text stringlengths 14 5.77M | meta dict | __index_level_0__ int64 0 9.97k ⌀ |
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Q: Docker, Nginx. PHP-fpm Upload progress bar not work I use docker-compose (php 7.2 FROM phpdockerio/php72-fpm:latest )
services:
webserver:
image: nginx:alpine
nginx.con
user nginx;
pid /var/run/nginx.pid;
events {
worker_connections 1024;
}
http {
include /etc/nginx/mime.types;
default_type application/octet-stream;
log_format main '$remote_addr - $remote_user [$time_local] "$request" '
'$status $body_bytes_sent "$http_referer" '
'"$http_user_agent" "$http_x_forwarded_for"';
access_log /dev/stdout main;
#sendfile on;
#tcp_nopush on;
keepalive_timeout 65;
gzip on;
server {
listen 80 default;
client_max_body_size 208M;
access_log /var/log/nginx/application.access.log;
root /application/public;
rewrite ^/index\.php/?(.*)$ /$1 permanent;
try_files $uri @rewriteapp;
location @rewriteapp {
rewrite ^(.*)$ /index.php/$1 last;
}
# Deny all . files
location ~ /\. {
deny all;
}
location ~ ^/(index)\.php(/|$) {
fastcgi_pass php-fpm:9000;
fastcgi_split_path_info ^(.+\.php)(/.*)$;
fastcgi_index app_dev.php;
send_timeout 1800;
fastcgi_read_timeout 1800;
fastcgi_param SCRIPT_FILENAME $document_root$fastcgi_script_name;
fastcgi_param PHP_VALUE "error_log=/var/log/nginx/application_php_errors.log";
fastcgi_buffers 16 16k;
fastcgi_buffer_size 32k;
include fastcgi_params;
}
# Statics
location /(bundles|media) {
access_log off;
expires 30d;
try_files $uri @rewriteapp;
}}
}
i create test controller to update progressbar
/**
* @Route("/progressTest", name="progressTest")
* @param Request $request
* @return \Symfony\Component\HttpFoundation\Response
*/
public function progressAction(){
ob_start();
header('Content-Type: text/event-stream');
header('Cache-Control: no-cache');
$total = 10;
for($i=0;$i<$total;$i++)
{
$percent = intval($i/$total * 100)."%";
sleep(1); // Here call your time taking function like sending bulk sms etc.
echo '<script>
parent.document.getElementById("progressbar").innerHTML="<div style=\"width:'.$percent.';background:linear-gradient(to bottom, rgba(125,126,125,1) 0%,rgba(14,14,14,1) 100%); ;height:35px;\"> </div>";
parent.document.getElementById("information").innerHTML="<div style=\"text-align:center; font-weight:bold\">'.$percent.' is processed.</div>";
</script>';
ob_flush();
flush();
}
echo '<script>parent.document.getElementById("information").innerHTML="<div style=\"text-align:center; font-weight:bold\">Process completed</div>"</script>';
return new Response('OK '.$i);
}
run it in template
<div class="col-md-12">
<div id="progressbar" style="border:1px solid #ccc; border-radius: 5px; "></div>
<div id="information" style="border:1px solid #ccc; border-radius: 5px; "></div>
</div>
<iframe name="loadarea" src="{{ path("progressTest") }}" id="loadarea" style="display:none2;"></iframe><br />
but have pending to end of loop, then get
<script>
parent.document.getElementById("progressbar").innerHTML="<div style=\"width:0%;background:linear-gradient(to bottom, rgba(125,126,125,1) 0%,rgba(14,14,14,1) 100%); ;height:35px;\"> </div>";
parent.document.getElementById("information").innerHTML="<div style=\"text-align:center; font-weight:bold\">0% is processed.</div>";
</script><script>
parent.document.getElementById("progressbar").innerHTML="<div style=\"width:10%;background:linear-gradient(to bottom, rgba(125,126,125,1) 0%,rgba(14,14,14,1) 100%); ;height:35px;\"> </div>";
parent.document.getElementById("information").innerHTML="<div style=\"text-align:center; font-weight:bold\">10% is processed.</div>";
</script><script>
parent.document.getElementById("progressbar").innerHTML="<div style=\"width:20%;background:linear-gradient(to bottom, rgba(125,126,125,1) 0%,rgba(14,14,14,1) 100%); ;height:35px;\"> </div>";
parent.document.getElementById("information").innerHTML="<div style=\"text-align:center; font-weight:bold\">20% is processed.</div>";
</script><script>
parent.document.getElementById("progressbar").innerHTML="<div style=\"width:30%;background:linear-gradient(to bottom, rgba(125,126,125,1) 0%,rgba(14,14,14,1) 100%); ;height:35px;\"> </div>";
parent.document.getElementById("information").innerHTML="<div style=\"text-align:center; font-weight:bold\">30% is processed.</div>";
</script><script>
parent.document.getElementById("progressbar").innerHTML="<div style=\"width:40%;background:linear-gradient(to bottom, rgba(125,126,125,1) 0%,rgba(14,14,14,1) 100%); ;height:35px;\"> </div>";
parent.document.getElementById("information").innerHTML="<div style=\"text-align:center; font-weight:bold\">40% is processed.</div>";
</script><script>
parent.document.getElementById("progressbar").innerHTML="<div style=\"width:50%;background:linear-gradient(to bottom, rgba(125,126,125,1) 0%,rgba(14,14,14,1) 100%); ;height:35px;\"> </div>";
parent.document.getElementById("information").innerHTML="<div style=\"text-align:center; font-weight:bold\">50% is processed.</div>";
</script><script>
parent.document.getElementById("progressbar").innerHTML="<div style=\"width:60%;background:linear-gradient(to bottom, rgba(125,126,125,1) 0%,rgba(14,14,14,1) 100%); ;height:35px;\"> </div>";
parent.document.getElementById("information").innerHTML="<div style=\"text-align:center; font-weight:bold\">60% is processed.</div>";
</script><script>
parent.document.getElementById("progressbar").innerHTML="<div style=\"width:70%;background:linear-gradient(to bottom, rgba(125,126,125,1) 0%,rgba(14,14,14,1) 100%); ;height:35px;\"> </div>";
parent.document.getElementById("information").innerHTML="<div style=\"text-align:center; font-weight:bold\">70% is processed.</div>";
</script><script>
parent.document.getElementById("progressbar").innerHTML="<div style=\"width:80%;background:linear-gradient(to bottom, rgba(125,126,125,1) 0%,rgba(14,14,14,1) 100%); ;height:35px;\"> </div>";
parent.document.getElementById("information").innerHTML="<div style=\"text-align:center; font-weight:bold\">80% is processed.</div>";
</script><script>
parent.document.getElementById("progressbar").innerHTML="<div style=\"width:90%;background:linear-gradient(to bottom, rgba(125,126,125,1) 0%,rgba(14,14,14,1) 100%); ;height:35px;\"> </div>";
parent.document.getElementById("information").innerHTML="<div style=\"text-align:center; font-weight:bold\">90% is processed.</div>";
</script><script>parent.document.getElementById("information").innerHTML="<div style=\"text-align:center; font-weight:bold\">Process completed</div>"</script>OK 10
How i can update progressbar ?
A: You are most probably missing a header X-Accel-Buffering, as described in Streaming a Response section of official documentation. Basically, your FPM does not buffer anything, but NGINX does, so at the end you will get everything in a bulk.
Try setting that header to no and see it it helps.
On a side note, returning a <script> tag like this seems like running with pair of scissors. I would suggest you refactor it completely and let the client side do that graphical manipulation solely on percentage.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 7,090 |
'use strict';
var _uniqs = require('uniqs');
var _uniqs2 = _interopRequireDefault(_uniqs);
var _postcss = require('postcss');
var _postcss2 = _interopRequireDefault(_postcss);
var _flatten = require('flatten');
var _flatten2 = _interopRequireDefault(_flatten);
function _interopRequireDefault(obj) { return obj && obj.__esModule ? obj : { default: obj }; }
var comma = _postcss.list.comma;
var space = _postcss.list.space;
function filterAtRule(css, declRegex, atruleRegex) {
var atRules = [];
var values = [];
css.walk(function (node) {
if (node.type === 'decl' && declRegex.test(node.prop)) {
return comma(node.value).forEach(function (val) {
return values.push(space(val));
});
}
if (node.type === 'atrule' && atruleRegex.test(node.name)) {
atRules.push(node);
}
});
values = (0, _uniqs2.default)((0, _flatten2.default)(values));
atRules.forEach(function (node) {
var hasAtRule = values.some(function (value) {
return value === node.params;
});
if (!hasAtRule) {
node.remove();
}
});
}
function hasFont(fontFamily, cache) {
return comma(fontFamily).some(function (font) {
return cache.some(function (c) {
return ~c.indexOf(font);
});
});
}
function filterNamespace(css) {
var atRules = [];
var rules = [];
css.walk(function (node) {
var type = node.type;
var selector = node.selector;
var name = node.name;
if (type === 'rule' && /\|/.test(selector)) {
return rules.push(selector.split('|')[0]);
}
if (type === 'atrule' && name === 'namespace') {
atRules.push(node);
}
});
rules = (0, _uniqs2.default)((0, _flatten2.default)(rules));
atRules.forEach(function (atRule) {
var _atRule$params$split$ = atRule.params.split(' ').filter(function (e) {
return e !== '';
});
var param = _atRule$params$split$[0];
var len = _atRule$params$split$.length;
if (len === 1) {
return;
}
var hasRule = rules.some(function (rule) {
return rule === param || rule === '*';
});
if (!hasRule) {
atRule.remove();
}
});
}
// fonts have slightly different logic
function filterFont(css) {
var atRules = [];
var values = [];
css.walk(function (node) {
if (node.type === 'decl' && node.parent.type === 'rule' && /font(|-family)/.test(node.prop)) {
return values.push(comma(node.value));
}
if (node.type === 'atrule' && node.name === 'font-face' && node.nodes) {
atRules.push(node);
}
});
values = (0, _uniqs2.default)((0, _flatten2.default)(values));
atRules.forEach(function (rule) {
var families = rule.nodes.filter(function (node) {
return node.prop === 'font-family';
});
// Discard the @font-face if it has no font-family
if (!families.length) {
return rule.remove();
}
families.forEach(function (family) {
if (!hasFont(family.value, values)) {
rule.remove();
}
});
});
}
module.exports = _postcss2.default.plugin('postcss-discard-unused', function (opts) {
opts = opts || {};
return function (css) {
if (opts.fontFace !== false) {
filterFont(css);
}
if (opts.counterStyle !== false) {
filterAtRule(css, /list-style|system/, /counter-style/);
}
if (opts.keyframes !== false) {
filterAtRule(css, /animation/, /keyframes/);
}
if (opts.namespace !== false) {
filterNamespace(css);
}
};
}); | {
"redpajama_set_name": "RedPajamaGithub"
} | 3,045 |
{"url":"https:\/\/www.ias.ac.in\/listing\/bibliography\/pmsc\/R._Balasubramanian","text":"\u2022 R Balasubramanian\n\nArticles written in Proceedings \u2013 Mathematical Sciences\n\n\u2022 Mean-value of the Riemann zeta-function on the critical line\n\nThis is an expository article. It is a collection of some important results on the meanvalue of$$\\left| {\\zeta (\\frac{1}{2} + it)} \\right|.$$\n\n\u2022 Effect of aspect ratio on the meridional circulation of a rotating homogeneous fluid\n\nThe effect of aspect ratio on the meridional circulation of a homogeneous fluid is analyzed. Aspect ratio is allowed to range between zero and unity. Relationships between possible horizontal and vertical length scales are obtained by length scale analysis as well as by solving an idealized problem. It is found that whenE1\/2 \u226a Z \u226a E1\/2\/\u03b4, whereE is the Ekman number, the stream lines are closely packed near the sidewall within a thickness ofO(E1\/2). The effect of stratification is unimportant within this depth range. In the depth rangeE1\/2\/\u03b4 \u226a Z \u226a 1\/ the vertical boundary layer in which the streamlines are packed is ofO(EZ\u03b4)1\/3. WhenZ \u226b 1\/E\u03b4 it is shown that the circulation decays algebraically with depth as 1\/Z.\n\n\u2022 On the frequency of Titchmarsh\u2019s phenomenon for \u03b6(s)-VIII\n\nFor suitable functionsH = H(T) the maximum of\u00a6(\u03b6(\u03c3 + it))z\u00a6 taken overT\u2264t\u2264T + H is studied. For fixed \u03c3(1\/2\u2264\u03c3\u2264l) and fixed complex constantsz \u201cexpected lower bounds\u201d for the maximum are established.\n\n\u2022 Proof of some conjectures on the mean-value of Titchmarsh series \u2014 III\n\nWith some applications in view, the following problem is solved in some special case which is not too special. LetF(s) =\u03a3n=1an\u03bbn\u2212s be a generalized Dirichlet series with 1 =\u03bb1 <\u03bb2 < \u2026,\u03bbnDn, and\u03bbn+1 -\u03bbnD\u2212 1\u03bbn+1\u2212 a where \u03b1>0 andD(\u2265 1) are constants. Then subject to analytic continuation and some growth conditions, a lower bound is obtained for$$(1\/H)\\int {_O^H |} F(it)|^2 dt$$. These results will be applied in other papers to appear later.\n\n\u2022 On the zeros of a class of generalised Dirichlet series-XIV\n\nWe prove a general theorem on the zeros of a class of generalised Dirichlet series. We quote the following results as samples.\n\nTheorem A.Let 0<\u03b8<1\/2and let {an}be a sequence of complex numbers satisfying the inequality$$\\left| {\\sum\\limits_{m = 1}^N {a_m - N} } \\right| \\leqslant \\left( {\\frac{1}{2} - \\theta } \\right)^{ - 1}$$for N = 1,2,3,\u2026,also for n = 1,2,3,\u2026let \u03b1nbe real and \u00a6\u03b1n\u00a6 \u2264 C(\u03b8)where C(\u03b8) > 0is a certain (small)constant depending only on \u03b8. Then the number of zeros of the function$$\\sum\\limits_{n = 1}^N {a_n \\left( {n + \\alpha _n } \\right)^{ - s} } = \\zeta \\left( s \\right) + \\sum\\limits_{n = 1}^\\infty {\\left( {a_n \\left( {n + \\alpha _n } \\right)^{ - s} - n^{ - s} } \\right)}$$in the rectangle (1\/2-\u03b4\u2a7d\u03c3\u2a7d1\/2+\u03b4,Tt\u2a7d2T) (where 0<\u03b4<1\/2)isC(\u03b8,\u03b4)T logT where C(\u03b8,\u03b4)is a positive constant independent of T provided TT0(\u03b8,\u03b4)a large positive constant.\n\nTheorem B.In the above theorem we can relax the condition on an to$$\\left| {\\sum\\limits_{m = 1}^N {a_m - N} } \\right| \\leqslant \\left( {\\frac{1}{2} - \\theta } \\right)^{ - 1} N^0$$ and \u00a6aN\u00a6 \u2264 (1\/2-\u03b8)-1.Then the lower bound for the number of zeros in (\u03c3\u2a7e1\/3\u2212\u03b4,Tt\u2a7d2T)is > C(\u03b8,\u03b4) Tlog T(log logT)-1.The upper bound for the number of zeros in \u03c3\u2a7e1\/3+\u03b4,Tt\u2a7d2T) isO(T)provided$$\\sum\\limits_{n \\leqslant x} {a_n } = x + O_s \\left( {x^2 } \\right)$$for every \u03b5 > 0.\n\n\u2022 On Ramanujan asymptotic expansions and inequalities for hypergeometric functions\n\nIn this paper we first discuss refinement of the Ramunujan asymptotic expansion for the classical hypergeometric functionsF(a,b;c;x), c \u2264a + b, near the singularityx = 1. Further, we obtain monotonous properties of the quotient of two hypergeometric functions and inequalities for certain combinations of them. Finally, we also solve an open problem of finding conditions ona, b > 0 such that 2F(\u2212a,b;a +b;r2) < (2\u2212r2)F(a,b;a +b;r2) holds for all r\u2208(0,1).\n\n\u2022 Some Zero-Sum Constants with Weights\n\nFor an abelian group \ud835\udc3a, the Davenport constant $D(G)$ is defined to be the smallest natural number \ud835\udc58 such that any sequence of \ud835\udc58 elements in \ud835\udc3a has a non-empty subsequence whose sum is zero (the identity element). Motivated by some recent developments around the notion of Davenport constant with weights, we study them in some basic cases. We also define a new combinatorial invariant related to $(\\mathbb{Z}\/n\\mathbb{Z})^d$, more in the spirit of some constants considered by Harborth and others and obtain its exact value in the case of $(\\mathbb{Z}\/n\\mathbb{Z})^2$ where \ud835\udc5b is an odd integer.\n\n\u2022 Density of Primes in \ud835\udc59-th Power Residues\n\nGiven a prime number \ud835\udc59, a finite set of integers $S=\\{a_1,\\ldots,a_m\\}$ and \ud835\udc5a many \ud835\udc59-th roots of unity $\\zeta^{r_i}_l,i=1,\\ldots,m$ we study the distribution of primes \ud835\udc5d in $\\mathbb{Q}(\\zeta_l)$ such that the \ud835\udc59-th residue symbol of $a_i$ with respect to \ud835\udc5d is $\\zeta^{r_i}_l$, for all \ud835\udc56. We find out that this is related to the degree of the extension $\\mathbb{Q}\\left(a^{\\frac{1}{l}}_1,\\ldots,a^{\\frac{1}{l}}_m\\right)\/\\mathbb{Q}$. We give an algorithm to compute this degree. Also we relate this degree to rank of a matrix obtained from $S=\\{a_1,\\ldots,a_m\\}$. This latter argument enables one to describe the degree $\\mathbb{Q}\\left(a^{\\frac{1}{l}}_1,\\ldots,a^{\\frac{1}{l}}_m\\right)\/\\mathbb{Q}$ in much simpler terms.\n\n\u2022 # Proceedings \u2013 Mathematical Sciences\n\nVolume 130, 2020\nAll articles\nContinuous Article Publishing mode\n\n\u2022 # Editorial Note on Continuous Article Publication\n\nPosted on July 25, 2019","date":"2020-01-29 20:19:00","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\": 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\": 0.8491998314857483, \"perplexity\": 1505.4942608957413}, \"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-2020-05\/segments\/1579251802249.87\/warc\/CC-MAIN-20200129194333-20200129223333-00556.warc.gz\"}"} | null | null |
Homeland Security's controversial facial recognition system to be tested at Texas border this summer
The Department of Homeland Security is testing facial recognition cameras at the Anzalduas Border Crossing in southern Texas, according to the Verge
The cameras will take photos of people arriving and departing the United States
Government officials will then match the photos with visas and passports
Part of DHS' biometric project, which also installed facial recognition at airports
By Annie Palmer For Dailymail.com
Published: 14:37 EST, 5 June 2018 | Updated: 15:43 EST, 5 June 2018
The Department of Homeland Security (DHS) is trialing a new facial recognition technology at US borders aimed at keeping track of people as the enter and exit the country.
Called the Vehicle Face System, the project is being spearheaded by Customs and Border Protection at the Anzalduas Border Crossing, located at the southern tip of Texas, in August, according to the Verge.
Sophisticated cameras will take photos of people arriving and departing the US and match them with government documents like visas and passports.
Scroll down for video
The Department of Homeland Security (DHS) is trialing a new facial recognition technology at US borders aimed at keeping track of people as the enter and exit the country
The cameras are expected to remain in operation at the crossing for a full year.
A customs spokesperson told the Verge that the purpose of the project will be to 'evaluate capturing facial biometrics of travelers entering and departing the US and compare those images to photos on file in government holdings'.
In the past, facial recognition technology struggled to correctly identify individuals behind a windshield due to glares and other obstructions.
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But the cameras at the crossing use technology that works in multiple focal lengths, which could allow the system to discern between people and reflections.
They're also fitted with ambient light sensors, range finders and remote speedometers.
'Specific technologies to be used may include digital single-lens reflex (DSLR) cameras in the visible and infrared, range finders, ambient light sensors and speedometers,' a document explaining the project states.
Called the Vehicle Face System, the project is being spearheaded by Customs and Border Protection at the Anzalduas Border Crossing, located at the southern tip of Texas, in August
The US Department of Homeland Security is testing facial recognition cameras at the Anzalduas Border Crossing, located at the southern tip of Texas.
It's being developed at Oak Ridge National Laboratory (ORNL) in Tennessee in partnership with Homeland Security.
The cameras will take photos of people arriving and departing the US and then officials will match the photos with visas and passports.
Few details about the cameras have been released, but they reportedly draw on light sensors to reduce the glass barrier.
This is possible because the cameras work in multiple focal lengths, which could allows it to discern between people and reflections in a car's windshield.
Hector Santos-Villalobos, a scientist who leads the work in ORNL's Electrical and Electronics Systems Research division, helped develop the plenoptic camera
Scientists at ORNL developed a 'plenoptic camera' that can capture photos of someone in motion, thanks to sophisticated lenses that show several elements in focus at once, unlike traditional cameras that typically show one object in focus.
The camera is also fitted with a ray-tracing algorithm that can capture the iris of subjects, an extremely accurate biometric identifier, even under challenging conditions.
Officials hope that the facial recognition system can take photos of people inside cars, even if they're wearing hats or a driver wasn't looking at the camera.
Cameras are also fitted with ambient light sensors, range finders and remote speedometers.
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'Visible images will be collected for different optics (e.g. focal lengths) and filters (e.g. attenuation and polarizers)'.
News of the trial comes after DHS announced in 2017 that it was looking for facial recognition technology to be used at the border.
Specifically, they hoped to devise a system that could take photos of people inside cars, even if they're wearing hats or a driver wasn't looking at the camera.
At the time, Customs and Border Patrol (CBP) said the system would make it so that fewer cars would have to stop at border crossings, reducing 'significant traffic delays'.
In the past, facial recognition technology struggled to correctly identify individuals behind a windshield due to glares and other obstructions. However, these cameras works in multiple focal lengths and could be able to discern between a person and their reflection
However, the photos would also be uesd to 'validate the identities of the occupants and document their entry or exit from the United States'.
The work is part of a wider biometric data project, which involved installing facial recognition systems at various airports across the country, including New York, Los Angeles and six other cities.
It's also not the only novel technology being tested at the border.
Last October, Border Patrol said that it's considering implementing a surveillance balloon that would quickly spot illegal activity, as part of an effort to see if more eyes in the sky translate to fewer illegal crossings over the border.
Agents in Texas recently finished a 30-day trial of the camera-toting, helium-filled balloon made by Drone Aviation Holding Corp.
The work is part of a wider biometric data project, which installed facial recognition systems at various airports across the country, including New York, Los Angeles and six other cities
Naturally, privacy advocates worry about how facial recognition technology at the border will be implemented and what, if any, impacts it will have on privacy.
'This is a way for the federal government to track people -- monitoring who goes where and and what they do there,' ACLU attorney Mitra Ebadolahi told the Verge.
'In a free society, we should all be able to safely live our lives without being watched, and targeted by the federal government'.
New Homeland Security system will bring facial recognition to land borders this summer - The Verge
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Depression, stress and loneliness weaken the body's immune system and could reduce the effectiveness of Covid-19 vaccines, study warns
Hunter-gatherer humans mirror the reproductive behaviours and social structures of mammals and birds living in the same areas, study finds
NASA Insight's 'Mole' bites the dust: Mars digger is declared dead after failing to burrow deep enough into the Red Planet to take its temperature after two years
Taking aspirin three times a week boosts chances of beating breast and bladder cancer by up to a third, study finds
Is SEAGRASS the key to clearing the oceans of plastic? 'Neptune balls' on the ocean floor sieve over 867 MILLION pieces of rubbish from the water every year
Faces of 'Siberian Tutankhamun' and his sacrificed concubine are reconstructed using their 2,600-year-old rotting skulls uncovered from a 262-foot wide burial mound
Covid-19 pandemic has reduced life expectancy in the US and UK by more than a YEAR - with men and ethnic minorities hit hardest
Spectacular fossil of an eight-foot SHARK that roamed the seas 150 million years ago and was one of the largest of its time is unearthed in Germany
Monkeys at a Bali temple steal PHONES from tourists and demand food before giving them back in 'unprecedented example of animal economics', scientists discover
Parents' sleep doesn't return to pre-pregnancy levels for up to six YEARS after the birth of their first baby - and Dad gets more than Mum!
iPad Pro review: Apple takes the tablet to new heights (at a price) Apple's new iPad is blazingly fast, gorgeous to look at, and quite simply the best tablet out there - and for a lot of people, probably the best computer out there.
The small smart display with big potential: Google Home Hub review Google is late to the game with its Home Hub, but the low price and AI features make it a great choice for controlling your home, showing pictures and even helping run your life.
'Good enough for most people': iPhone XR review On one hand, the XR lacks the high-resolution screen and dual-lens camera on the XS. but it is $250 cheaper and still get most of the other cutting-edge features found on the more expensive model.
The Pixel 3 outsmarts the iPhone (IF you trust Google with all your information) AI seems to permeate every part of its software, from the ability to answer calls for you to being able to almost perfectly predict your morning commute.
Bigger and better in every way: Apple's XS really does take the iPhone to the Max Apple's new iPhone XS and XS Max go on sale on Friday - and the biggest handset Apple has ever made is also its best (and possibly unsurprisingly, its most expensive).
The $250 beauty device that works like 'Photoshop for your face' Israeli beauty-tech firm Pollogen has launched its Geneo Personal device, which stimulates oxygen from beneath the skin's surface to give you a clearer, fresher face within minutes.
iOS 12 review: The update that really will improve your iPhone Rather than cram in a plethora of new features, Apple's latest update is about boosting stability, with improvements in everything from FaceID and battery life.
Naim Atom: The hifi that will change the way you listen to music It's eye-wateringly expensive at $2,999, but Naim's Uniti Atom is a revelation, an integrated amplifier than makes it easy to stream music at a quality you've probably never heard before.
The $1,000 wireless speaker that really IS worth the price: Naim Mu-so Qb review Naim's incredible Mu-So Qb takes you back to the good old days - where the music captivates and enthralls, rather that simply being something in the background.
The hi-tech $2,000 spin bike that really could change your life Peloton's hi-tech bike lets you stream live and on demand rides to your home - and it's one of the best examples of fitness technology out there - at a price.
The best all in one wireless speaker you'll ever hear: Naim Mu-so review It might not be a name familiar to the US market, but Naim is a legendary British brand hoping to make a splash with the American launch of its $1499 Mu:So speaker. | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 4,884 |
Aderlin Rodríguez (born November 18, 1991), nicknamed "A-Rod", is a Dominican Republic professional baseball corner infielder who is currently a free agent. He previously played for the New York Mets, Seattle Mariners, Baltimore Orioles and Detroit Tigers organizations, and for the Orix Buffaloes of the Nippon Professional Baseball (NPB).
Career
New York Mets
On July 2, 2008, Rodríguez signed a minor league deal with the New York Mets organization that included a $600,000 dollar signing bonus. He made his professional debut with the GCL Mets in 2009. He split the next year with the rookie ball Kingsport Mets and the Single-A Savannah Sand Gnats, slashing a combined .300/.350/.532 with 14 home runs and 59 RBI. He remained in Single-A for the 2011 season, hitting .221/.265/.372 with 17 home runs and 78 RBI in 131 games for Savannah. The next year, Rodríguez split the season between Savannah and the High-A St. Lucie Mets, batting .263/.321/.476 with 24 home runs and 83 RBI in 125 contests. He remained in St. Lucie in 2013, slashing .260/.295/.427 with 9 home runs and 41 RBI in 264 plate appearances. In 2014, Rodríguez slashed .242/.284/.366 in 89 games for St. Lucie. He began the 2015 season in Double-A with the Binghamton Mets, but was released on July 15, 2015 after batting .253/.288/.461 in 63 games.
Seattle Mariners
On July 21, 2015, Rodríguez signed a minor league deal with the Seattle Mariners and was assigned to the Jackson Generals. He finished the season in Jackson batting .206/.262/.335 with 3 home runs and 16 RBI. On November 6, 2015, Rodríguez elected free agency.
Baltimore Orioles
On January 18, 2016, Rodríguez signed a minor league deal with the Baltimore Orioles and received an invitation to Spring Training. He did not make the club out of spring and was assigned to the High-A Frederick Keys. He was named a Carolina League all-star in 2016, and batted .304/.359/.532 with 26 home runs and 93 RBI on the season. In 2017, Rodríguez played for the Double-A Bowie Baysox, hitting .279/.341/.471 with 22 home runs and 76 RBI in 125 games for the club. On November 6, 2017, Rodríguez elected free agency and re-signed with the Orioles on a new minor league contract on December 22. He spent the 2018 season with Bowie, hitting .286/.335/478 in 128 contests. On November 2, 2018, Rodríguez elected free agency.
San Diego Padres
On December 21, 2018, Rodríguez signed a minor league contract with the San Diego Padres and received an invitation to Spring Training. Rodríguez did not make the major league club and was reassigned to the El Paso Chihuahuas, with whom he would spend the entire season, slashing .321/.363/.634 with 19 home runs and 64 RBI. On November 4, 2019, he elected free agency.
Orix Buffaloes
On December 23, 2019, Rodríguez signed with the Orix Buffaloes of the Nippon Professional Baseball (NPB). On June 19, 2020, Rodríguez made his NPB debut. Rodríguez batted .218/.280/.363 with 6 home runs and 25 RBI in 59 games for the Buffaloes in 2020. On December 2, 2020, he became a free agent.
Detroit Tigers
On January 16, 2021, Rodríguez signed a minor league contract with the Detroit Tigers. Rodríguez was named Triple-A East Region MVP for the 2021 season, hitting .290 with 29 home runs and 94 RBI in 116 games. On November 9, 2021, Rodríguez declined a minor league assignment and became a free agent.
San Diego Padres (second stint)
On March 13, 2022, Rodríguez signed a minor league contract with the San Diego Padres. He was released on June 15, 2022.
Hanshin Tigers
On July 11, 2022, Rodriguez signed with the Hanshin Tigers of Nippon Professional Baseball. He became a free agent following the 2022 season.
References
External links
1991 births
Living people
Baseball third basemen
Binghamton Mets players
Bowie Baysox players
Dominican Republic expatriate baseball players in Japan
Dominican Republic expatriate baseball players in the United States
El Paso Chihuahuas players
Frederick Keys players
Gigantes del Cibao players
Gulf Coast Mets players
Hanshin Tigers players
Jackson Generals (Southern League) players
Leones del Escogido players
Kingsport Mets players
Nippon Professional Baseball first basemen
Orix Buffaloes players
Savannah Sand Gnats players
Scottsdale Scorpions players
Sportspeople from Santo Domingo
St. Lucie Mets players
Toledo Mud Hens players | {
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{"url":"http:\/\/math.stackexchange.com\/questions\/65896\/can-i-reverse-any-hash-algorithms-to-find-a-set-of-the-possible-orginals","text":"# Can I reverse any hash algorithms to find a set of the possible orginals?\n\nIf I map 1024 bits onto a 16 bit hash (just random numbers for conversation sake), I will have an average of 64 collisions per hash (assuming a good algorithm).\n\nI wonder if anyone knows any hash algorithms around today in which I could take a hash and extrapolate the ~64 1024 bit original values?\n\nI suppose that's not easy, but I don't know for sure.\n\nMy thought process is to see if I could tack an index number onto the end of the hash to enable me to extrapolate the original (perhaps at a significant cpu cost) later.\n\n-\nAs Henning points out, this is significantly more difficult than your question makes it out to be. And I have to say.. this is a very good thing! If it wasn't, there would be very little point of cryptographic hashing! Now granted, cryptographic hashing is going to have much more than 16 bits, but even so, if the math in this post were correct, it would be devastating for the security community. Of course, if it were correct, and they'd gone the last 50 years without realizing it, I'd feel a little safer :-) \u2013\u00a0 corsiKa Sep 19 '11 at 21:56\n\nIf your hash is only 16 bits, then on average there will be $2^{1008}$ different possible preimages for any hash value. It may be that you're only using 64 of those in practice, but you can't identify those from the hash alone, without using (very strong) additional information about the distribution of the actually occurring values.\nTheoretically, there is a set of values that get hashed to a particular hash value, so there is such a function taking hash values back to the unhashed $1024$ bit numbers. However, if the hash is a good one, it should be as hard as generating the hash values for all the $1024$ bit originals and recording the mapping. That is, it is possible, but should be impractical.\n@Henning: granted, $16$ bits is not a strong hash, but putting that aside, if it is a good $16$ bit hash, generating the list of possible sources should be as hard as generating all $1024$ bit patterns and correlating all the $16$ bit hashes with their source. \u2013\u00a0 robjohn Sep 20 '11 at 0:24","date":"2014-12-22 20:53:25","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\": 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\": 0.5116010308265686, \"perplexity\": 318.9360747989542}, \"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-2014-52\/segments\/1418802776563.13\/warc\/CC-MAIN-20141217075256-00122-ip-10-231-17-201.ec2.internal.warc.gz\"}"} | null | null |
FreeBookNotes found 2 sites with book summaries or analysis of I Live for This! Baseball's Last True Believer. If there is a I Live for This! Baseball's Last True Believer SparkNotes, Shmoop guide, or Cliff Notes, you can find a link to each study guide below.
Among the summaries and analysis available for I Live for This! Baseball's Last True Believer, there is 2 Book Reviews.
Depending on the study guide provider (SparkNotes, Shmoop, etc.), the resources below will generally offer I Live for This! Baseball's Last True Believer chapter summaries, quotes, and analysis of themes, characters, and symbols.
Sites like SparkNotes with a I Live for This! Baseball's Last True Believer study guide or cliff notes. Also includes sites with a short overview, synopsis, book report, or summary of Bill Plaschke's I Live for This! Baseball's Last True Believer.
Sites with a book review or quick commentary on I Live for This! Baseball's Last True Believer by Bill Plaschke. | {
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Sometimes I go weeks without hearing from anyone about business issues. Other times like the past several weeks I can't go five minutes without someone calling or e-mailing me with questions. This month has been unusually heavy and the predominant scenario has been like this.
Hello Mr. Rickman, my name is Jamie. I'm from bent grass, Nebraska and I was wondering if you could help me with a problem. I've been freelancing now for about 1 & 1/2 years and I think I'm a pretty good photographer but I can't seem to get work from any of the bigger magazines. What do you think I'm doing wrong?
Well Hello Jamie. You don't really have to call me Mr. Rickman. It makes me feel older than I already am. You say you're from Bent Grass. I used to go through there all the time when I used to work at the Des Moines Register. I'll bet you're starting to get a real good dose of that Nebraska humidity right about now huh.
Anyway, you say you want to get work from the major magazines? Well let's see. Have you put together a portfolio?
Oh yes sir Mr. Rickman I've got a bunch of portfolios on CD's and I've been sending them out to all the photo editors I can get the names of. It's taken me a lot of time to put all this together but I haven't heard from a single one of the people I've sent them out to.
Please Jamie, just call me Rick. It's OK. Well, not one response huh. Did you send a very interesting cover letter with the CD that you sent out?
I did send a letter. Do you want to hear it?
Sure Jamie, it will give me an idea of how you approached this portfolio mailing.
Dear Mary Ann, my name is Jamie Nelson and I live in Bent Grass Nebraska. I'm very interested in getting assignments from your magazine and I'd really like it if you could please look at my portfolio. I like the pictures and I think you will too. Your magazine runs such good pictures and I'd really like to have mine in your magazine as well. I know if I can get my pictures in your magazine my career will just take off. I hope to hear from you soon. Sincerely, Jamie Nelson.
Jamie, you're gonna have to call me back because I've got to pick up my daughter from school in the next 20 minutes and this conversation is gonna take longer than that. One thing I will tell you before I go. You need to go out and buy a good pair of travelin' shoes.
Jamie Nelson, (not his real name) is a classic example of what many photographers do to attempt to drum up business. Mistakenly believing that it's enough to send a CD of images off to a name at a magazine in New York and hoping that that act will generate a new client is like believing in the tooth fairy.
If you're like me you hate telemarketers. Break that hatred down and you'll see what this has to do with promoting new business. Telemarketers don't know you and you don't know them. They call you up at the most inconvenient times and want you to listen to their spiel when you have a million other things to do with your time.
When you send a CD of images to someone you've never met or established some kind of rapport with you are like a telemarketer. You're wanting someone who doesn't know you to drop what they are doing, take a few minutes of their already overloaded day and go through your pictures. How far down on the priority totem pole do you think that falls? You may as well take those CD's and hang them on the apricot tree to help keep the finches off the fruit.
So, Billy Bob, what's the answer? Well Jethro, it's a tried and true solution that isn't guaranteed but has a whole lot better chance than the blind CD approach.
First, get your list of the people you'd like to see together and get the phone numbers for those people shinnied right up next to the name. Start making calls to each one of them and introduce yourself. In the course of the conversation mention to them that you'd like to come to where ever it is they are and share some of your work with them.
Give them a date you'd like to be there and see if they will agree to make some time to sit with you and view your portfolio. (Make sure you have good pictures and a nice presentation ready.) Now one of the most important things. Put together several really solid story ideas that you can present to the editors. I've found that there is a really high likelihood that if you walk in the door with a good story idea you may walk out with an assignment.
I just returned from New York with 3 potential assignments on ideas I proposed while I was visiting photo editors. A good editor really likes a photographer that can generate viable ideas. It shows you are thinking and eager to work to be part of the team.
Second, once you've gotten a possible time squared away with these people call the travel agent and make your reservations. Get a hotel at the same time. Don't forget to dress nicely. First impressions are important and setting yourself apart from the "jeans wearing tee shirt adorned stereotype" is a good idea. I wouldn't wear a Hugo Boss double-breasted suit but a quality pair of slacks and nice shirt won't hurt.
Here's where your CD's could have real value. Photo Editors also like to have something you can leave behind. I usually leave promotional fliers and a business card. However a nice, easy to use CD, may do very well.
Third and maybe most importantly, once you've seen all the photo editors you're interested in impressing and have returned home don't forget to follow up. Send a nice letter earnestly thanking the person for their time and include a promo card with an image they haven't seen already in your portfolio.
This is called name re-enforcement. If you went there with a great portfolio and they liked it, this will remind the person that you are serious about working for them and re-enforce the fact that you can regularly produce quality images. It may also establish that you truly are a good person despite what your mother says.
One little extra item that you may want to try after your return is a monthly mailing. A very good friend of mine who is religious about this has had really good luck generating work with a monthly post card campaign. He sends out postcards that has his identity phrase on it and a nice image. People remember him because he contiguously sends these without fail. Name retention is the name of the game here. I saw several of his cards pinned up on the walls of several of the editors' offices that I went to see.
Sports Shooter Newsletter list and I hope you read this issue. If not, it just further-enforces the problem.
Before I go I have to address one item that deals with my last column. If you recall I wrote about the dire nature of the industry and how some publications were taking advantage of the situation by insisting that young photographer sign less than friendly contracts to work.
To ad insult to an already bad situation, establishments like the New York Times and AOL/Time have decided to try and get photographers to sign over all their rights to their work for abysmal compensation. The Associated Press started this trend several years ago by strong-arming their freelancers into doing work for them for almost nothing.
One reader who works for AOL online enterprises thought that I didn't delineate well enough between the Time publications and AOL online. I agree with her assessment. I want to make it clear that I was talking about Time publications not AOL enterprises. I also should have listed Time/AOL rather than vise versa. As of this moment AOL online doesn't do assignment work so there is no photographers contracts there to deal with. I told her that I would clarify my statement and so I am attempting to do just that.
Anyway, let's all get out there and do some great work and make some money. | {
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Q: How do I get the ec2 tag Name from my ec2 hosts? I'm wanting to extract the "Name" tag from ec2 instances. How do I do that? It doesn't seem to be part of ec2_facts
A: Ansible recommends using dynamic inventories to manage AWS EC2 instances.
The docs explain the basic setup, afterwards you can address an EC2 instance like any other host via tags. Say, your instance is called web, you can address it later in a playbook via
hosts: tag_Name_web
| {
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Biografia
Era figlio dello scultore Ludwig Moroder e di Adele Moroder. Non avendo i suoi genitori optato nel 1939 per la Germania, fu arruolato nell'esercito italiano con gli Alpini. Nel settembre 1943 fu deportato nei campi di prigionia tedeschi, prima in Pomerania quindi in Carinzia, dove lavorò in infermeria e come interprete.
Sposò Paola Grossrubatscher nel 1945 ed ebbe cinque figli Ulrike, Wolfgang, Egon, Ruth e Stefan.. Morì in seguito alle complicanze remote dell'epatite contratta nei campi di prigionia.
Attività
Alex Moroder si prodigò per la conservazione e la diffusione della cultura e della lingua ladina, impegnandosi attivamente come fondatore o socio delle seguenti associazioni:
Union di Ladins de Gherdëina (1951-2006)
Segretario dell'Union Generela di Ladins dla Dolomites (1975-1987)
Amministratore del giornale La Usc di Ladins, settimanale dei ladini delle Dolomiti (1974-1994)
Radio Ladin de Gherdëina (1955-1997)
Museum de Gherdëina, fondatore con Robert Moroder presidente, Hermann Moroder-Jumbierch, Heinrich Moroder-Doss Raimund Mureda, Luis Piazza e Vigil Prugger. (1958-2006)
Compagnia di Teatro ladino di Ortisei
Inoltre fu socio fondatore e collaboratore per molti anni delle seguenti associazioni:
Coro Parrocchiale di Ortisei (1941-2006)
Club Alpino Italiano-Alpenverein Südtirol Sezione Val Gardena, socio fondatore con Hans Sanoner, Batista Vinatzer, Flavio Pancheri, Norbert Mussner, Heinrich Moroder-Doss e Bruno Moroder
Associazione per il mantenimento dei costumi tipici gardenesi (1956-1968)
Patronato scolastico, presidente dal 1965 al 1985
Scritti e opere varie
Lecurdanzes de l'ultima gran Viëra, Calënder de Gherdëina, Union di Ladins de Gherdëina, Ortisei, Anno 1985, pag. 60. (ladino).
L fanatism fej uni vierces – il fanatismo acceca - Intervista con Ingrid Runggaldier, Allegato: Usc di Ladins, Ortisei 2006. (ladino).
Fu principale artefice con Edgar Moroder dello studio genealogico sulla famiglia Moroder.
Radio Ladin
Assieme a Bruno Moroder fondò nel 1955 Radio Ladin de Gherdëina, con lo scopo di produrre trasmissioni culturali e notiziari radiofonici in lingua ladina che venivano trasmessi dalla RAI.
Il Museo della Val Gardena custodisce una raccolta di oltre 500 bobine di nastri magnetici registrati nell'ambito di questa attività e che costituiscono un patrimonio documentale unico in Alto Adige. L'Archivio Radio Ladin Alex Moroder è stato digitalizzato ed è accessibile tramite la Mediateca della Provincia autonoma di Bolzano.
Onorificenze
Anello d'oro del Comune di Ortisei, il 7 dicembre 1991
Medaglia di merito dello Stato del Tirolo a Innsbruck, il 15 agosto 1999
Note
Bibliografia
Carl Insam, Storia di 40 ani dl Radio ladin (RAI), Calënder de Gherdëina, Union di Ladins de Gherdëina Ortisei, anno 1986 p. 125. (Ladino).
Vinzenz Peristi, N lecort de Alex (Alexander Franz) Moroder dl Rusina, Calënder de Gherdëina, Union di Ladins de Gherdëina Ortisei, anno 2007, pagine 36-41. (Ladino).
Altri progetti
Collegamenti esterni
Archivio Radio Ladin Alex Moroder (Luis Trenker all'80º compleanno)
Archivio Radio Ladin Alex Moroder (Intervista di Bruno Moroder con Luis Trenker in ladino)
Val Gardena | {
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Box Office Results for June 17, 2011
Tags: 20th Century Fox, Academy Award Winner, Apatow Productions, Avatar, Batman, Batman & Robin, Batman Begins, Blake Lively, box office results, Bridesmaids, Captain America: The First Avenger, Cars 2, Casino Royale, China, CinemaScore, Columbia Pictures, comic book, DC Entertainment, Disney, DreamWorks Animation Studios, DreamWorks SKG, Emma Roberts, Fox, Fox Searchlight Pictures, Freddie Highmore, Geoffrey Rush, GoldenEye, Green Lantern, Imagine That, InTru Digital 3D, Iron Man 2, J.J. Abrams, Jack Black, Jerry Bruckheimer Films, Jig, Jim Carrey, Johnny Depp, Jonah Hex, Judy Moody and the Not Bummer Summer, June 17 2011, Killers, Kung Fu Panda 2, Land of the Lost, Lions Gate Entertainment, Lionsgate, Man of Steel, Marmaduke, Martin Campbell, Marvel Studios, Metro-Goldwyn-Mayer Pictures, MGM, Midnight in Paris, Mr. Popper's Penguins, NBC Universal, New Line Cinema, Nickelodeon Movies, Night at the Museum: Battle of the Smithsonian, Paramount Pictures, PG-13, PG-rated, Pirates of the Caribbean: On Stranger Tides, Pixar Animation Studios, Prince of Persia: The Sands of Time, Real D Digital 3D, Regency Enterprises, Relativity Media, Ryan Reynolds, Shrek Forever After, Sony, Sony Pictures Classics, Spyglass Entertainment, Star Trek, Super 8, Superman, Superman Returns, Terminator Salvation, The A-Team, The Art of Getting By, The Halcyon Company, The Hangover, The Hangover Part II, The Karate Kid, The Lord of the Rings, The Proposal, The Return of the King, The Taking of Pelham 1 2 3, Thor, Tim Robbins, Time Warner, Titanic, toon, Touchstone Pictures, Toy Story 3, United Artists, Universal Pictures, Up, Viacom, Walt Disney Pictures, Warner Bros. Pictures, Woody Allen, X-Men: First Class, Year One
Tags: 1979, 2004, 2009, 20th Century Fox, 3D, action, Alice in Wonderland, Angels & Demons, Apatow Productions, Beginners, Blue Sky Studios, box office results, Brad Pitt, Bridesmaids, CinemaScore, Columbia Pictures, comic book, Dark Castle Entertainment, Disney, District 9, Drag Me to Hell, drama, DreamWorks Animation Studios, DreamWorks Pictures, DreamWorks SKG, Ewan McGregor, Fantastic Four, Fast Five, Focus Features, Fox, Fox Searchlight Pictures, Get Him to the Greek, Ghost House Pictures, HBO Films, Heather Graham, Ice Age: Dawn of the Dinosaurs, Imagine Entertainment, Imagine That, IMAX, Iron Man 2, J.J. Abrams, James Cameron, Jerry Bruckheimer Films, Johnny Depp, Jordana Beatty, Judy Moody and the Not Bummer Summer, June 10 2011, Killers, Kristen Wiig, Kung Fu Panda 2, Land of the Lost, Lions Gate Entertainment, Lionsgate, Marmaduke, Marvel Studios, Meet the Fockers, Metro-Goldwyn-Mayer Pictures, MGM, Midnight in Paris, NBC Universal, New Line Cinema, Nickelodeon Movies, Night at the Museum: Battle of the Smithsonian, Owen Wilson, Paramount Pictures, PG-13, PG-rated, Pirates of the Caribbean: On Stranger Tides, Pixar Animation Studios, Prince of Persia: The Sands of Time, QED International, R-rated, reboot, Regency Enterprises, Relativity Media, River Road Entertainment, sci-fi, Sean Penn, sequel, Sex and the City 2, Shrek Forever After, Silver Pictures, Smokewood Entertainment, Sony, Sony Pictures Classics, Splice, Spyglass Entertainment, Star Trek, Steven Spielberg, Super 8, super hero, Terminator Salvation, Terrence Malick, The A-Team, The Halcyon Company, The Hangover, The Hangover Part II, The Incredible Hulk, The Karate Kid, The Lord of the Rings: The Return of the King, The Proposal, The Taking of Pelham 1 2 3, The Tree of Life, Thor, Time Warner, Touchstone Pictures, TriStar Pictures, Universal Pictures, Up, Viacom, Vin Diesel, Walt Disney Pictures, Warner Bros. Pictures, wolf pack, Woody Allen, X-Men: First Class | {
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const RateLimiter = require('../../../structures/RateLimiter');
class UserGET {
constructor(controller) {
this.path = '/user/:id';
this.router = controller.router;
this.database = controller.database;
this.rateLimiter = new RateLimiter({ max: 10 }); // 10/10 limit
this.router.get(
this.path,
this.rateLimiter.limit.bind(this.rateLimiter),
this.run.bind(this)
);
}
async run(req, res) {
const userMe = req.headers.authorization
? await this.database.User.findOne({ token: req.headers.authorization }).select('-_id -__v -password -token').lean()
: null;
if (req.params.id === '@me' || (userMe && req.params.id === userMe.id)) {
if (!req.headers.authorization)
return res.status(400).send({ message: "Authentication required" });
if (!userMe)
return res.status(401).send({ message: "Invalid token" });
return res.status(200).send({ user: userMe });
}
const user = await this.database.User.findOne({ id: req.params.id, verified: true }).select('-_id -__v -password -token -email -savedTags -verified').lean();
if (!user)
return res.status(404).send({ message: "No user with that id" });
return res.status(200).send({ user });
}
}
module.exports = UserGET;
| {
"redpajama_set_name": "RedPajamaGithub"
} | 8,579 |
Jerusalem Post Israel News
Israel parole board refuses bank embezzler's request for early release
In February 2015, the Central District Court vetoed an early release for Alon after the prosecution opposed her early release and appealed an earlier parole board decision to let her go.
By YONAH JEREMY BOB
Updated: FEBRUARY 18, 2016 02:28
(photo credit: REUTERS)
The Prison Parole Board on Wednesday announced it will not grant Eti Alon's request for immediate early release, but will push off the decision until August 4, when it will likely release her.
The board conditioned the August release on continued rehabilitation and good behavior by Alon, but noted that even the state prosecution had shifted its position to likely supporting her early release in August.
In February 2015, the Central District Court vetoed an early release for Alon after the prosecution opposed it and appealed an earlier parole board decision to let her go.
Alon, a convicted embezzler, has served around 14 years of a 17-year sentence which would run until 2019 at maximum.
She was imprisoned in 2003 for the embezzlement of some NIS 300 million from the Trade Bank, where she had served as the deputy chief of investment.
In court, Alon had admitted to stealing sums of money for over a five-year period and said she did it to help her brother, Ofer Maximov, pay a gambling debt estimated at approximately NIS 100m., which was owed to organized crime groups.
Alon's theft caused the Trade Bank to collapse and cost the state half a billion shekels in deposit insurance.
Legislation was introduced in light of this case that prevents bank employees from having comparable access to funds in the future.
In December 2014, a Prisons Service parole committee provisionally decided to shorten Alon's sentence, but finalization was postponed and then rejected.
Jerusalem Post staff contributed to this report.
Tags crime rates in israel | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 9,447 |
Q: Cannot access drive mounted by sshfs using Ubuntu file manager I've run into a problem with sshfs that I haven't seen before.
I mount serverB to serverA by doing the following (while logged in as root on serverA):
mkdir serverBLink
sshfs root@serverB:/ /home/myname/Documents/serverBLink
Once I do that, from the commandline I'm able to see all the files on serverB via the serverBLink folder.
Business as usual.
However, I cannot access the serverBLink folder using File Manager on Ubuntu. I don't know why. I thought it might be a permissions thing because I'm technically signed into the computer as "dot" but in the commandline, I've switched to root... ??
As a test I tried running chmod 777 on the serverBLink folder to grant everyone access to everything inside but it still doesn't work.
Using File Manager, when I try to access the serverBLink folder, I get the error message:
Could not enter folder
Any suggestions?
A: Maybe try -o allow_other to allow users other than the mounter to access.
Even better, you don't need to be root to use sshfs, so you can simply create the directory and mount the remote directory as yourself (but with root@serverB).
From a security perspective, you need to establish a connection as root@serverB (which you do already), and then you need at least execute permission on the mount directory and access to the mount contents itself.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 7,831 |
\section{Introduction}
The interaction of magnetic fields and (often turbulent) fluid flows is a fundamental problem of geophysical and astrophysical fluid dynamics. Its importance lies in the fact that this interaction often controls the dynamics of geophysical and astrophysical objects, with amplification of the field via stretching by turbulent flows leading to dynamo action \citep[see e.g.][]{moffatt78} and the back-reaction of the magnetic field on the turbulent flows via the Lorentz force. This leads to, for example, the suppression and excitation of instabilities \citep{rkh_2013} and the modification of the mixing and transport properties of the flow \citep{moffatt_1983,GD_1994}. These interactions may occur in models of self-consistent dynamo action \citep[see e.g.][]{ds_2007}, magnetoconvection \citep{wp_2014} or stably stratified magnetic layers \citep{t_2010}.
In this paper, we shall be concerned with the interaction of magnetic fields in fluid layers that are stably stratified. Such layers are common in geophysics and astrophysics, with notable examples being the solar tachocline \citep[see e.g.][and the references therein]{hrw_2012}, the stably stratified layer at the core-mantle boundary \citep{gd_2013,buff_2014}, and possible stable layers in gas giants and exoplanets \citep{s_2003,cw_2008}. It is well known that stable stratification leads to strong anisotropy in flows with vertical (i.e. aligned with gravity) motions inhibited relative to horizontal ones. Because of this anisotropy, the dynamics in such layers is often modelled using reduced models of varying complexity; with thin-layer models, shallow water models and two-dimensional models all providing useful insights into the dynamics of such layers. Recently the more sophisticated of these models have been extended to MHD \citep[see e.g.][]{g_2000,mg_2004}, though much progress can still be made utilising basic two-dimensional models; it is this approach we use here, though we discuss generalisations to such models in the conclusions.
It is well known that rotating, stably stratified fluids exhibit correlations that can lead to the generation of large-scale flows. There are many explanations for such behaviour, but it is often argued that the existence of conservation laws and an inversion procedure plays a key role in this emergence of large-scale behaviour \citep{DM:2008}. For example in two-dimensional dynamics vorticity (and in quasi-two-dimensional dynamics potential vorticity) are important conserved quantities. \citet{TDH_2007} have demonstrated that the presence of even a weak magnetic field may lead to the suppression of the correlations that lead to the formation of large-scale flows. A central question then is what role the magnetic field may play in the modification of the Lagrangian conserved quantities of the flow, via the action of the Lorentz force \citep{KSD_2008}. Furthermore, as described below, it has been demonstrated that magnetic fields may inhibit shear flow instabilities and lead to the disruption of coherent structures such as vortices.
One key issue (often conveniently overlooked) for the modelling of astrophysical stable layers is that both the ionised plasma of stellar interiors and the liquid iron of the Earth's fluid outer core are fluids with
extremely low magnetic Prandtl number $Pm = Rm/Re = \nu/\eta$, where $\nu$ is the viscosity and $\eta$ is the magnetic diffusivity of the fluid. This has the consequence that the velocity or vorticity field dissipates at spatial scales much smaller than the magnetic field (which is itself at small scales owing to high values of $Rm$) \citep{tcb:2013}. Thus the description of low $Pm$ dynamics is a computationally difficult problem, and virtually all numerical investigations have been carried out with $Pm \sim {\cal O}(1)$.
Here we briefly mention some previous investigations of the interaction of weak magnetic fields with two dimensional flows. Note this body of work is distinct from that examining the dynamics of MHD turbulence with a strong guide field (where quasi two-dimensionality occurs in the plane perpendicular to the magnetic field; for a review see \citet{tcb:2013}). Weak magnetic fields are known to have a significant effect on two dimensional turbulence. Most striking is that the presence of a magnetic field can alter the direction of the spectral transfer of two dimensional turbulence, turning inverse cascades into forward cascades \citep[see e.g.][]{Pouquet_1978,sesh_etal_2014, Banpan_2014,Seshalex_2016}. The inverse cascade in two dimensional hydrodynamic turbulence is often ascribed to the global conservation of enstrophy and energy in the dissipationless regime; in the presence of magnetic field the global conservation of enstrophy is broken.
It has also been shown that magnetic fields can have strong effects on the linear and nonlinear evolution of shear flows in two dimensions \citep{fjrg_1996, jgrf_1997, bk_2002, phzh_2008}. Here magnetic fields can interact with the vortices that arise as a result of Kelvin-Helmholtz instability and also prevent roll-up occurring in the first place.
Perhaps the most subtle and interesting effect is that weak magnetic field can inhibit the transport (turbulent diffusion) of scalar fields as described for example by \citet{CV_1991,GD_1994,Cattaneo_1994,kht_2016}. Mixing and transport is often associated with the Lagrangian properties of fluid flows and so it is often argued that in order for a weak magnetic field to have an effect it must be subtly altering these properties, for example by breaking the material invariants of the flow. It is this effect that we shall investigate here.
All the calculations described above are performed with the magnetic Prandtl number of order unity; in this (unphysical) regime vortex filaments have the same spatial scale as current filaments, in contrast with the geophysical and astrophysical case where the vorticity dissipates on scales much smaller than the magnetic field. Moreover the presence of a finite amount of viscosity ensures that there are no conservation laws even in the hydrodynamic case --- therefore it is uninteresting to examine the role of weak magnetic field in modifying conservation laws. Finally in this case (with finite viscosity) it is very difficult to find exact hydrodynamic states to perturb with a magnetic field, so that little analysis is possible; at best plausible scaling arguments are possible.
In this paper we utilise a numerical scheme introduced by \citet{dt_2012}. This scheme, which was compared with pseudo-spectral methods for the problem of decaying MHD turbulence, allows the
integration of MHD flows at low $Pm$.
Our philosophy is to investigate the role of magnetic fields in modifying the behaviour of simple paradigm flows (Gaussian vortices and circular and elliptical vortex patches). This interaction of coherent structures with magnetic fields has been much studied in the context of flux expulsion \citep{weiss_1966, mk_1983, bbg_2001,gmt_2016}. This problem has the advantage that much can be done analytically \citep{gmt_2016}. Of particular interest is that the numerical scheme we utilise (which involves evolving contours advected by the flow) is perfectly suited to evaluating the role of magnetic field in modifying the evolution of (hydrodynamically) materially conserved quantities such as circulation; as far as we are aware this is the first evaluation of this effect in the literature.
The rest of this paper is organised as follows. In section
2 we give the mathematical framework of the model, including a description of the equations, scalings and numerical method. In section 3 we describe the results of asymptotic and numerical analysis of the interaction of magnetic fields with Gaussian vortices, circular and elliptical vortex patches, paying particular close attention to the breaking of conservation laws. We conclude in section 4 with a description of the implications of our results and possible future investigations.
\section{Mathematical framework}
\subsection{Governing equations}
We consider the two-dimensional incompressible MHD equations
in a doubly-periodic domain at
essentially zero Prandtl number (negligible viscosity), as in
\citet{dt_2012}. The magnetic field ${\boldsymbol B}$ is divided into a steady mean
component $B_0$ in the $x$ direction and a remaining variable part
$-{\boldsymbol \nabla}^\perp{A}$ represented by a magnetic potential $A(x,y,t)$, where
${\boldsymbol \nabla}^\perp{A}=(-A_y,A_x)$ in two dimensions and subscripts $x$ and
$y$ denote partial derivatives. That is, we take
\begin{equation}
\label{magfield}
{\boldsymbol B}=B_0\hat{\boldsymbol e}_x-{\boldsymbol \nabla}^\perp{A}.
\end{equation}
As the flow ${\boldsymbol u}$ is incompressible, it is convenient to introduce a
streamfunction $\psi(x,y,t)$ in terms of which ${\boldsymbol u}={\boldsymbol \nabla}^\perp\psi$.
Then, we can write the 2D MHD equations in terms of the vorticity
$\omega={\boldsymbol \nabla}^\perp\bcdot{\boldsymbol u}=v_x-u_y=\nabla^2\psi$ and
magnetic potential $A$ as follows:
\begin{align}
\label{voreq}
\omega_t+J(\psi,\omega) &=B_0 j_x-J(A,j), \\
\label{poteq}
A_t+J(\psi,A) &=B_0\psi_x-\eta j,
\end{align}
where $j={\boldsymbol \nabla}^\perp\bcdot{\boldsymbol B}=-\nabla^2{A}$ is the (vertical component of the)
current density (for unit permeability $\mu_0$), $\eta$ is the
magnetic diffusivity, and $J(a,b)=a_x b_y - a_y b_x$ is the Jacobian
operator. The terms on the r.h.s.\ of (\ref{voreq}) come from taking
the curl of the Lorentz force per unit mass. In the absence of a
magnetic field, the vorticity is materially conserved. Likewise, when
$\eta=0$, the total scalar potential $A+B_0 y$ is materially
conserved. However, $\eta>0$ appears to be necessary for regularity
of the equations, though this remains unproven \citep{cao_2017}.
\subsection{Scalings and parameters}
In the results below, we consider an initial state consisting of a
vortex of mean radius $R$ and characteristic vorticity $\omega_0$
(chosen so that the maximum velocity $U_0=\tfrac12\omega_0 R$).
The initial magnetic potential $A=0$. We additionally prescribe the
parameters $\eta$ and $B_0$. By choosing $R$ to be a characteristic
length, and $\tfrac12\omega_0$ to be a characteristic frequency, we can
form two dimensionless parameters from $\eta$ and $B_0$,
\begin{equation}
\label{nondim}
\delta=\frac{\sqrt{\eta/\omega_0}}{R} \quad\textrm{and}\quad
\gamma=\frac{B_0}{U_0\delta}\,.
\end{equation}
The parameter $\delta$ may be regarded as the ratio of the diffusive
length scale $\ell_\eta=\sqrt{\eta/\omega_0}$ to the mean
vortex radius $R$. Notably, the familiar magnetic Reynolds number $R_m=U_0
R/\eta=\tfrac12 \delta^{-2}$, so $\delta = (2 R_m)^{-1/2}$.
The second parameter $\gamma = (2 R_m)^{1/2} B_0/U_0$ measures
the ratio of the magnetic field --- after it has been fully
intensified by sharpened gradients in $A+B_0 y$ --- to the maximum
initial velocity $U_0$. Hence $\gamma = 1$ denotes the field strength that would in the absence of other, more subtle interactions, bring the small-scale field into equipartition with the flow. Note, diffusion limits the gradients in
$A+B_0 y$ to
${\mathcal{O}}(B_0 R/\ell_\eta)={\mathcal{O}}(B_0/\delta)$.
So, even a weak initial field can have a strong effect if $\eta$ is
sufficiently small.
\subsection{Conservation laws}
The presence of a magnetic field breaks many hydrodynamical conservation
laws, the most important of which is conservation of circulation
\begin{equation}
\label{circ}
\Gamma=\oint_{{\mathcal{C}}} {\boldsymbol u}\bcdot d{\boldsymbol x}
\end{equation}
where ${\mathcal{C}}$ is any material contour, and ${\boldsymbol x}$ lies on
${\mathcal{C}}$. In an inviscid fluid, considered here, $\Gamma$ remains
constant in the absence of a magnetic field,
a fundamental result known as Kelvin's circulation theorem. This result
is a direct consequence of material (pointwise) conservation of vorticity.
A magnetic field breaks this conservation. The tension created by
twisting field lines tends to retard the vortex rotation, reducing
circulation in magnitude (at least initially). The finite magnetic
diffusivity limits the build up of this tension, leading typically to
the expulsion of the field from the vortex core \citep{weiss_1966}.
In this way, only a fraction of the vortex circulation may be removed
by the action of the field. This process is subtle, indeed even in the kinematic regime it becomes apparent that it is the integrated effects of diffusion that
control the scaling of the maximum field strength \citep{weiss_1966,moffatt78}.
An expression for the rate of change of circulation can be obtained by
taking a time derivative of (\ref{circ}) using (\ref{voreq}). One finds
\begin{equation}
\label{dcirc}
\frac{d\Gamma}{dt}=\oint_{{\mathcal{C}}} j{\boldsymbol \nabla}(A+B_0 y)\bcdot d{\boldsymbol x}
=\oint_{{\mathcal{C}}} j\frac{d(A+B_0 y)}{ds}ds\,,
\end{equation}
where $s$ is any parametrisation of ${\mathcal{C}}$.
Therefore, $j$ and the tangential derivative of $A+B_0 y$ along
${\mathcal{C}}$ must correlate in order to change the circulation.
\subsection{Numerical Method}
We employ the `Combined Lagrangian Advection Method' \citep[`CLAM',
see][]{df_2010} used in a previous work investigating 2D MHD
turbulence at low Prandtl number \citep{dt_2012}. The method uses
material contours to represent part of the vorticity field alongside
two auxiliary gridded vorticity fields used to incorporate vorticity
forcing. The magnetic potential $A$ is also represented on a grid,
and the pseudo-spectral method is used to calculate accurately
derivatives and invert Laplace's operator on a square doubly-periodic
domain of side length $2\pi$. Nonlinear terms are de-aliased by
applying a circular filter in spectral space to all fields before they
are multiplied together on the grid. The filter removes all
wavenumbers whose magnitude exceeds $2k_{\mathsf{max}}/3$, where
$k_{\mathsf{max}}$ is the maximum wavenumber in $x$ and $y$. This is
less aggressive than the standard `2/3 rule', but is sufficient to
remove aliasing errors. Finally, a weak $\nabla^6$ hyperdiffusion is
applied to the small-amplitude, residual vorticity field with a
damping rate of $2\omega_{\mathsf{rms}}$ at the wavenumber
$k=k_{\mathsf{max}}$.
The vorticity field is primarily represented by contours, with a
contour interval chosen to be equal to the initial range of vorticity
divided by $80$. This is twice as fine as recommended
in \cite{df_2010} to provide higher accuracy. Each contour is
represented by a variable number of nodes which are frequently
redistributed to maintain resolution. This occurs each time the
`twist' $\tau$ exceeds $2.5$, where
\begin{equation}
\label{twist}
\tau=\int_{t_0}^{t} |\omega|_{\mathsf{max}}(t)dt
\end{equation}
and $t_0$ is the last time contour nodes were redistributed (or the
initial time). At these times, `contour surgery' is also performed to
regularise the contours, i.e.\ to remove small filaments and to
reconnect contours of the same level which are sufficiently close.
Every $20\tau$ time units, the contours are converted to an ultra-fine
grid having dimensions $16$ times larger in each direction than the
basic `inversion' grid, and combined with the residual vorticity field
(interpolated to the ultra-fine grid) to form a gridded vorticity
field fine enough to resolve the scale of contour surgery. This field
is then recontoured to form a new set of contours to be used for the
next $20\tau$ time units. Recontouring acts like contour surgery but
also largely prevents contour crossing errors arising from node
redistribution. Further details of the numerical method can be found
in \cite{df_2010} and references therein. This scheme has been demonstrated
to give extremely accurate representations of low $Pm$ dynamics;
comparable with
spectral schemes at significantly higher resolutions \citep{dt_2012}.
\section{Results}
In this section, we illustrate the flow evolution in a few
representative examples and quantify key diagnostics. In particular,
we examine the time evolution of the energy components, mean square
vorticity and current density, and the circulation. We determine an
appropriate scaling theory to estimate the amount of circulation
removed by the presence of a magnetic field, and contrast various
initial flow configurations: a Gaussian vortex, a Rankine vortex
(or circular vortex patch) and an elliptical vortex patch.
\subsection{Parameter settings}
In all results presented, without loss of generality we take the
characteristic vorticity within the vortex $\omega_0=4\pi$, corresponding to
a unit rotation period, and a mean vortex radius $R=5\pi/32\approx 0.49087$,
which is sufficiently small compared with the domain half width ($\pi$)
to have only a minor effect on the vortex evolution.
We consider basic `inversion' grid resolutions ranging from $128^2$ to
$1024^2$. This grid is the one used to evolve $A$ and the gridded
vorticity fields, as well as to carry out all spectral operations,
including determining the velocity field ${\boldsymbol u}$ from the vorticity
field. The latter is found from the contours (after a contour to grid
conversion) and a portion of the two other gridded vorticity fields,
as described in \cite{df_2010}. Note: the effective resolution of a
CLAM simulation is $16$ times greater in each direction, as
demonstrated in direct comparisons with a standard pseudo-spectral
method \citep{dt_2012}.
On a grid having a resolution of $n_g^2$, the magnetic diffusivity
$\eta$ is chosen as $\eta=\omega_0(\Delta x)^2$ where $\Delta
x=2\pi/n_g$ is the (basic) grid scale. This is sufficient to resolve
the magnetic diffusion length $\ell_\eta$, as judged by the downturn
in the current density power spectrum at large wavenumber. Note that
$\ell_\eta=\sqrt{\eta/\omega_0}=\Delta x$ with these choices of
parameters.
The two parameters we vary are $\delta=\ell_\eta/R$ and
$\gamma=B_0/(U_0\delta)$. The former is implicitly set by the grid
resolution, and here we have $\delta=12.8/n_g$. The second
parameter $\gamma$ is used to
determine the initial field strength $B_0$. Given
$U_0=\tfrac12\omega_0 R=10\pi^2/32\approx 3.084$, we choose a value of
$\gamma$ and determine $B_0$ from $B_0=\gamma\delta U_0$. For
example, for $n_g=512$, we find $\delta=0.025$, and if further
$\gamma=1$, we find $B_0\approx 0.077106$.
At the initial time $t=0$, we start with $A=0$ and one of three
vorticity distributions: (1) a Gaussian vortex with
$\omega({\boldsymbol x},0)=\omega_{\mathsf{max}}e^{-r^2/2R^2}$,
where $r=|{\boldsymbol x}|$ and
$\omega_{\mathsf{max}}=\omega_0/(2(1-e^{-1/2}))\approx1.27\omega_0$
is chosen so that the maximum velocity $U_0=\tfrac12\omega_0 R$
occurs at $r=R$; (2) a Rankine (circular) vortex with
$\omega({\boldsymbol x},0)=\omega_0$ for $r<R$ and zero otherwise; and
(3) an elliptical vortex patch having uniform vorticity $\omega_0$
within the ellipse $x^2/a^2+y^2/b^2=1$ and zero otherwise, where
$ab=R^2$ and $b/a=\lambda$, the prescribed vortex aspect ratio.
Actually, the requirement that the mean vorticity be zero within
the doubly-periodic domain implies that there is a uniform negative
compensating vorticity spread throughout the domain. The background
vorticity is approximately $-0.024\omega_0$ for the Gaussian vortex and
$-0.019\omega_0$ for both the circular and elliptical vortex.
\subsection{Qualitative description of the flow evolution}
\begin{figure}
\begin{center}
\includegraphics[width = \textwidth]{fig1.pdf}
\end{center}
\caption{Vorticity $\omega({\boldsymbol x},t)$ and magnetic field lines at the
times indicated (top to bottom) for an initially Gaussian vortex and
for $\gamma=0.125,\,0.5$ and $2$ (left to right). The vorticity
colourbar is indicated next to each image. The contour interval for
$A+B_0 y$ is $0.005$, $0.02$ and $0.08$ (left to right).}
\label{fig:q512g}
\end{figure}
\begin{figure}
\begin{center}
\includegraphics[width = \textwidth]{fig2.pdf}
\end{center}
\caption{As in figure~\ref{fig:q512g} but for the current density
$j({\boldsymbol x},t)$.}
\label{fig:j512g}
\end{figure}
We begin by discussing a few characteristic simulations. For this
purpose, we consider $\delta=0.025$ (corresponding to $n_g=512$) and
three different values of $\gamma$, namely $0.125$, $0.5$ and $2$,
corresponding to a weak, moderate and strong magnetic field (at full
intensity). For the initially Gaussian vortex, figure~\ref{fig:q512g}
shows the evolution of the vorticity field (colour) overlaid with
field lines (contours of $A+B_0 y$) for the three values of $\gamma$
(increasing from left to right). The corresponding current density
is shown in figure~\ref{fig:j512g}.
In the left column, the weak field has no discernible impact on the
vortex, which remains approximately circular and undiminished
throughout the evolution. The field itself is twisted rapidly and
field lines are broken by the magnetic diffusivity, leading to an
expanding region of nearly zero field --- this is the classic `flux
expulsion' phenomenon first described by \cite{weiss_1966}. Note that
the current sheets and strong field gradients developing in the
periphery are a consequence of periodicity; otherwise the region of
nearly zero field would continue expanding. These strong gradients
generate vorticity which subsequently destabilises and disrupts
the field in this region, away from the central vortex.
In the middle column for a stronger initial field, the initial
evolution is closely similar. Now however a weak spiral pattern in
vorticity is generated by the tightening field gradients before
diffusion erases them. Moreover, the outer gradients induced by
periodicity are much stronger and more disruptive at late times,
distorting the vortex into an elliptical shape and eroding it. The
expelled field in this case collapses back toward the vortex and
strongly interacts with it at late times --- again here the later dynamics
is a consequence of periodicity.
In the right column for the strongest initial field, again the early
evolution is similar. Also, spiral vorticity generation occurs but
this time the vorticity becomes comparable with that in the core, and
the alternating bands of vorticity destabilise by $t=12$. The
subsequent evolution is much more turbulent and noticeably affects the
vortex core itself, causing strong distortion and a loss of symmetry
at late times. In this case the field is never fully expelled
initially and the strong gradients collapse back more rapidly, leaving
weaker gradients only in the vortex core. A slightly higher initial
field strength ($\gamma=2.5$) leads to the complete destruction of the vortex
by $t=25$ (not shown).
We now contrast the Gaussian vortex with a circular vortex patch of
uniform initial vorticity. We choose the same $\delta$ and $\gamma$
values so that any differences may be attributed to the initial
vorticity profile. The vorticity (with superimposed field lines) and
current density are illustrated in figures~\ref{fig:q512p} and
\ref{fig:j512p} respectively. Compared with figures~\ref{fig:q512g} and
\ref{fig:j512g}, there are striking differences. First of all, in
general, the magnetic field amplification is much stronger for the patch
than for the Gaussian vortex, leading to greater disruption at late
times and indeed vortex destruction for $\gamma=2$. In that case, the
field is never expelled and interacts strongly with the vortex,
ultimately pulling it apart and leaving intense current sheets where
the vortex used to be. For moderate initial field strength
($\gamma=0.5$, middle column), the vorticity filament spiral outside
of the initial vortex destabilises, something only seen for $\gamma=2$
in the case of the Gaussian vortex. Even for weak initial field ($\gamma=0.125$, left column), there is evidence that the
field is disturbing the vortex boundary, which is no longer circular
but more polygonal. Evidently, the less regular flow associated with
the vortex patch, especially the discontinuity in shear at its edge,
gives rise to a much stronger local interaction with the magnetic
field. This is quantified below.
\begin{figure}
\begin{center}
\includegraphics[width = \textwidth]{fig3.pdf}
\end{center}
\caption{Vorticity $\omega({\boldsymbol x},t)$ and magnetic field lines at the
times indicated (top to bottom) for an initially uniform (Rankine) vortex and
for $\gamma=0.125,\,0.5$ and $2$ (left to right). The vorticity
colourbar is indicated next to each image. The contour interval for
$A+B_0 y$ is $0.005$, $0.02$ and $0.08$ (left to right).}
\label{fig:q512p}
\end{figure}
\begin{figure}
\begin{center}
\includegraphics[width = \textwidth]{fig4.pdf}
\end{center}
\caption{As in figure~\ref{fig:q512p} but for the current density
$j({\boldsymbol x},t)$.}
\label{fig:j512p}
\end{figure}
\subsection{Quantitative results}
We next discuss various quantitative aspects of the flow evolution
before developing a scaling theory to explain the results. An
important diagnostic is the vortex circulation $\Gamma$ defined in
(\ref{circ}), in particular its rate of change $d\Gamma/dt$, which may
be computed using (\ref{dcirc}). The circulation changes only as a
result of the magnetic field, and given that field lines are twisted
by the vortex, we expect {\it a priori} that the associated tension
will act to slow the vortex rotation, reducing its circulation. At
least this should happen initially.
\begin{figure}
\begin{center}
\includegraphics[width = \textwidth]{fig5.pdf}
\end{center}
\caption{The material contour (or contours) belonging to the
original circular tracer contour at times $t=5,\,10,\,15$ and
$20$ for the Gaussian vortex case with $\delta=0.0125$
($n_g=1024$) and $\gamma=2$. Only the inner portion of the
flow domain is shown. }
\label{fig:tracer}
\end{figure}
We compute the circulation using a material contour ${\mathcal{C}}$
which is initially a circle of radius $R$ centred at the origin. The
contour is evolved in just the same way as the vorticity contours,
except that it is never rebuilt. It may generally distort and even
split into various parts, but at all stages the collection of contours
belonging to the original contour is used in the contour integrations
required in (\ref{circ}) and (\ref{dcirc}). A more extreme example
showing how ${\mathcal{C}}$ may distort is provided in
figure~\ref{fig:tracer}. Here, at late times, ${\mathcal{C}}$ splits
into many parts, though most of these are very small. Nonetheless,
accurate contour integration can be performed around such contours.
Here, we use two-point Gaussian quadrature and the actual curved shape
of the contour between successive nodes. At the evaluation points,
the fields such as ${\boldsymbol u}$ and $j$ are interpolated from nearby gridded
values using bi-linear interpolation.
\begin{figure}
\begin{center}
\includegraphics[width = \textwidth]{fig6.pdf}
\end{center}
\caption{Time evolution of various diagnostics for the Gaussian vortex
case with $\delta=0.0125$ and $\gamma=2$, i.e.\ as in
figure~\ref{fig:tracer}. From left to right, we show energy,
enstrophy, circulation and the circulation rate of change. See text
for details.}
\label{fig:diag}
\end{figure}
Figure~\ref{fig:diag} shows $\Gamma$ and $d\Gamma/dt$ along with other
important diagnostics for an initially Gaussian vortex when
$\delta=0.0125$ and $\gamma=2$. This figure also shows the
hydrodynamic (or kinetic) and magnetic energy components,
respectively
\begin{equation}
\label{energy}
E_u=\frac{1}{2}\int_{-\pi}^{\pi}\int_{-\pi}^{\pi}|{\boldsymbol u}|^2 dx\,dy
\qquad\textrm{and}\qquad
E_b=\frac{1}{2}\int_{-\pi}^{\pi}\int_{-\pi}^{\pi}|\nabla{A}|^2 dx\,dy
\end{equation}
together with the total energy $E=E_u+E_b$, as well as the
hydrodynamic and magnetic `enstrophies' $\langle\omega^2\rangle$ and
$\langle j^2\rangle$, here defined as the domain mean values of
$\omega^2$ and $j^2$. Note that $E_b$ does not include the constant
part of the magnetic energy associated with the initial mean magnetic
field $B_0\hat{\boldsymbol e}_x$. For the hydrodynamic case the enstrophy $\langle\omega^2\rangle$ is conserved in the absence of viscosity, whilst for the ideal MHD case the total energy $E$ (magnetic plus kinetic) is conserved, whilst the enstrophy is not.
Note, in this limit $\langle j^2\rangle$ is
not conserved, however any functional of $A+B_0 y$ is, since this field
is materially conserved (and the flow is incompressible). However,
this limit is not relevant for the present purposes and is likely to
be mathematically ill-posed \citep{cao_2017}.
The case illustrated in figure~\ref{fig:diag} is broadly
representative of all simulations conducted. All share similar trends
albeit with different amplitudes and time scales. The kinetic energy
decays while the magnetic energy grows non-diffusively at first, as
evidenced by the conservation of the total energy at early times (red
curve). As field gradients increase, magnetic diffusion
and the Lorentz force begin
to act, ultimately halting the growth in magnetic energy and inducing
decay at later times. Note that the background magnetic energy
$\bar{E}_b=\tfrac12 B_0^2 (2\pi)^2$, which is ignored in $E_b$, is
typically small compared with the maximum $E_b$ observed. In this
example, $\bar{E}_b\approx 0.117$, which is less than $2\%$ of the
maximum $E_b$. The decay in kinetic energy $E_u$ is consistent with
the action of the field, forcing the vortex to slow down as
field lines twist. Only the breaking of field lines by the diffusion
allows the vortex to survive.
Regarding the enstrophy and current density, the mean square current density
$\langle j^2\rangle$
initially grows rapidly until approximately $t=6$, during which time
the hydrodynamic enstrophy $\langle\omega^2\rangle$ weakly decays.
Over this period, the vortex is mainly slowing down as it twists
magnetic field lines. Around $t=6$, magnetic diffusion begins to act
strongly, expelling the field from the vortex core and its immediate
vicinity. After this time, $\langle j^2\rangle$ grows more slowly but
$\langle\omega^2\rangle$ begins to grow rapidly, reaching a value more
than $17$ times its initial value by $t=19$ before subsequently
decaying. This growth is due to the vorticity production by the
strong current sheets created in the periphery of the vortex,
primarily around and after $t=6$ (cf.\ right column in
figure~\ref{fig:j512g}). Only when these sheets begin to decay
significantly at late times does $\langle\omega^2\rangle$ begin to
decay. This decay is not inviscid: numerical dissipation acting at
scales well below the grid scale are sufficient to cause a strong
decay when $\omega$ develops extensive fine-scale structure in the
form of filaments or sheets.
The time evolution of the circulation $\Gamma$ and its rate of change
$d\Gamma/dt$ are consistent with the foregoing description. Up to
$t=6$, the circulation continually decreases as the twisting magnetic
field lines slow the vortex rotation. The slowing decay after $t=3$
indicates that magnetic diffusion is already breaking field lines and
thus reducing the impact on the vortex. After $t=6$, the circulation
remains roughly constant (with a small rebound just after $t=6$),
despite the continued vorticity production beyond the vortex core.
This is because the contour ${\mathcal{C}}$ around which the
circulation is computed remains near the centre of the domain, as
shown previously in figure~\ref{fig:tracer}. Notably, since the
circulation of the entire domain must be zero in a doubly-periodic
domain, then the total circulation outside of ${\mathcal{C}}$ is just
$-\Gamma$. In particular, this means that despite the intense
vorticity production occurring beyond the vortex core, the net change
in total vorticity there is small after $t=6$.
\subsection{Scaling theory}
\begin{figure}
\begin{center}
\includegraphics[width = \textwidth]{fig7.pdf}
\end{center}
\caption{Scaled forms of $d\Gamma/dt$, as indicated, for
$\delta=0.0125,\,0.025,\,0.05,\,0.1$ and
$\gamma=0.0625,\,0.125,\,0.25,\,0.5,\,1,\,2$. The values of
$\delta$ are distinguished by line style: solid, dashed, dotted,
dash-dotted. The values of $\gamma$ are distinguished by colour:
black, blue, red, green, magenta and cyan. Panels (a) and (b)
pertain to the initially Gaussian vortex, while panels (c) and (d)
pertain to the initially circular vortex patch. The straight dashed
magenta line in panel (b) is the fit to equation
(\ref{gauss-dcirc-bis}). See text for further details.}
\label{fig:scaling}
\end{figure}
We next focus on the behaviour of $d\Gamma/dt$, in particular how its
evolution depends on the parameters $\delta$ and $\gamma$ as well as
on the initial vorticity distribution. Given the crucial role played
by the magnetic diffusivity, we expect the flow to evolve on an
appropriate diffusive time scale, which may (and does) depend on the
initial vorticity distribution. Moreover, the amplitude of
$d\Gamma/dt$ is expected to increase as $\delta$ and $\gamma$
increase. Figure~\ref{fig:scaling} summarises all of the results,
both for the Gaussian vortex (panels (a) \& (b)) and for the circular
vortex patch (panels (c) \& (d)), for 4 values of
$\delta\in[0.0125,0.1]$ differing by factors of two, and for 6 values
of $\gamma\in[0.0625,2]$ also differing by factors of two.
First consider panels (a) and (b) for the initially Gaussian vortex.
Panel (b) merely shows a restricted set of parameters, namely the
three smallest $\delta$ values and the three smallest $\gamma$ values.
This is done to show just how well the curves collapse for small
$\delta$ and $\gamma$, where one might expect a scaling theory to
apply. The results show a clear dependence on the scaled time
$\delta^{2/3}t$, rather than the $\delta^2 t$ dependence one might
expect for pure diffusive decay. This is due to the spiral wind-up of
the magnetic field (which at small $\gamma$ behaves like a passive
tracer), accelerating the diffusive decay ($\propto\eta^{1/3}$), as
originally shown by \cite{bbg_2001}. The quadratic dependence of
$d\Gamma/dt$ on $\gamma$ is just a consequence of the form of the
integrand in (\ref{dcirc}), where a quadratic product of quantities
proportional to the magnetic field appears.
The dependence on $\delta^{4/3}$ may be explained by considering the
early time evolution of $d\Gamma/dt$ and using Moffatt's approximate
inviscid solution for $A$,
\begin{equation}
\label{moffatt}
A(r,\theta,t)=B_0 r [\sin(\theta-\bar\Omega t) - \sin\theta]
\end{equation}
\citep{moffatt_1983}.
This assumes that the background flow is steady and axisymmetric, with
angular frequency $\bar\Omega(r)$ a function of $r$ only, and moreover
that $\gamma\ll 1$. This solution directly follows from
(\ref{poteq}), neglecting $\eta$, and can be seen most easily by
recognising that the total potential $\tilde{A}=A+B_0 y$ satisfies
(for a steady axisymmetric flow)
\begin{equation}
\tilde{A}_t+\bar\Omega\tilde{A}_\theta=0,
\end{equation}
implying $\tilde{A}=F(r,\theta-\bar\Omega t)$ for some function $F$.
This function is determined from the initial conditions,
$\tilde{A}(r,\theta,0)=B_0 y = B_0 r\sin\theta$, giving
$F(r,\theta)=B_0 r\sin\theta$, from which (\ref{moffatt}) follows.
Now, to estimate $d\Gamma/dt$ at early times (before diffusion has
a chance to act significantly), we also need the current density $j$.
Using Moffatt's solution (\ref{moffatt}) for $A$, we find
\begin{equation}
\label{jmoffatt}
j(r,\theta,t)=B_0 t(r\bar\Omega_{rr}+3\bar\Omega_r)\cos(\theta-\bar\Omega t)
+B_0 t^2 r\bar\Omega_r^2\sin(\theta-\bar\Omega t).
\end{equation}
Using this and $\tilde{A}_\theta=B_0 r\cos(\theta-\bar\Omega t)$ in
(\ref{dcirc}) written using the parametrisation $\theta$, we obtain
after elementary integration
\begin{equation}
\label{gauss-dcirc}
\frac{d\Gamma}{dt}=B_0^2 \pi t (r^2\bar\Omega_{rr}+3r\bar\Omega_r)_{r=R}
\end{equation}
(the $t^2$ term integrates to zero). But for the Gaussian vortex,
\begin{equation}
\label{gauss-omega}
\bar\Omega(r)=\omega_{\mathsf{max}}\frac{R^2}{r^2}
\left(1-e^{-r^2/2R^2}\right).
\end{equation}
After some algebra, one may show that
\begin{equation}
\label{nasty-term}
(r^2\bar\Omega_{rr}+3r\bar\Omega_r)_{r=R}=-\omega_{\mathsf{max}}e^{-1/2}.
\end{equation}
Next, using $B_0=\delta\gamma U_0=\tfrac12\delta\gamma\omega_0 R$
from (\ref{nondim}) in (\ref{gauss-dcirc}) together with
$\omega_{\mathsf{max}}=\omega_0/(2(1-e^{-1/2}))$, we obtain the
following explicit prediction for $d\Gamma/dt$:
\begin{equation}
\label{gauss-dcirc-bis}
\frac{d\Gamma}{dt}=-\delta^2\gamma^2\frac{\pi\omega_0^3 R^2}
{8\left(e^{1/2}-1\right)} t.
\end{equation}
This is plotted as the straight dashed magenta line in panel (b). It
coincides with the initially linear decrease in $d\Gamma/dt$.
Moreover, it shows that $\delta^{-4/3}\gamma^{-2}d\Gamma/dt$ should be
proportional to the scaled time $\delta^{2/3}t$, as observed. At
later times, $d\Gamma/dt$ is affected by magnetic diffusion, neglected
here. This arrests the change in circulation, ultimately reducing it
to near zero at late times.
This scaling is consistent with the early-time behaviour
described by \citet{gmt_2016}.
Next consider panels (c) and (d) for the circular vortex patch. In
(c), all of the results are plotted versus the unscaled time $t$ but
$d\Gamma/dt$ is scaled in such a way that the very early time
behaviour is closely similar: all 24 curves lie on top of each other
for $t<0.2$. In panel (d), we show that by plotting $d\Gamma/dt$
versus the scaled time $\delta^{1/2}t$ and appropriately scaling
$d\Gamma/dt$, the curves nearly collapse onto a single curve. Here
again only the three smallest $\delta$ values and the three smallest
$\gamma$ values are plotted. The collapse is not as good as for the
Gaussian vortex in panel (b), but nonetheless extends well into the
evolution, including the rebound after $\delta^{1/2}t=0.35$ (which is
much stronger than seen for the Gaussian vortex).
From the earliest time, diffusion plays an important role, and hence the
inviscid solution presented above for the Gaussian vortex does not
apply. Equation (\ref{gauss-dcirc}) is problematic for the vortex
patch, as the radial function there equals $-\omega_0 R \delta(r-R)$,
where here $\delta(s)$ is Dirac's delta function. In reality, $j$
immediately diffuses, and qualitatively should exhibit a
$1/\sqrt{\eta{t}}$ time dependence at $r=R$ based on the solution to
the heat equation. This would imply
\begin{equation}
\label{patch-dcirc}
\frac{d\Gamma}{dt} \sim -B_0^2 t \frac{\omega_0 R}{\sqrt{\eta t}}
\sim -\delta\gamma^2 \omega_0^2 R^2 \sqrt{\omega_0 t}
\end{equation}
(the constant of proportionality based on the solution of the heat
equation is $\sqrt{\pi}/8$). While this qualitatively explains the
observed nonlinear time dependence in $d\Gamma/dt$ in panels (a) and
(b), it represents only a crude fit. This is likely due to assuming
that $j$ evolves according to the heat equation while using the
inviscid solution for $A$. Nonetheless, (\ref{patch-dcirc}) explains
the dependence on $\delta\gamma^2$ exhibited in panel (c).
\begin{figure}
\begin{center}
\includegraphics[height = 0.333\textwidth]{jjcross.png}
\includegraphics[height = 0.333\textwidth]{atcross.png}
\end{center}
\caption{Scaled radial dependencies of $j$ and $\tilde{A}_\theta$
near the edge of a circular vortex patch, projected onto the
cosine and sine azimuthal modes (solid and dashed respectively)
at times $t=0.1$ (black), $0.2$ (blue) and $0.3$ (red). These
results are derived from a simulation starting from a circular
vortex patch with $\delta=0.0125$ and $\gamma=1$.}
\label{fig:cross}
\end{figure}
The actual radial cross sections of $j$ and $\tilde{A}_\theta$ near
the vortex edge, projected onto the $\cos(\theta-\bar\Omega t)$ and
$\sin(\theta-\bar\Omega t)$ azimuthal modes, are shown in
figure~\ref{fig:cross}. We find that the cosine projection of
$j$ indeed exhibits a roughly Gaussian dependence on $r-R$, while
the cosine projection of $\tilde{A}_\theta$ varies only weakly
across $r=R$. However, the sine projection of $\tilde{A}_\theta$
is a diffusive effect, and spoils any simple theoretical prediction
for $d\Gamma/dt$.
Finally, we remark that $|d\Gamma/dt|$ grows to much larger values for
the initially circular patch than for the Gaussian. As an example,
for the smallest $\delta$ and $\gamma$ values, the ratio in the
maximum values of $|d\Gamma/dt|$ is $6.45$. The circular patch
therefore is much more strongly affected by the magnetic field
than the Gaussian vortex.
\begin{figure}
\begin{center}
\includegraphics[height = 0.333\textwidth]{fig8a.png}
\includegraphics[height = 0.333\textwidth]{fig8b.png}
\end{center}
\caption{Scaled net reduction in circulation (a) for the initial
Gaussian vortex and (b) for the initial circular vortex patch,
as a function of $\delta$. The symbols indicate the value of
$\gamma$. In order of increasing $\gamma$, the symbols are
circle, triangle pointing down, triangle pointing up, square,
plus and diamond.}
\label{fig:netcirc}
\end{figure}
In nearly all simulations conducted for either vortex profile, the
circulation $\Gamma$ decreases and levels off at a nearly constant
value, particularly for small $\delta$ and $\gamma$ (when the vortex
is not greatly disrupted). The above scaling results can be used to
estimate the total reduction in circulation $\Delta\Gamma$. For the
initially Gaussian vortex, integrating $-d\Gamma/dt$ from $t=0$ to
$t\sim\delta^{-2/3}$ gives the estimate
$\Delta\Gamma\sim\delta^{2/3}\gamma^2$. This is shown to predict well
the actual change in circulation up to $t=0.5\delta^{-2/3}$, as shown
in panel (a) of figure~\ref{fig:netcirc}. We stress that, in order to
assess the ultimate role of the magnetic field in extracting
circulation from the vortex --- and therefore the ultimate fate of the
vortex, the {\it integrated} effects of the
Lorentz force must be calculated. The same integration for the patch
to $t=0.6\delta^{-1/2}$ gives the estimate
$\Delta\Gamma\sim\delta^{1/6}\gamma^2$. As seen in panel (b), this is
not accurate, and suggests that the dependence on $\gamma$ should be
different. However, by log-scaling the data and searching for best
fit curves, no simple relationship was found to collapse the data
significantly better than shown in panel (b). The circular vortex
patch is not nearly as simple as the Gaussian vortex.
\subsection{Initially elliptical vortex patches}
\begin{figure}
\begin{center}
\includegraphics[width = \textwidth]{fig9.pdf}
\end{center}
\caption{Vorticity $\omega({\boldsymbol x},t)$ and magnetic field lines at the
times indicated (top to bottom) for an initially elliptical vortex
with $\lambda=1/3,\,1$ and $3$ (left to right). The vorticity
colourbar is indicated next to each image. The contour interval for
$A+B_0 y$ is $0.04$ in all images.}
\label{fig:q512e}
\end{figure}
\begin{figure}
\begin{center}
\includegraphics[width = \textwidth]{fig9j.pdf}
\end{center}
\caption{As in figure~\ref{fig:q512e} but for the current density
$j({\boldsymbol x},t)$.}
\label{fig:j512e}
\end{figure}
We conclude this section by discussing the case of an initially
elliptical vortex patch whose boundary is given by
\begin{equation}
\label{epatch}
\frac{x^2}{a^2}+\frac{y^2}{b^2}=1
\end{equation}
with $\sqrt{ab}=R$ so that it has the same area for all aspect ratios
$\lambda=b/a$. One reason to study the ellipse is to understand the
role of the threading of the field lines in the subsequent evolution
of the vortex \citep[see e.g.][]{KSD_2008}.
Would a vortex threaded by more field lines
($\lambda>1$) be more affected by the magnetic field than one which is
threaded by fewer field lines ($\lambda<1$)? As a first qualitative
view, figures~\ref{fig:q512e} and \ref{fig:j512e} show the vorticity,
field lines and current density for three ellipses, with $\lambda=1/3$
(left), $\lambda=1$ (middle), $\lambda=3$ (right) --- all for
$\delta=0.025$ and $\gamma=1$. Note that an ellipse with
$\lambda<1/3$ or $\lambda>3$ is linearly unstable in the absence of a
magnetic field \citep{love_1893}. Here the field acts to circularise
the vortex. For both $\lambda=1/3$ and $\lambda=3$, the impact of the
field on the vortex is noticeably greater than for the circular
vortex, $\lambda=1$. It appears that $\lambda=3$ is most strongly
affected, but the argument that more field lines initially
threading the vortex
has a greater impact is clearly not correct. The circular vortex is
much less affected than the vortex with $\lambda=1/3$, which is
threaded by the fewest field lines.
\begin{figure}
\begin{center}
\includegraphics[width = \textwidth]{ellipse.pdf}
\end{center}
\caption{Accumulative diagnostics as a function of initial
vortex eccentricity ${\mathcal{E}}$. The diagnostics are
computed over $0\leq t \leq 10$ and show (a) the net circulation
reduction $\Delta\Gamma$, (b) the net growth in magnetic energy
$\Delta{E_b}$, (c) the net decline in kinetic energy
$\Delta{E_u}$, and (d) the net magnetic dissipation
$\eta\int_0^{10}\langle{j^2}\rangle\,dt$. All simulations
used the parameters $\delta=0.025$ and $\gamma=1$.}
\label{fig:ellipse}
\end{figure}
Instead, what appears to be important is the reach of the vortex in
sweeping through the background magnetic field. Then, both small and
large $\lambda$ would exhibit a similar behaviour, and would be more
affected than the circular vortex. This is borne out in
figure~\ref{fig:ellipse}, which plots various accumulative diagnostics
for over 200 simulations varying the vortex eccentricity
\begin{equation}
\label{eccen}
{\mathcal{E}}=\frac12\left(\lambda-\frac{1}{\lambda}\right)
\end{equation}
over the range $-15/8 \leq {\mathcal{E}} \leq 15/8$, corresponding to
$1/4 < \lambda < 4$. The results in figure~\ref{fig:ellipse} show that
the circular vortex is clearly anomalous. Yet, the circular vortex
also displays the greatest net reduction in circulation, despite
keeping it shape. Ellipses retain their initial circulation better,
not because they are less affected, but because the vorticity
production near the vortex edge is different: both increases and
decreases in vorticity occur within the vortex edge, whereas for a
circular vortex only decreases occur. This can be seen to some extent
in figure~\ref{fig:q512e}, where the plotted vorticity field levels
are higher for both $\lambda=1/3$ and $\lambda=3$ than for
$\lambda=1$. In short, the circulation changes occurring for
distorted vortices are more complex but tend to be weaker than those
occurring for an initially circular vortex.
Regarding the other diagnostics, there is very little dependence in
the gain in magnetic energy on vortex eccentricity, but a significant
dependence in the loss in kinetic energy. The initially circular
vortex exhibits the least loss in kinetic energy, consistent with the
images in figure~\ref{fig:q512e}, where the flow surrounding the
vortex is generally much less agitated compared with the elliptical
cases. Finally, the net magnetic dissipation is also weakest for the
initially circular vortex, consistent with the generally weaker field
of current density seen in the middle panels of
figure~\ref{fig:j512e}.
Finally, despite the fact that the ellipse is unstable for
$\lambda<1/3$ or $\lambda>3$ in the absence of a magnetic field, the
effect of the magnetic field in the examples shown (which here is not a
weak effect) dominates the flow evolution, rapidly causing the vortex to
become more circular in form. A weaker magnetic field might allow a
competition between the hydrodynamic instability and the action of the
field, but this is beyond the scope of the present study.
\section{Conclusions and Future Work}
In this paper we have examined the role of a weak magnetic field in
modifying Kelvin's circulation theorem in two-dimensional MHD at low
magnetic Prandtl number $Pm$. The circulation of the velocity field is
a materially conserved quantity in hydrodynamics and plays a key role
in determining the dynamics. That the magnetic field acts through the
Lorentz force to destroy these conservation properties is well known,
but quantifying the effect as a function of parameters (magnetic
diffusion and field strength) has hitherto not been achieved. We
consider three model flows that, in the absence of magnetic effects,
remain exact stable solutions of the two-dimensional Euler equations;
namely the Gaussian vortex, the circular vortex patch, and the
elliptical vortex patch.
As always in these situations, it appears as though the role of the
magnetic field is more subtle than first (or even second) imagined. As
noted by \citet{gmt_2016} the degree of circulation extracted from the
vortices {\it must} be determined via integrating the effects of the
Lorentz force over the entirety of the evolution, rather than by
hypothesising balances of crude instantaneous measures of the Lorentz
force, which will yield incorrect scalings. Furthermore, the roles of
diffusion and Lorentz force depend on the initial configuration of the
flow, with smooth vortices reacting rather differently from vortex
patches.
We note that the dynamics and role of the magnetic field is different at high $Rm$ fluids at low $Pm$ (such as astrophysical fluids) than it is for low $Rm$ fluids at low $Pm$ such as liquid metal experiments, and even some geophysical cases. The latter situation
can be investgated in detail, as then the Lorentz force that breaks Kelvin's theorem can be linearised about a background magnetic field. We are currently investigating the scalings that apply.
Although we have focussed on simple models with no background rotation
or stratification, it is clear that the results can (and should) be
extended to more geophysically and astrophysically relevant cases with
these included. Simple extensions that should be (and are being)
evaluated include incorporating rotation and stratification on
both a $\beta$-plane and a spherical surface. Here the key materially
conserved quantity is the absolute (potential) vorticity, which
includes the planetary and relative vorticity as well as density
variations. Since material conservation of this scalar field has a
significant effect on the dynamics (for example being implicated in
the formation of potential vorticity staircases, see
e.g.\ \cite{DM:2008}), then understanding the role of a magnetic field
in modifying this conservation property is an important next step in
understanding the dynamics of stably stratified magnetised
environments \citep[as described in][]{T_2005}.
\section*{Acknowledgements}
PHD and SMT would like to acknowledge the support of the Festival de Th\'eorie in Aix-en-Provence. Support for this research has come from the UK Engineering and Physical Research Council (grant nu. EP/H001794/1).
\bibliographystyle{jfm}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 2,286 |
Q: Вывод и замена элементов через react У меня есть отдельный js файл, в котором у меня храниться массив из объектов с данными.
const destination = [
{
id: 0,
title: "moon",
subtitle: "See our planet as you've never seen it before. A perfect relaxing trip away to help regain perspective and come back refreshed. While you're there, take in some history by visiting the Luna 2 and Apollo 11 landing sites.",
distance: "384,400 km",
travelTime: "3 days",
},
{
id: 1,
title: "mars",
subtitle: "Don't forget to pack your hiking boots. You'll need them to tackle Olympus Mons, the tallest planetary mountain in our solar system. It's two and a half times the size of Everest!",
distance: "225 mil. km",
travelTime: "9 months",
},
{
id: 2,
title: "europa",
subtitle: "The smallest of the four Galilean moons orbiting Jupiter, Europa is a winter lover's dream. With an icy surface, it's perfect for a bit of ice skating, curling, hockey, or simple relaxation in your snug wintery cabin.",
distance: "628 mil. km",
travelTime: "3 years",
},
];
export default destination;
И у меня есть отдельная страница, куда я должен выводить эти данные.
const Destination = () => {
return (
<main>
<div>
<button>moon</button>
<button>mars</button>
<button>europa</button>
</div>
<div>
<h1>Title</h1>
<p>subtitle</p>
</div>
</main>
);
};
Вопрос: У меня на странице 3 кнопки, подписаны соодветсвенно 1 - moon, 2 - mars, 3 - europa. Как мне сделать вывод только первого элемента, условно moon как стандартный, а при нажатии на 2 или 3 кнопку, контент с первой пропадал, и появлялся на 2 или 3 соответственно?
A: В React такой переключатель контента делается примерно следующим образом:
const Destination = () => {
const [dest, setDest] = useState(destination);
const [selection, setSelection] = useState(0);
return (
<main>
<div>
{dest?.map((it, idx) => <button onClick={() => setSelection(idx)}>{it.title}</button>)}
</div>
<div>
<h1>{dest[selection].title}</h1>
<p>{dest[selection].subtitle}</p>
</div>
</main>
);
};
Отрисовка кнопок должна идти с привязкой к текущему массиву, а не вбита "хардкорно".
Создаем кнопки из массива, кнопкам назначаем обработчик, который будет записывать в состояние выбранный номер элемента.
При изменении состояния, будет происходить ререндер компонента и будут выводиться данные выбранного элемента массива.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 7,684 |
Polycaena princeps är en fjärilsart som beskrevs av Charles Oberthür 1886. Polycaena princeps ingår i släktet Polycaena och familjen Riodinidae. Inga underarter finns listade i Catalogue of Life.
Källor
Äkta dagfjärilar
princeps | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 14 |
\section{Introduction}
\label{sec:intro}
The notion of (functional) safety is defined as a freedom from risk of damage to user, property or environment, and correct operation of a system in response to its inputs. Security, on the other hand, is the prevention of illegal access causing change and destruction of equipment, information and services~\cite{biro18a}. Traditionally, depending upon the domain and the background, software engineers mostly focused on designing systems, which are either safe or secure in nature. Typically, we find methods that investigate these concerns separately. While some exchange of ideas existed across these concerns, modern systems require their thorough, combined treatment since security concerns may affect safety and vice versa. This is particularly true for Cyber-Physical Systems or Internet of Things, whose components may be interconnected via the Internet and, hence, there is a good chance for safety concerns to be exposed and thus vulnerable to other types of failures caused by security attacks. Connected (and consequently exposed) safety systems must, therefore, be equipped with security mechanisms for protection against such attacks. Only recently, there has been a surge in research focusing on integrated modeling and development of safety and security systems~\cite{biro18a, wolf18a}.
Model-driven engineering~\cite{schmidt06a} is a development paradigm that focuses on creating models, which could be systematically transformed into (correct) pieces of software. The advantage is that developers can exclusively focus on modeling the problem rather than worrying about unnecessary and distracting implementation details. In that regards, model-driven engineering is appealing for addressing safety and security concerns where models play the integral role in describing and analyzing them.
Systematic mapping studies are meant to provide an overview of a research area through classification and counting contributions in relation to the categories of that classification. They involve searching the available literature in order to know what topics have been covered and where the corresponding papers have been published~\cite{petersen08a}. According to Kitchenham et al.~\cite{kitchenham10a}, the research questions in mapping studies are general as they aim to discover research trends (e.g., publication trends over time and topics covered in the literature). This is in contrast to systematic reviews, which intend to aggregate evidence and hence formulate a very specific goal (e.g., whether research results are practical and deployable for industry)~\cite{petersen15a}. The outcome of a mapping study is an inventory of publications on the selected topic mapped to a classification~\cite{wieringa05a}.
In this paper, we present a systematic mapping study on model-driven engineering of safety and security systems. The overall aim of this study is to collect relevant state-of-the-art in this field of research. Besides that, we answer some important questions like what are frequently used methods and tools in this field, what are their applicable development stages, and in which application domains they have been evaluated. We also identify where the community prefers to publish research results and what are recent publication trends in this field. We prudently select 95 publications out of 17,927 relevant search results through a rigorous and systematic process. These publications were proven very helpful in answering a set of six judiciously crafted research questions, providing gainful insights, and identifying the directions for future research.
The paper is organized as following: Sec.~\ref{sec:method} details the systematic mapping process including the research questions we investigate in this study. Sec.~\ref{sec:results} presents results of the mapping study. Sec.~\ref{sec:discussion} presents our analysis on the current state-of-the-art. Sec.~\ref{sec:threats} discusses the threats to validity of this study and the adopted mitigation strategies. The paper is concluded in Sec.~\ref{sec:conclusion}.
\section{Mapping study process}
\label{sec:method}
\paragraph{Time period}
We scope the time period of related studies published from 1992 to 2018. The earliest paper we could find in our mapping study was published in 1992, hence the starting time. We started this mapping study in December 2018, hence the ending time. Please note that we re-conducted the search in January 2019 in order to make sure that all results published until 2018 are included in our study.
\paragraph{Digital libraries}
Four digital libraries were used in this mapping study: ACM\footnote{\url{https://dl.acm.org}}, IEEE\footnote{\url{https://ieeexplore.ieee.org/Xplore/home.jsp}}, Springer\footnote{\url{https://link.springer.com}}, and Web of Science\footnote{\url{https://apps.webofknowledge.com}}. According to~\cite{chen10a}, these digital libraries are among the most popular sources in computer science and engineering that ensure a high coverage of potentially-relevant studies. Although Scopus\footnote{\url{https://www.scopus.com}} is also considered as an important source, it was not included in the study as it is not accessible in our institution. However, many venues indexed by Scopus are indexed by other included digital libraries as well. We did not include Google Scholar\footnote{\url{https://scholar.google.com}} in our mapping study as the search results of Google Scholar tend to be repetitive with respect to results from the included digital libraries, and its unique contribution to the search process is unclear~\cite{chen10a}.
\paragraph{Tool}
Conducting a systematic mapping study is a tedious and time consuming task. It usually involves search, collection, filtration, and classification of a huge amount of papers. Without a helping tool, this is a very difficult endeavor. In this work, we used Zotero~\cite{ahmed11a} and spreadsheets. These tools helped us in importing, organizing, and analyzing search results.
\subsection{Research questions}
The goal of this mapping study (following the guidelines presented in~\cite{kitchenham07b, petersen08a, petersen15a}) is to discover what is the current state-of-the-art in the field of model-driven engineering of safety and security systems (and how it can be advanced in the future). This goal leads to following precise research questions (RQs):
\begin{itemize}
\item RQ1: At which development stage the research was conducted?\\
Rationale: Model-driven engineering is a multi-stage development process. We want to know at which development stage this research was conducted. This information can help us identify which development stages are susceptible to be focused more for the engineering of such systems.
\item RQ2: Which methods and tools were employed during the research?\\
Rationale: The use of methods and tools is inevitable during any research and development activity. This information can help us identify what are frequently used methods and tools for the engineering of such systems.
\item RQ3: What is the classification of the contribution of the research?\\
Rationale: Through this question, we want to investigate what is the contribution type of articles. According to Wieringa et al.~\cite{wieringa05a}, contribution types refer to determining the type of intervention being studied. This could be a process, method,
model, tool, framework, etc.
\item RQ4: In which domain(s) research results were evaluated?\\
Rationale: Safety and security systems may belong to various application domains, e.g., railways, nuclear plants, and marine systems. By answering this question, we want to know what are the application domains in which the research results were evaluated. This information can help us identify which application domains have gained more interest of developers of such systems.
\item RQ5: Where the research was published? \\
Rationale: By answering this question, we want to find out whether researchers preferred to publish in journals, magazines, conferences, or workshops? Usually journals include more mature and concrete results, whereas conferences and workshops are targeted for timely discussion and early feedback. By answering this question, we can find out the maturity of results of this field.
\item RQ6: What is the research publication time-line and trend? \\
Rationale: Time-lines and publication trends tell us about novelty and frequency of research. By answering this question, we can find out how the community is building around this topic. Is the topic a relatively new one, gaining popularity in recent years, or just phasing out? This information can help us determine the potential of this research topic.
\end{itemize}
\subsection{Papers search and screening}
The mapping study was conducted in 6 steps as illustrated in Fig.~\ref{fig:approach}.
\begin{figure}
\centering
\includegraphics[width=0.5\linewidth]{Steps}
\caption{Steps for the search and selection process}
\label{fig:approach}
\end{figure}
\paragraph{Step 1 - Search in digital libraries}
The following query performed in aforementioned digital libraries produced 17,927 search results. Digital library-wise acquired results are shown in Tab.~\ref{tab:DLResults}.\\
\noindent \textit{(``model-driven'' OR ``model-based'') AND (``engineering'' OR ``development'') AND (``safety'' OR ``safe'') AND (``security'' OR ``secure'')}\\
The search terms were identified according to the study topic.
Similar to Kitchenam et al.~\cite{kitchenham07b}, we adopted the PICO (Population, Intervention, Comparison, Outcomes) criteria to formulate the search terms.
\begin{itemize}
\item Population: According to Kitchenam et al.~\cite{kitchenham07b}, population may refer to a specific software engineering role, a category of software engineers, an application area, or an industry group. In our case, population is the terms about ``safety/safe'' and ``security/secure''.
\item Intervention: According to Kitchenam et al.~\cite{kitchenham07b}, intervention may refer to a software methodology, a tool, a technology, or a procedure. In the context of this study, intervention includes terms ``model-driven'' or ``model-based''.
\item Comparison: The comparison part is not applicable in this mapping study because this mapping study does not involve the comparison of model-driven and other types of approaches.
\item Outcomes: Outcomes include the terms relevant to ``engineering'' or ``development'' activities.
\end{itemize}
We used the Boolean operator OR to join alternate words and synonyms in each part (i.e., population, intervention, outcomes), and the Boolean operator AND to join the terms from the three parts, respectively.
\begin {table}
\caption {Digital library-wise results distribution}
\label{tab:DLResults}
\begin{tabular}{|c|c|c|}
\hline
{\bf Digital library}& {\bf URL} & {\bf \# of results} \\
\hline
ACM & \url{dl.acm.org} & 193\\
\hline
IEEE Xplore & \url{ieeexplore.ieee.org} & 238 \\
\hline
Springer & \url{link.springer.com} & 17,383 \\
\hline
Web of Science & \url{apps.webofknowledge.com} & 113 \\
\hline
\bf{Total} & & {\bf 17,927}
\\
\hline
\end{tabular}
\end{table}
\paragraph{Step 2 - Inclusion and exclusion of results}
In order to make the study selection results objective, we defined selection criteria that were employed in the study selection process. The criteria is as following:
{\bf Inclusion criteria:}
\begin{itemize}
\item Peer-reviewed studies published in conferences, workshops, journals, magazines or books,
\item Studies classified as computer science publications, and
\item Studies published in the English language.
\end{itemize}
{\bf Exclusion criteria:}
\begin{itemize}
\item Studies published as courses or reference work entries,
\item Studies published in disciplines other than computer science,
\item Studies published in languages other than English, and
\item Studies presenting non-peer-reviewed results or gray literature.
\end{itemize}
In ACM and Web of Science digital libraries, the search process was simple. The basic search fields were enough to run the query, which required no further processing at this point. In the IEEE digital library, we had to use the advance search option. We wrote the query in the command search and obtained the results. The IEEE digital library also included courses on this topic in search results, which we excluded. We only included conferences, journals, magazines and early access articles. As shown in Tab.~\ref{tab:DLResults}, the Springer digital library produced the maximum amount of results. In order to focus on relevant results, we included only computer science publications, publications that were written in the English language, and publications that appeared as book chapters, conference papers or journal articles. We also excluded reference work entries from research results. This brought down the overall result count from 17,927 to 6,159 papers.
\paragraph{Step 3 - Meta-data lookup}
In this step, we carefully checked the available meta-data, e.g., keywords and abstracts, of results. We filtered out all those results, which were not explicitly focusing on safety and security. This brought down our results tally to 596.
\paragraph{Step 4 - Manual title search}
Despite the meta-data lookup, some publications could still be included in results, which are only remotely dealing with safety and security concerns. In order to ensure that the final result only includes high-quality relevant papers, we manually checked the title of each paper. We ensured that each paper title has something to do with both safety and security. As a result of this step, our result count became 44.
\paragraph{Step 5 - Check for duplicate results}
Once we individually checked results produced by each digital library, we merged all of them into a single repository. Since many digital libraries index same venues, the search results may be redundant. In order to have a list of only unique results, in this step we check the list of merged results for duplicates. All duplicates were consequently removed from the list of results and the publication count became 37.
\paragraph{Step 6 - Snowballing}
In this last step, we performed snowballing readings. In a snowballing reading, the lists of references of found papers are used to identify other relevant studies~\cite{wohlin14a}. We performed the backward snowballing, i.e., we went through lists of references of previously obtained papers and identified the potential relevant studies. For each paper identified for the possible inclusion, we applied the same criteria that were employed for the selection of papers in the first place. Then, we identified 58 further relevant studies in this step. After this, the final set of results reached the tally of 95 publications.
\subsection{Studies classification scheme}
The classification scheme used for this study follows a systematic process suggested by Petersen et al.~\cite{petersen08a, petersen15a}. We are using keywords as bases for studies classification. Initially, we read abstracts in order to find representative keywords and concepts. The set of extracted keywords from different studies are then unified in order to overview the nature and contribution of the research (e.g., as shown in Fig.~\ref{fig:methods}, different similar methods and tools are merged into a single category). This results into a set of categories which is representative of the underlying population. Sometimes meaningful keywords could not be extracted from the abstract alone. In such cases, either introduction and conclusion sections were studied, or complete papers were skimmed through. Upon selection of the final set of keywords, they are clustered and consequently used to form the categories. Where applicable, classifications were also based on the Software Engineering Body of Knowledge (SWEBOK)\footnote{\url{https://www.computer.org/education/bodies-of-knowledge/software-engineering}} structure (e.g., as shown in Fig.~\ref{fig:stages}, which are the main life-cycle activities of software engineering) or inspired from previous categorizations (e.g., as shown in Fig.~\ref{fig:category}, which is based on the work of Wieringa et al.~\cite{wieringa05a}).
In order to reduce any bias, we followed an iterative strategy. Initially, the first author classified all studies. The classifications were then reviewed by the second author and corrected, where necessary. In case of a disagreement, the third author independently reviewed the classification and gave his judgment. The opinion of majority prevailed. Although all authors of this paper are senior and experienced researchers, given the fact that this step involves human judgment, the threat of bias cannot be completely eradicated.
\subsection{Data extraction and synthesis}
To answer the RQs, we extracted specific data from selected publications. Tab.~\ref{tab:extractedItems} describes data items that have been extracted in this mapping study.
\begin {table}
\caption {Extracted research items}
\label{tab:extractedItems}
\begin{tabular}{|p{2cm}|p{4cm}|p{1.5cm}|}
\hline
{\bf Item name}& {\bf Description} & {\bf Relevant RQ} \\
\hline
Development stage & At which development stage was the approach applicable? & RQ1\\
\hline
Method/tool & What is the deployed method or tool? & RQ2\\
\hline
Contribution classification & What is the classification of contribution of the publication? & RQ3 \\
\hline
Application domain & Which application domain the study was applied to? & RQ4 \\
\hline
Publication type & In which publication type was the study published? & RQ5a\\
\hline
Publication venue & In which venue was the study published? & RQ5b\\
\hline
Publication year & In which year was the study published? & RQ6\\
\hline
\end{tabular}
\end{table}
Data synthesis targets to synthesize the extracted data to answer the RQs. The results of this task are discussed (also visually) in the following section.
\section{Mapping study results}
\label{sec:results}
In this section, we synthesize the extracted data to answer previously listed RQs.
\subsection{Development stages (RQ1)}
\label{subsec:stages}
As shown in Fig.~\ref{fig:stages}, only a few studies (4 out of 95) were covering the whole model-driven engineering spectrum, i.e., all development stages. Hassan et al.~\cite{hassan10a} were discussing the idea that how the Formal Analysis and Design for Engineering Security (FADES) approach can be used to support the model-based software engineering paradigm. Bloomfield et al.~\cite{bloomfield13a} use the structured safety cases approach to discuss the impact that security might have on an existing safety case. Apvrille et al.~\cite{apvrille16a} presented a similar idea based on the SysML-Sec environment covering all the development stages. However, all these studies did not use any application domain to evaluate the proposed approaches. The approach presented in~\cite{benyo16a}, on the other hand, discussed the design and development of a smart card application management infrastructure by specifying business and technological processes and associated security requirements.
Although the planning phase is very crucial for successful development of a system, very few studies (2 out of 95) have focused on this stage. In the first study, Park et al.~\cite{park16a} discuss how multi-agent systems and swarm intelligence can be exploited to boost counter-terrorism and public safety activities. In the second study, Park et al.~\cite{park16a} emphasize the idea of using cybersecurity considerations to make nuclear facilities even safer.
As anticipated, most of the studies (33 out of 95) were focusing at the level of requirements. 14~\cite{elliot95a, eames99a, novak07a, poslad09a, sun09a, pietre10b, amthor11a, oates13a, apvrille15a, hessami15a, troubitsyna16a, troubitsyna16b, brunner17a, ponsard18a} out of those 33 were focusing exclusively on requirements modeling of such systems. 16 studies~\cite{fischer10a, monakova12a, monakova12b, raspotnig12a, dong12a, kornecki13a, bieber14a, brunel15a, li15a, taguchi15a, ponsard16a, pereira17a, vistbakka17a, pawlik18a, troubitsyna18a, sangchoolie18a} were focusing on both requirements modeling and analysis. A few studies were either focusing solely on requirements analysis~\cite{pietre10a, roudier15a} or requirements traceability~\cite{katta13a}.
The architecture and design stage is of paramount importance in the development of any system; safety and security systems are no exceptions. 28 out of 95 studies were focusing on this stage. 4 out of those studies
~\cite{varrette09a, glasser10a, brunel14a, tverdyshev16a} were discussing architecture modeling. 10 studies~\cite{winther01a, preschern13a, steiner13a, kriaa14a, schmittner14a, woskowski14a, chen14a, macher15a, schmittner15a, subramanian16a} were discussing architecture analysis. 14 studies~\cite{glasser10b, jackson11a, banerjee12a, young13a, young14a, brunel14b, kriaa15b, chen15a, cimatti15a, schmittner16a, martin17a, hazell17a, amorim17a, friedberg17a} were discussing how to make architectural design of systems both safe and secure through modeling and analysis.
Testing also plays a pivotal role in systems development life-cycle. We found 3 studies focusing on testing in our mapping study. While Sojka et al.~\cite{sojka14a} were explicitly focusing on the testing of safety and security requirements within the automotive domain, Shahir et al.~\cite{shahir11a, shahir12a} were focusing on test case generation for safety and security of marine systems.
Development stages, such as implementation~\cite{kleidermacher12a, bagnara18a}, and deployment and reconfiguration~\cite{tariq18a}, were also mentioned in the literature, however, they were not the center of attention of researchers of this field.
A large amount of studies (22 out of 95) were not focusing on any development stage at all. They were either comparing safety and security concepts, e.g.,~\cite{burns92a}, discussing how one can help achieving the other, e.g.,~\cite{brewer93a}, making similarities and dissimilarities explicit between the two, e.g.,~\cite{blanquart12a}, analyzing how the two concepts can cross-fertilize each other, e.g.,~\cite{pietre13a}, etc.
\begin{figure}
\centering
\includegraphics[width=0.9\linewidth]{RQ1}
\caption{RQ1: Studies classification based on development stages}
\label{fig:stages}
\end{figure}
\subsection{Methods and tools (RQ2)}
\label{subsec:methods}
Fig.~\ref{fig:methods} graphically depicts the frequency of the applied methods and tools. Some approaches consisted of more than one method/tool. The methods whose use has been confined to only one study are being skipped here for the sake of brevity.
