
By contrast, from the late 1970s until the early 1990s courts abandoned civil liberties in favor of antidiscrimination principles with stunning blitheness. State courts went even further, expanding the compelling interest paradigm to antidiscrimination interests that don't even seem objectively important, much less constitutionally compelling. For example, the Alaska Supreme Court found that the state's interest in protecting unmarried heterosexual couples from housing discrimination is sufficiently compelling to override First Amendment rights.2
If judges routinely announced that the government's compelling interest in eradicating violent crime trumped the enforcement of constitutional rights, civil libertarians—in common with other thoughtful Americans—would strongly protest. Yet few civil libertarians protested when courts allowed the government to eviscerate civil liberties to pursue its interest in eradicating discrimination.3 Indeed, many liberal law professors with otherwise impeccable civil liberties credentials went out of their way to justify the courts' malfeasance. The professors argued that the Thirteenth, Fourteenth, and Fifteenth Amendments, passed largely to aid African Americans after the Civil War, create a governmental obligation to enforce equality among groups.4 This obligation, they contend, can in turn supersede explicit protections provided by the Bill of Rights, including the First Amendment.
This argument is wrong, both textually and historically. The Civil War amendments do not purport to guarantee substantive equality, much less to override the First Amendment. The Thirteenth Amendment abolished slavery, the Fourteenth Amendment required states to provide all persons with equal protection of the laws (not equality per se ), and the Fifteenth Amendment guaranteed African Americans the right to vote. None of the Civil War amendments established a right to be free from private-sector discrimination.
Some scholars argue, however, that First Amendment rights should be subordinated to antidiscrimination claims because the ''constitutional value'' of equality as reflected in the Fourteenth Amendment is in tension with the First Amendment ''value'' of freedom of expression.5 The Constitution, however, is first and foremost a legal document, not a mere expression of abstract values. The First Amendment's prohibition on government regulation of freedom of expression does not conflict with the Fourteenth Amendment's requirement that states may not deny equal protection of the laws. For example, an individual who engages in racist speech is protected by the First Amendment and is not violating the Fourteenth Amendment because he is neither an agent of the state nor denying anyone equal protection of the laws.
Arguments that courts should abstract egalitarian values from the Civil War amendments and find that those values trump the First Amendment are not only specious but also extremely dangerous. If courts were to accept such arguments, the slippery slope to broad censorship of speech would be short indeed. For example, public safety, like equality, is an important societal and constitutional value. Under a paradigm that important values override constitutional protections, the government could ban any incendiary speech that implicitly or explicitly encourages violence or criminal activity because such speech could be considered a threat to public safety.6 Any movie, book, or play with an outlaw hero would lose constitutional protection; say goodbye to Robin Hood , Antigone , Bonnie and Clyde , and virtually every Martin Scorsese movie. Moreover, if the constitutional values paradigm were adopted by the courts, the criminal procedure protections of the Fourth, Fifth, and Sixth amendments, such as the right to remain silent and the right to a jury trial, could ultimately be eviscerated. After all, these rights conflict with the ''constitutional value'' of public safety.
The lack of a sound constitutional justification for sacrificing civil liberties to antidiscrimination laws, combined with the increased encroachment of antidiscrimination laws on previously untouched elements of civil society, has led the Supreme Court to become increasingly protective of civil liberties. In 1992, the Court unanimously invalidated a hate speech law as unconstitutional government interference with free speech.7 Several years later, the Court unanimously held that Massachusetts had violated the First Amendment when it tried to force a privately sponsored St. Patrick's Day parade to allow a gay rights group to march under its own banner.8 Most recently, the Court, in a five-to-four decision, upheld the right of the Boy Scouts of America to exclude a gay scoutmaster whose sexual identity, according to the BSA, undermined the BSA's promotion of traditional sexual morality.9 In all these cases, the Court rejected the argument that the government's purported compelling interest in eradicating discrimination trumped the First Amendment.
* * *
In theory, the Constitution's protection of civil liberties is inviolate and therefore not subject to changing intellectual fashion. In practice, however, history teaches that when constitutional provisions lose the support of the public, and especially the support of the legal elite from which federal judges are drawn, those provisions are enervated. Judges will continue to pay lip service to such provisions, but they will fail to properly enforce them until eventually they lose all force.
Given this dynamic, the prospect for continued judicial protection of civil liberties when they impinge upon antidiscrimination concerns is uncertain. Many academics are already disparaging constitutional protection of freedom of expression. Over the last two decades, radical scholars, including many feminists and ''critical race'' theorists, have vociferously attacked the First Amendment as a barrier to the government's ability to pursue sexual and racial equality. Anti–free speech feminists have stated that they would ban what they call ''expressive means of practicing inequality,'' such as publishing ''academic books purporting to document women's biological inferiority to men . . . or [claiming] that reports of rape are routinely fabricated.''10 Critical race theorists, meanwhile, suggest that racist expression is ''so dangerous, and so tied to perpetuation of violence and degradation of the very classes of human beings who are least equipped to respond, that it is properly treated as outside of the realm of protected discourse.''11 From their ivory towers at Harvard, Yale, Chicago, and other elite universities, influential liberal law professors increasingly echo the feminists' and critical race theorists' views.12 The First Amendment is therefore in dire need of a powerful, consistent, defense.
The primary civil libertarian defense of freedom of expression from government suppression is that such freedom is necessary to ensure the existence of a robust marketplace of ideas. Advocates of this position suggest that freedom of expression helps ensure the triumph of reason over prejudice, of enlightened public opinion over entrenched political and economic power. This argument has some force, given the notable successes of the marketplace of ideas in recent American history. In the 1940s, Catholics and Jews were excluded from many universities, private clubs, and corporations; African Americans were segregated by law in the South and subjected to routine discrimination almost everywhere else; Japanese Americans were incarcerated in internment camps; American Indian children were frequently removed from their parents and forcibly assimilated in boarding schools; and male homosexuals were thought to be pedophiles and perverts, and with few exceptions felt obliged to live closeted lives. Sixty years later, the status of all of these groups has improved dramatically. The remarkable social and political transformation in the status of American minority groups was possible only because the Constitution's guarantee of freedom of expression prevented defenders of the discriminatory status quo from using government power to stifle challenges to orthodox attitudes.
Nevertheless, critics of freedom of expression argue that the marketplace of ideas paradigm is an inadequate justification for inhibiting government regulation of speech. They point out that the unregulated marketplace of ideas is highly imperfect, and indeed far less effective than an unregulated economic market when it comes to protecting minorities. Economists point out that a free economic market protects minorities from discrimination to some degree because businesspeople have an economic incentive to hire the most productive workers and to obtain the most customers. Concern for the financial bottom line mitigates the temptation of business owners to indulge their prejudices.
However, minorities get comparatively little innate protection in the political marketplace of ideas because individual citizens have no corresponding incentive (economic or otherwise) to overlook or overcome personal prejudices or opinions about minorities. The average citizen seeking an ideology to guide his voting and other political activity has virtually no incentive to seek and find truth, especially because his opinion is highly unlikely to be decisive on any given matter. Even voters who genuinely seek the truth regarding particular issues will have difficulty finding it. The human mind is cognitively limited and much more suited for certain tasks, such as pursuing economic self-interest, than for others, such as adopting sensible ideological positions. As Nobel economics laureate Ronald Coase points out, ''It's easier for people to discover that they have a bad can of peaches than it is for them to discover that they have a bad idea.''13 Moreover, while in competitive economic markets minorities can generally find safe havens in the private sector even if most organizations discriminate, there is no safe haven for minorities if racist ideas dominate politics and find their way into law.
If anything, then, restrictions on speech that denigrates vulnerable groups are more likely to protect minorities and women over time than are laws banning discrimination in employment. Free speech critics exploit the power of this point by criticizing liberal civil libertarians who vigorously oppose laissez faire economics, especially when it comes to protecting minorities from discrimination, but support an unregulated marketplace of ideas.14 If the government can make the economic marketplace fairer and more efficient by regulating it, they ask, why can the government not do the same for the less-efficient speech marketplace?
One answer, provided by law and economics luminaries such as Ronald Coase and Richard Epstein, is that government regulation of the economic marketplace is at least as wrongheaded as government regulation of the marketplace of ideas. Epstein therefore argues in favor of both the robust protection of First Amendment liberties and the repeal of antidiscrimination laws that apply to private parties.15 Indeed, Epstein suggests that these two policies are synergistic, because he doubts that the freedoms of speech and religion can ultimately be defended from antidiscrimination laws once it is conceded that an antidiscrimination norm is an appropriate legal limit on freedom of contract.
But even civil libertarians who strongly support basic employment and housing discrimination laws can offer a compelling rejoinder to those who advocate allowing such laws to run roughshod over the First Amendment. In contrast to the Panglossian straw men that censorship advocates build and demolish, realistic civil libertarians recognize that the free marketplace of ideas is imperfect, perhaps highly so. However, civil libertarians also recognize that they must still ask the most important question in political economy: compared with what? Although much private speech is wrongheaded or even dangerous, it is even more dangerous to put the government in charge of policing it.16
The alternative to allowing an unregulated speech marketplace is permitting government censorship, leaving ''the government in control of all the institutions of culture, the great censor and director of which thoughts are good for us.''17 For good reason, civil libertarians believe that the government cannot be trusted with the power to establish an official orthodoxy on any issue, cultural or political, or to ensure the ''fairness'' of political debate. As one scholar puts it, ''freedom of speech is based in large part on a distrust of the ability of government to make the necessary distinctions, a distrust of government determinations of truth and falsity, an appreciation of the fallibility of political leaders, and a somewhat deeper distrust of governmental power in a more general sense.''18
Freedom of expression is necessary to prevent government from entrenching itself and expanding its power at the expense of the public. As federal court of appeals judge Frank Easterbrook wrote in an opinion striking down an antipornography statute inspired by academic feminists, ''free speech has been on balance an ally of those seeking change. Governments that want stasis start by restricting speech.... Without a strong guarantee of freedom of speech, there is no effective right to challenge what is.''19 First Amendment scholar John McGinnis likewise notes that government officials have a natural tendency to suppress speech antithetical to their interests. As McGinnis notes, the free flow of information related to politics and culture threatens ''government hierarchies both by rearranging coalitions and revealing facts that will prompt political action.''20
The framers of the American Constitution also recognized that government is in constant danger of capture by factions that desire to use the government for their own private ends, a phenomenon known in modern academic literature as ''rent-seeking.'' The Constitution and Bill of Rights were intended to establish a system of government that limits such rent-seeking. The First Amendment's protection of freedom of expression is particularly important in this regard. The founders believed that once in power, factions would exploit any government authority to regulate speech in self-serving ways. The founders' insights have been confirmed by experience around the world and by modern research into human political behavior by economists and evolutionary psychologists. Permitting government regulation of information relating to politics or culture would come at a very high price to society.21
Contrary to the insinuations of some critics,22 then, all but the most starry-eyed civil libertarians recognize that freedom of expression can have many negative side effects, or, as economists put it, negative externalities. But civil libertarians are also familiar with the voracious lust for power and pursuit of self-interest endemic in politicians and their rent-seeking allies. Civil libertarians apply the cold calculus that the negative externalities caused by government regulation are likely to outweigh any negative externalities that arise from freedom of expression. Or, more simply put, civil libertarians believe that allowing politicians to decide the scope of freedom of speech is simply more dangerous than any damage the speech itself may cause. This is especially true in the United States. In contrast to more statist social systems, the United States has largely maintained a Tocquevillian nature, in which political and cultural innovations arise from the grass roots, not from the government. Freedom of expression is therefore necessary for economic and cultural progress.23
Some scholars recognize the dangers of government regulation of speech but still call for limited censorship to achieve what they consider particularly important antidiscrimination ends. Professor Andrew Koppelman of Northwestern University, for example, argues that there should be a presumption in favor of freedom of expression because ''[r]acist speech may be substantively worthless, but outlawing it would give the state the power to decide which political views are worthless because racist.'' However, although Koppelman acknowledges that government power to censor speech can be ''easily abused,'' he adds that censorship can be justified if the speech in question is ''exceedingly harmful.''24 Koppelman believes that in such cases ''a significant, but limited, infringement on free speech'' is appropriate. He says he would discard any speech restrictions once they had served their purpose of achieving ''work-place equality'' for previously excluded minorities and women.
Koppelman's proposal demonstrates the dangers of divorcing political philosophy from practical political economy. He never clarifies how the government could objectively determine which speech is sufficiently harmful to merit censorship. With the First Amendment effectively nullified under Koppelman's preferred regime, censorship decisions would ultimately be made through ordinary politics, in which voter ignorance, rent-seeking, and similar problems would arise. In the long run, speech restrictions would likely serve the interests of dominant political factions, with no guarantee that those factions would represent the progressive political forces Koppelman supports.
Moreover, even assuming speech restrictions could be limited to the goals set for them by Koppelman, he provides no guidance on how such restrictions would ultimately be abolished once they are in place. He fails to explain how Congress or state legislatures would reach a consensus that the speech restrictions' goals have been achieved, and how legislators would buck the lobbying power of the interest groups that would inevitably coalesce to defend the restrictions. For example, in the 80-plus years since the end of World War I, Congress has not been able to summon the will to permanently abolish the mohair subsidies that were enacted to ensure fabric availability for World War I military uniforms.25 It hardly seems likely, then, that Congress would have the wherewithal to abolish entrenched censorship rules.
* * *
Some civil libertarians argue that the government should force large private institutions, such as universities and large corporations, to adhere to ''First Amendment standards.'' In other words, the government should prohibit large private institutions from penalizing expression if the government itself could not lawfully punish that expression. For example, the California affiliate of the American Civil Liberties Union supported a state law that requires private high schools and universities to permit any speech that the First Amendment requires a public school to tolerate.26 The national ACLU then backed a bill introduced in the U.S. House and Senate that would have extended that rule to universities nationwide.27
As we have seen, the underlying rationale for the First Amendment is to protect the private sector from government regulation of speech. Moreover, the First Amendment—''Congress [and, under modern doctrine, the states] shall make no law''—applies only to the government. The ACLU's argument that the government should impose ''First Amendment standards'' on the private sector is therefore paradoxical. A constitutionally based, normatively sound civil libertarian perspective dictates instead that private entities must be free to adopt idiosyncratic policies regarding expression, even if powerful lobbying groups such as the ACLU believe such policies are unwise. As Professor Randall Kennedy of Harvard Law School suggests, the proper response to private-sector experimentation with speech rules is to ''let a thousand flowers bloom.''28 Indeed, Supreme Court precedent suggests that the First Amendment prohibits the government from interfering with private institutions as they promote and defend particular ideological orthodoxies.29
An exception to the principle that civil liberties concerns are not implicated when private institutions adopt speech rules arises when a private institution adopts a speech rule because the law requires it to do so. For example, a university speech code adopted to comply with sexual harassment laws is an indirect regulation of speech by the government, not a voluntary speech restriction by a private institution. From a First Amendment perspective, such indirect government censorship is just as problematic as direct government control over speech.
* * *
Some scholars, most prominently law professor and literary critic Stanley Fish of the University of Illinois at Chicago, argue that neutral protection of freedom of expression is impossible. In our society, the task of interpreting the First Amendment falls mainly to the judiciary, and Fish argues that judicial invocation of freedom of expression merely masks politically motivated actions. Therefore, according to Fish, the only question worth discussing is who will get the power to censor whom.30
Fish is correct that judges are not Platonic guardians immune from political motivation. However, that does not mean that judges are motivated solely, or even primarily, by politics. Fish's left-wing academic allies have faulted ''law and economics'' scholars for relying on too narrow a view of human nature. In particular, economists tend to treat individuals as rational utility-maximizers, while ignoring the powerful roles played by psychology and social norms in shaping behavior. Fish likewise ignores the role played by psychology and social norms in shaping judicial behavior. Judges who are trained from their law school days that the role of the judiciary is to fairly enforce constitutional rights will find their self-image bound up in their ability to eschew personal prejudices and act fairly. This has practical consequences. For example, federal judges in the late 19th and mid-20th century protected the rights of Chinese immigrants and African Americans, respectively, even though the judges often had little personal sympathy for these minority groups' aspirations, and even though local political culture was strongly hostile to those groups.31 Political temptations will always exist for judges, but they will remain tempered by the norm of judicial objectivity—unless Fish and his colleagues succeed in destroying that norm by persuading judges that law and politics are indistinguishable.
Another irony is that Fish and his allies attack claims of neutrality by ''employ[ing] an epistemology that denies all eternal verities.'' Simultaneously, however, ''they establish current notions of racial and gender equality as an unquestionable, transcendent truth.''32 For example, Fish writes that '''[f]ree speech' is just the name we give to verbal behavior that serves the substantive agendas we wish to advance; and we give our preferred verbal behaviors that name when we can, when we have the power to do so, because in the rhetoric of American life, the label 'free speech' is the one you want your favorites to wear.''33 Because the concept of freedom of expression is merely a political device to promote particular agendas, according to Fish, there is no reason to suffer racist and sexist expression in its name, given the dangers such speech poses to the dignity and equality of its targets.34 Yet if we accept Fish's view that there is ''no such thing as free speech'' because everything comes down to politics, then surely there can be no such thing as ''dignity'' or ''equality'' either. Those who argue that purportedly illusory notions of freedom of speech should be sacrificed to equalitarian commitments that are based on notions at least as delusive cannot possibly explain why.
* * *
Protecting freedom of expression from government regulation will ultimately benefit left-wing scholars who support censorship, such as radical feminists and critical race theorists, as much as anyone. These scholars advocate speech regulations while living primarily in the very left-wing academic world, where their views are only marginally out of the mainstream. Yet, if the First Amendment is weakened sufficiently by antidiscrimination law and the government gains the power to suppress speech more broadly, radical feminists and critical race theorists, as holders of views wildly at variance with those of the public at large, are likely to be among the new censorship's first victims. That leftists writing in a society that has long been, and continues to be, hostile to their ideologies would want to weaken the principle that government may not suppress unpopular expression seems counterintuitive and shortsighted, to say the least.35
Indeed, many critical race scholars and radical feminists argue that the United States is innately and irredeemably racist and sexist. One need not accept this vision to realize that the Critical-Race-and-Radical-Feminist-Party, if such a thing existed, would not exactly take the American electorate by storm, at least not anytime soon. Because many critical race theorists and feminists claim to believe that American society is so hostile to their values, they should find constitutional protections against the majority especially important.
Of course, left-wing censors imagine a world in which the government silences only their ideological enemies, and they advocate censorship as an integral part of a much broader scheme for reconstructing society along egalitarian lines. Yet, it should be a cardinal principle of political advocacy that one should not support a regime with regulatory powers that one would not want applied to oneself. Acceptance of this principle would not only reduce hypocrisy, it would also remind political activists that politics is unpredictable and driven by power rather than morality. Power granted to government is often ultimately used against those who advocated that the power be exercised against others. As Yale political science professor William Graham Sumner remarked many years ago, ''The advocate of [government] interference takes it for granted that he and his associates will have the administration of their legislative device in their own hands.... They never appear to remember that the device, when once set up, will itself be the prize of a struggle; that it will serve one set of purposes as well as another, so that after all the only serious question is: who will get it?''36
# 2. The Threat to Freedom of Expression
in the Workplace
Jerold Mackenzie worked at Miller Brewing Company for 19 years, eventually achieving executive status and a $95,000 salary. One day, he made the career-ending mistake of recounting the previous night's episode of the sitcom Seinfeld to his coworker Patricia Best. In the episode, Jerry Seinfeld cannot remember the name of the woman he is dating, but he does recall that she said kids teased her as a child because her name rhymes with a part of the female anatomy. Jerry and his friend George brainstorm, but the best guesses they can come up with are the unlikely ''Mulva'' and ''Gipple.'' Jerry's girlfriend breaks up with him when she realizes he doesn't know her name. As she leaves him forever, Jerry finally remembers the elusive rhyming name and calls after her, ''Delores!''
Mackenzie related the details of this episode to Best, but she told Mackenzie she did not get the joke. To clarify the somewhat off-color punch line, Mackenzie gave her a copy of a dictionary page on which the word ''clitoris'' was highlighted. Best—who was apparently known to use salty language at work herself—complained to Miller Brewing officials of sexual harassment, and Miller Brewing fired Mackenzie for ''unacceptable managerial performance.'' Mackenzie responded with a lawsuit alleging wrongful termination and other wrongs. At trial, Miller Brewing officials acknowledged that the direct cause of Mackenzie's termination was the Seinfeld incident and the ensuing fear of a sexual harassment lawsuit. The jury awarded Mackenzie $26.6 million, including $1.5 million in punitive damages against Best for interfering with Mackenzie's employment relationship with Miller Brewing. The verdict was later overturned on appeal because Wisconsin law does not have a law banning wrongful termination.1
Miller Brewing's firing of Mackenzie may seem like an absurd overreaction, but it was very much consistent with the counsel of employment law experts. They advise employers to enforce a zero tolerance policy for any type of sex-related remarks by employees, especially those made by supervisors or executives like Mackenzie. Consultant Beau Crivello suggests, ''A rule of thumb is that if you can't say it or do it in a house of worship or in front of children, then don't say it or do it at work.''2 The rather startling message from the experts is that speech generally protected from government sanction loses that protection the moment it enters the workplace. Frank Carillo, president of Executive Communications Group, warns that just because you hear something in the media ''doesn't mean you can say it [at work]. The media has a certain license to say things that the average person can't.''3 Consultant Monica Ballard concurs: ''People think that if they hear something on TV or the radio, they can say it at work. But that, of course, is not the case.''4 Jerold Mackenzie, among others, would agree.
The roots of all of this censorship lie in the ''hostile environment'' component of antidiscrimination law. Beginning in the late 1970s, feminist legal scholars argued that the ban on employment discrimination against women should include a ban on sexual harassment.5 Sexual harassment, they argued, includes the act of subjecting women to a ''hostile work environment'' by exposing them to offensive speech. The speech need not be directed at any individual woman to constitute harassment. For it to qualify as harassment of a woman coworker, it is enough that the speech could reasonably be construed as hostile to women generally. Further, the determination of whether a hostile environment existed does not depend on whether anyone intended to make any or all of their female coworkers feel unwelcome. An innocently offered comment can as easily be charged with creating a hostile environment as a deliberate slur or threat.
The feminists achieved a great victory when the Supreme Court held in 1986 that an illegal hostile work environment exists when ''the workplace is permeated with discriminatory intimidation, ridicule, and insult, . . . that is sufficiently severe or pervasive to alter the conditions of the victim's employment.''6 Thousands of lawsuits of varying degrees of legal merit followed. Legal filings grew exponentially after the attention given to the issue of sexual harassment during the Clarence Thomas–Anita Hill hearings. Government agencies quickly produced pamphlets that urged victims of sexual harassment to file complaints and that often defined ''hostile environment'' far more broadly than the law justified.
Many employers responded to the growth of hostile environment law by attempting to regulate the potentially offensive speech of their employees.7 The result was an implicit, but nonetheless chilling, nationwide workplace speech code that banned any speech that could offend women. The Supreme Court, perhaps realizing that it had opened a veritable Pandora's box of litigation, has recently emphasized that sporadic abusive language, gender-related jokes, and occasional teasing are not enough to meet the legal test for a hostile environment.8 Prudent employers still feel compelled, however, to enforce speech guidelines that go well beyond what the letter of Supreme Court precedent requires.
There are several reasons for this caution. First, as four Supreme Court justices have noted in a related context,9 the fuzzy guidance provided by hostile environment precedents simply does not give employers a clear indication of what they must do to remain within the confines of the law. For example, while a single offensive joke will not create liability, some courts have held that a pattern of jokes by different employees can create a hostile environment.10 The safest route for employers is to ban any banter with sexual connotations, lest the aggregation of speech by different employees constitute a hostile environment. Better to be safe (if silent) than sorry.
Second, and relatedly, the severe and pervasive liability standard is sufficiently vague, good counsel sufficiently expensive, and trial judges and juries sufficiently unpredictable that employers feel compelled to settle even highly dubious claims to avoid the risks and costs of litigation. After all, juries have awarded tens of thousands of dollars to plaintiffs in cases appellate courts later dismissed.11 Although clearly meritless claims rarely survive federal appellate review, no sensible attorney would advise his clients to depend on appellate courts—which can only overturn ''clearly erroneous'' jury verdicts—to save them from unjustified claims. This is especially true because fighting a claim to the appellate level can cost hundreds of thousands of dollars, with the costs disproportionately borne by the defendant. Victory may be sweet, but saving one's company six-digit sums by avoiding litigation entirely is even sweeter. Risk-averse employers will settle pending cases, and prevent future lawsuits by cracking down on potentially offensive speech.
Third, disgruntled employees or former employees can impose large costs on employers without going to the effort and expense of filing a lawsuit, simply by complaining of harassment to the Equal Employment Opportunity Commission. The EEOC is legally required to investigate every complaint of sex discrimination, no matter how weak or unconvincing a complaint seems. Even a trivial complaint can lead to a broad investigation of the underlying claim, costing the employer thousands of dollars in legal fees and lost time. And petty complaints are actually encouraged by official government pronouncements that propagate inaccurate, overbroad definitions of what constitutes illegal sexual harassment. For example, an official U.S. Department of Labor pamphlet states that harassment includes cases in which a coworker ''made sexual jokes or said sexual things that you didn't like, so long as the jokes made it hard to work.''12 A very sensitive or very religious person may find that any sex-oriented remarks make it hard to work. Such a person is encouraged by government publications to complain of sexual harassment the first time a coworker tells a dirty joke. The offended worker will likely lose, but not before her employer wastes resources on its defense.
Fourth, many states and localities have their own antidiscrimination laws with standards for hostile environment liability that are sometimes significantly broader than the federal laws' requirement of severe and pervasive harassment. For example, a New Jersey court held that under state law employees who forwarded one list of crude jokes to their colleagues via e-mail had created an illegal ''offensive work environment,'' even though this act would be unlikely to create liability under federal law.13 Even if state and local law are no broader than federal law, employers are often at a special disadvantage when a hostile environment complaint is filed under state or local law because, unlike in the federal system, in states administrative tribunals often make the initial ruling on hostile environment claims. Because these administrative bodies are part of executive branch agencies charged specifically with enforcing the relevant antidiscrimination laws, they naturally tend to be more sympathetic to discrimination claims and less sensitive to free speech concerns than are federal courts, which have broader responsibilities and are part of the judicial branch of government.
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Hostile environment law has spread well beyond the sex discrimination context, with claims successfully prosecuted for race, religion, and national origin harassment. One court, for example, found that publishing religious articles in a company newsletter and printing Christian-themed verses on company paychecks constituted ''harassment'' of a Jewish employee.14 Another court found that an employee who hung in her cubicle pictures of the Ayatollah Khomeini and of Iranian protestors burning an American flag was guilty of national origin harassment against an Iranian-American employee who happened to see the display.15 Court rulings and EEOC guidelines suggest that religious harassment includes both a religious employee proselytizing a coworker and a secular employee ridiculing a religious coworker for the latter's beliefs.16
As in the sex discrimination context, a hostile environment claim for race discrimination and other types of workplace discrimination can arise even when the speech in question was not directed at the plaintiff. For example, the EEOC charged a company with national origin harassment after a Japanese-American employee filed a complaint about the firm's advertising campaign. Some of the company's ads featured images of samurai, kabuki, and sumo wrestling to represent the firm's Japanese competitors. The employee also charged that officials of the company called Japanese competitors ''Japs'' and ''slant-eyes.'' The case was eventually settled for an undisclosed amount.17
Standards for racial and ethnic harassment are at least as vague as they are in the sexual harassment context, which leads to unpredictable jury verdicts. Even highly questionable claims can result in large verdicts, giving employers strong incentives to heavily regulate workplace speech as a preventive measure.
One especially meritless claim that led to a six-figure verdict involved Allen Fruge, a white Department of Energy employee based in Texas. Fruge unwittingly spawned a harassment suit when he followed up a southeast Texas training session with a bit of self-deprecating humor. He sent several of his colleagues who had attended the session with him gag certificates anointing each of them as an honorary ''Coon Ass''18—usually spelled ''coonass''—a mildly derogatory slang term for a Cajun. The certificate stated that ''[y]ou are to sing, dance, and tell jokes and eat boudin, cracklins, gumbo, crawfish etouffe and just about anything else.'' The joke stemmed from the fact that southeast Texas, the training session location, has a large Cajun population, including Fruge himself.
An African American recipient of the certificate, Sherry Reid, chief of the Nuclear and Fossil Branch of the DOE in Washington, D.C., apparently missed the joke and complained to her supervisors that Fruge had called her a ''coon.'' Fruge sent Reid a formal (and humble) letter of apology for the inadvertent offense, and explained what ''Coon Ass'' actually meant. Reid nevertheless remained convinced that ''Coon Ass'' was a racial pejorative, and demanded that Fruge be fired. DOE supervisors declined to fire Fruge, but they did send him to ''diversity training.'' They also reminded Reid that the certificate had been meant as a joke, that Fruge had meant no offense, that ''Coon Ass'' was slang for Cajun, and that Fruge sent the certificates to people of various races and ethnicities, so he clearly was not targeting African Americans. Reid nevertheless sued the DOE, claiming that she had been subjected to a racial epithet that had created a hostile environment, a situation made worse by the DOE's failure to fire Fruge.
Reid's case was seemingly frivolous. The linguistics expert her attorney hired was unable to present evidence that ''Coon Ass'' meant anything but ''Cajun,'' or that the phrase had racist origins, and Reid presented no evidence that Fruge had any discriminatory intent when he sent the certificate to her. Moreover, even if ''Coon Ass'' had been a racial epithet, a single instance of being given a joke certificate, even one containing a racial epithet, by a nonsupervisory colleague who works 1,200 miles away does not seem to remotely satisfy the legal requirement that harassment must be ''severe and pervasive'' for it to create hostile environment liability. Nevertheless, a federal district court allowed the case to go to trial,19 and the jury awarded Reid $120,000, plus another $100,000 in attorneys' fees.20 The DOE settled the case before its appeal could be heard for a sum very close to the jury award.
Even if a disgruntled worker decides not to take a case all the way to a jury, he can still impose costs on his boss or ex-boss by alleging that he was subjected to a hostile environment, even if he has scant supporting evidence. For example, a gay man named John Dill put his former employer, CPA Referral, in a pickle when he filed a complaint of employment discrimination with the Seattle Human Rights Department. Dill claimed that his ex-boss Bryan Griggs had created a ''hostile work environment'' for homosexuals in violation of a local antidiscrimination ordinance. According to Dill, Griggs's offensive behavior consisted of playing conservative and Christian radio shows that Dill felt conveyed an antigay message, posting a letter from a congresswoman in which she endorsed the military's policy of excluding gays, and having a note on his desk reminding himself to lobby against allowing gays to adopt children. Dill acknowledged that Griggs did not know he was gay, and Dill never told Griggs that any of Griggs's actions offended or upset him.
Dill had been employed by CPA Referral the previous fall, but Griggs had laid him off when business slowed. Griggs had allowed Dill to come back to work as a volunteer, promising him the first available paid job. Much to Griggs's surprise, Dill suddenly tendered his resignation in a letter stating that ''I feel I must 'come out' and stop playing 'don't ask, don't tell.' '' In his letter, Dill explained that he was leaving CPA Referral for ''a supportive environment.'' He then filed his complaint, and the SHRD launched a full investigation of CPA Referral.
The befuddled Griggs told the SHRD that he listened to the conservative talk shows to make sure they played the advertising he had paid for, and that he posted many letters from politicians to encourage political participation among his employees. Another gay employee signed an affidavit swearing that he had never perceived any antigay animus in the workplace. There seems to have been no evidence that Dill suffered antigay discrimination, and a cynic might surmise that Dill filed the complaint mainly to get revenge on Griggs for having fired him. Dill eventually withdrew his complaint, but only after Griggs had spent thousands of dollars on legal fees defending himself and his company.21 If Dill's goal was to punish Griggs, he managed to achieve it even without being formally vindicated by a court.
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Most hostile environment employment cases have focused on whether the behavior at issue crossed the line from merely annoying or offensive conduct into conduct sufficiently severe and pervasive to meet the law's definition of creating a hostile environment. A few private employers, however, have unsuccessfully tried to claim First Amendment immunity from speech-based hostile environment claims.
The first reported hostile environment lawsuit in which the defendant invoked a free speech defense involved Lois Robinson, a welder at a Florida shipyard, who brought a case in federal court alleging that her employer, Jacksonville Shipyards, countenanced a hostile environment by permitting photos of nude and partially nude women to be displayed in various areas of her workplace.22 She also complained about sexual and derogatory remarks made in her presence about her and other women, and about indecent and obscene graffiti directed at her.23 Jacksonville Shipyards responded that the First Amendment protected at least some of this speech and asked the court to prohibit Robinson from relying on constitutionally protected speech to support her hostile environment claim.
The court ruled that the First Amendment does not protect work-place speech from employment discrimination law.24 The court then issued an incredibly broad injunction that banned from the Jacksonville Shipyards' workplace not only pornography but also any ''sexually suggestive'' material. Employees on lunch break could no longer read Cosmopolitan magazine or Danielle Steel novels, or listen to Eminem or Britney Spears on a Walkman.
The court found that the First Amendment did not protect the workplace speech at issue for several reasons, none of which is persuasive. First, the court asserted that the company was not expressing itself through the offensive expression of its employees. What the court failed to discern was that because the company was being held liable for the speech of its employees, the relevant question was whether the employees' speech was constitutionally protected. There is no doubt that the Constitution protects such speech from government regulation, even when the speech conflicts with a broader regulatory scheme like hostile environment law.25 The court failed to recognize that employers may assert a First Amendment defense on behalf of their employees, and may have their own First Amendment right to refuse to prohibit workplace speech.26
Next, the court opined that the nude pinups and expressions of hostility toward women in the shipyard were not protected speech, but were discriminatory conduct in the form of creation of a hostile work environment. Here, the court was correct insofar as it pointed out that speech can sometimes be considered conduct—for example, threats, intimidation, libel, and other forms of misconduct engaged in through speech do not receive First Amendment protection. Similarly, quid pro quo harassment (e.g., ''Sleep with me or else!'') is not protected by the First Amendment. Arguably, the government may even regulate as an action harassing speech targeted at a particular person for discriminatory reasons. But merely labeling speech ''discrimination,'' as the Robinson court did, does not make it so. Posting a nonobscene pinup or expressing a politically incorrect opinion is protected outside of the workplace, and a mere change in venue from the sidewalk to the office cannot convert such protected speech into unprotected discriminatory action. Given that most adults spend much of their time in the workplace and that almost any speech beyond the most banal is likely to offend someone , allowing the government to regulate any offensive speech that occurs in the workplace would invite an incredibly broad assault on freedom of speech.
The Robinson court next determined that regulation of offensive workplace speech was a permissible regulation of the time, place, and manner of speech. Government can regulate these aspects of speech, restricting parades and protests to certain times of the day or limiting the volume of a megaphone in a residential area. But time, place, and manner restrictions can only be valid if they do not regulate speech on the basis of the speaker's viewpoint. Thus, a rule disallowing the use of megaphones during protests in residential neighborhoods may be valid, but a rule forbidding megaphones only when they are used to criticize affirmative action would be illicit viewpoint discrimination. Hostile environment law clearly discriminates based on viewpoint.27 For example, hostile environment law potentially penalizes expression of the viewpoint that ''women are stupid and incapable of being physicists,'' but not that ''women are brilliant and make excellent physicists.'' Therefore, hostile environment law cannot be considered an appropriate time, place, and manner regulation.
Finally, the court insisted that plaintiff Robinson was a ''captive audience'' in the shipyard and therefore the First Amendment did not protect speech that offended her. Yet we are all at times captive to expression we find offensive, in the sense that we must take action to avoid seeing or hearing it. Nevertheless, that speech is still constitutionally protected. Of course, avoiding some types of offensive speech is relatively easy, while avoiding offensive work-place speech by finding new employment can be difficult and costly. But if courts accepted Robinson 's view that the First Amendment does not protect offensive speech that is very difficult or costly to avoid, much of modern First Amendment law would need to be discarded. For example, contrary to Supreme Court precedent, strikers would not have the right to picket outside their workplace, and antiabortion protestors would not have the right to assemble outside abortion clinics.28 The Supreme Court has even protected the right of an individual to wear a jacket displaying the phrase ''Fuck the Draft'' inside a courthouse where many people who will see the profanity are truly a captive audience, in that they are legally required to be there.29 If offensive speech is thus protected when avoiding it would require committing a crime by refusing to show up in court when required, surely it must also be protected when avoiding it would only involve switching jobs. Even if the captive audience rationale could be used to justify speech restrictions in the workplace, any such restrictions would have to be viewpoint-neutral, which, as noted previously, hostile environment law is not.
Despite the seemingly fatal weaknesses in Robinson 's First Amendment analysis, many other courts have relied on it in rejecting First Amendment defenses in hostile environment cases.30 Most commonly in cases favorably citing Robinson , the plaintiff had been subjected to a pattern of severe individualized harassment, and the First Amendment defense applied only to a fraction of the behavior that allegedly created a hostile environment. However, nothing in Robinson limits its application to cases in which constitutionally protected expression is only a minor element. One court, in fact, cited Robinson favorably in a case in which the plaintiff's sole allegation was that her opponents for a union position had cirulated a satirical flyer during an election campaign.31 The satire featured a picture of the plaintiff's head superimposed over an anonymous woman's naked body. This was tasteless, to be sure, but it was also political speech clearly protected by the First Amendment, as indicated by a landmark Supreme Court opinion protecting an even more offensive satire of Jerry Falwell that appeared in Hustler magazine.32
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Just as the injunction granted in Robinson created an unprecedented prior restraint (proactively censoring speech before it is spoken) on sexist speech, the California Supreme Court recently upheld an unprecedented prior restraint on racist speech. A jury had found that an Avis Rent A Car outlet had engaged in employment discrimination, in part by allowing an employee to repeatedly utter racial epithets targeted at the Latino plaintiffs. Besides awarding damages, the trial court issued an injunction prohibiting Avis employees ''from using any derogatory racial or ethnic epithets directed at, or descriptive of, Hispanic/Latino employees of [Avis].''33 An appellate court limited the injunction to the workplace and attempted to narrow the scope of the injunction via a proposed list of specific words that the district court could ban. Not satisfied that these modifications made the injunction comport with the First Amendment, Avis appealed to the California Supreme Court.
A four-to-three majority of the state supreme court upheld the appellate court's decision. The three dissenters argued that the injunction amounted to a prior restraint on constitutionally protected speech. They pointed out that U.S. Supreme Court precedent shows that prior restraints are not allowed for speech that might, but won't necessarily, be illegal. The reason for this rule is that such restraints have a chilling effect on what could have been legal, protected speech. For example, a single future pejorative use of a racial epithet, although banned by the injunction, cannot be the severe and pervasive harassment required to create an illegal hostile work environment; in some contexts it might be severe, but a single comment cannot be ''pervasive.'' For that matter, racial epithets can be uttered in contexts that do not evince hostility. For example, epithets could be mentioned during ''diversity education'' or could be used ironically, yet these uses of the epithets would be equally banned by the injunction's prior restraint. Justice Clarence Thomas urged his colleagues to hear Avis's appeal to the U. S. Supreme Court because of the ''troubling free speech issues'' raised by the case,34 but he was not successful, and the injunction stood.
The ultimate outcome of the battle between the First Amendment and the speech-regulating aspects of hostile environment law thus remains unresolved and will remain that way until the Supreme Court chooses to resolve the issue. No court has yet held directly that the First Amendment prohibits workplace speech from being the basis of Title VII liability if that speech would be protected in other contexts. However, four Supreme Court justices have suggested that hostile environment law sometimes violates the First Amendment,35 and other federal courts have expressed alarm at hostile environment law's growing conflict with freedom of speech.36
Federal courts have also been sympathetic to First Amendment objections to prophylactic measures ordered by state and local governments to avoid creating a hostile environment in the public sector workplace. For example, courts have held that prohibiting prisoners and on-duty firefighters from reading Playboy unconstitutionally restricts expression, despite claims that allowing pornographic magazines to be read creates a hostile work environment for female prison guards and firefighters.37
In the absence of definitive Supreme Court guidance, however, hostile environment law marches on. In February 2002, for example, Anchorage, Alaska, fearing lawsuits by female firefighters, banned from its firehouse not only Playboy and other pornographic magazines, but also the slightly racy men's magazine Maxim .38 And the law continues to grow. The latest trend in this expansion is employees suing employers for not preventing hostile environments allegedly created by patrons. For example, the Equal Employment Opportunity Commission has declared that 12 Minneapolis librarians were subjected to a sexually hostile work environment when they were exposed to pornography accessed on the Internet by library patrons. If courts agree with the EEOC, all libraries, public and private, will need to ban Internet access to ''offensive'' sites or face hostile environment liability.39
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There are signs that the public is growing impatient with the corrosive effect of hostile environment law on freedom of expression. One of the more amusing manifestations of this disquiet is an episode of the animated series South Park . After a visit from the ''Sexual Harassment Panda,'' the children of South Park begin to sue each other for harassment over minor insults. Eventually, the children pursue deeper pockets, the school at which these insults take place. The school is bankrupted, while Kyle's attorney father, who represents all of the plaintiffs, becomes wealthy. This leads to the following exchange:
> Father: You see, son, we live in a liberal democratic society. The Democrats [sic—it was a mostly Republican EEOC and Supreme Court] created sexual harassment law, which tells us what we can and cannot say in the workplace, and what we can and cannot do in the workplace.
>
> Kyle: But isn't that fascism?
>
> Father: No, because we don't call it fascism.
# 3. The Threat to Artistic Freedom
In 1999, a San Francisco gym put up a billboard with an illustration of space aliens and a warning: ''When They Come, They'll Eat the Fat Ones First.'' Outraged activists for the overweight protested outside of the gym, holding signs that said ''Eat Me.'' The gym took the billboard down, but the activists used momentum from the protests to successfully lobby for a city ordinance banning discrimination based on height and weight.
Krissy Keefer, director of Dance Brigade, a company that produces political dance such as ''Dance of the Endangered Species,'' soon became the first San Franciscan to take advantage the new ordinance.1 The standards of modern ballet require dancers to be lithe and thin, because body fat obscures the separations between parts and, it is thought, unduly accentuates the trunk. Being thin also helps a dancer perform ballet moves quickly and artfully and makes it easier for a male dancer to lift his partner. Keefer, however, regards ballet's body-type criteria as a feminist issue, because, she says, they require a dancer to ''have an unhealthy relationship'' with her body, leaving ballerinas on diets so strict that they are vulnerable to eating disorders.
Keefer had a particularly keen interest in ballet's body-style requirements because of her medium-sized daughter, Fredrika. The elder Keefer had brought nine-year-old Fredrika to an audition for the San Francisco Ballet's preprofessional school. The school's Web site states that ''the ideal candidate is a healthy child with a well-proportioned body, a straight and supple spine, legs turned out from the hip joint, flexibility, slender legs and torso and correctly arched feet, who has an ear for music and an instinct for movement.'' The school promptly rejected Fredrika for not having the right body type to succeed as a professional ballet dancer.
The Ballet instead offered Fredrika a full scholarship to its Dance in Schools Program. School admissions officers said that if she could prove the school's initial impression wrong or if her body style changed, Fredrika could enter the preprofessional regimen later. But Krissy Keefer was not mollified. Like many stage moms, she was convinced that her daughter was destined for great things. Keefer persuaded herself that the narrow-mindedness of the ballet school was interfering with nine-year-old Fredrika's ''career.'' The elder Keefer told ABC's Good Morning America that ''I need a program for my daughter that actually could satisfy her professional aspirations.''
Keefer filed a complaint with the San Francisco Human Rights Commission, claiming height and weight discrimination and, because ballet schools enforce height and weight requirements less stringently for boys—largely because the pool of boys willing to pursue ballet is much smaller than the pool of girls—sex discrimination. Keefer told the media, ''I am mad at them for not seeing how talented she is, for having such a narrow, myopic view of what makes a dancer.'' The San Francisco Ballet, Keefer wrote in a press release, ''should have a program that reflects the real needs of San Francisco's citizens, and the SFB school should foster a program of physical, emotional and mental well-being of its female participants as it pursues artistic excellence.''
Keefer's complaint charged that Fredrika's rejection had caused her ''confusion'' and ''humiliation.'' Fredrika, however, actually seemed reasonably content. She told the San Francisco Chronicle that ''I'm sad I didn't get in, but I'm happy because I like the Pacific Dance Theater [the school she had been attending] a lot and I didn't want to lose that.'' In fact, any confusion and humiliation suffered by Fredrika may have been the result of her mother dragging her into a media circus. Krissy subjected Fredrika to press conferences and television interviews, forcing Fredrika to relive her ''rejection'' countless times and to have her body repeatedly held up to public scrutiny.
Keefer's legal action drew howls of protest from dancers and dance critics. Paul Ben-Itzak, editor of Dance Insider magazine, wrote that ''what we have here is a ballet mother whose vanity is vicariously wounded, and who is shamelessly, in the guise of public-spirited concern, trying to hurt the San Francisco Ballet because it, in her view, hurt her daughter Fredrika.'' Dance critic Octavio Roca added: ''We are in a world where artistic canons are devalued, and every opinion, no matter how biased or uninformed, is worth the same as every other....Inthe name of democracy, with the laudable goal of nondiscrimination, we end up bypassing excellence while propping up the mediocre and the bland.'' Even Lawrence Gold-huber, a six-foot-one, 350-pound modern dancer, mocked Keefer's complaint, and admitted that he preferred watching thin dancers, particularly in ballet. ''Short people don't get hired by the NBA,'' he noted, ''Should fat people be in the ballet?''
Critics also pointed out that little Fredrika was hardly being deprived of a potential career in dance. Many other dance styles, including musical theater, disco, modern dance, and most ethnic dance types, do not have stringent body type requirements. None of this swayed Keefer, however, who told a reporter that people act as if ''there's something sacred about ballet, so that it can't be legislated at all outside of the artistic view. It's not untouchable by the rest of the standards for society.'' Eva Patterson, an attorney for the Lawyers' Committee for Civil Rights, gushed that Keefer's case was ''really groundbreaking. I'm sure many people will pooh-pooh it but it sounds important because it could force us to reexamine our attitudes toward body image and culture.''
Unfortunately, in their intense zealousness to right the wrongs attributed to ballet's slim-centric aesthetic, Keefer and Patterson overlooked one small but important detail: the First Amendment. Properly interpreted, the Constitution's protection of free expression from government interference bars the City of San Francisco from legislating ballet standards. Larry Brinkin, a member of the San Francisco Human Rights Commission, recognized as much. He told the San Francisco Chronicle that the San Francisco Ballet school has a First Amendment right to choose to train only performers who meet the school's subjective criteria.
As of this writing, however, the case against the Ballet is still pending. Fredrika's dance career is going strong despite her rejection by the San Francisco Ballet; she won rave reviews for her lead role in a 2003 production of ''Einstein's Daughter.'' Meanwhile, another claimant under San Francisco's weight discrimination law, a five-foot-eight and 240-pound woman, forced Jazzercise, the nation's leading aerobic exercise company, to drop its requirement that instructors have a fit appearance.
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The Keefer case is an extreme illustration of an emerging trend of activists and government agencies trying to use antidiscrimination law to make artistic expression more politically correct. For example, in March 1998 a group of women artists calling itself the Title IX Task Force filed a complaint with the National Endowment for the Arts against three of New York's leading museums—the Museum of Modern Art, the Guggenheim Museum, and the Whitney Museum of American Art. The complaint alleged that these museums do not display enough paintings or sculptures created by women.
Title IX, an amendment to the 1964 Civil Rights Act, bans sex discrimination by institutions that receive federal funds, a definition that encompasses the three art museums named in the Task Force's complaint. Title IX is famously credited with substantially increasing the funding universities give to women's athletics. Activists for women's athletics ''so unequivocally succeeded in what they had set out to do, it inspired us,'' Task Force member Mary Beth Edelson remarked.2
Edelson claims that the paucity of art by women exhibited in the big three art museums is devastating to women's career prospects. ''Collectors will go to the museums and see work and think, 'This is the Good Housekeeping seal of approval'...and they go to a dealer and they buy that work,'' Edelson explained, ''If the museums don't include women . . . then the dealers have a very difficult time selling [art by] women.'' The museums' spokespeople respond that major exhibitions focus on the work of artists established over many years; therefore, if works by male artists are presently overrepresented at exhibitions, this reflects biases that shaped the art world years ago, not any biases currently informing the museums' choices.3 Regardless of who is correct, it hardly seems consistent with artistic freedom to have the government dictate whose work art museums should display.
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Antidiscrimination laws' threat to artistic freedom goes well beyond arts organizations such as the San Francisco Ballet and New York's leading art museums. Employers and university officials are increasingly facing the Hobson's choice of either removing ''offensive'' art from the workplace or facing antidiscrimination lawsuits. The ban on certain kinds of art is explicit in some jurisdictions. For example, Madison, Wisconsin, has a law specifically defining illegal ''sexual harassment'' to include ''repeated display of sexually graphic materials which is not necessary for business purposes.''4 The Montana Human Rights Commission's guide for employers similarly states that ''prohibited sexual harassment includes: [d]is-plays of magazines, books, or pictures with a sexual connotation.''5
At the end of the day, however, it is litigation or fear of litigation pursued under federal antidiscrimination law that lies at the root of most art censorship undertaken to satisfy antidiscrimination law. Title VII of the 1964 Civil Rights Act bans the creation of a ''hostile workplace environment'' for women as part of its judicially constructed prohibition on sexual harassment. For example, Penn State University took down a print of Goya's Naked Maja that had been hanging in a classroom when Nancy Stumhofer, an English professor, complained about its depicting a naked woman. Professor Stumhofer explained, ''Whether it was a Playboy centerfold or a Goya, what I am discussing is that it's a nude picture of a woman which encourages males to make remarks about body parts.''6
The Murfreesboro, Tennessee, city government removed from city hall an impressionistic painting by Maxine Henderson that depicts a nude woman with her breasts partially in view. The city was responding to a complaint by Laurie Crowder, an assistant school superintendent who did not work in city hall but passed the painting one day on the way to a meeting there. She threatened a hostile environment lawsuit, a move that led the city to take the painting off display.7 Crowder said, ''I personally find art in any form whether it be a painting, a Greek statue or a picture out of Playboy which displays genitals, buttocks, and/or nipples of the human body, to be pornographic and, in this instance, very offensive and degrading to me as a woman.''
After the city removed the painting, City Attorney Tom Reed remarked, ''I feel more comfortable siding with protecting the rights under the Title VII sexual harassment statutes than I do under the First Amendment.''8 Reed added, ''You really can't be too cautious. A sexual harassment judgment usually has six zeros behind it.''9 Ironically, Reed's caution did not save Murfreesboro from a lawsuit. Henderson, the artist, successfully sued the city for removing the painting in violation of Henderson's First Amendment rights.10 However, in stark contrast to the huge sum that Reed had worried about losing in a sexual harassment suit, Henderson recovered only one dollar along with her costs.11
Arguably, public schools like Penn State, local governments like Murfreesboro, and other government entities should, out of respect to prudish employees and citizens, avoid displaying nude art in public spaces. Despite the dubious First Amendment ruling in favor of Ms. Henderson, the objectionable aspect of the incidents described earlier is not that the art was removed—Penn State and Murfreesboro had no obligation to display the art in the first place—but rather that its removal was undertaken in response to threats of legal action. Stumhofer and Henderson turned issues of taste into issues of alleged illegal sexual harassment—developments that will give inevitable pause to any employer, public or private, who wishes to display potentially controversial art in the workplace.
* * *
Although many of the early sexual harassment complaints based on artistic displays involved feminist plaintiffs, individuals with conservative social views have also used sexual harassment law to promote censorship. For example, some Christian groups have argued that convenience stores should not be permitted to sell pornographic magazines, because the presence of such magazines creates a hostile environment for female and Christian employees.
For others, it is the combination of race and sex that proves especially provocative and objectionable. For example, University of South Florida freshman Nicole Ferry was offended by a photograph displayed in her art class. The photograph, titled ''Nigger Lover,'' showed a black man and a white woman locked in a simulated sexual embrace.12 It was the work of African American artist and class teaching assistant Derek Washington, who intended to use the arresting image to force viewers to examine their reactions to a depiction of interracial sex.
Washington, who also happened to be the black man in the photo, displayed the image in class as part of a lecture on controversial art. Although the explicit nature of Washington's photo may have surprised or bothered some students, it should not have come as a complete shock. Instructor Diane Elmeer had earlier warned students that they might find some images shown during this lecture offensive, and told them they were free to skip the presentation entirely or to leave at any time without being penalized.
Ferry apparently was not so sensitive as to skip the presentation, but Washington's photo made a strong negative impression on her. When she mentioned the photo to her father, he responded by sending an angry letter to the university, calling the photo ''pornographic'' and ''smut.'' The university was unresponsive to this complaint, which seemed little more than the prudish concerns of a conservative parent. In a later meeting with university officials, however, Mr. Ferry hit school officials where it hurt. He claimed ''sexual harassment'' had been perpetrated on his daughter—by ''an African American male,'' no less. The elder Ferry had clearly learned the proper buzzword (''sexual harassment'') to get university censorship gears in motion, and move the censors did. The university general counsel ordered Washington reassigned to another class, because it would ''penalize a victim of an alleged sexual harassment'' if Washington were to continue to have ''a position of power'' in the original class. Fine Arts Dean Ronald Jones told students that ''no sexual harassment claim or allegation made in my office or within my hearing will go unacted upon. I cannot tolerate an environment when something like that happens.''
Washington's reassignment prompted a sit-in protest of the university president's office by most of the other 250 students in the class. Sophomore Alexia Bridges expressed concern that Washington's reassignment would cause other instructors to avoid controversial subjects. ''Everybody is going to watch their step,'' she said, ''dot their I's and cross their T's.'' Students contended that other art displayed in the class was far more sexually explicit than Washington's piece, and that Ferry had singled out Washington's photo because of its depiction of interracial sex. Elmeer reportedly told her class that the incident ''reeks of racism.'' Following the protest, the university withdrew Washington's reassignment. All of this further upset Ferry, who alleged that she was being vilified for standing up to sexual harassment. Her father sent another letter to the university, this one accusing college officials of ''evoking [sic] the protest,'' and the younger Ferry filed a sexual harassment lawsuit against the school. The complaint lent support to those who thought Ferry's agitation had a racial subtext when it gratuitously volunteered that she was white and Washington was black. The university caved again, settling with the Ferrys for $25,000.
Not surprisingly, Washington was upset by the university's cravenness. ''This came down to a business issue,'' he said, ''and I just don't think money should supersede ethics.'' An explicit university policy prohibiting instructors from displaying sexually explicit materials in their classes would probably be within a state university's constitutional authority to set academic policy (see Chapter 5). No such policy, however, existed at the University of South Florida. Given that the controverted art was directly related to the subject matter of the class, Washington had every reason and right to assume that, in the absence of an explicit policy to the contrary, his academic freedom in displaying this art was protected. As the Ferry debacle shows, vague sexual harassment policies have unfortunately become a means for enforcing ad hoc artistic censorship policies.
* * *
Inevitably, antidiscrimination laws threaten not only highbrow art, but lowbrow art and entertainment as well. The Supreme Court has declared that ''the line between the transmission of ideas and mere entertainment is much too elusive for this Court to draw, if indeed such a line can be drawn at all.''13 Therefore, the First Amendment has been held to protect all forms of entertainment from government regulation, even those shows, books, and pictures that have no discernable value to society beyond entertainment. This principle, however, is being increasingly undermined by the enforcement of antidiscrimination laws.
In response to a ''hostile environment'' complaint on the basis of the prevalence of nude pinups at a shipyard, a federal court banned the display of any ''sexually suggestive, sexually demeaning, or pornographic'' material there.14 Another court upheld a $125,000 sex discrimination award based in part on the plaintiff's coworker's playing ''misogynistic rap music'' and displaying music videos depicting an array of sexually provocative conduct.15 The Americans with Disabilities Act has been held to require a comedy club to put a deaf interpreter on stage, even during a performance by an illusionist who must have the audience's full attention focused where he needs it to achieve his effects.16
Perhaps the most notorious case of antidiscrimination law impinging on lowbrow art involved actress Hunter Tylo. The producers of the steamy prime-time soap opera Melrose Place hired Tylo to play the show's latest promiscuous bimbo, ''Taylor McBride.'' Predictably, given Melrose Place 's emphasis on form (and especially female form) over substance, Tylo's contract included a clause forbidding any ''material change'' in her appearance. When Tylo became pregnant before the new season started shooting, the producers fired her, explaining that they did not want their bed-hopping vixen character to be played by an obviously pregnant woman. To get an idea of where the producers were coming from, picture this: in one pivotal scene, Tylo, who gained 47 pounds during her pregnancy, was to be filmed cavorting pool-side in a thong bikini.
Tylo sued for employment discrimination based on sex and pregnancy. The producers of the show responded that Tylo's prepreg-nancy appearance was a bona fide occupational qualification (BFOQ) reasonably necessary to the proper casting of the show. Therefore, they argued, Tylo's claim failed under federal law.17 The producers also claimed a First Amendment right to cast the part as they saw fit. The judge declined to dismiss the case on BFOQ or First Amendment grounds, and the jury found in Tylo's favor, awarding her $5 million. Tylo's attorney, Gloria Allred, enthused that Tylo ''is absolutely a living Susan B. Anthony and a Rosa Parks all rolled into one.''18 After the verdict, the case was settled for an undisclosed sum.
But it's not only Hollywood's free, if sometimes raunchy, expression that is being compromised. Antidiscrimination laws even endanger something as quaint and apparently innocuous as the period theme of a restaurant, raising the question of whether ambience is an element of artistic freedom protected by the First Amendment. Cock of the Walk, a southern seafood chain, tried to provide an atmosphere in keeping with its 1800s riverboat theme. The waiters, dressed in period costume, were meant to represent the legendary fighters who brawled for the privilege of steering the riverboats, which netted them the best-of-the-best title: Cock of the Walk. Only males were hired as servers because, as Mike Fink Corporation, the owner of the chain, explained, women did not work on riverboat crews in the 1800s. It was a simple matter of historical accuracy.
Susan Mathis applied for a server job at one of the chain's restaurants, arriving equipped with a hidden recorder that taped a restaurant manager turning her down for a server position because she was a woman. At Mathis's behest, the Equal Employment Opportunity Commission sued Mike Fink for sex discrimination. The company responded that given the restaurants' historical theme, being male was a BFOQ. A jury disagreed and found the restaurant liable for discrimination. Following the verdict, the company agreed to pay a $70,000 settlement. The company also agreed to hire women for server positions and to allow the EEOC to monitor its hiring practices for the next five years.19 Mathis's successful lawsuit led one frustrated commentator to ask, ''What's the next logical target for discrimination cleanup?. . . How about a guy in the Dallas Cowboys cheerleaders? How about featuring a guy in the Sports Illustrated annual swimsuit issue?''20
Mike Fink failed to raise a First Amendment defense in the case, so the court did not address the restaurant chain's constitutional rights. However, one federal appellate court has held that the (late) Sambo's restaurant chain had a First Amendment right to use its name, despite claims that the name created a hostile environment for African American patrons.21 A restaurant like Cock of the Walk may have a similar First Amendment right to create a particular historical ambience.
An opportunity for courts to decide whether a restaurant has the right to create a sexy ambience appealing to men was lost when the Hooters restaurant chain settled a sex discrimination complaint filed by the EEOC. The EEOC had sued Hooters, which relies on an image provided by voluptuous and tightly clothed waitresses, for refusing to hire male servers and for having a double-entendre name that suggested that only women could work there. Following a clever public relations campaign by Hooters, featuring a hairy, ugly ''Hooters guy'' —Hooters' comical take on being forced to abandon its female-only server policy—the EEOC backed off, but not before extorting $3.75 million from Hooters, and requiring Hooters to create three new gender-neutral categories of employees.22
In separate litigation, two women who worked at a New Orleans Hooters franchise won verdicts of $20,000 each after having their hours cut when they became pregnant. In response, the national chain expressed regret, and noted that corporate policy prohibits pregnancy discrimination and requires all of its restaurants to offer special maternity Hooters outfits to its staff. Not all patrons are pleased with this compromise, which is dictated by laws banning discrimination against pregnant women. ''Who wants to look at a belly button looking at you?'' asked Ryan Petty, a 22-year-old U.S. Air Force flight crew chief from Dallas with a talent for telling it like he sees it, ''Under the law, it's discrimination, but I don't want to see a pregnant Hooters girl, cottage-cheese legs and everything.''23 A similarly blunt bachelor party participant added that if ''the [Hooters] atmosphere was filled with 18 pregnant women in tights, we wouldn't be there.''
Regardless of how antidiscrimination law affects waiters at Cock of the Walk and Hooters, though, the grand American tradition of dinner theater, in which actors double as waiters during intermissions, is apparently not at risk from sex discrimination law. For purposes of determining whether sex discrimination by eating places is permissible, the EEOC draws a distinction between ''whether you're putting on a show or [just] serving food.''24 If servers at a restaurant actually perform gender-specific roles in a theatrical performance,25 then sex discrimination in hiring is okay. Otherwise, the EEOC generally considers sex discrimination to be impermissible under federal antidiscrimination laws. The basis for this policy is the famous ''Love Airlines'' case from the late 1970s, in which Southwest Airlines asserted the right to hire only sexy young women as flight attendants in order to cultivate an image that would appeal to male business travelers. A federal court ruled that because the essence of the airline's business was transporting passengers, not sexual allurement, the airline's employment policy was illegal sex discrimination.26 The implication, however, was that discrimination by a business that really was centered around sexual allurement would be licit. Ironically, then, Hooters' problem may be that its form of sexual entertainment is too subtle and tame. As an anonymous EEOC official noted, ''Hooters claimed that . . . they [sic] were providing vicarious sexual recreation . . . but all along they were primarily a food business.''27 A bemused commentator concluded that ''[i]f Hooters had wanted to avoid a civil rights lawsuit, and save $3.75 million, it should have dimmed the lights, bared the waitresses, and cut the menu down to nuts and nachos.''28
* * *
After generations in which controversial art, especially art considered sexually indecent, was ''banned in Boston'' and across the United States, American artists have finally won First Amendment protection for their work over the past several decades. The result has been a flourishing and diverse arts and entertainment scene unrivaled in the rest of the world. However, the growth of antidiscrimination law threatens this achievement. Feminists like Krissy Keefer and the Title IX Task Force, prudes like Laurie Crowder, prima donnas like Hunter Tylo, reactionaries like the Ferry family, and government bureaucrats like the EEOC officials who went after Hooters are all eager to use the force of antidiscrimination law to compel the arts and entertainment world to conform to their vision of a good society. Only the First Amendment's protection of artistic freedom stands between such individuals and a return to widespread artistic censorship under the guise of combating discrimination.
# 4. Political Speech as Illegal
Discrimination
One of the cornerstones of any healthy democracy is the citizenry's freedom to criticize and question government officials and policies. That is why the U.S. Constitution acknowledges a specific right to petition the government rather than relying on the general freedom of speech granted in the First Amendment to safeguard this essential liberty. Despite this crucial and clear protection, however, government officials are increasingly trying to punish the political speech they dislike as illegal discrimination.
Perhaps the most egregious example of this phenomenon involved an attempt to punish opponents of a proposed public housing project in Berkeley, California. Berkeley is divided between affluent neighborhoods in the coastal hills and the much poorer flatlands area. The liberal hills neighborhoods dominate local politics and elect representatives who vote to heavily invest city resources in public housing units, social services, and homeless shelters. Also in response to concerns of the affluent hills residents, the city places almost all these projects in the low-income neighborhoods of the flatlands, where the residents have traditionally been poorly organized and politically weak.
In May 1992, Resources for Community Development, a nonprofit housing developer, received a large grant from Berkeley to convert the run-down Bel Air Motel in the flatlands into a multifamily housing unit for the homeless.1 Opposition to the Bel Air conversion became a unifying cause among the flatlanders. As one resident put it, ''If the city wants to build low-income housing they should do so in an equitable fashion—everywhere within the city's districts— equally. It's time for other areas to participate in solving the 'affordable housing crisis.' ''2
Alexandra White, her husband, Joseph Deringer, and their neighbor Richard Graham—a group the media later dubbed ''the Berkeley three''—organized the opposition to the new housing units. Deringer and White's home abutted immediately against the Bel Air property, and Graham lived a few houses down the street. In newsletters and petitions, the Berkeley three asserted that the proposed location of the new center, near two liquor stores and a nightclub, was inappropriate because of the prevalence of alcoholism among the homeless population. They also noted the absence of local mental health and substance abuse treatment facilities, a factor seemingly neglectful of the needs of the many homeless who are mentally ill or addicted to drugs.
Despite this neighborhood opposition, led by the Berkeley three, and despite a lawsuit documenting irregularities in the process granting the needed zoning variance to the project, the Bel Air conversion ultimately went forward. However, bitter feelings remained, accompanied by a desire for revenge on the part of the housing activists who had supported the Bel Air project. Marianne Lawless, the director of Housing Rights, Inc., a federally funded housing advocacy group, decided to punish the Berkeley three for what she considered to be their politically incorrect community activism by filing a complaint with the San Francisco office of the federal Department of Housing and Urban Development claiming that the Berkeley three were guilty of discrimination against the disabled. Lawless's one-sentence complaint stated that the Berkeley three had tried to block the Bel Air project ''because they perceive[d] the primary residents of the facility would be the mentally disabled or the disabled through substance abuse.''3
Lawless's complaint relied on the 1988 amendments to the Fair Housing Act, which she contended banned political speech motivated by discriminatory animus that leads to the delay or cancellation of a project that would serve protected groups. HUD agreed, arguing that it could punish ''individuals [who] have engaged in speech advocating illegal acts.'' HUD asserted that such speech includes asking the government to halt a publicly funded housing project because the facility will serve those ''disabled'' by drug addiction and mental illness.4
Therefore, HUD vigorously investigated Lawless's claim, issuing subpoenas for everything the Berkeley three had written about the controversy, for minutes of public meetings, for lists of members of their coalition, and for any other relevant documents. HUD warned the Berkeley three that failure to cease their activism immediately or to comply with the subpoenas could result in fines of up to $100,000 each and jail sentences of up to one year. The Berkeley three were further informed that if the investigation turned up evidence of discrimination, they would be subject to fines of up to $50,000 each and might be liable for compensatory and punitive damages.5 Despite protests from the Berkeley three's attorney, HUD denied that its investigation impinged on their First Amendment rights. HUD soon announced the results of its preliminary investigation: the Berkeley three had violated the Fair Housing Act. HUD sent the case to the Justice Department for prosecution.
The Berkeley incident was just one of many during the early years of the Clinton administration in which HUD officials harassed and intimidated neighborhood activists.6 One victim summed up the effects of HUD's investigation as follows:
> It financially ruined the neighborhood association and terrified residents. HUD investigators pressured neighbors to turn informer. Residents were afraid to join the association or to speak out at public meetings. The government even tried to deprive us of legal representation by threatening to call our attorney as a witness. We couldn't take minutes at meetings of our board because these could be seized and used as evidence against us. We tried to settle the case, but the terms of the consent decree drafted by the government were intolerable. They would have required residents to undergo an enforced course of political re-education and proposed unconstitutional restraints on our right to speak, write and association.7
>
After a media outcry over HUD's disregard of First Amendment rights in the Berkeley case and other cases,8 the agency backed down, announcing that it would no longer investigate ''any complaint . . . that involves public activities directed toward achieving action by a governmental entity or official; and do not involve force, physical harm, or a clear threat of force or physical harm to one or more individuals.''9 HUD also announced that it was dropping the investigation of the Berkeley incident because, it concluded, the Berkeley three had acted within their First Amendment rights.10
This all sounds very sensible, but the new policy was opposed by Assistant Attorney General Deval Patrick of the Justice Department, which prosecutes lawsuits under the Fair Housing Act. Patrick ignored HUD's new guidelines and ordered the Justice Department to bring new lawsuits against community activists.11 He contended that ''Congress intended the [Fair Housing Act] to proscribe any speech if it leads to discrimination prohibited by the FHA.''12 Two years after HUD acknowledged that prosecuting neighborhood activists for expressing their political viewpoints was unconstitutional and unwise, Patrick continued to defend the Justice Department's attempted squelching of free speech in a Fair Housing Act case in Fort Worth, Texas. In doing so, he analogized political leaflets to baseball bats, remarking that bats ''are perfectly legal too. But if you wield one to keep people out of the neighborhood, we are going to use the bat as evidence of your intent to violate the civil rights laws.''13
The problem with Patrick's analogy is that there are huge differences, both constitutionally and morally, between wielding a baseball bat as a physical threat and using speech to try to peacefully persuade others that a point of view is correct. The essence of the First Amendment is that peaceful persuasion is permissible, even when the potential consequences of that persuasion are unpalatable. Patrick assumed that speech, like wielding a baseball bat, can be restricted simply because it may result in harm to someone, but he was wrong. The First Amendment protects freedom of speech even when the speech at issue could cause harm . For example, a person has the right to propagate nasty and incendiary theories, such as the truth of racial superiority or the need to boycott stores owned by a particular ethnic group, even though speech may cause grievous harm. This outcome may be distasteful, but it beats the alternative, of trusting the government to use political criteria to decide which speech is too offensive or too dangerous to tolerate. And let's not kid ourselves; political criteria, rather than some highfalutin' academic or philosophical theory, is exactly what the government will use.
Luckily, the federal judge overseeing the Fort Worth case had a better grasp of the First Amendment than did Patrick and rejected the latter's theory. The judge held that ''leafleting, petitioning, and soliciting'' against the placement of a group home in one's neighborhood are actions protected by the First Amendment.14 More generally, the federal courts have steadfastly protected First Amendment rights against legal assaults on neighborhood activists. For example, the Berkeley three successfully sued HUD in federal court for its violation of their constitutional rights.15 In that case, the court even took the unusual step of holding individual HUD employees personally liable for this violation because their conduct was so clearly and outrageously unconstitutional. In the few other cases that have squarely addressed the First Amendment issue, courts have similarly decided in favor of citizen activists and against HUD.16
However, one judge did leave the door open for future government lawsuits after dismissing a Fair Housing Act case filed by a real estate developer against Travis Compton. Compton had been appointed by the mayor of Fresno, California, to serve on an advisory committee charged with making recommendations on proposed development plans. As part of his duties, Compton voted and spoke out against a public bond issue for a low-income housing project. The developer who had hoped to build the project sued Compton for violation of the Fair Housing Act.
Tens of thousands of dollars in legal fees later, the judge found that the plaintiff failed to provide sufficient evidence to support his claim. But the judge also opined gratuitously that ''the First Amendment does not necessarily trump the Civil Rights Act or state and federal fair housing laws.... Unlawfully discriminatory conduct carried out by speech activities is not immunized by the First Amendment.''17 Cases in which developers sue citizens opposed to their plans are especially dangerous, because developers, unlike HUD officials, are not government officials and therefore cannot be sued for violating the First Amendment. Until the Supreme Court makes clear that citizen activists may not be punished under the Fair Housing Act for engaging in political speech, public housing developers will attempt to use the Fair Housing Act to intimidate their political opponents and bully their way past obstacles to their projects.
* * *
Neighborhood activists opposing housing projects are not the only lightning rods for attempts to suppress political speech. Anyone taking action to oppose the current orthodoxy on antidiscrimination principles is at risk of being silenced by the powers that be. Critics of affirmative action preferences in higher education seem especially likely to be threatened with censorship. For example, Professor James Bell of Chicago's Daley College mocked the school's affirmative action ''diversity'' policy in a sarcastic column for the teachers' union newspaper. He wrote the following:
> I think this is a marvelous idea, and because I also subscribe to the idea of diversity . . .
>
> . . . When I buy a dozen eggs I try to make sure that at least two or three of them are rotten.
>
> . . . I want a law passed that says one-fourth of all doctors must be incompetent.
>
> . . . now and then I make a point to date an ugly woman.
> . . . I believe we should encourage more Egyptians to come to the U.S. so that our country could also enjoy the advantages of female genital mutilation. . . . I think we should also welcome more Mauritanians and Sudanese to the United States, so we could also have human slavery in this country.
>
> . . . I think all colleges should be required to hire administrators and teachers with IQs below 80. (I was just told this law already exists; it's called ''affirmative action.'')
>
> . . . I think there should be a law forcing companies to hire employees even though they can't do the job. (Someone mentioned that there already was such a law; it's called ''affirmative action.'').
>
> . . . Finally, I think the President [of the College] should fire himself and the Vice-President in order to make room for more non-Hispanic administrators at Daley College.18
>
Not surprisingly, the column evoked some controversy. No doubt that was part of the author's intent, but those who disagreed with Bell did not seem willing to debate or share their views on the contentious issue. It was perhaps easier to muzzle the pesky messenger. The college's Board of Trustees filed a complaint against the union newspaper that had carried Bell's column with the Chicago Commission on Human Relations. The complaint relied on the Chicago Human Rights Ordinance, which bans discriminatory ''harassment in places of public accommodation.'' The complaint alleged that Bell's antidiversity article ''contribute[d] to deep-seated problems in attitude and behavior that makes students uncomfortable in an institution where comfort is essential for learning.'' According to the board, ''The First Amendment is not blanket authorization for provocative hate speech at a public institution.'' The Commission eventually dismissed the action, but only because it found that the newspaper at issue was not a ''place of public accommodation'' under the law.19
Other professors have also found themselves under fire for expressing politically incorrect sentiments outside of the classroom. David Deming, professor of geology and geophysics at the University of Oklahoma, wrote to the campus newspaper, The Oklahoma Daily ,20 responding to a syndicated pro–gun control editorial by Yale student Joni Klotter. Klotter's piece had stated that ''easy access to a handgun allows everyone in this country . . . to quickly and easily kill as many random people as they want.''
It wouldn't take a gun nut to object to Klotter's hyperbole, but Deming, a zealous gun rights advocate with a history of making eccentric statements, had an especially cantankerous reaction.21 His response letter stated that Klotter's ''easy access'' to a vagina enabled her to ''quickly and easily'' have sex with ''as many random people'' as she wanted. He added that her ''possession of an unregistered vagina equipped her to work as a prostitute and spread venereal disease.'' Deming concluded his letter by stating that he hoped Klotter was as responsible with her dangerous ''equipment'' as most gun owners are with theirs.
It was a strange and aggressive way to express a pro–gun rights position, and it is hard to imagine that Deming's analogy won over many readers, but his letter clearly argued the merits of a political position. A few days after Deming's letter appeared, Becky Herbert, director of the University of Oklahoma's campus ministry center, filed a sexual harassment complaint against Deming with university administrators. Herbert found it ''unacceptable'' that Deming had ''resort[ed] to using an individual's human sexuality as a means of entering into a debate.'' Herbert stated that ''having my [sic] vagina equated with a handgun is degrading, and for this to go unaddressed by the university is demoralizing.''22 She told the media that she wanted the university to reprimand Deming and require him to undergo sensitivity training on women's issues.23 Twenty more formal complaints from other members of the University of Oklahoma community followed.
Most observers would agree that Deming's letter was, at best, intemperate and vulgar, although Deming subsequently argued that he had simply tried to show that ''my gun no more makes me a killer than her vagina makes her an immoral person.''24 Regardless, a letter to a school paper making a political argument hardly comes within the standard definition of sexual harassment. Moreover, the letter was clearly political speech protected by the First Amendment, and the University of Oklahoma, as a public university, was obligated to abide by First Amendment rules.
The university nevertheless allowed a sexual harassment investigation to proceed. The dean of the College of Geosciences, John T. Snow, criticized Deming for upsetting students, alumni, and the administration, and he warned Deming that the controversy might affect his career.25 As proceedings against Deming progressed, university president and former U.S. senator David Boren declined to intercede on his behalf. Boren's primary concern, he told Deming, was not academic freedom but ''restoring civility to public debate.''26 Eventually, two libertarian-leaning organizations, the Center for Individual Rights and the Foundation for Individual Rights in Education, threatened to sue the university for violating Deming's First Amendment rights. In an astounding coincidence, shortly after receiving these threats the university's administration suddenly discovered that Deming's letter was actually not covered by the university's sexual harassment guidelines, and the university dismissed the complaints against him.
* * *
We have examined some very blatant and overt attempts at censoring unpopular political ideas, but antidiscrimination laws threaten freedom of expression in more subtle and insidious ways. Corporate CEOs, university presidents, members of the clergy, and other prominent individuals often develop a high profile outside of their work-places and are subsequently asked to speak about public issues. One would think that on these occasions the speaker could say what he liked, as he is speaking on his own private time and in his own personal capacity, but one would be wrong. As former Boston University president John Silber discovered the hard way, plaintiffs in employment discrimination lawsuits can use a prominent person's public statements against him.
Professor Julia Brown of BU's English Department sued the university when it denied her tenure.27 During trial and in his closing argument, her attorney discussed a speech that had been delivered by then-university president Silber, a vocal social conservative. In his speech, delivered a few years earlier to a policy group in Washington, D.C., Silber had expressed concern about the growing number of working women who he felt did not spend sufficient time and energy on child-rearing. Brown's attorney cross-examined Silber about this speech, and the judge jumped in, gratuitously asking, ''Some of those career women are in the universities, including your own? . . . And I suppose one way to get them back in the kitchen, is to get them out of the university; is that so?'' In his closing argument, Brown's attorney stated that based on Silber's views, ''at BU, women and not men carry the burden of being seen as wives and mothers and not just as scholars.''
The jury awarded Brown $215,000 and tenure. An appellate court criticized the trial court for admitting the evidence regarding Silber's speech. The court observed that the evidence presented was marginally relevant at best and that allowing evidence of a university official's political and social views to support a discrimination claim had the potential to chill academic freedom. The court nevertheless let the verdict stand, finding that the admission of the speech was ''harmless error'' that had not affected the verdict—a curious finding given the attention Brown's attorney had lavished on the evidence in his closing. Indeed, posttrial interviews with jurors revealed that while they liked Brown,28 they did not believe that BU had discriminated against her. They had nevertheless ruled in her favor because they felt that Silber was arrogant and sexist in believing that women should stay home and take care of their kids. Had the district court excluded the evidence of Silber's speech, BU would likely have won the case.
Courts have even used individuals' stated opposition to or distaste for antidiscrimination laws as evidence of discrimination. For example, one court began an opinion finding liability under the Equal Pay Act of 1963 by quoting a manager who had pronounced the law ''foolish'' when it was under congressional consideration.29 In another case, an appellate court upheld a verdict for the plaintiff in a sex discrimination lawsuit against Keene State College in part because a Keene State official had, in an unrelated letter, written to the president of Smith College for information on how that school had responded to a charge of sex discrimination because he was ''concerned that that form of anarchy may creep north into our virgin territory.''30 And when Forbes magazine was sued for age discrimination, the plaintiff relied on a column publisher Steve Forbes had written 15 years earlier opposing proposed laws that would end age-based mandatory retirement.31
This trend of admitting past remarks on legal or social policy law as evidence of current discrimination is disturbing. The fact that a defendant criticized an antidiscrimination law may be marginally relevant to the question of whether the defendant broke the law. However, most people obey even laws they disagree with, and allowing the plaintiff to present the defendant's critical remarks to the jury about popular law is grossly and unfairly prejudicial. Admission of such statements therefore violates standard rules of evidence.32 Moreover, allowing discrimination plaintiffs to rely on a defendant's past political speech creates a severe risk of chilling the exercise of First Amendment rights, a risk that is not worth taking for introducing evidence of minimal value.
* * *
Even criticisms of perceived government racism can get a speaker in trouble with civil rights authorities when the form of the criticism is deemed offensive. St. Paul, Minnesota's Human Rights Director, Tyrone Terrill, sought to punish the St. Paul Pioneer Press for running a biting editorial cartoon critical of the school's failure to properly educate black athletes. The cartoon, entitled ''The Plantation,'' depicted a basketball game with three anonymous African American University of Minnesota basketball players visible. Two middle-aged, well-dressed white males are watching the game from the stands, and one says, ''Of course we don't let them learn to read or write.''33 Cartoonist Kirk Anderson was protesting the UM athletic program's perceived exploitation of African American athletes— only one in four UM basketball players graduates from the university.
Terrill's complaint nevertheless alleged that the cartoon created an illicit ''hostile public environment,'' an allegation similar to the one leveled against the teachers' union newspaper in the Daley College case. Terrill claimed that by creating such an environment, the newspaper illegally ''discriminated against African American student-athletes past, present and future in the area of public accommodations on the basis of race.''34 Terrill told the Pioneer Press that he believed the cartoon was not protected by the First Amendment, because it was analogous to an employee hanging nude centerfolds in the workplace or directing racial epithets at coworkers, behavior other courts had punished (see Chapter 2). After meeting with the newspaper's attorney, Terrill agreed to drop the complaint, but only because the attorney persuaded him that the newspaper's editorial column could not have violated St. Paul's antidiscrimination ordinance, because an editorial column is not a ''place of public accommodation'' under the law.35
* * *
One of the most cherished freedoms Americans enjoy is the right to lobby and criticize their government. It is both frightening and sad, then, that this liberty is undergoing such a serious and increasing threat from antidiscrimination laws. The only thing that now stands between a citizen with a contrarian political view to express and the Deval Patricks, Tyrone Terrills, and other eager censors of the world is the First Amendment. If we allow antidiscrimination laws to erode this protection, we will find ourselves at the mercy of a power elite able to muzzle any dissent from its vision of an egalitarian political orthodoxy.
# 5. Censoring Campus Speech
Public universities, like all government entities, must comply with the First Amendment. Nevertheless, many public universities have established speech codes to censor expression potentially offensive to women, African Americans, or other groups protected by civil rights laws. Universities commonly justify these rules as being necessary to prevent the creation of an illegal ''hostile environment'' on campus. University officials have not, however, been able to reconcile suppression of potentially offensive expression with the First Amendment.
The first wave of public university speech codes appeared in the late 1980s, with the rise of censorious political correctness. The University of Michigan's code, for example, banned speech ''that stigmatizes or victimizes an individual on the basis of race'' or that ''has the purpose or reasonably foreseeable effect of interfering with an individual's academic efforts.''1 Another part of the code prohibited speech relating to sex or sexual orientation that ''creates an intimidating, hostile or demeaning environment for educational pursuits.''
In furtherance of its code, the university distributed a handbook with examples of illicit speech. For example, a student organization, the book stated, would violate the speech code if it ''sponsors entertainment that includes a comedian who slurs Hispanics.'' The handbook also noted that expression of certain politically incorrect opinions, such as remarks by male students that ''women just aren't as good in this field as men,'' were prohibited. Beyond these two examples, students could only guess at what speech was forbidden. A federal court concluded ''that the University had no idea what the limits of the [p]olicy were and it was essentially making up the rules as it went along.''
Ironically, complaints under the speech code overwhelmingly involved white students charging African Americans with hate speech. For example, the university punished an African American student for opining in class that homosexuality is a curable disease. Courts did not treat these early speech codes kindly: federal courts overturned on First Amendment grounds codes at Michigan,2 the University of Wisconsin,3 and Central Michigan University.4 Through the early 1990s, advocates of speech codes argued that, despite these lower court decisions, the Supreme Court's ''fighting words'' doctrine allowed government regulation of ''hate speech.'' Under the fighting words doctrine, the First Amendment does not protect speech likely to incite the listener to imminent violence.
In R.A.V. v. City of St. Paul ,5 however, the Supreme Court overturned a conviction under a hate speech law for cross burning. In its ruling, the Supreme Court held that the government may ban all fighting words but it may not ban only select fighting words on the basis of their content. The hate speech ordinance in question banned only racist fighting words and therefore violated the First Amendment.6 The upshot of R.A.V. is that, first, public universities may not restrict student speech that allegedly creates a hostile environment when the speech does not rise to the level of fighting words.7 Second, even when such speech does amount to fighting words, public universities may not enact speech restrictions that single out for punishment fighting words that offend only members of certain protected groups.8 The only possible exception to the latter rule is if a university can show that the racist fighting words it banned are more likely to incite imminent violence than are other fighting words, and that this greater danger from racist fighting words, and not a desire to squelch racist speech as such, was the sole reason the university prohibited racist fighting words.
Given these constitutional barriers, public university speech codes were on the way out until the federal Department of Education revived them in 1994. Male students at Santa Rosa Community College had posted anatomically explicit and sexually derogatory remarks about two female students in a discussion group hosted by the college's computer network.9 Several aggrieved students filed a complaint against the college with the DOE's Office for Civil Rights. The DOE found that the messages probably created a hostile educational environment on the basis of sex for one of the students. University toleration of such offensive speech, the government added, would violate Title IX, the law banning discrimination against women by educational institutions that receive federal funding. Under this standard, to avoid losing federal funds, universities must proactively ban offensive speech by students and diligently punish any violations of that ban.
The DOE failed to explain how its rule was consistent with the First Amendment. Speech codes enacted by public universities clearly violate the First Amendment even if the codes are enacted in response to the demands of the DOE, so requiring public universities to enact speech codes or forfeit public funds would obviously be unconstitutional. Nevertheless, facing this choice, public university officials have ignored the First Amendment issue and complied with DOE guidelines. Although a few schools may truly be concerned about the potential loss of federal funding, the prevailing attitude among university officials seems to be that the DOE's Santa Rosa decision provides a ready excuse to indulge their preference for speech codes. University officials implicitly reason that if the DOE can get away with ignoring the First Amendment, then so can they. Unfortunately, they may be right.
In any case, many public universities retain speech codes despite the lurking First Amendment issues. Some codes are so broad that, when taken literally, they are absurd. The University of Maryland's sexual harassment policy, for example, bans ''idle chatter of a sexual nature, sexual innuendoes, comments about a person's clothing, body, and/or sexual activities, comments of a sexual nature about weight, body shape, size, or figure, and comments or questions about the sensuality of a person.''10 So, at the University of Maryland, saying ''I like your shirt, Brenda'' is a punishable instance of sexual harassment. Further, because under Maryland's code the prohibited speech need not be specifically directed at an individual to constitute harassment, even saying ''I really like men who wear bow ties'' is out of bounds, at least if a man who wears bow ties hears about it.
Public university censorship to prevent a hostile environment extends well beyond the sex discrimination issues raised in the Santa Rosa case. Federal law also bans discrimination in education on the basis of race, religion, veteran status, and other criteria, and universities argue that they must censor speech to prevent a hostile environment for groups protected by those laws, as well. As a measure of just how far the law extends, consider the actions of the Office of Federal Contract Compliance Programs. That office charged illegal harassment based on Vietnam-era veteran status when an exhibit at Ohio State University displayed pictures and postings criticizing the actions of American military personnel during the Vietnam War.11 So much for academic freedom and the spirit of open debate in higher education.
A more typical case arose when a member of Phi Kappa Sigma at the University of California, Riverside, designed a T-shirt advertising a ''South of the Border'' party. The shirt featured a figure wearing a serape and sombrero sitting on a beach looking at the setting sun and holding a bottle of tequila, along with a picture of a set of steel drums and a wooden tiki head, in which was carved the word ''Jamaica.'' The bottom of the shirt depicted a smiling Rastafarian carrying a six-pack of beer while standing in a Mexican cantina frequented by Riverside students, humming a lyric from an antiracist song by Bob Marley: ''It doesn't matter where you come from long as you know where you are going.''12 Although not exactly a brilliant artistic gem, the shirt was nonetheless a little more creative and diverse than the average frat party ad.
Campus Latino activists, however, were not favorably impressed. They charged that the shirt ''dehumanizes and promotes racist views of Mexican people'' and they formally accused the fraternity of violating university rules by circulating ''offensive racial stereotypes.'' The fraternity president, Rich Carrez, apologized to the activists and pointed out that he was part Native American, the vice president of the fraternity was Latino, the T-shirt creator was Latino, and the fraternity was the most racially diverse on campus, with 25 white and 22 nonwhite members. The activists were unmoved and stubbornly clung to their view that the innocuous T-shirt promoted offensive stereotypes.
Ultimately, the university required fraternity members to destroy all of the T-shirts, apologize in writing, engage in community service, and attend two seminars on multiculturalism—an ironic punishment given that almost half the fraternity members were themselves minorities. The university also stripped the fraternity of its charter and expelled it from campus for three years. The university eventually lifted all of the sanctions, but only after legal intervention by the Individual Rights Foundation, a national network of lawyers that responds to threats to the First Amendment by college administrators and government officials.
Lawsuits, or even the threat of lawsuits, certainly seem to get campus officials' attention. At some public universities, civil libertarians have used the threat of legal action to persuade school officials to abandon their speech codes. For example, in 1997, the Office of Social Justice at West Virginia University published a brochure defining illicit discriminatory behavior as, among other things, expression of politically incorrect sentiments. An example of such forbidden discrimination was provided: claiming that ''women never do well'' in a particular science class regardless, apparently, of whether the statement is true.13 With such strict limits on what thoughts and feelings could be publicly shared, WVU students might well have had trouble finding anything neutral and sensitive enough to say to each other. But not to worry, the brochure provided helpful ''advice'' for encouraging a welcome environment, such as substituting ''friend, lover, or partner'' for the word boyfriend or girlfriend. The brochure further cheerfully suggested that failure to comply with its advice would be punishable.
Concerned faculty members wrote to the president of the university, David Hardesty Jr., seeking assurance that the brochure was not a speech and behavior code for students and faculty. Hardesty instead confirmed his correspondents' fears by writing that ''[t]he right to free speech and the concept of academic freedom do not exist in isolation,'' and that freedom of speech does not include the right ''to create a hostile environment on campus.''14 The university ultimately withdrew the brochure, but, as is no doubt becoming a familiar theme in these tales, only after the West Virginia Civil Liberties Union threatened to sue.15
* * *
Regardless of whether their universities have formal speech codes, public university officials frequently restrict ''offensive'' student speech on an ad hoc basis. For example, UCLA suspended an editor of the student newspaper for running an editorial cartoon ridiculing affirmative action preferences. In the cartoon, a student asks a rooster on campus how it got into UCLA. The rooster responds, ''affirmative action.'' After the editor was sanctioned by UCLA, student editor James Taranto reproduced the cartoon in the California State University, Northridge, student newspaper and criticized UCLA officials for suspending the paper's editor for engaging in constitutionally protected expression. Northridge officials suspended Taranto from his editorial position for two weeks for publishing controversial material ''without permission.'' However, when Taranto threatened a lawsuit, the school removed the suspension from his transcript.16 Taranto continued to pursue a career in journalism and currently edits Opinionjournal.com.
In another incident, administrators at the University of Minnesota, Twin Cities, prohibited the College Republicans from distributing at the school's orientation fliers critical of then-president Bill Clinton. Several fliers contained R-rated humor, and one of them vulgarly satirized the president's views on gay rights. University officials argued that the fliers violated the university's nondiscrimination policy, violated orientation guidelines that require orientation to provide students with an ''appreciation of diversity,'' and were not ''consistent with the goals of the university.''17
After severe criticism from the American Civil Liberties Union and the local media—especially the Minneapolis Star Tribune —the university relented and permitted the distribution of the fliers. However, university president Nils Hasselmo stubbornly insisted that the flyer incident had only had the ''appearance of'' suppressing speech.18 He maintained that the orientation regulations that the fliers had violated were constitutional and had only been suspended, not repealed. Subsequently, an outraged Minnesota law student sued the university for violating its students' constitutional rights. The university capitulated, agreeing not only to stop censoring student materials but also, in a welcome twist on the usual forced sensitivity training ritual, to have its administration attend a lecture on the protection of freedom of speech afforded by the First Amendment.19
* * *
This chapter has so far dealt only with public universities, which, as government actors, are subject to the limits of the First Amendment. However, it is important to remember that private universities are not government actors and therefore are immune from the dictates of the First Amendment. The Constitution does not stop them from enacting speech codes. In fact, private universities probably have a First Amendment expressive association right to set speech guidelines on campus (see Chapter 8). Many private university speech restrictions would exist regardless of government antidiscrimination regulations. For example, one hardly expects universities with a traditional religious mission to tolerate blasphemous comments from their students. Also, many elite private universities are controlled by politically correct administrators and professors who support stringent speech codes banning insensitive and intolerant comments regardless of legal requirements.
But although private universities have the right to enact and enforce voluntary speech codes, the First Amendment prohibits the government from requiring private universities to administer speech codes. Nevertheless, under the Santa Rosa case discussed previously, the government has threatened to strip private universities of federal funding if they don't enforce speech restrictions to ensure that their students are not exposed to a ''hostile environment.'' Moreover, individual students may sue universities for tolerating a ''hostile educational environment,'' in the same way that workers may sue their employers for tolerating a ''hostile workplace environment'' (see Chapter 2). There is no practical difference between the blatantly unconstitutional act of the government's directly censoring speech at private universities and what the government actually does, which is to enforce laws that create legal liability for private universities that fail to proactively censor speech. The latter course may be less obviously Orwellian than the former, but its effects, that is, government censorship, are the same.
Brad Kvederis, a student at Claremont McKenna College, a private school in Claremont, California, learned this lesson the hard way. He published for his dorm a gossip newsletter called the Wohlford Free Press . Like many college publications, the Free Press included sexually suggestive material. Depending on which account of the relevant events one reads, the newsletter was either a relatively sober, albeit profanity-laced, publication that occasionally mentioned sex or a scandal sheet reporting on the drinking and sexual hijinks of dorm residents. In any event, three female students— only one of whom was mentioned in the newsletter—filed hostile environment complaints against Kvederis with the university. Fearing liability, the university suspended Kvederis for a semester and required him to undergo sexual harassment sensitivity training.
The ACLU sued on Kvederis's behalf under a unique California law that prohibits private universities from regulating student speech (see Chapter 8). The court, however, dismissed the case on the grounds that Kvederis's publication had ''the potential to create a hostile environment and could have become the basis of sexual harassment claims'' if the college had not intervened.20 Federal anti-discrimination law supersedes state free speech law, the court ruled. Before appeal, the college and Kvederis settled for undisclosed terms.21
* * *
For any university to function, its administration must engage in content-based regulation of its faculty's speech. That is to say, the administrators must, to a certain extent, dictate what professors will or will not talk about in class and the subjects they will or will not teach. For example, for a university to run smoothly, the administrators must determine what courses will and will not be taught, and on the basis of the applicants' academic writings, which professors will or will not be hired and granted tenure.22 The inevitability of content-based regulation of academic expression on public university campuses suggests a strong civil libertarian case that government should not be in the business of running universities at all. After all, content-based speech restrictions are a clear no-no under the First Amendment. But once the government is allowed to control universities, university officials must be able to place reasonable restrictions on what their faculty members may say in the classroom.
Even the most hardcore proponent of academic freedom would have to concede that a professor assigned to teach 19th-century French literature can be penalized for using his class time to teach anthropology, in the same way that any other government employee can be punished for not doing his job. Similarly, a professor who uses his class as a forum to launch into irrelevant diatribes criticizing certain ethnic or religious groups may clearly be sanctioned for not doing his job. More problematic is the question of whether professors have the right to engage in classroom speech that is relevant to the topic at hand but that offends some students.
Academics, including the author of this book, generally believe that the danger to academic dialogue caused by restrictions on purportedly offensive speech outweighs the potential benefit of reducing offense to students. Indeed, sometimes the only way to get students to genuinely confront and engage in controversial issues is to risk offending them. The appropriate policy is one that fully protects professors' classroom speech, as long as the speech has a reasonable relationship to the topic at hand (there's no reason to tolerate a lecture on the glories of Mein Kampf from a woodworking professor), and as long as the offending speech does not constitute harassing behavior clearly directed at particular students .
Some federal court analyses of the constitutional issues involved in regulating professors' classroom speech adopt a similar analysis.23 Other decisions, however, suggest that public universities have a broader latitude than this to set general guidelines on appropriate speech in class. In essence, under these decisions, universities are free to regulate any classroom speech as long as they can show that such regulations are reasonably related to legitimate pedagogical objectives.24 For example, a university may bar the faculty from using obscene language during class, regardless of context, on the grounds that university officials have determined that any educational benefit that may be gained from using such language is outweighed by the fact that it will distract and upset many students, interfering with their ability to learn.25 (A law professor at such a university would have a difficult time teaching many First Amendment cases, including the important ''Fuck the Draft'' case mentioned in Chapter 2.) Under this line of cases, arguably a university may even declare that certain controversial subjects, such as whether racial differences in IQ exist, are off-limits in the classroom because they are too distracting to students.
The caveat is that to comply with the First Amendment's guarantees of free expression and the Fourteenth Amendment's guarantee of due process, public universities must clearly spell out any restrictions on professors' classroom speech in advance.26 However, because academic freedom is an extremely powerful and popular notion, few, if any, public universities promulgate detailed prospective speech regulations. Indeed, many universities spell out academic freedom guarantees in faculty contracts or in binding rules published in university handbooks. The threat of censorship remains, however, when universities adopt extremely vague guidelines banning ''harassment'' based on race, sex, and other attributes. The vagueness of these guidelines allows extremely sensitive or politically motivated students to launch harassment cases against unwary professors who offended them in class, which undermines the university's claimed commitment to academic freedom.
The case of Professor Donald Silva of the University of New Hampshire provides an instructive example. Silva's troubles started when, during his technical writing course, he used the concept of sexual intercourse to illustrate the process of focusing the thesis statement of a technical report. He told the class, ''I will put focus in terms of sex, so you can better understand it. Focus is like sex. You seek a target. You zero in on your subject. You move from side to side. You close in on the subject. You bracket the subject and center on it. Focus connects experience and language. You and the subject become one.'' In a later class, he used a famous remark about belly dancing—''like jello on a plate with a vibrator under the plate''—as an example of a vivid metaphor.
Silva had used these similes in class for many years, and he argued that they were effective in getting the attention of his students. Six of his students did not agree, although judging by the poor grammar and the spelling errors that plagued the written sexual harassment claim they filed against Silva, they could have used all the writing help they could get.27 One student wrote, somewhat incoherently, that ''Silva started talking in a sexual manner which I thought was very inappropriated [sic] and also very affending [sic].'' Another wrote, ''During class we were discussion [sic] our technical reports when Don Silva . . . made [sic] a vulgar, inappropriate description of a 'bowl of jello and a vibrator,' to describe the belly dancer.'' A third added, ''I had questions about our assignment on 26 Feb, but due to his use of sex as a 'focus,' I walked away rather than asked [sic] him to clarify again. I didn't want any more strange explainations [sic].'' Yet another student was ''very offended'' by Silva's ''sexual refferals [sic].''
Silva's comments were arguably in bad taste, but they hardly rose to the level of the severe and pervasive conduct normally required to support a sexual harassment claim. Moreover, the university's sexual harassment policy did not suggest that it regulated the comments at issue. The only examples the policy gave of remarks that could constitute sexual harassment were ''unwelcome sexual propositions,'' ''graphic comments about a person's body,'' ''sexually degrading words to describe a person,'' ''derogatory or sexually explicit statements about an actual or supposed sexual relationship,'' and ''derogatory gender-based humor.'' None of these examples applied to Silva's statements. Nevertheless, after several hearings that could most charitably be described as almost comically unfair, university officials found that Silva's ''focus'' discussion had violated the university's sexual harassment policy. The university suspended Silva without pay for one year and required him to attend psychological counseling sessions at his own expense.28
Silva responded by suing the university in federal court. The court issued a favorable preliminary ruling after finding, among other things, that the university likely violated Silva's First Amendment rights. The court acknowledged that under appropriate circumstances the university's sexual harassment policy could be applied to classroom speech because it ''seeks to address the legitimate pedagogical concern of providing a congenial academic environment.'' However, the policy was unconstitutional as applied to Silva's classroom speech because it ''employed an impermissibly subjective standard that unreasonably limited academic freedom.'' The strong theme running through the court's opinion is that a public-university professor may not be sanctioned for classroom speech unless he has been given prior notice that such speech is prohibited. Before the case could proceed further, the parties settled, with the university agreeing to all of Silva's demands.29
* * *
Much of the threat to academic freedom from antidiscrimination laws comes from campus radical feminists who seek to use the hostile environment component of sexual harassment law to stifle discourse they dislike. A University of New Hampshire women's studies professor's diatribe, reacting to Silva's vindication, exemplifies the anti–free speech sentiment of many (though certainly not all) feminist academics:
> Academia . . . has traditionally been dominated by white heterosexual men, and the First Amendment and Academic Freedom (FAF) traditionally have protected the rights of white heterosexual men. Most of us are silenced by existing social conditions before we get the power to speak out in any way where FAF might protect us. So forgive us if we don't get all teary-eyed about FAF. Perhaps to you it's as sacrosanct as the flag or national anthem; to us strict construction of the First Amendment is just another yoke around our necks.30
Ironically, preventing vague university antidiscrimination policies from becoming excuses to censor unpopular speech will ultimately benefit feminists and their anti–free speech allies in the multiculturalist and critical race theory movements as much as it benefits anyone else. One does not need much of an imagination to come up with examples of how antidiscrimination law could be used to silence left-wing academics like the New Hampshire women's studies professor. For example, men taking classes from extreme feminist professors sometimes claim that these professors create a hostile environment for them. These claims sometimes have a legitimate basis. After all, Professor Mary Daly of Boston College went so far as to ban men from her feminist ethics class over a 25-year period,31 ensuring that male students had no access to her academic environment at all. More often, however, male students are simply uncomfortable with feminist professors' radical viewpoints.
Highly questionable claims of discrimination by male students have already been reported. For example, a male undergraduate in a human sexuality course accused Toni Blake, a female graduate student teacher, of sexual harassment. Blake used a banana to demonstrate condom application and joked that men, like basketball players, ''dribble before they shoot.'' A male student complained that she ''objectified the penis'' and created a ''hostile environment for him as a man.''32 In another incident, a married male Christian student filed a sexual harassment lawsuit after a lesbian psychology professor presented a lecture on female masturbation. The student claimed to have felt ''raped and trapped'' by the lecture.33
While it would be unfair to speculate about the motives of these students, one can easily imagine situations in which students would bring such charges because they disliked their professors for ideological or other reasons. Unfortunately, that is exactly the spiteful behavior that hostile environment law invites. Even the weakest discrimination complaints can lead, at a minimum, to a mandatory investigation by the Department of Education. Michael Krauss of George Mason University's law school, for example, spent months responding to one such investigation based on a frivolous student complaint, which he believes was motivated by a prior dispute he had with the student over grading. The complaint arose from Krauss's query to a torts class about whether burning a cross and shouting ''kill the niggers'' in front of someone's home constituted the tort of assault.34 The student suggested that using the n-word in class was discriminatory per se. Such incidents make professors reluctant to discuss issues involving race relations, rape, and other extremely important issues for fear that an offended or vengeful student will file a complaint.
* * *
If left-wing professors wish to preserve their own academic freedom, they must learn to be more tolerant of those whose speech they currently seek to suppress. For the past several decades, the pressure to censor free speech on public university campuses has come primarily from the left. However, the current war against terrorism, and the frequent dissent within academe to that war, has shifted the censorship dynamic, putting many radical-left professors on the defensive. The First Amendment, and the values of academic freedom that have sprung up around it, will protect the vast majority of dissenters, but only because the radicals' war against the First Amendment has so far been largely unsuccessful. These academics would do well to consider what their plight might be should they ever succeed in doing away with constitutional protection of unpopular speech.
In Canada, left-wing academics are beginning to learn firsthand what it's like to have their own censorship vehicles used against them. For example, Professor Sunera Thobani of the University of British Columbia, a native of Tanzania, faced a hate crimes investigation after she launched into a vicious diatribe against American foreign policy. Thobani, a Marxist feminist and multiculturalist activist, had remarked that Americans are ''bloodthirsty, vengeful and calling for blood.''35 The Canadian hate crimes law was created to protect minority groups from hate speech, but in this case it was invoked to protect Americans. The police revealed the investigation to the media, despite a general policy against doing so, because, a hate crimes investigator explained, ''Here we have a complaint against someone who is obviously from a visible minority, whom the complainant feels is promoting hate. Normally, people think it's a white supremacist or Caucasians, promoting hate against visible minorities.... We want to get the message out that it's wrong, all around.''36
The police eventually decided not to file charges for undisclosed reasons, perhaps because Thobani's speech was sufficiently rambling that her perceived attack on Americans could alternatively be construed as an attack on the ''socially constructed'' American nation invoked by President George W. Bush. Although still potentially insulting to Americans, this would not violate the hate crimes law. So, Thobani, who seethes with contempt for the Western world and the bourgeois liberties it protects, will stay out of jail—for now. Nevertheless, the incident reminds us that those who oppose freedom of speech would likely become the first victims of its demise. As Albert Jay Nock once wrote, ''Whatever power you give the State to do things for you carries with it the equivalent power to do things to you.''37 With freedom of expression, as with much else in life, what goes around comes around.
# 6. Compelled Speech
Nothing is more repugnant to the First Amendment's protection of freedom of expression than the government's compelling individuals to express views contrary to their actual beliefs. As Justice Robert Jackson wrote for the Supreme Court almost 60 years ago, the nation cannot logically have a First Amendment that ''guards the individual's right to speak his own mind, but left [sic] it open to public authorities to compel him to utter what is not on his mind.''1
Despite these serious First Amendment considerations, an increasingly common method of punishing violators of antidiscrimination laws is to compel them to speak against their beliefs, as the case of Roy Frankhouser illustrates. Frankhouser, a Ku Klux Klan supporter with a long arrest record, harassed and intimidated Bonnie Jouhari, a fair-housing specialist for the Reading-Berks County Human Relations Council in Reading, Pennsylvania. Frankhouser sat on a public bench outside Jouhari's office and photographed her through the window. When Jouhari appeared on a television talk show, Frank-houser called in to warn her that ''we're always keeping an eye on you.'' Even more ominous, Frankhouser displayed a picture of her obtained from a local neo-Nazi Web site on his ''White Forum'' public access cable television show. As on the Web site, the picture shown on television had a threatening caption: ''Traitors like this should beware, for in our day, they will be hung from the neck from the nearest tree or lamppost.'' Jouhari decided to move to the West Coast—in part to get away from Frankhouser—but he continued to unnerve her until the last moment by appearing uninvited at the local bar that hosted her going-away party.2
The U.S. Justice Department and the local police declined to prosecute Frankhouser, because officials determined that his obnoxious behavior did not rise to the level of an actual threat, and he was therefore acting within his First Amendment rights. This decision was sound based on current First Amendment doctrine, which probably protects implicitly threatening speech more than it should. In January 1999, an administrative law judge with the federal Department of Housing and Urban Development did charge the owner of the neo-Nazi Web site with violating the Fair Housing Act by threatening Jouhari. The judge, however, found no reasonable cause for charging Frankhouser, who had ''reported'' the threat by discussing it on his television show, but had never explicitly endorsed it.
A month later, however, the assistant secretary for fair housing and equal opportunity ordered that misdemeanor charges be brought against Frankhouser. Ultimately, the impecunious, unemployable Frankhouser agreed to a settlement. He promised to stay 100 feet away from Jouhari and her daughter and to pay Jouhari five percent of his annual salary for 10 years, in the unlikely event that it ever exceeded $25,000.3 Frankhouser agreed to never mention Jouhari's name again and to attend HUD-sponsored sensitivity training. Frankhouser was also required to apologize to Jouhari on his ''White Forum'' television show and in letters to local newspapers, to broadcast HUD fair housing public service announcements as part of his television show, to read a government-scripted introduction to those announcements, and to display on the front of his house a poster produced by HUD, inveighing against discrimination in housing sales and rentals.
HUD Secretary Andrew Cuomo announced that ''this settlement makes a very loud statement, not just to this particular case but to anyone who would think of engaging or involving themselves in this hideous type of behavior.''4 Columnist Michael Kelly, by contrast, interpreted the ''statement'' made by the settlement as, among other things, that the government may force an individual ''to curtail his speech,'' to take reeducation classes, and to ''make statements contrary to his beliefs.''5
Not surprisingly, Frankhouser was not rehabilitated. ''Clinton and Andrew Cuomo can kiss my rebel derriere,'' Frankhouser told columnist Dennis Roddy. ''Yeah, I'm a sensitive guy. I'll end up liking gays, marry a [black] and maybe move to Mexico later on.'' Frank-houser said of his sensitivity training, ''Hey, if the taxpayers want to foot the bill, God bless 'em. If they don't give me lunch, I won't go.'' Roddy opined that ''[w]hen an irredeemable racist is sent to sensitivity training and made to say things he doesn't believe on a show that caters to an audience that won't listen, we are only left to remember how foolish a country gets to look when its secretary of housing becomes a closet attorney general.''6
Indeed, during the Clinton administration, HUD was the federal agency that most consistently violated civil liberties on behalf of an antidiscrimination agenda. HUD's overzealousness went well beyond the Frankhouser case. As part of its war against neighborhood organizations that oppose local group housing initiatives (see Chapter 4), HUD tried to compel these organizations not only to give up their right to express their opinions but also to affirmatively support HUD's objectives. For example, a Seattle citizens' group, the Capitol Hill Association for Parity, opposed the proposed establishment by Pioneeer Housing Services of a complex of five buildings on one block to house the mentally ill and recovering addicts. HUD accused CHAP of violating the Fair Housing Act, and offered a conciliation agreement to avoid litigation.7 Among other things, the agreement required the group to write to everyone on its mailing list in support of the PHS development, and to sponsor a block party ''to which all residents, including residents of PHS housing, will be invited.'' The agreement specified that the group ''shall solicit support for the block party from local businesses, and will ensure that free entertainment and inexpensive food are provided.'' HUD eventually dropped the case under public pressure.
Another case in which compelled speech was invoked as a remedy for discrimination involved Union Market, a store in Springfield, Massachusetts. After finding that a Union Market supervisor had discriminated against a Puerto Rican worker, the Massachusetts Commission Against Discrimination ordered standard remedies, including requiring back wages and emotional distress damages to be paid. However, the MCAD also required Union Market to ''sponsor an event celebrating the Latino history and culture, drawing upon the resources of leaders and civic organizations servicing the Springfield Latino community.''8
The MCAD justified this extraordinary remedy on the grounds that most of Union Market's employees and customers are Puerto Rican. ''It not only provides an opportunity for the market to demonstrate its goodwill,'' the hearing officer wrote, ''it sends a message to businesses . . . that they should honor the people they serve and show they appreciate their patronage.'' The MCAD did not attempt to explain how the commonwealth could require Union Market to ''honor'' customers of a certain ethnic group and to demonstrate that the store ''appreciates their patronage'' without violating the First Amendment. The First Amendment issue is especially problematic in this case because it was an employee, not a customer, who complained of discrimination, so it is difficult to argue that the compelled speech honoring Latino customers was necessary to remediate a specific harm caused by a violation of the law.
The MCAD also dictated speech to a Boston bar owner charged with discrimination. In February 2000, the owner put up a display comprising vines, stuffed monkeys, a large stuffed gorilla wearing a crown, a wooden figure holding a spear, and coconuts painted with black faces and large red lips. A sign behind the stuffed animals proclaimed, ''Hey, hey, we're the monkeys.'' The owner claimed he put up this display annually ''because it's the dead of winter. People are sick of winter and want to go into a bar with a tropical flair.''9 He noted that the tropical display was part of a rotating series— frogs in the spring, fish in the summer, elephants and donkeys at election time. However, a bartender allegedly told patrons that the display mocked Black History Month and that the regal gorilla represented Martin Luther King Jr. When a report of the incident appeared in the Boston Herald , the chairman of the MCAD initiated proceedings against the bar for allegedly creating a hostile environment for African American patrons.10 Rather than litigate, the bar owner agreed to the Commission's demands that he apologize and contribute money to events ''addressing the topic of the history and contributions of Irish Americans and African Americans.''11 Surprisingly, the MCAD did not respond to the bar owner's annual display of frogs by requiring him to contribute money to events addressing the topic of the history and contributions of French Americans.
* * *
Government authorities have also sought to dictate to commercial entities the content of their advertisements. The Fair Housing Act, for example, has been construed to regulate the content of real estate advertisements. Federal regulations—currently suspended while HUD completes a review of possible conflicts between its regulations and the First Amendment—state that to prevent an inference that an advertiser prefers tenants from certain groups, if human models are used in display advertising campaigns, ''the models should be clearly definable as reasonably representing majority and minority groups in the metropolitan area.''12 In other words, if you are a developer setting up a magazine ad to sell units in a new condominium complex, you had better be sure that some of those happy people cavorting in the pool and soaking up sun on their balconies are not white.
Liability for failure to use a suitably diverse group of human models extends not only to the party that places the ad but also to the newspaper publishing the ad and the ad agency that designed it. Several courts have agreed with HUD on this interpretation of the Fair Housing Act.13 One court held that an ordinary reader, seeing ads that contained only white models, ''would naturally infer from these ads . . . that white individuals were preferred as tenants.''14 Therefore, such ads violate the Fair Housing Act's ban on advertising that indicates a preference on the basis of race.
A federal appellate court rebuked the New York Times for suggesting that the only way to avoid a lawsuit—and potential liability for hundreds of thousands of dollars in damages15—under HUD's interpretation of the Fair Housing Act would be to institute quotas for African American models.16 Yet the Washington Post was soon compelled to do exactly that. The Post avoided litigation only by agreeing with a local activist group that the newspaper would require a minimum of 25 percent African American models in all housing display ads.17 One real estate company that faced claims for discriminatory advertising sought to avoid future liability by ending its use of human models entirely, only to be ordered by a federal court to first expiate its past sins by placing ads featuring racially diverse models.18
Fair housing laws protect many groups besides African Americans; in theory, advertisers who use human models and do not include Asians, Latinos, Hasidic Jews, disabled individuals, or families with children could be held liable for discrimination.19 (The ad that did comply with such silly standards would be decidedly amusing to behold. The Afro-Asian Lubavitcher and his wheelchair-bound Latino daughter . . .) A federal judge has specifically argued that advertisements that did not feature all groups protected by the Fair Housing Act in proportion to their representation in the local metropolitan area could be found to be discriminatory.20 Predictably, the result of all this has been that advertisers have given up on trying to meet such unreasonable standards; human models are now rarely used in real estate advertising. Ironically, the exception to this trend is on those occasions when HUD requires developers participating in certain federal housing programs to develop and implement ''affirmative fair housing'' marketing plans, which must include advertising specifically designed to appeal to groups that are not likely to apply for the housing.21
At one time, HUD's regulations clearly imposed liability for ''discriminatory advertising'' regardless of the intent of the advertiser. For example, the fact that it hadn't occurred to an apartment complex owner to include a couple of kids in the ad for downtown studios was no defense under the regulations to a charge of discrimination against families with children. HUD suspended those regulations as part of a general effort to get closer to the right side of the First Amendment, but the department stopped short of promulgating new regulations limiting liability to intentional discriminators. HUD currently takes no official position on whether discriminatory intent is necessary for advertising to violate the Fair Housing Act, instead leaving the issue up to the courts.22 Some courts, meanwhile, do require plaintiffs to prove intent in human model cases.23 One federal appellate court reasoned that forcing advertisers and newspapers that had no discriminatory intent to consider the race of advertising models would violate the First Amendment by chilling commercial speech.24
* * *
In contrast to HUD rules requiring real estate companies to have ''inclusive'' advertising if they advertise at all, the Equal Employment Opportunity Commission has prosecuted some employers for not advertising. The Chicago office of the EEOC has made something of a cottage industry out of suing small businesses that hire workers primarily through word of mouth, rather than through help-wanted ads placed in large-circulation newspapers. The department claims that the result of such hiring practices is a statistically determined ''underrepresentation'' of African Americans at the companies at issue.
For example, the agency went after Andrew Hwang, a Korean immigrant who owned Consolidated Service Systems, a small Chicago-based janitorial services company.25 Hwang found his employees mostly by word of mouth in the local Korean community and through the Korean Association of Greater Chicago.26 The EEOC decided that because 95 percent of the Chicago work force is composed of non-Asians, while Consolidated had mostly Korean employees, Consolidated was presumptively guilty of discrimination. The EEOC offered to settle if Consolidated agreed to pay $475,000 in ''back pay'' to non-Koreans who had applied to Consolidated and (like many Korean applicants) been rejected.27 Consolidated's annual revenues were only about $400,000, so accepting a $475,000 settlement offer was well beyond Hwang's means. Not surprisingly, Hwang declined to settle.
The EEOC then sued Hwang and Consolidated in federal court, but the trial court dismissed the EEOC's case. On agency appeal, Judge Richard Posner wrote a rousing opinion affirming the lower court's ruling. Posner first stated that small businesses are not required to actively seek out workers from the broad community. He noted that if an employer ''can obtain all the competent workers he wants, at wages no higher than the minimum that he expects to have to pay, without beating the bushes for workers—without in fact spending a cent on recruitment,'' he will do so to reduce his costs of doing business. Continuing, Posner stated that, notwithstanding the discriminatory impact it may have, word-of-mouth hiring cannot support an inference of intentional discrimination when it is clearly ''the cheapest and most efficient method of recruitment.'' Posner concluded that ''it is not discrimination, and it is certainly not active discrimination, for an employer to sit back and wait for people willing to work for low wages to apply to him. The fact that they are ethnically or racially uniform does not impose upon him a duty to spend money advertising in the help-wanted columns of the Chicago Tribune .''
Posner also focused on the important role that small, ethnically based businesses play in the upward mobility of immigrants. Immigrants, Posner wrote, ''tend to cluster in their own communities, united by ties of language, culture, and background.'' They often form small businesses, the ''first rung on the ladder of American success,'' and employ ''relatives, friends, and other members of their community, and they obtain new employees by word of mouth.'' Despite, or perhaps because of, ''their ambition and hard work,'' recent immigrants ''are frequent targets of discrimination, some of it violent.'' Posner suggested that ''it would be a bitter irony if the federal agency dedicated to enforcing the antidiscrimination laws succeeded in using those laws to kick these people off the ladder by compelling them to institute costly systems of hiring.''28 Alas, Hwang's legal triumph turned out to be Pyrrhic. The huge legal fees he expended in successfully fighting off the EEOC forced Consolidated Service Systems out of business.29
The Chicago office of the EEOC also targeted Ted Grezeskiewicz, a Polish immigrant. After working for 16 years at a spring-making plant that employed mainly fellow Polish immigrants, Grezeskiewicz left in 1966 to form his own business, O & G Spring and Wire Forms Specialty Company. He took many of his former coworkers with him. By the 1980s, Grezeskiewicz employed around 50 workers, almost all of them Polish or Latino immigrants, hired primarily through word of mouth.30
In 1988, the EEOC sued O & G because, according to the agency's statistical models, O & G's work force should have been 22 percent African American. Although the EEOC had received no complaints of discrimination, the agency found that O & G's disproportionate percentage of Polish and Hispanic workers evidenced discrimination.31 The district court sided with the EEOC and required O & G to place an ad in the Chicago Tribune inviting readers to submit claims against O & G.32 More than 400 people eventually submitted claims. Amazingly, the EEOC made no attempt to screen applicants to determine whether or not they had actually sought work at O & G. Instead, the agency demanded that the company pay all of them, at a total cost of $378,754. Some of these purported victims had been in jail during the relevant time periods or had held better paying jobs.33
Grezeskiewicz appealed, but the court sided with the EEOC. Judge Daniel Manion wrote a dissent sharply criticizing the statistical evidence relied upon by the EEOC, the district court, and the appeals court. He quoted Judge Posner's opinion in the Consolidated Services case and suggested that ''Judge Posner's prophecy has come to pass in this case.''34 As for O & G, besides the cost of the remedy, it had to endure 10 years of EEOC investigation and litigation, the company ultimately spending more than $400,000 defending itself.35
The EEOC's defenders observe that certain hiring policies can reinforce patterns of discrimination by allowing incumbent workers from dominant ethnic groups to choose their colleagues. The EEOC, for example, forced construction unions to adopt antinepotism policies. The unions in question not only had a history of excluding nonwhites but also restricted entry into their occupations through their unions' membership policies and through control of licensing boards.36 However, the Chicago cases are very different. Polish and Korean immigrants are not established, incumbent workers trying to maintain their status at the expense of African Americans. Rather, they themselves are trying to establish a foothold in the American economy while competing with other Americans who have the advantages of better language skills, more familiarity with the labor market, and often better access to traditional credit.
The reason the Chicago companies sued by the EEOC failed to advertise widely in the media is that newspaper advertisements were obviously an inefficient use of the companies' limited resources. The Chicago EEOC tried to force small companies that employ mainly immigrants to have the same employment advertising policies as IBM or General Motors, with a public job search for each position and a premium placed on ensuring ethnic diversity. However, for the most part, the jobs offered by the Chicago small businesses in these cases involved low wages and hard work—the type of work generally scorned by native-born Americans of all races. Had these Chicago companies tried to advertise widely for unskilled workers, they would likely have found little interest from the general public, and therefore would have received little bang for their buck.
In contrast, word-of-mouth employment recruitment lowers costs for employers of immigrants. Not only does it save advertising costs, but, as Professor Richard Epstein notes, ''It is easier and cheaper for everyone if Spanish-speaking workers work with Spanish-speaking workers and Polish-speaking workers with Polish-speaking workers, all other things held constant.''37 Moreover, employees hired through ethnic networks are likely to be reliable individuals, because current employees have vouched for them. Further, small immigrant manufacturing companies can compete with foreign competitors only because of their low labor costs relative to productivity. To the extent the EEOC forces higher employment costs on these businesses, it forces them closer to going out of business.
Finally, as Judge Posner has pointed out, African Americans have their own word-of-mouth job networks. Those would also be threatened by the EEOC's policies. For example, the Clarence Thomas– Anita Hill hearings revealed a network of African American Yale Law School alumni who refer job candidates to each other, which is how Thomas came to hire Hill. Notwithstanding the antagonistic end to the Thomas-Hill professional relationship, it hardly seems obvious that this sort of networking should be considered illegal discrimination as opposed to a welcome continuation of the African American self-help tradition.
* * *
As a condition of settlement of antidiscrimination lawsuits, the EEOC and private litigants are increasingly demanding that defendant corporations agree to have managers strongly consider supervisors' vigilance in implementing anti-harassment policies when evaluating those employees' performances. Even companies that have not been sued are adopting this policy to attempt to avoid future lawsuits. One common criterion used to judge an employee's zealousness in enforcing anti-harassment policies is whether the employee has expressed his personal support for the policies. An employment law expert asserts that managers must ''communicate to their employees that they agree with, personally believe in, and will enforce the harassment policy.''38 Yet anti-harassment policies are often controversial within a company, especially when they stifle speech or prohibit dating among coworkers. Employment law expert Walter Olson writes that unless the trend toward requiring absolute fealty to internal anti-harassment policies is reversed, ''those who dissent from the official line, harbor doubts or qualms about it, or for any other reason prove unwilling to announce their enthusiasm for it, will sooner or later find themselves excluded from positions of responsibility in the American corporation.''39
* * *
The Supreme Court has held that the ''right of freedom of thought protected by the First Amendment against state action includes both the right to speak freely and the right to refrain from speaking at all.''40 In a stirring opinion overturning a compulsory flag salute statute in the midst of World War II, the Court wrote,
> We set up government by consent of the governed, and the Bill of Rights denies those in power any legal opportunity to coerce that consent. Authority here is to be controlled by public opinion, not public opinion by authority. . . . If there is any fixed star in our constitutional constellation, it is that no official, high or petty, can prescribe what shall be orthodox in politics, nationalism, religion, or other matters of opinion or force citizens to confess by word or act their faith therein. If there are any circumstances which permit an exception, they do not now occur to us.41
>
We should not let antidiscrimination orthodoxy become the first of what would inevitably turn into many such exceptions.
# 7. Public Accommodations Laws and
the Threat to the Autonomy of
Private Organizations
In the late 1960s, John and Ruth Mallery founded a Boys' Club in a poor, blighted neighborhood in Santa Cruz, California. After John died, Ruth, inspired by her childhood memories of boys who got into legal trouble because they had nothing to keep them busy, donated $1.5 million to endow the Club. She stipulated that her gift was to be used only to help boys. Eight-year-old Victoria Isbister, a resident of the neighborhood in which the Boys' Club was located, probably did not understand or even know about Ruth's reasons for marking her donation for boys only. What Victoria did know was that she thought it was unfair that she could not use the only swimming pool in the neighborhood, the one at the Boys' Club. Her parents agreed, and with the help of local American Civil Liberties Union attorneys, Victoria sued the Boys' Club for excluding her from its facilities.1
Victoria's lawsuit hinged on a California law banning sex discrimination in all ''business establishments.'' The Club's attorneys argued that the Boys' Club was a charitable recreation facility, not a business establishment, so the law should not apply. The California Supreme Court held that because the Club had a fixed location, it was a business establishment within the meaning of the law. Dissenting Justice Stanley Mosk, a liberal civil libertarian, ridiculed his colleagues: ''The majority opinion conjures up visions of young boys, who have been skinny-dipping in their club pool, donning three-piece suits to attend the board meeting of their 'business establishment' where they may discuss such matters as the antitrust implications of a proposed takeover of girl scout cookies. Precocious indeed these teen and preteen youngsters must be.''
The Club's attorneys also asserted that it should be exempt from the law for public policy reasons. If enough girls decided to join the Boys' Club, it might need to drop its open-door policy and limit access to the club at certain hours. The Club's attorneys insisted that it had good reasons to spend its limited resources on boys—namely, that they are far more likely than girls to be arrested and to become the perpetrators or victims of violence. The California Supreme Court majority responded that the Club had presented no hard evidence ''that boys need the recreation offered by the Club more than girls, that a sex-segregated 'drop-in' recreational facility is more effective in combating juvenile delinquency than one open to both sexes, or that extension of membership to girls would cause an impractical net increase (or decrease) in membership.'' In the absence of hard evidence on these issues, the court saw only arbitrary and illegal discrimination.
In contrast, Justice Mosk saw an open and diverse philanthropic arena with room for all kinds of charitable clubs, including sex-specific ones. He observed that allowing philanthropists like Mallery to donate to sex-segregated clubs does not prohibit other donors from sponsoring coed clubs. On the other hand, requiring all children's organizations to be coed, as the California Supreme Court had now done, prevented those with a different vision of how to help children from trying to realize it. Mosk accused his colleagues of quashing ''pluralism [and] all the values that connotes—values such as a diversity of views, a variety of ideas, and preservation of traditions.'' Justice Otto Kaus, who also dissented, cited studies showing that boys and girls benefit from being separated from each other for at least part of their day. He added, ''Who are we to say it is unreasonable for the club's management to believe that there is a rational basis for giving boys a few hours a day when they do not have to carry their machismo on their sleeves?''
Chief Justice Rose Bird, concurring with the majority, wrote an opinion scoffing at the dissenters' defense of pluralism, which she reduced to defending the right of ''wealthy patrons who prefer to confer largess in a sexually discriminatory fashion.'' Bird saw Ruth Mallery and people like her not as kindly philanthropists trying to aid society as best they know how, but as a contemptible ''select few'' who wish to be ''insulated from the 20th century.'' Bird's intemperate opinion attacking an altruistic elderly widow became an issue in a reelection battle that ultimately cost Bird her seat on the state supreme court.
One result of bans on single-sex charitable organizations is that some donors are not able to fully satisfy their preferences. The logical response of these frustrated would-be donors is to either reduce their donations to children's charities or to stop donating at all. Although the California Supreme Court could dictate that Boys' Clubs must admit girls, it could not force donors to continue to fund the clubs. Mallery, upset that the court had thwarted her goal of helping boys, withdrew the unspent portion of her endowment of the Boys' Club. Her view was that if the ACLU and the California Supreme Court wanted Santa Cruz to have a ''Boys' and Girls' Club,'' they could go ahead and pay for it themselves.2
* * *
The Boys' Club case exemplifies the vast expansion of public accommodations law at the federal and especially state levels since the passage of the granddaddy of public accommodations laws, Title II of the federal 1964 Civil Rights Act. Title II bans discrimination on the basis of race, color, religion, or national origin in public accommodations.
The law was motivated in part by testimony before Congress that African Americans traveling in the South often had difficulty finding motels and restaurants that would serve them. Title II also reflected a growing belief that any establishment that holds itself out as being open to the public, and that is not otherwise selective about who it admits, should not be permitted to discriminate against members of minority groups.
A few libertarians objected to Title II because it conflicted with property rights and freedom of association. Novelist-philosopher Ayn Rand, for example, wrote that ''[j]ust as we have to protect a communist's freedom of speech, even though his doctrines are evil, so we have to protect a racist's right to the use and disposal of his own property.''3 Future Supreme Court nominee Robert Bork, who was more libertarian in those days, famously referred to legally compelled association as a ''principle of unsurpassed ugliness.'' He added that the issue was not ''whether prejudice or preference is a good thing but whether individual men ought to be free to deal and associate with whom they please for whatever reasons appeal to them.''4
Libertarian objections to Title II's regulation of public accommodations were largely overshadowed by southern congressmen's arguments that Title II violated ''states' rights'' by overturning Jim Crow laws that required segregation in public accommodations. Libertarian concerns regarding private accommodations, however, received a serious hearing. At the time, even very liberal members of the legal elite agreed that members of private clubs had a right to choose their associates without government interference. Supreme Court Justice Arthur Goldberg, for example, wrote that there is a constitutional right to close one's home or club ''to any person . . . solely on the basis of personal prejudices, including race.'' Several years later, Justice William O. Douglas proclaimed, ''The associational rights which our system honors permit all white, all black, all brown, and all yellow clubs to be formed. They also permit all Catholic, all Jewish, or all agnostic clubs to be established. Government may not tell a man or woman who his or her associates must be. The individual can be as selective as he desires.''5
Congress ultimately agreed to exempt private clubs from Title II's dictates, but this exemption begged the pivotal question of what makes a club ''private.'' Many restaurants in the South began to call themselves ''private'' in an attempt to evade Title II, but their alleged privateness was obviously pretextual, as all whites were admitted and all African Americans were excluded.6 Federal courts eventually developed a test to distinguish private clubs from public accommodations: the factors that weigh in favor of private status include selectivity in membership, limiting use of facilities and services to members and bona fide guests, nonprofit status, and an absence of advertising to the general public.