Our research shows that a multitude of methods and tools are being used in this field but none clearly stands out. Although there is an observable tendency among the community to use formal methods for such kind of engineering activities (23 studies are conducted using formal methods), yet no particular formal method can be classified as the method of choice. Among more frequently used formal methods, the use of Abstract State Machines has been found in five studies~\cite{glasser10a, glasser10b, jackson11a, shahir11a, shahir12a}, whereas the use of Event-B~\cite{troubitsyna16a, vistbakka17a, troubitsyna18a} and Alloy~\cite{brunel15a, brunel14a, brunel14b} has been mentioned in three studies apiece. However, please note that all applications of Abstract State Machines and Event-B method stemmed from single groups and targeted towards marine and industrial control systems, respectively.
The second most widely used set of techniques, after formal methods, was based on STAMP and its variants, i.e., STPA, STPA-Sec, and STPA-SafeSec (7 studies). Systems-Theoretic Accident Model and Processes (STAMP)~\cite{leveson03a} is an accident causality model based on systems theory and systems thinking. Systems-Theoretic Process Analysis (STPA)~\cite{ishimatsu10a} is a powerful hazard analysis technique based on STAMP. STPA-Sec~\cite{young14a} is a system-theoretic process analysis method explicitly focusing on security issues. STPA-SafeSec~\cite{friedberg17a} is an analysis methodology for both safety and security. The use of STAMP is mentioned in~\cite{troubitsyna16a}. The use of STPA is mentioned in~\cite{pereira17a}. The use of STPA-Sec is mentioned in~\cite{young13a, young14a, schmittner16a}. The use of STPA-SafeSec is mentioned in~\cite{friedberg17a}.
The use of UML and its variants, i.e., SysML and SysML-Sec is also relatively popular in this domain and has been found in 5 studies. The use of Unified Modeling Language (UML) is mentioned in~\cite{raspotnig12a}. The use of Systems Modeling Language (SysML) has been mentioned in~\cite{oates13a}. The use of SysML-Sec (an extended version of the SysML language to design safe and secure embedded systems) has been found in~\cite{apvrille15a, roudier15a, apvrille16a} .
Another approach relatively popular in this domain is based on Goal Structuring Notation (GSN) and safety cases. The use of these notations has been found in 4 studies. The use of GSN is mentioned in~\cite{preschern13a, troubitsyna16b, martin17a} and the use of safety cases is mentioned in~\cite{bloomfield13a, troubitsyna16b}.
Goal-oriented requirements engineering approaches, such as KAOS or NFR, also play an important role in this domain. Their use has been found in 4 studies. The use of Knowledge Acquisition in Automated Specification (KAOS) -- a goal-oriented requirements engineering approach -- has been found in~\cite{ponsard16a, ponsard18a}. The use of the Non-Functional Requirements (NFR) approach -- a goal-oriented technique that can be applied to determine the extent to which specific objectives are achieved by a design -- has been found in~\cite{kornecki13a, subramanian16a}.
Failure analysis is the process of collecting and analyzing data to determine the cause of a possible failure in a system. Failure analysis methods (e.g., FMEA, FMVEA, and FTA) are also commonly used in the engineering of safe and secure systems. Their use has been found in 4 studies. The use of Failure Mode and Effects Analysis (FMEA) is mentioned in~\cite{winther01a}. The use of Failure Mode, Vulnerabilities and Effects Analysis (FMVEA) -- a variant of FMEA -- has been found in~\cite{schmittner14a, schmittner15a}. The use of Fault Tree Analysis (FTA) has been found in~\cite{steiner13a}. An approach very similar to failure analysis is hazard analysis (e.g., HAZOP and CHASSIS). The use of hazard analysis approaches has been found in 3 studies, however, 2 of them were applied in combination with traditional failure analysis methods. The use of Hazard and Operability Study (HAZOP) in combination with FMEA is found in~\cite{winther01a} and in combination with Combined Harm Assessment of Safety and Security for Information Systems (CHASSIS) has been found in~\cite{katta13a}. The use of CHASSIS in combination with FMVEA has been found in~\cite{schmittner15a}.
Some researchers have also proposed different patterns in this domain, i.e., architectural safety patterns including security considerations~\cite{preschern13a}, safe \& sec case patterns~\cite{taguchi15a}, and systems engineering patterns for interlinking safety and security~\cite{amorim17a}.
There are many other methods and tools which have been used less frequently as compared to the aforementioned methods and tools. Following are the methods whose use has been found in 2 studies apiece. The use of AltaRica -- a high-level language designed for the modeling of systems -- has been mentioned in~\cite{bieber14a, brunel14b}. The use of Business Process Model and Notation (BPMN) -- a graphical representation for specifying business processes -- has been found in~\cite{monakova12a, monakova12b}. The use of Multi-Agent Systems (MAS) has been found in~\cite{poslad09a, park12a}. The use of Simulink -- a graphical programming environment for modeling, simulating and analyzing multi-domain dynamical systems -- has been found in~\cite{tariq18a, sangchoolie18a}. The use of the Spoofing, Tampering, Repudiation, Information Disclosure, Denial of Service (DoS), Elevation of Privilege (EoP) (STRIDE) approach -- a structured way to find security threats -- has been found in~\cite{preschern13a, macher15a}.
A large number of found studies (25) did not employ any particular method or tool in the conducted research. They were either characterizing the differences between safety and security, e.g.,~\cite{burns92a}, comparing the two approaches~\cite{raspotnig13a}, stressing the need of their integration, e.g.,~\cite{eames99a}, or demonstrating how they could possibly complement each other, e.g.,~\cite{brewer93a}.
\begin{figure}
\centering
\includegraphics[width=0.9\linewidth]{RQ2}
\caption{RQ2: Studies classification based on applied methods and tools}
\label{fig:methods}
\end{figure}
\subsection{Contribution classification (RQ3)}
\label{subsec:category}
As shown in Fig.~\ref{fig:category}, the contribution of a study can be classified into multiple categories. Most of the researchers were interested in deploying model-driven approaches for risk-related activities of safe and secure systems. 21 out of 95 studies focused on this aspect. While majority of researchers explicitly focused on risk analysis~\cite{winther01a, aven07a, young13a, brunel14b, brunel14a, kriaa14a, schmittner14a, young14a, macher15a, schmittner15a, kriaa15b, schmittner16a, martin17a, friedberg17a}, some also focused on risk assessment~\cite{bloomfield13a, katta13a, chen14a}, risk communication~\cite{fruth14a}, risk management~\cite{woskowski14a, hazell17a}, and risk modeling~\cite{sangchoolie18a}.
20 out of 95 publications~\cite{poslad09a, pietre10b, kornecki13a, steiner13a, bieber14a, brunel15a, sojka14a, nostro14a, chen15a, ponsard16a, troubitsyna16a, park16a, subramanian16a, troubitsyna16b, pereira17a, vistbakka17a, brunner17a, ponsard18a, troubitsyna18a, tariq18a} proposed an approach or a methodology based on an already existing method or tool. Their aim was to adapt an existing technology in such a way that it becomes exploitable for model-driven engineering of safety and security systems.
17 out of 95 studies belonged to the assorted class. We put those studies in this class which could not be classified otherwise. Most of these studies were either comparative or conceptual, i.e., some of them were comparing safety and security concepts, e.g.,~\cite{burns92a}, some of them were eliciting similarities and dissimilarities between the two concepts, e.g.,~\cite{blanquart12a}, some of them were arguing why the two concepts are vital for Cyber-Physical Systems and Internet of things, e.g.,~\cite{wolf17a}, some of them were aligning the two concepts with each other, e.g.,~\cite{skoglund18a}, etc.
10 out of 95 studies presented a framework, which could be useful in various phases of model-driven engineering of safety and security systems. These frameworks were based on either formal methods~\cite{sun09a, banerjee12a, dong12a, li15a}, SysML~\cite{oates13a}, or other various methods and tools~\cite{varrette09a, pietre10a, park12a, schmittner15b, benyo16a}.
9 out of 95 studies presented a model. The model could either be related to the collaborative modeling of safety and security properties~\cite{robinson-mallett14a}, a life-cycle model~\cite{novak07a, kleidermacher12a, kanamaru17a}, a process model~\cite{eames99a, raspotnig12a}, a reference model~\cite{pawlik18a}, or a business process model~\cite{monakova12a, monakova12b} for the development of safety and security systems.
8 out of 95 studies presented a language for the model-driven engineering of safety and security systems. The proposed languages were either formal languages~\cite{hassan10a, fischer10a, cimatti15a}, graphical modeling languages~\cite{apvrille15a, roudier15a, apvrille16a}, programming languages~\cite{bagnara18a}, or a language for presenting mishaps~\cite{stoneburner06a}.
Some researchers also presented some decision support systems~\cite{glasser10a, glasser10b, jackson11a, shahir11a, shahir12a}, patterns~\cite{preschern13a, taguchi15a, amorim17a}, and policies~\cite{amthor11a, tverdyshev16a} for the model-driven engineering of safety and security systems.
\begin{figure}
\centering
\includegraphics[width=0.9\linewidth]{RQ3}
\caption{RQ3: Studies classification based on contributions}
\label{fig:category}
\end{figure}
\subsection{Evaluation domains (RQ4)}
Fig.~\ref{fig:domains} graphically depicts the frequency of evaluation domains. Some publications used more than one domain for evaluation purposes. Domains confined to only one study are being skipped here for the sake of brevity.
Researchers dealing with safety and security were mostly interested in evaluating their proposed methodologies and tools in the automotive domain. 18~\cite{steiner13a, schmittner14a, sojka14a, robinson-mallett14a, apvrille15a, macher15a, roudier15a, schmittner15b, schmittner15a, ponsard16a, schmittner16a, schoitsch16a, amorim17a, martin17a, brunner17a, huber18a, skoglund18a, sangchoolie18a} studies were applied to automotive systems.
After automotive systems, researchers of this field were mostly interested in applying their methods and tools in control systems. 13 studies were applied to control systems. Control systems included general-purpose control systems~\cite{young13a, kleidermacher12a}, air traffic control systems~\cite{eames99a, raspotnig12a, katta13a}, access control systems~\cite{amthor11a}, industrial control systems~\cite{oates13a, kriaa15a, kriaa15b, troubitsyna16a, tverdyshev16a, vistbakka17a}, and network control systems~\cite{troubitsyna18a}.
After control systems, avionics and railway domains were most attractive for researchers of this topic. Both domains were used as a testbed in 6 studies apiece. The avionics domain has been featured in~\cite{banerjee12a, bieber14a, brunel14b, brunel14a, nostro14a, pereira17a}. Whereas, the railway domain has been featured in~\cite{winther01a, dong12a, hessami15a, pawlik17a, pawlik18a, ponsard18a}.
The use of marine systems as an evaluation domain has been mentioned in 5 studies~\cite{glasser10a, glasser10b, jackson11a, shahir11a, shahir12a}. However, an interesting point to note is that all of these publications stemmed from a single group applying a particular method: Abstract State Machines.
Automation and pipeline systems were mentioned in 4 studies each. Automation systems were further classified into building automation systems~\cite{novak07a, sun09a}, electrical substation automation systems~\cite{preschern13a}, and industrial automation systems~\cite{fruth14a}. Pipeline systems, on the other hand, were mainly dealing with the oil industry~\cite{kornecki13a, kriaa14a, li15a, subramanian16a}.
Business, medical, nuclear, and power grid systems have been used as an evaluation domain in 3 publications each. The use of business systems, mainly enterprise resource planning systems, has been mentioned in~\cite{fischer10a, monakova12a, monakova12b}. The use of medical systems has been mentioned in~\cite{varrette09a, banerjee12a, woskowski14a}. The use of nuclear systems has been mentioned in~\cite{pietre10a, chen14a, park16a}. The use of power grid systems has been mentioned in~\cite{pietre10a, friedberg17a, tariq18a}.
The use of defense~\cite{cimatti15a}, fire detection~\cite{brunel15a}, rescue~\cite{park12a}, road transportation~\cite{chen15a}, smart card~\cite{benyo16a}, and virtual organization~\cite{poslad09a} systems has been mentioned only once in the found literature.
As aforementioned in Sec.~\ref{subsec:methods}, many found studies did not employ any particular method or tool in their research. These studies were either characterizing the differences between safety and security or stressing the need of their integration. Naturally, such comparative or road-map studies were not always subject to evaluation. Consequently, a large number of studies (23) we found were not evaluated on any particular domain.
\begin{figure}
\centering
\includegraphics[width=0.9\linewidth]{RQ4}
\caption{RQ4: Studies classification based on evaluation domains}
\label{fig:domains}
\end{figure}
\subsection{Publication types and venues (RQ5)}
\paragraph{Publication types (RQ5a)}
In this study, only peer-reviewed publications (including books, journals, magazines, conferences and workshops) were considered. Fig.~\ref{fig:venues} provides an overview of the distribution of studies between these venues. An overwhelming majority of studies (64/95) were published in conferences followed by journals and workshops, respectively.
\begin{figure}
\centering
\includegraphics[width=0.9\linewidth]{RQ5a}
\caption{RQ5a: Studies classification based on publication types}
\label{fig:venues}
\end{figure}
\paragraph{Publication venues (RQ5b)}
Looking at mapping study results, it was clear which venues were mostly targeted by researchers of this domain. The top seven venues for this domain are shown in Fig~\ref{fig:topvenues}. The most favorite venue of researchers of this topic is undoubtedly the Conference on Computer Safety, Reliability, and Security (Safecomp). 21~\cite{eames99a, winther01a, bieber14a, brunel14a, fruth14a, kriaa14a, schmittner14a, woskowski14a, macher15a, cimatti15a, schmittner15b, taguchi15a, ponsard16a, schmittner16a, troubitsyna16a, amorim17a, martin17a, pereira17a, huber18a, skoglund18a, troubitsyna18a} out of 95 studies are published on this venue. Conference on Intelligence and Security Informatics (ISI)~\cite{glasser10b, jackson11a, shahir11a}, Proceedings of the IEEE~\cite{banerjee12a, wolf17a, tariq18a}, and Journal on Reliability Engineering \& Systems Safety~\cite{aven07a, pietre13a, kriaa15a} contained 3 publications each. Conference on Critical Information Infrastructures Security (CRITIS)~\cite{tverdyshev16a, chockalingam17a}, Journal on Security Informatics~\cite{park12a, shahir12a}, and Workshop on Software Engineering for Resilient Systems (SERENE)~\cite{bloomfield13a, vistbakka17a} hosted 2 papers apiece. All other venues had only 1 publication each.
\begin{figure}
\centering
\includegraphics[width=0.9\linewidth]{RQ5b}
\caption{RQ5b: Studies classification based on top publication venues}
\label{fig:topvenues}
\end{figure}
\subsection{Publication time-line and trend (RQ6)}
Fig.~\ref{fig:trend} shows the time-line and trend of publications in this area. As per our findings, the first study explicitly focusing on safety and security together was published in 1992~\cite{burns92a}. While the interest in this area was moderately increasing until 2011, a significant increase can be observed in 2012 onwards reaching its top in 2015. Since then, like a typical hype cycle, the community is perhaps slowly climbing the ``slope of enlightenment'' towards the ``plateau of productivity''. Nonetheless, the increase in the number of publications indicates that the area is considered highly relevant by the software engineering research community.
\begin{figure}
\centering
\includegraphics[width=0.9\linewidth]{RQ6}
\caption{RQ6: Studies classification based on publication time-line and trend}
\label{fig:trend}
\end{figure}
\section{Discussion}
\label{sec:discussion}
Regarding RQ1, we have found that majority of researchers are working at the level of requirements or architecture. Modeling and analysis activities are the primary focus at both these levels. Only few researchers are considering the whole model-driven engineering spectrum (i.e., all development life-cycle activities). While modeling and analysis of requirements and designs are important activities, it is also imperative to ensure that these models are eventually translated into implementations as seamlessly as possible. Detailed works showing such transformations are currently missing from the state-of-the-art and worth exploring in the future. Another important point we have observed in found studies is that testing is not a primary focus of researchers of this field. Although the code generated through a rigorous development process is, in principle, already verified and validated, this is not enough in case of critical systems. For such systems, the generated code also needs to be tested~\cite{bonfanti18a}. In our opinion, researchers of this field should also give priority to testing as it uncovers different set of problems than those found in earlier stages of development, e.g., if the code is later manually modified in order to introduce further implementation details, the designer can use tests in order to check that no faults are introduced inadvertently.
Regarding RQ2, we have found out that no single method or tool is prevalent in this domain. Although the use of formal approaches is common (which, by the way, makes perfect sense given the critical nature of safety and security systems), no particular formal method stands out. Formal methods, such as Abstract State Machines or Event-B, have been used in design and development of many systems. However, the use of these methods often stems from particular groups. The use of the STAMP method -- originally proposed for the safety domain -- also looks promising in this field and several variants of STAMP have recently been proposed to extend its capability towards security systems. However, it needs to be applied to more domains and projects before its actual suitability for safety and security systems can be truly evaluated. Additionally, the current use of this method is also confined to modeling and analysis of requirements and design artifacts. In the future, application of this method (by extension) to other stages of development could be an interesting topic of research. The use of graphical modeling languages, such as UML or SysML, is certainly lacking behind in this field. Even the applied work is mostly concentrated on modeling and analysis of requirements. Given the potential of these languages, there could be a niche for their users to demonstrate their effectiveness through their widespread applications to safety and security systems.
Regarding RQ3, we have found out that most researchers were interested in risk analysis of such systems. Risk analysis is a crucial activity in the domain of safety. This becomes even more crucial when safety is integrated with security. Variety of methods were used for risk analysis and mostly researchers worked at the architecture and design level. While hazard analysis (e.g., HAZOP) and failure analysis (e.g., FMEA or FTA) are already established methods for risk analysis, new approaches, such as FMVEA, STPA-SafeSec or SAHARA, are also emerging recently. Working towards maturity and improvement of these approaches by their further application to new domains and projects is also an exciting research topic. Another interesting observation we made was that most researchers are extending the capabilities of existing methods and tools to solve the challenges of this field (e.g., FMVEA is based on well-established FMEA or STPA-SafeSec is based on popular STPA) rather than presenting new frameworks and languages. Of course, new pertinent frameworks (e.g., SAFESCALE~\cite{varrette09a}) or languages (e.g., FADES~\cite{hassan10a}) are also surfacing, but relatively low in number.
Regarding RQ4, we have found out that most researchers used the automotive domain to evaluate their results. This is consistent with the emerging phenomenon of autonomous driving where both safety and security play equally critical roles. However, the prominence of research in model-driven engineering for the automotive domain predates autonomous driving and has more to do with the adoption of this paradigm by the automotive industry~\cite{broy12a}. Control systems were also a favorite testbed for the evaluation of such systems.
Regarding RQ5, we have found out that most researchers preferred to publish their results in conferences and especially in SAFECOMP (International Conference on Computer Safety, Reliability and Security). Articles appearing in journals were not only less in numbers but also distributed among different venues. The numbers indicate that this research field is still (relatively) young and evolving.
Regarding RQ6, we have found out that the interest of community is increasing in this research field. In past few years, more and more publications are appearing explicitly focusing on the model-driven engineering of safety and security systems.
We have observed in our research that a significant amount of publications did not mention any development stage, method, or evaluation domain in their results. This is mainly due to the fact that these publications were stressing the need of joint modeling and development of safety and security by either comparing the two concepts, discussing how one can help achieving the other, or analyzing how the two concepts can cross-fertilize each other. Naturally, such conceptual and road-map studies were not subject to classification in respective RQs.
In the end, we would like to express that, in our opinion, state-based formal methods\footnote{a primer on state-based formal methods is available in~\cite{mashkoor18a}} supporting the ``correct-by-construction'' development approach seem to be quite suitable for engineering of such kind of systems: they cover all stages of development life-cycle, variety of modeling and analysis tools are available at the disposal of developers, quality assurance is embedded within the development process, there is a support for translation of requirements and design artifacts into correct pieces of software, etc. The catch is that state-based formal models may be opaque, i.e., hard to read and write for many stakeholders~\cite{kossak16a, kossak14c}. In this case, such developments can be augmented by using graphical modeling notations such as UML or SysML. This not only provides cross-fertilization among various modeling tools but also enables developers to harness the true potential of each tool at the suitable development stage. Some tools (e.g., UML-B~\cite{snook06a}) and approaches (e.g., KAOS-Event-B~\cite{mashkoor10a}) already exist and worth exploring in this regard. As far as risk analysis is concerned, which generally does not fall within the jurisdiction of formal methods, further research is required towards its harmonization with formal methods such as shown by Khan et al.~\cite{khan18a}. Another problem with state-based formal methods is that while they offer effective tools for verification and validation, the support for automatic code generation is far from desirable~\cite{mashkoor16c}. These methods can, in principle, generate code artifacts from models, however, the generated code needs a lot of manual post processing. This may introduce some inconsistencies or errors in code, which may, in turn, compromise the integrity of previously applied rigorous quality assurance process. This also makes systems susceptible to extensive testing, which is already a weak link in the development chain of such systems. Hence, future methods for model-driven engineering of safety and security systems need to offer better tools and methodologies, especially for code generation and testing, respectively.
\section{Threats to validity}
\label{sec:threats}
There is always a threat of validity for such kind of research. We also face a number of threats in our systematic mapping process, which we discuss as following.
The first threat is related to research questions: are they the right kind of questions we should be asking? To minimize this threat, we judiciously crafted the questions in alignment with the overall aim of this work after having several internal discussions. The final set of research questions indeed reflect the goals of our work.
The second threat is related to the terms used in search queries. To minimize this threat, we adopted the PICO (Population, Intervention, Comparison, Outcomes) criteria~\cite{kitchenham07b} to formulate the search terms. The selected terms unequivocally represents the goals of our work. An associated issue corresponds to the frequently used acronyms for model-based/driven engineering. Although the query used did not explicitly include related acronyms, such as MDE (model-driven engineering), MDD (model-driven development), or MBSE (model-based software engineering), this would not result in missing relevant articles because such information is usually available (or redundant) in meta-data, e.g., keywords or index terms, hence accessible.
The third threat is regarding the source of the data. We used four digital libraries as a primary source for this research. All selected digital libraries are well known in the computer science discipline for including most relevant results~\cite{dyba07a}. Although Scopus is also considered as an important source, it was not included in the study due to its inaccessibility at our research institute. However, many venues indexed by Scopus are already indexed by other considered digital libraries. Additionally, Wohlin et al.~\cite{wohlin13a} state that having a larger set of papers is not necessarily better for mapping studies. The important thing is that found studies are a good representation of the population, which we ensured in this study by adopting a rigorous paper selection process.
The fourth threat is regarding the quality assessment. As found by Petersen et al.~\cite{petersen15a}, quality assessment is not common in mapping studies. This is also consistent with suggestions of Kitchenham et al.~\cite{kitchenham10a}, which state that quality assessment is not essential for mapping studies as their overall aim is to give a broad overview of the topic area. However, despite these observations, we have adopted a rigorous process for inclusion/exclusion and classification of papers, which ensures that only high-quality related papers are selected as primary studies.
\section{Conclusion}
\label{sec:conclusion}
In this paper, we have presented a systematic mapping study on model-driven engineering of safety and security systems. Our mapping study provides an overview of the current state-of-the-art in this field. Through a rigorous and systematic process, this study carefully selected 95 publications out of 17,927 relevant search results, which proved very helpful in answering the judiciously crafted research questions like what are the frequently used methods and tools, what are the applicable development stages, and what are the evaluation domains. Additionally, we identified the community's preference for publication venues and publication trends. Based on analysis of selected studies, we indicated several avenues for future research.
The current state-of-the-art provides effective support for modeling and analysis of requirements and design of safety and security systems. However, the state-of-the-art needs to be advanced in order to offer better tools and methodologies especially for code generation and testing, respectively. Better integration of graphical modeling languages with conventional formal notations and better harmonization of rigorous methods and risk analysis approaches will also help in this regard. We also welcome more studies encapsulating the whole spectrum of model-driven engineering applied to safety and security systems.
In the future,
we want to extend this study by asking qualitative questions like what is the maturity level of the presented contribution, how useful it is for the given task, which impetuses are required as input, and whether the contribution is applicable at the design time (static) or the runtime (dynamic).
\section*{Acknowledgement}
The research presented in this technical report has been partly funded by the LIT Secure and Correct Systems Laboratory and the Austrian Ministry for Transport, Innovation and Technology (BMVIT), the Federal Ministry for Digital and Economic Affairs (BMDW), and the Province of Upper Austria in the frame of the COMET - Competence Centers for Excellent Technologies - program managed by the Austrian Research Promotion Agency FFG.
| {
"redpajama_set_name": "RedPajamaArXiv"
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+----------------------------------------------------------+
Machinery's Reference Series
Each Number Is a Unit in a Series on Electrical and
Steam Engineering Drawing and Machine
Design and Shop Practice
NUMBER 70
STEAM ENGINES
CONTENTS
Action of Steam Engines 3
Rating and General Proportions of Steam Engines 11
Steam Engine Details 15
Steam Engine Economy 30
Types of Steam Engines 36
Steam Engine Testing 41
Copyright, 1911, The Industrial Press, Publishers of MACHINERY,
49-55 Lafayette Street, New York City.
CHAPTER I
ACTION OF STEAM ENGINES
A steam engine is a device by means of which _heat_ is transformed into
_work_. Work may be defined as the result produced by a force acting
through space, and is commonly measured in foot-pounds; a foot-pound
represents the work done in raising 1 pound 1 foot in height. The rate
of doing work is called _power_. It has been found by experiment that
there is a definite relation between heat and work, in the ratio of 1
thermal unit to 778 foot-pounds of work. The number 778 is commonly
called the heat equivalent of work or the mechanical equivalent of heat.
Heat may be transformed into mechanical work through the medium of
steam, by confining a given amount in a closed chamber, and then
allowing it to expand by means of a movable wall (piston) fitted into
one side of the chamber. Heat is given up in the process of expansion,
as shown by the lowered pressure and temperature of the steam, and work
has been done in moving the wall (piston) of the closed chamber against
a resisting force or pressure. When the expansion of steam takes place
without the loss of heat by radiation or conduction, the relation
between the pressure and volume is practically constant; that is, if a
given quantity of steam expands to twice its volume in a closed chamber
of the kind above described, its final pressure will be one-half that of
the initial pressure before expansion took place. A pound of steam at an
absolute pressure of 20 pounds per square inch has a volume of
practically 20 cubic feet, and a temperature of 228 degrees. If now it
be expanded so that its volume is doubled (40 cubic feet), the pressure
will drop to approximately 10 pounds per square inch and the temperature
will be only about 190 degrees. The drop in temperature is due to the
loss of heat which has been transformed into work in the process of
expansion and in moving the wall (piston) of the chamber against a
resisting force, as already noted.
Principle of the Steam Engine
The steam engine makes use of a closed chamber with a movable wall in
transforming the heat of steam into mechanical work in the manner just
described. Fig. 1 shows a longitudinal section through an engine of
simple design, and illustrates the principal parts and their relation to
one another.
The cylinder _A_ is the closed chamber in which expansion takes place,
and the piston _B_, the movable wall. The cylinder is of cast iron,
accurately bored and finished to a circular cross-section. The piston is
carefully fitted to slide easily in the cylinder, being made practically
steam tight by means of packing rings. The work generated in moving the
piston is transferred to the crank-pin _H_ by means of the piston-rod
_C_, and the connecting-rod _F_. The piston-rod passes out of the
cylinder through a stuffing box, which prevents the leakage of steam
around it. The cross-head _D_ serves to guide the piston-rod in a
straight line, and also contains the wrist-pin _E_ which joins the
piston-rod and connecting-rod. The cross-head slides upon the
guide-plate _G_, which causes it to move in an accurate line, and at the
same time takes the downward thrust from the connecting-rod.
The crank-pin is connected with the main shaft _I_ by means of a crank
arm, which in this case is made in the form of a disk in order to give a
better balance. The balance wheel or flywheel _J_ carries the crank past
the dead centers at the ends of the stroke, and gives a uniform motion
to the shaft. The various parts of the engine are carried on a rigid bed
_K_, usually of cast iron, which in turn is bolted to a foundation of
brick or concrete. The power developed is taken off by means of a belted
pulley attached to the main shaft, or, in certain cases, in the form of
electrical energy from a direct-connected dynamo.
[Illustration: Fig. 1. Longitudinal Section through the Ames High-speed
Engine]
When in action, a certain amount of steam (1/4 to 1/3 of the total
cylinder volume in simple engines) is admitted to one end of the
cylinder, while the other is open to the atmosphere. The steam forces
the piston forward a certain distance by its direct action at the boiler
pressure. After the supply is shut off, the forward movement of the
piston is continued to the end of the stroke by the expansion of the
steam. Steam is now admitted to the other end of the cylinder, and the
operation repeated on the backward or return stroke.
An enlarged section of the cylinder showing the action of the valve for
admitting and exhausting the steam is shown in Fig. 2. In this case the
piston is shown in its extreme backward position, ready for the forward
stroke. The steam chest _L_ is filled with steam at boiler pressure,
which is being admitted to the narrow space back of the piston through
the valve _N_, as indicated by the arrows. The exhaust port _M_ is in
communication with the other end of the cylinder and allows the piston
to move forward without resistance, except that due to the piston-rod,
which transfers the work done by the expanding steam to the crank-pin.
The valve _N_ is operated automatically by a crank or eccentric attached
to the main shaft, and opens and closes the supply and exhaust ports at
the proper time to secure the results described.
Work Diagram
Having discussed briefly the general principle upon which an engine
operates, the next step is to study more carefully the transformation of
heat into work within the cylinder, and to become familiar with the
graphical methods of representing it. Work has already been defined as
the result of force acting through space, and the unit of work as the
foot-pound, which is the work done in raising 1 pound 1 foot in height.
For example, it requires 1 x 1 = 1 foot-pound to raise 1 pound 1 foot,
or 1 x 10 = 10 foot-pounds to raise 1 pound 10 feet, or 10 x 1 = 10
foot-pounds to raise 10 pounds 1 foot, or 10 x 10 = 100 foot-pounds to
raise 10 pounds 10 feet, etc. That is, the product of weight or force
acting, times the distance moved through, represents work; and if the
force is taken in pounds and the distance in feet, the result will be in
foot-pounds. This result may be shown graphically by a figure called a
work diagram.
[Illustration: Fig. 2. Section of Cylinder, showing Slide Valve]
In Fig. 3, let distances on the line _OY_ represent the force acting,
and distances on _OX_ represent the space moved through. Suppose the
figure to be drawn to such a scale that _OY_ is 5 feet in height, and
_OX_ 10 feet long. Let each division on _OY_ represent 1 pound pressure,
and each division on _OX_ 1 foot of space moved through. If a pressure
of 5 pounds acts through a distance of 10 feet, then an amount of 5 x 10
= 50 foot-pounds of work has been done. Referring to Fig. 3, it is
evident that the height _OY_ (the pressure acting), multiplied by the
length _OX_ (the distance moved through), gives 5 x 10 = 50 square feet,
which is the area of the rectangle _YCXO_; that is, the area of a
rectangle may represent work done, if the height represents a force
acting, and the length the distance moved through. If the diagram were
drawn to a smaller scale so that the divisions were 1 inch in length
instead of 1 foot, the area _YCXO_ would still represent the work done,
except each square inch would equal 1 foot-pound instead of each square
foot, as in the present illustration.
[Illustration: Fig. 3. A Simple Work Diagram]
In Fig. 4 the diagram, instead of being rectangular in form, takes a
different shape on account of different forces acting at different
periods over the distance moved through. In the first case (Fig. 3), a
uniform force of 5 pounds acts through a distance of 10 feet, and
produces 5 x 10 = 50 foot-pounds of work. In the second case (Fig. 4),
forces of 5 pounds, 4 pounds, 3 pounds, 2 pounds, and 1 pound, act
through distances of 2 feet each, and produce (5 x 2) + (4 x 2) + (3 x
2) + (2 x 2) + (1 x 2) = 30 foot-pounds. This is also the area, in
square feet, of the figure _Y54321XO_, which is made up of the areas of
the five small rectangles shown by the dotted lines. Another way of
finding the total area of the figure shown in Fig. 4, and determining
the work done, is to multiply the length by the average of the heights
of the small rectangles. The average height is found by adding the
several heights and dividing the sum by their number, as follows:
5 + 4 + 3 + 2 + 1
----------------- = 3, and 3 x 10 = 30 square feet, as before.
5
[Illustration: Fig. 4. Another Form of Work Diagram]
This, then, means that the average force acting throughout the stroke is
3 pounds, and the total work done is 3 x 10 = 30 foot-pounds.
In Fig. 5 the pressure drops uniformly from 5 pounds at the beginning to
0 at the end of the stroke. In this case also the area and work done are
found by multiplying the length of the diagram by the average height, as
follows:
5 + 0
----- x 10 = 25 square feet,
2
or 25 foot-pounds of work done.
[Illustration: Fig. 5. Work Diagram when Pressure drops Uniformly]
The object of Figs. 3, 4 and 5 is to show how foot-pounds of work may be
represented graphically by the areas of diagrams, and also to make it
clear that this remains true whatever the form of the diagram. It is
also evident that knowing the area, the average height or pressure may
be found by dividing by the length, and _vice versa_.
Fig. 6 shows the form of work diagram which would be produced by the
action of the steam in an engine cylinder, if no heat were lost by
conduction and radiation. Starting with the piston in the position shown
in Fig. 2, steam is admitted at a pressure represented by the height of
the line _OY_. As the piston moves forward, sufficient steam is admitted
to maintain the same pressure. At the point _B_ the valve closes and
steam is cut off. The work done up to this time is shown by the
rectangle _YBbO_. From the point _B_ to the end of the stroke _C_, the
piston is moved forward by the expansion of the steam, the pressure
falling in proportion to the distance moved through, until at the end of
the stroke it is represented by the vertical line _CX_. At the point _C_
the exhaust valve opens and the pressure drops to 0 (atmospheric
pressure in this case).
As it is always desirable to find the work done by a complete stroke of
the engine, it is necessary to find the average or mean pressure acting
throughout the stroke. This can only be done by determining the area of
the diagram and dividing by the length of the stroke. This gives what is
called the mean ordinate, which multiplied by the scale of the drawing,
will give the mean or average pressure. For example, if the area of the
diagram is found to be 6 square inches, and its length is 3 inches, the
mean ordinate will be 6 / 3 = 2 inches. If the diagram is drawn to such
a scale that 1 inch on _OY_ represents 10 pounds, then the average or
mean pressure will be 2 x 10 = 20 pounds, and this multiplied by the
actual length of the piston stroke will give the work done in
foot-pounds. The practical application of the above, together with the
method of obtaining steam engine indicator diagrams and measuring the
areas of the same, will be taken up in detail under the heading of Steam
Engine Testing.
Definitions Relating to Engine Diagrams
Before taking up the construction of an actual engine diagram, it is
first necessary to become familiar with certain terms which are used in
connection with it.
[Illustration: Fig. 6. The Ideal Work Diagram of a Steam Engine]
_Cut-off._--The cut-off is the point in the stroke at which the
admission valve closes and the expansion of steam begins.
_Ratio of Expansion._--This is the reciprocal of the cut-off, that is,
if the cut-off is 1/4, the ratio of expansion is 4. In other words, it
is the ratio of the final volume of the steam at the end of the stroke
to its volume at the point of cut-off. For example, a cylinder takes
steam at boiler pressure until the piston has moved one-fourth the
length of its stroke; the valve now closes and expansion takes place
until the stroke is completed. The one-fourth cylinderful of steam has
become a cylinderful, that is, it has expanded to four times its
original volume, and the ratio of expansion is said to be 4.
_Point of Release._--This is the point in the stroke at which the
exhaust valve opens and relieves the pressure acting on the piston. This
takes place just before the end of the stroke in order to reduce the
shock when the piston changes its direction of travel.
_Compression._--This acts in connection with the premature release in
order to reduce the shock at the end of the stroke. During the forward
stroke of an engine the exhaust valve in front of the piston remains
open as shown in Fig. 2. Shortly before the end of the stroke this
closes, leaving a certain amount of steam in the cylinder. The
continuation of the stroke compresses this steam, and by raising its
pressure forms a cushion, which, in connection with the removal of the
pressure back of the piston by release, brings the piston to a stop and
causes it to reverse its direction without shock. High-speed engines
require a greater amount of compression than those running at low speed.
_Clearance_.--This is the space between the cylinder head and the piston
when the latter is at the end of its stroke; it also includes that
portion of the steam port between the valve and the cylinder. Clearance
is usually expressed as a percentage of the piston-displacement of the
cylinder, and varies in different types of engines. The following table
gives approximate values for engines of different design.
TABLE I. CLEARANCE OF STEAM ENGINES
Type of Engine Per Cent Clearance
Corliss 1.5 to 3.5
Moderate-speed 3 to 8
High-speed 4 to 10
A large clearance is evidently objectionable because it represents a
space which must be filled with steam at boiler pressure at the
beginning of each stroke, and from which but a comparatively small
amount of work is obtained. As compression increases, the amount of
steam required to fill the clearance space diminishes, but on the other
hand, increasing the compression reduces the mean effective pressure.
_Initial Pressure._--This is the pressure in the cylinder up to the
point of cut-off. It is usually slightly less than boiler pressure owing
to "wire-drawing" in the steam pipe and ports.
_Terminal Pressure._--This is the pressure in the cylinder at the time
release occurs, and depends upon the initial pressure, the ratio of
expansion, and the amount of cylinder condensation.
_Back Pressure._--This is the pressure in the cylinder when the exhaust
port is open, and is that against which the piston is forced during the
working stroke. For example, in Fig. 2 the small space at the left of
the piston is filled with steam at initial pressure, while the space at
the right of the piston is exposed to the back pressure. The working
pressure varies throughout the stroke, due to the expansion of the
steam, while the back pressure remains constant, except for the effect
of compression at the end of the stroke. The theoretical back pressure
in a non-condensing engine (one exhausting into the atmosphere) is that
of the atmosphere or 14.7 pounds per square inch above a vacuum, but in
actual practice it is about 2 pounds above atmospheric pressure, or 17
pounds absolute, due to the resistance of exhaust ports and connecting
pipes. In the case of a condensing engine (one exhausting into a
condenser) the back pressure depends upon the efficiency of the
condenser, averaging about 3 pounds absolute pressure in the best
practice.
_Effective Pressure._--This is the difference between the pressure on
the steam side of the piston and that on the exhaust side, or in other
words, the difference between the working pressure and the back
pressure. This value varies throughout the stroke with the expansion of
the steam.
_Mean Effective Pressure._--It has just been stated that the effective
pressure varies throughout the stroke. The mean effective pressure (M.
E. P.) is the average of all the effective pressures, and this average
multiplied by the length of stroke, gives the work done per stroke.
_Line of Absolute Vacuum._--In the diagram shown in Fig. 6, the line
_OX_ is the line of absolute vacuum; that is, it is assumed that there
is no pressure on the exhaust side of the piston. In other words, the
engine is exhausting into a perfect vacuum.
[Illustration: Fig. 7. Constructing a Steam Engine Work Diagram]
_Atmospheric Line._--This is a line drawn parallel to the line of
absolute vacuum at such a distance above it as to represent 14.7 pounds
pressure per square inch, according to the scale used.
Construction of Ideal Diagram
One of the first steps in the design of a steam engine is the
construction of an ideal diagram, and the engine is planned to produce
this as nearly as possible when in operation. First assume the initial
pressure, the ratio of expansion, and the percentage of clearance, for
the type of engine under consideration. Draw lines _OX_ and _OY_ at
right angles as in Fig. 7. Make _OR_ the same percentage of the stroke
that the clearance is of the piston displacement; make _RX_ equal to the
length of the stroke (on a reduced scale). Erect the perpendicular _RA_
of such a height that it shall represent, to scale, an absolute pressure
per square inch equal to 0.95 of the boiler pressure. Draw in the dotted
lines _AK_ and _KX_, and the atmospheric line _LH_ at a height above
_OX_ to represent 14.7 pounds per square inch. Locate the point of
cut-off, _B_, according to the assumed ratio of expansion. Points on the
expansion curve _BC_ are found as follows: Divide the distance _BK_ into
any number of equal spaces, as shown by _a_, _b_, _c_, _d_, etc., and
connect them with the point _O_. Through the points of intersection with
_BP_, as _a'_, _b'_, _c'_, _d'_, etc., draw horizontal lines, and
through _a_, _b_, _c_, _d_, etc., draw vertical lines. The intersection
of corresponding horizontal and vertical lines will be points on the
theoretical expansion line. If the engine is to be non-condensing, the
theoretical work, or indicator diagram, as it is called, will be bounded
by the lines _ABCHG_.
The actual diagram will vary somewhat from the theoretical, as shown by
the shaded lines. The admission line between _A_ and _B_ will slant
downward slightly, and the point of cut-off will be rounded, owing to
the slow closing of the valve. The first half of the expansion line
will fall below the theoretical, owing to a drop in pressure caused
by cylinder condensation, but the actual line will rise above
the theoretical in the latter part of the stroke on account of
re-evaporation, due to heat given out by the hot cylinder walls to the
low-pressure steam. Instead of the pressure dropping abruptly at _C_,
release takes place just before the end of the stroke, and the diagram
is rounded at _CF_ instead of having sharp corners. The back pressure
line _FD_ is drawn slightly above the atmospheric line, a distance to
represent about 2 pounds per square inch. At _D_ the exhaust valve
closes and compression begins, rounding the bottom of the diagram up to
_E_.
The area of the actual diagram, as shown by the shaded lines in Fig. 7,
will be smaller than the theoretical, in about the following ratio:
Large medium-speed engines, 0.90 of theoretical area.
Small medium-speed engines, 0.85 of theoretical area.
High-speed engines, 0.75 of theoretical area.
CHAPTER II
RATING AND GENERAL PROPORTIONS OF STEAM ENGINES
The capacity or power of a steam engine is rated in horsepower, one
horsepower (H. P.) being the equivalent of 33,000 foot-pounds of work
done per minute. The horsepower of a given engine may be computed by the
formula:
_APLN_
H. P. = ------
33,000
in which
_A_ = area of piston, in square inches,
_P_ = mean effective pressure per square inch,
_L_ = length of stroke, in feet,
_N_ = number of strokes per minute = number of revolutions x 2.
The derivation of the above formula is easily explained, as follows: The
area of the piston, in square inches, multiplied by the mean effective
pressure, in pounds per square inch, gives the total force acting on the
piston, in pounds. The length of stroke, in feet, times the number of
strokes per minute gives the distance the piston moves through, in feet
per minute. It has already been shown that the pressure in pounds
multiplied by the distance moved through in feet, gives the foot-pounds
of work done. Hence, _A_ x _P_ x _L_ x _N_ gives the foot-pounds of work
done per minute by a steam engine. If one horsepower is represented by
33,000 foot-pounds per minute, the power or rating of the engine will be
obtained by dividing the total foot-pounds of work done per minute by
33,000. For ease in remembering the formula given, it is commonly
written
_PLAN_
H. P. = ------,
33,000
in which the symbols in the numerator of the second member spell the
word "Plan."
_Example_:--Find the horsepower of the following engine, working under
the conditions stated below:
Diameter of cylinder, 12 inches.
Length of stroke, 18 inches.
Revolutions per minute, 300.
Mean effective pressure (M. E. P.), 40 pounds.
In this problem, then, _A_ = 113 square inches; _P_ = 40 pounds; _L_ =
1.5 feet; and _N_ = 600 strokes.
Substituting in the formula,
40 x 1.5 x 113 x 600
H. P. = -------------------- = 123.
33,000
The mean effective pressure may be found, approximately, for different
conditions by means of the factors in the following table of ratios,
covering ordinary practice. The rule used is as follows: Multiply the
absolute initial pressure by the factor corresponding to the clearance
and cut-off as found from Table II, and subtract the absolute back
pressure from the result, assuming this to be 17 pounds for
non-condensing engines, and 3 pounds for condensing.
_Example 1_:--A non-condensing engine having 3 per cent clearance, cuts
off at 1/3 stroke; the initial pressure is 90 pounds gage. What is the
M. E. P.?
The absolute initial pressure is 90 + 15 = 105 pounds. The factor for 3
per cent clearance and 1/3 cut-off, from Table II, is 0.71. Applying the
rule we have: (105 x 0.71) - 17 = 57.5 pounds per square inch.
_Example 2_:--A condensing engine has a clearance of 5 per cent. It is
supplied with steam at 140 pounds gage pressure, and has a ratio of
expansion of 6. What is the M. E. P.?
The absolute initial pressure is 140 + 15 = 155. The factor for a ratio
of expansion of 6 (1/6 cut-off) and 5 per cent clearance is 0.5, which
gives (155 x 0.5) - 3 = 74.5 pounds per square inch.
The power of an engine computed by the method just explained is called
the indicated horsepower (I. H. P.), and gives the total power
developed, including that required to overcome the friction of the
engine itself. The delivered or brake horsepower (B. H. P.) is that
delivered by the engine after deducting from the indicated horsepower
the power required to operate the moving parts. The brake horsepower
commonly varies from 80 to 90 per cent of the indicated horsepower at
full load, depending upon the type and size of engine.
In proportioning an engine cylinder for any given horsepower, the
designer usually has the following data, either given or assumed, for
the special type of engine under consideration: Initial pressure, back
pressure, clearance, cut-off, and piston speed.
These quantities vary in different types of engines, but in the absence
of more specific data the values in Table III will be found useful. The
back pressure may be taken as 17 pounds per square inch, absolute, for
non-condensing engines, and as 3 pounds for condensing engines as
previously stated.
TABLE II. FACTORS FOR FINDING MEAN EFFECTIVE PRESSURE
+--------------+-----------------------------------------+
| | Point of Cut-off |
| Percentage +------+------+------+------+------+------+
| of Clearance | 1/10 | 1/6 | 1/4 | 1/3 | 1/2 | 3/4 |
+--------------+------+------+------+------+------+------+
| 1.75 | 0.35 | 0.48 | 0.60 | 0.70 | 0.85 | 0.96 |
| 3.00 | 0.37 | 0.49 | 0.61 | 0.71 | 0.85 | 0.96 |
| 5.00 | 0.39 | 0.50 | 0.62 | 0.72 | 0.86 | 0.97 |
| 7.00 | 0.41 | 0.52 | 0.63 | 0.73 | 0.86 | 0.97 |
| 9.00 | 0.43 | 0.54 | 0.64 | 0.73 | 0.86 | 0.97 |
+--------------+------+------+------+------+------+------+
The first step in proportioning the cylinder is to compute the
approximate mean effective pressure from the assumed initial pressure,
clearance, and cut-off, by the method already explained. Next assume the
piston speed for the type of engine to be designed, and determine the
piston area by the following formula:
33,000 H. P.
A = -----------------------.
M. E. P. x piston speed
This formula usually gives the diameter of the piston in inches and
fractions of an inch, while it is desirable to make this dimension an
even number of inches. This may be done by taking as the diameter the
nearest whole number, and changing the piston speed to correspond. This
is done by the use of the following equation.
First piston speed x first piston area
-------------------------------------- = new piston speed.
new piston area
In calculating the effective piston area, the area of the piston rod
upon one side must be allowed for. The effective or average piston area
will then be (2_A_ - _a_)/2, in which _A_ = area of piston, _a_ = area
of piston rod. This latter area must be assumed. After assuming a new
piston diameter of even inches, its effective or average area must be
used in determining the new piston speed. The length of stroke is
commonly proportioned to the diameter of cylinder, and the piston speed
divided by this will give the number of strokes per minute.
_Example_:--Find the diameter of cylinder, length of stroke, and
revolutions per minute for a simple high-speed non-condensing engine of
200 I. H. P., with the following assumptions: Initial pressure, 90
pounds gage; clearance, 7 per cent; cut-off, 1/4; piston speed, 700 feet
per minute; length of stroke, 1.5 times cylinder diameter.
TABLE III. PRESSURE, CLEARANCE, CUT-OFF AND PISTON SPEED OF STEAM
ENGINES
+---------------------+------------+-----------+-------------+------------+
| | Initial | Clearance,| Cut-off, | Piston |
| Type of Engine | Pressure, | Per Cent | Proportion | Speed, Feet|
| | (Gage) | | of Stroke | per Minute |
+---------------------+------------+-----------+-------------+------------+
|Simple high-speed | 80 to 90 |4 to 10 | 1/4 to 1/3 | 600 to 800 |
|Simple medium-speed | 80 to 90 |3 to 8 | 1/4 to 1/3 | 500 to 700 |
|Simple Corliss | 80 to 90 |1.5 to 3.5| 1/4 to 1/3 | 400 to 600 |
|Compound high-speed | 130 to 140 |4 to 10 | 1/10 to 1/8 | 600 to 800 |
|Compound medium-speed| 130 to 140 |3 to 8 | 1/10 to 1/8 | 500 to 700 |
|Compound Corliss | 130 to 140 |1.5 to 3.5| 1/10 to 1/8 | 400 to 600 |
+---------------------+------------+-----------+-------------+------------+
By using the rules and formulas in the foregoing, we have:
M. E. P. = (90 + 15) x 0.63 - 17 = 49 pounds.
33,000 x 200
_A_ = ------------ = 192.4 square inches.
49 x 700
The nearest piston diameter of even inches is 16, which corresponds to
an area of 201 square inches. Assume a piston rod diameter of 2-1/2
inches, corresponding to an area of 4.9 square inches, from which the
average or effective piston area is found to be ((2 x 201) - 4.9)/2 =
198.5 square inches.
Determining now the new piston speed, we have:
700 x 192.4
----------- = 678.5 feet per minute.
198.5
Assuming the length of stroke to be 1.5 times the diameter of the
cylinder, it will be 24 inches, or 2 feet.
This will call for 678.5 / 2 = 340 strokes per minute, approximately, or
340 / 2 = 170 revolutions per minute.
CHAPTER III
STEAM ENGINE DETAILS
Some of the most important details of a steam engine are those of its
valve gear. The simplest form of valve is that known as the plain slide
valve, and as nearly all others are a modification of this, it is
essential that the designer should first familiarize himself with this
particular type of valve in all its details of operation. After this has
been done, a study of other forms of valves will be found a
comparatively easy matter. The so called Corliss valve differs radically
from the slide valve, but the results to be obtained and the terms used
in its design are practically the same. The valve gear of a steam engine
is made up of the valve or valves which admit steam to and exhaust it
from the cylinder, and of the mechanism which governs the valve
movements, the latter usually consisting of one or more eccentrics
attached to the main shaft.
[Illustration: Fig. 8. Longitudinal Section of Slide Valve with Ports]
The Slide Valve
Fig. 8 shows a longitudinal section of a slide valve with the ports,
bridges, etc. The valve is shown in mid-position in order that certain
points relating to it may be more easily understood. The valve, _V_,
consists of a hollow casting, with ends projecting beyond the ports as
shown; the lower face is smoothly finished and fitted to the valve seat
_AB_. In operation it slides back and forth, opening and closing the
ports which connect the steam chest with the cylinder. Steam is admitted
to the cylinder when either port _CD_ or _DC_ is opened, and is released
when the ports are brought into communication with the exhaust port
_MN_. This is accomplished by the movement of the valve, which brings
one of the cylinder ports and the exhaust port both under the hollow
arch _K_. The portions _DM_ and _ND_ of the valve seat are called the
bridges.
It will be seen by reference to Fig. 8 that the portions _OI_ and _IO_
are wider than the ports which they cover. This extra width is called
the _lap_, _OC_ being the outside lap and _DI_ the inside or exhaust
lap. The object of outside lap is that the steam may be shut off after
the piston has moved forward a certain distance, and be expanded during
the remainder of the stroke. If there were no outside lap, steam would
be admitted throughout the entire stroke and there would be no
expansion. If there were no inside lap, exhaust would take place
throughout the whole stroke, and the advantages of premature release and
compression would be lost. Hence, outside lap affects the cut-off, and
inside lap affects release and compression. A valve has _lead_ when it
begins to uncover the steam port before the end of the return stroke of
the piston. This is shown in Fig. 9, where the piston _P_ is just ready
to start on its forward stroke as indicated by the arrow. The valve has
already opened a distance equal to the lead, and the steam has had an
opportunity to enter and fill the clearance space before the beginning
of the stroke. The lead varies in different engines, being greater in
high-speed than in low-speed types.
[Illustration: Fig. 9. Illustration showing Lead of Slide Valve]
[Illustration: Fig. 10. Diagrammatical View of Eccentric]
The Eccentric
The slide valve is usually driven by an eccentric attached to the main
shaft. A diagram of an eccentric is shown in Fig. 10. An eccentric is,
in reality, a short crank with a crank-pin of such size that it
surrounds the shaft. The arm of a crank is the distance between the
center of the shaft, and the center of the crank-pin. The throw of an
eccentric corresponds to this, and is the distance between the center of
the shaft and the center of the eccentric disk, as shown at _a_ in Fig.
10. The disk is keyed to the shaft, and as the shaft revolves, the
center of the disk rotates about it as shown by the dotted line, and
gives a forward and backward movement to the valve rod equal to twice
the throw _a_.
[Illustration: Fig. 11. Relations of Crank and Eccentric]
In Fig. 11 let _A_ represent the center of the main shaft, _B_ the
crank-pin to which the connecting-rod is attached (see _H_, Fig. 1), and
the dotted circle through _B_ the path of the crank-pin around the
shaft. For simplicity, let the eccentric be represented in a similar
manner by the crank _Ab_, and its path by the dotted circle through _b_.
Fig. 12 shows a similar diagram with the piston _P_ and the valve in the
positions corresponding to the positions of the crank and eccentric in
Fig. 11, and in the diagram at the right in Fig. 12. The piston is at
the extreme left, ready to start on its forward stroke toward the right.
The crank-pin _B_ is at its extreme inner position. When the valve is at
its mid-position, as in Fig. 8, the eccentric arm _Ab_ will coincide
with the line _AC_, Fig. 11. If the eccentric is turned on the shaft
sufficiently to bring the left-hand edge _O_, Fig. 8, of the valve in
line with the edge _C_ of the port, the arm of the eccentric will have
moved from its vertical position to that shown by the line _Ab'_ in Fig.
11. The angle through which the eccentric has been turned from the
vertical to bring about this result is called the _angular advance_, and
is shown by angle _CAb'_ in Fig. 11. The angular advance evidently
depends upon the amount of lap.
If the valve is to be given a lead, as indicated in Fig. 12, the
eccentric must be turned still further on the shaft to open the valve
slightly before the piston starts on its forward movement. This brings
the eccentric to the position _Ab_ shown in Fig. 11. The angle through
which the eccentric is turned to give the necessary lead opening to the
valve is called the _angle of lead_, and is shown by angle _b'Ab_. By
reference to Fig. 11, it is seen that the total angle between the crank
and the eccentric is 90 degrees, plus the angular advance, plus the
angle of lead. This is the total angle of advance.
[Illustration: Fig. 12. Piston just beginning Forward Stroke]
The relative positions of the piston and valve at different periods of
the stroke are illustrated in Figs. 12 to 16. Fig. 12 shows the piston
just beginning the forward stroke, the valve having uncovered the
admission port an amount equal to the lead. The crank is in a horizontal
position, and the eccentric has moved from the vertical an amount
sufficient to move the valve toward the right a distance equal to the
outside lap plus the lead. The arrows show that steam is entering the
left-hand port and is being exhausted through the right-hand port.
[Illustration: Fig. 13. Steam Port fully Opened]
In Fig. 13 it is seen that the valve has traveled forward sufficiently
to open the steam port to its fullest extent, and the piston has moved
to the point indicated. The exhaust port is still wide open, and the
relative positions of the crank and eccentric are shown in the diagram
at the right. In Fig. 14 the eccentric has passed the horizontal
position and the valve has started on its backward stroke, while the
piston is still moving forward. The admission port is closed, cut-off
having taken place, and the steam is expanding. The exhaust port is
still partially open.
[Illustration: Fig. 14. Valve has started on Backward Stroke]
[Illustration: Fig. 15. Both Steam Ports Closed]
In Fig. 15 both ports are closed and compression is taking place in
front of the piston while expansion continues back of it. Release occurs
in Fig. 16 just before the piston reaches the end of its stroke. The
eccentric crank is now in a vertical position, pointing downward, and
exhaust is just beginning to take place through the left-hand port.
This completes the different stages of a single stroke, the same
features being repeated upon the return of the piston to its original
position. The conditions of lap, lead, angular advance, etc., pertain to
practically all valves, whatever their design.
[Illustration: Fig. 16. Exhaust Begins]
Different Types of Valves
In the following are shown some of the valves in common use, being, with
the exception of the Corliss, modifications of the plain slide valve,
and similar in their action.
[Illustration: Fig. 17. Engine with Piston Valve]
_Double-Ported Balanced Valve._--A valve of this type has already been
shown in Fig. 2. This valve is flat in form, with two finished
surfaces, and works between the valve-seat and a plate, the latter
being prevented from pressing against the valve by special bearing
surfaces which hold it about 0.002 inch away. The construction of the
valve is such that when open the steam reaches the port through two
openings as indicated by the arrows at the left. The object of this is
to reduce the motion of the valve and quicken its action in admitting
and cutting off steam.
[Illustration: Fig. 18. Section through Cylinder of Engine of the
Four-valve Type]
[Illustration: Fig. 19. Different Types of Corliss Valves]
_Piston Valve._--The piston valve shown in Fig. 17 is identical in its
action with the plain slide valve shown in Fig. 8, except that it is
circular in section instead of being flat or rectangular. The advantage
claimed for this type of valve is the greater ease in fitting
cylindrical surfaces as compared with flat ones. The valve slides in
special bushings which may be renewed when worn. Piston valves are also
made with double ports.
[Illustration: Fig. 20. Longitudinal Section through Corliss Engine]
[Illustration: Fig. 21. The Gridiron Valve]
_Four-Valve Type._--Fig. 18 shows a horizontal section through the
cylinder and valves of an engine of the four-valve type. The admission
valves are shown at the top of the illustration and the exhaust valves
at the bottom, although, in reality, they are at the sides of the
cylinder. The advantage of an arrangement of this kind is that the
valves may be set independently of each other and the work done by the
two ends of the cylinder equalized. The various events, such as
cut-off, compression, etc., may be adjusted without regard to each
other, and in such a manner as to give the best results, a condition
which is not possible with a single valve.
_Gridiron Valve._--One of the principal objects sought in the design of
a valve is quick action at the points of admission and cut-off. This
requires the uncovering of a large port opening with a comparatively
small travel of the valve. The gridiron valve shown in Fig. 21 is
constructed especially for this purpose. This valve is of the four-valve
type, one steam valve and one exhaust valve being shown in the section.
Both the valve and its seat contain a number of narrow openings or
ports, so that a short movement of the valve will open or close a
comparatively large opening. For example, the steam valve in the
illustration has 12 openings, so that if they are 1/4 inch in width
each, a movement of 1/4 inch of the valve will open a space 12 x 1/4 = 3
inches in length.
[Illustration: Fig. 22. The Monarch Engine with Corliss Valve Gear.--A,
Rod to Eccentric; B, Governor; C, Reach Rod; D, Radial Arm; E, Steam
Valve; F, Bell-crank; G, Wrist Plate; H, Exhaust Valve; K, Dash-pot]
_Corliss Valve._--A section through an engine cylinder equipped with
Corliss valves is shown in Fig. 20. There are four cylindrical valves in
this type of engine, two steam valves at the top and two exhaust valves
at the bottom. This arrangement is used to secure proper drainage. The
action of the admission and exhaust valves is indicated by the arrows,
the upper left-hand and the lower right-hand valve being open and the
other two closed.
Side and sectional views of different forms of this type of valve are
shown in Fig. 19. They are operated by means of short crank-arms which
are attached to a wrist-plate by means of radial arms or rods, as shown
in Fig. 22. The wrist-plate, in turn, is given a partial backward and
forward rotation by means of an eccentric attached to the main shaft and
connected to the upper part of the wrist-plate by a rod as indicated.
The exhaust valves are both opened and closed by the action of the
wrist-plate and connecting rods. The steam valves are opened in this
manner, but are closed by the suction of dash pots attached to the drop
levers on the valve stems by means of vertical rods, as shown.
[Illustration: Figs. 23 to 26. Action of Corliss Valve Gear]
The action of the steam or admission valves is best explained by
reference to Figs. 23 to 26. Referring to Fig. 23, _A_ is a bell-crank
which turns loosely upon the valve stem _V_. The lower left-hand
extension of _A_ carries the grab hook _H_, while the upper extension is
connected with the wrist-plate as indicated. Ordinarily the hook _H_ is
pressed inward by the spring _S_, so that the longer arm of the hook is
always pressed against the knock-off cam _C_. The cam _C_ also turns
upon the valve stem _V_ and is connected with the governor by means of a
reach rod as indicated in Fig. 23 and shown in Fig. 22. The drop lever
_B_ is keyed to the valve stem _V_, and is connected with the dash pot
by a rod as indicated by the dotted line. This is also shown in Fig. 22.
The end of the drop lever carries a steel block (shown shaded in Fig.
23), which engages with the grab hook _H_.
When in operation, the bell-crank is rotated in the direction of the
arrow by the action of the wrist-plate and connecting-rod. As the
bell-crank rotates, the grab hook engages the steel block at the end of
the drop lever _B_ and lifts it, thus causing the valve to open, and to
remain so until the bell-crank has advanced so far that the longer arm
of the grab hook _H_ is pressed outward by the projection on the
knock-off cam, as shown in Fig. 24. The drop lever now being released,
the valve is quickly closed by the suction of the dash pot, which pulls
the lever down to its original position by means of the rod previously
mentioned.
[Illustration: Fig. 27. Governor for Corliss Engine]
The governor operates by changing the point of cut-off through the
action of the cam _C_. With the cam in the position shown in Fig. 25,
cut-off occurs earlier than in Fig. 24. Should the cam be turned in the
opposite direction (clockwise), cut-off would take place later. A
detailed view of the complete valve mechanism described is shown
assembled in Fig. 26, with each part properly named. A detail of the
governor is shown in Fig. 27. An increase in speed causes the revolving
balls _BB_ to swing outward, thus raising the weight _W_ and the sleeve
_S_. This in turn operates the lever _L_ through rod _R_ and a
bell-crank attachment, as shown in the right-hand view. An upward and
downward movement of the balls, due to a change in speed of the engine,
swings the lever _L_ backward and forward as shown by the full and
dotted lines. The ends of this lever are attached by means of reach-rods
to the knock-off cams, this being shown more clearly in Fig. 22. The
connections between the lever _L_ and cam _C_ are such that a raising of
the balls, due to increased speed, will reduce the cut-off and thus slow
down the engine. On the other hand, a falling of the balls will lengthen
the cut-off through the same mechanism.
[Illustration: Fig. 28. Dash-pot for Corliss Engine]
[Illustration: Figs. 29 and 30. Plan and Longitudinal Section of
Adjustable Piston]
Mention has already been made of the dash pot which is used to close the
valve suddenly after being released from the grab hook. The dash-pot rod
is shown in Fig. 26, and indicated by dotted lines in Figs. 23 to 25. A
detailed view of one form of dash pot is shown in Fig. 28. When the
valve is opened, the rod attached to lever _B_, Figs. 23 and 24, raises
the piston _P_, Fig. 28, and a partial vacuum is formed beneath it which
draws the piston and connecting rod down by suction as soon as the lever
_B_ is released, and thus closes the valve suddenly and without shock.
The strength of the suction and the air cushion for this piston are
regulated by the inlet and outlet valves shown on the sides of the dash
pot.
Engine Details
Figs. 29 to 37 show various engine details, and illustrate in a simple
way some of the more important principles involved in steam engine
design.
[Illustration: Fig. 31. A Typical Cross-head]
[Illustration: Figs. 32 and 33. Methods Commonly Used for Taking Up Wear
in a Connecting-rod]
A partial cross-section of an adjustable piston is shown in Fig. 29, and
a longitudinal section of the same piston in Fig. 30. The principal
feature to be emphasized is the method of automatic expansion employed
to take up any wear and keep the piston tight. In setting up the piston
a hand adjustment is made of the outer sleeve or ring _R_ by means of
the set-screws _AA_. Ring _R_ is made in several sections, so that it
may be expanded in the form of a true circle. Further tightness is
secured without undue friction by means of the packing ring _P_ which
fits in a groove in _R_ and is forced lightly against the walls of the
cylinder by a number of coil springs, one of which is shown at _S_. As
the cylinder and piston become worn, screws _A_ are adjusted from time
to time, and the fine adjustment for tightness is cared for by the
packing ring _P_ and the coil springs _S_.
The points to be brought out in connection with the cross-head are the
methods of alignment and adjustment. A typical cross-head is shown in
cross and longitudinal sections in Fig. 31. Alignment in a straight
line, longitudinally, is secured by the cylindrical form of the bearing
surfaces or shoes, shown at _S_. These are sometimes made V-shaped in
order to secure the same result. The wear on a cross-head comes on the
surfaces _S_, and is taken up by the use of screw wedges _W_, shown in
the longitudinal section. As the sliding surfaces become worn, the
wedges are forced in slightly by screwing in the set-screws and clamping
them in place by means of the check-nuts.
[Illustration: Fig. 34. Outboard Bearing for Corliss Type Engine]
[Illustration: Fig. 35. Inner Bearing and Bed of Corliss Engine]
The method commonly employed in taking up the wear in a connecting-rod
is shown in Figs. 32 and 33. The wear at the wrist-pin is taken by the
so called brasses, shown at _B_ in the illustrations. The inner brass,
in both cases, fits in a suitable groove, and is held stationary when
once in place. The outer brass is adjustable, being forced toward the
wrist-pin by a sliding wedge which is operated by one or more
set-screws. In Fig. 32 the wedge is held in a vertical position, and is
adjusted by two screws as shown. The arrangement made use of in Fig. 33
has the wedge passing through the rod in a horizontal position, and
adjusted by means of a single screw, as shown in the lower view. With
the arrangements shown, tightening up the brasses shortens the length of
the rod. In practice the wedges at each end of the rod are so placed
that tightening one shortens the rod, and tightening the other lengthens
it, the total effect being to keep the connecting-rod at its original
length.
A common form of outboard bearing for an engine of the slow-speed or
Corliss type is illustrated in Fig. 34. The various adjustments for
alignment and for taking up wear are the important points considered in
this case. The plate _B_ is fastened to the stone foundation by anchor
bolts not shown. Sidewise movement is secured by loosening the bolts
_C_, which pass through slots in the bearing, and adjusting by means of
the screws _S_. Vertical adjustment is obtained by use of the wedge _W_,
which is forced in by the screw _A_, as required. The inner bearing and
bed piece of a heavy duty Corliss engine is shown in Fig. 35. The
bearing in this case is made up of four sections, so arranged that
either horizontal or vertical adjustment may be secured by the use of
adjusting screws and check-nuts.
Engines of the slide-valve type are usually provided either with a
fly-ball throttling governor, or a shaft governor. A common form of
throttling governor is shown in Fig. 36. As the speed increases the
balls _W_ are thrown outward by the action of the centrifugal force, and
being attached to arms hinged above them, any outward movement causes
them to rise. This operates the spindle _S_, which, in turn, partially
closes the balanced valve in body _B_, thus cutting down the steam
supply delivered to the engine. The action of a throttling governor upon
the work diagram of an engine is shown in Fig. 38. Let the full line
represent the form of the diagram with the engine working at full load.
Now, if a part of the load be thrown off, the engine will speed up
slightly, causing the governor to act as described, thus bringing the
admission and expansion lines into the lower positions, as shown in
dotted lines.
[Illustration: Fig. 36. Common Form of Throttling Governor]
The shaft governor is used almost universally on high-speed engines, and
is shown in one form in Fig. 37. It consists, in this case, of two
weights _W_, hinged to the spokes of the wheel near the circumference
by means of suitable arms. Attached to the arms, as shown, are coil
springs _C_. The ends of the arms beyond the weights are connected by
means of levers _L_ to the eccentric disk. When the engine speeds up,
the weights tend to swing outward toward the rim of the wheel, the
amount of the movement being regulated by the tension of the springs
_C_. As the arms move outward, the levers at the ends turn the eccentric
disk on the shaft, the effect of which is to change the angle of advance
and shorten the cut-off. When the speed falls below the normal, the
weights move toward the center and the cut-off is lengthened. The effect
of this form of governor on the diagram is shown in Fig. 39. The full
line represents the diagram at full load, and the dotted line when the
engine is under-loaded.
[Illustration: Fig. 37. Shaft Governor for High-speed Engine]
CHAPTER IV
STEAM ENGINE ECONOMY
Under the general heading of steam engine economy, such items as
cylinder condensation, steam consumption, efficiency, ratio of
expansion, under- and over-loading, condensing, etc., are treated.
The principal waste of steam in the operation of an engine is due to
condensation during the first part of the stroke. This condensation is
due to the fact that during expansion and exhaust the cylinder walls
and head and the piston are in contact with comparatively cool steam,
and, therefore, give up a considerable amount of heat. When fresh steam
is admitted at a high temperature, it immediately gives up sufficient
heat to raise the cylinder walls to a temperature approximating that of
the entering steam. This results in the condensation of a certain amount
of steam, the quantity depending upon the time allowed for the transfer
of heat, the area of exposed surface, and the temperature of the
cylinder walls. During the period of expansion the temperature falls
rapidly, and the steam being wet, absorbs a large amount of heat. After
the exhaust valve opens, the drop in pressure allows the moisture that
has collected on the cylinder walls to evaporate into steam, so that
during the exhaust period but little heat is transferred. With the
admission of fresh steam at boiler pressure, a mist is condensed on the
cylinder walls, which greatly increases the rapidity with which heat is
absorbed.
The amount of heat lost through cylinder condensation is best shown by a
practical illustration. One horsepower is equal to 33,000 foot-pounds of
work per minute, or 33,000 x 60 = 1,980,000 foot-pounds per hour. This
is equivalent to 1,980,000 / 778 = 2,550 heat units. The latent heat of
steam at 90 pounds gage pressure is 881 heat units. Hence, 2,250 / 881 =
2.9 pounds of steam at 90 pounds pressure is required per horsepower,
provided there is no loss of steam, and all of the contained heat is
changed into useful work. As a matter of fact, from 30 to 35 pounds of
steam are required in the average simple non-condensing high-speed
engine.
There are three remedies which are used to reduce the amount of cylinder
condensation. The first to be used was called steam jacketing, and
consisted in surrounding the cylinder with a layer of high-pressure
steam, the idea being to keep the inner walls up to a temperature nearly
equal to that of the incoming steam. This arrangement is but little used
at the present time, owing both to the expense of operation and to its
ineffectiveness as compared with other methods.
The second remedy is the use of superheated steam. It has been stated
that the transfer of heat takes place much more rapidly when the
interior surfaces are covered with a coating of moisture or mist.
Superheated steam has a temperature considerably above the point of
saturation at the given pressure; hence, it is possible to cool it a
certain amount before condensation begins. This has the effect of
reducing the transfer of heat for a short period following admission,
and this is the time that condensation takes place most rapidly under
ordinary conditions with saturated steam. This, in fact, is the
principal advantage derived from the use of superheated steam, although
it is also lighter for a given volume, and therefore, a less weight of
steam is required, to fill the cylinder up to the point of cut-off. The
economical degree of superheating is considered to be that which will
prevent the condensation of any steam on the walls of the cylinder up to
the point of cut-off, thus keeping them at all times free from moisture.
The objections to superheated steam are its cutting effect in the
passages through which it flows, and the difficulty experienced in
lubricating the valves and cylinder at such a high temperature. The
third and most effective remedy for condensation losses is that known as
compounding, which will be treated under a separate heading in the
following.
Multiple Expansion Engines
It has been explained that cylinder condensation is due principally to
the change in temperature of the interior surfaces of the cylinder,
caused by the variation in temperature of the steam at initial and
exhaust pressures. Therefore, if the temperature range be divided
between two cylinders which are operated in series, the steam condensed
in the first or high pressure cylinder will be re-evaporated and passed
into the low-pressure cylinder as steam, where it will again be
condensed and re-evaporated as it passes into the exhaust pipe.
Theoretically, this should reduce the condensation loss by one-half, and
if three cylinders are used, the loss should be only one-third of that
in a simple engine. In actual practice the saving is not as great as
this, but with the proper relation between the cylinders, these results
are approximated.
Engines in which expansion takes place in two stages are called compound
engines. When three stages are employed, they are called triple
expansion engines. Compounding adds to the first cost of an engine, and
also to the friction, so that in determining the most economical number
of cylinders to employ, the actual relation between the condensation
loss and the increased cost of the engine and the friction loss, must be
considered. In the case of power plant work, it is now the practice to
use compound engines for the large sizes, while triple expansion engines
are more commonly employed in pumping stations. Many designs of multiple
expansion engines are provided with chambers between the cylinders,
called receivers. In engines of this type the exhaust is frequently
reheated in the receivers by means of brass coils containing live steam.
In the case of a cross-compound engine, a receiver is always used. In
the tandem design it is often omitted, the piping between the two
cylinders being made to answer the purpose.
The ratio of cylinder volumes in compound engines varies with different
makers. The usual practice is to make the volume of the low-pressure
cylinder from 2.5 to 3 times that of the high-pressure. The total ratio
of expansion in a multiple expansion engine is the product of the ratios
in each cylinder. For example, if the ratio of expansion is 4 in each
cylinder in a compound engine, the total ratio will be 4 x 4 = 16. The
effect of a triple-expansion engine is sometimes obtained in a measure
by making the volume of the low-pressure cylinder of a compound engine 6
or 7 times that of the high-pressure. This arrangement produces a
considerable drop in pressure at the end of the high-pressure stroke,
with the result of throwing a considerable increase of work on the
high-pressure cylinder without increasing its ratio of expansion, and at
the same time securing a large total ratio of expansion in the engine.
In the case of vertical engines, the low-pressure cylinder is sometimes
divided into two parts in order to reduce the size of cylinder and
piston. In this arrangement a receiver of larger size than usual is
employed, and the low-pressure cranks are often set at an angle with
each other.
Another advantage gained by compounding is the possibility to expand the
steam to a greater extent than can be done in a single cylinder engine,
thus utilizing, as useful work, a greater proportion of the heat
contained in the steam. This also makes it possible to employ higher
initial pressures, in which there is a still further saving, because of
the comparatively small amount of fuel required to raise the pressure
from that of the common practice of 80 or 90 pounds for simple engines,
to 120 to 140 pounds, which is entirely practical in the case of
compound engines. With triple expansion, initial pressures of 180 pounds
or more may be used to advantage. The gain from compounding may amount
to about 15 per cent over simple condensing engines, taking steam at the
same initial pressure. When compound condensing engines are compared
with simple non-condensing engines, the gain in economy may run from 30
to 40 per cent.
TABLE IV. STEAM CONSUMPTION OF ENGINES
+-------------------------+--------------------------------+
| | Pounds of Steam per Indicated |
| | Horsepower per Hour |
| Kind of Engine +----------------+---------------+
| | Non-condensing | Condensing |
+-------------------------+----------------+---------------+
| { High-speed | 32 | 24 |
| Simple { Medium-speed | 30 | 23 |
| { Corliss | 28 | 22 |
| | | |
| { High-speed | 26 | 20 |
| Compound { Medium-speed | 25 | 19 |
| { Corliss | 24 | 18 |
+-------------------------+----------------+---------------+
Steam Consumption and Ratio of Expansion
The steam consumption is commonly called the _water rate_, and is
expressed in pounds of dry steam required per indicated horsepower per
hour. This quantity varies widely in different types of engines, and
also in engines of the same kind working under different conditions. The
water rate depends upon the "cylinder losses," which are due principally
to condensation, although the effects of clearance, radiation from
cylinder and steam chest, and leakage around valves and piston, form a
part of the total loss. Table IV gives the average water rate of
different types of engines working at full load.
The most economical ratio of expansion depends largely upon the type of
the engine. In the case of simple engines, the ratio is limited to 4 or
5 on account of excessive cylinder condensation in case of larger
ratios. This limits the initial pressure to an average of about 90
pounds for engines of this type. In the case of compound engines, a
ratio of from 8 to 10 is commonly employed to advantage, while with
triple-expansion engines, ratios of 12 to 15 are found to give good
results.
[Illustration: Fig. 38. Action of Throttling Governor on Indicator
Diagram]
[Illustration: Fig. 39. Effect of Shaft Governor on Indicator Diagram]
[Illustration: Fig. 40. Increasing Power of Engine by Condensing]
[Illustration: Fig. 41. Decreasing Steam Consumption by Condensing]
The _thermal efficiency_ of an engine is the ratio of the heat
transformed into work to the total heat supplied to the engine. In order
to determine this, the _absolute_ temperature of the steam at admission
and exhaust pressures must be known. These pressures can be measured by
a gage, and the corresponding temperatures taken from a steam table, or
better, the temperatures can be measured direct by a thermometer. The
absolute temperature is obtained by adding 461 to the reading in degrees
Fahrenheit (F.). The formula for thermal efficiency is:
_T__{1} - _T__{2}
-----------------
_T__{1}
in which
_T__{1} = absolute temperature of steam at initial pressure.
_T__{2} = absolute temperature of steam at exhaust pressure.
_Example_:--The temperature of the steam admitted to the cylinder of an
engine is 340 degrees F., and that of the exhaust steam 220 degrees F.
What is the thermal efficiency of the engine?
(340 + 461) - (220 + 461)
Thermal efficiency = ------------------------- = 0.15
(340 + 461)
The _mechanical efficiency_ is the ratio of the delivered or brake
horsepower to the indicated horsepower, and is represented by the
equation:
B. H. P.
Mechanical efficiency = --------
I. H. P.
in which B. H. P. = brake horsepower,
I. H. P. = indicated horsepower.
All engines are designed to give the best economy at a certain developed
indicated horsepower called full load. There must, of course, be more or
less fluctuation in the load under practical working conditions,
especially in certain cases, such as electric railway and rolling mill
work. The losses, however, within a certain range on either side of the
normal load, are not great in a well designed engine. The effect of
increasing the load is to raise the initial pressure or lengthen the
cut-off, depending upon the type of governor. This, in turn, raises the
terminal pressure at the end of expansion, and allows the exhaust to
escape at a higher temperature than before, thus lowering the thermal
efficiency.
The effect of reducing the load is to lower the mean effective pressure.
(See Figs. 38 and 39.) This, in throttling engines, is due to a
reduction of initial pressure, and in the automatic engine to a
shortening of the cut-off. The result in each case is an increase in
cylinder condensation, and as the load becomes lighter, the friction of
the engine itself becomes a more important part of the total indicated
horsepower; that is, as the load becomes lighter, the mechanical
efficiency is reduced.
Effect of Condensing
So far as the design of the engine itself it concerned, there is no
difference between a condensing and a non-condensing engine. The only
difference is that in the first case the exhaust pipe from the engine is
connected with a condenser instead of discharging into the atmosphere.
A condenser is a device for condensing the exhaust steam as fast as it
comes from the engine, thus forming a partial vacuum and reducing the
back pressure. The attaching of a condenser to an engine may be made to
produce two results, as shown by the work diagrams illustrated in Figs.
40 and 41. In the first case the full line represents the diagram of the
engine when running non-condensing, and the area of the diagram gives a
measure of the work done. The effect of adding a condenser is to reduce
the back pressure on an average of 10 to 12 pounds per square inch,
which is equivalent to adding the same amount to the mean effective
pressure. The effect of this on the diagram, when the cut-off remains
the same, is shown by the dotted line in Fig. 40. The power of the
engine per stroke is increased by an amount represented by the area
enclosed by the dotted line and the bottom of the original diagram.
Assuming the reduction in back pressure to be 10 pounds, which is often
exceeded in the best practice, the gain in power by running condensing
will be proportional to the increase in mean effective pressure under
these conditions. For example, if the mean effective pressure is 40
pounds when running non-condensing, it will be increased to 40 + 10 = 50
pounds when running condensing, that is, it is 50/40 = 1.25 times as
great as before. Therefore, if the engine develops 100 I. H. P. under
the first condition, its final power will be increased to 100 x 1.25 =
125 I. H. P. under the second condition.
Fig. 41 shows the effect of adding a condenser and shortening the
cut-off to keep the area of the diagram the same as before. The result
in this case is a reduction in the quantity of steam required to develop
the same indicated horsepower. The theoretical gain in economy under
these conditions will run from about 28 to 30 per cent for simple, and
from 20 to 22 per cent for compound engines. The actual gain will depend
upon the cost and operation of the condenser which varies greatly in
different localities.
CHAPTER V
TYPES OF STEAM ENGINES
There are various ways of classifying steam engines according to their
construction, the most common, perhaps, being according to speed. If
this classification is employed, they may be grouped under three general
headings: High-speed, from 300 to 400 revolutions per minute;
moderate-speed, from 100 to 200 revolutions; and slow-speed, from 60 to
90 revolutions; all depending, however, upon the length of stroke. This
classification is again sub-divided according to valve mechanism,
horizontal and vertical, simple and compound, etc. The different forms
of engines shown in the following illustrations show representative
types in common use for different purposes.
The Ball engine, as shown in Fig. 42, is a typical horizontal single
valve high-speed engine with a direct-connected dynamo. It is very rigid
in design and especially compact for the power developed. The valve is
of the double-ported type shown in Fig. 2, having a cover plate for
removing the steam pressure from the back of the valve. The piston is
hollow with internal ribs similar to that shown in Fig. 29, and is
provided with spring packing rings carefully fitted in place. The
governor is of the shaft type, having only one weight instead of two, as
shown in Fig. 37.
[Illustration: Fig. 42. The Ball Engine]
The Sturtevant engine shown in Fig. 43 is a vertical high-speed engine
of a form especially adapted to electrical work. Engines of this general
design are made in a variety of sizes, and are often used on account of
the small floor space required. In the matter of detail, such as valves,
governors, etc., they do not differ materially from the high-speed
horizontal engine.
Fig. 44 illustrates a moderate-speed engine of the four-valve type.
These engines are built either with flat valves, or with positively
driven rotary or Corliss valves, the latter being used in the engine
shown. It will be noticed that the drop-lever and dash-pot arrangement
is omitted, the valves being both opened and closed by means of the
wrist-plate and its connecting rods. This arrangement is used on account
of the higher speed at which the engine is run, the regular Corliss
valve gear being limited to comparatively low speeds. All engines of
this make are provided with an automatic system of lubrication. The oil
is pumped through a filter to a central reservoir, seen above the center
of the engine, and from here delivered to all bearings by gravity. The
pump is attached to the rocker arm, and therefore easily accessible for
repairs.
The standard Harris Corliss engine shown in Fig. 45, is typical of its
class. It is provided with the girder type of frame, and with an
outboard bearing mounted upon a stone foundation. The valve gear is of
the regular Corliss type, driven by a single eccentric and wrist-plate.
The dash pots are mounted on cast-iron plates set in the floor at the
side of the engine, where they may be easily inspected. The governor is
similar in construction to the one already described, and shown in Fig.
27. The four engines so far described are simple engines, the expansion
taking place in a single cylinder. Figs. 46 to 48 show three different
types of the compound engine.
[Illustration: Fig. 43. The Sturtevant Vertical Engine]
The engine shown in Fig. 46 is of a type known as the tandem compound.
In this design the cylinders are in line, the low-pressure cylinder in
front of the high-pressure, as shown. There is only one piston rod, the
high-pressure and low-pressure pistons being mounted on the same rod.
The general appearance of an engine of this design is the same as a
simple engine, except for the addition of the high-pressure cylinder.
The governor is of the shaft type and operates by changing the cut-off
in the high-pressure cylinder. The cut-off in the low pressure cylinder
is adjusted by hand to divide the load equally between the two
cylinders for the normal load which the engine is to carry.
[Illustration: Fig. 44. Moderate Speed Engine of the Four-valve Type]
The engine shown in Fig. 47 is known as a duplex compound. In this
design the high-pressure cylinder is placed directly below the
low-pressure cylinder, as indicated, and both piston rods are attached
to the same cross-head. The remainder of the engine is practically the
same as a simple engine of the same type.
[Illustration: Fig. 45. The Harris Corliss Engine]
Fig. 48 shows a cross-compound engine of heavy design, built especially
for rolling mill work. In this arrangement two complete engines are
used, except for the main shaft and flywheel, which are common to both.
The engine is so piped that the high-pressure cylinder exhausts into the
low-pressure, through a receiver, the connection being under the floor
and not shown in the illustration. One of the advantages of the
cross-compound engine over other forms is that the cranks may be set 90
degrees apart, so that when one is on a dead center the other is
approximately at its position of greatest effort.
Selection of an Engine
The selection of an engine depends upon a number of conditions which
vary to a considerable extent in different cases. Among these may be
mentioned first cost, size and character of plant, available space,
steam economy, and utilization of the exhaust steam. The question of
first cost is usually considered in connection with that of operation,
and items such as interest and depreciation are compared with the saving
made through the saving in steam with high priced engines.
[Illustration: Fig. 46. The Skinner Tandem Engine]
[Illustration: Fig. 47. American Ball Duplex Compound Engine]
The principal use of the stationary engine is confined to the driving of
electric generators and the furnishing of motive power in shops and
factories. For the first of these uses, in cases where floor space is
limited, as in office buildings, and where the power does not exceed
about 100 I. H. P., the simple non-condensing high-speed engine is
probably employed more than any other type. For larger installations, a
saving may usually be made by the substitution of the moderate-speed
four-valve engine. The question of simple and compound engines in this
class of work depends largely upon the use made of the exhaust steam. In
winter time the exhaust is nearly always utilized in the heating system,
hence steam economy is not of great importance, and the simple engine
answers all purposes at a smaller first cost. In localities where the
heating season is comparatively short and fuel high, there is a decided
advantage in using compound engines on account of their greater steam
economy when operated within their economical range as regards load.
[Illustration: Fig. 48. The Monarch Corliss Engine]
In large central plants where low cost of operation is always of first
importance, it is common practice to use the best class of compound
condensing engines of moderate or low speed. Those equipped with some
form of Corliss valve gear are frequently found in this class of work.
In the generation of power for shops and factories, where there is
plenty of floor space, low-speed engines of the Corliss type are most
commonly used. When space is limited, very satisfactory results may be
obtained by using the moderate-speed four-valve engine. In deciding upon
an engine for any particular case, the problem must be studied from all
sides, and one be chosen which best answers the greatest number of
requirements.
CHAPTER VI
STEAM ENGINE TESTING
The principal information sought in the usual test of a steam engine is:
1. The indicated horsepower developed under certain standard conditions.
2. The friction of the engine, from which is determined the mechanical
efficiency.
3. The steam consumption per indicated horsepower.
4. The general action of the valves.
5. The pressure conditions in the cylinder at different periods of the
stroke.
The ultimate object of an efficiency test is to determine the
foot-pounds of work delivered by the engine per pound of coal burned in
the boiler furnaces. The general method of finding the pounds of dry
steam evaporated per pound of coal has been treated in MACHINERY'S
Reference Series No. 67, "Boilers," under the head of "Boiler Testing."
In the present case it is, therefore, only necessary to carry the
process a step further and determine the foot-pounds of work developed
per pound of steam.
The apparatus used in engine testing, in addition to that used in boiler
testing, consists of a steam engine _indicator_ and reducing device for
taking diagrams, and a _planimeter_ for measuring them afterwards. If
the test is made independently of the boiler test, a calorimeter for
measuring the amount of moisture in the steam should be added to the
outfit.
It has already been shown how a diagram may be made to represent
graphically the work done in a steam engine cylinder during one stroke
of the piston. The diagrams shown thus far have been theoretical or
ideal cards constructed from assumed relations of the pressure acting
and the distance moved through by the piston. An indicator is a device
for making a diagram of what actually takes place in an engine cylinder
under working conditions. Such a diagram shows the points of admission,
cut-off, and release, and indicates accurately the pressures acting upon
both sides of the piston at all points of the stroke.
A common form of steam engine indicator is shown in Fig. 49. It consists
of a cylinder _C_ which is placed in communication at _E_ with one end
of the engine cylinder by a proper pipe connection, provided with a
quick opening and closing cock or valve. The cylinder _C_ contains a
piston, above which is placed a coil spring of such strength that a
given pressure per square inch acting upon the lower side of the piston
will compress the spring a definite and known amount. Extending through
the cap or head of cylinder _C_ is a stem attached to the piston below,
and connected by suitable levers with a pencil point _P_. The
arrangement of the levers is such that a certain rise of the piston
causes the point _P_ to move upward in a vertical line a proportional
amount.
The springs used above the piston vary in strength, and are designated
as 20-pound, 40-pound, 60-pound, etc. A 20-pound spring is of such
strength that a pressure of 20 pounds per square inch, acting beneath
the piston in cylinder _C_, will raise the pencil point 1 inch. With a
40-pound spring, a pressure of 40 pounds per square inch will be
required to raise the pencil 1 inch, and so on for the other strengths
of spring.
The hollow drum _D_ rotates back and forth upon a vertical stem at its
center, its motion being produced by the string _H_, which is attached
by means of a suitable reducing motion to the cross-head of the engine.
The return motion to the drum is obtained from a coil spring contained
within it and not shown. The paper upon which the diagram is to be drawn
is wound around the drum _D_, and held in place by the spring clip _F_.
In taking an indicator card, the length of stroke must be reduced to
come within the limits of the drum, that is, it must be somewhat less
than the circumference of drum _D_. In practice, the diagram is commonly
made from 3 to 4 inches in length. There are a number of devices in use
for reproducing the stroke of the engine on a smaller scale. The most
accurate consists of a series of pulleys over which the cord passes on
its way from the cross-head to the indicator drum.
The indicator is connected with the engine cylinder by means of special
openings tapped close to the heads and either plugged or closed by means
of stop-cocks when not in use. In some cases two indicators are used,
one being connected to each end of the cylinder, while in others a
single indicator is made to answer the purpose by being so piped that it
can be connected with either end by means of a three-way cock. After the
indicator is connected and the cord adjusted to give the proper motion
to the drum, a card is attached, after which the three-way cock is
opened and steam allowed to blow through the indicator to warm it up.
The cock is now closed and the pencil pressed against the drum to get
the so-called atmospheric line. The cock is again opened, and the pencil
pressed lightly against the drum during one complete revolution of the
engine. The cock is then thrown over to connect the indicator with the
other end of the cylinder and the operation is repeated.
[Illustration: Fig. 49. Steam Engine Indicator]
The indicator card obtained in this way is shown in Fig. 50. It is
sometimes preferred to take the diagrams of the two ends on separate
cards, but it is simpler to take them both on the same one, and also
easier to compare the working of the two ends of the cylinder.
The analysis of a card for practical purposes is shown in Fig. 51.
Suppose, for example, that the length of the diagram measures 3.6
inches; the distance to the point of cut-off is 1.2 inch; and the
distance to the point of release is 3.3 inches. Then, by dividing 1.2 by
3.6, the cut-off is found to occur at 1.2 / 3.6 = 1/3 of the stroke.
Release occurs at 3.3 / 3.6 = 0.92 of the stroke. Compression begins at
(3.6 - 0.5) / 3.6 = 0.86 of the stroke. The diagrams shown in Figs. 50
and 51 are from non-condensing engines, and the back-pressure line is
therefore above the atmospheric line, as indicated.
The indicator diagram gives a means of determining the mean effective
pressure, from which the power of the engine can be found from the
previously given equation
_APLN_
I. H. P. = ------.
33,000
The method of determining the mean effective pressure is as follows:
First measure the area of the card in square inches, by means of a
planimeter (an instrument described later), and divide this area by the
length in inches. This gives the mean ordinate; the mean ordinate, in
turn, multiplied by the strength of spring used, will give the mean
effective pressure in pounds per square inch. For example, suppose that
the card shown in Fig. 51 is taken with a 60-pound spring, and that the
area, as measured by a planimeter, is found to be 2.6 square inches.
Dividing the area by the length gives 2.6 / 3.6 = 0.722 inch as the mean
ordinate, and this multiplied by the strength of spring gives a mean
effective pressure of 0.722 x 60 = 43.3 pounds per square inch.
[Illustration: Fig. 50. A Typical Indicator Diagram]
In practice, diagrams taken from the two ends of the cylinder usually
vary more or less, due to inequalities in the valve action. Again, the
effective area of the piston on the crank end is less than that on the
head end, by an amount equal to the area of the piston rod. For these
reasons it is customary to compute the mean effective pressure of all
the cards separately, and take, for use in the formula, the average of
the various computations. The corrected value of the piston area is, as
already stated, equal to (2_A_ - _a_)/2, in which _A_ is the area of the
piston, and _a_ the area of the piston rod. Substituting these values
for _A_ and _P_ in the formula, together with the length of stroke and
average number of revolutions per minute, the indicated horsepower is
easily computed.
In making an ordinary test, diagrams are taken from both ends of the
cylinder at 10-minute intervals for several hours, depending upon the
accuracy required. The revolutions of the engine are counted for two or
three-minute periods each time a pair of cards are taken, or still
better, an automatic counter is used for the run, from which the average
number of revolutions per minute may be determined.
[Illustration: Fig. 51. Diagram for Illustrating Method of Computation]
The friction of the engine is determined by taking a pair of cards while
"running light," that is, with the belt thrown off, or the engine
uncoupled, from the dynamo, if part of a direct-connected outfit. The
friction load is then computed in horsepower from the indicator cards,
and subtracted from the indicated horsepower when loaded. Thus we obtain
the delivered or brake horsepower. The delivered horsepower divided by
the indicated horsepower gives the mechanical efficiency. This may be
expressed in the form of an equation as follows:
I. H. P. - friction loss
------------------------ = mechanical efficiency.
I. H. P.
Planimeter
The planimeter is an instrument for measuring areas in general, and
especially for measuring the areas of indicator cards. Some forms give
the mean effective pressure directly, without computations, by changing
the scale to correspond with the spring used in the indicator. A
planimeter of this type is shown in Fig. 52. The method of manipulating
this instrument is as follows. Set the arm _BD_ equal to the length of
the card _EF_, by means of the thumb screw _S_, and set the wheel at
zero on the scale, which must correspond to the spring used in the
indicator. Next, place the point _D_ at about the middle of the area to
be measured, and set point _C_ so that the arm _CB_ shall be
approximately at right angles with _BD_. Then move _D_ to the upper
left-hand corner of the diagram, and with the left hand move _C_ either
to the right or left until the wheel comes back exactly to the zero
point on the scale; then press the point firmly into the paper. Now, go
around the outline of the diagram with point _D_ from left to right,
finishing exactly at the starting point. The mean effective pressure may
now be read from the scale opposite the edge of the wheel.
When very accurate results are required, the tracer point _D_ may be
passed over the diagram several times, and the reading divided by the
number of times it is thus passed around. With short cards, 3 inches and
under in length, it is best to make the arm _BD_ twice the length of the
card, and go around the diagram twice, taking the reading directly from
the scale as in the first case.
Determining Steam Consumption
When it is desired to determine accurately the water rate of an engine,
a boiler test should be carried on simultaneously with the test upon the
engine, from which the pounds of dry steam supplied may be determined as
described in MACHINERY'S Reference Series No. 67, "Boilers." Knowing the
average weight of steam supplied per hour for the run, and the average
indicated horsepower developed during the same period, the water rate of
the engine is easily computed. Sometimes the average cylinder
condensation for a given type and make is known for certain standard
conditions. In this case an approximation may be made from an indicator
diagram which represents the average operation of the engine during the
test.
[Illustration: Fig. 52. General Construction of Planimeter]
A diagram shows by direct measurement the pressure and volume at any
point of the stroke, and the weight of steam per cubic foot for any
given pressure may be taken directly from a steam table. The method,
then, of finding the weight of steam at any point in the stroke is to
find the volume in cubic feet, including the clearance and piston
displacement to the given point, which must be taken at cut-off or
later, and to multiply this by the weight per cubic foot corresponding
to the pressure at the given point measured on the diagram. As this
includes the steam used for compression, it must be corrected, as
follows, to obtain the actual weight used per stroke. Take some
convenient point on the compression curve, as _Q_, in Fig. 53; measure
its absolute pressure from the vacuum line _OX_ and compute the weight
of steam to this point. Subtract this weight from that computed above
for the given point on the expansion line, and the result will be the
weight of steam used per stroke. The best point on the expansion line to
use for this purpose is just before release, both because the maximum
amount of leakage has taken place, and also because of the
re-evaporation of a portion of the steam condensed during admission. The
actual computation of the steam consumption from an indicator diagram is
best shown by a practical illustration.
_Example_--Let Fig. 53 represent a diagram taken from the head end of a
16 x 30-inch non-condensing engine, running at a speed of 150
revolutions per minute; the card is taken with a 60-pound spring; the
clearance of the engine is 6 per cent; the average cylinder condensation
is 20 per cent of the total steam consumption; the diameter of the
piston rod is 3 inches.
[Illustration: Fig. 53. Diagram for Calculating Steam Consumption]
Measuring the card with a planimeter shows the mean effective pressure
to be 48.2 pounds. The area of the piston is 201 square inches; the area
of the piston rod is 7 square inches; hence, the average piston area =
((2 x 201) - 7)/2 = 198 square inches, approximately. Then
198 x 48.2 x 2.5 x 300
I. H. P. = ---------------------- = 217.
33,000
In Fig. 53, _GH_ is the atmospheric line; _OX_ is the line of vacuum or
zero pressure, drawn so that _GO_ = 14.7 pounds on the scale; and _OY_
is the clearance line, so drawn that _ON_ = 0.06 _NX_. The line _PQ_ is
drawn from _OX_ to some point on the compression line, as at _Q_. From
_C_, a point on the expansion line, just before release, the line _CF_
is drawn perpendicular to _OX_. The following dimensions are now
carefully measured from the actual diagram (not the one shown in the
illustration), with the results given:
_OX_ = 3.71 _OP_ = 0.42
_NX_ = 3.50 _CF_ = 0.81
_OF_ = 3.20 _QP_ = 0.81
On the indicator diagram, being taken with a 60-pound spring, all
vertical distances represent pounds per square inch, in the ratio of 60
pounds per inch of height. The stroke of the engine is 30 inches or 2.5
feet. The length of the diagram _NX_ is 3.5 inches; hence, each inch in
length represents 2.5/3.5 = 0.71 feet. From the above it is evident that
vertical distances in Fig. 53 must be multiplied by 60 to reduce them to
pounds pressure per square inch, and that horizontal distances must be
multiplied by 0.71 to reduce them to feet. Making these reductions
gives:
_OX_ = 2.63 feet. _OP_ = 0.30 foot.
_NX_ = 2.49 feet. _CF_ = 48.6 pounds.
_OF_ = 2.27 feet. _QP_ = 48.6 pounds.
As a card from the head end of the cylinder is taken to avoid
corrections for the piston rod, the area is 201 square inches or 1.4
square foot. With the above data the volume and weight of the steam in
the cylinder can be computed at any point in the stroke. When the piston
is at _C_, the volume is 1.4 x 2.27 = 3.18 cubic feet. When the piston
is at _Q_, the volume is 1.4 x 0.30 = 0.42 cubic foot. From a steam
table the weight of a cubic foot of steam at 48.6 pounds absolute
pressure is found to be 0.116 pounds. Therefore, the weight of steam
present when the piston is at _C_ is 3.18 x 0.116 = 0.369 pounds. The
weight of steam present when the piston is at _Q_ is 0.42 x 0.116 =
0.049 pound. That is the weight of steam in the cylinder at release is
0.369 pound, and the weight kept at exhaust closure for compression is
0.049 pound.
The weight exhausted per stroke is therefore 0.369 - 0.049 = 0.32 pound.
The number of strokes per hour is 150 x 2 x 60 = 18,000, from which the
steam accounted for by the diagram is found to be 18,000 x 0.32 = 5760
pounds, or 5760 / 217 = 26.5 pounds per indicated horsepower per hour.
If the cylinder condensation for this type of engine is 20 per cent of
the total steam consumption, the water rate will be 26.5 / 0.8 = 33.1
pounds per indicated horsepower per hour.
In the present case it has been assumed, for simplicity, that the
head- and crank-end diagrams were exactly alike, except for the piston
rod. Ordinarily, the above process should be carried out for both head
and crank ends, and the results averaged.
*** | {
"redpajama_set_name": "RedPajamaBook"
} | 4,375 |
\section{Introduction}
\label{sec.1}
According to our current theory of the Early Universe, a phase of almost de-Sitter expansion known as cosmological Inflation~\cite{Guth:1980zm} is expected to drive the Universe towards homogeneity and flatness, setting the appropriate initial conditions for the subsequent Hot Big Bang Theory evolution and providing a compelling mechanism to explain the physical origin of the observed anisotropies in the Cosmic Microwave Background (CMB) radiation.
A \textit{unique} prediction of inflation theory is the existence of Primordial Gravitational Waves (PGWs), tensor perturbations on super-horizon scales sourced by a super-adiabatic amplification of zero-point quantum fluctuations during inflation~\cite{Starobinsky:1980te,Linde:1981mu,Vilenkin:1983xq,Ungarelli:2005qb,Guzzetti:2016mkm}. Their detection would provide direct evidence for inflation, opening an inestimable observational windows on fundamental physics. For this reason, significant experimental efforts have been devoted to the search for primordial tensor modes, above all by looking for B-modes polarization on large angular scales in the Cosmic Microwave Background angular power spectra~\cite{Baumann:2014cja,Kamionkowski:2015yta}. Nevertheless, despite the best efforts, a detection of primordial tensor perturbations is still missing and only upper bounds can be inferred by current data~\cite{BICEP:2021xfz,Akrami:2018odb}.
More precisely, within the simplest slow-roll scenario (where inflation is achieved by means of a single scalar field minimally coupled to gravity) the power spectrum of primordial tensor perturbations around the CMB scales can be well described by a two-parameter power-law parameterization:
\begin{equation}
\ln \mathcal P_{\rm T}(k)=\ln(r\,A_{\rm s}) + n_{\rm T}\,\ln(k/k_{\star}).
\label{PL}
\end{equation}
The first parameter, \textit{i.e.} the tensor amplitude $A_{\rm T}\doteq r\,A_{\rm s}$, is currently constrained to\footnote{We recall that $A_{\rm s}\simeq 2.1\times 10^{-9}$ is the amplitude of primordial scalar perturbations~\cite{Planck:2018jri}.} $r<0.032$ at 95\%CL~\cite{Tristram:2021tvh} when \textit{Planck}~\cite{Planck:2020olo} and BK18~\cite{BICEP:2021xfz} datasets are combined, together with BAO~\cite{eBOSS:2020yzd} and CMB lensing~\cite{Planck:2018lbu}. Hopefully, in the upcoming decade, new CMB experiments like BICEP3~\cite{BICEP3}, CLASS~\cite{CLASS} , SPT-3G~\cite{SPT-3G}, Advanced ACTPol~\cite{ACTPol}, LiteBIRD~\cite{LBIRD} and CMB-S4~\cite{CMB-S4} should reach a better sensitivity $r \sim 0.001$, possibly leading to the first detection of B-mode polarization.\\
As concerns the second parameter, \textit{i.e.}, tensor tilt $n_{\rm T}\doteq d\ln \mathcal P_{\rm T}/d\ln k$, within the simplest single-field slow-roll framework, its value is fully determined by the slow-roll consistency relation $n_{\rm T}=-r/8$ that implies an almost scale-invariant slightly red-tilted spectrum. However this relation can be violated in many non-standard realizations of inflation that range from multi-fields models to modified gravity theories\footnote{See, \textit{e.g.}, Refs~\cite{Mukohyama:2014gba,Namba:2015gja,Peloso:2016gqs,Giare:2019snj,Giare:2020vhn,Ozsoy:2020ccy,Stewart:2007fu,DEramo:2019tit, Baumann:2015xxa,Giovannini:2015kfa,Giovannini:2018dob,Giovannini:2018nkt,Giovannini:2018zbf,Odintsov:2020ilr,Giare:2020plo,Oikonomou:2021kql,Odintsov:2021kup,Baumgart:2021ptt,Odintsov:2022cbm}}. Depending on the underlying phenomenology, the tensor tilt can be still red ($n_{\rm T}<0$) or even become blue ($n_{\rm T}>0$). Therefore, constraining the tensor tilt (and in general the shape of the tensor spectrum) without any underlying assumption is a matter of interest to test possible hints for new physics as well as to test the validity of the standard scenario itself~\cite{Franciolini:2018ebs,Caldwell:2018giq,Clarke:2020bil}.
Relaxing the slow-roll consistency relation, the analysis of the CMB data only weakly constrains the tensor tilt to $-0.55<n_{\rm T}<2.54$ at 95\% CL~\cite{Akrami:2018odb}. However, important improvements in the upper limit can be achieved by exploiting other CMB-independent observables.
For instance, along with B-modes polarization, primordial tensor fluctuations may contribute also to the stochastic background of gravitational waves (SGWB), the analogous of CMB for gravitational waves~\cite{Caprini_2018}. Interestingly, if the spectrum is enough blue-tilted, according to Eq.\eqref{PL} the inflationary contribution should be much amplified on scales of direct gravitational wave detection so that we can use data from ground-based interferometers such as LIGO and VIRGO to infer constraints on $n_{\rm T}$. Indeed these experiments set an upper bound on the fraction of the energy-density of the Universe in gravitational radiation $\Omega_{\rm GW}\lesssim 10^{-7}$ ~\cite{LIGO_SGWB-2017,LIGO_SGWB-2019} in the frequency range $f\in\left(20\,\rm{-}\,85.8\right)$ Hz (which corresponds to the wave-number range $k_{\rm LV} \in \left(1.3\,\rm{-}\,5.5\right)\times 10^{16} \,\rm{Mpc}^{-1}$), leading to a more stringent upper limit $n_T < 0.52$ at 95\% CL ~\cite{Akrami:2018odb}. While this approach is largely used in the literature, it should be noted that these bounds are obtained by extrapolating the relation \eqref{PL} on frequencies (those probed by GWs experiments) where it is not granted that the spectrum still follows a power-law behavior. High wave-numbers $k$ correspond to modes that exit the horizon relatively close to the end of inflation where the spectrum may strongly depend on the higher-order terms in Eq.~\eqref{PL}~\cite{Giare:2020vhn} and therefore on the specific form of the inflationary potential~\cite{Kinney:2021nje}, making it extremely difficult to derive reliable model-independent bounds on the tensor-tilt.
Another interesting possibility to gain constraining power on blue-tilted models of inflation is to study the effects induced by PGWs in the early Universe, before the recombination epoch. Behaving as extra radiation, a sizable amount of tensor perturbations may significantly contribute to the energy budget of the Early Universe, increasing the effective number of relativistic species $N_{\rm eff}$. As we shall see, this contribution depends on the integrated energy-density in gravitational waves over all scales and it exponentially grows when $n_{\rm T}>0$. So, in principle, we can use the Big Bang Nucleosynthesis (BBN) limit on additional radiation ($\Delta N_{\rm eff}\lesssim 0.4$) to infer constraints on blue-tilted models of inflation. Also, this approach is largely followed in literature, leading to a limit $n_{\rm T}\lesssim 0.4$ that is more or less of the same order as those inferred by gravitational wave experiments, see \textit{e.g.} Refs.\cite{Allen:1997ad,Smith:2006nka,Boyle:2007zx,Kuroyanagi:2014nba,Ben-Dayan:2019gll,Aich:2019obd,Cabass:2015jwe}.
In the present work, we would like to focus a bit closer on this latter scenario. In \autoref{sec.2}, we review in details the basic theoretical aspects of gravitational wave propagation in the early Universe, while in \autoref{sec.3} we review the state-of-the-art analyses, outlining some important caveats and showing that the results share the same difficulties discussed so far. Also in this case the largest inflationary contributions to the effective number of relativistic species come from tensor modes that exit the horizon very close to the end of inflation, precisely when the slow-roll approximation is no longer valid and the power-law parametrization breaks down. Consequently, any calculation becomes model-dependent and accurate analyses are needed to correctly estimate the relic radiation resulting from primordial tensor modes. To prove this point and confer additional physical meaning to our findings, in \autoref{sec.4} we explicitly compute the energy budget of the Universe in several general Effective Field Theory (EFT) realizations of (blue and red) inflation. By integrating a set of differential equations we correctly predict the evolution of the spectrum (and all the other dynamical quantities) over the different cosmic epochs and scales. Finally, we present our conclusion in \autoref{sec.5}.
\section{Gravitational Radiation in the early Universe}
\label{sec.2}
We consider a spatially flat FLRW metric, whose perturbed line element
in synchronous gauge reads~\cite{Ma:1995ey}
\begin{equation}
d s^{2}=a^{2}(\eta)\left[d \eta^{2}-\left(\delta_{i j}+h_{i j}\right) d x^{i} d x^{j}\right]
\end{equation}
with $a$ and $\eta$ denoting scale factor and conformal time, respectively. In this picture, generic tensor perturbations are described by the transverse and traceless part of the symmetric $3 \times 3$ matrix $h_{ij}$. In the Fourier space, focusing on one particular polarization state and a given mode $k$, the gravitation weave field satisfies the usual equation of motion~\cite{Lyth:2009}
\begin{equation}
h_{k}^{\prime \prime}+2 \mathcal{H} h_{k}^{\prime}+k^{2} h_{k}=0
\label{eq:motion}
\end{equation}
where the prime indicates the derivative with respect to the conformal time and $\mathcal H = a^{\prime}/a$. Since here we are mainly interested in primordial gravitational waves, it is particularly convenient to characterize the gravitational field in terms of its power spectrum
\begin{equation}
\mathcal P_{\rm T}(k) = \frac{2 k^3}{\pi} \, \left |h_k(\eta_i)\right|^2
\end{equation}
where, for each mode $k$, $h_k(\eta_i)$ specifies the value of the field at some initial conformal time $\eta_i$. In this way, connecting this picture to inflation simply requires identifying the power spectrum of the gravitational field with the primordial spectrum of inflationary tensor modes.
In the early Universe, a satiable background of gravitational waves will clearly increase the energy-budget by providing an additional form of radiation. Here we parameterize this contribution in terms of corrections to the effective number of relativistic degrees of freedom $N_{\rm eff}$. Within the Standard Model of particle physics this parameter acquires the reference value of $N_{\rm eff} = 3.044$~\cite{Mangano:2005cc,2016JCAP...07..051D,Akita:2020szl,Froustey:2020mcq,Bennett:2020zkv}, counting three different families of relativistic neutrinos plus an additional contribution coming from the non-instantaneous neutrino decoupling. To understand how this reference value is modified in presence of additional gravitational radiation, we focus on temperatures $T\gtrsim \mathcal O(1)$ MeV when the relativistic species in the Universe were electrons (and their antiparticles, positrons) $e^{\pm}$, neutrinos $\nu$ and photons $\gamma$. Including also the contributions of gravitons, the total amount of radiation will read \cite{Maggiore:1999vm}
\begin{equation}
\rho_{\rm rad} = \frac{\pi^2}{30} \left[ 2 \, T_{\gamma}^4 + \frac{7}{4}\, T_{e^{\pm}}^4 + \frac{7}{4} \,N_{\rm eff}\, T_{\nu}^4 + 2 \, T_{\rm GW}^4 \right]
\end{equation}
where the factor 2 in front of $T_{\rm GW}$ counts the two different polarization states $(+,\times)$ of tensor perturbations. Apart from the gravitons, all the other species were in thermal equilibrium and shared the same temperature: $T_{\gamma}=T_{e^{\pm}}=T_{\nu}$. Therefore it is straightforward to see that we can describe gravitational radiation as an additional contribution to the effective number of relativistic species
\begin{equation}
\Delta N_{\rm eff}^{\rm GW} = \frac {8}{7} \frac{T_{\rm GW}^4}{T_{\gamma}^4}=\left. \frac {8}{7} \frac{\rho_{\rm GW}}{\rho_{\gamma}}\right|_{\rm T_{\gamma}\gtrsim \mathcal O(1) \,\text{MeV}}
\end{equation}
To re-scale this contribution to the present time, we must consider that after $T\gtrsim \mathcal O(1)\,\rm{MeV}$, as the the Universe expands, the gravitational wave energy-density decays as $\rho_{\rm GW}\sim 1/a^4$, while, assuming entropy conservation, the CMB photon energy-density evolves as $\rho_{\gamma} \sim 1 /\left(a^{4} g_{*, s}^{4 / 3}\right)$ with $g_{*, s}$ the number of entropic degrees of freedom. Therefore the present-day contribution will be given by
\begin{align}
\Delta N_{\rm eff}^{\rm GW} &=\left.\frac{8}{7}\left(\frac{g_{*, s}(T \gtrsim 1 \mathrm{MeV})}{g_{*, s}\left(T_{0}\right)}\right)^{\frac{4}{3}} \frac{\rho_{\mathrm{GW}}}{\rho_{\gamma}}\right|_{\rm Today}
\end{align}
with $g_{*, s}(T_0)\simeq 3.91$ the current number of entropic degrees of freedom.
While the present Cosmic Microwave Background energy density $\rho_{\gamma}$ is accurately measured~\cite{Planck:2019nip,Planck:2018jri,Aghanim:2018eyx}, the present-day fraction of the energy budget of the Universe in gravitational radiation (\textit{i.e.}, the ratio between the present GW energy density $\rho_{\rm GW}$ and the critical density, $\rho_c=3H^2/8\pi G$), can be easily computed by integrating the spectrum over all scales~\cite{Maggiore:1999vm,Boyle:2005se,Guzzetti:2016mkm}
\begin{equation}
\Omega_{\mathrm{GW}}=\frac{1}{12 H_{0}^{2}} \int \text{d} \ln k \, \mathcal P_{\rm T}(k) \, \frac{\text{d} T(\eta_0,k)}{\text{d}t}
\label{Eq:full_OmGW}
\end{equation}
where the contribution of each mode is weighted by (the time derivative of) the so-called transfer function
\begin{equation}
T(\eta,k)=\frac{h_k(\eta)}{h_k(\eta_i)}
\end{equation}
that takes into account the different time-evolution of modes with different $k$ according to Eq.\eqref{eq:motion}. Assuming that inflation is followed by a standard Hot Big Bang Theory evolution, (\textit{i.e.}, by radiation, matter, and dark energy dominated epochs), the transfer function admits relatively simple semi-analytic solutions and we can estimate the present time contribution at generic frequency $f=k/2\pi$ as~\cite{Akrami:2018odb,Bartolo:2016ami,Cabass:2015jwe,Stewart:2007fu,Graef:2018fzu,Liu:2015psa}
\begin{equation}
\Omega_{\mathrm{GW}}(f) \simeq\frac{\mathcal P_{\mathrm{T}}(f)}{24 z_{\mathrm{eq}}}
\label{OmegaGW}
\end{equation}
with $z_{\mathrm{eq}}\simeq 3400$ the redshift at equivalence and $\mathcal P_{\mathrm{T}}$ the spectrum of primordial tensor modes. By using Eq.\eqref{OmegaGW}, putting everything together, we finally get~\cite{Maggiore:1999vm}
\begin{equation}
\Delta N_{\rm eff}^{\rm GW} \simeq \frac{h_0^2}{5.6\times10^{-6}}\left(\frac{1}{24\,z_{\rm eq}}\right) \int_{f_{\rm min}}^{f_{\rm max}} \frac{\mathrm{d}f}{f}\, \mathcal P_{\rm T}(f)
\label{Int1}
\end{equation}
recovering the standard result that Gravitational Waves contribute to the effective number of relativistic species through the logarithmic integral of their power spectrum over frequencies.
\section{Parametric Analysis}
\label{sec.3}
\subsection{State-of-the-art analyses}
\label{sec.3.1}
Following the picture drawn in the previous section, we now turn to analyze the contribution of inflationary tensor modes to the effective number of relativistic degrees of freedom in the early Universe. From Eq.~\eqref{Int1} it is evident that such contribution will depend on (i) the frequency range $f\in[f_{\rm min}\,,\,f_{\rm max}]$ over which the integral runs and (ii) the (parametrization of) primordial tensor spectrum.
(i) The choice of the frequency range on which the integral runs is quite debated. In particular, the infrared cutoff can be safely set to $f_{\rm min} = 10^{-10}\,\rm{Hz}$ which approximately corresponds to the size of the comoving horizon at the time of BBN~\cite{Cabass:2015jwe,Pritchard:2004qp,Smith:2006nka}. Conversely, the ultraviolet cutoff is more arbitrary. Being primordial gravitational waves produced during inflation, we expect an ultraviolet cutoff of the size of the horizon at the end of inflation~\cite{Meerburg:2015zua} (as PGWs with smaller wavelengths cannot be produced). Anyway, the size of the horizon at the end of inflation depends on the reheating temperature $T_{\rm RH}$ at the end of inflation. Assuming an almost GUT-scale inflation and an instant reheating we can set $T_{\rm RH}\sim 10^{15}\,\rm{GeV}$ which corresponds to $k_{\rm end}\sim 10^{23}\,\rm{Mpc}^{-1}$ and thus $f_{\rm max}\simeq 10^{8}\,\rm{Hz}$~\cite{Cabass:2015jwe}. Nevertheless, inflationary models with (very) lower reheating temperatures $T_{\rm RH}\sim 10^{10} - 100\, \rm{GeV}$ have been proposed in the literature (see e.g., Refs.~\cite{Kawasaki:1999na,Kawasaki:2000en,Giudice:2000dp,Giudice:2000ex,Hannestad:2004px,Khoury:2011ii,Hasegawa:2019jsa,Hasegawa:2020ctq,Carenza:2021ebx,Freese:2017ace,Litsa:2020rsm}) and, although such scenarios are typically not easy to realize, in these models the ultraviolet cutoff may be much smaller, limiting the high-frequency contributions in the integral \eqref{Int1}, see also Refs.~\cite{Vagnozzi:2020gtf,Benetti:2021uea}.
(ii) The main purpose of this section is to study the dependence of the integral \eqref{Int1} from the parametrization used for the primordial tensor spectrum $\mathcal P_{ \rm T}$. The common practice in literature is to assume a power-law tensor spectrum given by Eq.~\eqref{PL} over the whole range of integration so that the integral \eqref{Int1} can be easily solved analytically:
\begin{align}
\Delta N_{\rm eff}^{\rm GW}& \simeq \frac{h_0^2}{5.6\times10^{-6}}\left(\frac{ r A_s}{24\,z_{\rm eq}}\right) \frac{1}{n_{\rm T}} \left[\left(\frac{f}{f_{\star}}\right)^{n_{\rm T}} \right]^{f_{\rm max}}_{f_{\rm min}}
\label{eq:limit1}
\end{align}
Interestingly, a blue tensor tilt exponentially amplifies the GWs production on ultraviolet frequencies - that therefore we expect to contribute mostly in Eq.~\eqref{Int1} - possibly leading to a sizable $\Delta N_{\rm eff}$ from PGWs. As we already discussed in the introduction, this effect is commonly used in literature to bound blue-tilted models of inflation, with several Implications also for gravitational waves observations~\cite{Vagnozzi:2020gtf,Benetti:2021uea,Vagnozzi:2022qmc} and fundamental physics~\cite{Calcagni:2020tvw}. For instance, assuming a GUT scale inflation ($f_{\rm max}\sim 10^{8}$ Hz) and a tensor amplitude $r\sim 0.001$, it is easy to see that the BBN limit on the the effective number of relativistic species ($\Delta N_{\rm eff}\lesssim 0.4$) is naturally translated into a limit $n_{\rm T}\lesssim 0.4$ by Eq.~\eqref{eq:limit1}, see also \autoref{fig:figure1} and \hyperref[sec.Appendix]{Appendix A} where an updated analysis of the observational constraints resulting from the BBN is carried out. We devote the rest of this section to studying how much robust these bounds are.
\subsection{Next-to-leading order parameterization}
\label{sec.3.2}
A first naive consideration is that the above mentioned result is derived assuming the tensor tilt to be exactly constant under the whole range of integration. Typically, in physical models of inflation where the tensor tilt can acquire such large positive values, it may also acquire a non-negligible scale dependence ~\cite{Giare:2019snj,Giare:2020plo}. Therefore, a first attempt to question the strength of this result is to study what happens extending the power low relation \eqref{PL} to its next-to-leading order generalization
\begin{equation}
\ln \mathcal P_{\rm T}(k)=\ln(r\,A_{\rm s}) + n_{\rm T}\,\ln(k/k_{\star}) + \alpha_{\rm T}\,\ln^2(k/k_{\star})
\label{PL2}
\end{equation}
where we parametrize the scale dependence of the tensor tilt by including its running $\alpha_{\rm T}\doteq dn_{\rm T} / d\ln k$.
In \autoref{fig:figure1}, we show the effect of a relatively small running of the tensor tilt on the calculation of $\Delta N_{\rm eff}^{\rm GW}$ finding that it can significantly change the results and so lead to a much tighter (relaxed) constraint on $n_{\rm T}$ represented by the horizontal dashed line in the figure. We postpone a rigorous analysis of the effects of a running of the tensor tilt on the observational constraints resulting from the BBN to \hyperref[sec.Appendix]{Appendix A}. Here we point out that a positive (negative) $\alpha_{\rm T}$ amplifies (suppresses) the power spectrum on high frequency and its contributions in the integral \eqref{Int1}, providing another important clue that properly accounting for the ultraviolet behavior of the tensor spectrum may be crucial in the calculation of $\Delta N_{\rm eff}^{\rm GW}$. In this regard, we notice that modes with frequency $f=k/2\pi$ will cross horizon $N_{k}$ e-folds before the end of inflation, where $N_{k}$ is given by~\cite{Martin:2013tda,Kinney:2021nje}
\begin{align}
\nonumber N_{k}\simeq&-\ln \left(\frac{k}{a_{0} H_{0}}\right)+\ln \left(\frac{H_{\star}}{H_{\rm {end}}}\right)-\frac{2}{3}\ln\left(\frac{T_{\rm RH}}{\Lambda}\right) \\ &\nonumber +\ln \left(\frac{T_{\rm{RH}}}{T_{\rm {\rm{eq}}}}\right)+\frac{1}{3} \ln \left(\frac{g_{* S}\left(T_{R H}\right)}{g_{* S}\left(T_{\rm{eq}}\right)}\right) \\ &+\ln \left(\frac{a_{\rm{eq}}H_{\rm{eq}}}{a_0 H_0}\right) .
\label{Nk}
\end{align}
In the equation above $a_0H_0= 2.248 \times 10^{-4} \rm{Mpc}^{-1}$ is the inverse of the comoving horizon size in the current Universe, $H_\star$ is the value of the Hubble parameter at the horizon exit, $H_{\rm end}$ is the Hubble parameter at the end of inflation, $\Lambda$ is the energy scale of inflation and the subscript "eq" denotes quantities evaluated at matter-radiation equality. Assuming a standard $\Lambda$CDM cosmology, we have $\ln \left[(a_{\rm{eq}} H_{\rm{eq}}) /(a_0 H_0) \right]\simeq 3.8$ and $T_{\rm eq}\simeq 8\times10^{-10}$ GeV~\cite{Martin:2013tda,Planck:2018jri,Forconi:2021que}. Approximating $H_{\rm end}\simeq H_{\star}$ and recalling that the energy scale of inflation can be related to the amplitude of tensor perturbations as $\Lambda\simeq r^{1/4}\times 3.3\times 10^{16}\rm{GeV}$, we can simplify Eq.~\eqref{Nk} to
\begin{align}
N_{k}\simeq 61-\ln \left(\frac{k}{a_{0} H_{0}}\right)+\frac{1}{3}\ln\left(\frac{T_{\rm RH}}{10^{15}\,\rm{GeV}}\right) +\frac{1}{6}\ln\left(r\right) \,.
\label{Nk}
\end{align}
Therefore the "high frequencies" in the integral \eqref{Int1} we are referring to, correspond to tensor modes that exit the horizon extremely close to the end of inflation ($N_k\lesssim 2$ for $k\gtrsim 10^{21}\,\rm{Mpc^{-1}}$ and $T_{\rm RH}\sim 10^{15}$ GeV and $r\sim 10^{-3}$). This is precisely where, at least in the simplest inflationary scenarios, the potential decreases very rapidly to approach its minimum, and the slow-roll dynamics breaks down. As pointed out in Refs.~\cite{Kinney:2021nje,Giare:2019snj}, it is not sure at all that a power-law parameterization (or even its next-to-leading order generalization) holds - even approximately - on such frequencies because the shape of the tensor spectrum will be strongly related to the shape of the inflationary potential. As a result, we argue the calculation of $\Delta N_{\rm eff}^{\rm GW}$ to be largely sensitive to the underlying model.
\begin{figure}[t]
\centering
\includegraphics[width=\columnwidth]{Figure1.png}
\caption{\small Inflationary tensor mode contribution to the effective number of relativistic degrees of freedom as a function of the tensor tilt and its running $\alpha_{\rm T}$. The black dashed line represents the contribution for $\alpha_{\rm T}=0$ while the horizontal dashed line represents the limit on additional radiation from the BBN bounds.}
\label{fig:figure1}
\end{figure}
\subsection{Higher-order stochastic reconstruction}
\label{sec.3.3}
A more general approach to the problem can be obtained by expanding (the log of) the tensor spectrum as a series of powers
\begin{align}
\ln \mathcal P_{\rm T}= \sum_{j=0}^{\infty} a_j (x-x_0)^j .
\label{EXP}
\end{align}
If we choose the CMB frequency as the center of the expansion ($x_0=\ln f_{\star}$) the coefficients $a_j$ can be trivially related to (the derivatives of) the tensor spectrum evaluated at the CMB scales. In particular, the tensor amplitude and the tensor tilt are simply given by
\begin{equation}
a_0= \ln(rA_S), \quad a_1=\frac{d\ln \mathcal P_{\rm T}}{ d\ln f}\equiv n_{\rm T}
\label{eq:a0a1}
\end{equation}
while the higher order coefficients are related to the higher order derivatives of the spectrum (or the tensor tilt) as:
\begin{equation}
\quad a_{j>1}=\frac{1}{j!} \frac{d^j\ln \mathcal P_{\rm T}}{ d\ln^j f} = \frac{1}{j!} \frac{d^{j-1} n_{\rm T}}{d\ln^{j-1} f}.
\label{eq:aj}
\end{equation}
Notice that if we stop the sum expansion at $j=1$ or $j=2$, we exactly recover Eq.\eqref{PL} or Eq.\eqref{PL2}, respectively. Therefore including more and more terms in the sum will clearly guarantee a more accurate reconstruction of the tensor spectrum at $x \gg x_0$ since it employs also the other higher-order terms in the expansion. However, if we want to adopt this parameterization in the integral \eqref{Int1}, we need to make sure that this sum will actually converge on the frequencies over which the integration runs. Although this depends on the specific model of inflation, in most models the tensor spectrum is a slow-evolving regular function of the frequency so that it is reasonable to expect a global convergence. For instance, the simplest slow-roll scenario is characterized by a hierarchy of parameters $n_{\rm T}=\mathcal O(\epsilon)$ and $d^{j} n_{\rm T} /d\ln^{j} f\lesssim \mathcal O(\epsilon^{j+1})$. Assuming such a scaling, the sum convergence can be easily proved by evaluating the radius of convergence
\begin{equation}
\frac{1}{R}\doteq\lim_{j\to \infty} \left|\frac{a_{j+1}}{a_j}\right| = \lim_{j\to \infty} \left|\frac{\mathcal O(\epsilon)}{j+1}\right|= 0.
\end{equation}
So, in principle, we can adopt this parameterization to predict the value of the tensor spectrum at $x\gg x_0$. Anyway, in practice, all the arbitrariness of the method is encapsulated into the coefficients $\{a_j\}$. Ultimately, fixing their values is equivalent to fixing a specific model of inflation. Here we sample different inflationary models by randomly varying the coefficients $\{a_j\}$ as follows:
\begin{itemize}[leftmargin = *]
\item We fix the tensor amplitude\footnote{ Notice that $\Delta N_{\rm eff}^{\rm GW}$ can be easily obtain for any generic $r$ simply re-scaling the value obtained for $r=10^{-3}$ as
$$ \Delta N_{\rm eff}^{\rm GW}(r) = \left(\frac{r}{10^{-3}}\right) \bigg[\Delta N_{\rm eff}^{\rm GW}\bigg]_{r=10^{-3}} $$} on the CMB scales to $r\sim 10^{-3}$ (which is the target of the next CMB experiments) so that $a_0$ is always fixed by Eq.\eqref{eq:a0a1};
\item We let the tensor tilt randomly vary in the range $n_{\rm T}\in [-0.5,1]$ thus evaluating $a_1$ according to Eq.\eqref{eq:a0a1}. In this way, we can explore both blue and red tilted models\footnote{Notice that we are relaxing the slow-roll consistency relation between the tensor tilt and the tensor amplitude ($n_{\rm T}\ne -r/8$) and considering the two parameters as independent.};
\item We randomly choose the higher-order coefficients $\{a_{j>1}\}$ to be extremely small such that $a_1\gg a_{j}\gg a_{j+1}$. This is done by assuming the $j$-order derivative of the tensor spectrum in Eq.\eqref{eq:aj} to be a Gaussian distributed with mean $\mu=0$ and standard deviation $\sigma\simeq 10^{-2j}$. While this is clearly an arbitrary assumption, in this way we can be sure that the spectrum follows a power-law \eqref{PL} on the CMB scales ($x\simeq x_0$) where such terms remain in fact negligible. In addition, this ensures a fast convergence of the sum expansion on high frequencies ($x \gg x_0$) while granting a certain freedom.
\end{itemize}
Following this scheme we simulate $10^{6}$ different shapes of the tensor spectrum as functions of frequency up to the order $j=10$ in the sum expansion\footnote{We checked that maintaining this scaling for parameters, the 10th order is enough to capture any relevant correction to the tensor spectrum.}. Examples of the spectra obtained within this method are provided in \autoref{fig:figure2}, together with a simple leading order power-law approximation (red line).
Notice that we consider both negative and positive coefficients $\{a_j\}$, so that, on high frequencies, the spectrum can be either suppressed or amplified. Indeed, while in the simplest cases we expect suppression of power because of the rapid decrease of inflationary potential (see also the subsequent discussion in \autoref{sec.4}), in more elaborated scenarios it is in principle possible to build inflationary models with ultraviolet amplification of tensor perturbations~\cite{Oikonomou:2022ijs,Barrow:1993ad,Peng:2021zon,Ota:2022hvh,Odintsov:2022sdk,Baumgart:2021ptt}. As explained in the introduction, in this latter case we may end up with large amounts of GW on the small scales as those probed by Gravitational interferometers. Therefore, for all the simulated spectra, we also checked that the amplitude $\mathcal P_{\rm T}(k)$ remains consistent with the LIGO/VIRGO limit, keeping only the models able to satisfy observations. This is the reason why in \autoref{fig:figure2} we get much more suppressed spectra than amplified ones. From the same figure, we can also appreciate how the usual power-law parametrization is a precise approximation only at frequencies corresponding to the CMB scales (as required by construction) while important deviations are observed at higher frequencies, in spite of our efforts for keeping small the parameters $\{a_j\}$.
\begin{figure}
\centering
\includegraphics[width=\columnwidth]{Figure2.png}
\caption{\small Examples of randomly generated tensor spectra (and the power-law extrapolation, red line) obtained by following the method outlined in \autoref{sec.3.3}.}
\label{fig:figure2}
\end{figure}
\begin{figure*}
\centering
\includegraphics[width=0.8\linewidth]{Figure3.png}
\caption{\small Primordial Gravitational Wave contribution to radiation energy-density in the early Universe parametrized as a correction to the effective number of relativistic species ($\Delta N_{\rm eff}^{\rm GW}$). All the inflationary models in the figure share the same tensor amplitude ($r\simeq 0.001$) and the same reheating temperature ($T_{\rm RH}\sim 10^{15} \text{GeV}$) but have different values of tensor tilt ($n_{\rm T}$) shown in the $x$-axis. The red thick line represents the predictions for $\Delta N_{\rm eff}^{\rm GW}$ inferred by extrapolating a power-law parameterization for the tensor spectrum (\autoref{PL}) over all frequencies. The gray dots represent the results of the parametric analysis carried out in \autoref{sec.3.3} where the spectrum is expanded as a sum of powers up to the 10th order (\autoref{EXP}) and randomly reconstructed. Finally, the magenta points represent the observable predictions of an ensemble of physical models randomly realized within the framework of the Effective Field Theory of inflation by means of a theoretical Monte Carlo. In this latter case, the spectrum is calculated by integrating a system of coupled differential equations (known as "Hubble Flow Equations"), as discussed in \autoref{sec.4}. The horizontal red band (dashed line) represents the current (future forecasted) observational limit on radiation.}
\label{fig:figure3}
\end{figure*}
Fixing the ultraviolet cutoff to $f_{\rm max}\simeq 10^{8}\,\rm{Hz}$, we numerically solve the integral \eqref{Int1} for all the different shapes of $\mathcal P_{\rm T}(f)$, thus computing the corresponding value of $\Delta N_{\rm eff}^{\rm GW}$. We ensure the computational relative error due to the numerical integration method to remain smaller than 1\%. In \autoref{fig:figure3} we show the results of our random analysis. Once again the red solid line represents the contribution $\Delta N_{\rm eff}^{\rm GW}$ obtained within the power-law parametrization \eqref{PL}. Instead, the gray dots represent the values of $\Delta N_{\rm eff}^{\rm GW}$ obtained by the numerical integration method of the randomly obtained tensor spectra.
Despite the intrinsic aleatory nature of this method, we can certainly draw some general conclusions. First of all, as evident from \autoref{fig:figure2}, the high-frequency behavior of the tensor spectrum may become basically uncorrelated with the value of the tensor tilt on the CMB scales. This goes in the direction of previous analyses already discussed in the literature, see \textit{e.g.}, Refs.~\cite{Graef:2018fzu, Kinney:2021nje}. In addition, the results displayed in \autoref{fig:figure3} lead weight to our previous considerations according to which the value of $\Delta N_{\rm eff}^{\rm GW}$ may be strongly sensitive to the high-frequency contributions in the integral \eqref{Int1}. Since on such frequencies the spectrum becomes uncorrelated with the behavior of the tensor tilt on the CMB scale, these findings lead us to believe that the BBN limit on additional radiation can hardly constrain the tensor tilt itself, unless without a full understanding of the underlying model. In this regard, we conclude with a final remark: so far we just performed a parametric analysis to investigate how different parameterizations of the tensor spectrum may impact the final calculation of $\Delta N_{\rm eff}^{\rm GW}$. While we believe that this discussion can be useful for pointing out caveats and weaknesses of the state-of-the-art analyses, clearly a reliable investigation of physical models of inflation, and their respective contribution to the energy budget of the early Universe, is still missing. This will be our goal in the next section.
\section{Physical Analysis}
\label{sec.4}
The lesson we have learned from the parametric analyses detailed in the previous section is that the calculation of relic radiation from primordial gravitational waves depends crucially on the behavior of the primordial tensor spectrum at ultraviolet frequencies. Given that assuming a power-law continuously on all frequencies is not reliable~\cite{Giare:2020vhn, Kinney:2021nje}, the calculation of $\Delta N_{\rm eff}^{\rm GW}$ becomes unreliable in turn. Motivated by these results, in this section we want to provide a definitive evidence that this issue persists in solid theoretical framework of inflation, conferring physical meaning to our findings. In addition, we want to quantify the typical error resulting from extrapolating a power-law parameterization by going through a precise evaluation of the radiation energy-density for a reasonable range of different models and possibilities.
In order to investigate the observable predictions of a very broad class of inflationary models in the most general framework, we follow a methodology based on the so-called Hubble Flow Equation~\cite{Hoffman:2000ue,Kinney:2002qn,Easther:2002rw,Friedman:2006zt}. The Hubble Flow Equations were first introduced by Hoffman and Turner~\cite{Hoffman:2000ue} for the simplest single-field slow-roll case where it is straightforward to define an infinite hierarchy of slow-roll parameters that, starting from the Hubble parameter $H$ and its derivatives with respect to the field, completely specify the evolution of the main observable quantities during inflation. Since the integration of the equations yields a trajectory in slow-roll parameter space that can be ultimately interpreted as a model whose dynamics is a solution of the flow equations, solving numerically a truncated system of Hubble Flow Equations for a set of suitably defined initial conditions has been proposed as a sophisticated algorithm for generating large numbers of slow-roll inflationary models, without relying on the explicit form of the action~\cite{Kinney:2002qn}.
Recently, in Ref.~\cite{Capurri:2020qgz} the method has been extended to the Effective Field Theory (EFT) framework of inflation to include a much broader class of beyond-standard inflationary models and explore a wide variety of possible high-energy corrections to the simplest slow-roll scenario. In this section, we follow this latter generalized approach to investigate in a more general and reliable way the actual contribution of inflationary tensor perturbations to the energy budget of the early Universe. We start reviewing the Hubble Flow Equations in the Effective Field Theory of Inflation, strictly following Ref.~\cite{Capurri:2020qgz}. Then we explain how we adapt this method to our investigation. Finally, we discuss the results.
\subsection{Hubble Flow Equations and EFT of Inflation}
The EFT of inflation~\cite{Cheung:2007st,Weinberg:2008hq} is a very general framework for describing fluctuations
around a quasi-de Sitter background. The general form of the effective action
in the comoving gauge reads
\begin{equation}
\begin{aligned} S=& \int d^{4} x \sqrt{-g}\left[\frac{1}{2} M_{\mathrm{pl}}^{2} R-c(t) g^{00}-\Lambda(t)+\right.\\ &+\frac{1}{2 !} M_{2}(t)^{4}\left(g^{00}+1\right)^{2}+\frac{1}{3 !} M_{3}(t)^{4}\left(g^{00}+1\right)^{3}+\ldots \\ &\left.-\frac{\bar{M}_{1}(t)^{3}}{2}\left(g^{00}+1\right) \delta K_{\mu}^{\mu}-\frac{\bar{M}_{2}(t)^{3}}{2} \delta K_{\mu}^{\mu 2}\right.\\ &\left.-\frac{\bar{M}_{3}(t)^{3}}{2} \delta K_{\nu}^{\mu} \delta K_{\mu}^{\nu}+\ldots\right] \end{aligned}
\label{eq:EFT_action}
\end{equation}
For the following discussion, it is useful to divide this action into two different blocks and analyze them separately.
The fist important block is given by the first line of Eq.~\eqref{eq:EFT_action} that we rewrite below for convenience:
\begin{equation}
S_{\rm{bg}}=\int d^{4} x \sqrt{-g}\left[\frac{1}{2} M_{\mathrm{pl}}^{2} R-c(t)g^{00}-\Lambda(t)\right]
\label{eq:background}
\end{equation}
It contains the standard Einstein-Hilbert action and terms that are linear perturbations around the background. Therefore, once that the time-dependent coefficients $c(t)$ and $\Lambda (t)$ have been specified, this part of the action completely fixes the background evolution during inflation. Notice also that the evolution of the parameters $c(t)$ and $\Lambda (t)$ can be related to the evolution of the Hubble parameter by the Friedmann equations
\begin{equation}
H^{2}=\frac{1}{3 M_{\mathrm{pl}}^{2}}[c(t)+\Lambda(t)] \quad \text { and } \quad \frac{\ddot{a}}{a}=-\frac{1}{3 M_{\mathrm{pl}}^{2}}[2 c(t)-\Lambda(t)]
\label{eq:lambda}
\end{equation}
so we need only two independent functions to fully characterize the background evolution that we choose to be $H(t)$ and $c(t)$, fixing $\Lambda(t)$ by Eq.~\eqref{eq:lambda}. Starting from Eq.~\eqref{eq:background}, we take a first step deriving the generalize Hubble Flow Equations for the background parameters. In analogy with the standard case, we take as our fundamental quantity the Hubble parameter as a function of inflaton field, $H(\phi)$. To switch from the time domain to field domain we can exploit a relation betweeen the time-derivative of the field, $c(\phi)$ and $H(\phi)$ that follows from a combination of the Friedmann equation and the continuity equation, namely:
\begin{equation}
\frac{\text{d}\phi}{\text{d}t}=-\frac{c(\phi)}{M_{\mathrm{pl}}^{2} H^{\prime}(\phi)}
\end{equation}
where, from now on, the prime indicates a derivative with respect to the field ($X^{\prime } = d X / d\phi$). Using the relation above, it is easy to see that the slow roll parameter $\epsilon$ becomes:
\begin{equation}
\epsilon=-\frac{\dot{H}}{H^{2}}=\frac{c(\phi)}{M_{\mathrm{pl}}^{2} H^{2}(\phi)}
\end{equation}
Starting from $\epsilon$, we can define the higher-order slow-roll parameters by iterated derivations:
\begin{equation}
\begin{aligned} \eta(\phi)=& \frac{c(\phi)}{M_{\mathrm{pl}}^{2}} \frac{H^{\prime \prime}(\phi)}{H(\phi) H^{\prime 2}(\phi)} \\ & \vdots \\{ }^{l} \lambda(\phi) &=\left(\frac{c(\phi)}{M_{\mathrm{pl}}^{2}}\right)^{l}\left(\frac{1}{H(\phi)}\right)^{l}\left(\frac{1}{H^{\prime}(\phi)}\right)^{l+1} \frac{d^{l+1} H(\phi)}{d \phi^{l+1}} \end{aligned}
\label{Htower}
\end{equation}
with $l \geq 2$ and $\eta(\phi)\equiv \, ^{1}\lambda(\phi)$. Notice however that, in contrast with the standard Hubble flow equations, now the evolution of $\epsilon$ and the other higher-order parameters will depend also on the additional unknown function $c(\phi)$. Therefore we need to define other new slow-roll parameters to describe the evolution of $c(\phi)$. Following the notation of Ref~\cite{Capurri:2020qgz} we introduce the parameter $\theta$
\begin{equation}
\theta \equiv-\frac{\dot{c}}{H c}=\frac{1}{M_{\mathrm{pl}}^{2}} \frac{c^{\prime}(\phi)}{H(\phi) H^{\prime}(\phi)}
\end{equation}
and the the other higher-order parameters by taking iterated derivations
\begin{equation}
\begin{aligned} \kappa(\phi) &=\frac{1}{M_{\mathrm{pl}}^{2}} \frac{c^{\prime \prime}(\phi)}{H^{\prime 2}(\phi)} \\ & \vdots \\ ^{l}{\xi}(\phi) &=\left(\frac{c(\phi)}{M_{\mathrm{pl}}^{2}}\right)^{l}\left(\frac{1}{H(\phi)}\right)^{l-1}\left(\frac{1}{H^{\prime}(\phi)}\right)^{l+1} \frac{1}{c(\phi)} \frac{d^{l+1} c(\phi)}{d \phi^{l+1}} \end{aligned}
\label{Ctower}
\end{equation}
always with $l \geq 2$ and $\kappa(\phi)\equiv \, ^{1}\xi(\phi)$. An explicit calculation of the equations above lead to derive the generalized Hubble flow equation for the background parameters~\cite{Capurri:2020qgz}:
\begin{equation}
\begin{cases}
\frac{\text{d}\epsilon}{\text{d}N}=\epsilon\,\left( \theta - 2\epsilon \right)\\
\frac{\text{d}\eta}{\text{d}N}= \eta\,\left( \theta - \epsilon -2\eta\right) +\,^{2}\lambda \\
\vdots
\\
\frac{\text{d} \, ^{l}\lambda }{\text{d}N} = \, ^{l}\lambda \, \left[ l\left( \theta -\epsilon \right) -\left(l+1\right)\eta \right] + \, ^{l+1}\lambda
\\
\\
\frac{\text{d}\theta}{\text{d}N}=\epsilon\,\kappa \, -\theta\,\left( \epsilon + \eta \right)\\
\frac{\text{d} {\kappa} }{\text{d}N} = -2\kappa\eta + \, ^{2}\xi\\
\vdots
\\
\frac{\text{d} \, ^{l}\xi }{\text{d}N} = \, ^{l}\xi \left[ \left(l-1\right)\left(\theta -\epsilon \right) -\left(l+1\right)\eta\right] + \, ^{l+1}\xi
\end{cases}
\label{eq:HFE_background}
\end{equation}
We stress that the integration of this system of coupled equations completely specifies the dynamics of the background during inflation.
The second block in the action~\eqref{eq:EFT_action}, involves the higher order operators that we have organized in powers of the number of perturbations and in terms of the
increasing number of derivatives:
\begin{equation}
\begin{aligned}
\Delta S = & \int d^{4} x \sqrt{-g}\left[ \sum_{n\geq 2} \frac{1}{n!}M_n(t)^{4}\left(g^{00}+1\right)^{n}\right. \\ &\left.-\frac{\bar{M}_{1}(t)^{3}}{2}\left(g^{00}+1\right) \delta K_{\mu}^{\mu}-\frac{\bar{M}_{2}(t)^{3}}{2} \delta K_{\mu}^{\mu 2}\right.\\ &\left.-\frac{\bar{M}_{3}(t)^{3}}{2} \delta K_{\nu}^{\mu} \delta K_{\mu}^{\nu}+\ldots\right]
\label{eq:DeltaS}
\end{aligned}
\end{equation}
These operators are turned on and off by the $M$ coefficients in the action, whose value will thus weight the relative effects. As we shall see, in their turn the coefficients $M$ can be related to physical quantities that can be in principle measured and constrained. Therefore, once we have reconstructed the background dynamics by solving the system~\eqref{eq:HFE_background}, it is useful to derive a further system
of equations to describe the evolution of the $M$ coefficients in Eq.~\eqref{eq:DeltaS} over that background. We can do so in a quite general and elegant way by noting that for any quantity described by a generic scalar function $Q(\phi)$, one can always define a slow-roll
parameter $\epsilon_Q$ as follows:
\begin{equation}
\epsilon_{Q}=-\frac{\dot{Q}}{H\,Q}=\frac{1}{M_{\mathrm{pl}}^{2}}\frac{c(\phi)}{H(\phi)\,H^{\prime}(\phi)}\,\frac{Q(\phi)}{Q^{\prime}(\phi)}
\label{eq:epsQ}
\end{equation}
In analogy to the discussion for the background parameters, we define also the higher-order parameters for the quantity $Q(\phi)$ by taking its derivatives:
\begin{equation}
\begin{aligned}
\rho_{Q}(\phi)&=\frac{1}{M_{\mathrm{pl}}^{2}} \frac{c(\phi)}{H^{\prime\,2}(\phi)}\frac{Q^{\prime \prime}(\phi)}{Q(\phi)}\\ & \vdots \\
{}^{l}\chi_{Q}(\phi)&=\left( \frac{c(\phi)}{M_{\mathrm{pl}}^{2}} \right)^l\,\left(\frac{1}{H(\phi)}\right)^{l-1}\,\left(\frac{1}{H^{\prime}(\phi)}\right)^{l+1}\,\frac{1}{Q} \frac{\text{d}^{l+1} \,Q}{\text{d}\phi^{l+1}}
\end{aligned}
\end{equation}
again with $l\geq 2$ and $\rho_{Q}(\phi)\equiv{}^{1}\chi_{Q}(\phi)$. By explicitly computing these relations, we eventually get the system of Hubble flow equations for $Q(\phi)$:
\begin{equation}
\begin{cases}
\frac{\text{d} \epsilon_{Q}}{\text{d} N}= \epsilon_{Q}\left(\theta - \epsilon -\eta -\epsilon_{Q} \right) + \, \epsilon\,\rho_{Q}\\
\frac{\text{d} \rho_{Q}}{\text{d} N}= \rho_{Q} \left(\theta - 2\eta -\epsilon_{Q}\right) + {}^{2}\chi_{Q}\\
\vdots
\\
\frac{\text{d} {}^{l}\chi_{Q}}{\text{d} N}= {}^{l}\chi_{Q} \left[l\theta -\left(l-1\right)\epsilon - \left(l+1\right)\eta -\epsilon_{Q} \right] + {}^{l+1}\chi_{Q}
\end{cases}
\label{eq:system_Q}
\end{equation}
Solving the system we can predict the evolution of any generic quantity $Q(\phi)$ that will depend also on the background via the slow-roll parameters $\epsilon$, $\eta$ and $\theta$, as expected. This means that, in principle, one can evolve all the $M$ coefficients in Eq.~\eqref{eq:DeltaS} and study different models of inflation in full generality.
\subsection{Theoretical Monte Carlo}
Our aim is to explore a reasonably large ensemble of physical models of inflation that can lead to a sizable gravitational wave production and calculate their contribution to the energy-density of the early Universe, accurately. In this regard, it is worth noting that taking into account all the operators in the quadratic effective action that induce tensor perturbations, one can derive the following leading order relation for the power-spectrum~\cite{Creminelli:2014wna,Noumi:2014zqa,Giare:2020vss}:
\begin{equation}
\mathcal P_{\rm T}= \frac{1}{c_{\rm T}}\left(\frac{H^2}{\pi^2\,M_{\mathrm{pl}}^{2}} \right)
\label{eq:PtCt}
\end{equation}
where $c_{\rm T}$ is the propagating speed of tensor modes that can be simply expressed in terms of $\bar{M}_3$ as $c_{\rm T}^{-2}=1 - \bar{M}_3^2 / M_{\mathrm{pl}}^{2}$ where $\bar{M}_3$ is defined in~\eqref{eq:EFT_action}. In this case, it is straightforward to see, from its definition, that the tensor tilt acquires a further correction
\begin{equation}
n_{\rm T}=-2\epsilon + \epsilon_{\rm T}
\label{ntt}
\end{equation}
where the evolution of the parameter
\begin{equation}
\epsilon_{\rm T}= - \frac{\dot{c}_{\rm T}}{H\,c_{\rm T}}
\label{ctepsilont}
\end{equation}
is clearly governed by the system \eqref{eq:system_Q}. It is also worth noting that in this framework the standard relation between the tensor amplitude and the tensor tilt does not hold anymore and more general consistency relations can be derived both in the absence and in presence of additional EFT operators, see Refs.~\cite{Giare:2020vss, Capurri:2020qgz} for detailed discussions. Anyway, all the cosmological observables can still be expressed in terms of the slow-roll parameters and in particular, the tensor spectrum and its evolution are fully determined by the evolution of the background and the parameter $\epsilon_{\rm T}$. This is an important achievement since through the flow equation method we can actually test the observable predictions of a large number of stochastically generated models, without relying on the specific form of their underlying actions. To optimize our model exploration, we proceed with a theoretical Monte Carlo as follows:
\begin{itemize} [leftmargin = *]
\item First and foremost, we notice that the hierarchy of flow equations must be truncated at finite order, which we choose to be the $4$th-order. Then, we draw a suitable set of randomly chosen initial conditions for the background parameters. In particular, we randomly choose the parameters introduced in the Hubble-tower \eqref{Htower} within the following ranges
\begin{gather*}
\epsilon_{\rm in}\in[0,0.8],\\
\eta_{\rm in}\in[-0.1,0.1],\\
^2\lambda_{\rm in}\in[-0.05,0.05],\\
^3\lambda_{\rm in}\in[-0.005,0.005],
\end{gather*}
while for the $c(\phi)$-tower \eqref{Ctower} the initial conditions are taken from the sets
\begin{gather*}
\theta_{\rm in}\in[-0.1,0.1],\\
\kappa_{\rm in}\in[-0.1,0.1],\\
^2\xi_{\rm in}\in[-0.05,0.05],\\
^3\xi_{\rm in}\in[-0.005,0.005].
\end{gather*}
These ranges are very similar to those in \cite{Kinney:2002qn} and \cite{Capurri:2020qgz}.
\item Once the initial conditions are chosen, we solve the Hubble flow equations \eqref{eq:HFE_background} for the background slow-roll parameters. Specifically, we integrate the equations forward in time for at most $\sim10^4$ e-folds of expansion. Then, apart from the unfortunate cases where the integration did not survive, we expect two possible outcomes: either we reach a fixed point (that we eliminate) or we manage to get the end of inflation defined by the usual relation $\epsilon=1$. In this latter case, we store all the background parameters as functions of the number of e-folds $N$ before the end of inflation (\textit{i.e.}, $N=0$ corresponding to $\epsilon=1$). Given a large number of repetitions ($\gtrsim 10^4$), approximately $90\%$ of the time the end of inflation is successfully reached.
\item We then check that the models stored in the previous point allow a sufficient long phase of expansion and are able to explain observations. To do so we use the values reached by parameters at the end of inflation as new initial conditions at $N=0$ and perform a backward-in-time integration up to the e-folds when the primordial observables are evaluated ($N=60$). Once more, we make sure to obtain a successful integration, that is, we do not end up with $\epsilon=1$ again. For the remaining models, we check whether the spectral index of scalar modes $n_s$ lies within the observed bounds. In particular, we reject all the results outside the range $0.94<n_s<0.98$, chosen conservatively around the Planck best-fit value, ending up with roughly $17\%$ of the total. We store the survived models and proceed to evolve all the other physical quantities involved in our analysis.
\item Particularly relevant for the evolution of the tensor spectrum are the quantities related to the propagating speed $c_T$, see also Eq.~\eqref{eq:PtCt}. To solve the system of equations~\eqref{eq:system_Q} we need to specify some initial conditions for $\epsilon_T$ and the other high-order tensor parameters that we randomly choose within the following ranges:
\begin{gather*}
\epsilon_{\rm T}\in[-0.1,0.1],\\
\rho_{\rm T}\in[-0.01,0.01],\\
^2\chi_{\rm T}\in[-0.001,0.001],\\
^3\chi_{\rm T}\in[-0.0001,0.0001].
\end{gather*}
To optimize the simulations and save computational time, for each realization of the background, our algorithm is able to perform simultaneous evolution of different physical quantities. In particular, starting from some initial conditions, we first perform a forward integration until the end of Inflation. Since we already did such an integration for the background (and given that all the other quantities do not affect the spacetime evolution), we can focus exclusively on the stability of the tensor-speed sector. We find that a small part of the total leads to an unsuccessful integration while most models require also a backward integration (for instance because they reach the controversial value $\epsilon_T=1$ during the integration or because they show non-physical behaviors for the other parameters). Once that all the consistency checks have been carried out, the model is either accepted or rejected. At the end of the process, only approximately $40\%$ of the attempts resolve in a successful inflation with a non-trivial tensor-speed sector.
\item As concerns the other physical quantities, we select a subgroup of models that share the same tensor amplitude $r\sim 0.001$ on the CMB scales ($N=60$) but that differ by the value of the tensor tilt $n_T$ that we estimate at $N=60$ according to Eq.~\eqref{ntt}. Finally, we evolve the tensor spectrum dynamically from $N=60$ up to the end of inflation by means of the Hubble flow Equations. For each spectrum, we calculate the corresponding contribution to the energy density of the early universe parametrized in terms of the effective number of relativistic degrees of freedom $\Delta N_{\rm eff}^{\rm GW}$. To do so, we evaluate the corresponding energy-density in gravitational waves $\Omega_{\rm GW}(f)$ by Eq.~\eqref{OmegaGW} and integrate it over frequency according to Eq.~\eqref{Int1}.
\end{itemize}
Using this procedure, we are able to collect a sufficiently large ensemble of physical models ($\simeq 10.000$) which spans a reasonable range of possibilities, from realization with a canonical tensor-speed sector (\textit{i.e.}, $c_{\rm T}=1$ and $\epsilon_T=0$) to more general cases with time-dependent tensor parameters. Nonetheless, our integration scheme is focused on a well-defined task, \textit{i.e.}, we are not interested in providing a comprehensive analysis of the model frequency distribution for the different observables as already done in full generality in Ref.~\cite{Capurri:2020qgz}, but rather to shed light on the correlation between $n_{\rm T}$ and the predictions for $\Delta N_{\rm eff}^{\rm GW}$. To achieve this task in the most direct and simple way we necessarily introduce some limitations on the models that we are actually able to explore, that deserve to be further justified and clarified.
A first major restriction comes from limiting our analysis to a small subgroup of models with a fixed tensor amplitude $r\sim 0.001$ on the CMB scales. This clearly introduces a limitation on the number of cases that we are able to reach within our Monte Carlo technique. Notice however that we do not expect this limitation to introduce a large bias on the frequency distribution of the values obtained for the tensor tilt as the consistency relation between $r$ and $n_T$ does not hold anymore and these two parameters can be regarded as independent. In addition, we are not particularly interested in studying the model frequency distribution, but rather in understanding whether models sharing similar parameters on the CMB scales may result into a significant different contribution to the energy budget of the early Universe because of their different evolutionary paths. Focusing only on models with the same $r$ at $N=60$ turns out to be particularly useful for this purpose since it ensures that the predictions for $\Delta N_{\rm eff}^{\rm GW}$ do not depend on the value of the tensor amplitude at the CMB scales (which is in fact common to all models). In this way at $N=60$ all the models will differ only by the value of the tensor tilt and comparing the values of $\Delta N_{\rm eff}^{\rm GW}$ predicted by models with a similar $n_{\rm T}$ one can have an immediate idea of the difference produced by the different evolution of the spectra from $N=60$ to $N=0$ and unequivocally understand whether $\Delta N_{\rm eff}^{\rm GW}$ and $n_{\rm T}$ are somehow correlated. Finally, we can directly compare the results obtained within our theoretical Monte Carlo with those derived in \autoref{sec.3.3} by means of a parametric reconstruction of the spectra (where the tensor amplitude was fixed to $r\sim 0.001$, as well), testing the consistency of these two methods. Last, but not least, $r\sim 0.001$ is the declared target of future CMB-S4-like experiments~\cite{CMB-S4}. Therefore we believe it should be particularly interesting to understand what kind of physical models future surveys may be able to probe. This is the ultimate reason why we have chosen such a value for the amplitude.
A second minor limitation is introduced by taking only positive initial conditions for the parameter $\epsilon$, without considering models resulting from a background evolution with $\epsilon_{\rm in}<0$, like it was done in Ref.~\cite{Capurri:2020qgz}. To understand the implications of this limitation, we recall that in the standard single-field models the Null Energy Condition (NEC) prevents the slow-roll parameter $\epsilon$ to be negative. However, this framework is quite general and can be applied also to more complicated scenarios where this possibility is viable, such as super-inflation models~\cite{Creminelli:2006xe,Gasperini:1992pa,Brustein:1995ah,Baldi:2005gk} (where $\epsilon$ can remain always negative) or models with intermittent NEC violation~\cite{Cai:2020qpu,Cai:2022nqv} (where $\epsilon$ can be negative for some e-folds and then come back to be positive, restoring the usual end of inflation at $\epsilon=1$). In this regard, we notice that starting with a positive $\epsilon$ as the initial condition does not preclude this parameter to acquire negative values during its evolution. Therefore the latter intermittent case is included in our Monte Carlo. Conversely, requiring $\epsilon_{\rm in}>0$ and the end of inflation to occur at $\epsilon=1$ exclude the super-inflation case. Indeed such models are characterized by an Hubble parameter that increases with time so that the end of inflation is no longer determined by the condition $\epsilon=1$ but must be forced by external factors, such as an additional field. In the framework of a theoretical Monte Carlo, it becomes very ambiguous to decide when inflation ends since we are not sensitive to the details of the mechanism. For this reason, one needs to choose an arbitrary point during the evolution, as done in Ref.~\cite{Capurri:2020qgz}, introducing an element of arbitrariness in the resulting predictions. In addition, this case should be considered separately because one needs to choose the range of integration very carefully in such a way that the energy scale at the end of inflation can lie whiting the observational upper bound ($H_{\rm fin} < 2.7 \times 10^{-5} \,\text{M}_{\rm pl}$~\cite{Akrami:2018odb}) and the lower limit (around the MeV scale to guarantees hydrogen and helium production during the BBN~\cite{Giudice:2000ex}). While neglecting these models clearly reduce the chance to populate the parameter-space with $n_{\rm T}>0$, our conclusions on $\Delta N_{\rm eff}^{\rm GW}$ cannot in any way rely on such exotic scenarios and therefore we can safely exclude them from our analysis, referring to Ref.~\cite{Capurri:2020qgz} for a systematic investigation of these controversial models.
\subsection{Observable Predictions}
\begin{figure}
\centering
\includegraphics[width=\columnwidth]{Figure4.png}
\caption{Three physical examples of the primordial tensor spectra (and their power-law extrapolation, orange line) obtained by integrating the Hubble Flow Equations as discussed in \autoref{sec.4}.}
\label{fig:figure4}
\end{figure}
\begin{figure}[tp]
\centering
\includegraphics[width=\columnwidth]{Figure5.png}
\caption{\small Observable predictions in the plane $(n_{\rm T}\,,\,\Delta N_{\rm eff}^{\rm GW})$. The magenta dots represent the models realized within the Hubble Flow Equation method discussed in \autoref{sec.4} while the red dashed line represents the power-law prediction. The dashed black lines define the regions of the plane that contain the 68\% and 95\% of the total models and are calculated by marginalizing over the point frequency distribution (displayed by the two histograms on the axes). }
\label{fig:figure5}
\end{figure}
We start discussing some useful insights about what is obtained following the integration method outlined in the previous subsection. In particular, in \autoref{fig:figure4} we show three controversial examples that we find particularly enlightening about the very diversified behavior that the tensor spectrum can acquire in physical models of inflation, validating the need to systematically investigate the observable predictions by means of a theoretical Monte Carlo.
In the top-side panel of the \autoref{fig:figure4}, we display the spectrum predicted by a red-tilted model of inflation where we evolved the background according to Eq.~\eqref{eq:HFE_background}, switching off all the other EFT operators. The shape of this spectrum is not very different from what we got by our previous parametric analysis (see also \autoref{fig:figure2}). Not surprisingly, near the CMB frequencies, the spectrum is well described by a power-law (orange line in the figure) and all the physics of the model is captured only by two parameters, the amplitude and the tilt. Conversely, on frequencies close to the end of inflation the power in gravitational waves is suddenly dismissed. As soon as the potential start approaching its minimum (\textit{i.e.}, $\epsilon \to 1$) the slow-roll dynamics breaks down and both the Hubble parameter and the tensor spectrum ($\mathcal P \propto H^2$) suddenly decrease. In this frequency range, the behavior of the spectrum is mostly determined by the shape of the potential (which is no more flat) and consequently, the gravitational wave production becomes strongly model-dependent~\cite{Kinney:2021nje}. Interestingly, if we compare the power spectrum integrated over the Hubble flow equations with a simple power-law extrapolation, we see that on high frequency there is a difference of almost two orders of magnitude between the two curves. We can easily quantify the impact in terms of $\Delta N_{\rm eff}^{\rm GW}$ by integrating both the spectrum and its power-law extrapolation through Eq.~\eqref{Int1}. For this particular model (and for models that show a similar behavior) we estimate a difference of a factor $\sim 10$ between the contributions obtained by integrating the Hubble flow equation ($\Delta N_{\rm eff}^{\rm GW}\simeq 1 \times 10^{-12}$) and the one inferred by a power-law extrapolation ($\Delta N_{\rm eff}^{\rm GW} \simeq 1 \times 10^{-11}$). In both cases, however, the contribution is extremely small and well beyond any current or future experimental sensitivity, as expected in red-tilted inflation.
The situation becomes even more intriguing if we turn to the study of blue-titled models of inflation. Within our framework, such models can be realized either taking $\epsilon<0$ at $N\sim 60$ or including corrections to the tensor spectrum coming from the extrinsic curvature perturbations in Eq.~\eqref{eq:EFT_action}. In the middle panel of \autoref{fig:figure4} we plot the tensor spectrum realized in one of the latter cases. In this particular model, the regime $n_{\rm T}>0$ is supported only for a few e-folds of inflation, corresponding to the frequency range during which the spectrum follows a blue-tilted power-law and the gravitational signal is amplified. After that, because of a combined effect of the background evolution and the evolution of parameter $\epsilon_{\rm T}$, the spectrum becomes very red-tilted and the power in the gravitational wave is suppressed at high frequencies. This model is similar to those discussed in Ref.~\cite{Benetti:2021uea} and in this case assuming a blue-tilted power-law spectrum over all scales leads to overestimating the gravitational wave signal by a factor of $10^{5}$. Repeating the exercise of computing the contribution to the radiation energy-density for both the integrated spectrum ($\Delta N_{\rm eff}^{\rm GW} \simeq 7 \times 10^{-14}$) and the power-law one ($\Delta N_{\rm eff}^{\rm GW} \simeq 2 \times 10^{-9}$) we end up with two completely different results. Therefore this is the "smoking gun" evidence that leads weight to all the concerns already emerged from our parametric analysis. It makes evident that extrapolating a power low spectrum over all scales can be an unreliable practice and can lead to strongly overestimating the gravitational wave contribution to the radiation energy-density (even by many orders of magnitude, as we have just proved). However one may ask to what extent such a model can be considered representative of the spectrum's behavior in blue-tilted inflation and how easily models like this one can be realized. As a counterexample, in the bottom panel of \autoref{fig:figure4} we show a blue-tilted spectrum realized within a model where a simple power-law extrapolation still provides a very good approximation of the gravitational wave production even on a frequency very close to the end of inflation, guarantying an accurate estimation of $\Delta N_{\rm eff}$. Notice that models like that are typically characterized by an extremely slow evolution of the inflationary parameters and hence by a very flat potential. Therefore one may argue that they may be not easy to realize, as well.
Clearly to provide a definitive answer and derive reliable results we need to study the inflationary gravitational wave production for a sufficiently large ensemble of randomly realized physical models where all the possibilities are studied exhaustively in the framework of a Theoretical Monte Carlo. In \autoref{fig:figure3} we compare the results for $\Delta N_{\rm eff}^{\rm GW}$ obtained by this latter approach (dark magenta dots in the figure) with those realized in \autoref{sec.3.3}. In \autoref{fig:figure5} we instead zoom-in on the $(n_{\rm T}\,,\, \Delta N_{\rm eff})$ plane, showing the distribution of the physical models. The dashed black lines in this latter figure define the regions of the plane where the 68\% and 95\% of the total models lie and are calculated by marginalizing over the point frequency distribution (displayed by the two histograms on the axes). An accurate analysis of this figure can reveal several interesting hints about the physics underlying the point distribution that is worthy of being discussed in details.
We start by analyzing the observable predictions for the tensor tilt. In particular, we notice that the vast majority of the models are characterized by slightly negative tilt ($n_{\rm T}\lesssim 0$). As partially explained in the previous subsection, this is due to the fact that, during the integration process, only a few blue-tilted models survive all the physical consistency checks and constraints. In fact, most of the survived models have a canonical tensor speed evolution ($c_{\rm T}=1$, $\epsilon_{\rm T}=0$) and respect the null energy condition ($\epsilon>0$) so that their observable predictions follow, or are very close to following, the usual slow-roll consistency relations. This also suggests that realizing well-defined blue-tilted models able to satisfy all the physical requirements (such as stability, causality and last but not least the observable constraints) may be a tricky avenue and in general red-tilted models are largely preferred by theoretical Monte Carlo simulations, as already pointed out in Ref.~\cite{Capurri:2020qgz}. Focusing on the survived blue-tilted models, it is also evident that only small values of the tensor tilt are realized and we remain far away from the controversial observational upper limit inferred for this parameter. As a matter of fact, the largest $n_{\rm T}$ we are able to get within our pipeline reads $n_{\rm T}\simeq 0.08$ (close to the middle panel of \autoref{fig:figure4}). The reasons why the case $n_{\rm T}>0$ is generally disfavored are several. For instance, such values can hardly arise from the extrinsic curvature corrections since this would imply a large $\epsilon_{\rm T}>0$ and, by Eq.~\eqref{ctepsilont}, a negative time derivative of the tensor speed that would thus be reduced close to the frequencies where it is instead constrained to be unitary by gravitational wave observations~\cite{GBM:2017lvd,Monitor:2017mdv}. As concerns the red-titled models, most of them show the same preference for very small tilt values ($-0.1<n_{\rm T}<0$ within the 95\% region), but a few exceptions with $n_{\rm T}\lesssim -0.2$ can be observed. While they represent a negligible part of the total points, it is interesting to notice that, in principle, such models do not violate any observable prediction. In our framework, a relatively large negative tilt can be realized by a combined effect of both the background evolution and the tensor speed evolution provided that $\epsilon_{\rm T}<0$. In this regard, it is worth pointing out that a negative $\epsilon_{\rm T}$ would imply $\dot{c}_{\rm T}>0$ and so a tensor speed that increases over time, around the CMB frequencies. Since the propagating speed of gravitational interactions is not (severely) constrained at those frequencies, the model may remain viable as long as $c_{\rm T}\in [0\,,\,1]$, see also Refs.\cite{Capurri:2020qgz,Giare:2020vss}. On the other hand, a significantly non-unitary $c_{\rm T}$ may be an element of concern because we are dealing with perturbative departures from General Relativity and so we do not expect large deviations. However, thanks to the narrowed window allowed for the initial conditions of the tensor-speed parameters, these models remain the very minority (we can count only 18 models with $n_{\rm T}\lesssim -0.2$) and in most of them, the background dynamics importantly contributes to this behavior. We, therefore, find this issue to be not particularly relevant to the general aim of this paper and leave it suitable for future investigation. There is yet another interesting aspect that deserves to be remarked: looking at \autoref{fig:figure5} we can spot a bunch of models that follow a power-law behavior very closely (dark magenta points that overlap with the red dashed line in the figure). All these models are characterized by a tensor tilt extremely close to zero. Because of Eq.~\eqref{ntt}, this means that both $\epsilon$ and eventually $\epsilon_{\rm T}$ need to be very close to vanishing, implying an extremely slow-roll dynamics and thus a very flat inflationary potential. They are nothing but models that behave like the one depicted in the bottom panel of \autoref{fig:figure4}. So, looking at \autoref{fig:figure5}, we can finally answer whether such models can be easily realized or not. In particular, we find that they are not in the densest region of the plane. Nonetheless, they still fall within the region containing the 95\% of the total models, actually contributing to a second (very) small peak in the histograms of $\Delta N_{\rm eff}$, see also \autoref{fig:figure5}.
We now turn to the study of the observable predictions for $\Delta N_{\rm eff}$ that is the point of interest for this analysis. First and foremost, most of the models predict a value very different from what one would expect by extending a power-law parameterization over all scales, see \autoref{fig:figure3}. The same conclusion can be derived from a different perspective by looking at \autoref{fig:figure5}. From the latter figure we can appreciate that, while the histogram of $n_{\rm T}$ is very sharped and most models share similar values of the tensor tilt, the histogram of $\Delta N_{\rm eff}^{\rm GW}$ is instead much broader and the regions containing the 68\% and 95\% of models are almost vertical, spanning a quite large range of values $\Delta N_{\rm eff}^{\rm GW}\simeq 10^{-10}\, - \, \simeq 10^{-14}$. This means that models that share the same inflationary parameters on the CMB scales (\textit{i.e.}, the same amplitude $r$ and the same tilt $n_{\rm T}$) can easily result in a completely different contribution to $\Delta N_{\rm eff}^{\rm GW}$. As already pointed out in \autoref{sec.3}, this depends on the different evolution of the spectra at high frequencies. More precisely, the results of theoretical Monte Carlo suggest that extrapolating a power-law behavior over ultraviolet frequencies, in most cases leads to overestimating the gravitational wave contribution to the energy budget of the Universe. As partially explained above, this is due to the fact that, close to the end of inflation, the potential necessarily undergoes a rapid phase of evolution towards its minimum that drives the Hubble parameter (and consequently the power spectrum) to be suddenly dismissed. This is evident in all the three physical spectra shown in \autoref{fig:figure4}. This feature is instead missed within a power-law extrapolation so that the power in gravitational waves is typically much overestimated on high frequencies, leading to a larger $\Delta N_{\rm eff}^{\rm GW}$. Nonetheless, we can observe a few models where the actual contribution to the effective number of relativistic species is larger than predicted by a power-law. While such points represent the vast minority of the models, it is still interesting to explain the physical reason underlyng this behavior. In particular, it is evident both from \autoref{fig:figure3} and from \autoref{fig:figure5} that this event is more frequent for those very few points that show a very red tensor tilt $n_{\rm T}\lesssim - 0.2$. As we pointed out in the previous paragraph, in these cases both the background dynamics (\textit{i.e.}, the value of $\epsilon$ at $N=60$) and the tensor-speed dynamics (\textit{i.e.}, the value of $\epsilon_{\rm T}$ at $N=60$) should significantly contribute to the final value of the tensor tilt on the CMB scales and to the evolution of the spectrum with frequency. Indeed, in all these models, $\epsilon$ must reach the value $\epsilon=1$ within $\Delta N=60$ e-folds of evolution (so that inflation can end) while $\epsilon_{\rm T}$ will undergo a similar evolution. If $\epsilon_{\rm T}$ evolves towards less negative values, it can mitigate the loss of power induced by $\epsilon$ and the spectrum may remain so much red-tilted only for a few e-folds. Consequently, in this case assuming continuously a power-law parameterization can lead to underestimating $\Delta N_{\rm eff}^{\rm GW}$.
We conclude this section with a final remark: all the models obtained with the Hubble Flow Equation method give an extremely small $\Delta N_{\rm eff}^{\rm GW}$. The histogram of this parameter is in fact centered around values $\Delta N_{\rm eff}^{\rm GW}\sim 10^{-12}$, with a second small peak of models at $\Delta_{\rm eff}^{\rm GW}\sim 10^{-10}$ (resulting from that class of models with an extremely slow evolution discussed in the previous paragraphs). These values are far away from the total amount of additional radiation allowed by data ($\Delta N_{\rm eff}^{\rm GW}\lesssim 0.3 - 0.4$) as well as from any current and future experimental sensitivity. Therefore one may ask whether this issue is in any way relevant for the purpose of mode-building. In this regard, we would like to point out that, while this method is quite general and allow precise calculation without relying on the details of the model, it does not cover all the possibilities proposed in the literature and blue-tilted models with larger gravitational wave production may be obtained by other viable physical mechanisms. On the other hand, the stochastic technique used in \autoref{sec.3.3} should embrace a much larger class of possibilities since we simply reconstruct the spectrum as a fraction of the frequency. It is also entirely plausible that such spectra can be obtained in well-motivated models, as we may argue by comparing the gray and dark magenta dots in \autoref{fig:figure3} and noticing that they share similar behavior. In any case a detailed study of the observational prospects of the field is beyond the aim of this manuscript where we believe to have already covered a reasonable range of different scenarios and possibilities, consistently getting conclusive evidence that assuming a power-law spectrum over all scales can lead to a wrong estimation of the gravitational wave contribution in the early Universe. In light of this result, we can definitively conclude that the calculation of $\Delta N_{\rm eff}^{\rm GW}$ proves to be remarkably model-dependent and more accurate analyses are needed before inferring any reliable conclusion on (blue-titled) inflationary models in light of the BBN bounds on additional radiation.
\section{Conclusions}
\label{sec.5}
In the simplest single-field models of slow-roll inflation, the isometries of the almost de Sitter background geometry constrain the power spectrum of inflationary gravitational waves to be slightly red-tilted and nearly scale-invariant and a small residual scale-dependence can be quantified through the same parameters that control also the amplitude of primordial tensor perturbations and the background dynamics. Nonetheless, many well-motivated physical mechanisms can break these standard (consistency) relations and induce different scale-dependence in the tensor two-point function that needs to be properly parametrized in cosmological and astrophysical data analysis.
Starting from this consideration, in this paper we revisit the calculation of the inflationary gravitational wave contribution to the radiation energy-density in the early Universe. Behaving as additional radiation, primordial gravitational waves may in fact increase the effective number of relativistic species ($N_{\rm eff}$) by a further correction that depends on the integrated energy-density in gravitational radiation over all scales, see Eq.~\eqref{Int1}. According to the Friedmann equations, extra radiation would imply a faster background expansion and consequently a different thermal evolution of the Universe, with several implications. For instance, a faster expansion would lead to a higher freeze-out temperature of the weak interactions, implying a higher fraction of primordial Helium and Deuterium to be forged during the Big Bang Nucleosynthesis epoch. This effect is particularly relevant, because it is commonly used to infer stringent bounds on the additional radiation energy-density and, in its turn, to constrain (blue-titled) models of inflation. Regarding the latter, the underlying assumption of (most of) the state-of-the-art analyses is that the spectrum of inflationary gravitational waves can be parametrized, \textit{continuously} over all cosmological epochs and scales, by a simple power-law with two free parameters: the amplitude $r$ and the tilt $n_{\rm T}$. While in most inflationary models such parameterization works very well on the frequencies probed by the CMB experiments (roughly corresponding to $N\sim 60$ e-folds before the end of inflation), as already pointed out in the literature~\cite{Giare:2020vhn,Kinney:2021nje} extrapolating a power-law behavior over all frequencies can be highly non-trivial and risky; above all on the high-frequencies corresponding to tensor modes that cross the horizon very close to the end of inflation, when the slow-roll dynamics breaks down and the gravitational wave production becomes strongly model-dependent.
First and foremost, in this paper we point out that these frequencies not only contribute to the integral~\eqref{Int1}, but they are also exponentially amplified within a power-law parameterization ($\mathcal P(f)\propto f^{n_{\rm T}}$). Therefore this problem becomes of primary relevance when evaluating the tensor modes contribution in the early Universe because the calculation crucially depends on a parameterization whose validity is anything but reliable.
Driven by this concern, in \autoref{sec.3}, we systematically study how (much) different parameterizations of the tensor spectrum
impact on the final predictions of $\Delta N_{\rm eff}^{\rm GW}$. We start the section by reproducing the standard calculation within the two-parameter power-law approach and providing a take-way summary of the state-of-the-art analysis and their caveats. Then, we generalize this parameterization by considering its next-to-leading order extension, Eq.~\eqref{PL2}, where a further scale-dependence is introduced in terms of a small running of the tensor tilt $\alpha_{\rm T}=d n_{\rm T} / d\log k$. In \autoref{fig:figure1} we show that allowing a $\sim \text{few} \%$ scale-variation of the tensor tilt, the resulting $\Delta N_{\rm eff}^{\rm GW}$ can be much amplified or suppress, depending on the sign of the running. This happens because a positive (negative) running will amplify (suppress) the power in gravitational waves on high frequencies that are those that contribute mostly to the calculation.
Once understood the nature of the problem, in \autoref{sec.3.3} we decide to perform parametric analysis. In particular, by expanding the spectrum in full generality as a sum of powers, we randomly collect $10^{6}$ different shapes of the spectrum in frequency, up to the tenth order of the expansion. We then keep only those spectra able to satisfy all the cosmological and astrophysical observational constraints, consistently towards all cosmological epochs and scales. We also ensure that around the CMB frequencies all the spectra are accurately described by a two-parameter power-law parameterization, as expected in most physical models of inflation. Finally, we integrate the remaining spectra over frequencies and evaluate the resulting $\Delta N_{\rm eff}^{\rm GW}$. We show the results in \autoref{fig:figure3} (gray dots). They prove that relaxing that assumption of power-law spectrum \textit{on high frequencies}, the value of the tensor tilt becomes basically uncorrelated with $\Delta N_{\rm eff}^{\rm GW}$ so that models with the same $n_{\rm T}$ can contribute very differently to the energy budget of the Universe.
However one may object that this analysis relies exclusively on the stochastic reconstruction of the spectrum as a function of frequency and not on a solid understanding of the underlying physics. In fact, this may call into question the applicability of our findings since the skeptical reader may speculate that this conclusion is rather an artifact of the method itself. In order to understand to what extent our result can be considered reliable when applied to physical models of Inflation, in \autoref{sec.4} we investigated the observable predictions of a very broad class of inflationary models. We work within the framework of the Effective Field Theory of inflation and follow a methodology based on the so-called Hubble Flow Equation: a system of coupled differential equations whose solution completely specifies the evolution of the main observable quantities during inflation. We solve numerically the truncated system of the Hubble Flow Equations for a set of suitably defined initial conditions (taking into account also a different combination of additional operators in the EFT of inflation) as a sophisticated algorithm for generating large numbers of slow-roll inflationary models without relying on the explicit form of the action. In this way, we produce an ensemble of very general physical models ($\simeq 10.000$) studying the resulting observable predictions. In particular, for each model, we dynamically evolve the primordial tensor spectrum over frequencies by means of the Hubble Flow Equations and calculate the resulting energy-density in primordial gravitational waves $\Omega_{\rm GW}(f)$. We then integrate over frequencies to obtain the corresponding contribution to the radiation energy-density of the early Universe, parametrized in terms of the additional effective number of relativistic species $\Delta N_{\rm eff}^{\rm GW}$. Examples of the spectra obtained by our method are shown in \autoref{fig:figure4} while the final results for $\Delta N_{\rm eff}^{\rm GW}$ are summarized both in \autoref{fig:figure3} and in \autoref{fig:figure5}. Both figures make it evident that most of the models predict a value for this quantity that is very different from what one would expect by extending a power-law parameterization over all scales. In most cases extrapolating a power-law behavior over 24 orders of magnitude in frequency leads to overestimating the power in gravitational waves, above all on the ultraviolet frequencies that are the most relevant in the calculation. As a result, the predicted relic energy-density in gravitational wave can be ultimately incorrect. The precise computations carried out in this analysis have proved also that the observable predictions for $\Delta N_{\rm eff}^{\rm GW}$ are largely sensitive to the underlying model of inflation. This seriously calls into question the validity of the observational constraints inferred on the tensor tilt by the indirect effect of additional radiation during the BBN epoch, motivating the need of more accurate calculations before inferring any reliable conclusion on inflation.
\section*{Acknowledgments}
WG thanks Martina Gerbino and Massimiliano Lattanzi for the useful comments at the early stage of this project and Fabrizio Renzi for valid suggestions on the manuscript. WG, MF and AM are supported by "Theoretical Astroparticle Physics" (TAsP), iniziativa specifica INFN. EDV is supported by a Royal Society Dorothy Hodgkin Research Fellowship.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 6,045 |
Q: Разные результаты от применения схожих по смыслу утилит Почему получилось так, что Валгринд показывает одно количество вызова сискола write a strace другое? Да, если ходить по узлам дерева которое построил Валгринд число сисколов меняется, что видимо соответствует количеству сисколов в развернутом узле дерева. Но у меня получилось, что Валгринд отобразил число намного большее, чем стрейс. Если брать сискол write то результаты 444 vs 360 а если read, то 412 vs 417
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 8,089 |
/**
* SSHHelper.java
* @author Ender
*/
package org.ender.sshutil;
import java.io.IOException;
import java.io.InputStream;
import java.util.HashMap;
import java.util.Map;
import com.jcraft.jsch.Channel;
import com.jcraft.jsch.ChannelExec;
import com.jcraft.jsch.JSch;
import com.jcraft.jsch.JSchException;
import com.jcraft.jsch.Session;
import com.jcraft.jsch.UserInfo;
/**
* @author Ender
* @Des use JSch SessionShell to execute a list of commands.
*/
public class SSHHelper {
public static final int PORT = 22;
/**
* @author Ender
* @since 2015.5.25
* @param host
* @param username
* @param password
* @param port
* @param command
* @return
*/
public static String execCommand(String host, String username, String password, int port, String command){
StringBuffer strbuf = new StringBuffer();
try{
JSch jsch=new JSch();
Session session=jsch.getSession(username, host, port);
session.setPassword(password);
UserInfo ui=new MyUserInfo();
session.setUserInfo(ui);
session.connect();
Channel channel=session.openChannel("exec");
((ChannelExec)channel).setCommand(command);
channel.setInputStream(null);
((ChannelExec)channel).setErrStream(System.err);
InputStream in=channel.getInputStream();
channel.connect();
byte[] tmp=new byte[1024];
while(true){
while(in.available()>0){
int i=in.read(tmp, 0, 1024);
if(i<0)break;
//System.out.print(new String(tmp, 0, i));
strbuf.append(new String(tmp, 0, i));
}
if(channel.isClosed()){
if(in.available()>0) continue;
//System.out.println("exit-status: "+channel.getExitStatus());
//System.out.println("result: \n"+strbuf.toString());
break;
}
try{Thread.sleep(1000);}catch(Exception ee){}
}
channel.disconnect();
session.disconnect();
}catch(Exception e){
System.out.println(e);
e.printStackTrace();
}
return strbuf.toString();
}
/**
* @author Ender
* @since 2015.5.25
* @param host
* @param username
* @param password
* @param command
* @return
*/
public static String execCommand(String host, String username, String password, String command){
return execCommand(host, username, password, SSHHelper.PORT, command);
}
/**
* @author Ender
* @since 2015.5.28
* @param host
* @param username
* @param password
* @param port
* @param command
* @return
* @throws JSchException
* @throws IOException
*/
public static Map execCommandWithExitCode(String host, String username, String password, int port, String command) throws JSchException, IOException{
StringBuffer strbuf = new StringBuffer();
Map result = new HashMap();
JSch jsch=new JSch();
Session session=jsch.getSession(username, host, port);
session.setPassword(password);
UserInfo ui=new MyUserInfo();
session.setUserInfo(ui);
session.connect();
Channel channel=session.openChannel("exec");
((ChannelExec)channel).setCommand(command);
channel.setInputStream(null);
((ChannelExec)channel).setErrStream(System.err);
InputStream in=channel.getInputStream();
channel.connect();
byte[] tmp=new byte[1024];
while(true){
while(in.available()>0){
int i=in.read(tmp, 0, 1024);
if(i<0)break;
//System.out.print(new String(tmp, 0, i));
strbuf.append(new String(tmp, 0, i));
}
if(channel.isClosed()){
if(in.available()>0) continue;
//System.out.println("exit-status: "+channel.getExitStatus());
//System.out.println("result: \n"+strbuf.toString());
result.put("ExitCode", channel.getExitStatus());
result.put("Result", strbuf.toString());
break;
}
}
channel.disconnect();
session.disconnect();
return result;
}
/**
* @author Ender
* @since 2015.5.28
* @param host
* @param username
* @param password
* @param command
* @return
* @throws JSchException
* @throws IOException
*/
public static Map execCommandWithExitCode(String host, String username, String password, String command) throws JSchException, IOException{
return execCommandWithExitCode(host, username, password, SSHHelper.PORT, command);
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 3,279 |
\section{Introduction}
The key to all matter-wave interferometry are coherent beamsplitters which divide each incident wave into separated wavelets with well-defined phase relations \cite{Cronin2009, Juffmann2013}. While modern atom interferometry often utilizes the momentum recoil of resonant laser light to split the atomic wave \cite{Borde1989, Kasevich1991}, mechanical masks \cite{Keith1988, Arndt1999} as well as optical phase \cite{Gould1986} or absorption \cite{Moskowitz1983} gratings can also be used to divide a matter-wave front. Since the universality of mechanical gratings is compromised by the van der Waals (vdW) potential it is important to ask to what extent it is possible to minimize this interaction by reducing the grating thickness. This technological feat - to actually create free-standing nanogratings in even a single layer of atoms \cite{Geim2007} - is accompanied by the fundamental question whether the path of a massive particle through the multi-slit array will become significantly entangled with the mechanical motion of the recoiling ultra-thin structure. If this were the case we would expect to observe loss of the interference contrast.\\
\section{Results and Discussion}
Using a focused ion beam we were able to mill a periodic diffraction grating into a single layer of graphene that was suspended over a silicon nitride (SiN$_\text{x}$) membrane (Fig. \ref{fig:gratings}a, see Appendix Sec.\ref{app:gratings} for details). The nanoribbons ($64\pm3$~nm wide) were written with a period of $88\pm3$~nm (Fig. \ref{fig:gratings}c). They spontaneously transform into carbon nanoscrolls \cite{Lucot2009}, here with a diameter down to $8$~nm (Fig. 1b and Appendix Sec.\ref{app:scrolls}). For shorter grating bars scanning transmission electron microscopy (STEM) reveals, however, stable flat single-layer graphene structures (Fig. \ref{fig:gratings}e).
We were also able to write gratings into bilayer graphene suspended across a lacey carbon mesh (Fig. \ref{fig:gratings}f). The second layer of carbon atoms suppresses the formation of nanoscrolls entirely on the observed scale. Bilayer graphene may also form bonds at open cuts and thus expose closed edges and a thicker wall than expected based on the number of layers alone \cite{Liu2009}. We compare these structures finally to an insulating structure of almost identical thickness, the carbonaceous biphenyl membrane \cite{Angelova2013} (also on lacey carbon, Fig. \ref{fig:gratings}g,) and reference all images to the diffraction of molecules at $45$~nm thick silicon nitride (Fig. \ref{fig:gratings}h) \cite{Juffmann2012}.
\begin{figure*}[htb]
\begin{center}
\includegraphics[width=16cm]{gratings.jpg}
\end{center}
\caption{Exploring the ultimate limit of nanomechanical diffraction gratings. (a) Gratings written into single-layer graphene suspended across a holey SiN$_\text{x}$ membrane. (b) Carbon nanoscrolls spontaneously form, when the aspect ratio of the graphene nanoribbons becomes too high (b) and (c). Folds and contaminations can prevent the membrane from curling. (d) STEM visualizes the hexagonal atomic structure of single-layer graphene. (e) Reducing the length of the $40$~nm wide nanoribbons to $250$~nm prevents the curling. (f) Adding another layer of carbon atoms (bilayer graphene) allows us to substantially extend the aspect ratio and to keep the grating flat. (g) Large area gratings can also be written into a carbonaceous biphenyl membrane. (h) Grating in silicon nitride of $45$~nm thickness}
\label{fig:gratings}
\end{figure*}
\begin{figure*}[htb]
\begin{center}
\includegraphics[width=16cm]{overview.jpg}
\end{center}
\caption{Influence of the membrane thickness and material composition of the van der Waals interaction in molecule diffraction. Top row: Grating type and thickness. (a) Period $d=105\pm1$~nm, (b) $d=88\pm3$~nm, (c) $d=107\pm9$~nm, (d) $d=113\pm4$~nm, (e) $d=101\pm2$~nm. Middle row: Fluorescence image of the PcH$_2$ diffraction image. With increasing flight time the molecules fall deeper in the gravitational field. Fast molecules arrive at the top, slow molecules arrive at the bottom of the detector. Bottom row: Each trace represents a normalized vertical 1D integral over the area under the white line, corresponding to the molecular velocity band centered at $220$~m/s. The experimental data can be approximated by Kirchhoff-Fresnel diffraction theory (see Appendix \ref{app:Kirchhoff}) by taking into account that the van der Waals forces reduce the effective slit width \cite{Grisenti1999}: (a) geometrical slit width $s= 50\pm2$~nm, effective slit width $s_\text{eff} = 15$~nm, (b) $s=65\pm6$~nm, $s_\text{eff} = 49$~nm, (c) $s=54\pm4$~nm, $s_\text{eff} = 28$~nm, (d) $s=62\pm8$~nm, $s_\text{eff} = 28$~nm, (e) $s=59\pm6$~nm, $s_\text{eff} = 35$~nm.}
\label{fig:overview}
\end{figure*}
Figure \ref{fig:gratings} demonstrates that stable structures can be written even into atomically thin membranes. The diffraction pattern behind a purely absorptive periodic mask - \emph{i.e.} without any phase modulation – can be described as the convolution of two contributions: the diffraction at each single slit of width $s$ and the diffraction at an array of infinitely thin slits of period $d$. The fringe positions are well described by wave theory. The fringe amplitudes are modulated by the single-slit diffraction pattern.
Comparing Fig. \ref{fig:overview}(a) - (e), we see immediately vast differences in the diffraction at geometrically similar gratings. For $45$~nm thick silicon nitride (Fig. \ref{fig:overview}a) we observe interference up to the $9$th diffraction order, which can only be understood if we complement the quantum wave model by the assumption that the position-dependent phases accumulated in the presence of vdW forces alter the effective transmission function. Approximating this interaction by reducing the effective slit width \cite{Grisenti1999} (see Appendix Sec.\ref{app:Kirchhoff}) allows us to estimate the strength of the vdW interactions. For silicon nitride the analysis yields an effective slit width of $15$~nm - a reduction of the open width by $s/s_\text{eff} =3.3$. This influence is strongly reduced for the single-layer graphene grating, the probably thinnest conceivable grating (Fig. \ref{fig:overview}e, $s/s_\text{eff} = 1.7$). As expected this leads to a strong suppression of all diffraction orders beyond the first one. This holds true - and even more so - for gratings made from nanoscrolls ($s/s_\text{eff} = 1.3$), which maximize the opening fraction, \emph{i.e.} the ratio of slit width to period.
In contrast to that, the diffraction pattern both behind the carbonaceous biphenyl membrane ($s/s_\text{eff} =1.9$) and the bilayer graphene ($s/s_\text{eff} = 2.2$) show substantial populations up to the fifth diffraction order. This indicates a stronger influence of the attractive van der Waals force. While the carbonaceous biphenyl membrane should be an insulator, the bilayer sample is conducting. However, both imprint similar phase shifts onto the transmitted molecules. We attribute the remaining van der Waals forces in particular also to the lacey carbon support structure which is thicker (up to $100$~nm) and spatially less well controlled than the SiN$_\text{x}$ support of the other ultra-thin gratings.
The central result of our diffraction experiments is the observation of high-contrast interference for all gratings, where the contrast reaches its maximum when the interference minima approach the zero (background) level. It is the absence of signal in these minima which contradicts any classical expectation the most. Our result relates to a thought experiment between Bohr and Einstein who elucidated the role of decoherence in double slit diffraction \cite{Bohr1949}. Einstein predicted that the observer should be capable of extracting which-path information from the recoil that the double slit receives upon diffraction of a particle (Fig. \ref{fig:Born}). Invoking Heisenberg's uncertainty relation, Bohr was able to demonstrate, however, that the recoil imparted by the diffracted particles remains within the momentum uncertainty of the grating if this is well positioned.
\begin{figure}[htb]
\begin{center}
\includegraphics[width=7cm]{einsteingraphene.jpg}
\end{center}
\caption{A nanomechanical implementation of the Bohr-Einstein debate: Can atomically thin gratings be compatible with high-contrast interference? A sketch of the diffraction setup using ultra-thin gratings is depicted on the left, corresponding to Bohr's double slit thought experiment on the right \cite{Bohr1949}. In analogy to a debate between Bohr and Einstein we ask: Can a flexible suspension of the mechanical mount encode which-path information of particles in transition through the double slit?}
\label{fig:Born}
\end{figure}
Different recent studies have realized the probably smallest double slits and analogs to this Einstein-Bohr debate using diatomic molecules as the diffraction elements in a photoionization process \cite{Zimmermann2008, Akoury2007, Liu2015}. They were destroyed in the diffraction process and therefore were capable of carrying away path information. Our carbon nanostructures are probably the thinnest durable realization of the Bohr-Einstein idea. These atomically thin membranes are flexible but they last for months and survive the diffraction of millions of molecules. The observed full contrast shows that coherence prevails, which we interpret as an indication that the momentum exchange with the grating remains within the intrinsic momentum uncertainty of the grating bars (see Appendix \ref{app:Heisenberg}) \cite{Bohr1949}. Hence, diffraction does not lead to a loss of fringe visibility even though it can cause a sizable matter-wave (vdW) phase shift.
Graphene gratings are ten times thinner than any other beamsplitter for atoms, molecules or clusters before and they are four orders of magnitude thinner than the width of a typical laser grating \cite{Gerlich2007}. Our results on single-layer graphene are the best approach with regard to the diffraction of high-mass molecules at nanomechanical gratings, since they show that the effect of molecule-surface interactions can be substantially reduced, even though they do not eliminate them entirely.
This property makes graphene nanogratings also appealing for use with other kinds of matter-waves. The reduced phase components may enable new coherence experiments with slow ions or anti-matter \cite{Hamilton2014}. It will also be interesting to explore atomically thin but insulating 2D sheets like boron nitride or molybdenum disulfide, in the future.
Even though van der Waals forces in thick gratings can be prohibitive for high-mass diffraction, they can also serve a purpose in metrology: our experiments show that a thick material grating (SiN$_x$, Fig. \ref{fig:overview}a) can act as a large momentum transfer beamsplitter. If we were to calibrate the momentum exchange between the extreme diffraction orders ($\pm9th$ order for $d=100$~nm) in units of the photon momentum ($\hbar k_\text{Rb}$) that is usually imparted in state-of-the-art beamsplitters \cite{Kasevich1991, Borde1989} for (rubidium) atoms, we see that the diffraction at our nanogratings amounts to $\Delta p=141\, \hbar k_\text{Rb}$. Photolithography can reliably provide thick gratings with a periodicity of better than $0.1$~nm over large areas \cite{Gerlich2007}. Stable thick membranes with narrow slits are predicted to provide a momentum transfer even beyond $500$~$\hbar k_\text{Rb}$.
\section{Conclusion}
Finally, our work shows that path-decoherence close to material gratings is still negligible in all settings discussed here. This applies in particular for the Bohr-Einstein Gedankenexperiment. Even the conceivably thinnest durable mechanical grating is still sufficiently massive and sufficiently localized not to encode sizable recoil-information. The intrinsic momentum uncertainty of each grating bar is larger than the recoil imparted on each diffracted molecule (see Appendix \ref{app:Heisenberg}).
This holds for all particles, independent of their mass, as long as we can keep their de Broglie wave-length, \emph{i.e.} their momentum, the same. For instance, quantum diffraction of insulin molecules seems conceivable once we can provide a directed molecular beam of about $20~$m/s velocity. Finally, it will also be intriguing to explore the role of quantum friction and path-decoherence \cite{Scheel2012, Anglin1997} which may become particularly relevant for polar molecules in the future.
\section*{Acknowledgements}
We acknowledge support by the European Commission (304886), the European Research Council (320694) and the Austrian science funds (DK CoQuS W1210-3). CB acknowledges the financial support of the Alexander von Humboldt foundation through a Feodor Lynen fellowship. JK acknowledges the Austrian Science Fund FWF for funding through project M 1481-N20. JM and CM acknowledge support from the Austrian science funds FWF project P 25721-N20. AW and AT acknowledge support of the DFG (SPP "Graphene" TU149/2-2, Heisenberg Program TU149/3-1). TJ acknowledges support by the Gordon and Betty Moore Foundation. We thank the group of Prof. Schattschneider, USTEM TU Vienna for assistance in recording image \ref{fig:gratings}(h). We thank Stefan Scheel and Johannes Fielder (Univ. Rostock) for fruitful discussions.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 2,310 |
Q: Html.OpenIdSelector in mvc3 I have the buttons rendering and here is the output:
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<input name="__RequestVerificationToken" type="hidden" value="M+ZFyksulpHW8asKultS/Y53gRs6eEli13rjL76+tc40ZB4WUbxAIpVMtsMnyGI2hXZ54DwyFypx/0UBlZqR+U7F/ALJRHiIGU9dCJpiohZHrlVEYZMgsF9HB14wruRia5A7jOidi4DlyfRriMjGrn63RMMJlLLHWIq5duSUiR4=" /><input
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name="openid_openidAuthData" type="hidden" value="" />
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it has the webresource css too.
However, clicking on the buttons does nothing. on the nerddinner sample it obv pops up the login box for the provider you select.
what do i need to do to make this work? is there a checklist of things i need to be aware of?
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 9,785 |
The 2018 Liga 2 was the second season of the Liga 2 under its current name, and the ninth season under its current league structure.
PSS won the title after a 2–0 win over Semen Padang in the final at Pakansari Stadium, Cibinong on 4 December 2018.
Overview
Player regulations
Clubs could register at least 18 players and a maximum of 30 players without age restriction like the previous season, but maximum 3 players over the age of 35 years. Like the previous season, the clubs also couldn't use foreign players.
Teams
Teams changes
The following teams have changed division since the 2017 season.
To Liga 2
Relegated from Liga 1
Persegres
Persiba
Semen Padang
Promoted from Liga 3
Blitar United
Persik Kendal
Aceh United
From Liga 2
Promoted to Liga 1
Persebaya
PSMS
PSIS
Relegated to Liga 3
Stadium and locations
Notes:
Personnel and kits
Note: Flags indicate national team as has been defined under FIFA eligibility rules. Players and coaches may hold more than one non-FIFA nationality.
Coaching changes
First round
West region
East region
Second round
This round began on 24 October 2018 and ended on 21 November 2018. Eight teams competed in this round.
Group A
Group B
Knockout round
Bracket
Semi-finals
Semen Padang won 3–2 on aggregate.
PSS won 2–0 on aggregate.
Third place
Final
Season statistics
Top scorers
See also
2018 Liga 1
2018 Liga 3
2018–19 Piala Indonesia
Notes
References
Works cited
Liga 2
Liga 2
Liga 2
Liga 2
Indonesia
Indonesia | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 7,580 |
Conference & Event Services
About TyndaleU
Contact TyndaleU
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Contact Tyndale Seminary
Open Learning Centre
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Tyndale Seminary Faculty Update
Tuesday, August 26, 2014 —
Tyndale Seminary has 24 faculty members researching and teaching across a diverse range of academic disciplines. The following are some recent contributions that faculty members have made to their field of research:
Dr. Ronald Kydd, Associate Professor of Church History, travelled to China from June 8 to July 3 2014 on a research trip to review and discover evidence of the presence of Christianity in China prior to 1400 AD. He travelled on an itinerary organized by a well-known Chinese archaeologist and former government official. They visited 16 museums, eight ancient cities that had Christian populations, four ancient Christian monasteries and numerous temples. Dr. Kydd was accompanied by groups of archaeologists in all places and was permitted to review many artifacts largely unknown outside of China. Also in summer 2014, Dr. Kydd authored the article, "Timothy I Looks at His Church," published in Studia Patristica. He also authored a review of Dr. Éric Rebillard's Christians and Their Many Identities in Late Antiquity North Africa, 200—450 CE in Church History (Cornell University Press, 2014).
Dr. John Kessler, Professor of Old Testament, authored "Torah and Character: A Kid and its Mother's Milk (Deut. 14:21, Exod. 23:19 and 34:26)," in Between the Lectern and the Pulpit: Essays in Honour of Victor A. Shepherd (Regent College Publishing, 2014). He also lectured at an international conference at the Israel Institute for Advanced Studies on the topic, "Patterns of Curse Formulae within the Hebrew Bible and ANE: The Case of Amos 4:6-12 and its Relationships to Deut. 28 and Lev. 26." The conference took place in Israel in May 2014, at the Hebrew University of Jerusalem. The theme of the conference, which brought together approximately 50 scholars from Europe, Israel, the US and Canada, was "The Pentateuch within Biblical Literature: Formation and Interaction." Dr. Kessler's paper was well received and will appear in an upcoming volume of conference papers published by Mohr Siebeck.
Dr. Rebecca Idestrom, Associate Professor of Old Testament, authored the chapter "Psalm 96: Declare His Glory Among the Nations," in Between the Lectern and the Pulpit: Essays in Honour of Victor A. Shepherd (Regent College Publishing, 2014). Dr. Idestrom is on a one-year sabbatical (2014-2015). She will be spending her sabbatical at Tyndale House in Cambridge, England, where she will be working on her book entitled Show Me Your Glory: The Glory of God in the Old Testament.
Dr. Dennis Ngien, Professor of Systematic Theology and Director of the Master of Theology program at Tyndale Seminary, was recently appointed as Research Professor of Theology at Wycliffe College, University of Toronto. In this role, Dr. Ngien will be teaching and supervising doctoral students.
Dr. Arnold Neufeldt-Fast, Associate Academic Dean and Associate Professor of Theology, authored "Menno Simons and Martin Luther on Christian Freedom," a chapter published in the book In Between the Pulpit and the Lectern: Essays in Honour of Victor A. Shepherd (Regent College Publishing, 2014). In June 2014, he was at Princeton Theological Seminary in Princeton, New Jersey, where he is a Fellow at the Center for Barth Studies. He is involved in a translation project of Karl Barth's Gottingen Dogmatics II as well as Karl Barth: Dialogues 1959-1962 (tentative title), edited by Dr. Karlfried Froehlich.
Dr. Grace Ko, Assistant Professor of Biblical Studies (CCSTTS), presented a paper entitled "The Placement of Ps. 90 in the Psalter: A Theological Consideration" at the International Congress of Ethnic Chinese Biblical Scholars held in Hong Kong in August 2014.
Dr. James Beverley, Professor of Christian Thought and Ethics, spoke at the Cesnur International Conference on Religions at Baylor University, in Waco, Texas, in June 2014. His lecture was titled "Texas Showdown: The Conflict between Mark 'Marty' Rathbun and David Miscavige, head of the Church of Scientology." It examined the conflict between the Rathbuns and the church and notes the parallel critiques given by each side. His lecture was based on intense discussions with Mark Rathbun and several Scientology leaders.
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Back to page topBack to page top Top | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 1,732 |
O Conselho Municipal de Estocolmo ( ou Stadsfullmäktige) é a direção política e administrativa da cidade de Estocolmo.
Está instalada na Casa da Cidade de Estocolmo (), o edifício-sede da comuna de Estocolmo, localizado na ponta oriental da ilha de Kungsholmen, perto da costa Norte da baía de Riddarfjärden, de cuja fachada podem-se observar as ilhas de Riddarholmen e Södermalm. É o local onde se realiza o banquete do Prémio Nobel e é uma das maiores atracções turísticas de Estocolmo.
Construções de Estocolmo
Arquitetura romântica nacional da Suécia | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 8,493 |
{"url":"https:\/\/projecteuclid.org\/euclid.im\/1323367278","text":"## Internet Mathematics\n\n### On the Approximability of Reachability-Preserving Network Orientations\n\n#### Abstract\n\nWe introduce a graph-orientation problem arising in the study of biological networks. Given an undirected graph and a list of ordered source\u2013target vertex pairs, the goal is to orient the graph such that a maximum number of pairs admit a directed source-to-target path. We study the complexity and approximability of this problem. We show that the problem is NP-hard even on star graphs and hard to approximate to within some constant factor. On the positive side, we provide an $\u03a9(log log n\/ log n)$ factor approximation algorithm for the problem on n-vertex graphs. We further show that for any instance of the problem there exists an orientation of the input graph that satisfies a logarithmic fraction of all pairs and that this bound is tight up to a constant factor. Our techniques also lead to constant-factor approximation algorithms for some restricted variants of the problem.\n\n#### Article information\n\nSource\nInternet Math., Volume 7, Number 4 (2011), 209-232.\n\nDates\nFirst available in Project Euclid: 8 December 2011","date":"2020-08-10 08:45:54","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\": 0.6444542407989502, \"perplexity\": 359.14339372973075}, \"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-2020-34\/segments\/1596439738653.47\/warc\/CC-MAIN-20200810072511-20200810102511-00471.warc.gz\"}"} | null | null |
// Copyright 2018 The Chromium Authors. All rights reserved.
// Use of this source code is governed by a BSD-style license that can be
// found in the LICENSE file.
#include "third_party/blink/renderer/core/css/style_environment_variables.h"
#include "third_party/blink/renderer/core/css/document_style_environment_variables.h"
#include "third_party/blink/renderer/core/css/style_engine.h"
#include "third_party/blink/renderer/core/dom/node_computed_style.h"
#include "third_party/blink/renderer/core/frame/local_frame.h"
#include "third_party/blink/renderer/core/frame/web_feature.h"
#include "third_party/blink/renderer/core/html/html_element.h"
#include "third_party/blink/renderer/core/style/computed_style.h"
#include "third_party/blink/renderer/core/testing/page_test_base.h"
#include "third_party/blink/renderer/platform/instrumentation/use_counter.h"
#include "third_party/blink/renderer/platform/testing/runtime_enabled_features_test_helpers.h"
#include "third_party/blink/renderer/platform/testing/unit_test_helpers.h"
#include "third_party/blink/renderer/platform/wtf/shared_buffer.h"
namespace blink {
namespace {
static const char kVariableName[] = "test";
// red
static const Color kTestColorRed = Color(255, 0, 0);
static const char kVariableTestColor[] = "red";
// blue
static const Color kAltTestColor = Color(0, 0, 255);
static const char kVariableAltTestColor[] = "blue";
// no set
static const Color kNoColor = Color(0, 0, 0, 0);
static const char kSafeAreaInsetExpectedDefault[] = "0px";
} // namespace
class StyleEnvironmentVariablesTest : public PageTestBase {
public:
void TearDown() override {
StyleEnvironmentVariables::GetRootInstance().ClearForTesting();
}
DocumentStyleEnvironmentVariables& GetDocumentVariables() {
return GetStyleEngine().EnsureEnvironmentVariables();
}
void InitializeWithHTML(LocalFrame& frame, const String& html_content) {
// Sets the inner html and runs the document lifecycle.
frame.GetDocument()->body()->setInnerHTML(html_content);
frame.GetDocument()->View()->UpdateAllLifecyclePhasesForTest();
}
void InitializeTestPageWithVariableNamed(LocalFrame& frame,
const String& name) {
InitializeWithHTML(frame,
"<style>"
" #target { background-color: env(" +
name +
"); }"
"</style>"
"<div>"
" <div id=target></div>"
"</div>");
}
void InitializeTestPageWithVariableNamed(LocalFrame& frame,
const UADefinedVariable name) {
InitializeTestPageWithVariableNamed(
frame, StyleEnvironmentVariables::GetVariableName(
name, /*feature_context=*/nullptr));
}
void SimulateNavigation() {
const KURL& url = KURL(NullURL(), "https://www.example.com");
GetDocument().GetFrame()->Loader().CommitNavigation(
WebNavigationParams::CreateWithHTMLBufferForTesting(
SharedBuffer::Create(), url),
nullptr /* extra_data */);
blink::test::RunPendingTasks();
ASSERT_EQ(url.GetString(), GetDocument().Url().GetString());
}
const String& GetRootVariableValue(UADefinedVariable name) {
CSSVariableData* data =
StyleEnvironmentVariables::GetRootInstance().ResolveVariable(
StyleEnvironmentVariables::GetVariableName(
name, /*feature_context=*/nullptr),
{});
EXPECT_NE(nullptr, data);
return data->BackingStrings()[0];
}
void SetVariableOnRoot(const AtomicString& name, const String& value) {
StyleEnvironmentVariables::GetRootInstance().SetVariable(name, value);
}
void RemoveVariableOnRoot(const AtomicString& name) {
StyleEnvironmentVariables::GetRootInstance().RemoveVariable(name);
}
void SetVariableOnDocument(const AtomicString& name, const String& value) {
GetDocumentVariables().SetVariable(name, value);
}
void RemoveVariableOnDocument(const AtomicString& name) {
GetDocumentVariables().RemoveVariable(name);
}
void SetTwoDimensionalVariableOnRoot(UADefinedTwoDimensionalVariable variable,
unsigned first_dimension,
unsigned second_dimension,
const String& value) {
StyleEnvironmentVariables::GetRootInstance().SetVariable(
variable, first_dimension, second_dimension, value);
}
};
TEST_F(StyleEnvironmentVariablesTest, DocumentVariable_AfterLoad) {
InitializeTestPageWithVariableNamed(GetFrame(), kVariableName);
SetVariableOnDocument(kVariableName, kVariableTestColor);
// Ensure that the document has been invalidated.
EXPECT_TRUE(GetDocument().NeedsLayoutTreeUpdate());
UpdateAllLifecyclePhasesForTest();
// Check that the element has the background color provided by the variable.
Element* target = GetDocument().getElementById("target");
EXPECT_EQ(kTestColorRed, target->ComputedStyleRef().VisitedDependentColor(
GetCSSPropertyBackgroundColor()));
}
TEST_F(StyleEnvironmentVariablesTest, DocumentVariable_Change) {
SetVariableOnDocument(kVariableName, kVariableAltTestColor);
InitializeTestPageWithVariableNamed(GetFrame(), kVariableName);
// Change the variable value after we have loaded the page.
SetVariableOnDocument(kVariableName, kVariableTestColor);
// Ensure that the document has been invalidated.
EXPECT_TRUE(GetDocument().NeedsLayoutTreeUpdate());
UpdateAllLifecyclePhasesForTest();
// Check that the element has the background color provided by the variable.
Element* target = GetDocument().getElementById("target");
EXPECT_EQ(kTestColorRed, target->ComputedStyleRef().VisitedDependentColor(
GetCSSPropertyBackgroundColor()));
}
TEST_F(StyleEnvironmentVariablesTest,
DocumentVariable_Override_RemoveDocument) {
// Set the variable globally.
SetVariableOnRoot(kVariableName, kVariableAltTestColor);
InitializeTestPageWithVariableNamed(GetFrame(), kVariableName);
// Check that the element has the background color provided by the global
// variable.
Element* target = GetDocument().getElementById("target");
EXPECT_EQ(kAltTestColor, target->ComputedStyleRef().VisitedDependentColor(
GetCSSPropertyBackgroundColor()));
// Change the variable value on the document after we have loaded the page.
SetVariableOnDocument(kVariableName, kVariableTestColor);
// Ensure that the document has been invalidated.
EXPECT_TRUE(GetDocument().NeedsLayoutTreeUpdate());
UpdateAllLifecyclePhasesForTest();
// Check that the element has the background color provided by the document
// variable.
EXPECT_EQ(kTestColorRed, target->ComputedStyleRef().VisitedDependentColor(
GetCSSPropertyBackgroundColor()));
// Remove the document variable.
RemoveVariableOnDocument(kVariableName);
// Ensure that the document has been invalidated.
EXPECT_TRUE(GetDocument().NeedsLayoutTreeUpdate());
UpdateAllLifecyclePhasesForTest();
// Check that the element has the background color provided by the global
// variable.
EXPECT_EQ(kAltTestColor, target->ComputedStyleRef().VisitedDependentColor(
GetCSSPropertyBackgroundColor()));
}
TEST_F(StyleEnvironmentVariablesTest, DocumentVariable_Override_RemoveGlobal) {
// Set the variable globally.
SetVariableOnRoot(kVariableName, kVariableAltTestColor);
InitializeTestPageWithVariableNamed(GetFrame(), kVariableName);
// Check that the element has the background color provided by the global
// variable.
Element* target = GetDocument().getElementById("target");
EXPECT_EQ(kAltTestColor, target->ComputedStyleRef().VisitedDependentColor(
GetCSSPropertyBackgroundColor()));
// Change the variable value on the document after we have loaded the page.
SetVariableOnDocument(kVariableName, kVariableTestColor);
// Ensure that the document has been invalidated.
EXPECT_TRUE(GetDocument().NeedsLayoutTreeUpdate());
UpdateAllLifecyclePhasesForTest();
// Check that the element has the background color provided by the document
// variable.
EXPECT_EQ(kTestColorRed, target->ComputedStyleRef().VisitedDependentColor(
GetCSSPropertyBackgroundColor()));
// Remove the global variable.
RemoveVariableOnRoot(kVariableName);
// Ensure that the document has not been invalidated.
EXPECT_FALSE(GetDocument().NeedsLayoutTreeUpdate());
}
TEST_F(StyleEnvironmentVariablesTest, DocumentVariable_Preset) {
SetVariableOnDocument(kVariableName, kVariableTestColor);
InitializeTestPageWithVariableNamed(GetFrame(), kVariableName);
// Check that the element has the background color provided by the variable.
Element* target = GetDocument().getElementById("target");
EXPECT_EQ(kTestColorRed, target->ComputedStyleRef().VisitedDependentColor(
GetCSSPropertyBackgroundColor()));
}
TEST_F(StyleEnvironmentVariablesTest, DocumentVariable_Remove) {
SetVariableOnDocument(kVariableName, kVariableTestColor);
InitializeTestPageWithVariableNamed(GetFrame(), kVariableName);
// Check that the element has the background color provided by the variable.
Element* target = GetDocument().getElementById("target");
EXPECT_EQ(kTestColorRed, target->ComputedStyleRef().VisitedDependentColor(
GetCSSPropertyBackgroundColor()));
// Change the variable value after we have loaded the page.
RemoveVariableOnDocument(kVariableName);
// Ensure that the document has been invalidated.
EXPECT_TRUE(GetDocument().NeedsLayoutTreeUpdate());
UpdateAllLifecyclePhasesForTest();
// Check that the element does not have the background color any more.
EXPECT_NE(kTestColorRed, target->ComputedStyleRef().VisitedDependentColor(
GetCSSPropertyBackgroundColor()));
}
TEST_F(StyleEnvironmentVariablesTest, MultiDocumentInvalidation_FromRoot) {
InitializeTestPageWithVariableNamed(GetFrame(), kVariableName);
// Create a second page that uses the variable.
auto new_page = std::make_unique<DummyPageHolder>(gfx::Size(800, 600));
InitializeTestPageWithVariableNamed(new_page->GetFrame(), kVariableName);
// Create an empty page that does not use the variable.
auto empty_page = std::make_unique<DummyPageHolder>(gfx::Size(800, 600));
empty_page->GetDocument().View()->UpdateAllLifecyclePhasesForTest();
SetVariableOnRoot(kVariableName, kVariableTestColor);
// The first two pages should be invalidated and the empty one should not.
EXPECT_TRUE(GetDocument().NeedsLayoutTreeUpdate());
EXPECT_TRUE(new_page->GetDocument().NeedsLayoutTreeUpdate());
EXPECT_FALSE(empty_page->GetDocument().NeedsLayoutTreeUpdate());
}
TEST_F(StyleEnvironmentVariablesTest, MultiDocumentInvalidation_FromDocument) {
InitializeTestPageWithVariableNamed(GetFrame(), kVariableName);
// Create a second page that uses the variable.
auto new_page = std::make_unique<DummyPageHolder>(gfx::Size(800, 600));
InitializeTestPageWithVariableNamed(new_page->GetFrame(), kVariableName);
SetVariableOnDocument(kVariableName, kVariableTestColor);
// Only the first document should be invalidated.
EXPECT_TRUE(GetDocument().NeedsLayoutTreeUpdate());
EXPECT_FALSE(new_page->GetDocument().NeedsLayoutTreeUpdate());
}
TEST_F(StyleEnvironmentVariablesTest, NavigateToClear) {
SetVariableOnDocument(kVariableName, kVariableTestColor);
// Simulate a navigation to clear the variables.
SimulateNavigation();
InitializeTestPageWithVariableNamed(GetFrame(), kVariableName);
// Check that the element has no background color.
Element* target = GetDocument().getElementById("target");
EXPECT_EQ(kNoColor, target->ComputedStyleRef().VisitedDependentColor(
GetCSSPropertyBackgroundColor()));
}
TEST_F(StyleEnvironmentVariablesTest, GlobalVariable_AfterLoad) {
InitializeTestPageWithVariableNamed(GetFrame(), kVariableName);
SetVariableOnRoot(kVariableName, kVariableTestColor);
// Ensure that the document has been invalidated.
EXPECT_TRUE(GetDocument().NeedsLayoutTreeUpdate());
UpdateAllLifecyclePhasesForTest();
// Check that the element has the background color provided by the variable.
Element* target = GetDocument().getElementById("target");
EXPECT_EQ(kTestColorRed, target->ComputedStyleRef().VisitedDependentColor(
GetCSSPropertyBackgroundColor()));
}
TEST_F(StyleEnvironmentVariablesTest, GlobalVariable_Change) {
SetVariableOnRoot(kVariableName, kVariableAltTestColor);
InitializeTestPageWithVariableNamed(GetFrame(), kVariableName);
// Change the variable value after we have loaded the page.
SetVariableOnRoot(kVariableName, kVariableTestColor);
// Ensure that the document has been invalidated.
EXPECT_TRUE(GetDocument().NeedsLayoutTreeUpdate());
UpdateAllLifecyclePhasesForTest();
// Check that the element has the background color provided by the variable.
Element* target = GetDocument().getElementById("target");
EXPECT_EQ(kTestColorRed, target->ComputedStyleRef().VisitedDependentColor(
GetCSSPropertyBackgroundColor()));
}
TEST_F(StyleEnvironmentVariablesTest, GlobalVariable_DefaultsPresent) {
EXPECT_EQ(kSafeAreaInsetExpectedDefault,
GetRootVariableValue(UADefinedVariable::kSafeAreaInsetTop));
EXPECT_EQ(kSafeAreaInsetExpectedDefault,
GetRootVariableValue(UADefinedVariable::kSafeAreaInsetLeft));
EXPECT_EQ(kSafeAreaInsetExpectedDefault,
GetRootVariableValue(UADefinedVariable::kSafeAreaInsetBottom));
EXPECT_EQ(kSafeAreaInsetExpectedDefault,
GetRootVariableValue(UADefinedVariable::kSafeAreaInsetRight));
EXPECT_EQ(
nullptr,
StyleEnvironmentVariables::GetRootInstance().ResolveVariable("test", {}));
}
TEST_F(StyleEnvironmentVariablesTest, GlobalVariable_Preset) {
SetVariableOnRoot(kVariableName, kVariableTestColor);
InitializeTestPageWithVariableNamed(GetFrame(), kVariableName);
// Check that the element has the background color provided by the variable.
Element* target = GetDocument().getElementById("target");
EXPECT_EQ(kTestColorRed, target->ComputedStyleRef().VisitedDependentColor(
GetCSSPropertyBackgroundColor()));
}
TEST_F(StyleEnvironmentVariablesTest, GlobalVariable_Remove) {
SetVariableOnRoot(kVariableName, kVariableTestColor);
InitializeTestPageWithVariableNamed(GetFrame(), kVariableName);
// Check that the element has the background color provided by the variable.
Element* target = GetDocument().getElementById("target");
EXPECT_EQ(kTestColorRed, target->ComputedStyleRef().VisitedDependentColor(
GetCSSPropertyBackgroundColor()));
// Change the variable value after we have loaded the page.
RemoveVariableOnRoot(kVariableName);
// Ensure that the document has been invalidated.
EXPECT_TRUE(GetDocument().NeedsLayoutTreeUpdate());
UpdateAllLifecyclePhasesForTest();
// Check that the element does not have the background color any more.
EXPECT_NE(kTestColorRed, target->ComputedStyleRef().VisitedDependentColor(
GetCSSPropertyBackgroundColor()));
}
TEST_F(StyleEnvironmentVariablesTest,
DISABLED_PrintExpectedVariableNameHashes) {
const UADefinedVariable variables[] = {
UADefinedVariable::kSafeAreaInsetTop,
UADefinedVariable::kSafeAreaInsetLeft,
UADefinedVariable::kSafeAreaInsetRight,
UADefinedVariable::kSafeAreaInsetBottom};
for (const auto& variable : variables) {
const AtomicString name = StyleEnvironmentVariables::GetVariableName(
variable, /*feature_context=*/nullptr);
printf("0x%x\n",
DocumentStyleEnvironmentVariables::GenerateHashFromName(name));
}
}
TEST_F(StyleEnvironmentVariablesTest, RecordUseCounter_IgnoreMediaControls) {
InitializeWithHTML(GetFrame(), "<video controls />");
EXPECT_FALSE(GetDocument().IsUseCounted(WebFeature::kCSSEnvironmentVariable));
EXPECT_FALSE(GetDocument().IsUseCounted(
WebFeature::kCSSEnvironmentVariable_SafeAreaInsetTop));
EXPECT_FALSE(GetDocument().IsUseCounted(
WebFeature::kCSSEnvironmentVariable_SafeAreaInsetLeft));
EXPECT_FALSE(GetDocument().IsUseCounted(
WebFeature::kCSSEnvironmentVariable_SafeAreaInsetBottom));
EXPECT_FALSE(GetDocument().IsUseCounted(
WebFeature::kCSSEnvironmentVariable_SafeAreaInsetRight));
}
TEST_F(StyleEnvironmentVariablesTest, RecordUseCounter_InvalidProperty) {
InitializeTestPageWithVariableNamed(GetFrame(), kVariableName);
EXPECT_TRUE(GetDocument().IsUseCounted(WebFeature::kCSSEnvironmentVariable));
}
TEST_F(StyleEnvironmentVariablesTest, RecordUseCounter_NoVariable) {
InitializeWithHTML(GetFrame(), "");
EXPECT_FALSE(GetDocument().IsUseCounted(WebFeature::kCSSEnvironmentVariable));
}
TEST_F(StyleEnvironmentVariablesTest, RecordUseCounter_SafeAreaInsetBottom) {
InitializeTestPageWithVariableNamed(GetFrame(),
UADefinedVariable::kSafeAreaInsetBottom);
EXPECT_TRUE(GetDocument().IsUseCounted(WebFeature::kCSSEnvironmentVariable));
EXPECT_TRUE(GetDocument().IsUseCounted(
WebFeature::kCSSEnvironmentVariable_SafeAreaInsetBottom));
}
TEST_F(StyleEnvironmentVariablesTest, RecordUseCounter_SafeAreaInsetLeft) {
InitializeTestPageWithVariableNamed(GetFrame(),
UADefinedVariable::kSafeAreaInsetLeft);
EXPECT_TRUE(GetDocument().IsUseCounted(WebFeature::kCSSEnvironmentVariable));
EXPECT_TRUE(GetDocument().IsUseCounted(
WebFeature::kCSSEnvironmentVariable_SafeAreaInsetLeft));
}
TEST_F(StyleEnvironmentVariablesTest, RecordUseCounter_SafeAreaInsetRight) {
InitializeTestPageWithVariableNamed(GetFrame(),
UADefinedVariable::kSafeAreaInsetRight);
EXPECT_TRUE(GetDocument().IsUseCounted(WebFeature::kCSSEnvironmentVariable));
EXPECT_TRUE(GetDocument().IsUseCounted(
WebFeature::kCSSEnvironmentVariable_SafeAreaInsetRight));
}
TEST_F(StyleEnvironmentVariablesTest, RecordUseCounter_SafeAreaInsetTop) {
InitializeTestPageWithVariableNamed(GetFrame(),
UADefinedVariable::kSafeAreaInsetTop);
EXPECT_TRUE(GetDocument().IsUseCounted(WebFeature::kCSSEnvironmentVariable));
EXPECT_TRUE(GetDocument().IsUseCounted(
WebFeature::kCSSEnvironmentVariable_SafeAreaInsetTop));
}
TEST_F(StyleEnvironmentVariablesTest, KeyboardInset_AfterLoad) {
// This test asserts that the keyboard inset environment variables should be
// loaded by default when the VirtualKeyboard runtime flag is set.
ScopedVirtualKeyboardForTest scoped_feature(true);
CSSVariableData* data =
StyleEnvironmentVariables::GetRootInstance().ResolveVariable(
StyleEnvironmentVariables::GetVariableName(
UADefinedVariable::kKeyboardInsetTop,
/*feature_context=*/nullptr),
{});
EXPECT_TRUE(data);
data = StyleEnvironmentVariables::GetRootInstance().ResolveVariable(
StyleEnvironmentVariables::GetVariableName(
UADefinedVariable::kKeyboardInsetLeft, /*feature_context=*/nullptr),
{});
EXPECT_TRUE(data);
data = StyleEnvironmentVariables::GetRootInstance().ResolveVariable(
StyleEnvironmentVariables::GetVariableName(
UADefinedVariable::kKeyboardInsetBottom,
/*feature_context=*/nullptr),
{});
EXPECT_TRUE(data);
data = StyleEnvironmentVariables::GetRootInstance().ResolveVariable(
StyleEnvironmentVariables::GetVariableName(
UADefinedVariable::kKeyboardInsetRight, /*feature_context=*/nullptr),
{});
EXPECT_TRUE(data);
data = StyleEnvironmentVariables::GetRootInstance().ResolveVariable(
StyleEnvironmentVariables::GetVariableName(
UADefinedVariable::kKeyboardInsetWidth, /*feature_context=*/nullptr),
{});
EXPECT_TRUE(data);
data = StyleEnvironmentVariables::GetRootInstance().ResolveVariable(
StyleEnvironmentVariables::GetVariableName(
UADefinedVariable::kKeyboardInsetHeight,
/*feature_context=*/nullptr),
{});
EXPECT_TRUE(data);
}
TEST_F(StyleEnvironmentVariablesTest, TwoDimensionalVariables_BasicResolve) {
ScopedCSSFoldablesForTest scoped_feature(true);
String env_contents("viewport-segment-top 1 0");
InitializeTestPageWithVariableNamed(GetFrame(), env_contents);
SetTwoDimensionalVariableOnRoot(
UADefinedTwoDimensionalVariable::kViewportSegmentTop, 1, 0, "red");
// Ensure that the document has been invalidated.
EXPECT_TRUE(GetDocument().NeedsLayoutTreeUpdate());
UpdateAllLifecyclePhasesForTest();
// Check that the element has the background color provided by the variable.
Element* target = GetDocument().getElementById("target");
EXPECT_EQ(kTestColorRed, target->ComputedStyleRef().VisitedDependentColor(
GetCSSPropertyBackgroundColor()));
}
TEST_F(StyleEnvironmentVariablesTest, TwoDimensionalVariables_UpdateValue) {
ScopedCSSFoldablesForTest scoped_feature(true);
String env_contents("viewport-segment-top 1 0");
InitializeTestPageWithVariableNamed(GetFrame(), env_contents);
SetTwoDimensionalVariableOnRoot(
UADefinedTwoDimensionalVariable::kViewportSegmentTop, 1, 0, "red");
// Ensure that the document has been invalidated.
EXPECT_TRUE(GetDocument().NeedsLayoutTreeUpdate());
UpdateAllLifecyclePhasesForTest();
// Check that the element has the background color provided by the variable.
Element* target = GetDocument().getElementById("target");
EXPECT_EQ(kTestColorRed, target->ComputedStyleRef().VisitedDependentColor(
GetCSSPropertyBackgroundColor()));
SetTwoDimensionalVariableOnRoot(
UADefinedTwoDimensionalVariable::kViewportSegmentTop, 1, 0, "blue");
EXPECT_TRUE(GetDocument().NeedsLayoutTreeUpdate());
UpdateAllLifecyclePhasesForTest();
EXPECT_EQ(kAltTestColor, target->ComputedStyleRef().VisitedDependentColor(
GetCSSPropertyBackgroundColor()));
}
TEST_F(StyleEnvironmentVariablesTest,
TwoDimensionalVariables_UndefinedFallsBack) {
ScopedCSSFoldablesForTest scoped_feature(true);
String env_contents(
"viewport-segment-width 10 20, env(viewport-segment-width 0 0, blue)");
InitializeTestPageWithVariableNamed(GetFrame(), env_contents);
SetTwoDimensionalVariableOnRoot(
UADefinedTwoDimensionalVariable::kViewportSegmentWidth, 1, 1, "red");
// Ensure that the document has been invalidated.
EXPECT_TRUE(GetDocument().NeedsLayoutTreeUpdate());
UpdateAllLifecyclePhasesForTest();
// Check that the element has the background color provided by the fallback.
Element* target = GetDocument().getElementById("target");
EXPECT_EQ(kAltTestColor, target->ComputedStyleRef().VisitedDependentColor(
GetCSSPropertyBackgroundColor()));
}
TEST_F(StyleEnvironmentVariablesTest,
TwoDimensionalVariables_IncorrectDimensionsFallsBack) {
ScopedCSSFoldablesForTest scoped_feature(true);
String env_contents("viewport-segment-width 0 0 0 0, blue");
InitializeTestPageWithVariableNamed(GetFrame(), env_contents);
SetTwoDimensionalVariableOnRoot(
UADefinedTwoDimensionalVariable::kViewportSegmentWidth, 0, 0, "red");
// Ensure that the document has been invalidated.
EXPECT_TRUE(GetDocument().NeedsLayoutTreeUpdate());
UpdateAllLifecyclePhasesForTest();
// Check that the element has the background color provided by the fallback.
Element* target = GetDocument().getElementById("target");
EXPECT_EQ(kAltTestColor, target->ComputedStyleRef().VisitedDependentColor(
GetCSSPropertyBackgroundColor()));
}
TEST_F(StyleEnvironmentVariablesTest,
TwoDimensionalVariables_NormalVariableWithDimensionFallsBack) {
ScopedCSSFoldablesForTest scoped_feature(true);
String env_contents("safe-area-inset-left 0, blue");
InitializeTestPageWithVariableNamed(GetFrame(), env_contents);
SetVariableOnRoot("safe-area-inset-left", "red");
// Ensure that the document has been invalidated.
EXPECT_TRUE(GetDocument().NeedsLayoutTreeUpdate());
UpdateAllLifecyclePhasesForTest();
// Check that the element has the background color provided by the fallback.
Element* target = GetDocument().getElementById("target");
EXPECT_EQ(kAltTestColor, target->ComputedStyleRef().VisitedDependentColor(
GetCSSPropertyBackgroundColor()));
}
TEST_F(StyleEnvironmentVariablesTest,
TwoDimensionalVariables_NegativeIndicesInvalid) {
ScopedCSSFoldablesForTest scoped_feature(true);
String env_contents("viewport-segment-top -1 -1, blue");
InitializeTestPageWithVariableNamed(GetFrame(), env_contents);
SetTwoDimensionalVariableOnRoot(
UADefinedTwoDimensionalVariable::kViewportSegmentTop, 0, 0, "red");
SetTwoDimensionalVariableOnRoot(
UADefinedTwoDimensionalVariable::kViewportSegmentTop, 1, 1, "red");
// Document should not have been invalidated since the value was a parse
// error and viewport-segment-left is not referenced.
EXPECT_FALSE(GetDocument().NeedsLayoutTreeUpdate());
// Check that the element has no cascaded background color.
Element* target = GetDocument().getElementById("target");
EXPECT_EQ(kNoColor, target->ComputedStyleRef().VisitedDependentColor(
GetCSSPropertyBackgroundColor()));
}
TEST_F(StyleEnvironmentVariablesTest,
TwoDimensionalVariables_NonCommaAfterIndexInvalid) {
ScopedCSSFoldablesForTest scoped_feature(true);
String env_contents("viewport-segment-left 1 1 ident");
InitializeTestPageWithVariableNamed(GetFrame(), env_contents);
SetTwoDimensionalVariableOnRoot(
UADefinedTwoDimensionalVariable::kViewportSegmentLeft, 1, 1, "red");
// Document should not have been invalidated since the value was a parse
// error and viewport-segment-left is not referenced.
EXPECT_FALSE(GetDocument().NeedsLayoutTreeUpdate());
// Check that the element has no cascaded background color.
Element* target = GetDocument().getElementById("target");
EXPECT_EQ(kNoColor, target->ComputedStyleRef().VisitedDependentColor(
GetCSSPropertyBackgroundColor()));
}
TEST_F(StyleEnvironmentVariablesTest,
TwoDimensionalVariables_NonIntegerIndicesInvalid) {
ScopedCSSFoldablesForTest scoped_feature(true);
String env_contents("viewport-segment-top 0.5 0.5, blue");
InitializeTestPageWithVariableNamed(GetFrame(), env_contents);
SetTwoDimensionalVariableOnRoot(
UADefinedTwoDimensionalVariable::kViewportSegmentTop, 0, 0, "red");
SetTwoDimensionalVariableOnRoot(
UADefinedTwoDimensionalVariable::kViewportSegmentTop, 1, 1, "red");
// Document should not have been invalidated since the value was a parse
// error and viewport-segment-left is not referenced.
EXPECT_FALSE(GetDocument().NeedsLayoutTreeUpdate());
// Check that the element has no cascaded background color.
Element* target = GetDocument().getElementById("target");
EXPECT_EQ(kNoColor, target->ComputedStyleRef().VisitedDependentColor(
GetCSSPropertyBackgroundColor()));
}
TEST_F(StyleEnvironmentVariablesTest,
TwoDimensionalVariables_NoIndicesFallsBack) {
ScopedCSSFoldablesForTest scoped_feature(true);
String env_contents("viewport-segment-height, blue");
InitializeTestPageWithVariableNamed(GetFrame(), env_contents);
SetTwoDimensionalVariableOnRoot(
UADefinedTwoDimensionalVariable::kViewportSegmentTop, 0, 0, "red");
// Document should not have been invalidated since the wrong dimensions can
// never resolve (and thus the variable has not been 'seen').
EXPECT_FALSE(GetDocument().NeedsLayoutTreeUpdate());
// Check that the element has the background color provided by the fallback.
Element* target = GetDocument().getElementById("target");
EXPECT_EQ(kAltTestColor, target->ComputedStyleRef().VisitedDependentColor(
GetCSSPropertyBackgroundColor()));
}
TEST_F(StyleEnvironmentVariablesTest, TwoDimensionalVariables_Removal) {
ScopedCSSFoldablesForTest scoped_feature(true);
String env_contents("viewport-segment-height 0 0, blue");
InitializeTestPageWithVariableNamed(GetFrame(), env_contents);
SetTwoDimensionalVariableOnRoot(
UADefinedTwoDimensionalVariable::kViewportSegmentHeight, 0, 0, "red");
// Ensure that the document has been invalidated.
EXPECT_TRUE(GetDocument().NeedsLayoutTreeUpdate());
UpdateAllLifecyclePhasesForTest();
// Check that the element has the background color provided by the variable.
Element* target = GetDocument().getElementById("target");
EXPECT_EQ(kTestColorRed, target->ComputedStyleRef().VisitedDependentColor(
GetCSSPropertyBackgroundColor()));
RemoveVariableOnRoot("viewport-segment-height");
EXPECT_TRUE(GetDocument().NeedsLayoutTreeUpdate());
UpdateAllLifecyclePhasesForTest();
// Check that the element has the background color provided by the fallback.
EXPECT_EQ(kAltTestColor, target->ComputedStyleRef().VisitedDependentColor(
GetCSSPropertyBackgroundColor()));
}
} // namespace blink
| {
"redpajama_set_name": "RedPajamaGithub"
} | 5,502 |
This week's word of the week was chosen in reference to my growing sense of needing to fight, whether for my beliefs, my sanity, my family, my varied interests, my identity, or my writing style. It's a tough job, this being a reporter while being a person.
I never quite realized how much people might start expecting me as a person to embody me as a journalist. As if I cannot have opinions, not be able to distinguish and separate one from the other, not be able to be a better reporter exactly because I am not an empty vessel to be steered according to the direction of whoever makes the strongest case. My job is to research, distill, expand upon and communicate. As a community reporter, I am in people's communities to shine a light on their issues, but also to frame it fairly, relevantly and thoroughly. It is not my job to simply spit out facts and give no analysis. Objectivity does not require obliviousness.
Then there is the fighting against pressures – whether from sources, family, superiors, colleagues or yourself – to live for others, for the job, not for yourself. It is awfully tempting to lose yourself in your job, especially when you enjoy it. But it is important that you maintain a sense of who you are and who you want to be, now and in the future.
I do enjoy realizing that I still have a spark in me.
These are some of the things I'm struggling with this week. Work is fine. Stories continue to be varied. No tragedies this week, knock on wood. Just lots of big news and changes and running out of page space for story content due to the coexistence with the classifieds and ads again. Some stories I'm proud of. But no worries, because I'm still fighting strong. | {
"redpajama_set_name": "RedPajamaC4"
} | 3,383 |
/*
* MIT Licence
* All Right Reserved
*/
package ec.edu.espe.isi.educat04.dao;
import ec.edu.espe.isi.educat04.model.CapacitacionAlumno;
import javax.ejb.Stateless;
import javax.persistence.EntityManager;
import javax.persistence.PersistenceContext;
/**
* Clase que registra la informcion de las capacitaciones del alumno. .
* @author: Cristhian J Arevalo.
* @version: 1/7/2017.
*/
@Stateless
public class CapacitacionAlumnoFacade extends AbstractFacade<CapacitacionAlumno> {
@PersistenceContext(unitName = "ec.edu.espe.isi.educat04_EducaT04-ejb_ejb_1PU")
private EntityManager em;
@Override
protected EntityManager getEntityManager() {
return em;
}
public CapacitacionAlumnoFacade() {
super(CapacitacionAlumno.class);
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 1,156 |
\section{Introduction}
The theoretical concept of creating artificial gauge potentials for neutral atoms
using spatially tailored light fields has now reached maturity
(see Ref.~\cite{DalGerJuz2011} for a comprehensive theoretical review).
The recent experiments in which an artificial magnetic field was created
in a rubidium Bose-Einstein condensate~\cite{lin_2009b},
has most notably led to the creation of quantized vortices~\cite{LinComJim2009},
spin-orbit coupling~\cite{lin_2011},
and strong effective magnetic fields in optical lattices~\cite{aidelsburger_2011}.
Being able to create artificial gauge fields, both Abelian and
non-Abelian~\cite{osterloh_2005,ruseckas_2005}, has opened up new avenues of research
such as creating exotic matter wave states~\cite{burrello_2010} (quantized vortices
being a simple example~\cite{LinComJim2009}), gauge potentials in optical lattices
allowing for the study of the Harper equation and Hofstadter butterfly~\cite{jaksch_2003},
the creation of Aharanov-Bohm-like effects in atomic gases~\cite{jacob_2007},
and the exploration of analogies and differences with condensed matter and
particle physics ideas~\cite{merkl_2010,lan_2011,mazza_2012}.
Current experiments with artificial gauge potentials rely on a number of different schemes.
In the continuous gas case Raman transitions have been used in order to tailor the dispersion
relation such that the resulting equation of motion for the center of mass is governed by an
effective gauge potential \cite{LinComJim2009}. In a similar fashion spin-orbit coupling has also
been created in a $^{87}$Rb BEC \cite{lin_2011,wang_2012}. Gauge potentials have also been created
in optical lattice settings where laser-induced tunneling between the adjacent sites is used,
which can give rise to a nonzero Peierl's phase \cite{aidelsburger_2011}. Similarly the lattice
configuration also allows for spin-orbit coupling \cite{cheuk_2012}. Nontrivial complex valued tunneling coefficients
can also be created in an optical lattice by mechanically shaking the lattice in a specific manner, and
thereby obtaining a time averaged tunneling coefficient which can mimic the presence of an effective
external magnetic field \cite{eckardt_2005,struck_2012,hauke_2012}.
Of particular interest for this paper is the fact that using Laguerre-Gaussian laser fields,
which carry orbital angular momentum, in interactions with a three-level atom,
can yield an induced gauge potential that acts as an effective flux tube~\cite{JRO:JPB:05}.
This is significant in that if the atom is trapped in a radially symmetric potential
and the flux tube pierces the potential, then varying the flux can vary
the angular-momentum properties of the trapped atom~\cite{SFLO:EPL:08,SonFor2009,Ohberg2011}.
The goal of the present paper is to initiate a line of research
involving artificial gauge potentials formed using quantum-mechanical applied light fields,
in particular, optical coherent-state superpositions~\cite{MilWal1994,GlaMac2008}.
The concept is that if the quantum nature of the applied light can be transferred
to the matter waves then we open up the possibility of exposing the atom simultaneously
to a superposition of two or more artificial gauge potentials.
To introduce and explore this possibility, we consider the example of an atomic quantum ring,
both idealized and in a harmonic trap. An atomic quantum ring involves ultracold atoms
that are trapped circumferentially on a ring that is pierced at its center by a flux tube
arising from the light-induced gauge potential due to
applied Laguerre-Gaussian fields~\cite{SonFor2009,Ohberg2011}.
With a finite flux piercing the ring, the ground state corresponds to a rotating state.
Here we show that by using optical coherent state superpositions to produce
light-induced gauge potentials, we can create a situation
in which the trapped atoms are simultaneously exposed to two distinct flux tubes,
thereby creating superpositions in atomic quantum rings.
In particular, we show that the ground state is a quantum superposition of counter-rotating atomic states.
Creation of quantum superposition is also studied for cold atoms in
a rotating ring lattice potential in Refs.~\cite{NAB08,NAB11}.
This paper is organized as follows: In Sec.~\ref{gaugepot} we overview the basic formulation
of the field-induced gauge potential for a single atom
in the electromagnetically induced transparency (EIT) configuration~\cite{DalGerJuz2011,JRO:JPB:05}.
An effective Hamiltonian for the dark-state atom and its eigensolutions
are given for the harmonic and ring potentials.
Section~\ref{optcat} extends the standard dark-state scheme to
the case of a nonclassical control field.
We show that the superposition of distinct motional states has a lower energy
than the statistical mixture of those states.
\section{Atomic quantum ring}\label{gaugepot}
For the sake of clarity in presentation, and to solidify notation,
in this section we review the basic physical ideas underpinning the atomic quantum ring
for classical applied fields as described by coherent states.
This idea is applicable both for a single atom and cold atomic ensemble~\cite{aidelsburger_2011} without collisions.
First we set up the model equations as described in Ref.~\cite{JRO:JPB:05},
and then we turn to dark states and the effective gauge potential and flux tube.
Finally we discuss the quantum motional eigenstates
for the cases of a ring geometry and harmonic trapping.