Consideration of these factors perhaps resulted in a narrower private club exemption than Congress had intended, and led to a broader definition of ''public accommodations'' than a literal interpretation of the phrase would allow. For example, courts applied Title II to such seemingly private organizations as a swim club, a hunting club, a youth football league, and an African American teachers' association.7 On the other hand, the Supreme Court rejected—over the dissent of three liberal Justices—an attempt to define all private organizations that receive government licenses and permits as ''state actors'' subject to the same prohibitions on discrimination as is the government.8
Many state and local public accommodations laws prohibit discrimination on bases not covered by Title II, such as sex, sexual orientation, weight, appearance, political affiliation, and even, in Minnesota, membership in a motorcycle gang.9 Moreover, some laws exempt only ''distinctly private'' clubs, a narrower category than the ''private'' clubs exempted by federal law. Some legislatures have even amended their states' laws to ensure that the term ''distinctly private'' is construed narrowly. New York State, for example, amended its public accommodations law to explicitly state that private clubs with more than 100 members that provide regular meal service are not ''distinctly private.'' This change in the law overturned a judicial decision holding that the Kiwanis Club and other large membership organizations are distinctly private.10
In other states, courts, rather than legislatures, have driven the expansion of public accommodations law. For example, in 1969, the New Jersey Supreme Court announced that it would give New Jersey's public accommodations law ''a broadly sympathetic construction'' to ''eradicate the cancer of discrimination.''11 A few years later, the court diverged from federal precedent and held that an organization need not meet in a fixed location to be considered a ''place of public accommodation.'' As a result, the Little League Baseball organization, though certainly not any kind of place at all in normal parlance, was held to be a ''place of public accommodation'' under New Jersey law and was therefore required to admit girls.12 A cat fanciers' club is also a ''place of public accommodation'' in New Jersey and therefore may not discriminate against Jews.13 Other state courts have held that such membership organizations as a boating club, the United States Jaycees, and the Boy Scouts of America are ''places of public accommodation,'' even though they have no fixed meeting place.14
Not content to merely redefine the word ''place,'' state courts have also ignored the ordinary meaning of the word ''private'' to reject private club defenses to the application of public accommodations laws. Perhaps the most egregious case along these lines involved three of Princeton's 13 historic private eating clubs.15 Although the clubs have no legal ties to Princeton University, they function as nonresidential fraternities, providing food, entertainment, and social services to most juniors and seniors at the school.
Princeton University junior Sally Frank filed a complaint under New Jersey's public accommodations law against three eating clubs that refused to admit women. New Jersey's law provided an exemption for private clubs, but Frank alleged that the clubs were actually public accommodations because they functioned as ''arms of Princeton.'' After several years of litigation, the New Jersey Supreme Court ruled in Frank's favor. The court acknowledged that the clubs had ''assiduously maintained legal separateness'' from the university: the clubs operated off-campus, in their own facilities, and they received no university funding. To find that the clubs were nevertheless public because of their purported ties to the university, the court focused instead on the ''gestalt'' of the clubs' relationship with the school.16 The state supreme court concluded that ''the Clubs and Princeton have an interdependent relationship that deprives the Clubs of private status.'' Frank , as the clubs' attorney, George McCarter, has written, is notable ''as an almost defiant exercise of raw judicial power, and for its indifference to traditional legal analysis.''17 One might add a similar note about the New Jersey Supreme Court's refusal to seriously consider the plain English meaning of the statutory language it was charged with interpreting.
Some state courts have interpreted their public accommodations laws much less expansively. Like federal courts, these courts have held that membership organizations with no fixed meeting place, such as the Boys Scouts of America, cannot be considered places of public accommodation.18 After all, they simply aren't places. Some courts have even held that organizations with fixed meeting places may use discriminatory criteria in selecting members, even when the clubs are not otherwise selective, because membership is not an ''accommodation.''19 However, the trend continues to favor an expansive definition of the phrase ''places of public accommodation.'' In 2001, for example, the Supreme Court held that under the Americans with Disabilities Act, the PGA tour is a place of public accommodation and therefore could not ''discriminate'' against disabled golfer Casey Martin by prohibiting him from using a golf cart.20 This was obviously a stretch, but the Court didn't stop there. For the ADA to apply to Martin, he had to be a ''customer'' of the PGA, and so the Court absurdly deemed him to be one—and a very strange customer he is, playing in the PGA tour on his Court-authorized motorized golf cart, sometimes collecting prize money but never seeming to buy anything from the PGA.
* * *
As we have seen, the battle over the scope of public accommodations laws has focused for the most part on the definition of ''public accommodation'' (or, in California, ''business establishment''). Whether Boys' Clubs, eating clubs, or other organizations must comply with antidiscrimination laws depends on whether these organizations fit the statutory definition of places of public accommodation, as construed by the courts.
However, there is more to this story. The expansion of public accommodations laws also has constitutional ramifications. The U.S. Supreme Court has acknowledged that the right to privacy, which arises out of the First and Fourteenth Amendments, protects a sphere of certain intimate relationships from antidiscrimination laws.21 Therefore, the question arises as to when membership in an organization is such a relationship. In determining whether the right to ''intimate association'' is implicated, courts must assess ''where [a] relationship's objective characteristics locate it on a spectrum from the most intimate to the most attenuated of personal attachments.''22 Protected relationships include, but are not limited to, ''creation and sustenance of a family—marriage, childbirth, the raising and education of children, and cohabitation with one's relatives.'' Between the extremes of a business association and a family lays ''a broad range of human relationships that may make greater or lesser claims to constitutional protection.''
The Supreme Court has not yet invalidated an antidiscrimination law as a violation of the right to intimate association, and no doubt the parameters of what constitutes a protected relationship will be clearer once it does. The Court, however, has, at least for the time being, put an outer limit on potential intimate association claims by holding that the Rotary Club, a national organization made up of local chapters, some quite small, was not an intimate association, because it lacked selectivity and had a business-oriented agenda.23 Most recently, the Court declined the Boy Scouts of America's invitation to determine whether its exclusion of gays is constitutionally protected by the right to intimate association, though it found for the Boy Scouts on other grounds (see Chapter 8).24 Lower courts, meanwhile, have been loathe in the absence of further Supreme Court guidance to find that the right to intimate association trumps antidiscrimination law in particular cases.
Two courts have, however, held that the right of intimate (or ''private'') association protects specific private clubs from antidiscrimination laws. One case arose in New Orleans, Louisiana—a city that proscribes discrimination by any club that has more than 75 members and provides regular meal service. An African American man filed a complaint with the city's Human Rights Commission against four social clubs, alleging that they had denied him membership because of his race. The Commission initiated an investigation of the clubs' membership policies and practices.
When the clubs sued in federal court seeking to enjoin the Commission from continuing the investigation, the Fifth Circuit Court of Appeals held that the Commission's investigation violated the intimate association rights of the clubs and their members.25 The court explained that the clubs existed exclusively for private, social purposes, and they prohibited the transaction or discussion of any commercial business on their premises. The clubs had very small memberships and very restrictive admission policies. There were no signs identifying the club's buildings to outsiders, and the clubs did not advertise to the public in any way. Club members shared common social interests and often preexisting family or religious ties, so there was a close nexus between the clubs' purposes and their membership criteria. Finally, the clubs rarely permitted guests. For these reasons, the clubs were held to be sufficiently private to be entitled to constitutional protection.
The court then turned to the issue of whether the Commission was violating the clubs' right of private association by merely investigating charges of discrimination. Association rights, the court noted, ''can be abridged even by government actions that do not directly restrict individuals' ability to associate freely.'' The court concluded that the investigatory techniques at issue did not adequately protect the clubs' private association rights, because the Commission had the authority to force the clubs to turn over their membership lists.26
Members of the Pacific Union Club in San Francisco also defeated an antidiscrimination investigation by invoking the right to intimate association.27 California's Franchise Tax Board had demanded the club's membership list so it could investigate whether members had illegally deducted club dues and expenditures. California tax law forbids members of private clubs that discriminate to deduct their club dues, and the club had admitted that it engaged in age discrimination. But the club argued that its members had a constitutional right to keep its membership list private.
The California Court of Appeal agreed. It found that the club had a purely social purpose; limited its size; did not actively recruit new members; required membership candidates to undergo a rigorous admissions process, including many personal interviews to assess the applicant's congeniality; excluded nonmembers from functions; and kept its membership list strictly private. The court concluded that ''the Club is more than sufficiently intimate'' to be entitled to claim the right of intimate association. Further, compelled disclosure of the club's membership list to the tax authorities would have a chilling effect on people's willingness to be members of the club, because their membership could lead to an audit. The court held that the goal of investigating potentially illegal tax deductions was not sufficiently compelling to override the privacy rights of the club and its members. The membership list stayed private.
* * *
Public accommodations laws are most effective against outliers who disagree with a broader societal consensus, such as when the rest of the United States imposed nondiscrimination norms on the recalcitrant South in the 1960s. More often, court decisions banning purely social discrimination target discrimination that is already in precipitous decline due to changing social attitudes and that would likely die a natural death if left alone. For example, most of Princeton's eating clubs had already begun admitting women by the time Sally Frank began her litigation in the 1970s. The litigation did not conclude until 1992,28 by which time changing social mores had led the very clubs Frank was suing to admit women regardless of the outcome of the court battle.29 Yale and Harvard's fraternal clubs also admitted women voluntarily. The last of Yale's single-sex secret societies, the Order of Skull and Bones, voted to admit women in 1991,30 and Harvard's last all-male club, the Fly Club, voted to admit women in 1993.31 The most positive thing one can say about Frank's litigation is that it may have forced sex integration to commence a bit earlier than it would have otherwise. Meanwhile, it established a damaging precedent for freedom of association in New Jersey.
Similarly, although the U.S. Supreme Court held in 1987 that states may force service organizations such as the Rotary Club to admit women (see Chapter 8), by 1992, very few states had chosen to enact such rules. Nevertheless, almost all major service organizations— a notable exception being the women-only Junior Leagues—had decided by then to admit both sexes nationwide to avoid the massive membership losses that could result from the perception that they are sexist and anachronistic. As we have seen, the California Supreme Court in 1983 ruled that Boys' Clubs in that state must admit girls. Few states followed California's lead but, by 1987, 80 percent of Boys' Clubs served girls and 60 percent of them admitted girls as members, continuing a trend that had begun before the California ruling for the pragmatic reason that many boys apparently found single-sex organizations to be ''uncool.'' In 1990, the organization officially changed its name to the Boys & Girls Clubs of America. The California court was ahead of the curve, but just barely.
On the other hand, if judicial interpretations of public accommodations laws stray beyond what society supports, the judiciary will generally back down. When she wrote her scathing concurrence in the Boys' Club case attacking single-sex youth organizations, Chief Justice Rose Bird suggested that such organizations were a relic of a less enlightened era and would soon be abolished. She was wrong. The Girls Clubs of America, for example, did not join the Boys' Clubs in turning coed. The GCA leadership continued to believe that many girls, especially girls growing up in poor urban neighborhoods in which teen pregnancy is rampant, benefit from a single-sex social environment. The GCA changed its name to ''Girls, Inc.'' and continues to offer programs tailored to at-risk girls, such as a program that discourages early sexual activity and attempts to reduce adolescent pregnancy rates. Those looking for single-sex youth organizations also still have the option of joining the Boy Scouts or Girl Scouts, among other organizations, while other groups, such as 4-H clubs and most religious youth groups, are coed. The California Supreme Court itself later backed away from the clear implications of its Boys' Club opinion when it held that the Boy Scouts of America is not a business establishment subject to antidiscrimination law. The public seems to support pluralism, and pluralism has triumphed—so far.
College fraternities have also survived the onslaught of antidiscrimination law. Unlike other single-sex social organizations, ''Greek'' fraternities have never been forced to go coed. Fraternities are explicitly exempt from the federal prohibition against sex discrimination in education (Title IX),32 from the Fair Housing Act,33 and from many states' public accommodations laws. Predictions that the Princeton eating clubs case would lead to the abolition of fraternities in New Jersey have not been vindicated and the California Supreme Court has indicated that, unlike Boys' Clubs and country clubs, fraternities are not business establishments and may engage in sex discrimination.34
The different treatment shown to discriminatory country clubs on the one hand and single-sex fraternities on the other is hardly a result of lesser government interest in eliminating discrimination by fraternities. All of the rationales for eliminating discrimination by other clubs apply to fraternities—for example, many important lifelong business contacts are made through friendships developed in fraternities. Yet the law has left fraternities alone because single-sex fraternities are still widely accepted as an appropriate form of socialization and because they have a significant political constituency. The public may be ready for the forced integration of golf and tennis clubs, but it is not willing to force frats to go coed, so the courts do not push it.
The inability of public accommodations laws to stray far beyond societal consensus stems from the U.S. system of government. Americans rely on democratically elected representatives to pass laws, and they look to judges, administrators, and juries to enforce them. There is little reason to believe that these government actors hold opinions far different than those of the public regarding whether traditional forms of social discrimination are harmful. Law can accelerate the process of social change somewhat, as voluntary social change is (or at least can be) a more drawn-out process than the enforcement of legislative edicts. The question is whether sacrificing freedom of association—with the attendant risk that the government will unnecessarily stifle pluralism or even ultimately codify regressive social norms, as it so disastrously did in the Jim Crow era—is worthwhile for slightly quicker social change and the suppression of a few outliers who refuse to conform to changing social attitudes.
This question is especially pertinent today, because the social context of discrimination has changed a great deal. At one time, public accommodations laws primarily targeted social organizations dominated by elite Protestant white males. The laws therefore arguably served the cause of pluralism by opening up such organizations to less-established outsiders. Today, by contrast, clubs with policies favoring the traditional elite are increasingly rare, while all-black (e.g., 100 Black Men of America), all-Jewish (e.g., B'nai B'rith), and all-female (e.g., the Junior Leagues), among others, are going strong and creating significant social and economic capital for their members. However, these organizations are at risk of being dissolved by public accommodations laws' nondiscriminatory membership policies because they practice social discrimination. The bottom line is that if the government is permitted to dictate policies to private social organizations, there is a strong chance that American society will be the worse for it.
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Many private organizations that promote political or social messages have been deemed to come within the purview of state public accommodations laws. If these ''expressive associations'' are forced to obey antidiscrimination mandates, the content of their messages will likely change. For example, B'nai B'rith, an all-Jewish fraternal organization, would likely promote or emphasize a different political agenda if the government required it to admit gentiles. The regulation of expressive associations implicates First Amendment concerns and is the subject of the next chapter.
# 8. Stifling Expressive Associations
Without a corresponding freedom to associate, the First Amendment rights to freedom of speech, assembly, and to petition government would be trivial because political and social movements advocating changes to the status quo could be easily suppressed by laws dictating the rules under which activists could interact.1 For example, a pro-vegetarian social movement would not get very far if the government said, ''Sure, you can sing the praises of greens and carrots all you like, but you're going to have to let members of a veal-and-pâté-worshipping religion into your group.'' This point was brought home more seriously and dramatically in the 1950s, when state governments in the South tried to defeat the civil rights movement by curtailing the associative rights of activists. The Supreme Court defeated this stratagem by recognizing the implicit constitutional right to associate for expressive purposes, now known as the right of ''expressive association.''2
In a series of decisions in the 1980s, however, the Supreme Court held that the expressive association right must yield to antidiscrimi-nation laws. Specifically, the Court reasoned that because the government has a compelling interest in eradicating discrimination, public accommodations laws that regulate the membership practices of private organizations trump the First Amendment rights of the organizations and their members. Fortunately, however, the Court seems to have recognized that its rulings created a grave danger to civil liberties and has recently backed away from these decisions.
The first case to reach the Supreme Court involving a clash between a public accommodations law and the First Amendment involved the United States Jaycees, an organization for young business leaders. The Jaycees originally accepted only men, but by the early 1970s it was admitting women as associate members. Associate members could participate in Jaycees activities, but they could not vote, run for office, or receive awards. Some chapters that wished to admit women to full membership, such as the Omaha Jaycees, formed two parallel, separate organizations under the same holding company. One of these organizations admitted women to full membership and conducted the day-to-day activities of the Jaycees. The other entity reserved full member status for men and served as the Jaycees' official link to the national organization. Other Jaycees chapters were free to follow the Omaha model, but two Minnesota chapters instead chose to sue the national organization under Minnesota's public accommodations law, which banned discrimination against women by membership organizations.
The litigation threatened to unalterably change the Jaycees' message. The Jaycees' charter established the organization's central purpose as ''promoting the interests of young men.'' It hardly seems likely that young women admitted as members would use their membership primarily to contribute to this purpose. Moreover, the national, state, and local chapters of the Jaycees (including the Minnesota chapter) took positions on a wide range of political issues. Given the ''gender gap'' in political views—women on average are more liberal on economic and military issues than are men—forcing the Jaycees to admit women would inevitably affect the Jaycees' political agenda.
For these reasons, a federal appeals court found that by forcing the Jaycees to admit women, Minnesota's public accommodations law violated the Jaycees members' First Amendment right of expressive association.3 Minnesota appealed to the Supreme Court, which ruled against the Jaycees in a 5–0 opinion written by Justice William Brennan, with Justices Sandra Day O'Connor and William Rehnquist concurring and two other justices recusing themselves.4
Justice Brennan acknowledged that the First Amendment protects the right to associate for expressive purposes, but he paid only lip service to that right. He found that the Jaycees had presented no valid evidence that the compelled acceptance of women as members would ''change the content or impact of the organization's speech.'' According to Brennan, the claim that admitting women would inherently change the Jaycees' message relied ''solely on unsupported generalizations about the relative interests and perspectives of men and women'' that ''may or may not have a statistical basis.'' Therefore, requiring the Jaycees to admit women did not violate anyone's expressive association rights.
Had Justice Brennan's opinion stopped there, it would not have been especially notable. Although critics have attacked Brennan's tendentiousness in ignoring the very real and predictable ways that the Jaycees' message would be changed by admitting women, if his opinion had confined itself to a fact-dependent analysis it would have had limited impact on the law. Instead, Brennan added that the Jaycees would have lost the case even if the Court had found that Minnesota's public accommodations law had infringed on the Jaycees' expressive association rights. He reasoned that because the law advanced the compelling interests of eliminating gender discrimination and ensuring ''equal access to publicly available goods and services,'' intrusion into First Amendment rights was permissible.
Reducing sex discrimination is an important goal, but merely stating that fact does not explain why the government's interest in forcing the Jaycees to admit women was sufficiently ''compelling'' to trump the First Amendment's protection of freedom of expression. Brennan did note that Minnesota claimed a longstanding interest in eradicating discrimination against women, but he failed to explain why a single state's public policy goal creates a federal constitutional interest powerful enough to override the First Amendment. More fundamentally, Brennan did not address the government's lack of a constitutionally legitimate —much less compelling —interest in eradicating discriminatory attitudes, beliefs, expressions, or associations. The very purpose of the free speech protections of the First Amendment is to prevent the government from squelching the expression or promotion of certain ideas, so it is difficult to see how the government's claimed interest in doing so can trump the First Amendment.
Perhaps the nadir of the Supreme Court's respect for expressive association rights was reached a few years after Jaycee s. The Court first extended the logic of Jaycees to hold that state governments could compel Rotary International to allow the admission of women as members. Then, adding insult to injury, the Court claimed that by approving government interference with RI's membership policies, the Court was serving the Rotarians' own best interests.5 The Court argued that its ruling would help RI achieve its stated objective of providing humanitarian service and encouraging high ethical standards. The addition of women, the Court added, would also likely promote RI's stated goal of ensuring that Rotary clubs represented a cross-section of their communities. Because the Court believed that admitting women advanced RI's stated goals, the Court reasoned that there was no violation of the right of expressive association. But, as in Jaycees , the Court volunteered that it would have ruled against RI even if RI's expressive association rights had been infringed. Public accommodations laws, the Court reiterated, ''plainly serv[e] compelling state interests of the highest order.''
With the Supreme Court signaling open season on any organization deemed by state law to be a public accommodation, the Boy Scouts of America soon became a leading target of antidiscrimination lawsuits. Activists accused the Scouts of violating state and local public accommodations laws by excluding gays, atheists, and girls. Gays are excluded because the Scouts' leadership believes that homosexual activity violates the Scout Oath, which requires scouts to be ''morally straight,'' a provision Scout leaders have construed to forbid nonmarital sex, including homosexual sex. Atheists and agnostics are excluded because the Scout Oath requires an acknowledgment of a scout's duty to God. Girls are excluded because the Scouts believes that the moral education of boys is best undertaken in a single-sex atmosphere.
Those who objected to the Scouts' policies were (and are) free to found the ''Straight and Gay Scouts'' or the ''Godless Scouts'' or the ''Boy and Girl Scouts.'' Dissident scouts also could join one of the many established youth organizations that do not discriminate on the basis of sex, religious belief, or sexual orientation. Some activists nonetheless sued the Scouts with the help of the American Civil Liberties Union, and eventually with help from local government antidiscrimination agencies. Several courts rejected these claims, but only because the Scouts was not a ''public accommodation'' subject to the relevant antidiscrimination law. Courts, meanwhile, consistently held that the Scouts had no constitutional expressive association right to discriminate to defend its creed.6 The Connecticut Supreme Court, for example, stated that the Scouts' assertion of a constitutional right to exclude women from serving as scoutmasters had ''little merit'' in light of Jaycees and Rotary International .7
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A 1995 case, Hurley v. Irish-American Gay, Lesbian & Bisexual Group of Boston ,8 suggested that the Supreme Court's deference to antidiscrimination laws at the expense of expressive association rights was waning. The Irish-American Gay, Lesbian & Bisexual Group (GLIB), a gay rights organization, claimed that Massachusetts's public accommodations law obligated the organizers of Boston's St. Patrick's Day Parade to permit GLIB members to march under GLIB's banner. The parade organizers responded that they had a First Amendment right to exclude any group that sought to convey a message (in this case, they claimed, a ''sexual message'') the organizers did not wish to convey.9 The trial court ruled in favor of GLIB,10 relying on Jaycees in holding that any ''incidental'' infringement on expressive association rights was justified by the government's interest in eradicating discrimination against homosexuals. On appeal, the Massachusetts Supreme Court agreed that the organizers had no viable First Amendment defense.11 So far, it was business as usual, with public accommodations law running roughshod over freedom of association.
The tide turned when the U.S. Supreme Court reversed the GLIB decision in a unanimous opinion written by Justice David Souter. The Court explained that the parade organizers had not excluded gays from the parade. Rather, they had excluded a group that had been formed for the express purpose of marching under its own banner in the parade ''in order to celebrate its members' identity as openly gay, lesbian, and bisexual descendants of Irish immigrants.'' The organizers had a First Amendment right not to promote this theme because ''the fundamental rule of protection under the First Amendment, is that a speaker has the autonomy to choose the content of his own message.'' Justice Souter distinguished Jaycees on the grounds that the Jaycees court found that enforcing Minnesota's public accommodations law did not affect the Jaycees' message, while enforcing the Massachusetts law would change the parade organizers' message. Souter ignored the compelling interest test, even though it loomed large in Jaycees and despite the fact that the trial court and GLIB's brief had relied on it.
Hurley's broader significance became apparent in 2000, when the case of Boy Scouts of America v. Dale came before the Supreme Court. James Dale had become a Cub Scout at the age of 8 and had remained in scouting until he turned 18, ultimately achieving the rank of Eagle Scout in 1988.12 In 1989, Dale applied for adult membership in the Scouts and became an assistant scoutmaster. Meanwhile, Dale ''came out'' and became active in his university's gay and lesbian advocacy organization. In 1990, a newspaper printed an interview with Dale about his advocacy on behalf of gay youth. Dale subsequently received a letter from the local scouting council revoking his adult membership, because the Scouts ''specifically forbid[s] membership to homosexuals.''
Dale sued the Scouts for violating New Jersey's public accommodations statute. After protracted litigation, the New Jersey Supreme Court ruled in Dale's favor. The court found that the Scouts' ability to disseminate its message of ''moral straightness'' was not significantly affected by forced employment of Dale. Moreover, the court added a familiar refrain: even if Dale's employment had infringed on the Scouts' expressive association rights, this infringement would have been justified under Jaycees by the government's ''compelling interest in eliminating discrimination based on sexual orientation.''
The U.S. Supreme Court overruled the New Jersey Supreme Court in a five-to-four opinion in favor of the Scouts, written by Chief Justice William Rehnquist. Rehnquist concluded that to force the Scouts to grant Dale a leadership position would violate the organization's right of expressive association because it ''would significantly burden the Scouts' right to oppose or disfavor homosexual conduct.'' ''Dale's presence in the Boy Scouts,'' Rehnquist wrote, ''would, at the very least, force the organization to send a message, both to the youth members and the world, that the Boy Scouts accepts homosexual conduct as a legitimate form of behavior.'' Just as the coerced presence of GLIB in Boston's St. Patrick's Day parade would have interfered with the parade organizers' choice not to propound a particular point of view, the presence of Dale as an assistant scoutmaster ''would surely interfere with the Boy Scouts' choice not to propound a point of view contrary to its beliefs.''
Rehnquist stressed that associations ''do not have to associate for the 'purpose' of disseminating a certain message'' to receive First Amendment protection. They merely have to ''engage in expressive activity.'' If the Scouts wants leaders to teach about sexual morality only by example, this subtle form of expression is protected by the First Amendment. Finally, Rehnquist also made clear that First Amendment protection is not limited to groups that take a strong stand against those they exclude. Rehnquist wrote that ''[t]he fact that the organization does not trumpet its views from the housetops, or that it tolerates dissent within its ranks, does not mean that its views receive no First Amendment protection.''
Because Dale did not explicitly overrule Jaycees , one might have expected Rehnquist to meaningfully explore whether New Jersey had a compelling interest in eradicating discrimination against gays, but he did not. Rather, he simply wrote that given the severe intrusion into the Scouts' right to expressive association, the state interests served by New Jersey's public accommodations law were not sufficient to overcome the Scouts' rights. Rehnquist implied that state interests in battling discrimination can overcome expressive association rights only when the infringement on such rights is minor, as the Court found was the case in Jaycees .
The four dissenters also did not focus on the compelling interest issue. Instead, they argued that the Scouts case was not sufficiently vociferous in its opposition to homosexual activity to have a First Amendment right to exclude gays. The Scouts' lack of virulence is intentional—the organization seeks to encourage traditional moral values while creating as little offense among its members and supporters as possible. Had they succeeded in limiting expressive-association rights to organizations vociferous in their support of discrimination, the dissenters would have ensured that those rights are available mainly to marginal, extremist organizations. As Northwestern University Law School Professor John McGinnis observes, ''the advantage of having a full range of civic associations lies in society's enjoyment of a range and intensity of views on an issue pressed from the different perspectives provided by associations with different civic purposes.''13 The constitutional world contemplated by the dissenters, by contrast, ''is one in which shrill advocacy alone supplements the norms encouraged by the government.''14
Another reason to protect freedom of expressive association from antidiscrimination laws is that government agencies charged with enforcing public accommodations laws tend to target groups with unpopular messages. For example, in 1994, the Nation of Islam, notorious for its racist, sexist, and anti-Semitic views (which are, of course, protected by the First Amendment), requested permission to rent the Cleveland convention center for a men-only meeting. The city of Cleveland sought a court ruling that the men's event would violate Ohio's public accommodations law by excluding women, and that denying the facility to the Nation would not violate the Nation's constitutional rights. The Nation, in turn, asked for a judgment permitting it to restrict its event to men, in accordance with its religious practice.15
A federal district court ruled in favor of the Nation on expressive association grounds, a ruling that now seems correct under Dale16 but that was possible at the time only because the court ignored Jaycees . The court stated that ''[i]f the City is allowed to make the public accommodation law requiring Minister Farrakhan to speak to a mixed audience, the content and character of the speech will necessarily be changed.'' After the decision was announced, Nancy Lesic, spokesperson for Cleveland mayor Michael White, told reporters that ''the city did not deny anyone's rights in this case. It is an unlawful and discriminatory practice to deny a person access to a public facility on account of factors such as gender. In this case, women were being denied access to public accommodations.''17 Yet it is difficult to imagine Cleveland similarly trying to force less controversial religious groups like Catholics, Orthodox Jews, or even Orthodox Muslims to hold coed meetings. Religious groups aside, it is also difficult to imagine Cleveland denying access to its convention center to the Junior League, the Girl Scouts, or other popular single-sex organizations.
* * *
Dale leaves many questions unresolved. For example, can for-profit businesses ever claim the right to expressive association in defiance of antidiscrimination laws, or, as Justice O'Connor suggested in her concurrence in Jaycees , can the right only be asserted by ''primarily expressive'' associations? If the latter, how does one determine whether a nonprofit organization is ''primarily commercial,'' as O'Connor thought the Jaycees to be, or primarily expressive? Under what circumstances must courts apply Jaycees' compelling interest test, and when, if ever, does the government have an interest sufficient to overcome the First Amendment's protection of expressive association? Despite these loose ends, the Court's decision in Dale is the greatest victory yet won by civil liberties partisans in the conflict between antidiscrimination laws and civil liberties.
The reaction to Dale , however, has largely divided along ideological lines. ''Conservatives'' generally support Dale , because in their eyes it prevents government from taking sides in the culture wars. ''Progressives,'' including many liberals who otherwise have strong civil libertarian instincts, oppose Dale because it seems to deal a blow to gay rights. Progressives also fear that organizations that wish to discriminate against other groups will rely on Dale for constitutional exemptions from antidiscrimination laws.
As a legal matter, however, Dale was not about the conflict between gay rights activists and their opponents, nor was it about a general right to discriminate. Rather, the underlying issue in Dale was whether a private, nonprofit expressive association has a First Amendment right to discriminate when needed to prevent dilution of its message. Although the right of expressive association can benefit people on either side of the political spectrum, for the past two decades the right has been primarily raised as a defense to antidiscrimination claims by African Americans, women, and especially homosexuals. As a result, left-leaning organizations have typically sought to limit the scope of the constitutional right, while conservatives have been more supportive of the autonomy of private associations. As discussed below, however, the left may soon find that the constitutional right to expressive association has its uses. It may save one of the left's favorite causes—affirmative action preferences at private universities—from interference by the government.
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Dale 's protection of the right of expressive association raises the issue of whether nonprofit expressive associations have a constitutional right to engage in race discrimination when needed to avoid dilution of their message. Even before Dale , one court recognized that the Ku Klux Klan had a right to discriminate. Thurmont, Maryland, had denied the KKK a parade permit because the Klan refused to allow African Americans to march in its parade. The Klan sued in federal court, and won.18 The court found that the Klan had a First Amendment right to exclude African Americans to prevent dilution of the Klan's message of racism and white superiority.
In contrast, the New York City Commission on Human Rights ruled that a black separatist organization had no constitutional right to exclude whites from its otherwise public meetings.19 The Commission acknowledged that the United African Movement had proved ''that there is a nexus between its racially discriminatory membership policies and the group's message that Caucasians and people of African descent should not mix.'' Therefore, forcing the Movement to admit whites to its meetings would dilute the group's message and consequently infringe upon its right to expressive association.20
The Commission concluded, however, that New York had a compelling interest in eradicating discrimination on the basis of race, an interest that trumped the Movement's First Amendment rights.21
Dale resolves the conflict between the Maryland and New York cases in favor of the expressive association rights of racist organizations. To force racist groups to integrate themselves, or even their audiences, would inhibit the ability of such organizations to preach racism at least as much as forcing the Boy Scouts to employ Dale would have interfered with the Scouts' antihomosexual activity message.
Many people are shocked by the idea that any organization— even a pro-racism advocacy group—has a First Amendment right to indulge in race discrimination when necessary to further its message. Yet, as in many other contexts, protecting the First Amendment rights of unpopular, outrageous, and contemptible organizations will ultimately protect the rights of mainstream and forward-thinking organizations as well. Overtly racist organizations are far from the only expressive groups that have an ideology that leads them to discriminate on the basis of race. Private universities almost universally engage in racial preferences in admission. Although the motivation for these preferences is benign—speeding the social and economic integration of racial minority groups—the preferences nevertheless quite literally involve race discrimination. What critics must realize is that if Dale protects the right of the Klan to discriminate against African Americans, it also protects the right of private universities to discriminate in their favor.
Racial and ethnic preferences on behalf of African Americans and Latinos are rampant in American academia. According to a study conducted by a supporter of affirmative action, among the most selective and prestigious law schools, 17.5 times as many African American students were admitted in 1991 as academic qualifications alone would have predicted.22 At the same time, approximately half of all African American matriculants to law school would not have been admitted to any law school purely on the basis of their grade point average and Law School Admission Test scores.23 Although grades and test scores don't tell the whole story about an applicant, these statistics show that racial preferences in law school admissions clearly go well beyond choosing the minority candidate when two candidates are equally qualified.
The legality of these preferences is dubious. In the famous Bakke case,24 four Supreme Court justices concluded that racial preferences always violate Title VI of the 1964 Civil Rights Act, which bans racial discrimination by schools that receive federal funds, a category that includes almost all American universities. A fifth justice, Lewis Powell, cast the deciding vote. Powell agreed that admissions quotas were illegal, but he concluded that racial preferences were permissible if they were used as a ''plus'' factor along the lines of other plus factors universities employ to diversify their student bodies.25
Some legal authorities, including one federal appellate court,26 assert that later Supreme Court decisions on racial preferences have overridden Bakke , and all racial preference programs by public or private universities now violate federal law. Others argue that Justice Powell's opinion in Bakke , as the necessary fifth vote on an issue that has not been directly revisited by the Supreme Court, is a binding statement of law, so that using race as a plus factor is still permitted. As of this writing, two cases that will clarify the law are pending before the U.S. Supreme Court. What the Court will certainly not do is endorse the legality of quotas.
It seems clear that any limitation on affirmative action decreed by the Court will be met with tacit and perhaps explicit resistance from many universities. Despite Bakke 's ban on quotas, for example, many universities continued to implicitly use them. Some universities discreetly violate the law but others do so overtly. For example, the administration of Rice University, a private school, believes that the law in its home state of Texas forbids it from considering the race or ethnicity of its applicants. Yet Rice's director of admissions boasted to the New York Times that the school engages in various subterfuges to defy the law. For example, Rice will not officially give a preference to an African American student for being black, but it will give credit for the student's involvement in a high school African American student club. As a result of such gambits, the percentages of African American and Latino students entering Rice barely changed after racial and ethnic preferences were banned.27 It would be logical to conclude that Rice not only continues to use race as a factor in admissions but also that it uses an implicit quota system.
Schools like Rice will eventually be targeted with reverse discrimination lawsuits. Private universities could respond to such lawsuits by claiming an expressive association exemption to antidiscrimination laws. The administrators of many universities sincerely believe that their schools should teach students the importance of assisting disadvantaged minorities and ensuring racial diversity in the upper echelons of American society. Not unreasonably, the administrators believe that if the law prohibits them from using racial preferences, they will see their schools' classes become overwhelmingly white (and, increasingly, Asian American) and it will become far more difficult to promote their schools' egalitarian ideals to their students. Just as employing Dale would have diluted the Boy Scouts of America's anti–homosexual activity message, forcing private universities to adopt race-neutral admissions policies would dilute their pro-diversity messages.
Moreover, a university that has a racially homogenous class—or faculty—inherently sends a negative or, at best, indifferent message to its students and the public at large about the importance of racial diversity. Engaging in explicit racial preferences to ensure a diverse student population sends the opposite message. To preserve racial preferences, universities can rely on Dale 's dictum that the Boy Scouts of America has a First Amendment right to teach ''by example,'' and argue that they too have a right to promote a moral vision unencumbered by government regulation.28 Conditioning federal funding of universities on the abolition of affirmative action preferences would place what constitutional scholars call an ''unconstitutional condition'' on that funding.
Some legal scholars argue that the 1976 Supreme Court case of Runyon v. McCrary29 suggests that, despite Dale, private universities cannot claim an expressive association right to discriminate on the basis of race. In Runyon , the Supreme Court rejected a freedom-of-association defense to a discrimination lawsuit against a whites-only private school. That opinion, and not Dale , is claimed by some to be the controlling precedent when expressive association rights conflict with laws banning race discrimination in education.
This understanding of Runyon is mistaken, because the Runyon defendants did not advance an expressive association argument. Instead, they made a very short, throwaway argument that compelled integration violated their general right to ''freedom of association.'' No such right appears in the Constitution, and the Supreme Court has never recognized a general right of association independent of any expressive goal. The Runyon defendants could have argued (but did not) that forced integration violated their First Amendment rights by impeding their ability to promote segregation to their students.30 Even that argument would have been problematic, however, because the schools involved in Runyon were organized on a commercial basis, and it is not clear whether commercial entities can claim expressive association rights.31 In short, the Runyon Court did not reach the issue of whether a noncommercial private school could successfully defend discriminatory policies as an exercise of expressive association rights.32 So, Runyon does not prevent universities from relying on Dale to protect their affirmative action programs from antidiscrimination suits.
If private universities acknowledged that they engage in racial preferences and successfully asserted an expressive association defense to any subsequent legal challenges, the current racial preferences in admissions would continue, but in a much more open and honest fashion. Because universities refuse to acknowledge that they engage in racial preferences, many otherwise well-informed people, including many of the beneficiaries of racial preferences, are unaware of their existence and scope.33
Some schools might not be able to successfully defend their racial preferences in the court of public opinion. On the other hand, if universities were more candid in their acknowledgment and defense of racial preferences in admissions, they might be able to develop a stronger constituency in favor of the preferences. Moreover, a frank acknowledgment by elite universities of the difficulty in finding African American (and to a lesser extent, Latino) applicants meeting the schools' regular standards34 might lead to some useful national soul-searching regarding the inferior educational opportunities given minority students.
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One commentator, writing before the Court's ruling in Dale , suggested that ''under the First Amendment, discrimination of any kind in choosing one's fellows in the conscience-forming enterprise must be viewed as protected expression.''35 At least with regard to nonprofit, expressive associations, this is now the law of the land. Political progressives have expressed dismay at the ruling in Dale and the potential consequences of the decision. Not only did Dale deal a blow to the gay rights movement, they complain; now any nonprofit, primarily expressive group with an ideology that requires discrimination may also have a First Amendment right to discriminate regarding membership, employment, and audience to prevent dilution of its message. The left's reaction is understandable. Many organizations with opprobrious ideas will evade antidiscrimination laws, using Dale as a defense.
On the other hand, protecting the liberty of those with deplorable views also protects one's own liberty. Dale may allow the Boy Scouts of America to discriminate against gays, but it should also provide protection for private universities that discriminate in favor of Latino and African American applicants. In short, Dale 's protection of the right of expressive association is about preserving pluralism by allowing organizations with diverse viewpoints to flourish. Given the vagaries of politics, where the majority can easily become a minority and vice versa, Dale 's protection of ideological diversity should be supported by Americans from all points on the political spectrum.
# 9. Regulating Religious Schools
The First Amendment protects the free exercise of religion and prohibits governmental establishment of religion, a concept that includes a prohibition on excessive government entanglement with religion. Accordingly, the Constitution prohibits the government from interfering in the hiring and firing of ''ministerial'' church employees, including clergy and religion teachers at church-sponsored schools.1 However, courts have held that antidiscrimination laws can still regulate the employment of teachers of secular subjects in religious schools.
One such teacher, Linda Hoskinson, felt a calling to teach in Christian schools so she ''could interpret her lessons with feelings [sic] from the Bible.''2 She found employment as a grade school instructor at Dayton Christian Schools, an affiliate of two of Dayton, Ohio's strict fundamentalist churches.3 DCS sought to employ only teachers who would ''carry with them into their classes the religious fervor and conviction felt necessary to stimulate young minds into accepting Christ as savior.'' Hoskinson seemed to have found her niche. Eventually, however, church doctrine and Hoskinson's personal life came into conflict. When Hoskinson informed the DCS administration that she and her husband were expecting a baby, she was told that her contract would not be renewed. The school's sponsoring churches believe that mothers of young children should not be employed outside of the home, so continuing to employ Hoskinson would flout church doctrine.4
Hoskinson consulted an attorney, who informed DCS that it was violating Hoskinson's rights under federal and state antidiscrimination laws, even though DCS had accepted no government funding. DCS responded by immediately firing Hoskinson for violating the ''Biblical Chain of Command,''5 a belief adhered to by some Christian sects, including DCS's sponsors, that all disputes among members of the church should be resolved within the church. Like all DCS employees, Hoskinson had agreed in her contract to abide by the Biblical Chain of Command, but had broken that agreement when she took her problems with church policy to an outside lawyer.6
Hoskinson filed a sex discrimination complaint with the Ohio Civil Rights Commission.7 The Commission investigated, and urged DCS to sign a settlement agreement that stipulated, among other things, that contrary to DCS's belief in resolving disputes within the church, DCS ''shall make clear in its employment contracts that employees may contact the Commission if they believe they are being discriminated against at any time.''
When DCS received the proposed agreement, it filed a suit in federal court asking that the court protect DCS's free exercise of religion by prohibiting the Commission from investigating and prosecuting the school. Joining DCS as plaintiffs were the two sponsoring churches, DCS officials, two parents who alleged that the investigation and potential prosecution of DCS ''burdens and endangers the ability of parents to choose a religious education for the children,'' and a teacher who charged that the investigation ''endangers the opportunity of religious teachers and administrators to carry out their religious vocation in the Christian formation and education of young people.''8
The court rejected DCS's free exercise claim, reasoning that the Commission's enforcement of Ohio's antidiscrimination law placed only ''a minimal burden'' on the plaintiffs' free exercise rights. No mothers with young children would be forced to work; DCS needed only to refrain from firing Hoskinson. The court did not address the plaintiffs' claim that by forcing DCS to employ a teacher who disobeyed church teachings, the law threatened the plaintiffs' ability to impress upon the students the importance of church doctrine. Although the court downplayed the importance of the case to the plaintiffs, it found that the state had a compelling interest in eliminating ''all forms of discrimination,'' and in preventing young people from being educated ''in an atmosphere of discrimination.''
An appeals court reversed the lower court decision, finding that the Commission's investigation violated the plaintiffs' free exercise rights, and that those rights were not trumped by the government's interest in eradicating discrimination.9 The Commission appealed to the Supreme Court. Although religious groups filed briefs uniformly supporting DCS, the case divided liberal civil libertarian organizations. The American Civil Liberties Union sided with the Commission, while Americans United for the Separation of Church and State supported the school's position. ''We are firmly opposed to discrimination,'' AUSCS executive director Robert Maddox said, ''but this principle must not override the right of churches or church schools to hire the pastors or teachers they believe can best teach their faith.''10 The Supreme Court ultimately sidestepped the civil liberties issue by reversing the appeals court on the grounds that the federal courts should not have interfered in ongoing state proceedings.11
Finally, after DCS had spent more than $100,000 defending itself, Hoskinson dropped her lawsuit. Hoskinson, who in the meantime had given birth to three children, and who had not returned to teaching, was unapologetic. She said, ''If a person who is in a religious institution cannot have the protection of the law, then I think we're in for some serious problems, because if they don't have the protection of the law, there's going to be a vacuum there they're just sucked into.''12 Recall, however, that Hoskinson had not been ''sucked into'' teaching in a school that taught and enforced conservative Christian values, but had actively sought out such an environment.
* * *
Other Christian schools have run afoul of antidiscrimination laws by trying to enforce religious doctrines that guide personal morality. In a virtual replay of the DCS case, the Michigan Supreme Court held that the government's compelling interest in eradicating discrimination trumped the Providence Christian School's claim of a free exercise right to refuse employment to female teachers with young children.13 Other cases have involved religious schools firing teachers who became pregnant out of wedlock—such pregnancy being compelling evidence of a violation of the schools' religious conviction against premarital intercourse. In these cases, courts agreed that religious schools' ''[r]estrictions on pregnancy are not permitted because they are gender discriminatory by definition.''14 In other words, the schools were discriminating by not firing any unmarried pregnant males! The more plausible legal defense for a school that fired an unmarried pregnant teacher would be to somehow persuade the jury that it would also have fired a male teacher who was discovered to have had sex outside of marriage, as this would be evidence of evenhanded treatment. But only a brave (or perhaps foolish) school administrator would risk his school's fiscal health on its attorneys' ability to prove this sort of counterfactual to a jury's satisfaction. The legal standard enunciated by the courts, then, would likely discourage most schools from enforcing their anti-fornication policies.
The standard itself makes little sense. Courts failed to consider that schools might reasonably choose to distinguish between a visibly pregnant female teacher and a male teacher whose fornication has come to the attention of a school's administration but not to the attention of his students. Christian educators could reasonably believe that sins by teachers that remain private can be overlooked, but employing a sinner whose transgressions have become public sends the wrong signal to students. As one Christian education manual states, teachers are expected to be role models. One such manual advises that students ''should see in their teachers the Christian attitude and behavior that is often so conspicuously absent from the secular atmosphere in which they live. Without this witness, living in such an atmosphere, they may begin to regard Christian behavior as an impossible ideal.''15 One court stated that if a school was concerned with the effect a teacher's visible pregnancy might have on impressionable high school students, it should have granted her a paid leave of absence during the term of her pregnancy. To fire her for getting pregnant, the court said, was ''inviting a sex discrimination lawsuit.''16 Where the typical financially overex-tended church school might find the money to finance a teacher's paid leave of absence, the court did not say.
* * *
Like their elementary and secondary school counterparts, religious universities have also been subjected to antidiscrimination claims when they tried to enforce their religious traditions. In the mid-1980s, Georgetown University, a Jesuit school in Washington, D.C., refused to extend ''university recognition'' to two gay student groups. Without university recognition, the groups could not get university funding and were not entitled to office space or a mailbox on campus. University recognition required the approval of the university's administration and was available only to organizations that were likely to be ''successful in aiding the university's educational mission in the tradition established by its founders.'' Although the university permitted the gay groups to meet on university property and to invite guest speakers, the groups were not eligible for university recognition because they flouted Catholic beliefs about sexual ethics.
The groups sued the university for violating the Washington, D.C., Human Rights Act's ban on discrimination against gays.17 The D.C. Court of Appeals acknowledged that a religious organization such as Georgetown could not be compelled to endorse a student group that encouraged or accepted homosexuality. However, the court found that D.C. law did not require Georgetown to actually endorse or accept the goals of the gay student groups, but merely to extend the same benefits to them that it offered to other student groups. Although D.C. had a compelling interest in eradicating discrimination against gays, the court said, the Act imposed a relatively minor burden on Georgetown's exercise of religion. The court reasoned that the university already provided limited benefits to the gay groups. The additional tangible benefits that would flow from university recognition were ''relatively insignificant.'' Ironically, the fact that Georgetown was generally tolerant of its gay students apparently meant that it received less constitutional protection than would have been granted to a virulently antigay school—a perverse message from a court delivering a lecture on the importance of not discriminating.
Disturbed by the court's ruling, Congress added an exemption for religious organizations to D.C.'s ban on discrimination against gays.18 But by this time, Georgetown had been so beaten down by a barrage of negative publicity it had received that it had lost the will to defend its restrictions on gay student groups. The university soon modified its rules, allowing any ''nonpolitical'' student group, including Georgetown's gay organizations, to receive funding and office space.19
* * *
South Carolina's Bob Jones University, which is famously sponsored by a strict fundamentalist Christian sect, screens its students for their religious beliefs to ensure compatibility with the school's mission, and the university requires all students to conform to a stringent code of conduct. Until 1971, the university excluded African American students. In 1971, the school, under pressure from federal civil rights authorities, began admitting married African American students. Following a 1975 court ruling requiring private colleges to admit African Americans, the university began admitting unmarried African American students as well. The university, however, contemporaneously banned interracial dating on penalty of expulsion. The university's founders claimed that the policy stemmed from a belief that the Bible prohibits interracial marriage, but others suspected that such explanations were merely a weak pretext for racial discrimination.20 And then the tax man got involved.
The Internal Revenue Service revoked Bob Jones' tax-exempt status when it concluded that the university's ban on interracial dating constituted discrimination in violation of public policy. The university sued, alleging that because the university was theologically opposed to interracial marriage, the IRS revocation infringed on the university's free exercise of religion. The case reached the Supreme Court, which acknowledged that IRS denial of tax benefits to universities that discriminated on religious grounds would ''inevitably have a substantial impact on the operation of private religious schools.''21 However, the Court held that this IRS policy was constitutionally permissible because the burden on universities was substantially outweighed by the government's ''fundamental, overriding interest in eradicating racial discrimination in education.''
There are legitimate grounds on which to justify the Court's decision in the Bob Jones case, but claiming that statutory antidiscrimination goals have a higher constitutional status than the First Amendment's protection of free exercise of religion, as the Court did in its opinion, is not one of them. Rather, given the university's historic discrimination against African Americans, the Court could reasonably have questioned the sincerity of the university's religious rationale for banning interracial dating.22 Indeed, the university abruptly gave up its purportedly ''sincere religious belief'' in banning interracial dating in 2000, after the university came under withering criticism following a visit by presidential candidate George W. Bush. Facing a loss of credibility, and possibly revenue, the university suddenly discovered that its ban on interracial dating was not theologically required, after all.23
* * *
Exactly how autonomous religious organizations should be from antidiscrimination laws has been a controversial question for decades. When it considered the 1964 Civil Rights Act, Congress debated how to deal with the potential conflicts with religious freedom that could arise under the act. Congress ultimately decided to exempt religious organizations from Title VII's prohibition against discrimination in employment, but only under narrow circumstances: when the discrimination is based on religion and the organization is engaging in religious activities.24 A 1972 amendment to the Civil Rights Act broadened this exemption so that it applied to religious organizations even when they were engaged in nonreligious activities.25
The Supreme Court upheld this provision against an Establishment Clause challenge in a case involving an employee of a Mormon church-owned gymnasium who was fired for failing to abide by church doctrine.26 The employee claimed that his dismissal constituted discrimination on the basis of religion, and that the religious organization exemption was an unconstitutional establishment of religion. The Court disagreed, finding that the exemption was an appropriate accommodation of religion by the government, not an illicit endorsement of religion.
Title VII's religious exemption remains limited in scope. Most courts, for example, have held that engaging in sex discrimination— even for religious reasons as in the DCS case—is not covered by the exemption. Courts consistently reject arguments from church defendants that they fired female employees who violated church doctrine over such issues as childbearing and child-rearing not because the employees were women, but because they had strayed from the church's religious teachings. Meanwhile, some states' employment discrimination laws, which are enforced on top of federal law, grant no religious exemptions at all.27
For many years, religious organizations and, to a lesser extent, individuals sought shelter from the mandates of antidiscrimination laws by relying on the free exercise clause of the First Amendment, as interpreted in the 1963 case of Sherbert v. Verner .28 In Sherbert , the Supreme Court dealt with the issue of generally applicable laws, such as antidiscrimination laws, that only incidentally interfere with the free exercise of religion. The Court held that free exercise rights trump such laws, unless the law in question serves a ''compelling governmental interest.'' In practice, this seemingly strict test was subsequently enforced so laxly that it provided religious organizations minimal protection from antidiscrimination laws.29 In 1990, the Supreme Court abandoned the compelling interest test, ruling instead that a generally applicable law that incidentally interferes with the free exercise of religion does not violate free exercise rights.30 Religious groups now receive no effective federal constitutional free exercise protection from antidiscrimination laws.
Religious organizations can, however, look elsewhere for protection. The Religious Freedom Restoration Act,31 passed by Congress in 1993, revived the compelling interest test that had been nixed for constitutional purposes in 1990. RFRA provides that laws could substantially burden the exercise of religion only if they constituted the least restrictive means of furthering a compelling governmental interest. Although the Supreme Court held RFRA unconstitutional as to state legislation because it was beyond the power of Congress to force states to define religious freedom so broadly,32 most courts have held that the RFRA still applies to federal legislation.33 Many states have passed their own versions of RFRA,34 and several state supreme courts have interpreted their state constitutions' free exercise clauses as demanding adherence to the compelling interest test. Some of these states have more clearly protected free exercise by adopting a narrow definition of what constitutes a ''compelling interest.''35
An even more important development is that religious organizations seeking a constitutional exemption from antidiscrimination laws can now rely on the right of expressive association. In the 2000 case of Boy Scouts of America v. Dale (see Chapter 8), the Supreme Court held that nonprofit, ideological organizations have a First Amendment expressive association right to set employment and membership policies consistent with their beliefs, even if antidiscrimination laws would normally make such policies illegal. Dale therefore implies that Christian schools like Dayton Christian Schools have an expressive association right to refuse to employ teachers who behave contrary to church doctrine; that Christian universities like Georgetown have an expressive association right to refuse to fund gay advocacy organizations; and that schools that have a religiously based racist outlook like Bob Jones claimed to have, have the right to discriminate based on race.36 Dale , in short, is likely to protect religious schools from having their free exercise rights violated by courts and agencies acting to enforce antidiscrimi-nation laws.
However, there are still some conflicts between religious freedom and antidiscrimination laws that Dale cannot resolve. For example, Dale only protects the rights of nonprofit associations, so parties that do not fit into that category, such as the religious landlords described in the next chapter, must either fall back on legislative exemption from antidiscrimination laws or on judicial enforcement of the compelling interest test to protect their freedom to exercise their religion.
# 10. Religious Landlords:
Antidiscrimination Law as a
Weapon in the Culture Wars
Paul Desilets and his wife Louise own 23 apartment units in Turners Falls, Massachusetts. The Desiletses are devout Roman Catholics who try to live according to their beliefs. Louise, for example, directs Sunday school at Our Lady of Czestochowa Church and works as a hospice visiting nurse, comforting dying patients. The Desiletses believe that renting an apartment to an unmarried couple would violate Catholic doctrine by facilitating fornication.1 Paul told the Seattle Times that ''allowing fornication to occur on property I own places my eternal soul at risk.''2
The Desiletses' lives changed the day Cynthia Tarail asked Paul about renting an apartment she intended to share with her boyfriend, Mark Lattanzi. According to Tarail, Paul asked if she intended to marry Lattanzi. When she replied that she was unsure, he told her, ''Then you'd be living in sin, and we don't go for that. Don't you know it's a criminal act to cohabitate and fornicate?''3 Paul acknowledges that he rebuffed Tarail but claims he politely informed her of his policy against renting to unmarried couples.
The couple filed a complaint with the Massachusetts Commission Against Discrimination, alleging discrimination on the basis of marital status, and the state attorney general filed suit against the Desiletses. Tarail, a graduate student in social work, described her politics as ''very left.'' ''I'm a feminist and a socialist,'' she told the Boston Herald , ''and our motivation here is not to stick up for unmarried couples but for tenants' rights. We believe strongly that housing is a right, not a privilege.''4 Lattanzi, a local coordinator for an anti-housing discrimination organization, expressed his disgust that ''the Desilets seem to think their religious beliefs allow them to discriminate.'' ''Housing is a commodity, like anything else,'' Lattanzi told the media.5 Paul Desilets responded, ''Must everything today come down to strictly economic terms, the lowest common denominator? Can't we raise our sights and deal with larger issues? We have laws that say I can't smoke in a public building, but people are allowed to fornicate on my property. Don't I have rights, too?''6
The trial court held that the Desiletses had violated the Massachusetts fair housing law, but found that the state constitution's protection of religious freedom from government interference precluded enforcing the statute against them. When the case was appealed to the state supreme court, three of the seven justices voted to affirm the lower court's ruling. In dissent, they argued that ''[n]either the court nor the Legislature can constitutionally give preference or priority to a so-called 'right' of cohabitation over the . . . guarantees of the free exercise of religion.''7
A four-justice majority, however, sent the case back to the trial court for further consideration of whether the fair housing statute could properly infringe on religious liberty. The majority opinion acknowledged that the statutory rights of Lattanzi and Tarail were of a ''lower order'' than the constitutional rights of the Desiletses, and the court strongly hinted that it expected the lower court to once again rule in the Desiletses' favor. The supreme court stated, for example, that it could not conclude that the ''simple enactment of the prohibition against discrimination based on marital status'' established that the comonwealth had a compelling interest in ending such discrimination.8 The majority added that to find for the state on remand, the lower court would need to find that Massachusetts had a specific compelling interest not just in combatting discrimination in general, but also ''in the elimination of discrimination in housing against an unmarried man and an unmarried women who have a sexual relationship'' and wish to rent housing together. The Massachusetts attorney general's office read between the lines and dropped the case, purportedly for lack of resources, but it warned that it reserved the right to prosecute other landlords who refused to rent to unmarried couples for religious reasons.9
The Desilets case is one of several in which unmarried heterosexual couples, hardly a beleaguered minority group, have charged religious landlords with discrimination for refusing to rent to them. Columnist George Will calls this ''the latest twist in the trivialization of the 'civil rights' movement.''10 In fact, as the Desilets case illustrates, these cases represent an even worse phenomenon—the use of antidiscrimination laws as a weapon in the ''culture wars'' between the secular left and the religious right.
While their case was being decided by the state supreme court, Lattanzi and Tarail married, but they declined to drop their claim. They told the media, ''Some people have said, 'If you're getting married, what's the big deal.' But that's not the issue. We don't want people telling us we have to be married. We want to be married when WE want to be.''11 This suggests that the couple's underlying complaint was not that they were denied needed housing, but that the Desiletses dared to disapprove of their living arrangements and had acted on that disapproval. The goal of Lattanzi, Tarail, and other cohabitating couples who sue religious landlords seems to have less to do with combating invidious discrimination—because unlike, say, African Americans in the 1960s, these couples can almost always find alternative housing quite easily—and more to do with trying to punish religious conservatives for refusing to accommodate liberal secular values. It is not so much a case of ''you've prevented me from finding a place to live,'' as it is a case of ''you've acted in a politically incorrect way and now you're going to pay.''
* * *
Anchorage, Alaska, landlord Tom Swanner lost his free exercise claim when he faced marital status discrimination charges for refusing to rent to three unmarried couples. After both a hearing examiner and a trial court ruled against Swanner, he appealed to the state supreme court.12 The court found that the verdict against Swanner could be upheld only if the state could demonstrate a compelling interest sufficient to overcome Swanner's free exercise rights.13 Swan-ner insisted that Alaska's interest in prohibiting discrimination against unmarried couples could not possibly be compelling, given that the state itself discriminated in favor of married couples in a variety of other contexts. The court disagreed, ruling that ''[b]ecause Swanner's religiously impelled actions trespass on the private right of unmarried couples to not be unfairly discriminated against in housing, he cannot be granted an exemption from the housing anti-discrimination laws.'' The circularity of this reasoning is evident; the court essentially reasoned that statutory antidiscrimination rights override free exercise rights because . . . they do. The court ordered Swanner to pay $1,000 plus all of the plaintiffs' legal costs.
The U.S. Supreme Court declined to review the case, sparking a vigorous dissent from Justice Clarence Thomas.14 At the time, the Religious Freedom Restoration Act, later invalidated as to its applicability to the states by the Court on constitutional grounds (see Chapter 9), suggested that Swanner had a federal statutory right to discriminate on the basis of religion unless the government could show it had a compelling interest in quashing the discrimination. Thomas wrote that ''if, despite affirmative discrimination by Alaska on the basis of marital status and a complete absence of a national policy against such discrimination, the State's asserted interest in this case is allowed to qualify as a 'compelling' interest—that is, a 'paramount' interest, an interest 'of the highest order'—then I am at a loss to know what asserted governmental interests are not compelling.''
* * *
Few laws explicitly protect unmarried couples from housing discrimination.15 Some jurisdictions do ban discrimination on the basis of marital status, but this bar was intended to aid recently divorced women who sometimes find it difficult to find housing because they have not established their own credit histories. Such bans on discrimination based on marital status arguably do not apply to landlords who willingly rent to single individuals but not to unmarried couples. After all, landlords who refuse to rent only to unmarried couples are not discriminating on the basis of the prospective tenants' marital status—such landlords would be perfectly willing to rent to these same prospective tenants individually—but on the basis of what the landlords perceive as immoral conduct .16
Several courts have nevertheless held that laws prohibiting marital status discrimination protect unmarried couples. The Minnesota Supreme Court is a rare but welcome exception. Layle French of Marshall, Minnesota, bought a new house for his family. Rather than selling his previous residence right away, he decided to rent it out until the real estate market picked up. He found a couple interested in the house and agreed to rent it to them, but then reneged on the agreement when he discovered that they were not married. French, a Sunday school teacher at a conservative Lutheran church, believed that premarital sex is a sin and that renting his house to an unmarried couple would aid in the commission of that sin or would at least create ''the appearance of evil.'' The rejected couple hired an attorney.
The state filed suit against French after the couple's attorney complained that French had ''illegally attempted to enforce his religious prejudices concerning marital status on the marketplace,'' and was thus ''guilty of violating the couple's civil rights.'' French recognized that he was a combatant in the culture wars. ''They're pretty consistent in telling us that we can't push our religion on somebody else,'' French remarked, ''Meanwhile, they are trying to push their beliefs on us.''17 An administrative law judge found that French had violated the Minnesota Human Rights Act and fined him over $1,000. In a four-to-three decision, the state supreme court reversed, holding that the act's prohibition on discrimination based on marital status did not extend to discrimination against unmarried heterosexual couples.18
Even if a fair housing law does protect unmarried heterosexual couples from discrimination, landlords may still have a federal or state constitutional right to follow the dictates of their consciences. As discussed previously (see Chapter 9), under federal constitutional precedent a religious believer usually cannot claim a free exercise exemption from general laws that happen to impinge on his religious beliefs. A three-judge panel of the Ninth Circuit Court of Appeals, however, held that fair housing laws that impinge on landlords' religious beliefs are an exception to this rule, because the laws also impinge on associational freedoms and property rights.19 The Ninth Circuit noted that the Supreme Court has held that when a litigant asserts a ''hybrid'' constitutional defense that joins a free exercise claim with an assertion of other constitutional rights (such as those protecting property and association), the law in question cannot be enforced unless it serves a compelling governmental interest. The Ninth Circuit panel concluded that there ''is simply no support from any quarter for recognizing a compelling government interest in eradicating marital-status discrimination.''20 The court, therefore, held that a landlord has a constitutional right to refuse to rent to unmarried couples for religious reasons. An opportunity to see whether the Supreme Court agreed with the panel's ruling was lost when the full Ninth Circuit reversed the panel's opinion on procedural grounds.21
Regardless of federal precedents, many state courts interpret their state constitutions as requiring them to apply the compelling interest test to general laws—including fair housing laws—that impinge on religious freedom. Three members of the majority in the French case, discussed earlier, stated that even if the statute applied to unmarried couples, French's right to exercise his religion under the freedom of conscience provision of Minnesota's constitution outweighed any interest of potential tenants to cohabitate before marriage.
The three dissenters, however, concluded that combating any type of invidious discrimination in housing is an overriding compelling state interest that trumps religious freedom. They justified this view on the grounds that ''housing is a basic human need regardless of a person's personal characteristics'' and ''an individual's marital or familial status . . . is irrelevant to . . . renting a house, because it bears no relation to the individual's ability to participate in and contribute to society.'' The dissenters, alluding to America's history of racial segregation, accused the majority of advocating a return to the days of ''separate but equal,'' during which individuals could keep ''undesirables'' out of their neighborhoods. Demonstrating an incredible lack of perspective, the dissenters argued that discrimination against the unmarried is no less invidious than discrimination against African Americans. The court ignored the fact that being an unmarried couple is a lifestyle choice, not an immutable characteristic like race, and that unmarried couples have not suffered centuries of slavery and persecution. Moreover, since marriage is widely regarded to be beneficial to society and especially to children, discrimination against cohabitating couples, to the extent it encourages them to get married, may actually serve the public interest.
* * *
But what happens when a court decides to focus on how hard it would be for the landlord to avoid discriminating rather than on how compelling the government's interest is in ending the discrimination? The California Supreme Court gave the free exercise issue this interesting twist in a case involving Evelyn Smith, an elderly widow who owned two duplexes in Chico, California, and offered the four apartments for rent.22 Two tenants gave Smith, a devout Presbyterian, a rental deposit, claiming they were married. When Smith discovered the tenants had lied and were actually single, she returned the deposit. The couple sued and won $454 in compensatory damages and $500 for emotional distress.
On appeal, the state supreme court addressed Smith's claim to a religious exemption. Instead of focusing on whether the government's interest was compelling, the court applied a ''substantial burden'' test, stating that if the law imposed a substantial burden on Smith's free exercise of religion, she would be entitled to an exemption. The court concluded that prohibiting marital status discrimination did not substantially burden Smith's practice of religion because she could voluntarily avoid the conflict without sacrificing her religious beliefs and ''without threatening her livelihood, by selling her units and redeploying the capital in other investments.'' The court, while still purporting to apply the substantial burden test, then disingenuously slipped in other considerations. It found that requiring a landlord to rent to unmarried couples is a relatively insubstantial burden on the landlord's religious freedom because allowing the landlord to rent only to married couples would affect the rights of third parties (that is, the unmarried couples who could not rent). The court did not, and obviously could not, explain how a burden on free exercise somehow diminishes merely because third parties are affected.
* * *
State supreme courts seem to be growing less sympathetic to discrimination claims by cohabiting couples. In 1997, the Illinois Supreme Court summarily reversed a lower court ruling that a religious landlord had no constitutional right to discriminate against an unmarried cohabitating couple.23 The lower court had found that the government's compelling interest in eradicating discrimination trumped the landlord's free exercise rights.
An even more dramatic reversal occurred in Michigan. Plaintiffs Kristal McCready and Keith Kerr, a cohabitating couple, had sought to rent an apartment from landlord John Hoffius, but he refused them as tenants for reasons of religious conscience. McCready and Kerr soon found another apartment, but they nevertheless filed suit in state court against Hoffius for marital status discrimination. The trial court ruled in Hoffius' favor, finding that the legislature could not possibly have meant to include unmarried couples in the class of people protected under Michigan's fair housing law, because cohabitation remained officially illegal in Michigan. Hoffius not only had the right to refuse to rent to McCready and Kerr, he could have reported them to the police. The state court of appeals affirmed.24
The Michigan Supreme Court, however, reversed, noting that the state anti-cohabitation law had not been enforced for decades. The court added that to the extent requiring Hoffius to rent to unmarried couples infringed on his free exercise rights, the infringement was justified under the compelling interest test, the applicable test under the Michigan constitution.25 Instead of engaging in an independent review of whether combating housing discrimination against unmarried couples is a compelling interest, the court deferred to the state legislature. The court explained that the compelling interest test was satisfied because ''[t]he Michigan Legislature has determined that the need for housing is so fundamental as to necessitate the passing of the Civil Rights Act.'' Meanwhile, Hoffius's ''fundamental''—and constitutionally protected—right to exercise his religious beliefs got short shrift. If Hoffius did not want to obey housing discrimination law, the court admonished, he should get out of the real estate business.
The court ordered the case remanded to the trial court for a trial to determine damages. McCready and Kerr, who had suffered no monetary damages and who were comfortably installed in another rental unit, claimed to be suffering from ''emotional distress'' because Hoffius had refused to rent to them. Hoffius was also potentially liable for the couple's attorneys' fees, which totaled more than $30,000. Before the damages case could be heard in the trial court, however, Hoffius filed a motion for rehearing. In the meantime, an election cycle had passed and new justices had joined the supreme court, including two justices who had decided in favor of Hoffius when they were lower court judges. Hoffius was in luck (or perhaps his prayers were answered). The supreme court granted the motion for rehearing and reversed its earlier ruling without published discussion.26
* * *
In the late 1990s, judicial decisions holding that landlords could refuse to rent to unmarried couples on religious grounds destroyed a broad coalition, ranging from religious conservatives to liberal civil liberties groups, that was seeking to enhance legislative protections for religious liberties. The coalition had been lobbying for congressional passage of a successor to the Religious Freedom Restoration Act, the Religious Liberty Protection Act, which would have evaded prior Supreme Court decisions and required courts to apply a compelling interest test when laws infringed on religious liberty. But some liberal groups, most prominently the American Civil Liberties Union, were appalled by the decisions upholding landlords' free exercise rights despite the government's assertion of its ''compelling interest'' in preventing discrimination.
The ACLU and other prominent civil libertarian groups supported the RLPA in principle. ACLU legislative counsel Christopher Anders testified in Congress that the RLPA would correct erroneous Supreme Court opinions that had construed the Constitution's guarantee of free exercise of religion too narrowly.27 The ACLU nevertheless felt compelled to oppose the RLPA because its religious exemptions would inevitably extend to antidiscrimination laws. Anders expressed particular concern that recent case law suggested that the RLPA would permit religious landlords to evade laws requiring them to rent to unmarried heterosexual couples. He also worried that laws protecting homosexuals, and perhaps other groups, from discrimination would also be weakened to some degree by the RLPA.28 But Anders and the ACLU never answered the $64,000 question: Why does an organization purportedly devoted to civil liberties believe that the constitutionally protected right to free exercise of religion should be trumped by antidiscrimination laws?
The ACLU and its allies insisted that the RLPA be amended to exempt antidiscrimination laws from its scope, but conservative groups refused to compromise on this issue. Left-wing groups then abandoned the coalition, effectively killing the legislation. Nathan Diament, director of the Union of Orthodox Jewish Congregations of America's Institute of Public Affairs, decried allegations by some coalition dropouts ''that right-wing religious groups were supporting RLPA in order to further their political agenda.'' Diament accused coalition defectors of being fair-weather friends of religious freedom, stating that ''[t]he real test of religious liberty is kind of like the real test of free speech. You defend the right of people even if they're politically incorrect. You really believe in religious liberty if you protect people whose religious views you disagree with.'''29
Despite criticism from Diament and others, civil liberties groups are increasingly unwilling to defend religious freedom when the price is a narrowing of antidiscrimination laws. These groups tend to consider all antidiscrimination laws, even trivial laws like those banning discrimination against unmarried heterosexual couples, as more important than the right to free exercise of religion. After several liberal Jewish civil libertarian groups abandoned the pro-RLPA coalition because of concerns about its effect on antidiscrimi-nation law, an unhappy Marc Stern of the American Jewish Congress attacked their implicit idolatry: ''The principle of equality is taking on a quasi-religious status,'' he complained, ''Maybe for some people questioning civil rights is like questioning God.''30
# 11. The Right to Privacy and the Right
to Be Left Alone
Ann Hacklander-Ready rented a four-bedroom house in Madison, Wisconsin, and sublet three of the bedrooms to female housemates. After two housemates moved out, Hacklander-Ready and her remaining housemate, Maureen Rowe, looked for replacements. They initially accepted a rent deposit from a woman named Caryl Sprague, whom they knew to be a lesbian. Upon further reflection, however, Hacklander-Ready and Rowe decided they were not comfortable sharing their living space with a lesbian, and they returned Sprague's deposit.
Sprague responded by filing a discrimination complaint against both Hacklander-Ready and Rowe with the Madison Civil Rights Commission. Sprague's claim relied on Madison's fair housing ordinance, which did not, on its face, indicate whether it applied to roommates. Hacklander-Ready and Rowe argued that it didn't; an administrative law judge decided that it did. The judge awarded Sprague $2,000 for emotional distress, $1,000 for punitive damages, and $300 for the security deposit she lost trying to secure another apartment, along with costs and attorney's fees. Rowe settled, but Hacklander-Ready, convinced that her civil liberties were being violated, appealed.
On appeal, the court agreed that the fair housing ordinance applied to Caryl Sprague's roommate situation. This result was remarkable, because shortly after Sprague filed her discrimination complaint, the Madison City Council had amended the housing ordinance to clarify that ''[n]othing in this ordinance shall affect any person's decision to share occupancy of a lodging room, apartment or dwelling unit with another person or persons.'' The city council was speaking directly to the Sprague case and making clear its support of Hacklander-Ready and Rowe's right to discriminate. The appellate court, however, refused to consider this amendment in resolving the ambiguity in the original law. The court also rejected Hacklander-Ready's argument that penalizing her for refusing to accept a lesbian housemate violated her constitutional rights to privacy and freedom of intimate association. The court held that these rights apply only in the ''home or family'' and that Hacklander-Ready gave up these rights when she ''rented housing for profit.'' The court did not explain how living with housemates to defray rental expenses and make ends meet constitutes renting housing ''for profit.''1
The Wisconsin and U.S. Supreme Courts declined to hear further appeals.2 Meanwhile, the Madison Civil Rights Commission determined that Hacklander-Ready was liable for the more than $23,000 in lawyers' fees Sprague had racked up over the course of the litigation, because the local antidiscrimination ordinance forced losing defendants to pay plaintiffs' expenses.3 Hacklander-Ready paid dearly for trying to defend her rights.
Nor were Hacklander-Ready's troubles unique. In May 1999, Melissa DeSantis, a young Filipina-American from San Jose, California, placed a sign in her window seeking a roommate to sublet the available bedroom in her two-bedroom apartment.4 Eric Campbell, an African American man, came to look at the room. Campbell, who was living at the Aconda Hotel at the time, complained that the rent was too high, that the bedroom was too small, and that he couldn't afford to pay the $150 security deposit upfront. He then asked to see the other, larger, room. DeSantis explained that the other room was her room, and was not for rent. For some reason, Campbell was disturbed by DeSantis's honest answer, and he belligerently insisted on seeing the unavailable room, only relenting when DeSantis informed him that her boyfriend was in that room.
Campbell apparently became convinced that DeSantis had refused to show him the larger room because he was black. He contacted Project Sentinel, a nonprofit group that investigates allegations of housing discrimination. The group sent two ''testers'' to the apartment, a white man and an African American man, to see if they could uncover any discrimination. DeSantis seemed inclined to rent to the white tester, but when the African American tester later inquired about what had become of his application, DeSantis claimed she did not know. DeSantis also offhandedly told the white tester, in regard to another prospective tenant, ''Actually, I don't really like black guys. I try to be fair and all, but they scare me.''
Armed with this information, Campbell turned the matter into a complaint with the California Fair Housing Commission. The Commission found that his testimony, which made various claims of discriminatory treatment, was internally inconsistent and not credible. The Commission further concluded that he had not been qualified to rent the room, because DeSantis had insisted that her roommate pay in advance the first month's rent and a security deposit, which Campbell could not afford. The Commission therefore found that Campbell was not the victim of illegal discrimination.
The Commission nevertheless awarded Campbell $240 in costs for the pay he lost for attending the hearing and $500 for emotional distress damages; Campbell had testified that when he learned of DeSantis's statement to the tester that she was afraid of black men, he had become upset because he felt he had been judged on the basis of his color. In other words, the Commission ultimately forced DeSantis to pay Campbell for losing work time to pursue a failed claim of housing discrimination and for having his feelings hurt by a comment she made to a ''tester'' employed specifically to discover such emotionally upsetting information. Strange logic, indeed.
This outcome seems even stranger when one considers that California's fair housing law explicitly exempts persons seeking ''boarders'' or ''roomers'' in a single-family house and says nothing about roommates in an apartment, apparently because the drafters did not imagine that the law might ever be applied to such a situation. So that the matter would fall under the law, the Commission treated DeSantis as if she occupied a single-family house, an inaccuracy which nevertheless would normally mean that she was exempt from the fair housing law because she was seeking a ''roomer.'' However, the Commission refused DeSantis this exemption because it only applies to persons who comply with another provision of the law making it ''unlawful for a person to make any statement with respect to the rental of a housing accommodation that indicates any preference, limitation, or discrimination based on race.'' The Commission found that DeSantis had violated this provision with her statement that she didn't like and was scared of black men.
Given constitutional constraints, one hardly expects that a person could be subject to liability for refusing to share an apartment with someone, much less be fined because of an offhand remark made in private conversation. Indeed, the Commission acknowledged in a footnote that ''this case raises significant issues of the constitutional protections of freedom of speech and the right to privacy and association.'' However, according to the Commission, as an administrative agency, it did not have power to declare a statute unenforceable on the basis of its being unconstitutional. This understanding of the Commission's responsibilities, though apparently settled law, is at odds with the accepted notion that all government officials are required to ensure that they act within constitutional strictures. If California law requires the Commission to ignore the federal Constitution, that law is itself unconstitutional. Overall, the Commission's ruling is consistent with the unfortunate tendency of administrative agencies charged with enforcing antidiscrimination laws to expansively interpret the laws and narrowly interpret constitutional rights.
* * *
Although federal, state, and local fair housing laws generally permit discrimination in selecting roommates or housemates, they still prohibit advertisers from mentioning their discriminatory preferences, except for specifying gender.5 The result is that persons who place classified ads for roommates waste their time, as well as the time of many of those who respond to their ads, by inviting and dealing with inquiries from persons who fail to meet the actual ''discriminatory'' criteria.
The advertising restriction can be particularly onerous in jurisdictions that ban housing discrimination on the basis of criteria beyond the standard categories of race, sex, religion, and age covered by federal law. For example, Washington, D.C., fair housing law prohibits discrimination on the basis of sexual orientation or political affiliation. In 1998, the Fair Housing Council of Greater Washington sued the Washington City Paper for publishing real estate advertisements for roommates and housemates that expressed illegal preferences. Among the examples of illicit advertisements raised in the complaint were the following:
* seeking a gay male to share two-bedroom, one-bath condo
* gay female seeking another gay female to share a house
* housemate needed for a spacious 30ish group house
* housemate needed, no pets, no Republicans
* women-of-color group house seeking a new member
* Jewish cooperative home starting6
Some of these ads represent attempts by members of minority groups to find housemates who share the same subculture; others express a desire to live with people of like-minded political views or who are at the same stage in life. In most of these cases, an advertisement that didn't specify the relevant discriminatory preferences would be nearly useless, because the advertisers would be inundated by calls from disfavored heterosexuals, gentiles, 20-year-olds, and so forth. The suit made little sense, but the City Paper appears to have capitulated; recent issues do not contain ads stating discriminatory preferences. This puts a great burden on persons with idiosyncratic roommate preferences: District of Columbia residents seeking to establish a group house for gay Jewish Libertarian women of color must either find new housemates by word of mouth or be willing to sift through the random mix of would-be renters that respond to a more generalized ad. Because of the advertisement restrictions, some persons may never be able to find roommates who match their preferences. Such governmental intrusion on the ability to form a relationship as intimate and private as the relationship between people who share living space is unjustifiable.
* * *
Approximately two million American women belong to women-only health clubs.7 Some women, such as those with religious objections to wearing revealing clothes in front of men, and abuse survivors who find it traumatic to display their bodies in front of unfamiliar men, use these clubs by necessity.8 Other women join these clubs to avoid unwanted male attention while they exercise. Still others, including overweight women and women who have had mastectomies, feel much less self-conscious exercising in an all-female environment. The owner of one women's health club boasts, ''I like to think we're for real women. We don't have everyone looking like a Barbie doll. They're average size and shape. And we don't let men in. We say, 'No men, no mirrors, no kids.'''9 The owner of a club that holds women-only aerobics classes explains, ''It's a privacy issue. The women are sweating, they don't have makeup on, and they feel that the guys are staring at their butts.''10
Some women find men to be a distraction when they go to coed gyms. Cynthia Parziale, director of research and development at the Naturally Women chain of fitness centers, opines, ''If you're really serious about your workout, it's distracting to have people of the opposite sex around. Women will spend time getting dressed or fixing their hair or putting on their lipstick before they come to the gym. The coolest thing about a women's gym is you can be ugly.''11< Joan Pirone, who patronizes a women-only exercise club in Anchorage, Alaska, told CNN that ''at coed clubs you feel like you're on TV, like the men are constantly looking at you. Some women enjoy the attention from men, but some of us are intimidated by it. I'm glad I have the choice of going to a women-only gym.''12
Other users of women's health clubs find that the women-only facilities are cleaner and smell better than coed gyms. Women's clubs also often emphasize the workout equipment that is used more frequently by women, and many even have special equipment built for women. The two women-only clubs in Anchorage, for example, have smaller-than-average Nautilus machines designed for women's bodies, with the weight stacks increasing by 3-pound increments instead of the usual 10. Women-only clubs also emphasize educational programs focusing on women's health concerns, such as preventing osteoporosis and losing weight gained during pregnancy.13
Despite their popularity and the privacy interests served by allowing women to work out free from male oglers, women-only clubs have sometimes run afoul of state laws banning sex discrimination in public accommodations. In 1988, the noted feminist attorney Gloria Allred filed a sex discrimination lawsuit on behalf of a Los Angeles man who was denied admission to a women's health club.14 Allred dismissed the concerns of women who join all-women gyms to avoid male ogling. She contended that the idea that all men ogle is a stereotype and that men who misbehave can be excluded from sex-integrated clubs on a case-by-case basis.15 Yet common experience suggests that heterosexual men are inclined to ''check out'' women, particularly women wearing skimpy shorts or tight leotards. Further, Allred did not explain how a club would enforce or prevent an anti-ogling policy on an individual basis. It would be very different to actually prove the subtle act of a man evaluating a woman's body (Mr. Jones, please stop undressing Ms. Smith with your eyes), and sensitive women could very well feel ogled whether or not it was actually happening. Despite these arguments, the Los Angeles club ultimately agreed to settle Allred's lawsuit and began admitting men.16 Successful lawsuits against women-only gyms in Minnesota; Orange County; California; and Wisconsin followed.17
Happily, the tide seems to have turned against applying sex discrimination laws to the membership policies of gyms. In 1997, a Massachusetts trial court ruled that a women-only health club, Healthworks Fitness Center, could not exclude men.18 The decision was met with dismay by the 40,000 female members of that and other such clubs throughout Massachusetts. Despite the National Organization for Women's objections, legislators responded to a flood of protests from angry female exercise enthusiasts by exempting single-sex health clubs from Massachusetts's public accommodations law.19 Since then, Alaska, Colorado, Hawaii, Illinois, New Jersey, and Tennessee have also passed laws specifically permitting single-sex health clubs, catering to either sex.20
The federal Equal Employment Opportunity Commission, meanwhile, has sued women's health clubs for refusing to hire male employees. The most significant case involved the Women's Work-out World chain of fitness clubs in the Chicago, Illinois, metropolitan area.21 After a showing that the chain hired only women, a federal judge granted summary judgment to the EEOC's claim of employment discrimination. In response, Women's Workout World filed a motion for reconsideration supported by a petition signed by more than 10,000 club members.22 In support of its motion, the chain noted that it specialized in individual attention for its members and that its members did not want men touching them during workouts or seeing them disrobed in the locker room.
The judge concluded that Women's Workout World had articulated a legitimate privacy interest with regard to nudity and withdrew the summary judgment, but he allowed the case to continue. After seven years of crippling litigation expenses, Women's Workout World settled. The company agreed to hire men for certain restructured positions that would (hopefully) maintain members' privacy, and to pay $30,000 to men who had been turned down for jobs. Other all-women clubs have also fought and sometimes lost sex discrimination lawsuits filed by men who were refused employment.23
* * *
As workplace use of and reliance on e-mail grows, employers are spending more and more energy monitoring and regulating their employees' e-mails and other computer communications to avoid potential liability under hostile environment law.24 Even if antidiscrimination law were not a factor, employers would engage in a certain level of monitoring and regulation to ensure that their workers were not frittering away the workday instant-messaging their friends and Web surfing. But many employers are going well beyond what is needed to maximize productivity, and are using sophisticated surveillance tools to monitor employee e-mail to head off potential discrimination complaints.25 One-quarter of all large corporations, for example, perform keyword or phrase searches to censor employee e-mails, usually looking for sexual, scatological, or racist language.26
Employers are using these techniques in response to a wave of hostile environment lawsuits brought by women and others who either received sexually suggestive e-mails, or who were simply offended to discover that their coworkers had swapped such e-mails among themselves.27 Almost every hostile environment case contains allegations of offensive workplace e-mails.28 While it is true that few hostile environment cases succeed solely on the basis of allegations that a corporate defendant tolerated offensive e-mails, such e-mails do hostile environment defendants no favors, so it is most sensible to prohibit them completely. As a leading First Amendment scholar points out, as long as e-mails can be used as part of a hostile environment claim, ''the cautious employer must restrict each individual instance of such speech....The employer must say, 'Do not circulate any material, even isolated items, that anyone might find racially, religiously, or sexually offensive, since put together such material may lead to liability.'''29
When employees are caught using offensive language by software filters or other monitoring devices, they often find that the breach of their privacy is not the worst of their worries. They may also be out of a job. The New York Times , for example, fired 20 staffers for sending inappropriate and offensive e-mail. The company ''cited a need to protect itself against liability for sexual harassment claims.''30 Jobs are at risk even when no third parties are involved, as two executives at Smith Barney discovered when the company dismissed them for accessing pornography at work and transmitting it between themselves. Although this might seem like excessive punishment, if a company looks the other way, or even lets its workers off with a stern warning, future plaintiffs in sexual harassment suits could use that tolerance as evidence that the company had a lax sexual harassment prevention policy.31 The looming threat of a hostile environment suit makes terminating an employee who e-mailed the wrong thing the most prudent course.
* * *
Discrimination lawsuits typically proceed with little regard for the privacy interests of the defendant, or even those of third parties not directly involved in the claim. This is an inevitable result of some types of discrimination claims. For example, if a female employee sues a company alleging that she received lower pay than similarly qualified male coworkers, in depositions and at trial the defendant will be forced to directly compare the plaintiff's performance and pay to that of any men with analogous responsibilities. The defendant may also find it useful to compare the performance and pay of other women employees with that of the plaintiff, or with that of other male employees, or with that of each other. To successfully navigate this process, the defendant will need to reveal details about deficiencies in various employees' work, give explanations of whether those deficiencies were related to personal crises, and provide other confidential information likely to embarrass the workers.
In one case, a female attorney sued her firm for sex discrimination after being passed over for partnership. By the time the plaintiff lost her case, everyone in the local legal community knew private details about other lawyers in the firm, including which associate ''offended the father-in-law of which senior partner,'' which associate frequently ''disappeared without notice,'' ''whose writing skills were seen as not being up to par,'' and who was perceived as ''more sizzle than steak.'' Everyone also knew who had said which of these things about whom.32
Although such revelations seem an unfortunate but necessary byproduct of some discrimination claims, some of the harm to privacy inflicted by discrimination cases seems gratuitous. For example, recent changes to the rules of evidence allow sexual harassment complaints to turn into massive assaults on privacy. Former president Bill Clinton is the most famous victim of this dynamic. Paula Jones filed a lawsuit against Clinton, claiming that when he was governor of Arkansas he exposed himself to her, made other sexual advances, and implicitly threatened her with retaliation in her job with the state if she refused him. Jones's lawyers, some of whom were at least as interested in embarrassing Clinton as in winning the case, desperately sought an excuse to question Clinton and others about Clinton's rumored affairs with several other women. According to a published report, Jones' husband, Steve, announced that Paula's legal team was going to use subpoena power to reconstruct the secret life of Bill Clinton. Every state trooper used by the governor to solicit women was going to be deposed under oath. ''We're going to get names; we're going to get dates; we're going to do the job that the press wouldn't do,'' Steve Jones said, ''We're going to go after Clinton's medical records, the raw documents, not just opinions from doctors, . . . we're going to find out everything.''33
Eventually, Jones's attorneys stumbled upon Federal Rule of Evidence 415, ironically signed into law by Bill Clinton only a few years earlier. Rule 415 allows plaintiffs in civil cases involving ''sexual assault'' to present evidence that the defendant engaged in similar acts of sexual assault, in order to show that the defendant had a propensity for abusing women. Sexual assault, as defined by Federal Rule of Evidence 413, includes ''contact, without consent, between any part of the defendant's body or an object and the genitals or anus of another person.'' To take advantage of Rule 415, Jones's attorneys promptly amended their complaint to include a new allegation that Clinton had ''put his hand on Plaintiff's leg and started sliding it toward the hem of Plaintiff's culottes, apparently attempting to reach Plaintiff's pelvic area.''34
Even with this allegation added to the complaint, it seemed like a stretch for Jones's attorneys to inquire about Clinton's past consensual affairs, because such affairs do not meet the rules' criteria for being considered prior sexual assaults. But Jones's lawyers successfully argued that ''[t]here is no practical means for this Court, in advance, to limit discovery to non-consensual sexual behavior because only after discovery can the existence of consent be determined.''35 Given the incredibly broad scope courts normally give to discovery requests, the judge had little choice but to accede to the lawyers' request. As a result, Jones's attorneys were able to subpoena the testimony of Monica Lewinsky, and to demand that she turn over her calendars, address books, journals, diaries, notes, letters, and other private information. Lewinsky's attorney filed a motion to quash the subpoena, arguing that complying with it would grossly invade his client's privacy. Before the court could rule on the motion, Kenneth Starr's independent counsel investigation interceded.36
Eventually, of course, Clinton's affairs with Lewinsky and other women became public knowledge, Clinton lied about his affairs under oath and to the American people directly, and the world was eventually treated to off-color tales of stained dresses and unusual uses for cigars. Clinton eventually settled the case, which had little if any legal merit, for $850,000—a testament to the blackmail potential of allowing lawyers to delve into the sex lives of their adversaries. One need not be a fan of Bill Clinton's to recognize that permitting sexual harassment complaints to become fishing expeditions for embarrassing information about the intimate lives of defendants is an open invitation to litigants to attempt to satisfy personal grudges, to blackmail defendants, and to otherwise abuse the legal process. All this comes at the expense of the privacy interests that civilized people hold dear. Conservatives did the cause of liberty no favors by helping to open this particular Pandora's box.
* * *
Despite countervailing privacy, academic freedom, and religious freedom considerations, antidiscrimination concerns have made it nearly impossible for colleges and universities to avoid scrutiny and regulation by the federal government, regardless of whether the schools have ever been accused of discrimination. Federal law bans discrimination based on race, sex, and other criteria by schools that receive federal funds, and these laws are accompanied by regulations requiring universities to proactively keep detailed records regarding the race and sex of their applicants, students, and staff.
Several small colleges, including Grove City College, a Christian liberal arts school in Pennsylvania, have tried to preserve their independence from government regulation by refusing all federal funding. Grove City even declined to participate in federal student aid programs that required the college's direct involvement. But these efforts to retain independence were not enough to stave off federal bureaucrats. In 1977, the Office for Civil Rights of the Department of Health, Education, and Welfare demanded that Grove City sign an ''assurance of compliance'' with federal regulations promulgated under Title IX of the Education Amendments Act of 1972, which bans collegiate sex discrimination. HEW claimed that while Grove City declined direct federal funding, it received indirect funding by accepting tuition payments subsidized by a federal program, even though students applied for this program without any input from or participation by the school. Therefore, according to HEW, Grove City was bound by Title IX.
Grove City's then-president, Charles MacKenzie, refused to sign the assurance of compliance, but he did affirm that the school had ''no argument with the spirit or intent of Title IX's support of nondiscrimination.''37 The college had accepted women since its founding in 1876 and had never been accused of sex discrimination, but Mac-Kenzie believed that if Grove City agreed to comply with Title IX, the result would be increased costs to the college, greater expenses for its students, threats to the Christian nature of the college, mandated affirmative action preferences based on race and sex, and a general loss of independence. HEW at least partially validated MacKenzie's suspicions when the department later informed Grove City that colleges subject to Title IX must maintain ''detailed records of all student and employee applications, enrollments, academic records, personnel files, suspensions, hirings, firings, promotions, denial of promotions, etc.—all broken down by race, age, sex, and ethnic origin—and submit them upon demand to federal authorities.''38
The college eventually filed a federal lawsuit against HEW, claiming that it was not a federally funded institution subject to Title IX and that, in any event, it had a First Amendment academic freedom right to refuse to comply with the government's intrusive information demands in the absence of any allegation that the college had discriminated. The college won a victory from a liberal federal trial judge, who admonished the government that it should be spending its resources combating discrimination instead of harassing innocent Grove City College.39 However, the Supreme Court disagreed and held that Title IX applied to Grove City because its students received financial aid from the federal government.40 The Court added that even if the college had a First Amendment right to refuse information demands by the government, the right had no bearing on the case because compliance with Title IX regulations was not mandatory: Grove City could avoid Title IX's dictates by refusing federal funds. Of course, the school already had refused federal funds, but to completely free itself of Title IX's reach it would have to stop accepting federally subsidized tuition payments. Only then could it duck the government's demand for information.
The Court tried to limit the damage its holding inflicted on the institutional independence of colleges by ruling that only Grove City's financial aid office was subject to Title IX, because only that part of the university was a recipient of federal aid. The rest of the institution, however, could maintain its autonomy from the federal government. Congress would have none of this. Under the ''Civil Rights Restoration Act,''41 Congress ensured that if a university receives any federal funds at all, including tuition payments from students who receive federal aid, as in Grove City's case, all educational programs at that university are subject to Title IX.
Grove City and other institutions of higher learning could either allow the government to regulate all of their programs or turn down all government aid to themselves and their students. Only a few extraordinary institutions could choose the latter option and still survive in the competitive educational marketplace. Grove City turned out to be one of these few institutions, but only because the federal government neglected to enforce Title IX's requirements against it for a decade after passage of the Civil Rights Restoration Act (it took until 1997 for the federal government to promulgate regulations under the Act).42 By that time, the college had raised enough private money to replace federal aid to its students.43 Almost every other college and university, however, has agreed to comply with federal Title IX regulations in exchange for federal money— not necessarily because they don't mind Title IX's intrusive meddling, but because they simply cannot survive without the federal funds. And once a school falls under Title IX, the regulations virtually take over. They dictate everything from what sports colleges must offer,44 to whether a university must favor feminist scholars in tenure disputes,45 to whether campus speech codes (see Chapter 5) are necessary. The degree to which American universities have lost their autonomy is staggering.
* * *
In the 1960s heyday of the civil rights movement, earnest advocates of antidiscrimination laws would never have imagined that such laws would ultimately forbid advertising for a Republican roommate, prohibit women-only gyms, encourage employers to closely monitor and regulate their employees' interpersonal communications, allow plaintiffs in discrimination lawsuits to go rummaging through defendant's sex lives, and require nearly every university in the United States to ''keep detailed records of all student and employee applications, enrollments, academic records, personnel files, suspensions, hirings, firings, promotions, denial of promotions, etc.—all broken down by race, age, sex, and ethnic origin.'' Yet, antidiscrimination laws have now expanded to the point at which all of these rules exist in some or all jurisdictions in the United States. That this expansion has occurred to general acclaim by— indeed, often at the behest of—antidiscrimination activists highlights the extent to which their movement has changed and demonstrates how little regard they now have for civil liberties.
# 12. The ACLU and the Abandonment of
Civil Liberties
The American Civil Liberties Union has a well-earned public image as a stalwart defender of civil liberties, even when the rights in question conflict with extremely popular and seemingly important legislation. Unfortunately, however, the ACLU, bowing to intellectual trends in left-liberal circles, is increasingly willing to support the enforcement of antidiscrimination laws at the expense of civil liberties. Perhaps the most egregious example of this backsliding is the ACLU's remarkable opposition to the 1999 Religious Liberty Protection Act, described in Chapter 10.
The national ACLU's opposition to the RLPA is just one of many examples of the organization's elevating antidiscrimination principles above free exercise rights. Indeed, the ACLU sided against free exercise in a number of the cases we have already examined. In 1983, for example, the ACLU filed a Supreme Court amicus brief against Bob Jones University, arguing that it was appropriate for the school to be stripped of its tax exemption by the IRS because of the university's (purportedly) religion-based ban on interracial dating (see Chapter 9).1 A few years later, the ACLU sided with the Ohio Civil Rights Commission and against free exercise of religion in the Dayton Christian Schools case (see Chapter 9).
State ACLU chapters, which act independently of the national ACLU, have also actively supported antidiscrimination cases that are hostile to free exercise rights. The Vermont chapter of the ACLU sued Catholic publisher Regal Arts Press for refusing a project from the abortion rights group Catholics for Free Choice.2 The Southern California branch of the ACLU filed a brief on behalf of a plaintiff attempting to force the Christian Yellow Pages, a publication created by and for evangelicals, to accept ads from non–born again Christians.3 In the Hoffius case (see Chapter 10), the ACLU of Michigan filed a brief supporting plaintiffs suing a landlord for refusing to rent to cohabiting unmarried couples for religious reasons.4
Religious freedom is hardly the only civil libertarian concern the ACLU has downgraded in favor of antidiscrimination concerns. The national ACLU, for example, believes that plaintiffs should be able to win antidiscrimination lawsuits by showing ''disparate impact'' (demonstrating the discriminatory effects of the defendant's actions, even if there was no discriminatory intent). This places defendants in a very vulnerable position—even if they acted completely innocently, they can be found liable—but the ACLU seems unconcerned. As Cornell University professor Jeremy Rabkin points out, the ACLU is ''obsessed with due process, except when it comes to civil rights litigation, where they want no due process for the other side.''5 ''There's a certain kind of logic to it,'' Rabkin adds, ''They genuinely think you're in the path of social progress if you object. It's not a personal comment on you; it's that you can't make an omelet without breaking eggs.''
To take another example, despite the ACLU's commitment to academic freedom, the organization vigorously supported the Civil Rights Restoration Act of 1987, which was passed in part to force small private colleges like Grove City College (see Chapter 11) to kowtow to heavy-handed government regulation of their admissions and employment policies.6 Once again, the ACLU was more concerned with paving the road of social progress than with any civil liberties it bulldozed on the way.
The ACLU has also advocated the expansion of state public accommodations laws (see Chapter 7), despite the high costs to freedom of association and to pluralism. For example, the ACLU represented Victoria Isbister in the case that forced the Santa Cruz Boys' Club to admit girls, and it represented Sally Frank in the litigation against the Princeton eating clubs. Even in expressive association cases that directly implicate the First Amendment, the ACLU has tended to take the government's side against private groups asserting their constitutional rights.
The ACLU has been particularly eager to subject the Boy Scouts of America's membership policies to government regulation. Various ACLU chapters have sued the Scouts to force the organization to accept gays and atheists as members and scoutmasters—an effort that was finally rejected by the Supreme Court in 2000 (see Chapter
8). Had the ACLU won its battle against the Scouts, civil liberties would have suffered great damage. For example, the ACLU sued the Scouts on behalf of a gay scoutmaster applicant named Timothy Curran, even though Curran acknowledged that he planned to violate Scouts policy by using his position to promote respect for gays among his youthful charges.7 By that logic, antidiscrimination laws that ban religious discrimination could require gay organizations to hire fundamentalist Christians who want to use their positions to proselytize against homosexuality. It's hard to imagine the ACLU showing equal enthusiasm for that case.
The ACLU argues—albeit not persuasively—that the Scouts is not truly a private organization, because it benefits from indirect government subsidies, such as the free use of public school facilities.8 By this logic, organizations ranging from the PTA to voluntary student Bible study groups are also not private. In any event, it is unlikely that the ACLU's position would change if the Scouts cut its ties to the public sector. An ACLU attorney representing a renegade scout differentiated between clearly ideological groups like the Ku Klux Klan, which the ACLU believes have the right to exist autonomously and spread their messages, and the Scouts, which the ACLU views as a nonideological group focused on teaching certain skills. ''You're talking about four million kids tying knots,'' he told the Washington Post . ''It's not the same thing.''9 Yet many parents enroll their children in the Scouts not because they learn to tie knots, but because the Scouts inculcates traditional moral values. The use of the phrase ''he's no Boy Scout'' to describe a reprobate is an indication of how much the Scouts' identity is tied to its production of morally upright citizens. One would think that the ACLU would be able to recognize that the Scouts' refusal to recognize avowed homosexuals as morally upright individuals is an ideological decision tied to a particular conception of morality, even though that conception happens to be one the ACLU does not share.
The ACLU's commitment to using government power to thwart discrimination is even threatening the organization's commitment to ''pure speech''—expression untied to any act of discrimination against any individual. Several years ago, John Powell, who was then legal director of the ACLU, argued that universities had an obligation to suppress speech that made African American students feel uncomfortable. He stated bluntly that his ''concern is less with the strength of the First Amendment than with the wave of racial harassment that has swept the country.''10 Powell also told a reporter that the most important issues for the ACLU were abortion and civil rights.11
Pro–free speech forces within the national ACLU, led by its president and strong free speech advocate Nadine Strossen, eventually gained the upper hand, and Powell moved on to a position as a professor at the University of Minnesota School of Law. But even Strossen has been forced to make concessions to the antidiscrimination lobby within the organization, and to left-wing critics who accuse the ACLU of sacrificing important egalitarian goals for abstract civil libertarian principles. Strossen has announced, for example, that the ACLU is committed to ''eliminating racial discrimination from society at large.''12 Strossen does not explain how this utopian goal can be actively pursued without resort to coercive means that would violate the restraints on government power that the ACLU has traditionally supported.
Indeed, although the ACLU has generally supported free speech rights over antidiscrimination laws, its record is far from perfect and increasingly reveals schisms within the organization. On the plus side, the Virginia ACLU defended a college fraternity's right to put on an ''ugly women'' skit;13 the Kansas City ACLU affiliate waged a long fight for the KKK's right to use a public access television channel,14 and the Illinois ACLU filed a brief on behalf of Matthew Hale, a law school graduate who was denied admission to the Illinois bar because of his racist beliefs.15 The ACLU also filed successful lawsuits against state university speech codes in Wisconsin and Michigan (see Chapter 5), and was active in defending neighborhood activists from the federal Department of Housing and Urban Development's charges that their political activities constituted illegal housing discrimination16 (see Chapter 4). The New York branch of the ACLU supported the right of the Ancient Order of Hibernians to exclude a contingent from the Irish Lesbian and Gay Organization in its New York St. Patrick's Day Parade.17 The District of Columbia branch of the ACLU, meanwhile, filed a friend of the court brief asking that Georgetown University not be forced to recognize and fund gay student groups18 (see Chapter 9).
On the minus side, the national ACLU took the opposite side of the Georgetown case. The national ACLU also declined to defend the right of organizers of a Boston St. Patrick's Day parade to exclude a gay rights group, even though, as in the New York parade, gay marchers were welcome as individuals but not as members of an organized group seeking to use the parade as a forum for gay rights advocacy (see Chapter 8).19 The Virginia ACLU filed a complaint with the Virginia Fair Housing Office against neighborhood activists opposing a home for AIDS sufferers, in part because the activists ''had made public statements designed to foster opposition to the . . . home . . . based on irrational prejudice, fear and animus toward those who will reside there.''20 After an investigation, the Fair Housing Office determined that the activists' actions were protected by the First Amendment.21 In that case, government bureaucrats were more supportive of the First Amendment than was the Virginia ACLU!
Meanwhile, all three California ACLU affiliates have endorsed government-imposed university speech codes. And while the national ACLU has generally opposed using otherwise protected speech as evidence of discrimination in harassment cases, and the Florida ACLU opposed the broad injunction against ''sexually suggestive'' speech in the Robinson case (see Chapter 2),22 the national organization supported the Northern California ACLU's brief advocating a broad injunction against offensive speech at an Avis Rent A Car outlet at the San Francisco International Airport23 (see Chapter 2).
* * *
The ACLU's growing preference for social equality over individual freedom, although antithetical to its stated purpose, is not new. The ACLU's support of civil liberties has been threatened by the temptation of egalitarian political goals since the organization's earliest years. Roger Baldwin, who founded the ACLU in 1920 and led the organization for decades, came out of the radical, pacifist, prolabor, socialist left of the World War I years. Baldwin flirted with Stalinist communism throughout the late 1920s and most of the 1930s,24 and in 1934 wrote that he favored civil liberties only to ultimately aid workers in gaining power. ''If I aid the reactionaries to get free speech now and then,'' he wrote, ''if I go outside of the class struggle to fight against censorship, it is only because those liberties help to create a more hospitable atmosphere for working class liberties.''25 Early ACLU policies reflected Baldwin's socialist agenda. For example, despite its purported commitment to free speech, the organization supported the National Labor Relations Board when it penalized the Ford Motor Company for handing out anti-union literature. The ACLU's paradoxical position was that Ford could say what it wanted to in newspapers or in the chamber of commerce, but the government could restrict Ford's speech in its own factories.26
Soviet communism lost its luster among many American leftists, including Baldwin, when Stalin formed a pact with Hitler in 1939. The following year, the ACLU board of directors voted to expunge all communist influence from the organization. The board declared that it was ''inappropriate for any person to serve on the governing committees of the Union or its staff, who is a member of any political organization which supports totalitarian dictatorship in any country, or who by his public declarations indicates his support of such a principle.''27 For the next 30 years or so, before its drift toward becoming an adjunct of the civil rights movement, the ACLU was a staunch and consistent defender of the First Amendment.
The growth of an aggressive antidiscrimination agenda at the ACLU at the expense of traditional civil liberties concerns has been a long, gradual process. According to Ira Glasser, longtime executive director of the ACLU, as late as the mid-1960s the ''received wisdom'' at the ACLU was ''that there was a distinction between civil liberties and civil rights, and that while we supported each other, the division of labor was that we handled civil liberties cases, and the NAACP handled civil rights.''28 When civil rights and civil liberties objectives clashed, the ACLU sided with civil liberties. For example, the NAACP opposed jury trials for violators of court decrees in civil rights cases out of fear that Southern juries would not convict such violators, while the ACLU supported jury trials as a matter of principle.29
Cracks in the ACLU's defense of civil liberties began to appear in the late 1960s, when the ACLU—which was founded in large part to defend the rights of labor unions—supported African American community activists asserting ''local control'' of Brooklyn public schools against claims by the teachers' union that its members were being denied due process.30 In 1972, the ACLU endorsed ''anti-blockbusting statutes which prohibit false or deceptive statements concerning changes in the racial, religious, or national character of a neighborhood, and/or the effect of those changes, made with the intent for commercial gain, to promote the sale of property.''31 This policy was sufficiently vague that it arguably did not conflict with First Amendment norms. But three years later, the board of directors voted down an amendment opposing fair housing laws to the extent the laws violated ''the constitutional guarantee of free speech.''32
Also in 1972, the ACLU reversed its long-standing opposition to government-mandated racial quotas in employment and university admissions. Many ACLU board members seemed more concerned with how the ACLU would be perceived among liberals than with whether racial quotas, particularly when mandated by the government, were actually consistent with civil liberties. One board member, for example, argued that liberals think that ''to be against quotas is to be against the aspirations of blacks and other minorities to achieve equality in employment,'' and the ACLU could not afford to be perceived by liberals as being hostile to minorities.33
Over time, the ACLU's commitment to civil liberties has progressively weakened. In the early 1970s, the ACLU's membership rose from around 70,000 to almost 300,000. Many new members were attracted by the organization's opposition to the Vietnam War and its high-profile battles with President Nixon, but such members were not committed to the ACLU's broader civil libertarian agenda. However, the organization's defense of the KKK's right to march in Skokie, Illinois, in the late 1970s weeded out some of these fair-weather supporters and attracted some new free speech devotees. But George H. W. Bush's criticisms of the ACLU during the 1988 presidential campaign again attracted many liberal members not especially devoted to civil liberties.
To maintain its large membership base, the ACLU recruits new members by directing mass mailings to mailing lists rented from a broad range of liberal groups.34 The result of the shift of the ACLU to a mass membership organization is that it is gradually transforming itself from a civil libertarian organization into a liberal organization with an interest in civil liberties. This problem has been exacerbated by the growth within the ACLU of autonomous, liberal, special interest cliques known as ''projects.'' These projects have included an AIDS Project, a Capital Punishment Project, a Children's Rights Project, an Immigrants' Rights Project, a Lesbian and Gay Project, a National Prison Project, a Women's Rights Project, a Civil Liberties in the Workplace Project, a Privacy and Technology Project, and an Arts Censorship Project. These projects tend to distract the ACLU from its traditional civil libertarian agenda—freedom of expression, free exercise of religion, freedom of assembly and association, and freedom from discriminatory government policies. This loss of focus has led Harvard Law School professor Alan Dershowitz to waggishly suggest that ''perhaps the Civil Liberties Union needs a civil liberties project.''35
Dershowitz explains that for a time the ACLU chose board members for affirmative action reasons (because they were African American, female, or gay) in preference to white males with stronger demonstrated commitments to civil liberties. These affirmative action appointees naturally felt that their primary function was to represent within the ACLU the interests of their groups, rather than to preserve civil liberties generally.36 According to one study, in 1948 the ACLU's traditional civil liberties agenda constituted 94 percent of the ACLU's cases; by 1987 this was down to 45 percent.37 Mark Lambert, former legislative director of the Iowa ACLU, explains that ''the changes started when the ACLU got involved in the civil rights movement. That opened the door for all of these other issues that have nothing to do with the First Amendment.''38
* * *
Perhaps the ACLU's current drift away from defending civil liberties in favor of antidiscrimination and other concerns could be arrested if the ACLU adhered to a formal constitution—an immutable statement of civil libertarian principles to which the organization could refer any time its mandate became cloudy. Instead, the ACLU makes its policy democratically, by majority vote of the 83 members of the board of directors, which includes all chairs of state affiliates. Immediate political considerations inevitably weigh against timeless principles, and, as Dershowitz notes, political expediency wins out far too often.39
Current ACLU president Nadine Strossen is by all accounts a strong, consistent civil libertarian—she even wrote a book defending the legality of pornography from its feminist critics. But Strossen cannot single-handedly reinvent the organization as one devoted solely to civil liberties, given the strong foothold other constituencies have achieved within the ACLU. Strossen concedes that when anti-discrimination laws and civil liberties conflict, the ACLU uses an ad hoc balancing test, choosing ''between them in the context of particular facts, weighing the potency and applicability in each instance of the general values of liberty and equality.''40 As the left has generally turned its back on civil liberties in favor of antidiscrimi-nation concerns, the ACLU has become increasingly reluctant to defend civil liberties at the expense of antidiscrimination laws. The ACLU has even given an honorary position to Georgetown University law professor Mari Matsuda, who is perhaps the nation's leading academic advocate of government censorship of ''hate speech.''41
To some extent, the slack left by the ACLU has been taken up by right-of-center groups, including the Individual Rights Foundation and the Center for Individual Rights, and by the Foundation for Individual Rights in Education, an ideologically ecumenical organization that focuses on protecting civil liberties on university campuses. Each of these organizations has been responsible for several civil libertarian triumphs over antidiscrimination laws described in this book. However, none of these organizations currently has the ACLU's resources, prestige, or long-standing civil liberties credentials. Nor, perhaps more crucially, do these organizations have the ACLU's credibility with left-liberals, although FIRE, the newest of these groups, seems to be gradually earning the civil libertarian left's respect.
The ACLU is desperately needed as a left-liberal voice willing to defend civil liberties even when they conflict with antidiscrimination laws. In his history of the ACLU, Samuel Walker has argued that the ACLU is distinguished from other liberal organizations by its ''skepticism of government power and a willingness to challenge extensions of that power justified in the name of social betterment.''42 In the antidiscrimination context, however, the organization has increasingly become the voice of statism, not civil liberties. The ACLU is at a crossroads: Will it live up to its reputation as a skeptic of government power and return to a defense of the First Amendment and other rights against the state, or will it continue to evolve into just another liberal organization that supports the evisceration of constitutional liberties in the name of ''eliminating discrimination''?
# Conclusion
As argued throughout this book, antidiscrimination laws should not be exempt from the First Amendment's and other constitutional provisions' limits on government power. The contrary position, increasingly promoted in law reviews, the popular media, and legislatures throughout the United States, is that antidiscrimination considerations should almost always override any competing concerns, including First Amendment rights. The primary rationale for antidiscrimination law is no longer bringing previously marginalized groups into the economic mainstream. Rather, antidiscrimination laws are justified on the ground that the offense taken by people who face discrimination is an especially serious moral harm—so serious, in fact, that even antidiscrimination laws with no direct economic impact should be exempted from the Constitution's protection of civil liberties. For example, many distinguished academics argue that because of the offense taken by the listener, even the core First Amendment protection of freedom of speech must yield to ''hate speech'' laws targeting malicious (and sometimes merely inadvertently offensive) speech.1
Punishing expression because it creates offense has absurd and totalitarian implications. This has been amply demonstrated on university campuses that have prohibited their faculties and students from offending each other in politically incorrect ways. Sarah Lawrence College, for example, a small liberal arts school in Bronxville, New York, punished a student for ''inappropriate laughter'' after snorting when his roommate called another student a ''fag.'' Other colleges have banned inconsiderate jokes, speech that threatens a student's self-esteem, inappropriate eye contact (or lack thereof), and licking one's lips in a provocative manner.2
More generally, campus intolerance of any speech deemed offensive to designated victim groups has led to serious miscarriages of justice, as campus activists groups use speech codes to suppress dissent from politically correct orthodoxy.3 One egregious example of the precarious state of freedom of expression on campus is the blind eye that is turned to the theft and destruction of campus newspapers containing stories or advertisements deemed offensive—a modern campus analogy to book burnings (worse, in a way, because book burners at least often own the books they incinerate). This widespread practice is generally tolerated by university administrations even though it evinces a decidedly authoritarian intolerance for open debate. Private universities have the right to enact and enforce foolish policies. Campus authoritarianism, however, may very well provide a glimpse at the sort of antidiscrimination policies that will be pursued at all levels of American government if civil liberties protections are not maintained.
One of the easiest ways to understand the frightening implications of eroding civil liberties with antidiscrimination policies is to take a look at English-speaking democracies in which the sensitivity police have made more gains than they have in the United States. In 1990, for example, the Canadian Supreme Court upheld hate speech laws against a freedom of speech defense. James Keegstra, a public high school teacher, had consistently propagated Holocaust denial and anti-Semitic views to his public high school students, despite repeated warnings from his superiors to stop. Even in the United States, someone in Keegstra's position could be disciplined, even fired, for ignoring his obligations to stick to his assigned curriculum, and for using his classroom as a forum for promoting hatred (see Chapter 5). Instead of merely firing Keegstra, the Canadian government arrested him. Keegstra was convicted of the crime of ''willfully promoting hatred against an identifiable group,'' which carries a penalty of up to two years in jail. On appeal, the Canadian Supreme Court upheld the conviction, despite the Canadian Constitution's protection of freedom of expression. Criminalizing hate speech, the Court stated, was a ''reasonable'' restriction on expression, and it therefore passed constitutional muster.4
Two years later, the Canadian Supreme Court held that obscenity laws are unconstitutional to the extent they criminalize material purely on the basis of its sexual content. However, any ''degrading or dehumanizing'' depiction of sexual activity—including material that the First Amendment would clearly protect in the United States—was deprived of constitutional protection to protect women and other ''victimized'' groups from discrimination.5 The opinion drew heavily on language from a brief coauthored by the feminist censorship advocate Catharine MacKinnon.
The inevitable result of these decisions has been the gradual but significant growth of censorship and suppression of civil liberties across Canada. The Canadian Supreme Court, meanwhile, turned down an appeal by a Christian minister convicted of inciting hatred against Muslims. An Ontario appellate court had found that the minister did not intentionally incite hatred, but was properly convicted for being willfully blind to the effects of his actions. Robert Martin, a professor of constitutional law at the University of Western Ontario, commented that he increasingly thinks that ''Canada now is a totalitarian theocracy. I see this as a country ruled today by what I would describe as a secular state religion [of political correctness]. Anything that is regarded as heresy or blasphemy is not tolerated.''6
Indeed, it has apparently become illegal in Canada to advocate traditional Christian opposition to homosexual sex. For example, the Saskatchewan Human Rights Commission ordered the Saskatoon Star Phoenix newspaper and Hugh Owens to each pay $1,500 (approximately $1,000 U.S.) to each of three gay activists as damages for publication of an advertisement placed by Owens conveying the message that the Bible condemns homosexual acts.7 The ad conveyed this message by citing passages from the Bible, with an equal sign placed between the verse references and a drawing of two males holding hands overlaid with the universal nullification symbol—a red circle with a diagonal bar. In another incident, after Toronto print shop owner Scott Brockie refused on religious grounds to print letterhead for a gay activist group, the local human rights commission ordered him to pay the group $5,000 (approximately $3,400 U.S.), print the requested material, and apologize to the group's leaders. Brockie, who always accepted print jobs from individual gay customers, and even did pro bono work for a local AIDS group, is fighting the decision on religious freedom grounds.8 An appellate court has upheld the fine, though it did add that it would have ruled the other way had the material in question impinged more directly on Brockie's ''core beliefs,'' such as a publication advocating homosexual behavior.9 As of this writing, another appeal is pending, with Brockie already having spent $100,000 (approximately $68,000 U.S.) in legal fees.10
Any gains the gay rights movement has received from the crack-down on speech in Canada have been Pyrrhic, because as part of the Canadian government's suppression of obscene material, Canadian customs frequently target books with homosexual content. Customs seizures have included Pornography , a book by MacKinnon collaborator and prominent feminist Andrea Dworkin, and several serious novels. A gay organization had to spend $14,000 (approximately $9,600 U.S.) in legal fees to force customs agents to allow The Joy of Gay Sex into the country. Police raids searching for obscene materials have disproportionately targeted gay organizations and bookstores. Two gay activists at the University of Toronto were fined for selling Bad Attitude, a lesbian magazine with sadomasochistic content.11 According to the ACLU, ''more than half of all feminist bookstores in Canada have had materials confiscated or the sales of some materials suspended by the government.''12 The Canadians are, therefore, living proof of the way progressive censorship rules can come back to bite the constituencies that endorsed them.
One Canadian incident, at least, had a satisfactory ending. The Canadian teachers' accreditation authority attempted to refuse accreditation to graduates of Trinity Western University, a private Christian institution in British Columbia, claiming that they are too bigoted to become teachers because they agree as students to abide by traditional Christian teachings about sex by refraining from ''pre-marital sex, adultery, and homosexual behavior.''13 The Canadian Supreme Court ordered that TWU alumni be deemed eligible for accreditation. Nevertheless, civil liberties in Canada remain in jeopardy, and a great deal more censorship in Canada seems inevitable. British Columbia, for example, has an extremely broad hate speech law that prohibits the publication of any statement that ''indicates'' discrimination or that is ''likely'' to expose a person or group or class of persons to hatred or contempt.14 It seems highly probable the worst is yet to come from the Canadian thought police.
Things look equally bleak in Australia. In 1998, The Australian Financial Review published a short opinion column on the Middle East by journalist Tom Switzer. In his piece, Switzer wrote that ''the Palestinians cannot be trusted in the peace process.'' Switzer also noted that since 1993 the Palestinians had engaged in more than 300 terrorist attacks against innocent Israeli civilians, and so ''it would appear that the Palestinians remain vicious thugs.'' When the local Palestinian Authority representative filed a complaint with the New South Wales Anti-Discrimination Board, a tribunal found the publisher guilty of inciting hatred against Palestinians in violation of the racial vilification provisions of the Anti-Discrimination Act. This ruling was later overturned on appeal, but in a narrow decision that gave little comfort to free speech advocates. Similarly, an Australian radio talk-show host was fined $6,000 (approximately $3,600 U.S.) for making disparaging comments about Aborigines while criticizing a recent fair housing decision.15 Meanwhile, outspoken left-wing Australian columnist Phillip Adams was investigated for ''racial vilification'' of Americans after he wrote an anti-American column in the wake of the terrorist attacks of September 11, 2001.16 This led an American wag to write to The Sydney Morning Herald , ''The next time [Adams] bitches the US out, even if she deserves it, he ought to consider the fact that, here at least, he would be left alone. Sorry, Phil. Them's the breaks, I guess.''17 Beyond their poor showing with regard to protecting speech deemed offensive to protected classes, Australian courts have also banned Jewish and age-specific dating services as discriminatory.18
The ban on Jewish dating services was eventually overruled, following public ridicule. But the authoritarian logic of the antidiscrimi-nation movement is inexorable, and supports the original anti– dating service ruling. If, as antidiscrimination activists argue, all discrimination against members of identifiable groups should be punished, then group-specific dating services, which inherently exclude other groups, should be banned. Never mind individual preferences in choosing compatible life partners—antidiscrimination goals are more important. An article in the Harvard Law Review even argued that race-specific personal ads should be banned (no more SWF or SBM), though the author conceded that enabling legislation is unlikely, for now.19
In fact, when one honestly applies the logic of the antidiscrimination movement, it is difficult to fault the law review article's conclusion that personal ads should be forcibly shorn of discriminatory preferences. Modern antidiscrimination ideology suggests that those who refuse to date (and, therefore, to ultimately marry) members of certain groups should be punished. After all, discriminatory dating not only offends those excluded, but, given the difference in median wealth among groups, it is also a leading cause of societal inequality. Taken to their logical ends, antidiscrimination principles suggest that singles in the dating market should be prohibited from preferentially choosing African Americans or whites, the able-bodied or the disabled, Catholics or Protestants, or even same-sex or opposite-sex partners, lest offense and inequality result.
Once the folly of this reductio ad absurdum is conceded, it becomes clear that some limits must be placed on the scope of antidiscrimination law. The only question is where to draw the line, and the First Amendment is the obvious place to start. Mainstream liberal civil libertarians, as represented by the ACLU, agree that the pursuit of antidiscrimination objectives must be limited by constitutional restraints on government power. However, they often believe that the First Amendment should only prohibit laws that regulate pure speech, such as hate speech laws and hostile environment regulations. By contrast, they believe that laws banning discriminatory acts—such as public accommodations laws that prohibit private organizations from banning gays from membership or employment discrimination laws that prevent church schools from firing teachers who get pregnant out of wedlock—should be beyond the reach of First Amendment. Defenders of such laws draw analogies to trespass, copyright and trademark infringements, and other acts that often have expressive aspects, but that can nevertheless be banned without violating the First Amendment.
Adopting this reasoning would have dangerous consequences because in contrast to trespass and other torts that may also have expressive aspects, antidiscrimination law has no clear definitional boundaries. The concept of antidiscrimination is almost infinitely malleable. Almost any economic behavior, and much other behavior, can be defined as discrimination. Is a school admitting students based on SAT scores? The U.S. Department of Education has proposed that using such tests in college admissions be considered discrimination against groups that get below-average scores.20 Is a credit card company denying applications to the non-creditworthy? That's discrimination based on financial status. (Sound absurd? Tell it to the New Zealand Human Rights Commission, a body modeled after American civil rights enforcement agencies, which has determined that refusing service on credit to a customer who is unemployed, has no credit card, earns less than $10,000 [approximately $5,500 U.S.] a year, and does not own a home is illegal discrimination on the grounds of employment status.)21 Is an employer hiring only the best qualified candidates? Well, that might be discrimination against everyone else!
The obvious retort from exasperated antidiscrimination activists is that only laws prohibiting ''real'' discrimination should receive constitutional exemption. Legislatures and courts should not allow the definition of discrimination to expand beyond what is reasonable. The problem is, of course, that there is no consensus about what constitutes ''real'' discrimination, nor does there appear to be any principled definition that legislatures have followed. What counts as discrimination will always depend on which interest groups have the power to influence legislatures to define their particular goals as antidiscrimination goals, and not on any objective definition of discrimination.
Already, definitions of discrimination have proven extremely tractable. Some define discrimination as treating the alike unequally on the basis of invidious preferences, but, even outside of the controversial area of affirmative action preferences, antidiscrimination law does not always follow this definition. The Americans with Disabilities Act defines discrimination not only as the unwillingness to treat the disabled and nondisabled alike but also as the unwillingness to make ''reasonable accommodations'' for the disabled. In the first enforcement action under the ADA, the government ordered a company to pay for a full-time sign translator for a hearing-impaired student in its review class for the CPA exam, even though the interpreter cost far more than the student's tuition.22 Undertaking this measure was obviously not treating the hearing-impaired student just like everybody else.
Similarly, Title VII of the 1964 Civil Rights Act's ban on discrimination based on religion actually mandates preferential treatment for religious employees. The statute requires that employers accommodate the religious beliefs and observances of their employees, unless doing so would cause the employer ''undue hardship.'' Some hardship to the employer, which in economic terms constitutes a subsidy to the religious employee, is mandated where necessary.23 If failure to give members of a group a subsidy constitutes discrimination, then just about any law can be defined as an antidiscrimination statute that is potentially exempt from constitutional limitations. In short, exempting antidiscrimination laws from the civil liberties protections manifested in the Constitution might destroy those protections.
* * *
Although much legal writing focuses on court decisions and the resulting legal precedent, responsibility for preserving civil liberties rests first and foremost with the legislative branch of government. Courts can only correct the constitutional mistakes of legislatures. Legislatures can avoid these mistakes in the first instance, and, when appropriate, provide protections for civil liberties that go beyond minimum constitutional requirements. Moreover, courts are influenced by the political winds, and are more likely to protect civil liberties when they see concern for such liberties emanating from legislatures.
Conscientious legislators should halt the expansion of antidiscrimination law, and, wherever possible, reduce its scope. There should be a presumption of freedom of association, both because such a presumption protects freedom in and of itself—what is freedom if it does not include some protection of the right to choose one's associates?—and because the growth of antidiscrimination law creates inevitable conflicts with civil liberties and diminishes the autonomy of the institutions of civil society that serve as buffers between the individual and the state.
A good start for legislatures concerned with civil liberties would be to roll back public accommodations laws (see Chapter 7) so that they apply only to truly public commercial entities such as restaurants, theaters, hotels, and stores—not to private clubs and associations. Other legislative tasks beckon. Sexual harassment law should be modified to explicitly prohibit constitutionally protected speech from being used to support a hostile environment claim (see Chapter 2). In addition, state universities should be more closely monitored to ensure that they are protecting student and faculty freedom of expression (see Chapter 5).
Given the precarious state of constitutional free exercise rights in the federal courts (see Chapter 9), legislatures have become the primary guardians of religious freedom from the excesses of antidiscrimination laws. A few states lack religious exemptions to their antidiscrimination laws, an oversight that should be remedied. Many states are protecting free exercise through state laws that create a presumption that religious activity should not be impinged upon by legislation. These laws should not be altered to include special exemptions for antidiscrimination laws, as the ACLU and many other liberal groups have advocated.
The religious exemptions that do currently exist should be broadened to explicitly include such things as allowing small-scale religious landlords to refuse to rent to unmarried couples. Such landlords have little effect on the housing market, but forcing them to rent to cohabitating unmarried couples interferes with their perceived religious duties (see Chapter 10). Church schools, meanwhile, should be free to fire teachers who disobey church doctrine, such as by getting pregnant out of wedlock (see Chapter 9). Even if the legislature believes that this is morally repugnant discrimination, ''its direct effects are purely internal to the religious group; only those who chose to become part of the religious community . . . are governed by its rules.''24 It is unfair and illogical to allow a teacher to claim the benefits of teaching at a religious school while retaining the right to sue the school for upholding the rules of its religion.
Legislatures must also monitor courts and administrative agencies to ensure that they are not interpreting antidiscrimination laws more broadly than is warranted either by the language of the statutes or by legislative intent. Some legislatures have been notably quiescent in this regard, allowing antidiscrimination laws to be applied wildly beyond their intended scope. The New Jersey legislature, for example, has allowed the New Jersey Supreme Court to make a mockery of its public accommodations law. As described previously (see Chapter 7), that court has held that the state's public accommodations law applies to everything from Little League baseball to small private eating clubs to cat fanciers' clubs to the Boy Scouts of America. Several states have allowed their administrative agencies and courts to interpret fair housing laws banning discrimination on the basis of marital status to include protections for unmarried heterosexual couples, despite rampant discrimination by the states themselves against such couples in other contexts (see Chapter 10). By contrast, the Madison, Wisconsin, City Council properly stepped in when local courts and agencies decided that the city's fair housing law applied to the residents' choice of roommates, albeit too late to save Ann Hacklander-Ready from a financially ruinous lawsuit (see Chapter 11).
The task for courts, meanwhile, is simple—do not give antidiscrimination laws special status, either in statutory interpretation or in constitutional analysis. On the statutory interpretation front, courts have been prone to expansively interpret antidiscrimination laws, to the point at which the language of the statutes in question cannot bear the weight of the interpretations. Courts justify this bias on the grounds that they are acting consistent with the ''purpose'' of the laws, such as when the Supreme Court asserted that ''eradicating discrimination'' was a ''central statutory purpose'' of Title VII of the 1964 Civil Rights Act.25 Yet an examination of the statute reveals that its provisions are consistent with the purpose of reducing discrimination, not eradicating it. For example, Title VII applies only to employers with more than 15 employees, contains special damage caps and limitations, requires Equal Opportunity Employment Commission approval before private plaintiffs may file suit, and contains a religious exemption.26 If Congress's goal had been to completely eliminate all discrimination, these caveats would not have been included.
With regard to constitutional analysis, from the mid-1970s through the early 1990s, the Supreme Court consistently favored antidiscrimi-nation laws over constitutionally protected civil liberties. The Court often did so by tendentiously construing the facts of cases to allow it to evade conflicts between antidiscrimination laws and the First Amendment. Beyond that, the Court suggested that when such conflicts do arise, preventing discrimination is such a ''compelling interest'' that, for reasons never clearly explicated, antidiscrimination statutes trump constitutional rights. Fortunately, the Court has recently backed away from such slipshod reasoning. The results of Boy Scouts of America v. Dale (see Chapter 8) suggest that all nine justices have all but abandoned the ''compelling interest'' reasoning, and that five of the justices are now willing to directly confront conflicts between antidiscrimination laws and civil liberties. Thankfully, the Court seems on the verge of treating antidiscrimination laws as normal statutes, subject to standard rules of constitutional and statutory interpretation.