\subsection{Model equations}
In a series of recent papers it has been shown how carefully shaped light beams
which are incident on cold atoms can be used for creating strong gauge potentials
in a cloud of neutral atoms.
This effect relies on the interplay between two laser beams and a $\Lambda$-type
level structure of the atoms, as shown in Fig.~\ref{fig1}.
In the following we consider a single atom which is characterized by two hyperfine ground levels
$|1\rangle$ and $|2\rangle$ of equal energies $\hbar\omega_1=\hbar\omega_2$,
and an electronic excited level $|3\rangle$ with energy $\hbar\omega_3$.
The atomic transition could involve, for example, $2\ {}^3S_1$ for the ground Zeeman states of ${}^4$He~\cite{AAKVC88} and $2\ {}^3P_1$ for the excited state.
The atom interacts with two laser beams.
The first beam, which we refer to as the probe beam,
is coupled with the transition $|1\rangle \leftrightarrow |3\rangle$,
whereas the second beam, the control beam, drives the transition $|2\rangle \leftrightarrow |3\rangle$.
The probe field is characterized by a wave vector $\bm{k}_p$, and a frequency $\omega_p=ck_p$.
The control laser, on the other hand, has a wave vector $\bm{k}_c$ and a frequency $\omega_c$.
We use Laguerre-Gaussian (LG) beams for the probe and control fields
having the lowest radial quantum number and distinct
orbital angular momenta per photon, which is $\hbar\ell_p$ for the probe field, and
$\hbar\ell_c$ for the control field, respectively.
Henceforth we choose the control and probe fields to have equal frequency $\omega_p=\omega_c=\omega$, equal magnitude of winding numbers of opposite sign $-\ell_p=\ell_c=\ell$, and take $\bm{k}_c$ and $\bm{k}_p$ collinear along the $z$ axis.
The Hamiltonian for the electronic degree of freedom of an atom interacting with quantized light fields
in the rotating-wave approximation is given by
\begin{eqnarray}\label{Hinternal}
\hat{h} (\bm{r})&=&\epsilon_{31}|3\rangle \lg 3|\nonumber\\
&-& \hbar \chi(\bm{r})\left(
\hat{a}_p e^{-i\ell \phi}|3\rangle \lg 1|
+\hat{a}_c e^{i\ell \phi} |3\rangle \lg 2|
+{\rm H.c.}
\right),\nonumber\\
\end{eqnarray}
where $\epsilon_{31}=\hbar (\omega_3-\omega_1-\omega)$
is the energy of the detuning from single-photon resonance,
with $\hbar \omega_j$ being the electronic energy of the atomic level $j=1,2,3$.
Here the Rabi frequency per photon, coupling the ground and excited states,
is denoted as $\chi (\bm{r})$.
The annihilation operators of a photon in the probe and control fields correspond to
$\hat{a}_p$ and $\hat{a}_c$, respectively.
In deriving the above Hamiltonian for the electronic degree of freedom,
we have assumed that the atomic motion is restricted to the two-dimensional plane $\bm{r}=(r,\phi)$
with $r=\sqrt{x^2+y^2}$, due to a tight confinement along the $z$ direction.
The spatial dependence of the Hamiltonian then comes from the space-dependent coupling
associated with the LG beams.
In this section we suppose that the control and probe fields may be described by coherent states
$|\alpha\rangle$ and $|\beta\rangle$, respectively.
The field state is then expressed by $|\Psi_f \rangle = |\alpha\rangle_c |\beta\rangle_p$
and the effective Hamiltonian for an atom
$\hat{h}_a(\bm{r}) \equiv \lg \Psi_f| \hat{h}(\bm{r}) | \Psi_f \rangle$ is given by
\begin{eqnarray}
\hat{h}_a(\bm{r})&=&\epsilon_{31}|3 \rangle\lg 3|\nonumber\\
&-&\hbar \chi (\bm{r})\left(\beta e^{-i\ell \phi}|3\rangle \lg 1|
+\alpha e^{i\ell \phi}|3\rangle \lg 2|+{\rm H.c.}
\right).
\end{eqnarray}
The eigensolutions, arising only from the Hamiltonian of electronic degree of freedom
$\hat{h}_a(\bm{r}) |X\rangle = \varepsilon_X |X\rangle$,
are denoted by $|D\rangle$, $|S\rangle$, and $|A\rangle$. The state
\begin{eqnarray}
|D\rangle = \frac{1}{\sqrt{\cal N}}(\alpha e^{i\ell \phi}|1\rangle - \beta e^{-i\ell \phi}|2\rangle)
\end{eqnarray}
is known as the {\it dark} state~\cite{A:PO:96,H:PT:97,L:RMP:03},
characterized by a zero eigenvalue $\varepsilon_D =0$.
Here ${\cal N} = |\alpha|^2+|\beta|^2$ is the normalization constant.
For $\epsilon_{31}=0$, namely, on resonance, the two other eigensolutions are given by the symmetric and antisymmetric superposition
of the {\it bright} state $|B\rangle$ and excited state $|3\rangle$,
\begin{eqnarray}
&&|S\rangle = \frac{1}{\sqrt{2}}(|B\rangle + |3\rangle),\\
&&|A\rangle = \frac{1}{\sqrt{2}}(|B\rangle - |3\rangle),
\end{eqnarray}
with eigenvalues $\varepsilon_S=|\chi({\bm r})|^2{\cal N}$ and $\varepsilon_A=-|\chi({\bm r})|^2{\cal N}$, respectively, where
\begin{eqnarray}
|B\rangle = \frac{1}{\sqrt{\cal N}}(\beta^* e^{i\ell \phi}|1\rangle + \alpha^* e^{-i\ell \phi}|2\rangle).
\end{eqnarray}
If the electronic state of an atom is prepared in the dark state $|D\rangle$,
the resonant control and probe beams induce the absorption paths
$|2\rangle \to |3\rangle$ and $|1\rangle \to |3\rangle$ which interfere destructively.
This is also the mechanism behind electromagnetically induced transparency~\cite{A:PO:96,H:PT:97,L:RMP:03}.
In such a situation, the transitions to the upper atomic level $|3\rangle$ are suppressed,
the atomic level $|3\rangle$ is weakly populated, and it is justified to neglect any losses
due to spontaneous emission from the excited state.
We shall hereafter assume that the trapped atom is prepared in the dark state.
The total Hamiltonian which accounts for both the electronic and motional dynamics is
\begin{eqnarray}\label{totalH}
\hat{H} = \frac{\hat{\bm{p}}^2}{2M}+\hat{V}(\bm{r}) + \hat{h}(\bm{r})
\end{eqnarray}
with $M$ being the atomic mass, $\hat{\bm{p}}=-i\hbar \bm{\nabla}$ the momentum operator, and
\begin{eqnarray}
\hat{V}(\bm{r}) = V_1(\bm{r})|1\rangle\lg 1|+V_2(\bm{r})|2\rangle\lg 2|+V_3(\bm{r})|3\rangle\lg 3|
\end{eqnarray}
is the trapping potential. The entire quantum state including both the atom and field can be written as
\begin{eqnarray}
|\Phi(\bm{r},t)\rangle = |\Psi_f\rangle\sum_{X=D,S,A}\Psi_X(\bm{r},t)|X\rangle,
\end{eqnarray}
where $\Psi_X(\bm{r},t)$ describes the translational motion of the atom
in one of the three electronic states.
By using this state and the total Hamiltonian~(\ref{totalH}) we arrive at the equation of motion for the three states $\bm{\Psi} = (\Psi_D,\Psi_S,\Psi_A)^T$,
\begin{eqnarray}
i\hbar \frac{\partial}{\partial t}\bm{\Psi} = \hat{H}^{\rm (eff)}\bm{\Psi},
\end{eqnarray}
where the effective Hamiltonian is given by
\begin{eqnarray}\label{Heff}
\hat{H}^{\rm (eff)}= \frac{1}{2M}(i\hbar \nabla - \bm{A})^2 + U
\end{eqnarray}
with
\begin{eqnarray}
&&\bm{A}_{X,X'}=-i\hbar \lg X|\nabla X'\rangle,\\
&&U_{X,X'}=\varepsilon_{X}\delta_{X,X'} + \lg X|\hat{V}| X'\rangle.
\end{eqnarray}
If the internal dynamics is much faster than the external one we can safely assume
the dynamics of the different states to be independent.
In other words, the adiabatic approximation is assumed to hold here.
\begin{figure}
\includegraphics[scale=0.5]{fig1.eps}
\caption{
The level scheme. A single atom is irradiated by two lasers:
the probe field that couples $|1\rangle$ and $|3\rangle$ with the amplitude $\beta$, winding number $\ell_p$, frequency $\omega_p$, and wavenumber $\bm{k}_p$,
and the control field that couples $|2\rangle$ and $|3\rangle$ with the
amplitude $\alpha$, winding number $\ell_c$, frequency $\omega_c$, and
wavenumber $\bm{k}_c$. Here we take $\ell = \ell_c = - \ell_p$.
}
\label{fig1}
\end{figure}
\subsection{Dark state and the effective flux tube}
In the following we assume that the atom remains dominantly in its dark state while moving in space.
The total effective Hamiltonian for the center-of-mass motion of the atom
in the dark state is given from Eq.~(\ref{Heff}) as
\begin{eqnarray}
\hat{H}^{\rm (eff)}_{DD}&=&\frac{1}{2M}(i\hbar \nabla - {\bm A}_{DD})^2 + V_{\rm eff}.
\end{eqnarray}
The resulting gauge potential is defined as
\begin{eqnarray}\label{ADD}
{\bm A}_{DD} = -i\hbar \lg D |\nabla D \rangle {\bm e}_\phi = \frac{\hbar \ell \sigma}{r}{\bm e}_\phi,
\end{eqnarray}
where
\begin{eqnarray}
\sigma \equiv \frac{|\alpha|^2- |\beta|^2}{{\cal N}}
\end{eqnarray}
is the mean spin of the two LG laser beams.
The effective potential is given by
\begin{eqnarray}
V_{\rm eff}=U + \varphi,
\end{eqnarray}
where
\begin{eqnarray}
\varphi=\frac{1}{2M}\sum_{X=S,A}\bm{A}_{D,X}\bm{A}_{X,D}.
\end{eqnarray}
For the dark state, the scalar potential is
\begin{eqnarray}
\varphi=\frac{\hbar^2}{2M}(\lg D | \nabla D \rangle^2 + \lg \nabla D | \nabla D \rangle),
\end{eqnarray}
and the effective Hamiltonian for the external motion of an atom in the dark state is
\begin{eqnarray}
\hat{H}^{\rm (eff)}_{DD}
&=& \frac{\hbar^2(-\nabla^2 + \lg \nabla D|\nabla D\rangle )}{2M}\nonumber\\
&&+\lg D | V(\bm{r}) | D\rangle-\frac{\hbar^2}{M}\lg D | \nabla D \rangle \nabla .
\end{eqnarray}
Note that with our Hamiltonian~(\ref{Hinternal}) and LG beams with the lowest radial quantum number,
the dark state depends only on the angle.
In this way, the effective trapping potential $V_{\rm eff}$ is composed of
the external trapping potential and the geometric scalar potential $\varphi$.
Drawing these results together the effective Hamiltonian becomes
\begin{eqnarray}
\hat{H}^{\rm (eff)}_{DD} =
-\frac{\hbar^2\nabla^2}{2M}+\frac{\hbar^2 \ell^2}{2Mr^2}+V(\bm{r})
-i \ell \sigma \frac{\hbar^2}{Mr^2} \frac{\partial}{\partial \phi} .
\end{eqnarray}
For simplicity in notation we hereafter omit the subscript $D$ for the dark state unless otherwise stated.
The angular-momentum operator for the dark-state atom is given by
\begin{eqnarray}
\hat{L}_z = |D\rangle \lg D|\left(-i \hbar \frac{\partial}{\partial \phi}\right) |D\rangle\lg D|,
\end{eqnarray}
which has an additional term that comes from the dark-state spatial variation,
\begin{eqnarray}
\lg D|\left(-i\hbar \frac{\partial}{\partial \phi}\right)|D\rangle
= - i\hbar \frac{\partial}{\partial \phi}+r A_{\phi},
\end{eqnarray}
where $A_{\phi} = \hbar \ell \sigma / r$ is the $\phi$ component of the gauge potential Eq.~(\ref{ADD}).
If the mean spin of two lasers $\sigma$ is non-integer,
the orbital angular momentum of the motional state is no longer quantized in the integer units of $\hbar$.
Finally, the effective magnetic flux induced by the effective gauge potential is given by
\begin{eqnarray}
\Phi_{\rm mf}=2\pi\hbar\sigma\ell.
\end{eqnarray}
The effective gauge potential due to the applied LG fields
therefore acts as a flux tube of strength $\Phi_{\rm mf}$.
\subsubsection{Ring geometry}\label{ringCS}
First we consider the case that the atom is tightly trapped circumferentially
on a ring of radius $R$ by an external annular potential, which greatly simplifies
the analysis~\cite{SonFor2009,Ohberg2011}.
The effective Hamiltonian at a fixed radius $r=R$ is
\begin{eqnarray}\label{H1D}
\hat{H}^{\rm (eff)} = \frac{\hbar^2}{2I}
\left(-\frac{\partial^2}{\partial \phi^2} + \ell^2
- 2i \ell \sigma \frac{\partial}{\partial \phi}\right),
\end{eqnarray}
where we have defined the rotational inertia $I = MR^2$.
The solutions of the eigenproblem $\hat{H}^{\rm (eff)}\Psi = E \Psi$
for the atomic motional state with the electronic state being the dark state are specified
only by angular-momentum quantum number $m$,
\begin{eqnarray}
&& E_m = \frac{\hbar^2}{2I}(\ell^2 + m^2 + 2 \sigma \ell m), \label{ene1D}\\
&& \Psi_m (\phi) = \frac{1}{\sqrt{2\pi}} e^{i m \phi}, \label{wf1D}
\end{eqnarray}
where $m \in \{0,\pm 1,\pm2,\dots\}$.
Generally the energy $E_m$ for a given value of $\sigma \ell$,
and $E_{-m}$ for the value $-\sigma \ell$ are degenerate.
The quantum number for the ground state $\check{m}$ is given by
\begin{eqnarray}\label{gsam1D}
\check{m}=-\lfloor\sigma \ell + 1/2\rfloor,
\end{eqnarray}
where $\lfloor s \rfloor$ denotes the floor function applied to the argument $s$.
We note that we have sgn$(\sigma \ell \check{m})<0$. This fact will be important
in the next section in evaluating the energy associated with the superposition.
The energy eigenvalues $E_m$, and the ground-state angular momentum $\check{m}$ for $\ell=4$ are plotted as a function of $\sigma \ell$ in Figs.~\ref{fig_R}(a) and (b), respectively.
Figure~\ref{fig_R}(c) plots the energy separation between the ground and the first excited states,
$\Delta E \equiv E_{\check{m}\pm 1}-E_{\check{m}}= (\hbar^2/2I)\left[\pm 2 (\check{m}+\sigma \ell)-1\right]$.
This energy gap becomes zero at half-integral values of the mean spin $\sigma$,
and the ground-state angular momentum $\check{m}$ changes at these points.
On the other hand, $\Delta E$ takes local maxima at integral values of $\sigma \ell$.
Because of the restriction of the atomic motion to the ring, the excitation energy
as a function of $\sigma \ell$ is independent of $\ell$.
\begin{figure}
\includegraphics[scale=0.5]{fig2.eps}
\caption{
(a) Energy eigenvalues $E_m/(\hbar^2/2I)$, (b) ground-state angular momentum $\check{m}$, and
(c) the lowest excitation energy $\Delta E/(\hbar^2/2I)$, as a function of the mean spin, for $\ell=4$.
}
\label{fig_R}
\end{figure}
\subsubsection{Harmonic trapping potential}
When the atom is trapped in a harmonic trap $V(r) = M\Omega^2 r^2/2$,
the eigenproblem for the motional state of the dark-state atom is also analytically solvable~\cite{SFLO:EPL:08}.
With the use of the zero-point oscillator length $r_0=\sqrt{\hbar/(2M\Omega)}$ as the length unit,
the Hamiltonian is
\begin{eqnarray}\label{2DH}
\hat{H}^{\rm (eff)}=\hbar \Omega \left[-\nabla^2+\frac{r^2}{4}+\frac{1}{r^2}\left(\ell^2 - 2i\ell \sigma \frac{\partial}{\partial \phi}\right)\right],
\end{eqnarray}
and its eigenvalues and eigenstates are given by
\begin{eqnarray}
&&E_{n,m}=\hbar \Omega (2n+\mu_{m} +1), \\
&&\Psi_{n,m}(\bm{r})=\frac{1}{\sqrt{2\pi}}e^{im\phi}f_{n,m}(r),
\end{eqnarray}
where $n \in \{0,1,\dots\}$ and $m \in \{0,\pm 1, \pm 2,\dots\}$.
The radial dependence of the eigenstate is obtained as
\begin{eqnarray}
f_{n,m}(r)= C_{n,m}\left(\frac{r^2}{2}\right)^{\mu_m/2} e^{-r^2/4}
{\cal L}_n^{\mu_m}\!\!\left(\frac{r^2}{2}\right),\label{fnm}
\end{eqnarray}
where $C_{n,m}=\sqrt{n!/\Gamma (n+\mu_m +1)}$ with $\Gamma(x)$ being the gamma function.
The function ${\cal L}_n^{\alpha}(x)$ is the generalized Laguerre polynomial,
parametrized with
\begin{eqnarray}
\mu_m = \sqrt{\ell^2 + m^2 + 2\sigma \ell m}.
\end{eqnarray}
Just like the case of the ring geometry, the eigenvalues $E_{n,m}$
for a given value of $\sigma \ell$ are degenerate with $E_{n,-m}$ for the value $-\sigma \ell$.
The quantum numbers $(\check{n},\check{m})$ of ground state are given by
\begin{eqnarray}\label{gsam}
\check{n}=0,\quad \check{m}=-\lfloor\sigma \ell +1/2\rfloor,
\end{eqnarray}
and therefore we again have sgn$(\sigma\ell\check{m})<0$ for the ground state.
The energy eigenvalues $E_{n,m}$ for various $n$ with $\ell=4$ are plotted
as a function of $\sigma\ell$ in Fig.~\ref{fig_H}(a).
\begin{figure}
\includegraphics[scale=0.5]{fig3.eps}
\caption{
(a) Energy eigenvalues $E_{n,m}/\hbar \Omega$ as a function of $\sigma \ell$. Here we fixed the winding number $\ell=4$.
(b) The lowest excitation energy for $\ell=4$ (line), 6 (dashed), and 10 (dotted).
(c) The lowest excitation energy at $\sigma=0$ as a function of $\ell$.
}
\label{fig_H}
\end{figure}
Figure~\ref{fig_H}(b) plots the energy separation $\Delta E$ between the ground and the first excited states.
This energy gap similarly becomes zero at half-integral values of the mean spin $\sigma$ and takes local maxima at integral value of $\sigma$.
In contrast to the ring case, for a fixed value of $\ell$ while changing the mean spin $\sigma$, the magnitudes of $\Delta E$ at different integral values of $|\sigma \ell|$
are different values as $\Delta E (\sigma\ell =0) \lesssim \Delta E(|\sigma \ell| = 1) \lesssim \Delta E(|\sigma\ell|=2)\lesssim \cdots$.
When we inspect the energy gap as a function of $\ell$ for a fixed value of mean spin (say, $\sigma=0$), $\Delta E$ is a monotonically decreasing function with respect to $\ell$ as shown in Fig.~\ref{fig_H}(c).
\section{Superposition in atomic quantum rings}\label{optcat}
The goal of this section is to demonstrate that by making the control field
a quantum superposition of coherent states, the trapped atom can be made to experience
a combination of flux tubes with opposite sign of flux~\cite{SFLO:EPL:08,SonFor2009,Ohberg2011}.
Furthermore we show that the ground state for both harmonic trapping and
a ring geometry is a superposition of rotating atomic states in the individual flux tubes.
In the following we consider a control field that is described by a quantum superposition of
coherent states $|\alpha_+\rangle$ and $|\alpha_-\rangle$ (Fig.~\ref{fig4}), whereas the probe field is
described by the single coherent state $|\beta\rangle$ as in the previous section.
More specifically we choose $\alpha_{\pm}$ as real and $\beta$ as complex
where a relative phase is included in $\beta$.
The total field state is then written as
\begin{eqnarray}
|\Psi_f \rangle \propto (|\alpha_+\rangle + e^{i\theta}|\alpha_-\rangle )|\beta\rangle ,
\end{eqnarray}
where $\theta$ is the relative phase between the two coherent state components in the control field.
\subsection{Atom-field states for different coherent states}
Let us first examine the nature of the atom-field state corresponding to each coherent-state component of the quantum superposition separately.
For the respective component associated with either of coherent states $|\alpha_\pm \rangle$,
the total quantum state, including field, and the atomic motional and internal states may be written as
\begin{eqnarray}
|\Phi_{\pm}(\bm{r}) \rangle = \Psi_{\pm}(\bm{r})|D_{\pm}(\phi)\rangle|\alpha_{\pm}\rangle |\beta\rangle,
\end{eqnarray}
where the dark state in each component is respectively given from the discussion in the previous section:
\begin{eqnarray}
|D_{\pm}(\phi)\rangle = \frac{1}{\sqrt{{\cal N}_{\pm}}}
\left(\alpha_{\pm} e^{i\ell \phi}|1\rangle -\beta e^{-i\ell\phi}|2\rangle\right) ,
\end{eqnarray}
with ${\cal N}_{\pm}=\alpha_{\pm}^2+|\beta|^2$ a normalization constant.
We also define the mean spin of each component as
\begin{eqnarray}
\sigma_{\pm}\equiv \frac{\alpha_{\pm}^2-|\beta|^2 }{\alpha_{\pm}^2+|\beta|^2}.
\label{sigmapm}
\end{eqnarray}
Now we describe our scheme more specifically: in particular, we want to choose the amplitudes $\alpha_\pm$ such that the two coherent-state components correspond to flux tubes of opposite sign which requires that the mean spins of the two components are opposite in sign $\sigma_+=-\sigma_-=\sigma$. Using Eq.~(\ref{sigmapm}) we find that the coherent-state amplitudes have to obey either of the following two conditions
\begin{eqnarray}\label{i}
{\rm (i)}\quad |\beta|^2 = \alpha_+ \alpha_-
\end{eqnarray}
or
\begin{eqnarray}\label{ii}
{\rm (ii)}\quad |\beta|^2 = - \alpha_+ \alpha_-.
\end{eqnarray}
When either of these two conditions is satisfied, the two components of the coherent state
correspond to situations in which the trapped particle will experience flux tubes with fluxes
$\Phi_{\rm mf}=\pm 2\pi\hbar|\sigma\ell|$ of equal magnitude but opposite sign.
From the perspective of the fragility of optical coherent-state superpositions
against interactions with their environment, case (i) above is preferable and we hereafter focus our
attention on this case. This follows since the optical coherent-state superpositions decay as
$\exp(-|\alpha_+ -\alpha_-|^2\gamma t/2)$~\cite{MilWal1994}, with $\gamma$ a constant
dependent on the specific dissipation mechanism.
Glancy and Macedo de Vasconcelos~\cite{GlaMac2008} have reviewed methods for producing
optical coherent-state superpositions.
For our present purposes we require a superposition of coherent states
that are macroscopically {\it distinguishable} but not necessarily macroscopically separated,
with the mean photon numbers $|\alpha_\pm|^2$ separated by only a few quanta.
The feasibility of creating such optical coherent state superpositions was already alluded to
in the seminal work of Ref.~\cite{SonCavYur1990}.
\begin{figure}
\includegraphics[scale=0.5]{fig4.eps}
\caption{
Level scheme to generate flux tubes with opposite sign. The control field is a superposition of coherent states $|\alpha_+\rangle$ and $|\alpha_-\rangle$.
}
\label{fig4}
\end{figure}
\subsection{Atom-field state for coherent-state superposition}
We next examine the normalized quantum state for the combined atom-field system
including both components of the coherent state
\begin{eqnarray}\label{swf}
|\Phi (\bm{r},t)\rangle = \frac{|\Phi_+\rangle + e^{i\theta}|\Phi_-\rangle}
{\sqrt{2[1+|\lg \Phi_+|\Phi_- \rangle |\cos(\theta+\psi)]}},
\end{eqnarray}
where $\lg \Phi_+|\Phi_- \rangle \equiv|\lg \Phi_+|\Phi_- \rangle| e^{i\psi} $.
We note that the relative phase between the field coherent-state components
also appears in the atom-field quantum state.
Consistency demands that the normalized state vector (\ref{swf}) obeys the Schr\"odinger equation
\begin{eqnarray}\label{Scheq}
i\hbar \frac{\partial}{\partial t}|\Phi(\bm{r},t)\rangle = \hat{H} |\Phi(\bm{r},t)\rangle,
\end{eqnarray}
where $\hat{H}$ is given by Eq.~(\ref{totalH}).
In choosing the form of the quantum state in Eq.~(\ref{swf}) we have tacitly assumed that it contains only the consistent dark-state components
$|\beta\rangle|\alpha_{\pm}\rangle|D_{\pm}\rangle$ of the Hamiltonian $\hat{h}_a (\bm{r})$ that are immune to decay from the excited state.
This choice of the form of the quantum state is motivated by the common notion that non-dark state components such as
$|\beta\rangle|\alpha_{\mp}\rangle|D_{\pm}\rangle$, for which the field and atomic states are incompatible for a dark state,
will decay due to spontaneous emission from the excited state. For example, one might venture an ansatz for the initial combined atom-field state as
$|\Psi_f\rangle (\Psi_+(\bm{r})|D_+\rangle+\Psi_-(\bm{r})|D_-\rangle)$, but following the decay of the non-dark-state components in this state vector leads to the quantum state
in Eq. (\ref{swf}) to within a normalization constant. In this connection we note that for case (i) above the two coherent states $|\alpha_\pm\rangle$, though not macroscopically separated, are macroscopically distinguishable,
meaning that $|\langle\alpha_-|\alpha_+\rangle| \ll 1$. The macroscopic distinguishability of the two coherent states is required to substantiate the claim of distinct decay properties for the dark and non-dark states above, and the requirement that they not be macroscopically separated is based on wanting to minimize the detrimental effects of decoherence on the field superposition.
Finally, we have assumed that any back action of the single atom back on the field is neglected: This is valid as long as the large amplitude $|\alpha_{\pm}|$ of the coherent state ensures that the mean photon number is much larger than unity. This is our case, because we only demand that $|\alpha_+-\alpha_-|$ be small, but $|\alpha_{\pm}|$ can be arbitrarily large. In such a case, any back action of atoms onto the large amplitude field will be small. We note, however, that the situation is much different in a cavity, where the mean number of photons is significantly restricted.
Our next goal is to derive equations of motion for the atomic motional wave functions $\Psi_\pm$
corresponding to the two coherent-state components.
However, this is complicated by the fact that $|\Phi_\pm\rangle$ need not be orthogonal
which originates from the fact that the coherent states $|\alpha_\pm \rangle$ are not orthogonal.
This means that cross terms between the components must be retained.
In particular, we need the matrix elements of the Hamiltonian
with respect to the dark states $|D_\pm\rangle$, which are given as
\begin{eqnarray}
&&\lg D_{\pm}|H|D_{\pm}\rangle
= \hat{K}-\frac{\hbar^2}{M}\lg D_{\pm} | \nabla D_{\pm} \rangle \nabla, \\
&&\lg D_{\pm}| H |D_{\mp} \rangle = \hat{K} \lg D_{\pm}|D_{\mp} \rangle
-\frac{\hbar^2}{M}\lg D_{\pm}|\nabla D_{\mp} \rangle\nabla, \label{ODH}
\end{eqnarray}
where
\begin{eqnarray}
\hat{K}\equiv \frac{\hbar^2}{2M}\left(-\nabla^2 + \frac{M^2 \Omega^2 r^2}{\hbar^2} + \frac{\ell^2}{r^2}\right)
\end{eqnarray}
for the harmonic potential, and
\begin{eqnarray}
\hat{K} \equiv \frac{\hbar^2}{2I}\left(-\frac{\partial^2}{\partial \phi^2} + \ell^2\right)
\end{eqnarray}
for the ring trap of radius $R$. The cross terms between different dark states are calculated as
\begin{eqnarray}
&&\lg D_{\pm}|D_{\mp}\rangle=\frac{\alpha_+\alpha_-+|\beta|^2}{\sqrt{{\cal N}_+{\cal N}_-}},\\
&&\lg D_{\pm}| \nabla D_{\mp} \rangle = \frac{i \ell (\alpha_+\alpha_--|\beta|^2)}{r\sqrt{{\cal N}_+{\cal N}_-}}.
\end{eqnarray}
The above results will be used to obtain the equations of motion for the wavefunctions $\Psi_\pm$ of the two coherent-state components by substituting the state vector in Eq. (\ref{swf}) into Eq. (\ref{Scheq}), and projecting onto the two (non-orthogonal) components.
In the following we deal with the two conditions set out in Eqs. (\ref{i}) and (\ref{ii}) separately.
\subsubsection{Case $ (i) \ |\beta|^2 = \alpha_+ \alpha_-$}
For this case the cross terms between the dark states reduce to
\begin{eqnarray}
\lg D_{\pm}|D_{\mp}\rangle = \sqrt{1-\sigma^2},\quad\lg D_{\pm}|\nabla D_{\mp} \rangle=0.
\end{eqnarray}
Then projection of the Schr\"odinger equation~(\ref{Scheq}),
multiplying $\lg D_{\pm}| \lg \alpha_{\pm} | \lg \beta|$ from the left,
generates the following set of equations for the wavefunctions $\Psi_{\pm}(\bm{r})$
for the atomic external degree of freedom
\begin{widetext}
\begin{eqnarray}
&&i\hbar \frac{\partial}{\partial t}[\Psi_+ + \epsilon e^{i\theta} \Psi_-]
=\left(\hat{K}-\frac{\hbar^2}{M}\lg D_+|\nabla D_+\rangle\nabla\right)\Psi_++\epsilon e^{i\theta}\hat{K}\Psi_-, \label{eqfora}\\
&&i\hbar \frac{\partial}{\partial t}[\epsilon e^{-i\theta} \Psi_++\Psi_-]
=\epsilon e^{-i\theta}\hat{K}\Psi_+ + \left(\hat{K}-\frac{\hbar^2}{M}\lg D_-|\nabla D_- \rangle \nabla\right)\Psi_- ,\label{eqforb}
\end{eqnarray}
\end{widetext}
where the following real parameter characterizes the non-orthogonality of two components
\begin{eqnarray}\label{paraeps}
\epsilon = \lg \alpha_+|\alpha_- \rangle\sqrt{1-\sigma^2}=e^{-|\alpha_+-\alpha_-|^2}\sqrt{1-\sigma^2}.
\end{eqnarray}
Figure~\ref{fig_eps} shows the dependence of $\epsilon$ on $\sigma$ and $|\alpha_+-\alpha_-|$, and shows that we may control the size of $\epsilon$ by controlling the difference between the coherent-state amplitudes $\alpha_\pm$. In keeping with case (i) reflected in Eq. (\ref{i}), if $\alpha_\pm$ have the same sign and differ in magnitude squared by a few quanta we may control $0\le\epsilon\le 1$ for a given $\sigma$. Typically we want $\epsilon$ small, say $1/10$, but not too small.
\begin{figure}
\includegraphics[scale=0.6]{fig5.eps}
\caption{
Parameter $\epsilon$ as functions of $|\alpha_+-\alpha_-|$ and $\sigma$.
}
\label{fig_eps}
\end{figure}
First we consider the ring geometry as this allows us to illustrate the basic ideas involved with the least complexity. For the ring case the atom is constrained to move on a circle of radius $R$ with position parametrized by the
azimuthal angle $\phi$. The atomic ring radius $R$ is typically a few micrometers, which is smaller than
the typical beam waist $w_0 \sim 100 \ \mu$m of the LG beams.
In order to evaluate the energy of superposition state in unit of $\hbar^2/(2I)$, we use the ansatz for the ground-state wavefunctions
\begin{eqnarray}\label{wf1d}
\Psi_{\pm} (\phi) \propto (\xi_{\pm} e^{i\check{m}\phi} + \zeta_{\pm} e^{-i\check{m}\phi})e^{-iEt/\hbar} ,
\end{eqnarray}
where $\xi_{\pm}, \zeta_{\pm}$ are $c$ numbers. This ansatz is motivated by the fact that in the approximation that the coherent-state components are treated as orthogonal $(\epsilon\rightarrow 0)$, the solutions of Eqs. (\ref{eqfora}) and (\ref{eqforb}) should coincide with those given
in Sec.~\ref{ringCS}. In particular, the solutions $\Psi_+ \propto e^{i\check{m}\phi}$ and $\Psi_- \propto e^{-i\check{m}\phi}$ correspond to
the rotating ground-state eigenfunctions of the Hamiltonian~(\ref{H1D}) for $+\sigma\ell$ and $-\sigma\ell$. Furthermore, the energies of the rotating eigenfunctions $\Psi_{\pm}$ are degenerate,
\begin{eqnarray}
E_0=\frac{\hbar^2}{2I}(\ell^2 + \check{m}^2 + 2 \sigma \ell \check{m}).
\end{eqnarray}
Figure \ref{fig_R} illustrates the degeneracy of the ground states for values $\pm\sigma\ell$ for the case with no cross coupling $\epsilon=0$. However, in the presence of cross coupling the angular momentum states with $\pm\check{m}$ become intermixed, hence the form of the ansatz (\ref{wf1d}). The key question to be addressed is whether cross coupling with $\epsilon\ne 0$ can lower the ground-state energy of the system. If so, then the state vector in Eq. (\ref{swf}), which represents a superposition of the atom trapped simultaneously on the two different flux tubes, will have an energy lower than a simple mixture state of the atom trapped on one or the other of the two flux tubes that has energy $E_0$. Furthermore, the energetically favored ground state will have the form of a quantum superposition of the atom in the counter-rotating angular momentum states $\pm\hbar\check{m}$.
To determine the ground-state energy in the presence of cross coupling, we substitute~(\ref{wf1d}) into Eqs.~(\ref{eqfora}) and (\ref{eqforb}), and
use the orthogonality of the spatial modes $e^{\pm i\check{m}\phi}$ to obtain equations for
$\xi_{\pm}$ and $\zeta_{\pm}$ as
\begin{widetext}
\begin{eqnarray}
&&\frac{\hbar^2}{2I}\left[
\begin{array}{cc}
\ell^2 + \check{m}^2 +2\sigma \ell \check{m}& e^{i\theta}\epsilon (\ell^2+ \check{m}^2)\\
e^{-i\theta}\epsilon (\ell^2 + \check{m}^2) & \ell^2+\check{m}^2-2\sigma \ell \check{m}
\end{array}
\right]
\left[
\begin{array}{c}
\xi_+\\
\xi_-
\end{array}
\right]
=E\bm{A}
\left[
\begin{array}{c}
\xi_+\\
\xi_-
\end{array}
\right], \\
&&\frac{\hbar^2}{2I}\left[
\begin{array}{cc}
\ell^2 + \check{m}^2 -2\sigma \ell \check{m}& e^{i\theta}\epsilon (\ell^2+ \check{m}^2)\\
e^{-i\theta}\epsilon (\ell^2 + \check{m}^2) & \ell^2+\check{m}^2+2\sigma \ell \check{m}
\end{array}
\right]
\left[
\begin{array}{c}
\zeta_+\\
\zeta_-
\end{array}
\right]
=E\bm{A}
\left[
\begin{array}{c}
\zeta_+\\
\zeta_-
\end{array}
\right],
\end{eqnarray}
\end{widetext}
where
\begin{eqnarray}\label{matA}
\bm{A}=\left[
\begin{array}{cc}
1 & \epsilon e^{i\theta}\\
\epsilon e^{-i\theta} & 1
\end{array}
\right].
\end{eqnarray}
These equations have common eigenvalues $E=\{E_+,E_-\}$,
\begin{eqnarray}
\left(\frac{\hbar^2}{2I}\right)^{-1}\!\!\! E_{\pm}=\ell^2+\check{m}^2 \pm \frac{2\sigma \ell \check{m}}{\sqrt{1-\epsilon^2}}.
\end{eqnarray}
Among these two eigenvalues, only $E_+$ is relevant here as it coincides with the degenerate ground-state
energy $E_0$ in the limit $\epsilon \to 0$.
The energy difference associated with the superposition $\delta E \equiv E_+-E_0$ is therefore given by
\begin{eqnarray}
\left(\frac{\hbar^2}{2I}\right)^{-1}\!\!\! \delta E = 2 \sigma \ell \check{m} \left(\frac{1}{\sqrt{1-\epsilon^2}}-1\right),
\end{eqnarray}
which is {\it negative} since sgn$(\sigma \ell \check{m})<0$ for the ground state [see the discussion surrounding Eq.~(\ref{gsam1D})].
The superposition state thus has a lower energy than that of the mixed states of two coherent-state components.
For small $\epsilon$ this reduction in energy is written as
$(\hbar^2/2I)^{-1} \delta E\simeq - |\sigma \ell \check{m}| \epsilon^2$, which scales as $\epsilon^2$.
However, we note that the order of magnitude $[\hbar^2/(2I)]^{-1}\delta E$ can be much larger than $\epsilon^2$ because of the prefactor $|\sigma \ell \check{m}|$. Remembering that the ground-state angular momentum is given by Eq. (\ref{gsam1D}), and that we can adjust so that $\sigma \ell$ is an integer, the prefactor $|\sigma \ell \check{m}|$ is a square of an arbitrary integer. Furthermore, as one can increase the OAM $\ell$~\cite{Zei12} and entangle OAM states in high dimensions~\cite{Dada11}, the energy gap can be as large as $\hbar^2/2I$ even if $\epsilon^2$ is small.
It is preferable to have a larger reduction in energy $|\delta E|$ in terms of robustness.
On the other hand, $|\delta E|$ should not be larger than the lowest excitation energy
$\Delta E$ from the ground state in the absence of superposition;
otherwise the ansatz~(\ref{wf1d}) is no longer valid.
Therefore, from an examination of the eigenvalue structure, we employ an integral value of $\sigma \ell$,
where the energy gap takes maximum value $\Delta E=\hbar^2/(2I)$ .
Figure~\ref{fig_1D_sup} plots the magnitude of the energy gain $|\delta E|$ in the region where $|\delta E| < \Delta E$. The corresponding parameter $\epsilon$ is also plotted.
When $|\delta E|/(\hbar^2/2I)$ is neither too small ($\sim 0$) nor too large ($\sim 1$), e.g., at $|\alpha_+-\alpha_-| \simeq 3$, the superposition is feasible.
The eigenvectors $\{\xi_{\pm}, \zeta_{\pm}\}$, corresponding to the eigenvalue $E_+$, give the admixture of the distinct rotational states with winding numbers $\pm\check{m}$ in the ground-state superposition. These eigenvectors are obtained as
\begin{eqnarray}
&&{}^t[\xi_+,\xi_-] \propto {}^t[-\epsilon e^{i\theta},1-\sqrt{1-\epsilon^2}],\\
&&{}^t[\zeta_+,\zeta_-] \propto {}^t[-\epsilon e^{i\theta},1+\sqrt{1-\epsilon^2}].\label{ieigenvec}
\end{eqnarray}
Thus for $\epsilon \ll 1$ we find
\begin{eqnarray}
\left | {\xi_-\over\xi_+}\right |^2 = \left | {\zeta_+\over\zeta_-}\right |^2 = {\epsilon^2\over 4} \ll 1 ,
\end{eqnarray}
which means that there is little mixing between the rotational states, and we have a superposition of counter-rotating states to a high degree.
Figure~\ref{fig_1D_sup} plots the magnitude of the energy reduction and the real parameter $\epsilon$
only in the region where $|\delta E|$ is smaller than the energy gap represented in Fig.~\ref{fig_H}.
\begin{figure}
\includegraphics[scale=0.48]{fig6.eps}
\caption{
Magnitude of energy reduction as functions of the integer values of $\sigma \ell$ and $|\alpha_+-\alpha_-|$
for $\ell=16$.
}
\label{fig_1D_sup}
\end{figure}
We now repeat the same procedure for the case of harmonic trapping which modifies the details but not the concept of the superposition state.
We employ a similar ansatz for wave functions,
\begin{eqnarray}\label{wf2d}
\Psi_{\pm}(r,\phi) \propto [\xi_{\pm} e^{i\check{m}\phi}+\zeta_{\pm}e^{-i\check{m}\phi} ]R_{\check{m}}(r) e^{-iEt/\hbar},
\end{eqnarray}
where
\begin{eqnarray}
R_{\check{m}}(r)&\equiv& f_{0{\check{m}}}(r)\nonumber\\
&=&\sqrt{\frac{2M\Omega}{\hbar \Gamma(\mu_{\check{m}}+1)}}
\left(\frac{M\Omega r^2}{\hbar}\right)^{\mu_{\check{m}}/2}e^{-(M\Omega/2\hbar)r^2}\nonumber\\
\end{eqnarray}
is the radial eigenfunction of Eq.~(\ref{fnm}) for the ground-state quantum numbers $n=0, m=\check{m}$.
Similar calculation as in the ring-geometry case yields equations for $\xi_{\pm}, \zeta_{\pm}$ for the harmonic-trapping case as
\begin{eqnarray}
&&\hbar \Omega\left[
\begin{array}{cc}
\eta+\sigma \ell \check{m}/\mu_{\check{m}} & e^{i\theta}\epsilon \eta\\
e^{-i\theta} \epsilon \eta & \eta-\sigma \ell \check{m}/\mu_{\check{m}}
\end{array}
\right]
\left[
\begin{array}{c}
\xi_+\\
\xi_-
\end{array}
\right]
=E\bm{A}
\left[
\begin{array}{c}
\xi_+\\
\xi_-
\end{array}
\right], \nonumber\\
&&\hbar\Omega\left[
\begin{array}{cc}
\eta - \sigma \ell \check{m}/\mu_{\check{m}} & e^{i\theta}\epsilon \eta\\
e^{-i\theta}\epsilon \eta & \eta + \sigma \ell \check{m}/\mu_{\check{m}}
\end{array}
\right]
\left[
\begin{array}{c}
\zeta_+\\
\zeta_-
\end{array}
\right]
=E\bm{A}
\left[
\begin{array}{c}
\zeta_+\\
\zeta_-
\end{array}
\right], \nonumber\\
\end{eqnarray}
where $\bm{A}$ is given by Eq.~(\ref{matA}), and
$\eta \equiv \mu_{\check{m}}+1 -\sigma\ell \check{m}/\mu_{\check{m}}$.
The common eigenvalues are
\begin{eqnarray}
\frac{E_{\pm}}{\hbar \Omega}
=\eta
\pm \frac{\sigma \ell \check{m}}{\mu_{\check{m}} \sqrt{1-\epsilon^2}},
\end{eqnarray}
and again $E_+$ is relevant, since in the limit $\epsilon\to 0$ it coincides with
the degenerate ground-state energy in the harmonic-trapping potential
$E_0 = \hbar \Omega (\mu_{\check{m}}+1)$.
The energy difference between the superposition and statistical mixture is
\begin{eqnarray}
\frac{\delta E}{\hbar \Omega} = \frac{\sigma \ell \check{m}}{\mu_{\check{m}}}\left(\frac{1}{\sqrt{1-\epsilon^2}}-1\right),
\end{eqnarray}
which is negative by virtue of the fact that sgn$(\sigma\ell\check{m})<0$, i.e., the superposition has a lower energy than the mixture.
For small $\epsilon$, this reduction in energy is written as
$\delta E /\hbar \Omega \simeq -|\sigma \ell \check{m}| \epsilon^2 / (2\mu_{\check{m}})$, which again scales as $\epsilon^2$ multiplied by the prefactor $\sigma \ell \check{m}/\mu_{\check{m}}$. In the harmonic-trapping case, $\mu_{\check{m}}$, which increases for a larger $\ell$, works to decrease the energy gap $\delta E$. Because of this factor, the ring case is more preferable than the harmonic-trapping case to a have more robust ground state. As the oscillator frequency, we employ $\Omega \simeq 2\pi \times 40$ s$^{-1}$, and the corresponding radius of the atomic cloud would be $20\ \mu$m. With this frequency $\Omega$, we note that the energy unit $\hbar \Omega$ is the same order of magnitude of the previous ring-trap case.
Thus, we have a superposition of counter-rotating states as a ground state in the case of the harmonic trapping, too.
\subsubsection{Case $(ii)\ |\beta|^2 = -\alpha_+ \alpha_-$}
In this case the cross terms of dark states reduce to
\begin{eqnarray}
\lg D_{\pm} | D_{\mp}\rangle = 0, \quad
\lg D_{\pm} | \nabla D_{\mp} \rangle = -\frac{i\ell}{r}\sqrt{1-\sigma^2}.
\end{eqnarray}
Following the same procedure as in case (i), the Schr\"odinger equation is obtained as
\begin{widetext}
\begin{eqnarray}
&&i\hbar \frac{\partial}{\partial t}\Psi_+(\bm{r})
=\left(\hat{K}-\frac{\hbar^2}{M}\lg D_+ | \nabla D_+ \rangle \nabla\right)\Psi_+(\bm{r})
+ \epsilon e^{i\theta} \frac{i \hbar^2 \ell}{Mr}\nabla \Psi_-(\bm{r}), \\
&&i\hbar \frac{\partial}{\partial t}\Psi_-(\bm{r})
=\epsilon e^{-i\theta}\frac{i\hbar^2 \ell}{Mr}\nabla \Psi_+(\bm{r})
+\left(\hat{K}-\frac{\hbar^2}{M}\lg D_- | \nabla D_- \rangle \nabla\right)\Psi_-(\bm{r}),
\end{eqnarray}
\end{widetext}
where $\epsilon$ is defined by Eq.~(\ref{paraeps}).
We again study the cases of ring potential, and harmonic potential, respectively, and
show only the results here without commentary.
With the use of the same ansatz~(\ref{wf1d}),
we obtain the difference in the energy of superposition and that of mixture $\delta E \equiv E_+ - E_0$ as
\begin{eqnarray}
\left(\frac{\hbar^2}{2I}\right)^{-1}\!\!\! \delta E =2\ell \check{m} (\sqrt{\epsilon^2 + \sigma^2}-\sigma),
\end{eqnarray}
where we again employed the solution that coincides with $E_0$ in the limit $\epsilon \to 0$.
For small $\epsilon$, this is expanded as
\begin{eqnarray}
\left(\frac{\hbar^2}{2I}\right)^{-1}\!\!\!\delta E \simeq \frac{\ell \check{m} \epsilon^2}{\sigma},
\end{eqnarray}
which is again negative, meaning that the superposition state is energetically favored.
For the integer values of $\sigma \ell$, the condition $|\delta E| < \Delta E$ turned out to be
identical to the case (i).
Eigenvectors for the ground state $E_+$ are
\begin{eqnarray}
&&{}^t[\xi_+,\xi_-] = {}^t[\epsilon e^{i\theta},\sigma-\sqrt{\epsilon^2 + \sigma^2}],\\
&&{}^t[\zeta_+,\zeta_-] = {}^t[\epsilon e^{i\theta},\sigma+\sqrt{\epsilon^2 + \sigma^2}],\label{iieigenvec}
\end{eqnarray}
and for $\epsilon \ll 1$ we have
\begin{eqnarray}
\left|\frac{\xi_-}{\xi_+}\right|^2 = \left|\frac{\zeta_+}{\zeta_-}\right|^2=\frac{\epsilon^2}{4\sigma^2} \ll 1.
\end{eqnarray}
This result again means that there is little mixing between the rotational states,
and we have a superposition of counter-rotating states to a high degree.
The ansatz~(\ref{wf2d}) leads to the energy difference
\begin{eqnarray}
\frac{\delta E}{\hbar \Omega} = \frac{\ell \check{m}}{\mu_{\check{m}}} (\sqrt{\epsilon^2 + \sigma^2} -\sigma),
\end{eqnarray}
and the corresponding eigenvectors are given by Eq~(\ref{iieigenvec}).
For $\epsilon \ll 1$,
\begin{eqnarray}
\frac{\delta E}{\hbar \Omega} = \frac{\ell \check{m}}{2\sigma \mu_{\check{m}}}\epsilon^2.
\end{eqnarray}
The energy associated with the superposition and the mixing rate of the rotational states are the order of $\epsilon^2$.
\section{Conclusion}\label{conclusion}
In summary, we have introduced the idea of using quantized light fields
for the creation of artificial gauge fields, and shown that it can yield superpositions
in atomic quantum rings. The underlying concept is that by using superpositions of optical coherent states,
one can expose an atom simultaneously to a combination of artificial gauge fields,
or in our specific example, to a combination of flux tubes.
For the atomic quantum ring this was shown to lead to a ground state that was
a superposition of counter-rotating atomic states.
It should be noted that a superposition of counter-rotating atomic states can also be created using synthetic spin-orbit coupling~\cite{lin_2011,jacob_2007,SonFor2009}. The gauge potential stems in this case from classical light fields and is also static, where each component of the resulting atomic pseudo spin can experience opposite constant magnetic fields. Artificial gauge potentials formed using quantum mechanical applied light fields, with the possibility of exposing the atom simultaneously to a superposition of two or more artificial gauge potentials, offers some intriguing concepts. Not only does it provide a route towards mesoscopic superposition states of quantum gases,
but it may also allow for creation of entanglement between light fields and motional degrees of freedom in the quantum gas. In addition it may provide a route to construct a back action between the gauge field and the atomic center-of-mass state by relying on strong coupling between the constituents, and by doing so simulate a dynamical gauge theory. From a quantum simulator point of view this would be important, as it would open up the possibility to emulate field theories known from particle physics and the standard model.
It is certainly tempting to extend these ideas in several ways including inclusion of many-body effects, treatment of more general quantized light fields, using squeezed light field for the pump and for the probe fields, coupling between the light and matter-wave fields in an optical cavity, and the application to more general geometries such as atomic motion in a combination of gauge fields of induced optical lattices.
P.\"O. acknowledges support from the UK EPSRC, and R.K. acknowledges support by Grant-in-Aid for Scientific Research from MEXT (Grant No. 23104712) Japan.
\ \ \\
\ \ \\
| {
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Master the Fourier transform and its applications (updated 11/2021)
MP4 | Video: h264, 1280x720 | Audio: AAC, 44.1 KHz
Language: English | Size: 1.53 GB | Duration: 6h 42m
Learn the Fourier transform in MATLAB and Python, and its applications in digital signal processing and image processing
Learn about one of the single most important equations in all of modern technology and therefore human civilization.
The fundamental concepts underlying the Fourier transform
Sine waves, complex numbers, dot products, sampling theorem, aliasing, and more!
Interpret the results of the Fourier transform
Apply the Fourier transform in MATLAB and Python!
Use the fast Fourier transform in signal processing applications
Improve your MATLAB and/or Python programming skills
Know the limitations of interpreting the Fourier transform.
A curious mind!
Some MATLAB or Python experience is useful but not required
High-school math (calculus is not necessary)
Previous knowledge of the Fourier transform is NOT necessary!
* Manually correct English captions *
The Fourier transform is one of the most important operations in signal processing and modern technology, and therefore in modern human civilization. But how does it work, and why does it work?
What you will learn in this course:
You will learn the theoretical and computational bases of the Fourier transform, with a strong focus on how the Fourier transform is used in modern applications in signal processing, data analysis, and image filtering. The course covers not only the basics, but also advanced topics including effects of non-stationarities, spectral resolution, normalization, filtering. All videos come with MATLAB and Python code for you to learn from and adapt!
This course is focused on implementations of the Fourier transform on computers, and applications in digital signal processing (1D) and image processing (2D). I don't go into detail about setting up and solving integration problems to obtain analytical solutions. Thus, this course is more on the computer science/data science/engineering side of things, rather than on the pure mathematics/differential equations/infinite series side.
This course is for you if you are an aspiring or established:
Computer scientist (MATLAB and/or Python)
Signal processing or image processing expert (or aspiring!)
Biologist
Curious independent learner!
What you get in this course:
>6 hours of video lectures that include explanations, pictures, and diagrams
pdf readers with important notes and explanations
Many exercises and their solutions! (Note: exercises are in the pdf readers)
MATLAB code, Python code, and sample datasets for applications
With >3000 lines of MATLAB and Python code, this course is also a great way to improve your programming skills, particularly in the context of signal processing and image processing.
Why I am qualified to teach this course:
I have been using the Fourier transform extensively in my research and teaching (primarily in MATLAB) for nearly two decades. I have written several textbooks about data analysis, programming, and statistics, that rely extensively on the Fourier transform. Most importantly: I have taught the Fourier transform to bachelor's students, PhD students, professors, and professionals, and I have taught to people from many backgrounds, including biology, psychology, physics, mathematics, and engineering.
So what are you waiting for??
Watch the course introductory video to learn more about the contents of this course and about my teaching style. And scroll down to see what other students think of this course and of my teaching style.
I hope to see you soon in the course!
Students who need to know the Fourier transform for courses.
Scientists who need to know the Fourier transform for research.
Data scientists who need to do spectral analysis.
Someone doing digital signal processing or image processing (filtering, signal separation, etc.)
Someone who learned the FT by solving integral equations but wants more insight into what it means.
Programmers looking for tips about optimizing code that involves FFT.
Someone who is curious what the Fourier transform is and why it's so important.
Someone who uses the FFT but wants a better understanding of what it means, why it works, and how to interpret the results.
Download from RapidGator
https://rapidgator.net/file/3f69132ff073bbcb340fd6e44efa979c/0jf31p21g1iy.part1.rar
https://rapidgator.net/file/9b29741c89576635e65132b1fbe6228f/d10q7b6i77ou.part2.rar
Download from DDownload
https://ddownload.com/s1hdhzh9in4f/3n615p1biij0.part1.rar
https://ddownload.com/bdeklbi8lu6d/cd52xk0jn864.part2.rar
2021-11-18Udemy - Master the Fourier Transform and its Applications (Updated 11.2021)
2021-11-10Master the Fourier transform and its applications (updated 11 2021)
2021-11-24Udemy; Master the Fourier transform and its applications
2019-11-19Master the Fourier transform and its applications
2021-09-28Understand The Fourier Transform And Its Applications
2019-12-09Lectures on the Fourier Transform and Its Applications (Pure and Applied Undergraduate Texts)
2013-04-24 The Fourier Transform and Its Applications (repost) - Removed
2012-04-06 Ronald N. Bracewell, "The Fourier Transform and Its Applications" (repost) - Removed
2011-08-07The Fourier Transform and its Applications – Stanford Video Course
2011-08-07The Fourier Transform and its Applications – Stanford Video Course
2011-08-04The Fourier Transform and its Applications - Stanford Video Course
2010-03-13The Fourier Transform and its Applications
2017-12-17[PDF] Fast Fourier Transform and Its Applications
No comments for "Master the Fourier transform and its applications (updated 11/2021)". | {
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{"url":"https:\/\/socratic.org\/questions\/how-do-you-simplify-4r-0-4","text":"# How do you simplify (4r^0)^4?\n\nJun 15, 2015\n\n=color(blue)(256 ( assuming r != 0)\n\n#### Explanation:\n\n(4r^0)^color(blue)(4\nHere, we need to multiply $\\textcolor{b l u e}{4}$ with the power of each term within the bracket.\n\n=4^color(blue)4 .r^(0. color(blue)(4)\n\n$= 256. {r}^{0}$\n\n$= 256. 1$ ------------- As (any non-zero number)$^ 0 = 1$\n\n=color(blue)(256","date":"2020-01-27 09:07:04","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 9, \"mathjax_inline_tex\": 1, \"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\": 0.7061746120452881, \"perplexity\": 7349.400562194204}, \"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-2020-05\/segments\/1579251696046.73\/warc\/CC-MAIN-20200127081933-20200127111933-00412.warc.gz\"}"} | null | null |
Q: Given a polynomial, prove the set $A$, the pre-image of $\{0\}$, is a closed subset of $\mathbb{R}^2$ I already proved that the set $A$ is non empty but showing there was a root value, which is essentially just the set $A$.
Now I have to prove $A$ is a closed subset of $\mathbb{R}^2$.
I was thinking about the Intermediate Value Theorem. Because the set $A$ consists of the roots of the polynomial, it is a subset of $R$. But I am not sure how to prove it is closed? Am I on the right track here?
A: Polynomials are continuous functions, so in particular, the inverse image of a closed set is closed. We know $D=p^{-1}(\{0\})$, and since $\{0\}$ is a closed set in $\mathbb{R}$, $D$ must be closed in $\mathbb{R}^2$.
A: Polynomials are continuous, as has been noted previously. I assume familarity with the fact: $f$ is continuous implies that $x_n \to x \implies f(x_n) \to f(x)$. We need a small lemma:
Lemma: Let $f$ be continuous and $A$ be closed. Then $f^{-1}(A)$ is also closed.
proof: Since $A$ is closed, it contains all of its limit points. Let $a_n \to a$ be a convergent sequence in $f^{-1}(A)$. We show that $a \in f^{-1}(A)$. Since $a_n \to a$, we know that $f(a_n) \to f(a)$, and $f(a) \in A$. by definition, the result follows.
Now for your problem: note that $\{0\}$ is closed in $\mathbb{R}$ .
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package org.apache.pig.newplan.logical.relational;
import java.util.Map;
import org.apache.pig.data.DataType;
import org.apache.pig.impl.logicalLayer.FrontendException;
import org.apache.pig.newplan.Operator;
import org.apache.pig.newplan.OperatorPlan;
import org.apache.pig.newplan.PlanVisitor;
import org.apache.pig.newplan.logical.expression.LogicalExpressionPlan;
import org.apache.pig.newplan.logical.expression.ProjectExpression;
import org.apache.pig.newplan.logical.relational.LogicalSchema.LogicalFieldSchema;
import org.apache.pig.parser.SourceLocation;
/**
* Operator to map the data into the inner plan of LOForEach
* It can only be used in the inner plan of LOForEach
*
*/
public class LOInnerLoad extends LogicalRelationalOperator {
private ProjectExpression prj;
private LOForEach foreach;
private boolean sourceIsBag = false;
public LOInnerLoad(OperatorPlan plan, LOForEach foreach, int colNum) {
super("LOInnerLoad", plan);
// store column number as a ProjectExpression in a plan
// to be able to dynamically adjust column number during optimization
LogicalExpressionPlan exp = new LogicalExpressionPlan();
// we don't care about type, so set to -1
prj = new ProjectExpression(exp, 0, colNum, foreach);
this.foreach = foreach;
}
public LOInnerLoad(OperatorPlan plan, LOForEach foreach, String colAlias)
throws FrontendException {
super("LOInnerLoad", plan);
// store column number as a ProjectExpression in a plan
// to be able to dynamically adjust column number during optimization
LogicalExpressionPlan exp = new LogicalExpressionPlan();
this.prj = new ProjectExpression( exp, 0, colAlias, null, foreach );
this.foreach = foreach;
}
public LOInnerLoad(LogicalPlan plan, LOForEach foreach,
ProjectExpression projectExpression) {
super("LOInnerLoad", plan);
this.prj = projectExpression;
this.prj.setInputNum(0);
this.prj.setAttachedRelationalOp(foreach);
this.foreach = foreach;
}
@Override
public LogicalSchema getSchema() throws FrontendException {
if (schema!=null)
return schema;
if (prj.findReferent().getSchema()!=null && prj.getFieldSchema()!=null) {
if (prj.getFieldSchema().type==DataType.BAG) {
sourceIsBag = true;
alias = prj.getFieldSchema().alias;
if (prj.getFieldSchema().schema!=null) {
LogicalFieldSchema tupleSchema = prj.getFieldSchema().schema.getField(0);
if (tupleSchema!=null && tupleSchema.schema!=null) {
schema = new LogicalSchema();
for (int i=0;i<tupleSchema.schema.size();i++)
schema.addField(tupleSchema.schema.getField(i));
}
}
}
else {
schema = new LogicalSchema();
schema.addField(prj.getFieldSchema());
}
} else if (!prj.isRangeOrStarProject()) {
schema = new LogicalSchema();
schema.addField(new LogicalFieldSchema(null, null, DataType.BYTEARRAY));
}
return schema;
}
@Override
public void resetSchema(){
super.resetSchema();
prj.resetFieldSchema();
}
public ProjectExpression getProjection() {
return prj;
}
@Override
public boolean isEqual(Operator other) throws FrontendException {
if (!(other instanceof LOInnerLoad)) {
return false;
}
return (getColNum() == ((LOInnerLoad)other).getColNum());
}
@Override
public void accept(PlanVisitor v) throws FrontendException {
if (!(v instanceof LogicalRelationalNodesVisitor)) {
throw new FrontendException("Expected LogicalPlanVisitor", 2223);
}
((LogicalRelationalNodesVisitor)v).visit(this);
}
public int getColNum() {
return prj.getColNum();
}
/**
* Get the LOForEach operator that contains this operator as part of inner plan
* @return the LOForEach operator
*/
public LOForEach getLOForEach() {
return foreach;
}
public boolean sourceIsBag() {
return sourceIsBag;
}
public String toString() {
StringBuilder msg = new StringBuilder();
if (alias!=null) {
msg.append(alias + ": ");
}
msg.append("(Name: " + name);
msg.append("[");
if( getProjection().getColAlias() != null )
msg.append( getProjection().getColAlias() );
else if (getProjection().isProjectStar())
msg.append("*");
else if (getProjection().isRangeProject())
msg.append(getProjection().getStartCol())
.append(" .. ")
.append(getProjection().getEndCol());
else
msg.append(getProjection().getColNum());
msg.append("]");
msg.append(" Schema: ");
if (schema!=null)
msg.append(schema);
else
msg.append("null");
msg.append(")");
if (annotations!=null) {
for (Map.Entry<String, Object> entry : annotations.entrySet()) {
msg.append(entry);
}
}
return msg.toString();
}
@Override
public void setLocation(SourceLocation loc) {
super.setLocation( loc );
prj.setLocation( loc );
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
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methods = {};
methods.unlock = function(callback) {
// Find a class on which the behavior had been set.
var behaviorData = Astro.utils.behaviors.findBehavior(this.constructor, 'lockable');
// set _lock fields to default values (remove lock)
this.set(behaviorData.lockFieldName + '.active', false);
this.set(behaviorData.lockFieldName + '.lockedBy', null);
this.set(behaviorData.lockFieldName + '.lockedAt', null);
// save document (saves also modified fields during lock - no extra doc.save necessary)
this.save(callback);
};
methods.lock = function(callback) {
// Find a class on which the behavior had been set.
var behaviorData = Astro.utils.behaviors.findBehavior(this.constructor, 'lockable');
// set _lock fields (activate lock and add meta information)
this.set(behaviorData.lockFieldName + '.active', true);
this.set(behaviorData.lockFieldName + '.lockedBy', Meteor.userId());
this.set(behaviorData.lockFieldName + '.lockedAt', new Date());
// save document (includes modified lock fields but also other fields)
this.save(callback);
};
methods.isLocked = function() {
// Find a class on which the behavior had been set.
var behaviorData = Astro.utils.behaviors.findBehavior(this.constructor, 'lockable');
return this.get(behaviorData.lockFieldName + '.active');
};
| {
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\section{Introduction}
Mean-variance portfolio selection problem is concerned about the tradeoff between the terminal return and the associated risk of the investment among a number of securities. It was first proposed and solved in the single-period setting by Markowitz \cite{Markowitz1952}. Zhou and Li \cite{Zhou2000} studied a continuous-time mean-variance problem and introduced an appropriate, effective framework in terms of stochastic LQ controls for this problem. In their paper, all the market parameters were assumed to be deterministic. Motivated by the need of more practical models, Lim and Zhou \cite{Lim2002} solved a mean-variance problem with random market parameters in a complete market. Zhou and Yin \cite{Zhou2003} studied the continuous-time mean-variance portfolio selection with regime-switching, they illustrated the influence of market trend change on portfolio selection by virtue of Markov chain. Lim \cite{Lim2004, Lim2005} studied the same problem in an incomplete market or with jumps, respectively. Based on the work of Lim \cite{Lim2004} and Yu \cite{Yu2013}, Lv et al. \cite{Lv2016} studied the mean-variance problem with random horizon in an incomplete market. Meanwhile, they proved that BMO martingales can be used to deal with the stochastic Riccati equations and the auxiliary BSDEs arising from various mean-variance problems. Shen et al. \cite{Shen2020} studied a mean-variance asset-liability management problem under non-Markovian regime-switching models. In their paper, Markov chain is no longer explicitly contained in the market parameters, but the model parameters are predictable with respect to the filtration generated by Markov chain and Brownian motion.
Most of classical financial economics are based on the hypothesis that the investors know with certainty about the eventual time of exit when they make investment decisions. But in practice, when many investors enter the market, they are not sure when they will exit. Therefore, it is of great significance to develop financial theory in random time horizon. Yaari \cite{Yaari1965} studied an optimal consumption problem for an individual with uncertain lifetime at the beginning. Then Hakansson \cite{Hakansson1969,Hakansson1971}, Richard \cite{Richard1975} etc. assumed that the random exit time is independent of all other uncertainties in the market. On the contrary, under the condition that the random exit time is fully dependent on the prices of underlying assets, Karatzas and Wang \cite{Karatzas2000} solved an optimal dynamic investment problem in a complete market. Bouchard and Pham \cite{Bouchard2004} and Blanchet-Scalliet et al. \cite{Blanchet2008} extended these two extreme cases to the situation that the horizon terminal is a general random time. By assuming all market parameters and the conditional distribution function of exit time were deterministic in \cite{Blanchet2008}, the authors obtained the explicit form of optimal portfolio for the constant relative risk aversion (CRRA) utility, which coincides with the outcomes under fixed time horizon. Then Yu \cite{Yu2013} and Lv et al. \cite{Lv2016} studied the mean-variance portfolio selection with random horizon in the complete market and incomplete market respectively. Huang, Wang and Wu \cite{Huang2020} studied a kind of optimal investment problem under inflation and uncertain time horizon. Wang and Wu \cite{Wang2020} studied mean-variance portfolio selection with discontinuous prices and random horizon in an incomplete market.
In this paper, we study a continuous-time mean-variance portfolio selection problem under non-Markovian regime-switching model with a general random time horizon and derive the closed form expressions for efficient portfolios and efficient frontier. In order to be more practical, we assume that all market parameters are predictable and the exit time is random. It is not a stopping time, which means that the exit time depends not only on the price information, but also on other uncertain factors in the market. This random horizon in deterministic case is first introduced by Blanchet-Scalliet et al. \cite{Blanchet2008} and we extend it to the stochastic case with Markov chain. We use a submartingale to characterize the conditional distribution of random time $\tau$ and reconstruct the mean-variance problem according to the Doob-Mayer decomposition theorem and some assumptions.
When we apply the LQ approach to the mean-variance problem, the key difficulty is to prove the global solvability of the so-called stochastic Riccati equation and the auxiliary regime-switching BSDE arising from the problem. When the time horizon is deterministic and the market parameters are random, however the SRE is a fully nonlinear singular BSDE for which the usual assumption (such as the Lipschitz and linear growth conditions) are not satisfied. Fortunately, the SRE has a nice structure. By BMO martingale and Girsanov theorem, Shen et al. \cite{Shen2020} obtained the existence and uniqueness of the solution of the SRE in the case. When the time horizon and the market parameters are both random which is the case concerned in this paper, the corresponding SRE is more complicated. In detail, there is an additional item destroying the nice structure. In this paper, we use a truncation technique to transform the SRE into a one-dimensional BSDE with quadratic grwoth. With the help of BMO martingale technique and comparison theorem and the result of Shen et al. \cite{Shen2020}, we obtain the existence and uniqueness of the stochastic Riccati equation and the auxiliary regime-switching BSDE. Then we get the efficient portfolios in a feedback form as well as the efficient frontier. In fact, the solutions of the two BSDEs completely determine the efficient portfolios and efficient frontier of the underlying mean-variance problem. In addition, we also derive the minimum variance explicitly. Because of the influence of uncertain exit time and Markov chain, the efficient frontier is no longer a perfect square (different from Lim and Zhou \cite{Lim2002}). As a result, the investors are not able to achieve a risk-free investment.
The rest of this paper is organized as follows. In section 2, we construct the non-Markovian regime-switching model with a random time horizon and formulate the corresponding mean-variance problem. In section 3, we investigated the feasibility property of the underlying model. In section 4, we show the global solvability of the stochastic Riccati equation and the auxiliary regime-switching BSDE. In section 5, we derive the solution of the unconstrained optimization problem. In section 6, we present the efficient portfolios and efficient frontier. Finally, we present the conclusion.
\section{Problem Formulation}
Let $\left({\it \Omega}, \mathcal{A}, \mathbb{F}, \mathbf{P} \right)$ be a complete filtered probability space. $W(t) = \left(W_1(t), W_2(t), \cdots, W_n(t) \right)^{\rm T}$ is an $\mathbb{R}^n$ valued standard Brownian motion (with $W(0) = \mathbf{0}$), where the superscript $M^{\rm T}$ denotes the transpose of any vector or matric $M$. And $\alpha(t)$ denotes a continuous-time finite state homogeneous Markov chain on this probability space.
We assume that the Brownian motion $W(\cdot)$ and the Markov chain $\alpha(\cdot)$ are independent. We further assume that $T > 0$ is a fixed time horizon and the filtration $\mathbb{F} = \{\mathcal{F}_{t}: 0 \leq t \leq T \}$ with ${\mathcal{F}}_T \subset \mathcal{A}$ is generated by $W(\cdot)$ and $\alpha(\cdot)$,
\begin{equation*}
\mathcal{F}_t := \sigma\{W(s), \alpha(s): 0 \leq s \leq t\} \vee \mathcal{N}({\mathbf{P}}),\quad\quad \forall t\in[0,T],
\end{equation*}
where $\mathcal{N}(\mathbf{P})$ denotes the collection of all $\mathbf{P}$-null events in this probability space so that $t \mapsto \mathcal{F}_t$ is continuous.
Throughout this paper, the state space of the Markov chain is identified with the canonical state space, that is, a finite set of unit vectors $\mathcal{E}:=\{e_1,e_2,\cdots,e_N\}\subset\mathbb{R}^N$, where the $j$th component of $e_i$ is the Kronecker delta $\delta_{ij}$, for each $i,j=1,2,\cdots, N$. We assume that the Markov chain $\alpha$ has a generator $Q=(q_{ij})_{N\times N}$ and stationary transition probabilities
\begin{equation}\label{transitionp}
p_{ij}(t)=\mathbf{P}(\alpha(t)=e_j | \alpha(0)=e_i), \quad t\geq 0,\ i,j=1,2,\dots,N.
\end{equation}
Since $q_{ij}\geq 0$, for $i\ne j$ and $\sum_{i=1}^N q_{ij}=0$, we have $q_{ii}<0$, for each $i=1,2,\cdots, N$. Based on the canonical representation of the state space, Elliott et al. \cite{Elliott1995} provided the following semimartingale representation of the chain $\alpha$:
\begin{equation*}
\alpha(t)=\alpha(0)+\int_{0}^{t} Q'\alpha(u)\mathrm{d}u +\textbf{M}(t),
\end{equation*}
where $\{\textbf{M}(t)| t\in [0,T] \}$ is an $\mathbb{R}^N$-valued, $(\mathbb{F}, \mathbf{P})$-martingale.
For each $i,j=1,2,\cdots,N$, with $i\ne j$, and $t\in [0,T]$, let $J^{ij}(t)$ be the number of jumps from state $e_i$ to state $e_j$ up to time $t$. Then
\begin{equation*}
\begin{aligned}
J^{ij}(t):=&\sum_{0<s\leq t}\langle\alpha(s-),e_i\rangle\langle\alpha(s),e_j\rangle=\sum_{0<s\leq t}\langle\alpha(s-),e_i\rangle \langle\alpha(s)- \alpha(s-),e_j\rangle\\
=&\int_0^t \langle\alpha(s-),e_i\rangle\langle\mathrm{d}\alpha(s),e_j\rangle=q_{ij}\int_0^t \langle\alpha(s-),e_i\rangle\mathrm{d}s+m_{ij}(t),
\end{aligned}
\end{equation*}
where $m_{ij}(t):=\int_0^t\langle\alpha(s-),e_i\rangle\langle \mathrm{d} \mathbf{M}(s), e_j\rangle$ is $(\mathbb{F},\mathbf{P})$-martingale. $\langle\cdot, \cdot \rangle$ denotes the inner product of the Euclidean space. The $m_{ij}$ are called the basic martingales associated with the chain $\alpha$.
Now, for each fixed $j=1,2,\cdots, N$, let $\Phi_j(t)$ be the number of jumps into state $e_j$ up to time $t$. Then
\begin{equation*}
{\it \Phi}_j(t):=\sum_{i=1,i\ne j}^N J_{ij}(t)=\sum_{i=1,i\ne j}^N q_{ij}\int_0^t\langle \alpha(s),e_i \rangle \mathrm{d}s +{\it \tilde{\Phi}}_j(t),
\end{equation*}
where $\tilde{\it \Phi}_j(t):=\sum_{i=1,i\ne j}^N m_{ij}(t)$ is again an $(\mathbb{F},\mathbf{P})$-martingale for each $j=1,2,\cdots, N$.
For each $j=1,2,\cdots, N$, let denote the compensator of ${\it \Phi}(t)$
\begin{equation*}
\lambda_j(t):=\sum_{i=1,i\ne j}^N q_{ij}\langle \alpha(s),e_i\rangle,
\end{equation*}
such that
\begin{equation*}
\tilde{\it \Phi}_j(t)={\it \Phi}_j(t)-\int_0^t \lambda_j(s) \mathrm{d}s.
\end{equation*}
To simplify our notation, we denote the vector of counting processes $\left\{{\it \Phi}(t)|t\in [0,T]\right\}$, intensity processes $\left\{\lambda(t)|t\in[0,T]\right\}$ and compensated counting processes $\{\tilde{\it \Phi}(t)|t\in [0,T]\}$ by ${\it \Phi}(t):=({\it \Phi}_1(t), {\it \Phi}_2(t), \cdots, {\it \Phi}_N(t))', \lambda(t):=(\lambda_1(t),\lambda_2(t),\dots, \lambda_N(t))'$ and $\tilde{\it \Phi}(t):= (\tilde{\it \Phi}_1(t), \tilde{\it \Phi}_2(t), \cdots,\tilde{\it \Phi}_N(t))'$, respectively, and these three processes are related as
$$\tilde{\it \Phi}(t)={\it \Phi}(t)-\int_0^t\lambda(s)\mathrm{d}s, \quad t\in [0,T].$$
Furthermore, it is worthwhile to point out that the jump of ${\it \Phi}(t)$, at any $t\in [0,T]$, can only take values on the set $\{0_N,e_1,e_2,\dots, e_N\}$, where $0_N$ is an $N$ dimensional vector of zeros. To be more precise, ${\it \Delta \Phi}(t)=e_j$, if there is a transition into state $e_j$ from any one of the other states at time $t$; otherwise, ${\it \Delta\Phi}(t)=0_N$, if there is no transition at all states at time $t$.
Now we introduce some space of stochastic processes and random variables.
\begin{itemize}
\item $L^2_{\mathbb{F}}(0,T;\mathbb{R}^m)$, the set of $\mathbb{R}^m$-valued $\mathbb{F}$-predictable processes $\varphi$ defined on $[0,T]$ such that
$$\mathbb{E}\int_0^T |\varphi(t)|^2 \mathrm{d}t < \infty;$$
\item ${\it\Pi}_{\mathbb{F}}^2(0,T;\mathbb{R}^N)$, the set of $\mathbb{R}^N$-valued $\mathbb{F}$-predictable processes $\varphi$ defined on $[0,T]$ such that
$$\mathbb{E}\int_0^T |\varphi(t)|^2\mathrm{d}{\it\Phi}(t)<\infty;$$
\item $L^{2,loc}_{\mathbb{F}}(0,T;\mathbb{R}^m)$, the set of $\mathbb{R}^m$-valued $\mathbb{F}$-predictable processes $\varphi$ defined on $[0,T]$ such that
$$\int_0^T |\varphi(t)|^2\mathrm{d}t < \infty \qquad \mathbf{P}-a.s.;$$
\item $L^{\infty}_{\mathbb{F}}(0,T;\mathbb{R}^m)$, the set of $\mathbb{F}$-adapted, uniformly bounded processes;
\item $S^2_{\mathbb{F}}(0,T;\mathbb{R}^m)$, the set of $\mathbb{R}^m$-valued $\mathbb{F}$-adapted, continuous processes $\varphi$ defined on $[0,T]$ such that
$$\mathbb{E}\left[\sup_{t\in[0,T]}|\varphi(t)|^2\right] < \infty ;$$
\item $S^{\infty}_{\mathbb{F}}(0,T;\mathbb{R}^m)$, the set of $\mathbb{F}$-adapted, uniformly bounded, continuous processes;
\item $L^{\infty}(\Omega, \mathcal{F}_T, \mathbf{P}; \mathbb{R}^m)$, the set of $\mathbb{R}^m$-valued, $\mathcal{F}_T$-measurable, bounded random variables;
\item ${\rm BMO}_{\mathbf{P}}(0,T;\mathbb{R})$, the space of $\mathbb{R}$-valued, {\rm BMO} martingales on $(\mathbb{F},\mathbf{P})$ equipped with the norm
$$\|\varphi\|_{{\rm BMO_{\mathbf{P}}(0,T;\mathbb{R})}}:=\sup_{\tau\in\mathcal{T}}\left\|\left\{\mathbb{E}\left[ |\varphi(T)-\varphi(\tau{-})|^2|\mathcal{F}_{\tau}\right]\right\}^{\frac{1}{2}}\right\|_{\infty}<\infty,$$
where $\mathcal{T}$ is the set of all $\mathbb{F}$ stopping time on $[0,T]$. Whenever there is no confusion, we abbreviate ${\rm BMO}_{\mathbf{P}}(0,T;\mathbb{R})$ as ${\rm BMO}_{\mathbf{P}}$. More details of BMO martingales can be seen in \cite{Kazamaki2006}.
\item $\mathcal{H}^2_{{\rm BMO}_{\mathbf{P}}}(0,T;\mathbb{R}^n)$, the space of $\mathbb{R}^n$-valued, $\mathbb{F}$-predictable processes $\varphi$ such that $\int_0^{\cdot}\varphi(t)^{\rm T}\mathrm{d}W(t)\\
\in {\rm BMO}_{\mathbf{P}}$, equipped with the norm
$$\|\varphi\|_{\mathcal{H}^2_{{\rm BMO}_{\mathbf{P}}}(0,T;\mathbb{R}^n)}:=\left\|\int_0^{\cdot}\varphi(t)^{\rm T} \mathrm{d}W(t) \right\|_{{\rm BMO}_{\mathbf{P}}}=\sup_{\tau\in\mathcal{T}}\left\|\left\{\mathbb{E}\left[\int_{\tau}^T|\varphi(t)|^2 \mathrm{d}t|\mathcal{F}_{\tau}\right]\right\}^{\frac{1}{2}}\right\|_{\infty}<\infty.$$
\item $\mathcal{J}^2_{{\rm BMO}_{\mathbf{P}}}(0,T;\mathbb{R}^N)$, the space of $\mathbb{R}^N$-valued, $\mathbb{F}$-predictable processes $\varphi$ such that $\int_0^{\cdot}\varphi(t)^{\rm T}\mathrm{d}\tilde{\Phi} (t)\\
\in {\rm BMO}_{\mathbf{P}}$, equipped with the norm
\begin{equation*}
\begin{aligned}
\|\varphi\|_{\mathcal{J}^2_{{\rm BMO}_{\mathbf{P}}}(0,T;\mathbb{R}^N)}:&=\left\|\int_0^{\cdot}\varphi(t)^{\rm T} \mathrm{d}\tilde{\it\Phi}(t) \right\|_{{\rm BMO}_{\mathbf{P}}}\\
&=\sup_{\tau\in\mathcal{T}}\left\|\left\{\mathbb{E}\left[\sum_{j=1}^N\int_{\tau}^T |\varphi(t)|^2 \mathrm{d}{\it\Phi}_j(t)\bigg|\mathcal{F}_{\tau}\right]\right\}^{\frac{1}{2}}\right\|_{\infty}<\infty.
\end{aligned}
\end{equation*}
\end{itemize}
Consider a market with $n+1$ securities, consisting of a bond and $n$ stocks are traded continuously. The bond price $P_0(t)$ satisfies the following equation:
\begin{equation}\label{bondprice}
\begin{cases}
\mathrm{d}P_0(t) = r\left(t\right)P_0(t) \mathrm{d}t, \quad t \in [0,T],\\
P_0(0) = p_0 > 0,
\end{cases}
\end{equation}
where $r(t)$ is given as the interest rate process. The price of each stock $P_1(t), P_2(t), \cdots, P_n(t)$, satisfies the stochastic differential equation:
\begin{equation}\label{stockprice}
\left\{
\begin{aligned}
&\mathrm{d}P_m(t) = P_m(t)\left\{\mu_m\left(t\right)\mathrm{d}t + \sum_{j=1}^n \sigma_{mj}\left(t\right) \mathrm{d}W_j(t)\right\}, \qquad t \in [0,T],\\
&P_m(0)=p_m > 0,
\end{aligned}
\right.
\end{equation}
where $\mu_m(t)$ is the appreciation rate process and $\sigma_m(t) := \big(\sigma_{m1}(t), \sigma_{m2}(t), \cdots, \sigma_{mn}(t)\big)$ is the volatility (or dispersion) rate process of the $m$th stock. Then define the volatility matrix $\sigma(t):=(\sigma_{mj}(t))_{n\times n}$.
\begin{assumption}\label{2.1}
The interest rate process $\{r(t)|t\in[0,T]\}$ is a positive, uniformly bounded, $\mathbb{F}$-predictable process; the appreciation rate processes $\{\mu_m(t)|t\in [0,T]\}$ for $m=1,2,\cdots,n$, are uniformly bounded, $\mathbb{F}$-predictable processes; the volatility processes $\{\sigma_{mj}(t)|t\in [0,T]\}$, for $m=1,2,\cdots,n$ and $j=1,2,\cdots,n$ are nonnegative, uniformly bounded, $\mathbb{F}$-predictable processes, and satisfy the non-degenerate condition, that is, for any $t\in [0,T]$, there exists a positive constant $\delta$ such that $\sigma(t)\sigma(t)^{\rm T} \geq \delta I_{n\times n}$.
\end{assumption}
\begin{remark}
In our model, all market parameters are assumed to be predictable with respect to the filtration generated jointly by Markov chain and Brownian motion. That is, they are completely stochastic rather than explicitly containing Markov chains. So our model is called non-Markovian regime-switching model.
\end{remark}
Consider an agent who invests the amount $\pi_m(t)$ of the wealth $x(t)$ in the $m$th stock ($m=1,2,\dots,n$). If the strategy $\pi(t)=\left( \pi_1(t), \pi_2(t), \cdots, \pi_n(t)\right)^{\rm T}$ is self-financing, the wealth invested in the riskless asset is $x(t) - \sum^n_{m=1} \pi_m(t)$, then the wealth process $x(\cdot)$, with the initial endowment $x_0$, satisfies the following SDE
\begin{equation}\label{wealths}
\left\{
\begin{aligned}
&\mathrm{d}x(t) =\left\{r(t)x(t)+\sum_{m=1}^n \left[\mu_m(t)-r(t)\right]\pi_m(t) \right\}\mathrm{d}t
+ \sum_{m=1}^n\pi_m(t) \sum_{j=1}^n \sigma_{mj}(t)\mathrm{d}W_j(t),\\
&x(0)=x_0>0.
\end{aligned}
\right.
\end{equation}
Setting
\begin{equation}
B(t) := \left(\mu_1(t)-r(t),\mu_2(t)-r(t),\cdots,\mu_n(t)-r(t)\right)^{\rm T},
\end{equation}
we can rewrite the wealth equation \eqref{wealths} as
\begin{equation}\label{wealth}
\left\{
\begin{aligned}
&\mathrm{d}x(t)=\left[r(t)x(t)+B(t)^{\rm T}\pi(t)\right]\mathrm{d}t+\pi(t)^{\rm T}\sigma(t) \mathrm{d}W(t)\\
&x(0)=x_0>0.
\end{aligned}
\right.
\end{equation}
\begin{definition}\label{Def2.3}
$\pi(t)$ is called an admissible portfolio if and only if $\pi(\cdot)\in \mathcal{U}:=L^2_{\mathbb{F}}(0,T;\mathbb{R}^n)$. It is easy to see that, for any admissible $\pi(\cdot)$, the corresponding SDE \eqref{wealth} has a unique solution $x(\cdot)\in S^2_{\mathbb{F}}(0,T;\mathbb{R})$ . In this case, we refer to $(x(\cdot),\pi(\cdot))$ as an admissible pair.
\end{definition}
\begin{remark}
In many literature, a portfolio named $u(\cdot)$ is defined as the proportion of wealth allocated to different stocks, i.e.
\begin{equation}\label{positive control}
u(t)=\frac{\pi(t)}{x(t)},\qquad t\in [0,T].
\end{equation}
\end{remark}
By this definition, the wealth equation \eqref{wealth} can be written as
\begin{equation}
\left\{
\begin{aligned}
&\mathrm{d}x(t)=x(t)\left\{\left[r(t)+B(t)^{\rm T}u(t)\right]\mathrm{d}t+u(t)^{\rm T}\sigma(t)
\mathrm{d}W(t)\right\},\\
&x(0)=x_0.
\end{aligned}
\right.
\end{equation}
It is easy to know that the above equation admits a unique positive solution when the initial endowment $x_0$ is positive from the standard SDE theory. In other words, with the definition of portfolio \eqref{positive control}, the corresponding wealth process must be automatic positive. However, the wealth process with zero or negative values is also sensible at least for some circumstance (see Zhou and Yin \cite{Zhou2003}).
In reality, the investor cannot know when the investment will exit certainly. We assume that the exit time of the investment is $\tau \wedge T$, where $\tau$ is a $\mathcal{A}$-measurable positive random variable. Under our assumption, $\mathcal{A}$ may be strictly bigger than $\mathcal{F}_T$. It means that the exit time relies on not only the uncertainties of prices, but also other uncertain factors in the market.
\begin{remark}
It is easy to see that $\tau$ is not a stopping time under our assumption.
\end{remark}
In this paper, we use the formulation of random time horizon similar to Blanchet-Scalliet et al. \cite{Blanchet2008}. We introduce the conditional distribution function of exit time by $F(t)=\mathbf{P} (\tau \leq t|\mathcal{F}_t)$. It is easy to verify that $F(t)$ is an $\mathbb{F}$-submartingale and the function $t\rightarrow \mathbb{E}[F(t)]$ is right-continuous. Then $F(t)$ has a right-continuous modification. From the Doob-Mayer decomposition theorem, we have $F(t)=A(t)+M(t)$, where $M$ is a martingale and $A$ is an increasing process. Then we give the following assumptions.
\begin{assumption}\label{2.7}
The process $A(\cdot)$ is absolutely continuous with respect to Lebesgue's measure, with a nonnegative bounded density $f(\cdot)$, i.e., $A(t)=\int_0^t f(s) \mathrm{d}s,\ t\in [0,T]$.
\end{assumption}
Under Assumption \ref{2.7}, we immediately get the boundedness of $A$, and then of the martingale $M$. From the martingale representation theorem, there exist processes $Z(\cdot) \in L^2_{\mathbb{F}}(0,T;\mathbb{R}^n)$ and $K(\cdot)\in {\it\Pi}_{\mathbb{F}}^2(0,T;\mathbb{R}^N)$ such that
$$M(t)=\int_0^t Z(s) \mathrm{d}W(s)+\int_0^t K(s) \mathrm{d}\tilde{\it \Phi}(s),\qquad t\in [0,T].$$
Actually, by the boundedness of $M$ and the Burkholder-Davis-Gundy inequality, there exists a constant $c_2$ such that
\begin{equation*}
\begin{aligned}
&\mathbb{E}\left[\int_0^T |Z(t)|^2 \mathrm{d}t\right]+\mathbb{E}\left[\int_0^T |K(t)|^2 \mathrm{d}{\it\Phi}(t)\right]\leq c_2\mathbb{E}\left[\sup_{t\in[0,T]}|M(t)|^2\right]<\infty.\\
\end{aligned}
\end{equation*}
But, we strengthen the above conclusion to the following
\begin{assumption}\label{2.8}
There exists a constant $C$ such that
\begin{equation*}
\int_0^T|Z(t)|^2\mathrm{d}t + \int_0^T|K(t)|^2\mathrm{d}{\it\Phi}(t) \leq C,\qquad \mathbf{P}-a.s..
\end{equation*}
\end{assumption}
\begin{assumption}\label{2.9}
There exists a constant $\varepsilon > 0$ such that $F(T)\leq 1-\varepsilon,\ \mathbf{P}-a.s.$.
\end{assumption}
\begin{remark}
Blanchet-Scalliet et al. \cite{Blanchet2008} assumed that the martingale $M\equiv 0$. Here, we weaken this condition.
\end{remark}
The agent's objective is to find an admissible portfolio $\pi(\cdot)$, among all such admissible portfolios whose expected terminal wealth $\mathbb{E}[x(\tau \wedge T)]=z$, for some given $z\in \mathbb{R}$, so that the risk measured by the variance of the terminal wealth
\begin{equation}
{\rm Var } [x(\tau \wedge T)]:=\mathbb{E}\big\{x(\tau \wedge T)-\mathbb{E}[x(\tau \wedge T)]\big\}^2 = \mathbb{E}[x(\tau\wedge T)-z]^2
\end{equation}
is minimized. Finding such a portfolio $\pi(\cdot)$ is referred to as the mean-variance portfolio selection problem with a random horizon.
From the definition of $F(t)=\mathbf{P}(\tau \leq t|\mathcal{F}_t)$, its decomposition $F(t)=A(t)+M(t)$ and Assumptions \ref{2.7}-\ref{2.9}, we have the following formulation by the same argument of Lemma 2.5 in Yu \cite{Yu2013},
\begin{equation*}
\begin{aligned}
\mathbb{E}[x(\tau \wedge T)] &=\mathbb{E}[\mathbbm{1}_{\{\tau\leq T\}}x(\tau)+\mathbbm{1}_{\{\tau >T\}}x(T)]
=\mathbb{E}\left[\int_0^T x(t) \mathrm{d}F(t)+\int_T^{\infty} x(T)\mathrm{d}F(t)\right]\\
&=\mathbb{E}\left[\int_0^T f(t)x(t)\mathrm{d}t+(1-F(T))x(T)\right].
\end{aligned}
\end{equation*}
Similarly, noting that $z=\mathbb{E}[x(\tau \wedge T)]$, we have
\begin{equation*}
{\rm Var } [x(\tau \wedge T)] = \mathbb{E} \left[\int_0^T f(t)(x(t)-z)^2\mathrm{d}t + (1-F(T))(x(T)-z)^2\right].
\end{equation*}
\begin{definition}\label{Del2.11}
Under Assumptions \ref{2.7}-\ref{2.9}, the mean-variance portfolio selection problem with random time horizon is formulated as a linearly constrained stochastic optimization problem, parameterized by $z \in \mathbb{R}$:
\begin{equation}\label{question}
\left\{
\begin{aligned}
&{\rm minimize}\ J_{MV}(\pi(\cdot)):=\mathbb{E}\left[\int_0^T f(t)(x(t)-z)^2\mathrm{d}t + (1-F(T))(x(T)-z)^2\right],\\
&{\rm subject\ to}\
\left\{
\begin{aligned}
&J_1(\pi(\cdot)):=\mathbb{E}\left[\int_0^T f(t)x(t)\mathrm{d}t+(1-F(T))x(T)\right]=z,\\
&(x(\cdot),\pi(\cdot)) \quad {\rm admissible}.
\end{aligned}
\right.
\end{aligned}
\right.
\end{equation}
\end{definition}
Moreover, an admissible portfolio $\pi(\cdot)\in \mathcal{U}$ is said to be a feasible portfolio for problem \eqref{question} if it satisfies the constraint $J_1(\pi(\cdot))=z$. If there exists a feasible portfolio, then problem \eqref{question} is said to be feasible. Problem \eqref{question} is called finite if it is feasible and the infimum of $J_{MV}(\pi(\cdot))$ over the set of feasible portfolios is finite. If problem \eqref{question} is finite and the infimum of $J_{MV}(\pi(\cdot))$ is achieved by a feasible portfolio $\pi^*(\cdot)$, then problem \eqref{question} is said to be solvable and $\pi^*(\cdot)$ is called an optimal portfolio. Finally, an optimal portfolio to problem \eqref{question} is also called an efficient portfolio corresponding to $z$, and the corresponding pairs $({\rm Var } [x(\tau \wedge T)],z)\in \mathbb{R}^2$ and $(\sigma_{x(\tau\wedge T)},z)\in \mathbb{R}^2$ are interchangeably called an efficient point, where $\sigma_{x(\tau\wedge T)}=\sqrt{{\rm Var } [x(\tau \wedge T)]}$ denotes the standard deviation of $x(\tau \wedge T)$. The set of all efficient points is called the efficient frontier.
\section{Feasibility}
Since the problem \eqref{question} involves a linear constraint $J_1(\pi(\cdot))=z$, in this section, we derive the conditions under which the problem is at least feasible. In fact, we have the following result on the feasibility of problem \eqref{question}.
\begin{proposition}\label{Prop3.1}
Let $\big(\psi(\cdot),\xi(\cdot),\hat{\xi}(\cdot)\big)\in S_{\mathbb{F}}^2(0,T;\mathbb{R})\times L_{\mathbb{F}}^2(0,T;\mathbb{R}^n)\times {\it\Pi}_{\mathbb{F}}^2(0,T;\mathbb{R}^N)$ be the solution of the following regime-switching BSDE:
\begin{equation}\label{feasible}
\left\{
\begin{aligned}
&-\mathrm{d}\psi(t)=\left[\psi(t)r(t)+f(t)\right]\mathrm{d}t-\xi(t)^{\rm T}\mathrm{d}W(t)- \hat{\xi}(t)^{\rm T}\mathrm{d}\tilde{\it\Phi}(t)\\
&\psi(T)=1-F(T).
\end{aligned}
\right.
\end{equation}
Then the mean-variance problem \eqref{question} is feasible for every $z\in\mathbb{R}$ if and only if
\begin{equation}\label{ftiao}
\gamma:=E\int_0^T |\psi(t)B(t)+\xi(t)^{\rm T}\sigma(t)|^2 \mathrm{d}t > 0.
\end{equation}
\end{proposition}
\proof
First, it is easy to see that the linear BSDE \eqref{feasible} admits a unique solution
In order to prove the sufficiency, we construct a family of admissible portfolios $\pi^{(\beta)}(\cdot)=\beta\pi(\cdot)$ for all $\beta \in \mathbb{R}$, where
\begin{equation}\label{pi}
\pi(t)= \psi(t)B(t)+\xi(t)^{\rm T}\sigma(t).
\end{equation}
Let $x^{(\beta)}(\cdot)$ be the wealth process corresponding to $\pi^{(\beta)}(\cdot)$ for any $\beta$. By linearity of the wealth equation \eqref{wealth}, it follows that $x^{(\beta)}(t)=x^{(0)}(t)+\beta y(t)$, where $x^{(0)}(\cdot)$ satisfies
\begin{equation}
\begin{cases}
\mathrm{d}x^{(0)}(t)=r(t)x^{(0)}(t)\mathrm{d}t, \quad t\in[0,T],\\
x^{(0)}(0)=x_0,
\end{cases}
\end{equation}
and $y(\cdot)$ satisfies
\begin{equation}\label{yy}
\begin{cases}
\mathrm{d}y(t)=\left[r(t)y(t)+B(t)^{\rm T}\pi(t)\right]\mathrm{d}t+\pi(t)^{\rm T}\sigma(t) \mathrm{d}W(t), \quad t\in [0,T],\\
y(0)=0,
\end{cases}
\end{equation}
respectively. The problem \eqref{question} is feasible for any $z\in \mathbb{R}$ if there exists a $\beta \in \mathbb{R}$ such that
\begin{equation*}
\begin{aligned}
z=J_1(\pi^{(\beta)}(\cdot)) &= \mathbb{E}\left[ \int_0^T f(t)x^{(0)}(t)\mathrm{d}t + (1-F(T))x^{(0)}(T) \right]\\
&\quad\quad+\beta \mathbb{E}\left[\int_0^T f(t)y(t)\mathrm{d}t+(1-F(T))y(T) \right].
\end{aligned}
\end{equation*}
In other words, problem \eqref{question} is feasible for any $z\in \mathbb{R}$ if
\begin{equation*}
\mathbb{E}\left[\int_0^Tf(t)y(t)\mathrm{d}t + (1-F(T))y(T) \right]\neq 0.
\end{equation*}
However, applying It\^o's formula to $\psi(t)y(t)$ on the interval $[0,T]$. Integrating from $0$ to $T$ and taking expectation, we have
\begin{equation}\label{psiy}
\begin{aligned}
\mathbb{E}\left[\int_0^T f(t)y(t)\mathrm{d}t+(1-F(T))y(T)\right]
&=\mathbb{E}\left\{\int_0^T \Big[\psi(t)B(t)+\xi(t)^{\rm T}\sigma(t)\Big]^{\rm T} \pi(t) \mathrm{d}t \right\}\\
&=\mathbb{E}\left\{\int_0^T \Big[\psi(t)B(t)+\xi(t)^{\rm T}\sigma(t) \Big]^2 \mathrm{d}t \right\}.
\end{aligned}
\end{equation}
Consequently, $\mathbb{E}y(T)\neq 0$ if \eqref{ftiao} holds.
Conversely, if problem \eqref{question} is feasible for any $z\in \mathbb{R}$, then there exists an admissible portfolio $\pi(\cdot)$ such that
\begin{equation*}
\mathbb{E}\left[\int_0^T f(t)x(t)\mathrm{d}t + (1-F(T))x(T)\right]=z.
\end{equation*}
We can decompose $x(t)=x^{(0)}(t)+y(t)$, where $y(\cdot)$ satisfies \eqref{yy}. This leads to
\begin{equation*}
\mathbb{E}\left[\int_0^Tf(t)x^{(0)}(t)\mathrm{d}t+(1-F(T))x^{(0)}(T)\right] + \mathbb{E}\left[\int_0^Tf(t)y(t)\mathrm{d}t+(1-F(T))y(T)\right]=z.
\end{equation*}
However $x^{(0)}(\cdot)$, which can be interpreted as the wealth process corresponding to the agent putting all the money in the bond, is independent of $\pi(\cdot)$, thus it is necessary that there exists a $\pi(\cdot)$ such that
\begin{equation*}
\mathbb{E}\left[\int_0^T f(t)y(t)\mathrm{d}t + (1-F(T))y(T)\right]\neq 0.
\end{equation*}
From \eqref{psiy},
\begin{equation*}
\mathbb{E}\left\{\int_0^T \Big[\psi(t)B(t)+\xi(t)^{\rm T}\sigma(t) \Big]^{\rm T}\pi(t)\mathrm{d}t\right\}\neq 0.
\end{equation*}
This implies \eqref{ftiao}. \hfill\rule{1mm}{3mm}
\begin{corollary}\label{Cor3.2}
Let
\begin{equation*}
z^{(0)}=\mathbb{E}\left[\int_0^T f(t)x^{(0)}(t)\mathrm{d}t + (1-F(T))x^{(0)}(T)\right],
\end{equation*}
\begin{equation*}
\gamma=E\int_0^T |\psi(t)B(t)+\xi(t)^{\rm T}\sigma(t)|^2 \mathrm{d}t.
\end{equation*}
We have:\\
{\rm (i)} if \eqref{ftiao} holds, then for any $z\in \mathbb{R}$, a feasible portfolio satisfying $J_1(\tilde{\pi}(\cdot))=z$ is given by
\begin{equation*}
\tilde{\pi}(\cdot)=\frac{z-z^{(0)}}{\gamma}\left(\psi(t)B(t)+\xi(t)^{\rm T}\sigma(t)\right);
\end{equation*}
{\rm (ii)} if \eqref{ftiao} doesn't hold, then for any admissible portfolio $\pi(\cdot)$, we have $J_1(\pi(\cdot))=z^{(0)}$.
\end{corollary}
\proof
(i) is immediately from the proof of the ``sufficient" part of Proposition \ref{Prop3.1}, and (ii) is from the proof of the ``necessary" part of Proposition \ref{Prop3.1}. \hfill\rule{1mm}{3mm}
\begin{remark}
The condition \eqref{ftiao} is very mild. On the one hand, since \eqref{feasible} is a linear BSDE, its unique solution $\psi$ has following representation:
\begin{equation*}
\begin{aligned}
\psi(t)=\mathbb{E}\left[(1-F(T)){\rm e}^{\int_t^T r(s)\mathrm{d}s }
+ \int_t^T f(s){\rm e}^{\int_t^s r(v)\mathrm{d}v }\mathrm{d}s |\mathcal{F}_t\right]
\end{aligned}
\end{equation*}
(see Theorem 3.3 in Zhou and Yin \cite{Zhou2003} and Proposition 4.1 in Lim and Zhou \cite{Lim2002}).
From Assumptions \ref{2.7}-\ref{2.9}, we know that $(1-F(T))\geq \varepsilon > 0$ and $f(s) \geq 0, s\in [0,T]$, and then $\psi(t) > 0$ for any $t\in[0,T]$. So \eqref{ftiao} is easily satisfied as long as there is one stock whose appreciation rate process is different from the interest rate process at any market mode, which is obviously a practically reasonable assumption. On the other hand, if \eqref{ftiao} fails, then Corollary \ref{Cor3.2}-(ii) implies that the mean-variance problem \eqref{question} is feasible only if $z=z^{(0)}$. This is a pathological and trivial case that does not warrant further consideration. So from this point, we shall assume that \eqref{ftiao} holds.
\end{remark}
After considering the feasibility, we proceed to study the issue of optimality. The mean variance problem with random horizon \eqref{question} is a dynamic optimization problem with a constraint $J_1(\pi(\cdot))=z$. In order to deal with the constraint, we employ the Lagrange multiplier technique. For any $\lambda\in \mathbb{R}$, define
\begin{equation}
\begin{aligned}
J(\pi(\cdot),\lambda)
:&=J_{MV}(\pi(\cdot))+2\lambda\left(J_1(\pi(\cdot))-z\right)\\
&=\mathbb{E}\left\{\int_0^Tf(t)\left[x(t)+(\lambda-z)\right]^2\mathrm{d}t + (1-F(T)) \left[x(T)+(\lambda-z)\right]^2\right\}-\lambda^2.
\end{aligned}
\end{equation}
Our first goal is to solve the following unconstrained problem parameterized by the Lagrange multiplier $\lambda$:
\begin{equation}\label{unquestion}
\begin{cases}
{\rm minimize} \ J(\pi(\cdot),\lambda)\\
{\rm subject \ to} \ (x(\cdot),\pi(\cdot)) \ {\rm admissible}.
\end{cases}
\end{equation}
This is a stochastic LQ optimal control problem, which will be solved in the next two sections.
\section{Related Stochastic Riccati Equation}
When we study the unconstrained stochastic LQ problem \eqref{unquestion}, an equation known in the literature as the stochastic Riccati equation (SRE) will arise naturally. The existence and uniqueness of SRE play a fundamental role in the solution of the stochastic LQ problem \eqref{unquestion}. In this section, we study the solvability of the SRE and the auxiliary regime-switching BSDE.
We introduce the following regime-switching BSDEs:
\begin{equation}\label{SRE}
\left\{
\begin{aligned}
&-\mathrm{d}p(t)=\Bigg[2f(t)+\left(2r(t)-\theta(t)\theta(t)^{\rm T}\right) p(t)-2\theta(t) {\it\Lambda}(t)- \frac{{\it\Lambda}(t)^{\rm T}{\it\Lambda}(t)}{p(t)} \Bigg] \mathrm{d}t \\
&\qquad \qquad \quad- {\it\Lambda}(t)^{\rm T}\mathrm{d}W(t)-\hat{\it \Lambda}(t)^{\rm T}\mathrm{d}\tilde{\it \Phi}(t),\qquad t\in[0,T],\\
&p(T)=2\big(1-F(T)\big),\\
&p(t)> 0, \quad t\in[0,T].
\end{aligned}
\right.
\end{equation}
\begin{equation}\label{nonhom}
\left\{
\begin{aligned}
&\mathrm{d}g(t)=\Bigg[\left(r(t)+\frac{2f(t)}{p(t)}\right)g(t)+\theta(t)\eta(t)-\frac{2f(t)}{p(t)} -\frac{\hat{\it\Lambda}(t)^{\rm T}\hat{\eta}(t)}{p(t)}\lambda(t) \Bigg]\mathrm{d}t\\
&\qquad \qquad+\eta(t)^{\rm T}\mathrm{d}W(t)+\hat{\eta}(t)^{\rm T}\mathrm{d}\tilde{\it\Phi}(t),\quad t\in[0,T],\\
&g(T)=1,
\end{aligned}
\right.
\end{equation}
where $\theta(t)=B(t)^{\rm T}\sigma(t)^{-1}$
The regime-switching BSDE \eqref{SRE} is a special case of the SRE associated with the general stochastic LQ optimal control problems. And the auxiliary regime-switching BSDE \eqref{nonhom} will be used to handle the nonhomogeneous terms involved in the problem \eqref{unquestion}.
Now we introduce a subset of $\hat{S}_{\mathbb{F}}^{\infty}(0,T;\mathbb{R})$ as follows:
\begin{equation*}
\begin{aligned}
\hat{S}_{\mathbb{F}}^{\infty}(0,T;\mathbb{R}):=\big\{\varphi(\cdot)\in S_{\mathbb{F}}^{\infty}(0,T;\mathbb{R}) \ | \ {\rm there\ exist\ two\ real\ numbers}\ 0<b<B<\infty, \\
{\rm such\ that}\ b\leq \varphi(t) \leq B\ {\rm for\ all}\ t\in [0,T] \big\}.
\end{aligned}
\end{equation*}
The general SRE is a highly nonlinear, matrix-valued BSDE, and there are many results on its solvability, for example, Bismut \cite{Bismut1976}, Peng \cite{Peng1992}, Tang \cite{Tang2003}, Lim and Zhou \cite{Lim2002}, Yu \cite{Yu2013}, Shen et al. \cite{Shen2020} and the references therein. With the help of regime-switching BSDE of quadratic-exponential growth introduced by Shen et al. \cite{Shen2020}, we shall prove the existence and uniqueness of solution of SRE \eqref{SRE}.
Let us begin with another simpler regime-switching stochastic Riccati equation introduced by Shen et al. \cite{Shen2020} as follows:
\begin{equation}\label{fSRE}
\left\{
\begin{aligned}
&-\mathrm{d}\bar{p}(t)=\left[\left(2r(t)-\theta(t)\theta(t)^{\rm T}\right)\bar{p}(t)-2\theta(t)\bar{\it \Lambda}(t) -\frac{\bar{\it \Lambda}(t)^{\rm T}\bar{\it \Lambda}(t)}{\bar{p}(t)}\right]\mathrm{d}t\\
&\qquad\qquad\quad -\bar{\it \Lambda}(t)^{\rm T}\mathrm{d}W(t) -\bar{\hat{\it \Lambda}}(t)^{\rm T}\mathrm{d}\tilde{\it \Phi}(t),\quad t\in [0,T],\\
&\bar{p}(T)=2(1-F(T)),\\
&\bar{p}(t)\geq 0,\quad t\in [0,T].
\end{aligned}
\right.
\end{equation}
\begin{lemma}[Shen et al. \cite{Shen2020}, Lemma 4.1]\label{4.1}
The SRE \eqref{fSRE} admits a unique solution $\big(\bar{p}(\cdot),\bar{\it\Lambda}(\cdot),\\ \bar{\hat{\it\Lambda}} (\cdot)\big) \in \hat{S}_{\mathbb{F}}^ {\infty}(0,T;\mathbb{R})\times \mathcal{H}^2_{{\rm BMO}_{\mathbf{P}}}
(0,T;\mathbb{R}^n)\times \mathcal{J}^2_{{\rm BMO}_{\mathbf{P}}}(0,T;\mathbb{R}^N)$, satisfying {\rm (i)} $\frac{\bar{\it\Lambda}(\cdot)}{\bar{p}(\cdot)}\in \mathcal{H}^2_{{\rm BMO}_{\mathbf{P}}}(0,T;\mathbb{R}^n), \ \\ \frac{\bar{\hat{\it\Lambda}}(\cdot)}{\bar{p}(\cdot)}\in \mathcal{J}^2_{{\rm BMO}_{\mathbf{P}}} (0,T;\mathbb{R}^N)$; {\rm (ii)} $\frac{\bar{\hat{\eta}}_k(\cdot)}{\bar{p}(\cdot)}\geq -1+\epsilon, \mathrm{d}t \otimes \mathrm{d}\mathbf{P} - a.e.$, for some $\epsilon >0$ and each $k=1,2,\cdots,N.$
\end{lemma}
\begin{theorem}\label{Thm4.2}
Suppose the Assumptions \ref{2.7}-\ref{2.9} hold. Then there exists a unique solution $(p(\cdot), {\it\Lambda}(\cdot), \hat{\it\Lambda}(\cdot)) \in \hat{S}_{\mathbb{F}}^ {\infty}(0,T;\mathbb{R})\times \mathcal{H}^2_{{\rm BMO}_{\mathbf{P}}} (0,T;\mathbb{R}^n)\times \mathcal{J}^2_{{\rm BMO}_{\mathbf{P}}} (0,T;\mathbb{R}^N)$ for the stochastic Riccati equation \eqref{SRE}, satisfying {\rm (i)} $\frac{{\it\Lambda}(\cdot)}{{p}(\cdot)}\in \mathcal{H}^2_{{\rm BMO}_{\mathbf{P}}}(0,T;\mathbb{R}^n), \ \frac{{\hat{\it\Lambda}}(\cdot)}{{p}(\cdot)}\in \mathcal{J}^2_{{\rm BMO}_{\mathbf{P}}} (0,T;\mathbb{R}^N)$; {\rm (ii)} $\frac{{\hat{\eta}}_k(\cdot)}{{p}(\cdot)}\geq -1+\epsilon, \mathrm{d}t \otimes \mathrm{d}\mathbf{P} - a.e.$, for some $\epsilon >0$ and each $k=1,2,\cdots,N.$
\end{theorem}
\proof
From Lemma \ref{4.1}, the SRE \eqref{fSRE} admits a unique solution $(\bar{p}(\cdot),\bar{\it\Lambda}(\cdot), \bar{\hat{\it\Lambda}}(\cdot))\in \hat{S}_{\mathbb{F}}^ {\infty}(0,T;\mathbb{R})\\ \times \mathcal{H}^2_{{\rm BMO}_{\mathbf{P}}} (0,T;\mathbb{R}^n)\times \mathcal{J}^2_{{\rm BMO}_{\mathbf{P}}}(0,T;\mathbb{R}^N)$. Without loss of generality, we assume that $b\leq \bar{p}(t) \leq B$ for any $t\in [0,T]$ with two constants $0<b<B<\infty$. We consider the following BSDEs:
\begin{equation}\label{ffSRE}
\left\{
\begin{aligned}
&-\mathrm{d}\bar{p}(t)=\left[\left(2r(t)-\theta(t)\theta(t)^{\rm T}\right)\bar{p}(t)-2\theta(t)\bar{\it\Lambda}(t) -\frac{\bar{\it\Lambda}(t)^{\rm T}\bar{\it\Lambda}(t)}{\bar{p}(t)\vee b}\right]\mathrm{d}t\\
&\qquad\qquad\quad -\bar{\it\Lambda}(t)^{\rm T}\mathrm{d}W(t) -\bar{\hat{\it\Lambda}}(t)^{\rm T}\mathrm{d}\tilde{\it\Phi}(t),\quad t\in [0,T],\\
&\bar{p}(T)=2(1-F(T)),\\
&\bar{p}(t)\geq 0,\quad t\in [0,T],
\end{aligned}
\right.
\end{equation}
and
\begin{equation}\label{fffSRE}
\left\{
\begin{aligned}
&-\mathrm{d}{p}(t)=\left[2f(t)+\left(2r(t)-\theta(t)\theta(t)^{\rm T}\right){p}(t)-2\theta(t){\it\Lambda}(t) -\frac{{\it\Lambda}(t)^{\rm T}{\it\Lambda}(t)}{{p}(t)\vee b}\right]\mathrm{d}t\\
&\qquad\qquad\quad -{\it\Lambda}(t)^{\rm T}\mathrm{d}W(t) -{\hat{\it\Lambda}}(t)^{\rm T}\mathrm{d}\tilde{\it\Phi}(t),\quad t\in [0,T],\\
&{p}(T)=2(1-F(T)),\\
&{p}(t)> 0,\quad t\in [0,T].
\end{aligned}
\right.
\end{equation}
Obviously, the unique solution $(\bar{p}(\cdot),\bar{\it\Lambda}(\cdot),\bar{\hat{\it\Lambda}}(\cdot))$ of SRE \eqref{fSRE} also hold for BSDE \eqref{ffSRE}. Since $f(\cdot)$, $r(\cdot)$, and $\theta(\cdot)$ are bounded and nonnegative, the driver $h(t,p,{\it\Lambda},\hat{\it\Lambda})=2f(t)+(2r(t)-\theta(t)
\theta(t)^{\rm T})p-2\theta(t){\it\Lambda}-\frac{{\it\Lambda}^{\rm T}{\it\Lambda}}{p\vee b}$ of BSDE \eqref{fffSRE} satisfies
\begin{equation*}
|h(t,p,{\it\Lambda},\hat{\it\Lambda})| \leq C(1+|p|+|{\it\Lambda}|^2),
\end{equation*}
where $C$ is a constant. Therefore, from Lemma A.1 in Shen et al. \cite{Shen2020}, there exists a unique bounded solution $(p^{(b)}(\cdot),{\it\Lambda}^{(b)}(\cdot),\hat{\it\Lambda}^{(b)}(\cdot)) \in {S}_{\mathbb{F}}^ {\infty}(0,T;\mathbb{R})\times \mathcal{H}^2_{{\rm BMO}_{\mathbf{P}}} (0,T;\mathbb{R}^n)\times \mathcal{J}^2_{{\rm BMO}_{\mathbf{P}}}(0,T;\mathbb{R}^N)$ for BSDE \eqref{fffSRE}. Next we apply the comparison theorem and from
\begin{equation*}
h(t,p,{\it\Lambda},\hat{\it\Lambda}) \geq (2r(t)-\theta(t)\theta(t)^{\rm T})p-2\theta(t){\it\Lambda}-\frac{{\it\Lambda}^{\rm T}{\it \Lambda}} {p\vee b},
\end{equation*}
we deduce that $p^{(b)}(t)\geq \bar{p}(t)\geq b$. Hence $(p^{(b)}(\cdot),{\it\Lambda}^{(b)}(\cdot),\hat{\it\Lambda}^{(b)}(\cdot)) \in \hat{S}_{\mathbb{F}}^ {\infty}(0,T;\mathbb{R})\times \mathcal{H}^2_{{\rm BMO}_{\mathbf{P}}} (0,T;\mathbb{R}^n)\\
\times \mathcal{J}^2_{{\rm BMO}_{\mathbf{P}}}(0,T;\mathbb{R}^N)$ is the unique solution of SRE \eqref{SRE}.
The proof of the solution's properties are similar to the proof in Appendix of Shen et al. \cite{Shen2020}, so we omit it. \hfill\rule{1mm}{3mm}
Then we show that the existence and uniqueness of solution of \eqref{nonhom}.
\begin{theorem}
Suppose the Assumptions \ref{2.7}-\ref{2.9} hold. Then there exists a unique solution $\big(g(\cdot),
\eta(\cdot),\hat{\eta}(\cdot)\big)\in S_{\mathbb{F}}^{2}(0,T;\mathbb{R})\times L_{\mathbb{F}}^2(0,T;\mathbb{R}^n)\times {\it\Pi}^2_{\mathbb{F}}(0,T;\mathbb{R}^N)$ for the BSDE \eqref{nonhom}. Moreover, we have $0<g(t)\leq 1$ for any $t\in [0,T]$ and if $r(t)>0,\ a.e.\ t\in [0,T]$, then $0<g(t)<1$ for all $t\in [0,T)$.
\end{theorem}
\proof
Since all the market parameters are bounded, the stochastic integral $-\int_0^t\theta(s)\mathrm{d}W (s)$ is a $\text{BMO}_{\textbf{P}}$ martingale. Then we define a probability measure $\mathbf{Q}_1$ equivalent to $\mathbf{P}$ as \begin{equation}\label{Q1}
\left.\frac{\mathrm{d}\mathbf{Q}_1}{\mathrm{d}\mathbf{P}}\right|_{\mathcal{F}_T}=\Theta_1:=\mathcal{E}\left(-\int_0^T \theta(s)\mathrm{d}W(s)\right).
\end{equation}
where the stochastic exponential $\mathcal{E}(M)$ is given by $\mathcal{E}(M)={\rm e}^{(M-\frac{1}{2}\langle M \rangle)}$. Under $\mathbf{Q}_1$, by Girsanov's theorem, the process
\begin{equation}
W^{\mathbf{Q}_1}(t):=W(t)+\int_0^t \theta(s)\mathrm{d}s
\end{equation}
is a $n$-dimensional standard Brownian motion, and $\tilde{\it\Phi}^{\mathbf{Q}_1}(t):=\tilde{\it\Phi}(t)$ has the same probability law as under $\mathbf{P}$ which is still an $\mathbb{R}^N$-valued jump martingale associated with the chain.
Since $\frac{\hat{\it\Lambda}}{p}\in \mathcal{J}^2_{{\rm BMO}_{\mathbf{P}}}(0,T;\mathbb{R}^N)$ and the probability measure $\mathbf{Q}_1$ is constructed as \eqref{Q1}, it can be shown as Theorem 3.3 in \cite{Kazamaki2006} that $\frac{\hat{\it\Lambda}}{p}\in \mathcal{J}^2_{{\rm BMO}_{\mathbf{Q}_1}} (0,T;\mathbb{R}^N)$. By the equivalence of $\mathbf{Q}_1$ and $\mathbf{P}$, we have that $\frac{{\hat{\eta}}_k(\cdot)}{{p}(\cdot)}\geq -1+\epsilon,\ \mathrm{d}t \otimes \mathrm{d}\mathbf{Q}_1-a.e.$. Hence, the techniques of \cite{Kazamaki2006} and the jump sizes ${\it\Delta \Phi}(t)$ can be used to show that $\mathcal{E}\left(\int_0^t \frac{\hat{\it\Lambda}(s)^{\rm T}}{p(s)}\mathrm{d}\tilde{\it\Phi} ^{\mathbf{Q}_1}(s)\right)$ is a uniformly integrable $(\mathbb{F}, \mathbf{Q}_1)$-martingale. Therefore, we can define a probability measure $\mathbf{Q}_2$ equivalent to $\mathbf{Q}_1$ as
\begin{equation}
\left.\frac{\mathrm{d}\mathbf{Q}_2}{\mathrm{d}\mathbf{Q}_1}\right|_{\mathcal{F}_T}=\Theta_2:=\mathcal{E}\left(\int_0^T \frac{\hat{\it\Lambda}(s)^{\rm T}}{p(s)}\mathrm{d}\tilde{\it\Phi}^{\mathbf{Q}_1}(s)\right).
\end{equation}
Under $\mathbf{Q}_2$, the $\mathbf{Q}_1$-Brownian motion $W^{\mathbf{Q}_1}$ is still a $n$-dimensional standard Brownian motion, which is denoted by $W^{\mathbf{Q}_2}(t):=W^{\mathbf{Q}_1}(t)$. And the process $\tilde{\it\Phi}^{\mathbf{Q}_2}(t):=\tilde{\it\Phi}^{\mathbf{Q}_1}(t)-\int_0^t\frac{\hat{\it\Lambda}(s)}{p(s)}\lambda(s) \mathrm{d}s$ is an $\mathbb{R}^{N}$-valued martingale associated with the chain $\alpha$. So the $\mathbf{Q}_2$-intensity of ${\it\Phi}$ is given by an $\mathbb{R}^N$-valued process:
\begin{equation}
\lambda^{\mathbf{Q}_2}(t):=\left[\lambda_1(t)\left(1+\frac{\hat{\it\Lambda}_{1}(t)}{p(t)}\right), \lambda_2(t)\left(1+\frac{\hat{\it\Lambda}_{2}(t)}{p(t)}\right),\dots, \lambda_N(t)\left(1+\frac{\hat{\it\Lambda}_{N}(t)}{p(t)}\right)\right]^{\rm T}.
\end{equation}
Therefore, the linear BSDE \eqref{nonhom} under $\mathbf{Q}_2$ becomes
\begin{equation}\label{QBSDE}
\left\{
\begin{aligned}
&\mathrm{d}g(t)=\left[-\frac{2f(t)}{p(t)}+\left(r(t)+\frac{2f(t)}{p(t)}\right)g(t)\right]\mathrm{d}t +\eta(t)^{\rm T}\mathrm{d}W^{\mathbf{Q}_2}(t)+\hat{\eta}(t)^{\rm T}\mathrm{d}\tilde{\it\Phi}^{\mathbf{Q}_2}(t),\\
&g(T)=1.
\end{aligned}
\right.
\end{equation}
It is easy to obtain the well-posedness of \eqref{QBSDE} which admits a unique square integrable solution $(g(\cdot),\eta(\cdot),\hat{\eta}(\cdot))$ under the probability measure $\mathbf{Q}_2$. Moreover, since $f(t)$ and $p(t)$ are bounded and $p(t)\geq b>0$, we have
\begin{equation*}
g(t)=\mathbb{E}^{\mathbf{Q}_2}\left[{\rm e}^{-\int_t^T\left(r(s)+\frac{2f(s)}{p(s)}\right) \mathrm{d}s }+\int_t^T \frac{2f(s)}{p(s)}{\rm e}^{ -\int_t^s \left(r(v)+\frac{2f(v)}{p(v)}\right)\mathrm{d}v}\mathrm{d}s|\mathcal{F}_t\right].
\end{equation*}
It is easy to see that $g(\cdot)$ is a bounded process and $g(t)>0$ for any $t\in [0,T]$. Next we introduce another BSDE:
\begin{equation}\label{ANBSDE}
\left\{
\begin{aligned}
&\mathrm{d}\tilde{g}(t)=\left[-\frac{2f(t)}{p(t)}+\frac{2f(t)}{p(t)}\tilde{g}(t)\right]\mathrm{d}t +\tilde{\eta}(t)^{\rm T}\mathrm{d}W^{\mathbf{Q}_2}(t)+\tilde{\hat{\eta}}(t)^{\rm T} \mathrm{d} \tilde{\it\Phi}^{\mathbf{Q}_2}(t),\\
&\tilde{g}(T)=1.
\end{aligned}
\right.
\end{equation}
Obviously, the unique solution is $(\tilde{g}(\cdot),\tilde{\eta}(\cdot),\tilde{\hat{\eta}}(\cdot))\equiv(1,0,0)$ to \eqref{ANBSDE}. Denoting $\bar{g}(\cdot)=\tilde{g}(\cdot)-g(\cdot)$, $\bar{\eta}(\cdot)=\tilde{\eta}(\cdot)-\eta(\cdot)$ and $\bar{\hat{\eta}}(\cdot)=\tilde{\hat{\eta}}(\cdot)-\hat{\eta}(\cdot)$, then $(\bar{g}(\cdot), \bar{\eta}(\cdot), \bar{\hat{\eta}}(\cdot))$ satisfies the following BSDE:
\begin{equation}
\left\{
\begin{aligned}
&\mathrm{d}\bar{g}(t)=\left[-r(t)g(t)+\frac{2f(t)}{p(t)}\bar{g}(t)\right]\mathrm{d}t +\bar{\eta}(t)^{\rm T}\mathrm{d}W^{\mathbf{Q}_2}(t)+\bar{\hat{\eta}}(t)^{\rm T} \mathrm{d} \tilde{\it\Phi}^{\mathbf{Q}_2}(t),\\
&\bar{g}(T)=0.
\end{aligned}
\right.
\end{equation}
Explicitly, $\bar{g}(t)=\mathbb{E}^{\mathbf{Q}_2}\left[\int_t^T r(s)g(s){\rm e}^{-\int_t^s\frac{2f(v)}{p(v)} \mathrm{d}v} \mathrm{d}s\right]$. Due to $r(t)\geq 0$ and $g(t)>0$, we obtain $\bar{g}(t)\geq 0$. From the definition of $\bar{g}(t)=\tilde{g}(t)-g(t)$, we get $g(t)\leq 1,\ t\in [0,T]$. Moreover, we have $g(t)<1$ for any $t\in[0,T)$, if the interest rate $r(t)>0,\ a.e.\ t\in [0,T]$. \hfill\rule{1mm}{3mm}
\section{Solution to the Unconstrained Problem}
Now we give the solution of the unconstrained problem \eqref{unquestion}.
\begin{theorem}\label{Thm5.1}
Under Assumptions \ref{2.7}-\ref{2.9}, the problem \eqref{unquestion} is solvable. The unique optimal feedback control for $t\in[0,T]$ is given by
\begin{equation}\label{optimalcontrol}
\pi^{(\lambda)}(t)=-\sigma(t)^{-1}\left(\theta(t)+\frac{{\it\Lambda}(t)}{p(t-)}\right)\left[ x^{(\lambda)}(t-) + (\lambda-z)g(t-) \right]-(\lambda-z)\sigma(t)^{-1}\eta(t)
\end{equation}
The corresponding optimal state trajectory is given by
\begin{equation}\label{SSSDE}
\begin{aligned}
\mathrm{d}x^{(\lambda)}(t)&=\Bigg\{r(t)x^{(\lambda)}(t)-\theta(t)\left(\theta(t)+\frac{{\it\Lambda}(t)} {p(t)}\right)\left[x^{(\lambda)}(t) +(\lambda-z)g(t)\right]-(\lambda-z)\theta(t)\eta(t)\Bigg\}\mathrm{d}t\\
&\quad\quad-\Bigg\{\left(\theta(t)^{\rm T}+\frac{{\it\Lambda}(t)^{\rm T}} {p(t)}\right)[x^{(\lambda)}(t)+(\lambda-z)g(t)] -(\lambda-z)\eta(t)^{\rm T}\Bigg\}\mathrm{d}W(t).
\end{aligned}
\end{equation}
And the associated optimal cost is given by
\begin{equation}\label{optimalcost}
\begin{aligned}
J(\pi^{(\lambda)}(\cdot),\lambda)
=\left[\frac{1}{2}p(0)g(0)^2+{\it\Delta}-1\right](\lambda-z)^2 +\left[p(0)g(0)x_0-2z\right](\lambda-z)+\frac{1}{2}p(0)x_0^2-z^2,
\end{aligned}
\end{equation}
where
\begin{equation}\label{Delta}
{\it\Delta}:=\mathbb{E}\left[\int_0^T f(t)|g(t)-1|^2+\frac{1}{2}p(t)\hat{\eta}(t)^2\lambda(t) \mathrm{d}t\right]\geq 0.
\end{equation}
\end{theorem}
Before proving this theorem, we verify that the strategy $\pi^{(\lambda)}(\cdot)$ is admissible.
\begin{lemma}\label{5.2}
Let Assumptions \ref{2.7}-\ref{2.9} hold. $\pi^{(\lambda)}(\cdot)$ defined by \eqref{optimalcontrol} is admissible.
\end{lemma}
\proof
Substituting the feedback control \eqref{optimalcontrol} into the wealth equation \eqref{wealth}, we have \eqref{SSSDE}. In \eqref{SSSDE}, the term $\Lambda(t)$ associated with the SRE \eqref{SRE} appears in the coefficients of the variable $x$ in both drift and diffusions. Although linear, the issue of existence and uniqueness of solution of \eqref{SSSDE} no longer lies in the domain of standard theory, which requires the coefficients of $x$ to be uniformly bounded. However, from Lemma 4.3 in Shen et al. \cite{Shen2020}, we directly get the desired results that the SDE \eqref{SSSDE} admits a unique strong solution. In addition, the left-limit processes $x^{(\lambda)}(t-)$, $p(t-)$ and $g(t-)$ are predictable as $x^{(\lambda)}(t)$, $p(t)$ and $g(t)$ are $\mathbb{F}$-adapted, ${\rm c\grave{a}dl\grave{a}g}$ processes. As a consequence that $\Lambda(t)$ and $\eta(t)$ are also predictable, we can deduce that the strategy $\pi^{(\lambda)}$ is predictable. Next we want to verify that $\pi^{(\lambda)}$ is square integrable.
Applying It\^o's formula to $p(t)(x^{(\lambda)}(t)+(\lambda-z)g(t))^2$, we have
\begin{equation}\label{ItoBSDE}
\begin{aligned}
&\mathrm{d}\left\{p(t)\left[x^{(\lambda)}(t)+(\lambda-z)g(t)\right]^2\right\}\\
&=\Bigg\{2p(t)\left[x^{(\lambda)}(t)+(\lambda-z)g(t)\right]\bigg\{r(t)x^{(\lambda)}(t)+B(t)\pi^{(\lambda)} (t)+(\lambda-z) \bigg[r(t)g(t)
+2\frac{f(t)}{p(t)}(g(t)-1)\\
&\quad\quad+\theta(t)\eta(t) -\frac{\hat{\it\Lambda}(t)^{\rm T}\hat{\eta}(t)}{p(t)}\lambda(t) \big)\bigg]\bigg\}
+p(t)\Big[\left(\sigma(t)\pi^{(\lambda)}(t))+(\lambda-z)\eta(t)\right)^2+(\lambda-z)^2\hat{\eta}(t)^2\lambda(t)\Big]\\ &\quad\quad-\left[x^{(\lambda)}(t)+(\lambda-z)g(t)\right]^2 \bigg[2f(t)+\big[2r(t)-\theta(t)\theta(t)^{\rm T}\big]
p(t)-2\theta(t){\it\Lambda}(t)-\frac{{\it\Lambda}(t)^{\rm T}{\it\Lambda}(t)} {p(t)}\bigg]\\
&\quad\quad+2[x^{(\lambda)}(t)+(\lambda-z)g(t)]\left({\it\Lambda}(t)\left[\sigma(t)\pi^{(\lambda)}(t)+(\lambda-z)\eta(t)\right]
+(\lambda-z) \lambda(t)\hat{ \it\Lambda}(t)\hat{\eta}(t)\right) \Bigg\}\mathrm{d}t\\
&\quad\quad +N^{(\lambda)}(t)\mathrm{d}W(t)+\tilde{N}^{(\lambda)}(t)\mathrm{d}\tilde{\it\Phi}(t)\\
&=\bigg\{p(t)\bigg[\sigma(t)\pi^{(\lambda)}(t)+(\lambda-z)\eta(t)+ \left(\theta(t)) +\frac{{\it\Lambda}(t)}{p(t)} \right)(x^{(\lambda)}(t)+(\lambda-z)g(t))\bigg]^2\\
&\quad\quad+2(\lambda-z)^2f(t)(g(t)-1)^2
+(\lambda-z)^2p(t) \hat{\eta}(t)^2\lambda(t)-2f(t)\left[x^{(\lambda)}(t)+(\lambda-z)\right]^2\bigg\}\mathrm{d}t \\
&\quad\quad +N^{(\lambda)}(t)\mathrm{d}W(t)+\tilde{N}^{(\lambda)}(t)\mathrm{d}\tilde{\it\Phi}(t)\\
&=\bigg\{ 2(\lambda-z)^2f(t)(g(t)-1)^2
+(\lambda-z)^2p(t) \hat{\eta}(t)^2\lambda(t)-2f(t)\left[x^{(\lambda)}(t)+(\lambda-z)\right]^2\bigg\}\mathrm{d}t \\
&\quad\quad +N^{(\lambda)}(t)\mathrm{d}W(t)+\tilde{N}^{(\lambda)}(t)\mathrm{d}\tilde{\it\Phi}(t)
\end{aligned}
\end{equation}
where
\begin{equation*}
\begin{aligned}
N^{(\lambda)}(t)=2p(t)\left[x^{(\lambda)}(t)+(\lambda-z)g(t)\right]\left[\pi^{(\lambda)}(t)\sigma(t)+(\lambda-z)\eta(t)\right] +{\it\Lambda}(t)\left[x^{(\lambda)}(t)+(\lambda-z)g(t)\right]^2,\\
\end{aligned}
\end{equation*}
\begin{equation*}
\tilde{N}^{(\lambda)}(t)=2(\lambda-z)p(t-)\hat{\eta}(t)\left[x^{(\lambda)}(t-)+(\lambda-z)g(t-)\right] +\hat{\it\Lambda}(t)\left[x^{(\lambda)}(t-)+(\lambda-z)g(t-)\right]^2.
\end{equation*}
For any given $t\in [0,T]$ and any given $\mathbb{F}$-stopping time $\tau$, we integrate \eqref{ItoBSDE} on $[0,t\wedge\tau]$ and get
\begin{equation*}
\begin{aligned}
&p(t\wedge \tau)\left[x^{(\lambda)}(t\wedge \tau)+(\lambda-z)g(t\wedge \tau)\right]^2-p(0)\left[x^{(\lambda)}(0)+(\lambda-z)g(0)\right]^2\\
&=\int_0^{t\wedge \tau}\bigg\{ 2(\lambda-z)^2f(s)(g(s)-1)^2
+(\lambda-z)^2p(s) \hat{\eta}(s)^2\lambda(s)-2f(s)\left[x^{(\lambda)}(s)+(\lambda-z)\right]^2\bigg\}\mathrm{d}s\\
&\quad\quad +\int_0^{t\wedge \tau}N^{(\lambda)}\mathrm{d}W(s)+\int_0^{t\wedge \tau}\tilde{N}^{(\lambda)}\mathrm{d}\tilde{\it\Phi}(s).
\end{aligned}
\end{equation*}
Since $\int_0^{t\wedge \tau} N^{(\lambda)}\mathrm{d}s$ and $\int_0^{t\wedge \tau} \tilde{N}^{(\lambda)} \mathrm{d}\tilde{\it\Phi}(s)$ are locally square integrable martingales, there exists a sequence of stopping times $\{\tau_i\}_{i=1}^{\infty}$ which increases and diverges $\mathbf{P}-a.s.$, as $i\rightarrow \infty$. It follows that
\begin{equation}\label{lemma1}
\begin{aligned}
\mathbb{E}&\left[p(t\wedge \tau \wedge \tau_i)\left(x^{(\lambda)}(t\wedge \tau \wedge \tau_i)+(\lambda-z)g(t\wedge \tau \wedge \tau_i)\right)^2\right]\\
&\leq p(0)\left[x^{(\lambda)}(0)+(\lambda-z)g(0)\right]^2
+\mathbb{E}\int_0^{t\wedge \tau\wedge \tau_i}(\lambda-z)^2\bigg\{ 2f(s)(g(s)-1)^2+p(s) \hat{\eta}(s)^2\lambda(s) \bigg\}\mathrm{d}s.
\end{aligned}
\end{equation}
Owing to $0<b\leq p(s)\leq B$, $f(\cdot),\ g(\cdot)$ are non-negative bounded and $\hat{\eta}(\cdot) \in {\it\Pi}^2_{\mathbb{F}} (0,T;\mathbb{R}^N)$, then it is easy to see that the integrand in the right-hand side of \eqref{lemma1} is non-negative. And we also know that the left-hand side is dominated by an integrable random variable $B\sup_{t\in [0,T]} |x(t)+(\lambda-z)g(t)|^2$. Therefore, by sending $i$ to $\infty$ and applying the dominated convergence theorem and the monotone convergence theorem to \eqref{lemma1}, we obtain
\begin{equation*}
\begin{aligned}
\mathbb{E}&\left[p(t\wedge \tau)\left(x^{(\lambda)}(t\wedge \tau)+(\lambda-z)g(t\wedge \tau )\right)^2\right]\\
&\quad\quad\leq p(0)\left[x^{(\lambda)}(0)+(\lambda-z)g(0)\right]^2
+\mathbb{E}\int_0^{t\wedge \tau}(\lambda-z)^2\bigg\{ 2f(s)(g(s)-1)^2+p(s) \hat{\eta}(s)^2\lambda(s) \bigg\}\mathrm{d}s.
\end{aligned}
\end{equation*}
Then we have
\begin{equation*}
\mathbb{E}\left[\left(x^{(\lambda)}(t\wedge \tau)+(\lambda-z)g(t\wedge \tau)\right)^2\right]< \infty.
\end{equation*}
Moreover, we can get
\begin{equation*}
\begin{aligned}
\mathbb{E}\left[\left|x^{(\lambda)}(t\wedge\tau)\right|^2\right]
&=\mathbb{E}\left[\left|\left(x^{(\lambda)}(t\wedge \tau)+(\lambda-z)g(t\wedge \tau)\right) -(\lambda-z)g(t\wedge \tau)\right|^2\right]\\
&\leq 2\mathbb{E}\left[\left|x^{(\lambda)}(t\wedge \tau)+(\lambda-z)g(t\wedge \tau)\right|^2\right] +2\mathbb{E}\left[\left|(\lambda-z)g(t\wedge \tau)\right|^2\right].
\end{aligned}
\end{equation*}
That is, for any $t\in [0,T]$ and any stopping time $\tau$, we obtain
\begin{equation}\label{jiben}
\mathbb{E}\left[\left|x^{(\lambda)}(t\wedge \tau)\right|^2\right]< \infty.
\end{equation}
Now, we show that \eqref{jiben} implies the admissibility of $\pi^{(\lambda)}(\cdot)$. Applying It\^o's formula, we have
\begin{equation*}
\begin{aligned}
|x^{(\lambda)}(t)|^2=x_0^2&+\int_0^t 2x^{(\lambda)}(s)\left[r(s)x^{(\lambda)}(s)+\pi^{(\lambda)}(s)^{\rm T}B(s)\right]\mathrm{d}s \\
& +\int_0^t|\pi^{(\lambda)}(s)^{\rm T}\sigma(s)|^2\mathrm{d}s
+\int_0^t 2x^{(\lambda)}(s)\pi^{(\lambda)}(s)\sigma(s)\mathrm{d}W(s).
\end{aligned}
\end{equation*}
From the inequality $-2xB\cdot \pi=-2(\sqrt{2}x\theta)\cdot(\pi \sigma /\sqrt{2})\leq 2x^2|\theta|^2+|\pi\sigma|^2/2$, we have
\begin{equation*}
\begin{aligned}
|x^{(\lambda)}(t)|^2\geq x_0^2&-\int_0^t 2|x^{(\lambda)}(s)|^2\left[|\theta(s)|^2-r(s)\right]\mathrm{d}s \\ &+\frac{1}{2}\int_0^t|\pi^{(\lambda)}(s)^{\rm T}\sigma(s)|^2\mathrm{d}s
+\int_0^t 2x^{(\lambda)}(s)\pi^{(\lambda)}(s)\sigma(s)\mathrm{d}W(s).
\end{aligned}
\end{equation*}
Note that $2x^{(\lambda)}(\cdot)\pi^{(\lambda)}(\cdot)\sigma(\cdot)\in L^{2,loc}_{\mathbb{F}} (0,T;\mathbb{R}^n).$ Therefore, there exists a localizing sequence of stopping times $\{\sigma_i\}_{i=1}^{\infty}$ which increases and diverges $\mathbf{P}-a.s.$, such that
\begin{equation*}
x_0^2+\frac{1}{2}\mathbb{E}\int_0^{T\wedge \sigma_i}|\pi^{(\lambda)}(t)\sigma(t)|^2\mathrm{d}t \leq \mathbb{E}\left[|x^{(\lambda)}(T\wedge \sigma_i)|^2\right]+2\mathbb{E}\int_0^{T\wedge \sigma_i}|x^{(\lambda)}(s)|^2\left[|\theta(s)|^2-r(s)\right]\mathrm{d}s.
\end{equation*}
By virtue of \eqref{jiben} and Assumption \ref{2.1}, we have
$$\mathbb{E}\int_0^{T\wedge \sigma_i}|\pi^{(\lambda)}(t)|^2\mathrm{d}t<\infty.$$
Sending $i$ to $\infty$, we can directly get
$$\mathbb{E}\int_0^{T}|\pi^{(\lambda)}(t)|^2\mathrm{d}t<\infty.$$
Then we get the admissibility of $\pi^{(\lambda)}(\cdot)$. Consequently, the corresponding wealth process $x^{(\lambda)}(\cdot) \in S^2_{\mathbb{F}}(0,T;\mathbb{R})$. \hfill\rule{1mm}{3mm}
Then we prove Theorem \ref{Thm5.1}.
\proof
Let $\pi(\cdot)\in\mathcal{U}$ be any given admissible control and $x(\cdot)$ be the corresponding state trajectory. Similar to Lemma \ref{5.2}, applying It\^o's formula to $p(t)\left(x(t)+(\lambda-z)g(t)\right)^2$, we obtain
\begin{equation*}
\begin{aligned}
p(t)&\left[x(t)+(\lambda-z)g(t)\right]^2+\int_0^t 2f(s)\left[x(s)+(\lambda-z)\right]^2\mathrm{d}s\\
&=\int_0^t \bigg\{p(s)\bigg[\sigma(s)\pi(s)+(\lambda-z)\eta(s)+ \left(\theta(s) +\frac{\Lambda(s)}{p(s)} \right)(x(s)+(\lambda-z)g(s))\bigg]^2\\
&\quad\quad+2(\lambda-z)^2f(s)(g(s)-1)^2
+(\lambda-z)^2p(s) \hat{\eta}(s)^2\lambda(s)\bigg\}\mathrm{d}s+p(0)\left(x(0)+(\lambda-z)g(0)\right)^2 \\
&\quad\quad +\int_0^t N(s)\mathrm{d}W(s)
+\int_0^t \tilde{N}(s)\mathrm{d}\tilde{\it\Phi}(s)
\end{aligned}
\end{equation*}
where
\begin{equation*}
\begin{aligned}
N(t)&=2p(s)\left[x(t)+(\lambda-z)g(t)\right]\left(\pi(t)\sigma(t)+(\lambda-z)\eta(t)\right) +{\it\Lambda}(t)\left[x(t)+(\lambda-z)g(t)\right]^2 \\
\tilde{N}(t)&=2(\lambda-z)p(t-)\hat{\eta}(t)\left[x(t-)+(\lambda-z)g(t-)\right] +\hat{\it\Lambda}(t)\left[x(t-)+(\lambda-z)g(t-)\right]^2
\end{aligned}
\end{equation*}
Similar to Lemma \ref{5.2}, integrating the above from $0$ to $T$ and taking expectations, we obtain
\begin{equation*}
\begin{aligned}
&\mathbb{E}\big[2(1-F(T))\left(x(T)+(\lambda-z)\right)^2\big]+\mathbb{E}\left[2\int_0^Tf(t)\left( x(t)+(\lambda-z) \right)^2\mathrm{d}t\right]\\
&=\mathbb{E}\int_0^T p(t)\left|\sigma(t)\pi(t)+\left(\theta(t)+\frac{{\it\Lambda}(t)}{p(t-)}\right)\left[ x(t-) + (\lambda-z)g(t-) \right]+(\lambda-z)\eta(t)\right|^2\mathrm{d}t\\
&\quad+p(0)\left[x_0+(\lambda-z)g(0)\right]^2+2(\lambda-z)^2\mathbb{E}\int_0^T f(t)\left(g(t)-1\right)^2\mathrm{d}t +(\lambda-z)^2\mathbb{E}\int_0^T p(t) \hat{\eta}(t)^2\lambda(t)\mathrm{d}t\\
\end{aligned}
\end{equation*}
Consequently,
\begin{equation*}
\begin{aligned}
J(\pi^{(\lambda)}(\cdot),\lambda)&=\mathbb{E}\left[\int_0^Tf(t)[x(t)+(\lambda-z)]^2\mathrm{d}t+(1-F(T)) [x(T)+(\lambda-z)]^2\right]-\lambda^2\\
&=\frac{1}{2}\mathbb{E}\int_0^T p(t)\left|\sigma(t)\pi(t)+\left(\theta(t)+\frac{{\it\Lambda}(t)}{p(t-)}\right)\left[ x(t-) + (\lambda-z)g(t-) \right]+(\lambda-z)\eta(t)\right|^2\mathrm{d}t\\
&\quad\quad+\frac{1}{2}p(0)\left[x_0+(\lambda-z)g(0)\right]^2+(\lambda-z)^2\mathbb{E}\int_0^T f(t)\left(g(t)-1\right)^2\mathrm{d}t\\
&\quad\quad+\frac{1}{2}(\lambda-z)^2\mathbb{E}\int_0^T p(t) \hat{\eta}(t)^2\lambda(t)\mathrm{d}t-\lambda^2.
\end{aligned}
\end{equation*}
Since $p(t)>0$ by Theorem \ref{Thm4.2}, it follows immediately that the optimal feedback control is given by \eqref{optimalcontrol} and the optimal value is given by
\begin{equation*}
\begin{aligned}
J(\pi^{(\lambda)}(\cdot),\lambda)
&=\frac{1}{2}p(0)\left[x_0+(\lambda-z)g(0)\right]^2+(\lambda-z)^2\mathbb{E}\int_0^T f(t)\left(g(t)-1\right)^2\mathrm{d}t\\
&\quad\quad +\frac{1}{2}(\lambda-z)^2\mathbb{E}\int_0^T p(t) \hat{\eta}(t)^2\lambda(t)\mathrm{d}t-\lambda^2\\
&=\left(\frac{1}{2}p(0)g(0)^2+{\it\Delta}-1\right)(\lambda-z)^2 +\left[p(0)g(0)x_0-2z\right](\lambda-z)+\frac{1}{2}p(0)x_0^2-z^2,
\end{aligned}
\end{equation*}
where ${\it\Delta}$ is defined by \eqref{Delta}. \hfill\rule{1mm}{3mm}
\section{Efficient frontier}
In this section, proceed to derive the efficient frontier for the original mean-variance problem \eqref{question}.
\begin{theorem}
Let Assumptions \ref{2.7}-\ref{2.9} and \eqref{ftiao} hold. Then
\begin{equation}\label{quadratic}
\frac{1}{2}p(0)g(0)^2+{\it\Delta}-1<0.
\end{equation}
Moreover, the efficient portfolio corresponding to $z$ is
\begin{equation}\label{opcontrol}
\pi^*(t):=\pi^{(\lambda^*)}(t)=-\left(\theta(t)+\frac{{\it\Lambda}(t)}{p(t-)}\right)\sigma(t)^{-1} \left[x(t-)+(\lambda^*-z)g(t-) \right]-(\lambda^*-z)\sigma(t)^{-1}\eta(t)^{\rm T},
\end{equation}
where
\begin{equation}\label{optimallambda}
\lambda^*-z=\frac{2z-p(0)g(0)x_0}{p(0)g(0)^2+2{\it\Delta}-2}.
\end{equation}
Furthermore, the optimal value of ${\rm Var} x(\tau\wedge T)$, among all the wealth processes $x(\cdot)$ satisfying $\mathbb{E}x(\tau\wedge T)=z$, is
\begin{equation}\label{optimalvalue}
\begin{aligned}
{\rm Var } x^*(\tau\wedge T)=\frac{2{\it\Delta}+p(0)g(0)^2}{2-2{\it\Delta}-p(0) g(0)^2} \left(z-\frac{p(0) g(0)}{2{\it\Delta}+p(0)g(0)^2}x_0\right)^2
+\frac{p(0){\it\Delta}}{2{\it\Delta}+p(0)g(0)^2}x_0^2.
\end{aligned}
\end{equation}
\end{theorem}
\proof
By condition \eqref{ftiao} and Proposition \ref{Prop3.1}, the mean-variance problem \eqref{question} is feasible for any $z\in \mathbb{R}$. By Theorem \ref{Thm5.1}, for every $\lambda\in \mathbb{R}$, the problem \eqref{unquestion} has a finite optimal value. Particularly, the problem \eqref{question} without the constraint $\mathbb{E}[x(\tau \wedge T)]=z$ is just the problem \eqref{unquestion} with $\lambda=0$, consequently it has a finite optimal value. Hence, \eqref{question} is finite for every $z\in \mathbb{R}$. Since $J_{MV}(\pi(\cdot))$ is strictly convex in $\pi(\cdot)$ and the constraint $J_1(\pi(\cdot))-z$ is affine in $\pi(\cdot)$, it follows from the duality theorem (see \cite{Luenberger1997} p.224 Theorem 1) that for any $z\in\mathbb{R}$, the optimal value of \eqref{question} is
\begin{equation}\label{fitness}
J^*_{MV}=\sup_{\lambda\in \mathbb{R}}\inf_{\pi(\cdot)\in \mathcal{U}}J(\pi(\cdot),\lambda)>-\infty.
\end{equation}
From Theorem \ref{Thm5.1}, $\inf_{\pi(\cdot)\in \mathcal{U}}J(\pi(\cdot),\lambda)$ is a quadratic function (see \eqref{optimalcost}) in $\lambda-z$. From the finiteness of the supremum value of this quadratic function, we have
\begin{equation*}
\frac{1}{2}p(0)g(0)^2+{\it\Delta}-1\leq 0.
\end{equation*}
But if $\frac{1}{2}p(0)g(0)^2+{\it\Delta}-1=0$, then due to \eqref{optimalcost} and \eqref{fitness}, we must have $p(0)g(0)-2z=0$, which is a contradiction for any $z\in \mathbb{R}$. So we prove \eqref{quadratic}.
On the other hand, we maximize the function \eqref{optimalcost} over $\lambda-z$. The optimal Lagrange multiplier $\lambda^*$ is given by \eqref{optimallambda}, and the optimal value of the variance ${\rm Var } x^*(\tau\wedge T)$ is given by \eqref{optimalvalue}. Finally, the optimal control \eqref{opcontrol} is obtained by \eqref{optimalcontrol} with $\lambda=\lambda^*$. \hfill\rule{1mm}{3mm}
The expression \eqref{optimalvalue} reveals explicitly the tradeoff between the reward and the risk at the terminal time. Different from the case without Markov chain \cite{Lim2002} and the case with deterministic exit time \cite{Zhou2000}, the efficient frontier in the present case with Markov chain and random exit time is not a perfect square. As a consequence, the agent is not able to achieve a risk-free investment. Owing to the influence of the exit timing risk and the independence between Markov chain and Brownian motion, the interest rate risk cannot be perfectly hedged by any portfolio consisting of the bank account and stocks. Then we give the minimum variance as follows, which can be achieved by a feasible portfolio.
\begin{corollary}[minimum variance]\label{6.2}
Let Assumptions \ref{2.7}-\ref{2.9} and \eqref{ftiao} hold. The minimum terminal variance is
\begin{equation}\label{c}
{\rm Var}x^*_{min}(\tau\wedge T)=\frac{p(0){\it\Delta}}{2{\it\Delta}+p(0)g(0)^2}x_0^2 \geq 0,
\end{equation}
which is achieved by the portfolio
\begin{equation}\label{cc}
\pi^*_{min}(t)=-\left(\theta(t)+\frac{{\it\Lambda}(t)}{p(t-)}\right)\sigma(t)^{-1}\left[x^*_{min}(t-)- z_{min}g(t-)\right]+z_{min}\sigma(t)^{-1}\eta(t).
\end{equation}
Moreover, the corresponding expected terminal wealth is given by
\begin{equation}\label{ccc}
z_{min}:=\frac{p(0)g(0)}{2{\it\Delta}+p(0)g(0)^2}x_0
\end{equation}
and the corresponding Lagrange multiplier $\lambda^*_{min}=0$.
\end{corollary}
\proof
We can easily get \eqref{c} and \eqref{ccc} from the expression \eqref{optimalvalue}. From \eqref{optimallambda} and \eqref{ccc}, we calculate $\lambda^*_{min}=0$. Finally, \eqref{cc} follows from \eqref{opcontrol}. \hfill\rule{1mm}{3mm}
\begin{remark}
As same as Lim and Zhou \cite{Lim2002}, Zhou and Yin \cite{Zhou2003} and Yu \cite{Yu2013}, due to the minimum variance, the parameter $z$ can be restricted on the interval $z\in [z_{min},+\infty)$ when we study the efficient frontier to the mean-variance problem \eqref{question}.
\end{remark}
Now we give the so-called mutual fund theorem.
\begin{theorem}[mutual fund theorem]
Let Assumptions \ref{2.7}-\ref{2.9} and \eqref{ftiao} hold. Let $\pi^*_{min}(\cdot)$ denote the minimum variance portfolio defined in Corollary \ref{6.2}, and $\pi^*_1(\cdot)$ is another given efficient portfolio corresponding to $z_1>z_{min}$. Then a portfolio $\pi^*(\cdot)$ is efficient if and only if there exists an $\beta\geq 0$ such that
\begin{equation}\label{aa}
\pi^*(t)=(1-\beta)\pi^*_{min}(t)+\beta\pi^*_1(t), \quad t\in [0,T].
\end{equation}
\end{theorem}
\proof
On one hand, we give the proof of the if part. For given $z_{min}$ and $z_1$, we write the expressions of the corresponding Lagrange multipliers and efficient portfolios:
\begin{equation*}
\begin{aligned}
&\lambda^*_{min}=z_{min}+\frac{2z_{min}-p(0)g(0)x_0}{p(0)g(0)^2+2{\it\Delta}-2}, \quad \quad \lambda^*_{1}=z_{1}+\frac{2z_{1}-p(0)g(0)x_0}{p(0)g(0)^2+2{\it\Delta}-2},\\
&\pi^*(t)=-\left(\theta(t)+\frac{{\it\Lambda}(t))}{p(t-)}\right)\sigma(t) ^{-1}\left[x^*_{min}(t-)+ (\lambda^*_{min}-z_{min})g(t-) \right]
-(\lambda^*_{min}-z_{min})\sigma(t))^{-1}\eta(t)^{\rm T},\\
&\pi^*(t)=-\left(\theta(t)+\frac{{\it\Lambda}(t)}{p(t-)}\right)\sigma(t) ^{-1}\left[x^*_{1}(t-)+ (\lambda^*_{1}-z_{1})g(t-) \right]
-(\lambda^*_{1}-z_{1})\sigma(t)^{-1}\eta(t)^{\rm T},\\
\end{aligned}
\end{equation*}
For any $\beta\geq 0$, we define $z=(1-\beta)z_{min}+\beta z_1$. By the linearities of $\lambda^*$ with respect to $z$, $x^*$ with respect to $\lambda^*$ and $\pi^*$ with respect to $x^*$, $\lambda^*$ and $z$, we have
\begin{equation*}
\begin{aligned}
&\lambda^*=(1-\beta)\lambda^*_{min}+\beta \lambda^*_1,\\
&x^*=(1-\beta)x^*_{min}+\beta x^*_1,\\
&\pi^*=(1-\beta)\pi^*_{min}+\beta\pi^*_1.
\end{aligned}
\end{equation*}
So a portfolio $\pi^*(\cdot)$ defined by \eqref{aa} is an efficient portfolio corresponding to $z=(1-\beta)z_{min}+\beta z_1$.
On the other hand, we give the proof of the only if part. When $\pi^*(\cdot)$ is an efficient portfolio corresponding to a certain $z\geq z_{min}$, we can write $z=(1-\beta)z_{min}+\beta z_1$ with some $\beta \geq 0$. The above analysis leads to that $\pi^*(\cdot)$ must be in form of \eqref{aa}. \hfill\rule{1mm}{3mm}
\begin{remark}
The mutual fund theorem implies that any efficient portfolio can be constructed as a combination of the minimum variance portfolio $\pi^*_{min}(\cdot)$ and another given efficient portfolio (called the mutual fund) $\pi^*_1(\cdot)$. In other words, the investor need only to invest in the minimum variance portfolio $\pi^*_{min}(\cdot)$ and the mutual fund $\pi^*_1(\cdot)$ to achieve the efficiency. The factor $\beta\geq 0$ means that the investor cannot short sell the mutual fund $\pi^*_1(\cdot)$.
\end{remark}
\begin{example}[numerical example]
Assume $r=0.1$, $\mu=0.3$, $\sigma=0.5$, $x_0=1$ and $T=1$. Then the efficient frontiers corresponding to the densities $f=0,\ 0.5,\ 0.8$ are plotted in Figure 1, respectively.
\end{example}
\begin{center}
\centerline
{\includegraphics[scale=0.6]{mean.eps}}\vskip3mm
\centering{\small {\bf Figure 1}\ \ Efficient frontier: f=0 (red), f=0.5 (blue) and f=0.8 (green) \label{fig1}}
\end{center}
Figure 1 shows that the larger the density of the random horizon is, the larger the variance of terminal wealth is. This is reasonable because a larger density implies that more extra uncertainty owing to the random horizon is added to the model, resulting in the increment of the overall risk.
\section{Conclusion}
In this paper, we have studied a continuous-time mean-variance portfolio selection problem under non-Markovian regime-switching model with random horizon. In our setting, an investor is uncertain about exit time. We assume that the exit time is $\tau \wedge T$, where $\tau$ is a $\mathcal{A}$-measurable positive random variable. It means that we have considered all uncertain factors affecting the investment, not just the price information. We use a submartingale to characterize the conditional distribution of random time $\tau$ and reconstruct the mean-variance problem according to the Doob-Mayer decomposition theorem and some assumptions. A key difficulty is to prove the global solvability of the stochastic Riccati equation. Using a truncation technique, we transform the corresponding SRE into a one-dimentional BSDE with quadratic growth. With the help of BMO martingales technique and comparison theorem, we proved the global solvability of the stochastic Riccati equation and the auxiliary regime-switching BSDE arising from the mean-variance problem.
For the mean-variance problem with regime-switching and random horizon, we obtained the efficient portfolios and efficient frontier in closed forms. Different from the case where the market is complete, the efficient frontier is no longer presented in a quadratic form. Due to the challenging structure of auxiliary regime-switching BSDE and ${\it\Delta}$, we obtained some results different from the existing works. We also proved that a risk-free investment is not able to be achieved. This phenomenon is reasonable because the random exit time and the Markov chain introduce new uncertainty, and such uncertainty can not be hedged by any portfolio consisting of the bond and stocks. In addition, we also present a minimum variance portfolio and a mutual fund theorem to illustrate.
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Q: Relation which is only locally a function Is there a term for a relation which is not a function (because it maps multiple inputs to the same output), but which looks like one locally? That is, for any $\langle x,y\rangle\in R$, there's some $\epsilon>0$ such that no $\langle x, y'\rangle\in R$ exists having $0<||y-y'||<\epsilon$. Also (and I'm not 100% that this is the proper formal definition I'm looking for) there's no $\langle x,y\rangle \in R$ having $\frac{dx}{dy} = 0$ -- that excludes relations like $\{\langle x,y\rangle|x^2+y^2=1\}$.
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{"url":"https:\/\/economics.stackexchange.com\/questions\/32522\/interest-rate-in-the-ramsay-cass-koopmans-model-in-a-closed-economy","text":"# Interest rate in the Ramsay-Cass-Koopmans model in a closed economy\n\nI am struggling to understand the optimal choices of firms in the Ramsey-Cass-Koopmans model. Specifically, everywhere I see there is the following optimality condition for the interest rate, $$r_{t}$$,\n\n$$r_{t} = f'(k_{t}) - \\delta_{k}$$\n\nThe information given to me is the following: Only one good is produced by competitive firms in the economy with the production function $$F(K_{t}, \\xi_{t}N_{t})$$ $$Y_{t} = K_{t}^{\\alpha}(\\xi_{t}N_{t})^{1 - \\alpha}$$\n\nwhere $$\\alpha$$ denotes the share of capital income and $$\\xi_{t}$$ a productivity term that grows at $$g = \\frac{\\dot{\\xi_{t}}}{\\xi_{t}}$$. Output can be consumed or invested $$Y_{t} = C_{t} + I_{t}$$\n\nCapital accumulates according to $$\\dot{K}_{t} = I_{t} - \\delta_{k}K_{t}$$\n\nwhere $$\\delta_{k}$$ is the depreciation rate of physical capital.\n\nFirms take input prices as given and choose how much labour to hire and capital rent to maximize their profit.\n\nThen letting $$f(k_{t}) = F(k_{t}, 1)$$ with $$k_{t} = \\frac{K_{t}}{\\xi_{t}N_{t}}$$, assuming firms pay a price $$r_{t}$$ for renting a unit of capital, optimal capital requires the above mentioned condition (i.e. $$r_{t} = f'(k_{t}) - \\delta_{k}$$).\n\nWithout making some sort of assumption about the interest rate I fail to see how to arrive to this FOC from the firm's problem. I found a text online () that stated the following:\n\nSince we assume that households understand precisely how the economy works, they can predict the future path of wages and interest rates. That is, we assume perfect foresight. Owing to this absence of uncertainty, the consequences of a choice are known. And rates of return on alternative assets must in equilibrium be the same. So the (short-term) interest rate in the bond market must equal the rate of return on real capital in equilibrium, that is $$r_{t} = \\hat{r_{t}} - \\delta_{k}$$ where $$\\delta$$ (\u2265 0) is a constant rate of capital depreciation. This no-arbitrage condition shows how the interest rate is related to the rental rate of capital.\n\nMy question then is, is this a condition that is given in the model and that my professor failed to mention? Or I am supposed to derive this from the information given?","date":"2019-12-12 13:59:12","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\": 16, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.9028238654136658, \"perplexity\": 585.090936346319}, \"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-2019-51\/segments\/1575540543850.90\/warc\/CC-MAIN-20191212130009-20191212154009-00235.warc.gz\"}"} | null | null |
SOCHI, Rus.—Canadian luge athletes Tristan Walker and Justin Snith will spend the summer fighting for the fractions of a second that cost them a shot at their first career podium on the Olympic Track in Sochi, Russia on Saturday.
Sitting in second spot after the opening bomb down the 2014 Olympic track, the 21-year-old Canadian duo struggled on the final descent, posting the 10th fastest time, to finish fourth with a time of 1:42.322 for the third straight week.
"The Austrians opened the door for us to get on the podium, and unfortunately Walker and Snith did not take gift that was presented on a silver plate to the podium. We just gave it away today," said Wolfgang Staudinger, head coach, Canadian Luge Team.
Walker, of Cochrane, Alta., and Calgary's Snith, may have missed first shot at a podium, but the young Canucks have enjoyed a breakthrough season. Battling their way into the top-10 at the start of the pre-Olympic year, Walker and Snith posted a historic fourth-place finish at the World Championships earlier this month on home ice in Whistler. They matched their career-best finish the following week in Lake Placid before heading to Russia for the final Olympic test.
Germany's Tobias Wendl and Tobias Arlt won the final World Cup race on Saturday with a time of 1:42.087. Austria's Peter Penz and Georg Fischler finished second at 1:42.221. Latvia's Andris Sics and Juris Sics slid to the bronze medal with a time of 1:42.243.
Earlier in the day, Calgary's Alex Gough finished as the top Canadian in the women's singles race. The 25-year-old Gough dropped two spots in rankings on her final trip down the track to finish sixth at 1:42.416. Calgary's Kim McRae completed a solid second year on the World Cup at just 20 years of age, finishing ninth with a two-run time of 1:48.802.
The Germans swept the women's podium. Tatjana Hufner was first at 1:41.922, while Natalie Geisenberger was second with a time of 1:41.960 and Anke Wischnewski slid to the bronze at 1:42.228.
Calgary's Arianne Jones rounded out the Canadian contingent finishing 15th at 1:43.132.
The final World Cup race of the season takes place in Sochi on Sunday with the men's singles and team relay events. | {
"redpajama_set_name": "RedPajamaC4"
} | 3,465 |
package jdbreport.source;
import java.text.MessageFormat;
import java.util.Collection;
import java.util.HashMap;
import java.util.Map;
import javax.swing.event.EventListenerList;
import jdbreport.model.ReportException;
import jdbreport.util.Utils;
/**
* @version 3.1 15.12.2014
* @author Andrey Kholmanskih
*
*/
public class BufferedDataSet implements MasterDataSet, DataSetListener {
private ReportDataSet ds;
private boolean inCache = false;
private boolean eof = false;
private boolean dsEof = false;
protected EventListenerList listenerList = new EventListenerList();
private boolean opened;
private Map<String, Object> linkedParams;
private boolean cursorChange;
private Object currentObject;
private Map<Object, Object> vars;
public BufferedDataSet(ReportDataSet ds) {
super();
this.ds = ds;
}
public BufferedDataSet(ReportDataSet ds, Map<Object, Object> vars) {
this(ds);
this.vars = vars;
}
public void setVars(Map<Object, Object> vars) {
this.vars = vars;
}
public Map<Object, Object> getVars() {
return vars;
}
public void open() throws ReportException {
if (isOpened())
return;
initValues();
dsEof = !ds.hasNext();
eof = !readToCache();
setOpened(true);
fireDataSetCursorChanged();
}
/**
* @throws ReportException
*/
private void initValues() throws ReportException {
currentObject = null;
}
public boolean reopen() throws ReportException {
inCache = false;
dsEof = !ds.reopen();
initValues();
eof = !readToCache();
setOpened(true);
cursorChange = true;
fireDataSetCursorChanged();
return !eof;
}
private void setOpened(boolean b) {
this.opened = b;
}
private boolean isOpened() {
return opened;
}
private boolean readToCache() {
if (inCache)
return !eof;
if (dsEof) {
return false;
}
inCache = true;
try {
currentObject = ds.getCurrentObject();
dsEof = !ds.next();
return true;
} catch (ReportException e) {
e.printStackTrace();
}
return false;
}
public boolean next() throws ReportException {
if (!isOpened())
throw new ReportException(MessageFormat.format(Messages
.getString("BufferedDataSet.not_opened"), getId()));
cursorChange = true;
inCache = false;
eof = !readToCache();
if (!eof) {
fireDataSetCursorChanged();
}
return !eof;
}
private String getFirstToken(String name) {
int p = name.indexOf('.');
if (p > 0) {
return name.substring(0, p);
}
return name;
}
public Object getValue(String name) throws ReportException {
return ds.getValue(currentObject, name);
}
@Override
public Object getValue(Object current, String name) throws ReportException {
return ds.getValue(current, name);
}
@Override
public boolean containsKey(String name) {
return ds.containsKey(name);
}
public boolean findColumn(String name) {
return ds.containsKey(name);
}
public String getId() {
return ds.getId();
}
public Object clone() {
try {
BufferedDataSet newDataSet = (BufferedDataSet) super.clone();
newDataSet.ds = (ReportDataSet) this.ds.clone();
return newDataSet;
} catch (CloneNotSupportedException e) {
e.printStackTrace();
}
return null;
}
public Collection<String> getColumnNames() throws ReportException {
return ds.getColumnNames();
}
public Object getNextValue(String name) throws ReportException {
if (!dsEof)
return ds.getValue(getFirstToken(name));
else
return null;
}
public boolean isDsEof() {
return dsEof;
}
public boolean isEof() {
return eof;
}
public void addDataSetListener(DataSetListener listener) {
listenerList.add(DataSetListener.class, listener);
}
public void removeDataSetListener(DataSetListener listener) {
listenerList.remove(DataSetListener.class, listener);
}
public void fireDataSetCursorChanged() {
Object[] listeners = listenerList.getListenerList();
if (listeners.length == 0)
return;
CursorChangedEvent e = new CursorChangedEvent(this);
for (int i = listeners.length - 2; i >= 0; i -= 2) {
if (listeners[i] == DataSetListener.class) {
((DataSetListener) listeners[i + 1]).cursorChange(e);
}
}
}
public DataSetParams getParams() throws ReportException {
return ds.getParams();
}
private boolean validateParams(MasterDataSet masterDS)
throws ReportException {
if (linkedParams != null)
return true;
linkedParams = new HashMap<>();
Collection<String> masterFields = masterDS.getColumnNames();
for (int i = 0; i < getParams().size(); i++) {
String paramName = getParams().getName(i);
if (masterFields.contains(paramName)) {
linkedParams.put(paramName, getParams()
.getValue(i));
}
}
if (linkedParams.size() == 0) {
masterDS.removeDataSetListener(this);
return false;
}
return true;
}
public boolean checkParamsChange(MasterDataSet masterDS) {
boolean result = false;
try {
if (!validateParams(masterDS))
return false;
for (String name : linkedParams.keySet()) {
Object paramValue = linkedParams.get(name);
Object dsValue = masterDS.getValue(name);
if (paramValue == null && dsValue == null)
continue;
boolean change = (paramValue != null && !paramValue.equals(dsValue))
|| (dsValue != null && !dsValue.equals(paramValue));
if (change) {
result = true;
linkedParams.put(name, dsValue);
getParams().setValue(name, dsValue);
}
}
} catch (ReportException e) {
Utils.showError(e);
masterDS.removeDataSetListener(this);
return false;
}
return result;
}
public void cursorChange(CursorChangedEvent evt) {
boolean change = checkParamsChange(evt.getMasterDataSet());
if (change) {
try {
reopen();
} catch (ReportException e) {
Utils.showError(e);
evt.getMasterDataSet().removeDataSetListener(this);
}
}
}
public String getMasterId() {
return ds == null ? null : ds.getMasterId();
}
public void resetCursorPos() {
cursorChange = false;
}
public boolean isCursorChange() {
return cursorChange;
}
public Object getCurrentObject() {
return currentObject;
}
public boolean hasNext() {
return !eof;
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 3,011 |
Latest in Culture
How to be a human being in the comments: A refresher
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Bose accused of secretly sharing your listening habits
Uber lets New York City drivers organize, with limits
It's not a union, but it gives ridesharing workers more of a voice.
Spencer Platt/Getty Images
Although Uber drivers have been organizing for a while, getting Uber to play along with those organizations has been difficult when it doesn't even want to treat workers as full-fledged employees. At last, though, there's some progress. Uber has partnered with the International Association of Machinists and Aerospace Workers to create the Independent Drivers Guild, the first labor group the ridesharing company officially recognizes. The Guild gives New York City's Uber drivers a collective voice in some issues, particularly when Uber kicks them out. It'll also reduce rates on everything from insurance to legal services.
This victory comes at a steep cost. The Guild can't actually unionize drivers (or have them treated as employees) for the next 5 years. That takes important labor issues off the table, including pay and workers' compensation. Moreover, the Guild has agreed to help push for state law changes that would lower taxes on hired rides and shrink Uber's expenses.
All the same, it's a big win for drivers that rarely have much recourse outside of lawsuits or jumping ship to work for rivals like Lyft. They'll get to communicate with Uber's management more often, and the firm says that savings from the reduced taxes would go into a benefits fund. While it's far from a perfect deal, it could make all the difference for regular drivers who have to fret over time off and lost wages.
In this article: culture, independentdriversguild, internet, labor, newyork, newyorkcity, ridesharing, services, transportation, uber | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 5,137 |
{"url":"https:\/\/brilliant.org\/problems\/problem-5\/","text":"# Problem 5\n\nHow many ordered triplets $$(a, b, c)$$ of non-zero positive integers satisfy\n\n$5a+6b+3c=50 ?$\n\n\u00d7","date":"2017-01-18 22:30:19","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\": 0.23346154391765594, \"perplexity\": 2455.9509474244023}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 5, \"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-2017-04\/segments\/1484560280364.67\/warc\/CC-MAIN-20170116095120-00545-ip-10-171-10-70.ec2.internal.warc.gz\"}"} | null | null |
package org.jetbrains.android.dom.transition;
import com.intellij.util.xml.DefinesXml;
@DefinesXml
public interface ChangeTransform extends Transition {
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 1,347 |
*Swoon*. Tina Fey and Amy Poehler will host the Golden Globes together.
The second Presidential debate is tonight. Follow @Feministing for live tweeting and minute-to-minute analysis.
Today is World Food Day. One of the best ways to enhance food security is to empower women with access to land, info and credit. Here are 3 things you can do to make a difference right now.
A new Tumblr chronicles academic men who explain things.
In a recent poll, thirty-one percent of female voters said birth control policy will be "extremely important" in influencing their vote. On a related note, the Guttmacher Institute estimates that unintended pregnancy costs American taxpayers roughly $11 billion each year.
Oh no! WHITE PRIVILEGE MAKE IT STOP!
A feminine hygiene company posted this hilarious response to a commenter complaining about them misrepresenting periods.
One billion women are set to enter the workplace in the next decade.
Our girl Katie appears in and co-wrote this satirical video on American foreign policy re: the 'war on drugs'. | {
"redpajama_set_name": "RedPajamaC4"
} | 8,187 |
On 'DAMN.,' Kendrick Lamar overloads us—and almost makes a classic album
Kendrick Lamar's 'DAMN.' is an epic statement, flame emoji and all.
Photo via Twocoms/Shutterstock (Licensed)
Ramon Ramirez— 2017-04-18 07:42 am | Last updated 2017-04-18 08:07 am
Kendrick Lamar is not the best rapper alive, but very few seem to work harder than the rapper from Compton, California. On DAMN., his dense and epic new album, Lamar is a wordy chameleon, burning through styles and lyrics like arcade quarters.
There are two Lamars dueling on DAMN.—the 29-year-old American who deftly understands his young nation's identity crisis, acting as its pent-up fury, and the divine healer who plays philosopher and grapples with his faith's ironclad tenets—a tension that's been building for years. On 2012's blistering major label debut good kid, m.A.A.d. city, Lamar proved to be a jaw-dropping storyteller who built a vivid world of class struggle and gang tussles, while 2015's To Pimp a Butterfly reveled in the heritage of subversive, black music.
On DAMN., which beamed onto streaming music services Thursday night, Lamar's hyper-aware self-mythologizing threatens to devalue his gifts as a vibrant performer. He takes on so many roles and ideas that listening to the album in one sitting is exhausting.
Lamar becomes the toxically masculine id of the fans who text about his work in superlatives adorned by flame emoji—but elsewhere he's a concerned romantic, for example. He's a paranoid philosopher rapping about The Matrix and I Am Legend with dated imagery, but then he's a community activist. He'll borrow lines and styles from Juvenile, Jay Z, and Andre 3000 because he's a studious rap fan eager to honor the legacy, but then he'll rhyme with evocative wit about his friends and mentors.
Lamar can't escape the impulse to appease record store puritans on DAMN. When he raps "Mr. One Through Five, that's the only logic / Fake my death, go to Cuba, that's the only option" on "ELEMENT.", he's writing to the peanut gallery of blogs like Nah Right and 2 Dope Boyz that hailed his ascent circa 2010. The aforementioned lyric riffs on a Tupac Shakur conspiracy theory. It also tries to end the debate that Lamar is one of the five best rappers in history by positing that he's actually all five of the best rappers in history, which is a joke from Chappelle's Show.
Lamar is a culture nerd who can pay homage to his faves with deft twists. He's a proud disciple of the blockbuster CD era and appears to follow suit here with a 14-song blueprint, an apparent nod to Jay Z's best albums. When he plays genre ambassador, however, he does poorly.
Lamar partners with U2 for choppy thought experiment "XXX.", but while Bono brings celebrity and perspective to the collaboration, he's otherwise superfluous. "It's not a place, this country is to be a sound of drum and bass," the Irishman lounge-sings on the chorus. Without the added wattage of U2, "XXX" remains a sprawling anecdote that juxtaposes the death of a friend's child with vengeful ethics. It serves as a harrowing microcosm of the shaky truces and faulty promises that bind the United States. Sonically, "XXX" is a booming suite that required all hands on deck from elite rap composers Anthony "Top Dawg" Tiffith, DJ Dahi, Sounwave, and Mike Will Made-It. "But is America honest, or do we bask in sin?" Lamar asks at the end. I dunno man, but Bono is weirding me out.
The rampant martyr imagery begins on album intro "BLOOD." and bookends DAMN. The skit finds Lamar helping a blind woman, struggling to walk in public, only to be shot and apparently killed by her. After the final song "DUCKWORTH.", the album spins backward and returns to the "I was taking a walk the other day" opening monologue. I like this reading of it from a commenter who annotated the lyrics on Genius:
Kendrick could be referencing Oedipus' blinding.
An analysis of Oedipus' blindness suggests, "blindness has in many myths represented a lack of power – in punishment and defeat". Kendrick could be suggesting that he is protecting those that have no power (since they have been ignored by those in power).
It's some gnarly, circle-of-life shit to be sure. This is fandom rap for people who want to unspool coded lyrics on Reddit. Hell, for a solid two days, die-hards were certain that Lamar would rise again and release a companion album called NATION. ahead of Easter Sunday. But if you want to don a foil hat while you listen to DAMN., just remember that what makes this album good are its visceral thrills.
Rihanna collaboration and possible song of the summer "LOYALTY." is the rush of pop. Tiffith and Terrace Martin arrange a soaring, 24-bit wave of G-funk, on which Rihanna continues her streak of being a cold-blooded mercenary who sings the best guest hooks. "DUCKWORTH." is Lamar in his most spellbinding pocket, rapping in curt cadences about how his dad was almost murdered by Lamar's manager. It's a market-fresh catch: Little Brother alum 9th Wonder found the song's soul sample from Ted Taylor's 1978 gem "Be Ever Wonderful" and warbled it with perfect drums and loops.
The seven-minute "FEAR." outlines the developmental pains of Lamar's childhood by writing from the perspective of his mom, chastising boyhood Lamar for scuffing up new shoes or complaining about food stamps. With artful detail, Lamar also spells out the everyday walkthroughs (buying weed at the apartment complex, miscalculating a friend's loyalty) that routinely threaten his life. He's a peer here, perfectly channeling your anxiety. His fluidity with cinematic dialogue stuns, even on throwaway lines like "I'm like an exit away" from "LOVE."
But Lamar is not the best rapper working, and you can tell it gets to him. Hip-hop in 2017 is more about vocalists and songwriters, and less about tongue-twisting writing. Sending warning shots to the industry by brandishing your pace and vocabulary is a dated game, one Lamar's rivals aren't playing. It would have been great fun to hear him square off against Eminem's platinum populism or Lil Wayne's codeine bender of freestyles. Today the world streams Drake's effortless charisma billions of times on Spotify. Future puts out lived-in, nonstop trap jams with sharper edges and regional identity. Chance the Rapper is a better youth pastor, manic in wordplay and boundless in optimism.
Even still, there's plenty on DAMN. to obsess over, like the way 50-year-old DJ Kid Capri plays hype man on it, a sort of bridge to the '90s that shaped Lamar's hip-hop ambition. It's a learned, experiential flourish from Lamar that provides just the right tinge of heritage. If our savior was roaming through the desert on Butterfly, conferencing with kings, he's come home with an album we won't forget.
Ramon Ramirez
Ramon Ramirez is the news director, and formerly the Dot's entertainment editor and evening editor. His work has appeared in the Washington Post, Grantland, Washington City Paper, Austin American-Statesman, and Austin Monitor.
Drake Hip Hop Jay-z Kendrick Lamar, Music | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 3,355 |
Jan Simon () est un pianiste tchèque, soliste de la radio tchèque et directeur de l'Orchestre symphonique de la radio de Prague (SOČR).
Biographie
Jan Simon vient d'une famille d'artistes : son père était le compositeur, pianiste et chef d'orchestre Ladislav Simon. Il commence le piano sous la direction de son père à sept ans.
Après des études au conservatoire de Prague avec Valentina Kameníková, il est lauréat de plusieurs concours depuis 2001 (Concours du printemps de Prague, Concours Chopin de Majorque, Concours William Kapell). Il travaille ensuite à l'Académie de musique (HAMU) avec Ivan Moravec, et obtient la médaille de bronze au Concours Reine-Élisabeth, à Bruxelles. Il complète sa formation par une année à Zurich avec Homeo Francesche et deux ans auprès de James Tocca, à Lübeck.
Nommé soliste, de l'orchestre de la radio à Prague en 1994, il en est également le directeur administratif depuis 2001. Il effectue des tournées régulièrement, non seulement avec son propre orchestre, le SOČR, mais en tant qu'invité de nombreux orchestres symphonique d'Europe.
L'enregistrement des concertos de Schulhoff a été primé au MIDEM classique de Cannes en 1995.
Discographie
Jan Simon a enregistré pour les labels Supraphon, BMG, Radioservis et Clarton.
Tomášek Concertos pour piano - Jan Simon, piano ; Orchestre symphonique de la radio de Prague, dir. Vladimír Válek (23-, Supraphon SU 3819-2)
Musique pour piano tchèque : Jan Ladislav Dussek, Bedřich Smetana, Leoš Janáček, Erwin Schulhoff, Bohuslav Martinů - (, Bonton)
Erwin Schulhoff, Concertos pour piano - Orchestre symphonique de la radio de Prague, dir. Vladimír Válek (1994, Supraphon)
Notes et références
Liens externes
Liste des ouvrages dans le catalogue de la bibliothèque nationale tchèque
Site web de la radio tchèque
Site web de l'agence ARSKONCERT
Naissance en mai 1966
Pianiste classique tchèque | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 3,647 |
**PROVENDER GLEED**
A _Bildungsroman_
**JAMES LOVEGROVE**
SOLARISBOOKS.COM
First published 2005 by Gollancz
Ebook published 2011 by Solaris
an imprint of Rebellion Publishing Ltd,
Riverside House, Osney Mead,
Oxford, OX2 0ES, UK
_www.solarisbooks.com_
ISBN: (epub) 978-1-84997-202-4
ISBN: (mobi) 978-1-84997-203-1
Copyright © James Lovegrove 2005
Cover Art by Pye Parr
The right of the author to be identified as the author of this work has been asserted in accordance with the Copyright, Designs and Patents Act 1988.
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of he copyright owners.
This is a work of fiction. All the characters and events portrayed in this book are fictional, and any resemblance to real people or incidents is purely coincidental.
**PART I**
From _Kin!_ magazine—"Your Weekly Guide to All That's Hot and All That's Not in the World of the Families':
**Provender Turns 25**
Provender Gleed hits the quarter century next Tuesday, and ClanFans all across the country will be holding street parties to celebrate.
But Prov himself has no plans for a bombastic birthday beano.
A Gleed Family spokesman commented: "The young master will treat the day just like any other. He attaches little importance to anniversaries and other such events."
Of course, with the Gleed summer ball this weekend, Provender will probably be all partied out by the time his personal silver jubilee comes round.
Blue-eyed Prov is very much the dark horse of the Gleed Family, a man of mystery who shuns the media spotlight, unlike the majority of his relatives.
Even at almost 25, he is still unmarried, which is a source of consternation among the Gleeds, with Provender being the firstborn (and only) male child on the Family's primogeniture bloodline.
Insider Gleed sources say that his mother Cynthia is tearing her hair out trying to match him with a suitable bride. But apart from last year's brief dalliance with Adèle Fforde-Nevant and a trial date with Inez Lamas, a distant cousin on his mother's side, Provender has not been successfully linked with any potential marriage material, Family or otherwise.
His continuing single status, however, is a ray of hope for countless female ClanFans. Organisations such as One Bride For One Provender and Thicker Blood have dedicated themselves to sourcing the Gleed heir a mate from the ranks of ordinary folk.
Members of The Brides of Provender have gone a step further, taking a vow of chastity that will end only when one of them is wed and bedded by the man himself.
Then there's Beardless, the militant gay pressure group who insist that Provender should not be forced into marriage when it is obviously against his inclination.
And what does Provender make of all this?
As he hardly ever ventures outside the grounds of Dashlands and never gives interviews, it's a moot point. The official Gleed line is: "No comment."
Still: happy birthday for Tuesday, Provender!
**Next week's _Kin!_ will carry full pictures of the arrivals at the Gleed ball, plus analysis and commentary by Family experts.**
From the Court and Social section of the _Daily Dynast_ :
The Gleed Summer Ball will be held at Dashlands, Berkshire, on Saturday June 30th
The theme is Renaissance Venice and guests are expected to attire themselves appropriately.
Start time is 8.30 p.m. for 9.00 p.m. Carriages at dawn.
Entry will be refused without valid invitation.
Unauthorised guests will be shot.
**1**
YOUR INVITATION TO the Gleed Summer Ball, had you one, would have arrived by courier six weeks in advance of the occasion. It would have come in a bonded-vellum envelope, eight inches by six, the flap sealed with a blob of crimson wax bearing the imprint of the Gleed Family seal, which depicts a nutmeg drupe, partially split open to reveal the kernel, and the legend "In Condimentis Pecunia". The invitation itself would be printed on card of extraordinary smoothness, with an icing-sugar-like finish which would seem to cry out to be stroked. Holding it close to your nose, you would detect a faint aroma which you would find delicious but hard to identify—sandalwood, cinnamon, ginger, something like that. The card would appear to have been impregnated with a scent redolent of the original source of the Gleed Family fortune, spices.
As for the text on it, this would have been printed in an elegant sans-serif font designed specially for the Gleeds some eighty years ago by none other than Eric Gill. Indeed, in printers" typeface catalogues the font is known by the name "Gleed". Its contrasting thick and thin verticals might suggest to you expansiveness coupled with caution, or perhaps, if you were of a more cynical bent, financial satiety gained through the impoverishment and starvation of others.
Be that as it may, you would not be paying much attention to the font, or even to the way the characters project from the card, thermographically raised, shinily black, like flecks of jet. Rather, you would be concentrating on the words themselves, and in particular that all-important opening line: "You are cordially invited to..."
Now, with this invitation you would be entitled to approach the main gates of Dashlands, the Gleed Family seat, on the appropriate date at the appropriate time. You would doubtless be clutching the invitation tightly as your vehicle turned off the M4 and began to navigate the tortuous labyrinth of country lanes leading, eventually, to those gates. Holding the invitation in your hand would not in any way hamper your driving abilities because you would not, of course, yourself be driving. A chauffeur would be doing that for you. If you did not have a chauffeur, if you were in some sort of automobile that was not a limousine, then you would not be attending the party in the first place. You would have no right to.
At the gates you would encounter the first line of security. Your car would be flagged down by a group of intense-looking, large-torsoed men dressed in jumpsuits and body armour, with sidearms holstered at their waists. They would peer in at you, scrutinise your invitation, check its watermark with a UV light, compare your face against a register of guest names and photographs, frown at you in much the same way that a hungry fox might frown at a hen, and eventually, and with seeming reluctance, wave you through. Meanwhile a mob of paparazzi and TV cameramen would be jockeying behind barriers for a clear shot of your face through the open window of your limo. Flashbulbs would be flickering like lightning. If recognised by this jostling journalistic throng, you would hear your name being called, howled, ululated, in order to get you to turn a certain way. In the unlikely event that you were someone nobody recognised, you would still be photographed but you might be subjected to a few sneers and jeers as well from the press pack. You might even hear such remarks as "Who are you?", said almost indignantly, and "You're nobody. Even you don't know who you are."
Kept further back from the gates than the newshounds, you would spy numerous ClanFans, popping away at your with their little cameras, their Instamatics, their Polaroids. You would not, if you had any sense or self-respect, pay these people any heed.
Past the gates—high gates, towering iron structures topped with gilded spikes, gates that would not disgrace the entrance to heaven—you would cruise along a drive lined with immense cedars. It being the height of summer, the trees would be at their lushest and most frondsome. They would resemble, you might say to yourself, great blue cumulonimbus clouds.
Then, a mile on, you would come to a second line of security, a manned barrier flanked by tank-traps—twists of steel girder wreathed in barbed wire. This second appraisal of your identity and your invitation would be to ensure that no one else had manifested inside your vehicle since you entered Dashlands—no one had emerged, perhaps, from a place of hiding under the seat or in the boot (this has happened in the past). It would also be to ensure that your limo had not, for some reason, left the drive and taken a detour across the grounds, an act which could only be construed as nefarious. In other words, you hadn't tried to smuggle in some gatecrasher and you didn't have some sinister ulterior motive for being on the Gleed estate.
Safely through the barrier, you would find yourself on the final approach to the ball. Dashlands House itself would just be coming into view. You would have a glimpse of its multiplicity of pitched and flat roofs, its jutting monolith-like towers, its sideways-protruding concrete balconies, its sliver-thin windows, its open-face stonework... and then your car would be guided off the drive by an official with fluorescent orange batons, who would direct you towards another similarly equipped official who, in turn, would direct you towards yet another such official who would instruct you, or rather your chauffeur, to park the limo in a cordoned-off area at the end of one of several long ranks of already-parked limos. Your vehicle would then become just one of many top-of-the-range marques and models—Cowley Torpedoes, VW Haifisches, BdM Atalantas, Dagenham Grey Spectres, Savage Ariels—and the splendour of its tailfins and hood ornament and whitewall tyres and running boards and spoiler and metallic paintjob would be signally diminished by proximity to cars of the same calibre, in the same way that an individual diamond, whatever its carat count, will lose its lustre when placed among a host of other diamonds, the dazzle of the whole subsuming the beauty of the one.
Still and all, this would not matter to you, for you would have a party to attend. You would be about to partake of the famously lavish Gleed hospitality. You would have your costume on. Let us say that in keeping with the theme of this year's ball you had adopted the traditional Venetian _bauta_ , consisting of a tricorn hat, a cape, a white mask, and a large black, full-cut mantle coming down from your head to cover the top half of your body—stifling to wear on such a warm night but striking apparel nonetheless. Or else you had come as a _dogaressa_ , a chief magistrate's wife, with a pointed cap and a high-collared brocade cloak worn over a silk ballgown. You would, quite naturally, be feeling resplendent, socially accepted, top of the tree, as you left the limo and followed a path towards the site of the soirée. The ball would not be taking place at the house itself but at a specially constructed venue set apart from the building. Not only would signposts be directing you towards it, the glow of light against the dusk-steeped sky would be drawing you, moth-like.
But before you got there, a third and final line of security. This one perhaps the most daunting of all.
Greeting you at the perimeter of the party site would be Carver. Carver, the Gleeds" major domo. Carver, the head of the under-the-stairs household. Carver, right-hand man to the wheelchair-bound Gleed patriarch, Great.
Carver would be standing there dressed in a frock coat finished with gold epaulettes and braid, his hands all but covered by lacy shirtcuffs, buckled shoes on his feet, a periwig perched on his head. You would catch sight of him, and whoever you were, however important you were, whatever your net worth, your status in the world, there would inevitably be a catch in your step, a falter in your stride, a brief, trepidatious hesitation.
For Carver is a forbidding presence. He would gaze on you with a respect that was somehow just a shade away from cold contempt. He would bow to you, ever so slightly, and as his eyes looked up at you through their beetling white brows they would be narrowed, ever so slightly.
It would strike you, if you had never set eyes on Carver before, that this was a very old man, in his eighth decade at least, if not his ninth. It would also strike you that this was a very tall man whom age had not, as it does so many, stooped. You would mark the breadth of his shoulders and the power that they still seemed to contain. You would note the economy of effort in that bow he made, and the lack of stiffness. This was not, you would conclude, someone who suffered from any of old age's physical shortcomings, or if he did, did not let it show.
Most of all your eye would be ineluctably drawn to the deep scar in Carver's left cheek, the result of a wound inflicted long ago in his youth. You would, if you knew anything of the life history of this domestic servant, recall that Carver served as an infantryman in the last world war but one. You would be aware that he accompanied Great Gleed as batman during the protracted and bloody Eastern Front campaign. You would know that he saw action in Riga, Gdansk and Poznan; that he helped defend the vital rail link between Vilnius and Minsk; and that he took part in the Siege of Prague, the final and decisive battle of the conflict, after which victory was pretty much a mopping-up operation. It was in Prague, on the Charles Bridge, before the big push into Wenceslas Square, that Carver received a bayonet-thrust in the face, courtesy of a trembling teenage Czech conscript who seemed more alarmed than elated at what he had done and became further alarmed when Carver seized the bayonet with his hand, calmly detached it from the barrel of the conscript's rifle, slid the blade out from his cheek, and proceeded to bury it hilt-deep in the conscript's own head. Eschewing medical attention, for the rest of that day Carver continued to fight using his right arm only, his left hand occupied with holding the two sides of the gash together.
So now this weathered face, with its disfigured left half, would be staring at you, waiting for you to say your name. You would be trying not to stare back, most of all trying not to fixate on the scar and how horribly puckered the scar was at its edges and the way the scar pulled down the outside corner of Carver's left eye... and then you would collect yourself, moisten your strangely dry tongue, and give your name.
Carver would then turn and announce you. In a voice sepulchrally deep, like the grating of a stone door in some vast cellar, he would let the guests already arrived know that one more had been added to their number. And then, instantly forgetting you, he would turn to the person waiting in line behind you; and you, not without some relief, would move on, stepping forward to immerse yourself in the brightness and bustle, the opulence, the sumptuousness, the sheer astonishing profligacy that was the Gleed Summer Ball.
Yes, all this would happen if you had an invitation.
But of course, you don't.
Who are you?
You're a nobody.
Even you don't know who you are.
And what do you think _you've_ done to deserve being invited to a Family occasion?
**2**
"WHERE _IS_ PROVENDER?" said Cynthia Gleed, and sighed, knowing full well the answer. _Not here_.
She was addressing her two daughters, Gratitude, the elder, and Extravagance, the younger. Both girls were dressed in billowing shot-silk gowns, both sported half-face masks with large noses that hid their only-somewhat-less-large real noses, and both wore wigs so ludicrously high-piled and heavy that they had to be supported by steel rods attached to purpose-built, truss-like undergarments. This arrangement restricted movement considerably, and Gratitude and Extravagance had spent much of the past week practising how to walk in their party get-up. What they had come up with was an oddly stately, swanlike gait which gave the impression of being effortless but was anything but. For the most part, so as not to exhaust themselves, they kept still.
Cynthia herself had opted for an equally fabulous gown—hers beaded with freshwater pearls and fitted with saucily revealing organdie panels—but she had decided against a wig, preferring a teeteringly tall tiara set atop her own hair. She was no longer young and did not think her spine would accept the weight of an enormous wig, truss or no truss. (Her daughters, she predicted, would be suffering for their vanity for days to come.) Like them, she did have a mask, but hers was a basic black domino framed an array of glossy blue-black magpie feathers and set, lorgnette-style, on the end of a wand so that she could cover her face if she wanted to but also reveal it if she wanted to. Cynthia knew she was still beautiful at fifty-three. She knew, too, that she devoted a great deal of money and effort to remaining beautiful at fifty-three. Why hide what was so hard-won?
Gratitude, in response to her mother's query, gave as much of a shrug as her outfit allowed. "Haven't seen him."
Extravagance assayed a nod. "Me either. Not since lunchtime."
Cynthia sighed again. Really, that son of hers...
"Bet he's still in his room," said Gratitude.
"Moping," said Extravagance.
"Probably not even in costume yet."
"He's such a miserable sod."
"And a party-pooper."
"Sometimes, you know, I can't believe we share the same DNA."
"Now, girls," warned Cynthia, although it was hard to contradict anything they had said. "None of that. Anyway, till your uncle Fortune arrives, strictly speaking the party hasn't started. So Provender's not late. Not yet."
"Wonder what Uncle Fortune will do for an entrance this year," said Gratitude. "He won't arrive by elephant again. Not after last year, when he fell out of the howdah and nearly broke his neck."
"Besides, the theme was maharajahs then," said Extravagance. "Do you think possibly he'll abseil from a helicopter again? Not very Venetian, I know..."
"Doubt it. And I'm certain the bungee jump from a hot-air balloon isn't going to get a repeat performance. Remember? They got the cord length wrong. An inch lower and he'd have smashed his skull open."
"Uncle Fortune," said their mother, "will try and top himself. Not literally, but you know what I mean. Outdo himself. Uncle Fortune always does." She brisked her palms together. "Now then, we can't stand around nattering to each other. We must go and mingle."
Obediently, Gratitude and Extravagance turned and, grimacing with exertion, glided off. Cynthia herself turned and surveyed the party.
So far, an hour in, things had gone swimmingly. There had been no upsets—nothing, at any rate, that she had been told about or observed. If there were crises happening behind the scenes, they clearly hadn't been so severe that the domestic and catering staff couldn't sort them out. Cynthia was all set to step in if summoned and straighten out any kinks in the smooth delivery of hospitality to her guests. She had, however, spent hundreds of hours organising the ball and drilling various employees on their roles and tasks, precisely in order to ensure that nothing went wrong that could be foreseen to go wrong.
All that hard work paid off here, at this moment, as she looked upon the replica of Venice which had been erected in her back garden. A team of set-builders from Pinewood Studios had come in and worked for a month re-creating all of _La Serenissima_ 's architectural features and landmarks. This second Venice of polystyrene, plywood and custom board, covering the equivalent of three football fields, was thronged now with the great and the good of Britain and a fair selection of the great and the good from other countries as well.
Cynthia was standing at one corner of the Piazza San Marco. To her right was the Basilica, wherein a sprung dancefloor had been installed and an orchestra waited to play later on in the evening. To her left rose the Campanile, thirty yards tall and, as in the real Venice, crowned with a Golden Angel. The party's version of the Grand Canal ran alongside the piazza's far edge, winding through the rest of the "city" on a circuitous loop, passing beneath a Bridge of Sighs and a Ponte de Rialto along the way. Gondolas and a couple of _vaporetti_ were plying the waterway, ferrying guests on round-trips or between different "boroughs" of the party site, perhaps to San Polo where the revellers could try their luck at the gambling tables on the Rialto itself or else to Castello where, at an ersatz Arsenale, they could shoot twelve-bores at luminous clay pigeons. There was a Lido (swimsuits, towels and changing rooms were supplied, although there would be few takers, few guests willing to unpick their elaborate costumes and hairdos just for a brief dip) and near that there was a stage where a troupe of circus performers were putting on a continuous programme of juggling, fire-eating, unicycling, and high-wire walking, some of them doing all four things simultaneously. Food, naturally, was in plentiful supply—nowhere were you out of sight of a buffet table—and waiting staff dressed as Harlequins and Columbines circulated bearing salvers of drinks.
Nothing had been left to chance. Many millions of pounds had gone to ensure no guest could claim, by the night's end, that he or she had not been thoroughly, amply, unstintingly, repletely entertained.
To judge by the faces Cynthia could see, lit up by the myriad strings of lightbulbs festooned across the piazza, the ball was well on its way to achieving that aim. There were smiles everywhere she looked, and where there weren't, there were frowns of the mildest sort—the frown of someone forced to choose between a dozen different kinds of stuffed olive, the frown of someone listening avidly to another's words, the frown of someone unable to decide which of the many amusements on offer to partake of next.
Her eye then alighted, however, on one disgruntled face which didn't have a mitigating excuse for its expression, a face which was genuinely, miserably frowning.
Great, parked halfway along the piazza's west side in his wheelchair, glared at the partygoers who flocked to and fro in front of him. The Gleed patriarch, oldest living member of the Family, was not happy.
But then, when was he ever?
Feeling a tug of reluctant obligation, Cynthia went over to him. Fluffing out her skirt and petticoats, she crouched in front of him like a deflating hovercraft, so that he and she were eye-level with each other. His glittering blue gaze settled on her and took a moment to place her. When it did, his scowl eased, if only slightly. The horizontal lines thinned but remained put, looking like a musical stave on which the many liver spots that dotted his brow (and the rest of his pate) resembled so many crotchets and minims.
Great tried to open his mouth, but all the action achieved was a drooping of one corner of his lower lip which exposed a couple of slanting brown teeth. At the same time, the only part of his anatomy other than his face that was not paralysed began to move. His left hand started to beat sideways against the wheelchair's armrest, his signet ring hitting the tubular-steel frame with a sharp, resonant tap.
"Hello, Great," said Cynthia. "You're having a nice time I trust."
The rhythm of Great's taps increased, becoming irregular.
"How many summer balls does this make it?" Cynthia went on. "A hundred and seven? Something like that."
Great's head jiggled in such a way that he could either have been nodding or shaking it.
"I hope it meets with your satisfaction. We've gone all-out this year, haven't we. No expense spared. After all, what use is it being Family if we can't show off the fact that we're Family?"
Cynthia fancied she saw agreement in his eyes. Great's eyes were the one feature of him that remained truly expressive. Usually baleful, sometimes they seemed to register approval of what they saw, as now. But that, Cynthia thought, might just be her own imagining. Eyes, when the face around them was slack and all but immobile, gave away very little.
"Carver's got another forty minutes or so till he's done with his announcing duties. I expect you'll be needing him by then."
Carver not only attended to all of Great's physical requirements, such as feeding him and changing his incontinence pants; he also had an uncanny, almost supernatural ability to interpret Great's thoughts and wishes. Having served Great for many a decade, first as batman, then as personal valet, Carver had developed an understanding of his master that went beyond intimacy and bordered on the psychic. Since the old man's paralysis had set in, Carver had become his mouthpiece, his messenger, his intermediary. When you spoke to Great in Carver's presence, you actually spoke to Carver, and when Carver replied, that was Great replying.
Which was why Cynthia liked to talk to Great when Carver was _not_ around. It might not be a dialogue as such, but at least she felt she was communicating with Great himself rather than with his glowering dragoman.
"Well, anyway," she said, rising. "Nice chatting with you, Great. I must go and grin at a few more guests."
Great's head jiggled again. The leathery wattle that hung below his jaw quivered.
"And," she added, with a speculative glance around the piazza, "if Provender doesn't show soon, I may have to go and roust him out from wherever he's hiding."
Mention of Provender's name appeared to excite further agreement (or perhaps disagreement) from Great. His head jiggled more agitatedly. His wattle quivered so much it almost vibrated.
Cynthia strode across the piazza. She had just spied her husband, whom she recognised without difficulty even though his features were almost entirely hidden beneath a _larva_ mask. Her husband was busy chatting up an attractive young woman. Cynthia made a beeline for him.
En route, she was accosted by: one of the most successful movie directors in the world; a Saudi princeling; the editor of the UK's most Family-friendly broadsheet newspaper and his tabloid counterpart; a Texan oil baron; Greta von Wäldchenlieb, wife of the head of the premier Teutonic Family; a pop star whose name Cynthia did not know but whose face she did because he had been given Gleed patronage and was riding high in the charts on the back of that; a duchess tangentially related to the British royals; and a peer of the realm who had done the Gleeds several favours in the House of Lords. While Cynthia could have happily stopped and made small talk with any of these, and indeed should have in order both to play the gracious hostess and to reinforce her and her Family's superiority over them, instead she bypassed them all with a wave and an airy smile. Her husband was her target and she could not afford to be diverted from reaching him. Just a few moments" delay, and next thing she knew, he would no longer be on the piazza and neither would the attractive young woman.
"Prosper!" she cried, pulling up alongside him. "I've been looking all over for you." She placed a hand gently but proprietorially on his elbow. "We must talk. Oh, but who's this lovely young creature?"
Prosper Gleed shot his wife the fiercest of glares before composing himself and introducing her to... "Ahh. Awfully sorry. I don't think I caught your name."
The attractive young woman was not amused. "Sophie," she said, in such a way that it was clear she had already told him, perhaps more than once. "Sophie Kilverton."
"Oh yes, that's right!" said Prosper. "And you're one of our artistic protégées, aren't you. A poet."
"A novelist."
"Yes, that's what I meant, a novelist."
Cynthia grinned at Sophie Kilverton—ostensibly a grin of greeting, really a grin of victory. She had been almost certain her husband would not have remembered the girl's name. Prosper was nothing if not predictable—predictably drawn to nubile females, predictably unmindful of such minor details as what they were called and what their occupations were.
"Well, Sophie," she said, "if you've no objection, I shall just drag my husband away."
"No objection," said Sophie Kilverton, frostily. "None at all."
"Cyn, honest, it wasn't how it looked," said Prosper, when they were out of the girl's earshot.
"Prosper, you know as well as I do that it was exactly how it looked. And while I couldn't give two hoots about your infidelities, attempted or otherwise—I'm way past caring about those—don't you think you could give it a rest, just for one evening? It is our party, after all. People are watching us."
"They wouldn't necessarily know it was me," Prosper said, touching his mask. The _larva_ was made of fine waxed cloth, with large eyeholes. Undoubtedly it disguised Prosper but it also left enough of his physiognomy visible that you could still tell he was good-looking, in an ageing, roguish, roué way. There were those grey eyes, in their charming beds of wrinkles. There was that bifurcated chin with its small underflap of skin that spoke of a man well-preserved for his age but displaying just an enticing hint of dissipation.
"Of course they'd know it's you," Cynthia said. "They'd know it's you by the puddle of drool around your feet. And anyway, why were you bothering with her?"
"What do you mean?"
"She's English. You've done England already. You've done all the major countries. It's only the smaller nations left on your checklist now. Djibouti, Tajikistan, Sao Tome and Principe, Vanuatu..."
Prosper had made it goal in life to commit adultery with at least one representative of every known country. He had never actually admitted as much to Cynthia but she had heard about it from reliable second-hand sources and indeed read about it in the Family column of one of the more scurrilous tabloid dailies. Prosper Gleed would, it seemed, not rest until he had philandered his way across the entire globe. Rather in the manner of the great empire builders of old, he hoped to see the map of the world coloured red with his conquests.
"Well, yes, but... You can't blame a chap for trying. Besides, I think she may have had some Welsh ancestry."
"But you've done Wales too."
"Wales. Ah yes, Wales." Prosper's eyes took on a wistful, faraway look. "There was certainly a welcome in _her_ valleys."
Cynthia ignored the remark. "So you're adding hybrids to the list now, is that it?"
"Actually, that's not a bad idea."
"Prosper..."
"No, dear. No, I'm not. Just kidding."
"Ha ha."
"So, what did you have to talk to me about?" Prosper snatched a flute of champagne from the tray of a passing Columbine, giving the girl the once-over as he did so. Sheer force of habit. "Something important? Or was it just a pretext to sabotage my chances with the delectable what's-her-name—Sophie?"
"Both. But mainly I was wondering if you'd seen Provender yet."
"Here? Can't say I have. Why, should he be here?"
"Of course he should. Apart from anything else, it's only polite. His absence will be noticed."
"Well, I'm sure he'll make it."
"I'm not."
"And I suppose the reason you want him here is you have some fine, marriageable little filly lined up for him to meet."
"Naturally. Two of them, in fact. You may recall my mentioning them at breakfast just this morning."
"Yes, absolutely," said Prosper, evidently having no memory of the conversation in any way, shape or form. About which Cynthia was not surprised. Half the time, things she said to her husband simply did not register. He might nod and go "Hmph", as though he were listening, but she knew the information was pouring down some bottomless hole in his brain as fast as it arrived there.
"You may also recall my saying that I have a good feeling about these two," Cynthia went on. "Neither's Family, but they're both well-born, interesting, intelligent, attractive..."
"Attractive?" Prosper perked up. "Don't suppose I ought to meet them, eh? You know, check them out beforehand. Vet them. Just to be on the safe side."
"Dearest husband, I am not letting you anywhere near those girls."
"Not even just a look?"
"Not even that."
"Spoilsport."
"Prosper." Cynthia was becoming annoyed now. "This may all seem terribly funny and trivial to you, but it's no laughing matter. We're talking about your son. We're talking about the last and only male on the primogeniture line. The only branch left on the trunk of the Family tree. The future of the Gleeds. Provender must marry. He must produce an heir. If he doesn't—if, God forbid, he dies without leaving a son—then we're sunk. We fade into obscurity. We lose continuity and status and all that makes us a Family. You know this as well as I do, and yet you still can't seem to take it seriously. And here I am, doing my best to get our son paired off, going to all this effort on the Gleeds" behalf, and I'm not even a born Gleed, I just married into your damn—"
She broke off, interrupted by a salutation from a guest, some jowly non-Family plutocrat whose name temporarily escaped her but whose obeisant overtures could not go unacknowledged. By the time she and her husband had finished assuring the plutocrat that yes, he was "in" with the Gleeds—and she had consented to the man's request of the honour of a dance later—Cynthia had lost the head of steam she had built up. She was still angry with Prosper, still incensed that she alone was bearing the burden of finding a mate for their son, but the moment had passed. Continuing to remonstrate with her husband was not going to get her anywhere. Tonight was not the time for it; the party was not the place.
"Look," she said, "I realise how you like to appear frivolous, Prosper. I realise how important it is to you to be the playboy, the rake, the frequenter of casinos and racetracks. It's all very lovely and beguiling, believe me. It's why I fell for you, and even as I married you I hoped I might be able to change you while knowing I never would. The point is, deep down I know you care about this Family as much as I do and I know you're keen to see Provender settled down and I know you wouldn't exactly hate the idea of a grandson—never mind the continuity a grandson represents—simply because you'd love to play grandfather to one. So just... help me, that's all. Support me. That's all I ask."
Prosper looked chastened, though not for long. Contrition wasn't really in his repertoire. "Whatever you say, Cyn," he said. "Point taken. You're the boss. No argument here. Et cetera, blah blah blah."
Cynthia, for the third time in the space of quarter of an hour, heaved a sigh. She wheeled away from her husband and took herself to the waterside end of the piazza, where she rested her elbows on the balustrade and peered out over the Grand Canal. The sky was twilight purple and the canal was dark, though its surface glittered intermittently with reflected light. The water itself came from the mains but had been dyed to an authentically green Venetian murk. A gondolier paddled past, yodelling an operatic aria. He was one of several dozen tenors from the Gleed Academy of Music, Drama and Dance who had undergone a fortnight's intensive coaching, courtesy of genuine Venetian gondoliers, in the art of propelling and steering that particular mode of transport. The genuine gondoliers had grumbled that no amateur should be piloting a gondola, even around a fake Venice. None of them, however, could sing opera, and that was the main criterion for the job at the ball. Besides, they had been well paid for sharing their expertise with the tenors, so the grumbling had been perfunctory, more for form's sake than anything. It allowed them to go home with their consciences clear, the Gleed money that stuffed their wallets rinsed satisfactorily of the taint of professional compromise.
Cynthia thought of this and all the other snags she had had to deal with on the way to making the ball a reality. It was the same every year—a horde of obstacles to overcome, pitfalls to anticipate, wounded egos to soothe—and no sooner was one ball over than she had to begin making plans for the next. She gave this Family her all. She did everything for them. She dedicated herself, sacrificed herself, for the greater good of the Gleeds, and asked little in return. And yet for all her efforts she was still unable to furnish them with the one thing they needed most. And this was becoming more and more anguishing to her.
_Oh Provender_.
Cynthia glanced up at the sky. When it was fully dark... No, when Uncle Fortune came. Then Provender would be joining the party, whether he liked it or not.
**3**
"I'M SCARED," SAID the Columbine, in a quiet voice. "Really scared."
"Don't be," said the Harlequin. "Everything'll be fine. This is going to work."
"But what if something goes wrong?"
"It won't."
"And what if he doesn't even notice me? What if he just ignores me?"
"He'll notice you, not a doubt about it. Especially with that little lot on show." The Harlequin gestured at the Columbine's breasts, which were naturally large and whose largeness the balconette bustier of her dress was doing very little to disguise. Her breasts, indeed, appeared to be in competition as to which of them was going to squeeze itself free of the bustier first.
The Columbine placed an arm across her cleavage, unhappy at the Harlequin's leering scrutiny.
"What's the problem?" the Harlequin said. "You shouldn't be ashamed. Tits like those. Should be proud. And anyway, it's not as if I haven't seen them before."
"It's different."
"If I remember rightly, you even wanked me off with them once."
"It's different," the Columbine insisted. "Things are different now." Colour had come to her cheeks and she could not meet the Harlequin's gaze. "I'm not your girlfriend any more."
"That could change."
"No, it couldn't."
The Harlequin let it lie, although his eyes said he didn't believe her. She was protesting too much. She still fancied him. Of course she did. Bloke like him? Strong? Worked out at the gym a lot? Smart? Committed? With a cause? Irresistible.
"Listen," he said, his voice softening, becoming almost gentle, "you're going to do fine. I mean it. The plan's sound. You—you're intelligent, beautiful. You'll play your part just right. I have every confidence in you."
The Columbine looked up at him again. In spite of her better judgement, against her every instinct she had, she was consoled by his words. She wanted to believe in him. He had hurt her in the past. He could be cruel. But she was convinced that at heart he was good. She was sure she could trust him. And if he had confidence in her, there was no reason why she shouldn't have the same confidence too.
"All right," she said, and she took a deep breath which helped stiffen her resolve and which was also, from the Harlequin's point of view, a good thing because it resulted in a temporary increase in the ratio of exposed breast flesh to unexposed. "All right," she said again, exhaling. "I'm fine. Everything's going to be fine."
She picked up a salver of drinks, the Harlequin did likewise, and together they exited the catering marquee, returning to Venice and the party.
**4**
UNCLE FORTUNE—FORT for short—had elected to arrive at the ball this year by parachute.
For him, in all sorts of ways, this was no mean feat. For one thing, Fortune was not of a naturally athletic build or disposition. He had the kind of figure that was most politely described as cuddly, the kind that, far from being aerodynamic, best lent itself to plummeting like a stone. For another thing, he was notoriously bibulous. He seldom did anything without alcohol in his veins (and that included eat breakfast).
The parachute instructor he hired to teach him, however, was aware of his reputation and impressed on him the unwisdom of skydiving while under the influence of alcohol. One might, the instructor said, if one jumped drunk, make a careless mistake. An irrevocable mistake. Such as, for example, forget to pull one's ripcord.
So it was a strange and novel experience for Fortune to embark on a potentially life-threatening enterprise without his customary cushion of inebriation. But he knuckled down and got on with it. First in tandem with the instructor, the two of them joined by a harness like Siamese twins, and then solo with the instructor alongside him, Fortune performed a series of jumps from his private dirigible at ever increasing altitudes. By the end of the course of lessons, he had become a proficient parachutist, able to hit a ten-foot roundel painted on the croquet lawn at the back of his manor house every time without fail. Apart from slightly spraining his ankle during one landing, he had not suffered any sort of injury and was proud of that.
Now, on the night of the ball, shortly before nine p.m., his dirigible nosed across Dashlands at a height of two thousand feet with its running lights doused so that it was all but invisible—if spotted, it would in all likelihood be taken for a cloud. Below, the party site glowed bright, unmissable. Fortune strapped on his parachute pack, went through his final equipment checks, slid open the cabin door, bid farewell to his pilot, reflexively groped for his hip-flask, remembered he hadn't brought it, and threw himself out into the night.
Everything went according to plan—almost. After a ten-second freefall Fortune yanked the ripcord, the parachute billowed open above him with the customary explosive _snap_ , his harness constricted around him, not unpainfully, and for a while he swung dizzyingly to and fro. When things settled down, he grabbed the guide-rope handles and began steering. Venice loomed beneath his feet and the partygoers swelled from milling dots to identifiably human shapes. The Piazza San Marco was his goal, although landing in the Grand Canal remained a possibility—he hated the idea of a soaking but the stunt would be funnier and more memorable if he came down with a splash.
Soon Fortune was low enough that he could even make out, or so he thought, his brother. He was about to yell out Prosper's name, and thus alert everyone to his imminent arrival, when a sudden crosswind caught him. In order to counter it he dipped one side of his parachute, but he could still feel himself being driven relentlessly and inexorably off-course, away from the piazza, towards the rooftops. The Campanile rushed up at him. _Please, O Lord, don't let me die_ , was Fortune's brief, fervent prayer. _Not like this. Not sober_. Then he screwed his eyes tight shut and braced himself for impact and possible impalement.
When he dared to open his eyes again, he found that he was dangling some thirty feet above the piazza's paving stones. A crowd had gathered beneath him and anxious voices were calling up, wanting to know if he was all right. He looked up and saw that his parachute had got hooked over the Golden Angel. He was suspended helplessly but harmlessly from the Campanile like some sort of novelty decoration.
Fortune began to chuckle.
When someone below informed him that a ladder was being fetched, he chuckled even more. "Tell them to bring up a snifter of brandy while they're at it," he called down.
Ten minutes later, Fortune was safely on the ground and receiving applause from the assembled partygoers. The applause, as was often the case, had a note of sycophancy to it. Applause usually did when you were Family. Nonetheless he accepted it with a gracious nod, and then he hugged Prosper, kissed sister-in-law Cynthia lavishly on both cheeks, made a typical bachelor-uncle fuss of nieces Gratitude and Extravagance, and in no time had a bottle of claret in each hand and was well on his wassailing way to total inebriation.
His costume, incidentally, was that of a devil. Red bodysuit, horns on his head, scarlet face-paint, short three-pronged pitchfork, and a fake goatee beard of hellish blackness.
UNCLE FORTUNE HAVING arrived, Cynthia could not put it off any longer. Provender would be coming to the ball even if she had to grab him by the scruff of the neck and drag him here.
She left the piazza. She threaded through the thoroughfares, the _salizade_ , the canalside _fondamente_ , till she reached the edge of Venice. Then she took off along a lamp-flanked path of crushed quartz that led towards the house. The party dwindled behind her, the sounds of conviviality fading, the shotgun reports from the Arsenale becoming nothing more than faint popcorn _cracks_. By the time she arrived at the house, all Cynthia could hear was the crunch of her own footfalls.
Dashlands House invited her in through a square archway into a courtyard which gave onto another courtyard via another square archway which in turn gave onto yet another courtyard via yet another square archway. The last courtyard, the largest of the three, boasted a rectangular lily pond which butted up against the lofty, narrow windows of the largest drawing room. A broad, low loggia led to one of the house's two main entrances. Twin teak-panelled doors swung inward, affording access to a chamber that was as much atrium as entrance hall—cylindrical, capped with a conical ceiling made up of arcs of iridescent glass. Gold-patinaed sconces held candle-shaped bulbs which shed a buttery light over the marble floor and the cuboid table-and-chair set that occupied a space next to the passageway into the drawing room. A rising concrete staircase hugged the inmost half of the wall, complete with wrought-iron handrail. But the hall's dominant feature was the twenty-foot chryselephantine statue which stood dead centre.
She was called Triumph and she held a pose that was part exaltation, part ecstasy, her legs together, her hips and breasts thrust forward, her head thrown back, one arm stretched in front of her, the other upraised with its fingers knifing to the heavens, like a gymnast about to begin floor exercises. Her face was incongruously inexpressive, with blank eyes and placid mouth, but then it did not need to convey much when her body was talking so eloquently. She was, it seemed, on the verge of something, some vast and longed-for release. Solid and gleaming and chunky, she had lines like a locomotive, and she waited, she only ever waited, poised, ready to commence. Triumph.
Depending on her mood, Cynthia could find the statue daunting, inspiring, oppressive, and, occasionally, vulgar. This evening, with certain matters weighing heavily on her mind, she thought Triumph looked silly and vain, an old tart in a posture too young for her, hoping for admiration. She passed around the statue and ascended the stairs, noting halfway up that Triumph's left shoulder bore a thick coating of dust. She would have a word with Carver about that.
Nowhere on all the acres of land it occupied was Dashlands House more than three storeys tall. It spread, it sprawled, but even its highest roof apex was a mere thirty feet from ground-level. Contained within it, however, was any number of midways and mezzanines. Rare was the room that shared the exact same horizontal plane as another room, and rare the corridor that did not terminate in a short flight of steps. Some of the larger rooms were in themselves multi-tiered, with platforms and pits denoting various separate sections. Sometimes, to Cynthia, the place felt like an indoor obstacle course. It was impossible to walk through it at any speed because every dozen or so paces you were obliged to break stride and turn a corner or go up or down. Frank Lloyd Wright had had a hand in its design, but you could be forgiven for thinking Maurits Cornelis Escher hadn't also been somehow involved.
Eventually she came to its northernmost wing. As she neared the door to Provender's suite of rooms, she heard the rattle of brass keyboard keys. Provender was at his videotyper, probably hammering out another entry in that journal of his. Cynthia tapped softly on the door with the rim of her mask, expecting that he would not hear this above the furious clatter he was making. He didn't, and so she opened the door uninvited, knowing that if Provender complained about the intrusion she would be able to tell him in all honesty that she _had_ tried knocking.
The blinds were drawn. All the lamps were switched off. The only illumination in the suite's main room came from the videotyper's screen, in front of which Provender sat hunched, staring fixedly into its small glowing oval. His brow was ploughed in concentration. His shaven head nodded as he typed. On the desktop beside him, the videotyper's operating unit whistled and droned in its brass housing. It was a Japanese make. In spite of the fact that the Gleeds owned several patents on British circuit-board technology, Provender insisted that the Japanese produced better machines and so purchased with money what everyone else in the Family could get for free. If medals were handed out for perversity, Provender would have a lapel-full.
Cynthia did not step into the room yet. She stood in the doorway and studied her son, who remained oblivious to her presence. She saw a slender, well-proportioned nearly-twenty-five-year-old who until recently had sported a head of lustrous Cavalier curls but now wore just a down of shorn hair, like a velvety pelt. She saw a grown man. But she also saw the infant Provender had been, the chubby, babbling creature whom she had held and fed, fussed with and dandled, and watched over through many a wakeful night. She could not look at him and not think of the clear, unblinking eyes that used to gaze up at her while he was at suck and not remember the smell of his fine-downed scalp, rich and yeasty like baking bread. His gestures, his mannerisms, had all been there, ready-formed, and had changed little in adulthood. Provender was and ever would be her baby boy, and come what may, she adored him.
But that didn't mean there weren't times when she thought he could do with a good hard smack.
Cynthia gazed on Provender for a further minute or so, then loudly and fulsomely cleared her throat.
**5**
_T HE QUESTION WHICH needs to be addressed_, wrote Provender, _is whether extreme wealth is incompatible with an ethical life._
_No doubt there are many people for whom this question would seem otiose, even absurd. They would love to be in a position to ask themselves such a question. They would love to have that luxury._
_But for those of us who do have that luxury, and have an ounce of self-awareness, it is the only question worth asking. It is the question._
_For an answer, one might look back to the early years of the Gleeds, in the seventeenth century, when the family was not yet a Family._
_Rufus Alexander Gleed (b.1649—d.1707) was a merchant trader, and a successful one, specialising in the import of spices, particularly nutmeg, which was then gaining currency in European cuisine._
_He did well in a cutthroat business. British spice traders were in perpetual competition with the Dutch, and Indonesia and most of the Southern Seas had become a virtual battleground. Merchantmen raced one another to secure the latest crop, and clashes between ships of either country were not uncommon as they homed in on the same harbour, each hoping to be the first into port to secure the best bargains. Since most merchantmen were accompanied by a naval escort for protection, the skirmishes were known to cost vessels and lives._
_Neither the British nor the Dutch government was any too happy to keep supplying military support in this manner. It was a huge drain on their budgets and resources. Yet they continued to do so, grudgingly, because the national economic interest demanded it._
_Rufus Gleed's stroke of genius, if one can call it that, was to decide to bypass government involvement. He began employing privateers to escort his trading fleet. He took on the defence of his own ships as a business expense. He was even able to defray the outlay against tax. He made piracy in effect a tax write-off._
_His privateers, unhindered by rules of engagement, were fiercer and more aggressive than any Dutch naval captain. They would attack without provocation. They harried Dutch ships mercilessly. With them there was never any parley. They argued with the voice of the cannonade._
_From being merely successful, Rufus became unimaginably successful. His ruthlessness (and that of his privateers) paid off to such an extent that he began to consider himself eligible for Family status. In a latter written to a nephew in 1693, and now kept at Dashlands in the Gleed archives, he states his intention thus:_
_"In that I am now among the richest men of Englande, and am blest with issue in the forme of three Sonnes and lately a Grand-sonne, it seems that it should be my purpose to raise myself and my progeny to the rank of Family; and this being so, to that end I have made Supplication to the Borgia de De'Medicis of Italy, who as the very first and original of the Families are endow'd with the Responsibility of bestowing or otherwise said Privilidge, and it is my full Expectation soon to be in receipt of Documents confirming their accession to my Desire..."_
_However, not long after his "Desire" became a reality, Rufus found himself in a direct conflict with a fellow spice trader, also recently Familied: Pieter van der Ebb. Van der Ebb had decided to adopt the same tactics as Rufus and furnish his fleet with a privateer bodyguard._
_What ensued was a protracted and violent spice war whose effects are still being felt to this day (its most trivial legacy may be found in certain Gleed forenames, including my own, embarrassing, never-to-be-mentioned-here middle name). Eastern Indonesia, and especially the tiny archipelago known as the Banda Islands, where most nutmeg is grown, saw an increasing incidence of bloodshed both on and off land. Down through the decades thousands of Bandanese were killed, caught in the crossfire between opposing groups of mercenaries employed by the Gleeds and the van der Ebbs. Several hundred Chinese immigrant workers met the same fate._
_The fighting was still going on even in the late 1800s, albeit sporadically. By then the van der Ebbs had, pardon the pun, ebbed in influence and power. As a result of a series of bad marriages and the premature deaths of a number of sickly offspring, more and more the van der Ebbs were finding themselves subsumed into the Kuczinski Family. Their name was dying out. The Kuczinskis were taking over their business interests and their lineage, and the van der Ebbs were shrinking to a rump. Over them fell the deepening shade of the Kuczinskis" rapidly expanding East European umbrella._
_Animosity toward the Gleeds, however, remained. The Kuczinskis subsumed that too. It entered into their bloodline and infected it, and has festered there ever since, bursting out at regular intervals and engulfing whole nations with its venom._
_It is also, undeniably, reciprocated. My father, for one, cannot mention the Kuczinski name without spitting._
_And this draws me to my point. There can surely be no Family which doesn't owe its fortune and status to the exploitation of others and the suffering of others. Somewhere in every Family's history there lies a heavy weight of guilt, never referred to, never expressed. We have built our empires on huge piles of nameless, forgotten corpses. We continue to sustain these empires in that way. We never admit it. It is too immense, too appalling a fact ever to be uttered._
_In the Gleeds" case, all we ever care to say—the official line, inculcated from birth—is that we started out earning our money from nutmeg._
_Such an innocent thing. Nutmeg. Everyone loves it. Everyone uses it. You put it in Béchamel sauce and mulled wine. Dopeheads say you can get high on it, although this is disputed. Its hallucinogenic properties are weak, if they exist at all. You have to ingest a hell of a lot to get a result, and more often than not that result is a bad case of vomiting follow by a cracking headache. I know this from experience. Never again._
_(Nutmeg also yields mace, a less innocent-sounding product, derived from the thin leathery tissue between the stone and pulp of the fruit. But mace, for all that by etymological accident it shares its name with a medieval weapon, is harmless. Merely another spice.)_
_So it eases the conscience just to say "nutmeg". It glosses over the awkward parts of Gleed history. In two soft syllables it sweetens the unpalatable past._
_How, then, to change that? How to tackle the truth of all the Gleed Family did—and still does—in the name of furthering its own ends and feathering its own nest? How to undo the sins of the forefathers?_
_I come up against this time after time. I wrestle with it at night. I ponder on it by day._
_The irony isn't lost on me that my sleepless nights are spent on a well-sprung bed between the softest of sheets, or that my daytime ponderings often find me strolling through a palatial house and a huge estate amid a host of domestic servants who call me Master Provender and would doubtless drop to their knees and lick my arse if I ordered them to (not that I ever would)._
_All the same, if I didn't have these thoughts and feelings, these doubts—this urge to somehow make amends—I would consider myself less than human._
_What I have yet to establish is how to go about_
The sudden throat-clearing shocked Provender out of his skin.
"Mother!" he yelped, crossly. "For God's sake! How long have you been standing there?"
"Not long," said Cynthia.
"Christ!" Provender rapidly tapped out a sequence of keystrokes, saving the journal entry and then blanking the file from the screen. "A man's entitled to some privacy, you know."
"Not when there's a party going on that he should be at." Cynthia strode into the room. Glancing through a doorway to her right she saw Provender's bed. His costume was laid out on it, untouched, exactly as she herself had left it that afternoon. Provender was still in his day clothes—open-necked shirt, corduroy trousers, brogues. "And you're not even dressed. Really, Prov, this isn't good enough."
"Um, what time is it?"
"Gone nine. You promised me. You promised me you wouldn't be late."
"I... lost track of time."
"I don't care. A promise is a promise. I'm very disappointed."
Provender tried to look as if her disappointment did not mean anything to him. "It's just a stupid party."
Cynthia tried to look as if she did not resent her summer ball being described as stupid. "In that case, then surely it needs someone like you to come along and raise the intellectual tone."
"Ooh, nice going there, Mum. Cunning piece of psychology."
"Yes, I thought so."
"And just how many nice young ladies are going to be paraded in front of me when I get out there?"
"I don't know what you're talking about."
"Come on. Two? Three?"
"It's possible I may have a couple of people I'd like you to meet."
"Female people?"
"Well, if you must be so gender-specific—yes."
"Mum." Provender reached down and switched the videotyper off. "You're a modern woman, wouldn't you say? Emancipated. Liberated. Doesn't this whole finding-Provender-a-wife malarkey strike you as just a bit, you know, anachronistic? Not to mention chauvinistic. At the very least, shouldn't I be left to do it myself, in my own time? You know, hunt my own fiancée fodder?"
Cynthia shrugged and nodded. "I can't disagree, it _is_ an anachronism. But it's also tradition, and Families are nothing if not traditional. Tradition is our bedrock. It's what people like about us. Bloodline. Take away the money, and that's the main source of public fascination: bloodline. I'm afraid it's your responsibility to be a part of that, and it's _my_ responsibility to make sure you discharge _your_ responsibility, and that's an end of it. Believe me, I'd happily let you, as you so charmingly put it, 'hunt your own fiancée fodder', if I thought there was the slightest chance of it happening. I would, I'd step aside and leave you to it like a shot. But since you don't seem able to even get up off your backside and start looking, I've no choice but to get all matchmaker on you. I'm sorry you find it all so irksome, but— Well, no, I'm not sorry at all. It's just tough _mierda_."
Provender, in spite of himself, smiled. His mother no longer believed, as she used to, that it was all right to swear in front of her children as long as she stuck to her native Spanish. However, the habit had become so ingrained that she continued to do it even now, when they understood perfectly well what she was saying. Not only that but, instead of preserving her children's innocence, she had managed instead to teach them a second set of obscenities to go along with the Anglo-Saxon ones they had picked up anyway from their schoolmates and peers. They were now, thanks to her, doubly proficient at swearing—expletive-bilingual.
" _Mierda_ , _madre_?" Provender said.
"Oh, don't start."
"Wherefore this Iberian invective?"
"I mean it. Stop."
"This Castilian castigation?"
"Stop it now. Put your costume on. Come to the party. Do as I say."
"This—"
"Provender!"
Her eyes flashed with pure exasperation. Anger would surely follow if Provender wasn't careful, and his mother's temper, when aroused, could be fearsome. It was the slumbering tiger you tiptoed around.
"OK, I'll come, I'll come," he said.
"Good. Thank you."
Cynthia crossed over to the row of windows that occupied all of one wall, giving access to a balcony. She rolled one of the windows open, to let in some air. The main room of Provender's suite was the size of a tennis court but even with all that space it could start to smell musty and stifling if he spent too much time there. A breeze wafted in around her ankles, bringing with it the scent and sound of waterfalls. There was a cascade directly below the balcony, a sequence of sluices and rock-pools that decanted into a stream and thence to a forest-fringed lake. Above the rushing water the night air thrilled with insects and misty spray.
Turning, she said, "Do you need a hand getting your outfit on?"
"Twenty-four, Mother," Provender replied, mock-wearily.
"I'll wait out in the corridor then."
"Do that."
"Five minutes."
" _Fine_."
**6**
FIVE MINUTES LATER, mother and son were making their way through the house. Ten minutes after that, they were approaching Venice.
By then Provender was already regretting his choice of costume. He had elected to go as the Medico from the Commedia dell'Arte, a kind of private joke since the character's look was derived from the outfits worn by real Renaissance doctors during times of plague. It amused Provender to think of himself at the ball as the one healthy individual among a batch of the diseased.
However, he was in a long black linen cape, which was hot and itchy, with a flat broad-brimmed hat, also hot and itchy, and worst of all was the mask, with its elongated beaklike nose and small round spectacles perched in front of the eyeholes. Navigating in this was phenomenally difficult. Wherever Provender looked, the nose was always in the way, obscuring a significant portion of his field of vision. He cursed himself for not having tried the mask on beforehand and wondered at what point he would be able to dispense with it—at what point he would feel his ironic statement had been sufficiently made.
On the plus side, he was equipped with a baton-like stick, like the ones the Medico (and the real Renaissance doctors) carried in order to be able to remove patients" garments from a safe distance. Even if no one "got" Provender's costume, there was always the option of whacking partygoers around the head with the stick to show them what he thought of them. No, not really. But he didn't doubt that he would at some point tonight be sorely tempted.
First to greet him on the Piazza San Marco was Uncle Fort, several sheets to the wind by now. Rocking unsteadily, Fort regaled Provender with an account of his arrival, pointing with pride to the parachute which still engulfed the Golden Angel like a squid, its severed ropes dangling tentacularly. "Thought I was a goner for sure this time!" Fort exclaimed, and his breath was the sweet-sour stench of a hundred vineyards, strong enough to assail his nephew's nostrils even through the Medico mask's prodigious proboscis.
Then came Gratitude, followed closely by Extravagance. Like galleons on a calm sea they sailed towards their brother, homing in. Cynthia, meantime, had melted into the crowd, and Provender knew it wouldn't be long before she was back with one or both of her marriage prospects in tow. He tried not to think about it.
His sisters gave him grief, in a sisterly fashion, for not turning up when he should have and for making their mother go to the trouble of fetching him. He in return, in a brotherly fashion, told them they could stick it up their wigs.
"You have obligations, Prov," said Gratitude. She was his elder by two years but often behaved as if it was more like ten.
"Fuck obligations," he replied. "I don't see why I should have to be here if I don't want to be."
"Oh, very mature," said Extravagance, who, though seven years younger than him, also behaved as if she were a decade his senior. "And what sort of costume is that? This is a ball, Prov, not a Halloween party."
"Really? So why are there witches here then?"
Extravagance went through an elaborate charade of not understanding the reference, then understanding. "Oh, I get. You mean us. Gratitude and I are witches. How clever. Sharp as ever with the putdowns, Prov. Obviously, spending hours on your own in your room does nothing to blunt the wit, does it."
"Is that the best you can do, 'Strav?" Provender replied. "Have a go at me for preferring my own company to that of others?"
"Oh no, I can do much better. I'm just getting warmed up. For instance, your slothfulness on the marriage front. I mean, what's it going to take for you to realise you _have_ to get some poor girl up the aisle, ASAP?"
"And if I don't, ASAP? What the worst that can happen? I get to spend a few more years single. Not such a bad alternative."
"Not for you maybe. Probably not for your putative wife either. But you know what's at stake, and still you faff around."
"I don't see you in any hurry to get hitched," Provender said. "You either, Grat."
"It's not so important for us" said Extravagance. "We can leave it as late as we like. No Y-chromosome. Sorry!"
"Best not leave it _too_ late. There's a limited shelf-life for the Y-chromosome-less, and spinsterhood can creep up unexpectedly. One moment you're young and lovely, the next you're a crocheting old hag."
"Cheap shot. But seriously, Provender, what if something happens to you? What if there's an accident or you get ill or something? What if—"
Gratitude stepped in. As the oldest sibling it usually fell to her to make peace between the other two. It had been that way since they were little, and she would not have minded so much if the level of the bickering between her brother and sister ever rose above childish, but it never did and probably never would.
"Listen, both of you," she said, low-voiced, stern. "Not now. Not here. We're on our best behaviour. You can argue all you want tomorrow. Tonight, we're one big happy Family. All right?"
Provender and Extravagance glared at each other, the tips of their masks" respective noses almost touching. Then both of them nodded, reluctantly, surlily. As the three siblings parted company, Extravagance turned and popped her tongue out at Provender. He, in response, brandished his stick at her. Each felt this constituted the last word and so was able to walk away satisfied, victorious.
Spying a Harlequin with a drinks salver, Provender made for him. He was almost at his goal when a partygoer stepped in the way, blocking his path.
"Provender. It is Provender, isn't it, under all that?"
"It is," said Provender, warily.
"Thought so. I'm pretty good on posture and gait. Got an eye for it. And yours are pretty distinctive. You always look like you're expecting something bad to happen."
It just did, Provender thought. "Arthur," he said.
"None other," said the partygoer, and executed a sweeping bow.
Provender's cousin had, like Provender, chosen his ball outfit from the ranks of the Commedia characters, but his was that of Scaramouche. Consisting of a multicoloured, gold-buttoned tunic, a feathered hat, a swirling moustache, and a sword at his side, the costume lent Arthur a swashbuckling look, which was let down somewhat by the fact that Arthur was a shade over five feet tall, five-two if he was wearing his lifts, and had ears that wouldn't have been out of place on a football trophy. Height, it would seem, was a prerequisite for successful swashbucklery, and so was a set of aural appendages that did not stick out sideways.
Arthur was the son of Prosper's other younger brother, the late Uncle Acquire. Uncle Ack, as he was known, had been the black sheep of that particular generation of Gleeds, turning his back on the Family and going off to live on a remote Scottish isle where he met, and for a while shared his humble croft with, a local girl who became Arthur's mother. Whether she and Uncle Ack were ever actually married was a question nobody dared ask. Ack died without mentioning her or her child in his will, at any rate, and so the Family chose to regard their union as not having the legality of even a common-law bond.
That was until the product of their union left the island in his late teens and came to the mainland, presenting himself at Dashlands and demanding to be treated as a proper Family member or else. What the "or else" consisted of was never made clear but it seemed likely to have something to do with the legitimacy or otherwise of Arthur's birth. Arthur appeared to be threatening to expose himself publicly as a Gleed bastard if he didn't get what he wanted, and rather than face that PR nightmare the Family decided instead to welcome him to its bosom, purchase him a fine London townhouse, furnish him with a handsome allowance, and help him get on in whatever trade or profession he might wish to pursue.
Arthur wished to pursue the craft of acting, and so was enrolled at the Gleed Academy of Music, Drama and Dance, from where he graduated _summa cum laude_ and stepped straight into his first starring role in a TV series in which he played a dashing police detective who solved crimes while moonlighting as a cabaret singer in his spare time. That Arthur was neither dashing, nor old enough to be a detective, nor any sort of singer, was not perceived as a hindrance to his getting the part. His principal qualification was that he was a Gleed. To have that surname in the cast credits guaranteed good viewing figures.
Thereafter, Arthur had never been out of work. Movies, comedy, radio drama, musicals—whatever type of role he set his heart on, he got. Some critics grumbled that he had no charisma or presence or discernible talent, that listening to him recite his lines was like listening to a washing machine running through its spin cycle. Not many critics expressed such opinions in their reviews, however, and few who did lasted long in their jobs. It wasn't a wise career move to be anything less than unstinting in your praise of a Gleed.
To say Arthur was smug would be an understatement. Being kind to him, one might aver that his smugness was warranted in so far as he had successfully blackmailed and bluffed his way into the Family's acceptance and then had shot to the top of the thespian tree despite his negligible acting ability. One might even admire him for his sheer nerve and gall.
Then again, one might, if one was Provender, dislike him intensely for that very reason. One might, indeed, make a point of trying to annoy him every time one encountered him, just to demonstrate one's feelings towards him.
"So, Art," Provender said, "how's tricks?"
Arthur did not care for "Art", but let Provender get away with it this time. "Not so bad."
"Haven't seen you on telly lately. Got any work? Or are you resting right now?"
Beneath the curlicued moustache, Arthur's lips went rigid. "'Resting', Prov?" he said.
_Gotcha_ , thought Provender.
During the time he had lived in England, Arthur had successfully managed to eradicate all traces of Scots brogue from his accent. He spoke Received Pronunciation with greater precision than many of those who were born to it.
"'Resting'," he said, in his archest, RP-est tones, "is a word used only people who aren't in showbusiness—people who like to think they're in with the jargon and know what's going on and what acting's all about. You will never, ever hear anyone in showbiz say 'resting'. No actor worth his salt would dream of letting the word pass his lips. And do you know why?"
Provender did, as a matter of fact. He had heard Arthur deliver this diatribe on at least two previous occasions, using almost the exact same words, with the exact same degree of pompous indignation. "Resting" was a red rag to this particular bull; or, if you prefer, it was the cue that invariably prompted Arthur to launch into a lengthy and probably self-penned soliloquy.
"Because," Arthur continued, "it isn't resting. It's anything but. When you're between jobs, you don't spend the time sitting at home making toast and waiting for your agent to ring. You're out there putting yourself about, going to audition after audition, callback after callback. You're phoning people, you're having meetings with producers, it's one long constant slog, and it's exhausting, let me tell you, it's not _resting_ , it's the complete bloody opposite."
"OK, right," said Provender. "Yes. Silly me. Thanks for setting me straight on that one."
"No problem. You're welcome. But honestly, it does get on my tits when I hear someone say 'resting'. They clearly have no idea what they're talking about."
"Clearly." Provender paused, then added: "But—forgive me, Art—but has there ever been a time when you've actually been between jobs? You seem to know all about it but, as far as I'm aware, you've never had a problem getting work and you're always saying how your diary's booked solid for the next three years."
Arthur's eyes narrowed, and his teeth came together with an audible _clack_ , and his neck straightened, and Provender congratulated himself on a hit, a palpable hit.
"I am speaking, not for myself, but for all actors," Arthur said stiffly. "All my brethren and sistren in the craft. All us jobbing thesps. I've been fortunate, yes, I won't deny it, luckier than most, but it's a precarious living, acting. Who knows, three years from now I might be looking at a diary full of blank pages. I doubt it but there's always the chance. Besides," he said, recovering some of his previous vim and vituperativeness, "at least I _have_ a job. At least I do something to earn a living. There are those of us who can't say the same, aren't there, Prov? Quite a few names spring to mind."
Provender tried not to flinch; not to let Arthur know that the barb had struck home. "You don't need to work, Arthur."
"And yet I do," Arthur replied. "I choose to. It would be perfectly possible for me to swan around all day long, the living epitome of the idle rich, all 'la la la, look at me, I've never put in a day's graft in my life"—but I don't. I get out there. I roll up my sleeves, muck in, _achieve_. And I have to say, doing that makes it a damn sight easier to look at myself in the mirror every morning."
Provender bit back the obvious retort. Too easy; and more to the point, he was suddenly finding himself on the losing end of the exchange, and a cheap crack about Arthur's looks would only incite his cousin to attack with even greater viciousness.
As it was, Arthur did not seem willing to relent just yet. "Yep," he said, "having a job sets you free, definitely. It sends you to bed with a clean conscience. It gives your life structure and focus. It prevents you from getting obsessed with yourself, bogged down in your own thoughts. Generally a good thing, Prov, work. Take it from one who knows. Oh, and in answer to your original question, yes I'm working right now. Well, not right this moment, but you know what I mean. I've no idea how it's passed you by, when _everyone's_ talking about it. I'm doing _Hamlet_ in the West End."
He left a pause, waiting for Provender to be impressed. When Provender just gave a noncommittal nod, he went on, "Yes, I've never tackled Shakespeare before, but it's only right and proper that I should. We're about to open at the Shortborn Theatre on New Aldwych. Previews tomorrow and Monday, first night Tuesday. It's a challenge, and frankly I'm nervous as hell about it, but then something would be wrong if I wasn't. You don't brave the Bard lightly."
"And you're playing...?"
"Who do you think I'm playing!"
"Well, I just thought I should check. You know, me not being part of the acting profession like you are, not a brethren or sistren thesp, somebody could say to me, 'I'm doing Shakespeare in the West End,' and for all I know they mean they're Third Servant or the stage manager or an usherette or something."
Arthur looked askance at his cousin, unable to decide if he was really as naïve as he sounded. "But I'm not somebody, Prov."
"No, that's true."
"And there can't be many actors better suited than me to portraying the Prince of Denmark. I do have a unique insight into that sort of world. Families in castles. Strange relatives and relationships."
"Yes?"
"Yes. In fact, you really ought to come and see it. I can arrange comp tickets for you. In the Family Box." Arthur struck Provender as surprisingly in earnest. "You'd enjoy yourself. It's quite a production. You could even attend the first night. You're not doing anything on Tuesday, are you?"
"Don't think so."
"No plans? Not likely to be otherwise detained?"
"Otherwise detained? Not as far as I know."