Ultimately, defending civil liberties from antidiscrimination laws is not only a job for courts and legislatures. Citizens, too, have a responsibility to organize and defend these civil liberties against the encroachment of laws promoting social equality. In some states, the ACLU is still dominated by traditional civil libertarians and these state chapters could become the nucleus for a movement to restore protection of civil liberties to the top of the national ACLU's agenda. A revitalized, consistently civil libertarian ACLU would lose some of its more authoritarian members, but it could lure back principled civil libertarians, such as author Nat Hentoff, who have quit in protest of the organization's neglect of, and sometimes outright opposition to, civil liberties. Such an ACLU would also attract libertarian-leaning conservatives who currently distrust the organization's creeping statism, giving the organization a broader and therefore more influential base.
Citizen support can also help other organizations fill at least part of the vacuum currently left by the ACLU's neglect of civil liberties. In particular, the Foundation for Individual Rights in Education, founded by attorney Harvey Silverglate and Professor Alan Kors of the University of Pennsylvania to protect civil liberties on college and university campuses, has the potential to become a broad-based, ecumenical, civil libertarian organization. The Center for Individual Rights has also done yeoman's work in defending civil liberties from antidiscrimination laws, and deserves support for its efforts.
Finally, if civil liberties are to be preserved, Americans will need to develop thicker skin. One price of living in a free society is having to tolerate those who intentionally or unintentionally offend you. The current trend, however, is to give offended parties a legal remedy, so long as the offense can be construed as ''discrimination.'' Yet the more the American legal system offers people remedies for offense, the more they are likely to feel offended. This is true for two reasons. First, as economists point out, when you subsidize something, you get more of it. Therefore, if the legal remedies of antidiscrimination law, particularly monetary remedies, subsidize feelings of outrage and insult, we will get more feelings of outrage and insult, a net social loss. Second, economists have also noted the psychological endowment effect, which, in effect, means that people tend to consider something they own to be more valuable than it would be if they did not own it. Similarly, once people are endowed with a right, they tend to overvalue it and react passionately when it is interfered with.
Unfortunately, Americans increasingly coddle and even reward the hypersensitive, perversely encouraging ever more hypersensitivity. In one notorious incident, a Washington, D.C., city official was forced to resign for using the word ''niggardly'' at a meeting because the word sounded like a racial epithet, even though it is actually a word of Scandinavian origin meaning ''miserly.''27 It should hardly be surprising, then, that people are suing for and winning damages when they are offended by colleagues at work, when they are excluded by private clubs or turned down as roommates, or when they are fired from church-run schools after reneging on promises to obey church doctrine. Nor should it be surprising that legislatures are increasingly succumbing to the temptation to expand the laws to protect from discrimination every group with a grievance, including the vertically challenged (short people, protected in San Francisco and Michigan), the body-pierced (among those protected in various jurisdictions, including Washington, D.C., that ban discrimination on the basis of personal appearance), recovering drug addicts (protected by the federal Americans with Disabilities Act and local equivalents), and the Hell's Angels (protected, along with other motorcycle gang members, in Minnesota).
Preserving the liberalism that defines the United States, and the civil liberties that go with it, requires Americans to show a certain level of virtue, including a phlegmatic tolerance of those who intentionally or unintentionally offend and sometimes—when civil liberties are implicated—even of those who blatantly discriminate. A society that undercuts civil liberties in pursuit of the ''equality'' offered by a statutory right to be free from all slights, protected by draconian antidiscrimination laws, will ultimately end up empty-handed with neither equality nor civil liberties to show for its efforts. The violation of civil liberties required to achieve this kind of equality will diminish constitutional restraints on the government, while the additional power garnered by the government, introduced for noble purposes, will end up in the hands of people who use it to promote their own interests.28 In these days of the Oprahization of public discourse, when even presidential candidates swear that they feel the public's pain, asking Americans to display a measure of fortitude in the face of offense and discrimination is asking for a lot. But in the end, it is a small price to pay for preserving civil liberties.
# Notes
Introduction
1. Susan Ferriss, ''Free Speech Advocates Find a Fight in Berkeley,'' San Francisco Examiner , July 22, 1994, p. A6.
2. Michelle Tauber, ''Dancer's Image: Charging Body-size Bias, Krissy Keefer Fights to Have Her 9-year-old Daughter Admitted to Ballet School,'' People , March 5, 2001, p. 79.
3. Al Knight, ''Webb Deaf to Free Speech,'' Denver Post , October 1, 2000.
4. Ganzy v. Allen Christian School , 995 F. Supp. 340, 348 (E.D.N.Y. 1998).
5. Carl S. Kaplan, ''In Library Filtering Case, an Unusual Ally,'' New York Times , October 2, 1998.
6. Kirsten Lagatree, ''Fighting Words: Efforts to Avoid Housing Discrimination Have Changed the Way Realty Ads Are Written,'' Los Angeles Times , February 12, 1995, p. 1.
7. The federal government has specified that using these phrases, along with other words and phrases that do not facially express a discriminatory preference, is permissible under federal law, but not all state and local agencies follow federal guidelines when enforcing their fair housing laws. See generally U.S. Department of Housing and Urban Development, Advertisements Under 804(c) of the Fair Housing Act, January 9, 1995, available at www.fairhousing.com/hud_resources/hudguid2.htm.
8. Stanley v. Lawson , 993 F. Supp. 1084 (N.D. Ohio 1997); Tom Puleo, ''Former Dairy Mart Manager in Ohio May Sue for Return of Her Job,'' Hartford Courant , January 13, 1992, p. A1.
9. Interview with Benjamin Bull, attorney for Ms. Stanley, January 11, 2002.
10. Senator Hubert H. Humphrey explained his support for the employment discrimination provisions of the federal 1964 Civil Rights Act this way: ''The Negro American is the principal victim of a vastly complex system of self-perpetuating practices, traditions, and processes that has denied him true parity in the national job market. He has consistently and effectively been kept from participating fully in the job opportunities developed by the American free enterprise system.'' Congressional Digest , March 1964, p. 76.
11. C. C. Burlingham, et al., Letter to the Editor, ''Faults Found in Ives Bill,'' New York Times , February 13, 1945. Not all civil libertarians shared this caution. Also in 1945, the ACLU called for federal and state fair employment practices laws, and restrictions on housing discrimination. Samuel Walker, In Defense of American Liberties: A History of the ACLU (New York: Oxford University Press, 1990), p. 168.
12. Hannah Arendt, ''Reflection on Little Rock,'' Dissent , No. 1, 1959, p. 45.
13. Elizabeth Jacoway and David R. Colburn, eds., Southern Businessmen and Desegregation (Baton Rouge: Louisiana State University Press, 1981); Robert Weems, Desegregating the Dollar: African-American Consumerism in the Twentieth Century (New York: New York University Press, 1998).
14. At common law, innkeepers and others who made a profession of public employment were prohibited from refusing, without good reason, to serve a customer. See Lane v. Cotton , 88 Eng. Rep. 1458, 1464–1465 (K.B. 1701) (Holt, C. J.).
15. At the time, hate speech laws were known as ''group libel'' laws. See Samuel Walker, Hate Speech: The History of an American Controversy (Lincoln, Neb.: University of Nebraska Press, 1994), pp. 85, 100.
16. See David E. Bernstein, Only One Place of Redress (Durham, N.C.: Duke University Press, 2001), p. 107.
17. Veto message of President George H. W. Bush, October 22, 1990.
18. See, for example, Terry Eastland, Ending Affirmative Action (New York: Basic Books, 1996), pp. 189–90.
19. Along with other, more minor incidents, for a period of several months during my childhood my family and I were subjected to anti-Semitic vandalism, taunts, and threats, a situation eventually resolved through police intervention. I mention this as a preemptive response to what I suspect is the inevitable ad hominem argument that my views result from insensitivity to the victims of discrimination, having never personally experienced it myself.
Chapter 1
1. George Kateb, ''The Value of Association,'' in Amy Gutmann, ed., Freedom of Association (Princeton, N.J.: Princeton University Press, 1998), p. 59.
2. Swanner v. Anchorage Equal Rights Comm'n , 874 P.2d 274 (Alaska 1994).
3. See, for example, Roberts v. United States Jaycees , 468 U.S. 609 (1984); Robinson v. Jacksonville Shipyards, Inc. , 760 F. Supp. 1486, 1542 (M.D. Fla. 1991).
4. See, for example, Akhil Reed Amar, ''The Case of The Missing Amendments: R.A.V. v. City of St. Paul ,'' Harvard Law Review 106 (1992): 124. Amar's argument is persuasively rebutted in Alex Kozinski and Eugene Volokh, ''A Penumbra Too Far,'' Harvard Law Review 106 (1993): 1639.
5. See, for example, Mari J. Matsuda, ''Public Response to Racist Speech: Considering the Victim's Story,'' in Mari J. Matsuda et al., Words That Wound: Critical Race Theory, Assaultive Speech, and the First Amendment (Colorado: Westview Press, 1993); Charles R. Lawrence III, ''If He Hollers Let Him Go: Regulating Racist Speech on Campus,'' in Mari J. Matsuda et al., Words That Wound , pp. 53, 61; Catharine MacKinnon, Only Words (Cambridge, Mass.: Harvard University Press, 1993), p. 71; Richard Delgado, ''Campus Antiracism Rules: Constitutional Narratives in Collision,'' Northwestern University Law Review 85 (1991): 343, 346; Mary Ellen Gale, ''Reimagining the First Amendment: Racist Speech and Equal Liberty,'' St. John's Law Review 65 (1991): 119, 162; Brian Owsley, ''Racist Speech and 'Reasonable People': A Proposal for a Tort Remedy,'' Columbia Human Rights Law Review 24 (1993): 323, 324. This argument has also infiltrated the civil libertarian community, and commands a great deal of support within the ACLU. See Dennis Cauchon, ''Civil Dispute within the ACLU,'' USA Today , March 31, 1993.
6. See Eugene Volokh, ''Freedom of Speech and the Constitutional Tension Method,'' University Chicago Roundtable 3 (1996): 223.
7. R.A.V. v. City of St. Paul , 505 U.S. 377 (1992).
8. Hurley v. Irish-American Gay, Lesbian & Bisexual Group of Boston , 515 U.S. 557 (1995).
9. Boy Scouts of America. v. Dale , 120 S. Ct. 2446 (2000).
10. Catharine MacKinnon, Only Words (Cambridge, Mass.: Harvard University Press, 1993), p. 107.
11. Mari J. Matsuda, ''Public Response to Racist Speech: Considering the Victim's Story,'' Michigan Law Review 87 (1989): 2320, 2359.
12. See, for example, Owen M. Fiss, Liberalism Divided: Freedom of Speech and the Many Uses of State Power (Boulder, Colo.: Westview Press, 1996), p. 115; Cass R. Sunstein, Democracy and the Problem of Free Speech (New York: The Free Press, 1993), pp. 186–95; Frank Michelman, ''Universities, Racist Speech and Democracy in America: An Essay for the ACLU,'' Harvard Civil Rights–Civil Liberties Law Review 27 (1992): 339, 351–52.
13. Thomas W. Hazlett, ''Looking for Results,'' Interview with Ronald Coase, Reason , January 1997, pp. 40, 45; see also R. H. Coase, ''The Economics of the First Amendment: The Market for Goods and the Market for Ideas,'' American Economic Review 64 (1974): 384; Aaron Director, ''The Parity of the Economic Market Place,'' Journal of Law and Economics 7 (1964): 1; Richard A. Epstein, ''Property, Speech, and the Politics of Distrust,'' University of Chicago Law Review 59 (1992): 41.
14. Fiss, see note 12; Morton Horwitz, ''The Constitution of Change: Legal Fundamentality without Fundamentalism,'' Harvard Law Review 107 (1993): 30; Frederick Schauer, ''Uncoupling Free Speech,'' Columbia Law Review 92 (1992): 1321; Sunstein, see note 12, p. 16; Cass Sunstein, ''Free Speech Now,'' University of Chicago Law Review 59 (1992): 255; see also Edwin Baker, ''Of Course, More Than Words,'' University of Chicago Law Review 61 (1994): 1181, 1187; Paul H. Brietzke, ''How and Why the Marketplace of Ideas Fails,'' Valparaiso University Law Review 31 (1997): 951.
15. Richard A. Epstein, Forbidden Grounds: The Case against Employment Discrimination Laws (Cambridge, Mass.: Harvard University Press, 1992).
16. See David F. McGowan and Ragesh K. Tangri, ''A Libertarian Critique of University Restrictions of Offensive Speech,'' California Law Review 79 (1991): 825; Michael S. Greve, ''Remote Control Tuning for Speech,'' Washington Times , November 9, 1996, p. D3.
17. American Booksellers Association v. Hudnut , 771 F.2d 323, 330 (7th Cir. 1985), aff'd mem. , 475 U.S. 1001 (1986).
18. Frederick Schauer, Free Speech: A Philosophical Inquiry (Cambridge, U.K.: Cambridge University Press, 1982), p. 86.
19. American Booksellers Association , 771 F.2d p. 330.
20. John O. McGinnis, ''Reviving Tocqueville's America: The Supreme Court's New Jurisprudence of Social Discovery,'' California Law Review 90 (2002): 485.
21. Ibid.
22. Stanley Fish, There's No Such Thing as Free Speech—And It's a Good Thing, Too (New York: Oxford University Press, 1994), p. 125.
23. McGinnis, see note 20.
24. Andrew Koppleman, Antidiscrimination Law and Social Equality (New Haven, Conn.: Yale University Press, 1996), p. 230.
25. See George Will, ''Reason One of the Few Things Not Included in Spending Bill,'' Seattle Post-Intelligencer , October 26, 1998, p. A9.
26. See Cal. Educ. Code § 943671(a) (West Supp. 1999); Cal. Educ. Code § 48950 (West 1993); Nat Hentoff, ''Magna Carta for Students,'' Washington Post , January 30, 1993, p. A21.
27. See Henry J. Hyde and George M. Fishman, ''The Collegiate Speech Protection Act of 1991: A Response to the New Intolerance in the Academy,'' Wayne Law Review 37 (1991): 1469. The bill stipulated that no university ''shall make or enforce any rule subjecting any student to disciplinary sanctions solely on the basis of conduct that is speech or other communication protected from governmental restriction by the first article of amendment to the Constitution of the United States.''
28. Transcript of discussion in Gary LaMarche, ed., Speech and Equality: Do We Really Have to Choose? (New York: New York University, 1996) p. 75; see also Michael S. Greve, ''The Libertarian Case for Speech Codes,'' Reason , July 1995, available at www.reason.com/9507/GREVEcol.jul.shtml.
29. Boy Scouts of America v. Dale , 120 S. Ct. 2446 (2000); see generally Henry Louis Gates Jr., ''Let Them Talk,'' New Republic , September 20 and 27, 1993, pp. 37, 42–43; Mari Matsuda, ''Public Response to Racist Speech: Considering the Victim's Story,'' Michigan Law Review 87 (1989): 2320, 2371.
30. Fish, see note 22.
31. Jack Bass, Unlikely Heroes (Tuscaloosa, Ala.: University of Alabama Press, 1986); David E. Bernstein, ''Lochner, Parity, and the Chinese Laundry Cases,'' William and Mary Law Review 41 (1999): 211.
32. James Weinstein, Hate Speech, Pornography, and the Radical Attack on Free Speech Doctrine (Boulder, Colo.: Westview Press, 1999), p. 5.
33. Fish, see note 22, p. 102.
34. Ibid., p. 109.
35. Weinstein, see note 32.
36. William Graham Sumner, ''Democracy and Plutocracy,'' in Robert Bannister, ed., On Liberty, Society, and Politics: The Essential Essays of William Graham Sumner (Indianapolis, Ind.: Liberty Press, 1985), p. 134.
Chapter 2
1. Mackenzie v. Miller Brewing Co. , 623 N.W.2d 739 (Wis. 2001).
2. Bernard J. Wolfson, ''Office Clinton Jokes Could Lead to Lawsuits,'' Orange County Register , October 5, 1998, p. A1.
3. Kathleen M. Moore, ''Workers' Talk Dwells on Case, But Discreetly Sensitive Issue at Water Cooler,'' Bergen Record , February 2, 1998, p. A6.
4. Yochi Dreazen, ''Talking Dirty: In Our Brazen Era of Monica and Viagra, What Subjects Should Be Off-limits at Work?'' Florida Times Union , August 16, 1998, p. F1.
5. The classic text is Catharine MacKinnon, Sexual Harassment of Working Women (New Haven, Conn.: Yale University Press, 1979).
6. Harris v. Forklift Systems, Inc. , 510 US 17, 21 (1993), quoting Meritor Savings Bank , FSB v. Vinson , 477 U.S. 57, 65, 67 (1986).
7. See generally Jonathan Rauch, ''Offices and Gentlemen,'' New Republic , June 23, 1997, p. 22; Eugene Volokh, ''What Speech Does Hostile Work Environment Harassment Law Restrict?'' Georgia Law Review 85 (1997): 627, 637; Jeffrey Rosen, ''In Defense of Gender-Blindness,'' New Republic , June 29, 1998, p. 25; Kingsley R. Browne, ''Title VII as Censorship: Hostile-Environment Harassment and the First Amendment,'' Ohio State Law Journal 52 (1991): 481, 539.
8. Oncale v. Sundowner Offshore Services, Inc. , 523 U.S. 75 (1998).
9. See Davis v. Monroe County Bd. of Educ. , 526 U.S. 629, 665, 682 (1999) (Kennedy, J., dissenting).
10. See, for example, Cardin v. Via Tropical Fruits, Inc. , 1993 U.S. Dist. LEXIS 16302, *24–25 and n. 4 (S.D Fla.).
11. See, for example, Baskerville v. Culligan Int'l Co. , 50 F.3d 428, 430 (7th Cir. 1995) (reversing jury award of $25,000); Black v. Zaring Homes, Inc., 104 F.3d 822, 823 (6th Cir. 1997) (reversing jury award of $250,000).
12. U.S. Department of Labor, ''Sexual Harassment: Know Your Rights'' (1994), discussed in Eugene Volokh, ''What Speech Does Hostile Work Environment Harassment Law Restrict?'' Georgia Law Review 85 (1997): 627, 633.
13. Olivant v. Department of Environmental Protection , 1999 WL 430770 (N.J. Admin. April 12).
14. Brown Transportation Corp. v. Commonwealth , 578 A.2d 555, 562 (Pa. Commw. 1990).
15. Pakizegi v. First National Bank , 831 F. Supp. 901, 908–909 (D. Mass. 1993).
16. Eugene Volokh, ''Thinking Ahead about Freedom of Speech and Hostile Work Environment Harassment,'' Berkeley Journal Employment and Labor Law 17 (1996): 305.
17. Ibid., pp. 307–08 (discussing EEOC v. Hyster , No. 88-930-DA [D. Or. filed August 15, 1988]).
18. For details, see Reid v. O'Leary , 1996 U.S. Dist. LEXIS 10627 (D.D.C. July 15, 1996).
19. Ibid.
20. Interview with Gary Simpson, attorney for the plaintiff, July 19, 2001.
21. Steve Miletich, ''Gay Man Withdraws His Complaint against Company,'' Seattle Post-Intelligencer , July 7, 1994, p. B2; Steve Miletich, ''Gay Man Claims Hostility at Work,'' Seattle Post-Intelligencer , June 21, 1994, p. B4; John Carlson, ''When Political Correctness Becomes Political Coercion,'' Seattle Times , June 21, 1994, p. B4.
22. Robinson v. Jacksonville Shipyards, Inc. , 760 F. Supp. 1486 (M.D. Fla. 1991).
23. Ibid., pp. 1492, 1502.
24. Ibid., p. 1535.
25. NLRB v. Local Union No. 3 , 828 F.2d 936 (2d Cir. 1987); Hospital & Serv. Employees Union , Local 399 v. NLRB , 743 F.2d 1417, 1428 n.8 (9th Cir. 1984).
26. NLRB v. Gissel Packing Co. , 395 U.S. 575, 617, 618 (1969); NLRB v. Douglas Div. , 570 F.2d 742, 747 (8th Cir. 1978); Sheet Metal Workers Int'l Ass'n v. Burlington N.R.R. Co. , 736 F.2d 1250, 1253 (8th Cir. 1984); Dow Chem. Co. v. NLRB , 660 F.2d 637, 644–45 (5th Cir. Unit A November 1981).
27. See, for example, Pacific Gas & Elec. Co. v. Public Util. Comm'n , 475 U.S. 1, 20 (1986); Consolidated Edison Co. v. Public Serv. Comm'n , 447 U.S. 530, 536 (1980).
28. Madsen v. Women's Health Center, Inc. , 512 U.S. 753 (1994) (discussing the right to protest outside an abortion clinic).
29. Cohen v. California , 403 U.S. 15, 21 (1971).
30. See, for example, Jenson v. Eveleth Taconite Company , 824 F. Supp. 847 (D. Minn. 1993); Berman v. Washington Times Corp. , 1994 WL 750274, *5 n.4 (D.D.C.); Baty v. Willamette Industries, Inc. , 985 F. Supp. 987 (D. Kan. 1997).
31. Bowman v. Heller , 1993 WL 761159, *1 (Mass. Super. Ct.) (unpublished disposition).
32. Hustler Magazine v. Falwell , 485 U.S. 46 (1988).
33. Aguilar v. Avis Rent A Car System, Inc. , 87 Cal. Rptr. 2d 132 (1999).
34. Avis Rent A Car System v. Aguilar , 120 S. Ct. 2029 (2000) (Thomas, J., dissenting from denial of cert.).
35. Davis v. Montrose County Bd. of Educ. , 119 S. Ct. 1661, 1682, 1690 (1999) (Kennedy, J., dissenting).
36. See, for example, DeAngelis v. El Paso Municipal Police Officers Ass'n , 51 F.3d 591, 596–97 (5th Cir. 1995).
37. Johnson v. County of Los Angeles Fire Dept. , 865 F. Supp. 1430, 1438, 1442 (C.D. Cal. 1994); Mauro v. Arpaio , 147 F.3d 1137, 1141 (9th Cir. 1998).
38. ''Anchorage Tells Fire Halls to Eliminate Risqué Magazines,'' Juneau Empire Online , February 18, 2002, available at www.juneauempire.com/stories/021802/sta_stbriefs.shtml.
39. See Eugene Volokh, ''Squeamish Librarians,'' www.reason.com/hod/ ev060401.html.
Chapter 3
1. This chapter's discussion of Keefer's lawsuit relies on Joan Acocella, ''A Ballerina Body,'' The New Yorker , March 5, 2001, p. 38; Paul Ben-Itzak, ''Keefer's Crazy Crusade: A Wounded Ballet Mom Strikes Out Blindly,'' available at www.danceinsider.com/f1213_1.html; Janice Berman, ''The Rejection Seat: Fredrika Near Keefer's Rejection from the San Francisco Ballet Company,'' Dance Magazine , March 1, 2001, p. 14; Edward Epstein, ''Girl Fights for a Chance to Dance: Complaint Filed over School's Body-type Rules,'' San Francisco Chronicle , December 7, 2000; Welton Jones, ''It's Unnatural Selection, but That's Ballet,'' San Diego Union-Tribune , January 28, 2001, p. F4; Joan Ryan, ''I Asked My Mother What Will I Be ...,'' San Diego Union-Tribune , December 24, 2000, p. G4; Michelle Tauber, ''Dancer's Image: Charging Body-size Bias, Krissy Keefer Fights to Have Her 9-year-old Daughter Admitted to Ballet School,'' People , March 5, 2001, p. 79; Joanna Weiss, ''Fight for Future of Dance Ideal Is Taking Shape: S. F. Ballet Battle Furthers Clash between Politics, Art,'' Boston Globe , January 16, 2001, p. E1; Good Morning America , Transcript, December 21, 2000.
2. Beth Gardiner, ''Stretching Title IX: N.Y. Group Seeks to Use Anti-bias Law to Get More Women's Artwork in Museums,'' Associated Press , www.s-t.com/daily/03-98/03-08-98/e04li202.htm; Beth Piskora, ''Artists Paint Bleak Picture of Museums,'' New York Post , January 27, 1998, p. 23; Tunku Varadarajan, ''Art World in Brush with US Women over Bias,'' Times of London , January 28, 1998.
3. Beth Gardiner, ''Women Artists Seeking the Benefits of Title IX; Group Argues Museums Should Put Them On Par with Female Athletes,'' Chicago Tribune , March 26, 1998, p. C8.
4. Wis. Stat. §§ 111.32 (13).
5. Montana Human Rights Commission, ''Model Equal Employment Opportunity Policy: A Guide for Employers'' (no date).
6. Nat Hentoff, ''Sexual Harassment by Francisco Goya,'' Washington Post , December 27, 1991, p. A21.
7. See Eugene Volokh, ''Thinking Ahead about Freedom of Speech and Hostile Work Environment Harassment,'' Berkeley Journal Employment and Labor Law 17 (1996): 305.
8. Ibid.
9. Jonathan Rauch, ''Offices and Gentlemen,'' New Republic , June 23, 1997, p. 22.
10. Henderson v. City of Murfreesboro , Tennessee, 960 F. Supp. 1292 (M.D. Tenn. 1997).
11. See Dave Kopel, ''Naked Justice,'' National Review Online , February 25, 2002.
12. Francis X. Gilpin, ''Unsettling Settlement,'' Tampa Bay Weekly Planet , July 26, 2001, available at http://www.weeklyplanet.com/2001-07-26/notebook.html; Kevin Graham, ''Art or Porn: USF Opts Not to Fight,'' St. Petersburg Times , July 4, 2001, p. A1; Joe Humphrey, ''Students Outraged by Removal of TA Who Showed Sex Photo to Student,'' USF Oracle , November 5, 1999, available at www.studentadvantage.lycos.com/lycos/article/0,4683,c4-i7-t41-a17728,00.html; www.oracle.usf.edu/archive/199911/19991108/.
13. Stanley v. Georgia , 394 U.S. 557, 566 (1969).
14. Robinson v. Jacksonville Shipyards, Inc. , 760 F. Supp. 1486, 1542 (M.D. Fla. 1991).
15. 2000 WL 272263, pp. *1, *3, *5-*7 (6th Cir. March 14).
16. David Patch, ''Panel Backs Deaf Patron's Claim against Club,'' Toledo Blade , March 6, 2001.
17. Federal law states that ''it shall not be an unlawful employment practice for an employer to hire and employ employees ..., on the basis of his religion, sex, or national origin . . . where religion, sex, or national origin is a bona fide occupational qualification reasonably necessary to the normal operation of that particular business.'' 42 U.S.C. § 2000e-2(e)(1).
18. Ruth Shalit, ''Melrose Case,'' New Republic , January 26, 1998.
19. EEOC v. Mike Fink Corp. , M.D. Tenn., No. 3-96-0790, consent decree approved 9/12/00; Stacey Hartmann, ''Male-Server Policy Loses Out in Court,'' The Tennessean , March 16, 2000.
20. Joe D. Jones, ''Have 'Equal' Employment Laws Gone Too Far?'' Mississippi Business Journal , April 3, 2000, available at www.msbusiness.com/archives/22v14n/ Editorial/9904.php.
21. Sambo's Restaurants, Inc. v. City of Ann Arbor , 663 F.2d 686 (6th Cir. 1981); but see Urban League v. Sambo's of Rhode Island (Rhode Island Commission for Human Rights, 1981), holding that prohibiting the use of the name ''Sambo's'' did not violate the First Amendment.
22. ''Hooters Agrees to Hire Men in Support Roles, but It Will Still Hire Scantily Clad Women,'' Baltimore Sun , October 1, 1997, p. 3C.
23. ''Hooters Moms Sue over Policy,'' Baton Rouge Sunday Advocate , December 17, 2000, p. I7.
24. Ralph Reiland, ''Selecting Targets,'' The Free Market , January 1998.
25. See 29 Code of Federal Regulations § 1604.2(2) (1997) (allowing sex to be considered in the hiring of actors).
26. Wilson v. Southwest Airlines Co. , 517 F. Supp. 292 (D.C. Tex. 1981).
27. Reiland, see note 24.
28. Ibid.
Chapter 4
1. See Heather MacDonald, ''Free Housing Yes, Free Speech No,'' Wall Street Journal , August 8, 1994, p. A12.
2. Debra Caldon, ''On Equity and Affordable Housing,'' Flatland News , February 1993, p. 2.
3. Fair Housing Issues: Hearings before the Subcommittees on Civil and Constitutional Rights of the House Comm. on the Judiciary, 103d Cong., 1st Sess. (1994).
4. White v. Lee , 227 F.3d 1214 (9th Cir. 2000).
5. Ibid.
6. See, for example, Sigfredo A. Cabrera, ''HUD Continues Its Assault on Free Speech,'' Wall Street Journal , June 7, 1995, p. A15; Lou Chapman, ''Free Speech an Issue in Suit against Ridgmar Group,'' Fort Worth Star-Telegram , November 19, 1994, p. 27; Editorial, ''Intimidating Political Protest,'' Washington Post , August 22, 1994, p. A16; Edmund Mahony, ''Judge Dismisses Suit against Neighborhood,'' Hartford Courant , February 12, 1995, p. B1; Joyce Price, ''Federal Government Sues Five for Fighting Group Home: Act of Getting a Restraining Order Called Discriminatory,'' Washington Times , May 31, 1995, p. A3; Joyce Price, ''HUD Sues Texans in Home-Sale Battle—Citizens Fought to Stop Deal in 1991,'' Washington Times , November 19, 1994, p. A4; Brian J. Taylor, ''No Retreat in Feds' War on Free Speech,'' Sacramento Bee , November 19, 1994, p. F1.
7. Mahony, see note 6, p. B1.
8. See, for example, Editorial, ''Free the Berkeley Three: HUD vs. Free Speech,'' Virginian-Pilot , August 18, 1994, p. A20; Editorial, ''No More Speech Police,'' Boston Herald , September 3, 1994, p. 12; Editorial, ''Intimidating Political Protest,'' see note 6; MacDonald, see note 1; Justin Raimondo, ''The Hidden Agenda of Radical Egalitarians,'' San Francisco Examiner , August 17, 1994, p. A17.
9. Memorandum from Roberta Achtenberg, Assistant Secretary for Fair Housing & Equal Opportunity, U.S. Department of Housing & Urban Development (September 2, 1994) (on file with author).
10. See Roberta Achtenberg, ''Sometimes on a Tightrope at HUD,'' Washington Post , August 22, 1994, p. A17.
11. See Editorial, ''Government by Intimidation,'' Washington Post , February 26, 1996, p. A18.
12. Achtenberg, see note 10, p. A17.
13. Deval L. Patrick, Letter to the Editor, Washington Post , February 19, 1996, p. A24.
14. United States v. Wagner , Civ. No. 3:94-CV-2540-H, 1995 WL 841924, p. *5 (N.D. Tex. December 11, 1995).
15. White v. Julian , 227 F.3d 1214 (9th Cir. 2000).
16. Salisbury House, Inc. v. McDermott , No. CIV.A.96-CV-6486, 1998 WL 195693, p. *10 (E.D. Pa. Mar. 24, 1998); Michigan Prot. & Advocacy Serv., Inc. v. Babin , 799 F. Supp. 695 (E.D. Mich. 1994).
17. Quoted in Jeremy Rabkin, ''Developers Nail Free Speech,'' American Spectator , December 2000, p. 46.
18. Robyn E. Blumner, ''Political Correctness Threatens to Swallow Free Speech,'' St. Petersburg Times , September 19, 1999; Eugene Volokh, ''Is Criticizing Affirmative Action Illegal in Chicago?'' Free Speech & Election Law News , Summer 1999, p. 10.
19. Volokh, see note 18.
20. For Deming's account, see David Deming, ''Free-Speech Hypocrisy at the University of Oklahoma,'' Front Page Magazine , January 25, 2001.
21. Lucia Perri, Letter to the Editor, The Oklahoma Gazette , available at Oklahoma Women Organizing for Change Web site, www.members.aol.com/okamwoc/deminged.html.
22. ''Bats in the Belltower: Sexual Harassment by Analogy,'' Clarion , Vol. 4, March/ April 2000, available at the Pope Center for Higher Education Web site, www.popecenter.org/clarion/2000/mar-apr/bats.html.
23. Ed Godfrey, ''Professor's Letter Draws Ire,'' February 26, 2000, available at Oklahoma Women Organizing for Change Web site, http://members.aol.com/okamwoc/ddeming.html.
24. Ibid.
25. ''Bats in the Belltower,'' see note 22.
26. Deming, see note 20.
27. See Brown v. Board of Trustees of Boston University , 891 F2d 337, 350–51 (1st Cir. 1989); J. Edward Pawlick, Freedom Will Conquer Racism and Sexism (Wellesley, Mass.: Mustard Seeds Incorporated, 1998), pp. 221–23.
28. Ibid., p. 227.
29. Wirtz v. Basic, Inc. , 786, 787 (D. Nev. 1966).
30. Sweeney v. Keene State College , 569 F.2d 169, 179 (1st Cir. 1978).
31. Walter Olson, The Excuse Factory (New York: Free Press, 1997), p. 256.
32. See, for example, Federal Rules of Evidence 403.
33. The cartoon can be viewed at www.detnews.com/AAEC/summer99/kirk/kirk.html.
34. ''St. Paul Human Rights Director Files Complaint over Pioneer Press Cartoon,'' Pioneer Press , June 10, 1999.
35. V. Cullum Rogers, ''Kirk Anderson Cartoon Stirs Tempest in St. Paul,'' www.detnews.com/AAEC/summer99/kirk/kirk.html.
Chapter 5
1. For details, see Doe v. University of Michigan , 721 F. Supp. 852, 867 (E.D. Mich. 1989).
2. Ibid.
3. UWM Post, Inc. v. Board of Regents of the University of Wisconsin System , 774 F. Supp. 1163, 1181 (E.D. Wis. 1991) (striking down the university's rule against directing discriminatory epithets at individuals as unduly vague and overbroad); Doe v. University of Michigan , 721 F. Supp. 852, 867 (E.D. Mich. 1989) (striking down speech limitation as overbroad).
4. Dambrot v. Central Michigan University , 55 F.3d 1177 (6th Cir. 1995).
5. R.A.V. v. City of St. Paul , 505 U.S. 377 (1992).
6. Ibid., pp. 383–84.
7. Some legal scholars argue that the Supreme Court's decision the following year in Wisconsin v. Mitchell , upholding a law providing sentence enhancements for hate crimes, essentially overruled R.A.V. by allowing extra punishment on the basis of the ideological motivation of the perpetrator. David E. Rovella, ''Critics See Threat to Free Speech as States Stiffen Penalties on Bias-motivated Crime,'' National Law Journal , August 29, 1994, p. A1. The cases are clearly distinguishable, however, because R.A.V. was charged under a law banning speech, while the defendant in Mitchell was charged with criminal conduct. That the Court itself recognized this distinction is evidenced by the fact that all of the justices who joined the majority opinion in R.A.V. also joined the unanimous opinion in Mitchell.
8. See Dambrot v. Central Michigan University , 55 F.3d 1177 (6th Cir. 1995).
9. For an account of the incident, see Eugene Volokh, ''Freedom of Speech in Cyberspace from the Listener's Perspective: Private Speech Restrictions, Libel, State Action, Harassment, and Sex,'' University of Chicago Legal Forum (1996): 377, 419, and n. 148.
10. The University of Maryland College Park's sexual harassment rules are described in www.inform.umd.edu/EdRes/Topic/WomensStudies/GenderIssues/SexualHarassment/UMDManual/handout1.
11. Conciliation Agreement between the U.S. Department of Labor, Office of Federal Contract Compliance Programs, and The Ohio State University, September 14, 1992.
12. See Nat Hentoff, ''Sombrero Scrap,'' Washington Post , January 1, 1994, p. A23.
13. The brochure's contents may be found at www.nas.org/affiliates/westvirginia/wvu98codes.htm.
14. See www.nas.org/affiliates/westvirginia/wvu98.html.
15. Ibid.
16. Richard Bernstein, Dictatorship of Virtue: Multiculturalism and the Battle for America's Future (New York: Alfred A. Knopf, 1994), p. 209; Alan Charles Kors and Harvey A. Silverglate, The Shadow University: The Betrayal of Liberty on America's Campuses (New York: The Free Press, 1998), pp. 180–81.
17. Doug Grow, ''College Republicans Can Thank 'U' Official for Their Sudden Fame,'' Minneapolis Star Tribune , September 19, 1993, p. 3B.
18. Maura Lerner, '' 'U' Backs off Ban on Literature Making Fun of Clinton,'' Minneapolis Star Tribune , September 22, 1993, p. 1B.
19. Maura Lerner, ''Did You Hear the One About . . . The Republican Student and the 'U' President?'' Minneapolis Star Tribune , April 27, 1994, p. 1A.
20. ''Free Speech or Sexual Harassment? Student Suspended for Material in Dorm Newsletter,'' Student Press Law Center Report , Fall 1997, p. 28; www.aclu-sc.org/news/openforum/of712.pdf.
21. ''Kvederis Lawsuit against CMC Settled on Confidential Terms,'' www.cmcstudent.com/kvederis.html.
22. Mary Becker, ''The Legitimacy of Judicial Review in Speech Cases,'' in Laura Lederer and Richard Delgado, eds., The Price We Pay: The Case against Racist Speech, Hate Propaganda, and Pornography (New York: Hill and Wang, 1995), pp. 208, 211.
23. See, for example, Hardy v. Jefferson Community College , 260 F.3d 671 (6th Cir. 2001).
24. See, for example, Dambrot v. Central Michigan University , 55 F.3d 1177 (6th Cir. 1995) (''An instructor's choice of teaching methods does not rise to the level of protected expression''). The Supreme Court has explicitly held that in public schools below college level, regulation of curriculum-related speech does not raise First Amendment concerns if it is ''reasonably related to legitimate pedagogical concerns.'' Hazelwood School Dist. v. Kuhlmeier , 484 U.S. 260, 268–69 (1988).
25. See, for example, Martin v. Parrish , 805 F.2d 583, 586 (5th Cir. 1986).
26. See, for example, Cohen v. San Bernardino Valley College , 92 F.3d 968 (9th Cir. 1996) (holding that a college's sexual harassment policy was too vague to be used against a professor who used explicit language and provocative examples in class); Dambrot v. Central Michigan University , 55 F.3d 1177 (6th Cir. 1995) (finding that a policy that vests authority in university administration to determine ex post what speech constitutes harassment is unconstitutional).
27. Silva v. University of New Hampshire , 888 F. Supp. 293 (D.N.H. 1994).
28. Ibid.
29. Center for Individual Rights, Docket Report, First Quarter, 1995. For a case in which a court held that a public university had the authority to sanction a professor for using obscene language after warning him that it was against university policy, see Bonnell v. Lorenzo , 241 F.3d 800 (6th Cir. 2001).
30. Kors and Silverglate, pp. 120–21.
31. Linda Chavez, ''Boston College Fires Feminist Prof for Excluding Men,'' Austin Review , September 15, 1999.
32. Kors and Silverglate, see note 16, p. 121.
33. Vicki Schultz, ''Reconceptualizing Sexual Harassment,'' Yale Law Journal 107 (1998): 1683, 1793.
34. Michael Krauss, ''When You Face the PC Inquisition,'' Washington Times , January 27, 1995, p. A27.
35. The text of the remarks can be found at www.print.indymedia.org/front.php3?article_id'923.
36. ''Police Get Hate-crimes Complaint against Thobani,'' National Post , October 10, 2001, p. A4.
37. Albert J. Nock, ''The Criminal State,'' American Mercury , March 1939.
Chapter 6
1. West Virginia v. Barnette , 319 U.S. 624 (1943).
2. Title VI Enforcement Agreement between the United States Department of Housing and Urban Development and Bonnie L. Jouhari/Pilar D. Horton and Roy E. Frankhouser, No. 03-98-0797-8 (August 28, 1998), available at www.splcenter.org/cgi-bin/oframe.pl?dirname'/egalaction&pagename'la1.html&anchorname'centerhud.
3. The text of the settlement may be found at www.splcenter.org/cgi-bin/frame.pl?dirname'/enterinfo&pagename'lci-15.html.
4. Michael Kelly, ''Cuomo's Thought Police,'' Washington Post , May 17, 2000.
5. Ibid.
6. Dennis Roddy, ''Deal Making Nazi a Martyr,'' Pittsburgh Post-Gazette , May 20, 2000.
7. See Editorial, ''Intimidating Political Protest,'' Washington Post , August 22, 1994, p. A16.
8. Torres v. Union Market , Mass. Comm'n against Disc., no. 94-SEM-0066 (December 7, 1998), reported in The Quincy Patriot Ledger , December 11, 1998, p. 6.
9. ''Other Ideas,'' Las Vegas Review Journal , April 1, 2000.
10. Jeff Jacoby, ''Banned in Boston,'' Boston Globe , April 6, 2000.
11. Eugene Volokh, ''Freedom of Speech, Cyberspace, Harassment Law, and the Clinton Administration,'' Law & Contemporary Problems 63 (2000): 299.
12. 24 C.F.R. 109.30a.
13. See, for example, Ragin v. New York Times Co. , 923 F.2d 995, 1000 (2d Cir. 1991).
14. Ragin v. Harry Macklowe Real Estate Co. , 801 F. Supp. 1213 (S.D.N.Y. 1992), aff'd in part and rev'd in part, 6 F.3d 898 (2d Cir. 1993).
15. Such damages were awarded in Spann v. Colonial Village, Inc. , 899 F.2d 24 (D.C. Cir. 1990); Fenwick-Schafer v. Winchester Homes , No. 90066002/CL110092 (Cir. Ct. Baltimore).
16. Ragin , 923 F. 2d, p. 100.
17. L. Pendlebury, ''Civil Rights Fight on Ads Leaves Bitter Aftertaste,'' Legal Times , July 20, 1987, p. 13.
18. Ragin v. Steiner, Clateman and Assocs. , 714 F. Supp. 709 (S.D.N.Y. 1989).
19. Michael E. Rosman, ''Ambiguity and the First Amendment: Some Thoughts on All-White Advertising,'' Tennessee Law Review 61 (1993): 289.
20. Housing Opportunities Made Equal, Inc. v. Cincinnati Enquirer, Inc. , 943 F.2d 644 1353 (6th Cir. 1991) (Keith, J., dissenting).
21. 24 C.F.R. 108.
22. www.hud.gov/fhe/109.html.
23. Spann v. Colonial Village, Inc. , 662 F. Supp., 541, 545 (D.D.C. 1987).
24. Housing Opportunities Made Equal, Inc. v. Cincinnati Enquirer, Inc. , 943 F.2d 644 1353 (6th Cir. 1991).
25. EEOC v. Consolidated Service Systems , 989 F.2d 233, 235 (7th Cir. 1993).
26. EEOC v. Consolidated Service Systems , 777 F. Supp. 599, 609 (N.D. Ill. 1991), aff'd , 989 F.2d 233 (7th Cir. 1993).
27. James Bovard, ''The Latest EEOC Quota Madness,'' Wall Street Journal , April 27, 1995, p. A14. See also James Bovard, Lost Rights (New York: St. Martin's Press, 1994), pp. 172–73.
28. 989 F.2d, pp. 237–38.
29. Michael A. Fletcher, ''Childhood Lessons Still Inspire New Leader of EEOC,'' Washington Post , November 30, 1998, p. A23.
30. Equal Employment Opportunity Commission v. O & G Spring and Wire Forms Specialty Company , 705 F. Supp. 400, 402 (N.D. Ill. 1988), aff'd , 38 F.3d 872 (7th Cir. 1994).
31. Bovard, see note 26.
32. Equal Employment Opportunity Commission v. O & G Spring and Wire Forms Specialty Company , 38 F.3d 872, 890 (7th Cir. 1994).
33. 38 F.3d 890, and ''Appellate Summaries, Civil Rights—Racial Discrimination,'' Chicago Daily Law Bulletin 1 (December 1, 1994).
34. 38 F.3d 893.
35. Ibid., p. 885.
36. See generally Seth Kupferberg, ''Civil Rights Law and Breaking Down Patterns of Segregation: The Case of Nepotism,'' Hofstra Labor and Employment Law Journal 16 (1999): 355.
37. Richard A. Epstein, Forbidden Grounds: The Case against Employment Discrimination Laws (Cambridge, Mass.: Harvard University Press, 1992), pp. 67–68.
38. Abraham McLaughlin, ''When Others Harass, Now Managers Lose Pay,'' Christian Science Monitor , September 10, 1999.
39. Ibid.
40. Wooley v. Maynard , 430 U.S. 705, 714 (1977).
41. West Virginia State Bd. of Educ. v. Barnette , 319 U.S. 624 (1943).
Chapter 7
1. Isbiter v. Boys' Club of Santa Cruz, Inc. , 707 P.2d 212, 214 (Cal. 1985).
2. ''The State,'' Los Angeles Times , November 6, 1985.
3. Ayn Rand, The Virtue of Selfishness: A New Concept of Egoism (New York: New American Library, 1964), p. 134.
4. Robert Bork, ''Civil Rights—A Challenge,'' New Republic , August 31, 1963, p. 21.
5. Moose Lodge No. 107 v. Orvis , 407 U.S. 163, 179–80 (1972).
6. See, for example, Katzenbach v. Jack Sabin's Private Club , 265 F. Supp. 90, 91–92 (E.D. La. 1967).
7. United States v. Lansdowne Swim Club , 713 F. Supp. 785, 790 (E.D. Pa. 1989), aff'd , 894 F.2d 83 (3d. Cir. 1990); Durham v. Red Lake Fishing & Hunting Club, Inc. , 666 F. Supp. 954 (W.D. Tex. 1987); United States v. Slidell Youth Football Ass'n , 387 F. Supp. 474 (E.D. La. 1974); Auerbach v. African Am. Teachers Ass'n , 356 F. Supp. 1046, 1047 (E.D.N.Y. 1973).
8. Moose Lodge No. 107 , 407 U.S. 163.
9. Minn. Stat. § 604.12, subd 2(a) (1998) (''A place of public accommodation may not restrict access, admission, or usage to a person solely because the person operates a motorcycle or is wearing clothing that displays the name of an organization or association.'')
10. N.Y. Exec. Law § 292(9) (McKinney 1993); Kiwanis Club of Great Neck, Inc. v. Board of Trustees of Kiwanis Int'l , 363 N.E.2d 1378 (N.Y. 1977).
11. Jackson v. Concord , 253 A.2d 793, 799 (N.J. 1969).
12. National Org. for Women v. Little League Baseball, Inc. , 127 N.J. Super. 522, 318 A.2d 33 (App. Div.), aff'd , 338 A.2d 198 (N.J. 1974).
13. Brounstein v. American Cat Fanciers Assoc. , 839 F. Supp. 1100 (D.N.J. 1993).
14. See, for example, Quinnipac Council, Boy Scouts of America, Inc. v. Commission on Human Rights and Opportunities , 528 A.2d 352, 354 (Conn. 1987); United States Power Squadrons v. State Human Rights Appeal Bd. , 452 N.E.2d 1199, 1204 (N.Y. 1983); United States Jaycees v. McClure , 305 N.W.2d 764, 772 (Minn. 1981).
15. Frank v. Ivy Club , 576 A.2d 241 (N.J. 1990).
16. Ibid., p. 257.
17. See George W. C. McCarter, ''Look Before You Leap: New Jersey's Experience with (Covert) Strict Gender Scrutiny,'' Seton Hall Constitutional Law Journal 6 (1996): 991–92.
18. See, for example, Seabourn v. Coronado Area Council , 891 P.2d 385 (Kan.1995); Schwenk v. Boy Scouts of America , 551 P.2d 465, 469 (Ore. 1976).
19. See, for example, Benevolent and Protective Order of Elks v. Reynolds , 863 F. Supp. 529 (W.D. Mich. 1994); Maine Human Rights Comm'n v. Le Club Calumet , 609 A.2d 285, 287 (Me. 1992).
20. PGA Tour, Inc. v. Martin , 121 S. Ct. 1879 (2001).
21. Roberts v. United States Jaycees , 468 U.S. 609 (1984).
22. Ibid.
23. Board of Dirs. of Rotary Int'l v. Rotary Club of Duarte , 481 U.S. 537, 546 (1987).
24. Boy Scouts of America v. Dale , 120 S. Ct. 2446 (2000).
25. Louisiana Debating and Literary Association, 42 F.3d 1483, 1493 (1995).
26. Ibid., p. 1498 (citing Lyng v. International Union, United Auto. Aerospace & Agric. Implement Workers of Am. , 485 U.S. 360, 367 [1988]).
27. Pacific-Union Club v. Superior Court , 283 Cal. Rptr. 287 (Ct. App. 1991).
28. After the New Jersey Supreme Court ruled in Frank's favor, the eating clubs challenged that ruling on constitutional grounds in federal court.
29. Meg Nugent, '' 'Eating Clubs' Settle Discrimination Suit,'' Newark Star-Ledger , June 4, 1992.
30. ''Last Yale Secret Society Votes to Allow Women,'' Orlando Sentinel Tribune , December 20, 1991, p. A16.
31. ''Nation in Brief,'' St. Petersburg Times , October 31, 1993, p. 7A.
32. 20 U.S.C. § 1681(a)(6) (1994).
33. 20 U.S.C. § 1144 (1994); 42 U.S.C. § 1975a(b)(1994).
34. See Warfield v. Peninsula Golf & Country Club , 896 P.2d 776, 790 (Cal. 1995).
Chapter 8
1. Roberts v. United States Jaycees , 468 U.S. 609, 622 (1984).
2. See, for example, NAACP v. Alabama ex rel. Patterson , 357 U.S. 449, 453 (1958); NAACP v. Button , 371 U.S. 415, 419 (1963).
3. United States Jaycees v. McClure , 709 F.2d 1560 (8th Cir. 1983), rev'd sub nom. Roberts v. United States Jaycees , 468 U.S. 609 (1984).
4. Roberts v. United States Jaycees , 468 U.S. 609 (1984).
5. Board of Dirs. of Rotary Int'l v. Rotary Club of Duarte , 481 U.S. 537, 546 (1987).
6. See, for example, Randall v. Orange County Council , Boy Scouts of America , 28 Cal. Rptr. 2d 53 (Ct. App. 1994); Anderson v. Boy Scouts of America, Inc. , 589 N.E.2d 892 (Ill. Ct. App. 1992); Quinnipiac Council, Boy Scouts of America, Inc. v. Comm'n on Human Rights & Opportunities , 528 A.2d 352, 356 n.5 (Conn. 1987). But see Welsh v. Boy Scouts of America , 993 F.2d 1267, (7th Cir. 1993) (Cummings, J., dissenting) (stating that if the issue arose, he would probably conclude that the Scouts has a First Amendment right to exclude atheists).
7. Anderson v. Boy Scouts of America, Inc. , 589 N.E.2d 892 (Ill. Ct. App. 1992).
8. 515 U.S. 557 (1995).
9. See Irish-American Gay, Lesbian & Bisexual Group of Boston v. City of Boston , No. 9-21518, 1993 WL 818674, p. *2 n.5 (Mass. Super. Ct. Dec. 15, 1993), aff'd , 636 N.E.2d 1293 (Mass. 1994), rev'd sub nom., Hurley v. Irish-American Gay, Lesbian & Bisexual Group of Boston , 515 U.S. 557 (1995).
10. Ibid., p. *14.
11. See Irish-American Gay, Lesbian & Bisexual Group of Boston v. City of Boston , 636 N.E.2d 1293, 1300 (Mass. 1994), rev'd sub nom., Hurley v. Irish-Am. Gay, Lesbian & Bisexual Group of Boston , 515 U.S. 557 (1995).
12. The background facts are found in Boy Scouts of America v. Dale , 120 S. Ct. 2446 (2000).
13. John O. McGinnis, ''Reviving Tocqueville's America: The Supreme Court's New Jurisprudence of Social Discovery,'' California Law Review 90 (2002): 485.
14. Ibid.
15. City of Cleveland v. Nation of Islam , 922 F. Supp. 56 (N.D. Ohio 1995).
16. As the Massachusetts Supreme Court has held in a similar case. Donaldson v. Farrakhan , 436 Mass. 94 (2002).
17. Richard Carelli, ''Court Denies Cleveland Bid to Avoid Legal Fees,'' Cleveland Plain Dealer , January 21, 1998, p. 2B.
18. Invisible Empire of the Knights of the Ku Klux Klan v. Mayor of Thurmont , 700 F. Supp. 281 (D. Md. 1988).
19. Southgate v. United African Movement , No. MPA 95-0851, PA 95-0031, 1997 WL 1051933 (N.Y.C. Com. Hum. Rts. June 30, 1997).
20. Ibid.
21. Ibid.
22. Linda F. Wightman, ''The Threat to Diversity in Legal Education: An Empirical Analysis of the Consequences of Abandoning Race as a Factor in Law School Admission Decisions,'' New York University Law Review 72, (1997): 1, 30, tbl. 6.
23. Ibid., p. 22, tbl. 5.
24. Regents of the Univ. of Cal. v. Bakke , 438 U.S. 265 (1978).
25. Ibid., pp. 314, 317–18 (Powell, J., concurring).
26. Hopwood v. Texas , 78 F.3d 932 (5th Cir. 1996).
27. John Roberts, ''It's Academic: Universities Discriminate Despite Court Orders,'' Washington Times , January 21, 2003, p. A17.
28. Boy Scouts of America v. Dale , 530 U.S. 640 (2000).
29. 27 U.S. 160 (1976).
30. Petitioner's Brief, Runyan v. McCrary , 427 U.S. 160 (1976) (No. 75-62).
31. Justice O'Connor, a member of the five-vote majority in Dale , has suggested that they cannot. Roberts v. United States Jaycees , 468 U.S. 609 (1984) (O'Connor, J., concurring).
32. Runyon v. McCrary , 427 U.S. 160, 175–76 (1976). See David E. Bernstein, ''The Right of Expressive Association and Private Universities' Racial Preferences and Speech Codes,'' William and Mary Bill of Rights Law Journal 9 (2001): 619.
33. Some minority students believe that many schools discriminate against them in admissions. As of early 2001 the official Web site of the Law School Admissions Council stated: ''We often hear . . . in the Office of Minority Affairs at Law School Admission Council: 'Is it okay to say I'm a minority student when I apply to law schools? I've heard it's better not to tell.' www.lsac.org/LSAC.asp?url/lsac/minorities-in-legal-education-selected-articles.asp. Needless to say, the Web site encouraged students to reveal their minority status.
34. See John E. Morris, ''Boalt Hall's Affirmative Action Dilemma,'' American Lawyer , November 1997, p. 4. For example, in 1996–97 only 103 African Americans and 224 Hispanics had a college GPA of 3.25 or above and LSAT scores at or above the 83.5 percentile, and only 16 African Americans and 45 Hispanics achieved the 92.3 (164 LSAT) percentile with a 3.50 or higher GPA. The latter credentials are lower than the averages at the elite ''Top 15'' law schools, which matriculate several thousand students each year.
35. Andrew R. Varcoe, ''The Boy Scouts and the First Amendment: Constitutional Limits on the Reach of Anti-Discrimination Law,'' Law and Sex. 9 (1999–2000): 163, 276.
Chapter 9
1. See, for example, E.E.O.C. v. Roman Catholic Diocese of Raleigh, N.C. , 213 F.3d 795 (4th Cir. 2000); Starkman v. Evans , 198 F.3d 173 (5th Cir.1999); E.E.O.C. v. Catholic Univ. of Am. , 83 F.3d 455, 461-63 (D.C. Cir.1996).
2. UPI, ''Religious Schools Await Supreme Court Ruling,'' Bergen Record , March 3, 1986, p. 10.
3. Ibid. The quotation here is from the news story, not from Mrs. Hoskinson.
4. Dayton Christian Schools v. Ohio Civil Rights Comm'n , 578 F. Supp. 1004, 1018–19, 1012 (D. Ohio 1984).
5. William Choyke, ''Supreme Court Will Rule on Church-School Dispute,'' Dallas Morning News , March 30, 1986, p. 4A.
6. 578 F. Supp. 1012–113.
7. 578 F. Supp. 1014.
8. Ibid.
9. Dayton Christian Schools v. Ohio Civil Rights Comm'n , 766 F. 2d. 932 (6th Cir. 1985).
10. UPI, ''Religious Schools Await Supreme Court Ruling,'' Bergen Record , March 23, 1986, p. O12.
11. Ohio Civil Rights Comm'n v. Dayton Christian Schools, Inc. 477 U.S. 619 (1986).
12. ''Church Worker Seeks Ruling on Job Bias,'' Houston Chronicle , March 27, 1986, p. 15.
13. McLeod v. Providence Christian School , 408 N.W.2d 146, 152 (Mich. 1987).
14. Ganzy v. Allen Christian School , 995 F. Supp. 340, 348 (E.D.N.Y. 1998); see also Dolter v. Wahlert High School , 483 F. Supp. 266 (N.D. Iowa 1980).
15. Sacred Congregation for Catholic Education, ''Lay Catholics in Schools: Witnesses to Faith,'' paragraph 32 (October, 15, 1982).
16. Dolter , 483 F. Supp. 270.
17. Gay Rights Coalition of Georgetown University Law Center v. Georgetown University , 536 A.2d 1 (D.C. 1987).
18. District of Columbia Appropriations Act, 1990, Pub. L. No. 101–168, 103 Stat. 1267, 1284 (1989).
19. Rebecca Sinderbrand, ''Taking Pride in Promoting Tolerance,'' The Georgetown Hoya , October 20, 1998, available at www.thehoya.com/features/102098/features3.htm.
20. See Bob Jones Univ. v. United States , 461 U.S. 574 (1983).
21. Ibid., p. 599.
22. See Mayer G. Freed and Daniel Polsby, ''Race, Religion and Public Policy: Bob Jones University v. United States ,'' Supreme Court Review 1(1984).
23. Brian Blomquist and Kenneth Lovett, ''Jones Reaches '18th Century' on New Dating Policy: McCain,'' New York Post , March 5, 2000, p. 18.
24. 42 USC § 2000e-1(a) (1970).
25. 42 USC § 2000e-1(a) (1994).
26. Corporation of the Presiding Bishop of the Church of Jesus Christ of Latter Day Saints v. Amos , 483 U.S. 327 (1987).
27. See, for example, Ohio Rev. Code Ann. § 4112.01(B) (providing no religious exemption).
28. 374 U.S. 398, 403–10 (1963).
29. As noted, Dayton Christian Schools claimed a rare victory in a federal appellate court under the Sherbert test.
30. Employment Division v. Smith , 494 U.S. 872 (1990).
31. 42 USC §§ 2000bb-2000bb-4 (1994).
32. Flores v. City of Boerne , 521 U.S. 507 (1997).
33. See, for example, Adams v. Comm'r of Internal Revenue , 170 F.3d 173 (3d Cir. 1999); In re Young , 82 F.3d 1407, 1416-17 (8th Cir. 1996).
34. See, for example, Conn. Gen. Stat. Ann. §§ 52-571b (West Supp. 1999); Fla. Stat. Ann. § 761 (West Supp. 1999); R.I. Gen. Laws §§ 42-80.1.3 (1997).
35. As of February 1999, among states interpreting their constitutions, approximately 15 apply a strong compelling interest test, 6 give less protection to religion, and the rest have not clearly spoken to the issue. Steve France, ''Not under My Roof You Don't,'' American Bar Association Journal 85 (April 1999): 26, 28.
36. See David E. Bernstein, ''Antidiscrimination Laws and the First Amendment,'' Missouri Law Review 66 (2001): 83; David E. Bernstein, ''The Right of Expressive Association and Private Universities' Racial Preferences and Speech Codes,'' William and Mary Bill of Rights Law Journal 9 (2001): 619.
Chapter 10
1. Attorney General v. Desilets , 636 N.E.2d 233, 234 (Mass. 1994).
2. Michael Matza, ''Rent and a Religious Landlord,'' Seattle Times , April 21, 1994, p. A3.
3. Ibid.
4. The Boston Herald , February 10, 1994, p. 20.
5. Professor Marie Failinger responds to this type of argument by noting that to ''discount such landlords' interests as merely economic is to send the wrong message about the kind of local communities we may hope to have. That is, it may signal that we do not want landlords who are interested in their tenants' needs or their tenants' misbehavior, that we want landlords who are indifferent to who their tenants are as persons, whose choices will be based solely on economics. To discount [a landlord] as merely a commercial enterprise is to move farther along to the day when the engaged landlord disappears, and our only landlords will be large corporations with absentee managers who govern through rules rather than relationships, who ignore disruptive tenants and habitability issues until it hurts their bottom line. The blessing of anonymity is also its curse: the landlord who may murmur disapproval at an indigent woman's poor choice in relationships is also the landlord who may fix the heat faster because she knows the woman's children.'' Marie A. Failinger, ''Remembering Mrs. Murphy: A Remedies Approach to the Conflict between Gay/ Lesbian Renters and Religious Landlords,'' Capital University Law Review 29 (2001): 383.
6. ''So Saith the Landlord,'' Boston Globe , February 13, 1994, p. 74.
7. Attorney General v. Desilets , 636 N.E.2d 233, 234 (Mass. 1994).
8. Desilets , 636 N.E.2d 240.
9. John Auerbach, ''Some Hail AG's Inaction on Tenant Case,'' Boston Globe , January 31, 1995.
10. George F. Will, ''Mass. Anti-Bias Law Clashes with Religious Rights,'' Chicago Sun-Times , March 13, 1994, p. 48.
11. Matza, see note 2.
12. Swanner v. Anchorage Equal Rights Comm'n , 874 P.2d 274 (Alaska 1994).
13. Ibid., p. 283–84.
14. Swanner v. Anchorage Equal Rights Comm'n , 513 U.S. 979, 982 (1994) (Thomas, J., dissenting from denial of cert.)
15. See Maureen E. Markey, ''The Landlord/Tenant Free Exercise Conflict in a Post-RFRA World,'' Rutgers Law Journal 29 (1998): 487 (21 states ban marital status discrimination in housing; none explicitly bans discrimination against unmarried heterosexual couples).
16. County of Dane v. Norman , 497 N.W.2d 714 (Wis. 1993) (making this argument in a related context).
17. Quoted in George Grant, ''Trial and Error: The American Civil Liberties Union and Its Impact on Your Family'' (undated), available at www.freebooks.commentary.net/freebooks/docs/a_pdfs/ggte.pdf.
18. 460 N.W.2d 2 (Minn. 1990).
19. Employment Division v. Smith, 494 U.S. 872 (1990).
20. Ibid., p. 717.
21. 220 F.3d 1134, 1137 (9th Cir. 2000).
22. Smith v. Fair Employment and Housing Comm'n , 913 P.2d 909 (Cal. 1996).
23. Jasniowski v. Rushing , 678 N.E.2d 743 (Ill. App.), judgment vacated, 685 N.E.2d 622 (Ill. 1997).
24. George C. Leef, ''Housing Discrimination Laws and the Continuing Erosion of Property Rights,'' Freedom Daily , May 1999, available at www.fff.org/freedom/0599e.asp.
25. McCready v. Hoffius , 586 N.W.2d 723 (Mich. 1998).
26. Cready v. Hoffius , 1999 WL 226862 (Mich.).
27. American Civil Liberties Union Statement on H.R. 1691 Religious Liberty Protection Act of 1999 before the Subcommittee on the Constitution of the House Committee on the Judiciary Presented by Christopher E. Anders, Legislative Counsel May 12, 1999.
28. Ibid.; see also Christopher E. Anders and Rose E. Saxe, ''Effect of a Statutory Religious Freedom Strict Scrutiny Standard on the Enforcement of State and Local Civil Rights Law,'' Cardozo Law Review 21 (1999): 663.
29. Eric Fingerhut, ''Jewish Groups Back Away from Religious Protection Act,'' Washington Jewish Week , October 7, 1999, p. 5.
30. Ibid.
Chapter 11
1. State ex rel. Sprague v. City of Madison , 555 N.W.2d 409 (Wis. Ct. App. 1996).
2. Sprague v. City of Madison , 207 Wis.2d 284 (1997); Hacklander-Ready v. Wisconsin ex rel. Sprague, 520 U.S. 1212 (1997).
3. Sprague v. Hacklander-Ready , Equal Opportunities Commission Case No. 1462 (February 9, 1995), available at www.ci.madison.wi.us/eoc/Cases/01462.htm.