"There you go, then. It's settled. I'll sort out tickets for all of you. You could make it a Family night out, the five of you."
"Well, we'll see."
"No, no, you have to come. Leave it with me. Now, I think there's someone over there I need to see. Nice chatting with you, Prov."
Arthur sauntered off, and belatedly it occurred to Provender that even if he didn't have anything planned for Tuesday night, he should have said he did. It was, after all, his birthday.
Well, Arthur could arrange tickets if he wanted to, and Provender's parents and sisters could go see Arthur's _Hamlet_ if they wanted to. Provender was pretty sure he would be staying put that night. He had no pressing urge to travel to London and watch his cousin massacre one of the great Shakespearian roles. Arthur's performance as the Dane would, he was sure, be tragic in all the wrong ways.
Provender scanned the piazza, looking both for someone with a drinks salver and for someone he might possibly want to talk to. Neither was immediately apparent. He swung his head this way and that, picturing the mask's nose as the barrel of a piece of field artillery, sighting along it and taking imaginary potshots at guests. He stopped when Great became his next "target". It didn't do to lob hypothetical artillery shells at your great-grandfather. Or was it great-great-grandfather? Or even great-great-great? Great being so old, so fantastically antiquated, there was some confusion about his genealogical status. The line of descent had become blurred, and nobody was quite sure any more where, exactly, he fitted in. It was possible he was not a direct ancestor at all, not several steps up the primogeniture bloodline from Provender but rather a distant uncle, a remote cousin several times removed. He was, though, undeniably the ultra-patriarch, the senior-most Gleed. For all his useless body, his threadbare scalp, his inability to communicate, his helplessness, he remained the root and figurehead of Britain's foremost Family.
Provender debated whether to go over and speak to him. What decided him against was the presence of Carver at Great's side. Carver stood sentinel, hands behind back, coldly viewing the party guests. Great's own expression seemed not much less cold. Nearby, Provender spotted a waitress bearing beverages. He made for her instead.
**7**
THE COLUMBINE DID not, at first, recognise who the dark figure swooping towards her in fact was. The hooknose mask, flat hat and swirling black cape made him a startling apparition, and, already in a state of heightened anxiety, the Columbine experienced something akin to mortal dread as he closed in on her with purposeful stride. For a few appalling seconds she thought this was, not some party guest, but rather punishment, nemesis, doom, all rolled into one, coming to claim her. Had the figure been carrying a scythe instead of a stick, it would not, to her, have seemed at all out of place.
In her consternation, she nearly dropped her salver. But the figure reached her just in time to seize her wrist and steady it, levelling the salver before the drinks slid off, and his grip was warm and firm and plainly that of an ordinary human being, and his voice was plainly that of an ordinary human being too as he said, "Whoops, careful there. Be a shame to waste all that booze before I've had a chance to sample some."
The Columbine blushed. She could scarcely believe her own foolishness. Thinking this was some supernatural entity. Honestly! How ridiculous was that? Get a grip on yourself, girl.
"Drink, sir?" she said, faltering only slightly over the words.
"Absolutely," said the partygoer, "now that they're not spilled all over the floor." He let go of her arm and she lowered the salver so that he could peruse the selection on it.
"I do apologise about that, sir."
"Oh God, don't worry. Accidents happen. Or don't, as the case may be." The partygoer's hand hovered to and fro over the various glasses like that of a chess player trying to decide which piece to move next. "Ah, bugger it, I can barely see what I'm doing." He grabbed his mask by the nose and yanked it down beneath his chin. "That's better. Now then..."
It was Provender Gleed, and the Columbine had realised that it was Provender Gleed an instant before he exposed his face. She ought to have known who he was as soon as she set eyes on him, and would have, had she been thinking straight. She had, after all, been told what costume Provender would be wearing tonight. It had been described to her in detail, right down to the fake spectacles on the nose. She had been supposed to be looking out for somebody dressed just like this.
Again, she told herself to get a grip. She needed to stay calm and focused. She needed to have all her wits about her. If she didn't pull herself together, she wasn't going to be able to do what the Harlequin wanted her to do, the plan would fail, everything would be in vain...
She remembered the Harlequin telling her earlier how he had faith in her. Even though they were no longer lovers, he had a way of making her feel capable of anything, everything. Not only that, his approval was still important to her, his happiness still mattered to her.
Thinking of which instilled her with strength. She could pull this off. She _would_. She peered across at Provender Gleed, who appeared unable to make up his mind.
"So, what'll it be?" she asked, and she accompanied the query with a small giggle. At the same time, she widened her eyes slightly, tilted her head to one side, and arched her back, thrusting her chest forward. Old tricks. Obvious tricks. But they seldom failed.
Provender noticed. He glanced up from the salver. His eyes flicked to her face. Searched there for a moment. Then he smiled.
It was, the Columbine noted, a nice smile. He was, indeed, a good-looking boy, better so in the flesh than in photographs. In some of the pictures of him she had seen, his nose looked enormous, as though transplanted from somebody else's face, someone twice his size. But up close, it fit. Big yet dignified. Characterful. A perfectly-in-proportion nose would have left him looking bland, she felt. Ordinarily handsome. A run-of-the-mill pretty-boy. The largeness of it gave him stature. And of course, such a nose was a physical trademark of his Family—without it, he would be far less of a Gleed. The shaven head worked for him as well. On someone else it might have looked thuggish. On him, it emphasised the sensitivity of his features, making him seem vulnerable and open. She vaguely recalled reading somewhere that that was the reason he had lopped off his long locks, as an outward expression of honesty. That, and to distance himself from the current vogue among young Family males for collar-length hair.
It crossed her mind that she oughtn't to be so taken with his looks. It seemed a betrayal of her principles. He was Family, and she hated the Families. She consoled herself with the thought that if she found Provender fanciable, there was no harm in that. It made what she had to do easier. She could play her role more credibly.
"There's champagne," she said. "White wine. Red. Rosé. That's a _kir Famille_ there. That's a margarita, of course. And there's a G and T, and that one's a vodka-tonic, I think. If you'd like something else, just say. Anything. Anything at all. If you don't like what you see..."
It was a perfect lead-in, but for some reason Provender didn't take advantage of it. Instead he said, "Did you know that every drop of alcohol on that tray comes from a Gleed Family vineyard or plantation?"
"I didn't know that, sir," replied the Columbine. "How fascinating." She widened her eyes a fraction more, and a fraction more breast flesh swelled into view just above the level of the salver. "It must be quite a thing, owning all those vineyards and plantations. I can't even imagine what it must be like."
"It's... As a matter of fact," he said, with a shrug, "it's pretty meaningless."
"Meaningless, sir?"
"I've no idea why I even brought it up. It doesn't bother me in the slightest where all that booze comes from, and I don't see why you should care either."
"Because, um, because I might be interested to know what I'm serving you with?" said the Columbine. "Its provenance?"
"Provenance?"
He grinned at her. Like his smile, his grin was nice too, the Columbine thought. Fresh and sincere, as if it was something he didn't do too often.
"That's a good word," he said. "Not one you hear every day. Provenance. I suppose if you hang around auction houses and museums you'd hear it a lot, but... Do you hang around auction houses and museums at all?"
The Columbine wasn't sure how to answer. Definitely, Provender was flirting with her, and that was good, that was the plan, that was the reason behind all her eye-flaring and her bosom-thrusting and her awed-ingénue remarks. His flirting, however, wasn't taking any form she was familiar with. He was attracted to her but showing it in none of the commonly accepted ways, by complimenting her, for example, or showing off. That line about vineyards had sounded sort of boastful but he had undercut it straight away. And now he wanted to talk about _auction houses_? One thing was for sure: Families were not like ordinary folk.
"Museums," she said. "Sometimes I'll go to a museum. But not that often, really. I've been meaning to visit the Gleed Gallery, the new one on Millbank, but... But... I haven't had the time."
"You're busy."
"I am."
"Doing jobs like this?"
"No. I mean, yes. Working, generally. Earning a crust. Some of us have to."
Provender was suddenly unsmiling. "The implication being some of us don't?"
"No. Oh no, sir." Idiot! "It was just a figure of speech. I didn't mean that—"
He waved a hand and laughed. "I was teasing. Sorry. Unfair of me. I apologise. "Earning a crust"—I like that, too. You come out with all sorts of interesting conversational wrinkles."
"So do you, sir."
"Do I? Thanks." He sounded genuinely flattered. "I like to talk with people. Properly. You know, not the standard hello-how-are-you-lovely-weather-we're-having crap, the nonsense that passes for conversation at occasions like these, everyone agreeing with everyone else. I like _discussing_ things, the way you and I are doing. Aren't we? I get bored out of my mind if there isn't some kind of depth to a conversation. I'd rather have an argument with someone than listen to them jabber on about mutual acquaintances and the last holiday they went on and isn't so-and-so looking positively radiant this evening? It's an attitude that doesn't make me very popular, but then life isn't a popularity conte—"
"Provender!"
Both he and the Columbine swung round in the direction of the cry. She saw a middle-aged woman striding towards them with another, younger woman in tow. The latter the Columbine did not recognise but the former she knew was Provender's mother. That afternoon, Cynthia Gleed had stood up before an assemblage of all the catering staff and told them what she expected of them at the party tonight (not much, just total dedication and immaculate efficiency). She had struck the Columbine then as a forceful personality, someone not to be messed with. Enviably beautiful, too. Now, resplendent in ballgown and mask, she looked no less beautiful and no less indomitable. She steered her young companion towards her son by the wrist, and it didn't take a genius to intuit what she had in mind for the two of them. The girl was in her twenties, slim, pretty in a vacant posh-girl way, and Provender's mother had a glint in her eye that said she was sure her son and this lissome lass were going to hit it off, and if they didn't, she would want to know the reason why.
"Prov, not interrupting anything, am I." It was not a question. Cynthia Gleed shot the Columbine a look that was mercilessly—or, depending on your viewpoint, mercifully—brief. It appraised and dismissed in the same instant. "Only, this is the most amazing coincidence. I was just talking to Gentian here and she, can you believe it, went to the same finishing school in Zurich as Cousin Inez. Isn't that a thing?"
Provender had no alternative but to fix on a smile and hold out his hand to the willowy Gentian. The Columbine, for her part, had no alternative but to shrink away with her salver. Cynthia Gleed's look had made it plain. The Columbine was not wanted there. Superfluous to requirements. She must look for someone else to serve.
Just before turning to meet Gentian, however, Provender had given the Columbine a wry roll of the eyes, then winked. Suddenly there was complicity between them, and in that complicity, connection. When the Harlequin sidled up to her a few moments later and said he'd spotted her talking to Provender and asked how it had gone, the Columbine was able to tell him, with complete honesty, that it had gone well. When the Harlequin then asked if she and Provender were going to be meeting up again later that night, she was able to say, also with complete honesty, that yes, she was certain they were.
And hearing this, the Harlequin smiled. A broad smile, but a wolfish one too. Not like Provender's. Not nice at all.
**8**
IT WASN'T UNTIL nearly midnight that Provender was able to speak to the Columbine again.
Dealing with Gentian took half an hour. She was a pleasant enough person, hard to find fault with. They talked about her horses, whom she loved, her parents, about whom she was more ambivalent, and about his cousin Inez, with whom, in Zürich, she had learned deportment, cooking, etiquette, and all the other hunting skills a girl needed in order to bag herself a well-to-do husband. She didn't balk when Provender made a joke about finishing schools being so called because they _finished_ any chance their pupils had of becoming independent, free-thinking individuals. She responded by saying, with just the right amount of rancour, that learning how to behave correctly in polite society didn't always mean turning into some kind of mindless social robot. You stayed who you were inside, just a little more polished on the outside. Did he think Inez had turned into a robot?
He didn't, and said, with truth, that he liked Inez a lot and didn't believe her time in Switzerland had inflicted any lasting damage.
"There, then," said Gentian, her point made.
Briefly, Provender recalled his date with Inez, which their mothers had fixed up. He had flown to Seville in the Gleed dirigible, met Inez for lunch at the Lamas Family hacienda, found her appealing but much too like his mother for comfort, and returned home the same day. His mother was still, a year on, smoothing the Lamas feathers that had been ruffled by his swift departure.
Gentian felt she had to prove that she wasn't as bland and conformist as Provender clearly thought she was, and told him of her three-day-eventing escapades, the nasty tumble she had taken just the other day at Hickstead, and her ambition to run a stud farm once she retired from competitive riding. She could see his interest waning by the second, and her opinion of him, at the same time, coagulated. He really was as stuck-up as everyone said. Not just Family-arrogant—intellectually arrogant. Thought he was smarter than everyone else, and thought that made him better than everyone else.
She was therefore relieved when Cynthia Gleed arrived with another girl for Provender to meet. Provender, likewise, was relieved... although his relief turned to dismay soon enough, as he was forced to spend the next hour in the company of Blaise Wynne.
Blaise made no bones about it: she wanted to marry into a Family. She didn't care which one and she didn't care whom she married. Provender Gleed would do as well as any.
Within five minutes of being introduced to him she had raised the subject of babies twice _and_ offered Provender a blowjob (with the bonus of simultaneous rectal stimulation, if he wished). Smoking incessantly, with quick hard sucks on liquorice-paper cigarillos, she talked of not having to work for the rest of her life, of knowing that men liked their wives to be whores in the bedroom, of injecting a shot of dynamism into a decadent household, and of looking forward to using the speedway circuit at Dashlands so that she could indulge in her favourite pastime, which was driving like a bloody loon. Provender barely got a word in edgeways. As she thundered on, however, he felt panic beginning to rise. Every instinct he had was urging him to get away from this woman. She was a shark—aggressive, relentless, tenacious. If he let her get her teeth into him, she would never let go.
He excused himself—needed to pee. When he emerged from the gents lavatory, in which he had spent an inordinate length of time, there she was, waiting patiently for him outside. Somehow she inveigled him into taking a gondola ride. They looped through the party site, and Provender was glad of the gondolier warbling at the stern, because the man was singing so loudly that Blaise could not make herself heard over him. However, near the end of the journey, Blaise decided to substitute deeds for words and lunged for Provender, her mouth wide. He genuinely thought she was going to bite him with those cigarillo-greyed gnashers of hers, but it turned out to be worse than that: an attempt to kiss him. He ducked his head to the side just in time and her lips mashed the side of his neck, harmlessly. But she wasn't done with him. As the gondola approached the candy-striped mooring posts at the edge of the Piazza San Marco, Provender felt her hand on his thigh, groping towards his crotch. There was still a gap of a few yards between the gondola and the piazza, but he leapt and somehow made it onto dry land. It was possible that in his fright he actually walked on water.
Thereafter, it became hunter and hunted, predator and prey, Provender scurrying through the crowds of merrymakers, Blaise stalking him. He bumped into his father, and Prosper Gleed was puzzled to see his son looking so hounded and harassed.
"What's up, Prov?"
Provender glanced over his shoulder. Prosper followed the direction of the look and saw Blaise Wynne at the other end of it, making her inexorable way towards them. He assessed the situation, grinned, and gave Provender a hearty slap on the arm. "Attaboy! Hard to get. Sometimes that's the way to play it."
Provender stumbled off and, not paying attention to where he was going, narrowly avoided a collision with Carver.
He recoiled, appalled that he had nearly touched the manservant. Carver: the bane of Provender's boyhood. Carver: like some ghost that haunted Dashlands. Carver: who, it seemed, had always been just around the corner when Provender accidentally broke a vase or put a scratch on a parquet floor or generally did something he ought not to have done. Carver had not ever scolded Provender—it was not his place—but his eyes had conveyed reproof far more sharply and eloquently than words ever could, and so too, in its way, had that scar of his.
Carver bowed deeply, with just a touch of obsequiousness. Great, beside him, was fast asleep. His chin was lodged on his collarbone, and every vein and tendon in his neck strained against the skin and looked ready to snap. His eyelids were so papery thin, his corneas stood proud through them like two buttons.
Provender backed away, mumbling an apology. He sought refuge in the jovial orbit of Fortune, catching the tail-end of the joke with which his uncle was regaling a small crowd:
"...so the third missionary, he's seen what's happened to the other two, he's watched through the chink in the wall of the mud hut as they've been buggered by every single tribesman and then allowed to stumble off into the jungle, and he thinks to himself, _Well, hold on, I'm a good Victorian gentleman, I'm a servant of the Lord, my body is His temple, I'm not going to allow these heathens to defile it in this ghastly manner_. So when the chief comes to him the next evening and makes the same offer, 'Death or ooga-booga', the missionary says, 'I choose death.' And the chief smiles a great big smile and says, 'Very well then. If that is what you wish. Death by ooga-booga!'"
As gales of laughter exploded around Uncle Fort, Provender turned away, and before he knew it he was in Blaise's clutches once more.
Realising that it was hopeless trying to flee from her, he adopted a different tactic, letting her know in no uncertain terms that he was not now or ever likely to be in the market for marrying a woman quite as pushy as she was. Weirdly enough, the blunter and ruder he got, the more, not less, confident Blaise became that he was the one for her.
"I like a man who speaks his mind," she said. "I like a bit of fire. There's nothing worse than a man who lacks spunk. In more ways than one."
Even as she chortled at her own crudity, Provender was forming the impression that Blaise Wynne was, in fact, completely mad. He was all for women who knew what they wanted, but this was a woman who didn't know anything other than what she wanted and who simply could not tell when what she wanted did not want her in return. Perhaps she had been normal once, and sane; if so, her dream of attaining Family status, whatever the cost, had driven her stark staring bonkers since then.
Rare was the occasion that Provender had cause to give thanks for his cousin Arthur, but at that moment, as the diminutive Scaramouche lurched into his eyeline, he could not have been more grateful.
Arthur, it seemed, wished to have words with Provender. Arthur, it also seemed, had recently visited a small room off one of the lesser piazzas where intoxicants of a non-alcoholic nature were available. His nostrils were red-rimmed and his eyes had a vacant, slightly belligerent sheen and did not appear to be focusing on the same thing as each other. Drugs, of course, couldn't _not_ be offered at a party like this one, and Cynthia Gleed, as any self-respecting hostess would, had laid on a premium selection—pure uncut Ecuadorian cocaine, some very pungent and potent sensimillia, and a smattering of downers and uppers to counteract the effects of the first two. At her insistence, their supply and ingestion was restricted to one discrete (and discreet) corner of the party site, so as not to offend the sensibilities of the more straight-laced guests. She herself didn't necessarily disapprove of the use of narcotics, but there was no need to rub people's noses in it.
Rubbing his own nose, Arthur lumbered up to Provender. His shoulder butted against Blaise's and he turned and peered at her as if he hadn't even realised she was there. Then, facing Provender again, he addressed him as though the two of them were already in the middle of an argument.
"And another thing, Prov," he said, "if anyone ought to be bloody on the bloody primogeniture line, it ought to be bloody me. I mean, I'm the bloody one with the acting career that's going bloody well even if I do say so my-bloody-self. I'm the one people bloody see on the TV and the cinema screen all the bloody time. Who'd be better as the next bloody Gleed heir? Who'd be better to carry on the bloody bloodline? Not bloody you, Prov, mate. Me! Bloody well me! Someone people know, someone people bloody see, not someone who bloody hides away all day. And someone whose bloody blood hasn't been bloody thinned like some bloody blood I could ment—"
"Arthur," said Provender, stemming the blood-flow, "have you met Blaise Wynne? Blaise, this is my cousin Arthur. In case you hadn't guessed, a Gleed."
Blaise required no further prompting. In an instant, Provender was forgotten. It was as if he had never existed. She grabbed Arthur by the arm, hard, sinking her claws into him. Arthur winced with pain and tried to prise himself free, but she held grimly on.
"Arthur Gleed!" she crooned. "Yes, I know you. Well, I've _seen_ you. I watched you in that series, what was it called...?"
Provender sidestepped smartly away. Only when there was a decent margin of safety between him and Blaise did he brave a look back. She was bent forward over Arthur, still clutching his arm. Arthur was shrinking from her, bewildered, trying to fathom what had just happened to him. Who was this woman? Why would she not let go? Provender saw him touch the hilt of his stage-prop sword, no doubt for reassurance, but perhaps wondering whether to draw it. Somehow Provender didn't think the weapon, wielded, would deter Blaise. She'd regard it, if anything, as a sexual come-on.
A quick check of his watch told him it was just gone half-past eleven. There was a fireworks display scheduled at midnight. Provender loved fireworks and knew he ought to get down to the southern end of the party site so as to find a spot with a good view. Of greater urgency, though, was the need for a drink. He was also keen to find a certain member of the waiting staff again. There were several Harlequins and Columbines within sight, all bearing beverages, but he ignored them. He was after one particular Columbine and would take a drink off no one else's salver.
He hunted for her through Venice. He could not say exactly what it was about her that had so intrigued him. She was extremely pretty, she had bright, clever eyes, was alluringly curvaceous—but looks alone were not the whole story. _Pert_ was the word that kept occurring to him. It seemed to sum her up. _Quirky_ also applied. And she hadn't been overawed by him, by what he was, and he liked that, too. She had called him "sir", but in her job that was how you addressed every man, it was just one of the rules; and even as she was being polite and deferential towards him, Provender had been able to tell that she didn't think he was any better than her. She wasn't Family-struck, as so many people were. She had given no indication that the accident of birth which made him a Gleed was, in fact, of any consequence to her. As far as she was concerned, he was a person, just as she was a person. They were, essentially, equals.
She had been in his thoughts while he was with Gentian and even more so while he was with Blaise. She had been lodged in his brain unshakeably from the moment he met her. Even if he had liked either of the other two women, they wouldn't have stood a chance. The Columbine towered head and shoulders above them. He must find her!
She wasn't anywhere he looked. She seemed to have vanished. He searched through every alley, every narrow Venetian street. Guests greeted him from time to time. He blanked them, forging past, head down. He could have put his mask back up in order to spare himself this awkwardness, but he didn't want to be hampered in any way. He needed his eyesight unconfined—full peripheral vision. Where was she? He scanned every piazza he came to. He began to wonder if she wasn't hiding from him, spooked, perhaps, by the way he had talked to her. Maybe she thought he was like his father, a chip off the old block, hounding after anything in a skirt. Or maybe she thought he was just _odd_. He might not have given the best account of himself during their brief exchange of words. But that simply made it all the more imperative that he find her, so that he could have a stab at redeeming himself.
Eventually, as midnight loomed, persistence was rewarded. Provender was crossing the Bridge of Sighs for what seemed like the dozenth time, and feeling, as he did so, the full appositeness of the bridge's name—and there she was, coming the other way. She spotted him at about the same time as he spotted her. As their eyes met, she looked pleased, and then she looked thankful—not quite the same thing. This perplexed Provender for all of a nanosecond. He had found her, that was all that mattered. She hadn't fled the party or anything. He hadn't scared her away. Here she was.
All at once, he was stuck for what to say. He stammered out a sentence, "So we meet again," something along those lines, fumbling and banal. She, with marginally greater confidence, said, "You never got a drink off me, did you?"
He said, "I never did."
She said, "Now's your chance, then."
He said, "Indeed."
She said, "Wine, maybe?"
He said, "Why not?", and cringed, because it sounded like an attempt at a pun. He grabbed a glass of rosé off the salver and downed it in a single, hurried gulp.
"So," he said, gasping.
"So," she said.
"They're going to start shortly."
"What?"
"Sorry. The fireworks."
"Ah."
"Do you like fireworks?"
The Columbine's mouth curved up at one corner. "I don't _dis_ like them."
At that moment, a Harlequin strode past, coming from the same direction the Columbine had. Provender threw him a glance—big, sturdy fellow, muscles bulking out his black-and-white diamond pattern leotard. He looked back to the Columbine. Her eyes, which had also been on the Harlequin, flicked back to Provender's face.
"Do you have a name?" Provender asked.
It was a straightforward enough question. He wanted to know the answer. But at the same time, both of them knew he was asking for a whole lot more. If she told him, she would be opening up the border between professional and personal, stamping his passport and giving him the go-ahead to walk through.
"I don't think I ought to—"
"No, no, of course."
She paused, deliberating, then said, "Is."
"Eh?"
"That's my name. Is."
"Really? Short for..."
"Just Is."
"Oh. Unusual."
"Says a man called Provender."
He smiled. "Yes. Quite. So then... Is. Those fireworks. Would you like to come and watch them with me?"
"I can't."
"Ah."
"I'd like to, but... you know, I have a job to do, and if my boss catches me watching fireworks when I should be serving drinks..."
"He'll give you a rocket."
This time the pun was intentional. That didn't make it any funnier, though.
"Right," said Is.
"Is that the only reason?"
"The only reason...?"
"You won't come and watch them with me."
She thought about it. "Yeah."
"Then not to worry. You won't get into trouble, I promise. I'll sort it out. I'll go and see your boss afterwards. I'll say I gave you permission to take half an hour off. I thought you'd been working so hard, you could do with a break. Actually, fuck it, why don't you take the rest of the night off? Spend it as my personal guest. On full pay."
"I don't think..." She shook her head uncomfortably. "No."
"OK, just the half an hour then. For the fireworks." Provender was thinking he had lost her. He had pushed too hard. Been greedy. "Please?"
But he hadn't, hurrah, lost her. "Perhaps," she said slowly, "just for the fireworks, I could, I suppose..."
"Brilliant!"
"You promise you'll talk to my boss afterwards."
"Swear. Cross my heart."
She took a deep breath. "All right then. Aren't they about to start?"
Provender consulted his watch. "Any minute. We'd better hurry if we're going to get a good position."
She nodded at her salver. "I need to find somewhere to put this down first."
"Leave it here."
"Can't do that. The catering marquee's just that way. It won't take a moment."
"I'll come with you."
She cocked her head. "If you like."
He followed her down one of the narrower alleys. His mother had told him the streets of Venice were categorised under various names, according to size and proximity to water. The narrow residential type, which this alley aped, was called a... _ruga_? Something like that. He thought about sharing this little factlet with the Columbine, Is. But he didn't want her to take him for a show-offy know-all.
Soon they were crossing the perimeter of the party site, and the catering marquee appeared in front of them, voluminous and candy-striped, like a huge canvas cake. From within came a clatter of cutlery and glassware, and also the sizzle of cooking and the sound of chefs shouting at one another. Is entered through one of the flaps, emerging empty-handed a moment later. Provender, eager, pointed towards Venice's south edge.
"That way," he said.
"Why don't we go over there instead?" said Is, gesturing past the side of the marquee.
Completely the opposite direction. Nothing lay that way except a copse of silver birches, an expanse of lawn, and beyond, the untended pasture and woodland which constituted the majority of the estate.
"There's a rise," she explained. "I saw it this afternoon. I bet up there we'll have an uninterrupted view. No one else around to get in the way."
Provender took this in; thought he knew what she was implying; liked it.
They headed off side by side, into the dark. Provender was delighted at how things were turning out. He didn't the least bit mind Is taking the lead in this way. He knew, of course, the rise she was referring to. He pictured her and him sitting atop it. She was wrong about the view from there being uninterrupted. Most of the ground-level detonations, the Roman candles and Catherine wheels, would be obscured by Venice, but the rockets and mortars, the big loud airbursting bangs which were really the point of a fireworks display—these would be visible in all their scintillating, percussive glory. And if his hand should happen to settle next to hers on the grass, if their fingers should brush, their shoulders touch... it would not be an unwelcome development at all. Provender was expecting no more than that. He wasn't expecting Is to pounce on him, Blaise-style. He didn't want her to, and didn't think she was that sort of girl. Just her presence beside him, her companionship, while the night sky exploded, was all he required.
They were passing the copse. The ground was starting to slope upwards. The light from the party site threw everything into dim relief.
To Provender's right, at the periphery of his vision, something moved. He thought it was the trunk of one of the silver birches, swaying in a sudden breeze.
Then he saw that it was a figure. He glimpsed diamond-shapes, black on white. Someone who had been perfectly camouflaged amid the piebald trees.
Bearing down on him.
Before he could say or do anything, an arm banded around his chest. A hand clamped over his mouth.
"Quick!" a hoarse voice yelled, right next to his ear.
Provender struggled, but the man holding him was stronger, much stronger, than him.
He saw Is fumbling among her skirts.
"Quick! Fucking get on with it!"
From a pocket she produced a small, thin, cylindrical object. It gleamed.
A hypodermic.
Provender struggled harder, but no more effectually. He yelled, but with his mouth muffled the yell came out a growl. Belatedly, he remembered the stick he was carrying. He had forgotten he still had it with him. He lashed backwards with it, going for his assailant's head, but the angle was awkward, he couldn't get in a decent blow.
With almost casual ease, the man batted the stick out of his grasp. It spun uselessly away.
Is moved in with the hypodermic. She grabbed the sleeve of Provender's cape and yanked it up to expose his bare arm.
A needle winked, poised over his biceps.
"Do it, for fuck's sake!"
Provender felt the jab. A sting, then deeper, muscular pain.
And suddenly brightness, a wash of crimson over the scene, followed immediately by a huge, hearty _thump_.
Distant cheering.
And further flashes of brightness followed, and a thunder peal of _thumps_. The tree trunks were lit up in a succession of colours. Is's face was lit up too. Provender watched her, even as his legs began to grow numb and crumple under him, even as the man braced him so that he remained upright. Is was growing further and further away, shrinking, and her face, as it receded and blurred, shifted through a palette of hues: sombre magenta, fierce scarlet, deep gold, shrewd green, cruel blue.
More cheering. Whoops of firework joy.
Coming from a far-off world.
Somewhere in dreams.
**9**
"WHERE _IS_ PROVENDER?"
This time Cynthia Gleed said the words less with a sigh, more with a frown.
A fusillade of explosions erupted overhead, like dandelions made of fire, one overlaying another in rapid succession The partygoers oohed their appreciated. Faces were upturned, mouths agape. Fireworks made children of everyone.
Cynthia, the only one not looking upward, studied the crowd by the flickering play of pyrotechnic light. No sign of her son in his sombre, somewhat sinister get-up. She could see Gentian, though, and Blaise, the latter with her arm around nephew Arthur (although the embrace, from certain angles, looked not unlike a headlock). Neither girl had found favour with Provender, and Cynthia, while disappointed, was also not surprised. In hindsight, Gentian was perhaps a little too winsome for him, and Blaise was definitely far too forward. Cynthia had had her hopes... but she perceived now that her choices had not been right. Ah well. She was learning from her mistakes. Soon she would have narrowed down the perfect woman for Provender. She already had the next couple of candidates in mind, and she also had a network of friends, relatives and acquaintances quietly, discreetly looking on her behalf, rifling through their address books, winnowing out likely young ladies to submit for her consideration. In time, she would find the Girl, the One.
There was a series of immense silver starbursts. Shrieking white dervishes whizzed off in all different directions.
Cynthia saw her husband. She saw her daughters. There was Uncle Fortune, sweaty and satanic. There was Great, craning his bony neck, peering up fiercely at the display.
All her Family. All her _family_.
Except Provender.
The likeliest explanation for his absence was that he had returned to the house; he was back in his suite, probably bashing away again on his damn videotyper.
Yet Provender loved fireworks. It was highly unusual that he wasn't here watching them.
On the ground, several dozen Roman candles ignited at once, and a host of golden sparks tumbled in a shimmering curtain.
Deep within her Cynthia felt the first faint pangs of misgiving.
She tried to ignore the feeling. She tried to convince herself she was being foolish.
She didn't quite succeed.
**PART II**
**10**
BETWEEN THEM, DAMIEN bearing most of the weight, they carried Provender's inert form to the car and bundled him into the boot.
This, for Is, was the riskiest and most terrifying part of the plan. Security personnel were patrolling the grounds. There was no way of pretending there was anything innocent about two people lugging the sedated body of Provender Gleed to the catering-staff car park and depositing him in the back of one of the vehicles there. It was not possible, if caught red-handed, to claim this wasn't what it appeared to be. Up till then, everything could be explained away: she was just chatting with Provender, they were just getting on with each other, they were just going for a walk in the grounds to find a vantage point to watch the fireworks from. Now, from the moment Damien grabbed Provender and she administered the muscle relaxant, there was no longer the safeguard of a plausible cover story. What they looked like they were doing was exactly what they were doing: they were kidnapping him.
But they made it to Damien's car safely. They saw no one. No one saw them. No one challenged them. The fireworks afforded the ideal diversion. Everyone's attention, including the security personnel's, was on the display. Plus, it provided illumination to see by.
Is hated to admit it, but Damien had thought the whole thing through really pretty well. He had had help, she knew, but nonetheless...
Damien lowered the lid of the boot and clumped it shut, leaning on it with all his weight. The catch was temperamental, sometimes not working and sometimes working too well, so that you had to thump the lid to get it to open. That was the problem with Chinese import cars like the Dragon Wind Compact. Not only were they unreliable but replacement parts, so often needed, were hard to come by. And with Dragon Winds in general there was the additional flaw of a crude catalytic converter which gave the exhaust emissions an unusually sulphurous stench. This had prompted motoring journalists to crack many a predictable joke about the brand name.
Tonight the god of felony was in a benign mood and the catch on the Compact behaved itself. Damien raised his hands slowly, experimentally. The boot lid did not spring open. He allowed himself a quick, tight smile.
"Right. Let's roll."
They drove out along one of the estate's back roads, the Dragon Wind's headlamps combing the dark. Is, in the passenger seat, sat with her fingernails digging into her palms. They weren't free and clear yet, far from it. There was the gate to get through. To be precise, there was the security presence at the gate to get past. She knew Damien had prepared for this contingency, but that didn't in any way help to calm her heart rate or unclamp the tightness in her belly. She was half-dizzy with fear and adrenaline.
Damien, by contrast, seemed to be thriving on the excitement. He was confident in the driving seat, his fingers tapping out a merry rhythm on the steering wheel. As Is looked at him, studying his profile, she remembered that he was handsome. It was an odd revelation. How could she have forgotten? But there it was. He had a near-spherical head which betokened, she thought, integrity, and eyes which, though a mite too deep-set, shone with a zealous gleam. His jaw, with its pronounced overbite, could have detracted from his looks but somehow didn't. _Piranha-esque_ , a girlfriend of hers had once called it, but Is didn't think that was quite right. (Besides, the remark was made after Is and Damien broke up, when slagging off the ex was considered fair game, indeed was a vital part of post-relationship the healing process.) He was well-built, too. Even wearing that absurd Harlequin outfit, he had physical presence. Damien was not someone people took lightly or dared laugh at.
Up ahead, the gate hove into view. Is glimpsed the brick-built guardhouse by the road's edge, with its open arched doorway. The guardhouse had been occupied by a member of the security staff when she and Damien had arrived this afternoon, a thickset monster of a man with hod-carrier shoulders and a face that looked like it had received more than its fair share of punches. He had leaned out to inspect their passes like some troll from its cave. Now, as far as she could tell, the guardhouse was empty.
Damien drew to a halt in front of the gate. "Better make this quick." He eyed the dashboard clock's phosphorescent dial. "We've got a half-hour window and it's closing."
Is leapt out of the car and hurried over to the guardhouse. As she neared the doorway she slowed and peered cautiously in, just to be sure. Yes, empty. The security man was off chasing shadows in the grounds. If interrogated, he would claim he heard suspicious sounds out in the woods and went to investigate. She couldn't imagine how large a bribe it must have taken to convince a trained security professional to abandon his post on a bogus pretext and, in so doing, jeopardise his entire career. All Damien had said was that it was a lot of money. He had also said that they had to be through the gate before the security man returned. If they were still there when he came back from his wild-goose chase, he would have no alternative but to challenge them. The elasticity of the man's conscience stretched only so far.
Is ventured into the guardhouse and quickly located the gate-operating mechanism, a wall-mounted control panel with two buttons on it, one with arrows pointing together, the other with arrows pointing apart. She punched the latter, and with a deep, heavy clank the gate unlocked itself. Its leaves swung ponderously apart and Damien steered the Dragon Wind through.
As Is got ready to hit the button that closed the gate, she thought she heard the thump of footfalls. Her breath caught in her throat. She leaned out of the guardhouse and scanned the darkened woods, her eyes panic-wide, expecting to see the security man come lumbering out from among the trees, sidearm drawn.
Not religious, she nevertheless sent up a small prayer. _Please, God, no_.
Then she heard the thumps again and realised it was the firework display. Three miles distant, a series of rockets detonated and then crackled like splintering tinder.
Slamming the gate-closing button, Is sprinted out of the guardhouse, darted through the narrowing gap between the gate leaves, ran to the car and jumped in. "Go."
Damien, seeing how spooked she was, smirked. "We were fine, you know. Five minutes to spare."
"I don't care. Fucking drive!"
It wasn't until they were a mile down the road that Is was able to draw a steady breath again. She vowed never to put herself through anything like that again. Ever.
"That stuff you injected Provender with," Damien said as he negotiated a junction that took them off the lane that ran alongside the perimeter of Dashlands and onto another lane. "The comatose thingy..."
"Comaphase."
"Thank you. How long's it supposed to last for, again?"
"It was fifteen migs. Should keep him down for three quarters of an hour."
Damien checked the dashboard clock. "Right, so in about twenty minutes, we find a lay-by, pull over and give him a second dose."
"If we have to. But he'll probably stay groggy even after he's come round. His head'll be fuzzy and he won't know what's going on. It's best not to give him two shots in a row if we don't have to. He might not react well."
"It's twenty miles to London. Half an hour at least."
"Let's risk it, Damien. Honestly, even if he wakes up, he'll be in a stupor. He won't be shouting for help or trying to escape or anything."
Damien remained unconvinced, but nodded. "OK, if you say so. But we hear the slightest funny noise from back there, anything at all, we stop and jab him. Agreed?"
"Agreed."
"So load up your hypodermic just in case."
She did, steadying herself against the car's rocking as she drew off a further 15 milligrams of the sedative from the ampoule which she had raided from the hospital supply closet and smuggled out of the building in her pocket. She flicked the syringe to raise the air bubbles, then depressed the plunger till a bead of clear fluid welled at the needle's tip. The needle, she noticed, was still smeared with Provender's blood.
Family blood.
When you looked at it, it was just blood, no different from anybody else's, same colour, same consistency. But to a Family it was everything. In what it represented, it was immeasurably precious.
For the first time, Is had an inkling that what Damien had in mind for Provender, the rest of his plan, was feasible. She hadn't dared believe this before. It had seemed dangerous to hope for so much. But the blood on the needle offered a kind of symbolic assurance. It said the Gleeds needed Provender returned to them. They would give anything, pay anything, accede to any demand, in order to get him back alive.
**11**
LEAFY BERKSHIRE—KEPT nice and rural because that was how the Gleeds liked their home county—gave way to the outskirts of London. The scattering of houses on either side of the dual carriageway became clusters of houses, then knots of houses, revealed by their lighted windows. A greater glare of light denoted Heathrow Aerodrome, where passenger and cargo airships swung at their tethers, white-bellied, like slumbering whales. The road veered towards then away from a stretch of tram track, part of the network that webbed the entire country, an automated transport system for the exclusive use of Family members. Beneath spark-spitting wires a lone tram was barrelling along, its lamp-lit interior furnished with leather armchairs and teak fixtures. No one was aboard. It was estimated that, on average, less than half of one per cent of the trams on the network were occupied at any time. An absurdly wasteful and costly means of getting about; yet the Families loved it, cherished it, and begrudged not one penny of the expense of running and maintaining it.
The glow of London brass-burnished the sky ahead. Suddenly the stars were gone. The city, jealous, would not have them. Suburbs stretched and flexed like a rising tide. Buildings crested upward, the troughs of streetlamp radiance in-between deepening. London massed itself; began to tower. Spikes and spires and skyscrapers, equalling Manhattan's for size, bristled all around. Height was the measure of a capital's worth, and London reached for altitude as keenly as any of its main rivals. Soon, if the Risen London Authority's plans went ahead, there would be cable cars operating between street-level and the summits of the tallest edifices. They were doing that in New York. They were doing it in Paris and Warsaw as well. They would be doing it here.
The road, single carriageway now, wound between the bases of the skyscrapers or sometimes tunnelled straight through. It rollercoastered along a series of elevated sections. It fissured off into slip-roads, or fused with an adjacent road. Traffic, at this hour, was light, and consisted primarily or taxis and electric buses, with the occasional freight lorry bumbling along on a fart of diesel fumes.
Now Damien steered the Dragon Wind off at the appropriate exit and, after negotiating a warren of dingy streets, drove through an entranceway that was neither gate nor outlet but rather indicated transition, a passage from state of existence to another. On one side, the rest of the world. On the other...
The name arched above the entranceway in iron:
NEEDLE GROVE
Each character was sharp and heavy, like a guillotine blade about to drop. You seldom went under them, even in a vehicle, without a reflexive hunching of the shoulders. And once you were through, the side on which the rest of the world stood seemed just that bit cleaner, just that but brighter, than where you were now. The difference was hard to define but there was definitely a difference.
The tower blocks of Needle Grove, numbering fifty in all, were thick-bodied and many-tiered. They didn't climb straight but rose in staggered sections, narrowing, like irregular ziggurats. They were thinner at top than at bottom and yet, confusingly, through some architectural optical illusion, the higher up you went the less space there seemed to be between them. They didn't, in all, behave as normal residential buildings, or any sort of buildings, should. Their bulk intimidated rather than inspired.
Threading between the blocks at almost every level there were overpasses and underpasses. There were cantilevered communal areas—concrete plazas suspended in mid-air, where, if you were lucky, some greenery grew, a tree, a shrub, a clump of grass, failing that a weed. There were spiralling outdoor staircases that threw off exit arms like spokes on a spindle. All these, from dawn to dusk, cast shade. They eclipsed one another and cumulatively occluded the ground. At any hour of the day, whatever the weather, down on the ground it was perpetual overcast twilight.
Damien drove along roadways where, if you saw another car, it was either in motion or a burned-out husk. Teenagers roamed, shrinking from the headlamp beams as though the light scalded their faces. They were kitted out according to various gang-tribe dress codes. Young Moderns sported slicked-down hairdos and three-piece suits with what appeared to be fob-watch chains across the front of the waistcoats (but they were longer than ordinary fob-watch chains and those switchblades at the end were no timepieces). The Radical Flappers looked like square-heeled good-time girls out for an evening's Charlestoning, but cross them and you'd soon learn what damage a wire-strung feather boa could do. The Technologists resembled robots as closely as it was humanly possible to do, while the Changelings, acknowledging that styles and fashions were protean and altered almost daily, wore a gallimaufry of types of clothing, diversity their uniform.
There were dozens of these gangs and night was their time. They roved in bands, bug-eyed on Tinct, looking for trouble and very rarely failing to find it. Fights were so commonplace, no one bothered calling the police to come in and break them up. A fatal knifing or shooting was an almost weekly occurrence, and when this happened the police _would_ turn up, but only to cart away the body and inform the deceased's parents, if no one else already had, that their son or daughter was dead. The crime was never investigated. As far as the cops were concerned, in Needle Grove, among a certain age group, a gang slaying was tantamount to death by natural causes.
At the foot of Block 26, Damien pulled up at the entrance to the basement garage. He wound down the driver's-side window, leaned out and entered a number into the code-lock mechanism, prodding the stiff steel keys firmly. With a _clunk_ , then a reverberant warping _twang_ , the segmented steel door began to rise.
Parked in his allotted space, Damien turned off the engine and rested his wrists on the wheel for a moment.
"Done it, Is," he said, looking sidelong at his accomplice. "We've done it. We've got him home."
"Not quite. We're not upstairs yet."
"Yeah, but. We've done the hard part. And I've got to say, you were brilliant. You really came through. I couldn't have managed it without you. You're a star."
"I did my best."
"No, I mean it. You're fantastic. You did everything absolutely right. The timing was perfect. You kept your nerve."
"There were moments..."
"But you didn't lose it. It's all right to be scared as long as you don't lose it, and you didn't, and that's true class."
"Thank you, Damien."
His eyes took on a mournful look which, alas, she knew only too well. "Why did we ever split up, Is?" he lamented. "What happened? What went wrong? Why did we just... fall apart like that?"
There were a hundred possible answers, and almost all of them ended with _...because you're a possessive, jealous, tantrum-prone egomaniac, Damien_. Is chose instead to deflect the question with a shrug, saying, "Let's just concentrate on this, eh?" She nodded towards the boot. "Leave the soul-searching for another time."
Damien studied the backs of his hands for several seconds, then opened the door and climbed out. Opening one of the rear doors, he learned in and took a pair of overcoats off the back seat. He handed one to Is and donned the other. With the overcoats buttoned up to the neck, their Harlequin and Columbine outfits were hidden.
From one pocket, Damien drew out a scarf-like length of fabric. Then, standing over the boot, he raised his fist and brought it down on a spot just above the catch. The lid creaked upward.
**12**
MINUTES (HOURS? SECONDS? weeks?) of juddering motion, in perfect darkness. Smells of oil, grease, sulphurous exhaust, warm metal. Up then down, down then up. Swaying this way, that way. Someone's knees butting intermittently against his chin.
_Those are my knees_ , Provender thought. _This is me, lying embryonic_.
It was a rare instance of lucidity, and it came in a flash and vanished almost as quickly. For the most part thoughts—any thoughts—were jigsaw-puzzle things that demanded a great deal of effort to piece together. Sometimes Provender seemed to have hold of a fully-formed concept, only to find it crumbled into fragments just when it was about to make sense.
There were memories, too. Strange, flitting-phantom recollections of recent events.
Is the Columbine, at the ball.
The Columbine Is.
The Columbine is—was—Is.
Leaving Venice with her.
Hypodermic.
Hypodermic.
And her face, in firework light. Colour-splashed with fields of brilliance.
And so now he was travelling. He managed to comprehend, eventually, that he was travelling. In motion.
And he was also lying paralysed, unable so much as to twitch a finger.
And the hour-second-week minutes rumbled by, until finally, abruptly, they stopped.
The travelling had stopped.
He had stopped.
Provender attempted to roll his head, because that seemed to him like something he might be able to do now that nothing else was in motion. His head lolled rather than rolled, but at least it moved. He had volition. Rollition. Lollition.
Then there was a booming _thud_ , and a sudden influx of yellowy light. He screwed up his eyes and loll-rolled his head sideways to escape the brightness. Next thing he knew, there was cloth over his eyes. The cloth was being tied behind his head. A blindfold. No more brightness. And the same hands that had put the blindfold on him then grabbed him under the armpits and manhandled him up, out, onto. He was jack-knifed over someone's shoulder. Fireman's lift. He was being carried, through some low-ceilinged, echoing place. Head dangling downward. Nose pressed into the fabric of someone's overcoat. Human lumber.
A soft _ping_.
A rumble of doors.
The vibration, sway, rattle, trundle of a lift ascending.
Ascending.
Ascending for a long time.
Halting.
Doors rumbling again.
"Coast clear?" said the voice of the overcoat, which was also the voice that had shouted by his ear when he was ambushed at the birch copse.
A pause, then "Yes". Another voice. He knew this one as well. The Columbine's.
More walking. More nosefuls of overcoat odour.
A door being unlocked; opening.
Provender was carried for a few more steps, and then the person bearing him dolloped him down on the floor with a grunt of effort, a hiss of relief.
"Fuck, _he_ wasn't getting any lighter, was he."
Provender lay on carpet. Coarse, cheap-feeling carpet. He didn't move. Didn't want to, even if he could have.
His brain was marginally clearer than it had been. Sense was becoming that much easier to make.
He was starting to grasp what was happening to him.
And not to move, not to draw attention to himself, not to do anything that might be construed as defiance or resistance—this, under the circumstances, seemed a very sensible course of action indeed.
**13**
"CARVER?"
"Mrs Gleed."
"A word, if you please."
"Of course, ma'am."
Cynthia drew Carver aside to a quiet corner of the Piazza San Marco. She did this without touching him, her hand hovering near his sleeve.
The sky was brightening, taking on a pewtery pre-dawn sheen. The ball was starting to wind down. Some guests had already tendered their thanks and left. There would soon be a mass exodus, once the sun rose and its gleam broke the spell of the night irrecoverably. A few diehards might linger on, dancing till the mist dispersed and the dew evaporated, but most partygoers understood that a perfect night finished when the night itself finished.
"Great's gone to bed?" Cynthia enquired.
"I wheeled him to the house and tucked him in a couple of hours ago. He would appear to have had a very pleasant time."
"I'm glad to hear it. So you have no other duties to attend to."
Carver decorously stifled a yawn. "I was anticipating being able to retire myself, in the not-too-distant future."
"Before you do, I've a small favour to ask."
"But of course."
Tallness in men was not something Cynthia had a problem with, _per se_ , but in Carver's case it wasn't an attractive or appealing quality. Whenever she spoke to him he hulked over her, demanding to be looked up _to_ as well as _at_. He knew he was doing it, and Cynthia considered it inappropriate in a domestic servant. Notwithstanding that Carver had been with the Gleeds far, far longer than she had, he remained an employee whereas she was Familial. He ought not to behave as if his decades of servitude meant that he outranked her.
She had the measure of him, however. You treated Carver as you would a dangerous dog: looked him straight in the eye, didn't betray an ounce of intimidation.
"I haven't seen Provender since well before midnight," she said.
"You've checked his room, I take it."
"Twice. He's not there. I've no idea where he can have got to, and I think... I have this feeling..." She faltered.
Carver's scar creased crookedly as he smiled. "You're worried something may have happened to him? Feminine intuition, ma'am?"
"It sounds foolish, I know."
"Not in the least. Who can fault a mother's instincts? More often than not they are right. However, in this instance, I would like to think they are mistaken, and indeed I'm sure they are. I'm sure no harm has befallen Master Provender. He is almost certainly somewhere on the premises, sequestered perhaps in some remote corner of Venice here. Perhaps a little drunk, who knows? He's apt to take after his uncle in that respect, especially on social occasions."
"I've scoured the party site."
"Nevertheless. It is a large site and you are just one person. But in order to set your mind at rest, ma'am, allow me to organise a more substantive search. I'll mobilise a number of security personnel and supervise them personally. We'll find him, have no fear of that."
"Thank you, Carver. It goes without saying you'll be discreet. I don't want anyone getting wind that anything might be amiss."
"Invisibly discreet, ma'am. Give me an hour and I shall undoubtedly be able to report back to you with good news."
AN HOUR PASSED, and the sun cracked free of the horizon, and the full flow of departures commenced. Cynthia fielded the guests" farewells automatically, clasping hands, pecking cheeks, scarcely knowing whom she was saying goodbye to, or caring. "Wonderful," some of the partygoers told her. "The best yet," other said. "Unsurpassable," said still others, as if throwing down the gauntlet for next year. Cynthia just grinned and nodded, while her gaze kept flicking to the left and right for sign of Carver. What was keeping him? Why was he taking so long to get back to her? She couldn't help but think that the longer the search continued, the less likely it was to yield a positive outcome. The misgiving in her belly was now a knot so tight it hurt. The worst of it was, she simply could not fathom what sort of awful thing might have happened to Provender. She just had this sense, this amorphous inkling, a formless notion of Badness, all the more disquieting because for it to have occurred within the confines of Dashlands, this most protected of places, the Family sanctum, it must be a very bad Badness indeed.
Threats were constantly being made against the Families—the Families in general, certain Families in particular, sometimes specific Family members. There was a lunatic fringe out there who, for no logical reason, found it impossible to feel anything in their hearts except hatred for those who happened to be better and wealthier than they were. These people penned and published anti-Family screeds, went on television to delivery anti-Family diatribes, made placards and gathered for anti-Family rallies in city squares. They were few in number, thank God, and they were, as a rule, reviled and repudiated by the general public, but still they existed, a virulently vocal minority. And sometimes their sentiments went beyond mere disapproval; sometimes they maintained that the Families were evil and must be destroyed. For the most part this was nothing more than impotent ranting, the caterwaul of lost, sad souls who needed someone else to blame for the mess that was their own lives. The Families were a convenient, high-profile scapegoat for all the ills of the world. But you could not be absolutely certain that one of these madman might not one day graduate from words to actions—indeed, it had happened. Hence a reasonable level of security was necessary at all times, a bulwark against the remote but tangible possibility that some mad, malevolent malcontent would try to take a Family life.
But how mad and malevolent would you have to be to strike at a Family member in the grounds of their own home? You would have to be utterly determined and quite unhinged. You would have to have no respect for life, your own or anyone else's.
Cynthia suspected she was letting her imagination run away with her. She was visualising wild-eyed psychopaths where there were none. Still, she couldn't shake the idea that her son was even now lying sprawled and cold on a lawn nearby, victim of a killer so crazed, so puffed up with self-righteous anger, that he actually felt he was doing the world a favour, ridding it of Provender Gleed.
_Come on, Carver. What the hell's keeping you? Put me out of my misery_.
Carver was, as it happened, standing right behind Cynthia as the imprecation ran through her mind, as if the same near-psychic affinity he had with Great enabled him to intuit _her_ thoughts as well. He alerted her to his presence with the most minuscule of coughs.
"Carver! You've found him, haven't you. You've found him and he's fine."
"Ma'am..." It was hard to tell if his mood was graver than normal. Carver habitually looked grave. It was his default demeanour. "There is something you ought to come and see."
He would not be persuaded to reveal more. When pressed, he simply reiterated that she had to come and see, in order to make up her own mind. He did not wish to prejudice her interpretation of the evidence.
Evidence?
Cynthia followed him, her thoughts in such turmoil that merely setting one foot in front of the other was a major accomplishment. They headed east out of the party site, exchanging ersatz cobbles and paving stones for morning-moist greensward. Soon they were nearing a small copse of silver birches, beside which stood a handful of security personnel. None of them could meet Cynthia's eye as she approached. Their attitude was one of furtiveness, almost of embarrassment.
"Well?" she said. It would have sounded more authoritative if her mouth hadn't suddenly gone dry.
"Over here, ma'am," said Carver, pointing. "This patch of grass. There are signs of trampling."
"So what?" She was doing her best to be haughty. Somehow that made it easier for her, gave her something to hide behind. "Nothing suspicious about that. Obviously some guests came out this way."
"Maybe, ma'am. But if I might draw your attention to..." Carver pointed again, this time with precise emphasis.
Cynthia looked.
On the ground, to the edge of the trampled area of grass, lay a short length of wood.
A stick.
Not a tree branch—a lathed utensil.
Cynthia tried to recall where she had seen it before. Sometime during the past few hours.
In Provender's hand.
The earth seemed to give a lurch. There was a dull hum in her ears. Carver was talking to her, saying something to the effect that this wasn't necessarily as sinister as it appeared, no one should jump to any conclusions, there might be a perfectly innocent explanation... Cynthia barely heard him. She stared at the stick, nestled there among those overlapping footprints, dropped, lost.
It seemed to point to something.
No, to nothing.
A headless arrow.
Provender...
**14**
SOME TIME AGO his captors had transferred him to a bathroom. He knew it was a bathroom by the cold tiles underneath him, the faint scents of soap and mildew, and the short shuffling echo that attended every sound. They had removed his cape and bound his wrists and ankles with lengths of plastic-coated cord—electrical flex? Then they had left him there, lying on his side on the floor, still blindfolded, with only his dread for company.
Nobody had told him he wasn't allowed to move. Nonetheless there was a kind of talismanic allure about staying still. Frightened animals did this, froze, hoping it would somehow render them invisible to carnivores prowling near. To be static was to invite harm to pass you by. So Provender had lain in the same fixed position, until eventually a severe case of cramp made it impossible to continue to do so. Slowly, with the utmost reluctance, he stretched out his arms and straightened his legs. Having completed this manoeuvre without inviting unpleasant consequences, he dared to ease his wrists and ankles around inside their bonds. His hands and feet tingled painfully as the blood flowed into them again.
By this stage, the effects of whatever drug his captors had injected him with had almost completely worn off. He still felt a little floaty, in a way that reminded him of when he was a child and had spent too long swimming in the sea—the up-and-down of the waves continued to wash within his body for some time after. His mind, however, had regained clarity. His thoughts weren't foggy and fuddled any more, although he might perhaps have preferred it if they were. He comprehended, now, exactly the predicament he was in, and wished he didn't.
He heard the bathroom door open. A pull-cord switch clicked and an extractor fan wheezed into life. No doubt a light must have come on too, but behind the tight-tied blindfold Provender remained in darkness.
He cringed as hands touched him, but he sensed almost immediately that the hands didn't belong to the man, the Harlequin. They were Is's.
"Sit up," she said.
He did, with her assistance, resting his back against the side of the bath.
"I'm just going to roll up your sleeve. OK?"
His body language must have conveyed why he didn't much like this idea.
"I'm not going to give you another injection. I'm taking your blood pressure, that's all."
The cuff of a sphygmomanometer was placed around his upper arm, secured with its Velcro fastenings, and inflated. Is then pressed the business end of a stethoscope into the crook of his elbow and let the air out of the cuff.
"One twenty-five over seventy," she said. "That's not bad, given how your heart rate's elevated. I'll check again later, but I'm sure you're going to be fine."
As she unfastened the cuff, she added, "You can speak, you know. You don't have to sit there like a statue."
"I can?"
"Just don't try yelling for help."
"Oh. No. Never crossed my mind."
"Because there's no point. That's why you're in the bathroom. No windows, no outside walls. Pretty good soundproofing. We'd hear you. No one else would."
"I understand." He gave an uncomfortable little cough. The back of his throat was feeling achey and constricted.
"Don't try removing the blindfold, either. We'll be able to tell if you have."
"What don't you want me to see? Your face? I already have."
"There are other reasons. Look, I realise you must be scared, Provender. All I can say is, if everything goes the way it should, there's no need to be."
He forced himself to ask, "And if everything _doesn't_ go the way it should?"
There was the minutest of pauses. "To be honest, how all this pans out isn't up to us. It's up to your Family. Their response determines _our_ response."
"We have money," Provender said quickly. "Lots of money. You know that. Name your price. Any amount. I'm sure my fath—"
"We'll discuss it later," said Is. There was a soft clatter as she gathered up her medical equipment. "I'll be back in an hour to do your BP again and give you some breakfast. Till then—please try not to worry, Provender. And get some sleep if you can."
The extractor fan rattled and whirred for a few minutes after she was gone, then lapsed into silence.
_Try not to worry. Get some sleep if you can_.
Provender would have laughed, if he hadn't felt so much like weeping.
**15**
IN THE OPEN-PLAN vastness of the second largest of Dashlands House's six main drawing rooms, Prosper Gleed, Cynthia Gleed, Gratitude Gleed and Extravagance Gleed all sat, none of them saying a word. In front of them, on various tables, lay trays of victuals. Clusters of untouched cups encircled cafetières of undrunk coffee and pots of cooled, stewed tea. Croissants and bread rolls, brought hot from the oven, were stacked stone-cold beside melting curls of butter. It was 9 a.m. Sunlight gleamed behind blinds that no one had thought to furl. Around the room several table lamps shed their own muted illumination. Each lamp took the form of a classical figurine, cast in spelter, either holding aloft or cavorting alongside a crackle-glass orb that served to shade the bulb. It was as though, in miniature, gods and nymphs were playing with planets.
On one sofa, Extravagance lay with her head resting in her mother's lap. Cynthia, in turn, was stroking her daughter's hair, just as she might have done when Extravagance was eight or nine. The action, performed mindlessly, soothed them both. Gratitude, meanwhile, had a faraway stare, and Prosper was absorbed in dark inward contemplation. The faces of all four showed, to a greater or lesser degree, a grey-tinged tautness—exhaustion compounded by shock, shock amplified by exhaustion. They had all changed out of their ball costumes into day wear. The party seemed to have happened a long time ago, and its pleasures and excesses had been consigned to memory along with the masks and the wigs and the makeup. The mood now was as sombre as it had been, for the duration of the night, frivolous.
Gratitude was the one who at last broke the long silence. "This better not be some stupid stunt he's pulling, that's all I can say. Some practical joke."
"He wouldn't, 'Tudey," said her mother. "He wouldn't dare. He knows I'd kill him."
"He's got such a strange brain, though. It might be his idea of fun. 'I'll go missing for a while. Pretend I've been kidnapped. Give everyone a scare.' He's probably feeling unappreciated and this is his way of getting everyone to notice him and take him seriously again."
"I was mean to him," Extravagance said. "At the ball. The last time we spoke we were sort of having an argument and I was sarcastic to him and—"
"Don't," said Cynthia, patting her. "Don't even think that way. This has nothing to do with anything you said to him, I'm quite certain of that."
"But I wish we hadn't been arguing."
"You two are always arguing," said Gratitude, meaning it as comfort.
"But if I'd known something like _this_ was going to happen..."
"But you didn't, 'Strav."
Extravagance settled her head in her mother's lap once more, disconsolately. "I promise I'm going to be nicer to him from now on. Every chance I get."
Implicit in this statement was the belief that Provender would be coming back to Dashlands sometime in the future, alive and well. Nobody thought to suggest to Extravagance that she was wrong to think that way. Nobody wanted to say such a thing aloud.
"If he has been kidnapped," Gratitude said, slowly, "if that _is_ what this is, then won't we be hearing from the kidnappers soon? You know, a message with their demands, or whatever."
"Let's hope so," said her mother. "And let's pray that all they're after is money."
"What would it be if it wasn't money?"
"They might"—Cynthia chose her words carefully—"try to make political capital out of holding Provender. They might try and blackmail us into making... compromises that would injure us as a Family. Force us to sacrifice certain rights and assets."
"Such as?"
"Our controlling stakes in major corporations, for one thing."
"Why?"
"To humiliate us, of course. Remember that Japanese Family a few years back, the Omarus? No, you wouldn't, either of you. You were both very small when it happened. Some radical activists, members of some kind of religious brainwashing cult, I forget what they called themselves, stole the youngest son of the main branch of the Family. He was barely a week old. He had been born premature, and they took him from the hospital, incubator unit and all, right under the noses of a dozen security guards. They just dressed up in white coats, pretended they were doctors, and wheeled the poor little thing out to a waiting car."
"I sort of have heard this story, I think. How horrid!"
"And then they went on TV and ordered Kenji Omaru—"
"Kenji was the baby's father?"
"Correct, and the head of the Omarus back then. They ordered him to sell off all Family stocks in the main Japanese _zaibatsus_ and then read out a speech on primetime television, which they'd written for him, basically saying he was corrupt, Families were evil, no one should have that much money, the wealth belonged to the people, it should be shared out more evenly, et cetera, et cetera. It was about twenty pages long, that speech, and Kenji was supposed to deliver it to camera with the whole world watching, and you know how the Japanese are about pride and honour. It was intended to break him. It was tantamount to a death sentence. Also, these people—the Cult of the Orange Shrine, something like that—they just hadn't thought the financial side of it through. If the Omarus tried to sell off that much stock all at once, there'd be a huge drop in share values across the board. The stock market would crash. The whole regional economy would collapse. Perhaps they wanted that as well. Social and economic chaos. Who knows how these people's minds work. Anyway..."
"What happened?"
The bitterness of Cynthia's tone gave way to wariness. "No, well, come to think of it, it's not such a relevant story after all."
"Mother, what happened?"
She shook her head. "I wish I hadn't brought it up now. The circumstances aren't similar to ours, not at all."
" _Mother_..."
"Kenji refused. Point-blank. Refused to do as they asked. He wasn't going to destroy himself and his whole Family, and heap financial ruin on so many others as well."
"He refused. So what about the baby? His son?"
"He... he thought it better to let the boy... It was his youngest son. He had three others."
"Oh my God."
"They... Police found the body a month later in marshland outside Kobe. They had a tip-off and apprehended the cultists too. There was a trial. Death sentences were passed."
"But he let the baby..."
"He had to. Had no choice. Too much else was at stake. He felt it was the right decision. He said Family is about more than parents and offspring and relatives."
"What a bloody wonderful little tale," said Extravagance from Cynthia's lap. "Thanks for sharing that with us, Mum. I feel a whole lot better now."
"I know, I'm sorry, it was just to illustrate what some people might be prepared to ask from us, how far they'd be willing to go. I really don't believe it's the same here with—"
"'Some people'," said Prosper. He, of all of them, was the one who had said the least since they assembled in the drawing room. His brooding had been deeper and more intense than anyone else's. Now that he had piped up, it was clear that he had come to some conclusions and wished to air them.
"Yes, dear?" Cynthia said.
Prosper looked at his wife and daughters, steely-eyed. "I don't think this was 'some people'. I don't think this is about ransom either."
"What is it about, then?"
His voice dropped so low, it was almost a growl. "I think we're under attack."
"What?"
"I think this is the opening salvo. Someone's gunning for us."
"Really?"
"Really."
"Where's the evidence? What makes you say this?"
"Instinct. Gut."
"Who, Dad?" said Gratitude. "Who's gunning for us?"
"Who do you think?"
"Another Family?"
"Not just any other Family. One particular Family."
It didn't take much hard thinking to work out who he was referring to.
"No," said Gratitude.
"They wouldn't," said Cynthia.
"Why not?" said Prosper.
"They—they wouldn't go this far," Cynthia said. "It's always been strictly business between us and them. Buyouts, takeovers, forced mergers. Yes, we fight them, but only in boardrooms, only in industry and commerce. We compete. We don't... It doesn't come to this. Not actually attacking Family members. I don't believe for one second they'd stoop that low."
"Don't you?" said her husband, flatly. "I'm not so sure. Face it, we've waged wars with them in the past. Literal wars. Twice this century we've virtually razed Europe, battling them. Oh, it _looked_ like it was about armies invading territory, annexation, occupation, political power blocs colliding— _we_ know it wasn't. This Provender situation, it's clearly just an extension of that. A new form of war. A new battlefront opening up."
"No, you're wrong, Prosper. This is paranoid talk. There's just no way they'd, out of the blue, they'd—"
One of the drawing room's three doors sprang wide open and Fortune came striding through.
"Right!" he said, thrusting the door shut behind him. He was still in his devil get-up, although he had relinquished his horns and pitchfork and, for the sake of warmth and decorum, had donned a smoking jacket borrowed from his brother. He was also still not entirely sobered up, although his drunkenness had been mostly alleviated by a sense of mission, and by several cups of espresso from the kitchen. "This is the situation out there. Prov's definitely not in the grounds. They've done sweeps of the estate, grid-pattern, military-style. Carver's running the whole shebang and you can take the man out of the army but you can't take the... and so forth. All the guests have gone. All the catering staff and that lot have been allowed to leave too. The set breakers have been put on hold. All they've been told is that we don't need them yet. The excuse is you lot want a lie-in, don't want to be disturbed by a bunch of blokes hammering away all morning. We'll have to let them come this afternoon at the latest, otherwise it'll look like things have gone awry."
Fortune pronounced the last word _or-ree_ , for reasons unknown even to himself. It was just one of his little verbal tics.
"So," he went on, "we've got the rest of the morning to keep searching, though somehow I don't think we'll have any more luck. The main thing is, as far as I'm aware nobody knows a thing about this except us and the security personnel, and we can be pretty sure they won't tell a soul. They're trained to keep schtum and they know that if one of them blabs and we find out who, he or she will never be employed anywhere else again ever. So that's your information blackout right there, Prosp. This isn't going public unless or until we want it to."
"Or the kidnappers want it to," said Cynthia. "Any idea how they got Provender off the estate?"
"Carver's looking into that. Seems there might be some sort of anomaly. Something to do with the catering staff. It may be relevant, it may not, who knows. Carver's on to it, at any rate. Frankly, if I was the chap in charge of catering and I'd made a goof of some sort, I'd be quaking in my boots right now."
"And has Great been informed?"
"Still asleep, apparently."
"He'll need to be told, but it should be broken to him gently. Someone in his state of health..."
"I'm sure the man with the scar will know how to handle it." Fortune eyed avidly the items of breakfast food ranged around the room. "Blimey, I'm famished. Mind if I tuck in?"
"It's not at its freshest. We could ring for more."
"Not too fussed about freshness." Within moments Fortune's cheeks were bulging with buttered and marmaladed roll, which he washed down with slurps of room-temperature coffee. Glancing up from his repast, he noticed that his arrival had done little to raise morale. The faces around him were as glum as when he had entered. This perturbed him. If Fortune Gleed had any particular talent, it was the ability to lift the mood of a room. Usually all he had to do was walk in.
"Oh come on," he said. "This is going to turn out fine. Of course it is." He took another look around. "Isn't it?"
**16**
IS SPOON-FED PROVENDER the last of the corn flakes and held up the glass of orange juice for him to sip. Some of the juice missed his mouth and dribbled down his chin. She swabbed the drips away with a wad of paper towel.
"I feel like I'm six months old," he said.
It wasn't much of a joke, and the laugh he chased it up with wasn't much of a laugh either. All the same, Is felt a prickle of admiration. In his position, would she be capable of making wisecracks?
"I wouldn't know about six months old," she said. "I've fed sixty-year-olds like this, though."
"You're a nurse, aren't you?"
She hesitated, cursing herself. Damien had been adamant that they gave away nothing about themselves. No clues to their identities whatsoever. She wasn't sure, however, if this was a practical precaution or if Damien was insisting on it because that was what kidnappers conventionally did: remained anonymous to their victims. When all was said and done, this wasn't a conventional kidnapping.
She decided it didn't matter. After all, she had already given Provender her real name. She hadn't meant to, but he had surprised her by asking for it at the ball, and her mind had gone blank. Instead of mustering up a false name, she had let the real one slip out. There was nothing she could do about that now, and similarly, there was no point trying to deny she was a nurse. Even if it wasn't obvious from the injection and the sphygmomanometer, that remark of hers about sixty-year-olds put it beyond doubt. She resolved, however, to be more careful in future.
"Good guess," she said. "Well done."
Provender nodded. "The way you are with that blood pressure thing. Very professional. And," he added, "you seem like you're used to caring for people."
"This an attempt to get on my good side? Win me over? Because if so, it's not going to work."
Had his eyes been visible, she knew she would have seen them wince.
"No, I only... It was an observation, nothing more."
"Right, then. Fine. Just so's you know. We're not going to be getting into any hostage—hostage-taker bonding here."
She clacked the empty juice glass into the cereal bowl, with finality, and stood up to go.
"Um, Is?"
"Yes?"
"I'm sorry, I don't want to be a pain or anything, but... I've been holding it off, and I can't any more."
"Holding what off? Oh. You need to pee."
"I need to pee. Quite badly, as a matter of fact."
She set down the glass and bowl. "All right. Listen, though. You're going to have to do this with my help because I'm not untying your hands or taking off the blindfold."
"I'm not all that comfortable with—"
"Tough. Now, stand up. I've got your arm. I'm taking your weight. Both feet flat on the floor. I know it's difficult with them tied together. Yes, that's it, there we go..."
She stationed Provender in front of the toilet, lifted the lid, and briskly unzipped his fly. As she delved into his trousers, he tried to bat her hand away.
"I can manage."
"No, you can't. Men have bad aim at the best of times. God knows what you'd be like blindfold."
"I could always sit."
"Don't be such a baby."
Provender fixed his jaw in an awkward jut as she groped through the flap in his underpants and fished out his penis.
Is had handled more strangers" penises than she cared to remember—all in the line of duty, naturally. Dealing with a male patient's appendage was one of a nurse's less agreeable tasks, although it was far from being the worst (wiping off vomit and cleaning up shit vied for _that_ honour). The trick was to think of the penis as just another anatomical part, no more interesting than a toe or a nose. Failing that, you had to try to regard it as just a functional object, a tube that just happened to be made of flesh. Normally, of course, she would be wearing latex gloves, a thin but crucial barrier between clinical and intimate. She made a mental note to buy some. This wasn't going to be the last time she had to help Provender pee.
"Your fingers," Provender said with a hiss. "Cold."
"That's your excuse, is it?"
"What?"
"Nothing. Sorry."
Provender screwed up his face, then gave a sigh.
"I can't. Nothing's coming."
"Relax. Try to pretend I'm not here."
"Difficult."
"Count yourself lucky. We did think about catheterising you."
"You wouldn't."
"But I could."
Again, Provender concentrated.
"Still nothing?"
"Nope," he said, pained.
"I'll run a tap."
Water spattered into the basin.
"I really—"
"Think watery thoughts. And unclench your pelvic floor."
He turned his head towards her, as though he could see her through the blindfold. "I don't have a pelvic floor. Do I?"
"Of course you do."
"I thought only women had..."
"Well, you're wrong."
The water continued to pour, but it was the only thing that did.
"Can we talk about something maybe?" Provender said. "You know, as a distraction. Take my mind off the problem at hand."
"What would you like to talk about?"
"How about the name Is? It's short for something, right? Isabel?"
"No."
"Isadora?"
"No."
"Isolde?"
"No."
"I'm all out of Is-es."
In spite of her earlier resolution, Is felt that giving him one more tiny nugget of information couldn't do any harm. He had half her name already, and the other half was identical to that half. Effectively, she was giving him nothing new.
"Isis."
"Isis?"
"Ancient Egyptian goddess. Wife of Osiris. Mother of Horus. Associated with nature and fertility. Symbolised by—"
"I know who Isis is. My parents spent a shit-load of money so that I'd be educated to know things like that."
"Ooh, well, aren't you the lucky one."
"No, I didn't mean it like that."
"How did you mean it, then?"
"I... I don't know. Not like that, though." He tried an ingratiating smile. "So it's Isis, is it? It's a nice name."
"My mum thought so. I don't."
"What's wrong with it?"
"For one thing, who wants to be named after a goddess? Talk about raising expectations. Also, it looks odd, written down. Repetitive. An "is" too far. So I shorten it."
"Why the second syllable, though? Normally people go for the first."
"Right, I'd really want to be called 'Ice'. I just prefer Is. Is is sort of... what it is. It just is."
"Very 'in the moment'."
"Don't mock."
"Very existential."
"I'm warning you."
"Ow! Not so tight!"
"Then don't mock, _Provender_. Hang on, what's this?"
"Oh, thank Christ. Finally." A smile of something close to bliss crescented Provender's lips.
"That's it. Don't lose it now. Keep going. Stay calm. Don't clench up. Relax."
"Oh, that is _so_ much better..."
**17**
PROSPER GLEED'S STUDY was a symphony in wood. Oak-panelled walls, inset with oak bookcases, stood between a parquet floor and a beech-beamed ceiling lined with cork tiles. A mahogany desk and matching chair dominated the centre, with a teak coffee table nearby on which various wooden ornaments rested, including a lacquered-ebony inro box—gift of the Takeshis, Japan's other main Family beside the Omarus—and a carved cherrywood bust of Rufus Gleed, the likeness of the Family's founder copied from the only extant portrait of him, which hung elsewhere in the house. The louvred window shutters, which stood open, were wood. The inkwell and even the fountain pen on the desktop were wood, as was the housing for Prosper's videotyper screen (for the record, dark-stained ash). The lighting sconces, shaped to resemble candelabra, were wood. Anywhere you looked, wherever wood could be used, wood would.
As Cynthia entered, she saw Prosper's Phone was stationed in one corner of the room, looking, it must be said, somewhat wooden himself. There wasn't much to do, when you were a Phone and not in use, except stand and stare into the middle distance, sentry-style. You must never yawn or shuffle your feet. Above all you must never give any sign that the communications unit strapped to you, all sixty pounds of it, was starting to get heavy. To be a Phone was a job only for those with a strong constitution and a high boredom threshold. Others need not apply.
Prosper, at his desk, was absorbed in contemplation of something on his videotyper screen. To judge by the red-highlighted figures in the right-hand margin, he was studying that subset of the Family accounts which related to the Gleeds" boardroom battles with the Kuczinskis, the only field of fiscal conflict in which the Family's losses currently outweighed its gains.
"Prosper?"
He looked up. Blinked.
"Would you send your Phone out for a moment?"
Prosper frowned, then turned to the man in the corner and clicked his fingers. The Phone stepped smartly out of the room.
Cynthia perched on the edge of the desk near her husband and folded her arms.
"Tell me you were showing off back there," she said, nodding in the direction of the second-largest drawing room. "Tell me it was just manly breast-beating."
"I don't know what you're—"
"You know perfectly well what I'm talking about. It was for the girls" benefit. So that you could look more like a father. You don't sincerely believe the Kuczinskis are behind all this."
"On the contrary, I'm trying to think of reasons why they might _not_ be."
"I gave you reasons. Plenty of them."
"And none, in my view, holds up against the fact that our two Families have been at loggerheads for two centuries, more or less. They hate us. They'd stop at nothing to undermine us. Won't you at least admit, Cynthia, that if any Family was responsible for kidnapping Provender, it would be the Kuczinskis?"
"I agree, but—"
"There we are, then."
"Let me finish. I was going to say, I agree, but without any form of proof, all you're doing is making wild and potentially dangerous accusations. Wouldn't it be better to wait till we know more? Till, for instance, we actually hear from the kidnappers?"
"And what if we don't hear from them? What if Provender is halfway to Warsaw by now? You have no idea what the Kuczinskis are like, Cynthia. You don't have to deal with them like I do. You don't have to sit with them at the Annual Family Congress and watch those beady red eyes and those white faces and those ridiculous filed teeth of theirs. You don't have to watch them sip blood from wine goblets and smack their lips with relish. Blood freely donated by East European ClanFans. Ugh! They're disgusting. They're worse than monsters—they're humans playing at being monsters. Real monsters, if such things exist, can't help being what they are. The Kuczinskis can. So don't tell me this isn't something they'd do, because I know them and this is exactly the sort of thing they'd do."
"Then why not contact them? Get the Phone back in and ring them right now? Speak to Stanislaw Kuczinski and ask him straight out: do you have my son?"
"Because, for one thing, it's mid-morning in Poland. They'll all be fast asleep. And for another thing, he'll almost certainly lie and say he doesn't have a clue what I'm talking about. And for a third thing, I've had a better idea."
"Which is?"
"All in good time. You know, though, Cynthia, it does upset me a bit."
"What does?"
"The fact that, here am I, I'm faced with a crisis, our son's been taken, our Family's been attacked in its own homestead, bearded in its lair, and I'm trying to do something about it, and all I get from you is grief. Not support. Not encouragement. My own wife, who's been harping on at me for years not to be such a wastrel and a layabout—and those are just some of the kinder names you've called me—my own wife is unwilling to back me to the hilt when I need her to."
"I'd back you, Prosper," Cynthia said. "Of course I would. If I believed you were doing the right thing. If I didn't feel you were about to take some precipitate course of action that could lead to God knows what."
"So much for a wife's unconditional love for her husband. So much for man and woman becoming one flesh. Were you asleep during our marriage vows?"
"Oh, _Dios mío_ , Prosper! Don't talk to me about 'unconditional love'. Don't you dare. _¡Hipócrita!_ This from a man who'll screw anything in a skirt. A man who'll disappear for days on end and I don't know if he's in a casino in Monte Carlo, at the Kentucky Derby, holed up in some high-class Bangkok brothel, or what! If I've given you anything over the years it's love, patience, tolerance, devotion, way above and beyond the call of duty. I've stood by you while any other woman would have divorced you long ago and made it as public and traumatic as possible. I've put up with your behaviour, I've taken more shit from you than anyone deserves, and damn it, if that doesn't give me the right to tell you when I think you're making a bad decision, I don't know what does. Bah!" She spat. " _¡Hijo de puta!_ Sometimes you disgust me."
"I understand you're upset by all this, Cynthia." Prosper's hands came up in a placatory gesture. "It's hardly surprising. We're all under incredible strain right now, and if—"
She hit him, open-handed, intending more to shock than to hurt. The fact that the blow clearly did hurt, however, a lot, was not exactly a source of displeasure to her.
When he had stopped rubbing his cheek and hissing through clenched teeth, Prosper said, "Well. Hmm. I'll put that down to heat of the moment. Lack of sleep. Time of the month, maybe."
"Put it down to whatever you like," she replied, icily. "You know as well as I do you've had it coming for ages."
"You won't change my mind, Cynthia. No matter how many times you slap me."
"A skull as thick as yours, it'd take a sledgehammer to get through to you."
"I'm convinced the Kuczinskis are behind this. Convinced. And the first thing I'm going to do is get them to confess it. And the next thing I'm going to do is threaten them with dire consequences if they don't give Provender back."
"You're mad."
"No, I'm someone who knows what's best for his Family and will do whatever it takes to protect his Family."
"This isn't just some game, Prosper. This isn't a spin of a roulette wheel or a draw at blackjack. Lives could be at stake here. Thousands, perhaps millions. You'd go to war with the Kuczinskis without even knowing for sure they're guilty?"
"I'll find that out first, and then, if war's what it has to be, then war it is. Phone!"
"Prosper, I'm begging you. Wait."
"Wait for what? The Kuczinskis to take Gratitude as well? Extravagance? _Phone!_ "
The study door open and the Phone poked his head in. "I'm sorry, sir, did you want me?"
"Dammit, man, are you deaf? I've been shouting for you for hours."
"Prosper..."
"Come over here," Prosper said to the Phone. To his wife he said, "I'm invoking an Extraordinary Family Congress. I'll get word out to Massimiliano Borgia de'Medici. He'll do the rest. I want Stanislaw Kuczinski to look me in the eye across the Congress Chamber and tell me he doesn't have my son. I want everyone to see that shifty vampire wannabe squirm as he lies to my face."
"Prosper, I can't condone—"
"Not asking you to." He snatched the receiver handset off the Phone's back. The Phone, meanwhile, reached over his own shoulder and hurriedly raised the retractable aerial on his backpack, then pressed a lever on his chestplate that flipped up the rotary dial.
"Prosper—"
"Borgia de'Medici," Prosper said to the Phone. "Come on, get on with it."
The Phone dialled the number, and Prosper tapped his fingers while waiting for the connection to be made.
Cynthia spoke her husband's name again, in vain.
"Hello! Yes!" Prosper barked into the receiver. "Signor Massimiliano? Prosper Gleed here. _Buòn giorno_. _Come sta_? No, not so good here, I'm afraid. Now listen..."
**18**
DAMIEN HAD ASKED to be woken at midday. Venturing into his bedroom, Is was struck by the messiness of it. Heaps of clothes cluttered the floor. Drawers were wide open, cupboard doors the same. The rattan window blinds hung at angles. Damien's collection of books, of which he was so proud, had fallen into disarray, filling their shelves haphazardly, most of them canted rather than upright. Worst of all, the whole room reeked. Unwashed laundry. Unkempt male. It had never, Is thought, been this untidy or this malodorous when _she_ had been a semi-regular occupant here. Back then, when she and Damien were lovers, he had made a concerted effort to clean and be clean. Six months on, that was no longer the case. When she had let him go, he had let himself go.
She spent a few moments inspecting the books, seeing if any new titles had appeared. This was Damien's ideological library, set apart from the run-of-the-mill hardbacks and paperbacks that could be found elsewhere in the flat. The books in the bedroom were the ones he returned to again and again, the ones he cherished. Academic treatises and works of political philosophy rubbed shoulders with less reasoned but more impassioned tomes. Anthologies of anti-Family writing. Tracts deploring the Families" stranglehold over ordinary people's lives. Angry denunciations of the public's fascination with all things Familial. And of course the famous what-if? novel, penned by Anonymous, _The Meritocrats_ , which posited a world where the Borgias and the de'Medicis had not joined forces in the Sixteenth Century and become _de facto_ rulers of Italy and therefore had not inspired the rise of Families in other nations. Utopic in outlook, and a dense and immensely dull read, _The Meritocrats_ had arrived on the anti-Familial underground scene roughly three years back and swiftly become a sensation. It was reputed to have found a home in more than a million households across the world, despite being available only in blurrily-printed and badly-bound foolscap _samizdat_ form, and was a particular favourite among university students, who passed it around like a naughty secret. Is herself did not know anyone other than Damien who owned a copy and thought the "million" estimate might be something of an exaggeration. She had also, despite several noble attempts, never managed to finish the book. She was somewhat ashamed of that. It was a seminal work. As Damien once said, "Anyone who hates the Families and hasn't read _The Meritocrats_ doesn't truly hate the Families." And maybe that was so and maybe Is didn't truly hate the Families—but she thought she did, and she thought that hatred wasn't all you needed to get you through to the end of Anonymous's seven-hundred-and-fifty-page doorstop. The patience of a saint and the endurance of a marathon runner were also required. It was a novel in name only. In lieu of plot there was a series of barely connected events. In lieu of characters there were a cast of ciphers who parroted the author's opinions. Each time she had borrowed Damien's copy, Is had vowed to plough all the way through. Each time, usually somewhere around page 50, it had defeated her.
She leaned down and shook Damien by the shoulder, and kept shaking him till he surfaced blearily and bleatingly from sleep. Swinging his legs over the side of the bed, he sat up and stared at his knees while he sorted his thoughts. Damien was never at his best, newly woken.
"Kettle's on," Is said.
He grunted approval.
"And Provender's fine," she added. "As fine as you'd expect, anyway."
He half nodded.
"I've fed him, relieved him." She paused. "He seems pretty docile. I was wondering..."
"If you're going to say what I think you are," Damien said thickly, "forget it."
"I doubt he'd try to escape."
"Of course he would."
"But he looks so uncomfortable."
"Boo-hoo. My heart bleeds."
"At least we could untie his ankles. Or if not that, take off the blindfold. He's seen my face already, for heaven's sake, and possibly yours too."
"That's not what the blindfold's there for. It's there to keep him disorientated. Standard military practice with captives: deprivation of light, to make them acquiescent. Like hooding a falcon."
"And to dehumanise him as well, maybe? So you don't have to look him in the eye?"
"Is." Damien fixed her with his gaze. "No. Let's not have any of this. No compassion for him. He's a Gleed, for fuck's sake."
"That's not _his_ fault."
"I can't believe you said that." Damien levered himself up off the bed. He was naked except for underpants, and the act of standing showed off his musculature to full effect. The whole of him tautened or flexed, a massed rippling of lean, fatless flesh. The rippling continued as he pulled on a plain shirt and a pair of cords. He wasn't innately graceful, but everything in his body moved and meshed just as it should and that lent him a kind of fundamental physical harmony.
Buttoning his shirt, he turned to face Is. "No Family member is innocent. You know that. They can't hide behind 'Ooh, it's not my fault, I didn't ask to be born'. They're part of the cabal from the moment they're conceived. Because it's genetic. It's in the blood. They go on about it all the time, don't they? Blood, lineage, and so on. It wouldn't matter if it wasn't all-important to them, but it is, and so they can't have it both ways. Either they're Family, every last one of them, or their entire massive con job falls apart. There are no exceptions. Think of it like the Catholics and Original Sin. They're all tainted, and no amount of denial or distancing's ever going to alter that."
He jabbed a finger at her.
"Are we clear?"
Is said, "It doesn't mean you and I can't show him a little humaneness."
"Humaneness," said Damien, "is what the Families have never shown towards the millions of people they've exploited, harmed and killed over time. Besides, we're not starving him. We haven't hurt him. If you ask me, he's come off pretty well, all things considered."
In the main room of the flat, the kettle began whistling. Damien strode out of the bedroom, and minutes later was to be found hunched at the table gulping down slices of toast and the first of several cups of tea. He had the television on, tuned to one of the news channels.
"Nothing about us," he said to Is, gesturing at the TV. "The Gleeds have sat on it, just like I thought they would. Keeping it in the Family." He smirked. "What I wouldn't give to be a fly on the wall at Dashlands House right now. I'd be able to watch them all flapping around like arseholes. _And_ I'd be able to leave little dots of shit all over their windowsills." The smirk became a guffaw. "Oh come on, Is, you have to admit that was pretty funny."
Is, rather than admit anything, got busy in the kitchen area, preparing a lunchtime sandwich for herself and for Provender.
Damien paid a visit to the bathroom, and she heard him chatting to their prisoner while he took a long and loud piss. Damien's tone was jovial but, she thought, mockingly so. This was confirmed when she looked in on Provender shortly afterwards. He didn't appear in any way happier about his situation. She noticed splash marks on the uppers of his shoes and a few dribbles of urine on the floor by his feet. _Damien_.
She gave Provender his sandwich and sat on the toilet seat to eat hers.
"Thanks," was all he said, when he had finished.
"Whatever he said to you," Is said, meaning Damien, "take it with a pinch of salt."
"Oh, he was very friendly. I'm your honoured guest, apparently. And if I have any complaints about the living conditions, I'm to take them up with the hotel manager, whose name is Mr Couldn't Give A Toss."
"That's his idea of a joke."
"No, really?"
Damien, when Is emerged from the bathroom, was on the phone. "Yup," he said, "all trussed up, nice and tight. He's not going anywhere."
He listened briefly, then said, "How long do you think I should leave it, then? I mean, they're expecting a note, aren't they? A phone call at the least."
More listening.
"Fair enough. And what's it like over there? What's your impression? All hell breaking loose?"
A grin appeared on his face, and broadened.
"Nice. Very nice."
The grin vanished.
"I wasn't gloating. I wouldn't call it that at all." For Is's benefit, he sneered and made a masturbatory gesture at the receiver with his free hand. "I was just... Yes, I know. Nope. Yes. No."
Now Damien began wagging his head from side to side, the universal sign language for The Person I'm Having This Phone Conversation With Is Beginning To Get On My Nerves.
"All right. So you'll call me when you want the next phase to start. OK. Yup. Fine. 'Bye."
He clanked the receiver onto its cradle, then said to the phone, "Your wish is my command, fuckwit."
"That was your insider?" Is said. "Your mole?"
"No, it was my mother."
She brushed the sarcasm aside. "So everything's going according to plan?"
"Seems that way."
"So why aren't you pleased?"
Damien pondered this. "I suppose because I'm the one meant to be running the show and yet I feel like I'm taking orders a lot of the time and that really wasn't how I saw this going."
"Why not tell him that? Your insider?"
"Who says it's a him?"
"Or her. Why not tell her?"
Damien shrugged. Is thought there was something furtive about the shrug, but then Damien was perennially touchy on the subject of his contact within Dashlands. Cagey as well. It was as if the less Is knew about the person, the less important it would be that Damien had needed inside help to formulate his kidnap plan. His vanity demanded that he appear solely in charge of the operation.
"Anyway..." Damien stood up, grabbing a jacket. "I'm off out. Breath of fresh air. Need anything from the shops?"
Is shook her head, then remembered she did need something. "Latex gloves, please."
"Eh?"
"Disposable ones."
"For what?"
She waggled a hand at him. "For this. For stuff I have to do with Provender."
"Oh. Oh, right. OK."
"Not washing-up gloves, either," she said, as Damien headed for the door. "Proper ones like I use at the hospital."
"I'm going to find those around here?"
"Don't see why not."
Damien sniffed. "Well, I'll try." From a small, low table by the door he took his wallet and another object. The wallet went into a pocket of his jacket. The other object he strapped to the back of his belt and carefully covered with the jacket flap. Then he went out.
Is pottered around the flat for a while, tidying, then glanced in on Provender once more. He was sitting crouched against the bath, as ever, head down. He looked small. Waiflike. Lost. She wanted to say something that would lift his spirits, even just slightly. Nothing sprang to mind. Gently, she shut the door.
**19**
AT SCHOOL DAMIEN had been known as Disgrace. The nickname was coined by a Fifth Form master, Mr Sudworth, who fancied himself something of a stand-up comedian though in truth was as tedious and mirth-free as the subject he taught, geography. Mr Sudworth's brilliant stroke of wit was to take Damien's name as it appeared on the school register, D. Scrase, and pronounce it in such a way that _it sounded like the word "disgrace"._
Hilarious!
Mr Sudworth thought so, at any rate, and never tired of the joke. Each time he addressed Damien as Disgrace, he would chortle heartily as if the nickname had only just occurred to him. Damien's classmates, for their part, found it amusing once, perhaps twice, but thereafter could barely muster a titter.
By rights, then, Disgrace ought not to have stuck. It wasn't an especially clever nickname, nor did it lend itself to shortening or further mutation. It was insulting but not terribly so. And perhaps it would not have stuck if Damien had objected to it strongly and put a stop to his peers calling him it by giving anyone who did a bash on the nose. But he hadn't, because deep down, almost at a subconscious level, he felt he deserved it. Disgrace summed up how he regarded himself and his life. He wore it like sackcloth and ashes; like tar and feathers. Even when juniors in the school knew him by it and used it to his face, he bore their jibes with a martyr's patience. Disgrace? Yes, that was him all right.
He had a father who scarcely spoke to anyone; a mother who was an avid, one might even say obsessive ClanFan; an older brother who had died aged seventeen, victim of a hit-and-run drunk-driving incident, and who was never mentioned; an older sister who had moved out to live with her boyfriend but spent as much time back home as she did at her boyfriend's flat because when he was out of work, as he often was, he became morosely depressed and then became too free with his fists; and a younger sister with Down's syndrome who needed more looking after than they could cope with and so had been packed off to live in care but came back to stay for one weekend a month. He had, in short, a family only in the loosest sense of the word, and Damien, as a sensitive boy and then a sensitive young man, always believed at the back of his mind that in some way he was to blame. It was _his_ fault that his father read the newspaper during mealtimes and whiled away all of his free hours down in the garden shed, allegedly fixing things but in fact quite evidently doing nothing. _He_ was the one who forced his mother to lose herself in a fantasy world of Families, collecting magazines and books about them, clipping out newspaper articles about them to paste into scrapbooks, buying all manner of Family-related bric-a-brac and memorabilia, and building what was effectively a shrine to all things Familial in one corner of the lounge—the walls smothered with posters, the carpet heaped with cheaply-produced souvenir tat, Family members" faces peering out into the Scrases" lives all day every day. _He_ was responsible for Jason being killed by that careering car and for Tanya hooking up with that godawful oaf Calvin. It was even possible that _he_ had somehow brought about little Adele's birth defect.
As an adult, Damien would realise that he took all this unwarranted guilt on himself simply because no one thought to tell him otherwise. It didn't occur to anyone sit him down and explain that some things happen just because they happen. His parents never even noticed that he was in a state of almost constant torment, agonising over the reasons why his family was so blighted by misfortune and misery (it was something he had done, it must be). As far as Mr and Mrs Scrase were concerned, thank God one of their children had turned out quiet, undemanding, normal. It was a relief to be able to ignore him. They could forget about Damien, in the way they couldn't forget about Tanya and her latest black eye, Adele shrieking through her weekend visits, or the hurtful memory of Jason.
It was around the age of eighteen that Damien had a moment of revelation, an epiphany almost. He was shortly to leave school, and his teachers had assured him that a university place was his for the taking if he only applied himself in his exams. His reports routinely described him as highly intelligent but lacking in drive and motivation. The headmistress promised him that if he made the effort and gained the requisite grades, she would do her utmost to obtain one of the Family-funded university scholarships for him, which would see him through his degree course.
In the lounge at home, Damien knelt at his mother's Family shrine. He studied the clusters of happy faces, the elegant poses, the immaculately-groomed hair, the backdrops of palatial residences and unimaginably expensive furnishings. This privileged international elite who led such perfect, carefree, untroubled lives. Look at them with their arms round one another. Look at their clothes. Look at the way members of each Family, or part of Family, were able to stand together to have their pictures taken. Where was the missing brother, taken too soon? The sullen, uncommunicative father? The sister with the bruises? Oh sure, the Families must have their problems. Damien wasn't so naïve as to think that things didn't wrong for them from time to time. But they had money, huge sums of it, and that made a difference. They also had unity. Every image in front of him said so. Screamed it. Unity radiated from every item of his mother's collection. It shone like the sun.
All at once, Damien understood that he hated them. No, not just hated. That wasn't strong enough a word. He _despised_ the Families. They were everything his family was not. They presented an ideal that it was impossible for others to live up to. Their capital F belittled every non-Family family in the world. Their wealth, even when they tried to disburse a tiny fraction of it as charity, mocked those who were poorer and less fortunate than themselves, which was everyone.
He knew, then, that he must dedicate his life to opposing the Families. He would fight them in whatever way he could. He would sacrifice himself to the task of damaging and perhaps even destroying them. It was his mission.
He flunked his exams abysmally. No hope of a Family scholarship then. He left home, moving from a small town just outside London's suburbs to the heart of the city. The night before he went, he did something which was appallingly mean and which he continued to regret but which at the time seemed like a necessity, even an act of generosity. He set fire to his mother's shrine. There were candles in front of it, which his mother would light occasionally to lend the shrine an even more votive air. They were aflame that evening, and Damien promised his mother when she went to bed that he would extinguish them when _he_ went to bed. He didn't. He "nodded off on the settee". One of the candles must have "accidentally fallen over". When he awoke, the whole shrine "was burning out of control". He tried to put out the flames "as fast as possible" but, obviously, "not fast enough".
The shrine was devastated. His mother was devastated. She was still in the lounge at dawn the next day, pawing distraughtly through the charred remnants of her collection, trying to salvage what she could of it. The last sounds Damien ever heard her make, as he sneaked out by the back door with a holdall containing all his clothes and possessions, were a series of helpless mewling sobs which degenerated into out-and-out lost-dog howling. The noise pursued him all the way down the street, onto the bus, into the city.
A decade on, if Mrs Scrase were by any chance to meet her younger son, she would almost certainly not recognise him. He was bulkier, thanks to a rigorous regime of bodybuilding (in any mission, physical strength was a must). He was harder-looking (to survive as a resident of Needle Grove you had to be hard-looking). His face had taken on a leaner, meaner air (never let it be said that the outer person did not reflect the inner). If Mrs Scrase had ever hoped that Damien might find himself a nice, secure profession, settle down, marry and give her grandchildren, she would have been disappointed. His career, such as it was, consisted of intermittent menial jobs which earned him enough to pay the rent and keep body and soul together, with a little left over for book-buying. Whatever kind of work he did, he carried it out with no more competence or enthusiasm than was necessary to avoid being sacked, and when he got bored and wanted to be sacked, he simply lowered his effort level that little bit further until his employers took the hint. As for settling down, he had had a string of short-lived affairs, glorified one-night stands many of them, and his only relationship of any significance was the year he had spent with Is, which he now looked back on as the happiest and maybe the only happy year of his life.
He had met her while he was working as a porter at St Fiacre's Hospital. Not porter in the sense of pushing beds and bodies around. He had been under that misapprehension himself when applying for the job. In fact, the position had been for a porter in the hospital's kitchen, where it pretty much meant dogsbody. He had pictured himself racing desperately ill patients to the operating theatre and wheeling dead patients to the morgue, both of which tasks had a kind of dark, noble glamorousness, but in the event his duties were preparing and serving food. He would have quit after the first day has a nurse called Isis Necker not entered the cafeteria that lunchtime and taken a portion of shepherd's pie and mixed vegetables from him.
She scarcely noticed him. She was busy talking to a friend, a fellow-nurse. She glanced at him for no longer than the time it took for him to ask her what she would like and for her to tell him and for him to give it to her. Then she strode away from the serving counter with her tray, and although she would insist later that he _had_ made an impression on her, he knew he hadn't. He was just the nonentity in the white smock and silly brimless cap who had slung some grub on a plate for her.
He stuck out the portering job for several months, just because of Is. Day after day he prepared and shovelled rank-smelling hospital meals, simply in hope of catching a glimpse of her. For long stretches of time he wouldn't see her. Her shifts changed; her hours and his didn't always overlap. Then she would be back, and he would have an opportunity to share a few words with her across the heat-lamps, maybe fire a quip at her, and always a smile. She made it all worthwhile. The smells of grease and boiled potato that seemed permanently suffused into his skin; the heat in the kitchen that left him dripping with sweat by day's end; the constant shouting of the chefs and the sullen bickering of the other porters; the numerous nicks in his fingers from knives and peelers; the dinning clatter of pots and pans—all worthwhile, all bearable, thanks to her.
What finally got them together was a chance remark about the Families. It was the day a new wing of the hospital was being opening, built with money endowed by one of the lesser British Families, the Graysons. The inauguration ceremony brought most of St Fiacre's to a standstill, with all the consultants and surgeons and registrars turning out in their best bib and tucker to applaud as Potiphar Grayson, the Family's head, made a lengthy speech about giving something back to the community and then applied scissors to ribbon. None of the nursing staff was invited to attend. Somebody, after all, had to carry on with the minor, inconvenient stuff like tending to patients and keeping the hospital ticking over. Is said as much to Damien as she took a helping of stew off him, and Damien nodded sympathetically and then said, "You know, it surprises me that a Family member even knows how to use a pair of scissors. Don't servants normally do that sort of thing for them?"
To which Is, amused, replied, "Lucky we have a casualty unit here, isn't it? Chances are he might give himself a nasty cut."
It felt naughty, a little bit seditious. Each of them sensed immediately that here was someone who didn't kowtow to the Families the way almost everyone else did. Each of them recognised a kindred spirit.
And it had been so great to begin with, Damien thought as he left his flat and took the lift down to Block 26's mid-level. So perfect. Him and Is. He had taken it upon himself to educate her. He had shared with her the benefit of his years of reading about the Families, learning about them, going on anti-Family rallies, joining various anti-Family discussion groups. Having fostered and nurtured his own resentment of the Families, he had been given the opportunity to foster and nurture someone else's, and he made the most of it. Where Is was sometimes unclear on Family history, he enlightened her. Where her take on anti-Family ideology was perhaps somewhat wonky, he had straightened her out. Pygmalion to her Galatea, he had taken the raw material of her opinions and fashioned it into a fine and focused credo.
And then—ungratefully?—she had dumped him.
It still rankled. After all he had done for her. All he had given her.
She had come out with some guff about two different perspectives on life, two strong personalities not always meeting each other halfway. She had said she still wanted to be friends even if they couldn't be lovers any more. She had tried, he had to admit, to let him down gently. But it had hurt. Still did.
One thing he could console himself with, though. When he had come to her with his proposal for kidnapping Provender Gleed, she had needed little persuasion to join in. And the credit for that, he liked to think, lay with him. His patient indoctrination of her. He had changed her for the better, and the change was permanent. Pat on the back for Damien "Disgrace" Scrase.
The lift bump-buffeted to a halt, and Damien stepped out into a murkily-lit shopping arcade. All of Needle Grove's indoor communal areas were bathed in the same low-wattage level of neon bulb, filtered through green plastic casings to cast everything in shades of that hue. The shopping arcade was no exception. The floors here were also green—lawn-coloured linoleum—and the walls, though not wholly green, sported a mural depicting a fir forest, the foliage of which was, of course, dark green. The mural was intended as a tribute to the expanse of coniferous woodland that had been present on this site prior to the estate being built. The name of the estate had been chosen with the same purpose in mind. But in the event, it all conspired to depress rather than uplift. It emphasised the kind of natural landscape that Needle Grove had erased and that its residents were unlikely ever to know.
Today being a Sunday, the majority of the arcade's shops were closed and had their protective shutters and grilles firmly up over their windows and doors, and even the premises that were open for business looked as if they were ready to shut at a moment's notice. Few shopkeepers put items of value on public display, for fear of smash-and-grab raids, so the windows were all but empty. Inside, likewise, care was taken not to offer too much in the way of temptation. Cash tills, for instance, were hidden away inside reinforced-glass kiosks, and shopkeepers more often than not served their customers from behind bars. Even with all these precautions, to work in retail in Needle Grove was to expose yourself to a certain level of risk, both fiscal and personal. Shrinkage ran at roughly thirty per cent. The mortality rate wasn't much lower.
Mr Ho's All-Day Emporium occupied a prime corner site and attracted, consequently, a higher than average share of theft and strife. Its proprietor nonetheless retained an almost touching level of faith in humanity, and that was partly why Damien was a regular customer. Optimists were few and far between on the estate and should be supported. The convenience of the shop's location was also a factor.
Loitering outside the All-Day Emporium now, as Damien approached, was a clutch of rag-clad kids who hunkered in various slovenly postures, each one apparently trying to out-slouch the rest. Damien recognised them as one of the more recent gang-tribes to emerge from Needle Grove's petri dish of youth culture, the Orphans. Their chosen theme was rejection of family in all its forms, including Family. They pretended their parents were dead. They squatted in vacant flats. They wore only what they could beg, borrow or steal. They considered themselves the absolute antithesis of everything to do with heredity, ancestry, consanguinity.
Damien, in that respect, could almost admire them.
In every other respect he abhorred them.
The Orphans bad-eyed him as he entered the shop. Damien didn't avert his gaze, neither did he stare back. He gave them a level, measured look that said they had nothing to fear from him as long as he had nothing to fear from them.
Mr Ho, behind his unbarred counter, greeted Damien with an ebullient wave.
"Mr Scrase."
"Mr Ho."
"How can I help you this fine day?"
"Just some cigarettes."
"You've given up."
"Not that I recall."
"I could swear, last month you told me never to sell you another packet. You made me vow."
"Well, I've changed my mind."
"Don't tell me. You've failed to get back together with that lady of yours."
"You can read me like a book."
Mr Ho shrugged. "She was the reason you took up smoking again the last time. You said the other day you had hopes of a reunion. Now you're buying cigarettes. It doesn't take a genius to work it out."
"It's a tense time for me generally, Mr Ho," Damien said, with a meaningful emphasis.
Mr Ho took the hint. "Fair enough. Say no more. It's Pedigree Milds, isn't it?"
"Ho ho, Mr Ho."
"No, of course not. Only Family-independent brands for you. Which narrows it down a bit." Mr Ho reached round and took a pack off the shelf behind him. The carton was festooned with Cantonese ideograms. "A twenty-pack of Parent Nation. China's finest. I'm afraid import duty has gone up again."
Damien took the cigarettes off him. "Can't be helped. Anyway, I don't mind. All in a good cause."
"Yes, China," said Mr Ho, with a sardonic glint in his eye. "The only real democracy in the world. Family-free for over half a century. A true paradise. I can't wait to return there."
"Oh come on, it's not that bad."
"Take it from me, Mr Scrase, China is a shit-hole. I know it offends you principles, but it's true. I couldn't wait to get out of there. Nothing works. Nothing gets done. Political corruption is off the scale."
"And this country's better?"
"It's not worse."
Damien remained resolutely unconvinced. He knew China wasn't perfect but it was trying its hardest. A decade after ousting its Families, it was a country still struggling to find its feet. He was sure that, in time, it would succeed. China was an experiment. It was setting the pattern which, one day, the rest of the world would follow.
"Let's agree to differ," he said.
"Fair enough," said Mr Ho. "Anything else I can get you?"
"Box of matches. Oh, and would you have latex gloves?"
"Latex gloves?" Mr Ho raised an insinuating eyebrow.
"Don't ask."
"It just so happens that the All-Day Emporium does stock latex gloves. You mean the disposable type, I take it. They're down the household aisle. If you want, I can get them for you..."
"No, I can do it."
"That's it. That's the aisle. A little bit further down. Yes, there you are, on your left. No, your other left. Look up now. Yes, there. Directly in front of your nose."
On his way back to the counter with the box of gloves Damien heard the chime of the electric bell over the shop door. A moment later he saw Mr Ho's welcoming-shopkeeper expression curdle into distaste. He turned in the direction Mr Ho was looking.
Three of the Orphans had come in and were standing slumped, hands in pockets, each pretending to examine a different display of groceries. They could not have looked more like three would-be shoplifters if they had tried.
"Listen, you lot," said Mr Ho. "I know you're not here to buy anything. Scram."
The Orphans peered at him from beneath their lank fringes. They all belonged to that category of teenager who was congenitally incapable of closing his mouth.
"Go on," Mr Ho said, with a flick of his hand for emphasis. "I mean it. Only good customers like Mr Scrase are welcome here."
One of the Orphans grabbed a tin of frankfurters in brine and held it up. "But I want this," he said. "I want to buy it off you. I want you to make a profit off of me with your enormous mark-up."
"No, you don't. You have no money. Put it back and leave."
The Orphan glared at Mr Ho. Mr Ho returned the glare.
Reluctantly, sullenly, the Orphan replaced the tin. He thought for a moment, then said, "Fuckin" Chinkie tampon."
Damien couldn't help himself. He snorted, half with laughter, half with derision. "What was that? What did you just say? Was it 'Chinkie tampon'?"
The Orphan, puzzled, nodded.
"Do you have any idea how asinine that sounds? 'Chinkie tampon'. It doesn't even make sense. It doesn't _mean_ anything."
"Yeah, it does," said the Orphan, defensively.
"Does it? What?"
"It, um... it means he's a fuckin" slitty-eyed Chinese shit-wanker."
"That doesn't mean anything either. For God's sake, if you're going to slag somebody off, at least make sure you do it coherently."
Baffled now, the Orphan groped further into the limited recesses of his vocabulary, found nothing there that was going to be of any use, and so hawked up a wad of phlegm and gobbed it onto the floor. Then he spun on his heel and hunched out of the All-Day Emporium. His two cohorts followed.
"Sorry about that," Damien said to Mr Ho.
"I'm used to it. I've been called worse. What gets me is that we went on that rent-strike two years ago to badger the Risen London Authority to improve conditions here, and when you see kids like those you have to wonder why we bothered. They don't deserve to have this place made better."
"Maybe, but the rest of us certainly do. And if this place is made better, perhaps those kids won't behave the way they do."
"Oh, I think they still will."
"Yeah, you're right, but perhaps the next generation of gang-tribes won't emerge. If this estate was somewhere they could take pride in..."
"It's a nice dream. Doomed to failure, though, if our last experience was anything to go by."
"Maybe," said Damien. "Maybe not. We'll see."
LEAVING THE ALL-DAY Emporium with his cigarettes, matches and box of latex gloves, Damien found the Orphans waiting for him outside. This wasn't exactly a surprise. It would have been naïve of him to think he could openly ridicule one of them and not be made to pay for it.
The Orphans had arranged themselves in a loose semicircle around the shop entrance. There were a dozen of them all told, and they were spaced out in such a way that Damien wouldn't be able to walk between any two of them without brushing at least one shoulder. The physical contact, however slight, would be construed as a shove. The shove, in turn, would be legitimate grounds for combat.
Damien halted in the shop doorway. He swivelled his head, taking in the Orphans one by one. Fully half of them had the reddened eye-whites and the receding gums of the habitual Tinct-user.
His face broke into a wide, fearsome grin. "Trust me, lads," he said. "I will kill you all. Gladly. One of you so much as lays a finger on me, you're dead, the lot of you. You do not fuck with someone like me. So what do we say you just step out of my way and there's an end of it? Hey?"
The Orphans frowned. He was supposed to be intimidated. Why wasn't he? There were a dozen of them and only one of him. Why was _he_ the one making the threats?
"Come on," Damien said. "I won't say it again. Do yourselves a favour. Get out of my way."
All it took was one of the Orphans to shuffle his feet uneasily. Straight away, their pack mentality collapsed and their ranks broke. The semicircle drifted apart and the various Orphans wandered off in twos and threes to regroup further down the arcade, where they began a fierce debate among themselves as to why and how it was that one man had managed to talk them out of kicking his head in. It was a mystery. Downright perplexing.
Meanwhile Damien, sauntering back to the lift, lit himself a Parent Nation. He dragged on the cigarette and felt the nicotine-hit scour through him. He had been on the cancer-stick wagon for far too long. Falling off it was like greeting an old, familiar friend.
Continuing to suck on the cigarette, his thoughts sharpening with every puff, he mused on his standoff with the Orphans. It was a truth not always universally acknowledged that in any confrontation with thugs your best weapon was your brain. Thugs were, almost by definition, thick. They were also, at heart, cowards. All you had to do was act more aggressively than them, state with utter conviction that this was a fight they couldn't win, browbeat them, and invariably they would back down.
Of course, it was crucial that you were prepared to enforce words with deeds if it came to that.
Damien could feel the pommel of his sheath knife pressing into the small of his back. The weight of the whole weapon was dragging down on his trouser belt. Cigarette in mouth, he reached behind him, slipped a hand under the fabric of his shirt and briefly stroked the knife's haft, his fingers tracing the ridged contours of deerhorn like a blind man reading Braille.
He was glad he hadn't been forced to use the knife.
And those Orphans should be thanking their lucky stars he hadn't.
**20**
GANGS OF CHEERFULLY whistling workmen dismantled Venice. With hammer and crowbar they clawed the city apart and loaded it section by section, shattered façade by shattered façade, onto the backs of flatbed lorries. What had taken days to construct was taking hours to deconstruct. The beautiful illusion of _La Serenissima_ was being reduced, little by little, to paint-and-plywood reality.
Late in the afternoon, with Venice all but gone, Cynthia came out and exchanged a few words with the foreman overseeing the demolition. If the foreman thought she seemed wan and listless, her conversation not at all sparkling, he put it down to the effects of a hard night's partying.
Back indoors, her duty discharged, Cynthia debated whether to try taking a nap again. She was bone-deep weary. However, she had gone to bed earlier in the afternoon and not managed so much as a wink of sleep, her head a churning vortex of suppositions and fears. She didn't think she would have any better luck this time.
Keep moving. Keep busy.
She headed for the eastern end of the house, where Great's quarters were. On the way, she passed Triumph. The statue's ivory eyes, gazing down from its golden face, seemed to taunt her as she went by. Cynthia, by way of rebuke, reminded herself that Triumph's beauty was purely superficial. Such a weight of soft metal and brittle tusk could not support itself unaided. Within the statue lay an armature of thick iron bars, the crude, mundane truth behind the magisterial illusion.
Great lived in what had come to be called the Granny Flat—a self-contained ground-floor annex with its own private patio outside and, inside, all the plush amenities you would expect. For Great's benefit, it was additionally kitted out with a panoply of medical and orthopaedic equipment, and there was a telephone hotline straight to the nearest hospital, in Reading, where the doctors were ready to drop everything and come running if an emergency arose. The annex was a more than agreeable place in which to spend the last few years of your life, and back in another age, before the events of this morning, before her world collapsed, Cynthia had always foreseen herself retiring happily here, conceding full run of the house to the next generation and its progeny. Anticipating that she would outlive her husband, she had looked forward to being a resident grandmother, on hand but not in the way. Now, all at once, the prospect of such a future seemed an unrealisable dream.
Her knock on the Granny Flat's main door went unanswered. She knocked again, with still no response, and so opened the door and strode in. Sounds of splashing drew her to the bathroom, and she tendered a "Hello?" as she neared it.
"One moment, ma'am."
Not one but several moments later, Carver emerged from the bathroom. He had an apron on and his shirtsleeves rolled up, and he was drying off his forearms with a towel.
"Great offers his apologies but he is taking a bath and cannot see you right now. If you were to come back in half an hour...?"
"As a matter of fact, Carver, it's you I want to talk to. Would that be possible?"
Carver glanced towards the bathroom doorway. "I'm sure I can spare a minute or so. Great will summon me back if he needs me. How may I be of assistance?"
Cynthia marshalled her thoughts. Deprived of sleep, her brain seemed to be mired in mud.
"My husband has left for the Island," she began.
"Indeed, ma'am. He and Master Fortune departed for the airfield an hour ago. I imagine the dirigible is taking to the sky even as we speak."
"He's called an Extraordinary Congress."
"That he has."
"I'm afraid he's going to do something rash."
"It's not my place to speculate on such matters."
"He's blaming the Kuczinskis for Provender's disappearance."
"The enmity between the two Families goes far back, ma'am."
"Do you think he's right, then?"
"I couldn't say."
"But you fought in the War."
"I fought against the Pan-Slavic Confederation army. I fought Eastern European soldiers. I didn't fight the Kuczinskis directly. I was a mere infantryman, as was my master."
"But war was sparked by a dispute between Gleeds and Kuczinskis."
"A spat at a Family Congress—that, as I recall, was the catalyst, ma'am. Wojtek Kuczinski believed that Basil Gleed made an insulting reference to his albinism. Allegedly Master Basil called him a 'white bastard' but in all probability what he said was 'right bastard'. Still an insult but not quite so personal. If only Master Basil had been able to overcome his speech impediment... It always flared up at moments of tension. But then it is said, isn't it, that the wheels of history turn on the tiniest of factors. Cleopatra's Nose and all that."
"And I'm concerned that history is about to repeat itself, Carver. Prosper has gone completely off the deep end. I've never seen him like this. It's as if he's suddenly discovered a purpose in life, after fifty-odd years of significantly failing to do so. But the thing is, he's spent so long doing nothing, just idling along, that now that there's a crisis he doesn't know how to react. He's _over_ reacted."
"Again, ma'am, not my place to speculate."
"I know. I know. I shouldn't really be burdening you with all this."
"However, ma'am, _were_ it my place, I would be expressing an opinion not entirely contrary to yours. I would add that it is good that that Master Prosper's brother has gone with him. My hope would be that Master Fortune might act as a calming influence on Master Prosper. Perhaps, when they get to the Island, Master Fortune will be able to mitigate anything Master Prosper might say to the head of the Kuczinskis. Serve as a buffer between the two of them, perhaps."
"I wish I shared your optimism."
Carver gave a broad-shouldered shrug. "Master Fortune's conviviality can be infectious. But I'm sensing, ma'am, that you're not here for just a sympathetic ear. You want something more from me. Perhaps some form of practical help...?"
"Carver," Cynthia said, nodding, "practical help would be immensely welcome."
"Specifically?"
"There has to be something we can do. _You_ can do. To find out who has Provender."
"Go to the police, perhaps."
"Not the police. Not yet."
"They have the resources. The manpower."
"They also don't know how to keep their mouths shut. Gone are the days when you could be sure the police would act on a Family's behalf quietly and discreetly. Now, you call them in, and next thing you know, one of them's gone to the press or a TV station and told all, and it becomes a circus."
"The modern media's interest in the Families is insatiable."
"There's money to be made out of us, that's the trouble."
"It's a debased age," Carver said, with feeling.
Cynthia did not demur. "So no, not the police. Not unless we absolutely have to. The longer we can keep this to ourselves, the better. What that leaves us with, however..."
Carver waited, then realised he was being asked to contribute. "What that leaves us with, ma'am," he said, "is some kind of private avenue of investigation."
"Yes."
"Some independent organisation without authority ties, looking into the matter."
"You sound," Cynthia said, "as though you may have something in mind."
"Not necessarily."
"Please say you do."
"There is one possibility that occurs, ma'am. I cannot guarantee it will bear fruit, but I do believe discretion could be assured, which is a significant factor."
"What is it? What do you have in mind?"
"I would require your permission to act in any way I see fit, and a substantial discretionary fund to draw on."
"You have both."
"I will not, however, be able to set anything in motion until tomorrow."
"Why not?"
"Late on a Sunday afternoon, I fear that I would not be able to contact those whom I need to contact."
"But you could first thing tomorrow?"
"I could, ma'am. First thing."
There came a tapping from the bathroom, the familiar arrhythmic drumming of Great's signet ring. Against the bath's ceramic side the ring made a sharper and more resonant sound than it did when striking the frame of Great's wheelchair.
"My master calls," Carver said. "I must go to him. You'll excuse me."
"Of course. Oh, but before you do, just one last thing. Fort mentioned something about an anomaly. Some kind of problem with the catering staff last night. He said you were looking into it."
"That's correct. I have indeed looked into it."
"And?"
"Master Prosper didn't inform you of my findings?"
"Obviously not." Cynthia had had no contact with her husband since slapping him in his study. She and he had been scrupulously avoiding each other all day.
"It may be that two members of the catering staff left the party early last night," Carver said. "The head count at the end of the proceedings came up short. Now, it's by no means certain that the two were the kidnappers. They may simply have got fed up with working and decided to leave."
"It's odd, though. They wouldn't have got paid."
"Very odd. Unfortunately, we have little further information to go on."
"We don't even have their names?"
"We have what appear to be false ones. It seems that the catering company is somewhat lackadaisical in its employment practices. It's very much a cash-in-hand, quick-turnover-of-staff type of business. I don't think a great amount of background vetting goes on."
"But that's appalling. We hired these people! They were doing the catering for a Family event!"
"I suspect, if it proves they _were_ at fault, they shan't be doing the catering for any kind of event ever again. But as I said, it's by no means certain this has any bearing on the situation whatever. There may even have been a miscount. I will continue to look into the matter and see what I can turn up."
"Do."
The tapping from the bathroom became louder and more insistent.
"And now, ma'am, if you don't mind, I really must attend to my master." Carver leaned close, dropping his voice. "Between you and me, Great isn't in the best of moods this evening. I'm due to give him his bimonthly prostate massage later—a procedure he seldom looks forward to. A procedure I can't say _I_ look forward to much either."
Cynthia wrinkled her nose. "Who would? Off you go then. And Carver?"
"Yes, ma'am?"
"Thank you."
She left the Granny Flat feeling comforted. She had been reluctant to go to Carver but was now pleased she had. He would do what he could. He hadn't held out any false hopes but he had at least given her _some_ hope where before there had been none.
She ate a light supper with Gratitude and Extravagance, and retired to bed straight afterward.
There was a bottle of Oneirodam in the drawer of her nightstand which Cynthia usually had recourse to when she found herself in bed alone. Tonight, however, she didn't need to take any of the sleeping pills. No sooner had she lain down than oblivion engulfed her in a warm, welcome wave. Her night was empty of dreams.
Monday dawn came.
**PART III**
**21**
IN AN INSALUBRIOUS borough of London, off an insalubrious street, down an insalubrious side-alley, you would come across the entrance to an insalubrious office building. Inside the building, if you mounted an insalubrious flight of stairs, through storeys that were of ever increasing insalubriousness, to a top floor that was the most insalubrious of all, you would find yourself on an in-no-way-salubrious landing. Passing along this landing, perhaps abandoning all hope of ever rediscovering salubrity, you would arrive at a door which may once have been tidy and shipshape, its paint not peeled, its mottled-glass windowpane not cracked, but which was now regrettably of a piece with its surroundings, a portal that was the epitome of insalubriousness. And on the windowpane you would see inscribed, in mostly intact transfer letters, the words:
MILNER & MOORE
ANAGRAMMATIC DETECTIVES
accompanied by the slogan:
" **HONESTLY**? OR **ON THE SLY**?
WE CAN TELL YOU WHICH!"
And if, during usual office hours, you were to pass through this door, you would almost inevitably discover two men sitting in the room within. Two besuited, unassuming-looking men whom you might, if you didn't know otherwise, take for accounts clerks or bank tellers. That punctiliousness in their faces. That air of needing everything to be exact and due. That sharply side-parted hair. Those analysing eyes.
Their full names were Merlin Milner and Romeo Moore, but their parents could hardly have christened them less appositely, since neither man lived up to his forename. There was nothing wildly wizardrous about Milner, nor anything dashingly romantic about Moore. Then again, both possessed abilities which some might say were magical, and both were passionate about words and wordplay to a degree that might be called amorous.
Their names, at any rate, had played a significant role in determining their choice of career. Born and brought up in different parts of the capital, at an early age Milner and Moore separately came to the same realisation. Each noticed that his forename and surname consisted of the same letters jumbled up. This led to an interest in anagrams and in word games generally, and, as time went by, interest blossomed into an overwhelming compulsion. Acrostics, telestichs, pangrams, chronograms, codes—all grist to the mill for Milner and Moore. But anagrams were their first love, and though they might dally for a while with palindromes, say, or rebuses, or even lipograms, to anagrams they would always faithfully return.
There was, it seemed to them, something almost mystical about the way one word or phrase could be reconstituted to form another word or phrase. It felt as if one were playing with the stuff of existence, the very building blocks of life. To manipulate the letters, to randomise, to induce chaos and then reassert order, a new order—it was a heady thrill, and one they could not tire of. Research told them they were not alone in this. Anagrammatising had a long and noble tradition, going back to the medieval Jewish Cabbalists and even further to the Ancient Greeks. The use of anagrams as a tool of divination was common to those two races and to many others.
By their mid-twenties, Milner and Moore, still separately, had both arrived at the same conclusion: there was much more to words than met the eye. Words were not merely symbolic representations of abstract and concrete concepts. In some strange way words _were_ the concepts. The two were indissolubly linked. When somebody spoke of a "dog", for instance, they weren't merely using the noun which by common consensus had become attached to the wild or domestic animal of the genus _Canis_ , they were also conjuring up the image of a dog in the mind of the listener. They were evoking the intrinsic notion of doggishness, the essence of dog with its attendant impressions of fur and slobber and devotion and implacable pursuit and cur-like cowardice, a whole raft of information compacted into that three-character monosyllable. It was impossible not to think of a dog when somebody said "dog". Everything you knew about dogs could be tapped into by mention of the word. It was the key to your entire mental archive on the subject, to your individual understanding of the nature of reality as far as dogs were concerned. If there was no word for dog, you might look at a dog and not know what it was. You might not even see it. It would be outside your sphere of comprehension. Without the appellation "dog", it was possible that dogs would cease to be.
Such was the power of words.
And if words could be pulled apart and reorganised into new shapes, perhaps this pertained to the things the words stood for as well. By moulding and refashioning the letters, you could reveal meanings no one even knew were there. You could expose the hidden connections of the world, the patterns which people followed subconsciously, the secret interleavings of existence.
It was, in a way, like playing God.
Or, indeed, playing dog.
It should be pointed out that at this stage in their lives, when they formulated their individual but identical theories about anagrams, both Milner and Moore were exceedingly frustrated young men. Each was working in an unchallenging, dead-end job—respectively, town planning and hotel management. Each was unmarried, living alone, parentless, loveless. Each was coming to that midlife cusp where the dreams and aspirations of youth had nearly all fallen away and a sense of limitation was creeping in, along with feelings of disappointment and the first intimations of mortality. Each, at about the same time, arrived at the same conclusion: it was time to change tack. Try something else while he could. While he was still young enough to resume his old job if things didn't work out. It was now or never.
Each thought, _Why not put into practice, somehow, my theories about words? Why not make use of all those hours I've spent absorbed in my linguistic hobby? Turn a pastime into an occupation?_
Thus, simultaneously, synchronicitously, at opposite ends of the city, two Anagrammatic Detective agencies were set up.
Neither thrived.
Clients came, but hardly in their droves, and most departed without engaging the services of Milner or Moore. Once their initial curiosity about how an Anagrammatic Detective actually worked had been satisfied, they laughed and left. Those who didn't laugh and leave were surprised to discover just how effective that particular system of investigation could be.
They were in such a small minority, however, that it made no difference. The money wasn't coming in. Overheads were not being met. Bills began to pile up. After a year, both Milner and Moore were finding that (a) self-employment was not all it was cracked up to be, and (b) being a private detective was not all it was cracked up to be either. Each man knew he was staring failure in the face. The prospect of re-entering the job market, dispiriting though it was, was beginning to look like the only course of action available.
That was when each learned about the other. Neither could quite believe there was another Anagrammatic Detective out there. They communicated, they met up at a vertiginously high rooftop bar in central London, the Old Hyde Park Tavern on Kensington Heights, and, in the space of one drunken evening, they compared notes, got on, and decided to pool their resources.
By sharing an office, each cut his overheads in half at a stroke. At the same time, neither was in competition with the other for the same jobs. Work began to pick up. The trickle of clients became... well, not a flood, but a slightly faster trickle. And the agency scored some notable successes. Not the sort that garnered headlines, nor the sort that won awards and honours, but still, achievements to be proud of, all of them adding to a lengthening backlist of Cases Solved.
There was, for example, the time they tracked down a missing person, a certain Andrew Riding who had vanished from his home in Portslade, near Brighton, taking all the family savings and leaving behind two small children and a wife who was beside herself with worry. It turned out that Riding had for many years been harbouring a repressed transexualism. The woman in him had been trying to force her way out, until eventually he could keep her contained no longer. Having used the family savings to pay for a sex-change operation overseas, Riding had then settled down in a small town in Gloucestershire, which was where Milner and Moore unearthed him, or rather her. ANDREW RIDING of PORTSLADE was now INGRID WARDEN of ADLESTROP, and although Ingrid was unhappy at first to have been located, the Anagrammatic Detectives were able to coax her into rejoining her family on the South Coast. Regular letters from both Ingrid and his/her wife kept Milner and Moore updated on the progress of this somewhat unorthodox household. Neighbours had got used to them. The children quite enjoyed having two mothers.
Then there was the case of the taxi firm whose owner was alarmed and baffled by a sudden, substantial drop in his profits. Milner and Moore, inspired by the equivalence of TAXIMETER to EXTRA TIME, took several rides anonymously in the firm's cabs, then compared the drivers" journey records to their own receipts. It was straightforward enough. A number of the drivers were fiddling their records and diddling their boss. Sackings ensued, and the grateful owner rewarded the Anagrammatic Detectives with a bonus on top of the agreed fee: a year's free use of his cabs.
There was the complicated affair of the SHORTCAKE and the TRACK SHOE. There was the THRENETICAL CHAIN-LETTER. There was the case of the restaurateur who was POISONED, although not lethally, by a rival, the proprietor of a seafood eaterie called the POSEIDON. There was the unusual job involving a group of south-east Londoners who had taken it upon themselves to find mates for lonely-hearts in the vicinity, bringing them together by surreptitious means so that they did not know they were being matched up—it became known as the SIDCUP CUPIDS case.
But such exciting and intellectually demanding investigations were, alas, the exception rather than the rule, and sometimes in order to make ends meet the Anagrammatic Detectives were obliged to take on assignments which did not call on their powers of wordplay at all—run-of-the-mill stuff that any private investigator could do. More often than not this meant snooping on errant husbands and wives, and to console themselves that there was some sort of wordplay involved, however tangentially, Milner and Moore filed such cases under the heading of BEDROOM BOREDOM. They argued, too, that adultery commonly took place within marriages where the APHRODITE had ATROPHIED or where an unmarried individual had got together with a MARRIED ADMIRER. Quite often the end-result of their evidence-gathering was a messy and combative divorce. That was when it became clear why the word MARITAL was just a letter-swap away from the word MARTIAL.
On this particular morning, the Monday after the Gleed Summer Ball, Milner and Moore had no work on, not even a BEDROOM BOREDOM case. There were no assignments pending, no invoices to be sent out. Their in-trays and out-trays were empty. Their bank accounts were starting to get that way too.
And so, as was their wont, they were sitting at their desks competing to see who could finish a cryptic crossword first. Each had a copy of the nation's highest-brow daily broadsheet and each was bent over its back page, forehead furrowed, pen poised, filling in the lights as fast as he could. Beating each other was part of the attraction, but devoting attention to the crossword meant, also, that for a few minutes they didn't have to think about their lack of work and the parlous state of their finances.
Milner was within a hair's breadth of solving the final clue when there was a rap at the door which not only shattered his concentration but came as such a shock that he half leapt out of his chair. Moore, lagging two clues behind, was no less startled. Each of the Anagrammatic Detectives looked over at the other, waiting for him to say something. Then each, in unison, stammered out an invitation to enter.
The tall, elderly man who walked into their office was a perturbing sight. Hulkingly large, bent like a lamp-post, and wearing a suit that would have set Milner or Moore back a year's salary, he strode in with a disdainful air, as though he begrudged every step of the journey that had taken him here to these tatty premises in this low-rent part of town. Having closed the door behind him, he rubbed fingers against thumb as if the doorknob left some kind of greasy residue. Then he cast an eye around the office, taking in the cracks in the ceiling plaster, the collection of dead flies inside the hemispherical light fixture, the shelves of old books bought by the yard to lend an air of respectability to the place, the arthritic electric fan flailing this way and that as it tried to lower the room temperature, the cheap metal-frame desks the Anagrammatic Detectives sat at, the clearance-sale typist's chairs they sat on, and finally the Anagrammatic Detectives themselves, with their shiny-kneed trousers, their nylon shirts, their fake leather slip-ons. Apparently none of what he saw met with his approval. Nevertheless he nodded in greeting to both men, and even attempted a smile, which caused the scar on his cheek to pucker and deepen in a very unwinning way.
"Gentlemen," he said, "the name is Carver."
This was news to Milner, but Moore had already recognised the Gleeds" major domo. Milner had little interest in Family affairs, whereas Moore, who affected indifference on the subject, was often to be found leafing furtively through the Family pages of the newspapers.
"And you'll be pleased to know that I'm here," Carver continued, "to offer you gainful employment."
**22**
AT AROUND THE same time that Carver stepped into the Anagrammatic Detectives" office, the dirigible carrying Prosper and Fortune was beginning its final approach to the Island. In the control car the captain barked out orders. "Pitch Helmsman, rear elevator up two degrees! Trim Helmsman, keep her steady! Engineer, reduce thrust on starboard fore prop by a quarter! That's it, boys. Nice and easy. Gently does it." The control car's atmosphere of apparent agitation belied a steely professional calm. There was noise and commotion but the captain had everything firmly in hand.
By contrast, in the dirigible's passenger lounge there was no discernible anxiety or urgency. Within both Prosper and Fortune, however, there was, to varying degrees, ferment. The day ahead promised to be eventful. Extraordinary Family Congresses seldom were not.
Fortune, breakfast Bloody Mary in hand, was leaning on the handrail of the for'ard-facing viewing gallery. Roughly five miles ahead, and getting closer by the minute, lay the Island. Set in a shimmer of Atlantic, it was an unprepossessing upthrust of volcanic rock, the kind that appeared virtually overnight, welling out of the waves during an eruption and hardening into a crack-contoured cone which was then colonised by only the hardiest and ugliest of vegetation—scrubby bushes with shallow roots and thorny stems, razor-edged grasses that could go for months without rain. Too small and too sheer-sloped to invite human occupation, for centuries the Island had sat at the far end of an archipelagic chain, unwanted, uninhabited, unnamed, an afterthought, an appendix, a full stop at the end of a sentence... until the Families came along and decided it was exactly what they were looking for.
In the wake of the First European War, it had seemed wise that there should be a place, neutral territory, where Family matters could be discussed, inter-Familial complaints worked out, and pan-Familial problems resolved. The Island fit the bill perfectly. Nobody else wanted it, it was centrally located, and it was going cheap. Every Family chipped in to have it built on and landscaped. In next to no time the Island had a Congress Chamber with several sets of living quarters attached, along with gardens, a beach, a harbour, and an aerodrome. The place served as a useful talking-shop, and everyone agreed that some potentially disastrous confrontations had been defused there. Everyone also agreed that the seeds of the _Second_ European War had been sown there, but it seemed better not to mention this. The Island's successes far outnumbered its failures. That was good enough.
It was on the aerodrome that Fortune's attention was presently focused. Situated on a southern peninsula which had been dynamited flat to accommodate it, the aerodrome offered mooring spaces for up to fifty dirigibles as well as hangars and a runway for the security planes that were even now patrolling the skies around the Island, protecting the arriving Family members against attack. For any normal Congress this was sufficient. Many Family heads preferred to travel by sea rather than by air, and the Island's harbour afforded ample room for yachts and cruisers. A hundred boats could berth there comfortably. With an Extraordinary Congress, however, time was of the essence. Summoned at short notice, you went by the fastest mode of transport available. This meant flying boat, which could dock at the harbour, but more usually it meant dirigible.
"I count about five gaps still free," Fortune commented. "We made it before they start having to do turnaround."
When spaces ran short at the aerodrome, the last few were utilised on a rota basis, each dirigible mooring for as long as was necessary for its passengers to debark, then taking off again. On the next island along in the chain, some ten miles away, there was a public aerodrome large enough to accommodate the overspill. Nobody was best pleased if their dirigible was one of those that couldn't get a permanent parking place. Therefore it was imperative to be punctual.
"Who's here already?" Prosper asked. He was reclining in an armchair with a steaming cup of coffee.
"Umm... I can see the von Wäldchenliebs" dirigible, I think. Theirs is the crest with the black eagle, right? And the Savages". They've got the eagle that isn't black. What is it with some people and eagles? What's wrong with having something small and unpretentious as your Family symbol? A piece of fruit, for instance. Speaking of which, there's the Maketsis" pineapple. And that looks to me like the al-Harouns" crossed date-palms. The Borgia de'Medicis have made it, of course. Nobody beats _them_ to the Island."
"They get a head start. They're always the first to be told."
"Being the ur-Family does have its privileges, doesn't it. Oh, and look. The Pongs. How the hell did _they_ get here so quickly, I wonder."
"Their dirigible has that new jet-propulsion system."
"Even so. How far away is Thailand?"
"I expect they were visiting someone at the time. My guess would be the Savages."
"Ah yes. What with all their marital and business links. The Savages and the Pongs. Imagine if they went the whole hog and merged. D'you think they'd call themselves the Savage-Pongs?" Fortune chuckled heartily.
"You're not the first to crack that joke, Fort," said Prosper, "and I seriously doubt you'll be the last."
"It's still funny." Fortune's expression abruptly turned sombre. "Oh-ho, what have we here? Can it be the famous Black Dirigible?"
Prosper sprang to his feet and joined his brother at the viewing gallery.
Halfway along the line of tethered dirigibles, almost all of which were the standard silvery-grey in colour, was one whose canvas shell was the deepest, darkest, most night-like shade of black conceivable. The crest on its flank was picked out in blood red and was a simplified silhouette representation of a bat in flight.
"The Kuczinskis," Prosper said, coldly, crisply.
"And to judge by the angle we're coming in at, I'd say we've been assigned the space next to them," said Fortune. "Luck of the draw? Or maybe someone down there in the control tower has a nasty sense of humour."
The Kuczinski dirigible loomed like a thundercloud. Its rudder fins continued the bat motif—they were scallop-edged, like a bat's wing. Also unusual about the aircraft were its windows. All, with the exception of those in the control car, were blacked out. The Kuczinskis found it necessary, and preferable, to travel in constant darkness.
"They seem to have made it here in very good time," Prosper observed. "Perhaps they knew they'd be coming."
"Steady on," Fortune warned. "Innocent until proven."
The Gleed dirigible nudged in alongside the Kuczinskis" and, with a whine of reverse propulsion, came rocking and bumping to a standstill. Ropes unfurled from the mooring cones at the nose and tail, and were gathered up by ground crew and secured to motor-driven winches. The dirigible's engines cut, bringing a sudden sonorous silence, and the winches took over and slowly hauled the aircraft down to earth.
Once the dirigible was secured and stabilised, a gangplank was extruded from its belly. Crewmen descended first, lining up in two rows, fingers slapping to foreheads in salute. Prosper and Fortune emerged, passing between the crewmen. The heat was sudden and ferocious, and became more so as they stepped out from the dirigible's shadow into the full flare of the subtropical sun. At a brisk march, the two Family members set off along the peninsula, heading for the Congress Chamber and the ancillary buildings clustered around it.
**23**
SOMEWHAT TO HIS own surprise, Provender had slept. He had woken up several times during the night and been obliged to ease out a kink in his spine or a cramp in his calf. He had never managed to get anywhere near comfortable, there on the bare bathroom floor, blindfolded, bound hand and foot. All the same, he had slept.
He knew it was morning because the building around him, having been silent for several hours, was now making noises again. They were dim sounds, and all bathroom-related: water gurgling, a badly-fixed pipe rattling. The bathroom he was in shared its plumbing system with countless others. He pictured people going about their ablutions, their ordinary Monday-morning routine. Shaving. Bathing. Brushing their teeth. Using the lavatory. Thinking about work, or school, or the duties of the day, or perhaps trying their best _not_ to think about any of these things. And all the while not having a clue, any of them, about the man being held captive in their midst, the man who could hear the results of what they were up to in their bathrooms, the man who would have given anything just to be able to stand up and wash his face as they were doing, perhaps check his chin for spots in the basin mirror, and then straddle the lavatory and partake of a long and blissfully unaided piss. How many flats were there in this building? How many bathrooms? From impressions he had collected, Provender guessed he was in a populous urban high-rise. There could be anything up to two thousand souls sharing this block with him, and each of them had a bathroom which was linked to this one by pipes and ducts. A connective maze of copper and ceramic tubing. The building's venous system. Clean water one way, waste water the other. It was, in some hard-to-describe way, reassuring. He was isolated but not wholly alone.
And then, very definitely, he was not alone. The door opened, the light switch clicked, the extractor fan started its bronchitic rattling again, and someone entered the room.
Straight away Provender knew it was Is's accomplice. The man had a heavy presence. He seemed to displace more air than most people.
Provender kept still, pretending he was asleep.
The man shuffled up to him barefoot and stood over him. His breathing was slow and steady. He jabbed a toe into Provender's midriff.
Provender flinched and braced himself, thinking the jab must be the prelude to a kick.
No kick came.
"'Morning, Provvie," the man said. "Wakey-wakey, rise and shine. Sleep well? I expect not."
Provender had decided on a policy of not talking to the man. The man seemed the sort you could antagonise without meaning to.
"Not at all what you're used to, eh?" the man said. "Nothing fancy about the accommodation here. I bet even boarding school wasn't as bad. Still, it's good for you. This way you get to experience how the rest of us live, the ordinary people your Family craps on all the time. Speaking of which..."
Provender heard the lavatory seat being flipped up and the sound of the man seating himself. What came next he wished he didn't have to listen to: the squeak and grunt of someone defecating just inches away from him. Even worse was the smell, so ripe he almost gagged.
"How's that then?" the man asked, to the accompaniment of unravelling toilet paper. "My partner's using a bucket out there in the main room. Says she couldn't "go" with you right next to her. Me? I'm not so squeamish. You could say I don't give a shit."
Provender couldn't restrain himself. He was too revolted. The retort sprang out of him. "That's because Is is a decent person and you're not."
There was a moment of deadly quiet, then the man said, "She told you her name. Stupid cow. I suppose it doesn't make a lot of difference, but even so... I told her not to. Oh, that's annoying."
Provender braced himself again, fearing that he would be taking the punishment for Is's slip-up.
As before, though, the man did not lay into him. Instead he said, "Well, I was going to do the decent thing and flush, but now I think I'll just leave it to marinade for a while. Nice chatting with you, Provvie."
The door closed, and soon afterwards Provender heard raised voices coming from the other side of it. Is and the man arguing. He didn't catch everything that was said but the odd phrase came through, giving him the over-all gist. Is was accused of treating their captive too leniently, not keeping a distance from him like she should. She defended herself by saying that the point of kidnapping him wasn't to torture him. She gave as good as she got but in the end the man's aggression won through. Provender heard Is's voice take on a conciliatory tone, and the volume of the conversation dwindled to inaudibility. Meanwhile the extractor fan churned away, toiling to cleanse the air in the bathroom, with little success. Eventually it timed out and lapsed into silence, as if exhausted from its efforts. The smell of the man's bowel movement lingered noxiously on.
Provender, taking care to breathe through his mouth, deliberated over what had just happened. At a stroke, two suspicions had been confirmed. One was that the man was a confirmed anti-Family type, close to pathological in his hatred of all things Familial. The other was that the relationship between the man and Is was strained and that Is was helping him, if not under duress exactly, then against her better judgement.
It came as something of a surprise to Provender that he was heartened by these two pieces of information. He realised he could, if he chose to, use them to his advantage. Through them he could maybe even engineer his escape.
Then again, if he didn't play his hand just right, he risked making an already bad situation worse.
What it hinged on, really, was whether or not he had the guts to try.
That, and his captors" reading habits.
**24**
"WHY US?"
It was a question that had to be asked, and Milner asked it with as much nonchalance as he could muster. He didn't want to sound as if he and Moore were unwilling to take on the case, but at the same time it was a case of such magnitude, such awesome importance, that he felt obliged to voice a note of reservation.
"Why you indeed," Carver said. "First of all, you aren't the police."
"That's for sure," Moore said. "COP LIE."
Carver shot him a quizzical look.
"We haven't had much luck in our dealings with the police," Milner explained. "They've taken the credit for a couple of cases _we_ cracked, and on the whole they've not been very cooperative. So we've anagrammatised POLICE to COP LIE. It's what we do."
"It's what _they_ do," Moore grumbled.
"I see," Carver said. "Then that's a further point in your favour. Not only are you not the police, but you'll have no qualms about keeping the police out of the equation."
"None whatever," said Milner.
"The other reason I chose to come to you," Carver went on, "is that you have scored a number of notable successes while still managing to maintain a low profile."
"You mean no one's heard of us."
"If you like. I'd rather see it as you have everything to prove and nothing to lose, which in this instance is a highly desirable combination. It means I can be assured of your utter loyalty and your wholehearted attention."
"So how did _you_ hear of us?" Milner said.
"You may recall you applied to the Gleeds for patronage last year."
"Did we? I don't think so."
"Um," said Moore, "as a matter of fact we did. Or at least, I did."
"What?"
"I didn't mention it at the time. We were going through one of our lean patches, and I thought, I'll put in an application for patronage, see if we can get the Gleeds to support us, no harm done if we can't, all it'll cost is the price of a stamp."
"And you didn't tell me?"
"I was going to, Merlin, if anything came of it. But nothing did. I got a pro forma reply acknowledging the application had been received, and that was that. Nothing else."
"Oh." Milner looked askance at his fellow Anagrammatic Detective, unable to decide if what he had done constituted a betrayal or not. He felt, on balance, that it didn't.
"I apologise that you didn't get any more than that," Carver said, "but as you can imagine, the Gleeds receive hundreds of requests for patronage every week. Sorting through them is a Herculean task and sometimes some of them, I regret to say, slip through the net. Yours, however, was given due consideration, believe me. I was on hand when the Family discussed it, and while Prosper Gleed was minded not to accept it, I myself made a mental note to remember you. Something told me I might have need of your services sometime." Again, he flashed that unenchanting smile of his. "And here I am. I cannot, of course, offer you patronage. That is solely within the Family's power to decide. But I can guarantee you this. If you help us, if you do manage to find young Master Provender, you will never have to worry about finding work again. No question about it. There won't be anyone in the world who won't have heard of Milner and Moore, the Anagrammatic Detectives. Your reputation will have been made. Your future prosperity will have been secured."
Milner and Moore avoided each other's glances. Neither wanted to see the look of wild avarice he knew was in his own eyes.
"Now," said Carver, "I take it you are going to accept the case."
What could either of the Anagrammatic Detectives do except say yes?
"I'm most pleased. A couple more points, then, before I leave you to get on with it. You will liaise with the Gleeds solely through me. I am going to give you a private phone number to contact me on. Any information you uncover, you report to me. Is that understood? The Gleeds have entrusted me with their full authority in this matter. You are to treat me as if I am the Family."
"Fine," said Milner.
"Also, you will doubtless be needing funds to cover your start-up costs, incidental expenses and the like." Carver reached into his inside jacket pocket and produced a thick wad of banknotes which he placed on the desk in front of Milner, just out of the Anagrammatic Detective's reach. "More, much more, is available should you require."
Milner and Moore stared at the money, agog. They estimated they were looking at the equivalent of an average year's income for the agency. Milner immediately thought about moving to more upmarket premises, while Moore entertained the idea of hiring a receptionist-cum-secretary. He had always fancied having a receptionist-cum-secretary in the office, someone young and attractive, with a trim figure and nice legs. She didn't even have to be particularly good at the job. Just sit there within his view, call him Mr Moore, make him coffee, dress smartly and sexily—that was all.
Carver butted in on his little reverie. "And naturally, should you succeed in bringing about a satisfactory resolution to the situation, the financial rewards will be great indeed."
_A fiftieth-floor office_ , Milner thought, _with commanding views of the city_.
_Not just one but_ two _receptionist-cum-secretaries_ , thought Moore, _so there's one for each of us and no squabbling over which of us she likes better_.
"But." Carver clamped a hand over the money, as if about to scoop it away. "Just to make matters absolutely clear, gentlemen." He looked at Milner, then at Moore. "No one else is to know about this. You are to do what you do in absolute isolation. Your lips are to stay hermetically sealed. For the duration of your investigation, you are to avoid mentioning to anyone what you are up to and why. The consequences of failing to comply with this stipulation... Well, I don't need to paint you a picture, do I?"
Milner and Moore both shook their heads.
"Though if I did," Carver continued, "it would be a picture not unlike the wilder imaginings of Bosch or Breughel. A canvas filled from corner to corner with suffering and hellfire and brimstone. Do I make myself clear?"
Milner and Moore both nodded.
"Crystal," said Milner, in a faint voice.
"Very well then." Carver let go of the money. "I look forward to hearing from you as and when you have made any progress. The very best of luck to you, gentlemen. Let us hope your endeavours bear fruit, and quickly."
**25**
FOR SEVERAL MINUTES after Carver left, a thunderstruck silence hung over the Anagrammatic Detectives" office. The money sat on Milner's desk, note stacked on note to an impressive, almost inconceivable height. Neither man dared touch it in case, like a conjuror's illusion, it vanished. Both just stared.
Finally Milner said, "I don't know which I'm more intimidated by—what he's asked us to do, or him himself."
"He didn't scare you, did he?" said Moore.
"Me? Oh no. You?"
"Not a bit."
Each looked the other in the eye and gave a shuddery laugh.
"Just out of curiosity," said Milner, "what's his first name?"
"Carver's? How should I know?"
"Oh come on. You're into the Families. You know."
"I am _not_ into the Families. I just... I like to keep up with current affairs, that's all. It's important in our line of work to have a healthy interest in everything that goes on in the world. And the Families definitely count as current affairs."
"So?"
"Neal. I'm pretty sure his first name is Neal."
"En, ee, eye, el?"
"En, ee, _a_ , el."
"NEAL CARVER." Milner tapped his lip contemplatively.
"LEAN CRAVER," Moore offered.
"I think we can do better than a simple metallege," his partner said.
"LANCE RAVER."
"Doesn't feel right. No, I've got it." Milner clapped his hands together. "CLAN REAVER. Quod erat demonstrandum."
Moore half-smiled. "CLAN REAVER. Yes, he's certainly the Gleeds" enforcer, isn't he. Their tame thug. Even at eighty-something years old."
"He's that old?"
"And a veteran of the last war."
"Really? God, no wonder we won."
"That's where this came from." Moore mimed a scar on his cheek. "He got it during the Siege of Prague. Bayonet in the face. Carried on fighting anyway."
"And you say you're not into the Families."
Moore blushed. "I have a retentive memory. Anyway, don't mock. We wouldn't have this case it all if it wasn't for me and my... interest."
"Actually, true," said Milner, nodding. "Full credit to you, Romeo."
Moore accepted the compliment magnanimously.
"And with that in mind," Milner said, "perhaps we should get cracking. Time, after all, as Mr Carver indicated, is of the essence."
Both men opened drawers in their desks. Milner took out a ringbound pad of unruled paper and a pen, while Moore produced a green felt bag tied with a drawstring. The bag contained dozens of square plastic tiles, each with a capital letter on it, taken from a well-known boardgame. He poured them onto the desktop, spread them out and began flipping the ones that were face-down face-up.
This was perhaps the most significant dissimilarity between the two men: the technique by which each generated anagrams. Milner preferred what he called "the old-fashioned method", the crossword solver's tried-and-trusted trick of writing the letters out in a jumble. Moore, on the other hand, found it easier and more convenient to use Scrabble tiles. All you had to do was keep swapping them around and swapping them around in various combinations. No wasting paper. No having to jot the letters down all over again if one jumble failed to yield a result. Milner thought Moore's technique noisy and untraditional. Moore thought Milner's crude and labour-intensive. Each had long since given up trying to persuade the other of the rightness of _his_ system.
And here was where the art began. Here was where Milner and Moore showed that there was more to being an Anagrammatic Detective than simply the ability to muck around with letters.
Because it wasn't just about making new words from old. Instinct was involved. A certain name or phrase could be rearranged into dozens of possible permutations. Knowing which was the correct permutation, which of all of them was the one you were looking for—that took a special talent. It was almost preternatural. Neither Milner nor Moore could easily explain it. Certain results just felt right. You saw them and you knew. Couldn't be put any more precisely than that. A tingle in the belly. A prickling at the back of the neck. The answer leapt out at you. You knew.
The sheer enormity of the case—a Family member, kidnapped—seemed to fall away as they set to work. Quickly it became a matter of words. The words were what counted. The words would reveal the truth. Milner scribbled, pondered, tore off a sheet, scribbled again. Moore lined up tiles, frowned, slid them around with his fingertips, lined them up afresh. An hour passed. Each man looked at names. People's names, the names of places. Every relevant reference he could think of. At one point Moore went scurrying off to retrieve Friday's newspaper from the waste-paper basket. He leafed through it, located the article he was looking for, and returned to the Scrabble tiles with renewed vigour. Milner, meanwhile, consulted a local London telephone directory and noted down with keenness what he found there.
They broke for coffee at eleven o'clock and briefly compared notes. To their surprise, they discovered they were at odds with their conclusions. Moore was becoming convinced that the kidnapping was an inside job, while Milner was of the view that some outside agency must be responsible. They seldom, if ever, disagreed over a case, and so they were perturbed. Each decided to follow up the other's line of approach to see if it had merit. Pen scratched. Tiles click-clacked. Another hour passed, and still neither man could descry how the other could possibly be correct.
"Look," said Moore, "it's obvious. Provender and his cousin Arthur—they don't get on. I've read about it. Arthur's this upstart from the wrong side of the bed. He's never made any secret of the fact that he thinks he'd be a better heir than Provender. Big chip on his shoulder about that."
"Big enough for him to kidnap his own cousin?"
"Why ever not? And for God's sake, his name screams it out. REGALED HURT. REAL RED THUG. RED LAUGHTER. HATRED GRUEL. 'E GLARED RUTH."
"Bit of a reach, that last one."
"I know, but still. For me, Arthur Gleed's your man. His name is a guilty party's name ten times over."
"Wasn't he at the ball when Provender was taken?"
"Yes, he was. I checked the invitee-acceptance list in the paper. But that doesn't mean he couldn't have masterminded the whole thing. Perfect alibi. He was there all along, in plain sight, partying away, while henchmen carried out the dirty deed. And look. Here's the clincher. He's an actor, right, and he's appearing in a play. There's a preview tonight and the premiere's tomorrow night. Guess where it's on at?"
Milner shrugged.
"The Shortborn Theatre."
"OK. SHORTBORN THEATRE. Let me think."
"I'll save you the trouble. BROTHER SON THREAT. Arthur is the son of Prosper Gleed's black-sheep brother Acquire. It all hangs together."
"Tenuously," said Milner. "I don't buy it. I don't buy the whole 'inside' angle at all. I've gone through the Gleeds, all of Provender's immediate kin, and they've all come up innocent. I've not got a 'hit' off any of them. Like his dad. PROSPER GLEED. GREED PROPELS. Now, no question, greed and Family go together. You can't have one without the other."
"And you're always likely to get GREED if there's GLEED involved."
"Quite. Practically an open goal. But greed, if you're Family, is hardly a motive to commit crime. It's more a way of life with them. Then there's Provender's mother. CYNTHIA GLEED. THE NICE G LADY. I even threw her maiden name into the mix. CYNTHIA LAMAS GLEED. Know what I got? CHEATING MALE'S LADY. Straightforward enough. Nothing sinister there. Her husband's famed for his extramarital affairs. Even I know about that. And THE LADY'S ANGELIC MA, that was my other one. Again, that would seem to sum her up, wouldn't it? And exonerate her."
Moore conceded the point, reluctantly.
"As for the oldest member of the Family," Milner went on, "GREAT GLEED got me AGED GELTER. He's certainly aged, I think you'd agree. And 'gelter'? Gelt is what a Family's all about. But as before, hardly a motive. I mean, if Provender's been kidnapped in order to be held to ransom, it _can't_ be an inside job. The Gleeds are filthy rich. They don't need to make money, and more to the point why would they try and hold _themselves_ to ransom?"
"Carver said there hadn't been a ransom note yet."
"Yet."
"But if Arthur's the culprit, maybe ransom isn't what he's after. Maybe it's recognition, or to get rid of his rival."
"You think this might be murder?"
"If it isn't already, it could become. Provender could just, you know, _disappear_. For ever."
Milner looked doubtful. "Somewhat extreme."
"We're talking about Families. Nothing's too extreme where they're concerned. With Provender out of the picture, Arthur stands to become the next head of the Family. Admittedly he'll have a hard task ahead of him. The chain of descendancy will have been broken. The Gleeds'll plummet in the Family ratings. But he'll be head all the same. And if the only thing that stands between him and that is Provender... Well, in his shoes, wouldn't you be tempted?"
"To kill my own cousin?"
"Arrange to have him killed. Keeping your own hands as clean as possible."
"I don't know. I'd like to think not." Milner tapped his ring-bound pad. "I still think you're barking up the wrong tree, though. I'm getting a definite reading from Provender himself. His name—"
"His name," Moore interjected, "doesn't ring any of _my_ bells. Look at it. PROVEN GREED-LED. You yourself said it. Greed and Family—virtually synonymous. And even with his middle name, Oregano, thrown into the mix..."
"Hold on, his middle name is Oregano?"
"It's something of a tradition with the Gleeds. They had their origins in the spice trade."
"I know that, but _Oregano_?"
Moore shrugged. "Provender itself isn't exactly normal, is it? Anyway, as I was saying, you throw Oregano into the mix..."
"For added flavour."
"Thank you. And you get GREEN ROAD DEVELOPER, with the letters G, O and N left over. Which sprang out at me, but I have so say, what the hell does it mean? I can't think of a context in which it would apply."
"And those left-over letters."
"Yes. Messy."
"Well, Romeo, to get back to what _I_ was saying—his name by itself isn't terribly productive, as you have just shown, but splice it together with his predicament..."
"As in?"
"As in PROVENDER GLEED STOLEN."
"And?"
Milner sucked on the cap of his pen. "And you get confirmation that this was an outside job. You even get where he's being held and a clue to the identity of the person holding him."
"Elucidate, please."
"You don't believe me."
"I'm a little sceptical."
"Then let me propose this, Romeo. As we each appear to have our own theory about the case, why don't we pursue our leads separately?"
"What?"
"I know. A radical departure for us but, as things stand, a sensible one. Clearly we're not going to see eye-to-eye over this, so let's make it a competition. Not unlike our morning crossword."
"Winner takes the dosh? Is that what you're saying?"
"Christ no. I'd never be that mercenary."
"Glad to hear it."
"No, just a gentlemanly challenge between friends. Your investigative skills against mine. We'll split this"—he pointed to the money—"so neither of us will be out of pocket. By the way—cash. We're not telling the accountant. Agreed?"
"Agreed."
"Good. So we split it, we go our separate ways, we work independently. It is a major case, after all."
"It's not just major, Merlin. It's the biggest case we've ever had. It's the one that'll make us."
"All the more reason, then, that we divide our forces. We can cover twice as much ground that way and double our chances of finding Provender. What d'you say?"
Moore couldn't fault his partner's logic. "And whichever of us cracks the case, we both share the fee? Equally?"
"Of course. Like I said, this isn't about the money. It's about intellectual satisfaction."
"And bragging rights."
"They might come into it."
Moore sat back in his chair. Milner, on the other side of the room, mirrored the action.
"All right," Moore said. "You're on."
Milner grinned. He would not have thrown down the gauntlet if he hadn't been so confident that he was on the right track and his colleague on completely the wrong one. By the same token, Moore would not have picked the gauntlet up if he hadn't thought his take on the case was correct and Milner's hopelessly misguided.
The main thing was, personal rivalry aside, they were going to crack the case. Both of them were confident that, one way or another, the Anagrammatic Detective Agency was going to win the day.
They were forgetting that in such SELF-ASSURANCE lay the potential for A CARELESS SNAFU.
**26**
MASSIMILIANO BORGIA DE'MEDICI, dapper little gent, comfortable with the weight of history and precedent that resided in his slender frame, a Family man to the marrow, called the Congress to order.
" _Signori, signore_." His voice, though slight, was clear and carried far thanks to the Congress Chamber's impressive acoustics—the domed ceiling and the suspended disc-shaped baffles that bounced sound around. "Gentlemen, ladies. I bid you all good afternoon and pray your attention."
Gradually conversation dwindled around the concentric hoop-shaped tables, silence spreading from innermost to outermost, from premier Family to lowest-ranked. The hundred-or-so Family representatives at the edge of the room, in the proverbial cheap seats, were the last to go quiet. They seldom did as they were told straight away. They liked to remind everyone else they were there.
"Thank you," said Borgia de'Medici. "You will see that we have a number of absentees. The missing Family heads have all tendered formal regrets. They have prior commitments. However, we exceed the three-quarters quorum, so business may be conducted."
He took care to keep his sentences short and leave gaps between them, for the benefit of the translators who accompanied several of the Family heads. A kind of massed whisper attended his statements, a Babel echo, as the translators did their job, leaning forward and murmuring in their employers" ears. Those Family heads who were conversant in English, the great majority, were allowed to bring along a companion in place of a translator, as moral support. By the rules of Congress, the companions were forbidden from speaking while the Congress was in session.
Fortune, who habitually fulfilled this function for his brother, found the no-speaking constraint almost unendurable. To compensate, he had devised a simple system of coughs and throat-clearings by which he could let Prosper know if he agreed or disagreed with the line Prosper was taking, and how vehemently. In extreme instances, when the system failed, he had been known to kick his brother in the leg, which usually achieved the desired effect.
He hoped that, today, no such drastic measures would be called for. He feared they would, though.
"An Extraordinary Congress is not lightly invoked," said Borgia de'Medici. "To ask the heads of Families to drop everything and come running is no mean thing. I say so not to undermine the reason for this meeting but to under _line_ it. We are here to give audience to an accusation of the utmost gravity. We must devote our fullest attention to it and discuss it as honestly and frankly as we can. I have no need to remind you that anything said in the Chamber goes no further than the Chamber. You may speak your minds freely."
Borgia de'Medici turned toward Prosper, who was three seats away from him on the central table.
"Signor Gleed," he said. "It is you who have summoned us here. Permit me to ask you to air your grievance."
"Of course." Prosper took a sip of water from the glass in front of him and stood up. Fortune, in the chair just behind him, reached forward to the table and grabbed his own glass, which contained a clear liquid which was not water. He took a sip and softly smacked his lips. Who said you had to be Russian to enjoy neat vodka?
Prosper ran his gaze around the central table till it came to rest on Stanislaw Kuczinski. For the space of several seconds he simply looked at his rival Family head, and Kuczinski simply looked back, red eyes fixed unwaveringly on Prosper's. Kuczinski was dressed in nothing but black, which set off the pallor of his skin and hair to extraordinary effect. Were it not for his eyes, and his rose-blush lips, he would have been devoid of all colour. He could have stepped straight out of a monochrome movie.
His companion, his twin sister Stanislawa, was similarly two-tone. Her outfit consisted of a black worsted two-piece with a sable tippet around her shoulders and, on her head, a black velvet Robin Hood cap topped with a raven's feather. Stanislawa shared with her brother the same sharp cheekbones, the same pointed chin, the same soft economy of gesture which in her was feline, in him effete. She also, if the rumours were to be believed, shared his bed. With the Kuczinskis, it wasn't just albinism that ran in the Family. There was a tradition of incest which earlier generations of Kuczinski had definitely indulged in—there was documentary proof—and which Stanislaw and Stanislawa at least _appeared_ to be perpetuating, if the gloved hand with which Stanislawa was stroking her brother's neck right now was anything to go by.
Of course, it could merely have been for show. This was a Family, after all, which wished the world to believe they were vampires. They drank human blood (two glass goblets of the stuff sat before them now). They shunned sunlight. If they were prepared to go to those lengths to maintain a reputation, then incest, or even the feigning of incest, was nothing.
It was Prosper who broke the eye contact between him and Stanislaw Kuczinski. He would have gladly carried on staring, but his distaste for Kuczinski, for the man's very appearance, was too great. It threatened to overwhelm him and make him incoherent with loathing. When he looked at Kuczinski he thought of all the times the Kuczinski Family had outsmarted the Gleeds—snatched away some juicy business proposition from under their noses, bankrupted a corporation they knew the Gleeds were eyeing up, triggered a stock-market plunge that always somehow left the Gleeds out of pocket, generally indulged in sharp practices with no other goal than to inconvenience their age-old enemies. Prosper invariably struck back, but he rarely seemed to give as good as he got. Stanislaw Kuczinski had a far better business brain than he did. That, although Prosper hated to admit it, was another reason he despised him.
"My fellow Family heads," Prosper said, and now it was his turn to be dogged by the susurrant translator echo. "I stand before you today, not as a Family head myself, nor as a Gleed, but simply as a father. A worried father. A frightened father."
_So far so good_ , thought Fortune. Appealing to a common bond. There were more than a few fathers in the room.
"My son Provender has been..."
Prosper faltered. Theatrically, in Fortune's view—but whatever got the point across.
"My son has been kidnapped."
Shock rippled out across the Chamber. The consternation was loudest around the outermost table, from where cries of outrage and sympathy resounded up to the sonic baffles.
"Please, please, everyone," said Massimiliano Borgia de'Medici. "Please, _silenzio_! Let Signor Gleed continue."
Prosper waited for the ruckus to die down, meanwhile gauging Stanislaw Kuczinski's reaction to his announcement. The white face did not perceptibly alter. The eyes perhaps widened a little, but that was all.
Which implied nothing. In the event that Kuczinski was innocent, he wouldn't know that he was about to be accused of the kidnapping. If he was guilty, he would register no surprise at what Prosper had just said. Either way, he was going to maintain that impassive expression. Why, before a quorum of assembled Family heads, was he going to show that he cared what had happened to his enemy's son?
"He was taken the night before last," Prosper continued, "during our annual ball. Provender, as you all well know, is the next Family head in line, and my only male offspring."
There were nods around the tables, and murmurs of concern.
"And," Prosper said, "I am convinced that the individual responsible for his abduction is in this very room."
That had the Family heads in ferment again. The Congress Chamber churned with shouts, demands, accusations, denials. Arms waved. Fists thumped tables. Prosper savoured the medley of uproar, and also the scowls that had manifested on the faces of both Kuczinski and his sister. They seemed well aware, the pair of them, what was coming next.
" _Prego! Prego! Silenzio!_ Silence!" Borgia de'Medici had to yell at the top of his voice to be heard. "Signor Gleed, you had better explain yourself. Such comments are highly inflammatory in this company."
"Oh, I'm going to explain myself all right, Massimiliano," said Prosper.
Fortune coughed gently, in a way which very clearly meant _Watch your step now, brother_.
"But," Prosper said, "I suspect most of you here have already guessed who I'm referring to."
Heads began to turn.
"In fact, I wouldn't be surprised if the guilty party were to stand up right now and say—"
Stanislaw Kuczinski was rising to his feet even as Prosper spoke. Halfway, he hesitated, realising he had been caught out. But it was too late. He straightened, drawing himself to his full height. His eyes flashed a baleful red glare at Prosper.
"Gleed," he said.
Uttering the name meant his lips pulled back, and his lips pulling back meant his teeth were revealed in all their jagged, filed-to-points hideousness.
"How dare you. How _dare_ you." Kuczinski turned to Massimiliano Borgia de'Medici. "This man is a liar. His accusation is groundless. Where is the proof? Let him show us his proof!"
"The proof," said Prosper, also addressing Borgia de'Medici, "is right in front of us. Kuczinski knew I was talking about him. By standing up, he was all but confessing his guilt."
"Nonsense! Gleed was making insinuations. Obvious insinuations. I knew I had to refute them."
"Do you deny you have my son?"
"I do. Emphatically. What would I have to gain by kidnapping him?"
"Oh, everything. Blackmail. Leverage over me. The humbling of my Family. An escalation in the longstanding feud between the Gleeds and the Kuczinskis. You name it."
"But there are certain codes of behaviour. You know what I am talking about. Among the Families. Certain lines one does not cross."
"Oh really?" said Prosper. "How interesting that you, of all people, should mention codes of behaviour, Kuczinski. Standing there with a glass of blood in front of you and your sister next to you. 'Sister', of course, being the least part of the intimate role she plays in your life."
" _Kurwy syn_!" Stanislawa snarled, while, behind Prosper, Fortune let loose another of those cautionary coughs.
"Mr Borgia de'Medici!" Kuczinski said, with a beseeching gesture. "Are you going to let him get away with this? First he falsely accuses me of a heinous deed, now he insults my Family and draws attention to our condition."
Prosper leapt in before Borgia de'Medici could say anything. "Your 'condition'? Well, I suppose you could call it that, in that it's a psychological delusion you all share. Vampires! You really get off on it, don't you? Makes you feel dangerous and different. Why not just admit it? You're not 'creatures of the night'. You don't drink blood to survive, it's simply an affectation. And sunlight will give you a nasty burn, what with that lack of skin pigmentation of yours, but it won't make you explode into flames. Oh, but if you didn't play at being vampires, you'd have nothing going for you, would you? You'd just be an ordinary Family with an unfortunate hereditary complaint. Call yourselves vampires and we won't all look at you and think, 'Now there's a perfect example of what inbreeding can—inbreeding can do to people.'"
The break and repetition in that last sentence was the result of Prosper being kicked in the calf by his brother, once, sharply. As soon as Fortune heard the word _inbreeding_ he knew Prosper had overstepped the mark. It was the one real taboo among Families, the one subject you did not raise under any circumstances. It was too close to home, too near the knuckle. In every Family represented in the Chamber there was at least one branch that had petered out into insanity, impotence, physical deformity, or any combination of the three. It was the risk you inevitably ran with a carefully cultivated bloodline. No one wished to be reminded of that fact.
Stanislaw and Stanislawa Kuczinski least of all.
Stanislawa bristled. Her hands became claws. As for her brother, he shot Prosper a look that would have curdled milk.
"Prosper Gleed." His voice was a feral hiss. "Is there nothing you will not stoop to?"
"I'm not the one who goes around abducting other people's sons."
"For the last time, I do not have your son. I do not know where your son is. Why say these things?"
"I don't believe you. I look at you and see a man acting very much like someone with something to hide. If you were truly innocent, you wouldn't be protesting your innocence so strongly."
"What chance does that give me, then? I might as well be guilty, if you're telling me I cannot even claim I am innocent."
"Don't claim your innocent. Prove it. Prove it by returning Provender to me."
"How can I? I don't _have_ him."
This exchange was conducted to the backdrop of a rumble of voices, which grew louder with each back-and-forth of the argument, becoming a thunder. It was the sort of noise you might hear from the audience at a boxing match as the two fighters slugged their way toward the knockout blow. The Family heads on the outermost table were almost baying in their excitement. A climax was looming. One or other of the combatants, Prosper Gleed or Stanislaw Kuczinski, was about to deliver some sort of devastating killer punch. The Family heads partly didn't want to see it land; partly they did. This dispute had been a long time brewing. The Gleed—Kuczinski antagonism, a constant of Family life, was particularly heartfelt between the representatives of the current generation, and yet before now had never exploded in quite such a manner. For everyone, not just the two men directly involved, there was a sense of release. That which had been pent-up was now in the open. The years of continual sniping and needling across the centre of the Congress Chamber were at last giving way to something more forthright and fierce. A long-swollen pustule was being lanced.
Massimiliano Borgia de'Medici was duty-bound to intervene. Even as he did, however, he understood it was futile. Gleed and Kuczinski were on the warpath. Whatever he said, neither man was likely to back down.
" _Signori_ , I beg you, let us sit down and think this through coolly. Prosper, you say he has kidnapped your son. Stanislaw, you say you have not. Either it is that one of you is lying, or one of you is mistaken. Now, as you are both men of honour—"
"Honour?" Prosper snapped. "That _thing_ over there wouldn't recognise honour if it came up and bit him on the neck."
"Thing! He calls me a thing! On top of all the other abuse he has heaped on me this day."
"Oh pipe down, Count Dracula. You can't have it both ways. Either you're a human being or you're one of the undead, and if it's undead than by definition you're a thing. Live with it. Or unlive with it, or whatever it is you do."
Stanislawa Kuczinski was on her feet now. "I cannot keep quiet any longer. I cannot sit here and say nothing while my brother's reputation and mine are—are _besmirched_ by this person."
"Signorina Kuczinski, I must ask you to resume your seat," said Borgia de'Medici. There were growls of agreement from other quarters. "The rules quite clearly state that—"
"To hell with the rules! The effrontery of Prosper Gleed knows no bounds. He has been breaking all sorts of rules. Moral rules. And not just today at this Congress. My brother and I are simply to accept all these insults from him without retaliating? No! How can we, when they come from a man who is a lifelong gambler, and a very bad one by all accounts. A notorious womaniser, too. A man who mocks the devotion of his loyal and trusting wife, to go around fucking any woman that moves. A man who cannot keep his _huj_ in his pants!"
"With respect to Miss Kuczinski," said Prosper, "I can think of one woman who I would definitely keep my _huj_ in my pants for. Assuming in the first place she was interested in any man other than the one she spent nine months in the womb with."
" _Psia krew! Kurwa mać! Spier dalej!_ "
You didn't have to be fluent in Polish to know that the words pouring from Stanislawa Kuczinski's mouth were not exactly a hallowing paean of praise. But in case the tone in which she said them and the look of sheer venom on her face were not enough, she followed them up with an action that put the matter entirely beyond doubt. Snatching up her half-drunk goblet of blood, she drew back her arm to throw it.
"Stasha! No!" cried her brother.
But too late. The goblet hurtled across the room. It missed Prosper, shattering against the edge of the table instead, but the result was almost as good as if it had been dead on-target. Blood sprayed everywhere. Some droplets hit Fortune in the face, and the Family heads to either side of the Gleeds, Desmond Maketsi and John-Paul Savage III, didn't escape a spattering. It was Prosper, though, who caught the lion's share. His shirtfront was covered in crimson. His face was a ghastly red-stippled mask. But even as the blood began to dribble down his forehead and cheeks in runnels, he was smiling. Taking a silk handkerchief from the breast pocket of his jacket, he began dabbing himself dry. Meanwhile, there was aghast silence in the Chamber. Around each of the concentric tables, jaws hung open.
"Well now," said Prosper, when he had cleaned the worst off. "First blood to you, Kuczinskis. It seems you've shown your true colours. Expect a response. Expect it swiftly. Expect it to be total and utter and overwhelming. You started this. Now you're going to pay for it. Dearly."
**27**
"DOES HE HIT you?"
Is was taken aback. Provender hadn't said a word since she entered the bathroom and started giving him his lunch. He seemed to have sunk into a mood of sullen resentment. Then, between mouthfuls of tinned tomato soup, this.
"Him out there," Provender said. "Your accomplice."
"I know who you meant. No. God, no. He doesn't hit me."
"He seems the type."
"Da—" She checked herself. She had nearly said Damien's name. "He has a temper. He's a very passionate person. What he feels, he feels strongly. But he's not violent. He never has been to me. For one thing, he wouldn't dare. If he'd so much as laid a finger on me, he'd have been walking funny for a week."
"He'd."
"Eh?"
"You said, 'If he'd so much as laid a finger on me'. Past tense."
"So?"
"So that implies not present tense. You and he aren't... you know. Any more."
Is busied herself with tipping another spoonful of soup between Provender's lips. "We shouldn't be talking like this."
"I know. He doesn't like it. Gets shirty about it. Was he this jealous when you _were_ going out?"
_Yes_ , Is thought. _Very much so_. Damien couldn't bear her even speaking to another man. Whenever she came in after a shift at St Fiacre's, he would quiz her about the patients she had tended to, with the emphasis on the male ones. What had she said to them? They to her? It reached the point where she would have to give every male patient she mentioned a qualifying tag, such as "He's only sixteen years old" or "He's in cardio, can barely raise an arm", so that Damien would know the person in question wasn't a potential rival. And on social occasions...! The hospital Christmas party, for instance. Damien had stuck next to her all evening, glowering at every man who approached her and scaring off most of the less intrepid ones. These were her friends, work colleagues, doctors and fellow nurses she'd known for years, and they were reluctant to come and chat because of the boyfriend-slash-bodyguard hovering at her shoulder.
Jealous? Oh yes, you could safely say that was among Damien's less appealing character traits.
"I'll take your lack of answer as a yes," Provender said.
"He's not a bad person," Is offered.
"He kidnapped me forcibly from my own home and he's holding me here against my will, and he's not a bad person? Forgive me if I give a little snort of incredulity."
"He's doing it for a reason."
"What reason?"
"I can't say. But it's all in a good cause."
"Oh well. Marvellous. That makes it all right then."
"He's altruistic."
"If by that you mean he hates the Families, then yes he is. What about you, though? Do you hate the Families?"
"I... I used to think I did."
"And now?"
"I'm not sure. I hate the way people worship you, but that's not the same thing. Maybe you should discourage them from doing that. But then why would you want to? It serves you well. You're the paragons, the ideal we're all supposed to aspire to. Wealth, power, a strong sense of kinship, rooted in heritage. As long as that's how people see you, you'll have their trust and keep your position."
"But nowadays everyone knows we're human and fallible. We used to have mystique, but then came all the magazines and the TV programmes. They love to show us up. Warts and all."
"And yet somehow that just makes the public love you even more. Probably because they feel they can identify with you. You have problems like they do. And yet still: wealth, power, kinship... It's the best of both worlds. You can slip up and yet you can still do no wrong."
"Lucky us."
"You _are_ lucky, Provender. Really, you have no idea how lucky you are."
"Remind me of that again, the next time I have to ask you to help me take a dump."
Is fed him the last morsel of soup. "This isn't for ever. This'll be over eventually."
"When?"
"Honestly, I have no idea. But it will be over."
"Is?"
"Yes?"
"This may sound like an odd question..."
"Try me."
"Would you believe me if I said _I_ hated the Families?"
She laughed, albeit softly, in case Damien overheard. "No."
"Why not?"
"Why would you? I could believe it, I suppose, if you were a surly adolescent and at that stage of your life where you just hated everything. Usually surly adolescents direct most of their rage against their own family. It's the most convenient target. But you should be past all that. You're a grown man."
"Try telling my sisters that. But actually, you misunderstood. I said the Families. Meaning the lot of them, not just my own. The whole institution."
"Then I really wouldn't believe you, no."
"What if I could prove it?"
"How?"
"Would it make you feel differently about me?"
"You answer my question first. How?"
IS CROSSED THE main room to the kitchen nook. Damien was slumped in front of the television, idly dialling between channels using the wired-in remote control. A cigarette smouldered between the first two fingers of his other hand. She had chastised him mildly about taking up smoking again. He had pretty much ignored her, although he had mumbled something about giving up for good after all this was over.
She deposited Provender's soup bowl in the sink with a clank and ran some water into it. Then, after a pause, she said, "Damien."
"Yup?"
"You know your copy of _The Meritocrats_?"
"Yeah. What about it? Oh, hold on." Damien sat up, twisting round in his chair. "You want to give it another go?"
He looked delighted, almost pathetically so. The strayed sheep Is, showing signs that she might be interested in returning to the fold.
Is felt vaguely ashamed of herself. "I thought I might try."
"It's hard work, I know," Damien said, "but my God, it's worth it. You just have to persevere. Everything that's wrong about the Families—it's in that book." He started to climb out of the chair. "I'll go fetch it."
"No, no, it's all right. I know where it is."
"Help yourself then." Damien settled back. "Enjoy. That Anonymous—he certainly nailed it. I'd love to meet him someday. Shake him by the hand. What a guy."
Is headed for the bedroom, thinking that if Provender was telling the truth, Anonymous was the last person Damien would have wanted to meet.
AND SHE COULDN'T see it, to begin with. _Read the first four paragraphs_ , Provender had said. _Study them carefully_. She sat on Damien's bed with the tattily-bound book open in front of her and she scanned through the first four paragraphs of Chapter One and she simply couldn't see what Provender was getting at. The clue to the novel's true authorship. The subtle little giveaway woven into the text.
She was, of course, familiar with the opening passage of _The Meritocrats_ from her previous unsuccessful assaults on the book:
Providence saw to it that Guy Godwin was born and brought up in a house at the confluence of three types of transportation. Road ran alongside the house. Overhead a railway viaduct arched. Very close to the end of the garden, a canal flowed. Every minute of every day, almost, Guy could look out of a window and see voyagers go by. Never did he not think of the world beyond his neighbourhood. Down on the canal, stately barges passed carrying rivermen and cargo to elsewhere. Electric trains thrummed on high, freighted with commuters. Rumbling traffic outside his front door ferried drivers and passengers to innumerable unknown destinations.
Guy Godwin, you would say, was fated to become a traveller himself. Late in life, looking back, he would perceive that it had been his destiny. Ever since birth there had been a restlessness in him. Ever since birth he had been conscious that journeying was man's natural state of being. Definitely, the urge to move outward and onward was inherent in all humans, and in him more than most.
When he was of an age to leave home, he did. Rolling up his belongings in a single small backpack, he began his wanderings on foot. Out into the world he went, to find what it had to offer. There could be no turning back. Even as he closed his parents" front door behind him, he knew this.
The very first person he encountered on his travels was the tramp Jack Holloway. Holloway was to become Guy's boon companion during his adventures. It could be said that without Holloway Guy would not have seen and experienced half the things he did. Sancho Panza to Guy's Don Quixote, Holloway was guide, governor, guardian and goad all rolled into one.
Reading the lines now, and rereading them, she recognised nothing other than the qualities she habitually divined and derided in the novel: the lugubriousness of the prose and the shallowness with which the two central characters were sketched. Perhaps in the parts of the book she had never got to, Guy Godwin and Jack Holloway were better fleshed out and became more believable, but she doubted it. Holloway, in particular, she found a hopelessly far-fetched figure, an idea of a tramp dreamed up by someone who had never actually met a tramp. Is knew tramps. They turned up in Accident and Emergency all the time. Not one of them was anything like Holloway. Holloway wasn't mad or methylated or both. He didn't reek of piss. He didn't mutter constantly and profanely. He wasn't prone to dropping his trousers and aggressively masturbating. He was an untarnished angel-of-the-road, there to steer the hero through his exploration of the book's fictional Family-less world, offering tips and sage observations along the way.
Is was close to resenting Provender for making her re-immerse herself in _The Meritocrats_. It really was—and she was surer than ever about this now—a bad book.
Then she saw it. On perhaps her seventh perusal of the four paragraphs, the answer suddenly blossomed. There it was, plain as day. She was stunned by the overtness, the sheer nerve of it.
_It must be a hoax_ , she thought. _Somebody having a laugh_.
But it wasn't. It was as clear and unambiguous a statement of copyright as could be imagined.
The first letter of each sentence.
Each paragraph denoting a separate word.
PROVENDER
GLEED
WROTE
THIS
**28**
THE JOURNEY TO the Island had been made under favourable conditions, a smooth flight. The journey home saw the Gleed dirigible bumping and buffeting through the air. It didn't help that the captain was under orders to make all speed and that they were running into a headwind. Instead of letting itself be buoyed and caressed by the air currents, the dirigible was hammering through. It also didn't help—at least in Prosper's view—that for the first couple of hundred miles they were following hard on the tail of the Black Dirigible.
"The Kuczinskis have something," he insisted, gripping the viewing gallery handrail. "Some kind of device that makes their wake choppier than normal."
"Don't be ridiculous," said Fortune. "It's just bad weather."
"Then why do they keep veering in front of us? Every time we turn to port, they turn to port. Every time starboard, the same."
"They're mucking around with us, that's why, Prosp. Don't you remember when we were lads, you, me and Acquire, and we'd take the cars out on the speedway circuit and Ack would always pull ahead and then stay dead in front, cutting us up so neither of us could overtake him?"
"Bloody annoying it was."
"Same principle here. Dog-in-the-manger tactics. They're angry and they're showing it."
Tutting in disgust, Prosper trod a staggering, swaying course aftward to the armchairs. His brother joined him, moving carefully so as not to spill a drop of his glass of single-malt.
"So, you picked a fight," he said. "And you got one. What now? Wait for them to make the next move?"
"Hell no. Keep the pressure on. Turn it up, if possible."
"Prosp, has it occurred to you that Kuczinski might not have been lying? He might have been on the level when he said he didn't know anything about Provender?"
" _Et tu_ , Fort?"
"Whoa, hold on there, big bro. Don't get all "Judas!" with me. Someone has to say these things to you."
"Someone already did." Prosper rubbed his cheek. "My face still hurts from it."
"Yes, well, hell hath no fury, blah-di-blah. That slap was long overdue, if you ask me." Fortune swilled his whisky around and drank a slug of it. "No, what I'm getting at is, it could be that your loathing of the Kuczinskis is muddying your thought processes. You might not be seeing quite straight here. You want them to be the villains of the piece so badly, you refuse even to consider the possibility that they aren't."
"You saw how they behaved. He blustered. She chucked blood at me. Blood!" The first thing Prosper had done after returning to the dirigible was go to his cabin, scrub his face clean and dig out a new shirt. He had rid himself of all physical traces of the blood, but he could not so easily erase the memory of having the wine goblet hurled at him and feeling the warm wet spatter of someone else's lifestuff on his skin. Even to think about it now left him nauseated.
"It might be argued that you provoked them."
"Or it might be argued that I called their bluff and they tipped their hand."
"Poker analogies don't seem proper somehow, under the circumstances."
"Why not? Life is a gamble."
"Oh what rot! Gambling's a gamble. Everything else is a matter of careful analysis and proportionate response."
"Says the man who nearly ended up with a spire up his arse the night before last. Says the man whose idea of proportion is 'three parts vermouth, one part gin, that's how you make a martini'."
Fortune gave a slow, forbearing blink. "You know I love and respect you, big bro. You know also that I'm one of the few people who can talk straight with you."
"Straight? You haven't been straight since you were seventeen."
"You know what I mean. I'm the one who can tell you to your face when I think you might be on the wrong track, and I'm doing so now. Tread cautiously, Prosp. It's probably a bit late for that but do it anyway. I dislike the Kuczinskis as much as you. But just because they're white-skinned blood-sucking bastards, that doesn't automatically make them evil. Remember that."
A FEW HOURS later, the Black Dirigible changed tack, heading off due east while the Gleed vessel continued on its north-eastward course. Progress was no calmer, even with the Black Dirigible gone. Objects rattled in the passenger lounge. The whole aircraft shuddered and strained. The bracing wires between the gas cells within the balloon sang and twanged distantly, like an Aeolian harp.
Alone, Fortune having retired to his cabin for a nap, Prosper brooded.
His brother did not understand. Could not. He had no children of his own. Provender was not _his_ son. Fortune didn't see that a father must do certain things when the life of an offspring was at stake. It was primal. An alpha-male instinct. An enemy threatened; one must bark and snap back.
And Prosper was right about the Kuczinskis. He knew it in his bones. Fortune would soon be eating several helpings of humble pie. He would concede with good grace, Prosper was sure. When the Kuczinskis surrendered Provender up. When, as the screws were tightened on them, those ersatz vampires caved in. Fortune would admit his older brother had played a masterful game. His strategy had been flawless. Well done. Bravo.
Prosper looked forward to that. More, he looked forward to seeing Cynthia grovel in apology. He loved his wife but knew she didn't think much of him as a husband and father. Well, he'd be showing _her_ , wouldn't he.
Ahead, through the windows of the viewing gallery, the coast of Spain was now visible on the far horizon, a faint brown blur beneath the misty purple of oncoming dusk. The dirigible was close enough to the landmass of Europe for Prosper to start making phone calls, via radio relay. He picked up the handset of the private line and began dialling.
It did not take long. A handful of calls, each as brief as the next. A word or two in the right ears—ears belonging to people who owed the Gleeds for their positions, who were in some way indebted or obligated to the Family. It wasn't so much what was said as what was left unsaid. His implication was quite clear. _Do this for me. I am Prosper Gleed_.
That, when you were Family, was how easy it was to spark off a war.
**29**
IS WAITED TILL Damien next went out. He hated to be housebound for too long. He said he began to feel like a caged tiger, and like a caged tiger he would pace and pace, endlessly circling. Is herself was feeling cooped-up and claustrophobic. The flat was not large, and seemed smaller still with one room effectively off-limits. But she was reluctant to leave. In Needle Grove a woman out on her own had to be careful, especially after dark. She also wasn't happy at the thought of Damien alone with Provender. And she herself wanted to be alone with Provender. So when Damien said he couldn't stand it in here any more, he _had_ to stretch his legs, she encouraged him to. She watched him strap on his sheath knife—his "necessary precaution", he called it. She chivvied him out of the door. He told her he wouldn't be gone long and threw a meaningful glance towards the bathroom. "Don't let him give you any bullshit."
"I won't go near him, I swear."
"Family try and twist people around their fingers. They can't help it."
"I'm going to sit and read." She pointed to _The Meritocrats_ , on the table.
"Good. That's fine by me."
No sooner had his footsteps faded down the hallway than Is grabbed the book and strode into the bathroom.
"Tell me this isn't true."
Provender raised his head to peer at her, as if there were no blindfold. "I take it you mean—"
"This." She waggled the book so that he could hear the pages flopping against one another. "You're not the author."
"I think pretty clearly I am. Who else would do that? Stick _my_ name and a claim of authorship right at the beginning?"
"It could be, I don't know, someone's idea of a joke."
"Kind of a pointless joke, if you ask me. Especially as no one is likely even to notice it."
"But how?"
"Don't you mean why?"
"No, I mean how. We'll come to why later. How did you write it? Get it out there?"
"I wrote it the way I imagine anyone writes a book: one word at a time. It took the best part of two years. I started when I was nineteen. I finished when I was just gone twenty-one. I have a lot of spare time. A lot of privacy too, if I want it. All in all, it was reasonably straightforward. Those first four paragraphs were the tricky part. The rest just sort of came out. Do you like it?"
"As a matter of fact, since you ask, no."
"Oh."
"It's almost unreadable."
"Ah."
"But I'm in a minority. I can think of one person who treats it pretty much like the Bible."
"Him."
"Him."
Provender almost laughed. "That's almost funny."
"No, it isn't," Is snapped. "It's sick. It's twisted. Where do you get off doing that? What kind of perverted pleasure do you get from fooling all those people?"
"Fooling? I didn't write _The Meritocrats_ to fool anyone. I wrote it because I had to, and I sent it out because I wanted to. It wasn't something I did on a whim. I printed off three manuscript copies and posted them to three radical anti-Family groups. Anonymously, of course. The addresses weren't hard to find. They're listed in the phone book under Political Organisations. I went for the three with the most colourful names. Kin Dread, that was my favourite. And then I just left it to them to do what they liked with the book. I thought, I hoped, it would get circulated. There was no copyright indicia, so they'd realise, if they had any sense, that they could run off pirated editions without getting sued. It was in the lap of the gods. The manuscripts might well have ended up being tossed in the bin. Instead..."
"Instead, anti-Family activists have taken the book to their hearts, little suspecting it was written by a Family member."
"Actually, I did worry that I'd be rumbled. Sticking my imprimatur in at the beginning like that—it was an arrogant thing to do. But I couldn't help myself. And nobody's spotted it so far, it seems."
"Unless you know to look for it, you'd never see it."
"I suppose. Or else, if somebody did spot it, they'd assume it was a joke, just as you did."
Is lowered the toilet lid and slumped down into it. "So now the why."
"Why write it? I told you. I had to."
"It was some sort of posh-boy challenge you set yourself, then. You were bored so you thought you'd write a subversive novel, see how well it did."
"No." Provender sounded offended. "It wasn't like that at all."
"But no one in your Family knows."
"Is, as far as I'm aware only two people in the world know I wrote it—you and me."
"So it's your amusing little secret. You've staked a claim on a little bit of independence from your upbringing."
"You've got me there," he conceded. "That is why I did it, partly. Late-teen rebellion."
"Not much of a rebellion, if nobody knows about it."
"Well, quite. Then again, the book's out there, I hope inspiring people to imagine a world without the Families. What do they say—a million copies doing the rounds? That's a pretty effective piece of propaganda, by anyone's standards. So why should I worry that my own blood-relations think I'm just lazy old Provender, loner, oddball, dragging his feet about getting married, confirmed dilettante? Doesn't bother me when I know my magnum opus is a success. It's worming its way through the public consciousness. It's gnawing away at the foundations of Family-run society. It's doing its bit to help bring about the Families" downfall."
"I don't believe I'm hearing this," Is said. "Provender Gleed, talking like an ardent anti-Familial."
"And meaning it. Every word."
Is stared at _The Meritocrats_ in her lap with its monochrome cover and its dog-eared, thumb-marked pages—Damien's holy text. If only Damien knew. If only everyone knew.
She returned her gaze to Provender. Something about his posture had altered, although perhaps she was imagining it. He seemed to be sitting up straighter, looking less hunched and humbled.
"If the Families were overthrown, and I don't think it very likely, but if—"
"They did it in China," Provender pointed out.
"Yes, and everybody looks at the mess _they're_ in now and says, 'Let's pray it never happens here.'"
"But it's possible."
"Anything's possible. But if it did happen, what about you? What would you do? The Chinese Families, after all, the Wings, the Cheungs, the Lees, they were either killed in the uprising or they had to go into exile with barely any of their wealth left."
"I know. I think most of the Wings are in Australia now, living on handouts from the Jacksons and the McIntyres. Rather ignominious. And the Lees, haven't they set up a restaurant chain in San Francisco or something?"
"Could you do that?"
"Go into catering? Doubt it. I'm a lousy cook."
"No, go from having everything to having next to nothing. What I'm saying is, have you really thought this through? You might want an end to the Families, but do you want an end to your lifestyle? The luxury. The not needing a job. The parties, for heaven's sake."
"The parties I could happily do without. You saw me the other night. Did I look like I was having fun? As for the rest—it depends."
"On?"
"The Families wouldn't have to be got rid of as violently as they were in China. That was mob hysteria. It needn't be like that anywhere else. There could be a quiet transition. We could be slowly edged out. We'd have our assets stripped from us bit by bit but we'd be allowed to hang on to the rump of our money. We'd have enough to keep going. We just wouldn't have the power and influence any more. Politicians wouldn't jump through hoops for us. We wouldn't be able to make or break a career with a single word. Lives wouldn't depend on our whims and whimsies."
"You want to get rid of your cake and eat it, that's what you mean."
"You make it sound like I'm being unrealistic. I think I'm being ultra-realistic. There's that bit in Chapter Thirty-Nine of _The Meritocrats_ where I talk about, or rather Jack Holloway talks about, capitalism and responsibility. Basically, are they mutually exclusive. You know the section I'm talking about?"
"Provender, I've never got beyond Chapter Six."
"You really hate my book, don't you."
"Don't be hurt."
"I'm not hurt. Well, yes I am. You have to understand, you're the first person I've met with a copy of it and you don't like it. That's not good for my author's ego. But I guess I can live with it. Your friend, after all, he loves it. Which is ironic, as I get the impression he'd happily stove my head in if I wasn't so valuable to him financially. That reminds me—how is the ransoming going? Have my Family agreed to cough up yet? How much am I worth?"
"I can't really talk about that."
"Can't or won't?"
"Can't. There's a lot to do with this business that I'm being kept in the dark about."
"What on earth for?"
"To protect me. The less I know, the safer I'll be if things go wrong."
"Your friend's idea? How chivalrous of him. Or maybe he doesn't trust you. Maybe he has an inferiority complex and can't bear the thought of you, a woman, being on an equal footing with him."
"Clumsy, Provender."
"What?"
Is stood up. "You were doing OK. This _Meritocrats_ thing. That was working. A trump card, and you played it nicely. You almost had me on your side. But then you overstepped the mark. I can't blame you for that. You're Family, and Family members don't know when enough's enough. But if you're going to win me over completely, you'll have to be a whole lot subtler and a whole lot smarter."
She exited the bathroom, slamming the door harder than she intended to. In the main room, she flung _The Meritocrats_ down and stomped over to the window. It was a full-length window that gave onto a small balcony. To open it took some effort; the runners were warped and rusty; it rolled grudgingly. Is forced it sideways till there was a gap large enough for her to slide through. On the balcony she stood and gazed down on Needle Grove. In the twilight, the shadows were growing. The hum of the surrounding city was abating and the estate's own cacophony was becoming more audible. Shouts echoed, ricocheting upwards between walls. Music blared from windows. Televisions jabbered. Down at the lowest, most lightless levels the gang-tribes were starting to gather for their after-dark wilding. Is could see them at their regular meeting-places, tiny figures. She knew they would be sharing bottles of cheap strong cider, shots of Tinct, and pugnacious jokes. Soon Needle Grove would be theirs again. All decent folk would stay locked in their flats till daybreak.
It could be better than this. Damien had promised her that. With money extorted from the Gleeds, Needle Grove could be brightened up, smartened, cleaned, made more liveable. There could be green areas—foliage-green, not paint-and-neon green. There could be improved lighting, and some kind of system of security patrols, maybe, to keep the kids off the streets until the kids got the message and stayed off the streets voluntarily. There could be new drains installed to replace the old ones which got clogged up during rainstorms and meant certain squares and underpasses flooded and were unusable for days. There could be playgrounds, safe zones that weren't vandalised or commandeered by the gang-tribes for their fights, places where the smaller children could actually _play_. Needle Grove could become an estate people wanted to live in, as opposed to an estate people ended up living in when there was nowhere else available, or were stuck living in because they didn't have the wherewithal to bribe someone high up in the Risen London Authority to get them out.
Is wanted to believe Damien when he said this. She wanted to think it was a vision that could become a reality. It was how he had sold her on the whole kidnapping plan. He had painted a picture of Gleed millions—money the Family could easily spare—being siphoned off into Needle Grove. He had described, in beguiling terms, a reversal of the usual model: money going from the rich to the poor, rather than the other way around. He had so enraptured her with this noble design of his that it was nearly, _nearly_ , like the old days, when they were first going out, before she got to know him too well. When he used to seem principled, rather than priggish; focused, rather than fanatical. When what he and she had in common was a bond of conviction and not, as it became, a bone of contention.
And now she was no longer sure. About anything. She was angry with Damien. Angry with Provender. Angry with herself. She was less and less happy about being a part of Damien's scheme. But if she backed out, she would be leaving Provender alone with Damien and she wasn't happy about that idea either. Perhaps Provender deserved whatever came to him. Then again, for all his faults, he wasn't a bad person. He was attempting, in his fumbling way, to be a good person. She wanted to hold _The Meritocrats_ against him but, damn it, she just couldn't. Terrible though it was as literature, at least it was a gesture in the right direction. And the more she saw him, trussed up and helpless in the bathroom, the more she felt that he was a hapless victim in all this, and the more she pitied him.
Is simply didn't know what to do any more. A dusky haze settled over Needle Grove, the tower blocks clustered against the darkening sky, lights flickered on, the estate's nightly nocturne of yelps and yammering swelled—and she didn't know what to do any more.
**PART IV**
**30**
OVERNIGHT, IT BEGAN.
Shortly after eleven p.m. GMT a battle group of British warships—three frigates and a destroyer—put out from Hull. Ostensibly on hastily-scheduled manoeuvres, they ploughed into the North Sea bearing due east on a course which soon took their radio transmissions within range of the listening post at Kolobrzeg in Poland.
Less than an hour later the German radar station at Zinnowitz detected ship activity at the naval yards at Gdansk and Köningsberg. Not just a battle group but fully half a division had begun steaming out into the Baltic. Polish military high command had not publicly announced any such deployment of vessels in advance. Messages flashed from Zinnowitz to Berlin, and thence to Stockholm, thanks to the intelligence-sharing pact between Germany and the Scandinavian countries instituted in the aftermath of the last war. Stockholm contacted Helsinki and Copenhagen, and all German and Scandinavian armed forces went from green alert condition to yellow.
Around three a.m., watchtowers to the west of the border between Germany and Poland were submitting reports of armoured brigades trundling along local roads on the Polish side. Similar reports came in from watchtowers along the German/Czech border and the Austrian/Hungarian. The German and Austrian armies responded in kind, sending out tanks from bases near Dresden, Passau and Güssing. To either side of the line dividing West Europe from East, the night air was shaken by the rumble of diesel engines and the clank of segmented steel tread on tarmac.
As dawn approached, troops were brought into play. On both sides, whole battalions had been roused from their billets and were marching eastward or westward to take up position a few miles from enemy territory. By this stage the premiers, presidents and prime ministers of every country in Europe were out of their beds and on the phone. For most, the events unfolding came as a surprise. They had believed the continent to be in a relatively stable state, everyone rubbing along contentedly enough, the odd dispute here and there, nothing that couldn't be solved through diplomatic means. They had had no idea that the peace that had endured these past five decades was, in the event, quite so fragile.
While the political hotlines from capital to capital crackled, the sun rose. Light moved east to west across the face of Europe, and with it came warplanes. Aerial visibility enabled takeoff. Reconnaissance craft, with fighter escorts, crisscrossed their own countries" airspace, coming near to but never quite entering enemy airspace. Strato-Class dirigibles also took flight, easing ponderously into positions of readiness in the upper atmosphere, at altitudes too great for fixed-wing aircraft and ground-based artillery to reach. These were huge creations, leviathans of the skies which made ordinary passenger dirigibles look like minnows, and they carried immense payloads of ordnance. City Smashers, they were colloquially called. Pregnant with death.
The national leaders, still on the phones, debated, soothed, squabbled, accused, objected, hectored, harangued, weaselled, wheedled, vilified, mollified, blustered, filibustered, postured, pontificated—and that was just with colleagues they knew to be allies. Within the bloc of West European states, a consensus started to form. Within the Pan-Slavic Federation, the same. Pledges of assistance were made to those countries on the front line of any potential conflict. _They invade you, they invade us_ , was what it boiled down to. England in particular was keen to form a part of any western military coalition. Troop carriers were placed on standby at airbases in Aldershot, Colchester and Peterborough, poised to take to the skies at a moment's notice.
It all happened fast, as if it had been waiting to happen, as if some fault-line was suddenly starting to flex and tremble once more, a political seismic fissure long thought dormant, largely forgotten. From Lisbon to Lugansk, from Hammerfest to Syracuse, people awoke to discover the Europe they had gone to bed in was not the same Europe in which they were yawning and stretching and blearily blinking. A shift had occurred. An old rupture was reopening. As they picked up their newspapers, as they switched on their radios and TVs, they felt a vague dread settle in their bones, strange yet familiar, new yet known. A sense shared by millions of civilian souls across the continent: _Here we go again_.
**31**
AS WITH ANY creative profession, being an Anagrammatic Detective entailed a highly disproportionate ratio of perspiration to inspiration. It was all very well shuffling letters around, making new words out of old. That was the fun part. But it was only the preliminary. The casting of the verbal runes, the reading of the orthographic tea leaves, the (in more than one sense) spelling—this was to lay the groundwork. Afterwards came the hard part, the standard gumshoe stuff, the gathering of proof, the amassing of evidence. The legwork.
For Romeo Moore, legwork had meant eighteen straight hours of covert pursuit and stakeout, with little to show for it except sore feet, the jitters from drinking too much coffee, and a notebook containing a breakdown of the movements of Arthur Gleed during the past afternoon, evening and night—a breakdown which, though meticulously detailed, was also sadly unenlightening.
Moore, stationed on a bench in the park at the centre of the Regency-era square where Arthur lived, was reviewing his notes now, by the early light of Tuesday morning. Birds were shrieking their aubade from the treetops. Traffic was beginning to move, London stirring from its rest. In the old parts of the city you heard and felt everything more clearly than you did in the metropolis's high-rise canyons. You got a glimpse of what London had been like before the aerial bombardments of the last war wiped 70% of it from the face of the map. These were little pockets of the past, miraculously preserved, history nestling in the shadows of the newer, upthrusting London. Porched and palinged, the housefronts spoke of genteeler, more sensitive times. As property, however, the houses themselves fetched premium prices and never changed hands without cutthroat haggling and gazumping. Gentility cost. A hunger for sensitivity brought out the worst in people.
Moore had written comments to this effect in his notebook entry headed 3.40 a.m., after the words "Still no apparent activity within the premises". During the small hours, when all Arthur seemed to be doing was sleeping, Moore's notebook entries had taken on an increasingly personal and ruminative bent, becoming less an account of his suspect's behaviour (or lack of it) and more an internal monologue, Moore addressing Moore. "I'll never be as rich as a Gleed" was a frequent refrain throughout the pages, along with "Merlin's going to be laughing on the other side of his face" and other similar affirmations that he, Romeo Moore, was on the right track and his partner wasn't. Then there were the lists he had made of possessions he might like to buy with some of the fee from the investigation. A new record-player and a more comfortable armchair for his flat were the common features of all the lists, and were probably the only things he _would_ buy. He was somewhat saddened by his lack of material ambition. In the notebook's margins he had made several attempts to divine Milner's approach to the investigation, of necessity using Milner's own anagrammatising technique. Nothing useful had resulted. There were, in addition, a few doodles, scrawled by lamplight.
It had been a long night.
He had picked up Arthur Gleed's trail yesterday shortly after two p.m. Arthur was returning to the Shortborn Theatre to resume rehearsals, following lunch at a nearby bistro with a couple of his fellow-actors. Moore's first note relayed his impression of Arthur's mood: "Seems upbeat. Confident. Makes his companions laugh with a joke. About nuns and soap(?)."
Later, Moore tried to gain access into the theatre via the lobby but was prevented from doing so by an usher. "Told I could buy a ticket from the box office for performance if wanted but not allowed to enter auditorium." His next entry, fifteen minutes on, read: "Stage door located in alley alongside theatre. Knocked on. Opened by large man. Bodyguard/doorman type. Tried to get on good side of. Claimed to be ClanFan autograph hunter. Bodyguard/doorman's good side not got on of. Claim believed but not effective. Told that Mr Gleed did not sign autographs. Persisted. Invited to 'f*** off'."
Arthur re-emerged from the theatre shortly after five, this time with a gaggle of people. Together they wended their way back along New Aldwych to the bistro and shared an early supper. Moore sat at a table within earshot and nursed several coffees in a row while Arthur and company raucously discussed the preview performance that was due to begin in a couple of hours" time. Moore noticed their affectation of addressing one another by their stage characters" names. Arthur took it one step further by referring to himself in the third person, as the Prince and the Dane, as in "Pass the Dane the salt please, Polonius, there's a good chap". Moore's notes, which he jotted surreptitiously, using a menu as a screen, included the comment: "Actors like nothing better than for other people in the vicinity to know they are actors." He also observed that their reactions and mannerisms were never normal, always exaggerated, as if they lived life at a higher pitch of intensity than everyone else. "'Laertes', describing event of trifling annoyance. Face aghast. Pinching bridge of nose. 'I was incan _des_ cent with rage!'"
The cast trooped back to the Shortborn. Moore followed in their wake. From then till eleven, all he did was stand across the street from the theatre and wait. A few people went in to watch the preview. Critics, he assumed, judging by the fact that most were carrying pads of paper. As a point of interest he noted that on the marquee outside the theatre, the name which appeared largest was that of the star of the show. The play's title and the playwright were both subordinate. Arthur Gleed merited as many yards of neon tubing as Hamlet and William Shakespeare combined.
The critics emerged three hours later, some looking pleased, some not. However mixed the reviews were, Arthur's performance would be singled out for praise. He invariably got a gentle ride. Moore could never forget how one TV critic had striven manfully to say something good about Arthur's execrable _Cabaret Cop_ series and come up with "Gleed's torch-singing is astonishing enough to stop any burglar in his tracks", which veered just the safe side of ambiguous. Arthur's Hamlet, in that spirit, would very likely be acclaimed a great Dane.
Roughly half an hour later Arthur himself came out. He did not look best pleased. "Stomping" was how Moore's notes put it. "Thundercloud above head. Not happy with perf? Or other reason?"
At a safe distance, Moore tailed the disgruntled Arthur to a Family tram stop. Arthur spoke his name into the microphone funnel by the gate. The gate rolled open and he proceeded through onto the platform to await the next tram.
Moore, at this point, was in an ecstasy of dismay. Arthur had stepped onto Family-only territory. He could be headed anywhere on the tram network. Moore was about to lose him—and if Arthur was holding Provender captive, now was exactly the time when he might visit his hostage cousin, to check on him, perhaps crow over him.
As luck would have it, a taxi happened along, For Hire light shining like a beacon. Moore hailed it, and once a tram arrived and Arthur got on board, Moore instructed the taxi driver to trail the tram wherever it went.
"I can't do that," said the driver. "There's laws against that sort of thing."
There weren't. At least, not proper laws. But there was the aura of untouchability that surrounded the Families, as good as a law to some folk.
Moore fished out a hefty wedge of his half of Carver's start-up money. "Are you sure about that?"
The taxi driver eyed the cash. Looked to the tram. Back to the cash.
"Wife's got a birthday coming up," he said, snatching the banknotes out of Moore's hand.
The pursuit was shorter-lived than Moore anticipated, and only once did the taxi driver seem in danger of losing the tram, when it plunged through a tunnel at the base of a building and he had to run a red light and screech around a couple of corners in order to catch up with it again. There was a near-miss with another car, as the driver's concentration on the tram momentarily eclipsed his concentration on the road. Other than that, the chase was problem-free. The tram lines, though hived off from the rest of the world by lofty chainlink fences, stuck close to the public highways, piggybacking on the existing transport infrastructure. Keeping up with a tram in another vehicle was, if due care and attention were paid, a relatively painless affair.
"Disappointment," read Moore's note, written after the taxi had deposited him near Arthur's destination. "A.G. alights at tram stop closest to his house." Appended to the note was a record of his outlay on the taxi ride, which he could not help commenting on with a large exclamation mark.
Outside his house, Arthur paused on his way to the front door to run a hand lovingly over the bodywork of a Dagenham Rapier convertible parked at the kerbside. The car was a sleek thing, low to the ground, with whitewall tyres, a bull-nosed radiator grille, and chrome headlamps that looked astonished at their own good fortune to be perched atop the front mudguards of so wondrous an automobile. Moore couldn't blame Arthur for stroking it like a pet. He would have done so too, had it been his.
Arthur paused again as a pair of ClanFans who were stationed near the house plucked up the courage to approach him, autograph books in hand. He spent a gracious five minutes with them, signing his name and letting them tell him how wonderful they thought he was. He parted from them with a show of great unwillingness, saying how tired he was. Then he went indoors, the ClanFans departed, thrilled, and Moore's midnight-to-dawn vigil in the park began.
He didn't think he slept. His handwriting was slightly slurred on a couple of entries but the very act of making regular notes kept him awake and alert. He left his post on the park bench only once, in order to find an all-night café where he had a torrential pee and then gulped down a pot's worth of coffee. He was gone for less than twenty minutes, and Arthur's house looked no different when he returned. Still darkened. Still nothing occurring within.
With the arrival of morning, Moore was disheartened but not despondent. He remained convinced that Arthur had Provender. Perhaps not here, though, at his house. That was too obvious a location. Cronies of his were keeping Provender somewhere else, somewhere remoter, isolated. Sometime today, before the first night of _Hamlet_ this evening, Arthur would undoubtedly pay a call on his cousin. And Moore would be dogging his steps all the way. His plan was to flag down a taxi perhaps an hour or so from now and have it sit idling at the kerbside, near Arthur's house. When Arthur left, whether he went by car or tram, Moore would follow him in the taxi, just like last night.
One of Moore's private mantras was that to maintain HOPEFULNESS one must PUSH ONESELF. When things looked unpromising, when you were tired and fed up, that was when you had to try harder.
He repeated the mantra to himself, as he huddled, stiff and bleary, on the park bench and waited for Arthur to wake.
To maintain HOPEFULNESS one must PUSH ONESELF.
MOORE'S PARTNER, MEANWHILE, was enjoying a pleasant breakfast after a good night's sleep, well earned after a long but profitable day's work. One thing troubled Merlin Milner this morning, and it had, as far as he could tell, no connection with the Gleed case. The news headlines were distinctly worrisome. Without warning, with shocking abruptness, Europe was lurching towards war. Politicians were talking about trade disagreements and about breaches of clauses of international convention so obscure that even legislative experts claimed not to have heard of them before. Live TV feeds from around the continent showed ambassadors shutting between embassies on urgent rounds of negotiation. The military build-up, however, hogged the greatest amount of airtime, since tanks, troops and warplanes in motion were far more rivetingly photogenic than middle-aged men in suits speaking into microphones or stepping out of limousines.
Milner chose to believe that the matter would resolve itself peacefully. Something which had blown up so quickly could not, ipso facto, be that serious. The louder the heads of state on either side rattled their sabres, the more probable it was that they weren't going to draw them. It was an elaborate charade of bluff, double-bluff and counter-double-bluff. You couldn't ignore that something bad was happening, just as you couldn't ignore the commonality of the words ANGERED, DERANGE, EN GARDE, ENRAGED, GRANDEE and GRENADE, all of which seemed applicable here. At the same time, LEADERS were also DEALERS. WARMONGERING could be broken down into three component parts, GAME, WORN and GRIN, which in almost any order pointed to a _realpolitik_ truth. What seemed MAD POLICY could in fact be DIPLOMACY. Those doing the SABRE RATTLING might equally be ARBITRAL GENTS.
More to the point, Milner was not prepared to let himself be distracted by outside events. The political situation was beyond his control. The Provender Gleed case was not, and needed his full attention.
Yesterday afternoon Milner had paid a visit to the Central London Library to check through the newspaper archives on microfiche. After an hour of scrolling he had found the article he was looking for, a short piece about tenant unrest on one of the capital's municipal housing estates. Next, he had gone to the Risen London Authority's records office, asked to see a list of tenants in a certain block on that estate, and been told by the registrar that thirty days" notice and a stamped endorsement from the RLA were required before such documents could be examined by a member of the public. In response, Milner had slipped the registrar a fifty, asked again, and shortly had the relevant paperwork in front of him and was busy jotting down the names of all those tenants whose initials were either D.S. or S.D.
The resulting list was long—some thirty individuals—and had to be winnowed down somehow. Back at his flat, Milner had spent the evening anagrammatising the names one after another. A bottle of wine was gradually emptied as the floor of the living room gradually filled up with discarded crumples of paper. Near midnight, Milner had reduced the list to seven. Each name, in one way or another, gave him a hit. Each could be refashioned into a phrase that sounded sinister, untrustworthy, or downright criminal.
Today, he planned to visit the estate and knock on the door of each of these seven tenants" flats. One of them would be the person he was looking for. Instinct, he was sure, would tell him which one. He would recognise the kidnapper straight away. He had seen enough guilt over the years to know the telltale signs. Over-friendliness. A tendency to talk too much. Distractedness. An underlying, ill-disguised aggression. One glance, and Milner would have his man.
Needle Grove was not a place he looked forward to visiting. It had a reputation. Teenage tearaways. Vandalism. Violence. Drugs. The joke went that the only needles you found there nowadays were on the tips of Tinct syringes.
Still, there was nothing he could do about that. The anagrams had spoken. The letters pointed just one way.
PROVENDER GLEED contained NEEDLE GROVE, and that had inspired Milner to try various phrases using Provender's name to see what they yielded. PROVENDER GLEED KIDNAPPED. PROVENDER GLEED TAKEN. PROVENDER GLEED CAPTURED.
It was PROVENDER GLEED STOLEN that worked. Stirred, mixed, muddled, reordered, the letters came out as NEEDLE GROVE RENT LOP D.S. or NEEDLE GROVE RENT LOP S.D.
The RENT LOP part had pricked a memory. A couple of years back residents of one block in Needle Grove had staged a protest about their living conditions, refusing to cough up their monthly dues unless their landlord, the Risen London Authority, acceded to a list of demands. The tenants barricaded themselves in the building, promising they would stay there for as long as it took, and were sternly, stalwartly militant right up until the moment the RLA offered them a small reduction in rent, at which point they caved in. It seemed they had had no real stomach for the fight, and the first excuse they got to back down, they took. The idea of a little more money in their pockets made everything else seem bearable. Of course all the other blocks on the estate demanded, and were given, the same rent reduction, but the Authority still won, in as much as the drop in its letting income was less than the amount it would have had to spent sprucing up Needle Grove to the standards the original protestors had been hoping for. Not only that but, if the RLA's track record elsewhere was anything to go by, rents at Needle Grove would have gradually, almost imperceptibly crept up over the past two years till they were back at the previous level. It wasn't just the Families who bled the common people dry. The common people were pretty good at doing it to each other too.
Block 26 was the one that had attempted and failed to persuade the Authority to clean up the estate, and so Block 26 was Milner's destination this morning. He finished breakfast, showered, shaved, dressed, and, with his short-list of seven names in his pocket, sallied forth from his flat and caught a bus that ferried him cross-town to a stop within ten minutes" walk of Needle Grove.
The walk, in the event, took more like twenty minutes. Milner's pace was that slow, that trepidatious. At last, however, he reached the entrance to the estate. Standing before the arc of iron letters, he nerved himself with a deep breath, squared his shoulders, straightened his neck, and, like Theseus about to enter the labyrinth in pursuit of the Minotaur, stepped forward.
**32**
PROVENDER WAS HOME. He was lying in his bed, sleeved in sheets of Egyptian cotton. He could hear the rumble-hiss of the cascades outside his window. There was a vague memory of unpleasantness. Something bad. He had been... held prisoner? Something like that. But it was in the past, long ago. He was home again, and warm in bed, and it was bliss. He could stay here for ever, lying here, free to loll and luxuriate. He could straighten his legs—
—his feet hit an obstruction—
—and he could stretch out his arms—
—his knuckles cracked against a hard surface—
—and he could wallow in the depression his body made in the mattress—
—only there was no mattress.
There was just the bathroom floor that had been under him for more than forty-eight hours now. The blindfold was still fastened around his head. His wrists and ankles were still bound with electrical flex.
It was not as heart-sinking an experience as it might have been, awaking from a dream of home to find himself, as before, in captivity. Bathroom and blindfold and bindings had, in the course of the two days, become the norm. A kind of tired passivity had settled in him. He could, with a strange calmness, foresee spending the rest of his life like this, sightless and helpless, never to look on another human face again, dying an old man on this very spot. There was a contentment in believing that that would be his fate. He was rid of the tormenting hope that somehow, at some point, he was going to be freed. To be back in his bed at Dashlands? Yes, that was truly a dream.
He lay and listened to the building's morning gush of water, the pipes, the ducts, the inner purging, till eventually Is arrived with something for him to eat and drink.
He realised immediately that there was something different about her this morning. A tremor in her voice, a tautness.
"What's up?"
"On the news. The TV. It's incredible. Dreadful."
"What is?"
"I think... They're all saying we could be going to war."
"Eh?"
"War, Provender. As in everyone kills everyone else."
"Where did that come from? I mean, who's going to war with whom?"
"The Pan-Slavic Federation. The western European countries. Just like last time and the time before. It's happening all over again."
"But that's bonkers! We're at peace with the Pan-Slavic Federation. Europe's all one big happy family. Why would...?"
"Why would what, Provender?"
_One big happy family_.
But not one big happy Family.
Had Provender's hands not been tied, he would have slapped his forehead with one of them.
"Has anyone said what the reason for war is?"
"There's some sort of mumbling about treaties that haven't been honoured and other stuff like that, but the main thing is the Federation have started moving troops and warships around in a threatening way and we've had to respond in kind."
"So nobody's invaded anywhere yet?"
"Not as far as I can tell."
"You realise what this is, don't you?"
Is paused to ponder. "You think _you_ —"
"I don't think. I know."
"Your Family."
"My father, to be precise."
"Your father's starting a war because of you? How is that going to help?"
"It isn't. At least, he think it's going to help but that's because he's clearly grasped the wrong end of the stick."
"What do you mean?"
It didn't take Provender long to sketch out the state of antagonism that existed between the Gleeds and the Kuczinskis. Is knew about the feud. Most people did. What she and most people didn't know was just how deep the mutual hatred ran. Provender was certain that his father had pinned the blame for his kidnapping on the Kuczinskis and was taking steps to force them to hand him back. The Kuczinskis, in return, were responding in the only way they could. They didn't have Provender, and they had no doubt told his father that in no uncertain terms. They couldn't, though, simply sit back and let western Europe mobilise for war against eastern Europe. They had no choice but to meet the threat of aggression with the threat of aggression.
"Families can do that? They can throw a whole continent into chaos just because one of them doesn't much like another of them?"
"Is, think about it. There isn't a politician in office who doesn't owe his or her position to Family influence, or else wants to get on a Family's good side. They're like chess-pieces to the Families. Or, no, like trading cards. To be bought, sold, swapped, trumped, disposed of. Politicians, in a sense, are the biggest ClanFans of all. The Families" power just mesmerises them. Being a politician is the closest they can get to being Family."
"Well, yes, I know all that. What I meant is, Families are _prepared_ to do that? They'll start wars over nothing?"
"I think I'm a little bit more than nothing, at least to my dad, but still, I take your point. And the answer's yes. My father's been itching for an excuse to get back at the Kuczinskis. I'm it. Tell me, was there by any chance an Extraordinary Family Congress yesterday?"
It had been mentioned on the news. "Yes."
"My dad," said Provender, nodding. "He called it. And I bet it didn't go well. I bet he and Stanislaw Kuczinski got right up each other's noses."
"But the Congress resolves Family disputes. That's the whole point of it."
"In theory. In practice, when it's not just all the Family heads getting together and having a 'we're so wonderful' knees-up, it's a massive bitch-fest. Everyone yells at everyone else, there's a lot of nasty name-calling, then they all go home again. Cathartic, I suppose, but otherwise essentially useless."
"So it wouldn't stop a potential war."
"The opposite. Any Family worth its salt, after all, has a munitions-manufacturing plant somewhere in its business portfolio, and an aeronautical engineering firm, and a shipwright's. War brings profits. It's an old maxim but still true. Those air forces will need new planes when their existing ones get shot down. Those navies will need new ships when their existing ones are sunk. And then of course there's the rebuilding. My Family made a killing from the reconstruction of London after the last war. We razed the old Dashlands House and built a brand new one just to celebrate how much profit we'd made."
"It's about money."
"It's always about money, Is. Not for my father right now, maybe, or for the Kuczinskis, but for the rest of them. They might have made disapproving noises are the Extraordinary Congress, some of them, but really each and every Family head was rubbing his hands and totting up the potential revenue."
"That's disgusting."
"Tell me about it."
"But no one on the television mentioned anything about your Family or the Kuczinskis."
"Why would they? Who, ultimately, owns those TV stations?"
"The Families."
"Exactly. You won't get TV reporters reporting things the Families don't want them to, not the things that really matter."
Provender heard Is let out a sharp hiss of contempt. For a minute after that she spooned breakfast cereal into his mouth, saying nothing. He could almost hear her thinking, the motor of her brain as troubled but as stoic as that of the extractor fan. Then she said, "If we got you back to your Family, would that mean—"
The sentence was cut short by the sound of the door being flung open. There was a moment when everything seemed to stop, even the extractor fan. Provender pictured Is, startled, peering round. In the doorway: her accomplice. Provender had built up a mental impression of how the man looked. He imagined, now, a face that was cruel to begin with, further uglified, contorted with rage. The man had been eavesdropping at the door. He had overheard what Is just said. For all Is's protestations that he wouldn't dare lay a finger on her, Provender felt that, if pushed far enough, he would. And surely her unfinished question, what it implied, was "far enough".
Absurd notions flashed through Provender's mind. Leaping, somehow, to Is's defence. Interposing himself between her and the man. Taking, on her behalf, whatever the man dished out.
It was easy to be heroic when there was, in fact, little he could do.
Then the man spoke, and Provender was surprised at how even his voice was. Not the fusillade of fury he was expecting at all.
"You done here yet?"
"Nearly."
"Only I need the bog."
"Use the bucket."
"Fuck that."
"I'll be a couple minutes more."
"OK. Hurry."
No sooner had the door closed than Is let out a long, breathless "Oh God."
"Did he hear what you said?" Provender whispered.
"I don't think so. Christ, I hope not."
"Did you...?" Provender hesitated. "Did you mean what you said?"
"I don't know. Maybe. Shit, no, it's madness. What am I thinking?"
"You're thinking that if you help me, you may just be able to prevent the whole of Europe turning into a bloodbath."
"Yes, but—I don't know. I don't know how I could do it. I might not get the chance."
"Does he go out ever? Leave you alone here?"
"Yes. But I never know how long he's going to be gone for. If he caught us trying to..."
"Is. Look at me."
"I already am."
"OK. Good. You see me? You see I'm not the inbred Family cretin you thought I was? You see what getting me out of here, getting me back to Dashlands, is worth? This isn't about ransom any more, or whatever the hell the reason is you kidnapped me. The stakes are much higher. This is a whole different business now."
"Maybe I could talk to him. Explain what you said. About the war and the Kuczinskis and all that. It might change his mind."
"You honestly think it would?"
"Honestly, no."
"Me too. And you talk like that to him, it could rouse his suspicions. He could decide not to go out at all. Best not say anything. Act normal. Wait for an opportunity. It'll come."
"I'm not sure, Provender."
"Is, please. You know it's what's right."
"It's crazy."
"Often the same as what's right, unfortunately."
**33**
IT WAS KNOWN as the Chapel, but that was a misnomer and something of a bitter joke. It was no House of God. It was a folly built on a rise about half a mile west of Dashlands House, close to the site of the original house before the original house was flattened and replaced with the newer one. A cylindrical structure capped with a dome, it mirrored the observatory which stood on another, higher rise a mile due south-east. Externally, the sole difference between the two edifices was that one had a high-powered refractor telescope protruding from its roof.
The superficial similarity was no accident. Both Chapel and observatory had been erected in the mid-eighteen-hundreds by Prosper's great-grandfather, Cardamom, amateur astronomer and ardent atheist. The observatory peered up into the universe and saw only stars and space. No God up there. Plenty of beauty and scientific wonderment, but no God.
The Chapel, by contrast, was blind. It didn't have an eye on the heavens. It was deliberately purposeless. Inside, there was a flagstone floor, a low circular dais at the centre, and, set equidistantly around the wall, alcoves of the kind that could have held idols, statues of saints, representations of gods, something like that, but here were left ostentatiously empty. The message was clear. Deities had no place in the Gleed scheme of things. The Chapel was a parody of a church, a mock temple, blasphemous in its bareness. There was nothing within it to genuflect before, not even an effigy of Mammon.
This, nevertheless, was where Cynthia came when she needed to pray. There was nowhere else to go, nowhere else where she could be guaranteed solitude and silence and stillness, nowhere else on the estate that even vaguely resembled a place of worship. The cool air, the damp smell of stone, and the hollow, hushed echoes, all reminded her of the cathedrals of her childhood. The Lamases were rare among Families in that they had not wholly dispensed with religion. Perhaps it was because the trappings of Catholicism, especially Roman Catholicism, were reassuringly gilded and grandiose. Equally it might be because, as Cynthia's father often said, it was wise not to reject the Almighty altogether, on the off-chance that He did exist. Confession, too, and the taking of the Sacrament, and general prostration before a higher power, did much to shrive the wealthy of their guilt about being wealthy (assuming they felt such guilt in the first place). Attending a two-hour Mass every Sunday was a small investment of time, given the psychological and spiritual dividends one stood to gain from it.
As a girl Cynthia used to love going to Mass: the otherworldly elegance of the Latin catechisms, the fragrant fume trails left in the air by the huge swinging silver censers, and the fact that everyone in the congregation, not least herself, was decked out in their very best clothes—the men in crisp blazers and trousers, the women a froth of underskirts and mantillas, black cloth everywhere, wave upon wave of it in the pews, a sea of dark, solemn self-effacement. She had been Confirmed. She had learned her _Ave Maria_ and was given a jade rosary by her parents on which to toll it, all one hundred and fifty times, to expiate her sins. She had believed everything the Church claimed, implicitly, perfectly. She was so devout, her mother even began to ask her, half jokingly, if she was thinking of becoming a nun.
But Faith had ebbed from her as she reached adulthood. Faith, it seemed, was for children, who were innocent enough to accept it at face value, and for very old people, who had to have something to cling to as the shadow of extinction loomed ever larger. The world was infinitely more complicated than religion could account for. Life had shades and hues that the Church's broad primary-colour statements simply could not match.
Cynthia was not lapsed. A belief, of some sort, persisted, like a high tide mark in her soul. She returned to Faith whenever she needed it, and was always somewhat surprised to find it there where she had left it, more or less intact, a little rusty but still serviceable. The Chapel, which she was just about the only person ever to visit, had become a sanctuary for her when things got difficult—and being married to Prosper Gleed, not to mention being mother to Provender Gleed, meant things often got difficult for Cynthia. She still had her jade rosary too, and to sit for an hour in the Chapel's emptiness, thumbing the beads one by one about their silk thread and murmuring the words of the _Ave_ till they lost all meaning, brought solace in even her darkest moods. The unadorned walls and vacant alcoves were a far cry from the stained-glass splendour and seething iconography she had known in her youth, but such plainness was, in a way, better. It was a closer reflection of how she felt inside.
Perhaps, after all, she should have taken the veil. A part of her still seemed to yearn for a life of nun-like simplicity and contemplation.
As a nun, for instance, Cynthia would not be sitting here this morning in the Chapel, consumed with anger and despair; would not be tolling a very unusual rosary, a substitute for her jade beads; and would not be considering an act of awful, soul-imperilling sinfulness.
She had heard the reports on the radio as she ate her breakfast—the cogs of the machinery of war, starting to turn. She had known, though, when Prosper arrived home in the small hours of last night, what he had done. He had crashed around their bedroom for a while, clumsily undressing in darkness, then headed off to one of the spare rooms to sleep. He had been unwilling to get into bed with her. He had been afraid to talk to her. She, for her part, had pretended to sleep, afraid in her own way to talk to him, not wanting to hear what he had to say. She had known. He had done everything he had threatened to. The news of the radio only confirmed it. Things had gone so far. So badly out of control.
Now, in the middle of the Chapel dais, Cynthia knelt. She was no longer young. It hurt her knees to kneel on bare stone. Nonetheless she did.
She was cold. Even in summer, the Chapel retained the chill of night through to midday at the earliest. The sun took that long to warm it. She had on an ash-coloured vicuña sweater but still she was shivering. Her breath emerged in pale wisps.
Her rosary consisted of little yellow pills—Oneirodam tablets from the bottle by her bedside.
With a trembling fingertip she shifted them across the floor, one by one, left to right.
" _Ave Maria, gratia plena; Dominus tecum_..."
Another pill was shunted across.
" _Ave Maria, gratia plena; Dominus tecum_..."
And another pill.
Could she? Should she? Dare she?
" _Ave Maria, gratia plena; Dominus tecum_..."
And another.
**34**
IS WATCHED DAMIEN watching the news. She wondered if he was going to make the connection. The war. Provender. She prayed he would. She prayed it would dawn on him that _he_ was the root cause of all this. His conscience would do the rest. He was still, all said and done, a man of conscience.
But, although Damien voiced concern about the situation, which was getting steadily graver, he didn't appear to care that much. He was preoccupied. Once or twice he mentioned getting the ransom demand out, saying it was long past due. He was expecting his Family insider to call soon and give him the go-ahead. That call, too, was long past due. Is could see he was chafing, champing at the bit. Less and less was he liking the fact that he was not in sole charge of the Provender kidnapping and that he had to be accountable to someone else. She still could not fathom his relationship with this unknown Family member. She understood only that in order to get what he was after, the money to renovate Needle Grove, Damien had entered into a pact with a representative of his very worst enemy. He had done a deal with, if not the Devil, then one of the Devil's minions. To Damien, this was not a compromise but an alliance forged by necessity. He remained, however, not best pleased about it.
On the television, the politicians kept talking about a diplomatic resolution, even as the military build-up continued. Whether they were genuinely hopeful of a peaceful outcome or just saying what an alarmed populace needed to hear, Is couldn't tell, but she felt that at the very least they were going to take things right to the brink. Like Damien, they too were at the behest of unseen masters, in this case Stanislaw Kuczinski and Prosper Gleed. Is found it bizarre to think that just two days ago she had been serving drinks to the latter, had stood within a few inches of him, had suffered him to ogle her boobs. A lecherous middle-aged man, similar to countless others she had come across, all too easily captivated by the sight of a generous chest—and yet he had the wherewithal to trigger a continent-wide conflict, almost without effort. Serially unfaithful to his wife, by all accounts, and addicted to gambling—and yet, with just a word, he could set one half of Europe against the other. That was wrong. That should not be. So much responsibility should not reside in the hands of someone so irresponsible.
The phone rang.
Damien snapped the TV off and picked up the receiver.
"Yeah?... Oh good. About time you got in touch again. I was beginning to think—... Right, right. Yes, I've been watching it. Not good... Uh-huh. Yes... Really? Jesus! ...You think so? It won't make matters worse? ...So the one I've already written is no good any more... No, I told you, I don't own a videotyper. Can't afford one. I use the public-use one at the local library... All right then... I know, keep it simple, don't say too much... Fine. And then the drop-off plan as before? ...Well, that's something... OK. Nice one. 'Bye."
He replaced the receiver and looked at Is with a broad, almost boyish smirk.
"Remarkable," he said.
"What is?"
"Well, I had a feeling that all that stuff"—he jerked at thumb at the television—"might have something to do with him." The thumb jabbed in the direction of the bathroom. "It was too much of a coincidence otherwise. But I couldn't think how the one joined up with the other till that person"—now the thumb indicated the telephone—"said the Gleeds think the Kuczinskis are behind the kidnapping."
"Oh," said Is, trying to pretend this was news to her.
"Yeah, so now we've got an even bigger stick to beat the Gleeds with. We can ask for twice as much as we were going to."
"How do you get that?"
"Because, Is, the Gleeds are desperate. They think their arch-enemies have Provender, and when they find out they don't, they'll be so damn relieved they'll cough up any amount of cash."
"I hate to say this, but isn't that a bit greedy, Damien? And isn't it wrong to use what's going on to your own advantage? An international crisis—"
"No, Is," said Damien, very firmly. "No, it's not wrong. The end justifies the means. The end damn well justifies the means. We were going to ask for five million for Provender, weren't we? We could do a lot for the estate with five million, but think what we could do with ten. Fuck it, with fifteen. Transform this place beyond recognition. Make thousands of lives better."
"At the risk of making hundreds of thousands of lives worse if this war goes ahead."
"But it won't go ahead. Once the ransom note's delivered, the Gleeds will know it isn't the Kuczinskis who have their precious boy and they'll call off the dogs."
"What if it's too late?"
"It won't be too late."
"You can't know that for sure. If the momentum keeps building the way it is, events could spin out of control. Something could start that just can't be stopped. Whereas all you have to do is phone the Gleeds now, tell them everything's all right, you're the one holding Provender and not the Kuczinskis..."
"The money, Is. _More_ money."
"At what point, Damien, does blackmail become extortion?"
"At what point, Is, does disagreement become mutiny?"
"That's ridiculous. All I'm doing is telling you—"
Two swift strides took Damien to within arm's reach of Is. She didn't, to her surprise, shrink away from him, though every instinct she had was ordering her to. Somehow her spine stayed straight, her head remained defiantly high.
"All you're doing is telling me you haven't the guts to do this any more," he spat. "Telling me Rich Kid has got to you. Telling me you'd rather hand him back for nothing than try and get the most we can out of him. Is that it, Is? Is he more important to you than us?"
"Us?" she replied, more calmly than she could have thought possible. "You're talking about everyone on the estate, I take it."
Damien blinked. "Yes. Exactly. Yes, I am. Is he more important than everyone on the estate?"
"No. I'm just saying I think you've lost sight of what this is supposed to be about. And—and I think this war thing has gone to your head. Suddenly you've got a tremendous amount of power, suddenly you have the capacity to prevent something truly terrible from happening, and what do you do? First thing you think of is "What can I, Damien Scrase, get out of this? How can _I_ benefit?" Which, in my book, makes you no better than the people you've been fighting against all your adult life. It makes you no better than Family, Damien."
She wished, as soon as she uttered the last sentence, that she could take it back. To compare Damien to Family was the worst insult imaginable for him. She might as well have called him a vivisectionist or a child-molester.
"Oh, Is," he said. His tone was deadly smooth. His eyes had gone dull and hard. "Oh, that's not kind of you at all."
Is didn't see it coming. She heard it coming, a whirr of displaced air, a sound she had no way of recognising, but she didn't actually see Damien's hand swinging at her, knuckles first. It blindsided her. It came at her too fast.
Then there was lightning.
Then there was the feel of carpet under one side of her face, and a ringing, droning hum in her skull, and her eyes were watering and the floor was pulsing up and down woozily, as though she were at sea, and Damien, from some deep distant cavern, miles away, was lecturing her, telling her she had asked for it, she had deserved it, and he was sorry—he didn't sound sorry but he said he was—and he was heading out in a mo and she could lie there if she wanted to, that was fine by him, but she should remember she had deserved it, and he wasn't that sort of bloke, he hated that sort of bloke, the type that hit women, but she had provoked him, it was her fault, she should think about that, she could think about it while he was gone, all right?
All right?
And then he was gone. Is heard him leave. The door slammed. A key turned in the lock. The floor oozed around her. The entire flat warped and distended, as though testing its own cubic dimensions.
Faintly, from far away, Provender was calling out her name: "Is? Is? Are you there, Is? Are you OK?"
**35**
A CAR STARTED, stuttering, then belching out a great four-cylinder roar. The driver revved the engine a few times, to get its juices flowing, then shifted out of neutral. The engine note changed from a growl to a purposeful purr.
Romeo Moore heard these sounds, identified them straight away as belonging to a sports-model vehicle, and mused happily on the fact that well-engineered automobiles always had such nice voices. In addition to looking good, a car had to sound good. There was no point in owning a Dagenham Rapier, say, if what lay under its bonnet produced a pathetic little fart of noise. You needed the whole package, aural as well as visual. Otherwise—
A Dagenham Rapier!
Moore's eyes flashed open. He started from the park bench. He was on his feet and running almost before he knew what he was doing.
He reached the park railings just in time to see Arthur Gleed's Rapier pull out from its space, Arthur at the wheel. He watched Arthur ease into the roadway then accelerate. Tyres pained tarmac. With a squeal and a roar and a burst of blue fumes, the Rapier shot away. A moment later, it was at one of the exits from the square. A moment after that, it was gone.
Asleep!
Damn and blast it, he had fallen asleep!
Moore checked his watch. Gone eleven. The last time he remembered looking, it had been nine.
Nodded off. Hadn't hired a taxi as he had planned to.
Stupid. Careless. Unprofessional.
He had lost his suspect's trail. Arthur was doubtless on his way to look in on Provender. Moore, through his own incompetence, had fluffed his chance of following him.
He cast around, hoping against hope to see a taxi cruising by through the square. There was none. It would have been a miracle if there had been.
With a groan, he lowered his head till his brow came to rest on the tip of a railing spike.
It hurt.
That was good.
HULKING CLEF!
**36**
PROVENDER CRAWLED FOR the bathroom door. It wasn't easy. He had to move like a caterpillar, sliding his arms forward, following with his torso, then arching his back and bringing his legs in behind. It also wasn't easy because he wasn't sure of the door's precise location. In the end, though, he did find it. Through sheer good luck, he crawled in exactly the right direction. Through sheer bad luck, he didn't know that until after he made one of his torso lunges and banged the door with his head.
When the pain faded, he called out to Is again. As before, there was no answer. He had listened to her arguing with her accomplice. He had heard their voices rise and then that final, climactic _thwack_ , followed by the sound of someone falling. A short while later, a door had slammed shut. He hoped that meant that the man had stormed out of the flat. He hoped that what had gone before signified that Is had been struck but nothing more serious.
But if it _was_ nothing more serious, how come she wasn't answering? And had the man actually stormed out? The door which had slammed might not necessarily be the front one.
Provender decided it didn't matter. He thought his interpretation of the sounds was correct, and if it wasn't, he would simply have to take the consequences.
Hunkering back on his knees, he raised his hands and hooked his thumbs under the blindfold. Lately the urge to do this had become all but unbearable. In spite of Is's warning he had been desperate to take a peek at his surroundings, just to be able to use his eyes again, see _something_. He had resisted. Now, he put such considerations aside.
Up the blindfold went.
The bathroom was dim. What light there was came in from under the door. Nevertheless Provender, having been sightless for two whole days, was dazzled. He winced. He screwed his eyes shut. After several moments he prised his eyelids apart again. The line of light under the door was a strip of pure supernova. It razored his retinas. He forced himself to keep looking at it, despite the agony. The sooner his vision adjusted, the sooner he could get out there and find out what had become of Is.
Gradually supernova became magnesium flare, which became white-hot metal, which became bright sunlight, then filtered sunlight, and finally cloudy sunlight. Provender looked around at the glimmering outlines of the bathroom's fixtures and fittings, shapes he had till now known only by feel. The bathroom was not large but it was bigger than he had thought. In the utter darkness of his captivity, it had seemed tiny and close-confining.
His eyesight was blurry but good enough, he thought, for him to venture out. He reached for the door handle and yanked it down.
Brilliance flooded in, a world of glare and shine. Provender thrust the door wide and groped his way over the threshold. Blinking hard, he tried to take stock of where he was. The main room of a smallish flat. Over there, a galley kitchen. Over there, the door to a bedroom, ajar. That was a relief. It couldn't, then, be the door that had slammed shut. The man _was_ out.
His eyes watered and began to sting. He rubbed them and reopened them.
The flat was shabby, cheaply furnished, low-rent. He saw a couple of plywood bookcases crammed with paperbacks and a pine table with spindly legs and a set of chairs to match. The table was just that bit too large for the place, occupying more than its fair share of floor. A tall window afforded a view of... It was too bright out there. Provender couldn't look directly at the view. He turned his gaze to the TV set and armchairs adjacent to the window. Just past them, poking out, he spied a pair of legs. Woman's legs.
He caterpillar-crawled over as fast as he could.
The legs belonged to Is. She was lying supine, with her head turned. Her eyes were glazed. A large red welt had formed on her left cheek. The swelling was spreading to her lower left eyelid.
"Is?"
Her eyes flicked, a minuscule movement, the irises shifting a degree or so.
"Is, it's Provender. I'm here. Are you all right?"
What an absurd question! Of course she wasn't all right. What was he thinking?
"Listen, I don't know what to do. I can't do anything. I'm still tied up. You've got shock or concussion or something, I don't know what. You're the one with the medical training, not me. But you've got to come round. You've got to help me. Then I can help you. Is! Please!"
Her eyes moved again.
"He could be coming back any minute, couldn't he. This is our chance. Come on!"
Her head rolled. She let out a murmur. Provender thought what she said was _water_.
He crossed the floor to the kitchen in his ungainly caterpillar style. Rising to his knees, he planted his elbows on the worktop and hauled himself to standing. He took a glass tumbler from the sink draining basket, filled it at the tap, then made his way back to Is in a series of small hops, cradling the tumbler in both hands. By the time he got to her at least half the water had slopped out over his fingers. More was lost as he lowered himself thumpingly down into sitting position. Still, there was some left. He brought the tumbler to Is's lips and tipped it carefully. A dribble went into her mouth, while the rest splashed onto the carpet. It wasn't the water itself that counted so much as the act of drinking. Slowly Is's eyes gained focus. She stirred, moving her arms, shifting her legs. Her hand went to her injured cheek and explored the swelling there. She was as gentle and tentative as she could be but still made herself hiss a few times. Finally, she made to sit up. Provender did what he could to assist, propping his hands beneath her back and lifting. Is, though, did most of the work. She moaned as her head came up. The colour drained from her face and she looked, to Provender, as though she might pass out. A clenching of teeth, a furrowing of brow, sheer willpower, kept her conscious.
"More water?" Provender asked.
"No," she said, thickly. "Just give me a second. Wait for... I just need to..."
Deep breaths. A gingerly turning of the head to one side then the other. A flexing of the fingers. Little by little she steadied herself, re-establishing her equilibrium.
"OK," she said at last. "Now." She looked at the knots that bound Provender. "In the kitchen. Drawer by the hob. Big carving knife."
Provender found the knife and hopped back with it, holding it out at arm's length in case he stumbled. Is took it from him, he knelt down beside her, she told him to stick out his wrists, he did so, and she inserted the knife blade between his forearms and began sawing at the innermost loop of the electrical flex.
Provender thought about telling her to be careful but then thought it was better to say nothing. Time was of the essence, and he would rather she worked swiftly and he received the odd nick than she sacrificed speed for precision.
The rubber insulation on the flex parted easily. The copper wire inside put up more resistance. Is worked the knife up and down, and Provender did his bit by keeping his arms rigid so that the flex was taut against the blade's cutting edge. He wondered if Is had any idea how long her accomplice was going to be absent. He was reluctant to ask. He wasn't sure he wanted to know.
The blade was through the copper wire. The last bit of insulation split apart. The loop of flex sprang open, and rapidly the other loops loosened and unspooled. Provender parted his hands. Never had such a straightforward action brought such joy. He felt like waving his arms around all over the place, just because he could. He managed to refrain from doing so, and instead kept himself perfectly still as Is set to work on the flex at his ankles. The knife cleaved. His feet were free. Kicking off the sundered flex, Provender extended each leg in turn and rotated each foot. His hands and feet tingled as full circulation returned to them. Provender felt, for the first time in two days, whole.
He flipped the blindfold off his head, stood shakily, then reached down and helped Is up.
"Thank you," he said, simply and, he hoped, humbly.
"Welcome," said Is.
"I take it the, er..." He gestured at her cheek. "The romance is over."
"Don't push it," she shot back.
"Sorry."