4. Department of Fair Employment and Housing v. DeSantis , FEHC Dec. No. 02-12, 2002 WL 1313078 (Cal. F.E.H.C. 2002).
5. See, for example, 24 C.F.R. §§ 109.20(b)(5) (withdrawn). This regulation has been withdrawn, directive no. FR-4029-F-01, effective May 1, 1996, but it probably still reflects HUD's interpretation of the Fair Housing Act. This section was withdrawn because of concern that its restrictions on specific wording of advertising swept too broadly. See Memo from HUD Assistant Secretary Roberta Achtenberg, Guidance Regarding Advertisements under 804(c) of the Fair Housing Act, available at www.fscn.com/members/text/hudadmem.htm. But experts believe that the general policy of prohibiting discriminatory advertising is still in place. See www.fairhousing.com/legal_research/regs/ fhr_109-20.htm; www.fscn.com/members/text/c2fhous.htm.
6. Complaint, In re Fair Housing Council of Greater Washington v. Washington City Paper , www.fairhousing.org/Casenotes/docs/CityPaper/dcComplaint.rtf.
7. Ellen Goodman, ''Desire for Women-only Health Clubs Is No Show of Strength,'' Fresno Bee , February 13, 1998, p. B7.
8. Ibid.
9. Doug Thomas, ''Female-friendly Fitness Curves for Women Centers Are Designed to Make the Average Woman Comfortable with Getting Fit without Distractions,'' Omaha World-Herald , December 18, 2000.
10. Michael R. Zahn, ''Bias Case against Fitness Club Dropped,'' Milwaukee Journal , December 20, 1993, p. B1.
11. Hanna Miller, ''Exercising Their Fitness Options,'' Arizona Daily Star , March 8, 2001, p. F8.
12. Suzanne Schlosberg, ''Women-Only Health Clubs Gain Popularity, Draw Controversy,'' CNN , May 31, 2000, available at www.cnn.com/2000/HEALTH/diet.fitness/05/31/women.only.wmd/.
13. Miriam A. Cherry, ''Exercising the Right to Public Accommodations: The Debate over Single-Sex Health Clubs,'' Maine Law Review 52 (2000): 97, 104–07.
14. Laura-Lynne Powell, ''Anaheim activist Roots Out Bias against Men,'' Orange County Register , April 17, 1992, p. 1.
15. Ibid.
16. ''Health Club to Admit Men,'' Los Angeles Times , August 3, 1988, p. Metro 2.
17. ''St. Paul Man Files Sex Discrimination Suit against Women-Only Health Club,'' Minneapolis Star Tribune , March 20, 1990, p. 7B; Powell, see note 14; Zahn, see note 10.
18. ''Women Only,'' Providence Journal Bulletin , November 3, 1997, p. C1.
19. J. M. Lawrence, ''Law Lets Women Sweat Where the Boys Aren't,'' Boston Herald , February 7, 1998, p. 7.
20. ''The International Health, Racquet & Sportsclub Association, Single Sex Health Clubs,'' available at www.ihrsa.org/publicpolicy/industryissues/womenonly.html.
21. EEOC v. Sedita , 755 F. Supp. 808 (N.D. Ill. 1991).
22. Ibid.
23. Cherry, see note 13, p. 126.
24. For citations on this point, see Eugene Volokh, ''Freedom of Speech, Cyberspace, Harassment Law, and the Clinton Administration,'' Law and Contemporary Problems 63 (2000): 299.
25. Paul McNamara, ''Keeping an Eye on E-mail,'' Network World , October 5, 1998, p. 80.
26. Dana Hawkins, ''Lawsuits Spur Rise in Employee Monitoring,'' U.S. News & World Report , August 13, 2001.
27. Volokh, www.law.ucla.edu/faculty/volokh/harass/cyberspa.htm.
28. Hawkins, see note 26.
29. Volokh, www.law.ucla.edu/faculty/volokh/harass/cyberspa.htm.
30. Ibid.
31. Ibid.
32. ''Victory in Sex Bias Suit Would Only Do So Much,'' New York Times , August 21, 1992. See Ezold v. Wolf, Block, Schorr and Solis-Cohen , 983 F.2d 509 (3d Cir. 1992).
33. Ambrose Evans-Pritchard, The Secret Life of Bill Clinton (Washington: Regnery Publishing, 1997), p. 363.
34. See Jeffrey Rosen, ''I Pry,'' New Republic , March 16, 1998.
35. Quoted in Jeffrey Rosen, ''Privacy in Public Places,'' Cardozo Studies of Law and Literature 12 (2000): 167, 183.
36. Ibid.
37. Becky Rees, Grove City College v. T.H. Bell, Secretary, U.S. Dept. Of Education , available at Grove City College Web site, www.gcc.edu/pr/Rees.asp.
38. Ibid.
39. Grove City College v. Harris , 500 F. Supp. 253 (D.C. Pa. 1980).
40. Grove City College v. Bell . 465 U.S. 444 (1984).
41. 20 U.S.C. §§ 1687, 29 U.S.C. §§ 794, 42 U.S.C. §§ 2000d-4a, and 42 U.S.C. §§ 6101.
42. John Leo, ''Gender Police: 'Pull Over,''' U.S. News & World Report , March 23, 1998, p. 11.
43. John Ritter, ''School Puts Its Principles First,'' USA Today , December 9, 1996.
44. See Jessica Gavora, Tilting the Playing Field: Schools, Sex, Sports and Title IX (San Francisco: Encounter Books, 2002).
45. Lynn v. Regents of the University of California , 656 F.2d 1337 (9th Cir. 1981).
Chapter 12
1. The ACLU's position was that because Bob Jones was still free to express its opposition to interracial dating and marriage, the university's constitutional rights were secure. Brief of the American Civil Liberties Union and the American Jewish Committee, Amici Curiae in support of Affirmance at 37-38, Bob Jones Univ. v. United States , 461 U.S. 574 (1983).
2. William A. Donohue, The Politics of the American Civil Liberties Union (New Brunswick, N.J.: Transaction Books, 1985), p. 131.
3. Pines v. W. R. Tomson , 206 Cal. Rptr. 866 (Cal. App. 1984).
4. McCready v. Hoffius , 586 N.W.2d 723 (Mich. 1998).
5. Quoted in Daniel J. Popeo, Not Our America (Washington: Washington Legal Foundation, 1989), p. 71.
6. Nadine Strossen, ''Regulating Racist Speech on Campus: A Modest Proposal,'' Duke Law Journal (1990): 484, n. 343.
7. Curran v. Mount Diablo Council of the Boy Scouts of America , 17 Cal. 4th 670, 674, 952 P.2d 218 (1998).
8. See, for example, Linda Hills, ''Court Decision Tarnishes Justice and Boy Scouts,'' San Diego Union-Tribune , March 27, 1998. (The executive director of the San Diego ACLU writes that the Boy Scouts of America should be regulated because it receives ''significant support from government.'')
9. Julie Makinen Bowles, ''D.C. Panel to Examine Boy Scouts' Ban on Gays,'' Washington Post , January 20, 1998, p. B1.
10. Jonathan D. Karl, ''Stifled Speech on Campus,'' Christian Science Monitor , August 23, 1990, p. 19.
11. Charles Oliver, ''The First Shall Be Last?'' Reason , October 1990, pp. 20, 25.
12. Strossen, see note 6.
13. See Iota Xi Chapter of Sigma Chi v. George Mason Univ ., 773 F. Supp. 792 (E.D. Va. 1991).
14. Samuel Walker, In Defense of American Liberties: A History of the ACLU (New York: Oxford University Press, 1990), p. 373.
15. Evan Osnos and James Janega, ''ACLU Sides with Supremacist on Right to Obtain Law License,'' Chicago Tribune , August 8, 1999.
16. See Guy Gugliotta, ''ACLU Alleges Free Speech Violations in HUD Probes,'' Washington Post , August 17, 1994, p. A20.
17. Rita Delfiner, ''St. Pat's Parade Heads to Court,'' New York Post , January 25, 1992, p. 7.
18. ''ACLU v. ACLU,'' Legal Times , November 7, 1987, p. 3.
19. The ACLU's brief before the Supreme Court supported neither party. The brief acknowledged that private parades are inherently expressive and are entitled to full First Amendment protection, but concluded that the case should be sent back to the trial court for a determination regarding whether the parade in question was truly private. That issue had already been raised in the courts below, rejected, and was not appealed, but apparently the ACLU simply could not bring itself to oppose enforcement of the antidiscrimination law in question.
20. Nat Hentoff, ''Government's Place,'' Sacramento Bee , September 24, 1994, p. B6.
21. Alan Cooper, ''Organization Fighting AIDS Homes Wins Round,'' Richmond Times-Dispatch , October 13, 1994, p. B5.
22. Nat Hentoff, ''The Onliest Robyn Blumner,'' Village Voice , November 4, 1997, p. 20.
23. John Leo, ''Watch What You Say,'' U.S. News & World Report , March 20, 2000.
24. Upon returning from a trip to the Stalinist Soviet Union in 1928, he criticized the ''bourgeois mind'' concerned with ''individual liberties'' instead of the economic freedom purportedly enjoyed by Soviet peasants, ''a freedom vastly more real to the average worker than shadowy intellectual liberties.'' Roger N. Baldwin, Liberty under the Soviets (New York: Vanguard Press, 1928), p. 24. In 1934, when millions of Soviet citizens were dying in government-engineered famines, Baldwin defended the Soviet dictatorship on the grounds that ''the Soviet Union has already created liberties far greater than exist elsewhere in the world.'' Quoted in Cletus E. Daniel, The ACLU and the Wagner Act (Ithaca, NY: Cornell ILR Press, 1980).
25. Daniel, see note 24.
26. Peggy Lamson, Roger Baldwin: Founder of the American Civil Liberties Union (Boston: Houghton Mifflin Co., 1976), p. 217.
27. See Robert C. Cottrell, Roger Nash Baldwin and the American Civil Liberties Union (New York: Columbia Univeristy Press, 2001), pp. 216–17.
28. Tamar Lewin, ''A.C.L.U. Boasts Wide Portfolio of Cases, but Conservatives See Partisanship,'' New York Times , October 2, 1988, § 1, p. 24.
29. See Sanford Levinson, ''Investigatory Bodies and the Due Processes of Law,'' in Robert I. Rotberg and Dennis Thompson, eds., Truth v. Justice: The Moral Efficacy ofTruth Commissions: South Africa and Beyond (Princeton University Press, forthcoming); Loren Miller, ''A Color-Blind Commonwealth,'' in Alan Reitman, ed., The Price of Liberty (New York: W. W. Norton and Co., 1968), pp. 187, 200.
30. Walker, see note 14, pp. 275–76.
31. Donohue, see note 2, p. 71.
32. Ibid.
33. Jessica Gavora, ''The Quota Czars,'' Policy Review , May 15, 1997, p. 22.
34. Oliver, see note 11, p. 24.
35. John T. Leeds, ''The A.C.L.U.: Impeccable Judgments or Tainted Policies?'' New York Times Magazine , September 10, 1989, p. 72.
36. Interview with Alan Dershowitz, February 26, 2002. Former ACLU of Florida president Robyn Blumner makes the same point. Robyn Blumner, ''Glasser Will Leave a Lasting Imprint on the ACLU,'' Jewish World Review , September 6, 2000.
37. Mark S. Campisano, ''Card Games: The ACLU's Wrong Course,'' The New Republic , October 31, 1988, p. 10.
38. Oliver, see note 11, p. 23.
39. See Dennis Cauchon, ''Civil Dispute within the ACLU,'' USA Today , March 31, 1993.
40. Mary Ellen Gale and Nadine Strossen, ''The Real ACLU,'' Yale Journal of Law and Feminism 2 (1989): 161, 172.
41. Blumner, see note 36.
42. Walker, see note 14, p. 5.
Conclusion
1. See, for example, the influential article by Mari J. Matsuda, ''Public Response to Racist Speech: Considering the Victim's Story,'' Michigan Law Review 87 (1989): 230.
2. All of these restrictions are noted in John Leo, ''A Tangled Web of Incorrect Thoughts,'' ex Femina , June 2001, available at www.iwf.org/pubs/exfemina/June2001h.shtml.
3. Many of these incidents are documented in Alan Charles Kors and Harvey A. Silverglate, The Shadow University: The Betrayal of Liberty on America's Campuses (New York: The Free Press, 1998).
4. R. v. Keegstra , 3 S.C.R. 687 (1990).
5. R. v. Butler , 1 S.C.R. 452 (1992).
6. Mirko Petricevic, ''Preaching . . . or Spewing Hate? A Thin Line Separates the Right of Canadians to Free Expression and the Crime of Promoting Hatred,'' The Record (Kitchener-Waterloo, Ontario), February 1, 2003, p. J8.
7. Ian Hunter, ''Worshiping the God Equality,'' Globe and Mail , July 5, 2001, p. A15.
8. Susan Martinuk, ''Religious Freedom Goes Public, Sort Of,'' National Post , May 21, 2001, p. 14.
9. Brillinger v. Brockie , No. 179/00 (Ont. Super. Ct. June 17, 2002).
10. Royal Hamel, ''Can Christians Let the Gospels Be Muzzled?'' Guelph Mercury , October 4, 2002, available at 2002 WL 26223201.
11. Zacharias Margulis, ''Canada's Thought Police,'' Wired , March 1995.
12. ''Why the ACLU Opposes Censorship of 'Pornography,'' available at www.eff.org/Censorship/aclu_opposes_porno_censorship.article.
13. Denise O'Leary, ''A Velvet Oppression,'' Christianity Today , April 2, 2001.
14. British Columbia Human Rights Act, Ch. 22, Pt. 1, § 2(1).
15. Both cases are described in Richard Ackland, ''Defending the Right to Be Obnoxious,'' Sydney Morning Herald , August 4, 2000, available at www.smh.com.au/news/0008/04/text/features2.html.
16. Quoted in Tim Blair, ''May I Speak Freely Here?'' The Australian , December 11, 2001.
17. Letter to the Editor, ''Phillip Adams and the Case for a Bill of Rights,'' Sidney Morning Herald , December 8, 2001.
18. JDC Enterprises Pty Ltd., Tribunal Reference No. 28/98, April 2, 1998.
19. Note, ''Racial Steering in the Romantic Marketplace,'' Harvard Law Review 107 (1994): 877.
20. John Leo, ''The Feds Strike Back,'' U.S. News & World Report , May 31, 1999, p. 16.
21. N. v. E. , Complaints Division W31/99 (N.Z. Human Rights Comm'n October 26, 1999), available at www.hrc.co.nz/org/legal/teritojuly00.htm.
22. Walter Olson, The Excuse Factory: How Employment Law Is Paralyzing the American Workplace (New York: The Free Press, 1997).
23. Equal Employment Opportunity Act of 1972, Pub. L. No. 92-261, §§ 2(7), 86 Stat. 103 (codified as amended at 42 U.S.C §§ 2000e(j) (1994)); Americans with Disabilities Act, 42 U.S.C. §§ 12112(b)(5)(A) (1994); 34 C.F.R. §§ 104.12(b)(2) (1999); 42 U.S.C. §§ 12111(10)(B) (1994) (definition of ''undue harship'').
24. Michael W. McConnell, ''Free Exercise Revisionism and the Smith Decision,'' University of Chicago Law Review 57 (1990): 1109.
25. Albemarle Paper Co. v. Moody , 422 U.S. 405, 421 (1975).
26. See 42 U.S.C. §§ 2000e(b) (1994); 42 U.S.C. §§ 1981a(b)(3) (1994); 42 U.S.C. §§ 2000e-5 (1994); 42 U.S.C. §§ 2000e-1(a) (1994).
27. Yolanda Woodlee, ''Top D.C. Aide Resigns over Racial Rumor,'' Washington Post , January 27, 1999, p. B1.
28. This is a paraphrase of Milton and Rose Friedman, Free to Choose (New York: Harcourt Brace Jovanovich, 1980), p. 159.
About the Author
David E. Bernstein is an associate professor at the George Mason University School of Law. He is a graduate of Yale Law School, where he was senior editor of the Yale Law Journal and a John M. Olin Fellow in Law, Economics, and Public Policy. After clerking for Judge David Nelson of the Sixth Circuit Court of Appeals and working as a litigator at Crowell & Moring, he served as a Mellon Foundation Research Fellow at Columbia University School of Law. Professor Bernstein is the author of more than 60 scholarly articles, book chapters, and think tank studies. He is author of Only One Place of Redress: African-Americans, Labor Regulations, and the Courts from Reconstruction to the New Deal (Duke University Press, 2001), coeditor of Phantom Risk: Scientific Inference and the Law (MIT Press, 1993), and coauthor of The New Wigmore: Volume on Expert and Demonstrative Evidence (forthcoming). He has been named one of the most-cited professors among those who have entered law teaching since 1992.
Cato Institute
Founded in 1977, the Cato Institute is a public policy research foundation dedicated to broadening the parameters of policy debate to allow consideration of more options that are consistent with the traditional American principles of limited government, individual liberty, and peace. To that end, the Institute strives to achieve greater involvement of the intelligent, concerned lay public in questions of policy and the proper role of government.
The Institute is named for Cato's Letters, libertarian pamphlets that were widely read in the American Colonies in the early 18th century and played a major role in laying the philosophical foundation for the American Revolution.
Despite the achievement of the nation's Founders, today virtually no aspect of life is free from government encroachment. A pervasive intolerance for individual rights is shown by government's arbitrary intrusions into private economic transactions and its disregard for civil liberties.
To counter that trend, the Cato Institute undertakes an extensive publications program that addresses the complete spectrum of policy issues. Books, monographs, and shorter studies are commissioned to examine federal budget, Social Security, regulation, military spending, international trade, and myriad other issues. Major policy conferences are held throughout the year, from which papers are published thrice yearly in the Cato Journal. The Institute also publishes the quarterly magazine Regulation .
In order to maintain its independence, the Cato Institute accepts no government funding. Contributions are received from foundations, corporations, and individuals, and other revenue is generated from the sale of publications. The Institute is a nonprofit, tax-exempt, educational foundation under Section 501(c)3 of the Internal Revenue Code.
CATO INSTITUTE
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Washington, D.C. 20001
www.cato.org
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Q: Android error: You must specifiy a valid layout reference. The layout ID. in elcipse I have been working with elcipse for a couple of weeks now. My code has functioned properly but all of a sudden it has stopped working. I get this error,
main.xml: You must specifiy a valid layout reference. The layout ID @layout/required is not valid.
my XML code
<?xml version="1.0" encoding="utf-8"?>
<ScrollView xmlns:android="http://schemas.android.com/apk/res/android"
android:layout_width="fill_parent"
android:layout_height="fill_parent" >
<LinearLayout xmlns:android="http://schemas.android.com/apk/res/android"
android:layout_width="fill_parent"
android:layout_height="wrap_content"
android:orientation="vertical">
<!-- select between BIN or auction -->
<LinearLayout
xmlns:android="http://schemas.android.com/apk/res/android"
android:layout_width="match_parent"
android:layout_height="wrap_content"
android:gravity="center_horizontal"
android:orientation="horizontal" >
<Button
android:id="@+id/AuctionButton"
android:layout_marginLeft="82dp"
android:layout_width="119dp"
android:layout_height="wrap_content"
android:onClick="showAuctionOptions"
android:text="Auction" />
<Button
android:id="@+id/BINButton"
android:layout_marginLeft="-2dp"
android:layout_width="119dp"
android:layout_height="wrap_content"
android:onClick="showAuctionOptions"
android:text="Buy it now" />
</LinearLayout>
<include android:id="@+id/cell1" layout="@layout/required"/>
<include android:id="@+id/cell2" layout="@layout/gray_line" />
<!--** Show if Buy it now is selected **-->
<include android:id="@+id/cell3" layout="@layout/buyitnow" />
<!-- ** End Buy it now display ** -->
<!--** Show if auction selected ** -->
<include android:id="@+id/cell4" layout="@layout/auction" />
<include android:id="@+id/cell5" layout="@layout/gray_line" />
<include android:id="@+id/cell6" layout="@layout/addons" />
<include android:id="@+id/cell7" layout="@layout/calculate" />
</LinearLayout>
</ScrollView>
the error is with the first include, however if I remove that, I just get an error with the second include. If I remove all of the include, I get a 'could not resolve R' error within my java code.
What I have tried,
*
*cleaning the project
*restarting eclipse
*rebooting my computer
this is my AndroidManifest XML file,
<?xml version="1.0" encoding="utf-8"?>
<manifest xmlns:android="http://schemas.android.com/apk/res/android"
package="toggler.state"
android:versionCode="1"
android:versionName="1.0" >
<uses-sdk android:minSdkVersion="10" />
<application
android:icon="@drawable/ic_launcher"
android:label="@string/app_name">
<activity
android:name=".TogglerActivity"
android:label="@string/app_name">
<intent-filter>
<action android:name="android.intent.action.MAIN" />
<category android:name="android.intent.category.LAUNCHER" />
</intent-filter>
</activity>
</application>
</manifest>
none of which have worked.Could anyone help please?
Thanks
A: The error is probably caused elsewhere in the layout. Remove the extra two xmlns:android="http://schemas.android.com/apk/res/android"
The xmlns is used to define a namespace. Only the top element can have it in most cases.
Take a look at What does "xmlns" in XML mean? if anyone wants to read about the xmlns explanation.
Also check to make sure your XML files are all lowercase.
Also try to see if you have the correct package specified in your manifest. Taken from https://stackoverflow.com/a/7496766/935779
It is worth checking in AndroidManifest.xml. The attribute package has
the correct value.
That is, <manifest
xmlns:android="http://schemas.android.com/apk/res/android"
package="your.correct.package.name" ...
After you change that, the R.java will be re-generated.
<?xml version="1.0" encoding="utf-8"?>
<ScrollView xmlns:android="http://schemas.android.com/apk/res/android"
android:layout_width="fill_parent"
android:layout_height="fill_parent" >
<LinearLayout
android:layout_width="fill_parent"
android:layout_height="wrap_content"
android:orientation="vertical">
<!-- select between BIN or auction -->
<LinearLayout
android:layout_width="match_parent"
android:layout_height="wrap_content"
android:gravity="center_horizontal"
android:orientation="horizontal" >
<Button
android:id="@+id/AuctionButton"
android:layout_marginLeft="82dp"
android:layout_width="119dp"
android:layout_height="wrap_content"
android:onClick="showAuctionOptions"
android:text="Auction" />
<Button
android:id="@+id/BINButton"
android:layout_marginLeft="-2dp"
android:layout_width="119dp"
android:layout_height="wrap_content"
android:onClick="showAuctionOptions"
android:text="Buy it now" />
</LinearLayout>
<include android:id="@+id/cell1" layout="@layout/required"/>
<include android:id="@+id/cell2" layout="@layout/gray_line" />
<!--** Show if Buy it now is selected **-->
<include android:id="@+id/cell3" layout="@layout/buyitnow" />
<!-- ** End Buy it now display ** -->
<!--** Show if auction selected ** -->
<include android:id="@+id/cell4" layout="@layout/auction" />
<include android:id="@+id/cell5" layout="@layout/gray_line" />
<include android:id="@+id/cell6" layout="@layout/addons" />
<include android:id="@+id/cell7" layout="@layout/calculate" />
</LinearLayout>
</ScrollView>
A: I had a similar problem and was able to fix it by providing a layout_width and layout_height to the include tag.
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| 3,122
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Q: How to make my comments in the code grey in the latex doc? I have to insert some mathematica code in my latex document. For that, I'm using the answer given here by user Ronny. Is it possible to add sth that would make my comments look grey in the resulting pdf document?
Thanks
A: You can use commentstyle=\color{gray}. Taking the code from answer linked by OP in the question:
\documentclass{article}
\usepackage{listings,framed,xcolor,amsmath}
\colorlet{shadecolor}{blue!20}
\lstnewenvironment{mat}
{\lstset{language=mathematica,mathescape,columns=flexible,commentstyle=\color{gray}}}
{}
\begin{document}
\begin{align}
\nonumber W_{r → ∞}=&-∫_{r}^{∞}\!F\,\mathrm{d}y=- ∫_r^∞ \! \dfrac{1}{4π\epsilon₀} \dfrac{q²}{\alpha²} \dfrac{\alpha³}{y³}\left(1- \dfrac{\alpha²} {y²}\right)⁻²\,\mathrm{d}y\\
=&-\dfrac{1}{4π\epsilon₀} \dfrac{q²}{\alpha²}\alpha³ \underbrace{∫_r^∞ \! y⁻³ \left(1-\dfrac{\alpha²} {y²}\right)⁻² \,\mathrm{d}y}_{I} \label{eq:WcondI}
\end{align}
\begin{shaded}
\begin{mat}
In[1]:= Integrate[{y^(-3)*(1-(a/y)²)^(-2)},{y,r,Infinity}]
Out[1]= {ConditionalExpression[$\displaystyle-\frac{1}{2(a²-r²)}$, Im[r]
Re[a] $ ≠ $ Im[a] Re[r] || (( $a+r>0$ || $a+r ∉ $ Reals) && ($a<r$ ||
$a-r ∉ $ Reals) || $r ∉ $ Reals )]} (* this is a comment *)
\end{mat}
\end{shaded}
\end{document}
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{"url":"https:\/\/www.physicsforums.com\/threads\/linear-algebra-ga-rref-a.255377\/","text":"Linear Algebra, GA=rref(A)\n\n1. Sep 11, 2008\n\nrocomath\n\nSo I found the elimination matrices such that $$G_3G_2G_1A=rref(A)$$ which, but it took way too long. Is there a shorter method?\n\n2. Sep 11, 2008\n\nDefennder\n\nI don't understand what were you trying to find. You want to find the matrix E such that EA = reduced row-echelon form of A ?\n\nIf so, I don't see any easy way to get it. Note that the elementary matrix corresponding to a row operation is simply the identity matrix with that same row operation performed on it. Just keep a simple record of all the types of row reduction you did, then you can easily get E from them.\n\n3. Sep 11, 2008\n\nDefennder\n\nJust thought about this a little longer and realised that if all you want is the final matrix G which is a matrix product of all the E's, then one way you could get it would be to juxtapose the identity matrix next to A and and row reduce A to it's reduced row echelon form. The resultant matrix next to rref(A) would be G. If you want the composite E's you'll have to solve as above.\n\n4. Sep 11, 2008\n\nrocomath\n\nThat's what my classmate told me as well, I haven't verified that method yet.\n\nI did what you said in the first post, took me forever to get G through all the E's, LOL.\n\n5. Sep 11, 2008\n\nrocomath\n\nLol much quicker!!! )\n\n6. Sep 11, 2008\n\nDefennder\n\nWell the quickest way of course would be to use MATLAB. But that's cheating.","date":"2017-03-29 13:35:10","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.7940947413444519, \"perplexity\": 387.2985122248704}, \"config\": {\"markdown_headings\": false, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2017-13\/segments\/1490218190295.65\/warc\/CC-MAIN-20170322212950-00413-ip-10-233-31-227.ec2.internal.warc.gz\"}"}
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Q: Invalid javascript Date in Google Chrome The below javascript convertion returns invalid date while ruuning application in google Chrome.But it returns correct datetime in Internet Explorer.
var custDate=new Date("05/23/2104 10:15PM");
Please help.
A: Have a look at this article.
new Date("05/23/2104 10:15:00 GMT");
Examples:
var d = new Date(2011, 01, 07); // yyyy, mm-1, dd
var d = new Date(2011, 01, 07, 11, 05, 00); // yyyy, mm-1, dd, hh, mm, ss
var d = new Date("02/07/2011"); // "mm/dd/yyyy"
var d = new Date("02/07/2011 11:05:00"); // "mm/dd/yyyy hh:mm:ss"
var d = new Date(1297076700000); // milliseconds
var d = new Date("Mon Feb 07 2011 11:05:00 GMT"); // ""Day Mon dd yyyy hh:mm:ss GMT/UTC
A: also,
new Date() // current date and time
new Date(milliseconds) //milliseconds since 1970/01/01
new Date(dateString)
new Date(year, month, day, hours, minutes, seconds, milliseconds)
or
d1 = new Date("October 13, 1975 11:13:00")
d2 = new Date(79,5,24)
d3 = new Date(79,5,24,11,33,0)
A: for chrome use this syntax :
new Date("05/23/2014 22:15");
normaly, it will solved
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{"url":"https:\/\/www.omnimaga.org\/the-axe-parser-project\/bug-reports\/45\/","text":"### Author Topic: Bug Reports \u00a0(Read 161669 times)\n\n0 Members and 1 Guest are viewing this topic.\n\n#### Eeems\n\n\u2022 Mr. Dictator\n\u2022 LV13 Extreme Addict (Next: 9001)\n\u2022 Posts: 6161\n\u2022 Rating: +318\/-36\n\u2022 C'est la vie\n##### Re: Bug Reports\n\u00ab Reply #45 on: February 22, 2010, 10:39:24 pm \u00bb\nAh ok XP\n\/e\n\n#### Eeems\n\n\u2022 Mr. Dictator\n\u2022 LV13 Extreme Addict (Next: 9001)\n\u2022 Posts: 6161\n\u2022 Rating: +318\/-36\n\u2022 C'est la vie\n##### Re: Bug Reports\n\u00ab Reply #46 on: February 23, 2010, 06:16:54 pm \u00bb\nok, so this isn't really a bug, but it's a warning...if you run this code:\nCode: [Select]\n[0011223344556677]->pic17->DFor(C,0,50)D+1->DIf D=80->DEndFor(A,0,12)For(B,0,7)pt-on(A*8[+D],A*8+D,pic1EndEndDispGraphEnd(note: [+D] is optional (take out the [] ))\nyou will with the extra +D on the completion of the program if you go to a menu and then back to homescreen your cursor will change to a insert-2nd one, and then your calc will crash and ram clear, if you exclude the extra +D then you will brick your calc...the same thing happens but instead of a insert-2nd cursor it is a lowercase-alpha cursor. and your calc will not crash but stay on that screen, and I tried pulling the batteries (all of the AAA's) out to no avail.\nI was able to fix it though by linking a classmate's 84+ to mine and sending an empty L1 to my 83+, and upon the 84+ erroring because there was nothing receiving, my 83+ on the other-hand unfroze and I was able to do things with it, although the alpha cursor was stuck on lowercase... when I didn't try to clear the ram right away it froze again, and I had to send L1 again. the second time I immediately cleared my RAM and my calc is now fixed.\n\ntl-dr;\ndon't display sprites off of the screen on the bottom, or to the right by 8 and then quit out of the program, bad things happen...\n\/e\n\n#### Quigibo\n\n\u2022 The Executioner\n\u2022 CoT Emeritus\n\u2022 LV11 Super Veteran (Next: 3000)\n\u2022 Posts: 2031\n\u2022 Rating: +1075\/-24\n##### Re: Bug Reports\n\u00ab Reply #47 on: February 23, 2010, 07:05:52 pm \u00bb\nRight, I haven't clipped the sprites yet, so that means it actually draws the sprite into the memory immediately after the buffer which contains a lot of important information the calc needs...\u00a0 so it will corrupt that data and do a RAM clear most likely.\u00a0 Might be fixed in the next version.\n___Axe_Parser___\nToday the calculator, tomorrow the world!\n\n#### Eeems\n\n\u2022 Mr. Dictator\n\u2022 LV13 Extreme Addict (Next: 9001)\n\u2022 Posts: 6161\n\u2022 Rating: +318\/-36\n\u2022 C'est la vie\n##### Re: Bug Reports\n\u00ab Reply #48 on: February 23, 2010, 07:13:47 pm \u00bb\nyeah, I figured that out...and wow that was some bad corruption\n\/e\n\n#### DJ Omnimaga\n\n\u2022 Now active at https:\/\/codewalr.us\n\u2022 CoT Emeritus\n\u2022 LV15 Omnimagician (Next: --)\n\u2022 Posts: 55821\n\u2022 Rating: +3151\/-232\n\u2022 CodeWalrus founder & retired Omnimaga founder\n##### Re: Bug Reports\n\u00ab Reply #49 on: February 23, 2010, 07:16:04 pm \u00bb\nsprite clipping is something I would like to have personally. It makes it easier to code certain engines. Make sure clipping also does all 4 screen sides. xLIB used to not do the upper side and instead gave RAM Clears\nIn case you are wondering where I went, I left Omni back in 2015 to form CodeWalrus due to various reasons explained back then, but I stopped calc dev in 2016 and am now mostly active on the CW Discord server at https:\/\/discord.gg\/cuZcfcF\n\n#### Builderboy\n\n\u2022 Physics Guru\n\u2022 CoT Emeritus\n\u2022 LV13 Extreme Addict (Next: 9001)\n\u2022 Posts: 5673\n\u2022 Rating: +613\/-9\n\u2022 Would you kindly?\n##### Re: Bug Reports\n\u00ab Reply #50 on: February 23, 2010, 07:40:09 pm \u00bb\nMost definetaly, as of now in the program i'm writing i needed to take super special extra care that the object didn't go one pixel off the screen, and there are going to be cases where you are going to want that anyway, like for smoothscrolling maps and such\n\n#### DJ Omnimaga\n\n\u2022 Now active at https:\/\/codewalr.us\n\u2022 CoT Emeritus\n\u2022 LV15 Omnimagician (Next: --)\n\u2022 Posts: 55821\n\u2022 Rating: +3151\/-232\n\u2022 CodeWalrus founder & retired Omnimaga founder\n##### Re: Bug Reports\n\u00ab Reply #51 on: February 23, 2010, 07:50:25 pm \u00bb\nI think i lost Metroid II progress 4 times due to accidentally displaying stuff outside of the screen\nIn case you are wondering where I went, I left Omni back in 2015 to form CodeWalrus due to various reasons explained back then, but I stopped calc dev in 2016 and am now mostly active on the CW Discord server at https:\/\/discord.gg\/cuZcfcF\n\n#### ztrumpet\n\n\u2022 The Rarely Active One\n\u2022 CoT Emeritus\n\u2022 LV13 Extreme Addict (Next: 9001)\n\u2022 Posts: 5712\n\u2022 Rating: +364\/-4\n\u2022 If you see this, send me a PM. Just for fun.\n##### Re: Bug Reports\n\u00ab Reply #52 on: February 23, 2010, 09:38:05 pm \u00bb\nWow.\nSo far I've cleared my ram twice (infinite loops, pulled battery) and corrupted a group with Axe (but I have no idea how).\n\nI'm liking Axe, but not the annoying glitches.\u00a0 Axe is still awesome!\nIf I'm wrong, please correct me!\nUnfinished Projects:\n Elmgon 14% Basic Movement Demo Homescreen Game Pack 80% Basic Latest Release Cube Droid Saves the Galaxy 65% Axe Demo Detonate 70% Axe\nCompleted Projects:\nExodus | Midnight |Drifter | Axe Snake | Jump! | Factory Theta | Spider | Plot Drop | Papi Jump | Numb3rs | Nibbler | Boost | Duel Tile Map Editor | Homescreen Map Editor | Key Group Check | Oasis\n\n#### DJ Omnimaga\n\n\u2022 Now active at https:\/\/codewalr.us\n\u2022 CoT Emeritus\n\u2022 LV15 Omnimagician (Next: --)\n\u2022 Posts: 55821\n\u2022 Rating: +3151\/-232\n\u2022 CodeWalrus founder & retired Omnimaga founder\n##### Re: Bug Reports\n\u00ab Reply #53 on: February 23, 2010, 09:40:31 pm \u00bb\nglitches are inevitable really, with most apps. To say it's even possible to crash a calculator without any ASM...\nIn case you are wondering where I went, I left Omni back in 2015 to form CodeWalrus due to various reasons explained back then, but I stopped calc dev in 2016 and am now mostly active on the CW Discord server at https:\/\/discord.gg\/cuZcfcF\n\n#### Quigibo\n\n\u2022 The Executioner\n\u2022 CoT Emeritus\n\u2022 LV11 Super Veteran (Next: 3000)\n\u2022 Posts: 2031\n\u2022 Rating: +1075\/-24\n##### Re: Bug Reports\n\u00ab Reply #54 on: February 23, 2010, 10:17:38 pm \u00bb\nYou guys all complain about \"RAM clears\" and \"corrupted memory\".\u00a0 Have you ever tried to program in assembly?\u00a0 There are so many leaks and corruptions that happen, not to mention all the frustration of trying to find logical errors in the code, that almost all ASM programmers run their works in progress on emulators just in case and to speed up the process.\u00a0 I can guarantee that if you tried to make the same program in assembly (unless you're highly experienced with it), you would have had at least an order of magnitude more problems with the code.\n\nRemember, me giving you the freedom to run lower level assembly code and commands is a trade-off with the safety of running it.\n\nNow, if you get an unexpected error either at compile time or at run time, I really need to know about that so I can fix it.\u00a0 I currently am aware of 2 mysterious bugs.\u00a0 One is that the compiler sometimes gives a random error if the program was just modified but parsing a second time always works.\u00a0 I have no idea what is causing that.\u00a0 Another error mysteriously vanished when I added some code unrelated to the error, so it will probably come back to haunt me sometime.\u00a0 I think it had something to do with automatic parenthesis in math operations.\n___Axe_Parser___\nToday the calculator, tomorrow the world!\n\n#### Builderboy\n\n\u2022 Physics Guru\n\u2022 CoT Emeritus\n\u2022 LV13 Extreme Addict (Next: 9001)\n\u2022 Posts: 5673\n\u2022 Rating: +613\/-9\n\u2022 Would you kindly?\n##### Re: Bug Reports\n\u00ab Reply #55 on: February 23, 2010, 10:29:47 pm \u00bb\nMmmmmm i think i had that happen to me once.\u00a0 I got an Error Block on one of my programs after transferring to wabbit, but then it went away after trying it again.\u00a0 I wonder if changes are being made to the app or program?\u00a0 Seems unlikely, must be something else, and i don't pretend to be an expert in the ways of Asm\n\nAnd thats a good point about the RAM clears Us Basic programmers are used to other things, so you'll just have to put up with our complaints for the time being Plus its still an alpha release, and an untested one at that.\n\n#### Eeems\n\n\u2022 Mr. Dictator\n\u2022 LV13 Extreme Addict (Next: 9001)\n\u2022 Posts: 6161\n\u2022 Rating: +318\/-36\n\u2022 C'est la vie\n##### Re: Bug Reports\n\u00ab Reply #56 on: February 23, 2010, 11:17:45 pm \u00bb\nUg...tell me about it...I had some of the worst memory leaks on hunt, and it took me forever to fix them\nthe random error tat isn't an error usually comes up with me if prgmLOL is exsisting, so deleting it before compiling will usually keep it from happening, but sometimes it won't.\nHmm, how hard would it be to add something that when it errors it tells you what line it's on?\n\/e\n\n#### Builderboy\n\n\u2022 Physics Guru\n\u2022 CoT Emeritus\n\u2022 LV13 Extreme Addict (Next: 9001)\n\u2022 Posts: 5673\n\u2022 Rating: +613\/-9\n\u2022 Would you kindly?\n##### Re: Bug Reports\n\u00ab Reply #57 on: February 23, 2010, 11:31:57 pm \u00bb\nHmm, how hard would it be to add something that when it errors it tells you what line it's on?\n\nAh, yes that would be very useful!\u00a0 Many a times i have gone editing to try to find out what was causing the problem.\n\n#### DJ Omnimaga\n\n\u2022 Now active at https:\/\/codewalr.us\n\u2022 CoT Emeritus\n\u2022 LV15 Omnimagician (Next: --)\n\u2022 Posts: 55821\n\u2022 Rating: +3151\/-232\n\u2022 CodeWalrus founder & retired Omnimaga founder\n##### Re: Bug Reports\n\u00ab Reply #58 on: February 23, 2010, 11:34:50 pm \u00bb\nYou guys all complain about \"RAM clears\" and \"corrupted memory\". \u00a0Have you ever tried to program in assembly? \u00a0There are so many leaks and corruptions that happen, not to mention all the frustration of trying to find logical errors in the code, that almost all ASM programmers run their works in progress on emulators just in case and to speed up the process. \u00a0I can guarantee that if you tried to make the same program in assembly (unless you're highly experienced with it), you would have had at least an order of magnitude more problems with the code.\n\nRemember, me giving you the freedom to run lower level assembly code and commands is a trade-off with the safety of running it.\nOh I do know in ASM it is worse. I did not code it, but I do know in ASM you have direct access to the calc memory, thus easier to break stuff. It is even possible to delete the calc OS sending certificate IIRC, causing it to no longer be able to receive a new OS anymore, so if your OS gets deleted, your calc is bricked for good. However we still have a right to complain as lib-enhanced BASIC\/other languages programmers because in our case, we program directly on the machine the program is gonna be tested on, meaning that unlike you, if our program crashes, we lose everything we didn't backup. It may be much easier for us to debug these errors, but at least on your side you don't have to backup your progress everytime they happen. In BASIC we also have to cope with rare TI-OS bugs that causes some BASIC programs to behave weirdly for absurd reasons (such as lone If statements inside a For( loop that doesn't have its closing parhentesis or when storing a very large set of concatened strings in one STO command). Fortunately, in pure-BASIC we no longer have to deal with extremly bad OS bugs that can cause RAM Clears such as when having a large PRGM list on OS 1.13 and the Equ>String glitch.\n\u00ab Last Edit: February 23, 2010, 11:41:05 pm by DJ Omnimaga \u00bb\nIn case you are wondering where I went, I left Omni back in 2015 to form CodeWalrus due to various reasons explained back then, but I stopped calc dev in 2016 and am now mostly active on the CW Discord server at https:\/\/discord.gg\/cuZcfcF\n\n#### ztrumpet\n\n\u2022 The Rarely Active One\n\u2022 CoT Emeritus\n\u2022 LV13 Extreme Addict (Next: 9001)\n\u2022 Posts: 5712\n\u2022 Rating: +364\/-4\n\u2022 If you see this, send me a PM. Just for fun.\n##### Re: Bug Reports\n\u00ab Reply #59 on: February 24, 2010, 04:31:06 pm \u00bb\nSince it's such an early release then I'm fine with lots of errors now.\u00a0 However, when you come out with a full version I think it should be close to error free because some people will get a RAM Clear and never us Axe again.\n\nI've gotten a lot of Err:Blocks randomly, so I just would open the source, look for a glitch, change something irrelevant, and recompile.\n\nCould you add a \"Where is this glitch\" feature?\nOh, and can you add the Axe Header to all source files so we don't have to comb through our huge lists?\u00a0 Thanks! (This is a big one for me, as I have to hold down for about 45 seconds before I get to my programs in RAM.)\n\u00ab Last Edit: February 24, 2010, 04:31:20 pm by ztrumpet \u00bb\nIf I'm wrong, please correct me!\nUnfinished Projects:\n Elmgon 14% Basic Movement Demo Homescreen Game Pack 80% Basic Latest Release Cube Droid Saves the Galaxy 65% Axe Demo Detonate 70% Axe\nCompleted Projects:\nExodus | Midnight |Drifter | Axe Snake | Jump! | Factory Theta | Spider | Plot Drop | Papi Jump | Numb3rs | Nibbler | Boost | Duel Tile Map Editor | Homescreen Map Editor | Key Group Check | Oasis","date":"2019-09-21 15:44:14","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.28189218044281006, \"perplexity\": 7222.8000011680215}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2019-39\/segments\/1568514574532.44\/warc\/CC-MAIN-20190921145904-20190921171904-00503.warc.gz\"}"}
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Q: How can I split a Windows 7 image on to multiple CDRs that I can boot from to install? Is there a way that I can do this? I'd appreciate any help / pointers.
A: Could you use something like Plop? You could make a bootable USB flash drive with Windows 7 on it and boot from Plop, which could then allow you to boot from the flash drive.
edit: I realize this isn't exactly the question you're asking, but it might work for the situation you're in...
A: The Windows Automated Installation Kit (AIK) includes a utility called imagex, which will split a .wim image, among other things. The AIK is really the way to go for building customized Windows installations.
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Ochna andravinensis är en tvåhjärtbladig växtart som beskrevs av Henri Ernest Baillon. Ochna andravinensis ingår i släktet Ochna och familjen Ochnaceae. Inga underarter finns listade i Catalogue of Life.
Källor
Malpigiaordningen
andravinensis
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\section{Introduction}
The notion of a generalized complex structure has been introduced by N. Hitchin
\cite{Hit}. It generalizes both the concept of a complex structure and that of a
symplectic one and can be considered as the complex analog of the notion of a Dirac
structure introduced by T. Courant and A. Weinstein \cite{Cou,CouWei} to unify Poisson
and symplectic geometries. The generalized complex geometry has been further developed
by M. Gualtieri \cite{Gu} and has recently attracted the interest of many
mathematicians and physicists, see, for example,
\cite{AbBo,Ba,BaBo,Ber,Ca,Cr,GrMiPeTo-2,Hu,IgWa,Ik,Je,KaLi,Li,LiMiToZa,Zab,Zuc} and the
literature quoted there.
A generalized complex structure on a smooth manifold $N$ is an endomorphism $J$ of
the bundle $TN\oplus T^{\ast}N$ satisfying the following conditions: $(a)$ $J^2=-Id$,~
$(b)$ $J$ preserves the natural metric $<X+\xi,Y+\eta>=\frac{1}{2}(\xi(Y)+\eta(X))$,
$X,Y\in TN$, $\xi,\eta\in T^{\ast}N$,~ $(c)$ the $+i$-eigensubbundle of $J$ in
$(TN\oplus T^{\ast}N)\otimes {\Bbb C}$ is involutive with respect to the bracket
introduced by T. Courant \cite{Cou}. If $J$ satisfies only the conditions $(a)$ and
$(b)$, it is called generalized almost complex structure. The integrability condition
$(c)$ is equivalent to vanishing of the Nijenhuis tensor of $J$ defined by means of the
Courant bracket instead of the Lie one. Every complex and every symplectic structure on
$N$ induce generalized complex structures on $N$ in a natural way. Examples of
generalized complex structures that cannot be obtained from a complex or a symplectic
structure have been given in \cite{CaGu,Ca,Gu}. The main purpose of the present paper
is to provide other examples of this type by means of the twistor construction.
The twistor theory has been created by R. Penrose \cite{Pen, PeWa} to solve problems in
Mathematical Physics. The construction of a twistor space in the framework of
Riemannian Geometry has been developed by M. Atiyah, N. Hitchin and I. Singer
\cite{AtHiSi}. Following the Penrose ideas, they have defined a natural almost complex
structure on the twistor space of an oriented Riemannian four-dimensional manifold and
found its integrability condition. J. Eeells and S. Salamon \cite{EeSa} have introduced
another almost complex structure on the twistor space of a $4$-manifold which although
is never integrable plays an important role in the harmonic maps theory. The twistor
construction has been generalized to any even-dimensional Riemannian manifold by L.
B\'erard-Bergery and T. Ochiai \cite{BeOch}, N. O'Brian and J. Rawnsley \cite{OBrRaw},
P. Dubois-Violette \cite{D-V}, I. Skornyakov \cite{Sk}. It has been extended to the
class of quaternionic K\"ahler manifolds by S. Salamon \cite{Sal}, L. B\'erard-Bergery
(unpublished, see \cite[Sec. 14G]{Besse}, \cite{BeOch}), C. LeBrun \cite{LeBr}.
Let $M$ be an even-dimensional smooth manifold. Following the general scheme of the
twistor construction, we consider the bundle ${\mathcal G}$ over $M$ whose fibre at a point
$p\in M$ consists of all generalized complex structures on the vector space $T_pM$
(i.e. endomorphisms satisfying conditions $(a)$ and $(b)$ above) which yield the
canonical orientation of $T_pM\oplus T_p^{\ast}M$. The general fibre of ${\mathcal G}$
admits a complex structure (in the usual sense) and this fact allows one to define two
natural generalized almost complex structures ${\mathcal J}_1$ and ${\mathcal J}_2$ on the
manifold ${\mathcal G}$ when the base manifold $M$ is endowed with a linear connection.
These are analogs of the Atiyah-Hitchin-Singer and Eells-Salamon almost complex
structures. Suppose that the given connection is torsion-free. Under this condition,
the main result of the present paper states that if $dim\, M=2$, then the structure
${\mathcal J}_1$ is always integrable, while if $dim\, M\geq 4$, it is integrable if and
only if the given connection on $M$ is flat (i.e. $M$ is an affine manifold). In
contrast, the structure ${\mathcal J}_2$ is never integrable. The complex structure on the
fibres of ${\mathcal G}$ is K\" ahlerian with respect to a natural metric induced by the
metric $<~,~>$. The corresponding K\" ahler form yields a generalized complex structure
on the general fibre of ${\mathcal G}$ and one can define two new generalized almost
complex structures on ${\mathcal G}$. It is not hard to see that these structures are also
never integrable.
\section{Generalized complex structures}
Let $W$ be a $n$-dimensional real vector space and $g$ a metric of signature $(p,q)$
on it, $p+q=n$. We shall say that a basis $\{e_1,...,e_{n}\}$ of $W$ is {\it
orthonormal} if $||e_1||^2=...=||e_p||^2=1$, $||e_{p+1}||^2=...=||e_{p+q}||^2=-1$. If
$n=2m$ is an even number and $p=q=m$, the metric $g$ is usually called {\it neutral}.
Recall that a complex structure $J$ on $W$ is called {\it compatible} with the metric
$g$, if the endomorphism $J$ is $g$-skew-symmetric. Suppose that $p=2k$ and $q=2l$, and
let $J$ be a compatible complex structure on $W$. Then it is easy to see by induction
that there is an orthonormal basis $\{e_1,....,e_{n}\}$ of $W$ such that
$e_{2i}=Je_{2i-1}$, $i=1,..,k+l$.
\vspace{0.1cm}
Now let $V$ be a $2n$-dimensional real vector space and $V^{\ast}$ its dual space. Then
the vector space $W=V\oplus V^{\ast}$ admits a natural neutral metric defined by
\begin{equation}\label{eq 0.0}
<X+\xi,Y+\eta>=\displaystyle{\frac{1}{2}}(\xi(Y)+\eta(X))
\end{equation}
(we refer to \cite{Gu} for algebraic facts about this metric).
\begin{lemma}\label {pi_1,2-basis}
Let $V$ be a $2n$-dimensional real vector space and let $\{e_i+\eta_i\}$, $i=1,...,4n$,
be an orthonormal basis of the space $V\oplus V^{\ast}$ endowed with the neutral metric
{\rm {(\ref{eq 0.0})}}. Then $e_1,...,e_{2n}$ is a basis of $V$ and
$\eta_1,...,\eta_{2n}$ is a basis of $V^{\ast}$ (similarly for $e_{2n+1},...,e_{4n}$
and $\eta_{2n+1},...,\eta_{4n}$).
\end{lemma}
\begin{proof}
Assume that $\sum_{k=1}^{2n}\lambda_k e_k=0$ for some $\lambda_1,...,\lambda_{2n}\in
{\Bbb R}$. Then we have \\ $\sum_{k=1}^{2n}\lambda_k\eta_l(e_k)=0$ for every
$l=1,...,2n$. Denote by $P$ the matrix $[\eta_l(e_k)]$, $1\leq l,k\leq 2n$. Let $I$ be
the unit $2n\times 2n$-matrix. Then the matrix $S=P-I$ is skew-symmetric since
$\eta_l(e_k)+\eta_k(e_l)=2\delta_{lk}$. Therefore
$(det\,P)^2=det\,(P\,^tP)=det\,(I-S^2)$. Let $\beta_1,...,\beta_{2n}$ be the
eigenvalues of the symmetric matrix $S^2$. Then $\beta_k\leq 0$ since the matrix $S$ is
skew-symmetric. Thus $(det\,P)^2=\Pi_{k=1}^{2n}(1-\beta_k)\geq 1$, in particular
$det\,P\neq 0$. Therefore all $\lambda_k$' s must be zero.
\end{proof}
\vspace{0.1cm}
Let $\{e_i\}$ be an arbitrary basis of a real vector space $V$ and $\{\alpha_i\}$ its
dual basis, $i=1,...,2n$. Then the orientation of the space $V\oplus V^{\ast}$
determined by the basis $\{e_i,\alpha_i\}$ does not depend on the choice of the basis
$\{e_i\}$. Further on, we shall always consider $V\oplus V^{\ast}$ with this {\it
canonical orientation}.
The next lemma is of technical character and will be used in the last section.
\begin{lemma}\label {Orient}
Let $V$ be a $2$-dimensional real vector space and let $\{Q_i=e_i+\eta_i\}$, $1\leq i\leq 4$,
be an orthonormal basis of the space $V\oplus V^{\ast}$ endowed with its natural
neutral metric {\rm {(\ref{eq 0.0})}}. Then:
$$
\begin{array}{lll}
e_3=a_{11}e_1+a_{12}e_2 \\
e_4=a_{21}e_1+a_{22}e_2
\end{array}
$$
where $A=[a_{kl}]$ is an orthogonal matrix. If $det\,A=1$, the basis $\{Q_i\}$ yields
the canonical orientation of $V\oplus V^{\ast}$ and if $det\,A=-1$ it yields the
opposite one.
\end{lemma}
\begin{proof}
According to Lemma~\ref{pi_1,2-basis},
$$
\begin{array}{lll}
e_3=a_{11}e_1+a_{12}e_2 \hspace{0.3cm}\mbox { and }\hspace{0.3cm}
e_1=b_{11}e_3+b_{12}\,e_4\\
e_4=a_{21}e_1+a_{22}e_2 \hspace{1.5cm} e_2=b_{21}e_3+b_{22}e_4
\end{array}
$$
where $[b_{kl}]=[a_{kl}]^{-1}$. Since the basis $\{Q_i\}$ is orthonormal, we have
$\eta_i(e_j)+\eta_j(e_i)=0$, $i\neq j$, $1\leq i,j\leq 4$ and
$\eta_1(e_1)=\eta_2(e_2)=1$, $\eta_3(e_3)=\eta_4(e_4)=-1$. The latter identities and
the identities $\eta_1(e_3)+\eta_3(e_1)=0$, $\eta_1(e_4)+\eta_4(e_1)=0$,
$\eta_3(e_4)+\eta_4(e_3)=0$ imply
$$
\begin{array}{c}
a_{12}\eta_1(e_2)+b_{12}\eta_3(e_4)=b_{11}-a_{11} \\
a_{22}\eta_1(e_2)-b_{11}\eta_3(e_4)=b_{12}-a_{21}.
\end{array}
$$
It follows that
\begin{equation}\label{eq I-b-row}
b_{11}^2+b_{12}^2=1.
\end{equation}
Similarly, we see that
\begin{equation}\label{eq rest}
b_{21}^2+b_{22}^2=1,~a_{11}^2+a_{12}^2=1,~a_{21}^2+a_{22}^2=1.
\end{equation}
Expressing $b_{kl}$' s in terms of $a_{kl}$' s, we get from (\ref{eq I-b-row}) and
(\ref{eq rest}) that
$$
(a_{11}a_{22}-a_{12}a_{21})^2=1.
$$
It follows that the matrix $A=[a_{kl}]$ is orthogonal.
To prove the second part of the lemma, let us denote by $\{\alpha_1,\alpha_2\}$ the dual basis
of the basis $\{e_1,e_2\}$ of $V$. Then
$$
\begin{array}{c}
\eta_1=\alpha_1+c\alpha_2,\> \eta_3=d_{11}\alpha_1+d_{12}\alpha_2\\
\eta_2=-c\alpha_1+\alpha_2,\> \eta_4=d_{21}\alpha_1+d_{22}\alpha_2
\end{array}
$$
for some constants $c$ and $d_{kl}$. For the coefficients $d_{kl}$ we have
$$
\begin{array}{lll}
d_{11}=\eta_3(e_1)=-\eta_1(e_3)=-(a_{11}+ca_{12}),\\
d_{12}=\eta_3(e_2)=-\eta_2(e_3)=-(-ca_{11}+a_{12}),\\
d_{21}=\eta_4(e_1)=-\eta_1(e_4)=-(a_{21}+ca_{22}),\\
d_{22}=\eta_4(e_2)=-\eta_2(e_4)=-(ca_{21}+a_{22}).\\
\end{array}
$$
Thus, if we set $c_{11}=c_{22}=1$ and $c_{12}=-c_{21}=c$, then
$[d_{kl}]=-[a_{kl}][c_{lk}]$. Set $C=[c_{kl}]$ and let $I$ be the unit $2\times
2$-matrix. Then the transition matrix from the basis $\{e_1,e_2,\alpha_1,\alpha_2\}$ to
the basis $\{Q_1,Q_2,Q_3,Q_4\}$ has the form
$$
\left[
\begin{array}{cc}
I & C \\
A & -AC^{t}
\end{array} \right]
$$
The determinant of this matrix is equal to $4det\,A$, which proves the lemma.
\end{proof}
\vspace{0.1cm}
A {\it generalized complex structure} on a real vector space $V$ is, by definition, a
complex structure on the space $V\oplus V^{\ast}$ compatible with its natural neutral
metric \cite{Hit}. If a vector space admits a generalized complex structure, it is
necessarily of even dimension \cite{Gu}. We refer to \cite{Gu} for more facts about the
generalized complex structures.
\vspace{0.1cm}
\noindent {\bf Examples}~\cite{Gu,Hit}. Let $V$ be a $2n$-dimensional real vector
space.
\noindent{\bf 1}. Let $K$ be a complex structure on $V$ and define a complex structure
$K^{\ast}$ on $V^{\star}$ by setting $(K^{\ast}\alpha)(X)=\alpha(KX)$, $\alpha\in
V^{\ast}$, $X\in V$. Then the endomorphism $J$ on $V\oplus V^{\ast}$ defined by $J=K$
on $V$ and $J=-K^{\ast}$ on $V^{\star}$ is a generalized complex structure on $V$. This
structure yields the canonical orientation of $V\oplus V^{\ast}$ (the orientation
induced by $J$ is defined by means of a basis of the form
$Q_1,JQ_2,...,Q_{2n},JQ_{2n}$) .
\noindent{\bf 2}. Let $\omega$ be a symplectic form on $V$ (i.e. a non-degenerate
$2$-form). Then the map $X\to \imath_X\omega$ is an isomorphism of $V$ onto
$V^{\star}$. Denote this isomorphism also by $\omega$ and define a complex structure
$S$ on $V\oplus V^{\ast}$ by setting $SX=\omega(X)$ and $S\alpha=-\omega^{-1}(\alpha)$
for $X\in V$ and $\alpha\in V^{\ast}$. Then $S$ is compatible with the natural neutral
metric of $V\oplus V^{\ast}$, so $S$ is a generalized complex structure on $V$. The
structure $S$ induces the canonical orientation of $V\oplus V^{\ast}$ if and only if
$n=\frac{1}{2}dim\,V$ is an even number.
Now let $g$ be a metric on $V$ (of any signature) and $K$ a complex structure on $V$
compatible with the metric $g$. Then the generalized complex structures $J$ and $S$
yielded by $K$ and the $2$-form $\omega(X,Y)=g(KX,Y)$ commute.
\noindent{\bf 3}. The direct sum of generalized complex structures is also a
generalized complex structure.
\noindent{\bf 4}. Any $2$-form $B\in \Lambda^{2}V^{\ast}$ acts on $V\oplus V^{\ast}$
via the inclusion $\Lambda^{2}V^{\ast}\subset \Lambda^{2}(V\oplus V^{\ast})\cong
so(V\oplus V^{\ast})$; in fact this is the action $X+\xi\to \imath_{X}B$;~ $X\in V$,
$\xi\in V^{\ast}$. Denote the latter map again by $B$. Then the invertible map $e^{B}$
is given by $X+\xi\to X+\xi+\imath_{X}B$ and is an orthogonal transformation of
$V\oplus V^{\ast}$. Thus, given a generalized complex structure $J$ on $V$, the map
$e^{B}Je^{-B}$ is also a generalized complex structure on $V$, called the $B$-transform
of $J$.
Similarly, any $2$-vector $\beta\in \Lambda^{2}V$ acts on $V\oplus V^{\ast}$. If we
identify $V$ with $(V^{\ast})^{\ast}$, so $\Lambda^{2}V\cong
\Lambda^{2}(V^{\ast})^{\ast}$, the action is given by $X+\xi\to \imath_{\xi}\beta\in
V$. Denote this map by $\beta$. Then the exponential map $e^{\beta}$ acts on $V\oplus
V^{\ast}$ via $X+\xi\to X+\imath_{\xi}\beta+\xi$, in particular $e^{\beta}$ is an
orthogonal transformation. Hence, if $J$ is a generalized complex structure on $V$, so
is $e^{\beta}Je^{-\beta}$. It is called the $\beta$-transform of $J$.
\vspace{0.1cm}
Let $W$ be a $2m$-dimensional real vector space equipped with a metric $g$ of
signature $(2p,2q)$, $p+q=m$. Denote by $J(W)$ the set of all complex structures on $W$
compatible with the metric $g$. The group $O(g)$ of orthogonal transformations of $W$
acts transitively on $J(W)$ by conjugation and $J(W)$ can be identified with the
homogeneous space $O(2p,2q)/U(p,q)$. In particular, ${\it dim}\,J(W)=m^2-m$. The group
$O(2p,2q)$ has four connected components, while $U(p,q)$ is connected, therefore $J(W)$
has four components.
\vspace{0.1cm}
\noindent {\bf Example 5}. The space $O(2,2)/U(1,1)$ is the disjoint union of two
copies of the hyperboloid $x_1^2-x_2^2-x_3^2=1$. It seems instructive to see this in
the context of compatible complex structures. Let $W$ be a $4$-dimensional real vector
space equipped with a neutral metric and $e_1,...,e_4$ an orthonormal basis of $W$. Set
$\varepsilon_k=||e_i||^2$, $k=1,...,4$, and define skew-symmetric endomorphisms of $W$
by setting $S_{ij}e_k=\varepsilon_k(\delta_{ik}e_j - \delta_{kj}e_i)$, $1\leq i,j,k\leq
4$. Then the endomorphisms
$$
\begin{array}{lll}
I_1=S_{12}-S_{34}, & & J_1=S_{12}+S_{34}, \\
I_2=S_{13}-S_{24}, & & J_2=S_{13}+S_{24}, \\
I_3=S_{14}+S_{23}, & & J_3=S_{14}-S_{23}
\end{array}
$$
constitute a basis of the space of skew-symmetric endomorphisms of $W$ subject to
following relations: $I_1^2=-Id$, $I_2^2=I_3^2=Id$, $J_1^2=-Id$, $J_2^2=J_3^2=Id$,
$I_rI_s=-I_sI_r$, $J_rJ_s=-J_sJ_r$, $1\leq r\neq s\leq 3$ and $I_rJ_s=I_sJ_r$, $1\leq
r,s\leq 3$. Let $K$ be a complex structure on W compatible with the metric and let us
set $K=\sum_{r=1}^{3}(x_rI_r+y_rJ_r)$. Then we have
$$
(-x_1^2+x_2^2+x_3^2-y_1^2+y_2^2+y_3^2)Id+2\sum_{r,s=1}^{3}x_ry_sI_rJ_s=-Id
$$
Evaluating the latter identity at $e_1,...,e_4$, we see that
$$
-x_1^2+x_2^2+x_3^2-y_1^2+y_2^2+y_3^2=-1 \mbox { and } x_ry_s=0 \mbox { for } r,s=1,2,3.
$$
Therefore $K^2=-Id$ if and only if either $x_1^2-x_2^2-x_3^2=1$ and $y_1=y_2=y_3=0$ or
$y_1^2-y_2^2-y_3^2=1$ and $x_1=x_2=x_3=0$.
\vspace{0.1cm}
Consider $J(W)$ as a (closed) submanifold of the vector space $so(g)$ of $g$-skew-symmetric
endomorphisms of $W$. Then the tangent space of $J(W)$ at a point $J$ consists of all
endomorphisms $Q\in so(g)$ anti-commuting with $J$. Thus we have a natural $O(g)$ -
invariant almost complex structure ${\mathcal K}$ on $J(W)$ defined by ${\mathcal K}Q=J\circ
Q$. It is easy to check that this structure is integrable.
Fix an orientation on $W$ and denote by $J^{\pm}(W)$ the set of compatible complex
structures on $W$ that induce $\pm$ the orientation of $W$. The set $J^{\pm}(W)$ has
the homogeneous representation $SO(2p,2q)/U(p,q)$ and, thus, is the union of two
components of $J(W)$.
\vspace{0.1cm}
\noindent {\bf Example 6}. Under the notations of Example 5, let $e_1,e_2,e_3,e_4$ be
an oriented orthonormal basis of $W$. Then it is easy to see that $J^{+}(W)$ is the
hyperboloid $\{\sum_{r=1}^{3}x_rI_r:~x_1^2-x_2^2-x_3^2=1\}$.
\vspace{0.1cm}
Further on, given an even-dimensional real vector space $V$, the set $J^{+}(V\oplus
V^{\ast})$ of generalized complex structures on $V$ inducing the canonical orientation
of $V\oplus V^{\ast}$ will be denoted by $G(V)$.
The group $GL(V)$ acts on $V\oplus V^{\ast}$ by letting $GL(V)$ act on $V^{\ast}$ in
the standard way. This action preserves the neutral metric (\ref{eq 0.0}) and the
canonical orientation of $V\oplus V^{\ast}$. Thus, we have an embedding of $GL(V)$ into
the group $SO(<~,~>)$ and, via this embedding, $GL(V)$ acts on the manifold $G(V)$ in a
natural manner.
\vspace{0.1cm}
{\it A generalized almost complex structure} on an even-dimensional smooth manifold $N$
is, by definition, an endomorphism $J$ of the bundle $TN\oplus T^{\ast}N$ with
$J^2=-Id$ which preserves the natural neutral metric of $TN\oplus T^{\ast}N$. Such a
structure is said to be {\it integrable} or {\it a generalized complex structure} if
its $+i$-egensubbunle of $(TN\oplus T^{\ast}N)\oplus {\Bbb C}$ is closed under the
Courant bracket \cite{Hit}. Recall that if $X,Y$ are vector fields on $N$ and
$\xi,\eta$ -- $1$-forms, the Courant bracket \cite{Cou} is defined by the formula
$$
[X+\xi,Y+\eta]=[X,Y]+{\mathcal L}_{X}\eta-{\mathcal
L}_{Y}\xi-\frac{1}{2}d(\imath_X\eta-\imath_Y\xi),
$$
where $[X,Y]$ on the right hand-side is the Lie bracket and ${\mathcal L}$ means the Lie
derivative. As in the case of almost complex structures, the integrability condition
for a generalized almost complex structure $J$ is equivalent to the vanishing of its
Nijenhuis tensor $N$, the latter being defined by means of the Courant bracket:
$$
N(A,B)=-[A,B]-J[A,JB]-J[JA,B]+[JA,JB], \> A,B\in TN\oplus T^{\ast}N.
$$
\vspace{0.1cm}
\noindent {\bf Example 7}. Let $J$ be a generalized almost complex structure on a
manifold $N$ and let $B$ be a smooth $2$-form on $N$. Then, according to Example 4,
$e^{B}Je^{-B}$ is a generalized almost complex structure on $N$. The exponential map
$e^{B}$ is an authomorphism of the Courant bracket (i.e.
$[e^{B}(X+\xi),e^{B}(Y+\eta]=e^{B}[X+\xi,Y+\eta]$) if and only if the form $B$ is
closed \cite{Gu}. In this case the structure $e^{B}Je^{-B}$ is integrable exactly when
the structure $J$ is so.
\section{The twistor space of generalized complex structures}
Let $M$ be a smooth manifold of dimension $2n$. Denote
by $\pi:{\mathcal G}\to M$ the bundle over $M$ whose fibre at a point $p\in M$ consists of
all generalized complex structures on $T_pM$ that induce the canonical orientation of
$T_pM\oplus T^{\ast}_pM$. This is the associated bundle
$$
GL(M)\times_{GL(2n,{\Bbb R}
)} G({\Bbb R}^{2n})
$$
where $GL(M)$ denotes the principal bundle of linear frames on $M$.
Let $\nabla$ be a linear connection on $M$. Following the standard twistor
construction, we can define two generalized almost complex structures ${\mathcal
J}_{1}^{\nabla}$ and ${\mathcal J}_{2}^{\nabla}$ on the manifold ${\mathcal G}$ in the
following way: The connection $\nabla$ gives rise to a splitting ${\mathcal V}\oplus {\mathcal
H}$ of the tangent bundle of the associated bundle ${\mathcal G}$ into vertical and
horizontal parts. The vertical space ${\mathcal V}_J$ of ${\mathcal G}$ at a point $J\in {\mathcal
G}$ is the tangent space at $J$ of the fibre through this point. This fibre is the
manifold $G(T_pM)$, $p=\pi(J)$, which admits a natural complex structure ${\mathcal K}$
defined in the previous section and we set ${\mathcal
J}_{\alpha}^{\nabla}=(-1)^{\alpha+1}{\mathcal K}$ on ${\mathcal V}_J$ and ${\mathcal
J}_{\alpha}^{\nabla}=(-1)^{\alpha}{\mathcal K}^{\ast}$ on ${\mathcal V}_J^{\ast}$,
$\alpha=1,2$. Thus ${\mathcal J}_{\alpha}^{\nabla}U=(-1)^{\alpha+1}J\circ U$ for every
$U\in {\mathcal V}_J$ ($U$ being considered as an endomorphism of $T_pM\oplus T^{\ast}_pM$)
and $({\mathcal J}_{\alpha}^{\nabla}\omega)(U)=(-1)^{\alpha}\omega(J\circ U)$ for
$\omega\in {\mathcal V}_J^{\ast}$. The horizontal space ${\mathcal H}_J$ is isomorphic via the
differential $\pi_{\ast J}$ to the tangent space $T_{p}M, p=\pi(J)$. Denoting
$\pi_{\ast J}|{\mathcal H}$ by $\pi_{{\mathcal H}}$, we define ${\mathcal J}_{\alpha}^{\nabla}$ on
${\mathcal H}_J\oplus {\mathcal H}_J^{\ast}$ as the lift of the endomorphism $J$ by the map
$\pi_{{\mathcal H}}\oplus (\pi_{{\mathcal H}}^{-1})^{\ast}$.
\vspace{0.1cm}
\noindent
{\bf Remark}. The fibre of ${\mathcal G}$ at any point $p\in M$ contains generalized
complex structures on $T_pM$ which do not preserve $T_pM$ as well as structures which
do not send $T_pM$ onto $T_{p}^{\ast}M$. This shows that the generalized almost complex
structures structures ${\mathcal J}_{1}^{\nabla}$ and ${\mathcal J}_{2}^{\nabla}$ are not
induced by an almost complex or a symplectic structure.
\vspace{0.1cm}
Further the generalized almost complex structure ${\mathcal J}_{\alpha}^{\nabla}$ will be
simply denoted by ${\mathcal J}_{\alpha}$ when the connection $\nabla$ is understood. The
image of every $A\in T_pM\oplus T_p^{\ast}M$ under the map $\pi_{{\mathcal H}}^{-1}\oplus
\pi_{{\mathcal H}}^{\ast}$ will be denoted by $A^h$. The elements of ${\mathcal H}_J^{\ast}$,
resp. ${\mathcal V}_J^{\ast}$, will be considered as $1$-forms on $T_J{\mathcal G}$ vanishing
on ${\mathcal V}_J$, resp. ${\mathcal H}_J$.
\vspace{0.1cm}
Let $A(M)$ be the bundle of the endomorphisms of $TM\oplus T^{\ast}M$ which are skew-
symmetric with respect to its natural neutral metric $<~,~>$. Consider the twistor
space ${\mathcal G}$ as a subbundle of $A(M)$. Then the inclusion of ${\mathcal G}$ is
fibre-preserving and the horizontal space of ${\mathcal G}$ at a point $J$ coincides with
the horizontal space of $A(M)$ at that point since the inclusion $G({\Bbb
R}^{2n})\subset so(2n,2n)$ is $SO(2n,2n)$-equivariant. Let $(U,x_1,...,x_{2n})$ be a
local coordinate system of $M$ and $\{Q_1,...,Q_{4n}\}$ an orthonormal frame of
$TM\oplus T^{\ast}M$ on $U$. Set $\varepsilon_k=||Q_k||^2$, $k=1,...,4n$, and define
sections $S_{ij}$, $1\leq i,j\leq {4n}$, of $A(M)$ by the formula
\begin{equation}\label{eq Sij}
S_{ij}Q_k=\varepsilon_k(\delta_{ik}Q_j - \delta_{kj}Q_i).
\end{equation}
Then $S_{ij}$, $i<j$, form an orthogonal frame of $A(M)$ with respect to the metric
$<a,b>=\displaystyle{-\frac{1}{2}}Trace\,(a\circ b);\, a,b\in A(M)$; moreover
$||S_{ij}||^2=\varepsilon_i\varepsilon_j$ for $i\neq j$. Set
$$\tilde x_{l}(a)=x_{l}\circ\pi(a),~ y_{ij}(a)=\varepsilon_i\varepsilon_j<a,S_{ij}>$$ for
$a\in A(M)$. Then $(\tilde x_{l},y_{ij})$, $1\leq l\leq 2n$, $1\leq i < j\leq 4n$, is a
local coordinate system of the manifold $A(M)$.
Let
$$
V=\sum_{i<j}v_{ij}\frac{\partial}{\partial y_{ij}}(J)
$$
be a vertical vector of ${\mathcal G}$ at a point $J$. It is convenient to set
$v_{ij}=-v_{ji}$ for $i\geq j$, $1\leq i,j\leq {4n}$. Then the endomorphism $V$ of
$T_{p}M\oplus T_{p}^{\ast}M$, $p=\pi(J)$, is determined by $VQ_i=\sum_{j=1}^{4n}
\varepsilon_iv_{ij}Q_j$. Moreover
\begin{equation}\label{cal J/ver}
{\mathcal J}_{\alpha}V=(-1)^{\alpha+1}\sum_{i<j}
(\sum_{k=1}^{4n}v_{ik}y_{kj}\varepsilon_k)\frac{\partial}{\partial y_{ij}}.
\end{equation}
Note also that, for every $A\in T_{p}M\oplus T_{p}^{\ast}M$, we have
\begin{equation}\label{cal J/hor}
A^h=\sum_{i=1}^{4n}(<A,Q_i>\circ\pi)\varepsilon_i Q_i^h \mbox { and } {\mathcal
J}_{\alpha}A^h=\sum_{i,j=1}^{4n}(<A,Q_i>\circ\pi)y_{ij}Q_j^h.
\end{equation}
For each vector field
$$X=\sum_{i=1}^{2n} X^{i}\frac{\partial}{\partial x_i}$$
on $U$, the horizontal lift $X^h$ on $\pi^{-1}(U)$ is given by
\begin{equation}\label{eq 3.1}
X^{h}=\sum_{k=1}^{2n} (X^{l}\circ\pi)\frac{\partial}{\partial\tilde x_l}-
\sum_{i<j}\sum_{p<q}
y_{pq}(<\nabla_{X}S_{pq},S_{ij}>\circ\pi)\varepsilon_i\varepsilon_j\frac{\partial}{\partial
y_{ij}}
\end{equation}
where $\nabla$ is the connection on $A(M)$ induced by the given connection on $M$.
Let $a\in A(M)$ and $p=\pi(a)$. Then (\ref{eq 3.1}) implies
that, under the standard identification of $T_{a}A(M)$ with the vector space of
skew-symmetric endomorphisms of $T_{p}M\oplus T_{p}^{\ast}M$, we have
\begin{equation}\label{eq 3.2}
[X^{h},Y^{h}]_{a}=[X,Y]^h_a + R(X,Y)a
\end{equation}
where $R(X,Y)a$ is the curvature of the connection $\nabla$ on $A(M)$ (for the
curvature tensor we adopt the following definition: $R(X,Y)=\nabla_{[X,Y]}-
[\nabla_{X},\nabla_{Y}]$).
{\it Notations}. Let $J\in {\mathcal G}$ and $p=\pi(J)$. Take an oriented orthonormal basis
$\{a_1,...,a_{4n}\}$ of $T_pM\oplus T_{p}^{\ast}M$ such that $a_{2l}=Ja_{2l-1}$,
$l=1,..,2n$. Let $\{Q_i\}$, $i=1,...,4n$, be an oriented orthonormal frame of $TM\oplus
T^{\ast}M$ near the point $p$ such that
$$
Q_i(p)=a_i \mbox { and } \nabla Q_i|_p=0, \> i=1,...,4n.
$$
Define a section $s$ of ${\mathcal G}$ by setting
$$
sQ_{2l-1}=Q_{2l}, ~ sQ_{2l}=-Q_{2l-1},\> l=1,...,2n.
$$
Then, considering $s$ as a section of $A(M)$, we have
$$
s(p)=J, ~ \nabla s|_p=0.
$$
Thus $X^h_J=s_{\ast}X$ for every $X\in T_pM$.
Further, given a smooth manifold $N$, the natural projections of $TN\oplus T^{\ast}N$
onto $TN$ and $T^{\ast}N$ will be denoted by $\pi_1$ and $\pi_2$, respectively.
We shall use the above notations throughout this section.
\vspace{0.1cm}
To compute the Nijenhuis tensor of the generalize almost complex structure ${\mathcal
J}_{\alpha}$, $\alpha=1,2$, on the twistor space ${\mathcal G}$ we need some preliminary
lemmas.
\vspace{0.1cm}
\begin{lemma}\label {brackets}
If $A$ and $B$ are sections of the bundle $TM\oplus T^{\ast}M$ near $p$, then:
\begin{enumerate}
\item[$(i)$]
$[\pi_1(A^h),\pi_1({\mathcal
J}_{\alpha}B^h)]_J=[\pi_1(A),\pi_1(sB)]^h_J+R(\pi_1(A),\pi_1(JB))J.$ \vspace{0.2cm}
\item[$(ii)$]
$[\pi_1({\mathcal J}_{\alpha}A^h),\pi_1({\mathcal
J}_{\alpha}B^h)]_J=[\pi_1(sA),\pi_1(sB)]^h_J+R(\pi_1(JA),\pi_1(JB))J.$
\end{enumerate}
\end{lemma}
\begin{proof}
Set $X=\pi_1(A)$. By (\ref{eq 3.1}), we have $X_J^h=\sum_{l=1}^{2n}
X^l(p)\frac{\partial}{\partial\tilde x_l}(J)$ since $\nabla S_{ij}|_p=0$,
$i,j=1,...,4n$. Then, using (\ref{cal J/hor}), we get
$$
[X^h,\pi_1({\mathcal J}_{\alpha}B^h)]_J=
$$
$$
\sum_{i,j=1}^{4n}<B,Q_i>_py_{ij}(J)[X^h,\pi_1(Q_j)^h]_J +
X_p(<B,Q_i>)y_{ij}(J)(\pi_1(Q_j))^h_J.
$$
Moreover, $sB=\sum_{ij}<B,Q_i>(y_{ij}\circ s)Q_j$ since $({\mathcal J}_{\alpha}B^h)\circ
s=(sB)^h\circ s$. Now formula $(i)$ follows by means of (\ref{eq 3.2}). Similar
computations give $(ii)$.
\end{proof}
\begin{lemma}\label {Lie deriv}
Let $A$ and $B$ be sections of the bundle $TM\oplus T^{\ast}M$ near $p$, and let $Z\in
T_pM$, $W\in {\mathcal V}_J$. Then:
\begin{enumerate}
\item[$(i)$]
\hspace{0.2cm}$({\mathcal L}_{\pi_1(A^h)}{\pi_2(B^h)})_J=({\mathcal
L}_{\pi_1(A)}{\pi_2(B)})^h_J.$ \vspace{0.2cm}
\item[$(ii)$]
\hspace{0.2cm}$({\mathcal L}_{\pi_1(A^h)}{\pi_2({\mathcal J}_{\alpha}B^h)})_J=({\mathcal
L}_{\pi_1(A)}{\pi_2(sB)})^h_J.$ \vspace{0.2cm}
\item[$(iii)$] \ \\
$
\begin{array}{lll}
({\mathcal L}_{\pi_1({\mathcal J}_{\alpha}A^h)}\pi_2(B^h))_J(Z^h+W)=\\
\\
({\mathcal L}_{\pi_1(sA)}\pi_2(B))^h_J(Z^h)+(\pi_2(B))_p(\pi_1(WA)).
\end{array}
$
\vspace{0.2cm}
\item[$(iv)$] \ \\
$
\begin{array}{lll}
({\mathcal L}_{\pi_1({\mathcal J}_{\alpha}A^h)}\pi_2({\mathcal J}_{\alpha}B^h))_J(Z^h+W)=\\
\\
({\mathcal L}_{\pi_1(sA)}\pi_2(sB))^h_J(Z^h)+(\pi_2(JB))_p(\pi_1(WA)).
\end{array}
$
\end{enumerate}
\end{lemma}
\begin{proof}
Formula $(i)$ follows from (\ref{eq 3.2}). Simple computations involving (\ref{cal
J/hor}) and (\ref{eq 3.2}) give $(ii)$, $(iii)$ and $(iv)$.
\end{proof}
\vspace{0.1cm}
The next lemma is also easy to prove by means of (\ref{cal J/hor}) and (\ref{eq
3.2}).
\begin{lemma}\label {Half-diff}
Let $A$ and $B$ are sections of the bundle $TM\oplus T^{\ast}M$ near $p$. Let $Z\in
T_pM$ and $W\in {\mathcal V}_J$. Then:
\begin{enumerate}
\item[$(i)$]
\hspace{0.2cm}$(d\>\imath_{\pi_1(A^h)}\pi_2(B^h))_J=(d\>\imath_{\pi_1(A)}\pi_2(B))^h_J$
\vspace{0.2cm}
\item[$(ii)$] \ \\
$
\begin{array}{lll}
(d\>\imath_{\pi_1(A^h)}\pi_2({\mathcal J}_{\alpha} B^h))_J(Z^h+W)= \\
\\
(d\>\imath_{\pi_1(A)}\pi_2(sB))^h_J(Z^h)+ (\pi_2(WB))_p(\pi_1(A))
\end{array}
$
\vspace{0.2cm}
\item[$(iii)$] \ \\
$
\begin{array}{lll}
(d\>\imath_{\pi_1({\mathcal J}_{\alpha}A^h)}\pi_2(B^h))_J(Z^h+W)= \\
\\
(d\>\imath_{\pi_1(sA)}\pi_2(B))^h_J(Z^h)+ (\pi_2(B))_p(\pi_1(WA))
\end{array}
$
\vspace{0.2cm}
\item[$(iv)$] \ \\
$
\begin{array}{lll}
(d\>\imath_{\pi_1({\mathcal J}_{\alpha}A^h)}\pi_2({\mathcal J}_{\alpha}B^h))_J(Z^h+W)= \\
\\
(d\>\imath_{\pi_1(sA)}\pi_2(sB))^h_J(Z^h)+ (\pi_2(WB))_p(\pi_1(JA))+
(\pi_2(JB))_p(\pi_1(WA)
\end{array}
$
\end{enumerate}
\end{lemma}
\vspace{0.1cm}
For any (local) section $a$ of $A(M)$, following \cite{Gaud}, denote by
$\widetilde a$ the vertical vector field on ${\mathcal G}$ defined by
\begin{equation}\label{eq tilde a}
\widetilde a_J=a+J\circ a\circ J.
\end{equation}
Let us note that for every $J\in {\mathcal G}$ we can find sections $a_1,...,a_m$,
$m=4n^2-2n$, of $A(M)$ near the point $p=\pi(J)$ such that $\widetilde
a_1,...,\widetilde a_m$ form a basis of the vertical vector space at each point in a
neighbourhood of $J$.
\vspace{0.1cm}
\begin{lemma}\label {H-V brackets}
Let $J\in {\mathcal G}$ and let $a$ be a section of $A(M)$ near the point $p=\pi(J)$. Then,
for any section $A$ of the bundle $TM\oplus T^{\ast}M$ near $p$, we have:
\begin{enumerate}
\item[$(i)$] $[\pi_1(A^h),\widetilde a]_J=(\widetilde{\nabla_{\pi_1(A)}a})_J$
\vspace{0.2cm}
\item[$(ii)$] $[\pi_1(A^h),{\mathcal J}_{\alpha}\widetilde a]_J=
(-1)^{\alpha+1}J\circ (\widetilde{\nabla_{\pi_1(A)}a})_J$ \vspace{0.2cm}
\item[$(iii)$] $[\pi_1({\mathcal J}_{\alpha}A^h),\widetilde
a]_J=(\widetilde{\nabla_{\pi_1(JA)}a})_J-\pi_1(\widetilde a(A))^h_J$
\vspace{0.2cm}
\item[$(iv)$] $[\pi_1({\mathcal J}_{\alpha}A^h),{\mathcal J}_{\alpha}\widetilde
a]_J=(-1)^{\alpha+1}[J\circ (\widetilde{\nabla_{\pi_1(JA)}a})_J-\pi_1((J\circ\widetilde
a)(A))^h_J]$
\end{enumerate}
\end{lemma}
\begin{proof}
Let $a(Q_i)=\sum_{j=1}^{4n}\varepsilon_ia_{ij}Q_j$, $i=1,...,4n$. Then, in the local
coordinates of $A(M)$ introduced above,
$$
\widetilde a=\sum_{i<j}\widetilde a_{ij}\frac{\partial}{\partial y_{ij}}
$$
where
$$
\widetilde
a_{ij}=a_{ij}\circ\pi+\sum_{k,l=1}^{4n}y_{ik}(a_{kl}\circ\pi)y_{lj}\varepsilon_k\varepsilon_l.
$$
Let us also note that for every vector field $X$ on $M$ near the point $p$, in view of
(\ref{eq 3.1}), we have
$$
[X^h,\frac{\partial}{\partial y_{ij}}]_J=0,~X_J^h=\sum_{i=1}^{2n}
X^i(p)\frac{\partial}{\partial\tilde x_i}(J),
~(\nabla_{X_p}a)(Q_i)=\sum_{j=1}^{4n}\varepsilon_iX_p(a_{ij})Q_j
$$
since $\nabla Q_i|_p=0$ and $\nabla S_{ij}|_p=0$. Now the lemma follows by simple
computations making use of (\ref{cal J/ver}) and (\ref{cal J/hor}).
\end{proof}
\vspace{0.1cm}
The proof of the next lemma is easy and will be omitted.
\begin{lemma}\label {H-V Lie der&diff}
Let $A$ be a section of the bundle $TM\oplus T^{\ast}M$ and $V$ a vertical vector field
on ${\mathcal G}$. Then:
\begin{enumerate}
\item[$(i)$] ${\mathcal L}_{V}\pi_2(A^h)=0$; \hspace{0.2cm}$\imath_{V}\pi_2(A^h)=0$.
\vspace{0.2cm}
\item[$(ii)$] ${\mathcal L}_{V}\pi_2({\mathcal J}_{\alpha}A^h)=\pi_2(VA)^h$;
\hspace{0.2cm} $\imath_{V}\pi_2({\mathcal J}_{\alpha}A^h)=0$.
\end{enumerate}
\end{lemma}
\vspace{0.1cm}
{\it Notations}. Take a point $J\in {\mathcal G}$ and fix a basis $\{U_{2r-1},U_{2r}={\mathcal
J}_1U_{2r-1}\}$, $r=1,...,2n^2-n$, of the vertical space ${\mathcal V}_J$. Now let us take
sections $a_{2r-1}$ of $A(M)$ near the point $p=\pi(J)$ such that $a_{2r-1}=U_{2r-1}$
and $\nabla a_{2r-1}|_p=0$. Define vertical vector fields $\widetilde a_{2r-1}$ by
(\ref{eq tilde a}). Then $\{\widetilde a_{2r-1},{\mathcal J}_1\widetilde a_{2r-1}\}$,
$r=1,...,2n^2-n$, is a frame of the vertical bundle on ${\mathcal G}$ near the point $J$.
Denote by $\{\beta_{2r-1},\beta_{2r}\}$ the dual frame. Then $\beta_{2r}={\mathcal
J}_1\beta_{2r-1}$.
Under these notations, identity (\ref{eq 3.2}) and Lemmas~\ref{brackets} and \ref{H-V
brackets} imply the following
\vspace{0.1cm}
\begin{lemma}\label {H-Vstar Lie der}
Let $A$ be a section of the bundle $TM\oplus T^{\ast}M$ near the point $p=\pi(J)$. Then
for every $Z\in T_pM$ and $s,q=1,....,4n^2-2n$, we have
\begin{enumerate}
\item[$(i)$]$({\mathcal L}_{\pi_1(A^h)}\beta_s)_J(Z^h+U_q)=-\beta_s(R(\pi_1(A),Z)J).$
\vspace{0.2cm}
\item[$(ii)$]$({\mathcal L}_{\pi_1({\mathcal
J}_{\alpha}A^h)}\beta_s)_J(Z^h+U_q)=-\beta_s(R(\pi_1(JA),Z)J).$
\end{enumerate}
\end{lemma}
\vspace{0.1cm}
\begin{prop}\label {Nijenhuis}
Suppose that the connection $\nabla$ is torsion-free and let $J\in {\mathcal G}$, $A,B\in
T_{\pi(J)}M\oplus T_{\pi(J)}^{\ast}M$, $V,W\in {\mathcal V}_J$, $\varphi,\psi\in {\mathcal
V}_J^{\ast}$. Then:
\begin{enumerate}
\item[$(i)$] \ \\
$
\begin{array}{lll}
N_{\alpha}(A^h,B^h)_J &=&-R(\pi_1(A),\pi_1(B))J+(-1)^{\alpha}J\circ R(\pi_1(A),\pi_1(JB))J\\
\\
& &(-1)^{\alpha}J\circ R(\pi_1(JA),\pi_1(B))J+R(\pi_1(JA),\pi_1(JB))J
\\
& &\hspace{3.5cm} -\displaystyle{\frac{1}{2}[1+(-1)^{\alpha}]} \omega_{A,B},
\end{array}
$
where $\omega_{A,B}$ is the vertical $1$-form on ${\mathcal G}$ given by
$$
\begin{array}{lll}
\omega_{A,B}(W)&=&\pi_2(JA)(\pi_1(WB))+\pi_2(WB)(\pi_1(JA)) \\
& &-\pi_2(JB)(\pi_1(WA))-\pi_2(WA)(\pi_1(JB))
\end{array}
$$
for every $W\in {\mathcal V}_J$.
\item[$(ii)$] \ \\
$N_{\alpha}(A^h,V)_J=[1+(-1)^{\alpha}]((J\circ V)A)^h_J$
\item[$(iii)$] \ \\
$N_{\alpha}(A^h,\varphi)_J\in {\mathcal H}_J\oplus {\mathcal H}_J^{\ast}$ ~ and \ \\
\ \\
$
\begin{array}{lll}
<\pi_{\ast}N_{\alpha}(A^h,\varphi)_J,B>=-\frac{1}{2}\varphi(N_{1}(A^h,B^h)_J)\\
\\
-\frac{1}{2}[1+(-1)^{\alpha}]
\varphi(J\circ R(\pi_1(A),\pi_1(JB))J+J\circ R(\pi_1(JA),\pi_1(B))J).
\end{array}
$
\item[$(iv)$] \ \\
$N_{\alpha}(V+\varphi,W+\psi)_J=0$.
\end{enumerate}
\end{prop}
\begin{proof}
Set $p=\pi(J)$ and extend the vectors $A,B$ to (local) sections of $TM\oplus T^{\ast}M$,
denoted again by $A,B$, in such a way that $\nabla A|_p=\nabla B|_p=0$.
Let $s$ be the section of ${\mathcal G}$ defined above with the property that
$s(p)=J$ and $\nabla s|_p=0$ ($s$ being considered as a section of $A(M)$).
According to Lemmas~\ref{brackets}, \ref{Lie deriv} and \ref{Half-diff}, the
part of $N_{\alpha}(A^h,B^h)_J$ lying in ${\mathcal H}_J\oplus {\mathcal H}^{\ast}_J$ is given
by
$$
({\mathcal H}\oplus {\mathcal
H}^{\ast})N_{\alpha}(A^h,B^h)_J=(-[A,B]-s[A,sB]-s[sA,B]+[sA,sB])^h_J.
$$
Note that we have $\nabla\pi_1(A)|_p=\pi_1(\nabla A|_p)=0$ and $\nabla\pi_1(sA)|_p=
\pi_1((\nabla s)|_p(A)+ s(\nabla A|_p))=0$. Similarly, $\nabla\pi_2(A)|_p=0$ and
$\nabla\pi_2(sA)|_p=0$. We also have $\nabla\pi_1(B)|_p=0$, $\nabla\pi_1(sB)|_p=0$ and
$\nabla\pi_2(B)|_p=0$, $\nabla\pi_2(sB)|_p=0$. Now, since $\nabla$ is torsion-free, we
easily get $({\mathcal H}\oplus {\mathcal H}^{\ast})N_{\alpha}(A^h,B^h)_J=0$ by means of the
following simple observation: Let $Z$ be a vector field and $\omega$ a $1$-form on $M$
such that $\nabla Z|_p=0$ and $\nabla\omega|_p=0$. Then for every $T\in T_pM$
$$
({\mathcal L}_{Z}\omega)(T)_p =(\nabla_{Z}\omega)(T)_p=0 ~\mbox { and
}~(d\,\imath_{Z}\omega)(T)_p=(\nabla_{T}\omega)(Z)_p=0.
$$
By Lemmas~\ref{brackets}, \ref{Lie deriv} and \ref{Half-diff} the vertical part of
$N_{\alpha}(A^h,B^h)_J$ is equal to
$$
\begin{array}{lll}
{\mathcal V}N_{\alpha}(A^h,B^h)_J&=&
-R(\pi_1(A),\pi_1(B))J - {\mathcal J}_{\alpha}R(\pi_1(A),\pi_1(JB))J \\
& &-{\mathcal J}_{\alpha}R(\pi_1(JA),\pi_1(B))+R(\pi_1(JA),\pi_1(JB))J\\
\end{array}
$$
The part of $N_{\alpha}(A^h,B^h)_J$ lying in ${\mathcal V}^{\ast}_J$ is the $1$-form whose
value at every vertical vector $W$ is
$$
\begin{array}{lll}
({\mathcal V}^{\ast}N_{\alpha}(A^h,B^h)_J)(W)= \\
-\frac{1}{2}[\pi_2(JA)(\pi_1(WB))+\pi_2(WB)(\pi_1(JA)) \\
\hspace{2.5cm}+(-1)^{\alpha}\pi_2(B)(\pi_1((J\circ W)A))+(-1)^{\alpha}\pi_2((J\circ W)A)(\pi_1(B))] \\
\\
+\frac{1}{2}[\pi_2(JB)(\pi_1(WA))+\pi_2(WA)(\pi_1(JB)) \\
\hspace{2.5cm}+(-1)^{\alpha}\pi_2(A)(\pi_1((J\circ W)B))+(-1)^{\alpha}\pi_2((J\circ
W)B)(\pi_1(A))].
\end{array}
$$
The endomorphism $W$ of $T_pM\oplus T^{\ast}_pM$ is skew-symmetric with respect to the
natural neutral metric and anti-commutes with $J$, so $<JA,WB>=\\ <(J\circ W)A,B>$.
This gives
$$
\begin{array}{c}
\pi_2(JA)(\pi_1(WB))+\pi_2(WB)(\pi_1(JA))= \\
\pi_2(B)(\pi_1((J\circ W)A))+\pi_2((J\circ W)A)(\pi_1(B)).
\end{array}
$$
It follows that
$$
\begin{array}{lll}
{\mathcal V}^{\ast}N_{\alpha}(A^h,B^h)_J=-\frac{1}{2}[1+(-1)^{\alpha}]
[\pi_2(JA)(\pi_1(WB))+\pi_2(WB)(\pi_1(JA)) \\
\hspace{5.8cm} -\pi_2(JB)(\pi_1(WA))-\pi_2(WA)(\pi_1(JB))].
\end{array}
$$
This proves $(i)$.
To prove $(ii)$ take a section $a$ of $A(M)$ near the point $p$ such that $a(p)=V$
and $\nabla a|_p=0$. Let $\widetilde a$ be the vertical vector field defined by
(\ref{eq tilde a}). Then it follows from Lemmas~\ref{H-V brackets} and \ref{H-V Lie
der&diff} that
$$
N_{\alpha}(A^h,V)_J=\frac{1}{2}N_{\alpha}(A^h,\widetilde a)_J= ((J\circ
V)A+(-1)^{\alpha}(J\circ V)A)^{h}_J.
$$
To prove $(iii)$ let us take the vertical coframe $\{\beta_{2r-1},\beta_{2r}\}$,
$r=1,...,2n^2-n$, defined before the statement of Lemma~\ref{H-Vstar Lie der}. Set
$\varphi=\sum_{s=1}^{4n^2-2n}\varphi_s\beta_s$, $\varphi_s\in {\Bbb R}$. Let $E_1,...,
E_{2n}$ be a basis of $T_pM$ and $\xi_1,...,\xi_{2n}$ its dual basis. Then, by
Lemma~\ref{H-Vstar Lie der}, we have \vspace{0.1cm}
\begin{equation}\label{eq H-Vstar Nij}
\begin{array}{lll}
N_{\alpha}(A^h,\varphi)_J=\sum_{s=1}^{4n^2-2n}\varphi_s N_{\alpha}(A^h,\beta_s)_J=\\
\\
\sum_{s=1}^{4n^2-2n}\sum_{k=1}^{2n}\varphi_s\{[\beta_s(R(\pi_1(A),E_k)J)+
(-1)^{\alpha+1}\beta_s(J\circ R(\pi_1(JA),E_k)J)](\xi_k)^h_J \\
\\
+[\beta_s(R(\pi_1(JA),E_k)J)-(-1)^{\alpha+1}\beta_s(J\circ
R(\pi_1(A),E_k)J)](J\xi_k)^h_J\}.
\end{array}
\end{equation}
Moreover, note that
$$
<\xi_k,B>=\frac{1}{2}\xi_k(\pi_1(B)) \mbox { and }
<J\xi_k,B>=-<\xi_k,JB>=-\frac{1}{2}\xi_k(\pi_1(JB)),
$$
therefore
$$
\sum_{k=1}^{2n}<\xi_k,B>E_k=\frac{1}{2}\pi_1(B) \mbox { and }
\sum_{k=1}^{2n}<J\xi_k,B>E_k=-\frac{1}{2}\pi_1(JB).
$$
Now $(iii)$ is an obvious consequence of (\ref{eq H-Vstar Nij}) and formula $(i)$.
Finally, identity $(iv)$ follows from the fact that the generalized almost complex structure
${\mathcal J}_{\alpha}$ on every fibre of ${\mathcal G}$ is induced by a complex structure.
\end{proof}
\section{The integrability condition}
\begin{tw}\label {Integrability}
Let $M$ be a $2n$-dimensional manifold and $\nabla$ a torsion-free linear connection on
$M$. Let ${\mathcal J}_{\alpha}={\mathcal J}_{\alpha}^{\nabla}$, $\alpha=1,2$, be the
generalized almost complex structures induced by $\nabla$ on the twistor space ${\mathcal
G}$ of $M$. Then:
\begin{enumerate}
\item[$(i)$] If $n=1$, the structure ${\mathcal J}_1$ is always
integrable.
\item[$(ii)$] If $n\geq 2$, the structure ${\mathcal J}_1$ is integrable if and only if the
connection $\nabla$ is flat.
\item[$(iii)$] The structure ${\mathcal J}_2$ is never integrable.
\end{enumerate}
\end{tw}
\begin{proof}
$(i)$~Let $J\in {\mathcal G}$ and let $\{Q_1, Q_2=JQ_1, Q_3, Q_4=JQ_3\}$ be an orthonormal basis
of $T_pM\oplus T_p^{\ast}M$, $p=\pi(J)$. By Proposition~\ref{Nijenhuis}, the Nijenhuis
tensor $N_1$ of ${\mathcal J}_1$ vanishes at the point $J$ if and only if
$N_1(Q_1^h,Q_3^h)=0$ (in view of the fact that $N_1({\mathcal J}_1E,F)=N_1(E,{\mathcal
J}_1F)=-{\mathcal J}_1N(E,F)$ for $E,F\in T{\mathcal G}$).
Let $\pi_1(Q_i)=e_i$, $i=1,...,4$. Then, according to Proposition~\ref{Nijenhuis},
$$
N_1(Q_1^h,Q_3^h)=([-R(e_1,e_3)J+R(e_2,e_4)J]-J\circ[R(e_1,e_4)J+R(e_2,e_3)J])^h_J.
$$
Both summands in the above formula vanishes since, by Lemma~\ref{Orient},
$e_3=\cos{t}\,e_1+\sin{t}\,e_2$, $e_4=-\sin{t}\, e_1+\cos{t}\,e_2$ for some $t\in {\Bbb
R}$.
\vspace{0.1cm}
$(ii)$~ Let $dim\, M=2n\geq 4$ and assume that the generalized almost complex structure
${\mathcal J}^{\nabla}_1$ is integrable. Then, by Proposition~\ref{Nijenhuis}, for every
$p\in M$, every (genuine) complex structure $K$ on $T_pM$ and every $X,Y\in T_pM$ we
have
$$
R(X,Y)K+K\circ R(X,KY)K+K\circ R(KX,Y)K-R(KX,KY)K=0,
$$
where $R$ is the curvature tensor of the connection $\nabla$. The latter identity, as
is well-known, is the integrability condition for the Atiyah-Hitchin-Singer almost
complex structure on the twistor space of complex structures on the tangent spaces of
$M$ (see, e.g., \cite[Theorem 1 or Theorem 3]{OBrRaw}). Then, according to the
arguments of \cite[pp. 42 - 43]{OBrRaw}, there exists a bilinear form $\mu$ on
$TM\times TM$ such that
\begin{equation}\label{eq curv}
R(X,Y)Z= \mu(X,Y)Z-\mu(Y,X)Z+\mu(X,Z)Y-\mu(Y,Z)X.
\end{equation}
Now let $p\in M$ and let $\{E_1,...,E_{2n}\}$ be an arbitrary basis of $T_pM$. Denote
by $\{\eta_1,...,\eta_{2n}\}$ its dual basis. Let $J$ be the complex structure on
$T_pM\oplus T^{\ast}_pM$ for which $JE_{2k-1}=\eta_{2k}$, $JE_{2k}=-\eta_{2k-1}$,
$k=1,...,n$. This structure is compatible with the natural neutral metric of
$T_pM\oplus T^{\ast}_pM$, so we get a generalized complex structure sending $T_pM$ onto
$T^{\ast}_pM$ and vice versa (it is similar to the structure in Example 2, Section 2).
If $n$ is an even number, the structure $J$ yields the canonical orientation of
$T_pM\oplus T^{\ast}_pM$, hence $J\in {\mathcal G}$. So, suppose that $n$ is even and let
$X,Y\in T_pM$. Then, by Proposition~\ref{Nijenhuis}\,$(i)$, we have $R(X,Y)J=0$. The
latter identity is equivalent to the following identities
$$
R(X,Y)\eta_{2k}-JR(X,Y)E_{2k-1}=0,~ R(X,Y)\eta_{2k-1}+JR(X,Y)E_{2k}=0,
$$
$k=1,...,n$. It follows that for every $Z\in T_pM$, we have
$$
2[\mu(X,Y)-\mu(Y,X)]\eta_{2k}(Z)+\mu(X,Z)\eta_{2k}(Y)-\mu(Y,Z)\eta_{2k}(X) $$
$$
+\mu(X,E_{2k-1})(JY)(Z)-\mu(Y,E_{2k-1})(JX)(Z)=0
$$
and
$$
2[\mu(X,Y)-\mu(Y,X)]\eta_{2k-1}(Z)+\mu(X,Z)\eta_{2k-1}(Y)-\mu(Y,Z)\eta_{2k-1}(X) $$
$$
-\mu(X,E_{2k})(JY)(Z)+\mu(Y,E_{2k})(JX)(Z)=0.
$$
Let $k\neq l$, $1\leq k,l\leq n$, be two indexes. Putting $X=E_{2k-1}$, $Y=E_{2k}$,
$Z=E_{2l-1}$ into the above identities, we get $\mu(E_{2k-1},E_{2l-1})=0$ and
$\mu(E_{2k},E_{2l-1})=0$; putting $X=E_{2k}$, $Y=E_{2k-1}$, $Z=E_{2l}$, we get
$\mu(E_{2k-1},E_{2l})=0$ and $\mu(E_{2k},E_{2l})=0$. Moreover, setting $X=Z=E_{2l-1}$,
$Y=E_{2k}$ and $X=Z=E_{2l}$, $Y=E_{2k}$ into the first of the above identities, we
obtain $\mu(E_{2l-1},E_{2l-1})=0$ and $\mu(E_{2l},E_{2l})=0$. Now take the basis
$E_1'=E_1$, $E_2'=E_3$, $E_3'=E_2$, $E_4'=E_4$,...,$E_{2n}'=E_{2n}$. Then the
identities $\mu(E_1',E_3')=\mu(E_3',E_1')=0$ give $\mu(E_1,E_2)=\mu(E_2,E_1)=0$. It
follows that $\mu(E_{2k-1},E_{2k})=\mu(E_{2k},E_{2k-1})=0$. Therefore $\mu=0$, thus
$R=0$ by (\ref{eq curv}).
Now assume that $n=2m+1$ is an odd number. Let $X,Y\in T_pM$ be two linearly
independent tangent vectors. Let $\{E_1,...,E_{2n}\}$ be an arbitrary basis of $T_pM$
with $E_1=X$, $E_2=Y$. Denote by $\{\eta_1,...,\eta_{2n}\}$ its dual basis. Let $J$ be
the complex structure on $T_pM\oplus T^{\ast}_pM$ for which $JE_{2k-1}=\eta_{2k}$,
$JE_{2k}=-\eta_{2k-1}$, $k=1,...,m$, and $JE_{4m+1}=E_{4m+2}$,
$J\eta_{4m+1}=\eta_{4m+2}$. Then $J\in {\mathcal G}$ and the preceding arguments show that
$$
R(X,Y)E_i=0 \mbox { for } i=1,...,4m.
$$
Applying the latter identity for the basis $\{E_1, E_2, E_{4m+1}, E_{4m+2},
E_3,...,E_{4m}\}$, we see that $R(X,Y)E_{4m+1}=R(X,Y)E_{4m+2}=0$. It follows that
$R=0$.
\vspace{0.1cm}
$(iii)$~ Let $J\in {\mathcal J}$ and let $\{Q_1, Q_2=JQ_1,..., Q_{4n-1},
Q_{4n}=JQ_{4n-1}\}$ be an orthonormal basis of $T_pM\oplus T_p^{\ast}M$, $p=\pi(J)$.
Define endomorphisms $S_{ij}$ of $T_pM\oplus T_p^{\ast}M$ by (\ref{eq Sij}). Then
$V=S_{13}-S_{24}$ is a vertical vector of ${\mathcal G}$ at the point $J$ and it follows
from Proposition~\ref{Nijenhuis}$\,(ii)$ that $N_{2}(E_1^h,V)_J=2(Q_4)_J^h\neq 0$.
\end{proof}
\vspace{0.1cm}
\noindent {\bf Remarks.} {\bf 1}. Concerning Theorem 1$(ii)$, let us note that that
every flat torsion-free connection on a manifold induces an affine structure on it,
i.e. local coordinates whose transition functions are affine. If, in addition, the
connection is complete, then the manifold is the quotient of an affine space by a
group of affine transformations acting freely and properly discontinuously on it (see,
for example, \cite{Wolf}).
\noindent {\bf 2}. The complex structure ${\mathcal K}$ on the fibres of ${\mathcal G}$ is
K\"ahlerian with respect to the metric $<a,b>=\displaystyle{-\frac{1}{2}}Trace\,(a\circ
b)$. Let ${\mathcal S}$ be the generalized complex structure on the vertical spaces of
${\mathcal G}$ induced by the K\"ahler form of K\"ahler structure $({\mathcal J},<~,~>)$ (see
Example 2, Section 2). Then, given a connection $\nabla$ on $M$, we can define two new
generalized almost complex structures ${\mathcal I}_{\alpha}$ on the twistor space ${\mathcal
G}$ by setting ${\mathcal I}_{\alpha}=(-1)^{\alpha+1}{\mathcal S}$ on ${\mathcal V}\oplus {\mathcal
V}^{\ast}$ and ${\mathcal I}_{\alpha}={\mathcal J}_{1}^{\nabla}\,(={\mathcal J}_{2}^{\nabla})$ on
${\mathcal H}\oplus {\mathcal H}^{\ast}$, $\alpha=1,2$. It is easy to see that the structures
${\mathcal I}_{\alpha}$ are never integrable. Indeed, let us adopt the notations used in
part $(iii)$ of the proof of Theorem~\ref{Integrability}. Then Lemma~\ref{H-V brackets}
implies that the projection of the Nijenhuis tensor $N_{{\mathcal I}_{\alpha}}(E_1^h,V)_J$
onto ${\mathcal H}_J$ is equal to $(Q_4)_J^h$.
\vspace{0.1cm}
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
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import { Component } from 'angular2/core';
@Component({
selector: 'people-route',
template: require('./people.route.html')
})
export class PeopleRoute {
constructor() {}
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 36
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{"url":"https:\/\/followtutorials.com\/2019\/04\/c-error-handling.html","text":"C Error Handling\n\nFor handling of errors and exceptions, C language does not provide any direct support. However, there are many ways through which error handling can be done in C programming. These error codes are defined under the header file \u2018error.h\u2019 which will point out the error using return statement in a function. It is the task of the programmer to prevent errors in the first place and test return values from the function. A function will return -1 or a NULL value if errors are encountered and set the global variable errno. So the return value is an indication of error while programming. In the context of Socket [progrmming, the errors are determined by checking the returned value of functions like socket(), listen(), etc.\n\nWhat is errno in C?\n\nWhenever you call a function is called in C, a variable named errno is designated to it. The errno is a global variable, which can be used to identify the type of error encountered while executing the function based on its value. It will indicate an error occurred during any function call and defined in the header file \u2018errno.h\u2019.\n\nBelow you will see the list different error values along with its corresponding meaning.\n\nerrno valueError\n1Operation not permitted\n2No such file or directory\n3No such process\n4Interrupted system call\n5I\/O error\n7Argument list too long\n8Exec format error\n10No child processes\n11Try again\n12Out of memory\n13Permission denied\n\nThe C language will implement the functions like perror() and strerror() functions for printing the message associated with the errno.\n\n\u2022 perror(): The function perror() will return the string that is passed to it. It also returns the textual representation of the current errno value followed by a colon and space.\n\u2022 \u00a0strerror(): The function strerror() is defined under the library \u2018string.h\u2019. This method will return a pointer to the string which is the representation of the current value.\n\nExample of error handling\n\nCode:\n\n#include <stdio.h>\n#include <errno.h>\n#include <string.h>\n#include<stdlib.h>\nint main ()\n{\nFILE *fp;\nfp = fopen(\"AbsentFile.txt\", \"r\");\nif (fp == NULL)\n{\nprintf(\"Value of errno is %d\\n \", errno);\nprintf(\"The error message is %s\\n\", strerror(errno));\nperror(\"The Message displayed from perror\");\nexit(EXIT_FAILURE);\nprintf(\"I will not be printed\\n\");\n}\n\nelse\n{\nfclose (fp);\nexit(EXIT_SUCCESS);\nprintf(\"I wont be printed at this point \\n\");\n}\nreturn 0;\n}\n\n\nThe above example is a very simple example of a program implementing the concept of error handling. Here, when the program executes the program won\u2019t find the file named \u2018AbsentFile\u2019. hence this file could not be opened. As this sort of error holds the value \u20182\u2019. So the value of errno is \u20182\u2019. And the function perror() will return the\u00a0textual representation of the current errno value.\n\nThe above code will display its output as below.\n\nOutput:\n\nValue of errno is 2\nThe error message is No such file or directory\nThe message displayed from perror: No such file or directory\n\nWhat is divide by zero error?\n\nA common mistake that a programmer makes during programming is not checking if the divisor is zero before executing the division command. In such a situation, nothing can be done to resolve the error. This error will lead to unwanted behavior and may even create a problem in the system. So in this case, the only thing we can do is to avoid the occurrence of such errors. The only possible way to avoid such error is by checking the denominator before using it in the program in the division operations. We can check for such errors by using the \u2018if\u2019 condition and if the denominator is found to be zero then display the message to alert the programmers about the possible error on the way and jump out of the function.\n\nCode:\n\n#include <stdio.h>\n#include <stdlib.h>\n\nmain() {\n\nint numerator, denominator, quotient;\nprintf(\"Enter the numerator: \");\nscanf(\"%d\", &numerator);\nprintf(\"Enter the denominator: \");\nscanf(\"%d\", &denominator);\nif( denominator == 0){\nfprintf(stderr, \"ALert! Divide error by zero is encountered in your program. \\n\");\nexit(-1);\n}\n\nquotient = numerator \/ denominator;\nfprintf(stderr, \"Value of quotient is %d\\n\", quotient );\n\nexit(0);\n}\n\nThe above code will display its output as below.\n\nOutput:\n\nEnter the numerator: 5\nEnter the denominator: 0","date":"2021-10-26 21:17:15","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.3859770596027374, \"perplexity\": 1902.9540661579124}, \"config\": {\"markdown_headings\": false, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-43\/segments\/1634323587926.9\/warc\/CC-MAIN-20211026200738-20211026230738-00027.warc.gz\"}"}
| null | null |
{"url":"https:\/\/mathematica.stackexchange.com\/questions\/91297\/show-scientific-form-number-in-epilog-on-a-plot","text":"# Show scientific form number in Epilog on a plot\n\nI'd like to overlay a scientific form number on a ListPlot at a particular position.\n\nSimply using Text[ToString@value, {xpos,ypos}] separates the exponent from the number and increases the font size. I found several posts about exponential notation for axes labels etc but I've not found one for this. I think one way would be to somehow convert the ScientificForm object into a Graphics object, then I could place it anywhere.\n\nI think this must be a duplicate question as it seems so fundamental but I'm clearly searching for the wrong expressions!\n\n\u2022 Note that an Inset does not need to be a Graphics. Aug 10 '15 at 17:58\n\u2022 Aug 10 '15 at 17:58\n\u2022 Thank you MarcoB! Inset is exactly what I needed. Inset[value,Scaled[{xpos,ypos}]]; Aug 10 '15 at 18:05\n\u2022 As an example, you could use Epilog -> Inset[Style[ScientificForm[N@value], Red, FontSize -> 14], Scaled[{xpos, ypos}]] to have control over the color, font size, positions, etc. of the text you want overlaid. Aug 10 '15 at 18:06\n\u2022 @march. That's not a good coding example. The use of string operations in generating the label is totally unnecessary. One can just use Row. Aug 11 '15 at 1:35\n\nYou can use the Text graphics primitive to place a ScientificForm expression anywhere in a graphics pane without resorting to string conversion. For example,\nGraphics[{\n\nI didn't bother to introduce Epilog here, but Text expression like this one are perfectly acceptable in a list of graphic primitives given to Epilog.","date":"2021-11-27 18:28:00","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.42410385608673096, \"perplexity\": 1756.3318469696098}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-49\/segments\/1637964358208.31\/warc\/CC-MAIN-20211127163427-20211127193427-00617.warc.gz\"}"}
| null | null |
{"url":"https:\/\/en.m.wikipedia.org\/wiki\/Factorization","text":"# Factorization\n\nThe polynomial x2\u00a0+\u00a0cx\u00a0+\u00a0d, where a\u00a0+\u00a0b\u00a0=\u00a0c and ab\u00a0=\u00a0d, can be factorized into (x\u00a0+\u00a0a)(x\u00a0+\u00a0b).\n\nIn mathematics, factorization (also factorisation in some forms of British English) or factoring consists of writing a number or another mathematical object as a product of several factors. For example, 3 \u00d7 5 is a factorization of the integer 15, and (x \u2013 2)(x + 2) is a factorization of the polynomial x2 \u2013 4.\n\nFactorization is not usually considered for rational and real numbers, because, for every pair (x, y) of nonzero such numbers, there is a factorization x = y z, with z = x \/ y.\n\nFactorization has been considered first by ancient Greek mathematicians, in the case of integers. They proved the fundamental theorem of arithmetic, which asserts that every positive integer may be factorized into a product of specific integers called prime numbers, that have the property of not having any factorization in factors different of one. Moreover, this factorization is unique up to the order of the factors. Factorization is, somehow, the inverse operation of multiplication. However, in the case of large integers, integer factorization is much more difficult than multiplication, and this is widely used in public-key cryptography, typically through the RSA cryptosystem.\n\nPolynomial factorization is also considered since a long time. Polynomials with integer coefficients or coefficients in a field have the unique factorization property, that is verify a theorem that is very similar to the fundamental theorem of arithmetic, with prime numbers replaced by irreducible polynomials. In particular, a univariate polynomial with complex coefficients, admits a unique (up to the order of the factors) factorization into linear polynomials; this is the fundamental theorem of algebra. In this case, the factorization is usually done with root-finding algorithms. The case of polynomials with integer coefficients is fundamental for computer algebra. There are algorithms for computing the (complete) factorization of any polynomial with integer coefficients (see factorization of polynomials); although they are very efficient for a computer usage, they are generally too complicate for being used in paper-and-pencil computation.\n\nThe commutative rings in which unique factorization property holds are called unique factorization domains. There are number systems which are not unique factorization domains. This is the case of many rings of algebraic integers. However, these are Dedekind domains, which means that unique factorization property holds if one replaces factorization into algebraic integers by factorization into ideals.\n\nFactorization is often used for the decomposition of a mathematical object into the product of objects of a more specific type. For example every function may be factored into the composition of a surjective function with an injective function. For matrices, there are many kinds of such matrix factorizations. For example, every matrix has a LUP factorization as a product of a square lower triangular matrix L with all diagonal entries equal to one, an upper triangular matrix U, and a permutation matrix P.\n\n## IntegersEdit\n\nBy the fundamental theorem of arithmetic, every integer greater than 1 has a unique (up to the order of the factors) factorization into prime numbers, which are those integers which cannot be further factorized into the product of integers greater than one.\n\nFor computing the factorization of an integer n, one needs an algorithm for finding a divisor q of n or deciding that n is prime. When such a divisor is found, the repeated application of this algorithm to the factors q and n \/ q gives eventually the complete factorization of n.[1]\n\nFor finding a divisor q of n, if any, it suffices to test all values of q such that 1 < q and q2n. In fact, if r is a divisor of n such that r2 > n, then q = n \/ r is a divisor of n such that q2n.\n\nIf one tests the values of q in increasing order, the first divisor that is found is necessarily a prime number, and the cofactor r = n \/ q cannot have any divisor smaller than q. For getting the complete factorization, it suffices thus to continue the algorithm by searching a divisor of r that is not smaller than q and not greater than r.\n\nThere is no need to test all values of q for applying the method. In principle, it suffices to test only prime divisors. This needs to have a table of prime numbers that may be generated for example with the sieve of Eratosthenes. As the method of factorization does essentially the same work as the sieve of Eratosthenes, it is generally more efficient to test for a divisor only those numbers for which it is not immediately clear whether they are prime or not. Typically, one may proceed by testing 2, 3, 5, and the numbers > 5, whose last digit is 1, 3, 7, 9 and the sum of digits is not a multiple of 3.\n\nThis method works well for factoring small integers, but is inefficient for larger integers. For example, Pierre de Fermat was unable to discover that the 6th Fermat number\n\n${\\displaystyle 1+2^{2^{5}}=1+2^{32}}$\n\nis not a prime number. In fact, applying the above method would require more than 10,000 division, for a number that has 10 decimal digits.\n\nThere are more efficient factoring algorithms. However they remain relatively inefficient, as, with the present state of the art, one cannot factorize, even with the more powerful computers, a number of 500 decimal digits that is the product of two randomly chosen prime numbers. This insure the security of the RSA cryptosystem, which is widely used for secure communications on Internet.\n\n### ExampleEdit\n\nFor factoring n = 1386 into primes:\n\n\u2022 Start with division by 2: the number is even, and n = 2 \u00b7 693. Continue with 693, and 2 as a first divisor candidate.\n\u2022 693 is odd (2 is not a divisor), but is a multiple of 3: one has 693 = 3 \u00b7 231 and n = 2 \u00b7 3 \u00b7 231. Continue with 231, and 3 as a first divisor candidate.\n\u2022 231 is also a multiple of 3: one has 231 = 3 \u00b7 77, and thus n = 2 \u00b7 32 \u00b7 77. Continue with 77, and 3 as a first divisor candidate.\n\u2022 77 is not a multiple 3, since the sum of its digits is 14, not a multiple of 3. It is also not a multiple of 5 because its last digit is 7. The next odd divisor to be tested is 7. One has 77 = 7 \u00b7 11, and thus n = 2 \u00b7 32 \u00b7 7 \u00b7 11. This shows that 7 is prime (easy to test directly). Continue with 11, and 7 as a first divisor candidate.\n\u2022 As 72 > 11, one has finished. Thus 11 is prime, and the prime factorization is\n1386 = 2 \u00b7 32 \u00b7 7 \u00b7 11.\n\n## PolynomialsEdit\n\nModern techniques for factoring polynomials are fast and efficient, but use sophisticated mathematical ideas (see Factorization of polynomials). These techniques are used in the construction of computer routines for carrying out polynomial factorization in computer algebra systems. The more classical hand techniques rely on either the polynomial to be factored having low degree or the recognition of the polynomial as belonging to a certain class of known examples; these hand techniques are not very suitable for computer implementation. This article is concerned with these classical techniques.\n\nWhile the general notion of factoring just means writing an expression as a product of simpler expressions, the vague term \"simpler\" will be defined more precisely for special classes of expressions. When factoring polynomials this means that the factors are to be polynomials of smaller degree. Thus, while ${\\displaystyle x^{2}-y=(x+{\\sqrt {y}})(x-{\\sqrt {y}})}$\u00a0 is a factorization of the expression, it is not a polynomial factorization since the factors are not polynomials.[2] Also, the factoring of a constant term, as in ${\\displaystyle 3x^{2}-6x+12=3(x^{2}-2x+4)}$\u00a0 would not be considered a polynomial factorization since one of the factors does not have a smaller degree than the original expression.[3] Another issue concerns the coefficients of the factors. In basic treatments it is desirable to have the coefficients of the factors be of the same type as the coefficients of the original polynomial\u2014that is, factoring polynomials with integer coefficients into factors with integer coefficients, or factoring polynomials with real coefficients into polynomials with real coefficients. It is not always possible to do this, and a polynomial that can not be factored in this way is said to be irreducible over this type of coefficient. Thus, x2 \u2013 2 is irreducible over the integers and x2 + 4 is irreducible over the reals. In the first example, the integers 1 and 2 can also be thought of as real numbers, and then ${\\displaystyle x^{2}-2=(x+{\\sqrt {2}})(x-{\\sqrt {2}})}$\u00a0 shows that this polynomial factors over the reals (sometimes it is said that the polynomial splits over the reals). Similarly, since the integers 1 and 4 can be thought of as real and hence complex numbers, x2 + 4 splits over the complex numbers, i.e. ${\\displaystyle x^{2}+4=(x+2i)(x-2i)}$\u00a0.\n\nThe fundamental theorem of algebra can be stated as: Every polynomial of degree n with complex number coefficients splits completely into n linear factors.[4] The terms in these factors, which are the roots of the polynomial, may be real or complex. Since complex roots of polynomials with real coefficients come in complex conjugate pairs, this result implies that every polynomial with real coefficients splits into linear and\/or irreducible quadratic factors with real coefficients (because when two linear factors with complex conjugate terms are multiplied together, the result is a quadratic with real coefficients). Even though the structure of the factorization is known in these cases, finding the actual factors can be computationally challenging, and by the Abel\u2013Ruffini theorem the coefficients and additive terms in the factors may not be expressible in terms of radicals.\n\n### History of factoring polynomialsEdit\n\nStudents who are introduced to factoring as a primary method of solving quadratic equations might be surprised to know it is one of the newest methods of solving them. Vera Sanford points out in her A Short History of Mathematics (1930)[5] that \u201cIn view of the present emphasis given to the solution of quadratic equations by factoring, it is interesting to note that this method was not used until Harriot\u2019s work of 1631. Even in this case, however, the author ignores the factors that give rise to negative roots.\u201d Harriot died in 1621, and like all his books, this one, Artis Analyticae Praxis ad Aequationes Algebraicas Resolvendas, was published after his death. An article on Harriot at the Univ of Saint Andrews math history web site says that in his personal writing on solving equations Harriot did use both positive and negative solutions, but his editor, Walter Warner, did not present this in his book. Harriot\u2019s method of factoring may look different than what modern students expect. In the first section (Sectio Prima) Harriot draws tables to illustrate the addition, subtraction, multiplication and division of monomial, binomial, and trinomial terms. Then in the second section he shows a more direct multiplication that provides the foundation to his factoring method. He sets up the equation aaba + ca = + bc, and shows that this matches the form of multiplication he has previously provided as,\n\n a \u2212 b aa \u2212 ba (===) (Harriot uses the long equal sign introduced by Robert Recorde) a + c ca \u2212 bc\n\nthus factoring the four terms of the adjusted expression aaba + cabc. This example can be seen on page 16 of the Artis Analyticae Praxis ad Aequationes Algebraicas Resolvendas.\n\nHarriot writes out a form for each of the possibilities of (a \u00b1 b)(a \u00b1 c) with a being the unknown (where we might use x today) and then when he needs to factor he picks on one of the forms that match. By separating out the linear coefficient into two parts he is able to break the problem into one of the forms.\n\n### General methodsEdit\n\nThere are general algorithms which always produce the complete factorization of any polynomial, in either one variable (the univariate case) or several variables (the multivariate case); see Factorization of polynomials. These algorithms are implemented and are available in most computer algebra systems. They involve advanced properties of polynomials, and are too complicated for hand-written computation. There are also a few elementary methods which are well\u2013suited for hand-written computation, and do not always allow finding the complete factorization in degree higher than four.\n\n#### Highest common factorEdit\n\nFinding, by inspection, the monomial that is the highest common factor (also called the greatest common divisor) of all the terms of the polynomial and factoring it out as a common factor is an application of the distributive law. This is the most commonly used factoring technique. For example:[6]\n\n${\\displaystyle 6x^{3}y^{2}+8x^{4}y^{3}-10x^{5}y^{3}=(2x^{3}y^{2})(3)+(2x^{3}y^{2})(4xy)+(2x^{3}y^{2})(-5x^{2}y)=(2x^{3}y^{2})(3+4xy-5x^{2}y).}$\n\n#### Factoring by groupingEdit\n\nA method that is sometimes useful, but not guaranteed to work, is factoring by grouping.\n\nFactoring by grouping is done by placing the terms in the polynomial into two or more groups, where each group can be factored by a known method. The results of these partial factorizations can sometimes be combined to give a factorization of the original expression.\n\nFor example, to factor the polynomial\n\n${\\displaystyle 4x^{2}+20x+3xy+15y}$\u00a0:\n1. group similar terms, ${\\displaystyle (4x^{2}+20x)+(3xy+15y),}$\n2. factor out the highest common factor in each grouping, ${\\displaystyle 4x(x+5)+3y(x+5),}$\n3. again factor out the binomial common factor, ${\\displaystyle (x+5)(4x+3y).}$\n\nWhile grouping may not lead to a factorization in general, if the polynomial expression to be factored consists of four terms and is the result of multiplying two binomial expressions (by the FOIL method for instance), then the grouping technique can lead to a factorization, as in the above example.\n\n#### Using the factor theoremEdit\n\nFor a univariate polynomial, p(x), the factor theorem states that a is a root of the polynomial (that is, p(a) = 0, also called a zero of the polynomial) if and only if (xa) is a factor of p(x). The other factor in such a factorization of p(x) can be obtained by polynomial long division or synthetic division.\n\nFor example, consider the polynomial ${\\displaystyle x^{3}-3x+2.}$\u00a0 By inspection we see that 1 is a root of this polynomial (observe that the coefficients add up to 0), so (x \u2013 1) is a factor of the polynomial. By long division we have ${\\displaystyle x^{3}-3x+2=(x-1)(x^{2}+x-2).}$\n\n#### Univariate case, using the properties of rootsEdit\n\nWhen a univariate polynomial is completely factored into linear factors (degree one factors), all of the roots of the polynomial are visible and by multiplying the factors together again, the relationship between the roots and the coefficients can be observed. Formally, these relationships are known as Vieta's formulas. These formulas do not help factorizing the polynomial except as a guide to making good guesses at what possible roots may be. However, if some additional information about the roots is known, this can be combined with the formulas to obtain the roots and thus the factorization.\n\nFor example,[7] we can factor ${\\displaystyle x^{3}-5x^{2}-16x+80}$\u00a0 if we know that the sum of two of its roots is zero. Let ${\\displaystyle r_{1},r_{2}}$\u00a0 and ${\\displaystyle r_{3}}$\u00a0 be the three roots of this polynomial. Then Vieta's formulas are:\n\n{\\displaystyle {\\begin{aligned}r_{1}+r_{2}+r_{3}&=5\\\\r_{1}r_{2}+r_{2}r_{3}+r_{3}r_{1}&=-16\\\\r_{1}r_{2}r_{3}&=-80.\\end{aligned}}}\n\nAssuming that ${\\displaystyle r_{2}+r_{3}=0}$\u00a0 immediately gives ${\\displaystyle r_{1}=5}$\u00a0 and reduces the other two equations to ${\\displaystyle r_{2}^{2}=16.}$\u00a0 Thus the roots are 5, 4 and \u20134 and we have ${\\displaystyle x^{3}-5x^{2}-16x+80=(x-5)(x-4)(x+4).}$\n\n##### Finding rational rootsEdit\n\nIf a (univariate) polynomial, f(x), has a rational root, p\/q (p and q are integers and q \u2260 0), then by the factor theorem f(x) has the factor,\n\n${\\displaystyle \\left(x-{\\frac {p}{q}}\\right)={\\frac {1}{q}}(qx-p).}$\n\nIf, in addition, the polynomial f(x) has integer coefficients, then q must evenly divide the integer portion of the highest common factor of the terms of the polynomial, and, in the factorization of f(x), only the factor (qxp) will be visible.\n\nIf a (univariate) polynomial with integer coefficients, say,\n\n${\\displaystyle a_{0}x^{n}+a_{1}x^{n-1}+\\ldots +a_{n-1}x+a_{n}}$\n\nhas a rational root p\/q, where p and q are integers that are relatively prime, then by the rational root test p is an integer divisor of an and q is an integer divisor of a0.[8]\n\nIf we wished to factorize the polynomial ${\\displaystyle 2x^{3}-7x^{2}+10x-6}$\u00a0 we could look for rational roots p\/q where p divides \u20136, q divides 2 and p and q have no common factor greater than 1. By inspection we see that this polynomial can have no negative roots. Assume that q = 2 (otherwise we would be looking for integer roots), substitute x = p\/2 and set the polynomial equal to 0. By multiplying by 4, we obtain the polynomial equation ${\\displaystyle p^{3}-7p^{2}+20p-24=0}$\u00a0 that will have an integer solution of 1 or 3 if the original polynomial had a rational root of the type we seek. Since 3 is a solution of this equation (and 1 is not), the original polynomial had the rational root 3\/2 and the corresponding factor (2x - 3). By polynomial long division we have the factorization ${\\displaystyle 2x^{3}-7x^{2}+10x-6=(2x-3)(x^{2}-2x+2).}$\n\nFor a quadratic polynomial with integer coefficients having rational roots, the above considerations lead to a factorization technique known as the ac method of factorization.[9] Suppose that the quadratic polynomial with integer coefficients is:\n\n${\\displaystyle ax^{2}+bx+c}$\n\nand it has rational roots, p\/q and u\/v. (If the discriminant, ${\\displaystyle b^{2}-4ac}$\u00a0, is a square number these exist, otherwise we have irrational or complex solutions, and there will be no rational roots.) Both q and v must be divisors of a so we may write these fractions with a common denominator of a, that is, they may be written as -r\/a and -s\/a (the use of the negatives is cosmetic and leads to a prettier final result.) Then,\n\n${\\displaystyle ax^{2}+bx+c=a\\left(x^{2}+{\\frac {b}{a}}x+{\\frac {c}{a}}\\right)=a\\left({\\frac {1}{a}}(ax+r){\\frac {1}{a}}(ax+s)\\right)={\\frac {(ax+r)(ax+s)}{a}}.}$\n\nSo, we have:\n\n${\\displaystyle a^{2}x^{2}+abx+ac=(ax+r)(ax+s),}$\n\nwhere rs = ac and r + s = b. The ac method for factoring the quadratic polynomial is to find r and s, the two factors of the number ac whose sum is b and then use them in the factorization formula of the original quadratic above.\n\nAs an example consider the quadratic polynomial:\n\n${\\displaystyle 6x^{2}+13x+6.}$\n\nInspection of the factors of ac = 36 leads to 4 + 9 = 13 = b.\n\n{\\displaystyle {\\begin{aligned}6x^{2}+13x+6&={\\frac {(6x+4)(6x+9)}{6}}\\\\&={\\frac {2(3x+2)(3)(2x+3)}{6}}\\\\&=(3x+2)(2x+3)\\end{aligned}}}\n\n### Recognizable patternsEdit\n\nWhile taking the product of two (or more) expressions can be done by following a multiplication algorithm, the reverse process of factoring relies frequently on the recognition of a pattern in the expression to be factored and recalling how such a pattern arises. The following are some well known patterns.[10]\n\n#### Difference of two squaresEdit\n\nA common type of algebraic factoring is for the difference of two squares. It is the application of the formula\n\n${\\displaystyle a^{2}-b^{2}=(a+b)(a-b),}$\n\nto any two terms, whether or not they are perfect squares.\n\nThis basic form is often used with more complicated expressions that may not at first look like the difference of two squares. For example,\n\n{\\displaystyle {\\begin{aligned}a^{2}+2ab+b^{2}-x^{2}+2xy-y^{2}&=(a^{2}+2ab+b^{2})-(x^{2}-2xy+y^{2})\\\\&=(a+b)^{2}-(x-y)^{2}\\\\&=(a+b+x-y)(a+b-x+y).\\end{aligned}}}\n\n#### Sum\/difference of two cubesEdit\n\nA visual representation of the factorization of cubes using volumes. For a sum of cubes, simply substitute z=-y.\n\nAnother formula for factoring is for the sum or difference of two cubes. The sum can be factored by\n\n${\\displaystyle a^{3}+b^{3}=(a+b)(a^{2}-ab+b^{2}),}$\n\nand the difference by\n\n${\\displaystyle a^{3}-b^{3}=(a-b)(a^{2}+ab+b^{2}).}$\n\n#### Difference of two fourth powersEdit\n\nTwo formulas for factoring the difference of two fourth powers are as follows:\n\n${\\displaystyle a^{4}-b^{4}=(a^{2}+b^{2})(a^{2}-b^{2})=(a^{2}+b^{2})(a+b)(a-b),}$\n${\\displaystyle a^{4}-b^{4}=(a-b)(a^{3}+a^{2}b+ab^{2}+b^{3}).}$\n\n#### Sum\/difference of two nth powersEdit\n\n\u2022 Difference, even n\n\nThe above factorizations of differences or sums of powers can be extended to any positive integer power n.\n\nFor even n, we have\n\n${\\displaystyle a^{n}-b^{n}=(a^{n\/2}-b^{n\/2})(a^{n\/2}+b^{n\/2}).}$\n\nThe first parenthetical term, and possibly the second one, can be further factored using the following formulas.\n\n\u2022 Difference, even or odd n\n\nFor any n, a general factorization is:\n\n${\\displaystyle a^{n}-b^{n}=(a-b)(a^{n-1}+ba^{n-2}+b^{2}a^{n-3}+\\ldots +b^{n-2}a+b^{n-1}).}$\n\u2022 Sum, odd n\n\nThe corresponding formula for the sum of two nth powers depends on whether n is even or odd. If n is odd, b can be replaced by \u2212b in the above formula, to give\n\n${\\displaystyle a^{n}+b^{n}=(a+b)(a^{n-1}-ba^{n-2}+b^{2}a^{n-3}-\\ldots -b^{n-2}a+b^{n-1}).}$\n\u2022 Sum, even n\n\nIf n is even, we consider two cases:\n\n1. If n is a power of 2 then ${\\displaystyle a^{n}+b^{n}}$\u00a0 is unfactorable (more precisely, irreducible over the rational numbers).\n2. Otherwise, ${\\displaystyle n=m\\cdot 2^{k},m>1,k>0}$\u00a0 where m is odd. In this case we have,\n${\\displaystyle a^{n}+b^{n}=(a^{2^{k}}+b^{2^{k}})(a^{n-2^{k}}-a^{n-2\\cdot 2^{k}}b^{2^{k}}+a^{n-3\\cdot 2^{k}}b^{2\\cdot 2^{k}}-\\ldots -a^{2^{k}}b^{n-2\\cdot 2^{k}}+b^{n-2^{k}})=(a^{2^{k}}+b^{2^{k}})\\sum _{i=1}^{m}a^{(m-i)2^{k}}(-b^{2^{k}})^{i-1}.}$\n\u2022 Examples\n\nSpecifically, for some small values of n we have:\n\n${\\displaystyle a^{5}+b^{5}=(a+b)(a^{4}-a^{3}b+a^{2}b^{2}-ab^{3}+b^{4}),}$\n${\\displaystyle a^{5}-b^{5}=(a-b)(a^{4}+a^{3}b+a^{2}b^{2}+ab^{3}+b^{4}).}$\n${\\displaystyle a^{6}+b^{6}=(a^{2}+b^{2})(a^{4}-a^{2}b^{2}+b^{4}),}$\n${\\displaystyle a^{6}-b^{6}=(a^{3}+b^{3})(a^{3}-b^{3})=(a+b)(a-b)(a^{2}-ab+b^{2})(a^{2}+ab+b^{2}).}$\n${\\displaystyle a^{7}+b^{7}=(a+b)(a^{6}-a^{5}b+a^{4}b^{2}-a^{3}b^{3}+a^{2}b^{4}-ab^{5}+b^{6}),}$\n${\\displaystyle a^{7}-b^{7}=(a-b)(a^{6}+a^{5}b+a^{4}b^{2}+a^{3}b^{3}+a^{2}b^{4}+ab^{5}+b^{6}).}$\n\n#### Sum\/difference of two nth powers over the field of the real algebraic numbersEdit\n\nThe above factorizations give factors with coefficients in the same field as those of the expression being factored\u2014for example, a polynomial with rational coefficients (\u00b11 in many cases above) is split into factors which themselves have rational coefficients. However, a factorization into factors with algebraic numbers (numbers that are the solution of some polynomial equation) as coefficients can yield lower-degree factors, as in the following formulas which can be proven by going through the complex conjugate roots of ${\\displaystyle f(a)=a^{n}\\pm b^{n}.}$\u00a0 (The cosine expressions are algebraic numbers because they are trigonometric numbers.)\n\nThe sum of two terms that have equal even powers is factored by\n\n${\\displaystyle a^{2n}+\\ b^{2n}=\\prod _{k=1}^{n}{\\Bigl (}a^{2}\\ \\pm \\ 2ab\\cos {\\frac {(2k-1)\\pi }{2n}}\\ +\\ b^{2}{\\Bigl )}.}$\n\nThe difference of two terms that have equal even powers is factored by\n\n${\\displaystyle a^{2n}-\\ b^{2n}=(a\\ -\\ b)(a\\ +\\ b)\\prod _{k=1}^{n-1}{\\Bigl (}a^{2}\\ \\pm \\ 2ab\\cos {\\frac {k\\pi }{n}}\\ +\\ b^{2}{\\Bigl )}.}$\n\nThe sum or difference of two terms that have equal odd powers is factored by\n\n${\\displaystyle a^{2n+1}\\ \\pm \\ b^{2n+1}=(a\\ \\pm \\ b)\\prod _{k=1}^{n}{\\Bigl (}a^{2}\\ \\pm \\ 2ab\\cos {\\frac {2k\\pi }{2n+1}}\\ +\\ b^{2}{\\Bigl )}=(a\\ \\pm \\ b)\\prod _{k=1}^{n}{\\Bigl (}a^{2}\\ \\pm \\ 2ab(-1)^{k}\\cos {\\frac {k\\pi }{2n+1}}\\ +\\ b^{2}{\\Bigl )}.}$\n\nFor instance, the sum or difference of two fifth powers is factored by\n\n${\\displaystyle a^{5}\\pm b^{5}=(a\\pm b){\\Biggl (}a^{2}\\mp {\\frac {1-{\\sqrt {5}}}{2}}ab+b^{2}{\\Biggl )}{\\Biggl (}a^{2}\\mp {\\frac {1+{\\sqrt {5}}}{2}}ab+b^{2}{\\Biggl )},}$\n\nand the sum of two fourth powers is factored by\n\n${\\displaystyle a^{4}+b^{4}=(a^{2}-{\\sqrt {2}}ab+b^{2})(a^{2}+{\\sqrt {2}}ab+b^{2}).}$\n\n#### Binomial expansionsEdit\n\nVisualisation of binomial expansion up to the 4th power\n\nThe binomial theorem supplies patterns of coefficients that permit easily recognized factorizations when the polynomial is a power of a binomial expression.\n\nFor example, the perfect square trinomials are the quadratic polynomials that can be factored as follows:\n\n${\\displaystyle a^{2}+2ab+b^{2}=(a+b)^{2},}$\n\nand\n\n${\\displaystyle a^{2}-2ab+b^{2}=(a-b)^{2}.}$\n\nSome cubic polynomials are four term perfect cubes that can be factored as:\n\n${\\displaystyle a^{3}+3a^{2}b+3ab^{2}+b^{3}=(a+b)^{3},}$\n\nand\n\n${\\displaystyle a^{3}-3a^{2}b+3ab^{2}-b^{3}=(a-b)^{3}.}$\n\nIn general, the coefficients of the expanded polynomial ${\\displaystyle (a+b)^{n}}$\u00a0 are given by the n-th row of Pascal's triangle. The coefficients of ${\\displaystyle (a-b)^{n}}$\u00a0 have the same absolute value but alternate in sign.\n\n#### Other factorization formulasEdit\n\n{\\displaystyle {\\begin{aligned}x^{2}+y^{2}+z^{2}+2(xy+yz+xz)\\,&=(x+y+z)^{2}\\\\x^{3}+y^{3}+z^{3}-3xyz\\,&=(x+y+z)(x^{2}+y^{2}+z^{2}-xy-xz-yz)\\\\x^{3}+y^{3}+z^{3}+3x^{2}(y+z)+3y^{2}(x+z)+3z^{2}(x+y)+6xyz\\,&=(x+y+z)^{3}\\\\x^{4}+x^{2}y^{2}+y^{4}\\,&=(x^{2}+xy+y^{2})(x^{2}-xy+y^{2}).\\end{aligned}}}\n\n### Using formulas for polynomial rootsEdit\n\nAny univariate quadratic polynomial (polynomials of the form ${\\displaystyle ax^{2}+bx+c}$\u00a0) can be factored over the field of complex numbers using the quadratic formula, as follows:\n\n${\\displaystyle ax^{2}+bx+c=a(x-\\alpha )(x-\\beta )=a\\left(x-{\\frac {-b+{\\sqrt {b^{2}-4ac}}}{2a}}\\right)\\left(x-{\\frac {-b-{\\sqrt {b^{2}-4ac}}}{2a}}\\right),}$\n\nwhere ${\\displaystyle \\alpha }$\u00a0 and ${\\displaystyle \\beta }$\u00a0 are the two roots of the polynomial, either both real or both complex in the case where a, b, c are all real, found with the quadratic formula.\n\nThe quadratic formula is valid for all polynomials with coefficients in any field (in particular, the real or complex numbers) except those that have characteristic two.[11]\n\nThere are also formulas for cubic and quartic polynomials which can be used in the same way. However, there are no algebraic formulas in terms of the coefficients that apply to all univariate polynomials of a higher degree, by the Abel\u2013Ruffini theorem.\n\n### Factoring over the complex numbersEdit\n\n#### Sum of two squaresEdit\n\nEven if a and b represent real numbers, the sum of their squares can be written as the product of non-real complex numbers. This produces the factorization formula:\n\n${\\displaystyle a^{2}+b^{2}=(a+bi)(a-bi).}$\n\nFor example, ${\\displaystyle 4x^{2}+49}$\u00a0 can be factored into ${\\displaystyle (2x+7i)(2x-7i)}$\u00a0.\n\n## NotesEdit\n\n1. ^ Hardy; Wright (1980). An Introduction to the Theory of Numbers (5th ed.). Oxford Science Publications. ISBN\u00a0978-0198531715.\n2. ^ Fite 1921, p.\u00a020\n3. ^ Even if the 3 is thought of as a constant polynomial so that this could be considered a factorization into polynomials.\n4. ^ Klein 1925, pp.\u00a0101\u2013102\n5. ^ Sanford, Vera (2008) [1930], A Short History of Mathematics, Read Books, ISBN\u00a09781409727101\n6. ^ Fite 1921, p.\u00a019\n7. ^ Burnside & Panton 1960, p.\u00a038\n8. ^ Dickson 1922, p.\u00a027\n9. ^ Stover, Christopher AC Method - Mathworld\n10. ^ Selby 1970, p.\u00a0101\n11. ^ In these fields 2 = 0 so the division in the formula is not valid. There are other ways to find roots of quadratic equations over these fields.\n\n## ReferencesEdit\n\n\u2022 Burnside, William Snow; Panton, Arthur William (1960) [1912], The Theory of Equations with an introduction to the theory of binary algebraic forms (Volume one), Dover\n\u2022 Dickson, Leonard Eugene (1922), First Course in the Theory of Equations, New York: John Wiley & Sons\n\u2022 Fite, William Benjamin (1921), College Algebra (Revised), Boston: D. C. Heath & Co.\n\u2022 Klein, Felix (1925), Elementary Mathematics from an Advanced Standpoint; Arithmetic, Algebra, Analysis, Dover\n\u2022 Selby, Samuel M., CRC Standard Mathematical Tables (18th ed.), The Chemical Rubber Co.","date":"2018-03-19 16:55:23","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 69, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.7680366635322571, \"perplexity\": 327.77729671289273}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.3, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2018-13\/segments\/1521257647003.0\/warc\/CC-MAIN-20180319155754-20180319175754-00206.warc.gz\"}"}
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Q: Using jquery toggle() inside a custom polymer element I want to use a button to toggle a word on click like this:
function toggle() {
$("#secret").toggle();
}
<script src="//ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<body>
<button onClick="toggle()"> toggle </button>
<p id="secret" style="display: none"> secret </p>
</body>
This works without problems but when using the code inside a custom Polymer element, the word is only shown but not hidden again.
<script src="//ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<script src="//www.polymer-project.org/components/polymer/polymer.js"></script>
<polymer-element name="test-element">
<template>
<button on-tap="{{toggle}}"> toggle </button>
<p id="secret" style="display: none"> secret </p>
</template>
<script>
Polymer({
toggle: function() {
$(this.$.secret).toggle();
}
});
</script>
</polymer-element>
<test-element></test-element>
However, using show() and hide() works:
<script src="//ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<script src="//www.polymer-project.org/components/polymer/polymer.js"></script>
<polymer-element name="test-element">
<template>
<button on-tap="{{toggle}}"> Toggle </button>
<p id="secret"> secret </p>
</template>
<script>
Polymer({
toggle: function() {
if ($(this.$.secret).css("display") == "block") {
$(this.$.secret).hide();
} else {
$(this.$.secret).show();
}
}
});
</script>
</polymer-element>
<test-element></test-element>
Why is the toggle() function working itself but not working inside a custom polymer element when show() and hide() are working ?
A: I don't think you have to use jQuery for "toggling" you can do that in more polymeric way:
<script src="//www.polymer-project.org/components/polymer/polymer.js"></script>
<polymer-element name="test-element">
<template>
<button on-tap="{{toggle}}">Toggle</button>
<p id="secret" hidden?="{{!showingSecret}}">secret</p>
</template>
<script>
Polymer({
toggle: function() {
this.showingSecret = !this.showingSecret;
}
});
</script>
</polymer-element>
<test-element></test-element>
A: i don't think jquery works inside polymer elements. and if so maybe not fully working. but it's easy to fix. you could use https://www.polymer-project.org/docs/elements/core-elements.html#core-collapse
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Home > node > Prom 5, Pelléas et Mélisande, Glyndebourne review - for the ears, not the eyes
Prom 5, Pelléas et Mélisande, Glyndebourne review - for the ears, not the eyes | reviews, news & interviews
Prom 5, Pelléas et Mélisande, Glyndebourne review - for the ears, not the eyes
Semi-staged Debussy is visually confused, musically mostly excellent
by Stephen WalshWednesday, 18 July 2018
Christina Gansch, Christopher Purves and John Chest: disrupted family linesBBC/Chris Christodoulou
What a fabulous score Pelléas et Mélisande is, and what a joy to be able to hear it in a concert performance without the distraction of some over-sophisticated director's self-communings. Well, if only. What last night's Prom in fact served up was a kind of abstract of Stefan Herheim's Glyndebourne production, semi-staged by Sinéad O'Neill without its organ-room setting and all that that entailed, but with a great deal of its dramaturgical clutter still intact.
This was emphatically a performance for the radio. I was in the Albert Hall, but I suspect the orchestral playing will have sounded about as technically and musically refined over the air as one could possibly wish, and even in the hall – if you could shut your eyes (and occasionally ears) to the downstage nonsense – the orchestral sound, under Robin Ticciati, was as nearly perfect as anything I've heard in these profound spaces for a very long time. The curious thing about this is that Debussy only orchestrated the opera – or at least only wrote the orchestration down – some years after the music itself was completed. Yet the whole score – voices and orchestra – sounds like a single, completely integrated concept, imagined all of a piece, and of an expressive subtlety and precision that perhaps only Mozart at his best ever surpassed.
The director needs to clarify these things, not obscure themDavid Nice has already done the necessary Beckmesser job on Herheim's dark fantasies, whose essence seems to survive in O'Neill's actually somewhat more than semi staging. If these ideas – the incessant comings and goings of assorted servants, the seemingly irrelevant paintings and empty easels, Yniold's sudden transgendering in his/her scene with Golaud, Golaud's physical presence, acknowledged by Mélisande, throughout the final love scene, Pelléas's reappearance as a walking corpse and Mélisande's love-death in the final scene: if these ideas were baffling to a Glyndebourne audience who at least had the full context, imagine what any Prommer not acquainted with this marvellous and essentially lucid work might make of them.
One even asked me in the interval what Yniold's sex change with skirt and long hair meant. I struggled: well, hair is something of a motif (isn't it?); Yniold is a boy played by a girl (isn't he – well actually not originally, but let that pass). The worst of all this is that it blocks out the real significance of the scene, Golaud punishing his first wife (Yniold's dead mother) for his failure with his second. Among other things Pelléas (like its near contemporary, Janacek's Jenufa) is about disrupted family lines. The director needs to clarify these things, not obscure them. Vocally, though, the cast did well. I liked the Pelléas, John Chest, somewhat more than David Nice did, Christina Gansch's Mélisande perhaps a fraction less. Chest may have profited from the acoustic space, but I thought his voice good for the part: a baritone slightly biased towards the top (this is said to have been Debussy's own range, though heaven knows what his singing was like). Gansch also suits this music very nicely, but overacted, turning Mélisande into a nonstop Rossetti mobile, with waving body, flailing arms, and not much mystery.
Christopher Purves will have sounded a strong Golaud on the airwaves, but was damaged onstage by his crusty, too-elderly image and too coarse persona. Golaud is a plain man but not a bad one, mystified by Mélisande but violent towards her only when her uncommunicativeness finally unhinges him.
The Arkel, Brindley Sherratt, and the Geneviève, Karen Cargill (pictured above with John Chest), were strong by any standards, and Chloé Briot was a sound Yniold, though a boy is really needed, however hard to find. But the real heroes of the evening were unquestionably Ticciati and the London Philharmonic Orchestra. Whenever I found my irritation with the stage boiling over, I took refuge in the orchestra and the conducting and they never let me down.
Listen to this Prom for the next month on the BBC iPlayer
Read more classical music reviews on theartsdesk
Technically and musically refined as you could wish, if you could shut your eyes
Pelléas et Mélisande, Glyndebourne review - frigid metatheatre
Hänsel und Gretel, Glyndebourne Festival Opera, Ticciati, Royal Albert Hall
Pelléas et Mélisande, LSO, Rattle, Barbican
Prom 1, BBCSO, Oramo review – spectacular First Night of the Proms
Pelléas et Mélisande, Garsington Opera review - brilliant but frustrating
opera directors
This performance also lacked
Permalink Submitted by Alan T (not verified) on Wed, 18/07/2018 - 13:35
This performance also lacked another traditional element of Proms opera performances: a libretto in the programme-book. Instead there were projected surtitles - which meant that, to follow the action, you had to look (more or less) in the direction of the stage. Paying attention where it most belonged, to the orchestra, was very difficult except for the orchestral interludes as a result. As the surtitles were only in English, it also meant that it was harder to appreciate Debussy's careful word-setting in French, and how that was enunciated and projected by the singers. It was a huge disservice to the audience.
And having one's head buried
Permalink Submitted by David Nice on Wed, 18/07/2018 - 23:46
And having one's head buried in the programme book would have made 'paying attention where it most belonged' any easier? Harder, I would have thought. Please don't give the Proms food for not having supertitles - we battled so hard for them in the past few seasons. Not having them for The Makropoulos Case left so many people bewildered. By the time they realised they should have bought a programme two-thirds of the opera was over.
Thank goodness for the
Permalink Submitted by Linda Rose (not verified) on Thu, 19/07/2018 - 08:29
Thank goodness for the surtitles!! The direction was totally baffling and I cannot agree more with the above article saying the direction should be to explain and demystify the story, not to confuse even more. It would be better not to 'stage' it at all than put odd and inexplicable props like the easels which supposedly doubled as the Tower etc. The acting around the long hair was ludicrous, the 3 peasants creeping on were bizarre, the use of the easels didn't work and had no suggestion of a tower at all, and the weird disturbing morphing somewhat sexually charged scene with the 'son' at the end of the first half was highly disturbing. We left at that point as my family didn't wish to stay for such a lengthy opera when it was so confused, disturbing, and poorly directed. I had chosen this night of the Proms to come to as I thought it would be more exciting having a part staged performance than simply the orchestra, but I agree again with the above author that it was by far the best when I closed my eyes and let the music wash through me. Shame on the director for damaging an otherwise excellent musical performance. My family will never be willing to attend another opera now.
Correct that immediately, if
Permalink Submitted by David Nice on Thu, 19/07/2018 - 09:56
Correct that immediately, if you can afford it, by taking them to see Ariadne auf Naxos at Opera Holland Park. There's a production which tells a funny and magical story with the utmost clarity. It does seem a shame that Glyndebourne couldn't shuck Herheim's obscure, messy vision when it visited the Proms. It made an opera I love almost unbearable to watch in the production proper.
I agree that the stage
Permalink Submitted by Kevin Nash (not verified) on Thu, 19/07/2018 - 09:50
I agree that the stage "direction" was a major distraction, but at the same time it was intentionally symbolist, even surrealistic; and it didn't always fail. The idea that each character was painting their own image of reality on a false canvas had some merit. What I found to be a greater distraction was the musical direction. I am (always have been) a great fan of Robin Ticciati, but I feel his reading of the score was miscalculated. At least the stage director tried to encapsulate the symbolist ideas of Debussy and Maeterlinck, while Ticciati seemed more intent on reimagining the music as late Romantic. There was far more allusion to Wagner and even Brahms than to the future soundscapes of Stravinsky that I believe Debussy anticipated. As "pretty" as the music sounded, this was not, for me, what Pélleas is all about.
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\section{Introduction}
\section{Introduction}
Let $\mathbb{D}_r$ be the disc centered at the origin with radius $r$, that is, \[\mathbb{D}_r:=\{x\in\mathbb R^2\mid x=(x_1,x_2), |x|:=x_1^2+x_2^2<r\}.\]
In this note, we shall study the radial symmetry property of solutions to the two-dimensional incompressible Euler equations in $\mathbb{D}_r$
\begin{equation}\label{euler}
\begin{cases}
\partial_t\mathbf{v}+(\mathbf{v}\cdot\nabla)\mathbf{v}=-\nabla P, & (x,t)\in\mathbb{D}_r\times\mathbb R_+, \\
\nabla\cdot\mathbf{v}=0,\\
\mathbf{v}\cdot\mathbf{n}=0, & x\in\partial\mathbb{D}_r, \\
\mathbf{v}|_{t=0}=\mathbf{v}_0,
\end{cases}
\end{equation}
where $\mathbf{v}=(v_1,v_2)$ is the velocity field, $P$ is the scalar pressure and $\mathbf{n}$ is the outward unit normal of $\partial \mathbb {D}_r$. The boundary condition $\mathbf{v}\cdot\mathbf{n}=0$, which is usually called the impermeability boundary condition, means that there is no matter flow through $\partial \mathbb{D}_r$. By introducing the scalar vorticity $\omega:=(\partial_{x_1}v_2-\partial_{x_2}v_1)$, the Euler system can be simplified as a single equation for the vorticity
\begin{equation}\label{vor}
\begin{cases}
\partial_t\omega+\nabla^\perp(\mathcal{G}\omega)\cdot\nabla\omega=0,&(x,t)\in\mathbb{D}_{r}\times \mathbb R_+,\\
\omega|_{t=0}=\omega_0,&x\in\mathbb{D}_r,
\end{cases}
\end{equation}
where $\nabla^\perp:=(\partial_{x_2},-\partial_{x_1})$ and $\mathcal{G}_r\omega(x):=\int_{\mathbb{D}_r}G_r(x,y)\omega(y)dy,$ with $G_r$ being the Green function for $-\Delta$ in $\mathbb{D}_r$ with zero Dirichlet data
\[G_r(x,y)=-\frac{1}{2\pi}\ln|x-y|-h_r(x,y),\,\,\,h_r(x,y)=-\frac{1}{2\pi}\ln\left|\frac{rx}{|x|}-\frac{|x|y}{r}\right|.\]
Equation \eqref{vor} is usually called the vorticity equation. For weak solutions of the vorticity equation with initial vorticity $\omega_0\in L^\infty(\mathbb{D}_r)$, the global well-posedness result was proved by Yudovich \cite{Y}. See also \cite{MB}, Chapter 8. Since $\nabla^\perp(\mathcal{G}\omega)$ is a divergence-free vector field, it is easy to see that the distribution function of the solution of \eqref{vor} is independent of the time variable $t$, that is,
\[|\{x\in\mathbb D_r\mid \omega(x,t)>a \}|=|\{x\in\mathbb D_r\mid \omega_0(x)>a \}|\]
for all $a\in\mathbb R$ and $t\in \mathbb R_+$. Here and in the sequel, we use $|\cdot|$ to denote the two-dimensional Lebesgue measure. As a consequence, if the initial vorticity $\omega_0$ is a constant multiple of the characteristic function of some measurable set $D\subset \mathbb D_r$, that is, $\omega_0=\lambda I_{D}$, where $\lambda\in\mathbb R$ represents the vorticity strength, then the evolved vorticity $\omega(\cdot,t)$ must be of the form
$\omega(\cdot,t)=\lambda I_{D_t}$ with $|D_t|=|D|$ for all $t>0$. The preservation of regularity for the boundary of an evolving vortex patch was firstly proved by Chemin \cite{Chemin} for the whole plane case and then was extended to bounded domains by Depauw \cite{Depauw}.
In this paper, we are mainly concerned with rotating solution, also called $V$-state, of the Euler equations, that is, solution with the form
\begin{equation}\label{1-2}
\omega(x,t)=w(e^{-i\Omega t}x),
\end{equation}
where $e^{-i\Omega t}x$ denotes clockwise rotation through $\pi/2$ of $x$, and $\Omega\in\mathbb R$ is the angular velocity of the rotating solution. It is easy to see that the solution rotates clockwisely if $\Omega<0$, and rotates anticlockwisely if $\Omega>0$. If $\Omega=0$, then obviously $w$ is a steady solution.
For smooth $w$, we can substitute \eqref{1-2} into the vorticity equation \eqref{vor} to obtain
\begin{equation}\label{1-3}
\nabla\cdot(w(x)\nabla^\perp(\mathcal G_r w(x)+\frac{\Omega}{2}|x|^2))=0.
\end{equation}
Since we are going to deal with solutions with discontinuity, we need to interpret \eqref{1-3} in the following weak sense
\begin{equation}\label{1-4}
\int_{\mathbb D_r}w(x)\nabla^\perp(\mathcal G_r w(x)+\frac{\Omega}{2}|x|^2)\cdot \nabla\phi(x)dx=0,\,\,\forall\,\phi\in C_c^\infty(\mathbb D_r).
\end{equation}
In fact, \eqref{1-3} can be obtained by integration by parts(notice that $\nabla^\perp(\mathcal G_r w(x)+\frac{\Omega}{2}|x|^2))$ is divergence-free).
We call $\omega$ a rotating vortex patch, or just rotating patch for brevity, if it satisfies \eqref{1-4} and has the form
\begin{equation}\label{form}
\omega(x,t)=w(e^{-i\Omega t}x), \,\,w=\lambda I_{D},
\end{equation}
where $\lambda$ is a parameter representing the vorticity strength of the patch.
In the sequel we shall also call the set $D$ in \eqref{form} a rotating patch.
It is not difficult to check that if $D$ is rotating patch with $C^1$ boundary and $\lambda\neq 0$, then $\lambda \mathcal G_r I_D+\frac{\Omega}{2}|x|^2$ is a constant on each connected component of $\partial D$(although on different components the constants may be different). In fact, since $D$ is a rotating patch, we have
\begin{equation}\label{1-101}
\lambda\int_{D}\nabla^\perp(\lambda\mathcal G_r I_D(x)+\frac{\Omega}{2}|x|^2))\cdot \nabla\phi(x)dx=0,\,\,\forall\,\phi\in C_c^\infty(\mathbb D_r).
\end{equation}
Then by integration by parts, we obtain
\begin{equation}\label{1-102} \int_{\partial D}\phi(x)\nabla^\perp(\lambda\mathcal G_r I_D(x)+\frac{\Omega}{2}|x|^2))\cdot\vec{\nu}(x)d\mathcal H^1=0,
\end{equation}
where $\vec{\nu}$ denotes the outward unit normal of $\partial D$ and $d\mathcal H^1$ denotes the one-dimensional Hausdorff measure. Taking into account the fact that $\phi$ can be chosen arbitrarily in $C_c^\infty(\mathbb D_r)$, we get
\[\nabla^\perp(\lambda\mathcal G_r I_D(x)+\frac{\Omega}{2}|x|^2))\cdot\vec{\nu}(x)\equiv0,\,\, x\in\partial D,\]
which leads to the desired result.
In the literature, there are a large number of results on existence and stability of rotating patches(including stationary patches) in the whole plane and in the disc. For existence, roughly speaking, there are mainly two types of rotating patches in the literature. The first one is of desingularization type. As the name suggests, it is about the desingularization of point vortices. More precisely, desingularization of point vortices is to construct a family of rotating(steady) vortex patches of the Euler equations that ``shrinks" to a given rotating(steady) system of point vortices. We point the interested reader to \cite{CWW}\cite{CWWZ}\cite{W} and the references listed therein. The second type of rotating patches is of bifurcation type. It consists of finding a new rotating patch bifurcating from a given one(for example, a disc, an annulus or a Kirchhoff ellipse). Related references are \cite{Burbea}\cite{dHHM}\cite{dHMV}\cite{DZ}\cite{HMV}. There are also many efforts that have been devoted to establishing the stability or instability of rotating patches. See \cite{GHS}\cite{Ta}\cite{W} for example. It should be noted that steady patches in general bounded domains have also been studied by many authors in recent years. See \cite{CPY}\cite{CW}\cite{CW3}\cite{T} for example.
Now we come back to rotating patches in the disc $\mathbb D_r$. It is easy to see that if $D$ is a disc centered at the origin, then it must be a rotating patch with arbitrary angular velocity. Now a very natural problem arises: \textit{under what conditions on $\lambda, r, \Omega$ must a rotating patch $D$ be a disc centered at the origin?}
To answer this question, we first notice the following fact which can be easily checked by using the scaling property of the vorticity equation \eqref{vor}: $D$ is a rotating patch in $\mathbb D_r$ with vorticity strength $\lambda$ and angular velocity $\Omega$ if and only if $D/r:=\{x\in\mathbb R^2\mid rx\in D\}$ is a rotating patch in $\mathbb D_1$ with vorticity strength $1$ and angular velocity $\Omega/\lambda$. For this reason, we will only consider the case $\lambda=1$ and $r=1$ in the rest of this paper.
Before we state our main result, we shall briefly review some known results on the radial symmetry property of rotating patches, both in the whole plane and in the unit disc. For rotating patches in the whole plane, Hmidi \cite{Hm} proved that any $C^1$ simply-connected rotating patch with angular velocity $\Omega$ must be radial if $\Omega=1/2$, or $\Omega<0$ but with some extra convexity assumption. For each $\Omega\in(0,1/2)$, de la Hoz--Hmidi--Mateu--Verdera \cite{dHMV} proved existence of non-radial rotating patches with $m$-fold symmetry bifurcating at $\Omega$. Recently, G\'omez-Serrano--Park--Shi--Yao \cite{GPSY} completely solved the radial symmetry problem for rotating patches by showing that any $C^1$ rotating patch(can be non-simply-connected) with angular velocity $\Omega\in(-\infty,0)\cup[1/2,+\infty)$ must be radially symmetric, and if $\Omega=0,$ then this rotating patch must be radially symmetric up to a translation.
As for rotating patches in the unit disc, to our knowledge, there is no result on radial symmetry in the literature by now. Here we only recall two existence results. In \cite{dHHM}, based on bifurcation theory, de la Hoz--Hassainia--Hmidi--Mateu proved that for any $b\in(0,1)$ and $m$ a positive integer, there exists a family of $m$-fold symmetric rotating patches bifurcating from the steady patch $\mathbb D_b$, $b\in(0,1)$, with angular velocity $\Omega_m=(m-1+b^{2m})/(2m)$. These rotating patches are simply-connected, moreover, the angular velocity lies in the interval $(0,1/2)$ just as the whole plane case. In \cite{CWWZ}, Cao-Wan-Wang-Zhan studied the existence of rotating patches of desingularization type in the unit disc. They proved that for any fixed $\Omega>0$, there exists a family of $C^1$ simply-connected rotating patches $\omega^\lambda=\lambda I_{D^\lambda}(e^{-i\Omega t}x)$ with $\lambda$ sufficiently large, moreover, $D^\lambda$ is supported in a very small region near some point $x_\Omega$ with $|x_\Omega|=0$ if $\Omega\leq (2\pi)^{-1}$ and $|x_\Omega|=(1-(2\pi\Omega)^{-1})^{1/2}$ if $\Omega> (2\pi)^{-1}$. It is easy to see that in this situation the angular velocity still lies in the interval $(0,1/2)$.
One may ask whether all the non-radial rotating patches in the unit disc possess an angular velocity in the interval $(0,1/2)$. This is in general a difficult problem. In this paper, we partially solve this problem by showing that for any $C^1$ simply-connected rotating patch with vorticity strength $1$ and angular velocity $\Omega$, if $\Omega\geq \max\{{1}/{2},({2 l^2})/{(1-l^2)^2}\}$ or $\Omega\leq -({2 l^2})/{(1-l^2)^2}$, where $l=\sup_{x\in D}|x|$, then $D$ must be radial.
The proof is inspired by a recent paper \cite{GPSY} by G\'omez-Serrano--Park--Shi--Yao. The basic idea is as follows.
Define
\begin{equation}\label{E}
E_\Omega(D):=\frac{1}{2}\int_D\int_DG_1(x,y)dxdy+\frac{\Omega}{2}\int_D|x|^2dx,
\end{equation}
where $G_1$ is the Green function in $\mathbb D_1$.
Since $D$ is a rotating patch, we can easily check that $E_\Omega$
is a critical point on the following rearrangement class
\[\mathcal R(D):=\{K\subset \mathbb D_1\mid |K|=|D|\}\]
in the sense that if we deform $D$ without changing its area, the variation of $E_\Omega$ is zero. On the other hand, we can choose a suitable divergence-free field $\mathbf{w}$ to deform $D$ and calculate the variation of $E_\Omega$. We will show that if $D$ is not a disc centered at the origin, then the variation of $E_\Omega$ is not zero for sufficiently large $|\Omega|$.
This paper is organized as follows. In Section 2 we state the main result and give several remarks. In Section 3 we prove the main result.
\section{Main Result}
In the rest of this paper, we will only focus on rotating patches in $\mathbb D_1$ with unit vorticity strength. For brevity, we will use $G$(rather than $G_1$) to denote the Green function in $\mathbb D_1$, that is,
\[G(x,y)=-\frac{1}{2\pi}\ln|x-y|-h(x,y),\,\,h(x,y)=-\frac{1}{2\pi}\ln\left|\frac{x}{|x|}-|x|y\right|.\]
The corresponding Green operator $\mathcal{G}$ is defined by
\[\mathcal{G}\omega(x):=\int_DG(x,y)\omega(y)dy.\]
Our main theorem can be stated as follows.
\begin{theorem}\label{thm}
Let $D$ be a $C^1$ simply-connected rotating vortex patch in $\mathbb D_1$ with vorticity strength 1 and angular velocity $\Omega$, that is, $I_{D}(e^{-i\Omega t}x)$ is a solution to the vorticity equation \eqref{vor} with $r=1$. If $\Omega\geq\max\{\frac{1}{2},\frac{2 l^2}{(1-l^2)^2}\}$ or $\Omega\leq-\frac{2 l^2}{(1-l^2)^2}$, where $l=\sup_{x\in D}|x|$, then $D$ must be a disc centered at the origin.
\end{theorem}
\begin{remarks}
We should point out that the conclusion in Theorem \ref{thm} still holds true if $D$ is a steady patch, that is, $\Omega=0$. This can be deduced from the following radial symmetry property of semilinear elliptic equations with monotone nonlinearity. Fraenkel (\cite{Frae}, Corollary 3.9) proved that if $\psi$ is the solution to the following semilinear elliptic equation
\begin{equation}\label{semi}
\begin{cases}
-\Delta\psi=f(\psi), &\mbox{in } \mathbb D_1, \\
\psi>0,&\mbox{in } \mathbb D_1,\\
\psi=0, & \mbox{on }\partial\mathbb D_1,
\end{cases}
\end{equation}
where $f$ has a decomposition $f=f_1+f_2$ such that $f_1:[0,+\infty)\to\mathbb R$ is locally Lipschitz continuous and $f_2:[0,+\infty)\to\mathbb R$ is nondecreasing and $f_2\equiv0$ on $[0,\kappa]$ for some $\kappa>0$, then $\psi$ must be a radial function. The proof is based on the moving plane method. From Fraenkel's result, we can easily get radial symmetry for simply-connected patches if $\Omega=0$, since in this situation the stream function $\psi:=\mathcal G I_D$ satisfies
\begin{equation}\label{psi}
\begin{cases}
-\Delta\psi=I_{\{\psi>\mu\}}, &\mbox{in } \mathbb D_1, \\
\psi=0, & \mbox{on }\partial\mathbb D_1
\end{cases}
\end{equation}
for some $\mu>0$. The above argument has been used by Hmidi in \cite{Hm} to prove radial symmetry for simply-connected rotating patches if $\Omega<0$ for the whole plane case, but with some additional convexity assumption. Although radial symmetry for steady patches indeed holds true,
our method in this paper are not able to deal with this simple case, since the boundary of the disc causes some inevitable trouble as we will see in the proof.
\end{remarks}
As mentioned in Section 1, $D$ is a rotating patch in $\mathbb D_r$ with vorticity strength $\lambda$ and angular velocity $\Omega$ if and only if $D/r:=\{x\in\mathbb R^2\mid rx\in D\}$ is a rotating patch in $\mathbb D_1$ with vorticity strength $1$ and angular velocity $\Omega/\lambda$. Therefore we can easily deduce the following radial symmetry property for rotating patches in $\mathbb D_r.$
\begin{corollary}\label{cor1}
Let $D$ be a $C^1$ simply-connected rotating vortex patch in $\mathbb D_r$ with vorticity strength $\lambda$ and angular velocity $\Omega$. If $\Omega\geq\max\{\frac{\lambda}{2},\frac{2\lambda l^2r^2}{(r^2-l^2)^2}\}$ or $\Omega\leq-\frac{2\lambda l^2r^2}{(r^2-l^2)^2}$, where $l=\sup_{x\in D}|x|$, then $D$ must be a disc centered at the origin.
\end{corollary}
\begin{remark}
By letting $r$ tend to infinity, we can easily get the result proved by G\'omez-Serrano--Park--Shi--Yao in \cite{GPSY}.
\end{remark}
If $D$ is a $C^1$ rotating patch in $\mathbb D_1$ with vorticity strength $1$ and angular velocity $\Omega$, then $D^c:=\{x\in\mathbb D_1\mid x\notin D\}$ is a rotating patch with angular velocity ${1}/{2}-\Omega$. In fact, we need only notice that $\mathcal{G}I_D+\frac{\Omega}{2}|x|^2=$constant on $\partial D$ implies $\mathcal{G}I_{D^c}+(\frac{1}{4}-\frac{\Omega}{2})|x|^2=$constant on $\partial D^c$. Taking into account Theorem \ref{thm}, we can easily get the following corollary.
\begin{corollary}\label{cor}
Let $D\subset\mathbb D_1$ be the complement of a $C^1$ simply-connected domain.
If $D$ is a rotating vortex patch with vorticity strength 1 and angular velocity ${\Omega}$ with $\Omega\leq\max\{0,\frac{1}{2}-\frac{2l^2}{(1-l^2)^2}\}$ or $\Omega\geq\frac{1}{2}+\frac{2l^2}{(1-l^2)^2}$, $l=\sup_{x\in D^c}|x|$, then $D$ must be an annulus.
\end{corollary}
\section{Proof}
In this section, we give the proof of Theorem \ref{thm}. To begin with, let us explain the basic idea of the proof.
As mentioned in Section 1, we need to deform $D$ under a suitable area-preserving flow, and show that if $D$ is not a disc centered at the origin, then the variation of the energy function $E_\Omega$(defined by \eqref{E}) is strictly positive or strictly negative if $|\Omega|$ is very large, which will lead to a contradiction. More specifically, for any divergence-free vector field $\mathbf{w},$ we define the area-preserving flow $\Phi_s$ by solving the following ordinary differential equation
\begin{equation}\label{ORD}
\begin{cases}\frac{d\Phi_s(x)}{ds}=\mathbf{w}(\Phi_s(x)), &s\in\mathbb R, \\
\Phi_0(x)=x.
\end{cases}
\end{equation}
We consider the variation of $E_\Omega$ along the flow $\Phi_s$, that is, $\frac{dE_\Omega(D_s)}{ds}\big|_{s=0}$ with \[D_s=\Phi_s(D):=\{\Phi_s(x)\mid x\in D\}.\]
By direct calculation, we have
\[\frac{dE_\Omega(D_s)}{ds}\bigg|_{s=0}=\int_D\nabla(\mathcal{G}I_D(x)+\frac{\Omega}{2}|x|^2)\cdot\mathbf{w}dx.\]
For sufficiently smooth $\mathbf{w}$ defined in $\mathbb D_1$, we can easily check $\frac{dE_\Omega(D_s)}{ds}\big|_{s=0}=0$ by integration by part. In the following lemma, we show that $\mathbf{w}\in H^1(D;\mathbb R^2)$ is sufficient.
\begin{lemma}\label{lem}
Let $\mathbf{w}\in H^1(D;\mathbb R^2)$ be a divergence-free vector field in $D$. Then
\begin{equation}\label{w}\int_D\nabla(\mathcal{G}I_D(x)+\frac{\Omega}{2}|x|^2)\cdot\mathbf{w}(x)dx=0.\end{equation}
\end{lemma}
\begin{proof}
Since $D$ is a rotating patch with angular velocity $\Omega$, we have $\mathcal{G}I_D+\frac{\Omega}{2}|x|^2=\mu$ on $\partial D$ for some $\mu\in \mathbb R$.
Moreover, by elliptic regularity theory we have $\mathcal{G}I_D+\frac{\Omega}{2}|x|^2\in C^1(\overline{D};\mathbb R^2)$. To verify \eqref{w}, we firstly assume $\mathbf{w}\in C^1(\overline{D};\mathbb R^2)$. By integration by parts we have
\begin{equation}\label{den}
\begin{split}
&\int_D\mathbf{w}(x)\cdot\nabla(\mathcal{G}I_D(x)+\frac{\Omega}{2}|x|^2)dx\\
=&\int_D\nabla\cdot(\mathbf{w}(x)(\mathcal{G}I_D(x)+\frac{\Omega}{2}|x|^2))dx-\int_D\nabla\cdot\mathbf{w}(x)(\mathcal{G}I_D(x)+\frac{\Omega}{2}|x|^2)dx\\
=&\int_{\partial D}(\mathcal{G}I_D(x)+\frac{\Omega}{2}|x|^2)\mathbf{w}(x)\cdot\vec{\nu}(x)d\mathcal{H}^1-\int_D\nabla\cdot\mathbf{w}(x)(\mathcal{G}I_D(x)+\frac{\Omega}{2}|x|^2)dx\\
=&\mu\int_{\partial D}\mathbf{w}(x)\cdot\vec{\nu}(x)d\mathcal{H}^1-\int_D\nabla\cdot\mathbf{w}(x)(\mathcal{G}I_D(x)+\frac{\Omega}{2}|x|^2)dx\\
=&\mu\int_{D}\nabla\cdot\mathbf{w}(x)dx-\int_D\nabla\cdot\mathbf{w}(x)(\mathcal{G}I_D(x)+\frac{\Omega}{2}|x|^2)dx,\\
\end{split}
\end{equation}
where $\vec{\nu}$ is the outward unit normal of $\partial D$. Since $C^1(\overline{D};\mathbb R^2)$ is dense in $H^1(D;\mathbb R^2)$, so by density argument \eqref{den} in fact holds for any $\mathbf{w}\in H^1(D;\mathbb R^2)$. Therefore the lemma is proved by the fact that $\mathbf{w}$ is a divergence-free field.
\end{proof}
To continue, we need to choose a suitable $\mathbf w$. Here we follow the choice in \cite{GPSY}, that is, $\mathbf w=x+\nabla p,$ where $p\in H^1_0(D)$ is the solution of the following elliptic problem
\begin{equation}\label{p}
\begin{cases}
-\Delta p=2, & x\in D, \\
x=0, & x\in\partial D.
\end{cases}
\end{equation}
In the following we begin to calculate the quantity $\int_D\nabla(\mathcal{G}I_D(x)+\frac{\Omega}{2}|x|^2)\cdot\mathbf{w}(x)dx$. For simplicity, we denote
\[\mathcal{I}_\Omega:=\int_D\nabla(\mathcal{G}I_D(x)+\frac{\Omega}{2}|x|^2)\cdot(x+\nabla p(x))dx,\]
\[\psi_\Omega(x):=\mathcal{G}I_D+\frac{\Omega}{2}|x|^2.\]
We will show that if $D$ is not a disc centered at the origin and $|\Omega|$ is sufficiently large, then $|\mathcal I{}_\Omega|>0$, which leads to a contradiction.
By direct calculation, we have
\begin{equation}\label{calculation}
\begin{split}
\mathcal{I}_\Omega&=\int_D(x+\nabla p)\cdot\nabla \psi_\Omega dx\\
&=\int_Dx\cdot\nabla_x\int_DG(x,y)dydx+\Omega\int_D|x|^2dx+\int_D\nabla p(x)\cdot\nabla \psi_\Omega(x) dx\\
&=\int_Dx\cdot\nabla_x\int_D-\frac{1}{2\pi}\ln|x-y|-h(x,y)dydx+\Omega\int_D|x|^2dx-\int_Dp(x)\Delta \psi_\Omega(x) dx\\
&=-\frac{1}{2\pi}\int_D\int_D\frac{x\cdot(x-y)}{|x-y|^2}dxdy-\int_Dx\cdot\nabla_x\int_Dh(x,y)dydx+\Omega\int_D|x|^2dx-\int_Dp(x)\Delta \psi_\Omega(x) dx\\
&=-\frac{1}{4\pi}\int_D\int_D\frac{|x-y|^2}{|x-y|^2}dxdy-\int_Dx\cdot\nabla_x\int_Dh(x,y)dydx+\Omega\int_D|x|^2dx-\int_Dp(x)\Delta \psi_\Omega(x) dx\\
&=-\frac{1}{4\pi}|D|^2-\int_Dx\cdot\nabla_x\int_Dh(x,y)dydx+\Omega\int_D|x|^2dx+(1-2\Omega)\int_Dp(x)dx\\
&=(2\Omega-1)\left(\frac{1}{4\pi}|D|^2-\int_Dp(x)dx\right)+\Omega\left(\int_D|x|^2dx-\frac{1}{2\pi}|D|^2\right)-\int_Dx\cdot\nabla_x\int_Dh(x,y)dydx,
\end{split}
\end{equation}
where we used the antisymmetry of the function $\frac{x\cdot(x-y)}{|x-y|^2}$ and the fact $-\Delta\psi_\Omega=1-2\Omega$ in $D$.
Therefore we need to deal the following three terms in \eqref{calculation}
\[\mathcal{J}_\Omega:=(2\Omega-1)\left(\frac{1}{4\pi}|D|^2-\int_Dp(x)dx\right)\]
\[\mathcal{K}_\Omega:=\Omega\left(\int_D|x|^2dx-\frac{1}{2\pi}|D|^2\right)\]
\[\mathcal{L}:=-\int_Dx\cdot\nabla_x\int_Dh(x,y)dydx.\]
To deal with $\mathcal J_\Omega$, we need the following result proved by Talenti in \cite{Talenti}.
\begin{proposition}[\cite{Talenti}, Theorem 1]\label{talenti}
Let $D$ be a planar bounded domain with $C^1$ boundary, and let $p$ be the solution of the following equation
\begin{equation}\label{p2}
\begin{cases}
-\Delta p=2, & x\in D, \\
x=0, & x\in\partial D.
\end{cases}
\end{equation}
Then we have
\[\int_Dp(x)dx\leq\frac{1}{4\pi}|D|^2.\]
Moreover, the equality is achieved if and only if $D$ is a disc.
\end{proposition}
To deal with $\mathcal{K}_\Omega,$ we need the following lemma.
\begin{lemma}\label{K}
Let $D$ be a measurable set in $\mathbb R^2$. Then we have
\[\int_D|x|^2dx\geq\frac{1}{2\pi}|D|^2+\frac{1}{\pi}|D\setminus B|^2,\]
where $B$ is the disc centered at the origin with the same area as $D$. Moreover, the equality is achieved if and only if $D$ is an annulus centered at the origin.
\end{lemma}
\begin{proof}
Notice that
\[\int_D|x|^2dx=\int_B|x|^2dx+\int_{D\setminus B}|x|^2dx-\int_{B\setminus D}|x|^2dx=\frac{1}{2\pi}|D|^2+\int_{D\setminus B}|x|^2dx-\int_{B\setminus D}|x|^2dx.\]
So it suffices to prove
\[\int_{D\setminus B}|x|^2dx-\int_{B\setminus D}|x|^2dx\geq\frac{1}{\pi}|D\setminus B|^2.\]
To this end, we notice that for $|D\setminus B|$ being fixed, $\int_{D\setminus B}|x|^2dx$ attains its minimum value if and only if $D\setminus B$ is an annulus with its inner boundary coinciding with $\partial B$. Similarly, for $|B\setminus D|$ being fixed, $\int_{B\setminus D}|x|^2dx$ attains its maximum value if and only if $B\setminus D$ is an annulus contained in $B$ with its outer boundary coinciding with $\partial B$. Therefore by direct calculation we can easily get
\[\int_{D\setminus B}|x|^2dx\geq \frac{2|B||D\setminus B|+|D\setminus B|^2}{2\pi},\]
\[\int_{B\setminus D}|x|^2dx\leq \frac{2|B||D\setminus B|-|D\setminus B|^2}{2\pi}.\]
Now we can subtracting the above two inequalities to get the desired result.
\end{proof}
By Proposition \ref{talenti} and Lemma \ref{K} we see that if $\Omega\geq{1}/{2}$, then $\mathcal I_\Omega+\mathcal J_\Omega\geq \frac{\Omega}{\pi}|D\setminus B|^2$, and if $\Omega\leq0$ and $|\Omega|$ is sufficiently large, then $\mathcal I_\Omega+\mathcal J_\Omega\leq \frac{\Omega}{\pi}|D\setminus B|^2$. If $|D\setminus B|>0$, in order to get a contradiction, we need to show that $|\mathcal L|$ is controlled by a reasonable constant multiple of $|D\setminus B|^2$. This is exactly what we will do in the following lemma.
\begin{lemma}\label{L}
For any measurable set $D\subset \mathbb D_1,$ define $l=sup_{x\in D}|x|$. Then the following inequality holds
\[\left|\mathcal{L}\right|\leq \frac{2l^2}{\pi(1-l^2)^2}|D\setminus B|^2.\]
\end{lemma}
\begin{proof}
Recall
\[h(x,y)=-\frac{1}{2\pi}\ln\left|\frac{x}{|x|}-{|x|y}\right|.\]
By direct calculation, we have
\begin{equation*}
\begin{split}
\mathcal{L}=-\int_Dx\cdot\nabla_x\int_Dh(x,y)dydx&=\frac{1}{2\pi}\int_Dx\cdot\nabla_x\int_D\ln\left|\frac{x}{|x|}-|x|y\right|dydx\\
&=\frac{1}{4\pi}\int_Dx\cdot\nabla_x\int_D\ln(1-2x\cdot y+|x|^2|y|^2)dydx\\
&=\frac{1}{2\pi}\int_D\int_D\frac{|x|^2|y|^2-x\cdot y}{1-2x\cdot y+|x|^2|y|^2}dxdy
\end{split}
\end{equation*}
So it suffices to prove
\begin{equation}\label{divi}
\left|\frac{1}{2\pi}\int_D\int_D\frac{|x|^2|y|^2-x\cdot y}{1-2x\cdot y+|x|^2|y|^2}dxdy\right|\leq\frac{2l^2}{\pi(1-l^2)^2}|D\setminus B|^2.
\end{equation}
For simplicity we denote \[L(x,y):=\frac{1}{2\pi}\frac{|x|^2|y|^2-x\cdot y}{1-2x\cdot y+|x|^2|y|^2}.\]
We divide the integral in \eqref{divi} into the following nine parts
\begin{equation}\label{nine}
\begin{split}
\int_D\int_DL(x,y)dxdy&=\int_B\int_BL(x,y)dxdy-\int_B\int_{B\setminus D}L(x,y)dxdy+\int_B\int_{D\setminus B}L(x,y)dxdy\\
&-\int_{B\setminus D}\int_BL(x,y)dxdy+\int_{B\setminus D}\int_{B\setminus D}L(x,y)dxdy-\int_{B\setminus D}\int_{D\setminus B}L(x,y)dxdy\\
&+\int_{D\setminus B}\int_BL(x,y)dxdy-\int_{D\setminus B}\int_{B\setminus D}L(x,y)dxdy+\int_{D\setminus B}\int_{D\setminus B}L(x,y)dxdy\\
&=\int_B\int_BL(x,y)dxdy-2\int_B\int_{B\setminus D}L(x,y)dxdy+2\int_B\int_{D\setminus B}L(x,y)dxdy\\
&+\int_{B\setminus D}\int_{B\setminus D}L(x,y)dxdy+\int_{D\setminus B}\int_{D\setminus B}L(x,y)dxdy-2\int_{D\setminus B}\int_{B\setminus D}L(x,y)dxdy,
\end{split}
\end{equation}
where we used the symmetry of the function $L$.
Now we claim
\begin{equation}\label{claim}
\int_B\int_BL(x,y)dxdy=\int_B\int_{B\setminus D}L(x,y)dxdy=\int_B\int_{D\setminus B}L(x,y)dxdy=0.
\end{equation}
To prove \eqref{claim}, we prove a more general result, that is, for any measurable set $E$ there holds
\begin{equation}\label{clai}
\int_B\int_EL(x,y)dxdy=\int_E\int_{B}L(x,y)dxdy=0.
\end{equation}
In fact, by using the polar coordinates we have
\[\int_E\int_{B}L(x,y)dxdy=\int_E\int_0^b\int_0^{2\pi}\frac{1}{2\pi}\frac{\rho^2|y|^2-\rho|y|\cos(\theta)}{1-2\rho|y|\cos(\theta)
+\rho^2|y|^2}d\theta d\rho dy,\]
where $b$ is the radius of $B$. Notice that for fixed $\rho,y$, we have $\rho|y|\in(0,1)$. We can use Cauchy's residue theorem to calculate the above integral to obtain
\[\int_0^{2\pi}\frac{1}{2\pi}\frac{\rho|y|\cos(\theta)-\rho^2|y|^2}{1-2\rho|y|\cos(\theta)
+\rho^2|y|^2}d\theta =0\]
for fixed $y$ and $\rho$, which proves \eqref{clai}.
We continue to estimate $\mathcal{L}$. From the above claim we deduce
\[|\mathcal{L}|=\left|\int_{B\setminus D}\int_{B\setminus D}L(x,y)dxdy+\int_{D\setminus B}\int_{D\setminus B}L(x,y)dxdy-2\int_{D\setminus B}\int_{B\setminus D}L(x,y)dxdy\right|.\]
By simple calculation, we can obtain the following
upper bound and lower bound for $L(x,y)$
\[L(x,y)\geq -\frac{l^2}{2\pi(1-l^2)},\,\,\forall\,x,y\in B\cup D,\]
\[L(x,y)\leq\frac{l^2(1+l^2)}{2\pi(1-l^2)^2},\,\,\forall\,x,y\in B\cup D,\]
where $l=\sup_{x\in D}|x|$.
Thus we obtain
\[|\mathcal{L}|\leq \frac{2l^2}{\pi(1-l^2)^2}|D\setminus B|^2,\]
which completes the proof.
\end{proof}
\begin{proof}[Proof of Theorem \ref{thm}]
Assume that $D$ is not a disc centered at the origin, or equivalently $|D\setminus B|>0$. We will deduce a contradiction if $\Omega\geq\max\{\frac{1}{2},\frac{2 l^2}{(1-l^2)^2}\}$ or $\Omega\leq-\frac{2 l^2}{(1-l^2)^2}$.
First we consider the case $\Omega\geq\max\{\frac{1}{2},\frac{2 l^2}{(1-l^2)^2}\}$. By Proposition \ref{talenti}, Lemma \ref{K} and Lemma \ref{L}, we obtain
\[0=\mathcal I_\Omega=\mathcal J_\Omega+\mathcal K_\Omega+\mathcal L\geq \frac{\Omega}{\pi}|D\setminus B|^2-|\mathcal{L}|\geq \frac{\Omega}{\pi}|D\setminus B|^2- \frac{2l^2}{\pi(1-l^2)^2}|D\setminus B|^2.\]
If $\Omega>\frac{2 l^2}{(1-l^2)^2}$, then we get an obvious contradiction. If $\Omega=\frac{2 l^2}{(1-l^2)^2},$ then $D$ must be an annulus centered at the origin. In fact, if $D$ is not an annulus centered at the origin, then the inequality in Lemma \ref{K} is strict, which leads to the following contradiction
\[0=\mathcal I_\Omega=\mathcal J_\Omega+\mathcal K_\Omega+\mathcal L> \frac{\Omega}{\pi}|D\setminus B|^2-|\mathcal{L}|\geq \frac{\Omega}{\pi}|D\setminus B|^2- \frac{2l^2}{\pi(1-l^2)^2}|D\setminus B|^2= 0.\]
But once $D$ is an annulus centered at the origin, we can repeat the calculation of \eqref{clai} to obtain $\mathcal{L}=0$,
thus
\[0=\mathcal I_\Omega=\mathcal J_\Omega+\mathcal K_\Omega+\mathcal L> \frac{\Omega}{\pi}|D\setminus B|^2-|\mathcal{L}|=\frac{\Omega}{\pi}|D\setminus B|^2>0,\]
which is also a contradiction.
Now we consider the case $\Omega\leq-\frac{2 l^2}{(1-l^2)^2}$. By Proposition \ref{talenti}, Lemma \ref{K} and Lemma \ref{L}, we obtain
\[0=\mathcal I_\Omega=\mathcal J_\Omega+\mathcal K_\Omega+\mathcal L\leq\frac{\Omega}{\pi}|D\setminus B|^2+|\mathcal L|\leq \frac{\Omega}{\pi}|D\setminus B|^2+ \frac{2l^2}{\pi(1-l^2)^2}|D\setminus B|^2.\]
If $\Omega<-\frac{2l^2}{(1-l^2)^2}$, then we get an obvious contradiction. If $\Omega=-\frac{2l^2}{(1-l^2)^2}$, we can still deduce that $D$ is an annulus centered at the origin. If otherwise, by Lemma \ref{K} we have
\[0=\mathcal I_\Omega=\mathcal J_\Omega+\mathcal K_\Omega+\mathcal L<\frac{\Omega}{\pi}|D\setminus B|^2+|\mathcal L|\leq \frac{\Omega}{\pi}|D\setminus B|^2+ \frac{2l^2}{\pi(1-l^2)^2}|D\setminus B|^2=0,\]
which is a contradiction. But once $D$ is an annulus centered at the origin, we immediately know $\mathcal{L}=0,$ therefore
\[0=\mathcal I_\Omega=\mathcal J_\Omega+\mathcal K_\Omega+\mathcal L\leq\frac{\Omega}{\pi}|D\setminus B|^2+\mathcal L= \frac{\Omega}{\pi}|D\setminus B|^2<0,\]
which also leads to a contradiction.
\end{proof}
From the proof, we see that the bound $\Omega\geq\max\{\frac{1}{2},\frac{2 l^2}{(1-l^2)^2}\}$ or $\Omega\leq-\frac{2 l^2}{(1-l^2)^2}$ is not optimal. In fact, one can improve this bound by giving $\mathcal L$ a more accurate estimate. But for a general domain $D$ this is usually very difficult.
\noindent{\bf Acknowledgments:}
We would like to thank Piye Sun for the useful discussion about the estimate of $\mathcal L.$
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