"But I suppose I have been put straight on a couple of things."
Provender was indignant. "'Put straight'! Like a woman needs the sense knocked into her from time to time."
"Not what I meant. I meant I don't have any illusions about Damien any more."
"Damien."
"No call for secrecy now. Yes. Damien Scrase is his name. And this is Needle Grove. And we're getting the hell out of here while we can."
"I like the sound of that." Provender didn't know much about Needle Grove and what little he did know hardly filled him with delight. Getting out of there seemed, on every level, a good idea. "Oh, and by the way, Is? Today's my birthday. Were you aware of that? My twenty-fifth. And I have to say you've just given me the best present I've ever received."
"Happy birthday, Provender," Is said tightly. "But how about you save the gratitude till we're far away and out of trouble?"
**37**
THE TRUST BETWEEN her and Damien was well and truly breached. As if the throbbing great haematoma on her cheek wasn't already enough of an indication, Is quickly discovered that Damien now regarded her as no less of a prisoner than Provender. The front door was locked, and her own door key was gone—Damien had pilfered it from her shoulder-bag. The emergency spare key Damien kept in a drawer in the kitchen was also gone. The door itself was sturdy, a common feature of Needle Grove flats. The original doors on the estate had been thin and skimpy, little better than sheets of plywood, easy to break down. Rather than keep replacing them all the time, the Risen London Authority had seen the economic advantage in installing heavier, more solider versions so that would-be thieves could not simply barge their way in. The corollary of this, unfortunate in the present circumstances, was that would-be escapees could not simply barge their way out.
Damien had also taken the precaution of rendering the telephone inoperable. He had removed the coiled cable which connected the receiver to the body of the phone. Is and Provender could not summon help.
"What about that way?" Provender pointed towards the windows, squinting.
"We're forty-five storeys up."
"Even so. Isn't there a balcony out there?"
"Yeah. So what?" Is thought for a moment. "Hang on, you might have something."
"I might?"
Is grappled with the sliding window and managed to haul it open. The exertion brought on a wave of light-headedness, which she did her best to ignore. She stepped out onto the balcony and looked left.
Each flat in each block had one of these balconies, a little square protrusion of outdoor space. Each flat was also a mirror image of its next-door neighbour, an architectural feature intended to make the residents feel marginally less like convicts in identical cells or battery hens in matching cages. This meant that the balconies were positioned alternately close together and far apart. The balcony to the right of the one Is was on was a good thirty feet away. The balcony to the left, however, was much nearer, no more than six feet.
Provender appeared behind her, shielding his eyes against the daylight.
"Who lives there?" he asked, nodding to the left-hand balcony.
"Mrs Philcox. Those are her pot-plants, or the dead remains of." There was a range of clay pots on the balcony in which nothing sprouted except clumps of moss. "She's getting on a bit, and not quite all there any more. The good news is, she'll definitely be in. Housebound, pretty much."
"But do you think you can jump that far?"
Is studied the gap. "Maybe, with a run-up, but not from a standing start. And not with that kind of drop below. You think _you_ can?"
Provender took a look over the balcony parapet and jerked back. "Even if I thought I could, I wouldn't want to try."
Is's shoulders sagged. "Then it's hopeless."
Provender seemed to agree. He looked indoors, surveying the layout of the flat. "How about if we ambush him—Damien—when he returns? We could lie in wait behind the door, in the kitchen bit, leap out, bring him down. There's two of us and only one of him."
"Have you seen him, Provender?"
"Rhetorical question, right?"
"Right."
"I got a glimpse of him, before you stuck that needle in me, but..."
"He's more than a match for both of us. Trust me."
"Even with the element of surprise?"
"Even with."
"There's that carving knife."
"Have you ever stabbed anyone?"
"No, but if I was ever going to, it'd be him."
"Big talk, but it's far easier said than done. Besides, Damien carries a knife. Sheath knife. Big one. Nine-inch blade. And he knows how to use it, and would, too."
"On me? His precious ransom cheque?"
"He doesn't have to kill you with it. He could do worse than simply kill you."
"Good point. Or he could use it on _you_." Provender frowned unhappily, then brightened. "I don't suppose you've any of that stuff left?"
"Stuff?"
"What you injected me with."
"As a matter of fact I do. There's an extra dose lying around somewhere. I kept it ready as a precaution."
"We could inject Damien, couldn't we, then. I grab him, hold him, you shoot him full of sedative or whatever."
"Well, it's a nice idea, but again we have the problem—don't take this the wrong way, Provender, but he's twice your size and you're hardly the big bad fighting type, are you? You could grab him but I don't think you could hold him. Not even for a moment."
She could see Provender trying hard not to look crestfallen. She hated to be the one to prick the bubble of his male pride, but it was best to be honest. Physically, in terms of sheer aptitude for violence, Damien was several leagues above Provender. In a straight contest between the two of them, Provender would not have a prayer.
"So we're stuck." He let out an angry gasp. "Unless we can somehow find something to bridge a six-foot gap between— Hold on."
Is had the idea almost at the same time he did.
"The table."
THEY MANHANDLED THE table out through the window, which was just wide enough to accommodate it sideways, legs horizontal; they manoeuvred the table onto its back; they manipulated it onto the balcony parapet. Then they had to shove it straight out, swing it around and slide it across to the other balcony. All this they accomplished with much effort and grunting and the occasional curse. They were hurrying and at the same time trying not to hurry, a recipe for grazed knuckles and squashed fingers if ever there was one.
The table, as its leading edge neared the lip of the other balcony, became increasingly heavy and difficult to control. It dipped down and wanted to slip out of their grasp and fall. Is and Provender hauled on a leg each, using it like a lever. Both heard ominous creaks coming from where the legs were screwed into place.
"Don't break," Is begged.
"Cheap piece of _mierda_ ," Provender muttered under his breath.
Finally, with a thumping scrape of wood on concrete, the far end of the table made contact with the side of Mrs Philcox's balcony. With a little further straining, Is and Provender got the table surface to overlap the parapet. They let go of the legs. The table stayed put. They had done it. The gap was bridged.
"Only one problem," Provender observed.
Is nodded. The overlap at either end was barely an inch. Not, under the circumstances, much of a margin for error.
Provender peered out over the edge of the balcony again. "Look on the bright side. You might not fall all the way."
"No?"
"No, there's an overpass about halfway down. You'd hit that first, most likely."
His bravado would have been more convincing if his face hadn't been so pale.
"Is," he said. "You don't have to do this. I do. You can stay. Tell Damien I got away. Pretend I overpowered you or something."
Is snorted. "He's really going to believe that!"
Again, that crestfallen expression, badly disguised.
"The point is, Provender," she went on, apologetically, "this whole thing has been a mistake. I should never have got involved in the first place. Somehow I've got to make amends."
"You already have."
"Then, also, I've no great urge to be here when Damien gets back."
"Fair enough." Provender surveyed the table, precariously poised, a slender traverse, all that stood between the person crossing it and a drop of several hundred feet. Just a few thin planks. Certain death below.
He turned to Is. "Ladies first?"
**38**
GRATITUDE GLEED WENT in search of her father and found him where he had been all morning, in the television room, sitting on a sofa, transfixed by the images being projected over his head via a system of magnifying lenses onto the bare white wall in front of him. A Phone was waiting in a corner of the room—there, clearly, for when the Kuczinskis rang to talk terms.
Hearing his daughter enter, Prosper Gleed patted the space next to him on the sofa. Gratitude declined the invitation.
"I just came to say we're about to have lunch, Dad. In the solarium."
"Have someone bring something through for me."
"Also, Arthur's dropped by. What are we supposed to tell him? About Provender."
"Tell him whatever you like. Might as well tell him the truth. He is Family."
_Not exactly_ , Gratitude thought. _Step-Family perhaps. If you wanted to be totally, brutally accurate: halfling bastard_.
"If you say so," she said. "Dad?"
She waited for him to look round.
On the wall, a reporter with an enormous microphone was addressing the camera from beside a road. _Lower Saxony_ read the caption below him. Behind him, a convoy of armoured personnel carriers was rolling past, against a background of flat green plains. Dust clouds and engine thunder were making it difficult for the reporter to do his job. He kept half ducking and swatting the air in front of his nose. About one in every three words he said was intelligible.
The glow of the epidiascoped image on the wall lit up Prosper Gleed's face. It flickered and moved there, throwing his features into shifting relief. His expression, though, beneath the changing light, stayed firm. Resolute. His eyes, bright-wide, drank in all they were seeing.
"Dad?"
Again he did not look round, and Gratitude wondered if he realised she was still there. All she wanted from him was a word of reassurance. All he had to do was turn and say, _This will get your brother back_.
He continued to gaze straight ahead.
Silently, Gratitude slipped out of the room.
UNCLE FORTUNE WAS in the solarium, as were Extravagance, Arthur, Great and Carver. They were ranged around the circular glass table with glass flatware and glass-handled cutlery set before them, all of them in glass chairs except Great who was in his wheelchair. Sunshine drenched the room and permeated its many transparent surfaces, some of which refracted the light prismatically and sent lozenges of rainbow-pattern brilliance scattering in a dozen different directions.
Gratitude arrived just as the first course, gazpacho soup, was being served. Everyone tucked in apart from Arthur, who was halfway through a thespian anecdote and would not be diverted from finishing it. When he was done with his tale of a faulty camera and the perfect take that was never captured on film, he paused and looked around, expecting some display of appreciation from his audience. He was taken aback when none came.
"I'm sorry, am I missing something here?"
The others exchanged glances.
"Only, I've played to livelier crowds of old-age pensioners." He bowed to Great. "Begging your pardon, of course, Coriander."
Great glared glitteringly back at him, as if to say, _Why are you using my first name? Why are you even here?_
"Good soup," said Fortune, slurping. "Prosp not joining us, Gratitude?"
"Busy."
"And Cynthia?"
"Still up at the Chapel, I think," said Extravagance.
Gratitude shot her sister a look.
"What?" Extravagance demanded.
In spite of her father's edict, Gratitude was loath to let Arthur in on the situation. It was none of his business. He took liberties as it was—for instance, turning up at Dashlands whenever he felt like it, uninvited. He behaved like he was one of the Family, this cuckoo-cousin, and he wasn't, not really, and Gratitude, whenever she could, did what she could to remind him of that fact.
"The Chapel, eh?" Arthur said. "So what's wrong?"
"Nothing," Gratitude replied, quickly. Too quickly.
"Oh, come off it. Aunt Cynth retreating to the Chapel? That's a sure sign all's not well. Has your dad made another conquest? Carved another notch on someone else's bedpost?"
"No."
"What, then?"
"Perhaps," said Carver, turning round from feeding Great, "Mrs Gleed is simply concerned about the rather tense state of affairs in Europe."
"Yeah, could be," Arthur said. "Bad business, that. You know, my director actually phoned me this morning, wondering if we shouldn't cancel tonight's performance because of it. I told him, 'Never.' I said, 'In troubled times, people need the solace of art more, not less.' I said, 'Even if only one ticket-holder turns up tonight and all the rest stay home, frightened, we will play to that person as if to a full house. We will bring that courageous soul the Shakespearian consolation he is seeking.' That pretty much settled it. Anyway, I'm sure it'll all blow over. I imagine that's what Uncle Prosper is busy doing right now. Trying to calm things down. Smoothing ruffled feathers. What else is a Family head for? Correct?"
He looked round the table. Silence and sombre faces told him he was way off the mark.
"Not correct. Oh dear. Oh yes, how obvious. The Poles. Our blood-guzzling chums the Kuczinskis. What's happened? They must have made some serious blunder."
"You may as well know," said Fortune, and explained.
The news that Provender had been abducted, possibly by the Kuczinski Family, had Arthur going through paroxysms of incredulity and anguish. He waved his hands about; he shook his head; he gasped "No!" loud enough to be heard in the back row of the stalls. It was all very histrionic, Gratitude thought, but then with Arthur the boundary between profession and life had long since become blurred. Drama was his natural state of being. Everything was an act.
"My God, and there we were at the party just the other night," he said, "me and Provender, having a lovely time. Rubbing along like we always do. And then—somebody nabbed him. Right from under our noses. I can't believe it."
"None of us can," said Extravagance.
"I even invited him to the show tonight. All of you, too. I insisted he come. That feels so—so _trivial_ now."
"So perhaps you will cancel tonight's performance after all," Gratitude suggested. She said it with just a soupçon of viciousness, hoping Arthur's answer would confirm her low opinion of him.
It did.
"Hell, no." Arthur bent over his soup and dipped his spoon in. "Show must go on and all that." He glanced up. "I mean, it's what Provender would want, isn't it? Surely?"
**39**
WHAT PROVENDER WOULD have wanted, right then, was not to have to crawl across an upturned pine table, forty-five storeys up, with no guarantee whether that the table would support his weight or that it would remain securely perched on the two balcony parapets while he was on it. He would have wanted anything but this sickened feeling in the pit of his stomach, this sense that every last drop of moisture in his mouth had somehow transferred itself to the palms of his hands, above all this fear that if fate was going to choose any day for him to meet a messy, spectacular death, why not today, the twenty-fifth anniversary of his birth? Fate had a nasty sense of humour, after all. This was not the day for him to be inviting it to play one of its grim practical jokes.
Then again, he had no desire to remain in Damien Scrase's flat, and the table was his only viable means of escape.
The opportunity for Provender to entertain these thoughts arose because Is had left him alone on the balcony. Saying she had just remembered something, she had ducked back into the flat, and Provender was waiting for her to come out again. He wasn't crossing the table without her holding one end of it down as they had planned. What she was actually doing in the flat, he had no idea. A part of him wished she would get on with it. A part of him didn't.
Finally she emerged. She had with her a hypodermic syringe and a medical ampoule containing some sort of fluid. She showed them to Provender, then bundled them up in a cloth and stuck the bundle in her shoulder-bag.
"Just in case," she said.
"Not for me, then."
"Not this time."
"Funny. I could do with being unconscious right now."
"Me too."
Provender gestured at the table and looked plaintive. "Are you sure you don't want to go first?"
"You're heavier than me. If it can take you, it'll take me."
"What if it can't take me?"
"It will."
"You know that for certain?"
"Stop fannying about and get on the table, Provender."
Is placed her hands close together on the end of the table and pressed down with all her might. Provender, feeling his heart start to pound, slid himself into the gap between her left arm and the table leg nearest the building. He eased himself out across the table's underside, lying flat, braced on his forearms. His feet were still on the balcony floor, taking most of his weight. Cautiously he lifted one leg, then the other. His weight was transferred to his torso.
The table creaked. Provender froze, his legs sticking straight out behind him.
"Can't do this," he breathed. "It's going to break."
"It's not. Keep going."
Little encouraged, Provender wriggled a few inches further forward.
The table creaked again, a deeper, sadder sound this time—the sound of resignation, almost, as if the table accepted it wasn't going to survive this ordeal.
Provender thought of the drop beneath him. He thought of the thickness of the wood that was keeping him from falling, or rather the thinness of it. An inch at most. Closer on three quarters of an inch.
Three quarters of an inch of cheap pine. It was nothing. Nothing. He might as well be lying on a sheet of balsa.
"Provender."
Is's voice. Urging.
But what Provender was listening to was the sound of space around him. The faint breeze thrumming through Needle Grove's canyons. Distant shouts that echoed nebulously. The height—and depth—of the world he had now ventured into. Air. Immensity.
He quailed inside. He clenched his eyes shut. He wanted to slide back onto the balcony where Is was, where safety was, but he couldn't. He couldn't move.
A table. A few glued-together planks.
He was going to die.
"Provender, listen to me. You've just got to go forward. There's nothing else you can do. You'll be fine."
"Is..."
"I mean it. I promise."
She meant it. She promised.
How could she promise something like that? That he would be fine?
She couldn't.
But what mattered was that she said she could.
Provender took a breath; held it. He clamped his teeth together. Eyes still tight shut, he threw himself fully onto the table. He slithered forward. He did it fast. Knees, elbows, scrambling, and there was a noise coming out of him, a fusion of expelled breath and battle cry, low-pitched, rising. The table flexed beneath him. The table jumped. The table juddered and groaned. He heard a yelp from Is. He fell.
Forward.
A short plunge.
Landed hands first on Mrs Philcox's balcony.
Tumbled.
Rolled.
Fetched up with his head between two plant pots.
He lay dazed, glad, numb, exultant. Alive.
Then he levered himself up onto his elbows and craned his neck to peer over the parapet at Is. He was about to say something blithe and plucky like "Nothing to it" or "Hop on over then", until he saw Is's face... and realised that the table was no longer there, suspended between the two balconies.
At that precise instant, from far below there came a faint but fulsome _crash_.
**40**
MERLIN MILNER HAD had a busy but so far fruitless morning in Needle Grove. He had crossed off five names on his list of seven. He had not yet found the person he was after.
Still, he refused to be discouraged.
Even when a pine table plunged from the sky and almost killed him.
Shortly before this incident occurred, Milner had decided to take a breather, grab a bite to eat, and assess the state of his investigations. It never hurt to take time out to regroup and retrench—especially after having come across five of the least savoury individuals he had ever had to misfortune to encounter, in surroundings that were not, anyway, conducive to feelings of goodwill toward one's fellow-men. Moreover, Milner wasn't looking forward to tackling the last two names on the list, and certainly didn't want to do it on an empty stomach.
Midway up Block 26 there was a mezzanine area which boasted a shopping arcade, along with a café and various other communal amenities. Milner had glimpsed it a couple of times on his way between different flats, as the lift had a tendency to stop at that floor to let people in or out. At the café he purchased a ham sandwich and a bottle of orange juice. The sandwich was so dry as to be near inedible, the juice so sharp as to be near undrinkable. He persevered with both while sitting at a cigarette-singed plastic table and perusing his list of suspects and the notes he had appended to the names of the ones he had already approached.
First in line, alphabetically, came Sable di Santis, who lived at Flat 37J. She had opened her door circumspectly—it proved to be a common habit among the denizens of Needle Grove—and had glared at Milner with an unnerving mixture of aggression and dismissal. She was taller than him by nearly a foot and had short spiky hair that matched the short-spiked dog collar she was wearing. The towelling bathrobe she had on revealed a glimpse of leather corsetry. While greeting her and introducing himself, Milner glanced past her and noticed an array of implements mounted on one wall of the main room—whips, manacles, ball-gags, and some large, long, nobbly devices the sight of which, frankly, alarmed him. He was still speaking when a muffled female voice called out from an adjoining room in the flat, asking Sable if she was coming back. Sable snapped a reply: "Shut your mouth, bitch!" Then, not much more pleasantly, she told Milner she was busy with a client, he should state his business, otherwise fuck off. Milner apologised, said he'd made a mistake, got the wrong flat, sorry for bothering her, goodbye.
So much for SABLE DI SANTIS—LESBIAN SADIST.
Next up was Serena Drummer, down on the fourth floor, flat number 4P. Milner had arrived just in time to find her locking her door, on her way out with a group of snivelling, clamouring children around her legs. "Miss Drummer?" he had asked, and had been firmly and tartly corrected: "Mrs." She wasn't any more warm or agreeable a woman than Sable di Santis, and during her conversation with Milner broke off to scold each of her children at least once. She had dull, grainy skin, lank hair, a chipped front tooth, an all-over air of harassment. She was, however, surprisingly forthcoming. She was just off with the kids to visit her husband, she explained. Went every Tuesday. He was inside, she said. Been banged up for killing someone eight years ago. Brixton Towers jail. He didn't do it, though. Well, he did. But the bastard had it coming. Fiddled with one of the kids, didn't he. "Anyway," she said, "if yer another journalist after me story, I in't talkin" to yer. Not till we've discussed terms." Milner informed her he wasn't a journalist. "Why you wastin" my fuckin" time then?" she snorted, and strode off with her brood in tow. Milner couldn't help but wonder if her husband, after all this time in clink, found it curious that at least three of her offspring were under eight years old. Did he ask himself how she kept getting pregnant? Or were conjugal visits less well supervised than Milner had been led to believe?
Not his problem, though. And SERENA DRUMMER, MURDER MAN SEER, wasn't his problem either.
Sherman Dungate, of Flat 19C, answered his door in vest and underpants but appeared fully clothed thanks to the tattoos that covered his torso to the neck, his arms to the wrists and his legs to the ankles. There were skulls, roses, angels and naked women on his body but the majority of the tattoos were non-representational, zigzags and swirls and interlocking knots, like a kind of animal marking, blue-ink camouflage. He was liberally pierced, too, with a dozen earrings, a nose stud, a lip ring, and a nipple ring prominent through the fabric of his vest. He was skeletal-skinny, with rodent eyes, and the moment he caught sight of Milner his expression turned peevish and sullen. "You're new, aintcha," he said. "All right, I'll give you your bung. But tell your Super I can't keep paying off every fucking one of you who turns up at my door. I got a business to run here, you know." Before Milner could say anything, Dungate disappeared into the flat and returned with a wad of greasy, crumpled banknotes. "Fifty usually covers it," he said, licking a finger and peeling off five tenners. "Cop tax," he sneered, holding out the money. At last it dawned on Milner what was going on, and he assured Dungate that he wasn't a policeman, at which the other man brightened. "Oh, you're here for some stuff then, are you?" Milner said no, not that either. Now Dungate became resentful. "So why you fucking bothering me? There's half a dozen buyers probably been scared off by seeing you here. You're costing me money, man." Milner tried to apologise but Dungate launched into a volley of invective, using all sorts of unflattering terms to describe Milner, _time-waster_ being the least offensive. Milner beat a retreat.
SHERMAN DUNGATE was many things, including a MEAN DRUGS THANE, but he was not, Milner was quite sure, Provender Gleed's kidnapper.
Fourth on the list came Dudley St Barstow, and although Milner did not actually meet the man face to face, what he heard through the door to Flat 48F was enough to convince him that St Barstow was not holding Provender on the premises. He seemed to have plenty of livestock in there, however, to judge by the clucks and squawks and woofs and oinks that emanated from within, and he seemed to be enjoying an unnatural relationship with several of them. Milner, ear pressed to the door, heard a crooning male voice compliment a bird on its alluring tail feathers, refer admiringly to some mammal's shanks, and entice another mammal to come over and snuffle around for a treat he had hidden somewhere in his lap. St Barstow cracked jokes with the animals. He sounded a lot like an Arab sheik immersed in his harem, doting on his many concubines. Milner did not knock on the door. Nothing on earth would have persuaded him to meet the man inside.
And so DUDLEY ST BARSTOW, exponent of WRY ODD BEAST LUST, was eliminated from Milner's enquiries.
It was with some haste that Milner had moved on to Dennis Sandringham, who proved to be the best of a bad bunch. Sandringham looked, dressed, was coiffed, above all _smelled_ , like the perfect lothario. As the flat door opened, a waft of cologne greeted Milner, then Sandringham did too. Immaculate in blazer and cravat, late-middle-aged but not looking it, he invited Milner in, offered him a nip of sherry, behaved like the most beneficent of hosts, and did not bat an eyelid when Milner asked to use his bathroom, a pretext for taking a sneaky peek around the entire flat. The phone rang while he was doing so, and when he returned to the main room, satisfied that Provender was not here, he found Sandringham cradling the receiver and chatting in such a way that Milner had no doubt the person on the other end of the line was a favoured female. "One of my ladyfriends," Sandringham explained after he hung up. "Wants me to drop round and see her. Can't say no, can I? She'll want me to stick my todger in that dried-up crack of hers, worse luck, but a chap has to earn a living somehow. Speaking of which," he added, insinuatingly, "I could fit you in if you like." Milner made his excuses. "I do men as well, you know," said Sandringham. Milner made more excuses, vehement ones this time, and left.
DENNIS SANDRINGHAM, DAMN DASHING SINNER, had not been the likeliest candidate for the role of Provender's kidnapper. Milner had felt obliged to check him out anyway, just to be sure. He rather wished he hadn't.
So, five down, two to go; and the final two were the ones Milner was most hopeful about, and most dreading meeting. Their names had given him the strongest hits out of all the seven. Last in alphabetical order was Demetrius Silver, who lived at the very top of the block in Flat 60M. DEMETRIUS SILVER, the anagrams said, IS DEVIL MUSTERER. Milner envisaged a goateed Satanist in a flat adorned with pentacles and inverted crucifixes, black candles guttering everywhere, the curtains permanently drawn.
It was an unappetising image, but the question was whether or not it was preferable to the impression Milner had built up of the resident of Flat 45L, one Damien Scrase.
From DAMIEN SCRASE Milner had extracted a plethora of anagrams, none of which was exactly a source of great comfort: SCARES MAIDEN, CRANIA MESSED, MEAN CAD RISES, INCREASES MAD, I END MASSACRE... The anagrams spake sooth. This Scrase fellow was not someone to be taken with a pinch of salt. He was, if not unhinged, then close to it. Potentially very dangerous. I END MASSACRE could, Milner supposed, be regarded as a good attribute rather than a bad. Then again, a person who ended a massacre might well be the very same person who started it, and in the light of the other anagrams Milner was more inclined towards the negative interpretation of the phrase rather than the positive.
The Satanist or the madman? It was a tough call, and in order to defer the decision, Milner found an exit from the shopping arcade and went outdoors.
He was on an overpass. The sun, now at its zenith, sent a hard white light straight down on his head. He shaded his eyes and basked in the brilliance, thinking that in these slivers of space between buildings the presence of direct sunshine must be a rarity and a blessing. He wondered if areas of Needle Grove ever even saw the sun during winter, when it was low and usually behind cloud.
He decided he would amble the length of the overpass, to the adjacent block, and come back. Idly he mused on Romeo Moore. How was he getting on? How far had he got in his quest to nail Arthur Gleed as the culprit? Not far at all, Milner suspected. Moore was a good anagrammatic detective but not, to be perfectly honest, as good an anagrammatic detective as Milner. Often Milner felt he was carrying Moore, doing a greater than fair share of the work. In any partnership, however much of a meeting of equals it appeared to be, there was inevitably one person who was superior to the other. An unwelcome truth but it had to be acknowledged. And if the current divergence of investigative paths proved anything, it would prove that.
On this uncharitable note, Milner sallied forth along the overpass... and that was when the table, like a divine judgement, came hurtling down from heaven.
It missed him by inches. It landed slap bang in front of his right toecap. If he had been half a stride further on, if he had started walking a split-second sooner, Milner would have been right under it. He would have been killed instantly.
He watched the table, as if in slow motion, hit the concrete in front of him. It seemed to dismantle itself, shrugging into its component parts, the planks of its top separating, its legs splaying, its bracing timbers splintering in all directions. The impact made an almighty _whump_ but was also somehow soundless, too stunningly loud for Milner's ears to comprehend. Fragments and flinders flew. The bulk of the table collapsed, plank bouncing off plank, shard off shard, slithering, spreading, coming to rest. Milner found himself staring at a heap of firewood at his feet, and he thought, _That used to be a table_ , and then he thought, _Was that a table?_ It seemed inconceivable that the wreckage just seconds ago had had shape, had been functional, had been a Thing and not merely Stuff.
Reflexively he anagrammed the word _table_.
TABLE—BLEAT.
That was all. Only BLEAT.
Then sense returned. His scattered wits came thronging back. He glanced up where the table had come from, not really looking. He saw tower blocks, balconies, windows, sky, sun. An impression of Needle Grove bearing down angrily upon him. He spun on his heel. He headed for the exit he had come out of. He plunged back into the shopping arcade, back into apparent safety, into a place where tables did not, could not, fall on you from a great height. He fetched up against a shopfront. He leaned into it for support, panting. Adrenaline surged through him like jolts of electricity. His legs went weak. He slumped. His heart rat-a-tat-tatted. He stayed there, shellshocked, for he didn't know how long.
Death. Death had come within a hair's breadth of getting him.
Gradually Milner began to realise how lucky he had been. How fortunate he was to be alive still. With that realisation a calm began to descend on him, and his breathing slowed and so did his heart rate.
What he would never know was that the falling table incident was a near-miss in more ways than one.
Had he remained outdoors a moment longer, had he kept looking up, Milner would have seen two heads appear, looking down from adjacent balconies directly overhead, fifteen storeys above the overpass. He would, if he had been in full possession of his faculties, surely have recognised one of the heads as belonging to none other than Provender Gleed.
That was how close Merlin Milner came top cracking the Provender Gleed case, and in the process winning his gentlemen's bet with Romeo Moore.
Painfully close.
Lamentably close.
Tragically close.
**41**
IS FELT MANY things when the table dropped away. The first was annoyance. If Provender hadn't scuttled across in such a frantic hurry, the table would not have started bouncing and the end she was holding down would not have slipped out of her grasp. The next thing she felt was chagrin. She should have held on tighter. She was to blame for the table falling, not Provender. Then came exasperation, as an old, familiar thought-routine welled to the surface: _Typical Family, taking everything, leaving nothing for anyone else_. Finally there was a peculiar kind of guilt, as she recalled the real reason she had gone back into the flat before Provender set off across the table—not to fetch the hypodermic, as she had claimed, but to leave a kind of time-bomb for Damien. She had committed an act of petty vengeance, and already karma had caught up with her. She had done something she should never have stooped to doing, and here was her reward, to be stranded on the balcony with her means of escape well and truly gone.
All these emotions came and went in a flash. It then occurred to her that there might have been somebody below when the table fell. She poked her head out over the parapet. Provender, on Mrs Philcox's balcony, did the same.
The table had struck the overpass. It was in about a thousand pieces but none of those pieces, thank God, was embedded in the anatomy of a human being. There was no one on the overpass. The only person adversely affected by the table's fall was Is herself.
"Shit," she sighed. She looked across at Provender. His body language said _puzzled_ and also _sheepish_. "Well, that's that, then. What the hell am I going to do now?"
"Erm..." Provender scratched his head. "No idea. Bugger. I'm sorry, Is. I don't even know how it happened." His expression turned hopeful. "Look, I could go into Mrs What's-her-name's flat and asked to use her phone. Call the police."
"We've no idea how quickly they'll get here."
"If they hear my name, pretty quickly."
"They might think it's a hoax call."
"I didn't think of that. Still, it's our best chance."
"But if Damien gets back from the library before the police arrive..."
Provender nodded. "Then you just have to jump."
"Are you joking?"
"Nope. Deadly serious."
"I can't jump that distance. We already established that."
"Why not? You could if we were on the ground."
"Maybe. But we're not on the ground. If we were it wouldn't matter, I could jump and miss. Here, I can't."
"But you won't miss. You'll make it."
"Says who?"
"Says me. Is, a moment ago you promised me I'd get across that table safely. Lo and behold I did. Now I'm making you the same promise. You _will_ jump across. You _will_ reach this side. And I'll be here to catch you. Just do it."
There was complete earnestness in his face and voice. He believed implicitly what he was saying. He was trying to make her believe it implicitly too.
To her surprise, Is found herself clambering up onto the parapet.
The building swooped away beneath her. Her entire body went numb. Her head became as empty as a balloon.
She lurched back down onto the balcony and stood there clutching the parapet and trying not to vomit. She wasn't scared of heights, but that meant nothing when you were teetering five hundred feet above the earth, contemplating a six-foot jump onto a foot-wide concrete wall. Then, the natural terror of falling took hold and overrode all else. It wasn't even a tussle between instinct and logic. There simply was no logic in what Provender was encouraging her to do.
"Is," he said, "get up there again and jump."
"Fuck off, rich boy. You do it, if it's so easy."
"Just spring forward. Throw yourself. I'll be here. I'll grab you, cushion your landing."
"You won't cushion my landing because I'll be landing right fucking down there and unless you plan to be standing under me like a one-man firemen's blanket..."
"Do you want to be there when Damien gets home?"
"I don't have a choice, do I."
"Yes, you do, and it's jump."
Is thought of Damien coming home and finding her alone in the flat. She could undo her "time-bomb", that wasn't a problem, but there would be no getting around the fact that Provender had absconded. That was something she could not undo, and there was just no predicting how Damien would react. The lump on her cheek was testament to that, not to mention the way her left eye was starting to puff shut.
She heaved herself, trembling, back up onto the parapet. There, she clutched the side of the building, shuffled her feet forward till the tips of her toes were at the parapet's outermost edge, and waited for an upsurge of courage.
And waited.
And waited.
Courage didn't seem to want to arrive. Every nerve in her was telling her to step back. Every cell in her recoiled from the drop in front of her.
If she leapt, for a moment she would be in flight between the balconies, nothing below her, greedy gravity eager to gets its hands on her and drag her down.
She could not see herself doing it.
Then she was doing it.
She did not know how or why. She had no idea what impelled her. All at once, obeying some subconscious command, she crouched, tensed her legs, put everything she had into it, and sprang.
There was no sense of transition. No notion of flight. One moment she was on Damien's balcony, the next she was on Mrs Philcox's.
Or _almost_ on Mrs Philcox's.
One foot scraped the parapet. Then the lip of the parapet jarred into her knee. Then she was sliding, flailing, tumbling. She knew she had failed. She was going to fall.
Then Provender had her. His arms were around her torso, his hands scrabbling for purchase, finding it in her clothing, in the strap of her shoulder-bag. She dangled, clinging onto him, he clinging onto her, and then she began kicking against the parapet, pushing herself up against it with her toes, mad, panicked, desperate to get onto the balcony, not caring what it took, screaming, yelling, clawing, fighting, and Provender hauled backwards, and the parapet was under her belly and then the balcony was beneath her and Provender was spreadeagled next to her, and Is caressed the solidity of the balcony's concrete floor, loved it like she had loved nothing before.
A long time later, still sprawled flat out, Is said, "Did you honestly believe I'd manage it?"
"Not for a second," Provender replied.
"You absolute fucking bastard."
"I know."
"When all this is over, I'm going to kill you. You know that, don't you?"
Provender grinned. "It will be a sweet death."
She punched him. It was the least he deserved.
**42**
LUNCH WAS DONE and Arthur took his leave. Threading his way through the house, he got a little lost. He was still not totally familiar with the layout—really, the place was a maze—but with time and a few further visits he would, he felt, have it solved.
He emerged into one of the drawing rooms, expecting it to be an entrance hall. There he came upon his aunt, Cynthia, who was sitting with several string-bound stacks of post in front of her. She looked—and it was hardly surprising—desolate.
"Arthur?"
"I know all about it," Arthur said, going over to her. "I am so, so sorry."
She made a vague gesture of acknowledgement which turned into a trembling caress of her forehead. "Birthday cards," she said, indicating the letters. "For Provender. Most arrived today. From well-wishers out there. You do know it's his birthday?"
"He mentioned it the other night."
"Twenty-five. Not a special age, like twenty-one or forty. Not a milestone. But still, a quarter of a century."
Arthur laid a hand on Cynthia's shoulder.
His own mother he loved. She was outspoken, forthright in her feelings, handsome in a rough-hewn Hebridean way, and she had defended him throughout his boyhood against the taunts and jibes that were frequently flung at him, while also encouraging him to stand up for himself (it had not been easy, growing up a Gleed in a small island community). For all that, she was not a woman like Cynthia Gleed. Arthur was in awe of his aunt. She was glamorous, ethereal, saintly, compassionate, forgiving... In a word, perfect. The kind of mother every son should have. The kind of son he, in furtive, wistful moments, wished _he_ had had.
His heart went out to her now, and at the same time he inwardly damned Provender for any and all of the distress he had caused Cynthia over the years, the long litany of upsets and disappointments he had brought to this fine, upstanding, blameless woman.
"If there's anything I can do to help..."
Cynthia patted his hand. "Thank you, Arthur, no. I can't think of anything."
"If you like, I could go back to the Chapel with you. We could pray together." Arthur had never prayed for anything in his life, but for Cynthia he would. Happily.
"No need, Arthur. That's kind, but it's all under control. I know what I have to do."
"Oh. Well. If you're sure..."
She nodded, sure.
"I'll be getting back to town, then," Arthur said. "We're having a full-dress run-through this afternoon. Clear up a few snags that happened last night. The director said it isn't necessary, but I wasn't completely happy with the performance, and when a Gleed's not completely happy there's no rest until he or she is. Isn't that right?"
"I agree," said Cynthia, with definiteness.
"Anything and everything must be done to bring about the right conclusion."
"Absolutely."
She seemed cheered, and all through the drive back to London Arthur was pleased to think he had brought her comfort with his words. A better son than her own son, he opined. Far more deserving of her maternal affections than Provender would ever be.
**43**
WINIFRED PHILCOX WAS surprised to see her son Barry standing on her balcony, tapping on the window. He hadn't rung to tell her he was visiting. Come to think of it, he hadn't called in ages, and she couldn't remember when he had last dropped round. A month ago? A year? Time was strange, wasn't it. Sometimes it shot by and sometimes it didn't seem to pass at all.
Winifred made her way to the window as fast as her trick hip would allow. She signalled to Barry that she would need his help sliding it open. Oh, and look. Barry had brought his girlfriend with him. Andrea, Angela, something like that. Winifred had met her twice previously. They hadn't got on. Not good enough for Barry, that was the trouble. Barry was a prize and that Andrea/Angela girl simply didn't deserve him.
Still, Winifred was impeccably polite as she greeted them. She told them to come in, come in. She went to hug Barry and he seemed startled, but he returned the hug. Winifred then held out her hand to Andrea/Angela and said it was nice to see her again.
"I'm sorry," she added, "you'll have to remind me. Is it Andrea or Angela?"
"Neither," said the girl. "Don't you recognise me, Mrs Philcox?"
"Of course I do," Winifred said with a sniff. "You're Barry's Andrea. Or Angela."
"No, I'm Is. I used to live next door, sort of. With Damien."
"Don't be daft. You're Andrea or Angela. I remember that Is. She looked nothing like you. Lovely girl, though." Winifred turned to Barry. "Now then, young man, why have I seen so little of you lately?"
"Erm... Because I've been holed up in an ashram in the Himalayas for the past decade, pondering on _koan_ s?"
Andrea/Angela hissed at him sharply, which Winifred chose not to comment on. Really, though, a girl should never backchat her man like that. No wonder she had that big bruise on her cheek and that swollen eye. Probably asked for it.
"Mrs Philcox," Andrea/Angela said, "actually we haven't got time to stop and talk. Could we use your phone?"
Winifred turned round again. "All right, I've been very patient with you, young lady, but even I have my limits. I was speaking to my son and I'll thank you not to interrupt. When and if you want to ask me something, you can jolly well wait until the right moment arises. Otherwise keep yourself to yourself." She clucked her tongue, uttered a little snarl, and shook her head. Honestly!
"As a matter of fact, er, Mum," said Barry, "we do rather need to use the phone."
"Go on then," Winifred said, somewhat irritably. That girl had put her in a bad mood. Completely ruined what should have been a happy reunion. It hadn't escaped Winifred's notice that Barry appeared not to have shaved for three days. The blame for this clearly lay with Andrea/Angela. She was a bad influence on him in so many ways. He used to be such a clean and tidy lad.
"Dead," Barry said, with his ear to the phone receiver. "No dial tone. Nothing."
"Are you sure, Prov—Barry?" said Andrea/Angela.
"If Barry says it's dead, it's dead," said Winifred. "Is it really, Barry?"
"As a dodo. When did you last pay your bill, Ma?"
"I don't know. Can't remember. I'm sure it was recently."
"Well, I'm afraid you've been cut off."
A light dawned in Winifred's head. "That'll be why you haven't rung in a while. I bet you've been trying and trying to get through."
"Yes. Quite. That's it."
"Payphone, then," said Andrea/Angela. "That's our best chance."
Barry agreed, and together the two of them made for the door.
"You're going?" said Winifred, not even trying to hide her dismay. "Already?"
"I'm sorry, we have to," Barry said. "It's been great to see you. I'll call again soon, I promise."
"You won't even stay for a cup of tea?"
"We'd love to but we just can't. Next time."
"Well, take care then. Look after yourself."
"Thanks. I fully intend to."
IT MIGHT BE argued that Mrs Philcox, mild senile dementia notwithstanding, was not in fact wrong to mistake Provender for her own son. After all, Family members were in some sense members of everyone's family. People knew them as well as, and sometimes better than, their own kin. And people often preferred them, or the idea of them, to their own kin.
Certainly Barry's visit, brief though it was, left Mrs Philcox with a warm glow of happiness that lasted the remainder of the day. Her son, whom it so happened she had not seen in nearly four years, still loved her. Her son, who in fact couldn't stand the sight of her any more, still cared.
**44**
ANXIETY DOGGED THEIR steps as they headed along the corridor towards the lift bank. It seemed that at any moment Damien might appear. He might be riding a lift up to this floor right now. The lift car would stop, the door would roll open, he would step out—and there would be Provender and Is straight in front of him, not where they were supposed to be, and with nowhere to hide.
Reaching the lift bank, Is stabbed the call button urgently. Nothing appeared to happen, but the lifts in this block, as in all of them, were notoriously sluggish and sometimes simply refused point-blank to work, for reasons no repairmen could fathom. If lifts had souls, the ones in Needle Grove were as downtrodden and surly as those of long-abused slaves. They bore a grudge about their lives of constant hard labour and all the times they had been pissed in and shat in and the fact that the legal minimum of maintenance work was done to keep them going. They resented their own existences, and it showed.
Is couldn't bear to be out here in the corridor, exposed, waiting for a lift to deign to come. She tried the button a couple more times, then jerked her thumb towards a nearby access door and said, "The stairs."
**45**
"MAY I BE of assistance?"
The voice was mildly accented and polite but with an undertow of quiet warning. It belonged to an Asian man—Chinese, Milner thought—with a soft round face, hair that had receded to the crown, and eyes that were deep-set and yellowed and, at this moment, wary.
"Only," the man continued, "you're leaning against my shop window, and I'm always a bit concerned when people lean against my shop window." He gave a wry grimace. "It often precedes people breaking my shop window."
Milner immediately straightened up, to prove that he was not the type of person who did that type of thing.
"Sorry. Wasn't really thinking. I was taking a rest. I've just had a bit of a sort of close shave, you see."
The shopkeeper nodded, understanding only too well. "Ah yes. You're not a resident, are you? I can tell. Needle Grovers have a certain look about them, and you don't have it. Though you seem to be well on your way to having it. What happened? Run into one of the gangs? Get stuck in a lift for an hour?"
"No, I just grabbed a bite to eat from that café over there—"
"Say no more. The food there is a traumatic experience."
"No, it wasn't that. Then I stepped outside for a breath of what passes for fresh air in this city, and somebody went and dropped a table on me."
The shopkeeper shrugged, as if such an event was a daily occurrence in Needle Grove. "They missed, though."
"Just barely. I swear to God, an extra layer of skin and I'd have been a dead man."
"You're lucky."
"Don't I know it."
"Lyman Ho," said the shopkeeper, extending a hand.
"Merlin Milner," said Milner, shaking it.
"I am, as you might have guessed, the proprietor of this establishment." Mr Ho rapped an affectionate knuckle on the shop window. "Mr Ho's All-Day Emporium. Robbed and/or vandalised a grand total of seventy-eight times since I took over the lease, and still in business."
"That's a record to be proud of."
"I like to think so. Would it be rude of me to ask why you've come to the Grove? It's simply that we get very few outsiders here and you seem, if I might say so, not the typical visitor. A cut above that."
Milner was only too happy to accept the compliment. "I'm here on business. I can't really tell you much more than that. It's confidential and rather serious."
"Forgive my enquiry. I'm famously nosy. I like to know everything that's going on. It's a useful trait for a shopkeeper, to be interested in the lives of all his customers and potential customers, but sometimes, I realise, I go too far. I cross the boundary of good manners. You English and your good manners—it's very confusing for a foreigner like me. You all know where the lines are drawn but you're damned if you're going to let anyone else in on the secret."
Milner smiled. Already he liked Mr Ho, and Milner wasn't someone who warmed to people easily. Then there was Mr Ho's name, his full name, Lyman Ho. It hardly even needed anagrammatising. Just swap forename and surname around, and hey presto, instant trustworthiness.
"You must be from Hong Kong, correct? Anglo-Saxon first name like that."
"Indeed. Son of very prestigious banking family. Not Family, not quite, though we had aspirations to be. Perhaps a couple more generations and we'd have made it. But it wasn't to be."
"The Shanghai Uprising."
"The great revolution." Mr Ho sneered. "When the Four Acquaintances took power and the people of China became a single, billion-strong Family. And my own family, like many others, was obliged to... 'pool our assets', the phrase was. 'Had our assets stolen by the government', more like. We were truly Shanghaied. No more rich, no more poor. Everyone equal. No Families lording it over everyone else. And look how well it turned out."
"And naturally you emigrated, and you ended up here. Running this place."
"It's not glamorous, it's not lucrative, but it's a living. And, if all goes well, it's a start. Three, four generations from now, maybe there'll be All-Day Emporiums across the entire country, and maybe a couple of generations after that the Hos will be a Family. It's possible. Anything's possible."
Milner looked from Mr Ho's modest retail enterprise to Mr Ho's dreamy expression, and saw a gulf between the two that all the ambition in the world could not bridge.
Time to change the subject. It was obvious to Milner that Mr Ho was an unparalleled source of local knowledge and might be able to help him with the dilemma he presently faced. Chances were Mr Ho knew at least one of the two names remaining on his list, if not both. Some inside info on Damien Scrase and Demetrius Silver would come in handy.
As Milner opened his mouth to speak, there was a commotion at the far end of the shopping arcade. Turning, Milner saw a bustling group of about thirty people come into view. They were a mixed lot: elderly women, overweight middle-aged males, some teenagers, a smattering of children. What they had in common was an air of eager excitement and the fact that each was carrying a candle.
The group passed by Mr Ho's shop and headed out into daylight.
"ClanFans," observed Mr Ho. "If I'm not mistaken, the official Needle Grove Block Twenty-Six ClanFan Society."
"Where are they off to? What are the candles for?"
"To hold a vigil. Didn't you know? It's Provender Gleed's birthday today."
"Oh. Ah." Milner hadn't known. But then, unlike his partner, he didn't follow the Families.
"Yes, they'll stand in a ring, sing 'Happy Birthday'. It's a ritual they have."
_Little do they realise_ , Milner thought to himself, _that the person whose birthday they're celebrating is actually here. Provender might even be able to hear them singing_.
"Mr Ho," he said, trying his best to make it sound as if what he was about to say had no connection with the foregoing exchange, "a short while ago you asked if you could be of assistance. As it happens, you can."
"You'd like to buy something?" Mr Ho started to usher him towards the shop entrance. "Be my guest."
"No, it's not that. It's more to do with... I'm looking for someone. Two people, to be exact. One's called Demetrius Silver, and he's—"
Mr Ho's expression turned sour. "Don't. Don't mention that person. A wicked, wicked man. They say he sacrifices babies. I don't believe it myself, but I do know that he's involved in some very dark practices. He keeps coming in and asking if I could get a goat's skull in stock. A goat's skull! As if I can just ring up my wholesaler and order half a dozen. He offers to pay me handsomely for it, but that makes no difference. I'd rather not help a Black Magician if I can avoid it. He does have a fondness for tinned apricots, however. Don't ask me why."
"The other person is Damien Scrase," said Milner. "Would you by any chance know him too?"
"Damien? I know him well."
"What's he like?"
"Damien... Thoroughly decent. A prince among men."
Milner frowned. That didn't seem right. It didn't tally with the anagrams. Maybe Silver was the perpetrator of the kidnapping after all.
"Yes," Mr Ho went on, "a good man who's quite out of place in this rat-hole. He wants a better world. He wants to get rid of the Families. I try to explain to him that that might not be a good thing, but he never listens. You have to admire altruism like his even if you don't agree with it."
"He doesn't like the Families?"
"Didn't you hear what I said? He detests them."
Milner was feeling a quickening of the blood. "Why is that, do you think?"
"Who can say? He just believes we'd be better off without them. And he can't stand people like that lot who went past just now, those ClanFans. If he'd been standing here with us, he'd have laid into them verbally. Called them suckers and slaves and morons and sheep. I've seen him do it. It doesn't win him friends, but then with beliefs like his you can't expect to be popular. There was a rent protest a couple of years back. Maybe you read about it."
"I did."
"Damien was one of the prime movers of that. Helped organise it. Rallied tenants to the cause. But because he's such an anti-Familial he didn't have everyone's full respect, and when it came to the crunch, when the RLA tried to fob us off with a minor rent reduction which we knew they wouldn't keep to for long, Damien advised against accepting it. He told everyone to hold out for better terms. And no one listened. The rebels rebelled against one of their ringleaders and the protest fell apart. _That's_ the drawback with hating the Families. You get hated in turn."
Milner was beyond excited now. He knew— _knew_ —that he had his man.
"Have you, um, have you seen him lately?" he enquired.
"Yesterday. No, I tell a lie, the day before yesterday. He came in for cigarettes. He'd given up smoking for a couple of months but he was back on the fags again. Which is usually a sign that he's under strain of some sort. In this case it's a woman. He's been in an on-off relationship for a while. More off than on. For all his apparent self-assurance, Damien is sensitive when it comes to things that matter to him." Mr Ho thumped himself in the chest, over the heart. "Matter to him here. He also," Mr Ho added, "needed latex gloves for some reason."
That clinched it, as far as Milner was concerned. The smoking might be connected to a woman but the likelier reason for it was the kidnapping and holding captive of a certain Family member, which would surely put anyone on-edge. And the latex gloves—to prevent leaving fingerprints, obviously.
"And at this point," Mr Ho said, "I suppose I should ask what your interest in Damien is, why you're looking for him. I've told you a great deal about him. Now you tell me about _you_."
"That's easier said than done."
"You aren't plainclothes police. You look a bit like it but you aren't. But you're here in some kind of official capacity. What?"
"Would it be all right if I said you'll know in a day's time?"
Mr Ho chuckled. "It would be fine. I don't much care. I'm just a natural gossip. I'd tell you anything you wanted to know. Also, Damien's an idiot, really."
"I thought you said—"
"I said I admire him. I said he's a good, decent man. I never said I _like_ him. I don't. Not a bit. And if he's done something wrong, committed some offence, then more fool him. He deserves to be caught." Mr Ho clapped Milner on the back. "Now, if I really can't tempt you to make a purchase, I'd better be getting back inside. Off you go. Hunt him down. Good luck. And watch out for any more falling tables!"
With that, Mr Ho disappeared into his shop, leaving Milner bemused, enlightened, but, above all else, elated.
Damien Scrase.
The intimidating anagrams were all at once unimportant. They were relegated to a position way down on the list of considerations, ousted by the sheer rapture Milner felt at knowing that his detective work had paid off and that the biggest case-bust of his career, probably ever, was now mere minutes away. He almost didn't need to pay a visit to Flat 45L, so confident was he that Damien Scrase was the guilty party. Caution, however, not to mention thoroughness, dictated that he should. As well as a location for the kidnapper, he wanted to be able to supply a first-hand physical description of the man before he picked up a phone and called the CLAN REAVER.
The lifts beckoned. Milner sauntered towards them with his head held high and a spring in his step.
**PART V**
**46**
FOR THE BLOCK 26 ClanFan Society, it was a special day, and about to get even more special.
They didn't hold a candle vigil on just anyone's birthday. Like most ClanFan groups they had their favourites, the Family members they liked above all others. By common consent, the Block 26 Society held Cynthia Gleed in the highest regard. Plenty of societies did. But they also greatly admired Llewellyn Madoc, head of Wales's pre-eminent Family; Detver von Wäldchenlieb, that most Anglophile of Germans, who with tweeds and monocle and muttonchop whiskers and cries of "Toodle-pip old chap!" was a living parody of a country squire (and perhaps the whole thing was a sly dig at the English, although given the impenetrability of the Teutonic sense of humour, who knew?); Siobhan Beauchamp-Dalziel-Featherstonehaugh, a tangential relative of one of the lesser British Families, who possessed the hardest-to-pronounce name known to man and who made up in camp outrageousness what she lacked in lineage; J.B. Bannerjee, hailed throughout the world for his philanthropic works, the most good-hearted spendthrift the planet had ever known; and last but not least, Provender.
They liked Provender largely because they liked his mother, but also because he was an unknown quantity. There was something wilfully romantic about a Family member who shunned the limelight, who kept his privacy while all around him were squandering theirs, who was handsome and intelligent yet chose neither to flaunt nor to exploit these attributes. Provender was a blank slate on which the Block 26 ClanFans could write their own dreams, a cloud whose shape they could interpret any way they wanted.
For some of the Society's female constituents, and a couple of the male, he was a heartthrob, the one they would fantasise about during their erotic daydreams or perhaps think about while making love with someone else. For the Society's junior contingent, he was just still young enough to be considered cool. For the older ladies among their number—and the Block 26 ClanFan Society was predominantly made up of women of mature years—he was the son they wished they'd had. He brought out the maternal instinct in them far more strongly than their own offspring ever had.
The Society assembled, as was its wont, on the shopping level of Block 26, then trooped outdoors, because it was a nice day and why not make the most of it? They skirted around the remains of a smashed table. As resident Needle Grovers it scarcely occurred to them to wonder what _that_ was doing there. You came across displaced objects all the time on the estate. They crossed the overpass to Block 31 and descended to an outdoor plaza some ten storeys lower, a recreation area protruding platform-like from Block 31's western flank.
This was where they habitually went. It was a recreation area in name only. The tennis court there had no nets, the netball court likewise. In the children's section, the climbing frame was a hazard to life and limb—the RLA had posted KEEP OFF signs on it and kept promising to have it dismantled. The sandpit had become a litter tray used by every cat in the neighbourhood, and no self-respecting parent let their kids go anywhere near. As for the seesaw and the merry-go-round, there were concrete stumps where those once sat. Magically, mysteriously stolen.
Today, a handful of Young Moderns had gathered on the site, but they cleared off, conceding it to the ClanFan Society. One kind of gang-tribe recognised another kind, and the Moderns saw in the ClanFans a degree of fanaticism that in their view was not healthy. It was one thing to base your lives around a mode of fashion, quite another to base your lives around certain people—people, moreover, you had never met and would never meet. The Moderns didn't even think about picking a fight. They just upped and left, wanting to put distance between themselves and the candle-toting nut-jobs.
The Block 26 ClanFan Society spread themselves out in a circle on the netball court. In an atmosphere of joyous fervour, a match was struck, a candle lit, and then the flame was passed from wick to wick both ways around the circle until some thirty-odd candle-tongues were flickering in the breeze. Laughing and chattering, the ClanFans stood like a human birthday cake. They were waiting for one of them to start the singing. They were, at heart, a shy lot. En masse they had a robust strength but individually none like to stand out.
At last one brave soul overcame her reticence and began the song in a warbling contralto:
"Happy birthday to you..."
Swiftly the rest joined in, at various different tempos, in a range of keys. The first two lines were a complete cats" chorus, but by "dear Provender" everything came together and the final line was delivered in rousing, gusto-filled unison. Then there were hip-hip-hoorays and someone embarked on "For He's A Jolly Good Fellow", which the others sang along to with relish.
Traditionally what came next was a series of personal testimonials. Each ClanFan in turn uttered a statement about the birthday boy or girl, which could take the form of a paean of praise, a humble confession of admiration, a direct personal address as if the Family member were actually there, or perhaps a story, anecdotal or fictional, about what he or she meant to the storyteller.
The ClanFans had come prepared, each with speech notes set out on slips of paper. The statements were made in halting voices, stammered out, stumbled over. Each was listened to in respectful silence.
"...I wish he would make up his mind and marry, make his mother happy..."
"...know that if only we met, he would see straight away that I was the one for him..."
"...yeah, so if I had all that money like he does, I'd, like, build this enormous house with all games and that in it, and all my friends could come and live there, and if he did that I'd be one of his friends and we could..."
"...if royalty meant anything any more, he'd make a great king..."
"...and Provender, please, if you can, don't let there be a war, in fact I have faith you're doing everything you can to stop there being one..."
"...and he said to me, 'Of course, what a great idea, why don't you come and live at Dashlands and be the official Gleed biographer?'..."
"...I'm not asking for much, just enough to keep me going till I'm back on my feet and have a job again, and he's got so much cash to spare he wouldn't even notice, I mean we're talking pocket change for him, and oh. My. God. Oh my sweet Jesus. He's right over there. It's him. He's coming right this way. I swear. I don't believe it. He's there!"
The ClanFan speaking, a man who had been out of work and living on benefit handouts for the past sixteen years, raised a trembling finger and pointed. The other ClanFans at first weren't sure what to make of this. What was he jabbering on about, Provender here? None of them wanted to turn and look in case it was just a practical joke, as when somebody yelled "Behind you!" and there wasn't anyone behind you.
But the man kept urging his fellow ClanFans to look. His face had gone white. His eyes were out on stalks. He could barely draw breath.
So the other ClanFans did eventually look, and rapidly their faces went the way of the pointing man's. A couple of them dropped their candles. One woman spilled molten wax on her hand and didn't feel a thing. Another, unnoticed by the rest, fainted.
Like some miracle, like some visitation from on high, like a sighting of the Blessed Virgin Mary or an alien from a spacecraft, the impossible made real, over the recreation area at a fast lick he came.
Loping, stubble-bearded.
Provender Gleed.
**47**
ON THE TWENTIETH floor of Block 26, Is and Provender were beginning to tire. They had lost count of the number of flights of stairs they had descended. They seemed to have become lost in a continuum of downward clockwise winding, their future an endless set of concrete risers coming up to meet them. The twentieth-floor landing offered release. There was a glass door leading out to a kind of cloister, which led in turn to a covered, colonnaded overpass, which terminated at the apex of a spiral staircase, which helter-skeltered all the way to the ground with overpasses radiating off from it at intervals. Still overdosed on stairs, the two fugitives exited at the first opportunity, heading across to Block 31. Is had calculated that there was little likelihood now of their and Damien's paths crossing. The estate library was on the other side of 26. He had no reason to be coming through 31. Still she wouldn't be wholly happy until she and Provender had found a phone, in fact until they had got clear of Needle Grove and were somewhere, _any_ where else.
The overpass decanted them onto a recreation area attached to 31, and finding their way into the block itself seemed a simple matter. A recreation area invariably had easy access to and from the block it belonged to. The gathering of people on the netball court scarcely gave Is pause. They weren't a gang-tribe, just a bunch of ordinary Needle Grovers having a chat in a circle. Some kind of residents" discussion group? Probably. Is did not give them a second glance as she and Provender passed along the netball court's perimeter.
Then the residents started shouting Provender's name.
It was something that Is hadn't thought about, something that hadn't even fleetingly entered her mind. She was out in public with a Family member. Provender's might not be the best-known Family face but it was famous nonetheless. A coating of stubble didn't do much to disguise it.
Then she noticed that the people on the netball court had lit candles in their hands, and the penny dropped. ClanFans. She and Provender had had the awesome misfortune to stumble across a crowd of ClanFans who were out celebrating Provender's birthday.
"Fuck my luck." Is seized Provender by the arm. "Come on, we need to get moving."
She said this because the ClanFans were themselves getting moving. A handful of them had broken away from the group and were stalking towards Provender, hesitant but with mounting confidence. They and the ones who remained rooted to the spot all had loose, inane grins on their faces and kept looking at one another—that was, when they could tear their eyes off Provender for a second—to seek reassurance that this was really happening, the person in front of them really was who they thought. They continued to call out to him, repeating the three syllables of his name in high, querulous voices like hatchlings in the nest vying for mother bird's attention. Then, all at once, the entire group surged forward, apart from the one they had left behind, who lay prone on the ground, insensible. With their hand outstretched, the ClanFans beelined for the object of their adoration...
...who stood immobile, uncomprehending. Is yanked on his arm. His body sagged in her direction but his feet stayed where they were.
"ClanFans, Provender," she said.
Her words had no meaning to him. He didn't seem to know what he was looking at, why these people were calling to him. He was as mesmerised by them as they were by him.
Is's medical training kicked in. Procedures for rousing or getting attention of semi-conscious patients. Either: pinch the earlobe. Or: rub knuckles up and down median line of sternum.
The latter worked only if the patient was lying down. Otherwise you couldn't get any leverage. There was nothing to push against.
Is reached up and dug the nails of thumb and forefinger into Provender's earlobe.
"Oww!"
"Run. Now. Us. Fast."
The ClanFans were a dozen paces away as Provender, galvanised, finally began to move.
IT WAS LOVE, pure and simple.
It was the need to touch, to grab hold of, to be sure of.
It was wanting to know if the person before them was flesh and not some figment of their imaginations.
It was the desire to lay hands on.
It was a form of lust.
It was worship.
It was greed.
It was all these things, and yet to the ClanFans it felt like nothing. A blinding urge. Indefinable. Primal.
When Provender was standing still, they had to home in on him.
When Provender took flight, they had to give chase.
ACROSS THE RECREATION area.
A square cavity in the side of Block 31.
A concrete tunnel burrowing into the building.
A narrower tunnel that jinked off to the side.
Stairs.
Is ran, pulling Provender after her. She ran in the knowledge that this was absurd, ridiculous. They were fleeing from a bunch of people who, by rights, were harmless. Ordinary individuals who normally wouldn't hurt a fly. Yet, in their devotion, their love for Provender, they might well tear him to pieces if they caught up with him. If nothing else, they were drawing attention to him, and that was exactly what he and Is did not need.
So she kept running, even as hilarity bubbled inside her, threatening to become hysteria. Had there been a moment to pause, had the ClanFans not been pressing hard on her and Provender's heels, she would have stopped and given in and laughed herself hoarse. But the ClanFans were right behind, yelping and imploring, a mass of needy arms, a rumble of desperate footfalls. "Provender!" they cried. "Provender, please! Please!"
She hit a landing, Provender still in tow, and barged through a doorway, which a woman with an armful of groceries was trying to negotiate from the opposite direction. Is shouldered her out of the way and the woman swore at her ripely and profusely. Next moment, the stampeding ClanFans burst through the doorway, and the woman and her groceries were sent flying.
Into an arcade, similar to the one in Block 26. Shops blurred by on either side. Ahead: a defunct indoor fountain, which a cluster of Orphans had commandeered— _our spot_. The Orphans, loaded to the gills with Tinct, chortled to see two adults come sprinting by, and laughed even harder at the sight of their pursuers, an assortment of grown-ups and children, all huffing and puffing frantically.
Beyond the fountain, a ramp. Down that, out onto a plaza, diagonally across to its only exit point, down another ramp to a disused swimming pool that had a residue of grimy water at the bottom in which car tyres and a rusty bicycle frame formed a reef. Around the pool, onward, till there were stairs, and more stairs, and yet more stairs, and suddenly, just like that, the ground.
They paused, Is and Provender, to take stock. They had managed to put some distance between themselves and the ClanFan pack, not much but enough to allow a brief respite from running. Compared with the majority of the ClanFans, they were young and relatively fit. Indeed, although they couldn't know it, there had been attrition among their pursuers. A few of the older and fatter ClanFans had had to abandon the chase and were strung out at intervals along the route, bent double, wheezing, experiencing all sorts of unpleasant palpitations to accompany the ache of anguish and frustration in their bellies. The rest, however, were still coming, undeterred by the fact that their quarry appeared to be getting away from them. They were relentless. They would keep after Provender as long as they were able to. Their lives had condensed down to a single objective: catch up with Provender, be with him, unite with him, embrace and cling to this avatar of Family, for ever. And as for that girl who was with him—what girl?
Is, panting hard, cast her gaze around. She didn't know Needle Grove all that well anyway, and down here on the ground it was another country, a gloom-hung, alien place, hostile territory. There were few map diagrams that hadn't had graffiti slapped over them and few signposts that hadn't been torn down, and the only other landmarks were car husks, which looked virtually identical, and trenches which the gang-tribes had dug out and fortified with rubble in the course of their perpetual turf-wars. The roads that wound through led somewhere but not necessarily out into London. Is could have navigated her way out of the estate if they had been standing at the foot of Block 26, somewhere near the parking garage entrance, since she knew that route reasonably well. But they were standing at the foot of 31, on the far side of the block from 26. She had only the vaguest notion of which way to go.
Above, on the staircase, the ClanFan clamour was growing louder. The front-runners of the group were closing in.
"Where now?" Provender gasped.
"There," said Is, pointing along a road that ran to the right, and added, "I think."
"You think."
She rounded on him. "Would you like me to leave you here?" She nodded upwards. "To meet your adoring public?"
"Uh, no."
"Then shut up and follow me."
**48**
WALKING BACK FROM the library, videotyped ransom demand in hand, Damien reflected on what he had done to Is. He felt terrible about it, even if he hadn't hit her that hard, just a backhand swipe, barely even a tap. It wasn't right. He should have been able to control his temper. Whatever the provocation—and boy had he been provoked—he shouldn't have lashed out like that. He had probably ruined any chance he had of getting back together with her. She wasn't going to forgive him in a hurry, that much was certain. Yet he remained hopeful that he could make it up to her somehow and that he and she could be reconciled. Perhaps once this kidnap business was over, when Provender wasn't there any more in the flat, when the money had arrived and the regeneration of Needle Grove commenced—then Damien could say to her, "Look. See? It was worth it. All we went through, all the hassle and strife—all worth it."
Is didn't know true love when she saw it. That was her problem. That and getting a bit too chummy with Provender fucking Gleed. But Damien couldn't even fault her there, not really. It was Is's nature to be kind, to see the best in people. That was one of the things he loved about her.
As the lift hauled him up to the forty-fifth floor, Damien contemplated stopping off at Mr Ho's along the way and buying some flowers. It would, however, be too corny and obvious a gesture. Is might even take it the wrong way: as if a bunch of flowers could just wave everything away like a magic wand. No, humility would be best. Honest, sincere contrition.
He was formulating his apology as he stepped out of the lift. He was still working on it as he unlocked the door to the flat. Composing himself, he swung the door open and began, "Is, I've just got to tell you..."
She wasn't there.
She wasn't on the floor. She wasn't sitting in a chair. A glance through the bedroom doorway told him she wasn't in there either.
The flat was silent. Shockingly, tellingly silent.
What was the balcony window doing open?
_Where the fuck was the table?_
Then Damien caught sight of the loops of severed flex on the floor not far from where Is had been lying when he left. That was when he knew what had happened, but he strode over to the bathroom and flung the door wide, because he had to be sure, he had to see it with his own eyes...
And when he did, when the bathroom's emptiness gaped at him, he felt a tremendous downward rush, as though the building had vanished and he was plummeting to earth, five hundred feet straight down. Weak, he grabbed the door frame for support. He croaked, "No," and then "No" again, as though by denying it he could somehow make it not have occurred. He lowered his head, closed his eyes, reopened them and looked up, hoping against hope that Provender would be there again, bound and helpless on the floor.
Of course he was not. The bathroom remained empty.
But not completely empty. Something was there which should not be there. Something had been placed there for him to find.
Bending forward, Damien reached out a numb hand and picked up his copy of _The Meritocrats_ , which was on the floor next to the bath in the exact spot where Provender should have been.
There was handwriting on the front cover. Damien held the book up to the light and read:
Look on page 1.
This is how misguided and gullible you are.
He knew the handwriting was Is's, and although he resented being called misguided and gullible he resented even more that she had defaced his copy of the book. It wasn't in the best of condition to start with, admittedly, but to scribble on the front like that was just plain vandalism. Sacrilege, even.
_Look on page 1_.
Damien's fingers felt thick and clumsy as he obeyed the instruction. He leafed the book open to the start of the story, wondering what Is had done there. More defacing, he reckoned. That bitch.
He knew he should be out looking for her and Provender. He should be scouring the estate for them. He couldn't let them get away.
But first this. He had to see what was on page 1. Why he was allegedly so misguided, so gullible?
Here was the page. Initially Damien couldn't discern anything different about it. What was he meant to be looking at?
Then he noticed that certain letters had been underlined—the first letter of each sentence of the first four paragraphs.
Providence saw to it that Guy Godwin was born and brought up in a house at the confluence of three types of transportation. Road ran alongside the house. Overhead a railway viaduct arched. Very close to the end of the garden, a canal flowed. Every minute of every day, almost, Guy could look out of a window and see voyagers go by...
And as he read, and as he perceived, and as he understood, there came that downrush again, that giddying sense of freefall, but worse this time, as though all certainties were collapsing, as though support columns were giving way and the structure of Damien's life was crumbling to pieces beneath him.
Now he couldn't hold himself up. He buckled to his knees. He began moaning, rocking his head from side to side, not willing to believe that such a huge, monstrous trick could have been perpetrated on him. Not just on him but on thousands of others. The magnitude of it. The evil of it!
How long he knelt there, he couldn't say. Abject in his misery, he went into a state of withdrawal, distant from the world, outside time. There was no meaning. There was no fairness. Everything was a hoax, a cruel prank. He seriously considered ending it all, there and then. Draw his knife from its sheath, plunge it into his guts like a dishonoured samurai. But his arms were nerveless. He couldn't reach behind him. He lacked the strength.
What finally roused him from his stupor was a rap at the door and a quiet voice saying, "Excuse me."
He had left the door open.
A man he didn't recognise was peering into the flat.
The man rapped again on the door, a formality, looking directly at Damien as he did so. Puzzled that Damien was crouched there in the bathroom doorway. Nervous.
"Yeah?" Damien intoned, bleakly, wearily.
"I'm, umm... I'm looking for Damien Scrase," said the man. "Would you be he?"
**49**
MILNER FULLY EXPECTED the answer to his enquiry to be no. He had the correct flat, 45L, but the man slumped in the bathroom doorway could not have corresponded less with his vision of Damien Scrase. He looked confused, helpless, broken, lost. He looked like someone who couldn't, at this moment and maybe at any moment, tell his BOWEL from his ELBOW, or for that matter his ARSE from his EARS. No way could he be Provender Gleed's kidnapper. And no way could this flat, with its front door wide open, be where Provender was being held captive. As far as Milner was able to see, it was empty, the slumped man its sole occupant.
Provender, he concluded, was elsewhere, and so was Scrase.
Maybe with Demetrius Silver? Were Scrase and Silver in it together, co-conspirators?
Such a prospect was not at all comforting, and Milner felt it was time to cut his losses and run. He would get a call out to Carver. Carver would do the rest.
"My mistake," he said. "Didn't mean to bother you. I'll just—"
"Who are you?" the man demanded.
"Uh, nobody."
"No, you said my name. You came to see me. Who the fuck are you?"
Milner was lost for words—a rare occurrence for him, a dereliction of duty, almost anathema. His mouth opened and shut soundlessly, even as his mind raced to come up with some sort of excuse for his being there and knowing Scrase's name. He grasped the enormity of the blunder he had made. He had assumed the man was not his suspect, and he had been wrong.
"I, um, I thought..."
Scrase moved fast—shockingly fast. He sprang to his feet and lunged. Milner barely had time to flinch, let alone take evasive action. All at once Scrase had grabbed him by the shirtfront and was hauling him into the flat. Scrase kicked the door shut, slammed Milner backwards against the wall, and thrust his face so close to Milner's that the Anagrammatic Detective could hear the breath whistling in and out of his nostrils.
Milner knew then that the anagrams had not lied. The furious, staring eyes that filled his field of vision were all the proof he needed. MEAN CAD RISES. INCREASES MAD.
_SCARES MAIDEN?_ he thought, remotely. _SCARES ME AND I!_
"What do you know?" Scrase snarled. His breath reeked of tobacco. "Where is he? What have you done with him?"
"I have no idea what you're—"
With a soft _zing_ , just like that, a knife appeared. Scrase held it up in his right hand while his left continued to grip Milner's shirtfront in a tight knot at his throat. Milner's stomach went hollow, and for a moment he thought he was going to soil himself. Everything seemed to have turned upside down. Reality was gone and there was only an insane nightmare: the knife poised in front of him, its blade about a foot long or so it seemed, light playing along honed steel, Scrase's eyes behind the weapon looking hard and lifeless and pitiless, knifelike themselves.
"I'll ask again," Scrase said with bitten-lip patience, "and you will answer in a straightforward and completely truthful manner. I'm not in the mood for mucking around. First off, who are you?"
"Merlin Milner."
"And you're here because...?"
Milner didn't dare tell Scrase the truth: _I'm here because I've found the person who kidnapped Provender Gleed—you_. That would be nothing short of suicidal. He struggled to come up with some sort of cover story, and did. It wasn't much of one but it would have to do.
"Authority," he said. "I'm from the Risen London Authority. We, er, we're following up on that rent business a while back. You know, the protest. We're canvassing residents" views. How are we going, have things improved, and so forth."
Scrase took the information on board and, with a nod, appeared to accept it as an explanation. The knife wavered in the air, then drew away from Milner's face. Milner allowed himself to relax. There. A nice piece of lying. A plausible tale plausibly told.
Then, almost a sigh, he heard Scrase say, "Rubbish."
There was a flash of metal, and a faint ripping sound, and a feeling like an icicle being drawn sideways across his cheek, and a moment later a sensation of warmth, of wetness, and then a sudden sharp sting of pain which opened up into something fiercer, fierier, more deep-seated.
Milner moaned, and his hand flew to his cheek to clutch the wound. At the same time Scrase relinquished his grip on him and stepped back a couple of paces, like an artist wishing to observe his handiwork.
"You're not RLA," he said. "The RLA doesn't do follow-ups. The RLA couldn't give a big fat hairy shit about this place. Authority officials come here once in a blue moon, and when they do it's always in groups, never alone. They're not stupid. _You_ are, thinking I'd fall for that load of bollocks."
Milner wanted to say something indignant. Through the pain, through the sight of his blood on his fingers, he wanted to tell Scrase he had no right to do that—cut him like that. He felt violated. It was an outrage for this man to have slashed his face, split his skin, simply as punishment for not being honest. It was disproportionate and spiteful and unjust.
Sensibly, however, Milner kept his opinion to himself. Instead, in humble, faltering tones, he said, "Please, let me go. I won't tell anyone anything. I'll leave and not come back. You'll never see me again. Just... don't hurt me."
Scrase studied him sidelong. "Well now, that depends. I'm having a pretty shitty day, as you can probably tell. Things that were supposed to be... working, haven't. I find out I've been lied to and cheated on in all sorts of ways. And then you come waltzing up to my door and I reckon you know something about what's going on here, you're involved in this somehow, and you won't give me any straight answers, so..." He shrugged. "So you've paid the price for that. And I don't think you'd be so daft as to try it on with me a second time. Right?"
Milner nodded eagerly.
"Right. What I think would be best is if you come over and sit down and you and I have a nice little chat. Discuss a couple of things."
Scrase motioned to a chair, and Milner, on weak, wobbly legs, tottered over to it and sat down. Scrase pulled up another chair and seated himself opposite, laying the knife across his lap. The knife was angled towards Milner but not pointing directly at him. Milner chose to regard this as a positive sign, cause for optimism.
"That's, erm, an impressive-looking utensil you've got there," he said. Admiring the knife seemed a good way of defusing its dangerousness. A compliment about the knife was a compliment about its owner.
"Bought it at an army-surplus shop," Scrase said. "See that?" He indicated the haft, which was gnarled and muddy brown for the most part, shading to white near the pommel, colours like an Irish coffee. "'Stag-handled' is the technical term for it, but it's deerhorn to you and me. Kind of ironic, since it's a knife designed specifically for gutting and skinning deer. Talk about adding insult to injury. See those serrations along the top edge of the blade? That's to prevent it slipping out too easily when you're using it. And now that we've established that my knife is a handsome, well-made piece of kit, let's get down to business, Mr Milner. Because I think we're past the pleasantries stage, and I think if you're trying to delay me for some reason, that would be very unwise of you."
Milner nodded to show he was in complete agreement with that last remark. "It would be, and I'm not trying to delay you."
"Good the hear. So now you're going to come clean about everything. Who, when, what, why."
Honesty, Milner told himself. SAY TRUTH and STAY HURT— _stay_ as in _prevent_.
He started speaking, and what he said elicited head-shakes from Scrase, and a hardening grimace, and eventually a hiss of dismay. And when he was done—when he had explained who he was, what an Anagrammatic Detective did, who had employed him, and how he had found Scrase—there was a long silence from the other man. Scrase's eyes were narrowed, calculating. The silence stretched on, and Milner began to believe that he had won himself his life and liberty. Just as his lying had been punished, his candour would be rewarded.
"You have no idea where Gleed is then?" Scrase said at last.
"None whatsoever. He should have been here."
"Well, he isn't, is he. The fucker escaped. I don't know how but I know he had help. She helped him."
"She?"
Scrase flicked a hand. "Not important. You don't need to know. You mentioned you have a partner, another Anagrammatic Detective. You said he's pursuing a different line of enquiry. He thinks the kidnapping is an inside job."
"When it so obviously isn't."
"So obviously."
"Yes. Poor old Romeo." Milner was keen to continue to be helpful. He had gained Scrase's trust, he was certain of that, but it wasn't a bad idea to ingratiate himself further if he could, so as to ensure his safety beyond all doubt. "He's barking up totally the wrong tree. He's convinced one of the Gleeds is behind everything. Absurd, really. I mean, why?"
"Which Gleed?"
"Provender's cousin. The actor. What's his name... Arthur. Romeo bases that conclusion—he's a bit of a closet ClanFan, not like me, I'm not that way at all, if anything I'm anti-Familial—but Romeo, he says there's no love lost between the two of them, Provender and Arthur. If anyone had something to gain by Provender being out of the picture, it would be Arthur." Milner spread out his hands and pulled a face to show what he thought of Family in-fighting. "But there you have it. Romeo's down on New Aldwych, hanging around outside the Shortborn Theatre, and wasting his time there, all because he thinks this is a spat between cousins. Whereas I know, and you know, Mr Scrase, that this is a political act, isn't it? A show of strength. Us versus them. Right?"
Scrase did not reply. He was thinking again—that calculating look.
Then he took hold of the knife, and Milner knew he was going to sheathe it. Scrase stood up, and Milner knew he was going to put the knife away and was then going to thank the Anagrammatic Detective for being so co-operative and invite him to depart. Milner knew he had just talked his way out of the stickiest predicament he had ever been in (literally sticky, in that the blood from the gash in his cheek had started to congeal—he could feel the dribbles of it tightening the skin on his face and neck). Milner knew he had just been through one of those life-threatening, life-changing experiences which only ever seemed to happen to others. It was an anecdote he would be able to regale people with for years to come. The near-miss with the table was nothing. _This_ —being held at knifepoint by a stone-eyed psycho and actively winning his freedom through words alone; you might almost call it playing CHARADES with a HARD-CASE—this was the stuff of heroism. A true adventure. And he was determined that he was going to be a better man for it. More patient, more tolerant, not as snooty as he knew he could sometimes be. What was the point in a brush with death if it didn't make you reassess your life and want to change?
Milner's moment of epiphany lasted right up until the knife plunged into his stomach.
He didn't understand.
What was this?
It felt as if he had been punched in the gut, but no mere fist-blow could go so deep and feel so wrong.
Scrase tugged the knife out and plunged it in again.
The blade grated against the bottom of Milner's ribcage. Milner felt it glance off the bone, angling upwards into his chest cavity.
He couldn't breathe. He wheezed for air. He choked, and there was liquid at the back of his throat and a taste like a nosebleed.
Scrase was crying.
Milner found that the oddest part of what was happening.
A third stab of the knife, and tears were spilling from Scrase's eyes and he was sobbing.
Dimly Milner thought, _I should be the one who's sad, not him_.
Then came an inrush of darkness.
An emptying-out.
A seizing-up.
And a final anagram, one last scattering and regathering.
DEATH.
HATED DEATH.
**50**
THE BAYING OF the ClanFans was a sad and distant sound and getting fainter by the minute. That, undeniably, was good. What was not so good was that Provender and Is had not reached an exit from Needle Grove. They didn't even seem to be near the edge of the estate. If anything, they were heading deeper into it. They moved from the shadow of one block to the shadow of another, hoping with every corner they turned that a way out would present itself. They were repeatedly disappointed. En route, they passed several payphones and, likewise, were repeatedly disappointed. Each had been wrecked beyond repair and the majority were nothing more than hollow shells, kiosk-shaped steel skeletons, glassless and scorch-marked.
"This," Provender commented at one point, as they were hurrying across a patch of hummocky grey wasteground, "is like Hell. No one should have to live in a place like this."
"Welcome to the real world, Provender," Is replied. "There are dozens of estates like it, and that's just in London alone. This is the world you Family members never even get a glimpse of."
"Estate," Provender said with a dry chuckle. "Funny how my understanding of the word is so different."
"Hilarious. Now how about we do less of the talking and more of the getting us out of here?"
"I thought that was what we were doing. Or rather, _you_ were doing."
"I am. So shut up and let me concentrate."
"And you're making such a fine job of it too."
"Provender!"
"All right. Sorry."
They roamed onward, and Is wondered whether Damien had returned to the flat yet and, if so, whether he had found her "time-bomb". How would he react to the discovery that his favourite book, his wellspring of inspiration, had been written by none other than Provender? Not calmly. If she knew Damien, it would cut the legs from under him. He would be livid. He deserved it, though. Perhaps she had overstepped the mark in accusing him of being misguided and gullible, perhaps it was an unnecessary twisting of the knife. But then he deserved that too. She was surprised, now, that she could once have been his girlfriend. It was strange to think she had loved him when she wasn't sure she had ever even liked him. It was stranger still to think that he had somehow been able to convince her that kidnapping Provender was a good idea. Six months after they had officially become Just Friends, his brooding charisma continued to be effective on her. She didn't know if that reflected well on him or badly on her. Probably a bit of both.
Is permitted herself this brief, introspective lull while still maintaining a level of alertness and apprehension. Daytime down here on the ground in Needle Grove wasn't as dangerous as nighttime, but you nonetheless had to be careful. She and Provender had slowed to a walk now, both believing they had managed to give the ClanFans the slip. The ClanFans, however, had hardly been a threat. A nuisance, more than anything. On the ground, even in the early afternoon, genuine hazards lurked.
Such as a group of Changelings.
At first, Is had only a vague suspicion that she and Provender were being followed. She thought it might be the ClanFans again—somehow they had caught up—but she dismissed the notion immediately. The ClanFans would have been making plenty of noise; it would be impossible to miss them. Whereas, as far as she could see, there was nobody around. There was simply the feeling that someone was nearby, lurking, looking. This was a world of hiding places—doorways, the struts that held up overpasses, deep shadows everywhere. Eyes could be watching from any of them. From all of them.
Is's pace quickened. Provender, catching her mood, followed suit.
Somewhere over to their left, gravel crunched. No one there. Then, over to the right, what sounded like a cross between a giggle and a whisper. No one there either.
"Are we—?" Provender began.
"Look straight ahead," Is said. "Keep moving. If I give the word to run, run like fuck."
If it was a gang-tribe, and it must be, Is doubted she and Provender would be able to outrace them. But what else could you do? Stop and reason with them? Not likely, especially not if they were off their heads on Tinct.
The first gang-member sauntered into view ahead. His Changeling garb consisted of a flock-pattern waistcoat, a denim shirt, a tartan kilt and sandals. He was grinning, and not in a friendly manner. A cudgel hung loosely from his hand.
Is did not need to turn round to know that there were other Changelings behind her, but she turned round regardless. Sure enough, two more of the gang-tribe had emerged from concealment. One was rag-clad like a scarecrow, while the other was like two people put together, his top half clad in dinner jacket and bowtie, his bottom half in stripy leggings and, bizarrely, a tutu.
Now four more Changelings came in from either side, and one of them, Is noted, had a cricket jersey on and was carrying a cricket bat, and another sported a jockey's cap and his weapon of choice, appropriately enough, was a riding crop.
Her heart pulsed in her throat. No point in telling Provender to run. It was too late for that now.
The Changelings closed in.
And then Provender did something unbelievably foolhardy.
**51**
AS FAR AS Provender was concerned, of course, it was not unbelievably foolhardy. On the contrary, it was eminently sensible, even cunning.
He raised his arms. Hands aloft, high enough to be pacificatory but not quite a gesture of surrender, he took a step towards the Changeling in front. With as winning a smile as he could muster, he said, "Do you know who I am?"
He knew they were not ClanFans. They were skinny, wiry youths, none older than nineteen, and they were armed and clearly out for trouble. They had the hunched, leering look of hyenas and the irises of their eyes swam in baths of blood-pinkened white. Anyone could tell they weren't the sort to be impressed by Family.
Nonetheless...
The Changeling in front gave Provender the once-over, head to toe, and something dawned in those feral eyes, a spark of recognition.
Provender pivoted through 360º so that the others could get a clear look at him too. In the process he saw Is with a worried question in her eyes: _what the hell are you up to?_ He tried, with a look, to reassure her that he knew what he was doing.
"Gleed," said the front Changeling. "The son. Weird name. Property?"
"It's Propeller," another of the Changelings offered, and that triggered a bombardment of suggestions.
"Probable."
"Providence."
"Pronto."
"Prostitute."
This last got all the gang-members laughing.
Provender laughed along, complaisantly, then said: "As a matter of fact it's Provender."
"As a matter of fact," the Changeling in front replied, "we couldn't give a toss. Family? What the fuck's Family ever done for us?"
Murmurs of assent did the rounds.
"You think you being Family means you can just wander through out turf, bold as you like, and get away with it? I don't think so. Actually, what _are_ you doing here? The Grove isn't the sort of place your kind hang out in."
"Ah, thereby hangs a tale," Provender said. "Would you believe—"
The Changeling cut him off with a wave of the hand. "Not interested. I only asked 'cause I thought I should. What I really want to know is how much of a fight are you going to put up."
"I was hoping it wouldn't have to come to that." There was just the slightest of wavers in Provender's voice, a hint of a tremble. "I was hoping, instead, that we could come to some sort of accommodation."
"Ooh, 'accommodation'," the Changeling echoed. "Hear that, everyone? Prompter here wants to come to an 'accommodation'. Whatever the fuck that is."
"All I meant was—"
"You'd like to buy us off."
"Yes."
"With cold, hard cash."
"Absolutely. See, the thing is, I'm lost." Provender tipped his head in Is's direction. "We're lost. We've been wandering around searching for an exit and we've got turned about and back-to-front and completely confused."
"And you'd like us to escort you out maybe?"
"God, would you? That would be fantastic."
The Changeling looked over at Is. "And you're with this bloke? Yes? No? Bruise-face woman, I'm talking to you."
Is, in spite of herself, was doing all she could to distance herself from Provender. She was angled away from him, her body language proclaiming that she and he were nothing to do with each other, he was just someone she'd happened to be walking beside. In truth, she was wondering what had come over him. All of a sudden he was behaving like an upper-class nitwit and she couldn't decide if this was bluff or, possibly, the real Provender coming to the surface at last.
Eventually, under the Changeling's continued scrutiny, she gave a cautious nod. "Yes."
"You Family too?"
"No."
"He your boyfriend?"
With vehemence: "No."
"But you want to get out of the Grove as much as he does?"
"Yes, I suppose so. Yes."
The Changeling turned back to Provender, cocked his head and scratched the underside of his chin. "How much money are we talking here?"
"You tell me."
"A grand?"
"Sounds fine to me."
The Changeling barked a laugh. "Seriously? No bullshit? One thousand notes?"
"Is that enough?"
"Oh, I'd say so. Wouldn't you, boys? Wouldn't you say a grand was enough to buy these people an escort off the estate?"
The Changelings bellowed in general agreement.
Is held her breath and braced herself. She was quite certain this was when the gang-tribe would weigh in. They were just toying with her and Provender. She was set to retaliate with everything she had—teeth, nails, knee to the groin, whatever it took. The Changelings would come at her expecting a pushover and find a hellion.
"Prognosis," said their spokesman, "you have yourself a deal." He stuck out a hand. "Shake on it."
Provender, with manly forthrightness, pumped the proffered hand.
Moments later, he and Is were striding through the estate accompanied by their very own gang-tribe honour guard. As they walked the Changelings amused themselves by coming up with yet more words with a "Pro-" prefix. Provender, meanwhile, kept darting jubilant glances at Is, which she refused to acknowledge. Her face was set in a scowl of frank incredulity. This couldn't be right. There must be some drawback here, some catch. The Changelings surely weren't going to see them to the gate and then just wave them off, were they? It couldn't be that simple. She and Provender couldn't have got that lucky.
**52**
THE CHANGELINGS DISCHARGED their half of the bargain and deposited their two-person cargo safely at the perimeter of the estate. Then, in the middle of the road, beneath the arching entranceway sign, the members of the gang-tribe huddled together expectantly, waiting for Provender to hand over the agreed-on sum. It seemed reasonable to them that he must have the money on his person, and although it had crossed their minds more than once that if he was carrying that much cash on him they could simply take it off him by force, there was something oddly satisfying about earning it. Earning it so easily, as well. All that dosh in return for a stroll through their own backyard, ten minutes" work, nothing to it. Maybe their attitude towards Family needed reconsidering, if this experience with Provender Gleed was anything to go by. Maybe there was something to be said for people who were burdened with so much wealth that they could spill it around so casually, so liberally.
"This is so great of you," Provender said, looking from one Changeling to the next. "Thank you all, very much. We really appreciate this. What I need now is to take down your names. Or the name of just one of you, if you prefer. You." He pointed to the Changeling with whom he had struck the deal. "Why not you?"
"Huh?" said the Changeling, with a slow, nonplussed blink. "What d'you want my name for?"
"So I can write you a cheque, of course. Which you can then take to a bank and cash and divvy up between all of you. Seven into a thousand goes... Well, I'm not sure. I'll leave it to you to do the maths."
"No, see, that's not going to work," said the Changeling. "Not a bit. Cheque won't do. Cash or nothing."
"Surely a Family cheque—"
"Cash or nothing."
"Fine then. Cash. I can always send it registered delivery. But in that case I'll need an address as well as a name."
"No," said the Changeling. "Now. Not later by post. Cash now."
"But I don't have that much..." Provender's voice tailed off, as if only now was it dawning on him that he and the Changelings had got their wires hopelessly crossed.
"Tell me you're joking," the Changelings" spokesman said to Provender. "You're taking the piss, right?" The other gang-members were muttering in low voices to one another, and their various weapons, which had been lowered, began to rise, going from at-ease to port-arms.
"I wish I was," Provender replied, feebly. With somewhat more force he added, "But look, I swear you'll get it. First opportunity I have, I'll send it. In fact, let's make it two grand, shall we. Just to show there's no hard feelings."
"Make it ten, it won't matter. You tricked us. Good as fucking lied to us."
"I didn't. It was an honest misunder—"
"Get 'im," the Changeling said, in a grim low growl.
At that selfsame instant, Provender grabbed Is's arm and started running.
IT WASN'T FUNNY this time. There was no element of absurdity about it, as there had been when they were fleeing from the ClanFans. It was in earnest. It was sheer blind panic. It was a flat-out sprint in order to get away from a foe who was manifestly dangerous and whose reason for wanting to catch them was not, as the ClanFans" had been, overwhelming love but quite the opposite.
The Changelings, as it happened, were not as quick off the mark as they might have been. Provender had surprised them by taking action so abruptly. Catching them on the hop, he gained himself and Is a few seconds" head start.
Once they had roused themselves, though, the Changelings gave chase with a vengeance. Provender and Is heard the clatter of their footfalls behind him and both knew they weren't going to be able to stay ahead for long. As far as Provender could see, their only hope lay in finding some busy part of town, a street filled with passers-by, where either the Changelings would think twice before assaulting them in front of so many witnesses or they could lose themselves in the crowd. Being in a populous public place did not guarantee immunity from attack, of course, and it was by no means certain they would get to one before the Changelings caught up, but it was all Provender could think of to do. He was barely even conscious of thinking it. It was an instinct more than anything, the natural desire of pursued prey to seek refuge in numbers. In Is's brain much the same notion had formed.
Together they hurtled along pavements, turning left, turning right, into side-streets, down alleyways, out into main streets again, weaving through the city's grid pattern but unable to shake off the Changelings at their heels. They soon found themselves beyond breath, beyond tiredness, in a world where the only thing that mattered was to carry on running, running, running. Both felt their lungs starting to rasp, their legs starting to ache. But these pains were far-off, ignorable, needing to be ignored.
On main roads, traffic roared past them. Occasionally a horn tooted, in mockery, in exhortation, who knew? The drivers in their vehicles were faceless entities, irrelevant. The vehicles themselves were irrelevant except when Provender and Is reached a junction and had to cross. Then they were moving metal obstacles to be darted in front of or around. Then, too, the horn beeps were rapid tattoos that more often than not came between a squeal of brakes and an angry out-of-the-window curse.
There were pedestrians around, but only a few, never enough to constitute a crowd, and invariably when they caught sight of Provender and Is running towards them they moved out of the way, not wanting to get involved; they even scurried over to the other side of the street if they had time to. It was early afternoon on a weekday in a more or less residential area. At this hour, this portion of London was hardly teeming.
And the Changelings were gaining. Hard as Provender and Is ran, the staccato slap of the Changelings" shoe soles was getting ever louder, ever closer, their shouts and panting likewise. Neither of the pursued dared look over their shoulders. They dashed onward, dragging each other along.
Then, up ahead, Provender caught a glimpse of something that was as good as a crowded space, if not far better.
He yanked on Is's arm and gesticulated. She peered and saw a chainlink fence, a high-sided enclosure running parallel with the next street they were coming to. She looked harder, not understanding why Provender was so excited about this, and then she got it.
They rounded the corner, and Provender's spurt of hope became a full-blown flood of happiness.
It wasn't just that they had stumbled across the Family tram system.
About half a mile away, there was a break in the chainlink fence. There was a gateway, and beyond it a platform.
He took a tighter hold on Is's arm, dug deep within himself, and gave his all in a final, fraught dash for sanctuary.
**53**
TINCT, LIKE ANY street drug, did more harm than good. For a while after injection it brought euphoria, clarification of the senses, a feeling of near-invulnerability. The metabolism was sharpened, the pain receptors were dampened, and the synapses fired like machineguns. On Tinct, you could accomplish extraordinary physical feats. Your body was on overdrive and refused to acknowledge fatigue. It was a warrior's drug and for that reason a favourite among the gang-tribes.
The downside? The effects were only temporary, and when they went, the drug's absence was felt like a sucking vacuum. Tinct's influence didn't fade, it vanished. One minute you were on top of the world, the next the world was on top of you.
Then there was the physical damage done during the periods when the drug was active. Muscles and joints could suffer excessive wear and tear which, if not allowed time to mend, became a cumulatively worsening problem. Habitual Tinct users invariably became stiff and arthritic in early middle age. And of course the metabolism adjusted. In order for the user to gain the same intensity of result, larger and larger doses were necessary, and in high concentrations Tinct could kill. Hardened Tinct-heads had been known to drop dead from heart attack, pulmonary oedema, deep vein thrombosis, even brain haemorrhage.
None of which occurred with the Changelings who were chasing Provender and Is, for all that the latter pair might have wished it would.
What did occur, though, was that the exertion began to take its toll on the gang members. For a while the Changelings felt as if they could keep going for ever. They could run and never stop. Then, just as Provender and Is reached the street with the tram track beside it, the Changelings started to crash. They had shot up together, using the same needle, so the comedown was pretty much simultaneous. The Tinct had burned through their systems like wildfire, the flames fanned by the adrenal rush of the pursuit. Then, all at once, it snuffed itself out. There was no more.
The Changelings didn't come to a screeching halt but there was an abrupt and marked decline in their rate of progress. To them, it was as though their legs had hollowed out, all muscle gone. They carried on running but it was momentum more than anything that bore them along. Searing pain seeped into their lungs. Their heads went swimmy with oxygen deprivation. One of them, without breaking stride, puked bile down his chest.
A gap opened between them and their intended victims. A half-dozen yards became a dozen, a dozen a score.
Provender and Is failed to notice because they were concentrating on one thing only: the tram stop ahead. They didn't even notice that the racket made by their pursuers was dwindling. All they could hear was their own breathing, their own thumping hearts. Ears, eyes, everything they had was focused on the tram stop's gate, getting to the gate, the swiftly nearing gate...
The gate.
They arrived at it and almost shot straight past. It appeared beside them with such surprising suddenness that they could scarcely believe it was there. Belatedly their brains told them to halt, and they both skidded to a standstill. Provender then bent to the microphone funnel and tried to heave out the two words that would activate the gate opening mechanism: his name.
The first time, what came out of his mouth didn't sound like language, just a muddled mishmash of syllables. The voice recognition system didn't register it as an entry attempt. The small display screen mounted above the microphone funnel remained starkly blank.
Provender sucked in air and had another go.
The second time, what he said was recognisably _Provender Gleed_ but it came out in a garbled splurge, as though a single word. The voice recognition system failed to accept it as valid. The display screen flashed up a curt response:
VOICE UNFAMILIAR
TRY AGAIN
While Provender collected himself for a third try, Is looked left and was astonished to see how far the Changelings had fallen behind. They were still coming, however, white-faced and gasping but still staggering on along the pavement. She shook Provender and told him to stop mucking around and get the ruddy gate _open_.
Provender ordered himself to be calm, to say the words slowly, clearly and audibly. At the back of his mind lurked the knowledge that the voice recognition system often did not work. The technology was reasonably new and therefore prone to glitches. The waveform-comparison generator was not sensitive to extreme fluctuations in the human voice and so didn't allow for a large margin of difference when matching a spoken name against the recorded version stored in its memory bank. Also, the company which owned the patent on and constructed the system was a Kuczinski holding, and it was believed that the Kuczinskis had arranged for a special design flaw to be installed with the express purpose of inconveniencing one other Family and one other Family alone. The jury was still out as to whether this was anything more than paranoia on the Gleeds" part. No statistical evidence existed to support the theory that the system failed more frequently for a Gleed than for anyone else. Then again, it seemed to certain members of Provender's Family that such sabotage was just the sort of thing the Kuczinskis would do, a suspicion given weight buy the fact that, were the roles reversed, were the voice recognition system a technology owned by the Gleeds, then rigging it so that it gave the Kuczinskis trouble was just the sort of thing _they_ would do.
Ignoring this thought as best he could, Provender brought his lips right up to the mouth of the microphone funnel, close enough for kissing, and uttered his name. He enunciated every syllable of it with an elocution master's precision. There was a pause, during which he could have sworn he heard a tiny mechanical giggle, the system snickering to itself, and the display screen cleared the extant message but seemed reluctant to put up anything in its stead, and he understood that the Kuczinskis had, if the belief about their mischief-making had a basis in fact, just condemned him and Is to a vicious beating and perhaps worse.
Then, like a prayer answered, a new message appeared:
VOICE FAMILIAR
PROVENDER GLEED
ACCESS PERMITTED
At the same instant, the gate unlocked itself. Bars retracted. Bolts were unshot. Pistons hissed. The gate eased inward.
Provender thrust Is through and followed right behind, then swung round and grabbed the gate. The gates on the tram network were notoriously slow in closing, which had never struck anyone as a problem till now. He leaned hard on this one to expedite the process. Out of the corner of his eye he could see the Changelings, the frontmost of them now within spitting distance. The gate would not be hurried. The hydraulics did not like to go at anything but their own speed. Is squeezed in beside him and pushed too. The gate groaned in protest. The Changeling, who was the one armed with a cricket bat, drew level and lunged exhaustedly.
The gate clanked shut at the very moment his hand grabbed it. Enraged, he drew back, brandishing his weapon. He swung the bat behind his head and brought it forward. The blow, which was aimed at Provender's fingers, missed, Provender having let go of the gate a split-second earlier. The bat struck ironwork with a resonant, shivering _clanggg_. Provender and Is drew back as the Changeling dropped the bat and threw himself at the gate, thrusting an arm through and grabbing for them. The other Changelings joined him, reaching through the bars and pawing at the air. Their movements were feeble, desperate, a last flailing effort to get at their quarry. They knew Provender Gleed and the girl with him had escaped, but they could not yet admit it to themselves. One of them made an attempt to clamber up the fence but did not get far, unable to find a decent toehold in the chainlink. Another tugged on the gate as if he truly believed he had the wherewithal to rip it loose from its frame, but there was little strength left in his arms. Eventually all of them were reduced to cursing and hawking gobs of sputum at Provender and Is, and soon they didn't even have the energy for that as the post-Tinct lethargy took a firm hold.
Provender and Is retreated to the tram platform, from where they watched their pursuers succumb to lassitude. Some of the Changelings sagged against the fence and gate while others sank to the ground, looking for all the world like marionettes whose puppeteer had grown bored of conducting the show. It seemed an ignominious finish to such a frantic chase, but Provender and Is weren't complaining. Exhausted themselves, though nowhere near as depleted as the gang-tribe, they settled down on the platform and got comfortable. For a while neither could speak and so they simply looked at the Changelings, who stared stuporously back with eyes that suggested they had forgotten why they were there and who the people on the platform were. During this curious stalemate one of the Changelings even managed to fall asleep, nodding off where he stood, kept upright solely by virtue of his fingers being hooked through the chainlink.
Provender, when his face was no longer such a hectic shade of scarlet, said, "I never thought we'd manage that. I thought they had us for sure."
"Tinct crash," Is replied.
"Oh. What?"
She outlined the pathology of the drug.
"Ah. Still, good for us that we ran so fast, eh?"
"Tell me that when I've stopped feeling so ill. How long till a tram comes?"
Provender glanced both ways along the track. "Should be soon. The most anyone's ever waited is half an hour. It depends on where the nearest one is when you activate the gate."
Just as he said this, as if on cue the overhead cables started to crackle and the steel rails began to hum.
**54**
THE TRAM ARRIVED, coasting to a halt alongside the platform. Accordion doors hissed open, and Provender, with a gentlemanly gesture, invited Is to step aboard, then hopped in after her.
Depressing a brass handle triggered the door-closing mechanism. Provender then ambled to the front of the car where the control console was situated, a sloping bank of switches, levers and lightbulbs. He frowned at it, hesitant.
"Tell me you know how to drive this thing," Is said.
"To be honest, this is the first time I've travelled in one on my own. Not on my own exactly, but you know. Without another Family member."
"Don't get out much, do you."
"Not till lately. However..." Provender toggled a switch and several bulbs lit up on the console. "It isn't that difficult, I think. If Extravagance can manage it, I can. All you have to do is—yes." Another switch brought illumination to a display window marked DESTINATION. "Then you just dial in the place you want to..." He manipulated a pair of knurled knobs, one of which caused the display window above it to scroll through a list of regions throughout the country, the other of which summoned up a sub-list of tram stops located within each of those regions. Finding BERKSHIRE with the first knob led him to find DASHLANDS easily with the second. "And then," he said, "with just a press of this button— _voilà_. We are on our way."
The tram car gave a lurch and began to roll, pulling away from the platform, the stop and the inert Changelings. It picked up speed and in no time was cruising at a steady 20 m.p.h. through west London. The city trundled by outside; the wires above gave off enthusiastic fizzes and sparks; the wheels drummed. Provender ensconced Is in an armchair, then went to the bar at the rear and fixed them both a whisky, adding ice from an ice-cube maker. They sipped the drinks facing each other, and Provender felt the weight of his recent travails begin, at last, to lift. He was truly out of harm's way now. In little over an hour, he would be back home. The whole horrible escapade was over.
"You, er, you didn't think that was really me back there, did you?" he said.
"What?"
"When I was talking to those kids. Offering them a bribe. Acting like a twit. I was just putting it on."
"Could have fooled me."
"No, really, I was— Oh, I see. You're mocking."
"Frankly, Provender, at the time I wasn't sure what to think. I thought you might have gone mad. I also thought there was no way they were going to fall for it."
"Neither did I, but I reckoned it was worth a shot. They were going to beat us up anyway, but I thought if I could persuade them to take us out of the estate first, we'd have a better chance of getting away from them before they started. It worked. I'm stunned that it did, but it did."
"Must be the Family mystique."
"Must be. Also, there is a kind of magic in behaving like a blithe, posh nincompoop. It protects you like a charm. People are disarmed by it. I don't do it myself as a rule, but I've seen it work for others. My uncle Fort, for instance. He does it all the time. Acts the buffoon and get away with murder. Mind you, with him I'm not sure it's an act."
Provender drained his whisky tumbler at a gulp, much as his uncle might have done, and asked Is if she wanted hers refreshed. She shook her head, then changed her mind and said yes.
Second whiskies in hand, they gazed out of the tram's windows as the turrets of Acton and then the tenements of Old Ealing passed by.
"I have to ask now," Provender said. "I can't not. What was it all about? Why was I kidnapped? What did your friend Damien want with me?"
"Money."
"That's it? Just the money?"
"Isn't that enough of a reason? He wanted several million from your Family, money he would put to use renovating Needle Grove, to make it a nicer place, not the sort of place that breeds gangs like that lot back there."
"But... he wouldn't expect to get away with it, surely. It's hardly subtle or covert. He gets the money, hands me over, next thing we know someone's spending a fortune doing up a slum housing estate. If he wanted to draw attention to himself, if he wanted everyone to know who the kidnap culprit was, he couldn't do much better than that. My Family would be on it like a shot. We'd have him. He'd be in jail faster than you can breathe."
"Don't think Damien didn't realise that."
"But he was still prepared to take the risk. D'you know, I'm almost starting to admire him."
"No, because there was no risk." Is studied her tumbler, swilling the liquor around inside it and making the ice cubes clink. "Look, I suppose you ought to know. It's only fair. Damien wasn't acting alone."
"He had you with him, yes. And if you're worried about that, don't be. My Family will go after him, have no fear, but you are going to be absolutely safe. I'll see to that. You'll have complete protection. No one's going to prosecute you or anything."
"Do you actually listen to me when I'm talking, Provender? Sometimes I think you only hear what you want to hear. I'm not referring to me when I say he wasn't acting alone. Clearly I was an accomplice. That's pretty bloody obvious."
"There was someone else? A third party?"
"Genius! And they say Family inbreeding lowers the IQ."
"Hey!"
He looked genuinely wounded. Isis waved a hand at him in apology. "You're right, that was uncalled-for. It's just—I don't like to have to be the one to break this to you."
"Go on."
"Because you're not going to like it."
"I'll be the judge of that."
"He had help. Damien. Inside help."
"Help."
"From Family. From someone in your Family."
"No!"
"And before you ask, I have no idea who. He wouldn't tell me. Said I was safer off not knowing."
"Oh, but that's preposterous. No one in my Family would do anything like this. He must have been having a joke with you."
"Believe me, he wasn't. I saw him have phone conversations with this person. He didn't like having to rely on a Family member, it didn't sit well with him at all, but he did it anyway. He—we—couldn't have pulled off your kidnap otherwise. Somebody had to buy off the security guard so that he wouldn't be at his post when we were leaving Dashlands, and Damien didn't have access to those sort of funds. And of course another part of the arrangement was that when Damien got the ransom money, he'd be guaranteed immunity from prosecution and from anything else the Gleeds might have in mind for him. He could spend the money how he wanted and not get caught for it."
"And this is somebody in my immediate Family?"
"I don't know. I suppose so."
Provender wagged his head wonderingly. "It can't be. I mean, who? My mother? Never. My father? Unlikely. Gratitude or Extravagance? It wouldn't be Grat, no way, and 'Strav, she and I don't get on but she'd hardly stoop to something like this, not even as a practical joke. Far too much like effort. Then there's Great, but he wouldn't. He _couldn't_. And Uncle Fort... He's a troublemaker, a piss-head, fond of himself, no question, but not—it's just isn't him. What would he gain from it? What would any of them gain from it? No, I don't accept this. I refuse to."
"Provender, you have to. It's the truth."
"It's someone in my Family?"
Impatiently: "Yes."
"My immediate Family?"
"I told you, I don't know. How immediate is immediate?"
"Well, a cousin... Oh."
"What?"
Provender rubbed his temples, his brain churning. "A cousin. Oh _mierda_ , yes. Arthur. That little _pendejo_ rat-bastard."
"This obviously sounds like one of your favourite relatives."
"Hmm? Arthur? Oh no, far from it."
"Sarcasm, Provender."
But even Is's admission of sarcasm was wasted on him. He was pondering too hard, too deep in concentration.
"Arthur," he said, "Arthur doesn't like me, and that's fine, no problem, the feeling's reciprocated, but would he go so far as to...? He might. He definitely might. Just to fuck up my life. And maybe, maybe... To annoy my father? To get him to resent me for costing him a chunk of money? That's like Arthur. And then, while I'm off the scene, tucked away in a Family-hater's bathroom, Arthur could always swan over to Dashlands and pretend to be all concerned, show sympathy, come across as the perfect cousin. Jockeying for position. Reminding everyone who he is, how wonderful he is, isn't he better than Provender?"
"I'll just join in the conversation when you're ready."
"And then at the party... Good God yes. That tirade of his about actors. His attempt at the world record for the most uses of the word 'bloody' in a single sentence. And, no, before that, when he was talking about his play. Offering me tickets. He said—he said I should come if I wasn't doing anything else."
"Any time you want some input, you only have to ask."
"No, he didn't say that, it was more specific than that. What the hell was it? If I'm not... otherwise detained! _Detained_. Christ, that cocky little _cabrón_ , he was telling me, he was just about giving it away. This was what was going to happen to me. I wouldn't be going to his _Hamlet_ first night because I'd be fucking being held hostage!"
"I'll sit here quietly minding my own busi—"
Provender sprang to his feet and hurried over to the control console.
"What are you doing?" Is asked.
"What's it look like?" He grabbed one of the destination knobs. "I'm diverting us."
"We're not going to Dashlands?"
"Nope."
"But we have to."
"No, we don't."
"Yes, we do. Your father. If your father sees you, if he knows you're safe, he can get the politicians to back down. There won't be a war."
"It can wait."
"It damn well can't." Is stormed up to the front of the car and seized Provender's arm. "What's more important, Provender? Going after your cousin or pulling a continent back from the brink of conflict?"
"Going after Arthur."
"You don't mean that."
"I do. I want to catch him unawares. I want to see his face when I turn up on his doorstep, free. I want to watch him gape and gulp like a stranded goldfish."
"Fine, then do that, but leave it till after we've been to Dashlands."
"No way. If all of a sudden everyone starts suing for peace, Arthur will know the game's up. Whereas if everything remains as it is, just for now, I can walk right up to him and he won't be expecting it. It's the only way I'll ever know if he's involved in the kidnapping."
"No, it isn't. Damien could rat him out. To the police. If he was arrested and being interrogated."
"Arthur would deny it. There's no proof of a connection between them, I bet. No physical evidence. Just phone calls. Just Damien's word against a Gleed's. Guess who everyone'll believe. Especially," he added, with an ironic leer, "when one of them's a much-loved star of stage and screen."
"But what if everything goes wrong? What if war is declared? For all we know it could already have been. We haven't exactly been keeping up with current events this past couple of hours."
"There's an entertainment system somewhere in the tram, with a radio. You could turn it on and listen."
"That isn't the point."
"An hour, Is. All I need. One measly hour."
**55**
ROMEO MOORE—NOW, although he was as yet blissfully unaware of the fact, the world's only remaining Anagrammatic Detective—was at his post outside Arthur Gleed's house. He couldn't think of anywhere else to be. The shame of letting Arthur slip through his fingers that morning had abated, but he still couldn't think about what he had done without feeling a smart of self-recrimination. Determined not to repeat the mistake, he had contacted the cab firm whose owner he and Milner had once helped—the TAXIMETER/EXTRA TIME case—and had hired the exclusive use of one of his cars for the entire day. The year-long free-travel offer had expired a while ago but the owner still held Moore in enough esteem that he was able to negotiate a decent rate. The taxi was now sitting at a corner of the square, engine running. Moore would have been in the back, in a far more comfortable seat than the park bench he was on, but for the fact that the driver was one of those garrulous types who not only couldn't stop talking but couldn't seem to take the hint that his passenger was in no mood for trivial chitchat. After half an hour of listening to the driver bang on about any subject that crossed his mind, a torrent-of-consciousness rant, apparently unstoppable, Moore had excused himself, saying the park was the better vantage point, with a more direct view of the house. The driver had carried on talking even as Moore exited the taxi. For all Moore knew, he was still talking now.
The newspaper crossword was done-and-dusted a long time ago, Moore winning his battle of wits with the setter in just six minutes. The newspaper itself, with its disturbing reports of potential armed conflict, had been perused from cover to cover. Moore was pleased to note that the review of last night's performance of _Hamlet_ was more or less as he had predicted: the paper's theatre critic was ho-hum about the production itself but Arthur Gleed had "essayed a unique Hamlet, inhabiting the role of arch-vacillator as though born to it". The comment had more edges than an icosahedron.
As for the threat of war, Moore had seen little evidence that people were unduly concerned. Everybody seemed to be going about their business as normal. Shops were open and there was no panic-buying as one might have expected, nor was there any sign of an imminent exodus into the countryside. London was proceeding at its customary pace, hectic but no more so than usual. Doubtless things would change if war was declared. Then again, _Homo sapiens_ was on the whole a phlegmatic species, and sometimes events were so momentous that they simply had to be ignored. Unless bombs were actually raining down on the capital, life would go on with the minimum of disruption. The taxi driver had touched on this, when flitting from one unrelated topic to the possible war to another unrelated topic. "Not a sod I can do about it," he had said. "I just drive a cab. Unless it's stopping me driving my cab, I'll just carry on doing that."
And Moore was an Anagrammatic Detective and it wasn't stopping him doing _his_ job, so he was carrying on too.
Needing something to occupy his thoughts till Arthur returned, Moore set himself the task of devising a word game. It was what he often did during idle moments, a way of pressure-valving his philologically hyperactive brain. Initially he came up with the idea of forming words from the letter sequences on vehicle licence plates. He tried it out with the cars parked in the square and it was satisfactorily entertaining but not much of a challenge. Looking for something a bit more taxing, he hit on the notion of finding words in which you could substitute one vowel with any of the other four vowels and create a valid new word each time. This was altogether more intellectually demanding, and Moore put his brain to work on it, mindful not to get too wrapped up in case Arthur reappeared and he didn't notice. He thought Milner would be pleased by the game, and wondered what he might call it. A Latinate or Hellenic name was conventional. Varivocalis? Pentalogue?
Before the astonishing event occurred—before the resolution to the Provender Gleed case all but fell into his lap—Moore managed to identify two strings of words which fulfilled the game's criterion. One was pack, peck, pick, pock, puck. The other was mate, mete, mite, mote, mute. He was racking his brains to find a third, preferably something more than four letters long, when two people walked into the square via its eastern end, emerging from the street which led to the nearest Family tram stop. Moore registered them, thought them of no significance—a young man and a young woman, perhaps a couple but, if so, they were in the throes of a lovers" squabble, not getting along, because he was a few paces ahead of her and she had her arms folded across her stomach in a manner that reeked of discontent—and then Moore blinked, hard, then rubbed his eyes as if to wipe them clean and start afresh, because his eyes were faulty, surely, some defect was causing them to tell him he was looking at the kidnappee, the Gleed heir-apparent, the reason for his vigil outside Arthur's house, Provender, who was now striding round the square's perimeter, heading for that selfsame residence, and it must be a vision problem, brought on perhaps by lack of sleep, a hallucination, and further blinking and rubbing would get rid of it, but this didn't work, not even banging a hand on the side of his head would do the trick, Moore tried it, a few hefty knocks with an open palm, but what would usually fix a television set when the picture wasn't right did not have the same effect on the mechanism of the human cranium and the Provender apparition did not correct itself, there he still was, with his companion a few steps behind him, climbing the steps to his cousin's front door and prodding the doorbell button with a forthright forefinger...
Finally Moore galvanised himself to move. It was the faint ringing of the doorbell within the house that did it, that proved he wasn't imagining what he saw. Hallucinations, he reasoned, couldn't make doorbells ring, could they? Leaping to his feet, he hastened feverishly out of the park and arrowed towards Provender.
_I was right, Merlin_ , he thought. _I don't know why it's turned out the way it has, I didn't think this was how I would find him, but I have, I've done it, I've won our bet, dammit I was right!_
**56**
"HE'S NOT HOME."
Provender wheeled round.
The man who had spoken was a timid-looking individual, slight of stature and dressed in a cheap, rumpled suit. He stood on the pavement clutching the bottom of his jacket and rocking on his heels like a nervous schoolboy. Is was peering at him quizzically, and Provender couldn't help but do the same.
"And you are...?"
"Oh, yes, forgive me. Romeo Moore, Anagrammatic Detective."
"Whatsis detective?" said Is.
"I have a card." The man reached inside his jacket and rummaged. "They're in here somewhere. I'm a private investigator. A special sort of private investigator. Oh dear, can't find them. I've been charged with the duty of— A-ha!" He produced a sheaf of business cards and handed one to Is, then climbed the front steps and proffered another of the cards to Provender, who took it, glanced at it, saw that it said _Milner and Moore, Anagrammatic Detectives_ together with an address and phone number, and tucked it away in a pocket.
"Charged with the duty of...?" Provender prompted.
"Uh, well, you, I suppose."
"Me."
"Yes," said Moore, and added, "Sir."
"No need for 'sir'. What about me? What duty?"
"Finding you."
"Right. Which you appear to have done."
"I know."
"Congratulations."
"Thank you. Your Family, you see, hired my colleague and myself to locate you after you... er, went missing. They had reason to believe you'd been taken against your will, but now... umm." Moore threw a look at Is. "Perhaps they were mistaken and it wasn't involuntary after all."
Provender saw what the Anagrammatic Detective was implying. "Trust me, it was. Very much so. My Family hired you?"
"Along with my colleague, yes. Courtesy of the Clan Reav— Of a certain Mr Carver. And so here I am." Moore's mouth flirted with the idea of a smile. "Case successfully solved. I can call Mr Carver and inform him that Provender Gleed is alive and well and no longer a captive. I can, can't I?"
Provender was frowning. "But you're here. Outside Arthur's pad. Which means you think Arthur..."
"...kidnapped you? I did think that. Current evidence would appear to indicate otherwise."
"Not necessarily. What reason do you have for thinking it was Arthur?"
"The anagrams."
"The anagrams?"
"The anagrams."
"What anagrams?"
"Of Arthur Gleed. There were all sorts. His name positively dripped guilt. My colleague had a different theory about your disappearance, but me, I had your cousin in the frame from the very start. Turns out I was wrong, but my roundabout route brought me to the right destination in the end. That's how it is with the anagrams sometimes. They move in mysterious ways, their wonders to perform."
"Let me get this straight. You're a private investigator who uses _anagrams_ to solve crimes?"
Moore beamed proudly. "I am."
Provender shook his head in mild disbelief. "And my Family took you on to find me. Just you?"
"And my colleague, Merlin Milner."
"Of course, your colleague. But no one else."
"Not that I know of."
Provender let out a hollow laugh. "Thanks for trying, everyone. No disrespect to you, Mr Moore, but you're hardly the thorough search party I'd have hoped for. A small army of private investigators I could understand, but two people who use anagrams...?"
"We were told that discretion was paramount." Moore was trying not to look as though his feelings were hurt. "A low-key approach. Obviously not good enough for some people, but I would submit that the results speak for themselves."
"Yes, yes, they do," Provender said, mollifying. "I really wasn't trying to cause offence."
"Though you did," Is chipped in.
"And," Provender went on, "it so happens, Mr Moore, that I believe you're on the right track. Arthur _is_ involved. He arranged for me to be kidnapped. He's the brains behind the operation."
" _Yes_ ," said Moore under his breath. "But you've escaped."
"I have, and I'm here to confront the little creep and get him to 'fess up."
"And he's not home, as I told you. He's elsewhere."
"Where?"
"I wish I knew."
"You don't have any idea? There isn't anywhere else he could be?"
"Well," said Moore, cautiously, "there is one place I've been staking out apart from here."
"Which is?"
"The theatre where his play's on. On New Aldwych. The Shortborn."
"Could he be there now?"
"I doubt it." Moore consulted his watch. "Curtain doesn't go up for another four hours. I don't think makeup and costuming takes that long."
"What do you say, Is? You think we should try there?"
"Don't ask my opinion. My opinion apparently doesn't count for anything."
"Well, I think we should. Back to the trams. Mr Moore, thanks for your help. It will be remembered."
"Very kind. Might I just say, though, that I have a taxi waiting. It might be quicker, more convenient."
"A taxi?" Provender pondered. "Yeah, good idea. A taxi. Why not?"
**57**
THE TELEVISION ROOM stank of sweat, of body odour, of manly musk, of maleness. Prosper had infused it with himself over the course of the day. Just by being there he had scent-marked it as his, a section of Dashlands House that was now Prosper Gleed's exclusive territory.
Or so Cynthia felt as she cracked the door open and tentatively entered. The smell might have been in her imagination, her senses confirming what she wanted to believe. She wanted the television room to have an offensive aroma, thus it did.
Prosper was on the sofa, fixated as ever on the projected TV image on the wall. The Phone was in the corner, dozing where he stood, poor fellow. Prosper ought at least to have instructed the man to sit—it wasn't against the rules—but no, he was too preoccupied, too absorbed in his own fermenting megalomania, too drunk with amazement at the turmoil he had instigated, to think of anyone but himself.
The glint in Prosper's eyes, as he watched a report being transmitted from a forward command post somewhere in the Sudetenland, was all but indistinguishable from the one that appeared when he was making a move on some nubile young creature. There was the same avarice in it, the same thrill in exerting his influence. Girls fell at Prosper's feet because he was handsome, certainly, but also because of who he was, his surname, his status. Cynthia understood this all too well, since she herself had been one of those girls, a long time ago. He had been utterly captivating back then, youth giving his charm a freshness, an innocence almost. Although Cynthia had been Family too, and therefore in theory his equal, looks coupled with the aura that hung around the word _Gleed_ had made Prosper an irresistible package. Naïve as she had been, she had found him endlessly, fascinatingly sophisticated, and when it became clear that he was courting her, wooing her, she could scarcely believe her luck. Nor could her parents. For the Lamases, a union with the Gleeds was several steps up. Their Family status would be immensely enhanced by the association. It was a match made in heaven. How could she not have been happy about it?
After almost thirty years—and countless infidelities—the question now was, how could she be happy about it any more? And the answer was, she had adapted. She had adjusted. Incrementally, as time went by, she had hardened herself to the disappointment and the betrayal. She hardly felt his indifference to her.
And then this. On top of her son being gone, her only boy, his absence like one of her own organs having been torn out of her, she was confronted with a husband who was no longer content with fucking his way through the women of the world and was now trying to fuck the world itself. Cynthia despised coarseness but there it was. Fucking. That was what Prosper was doing, there was no other word for it. Fucking like some maddened rapist, not caring who got hurt so long as he exerted his power.
Well, no more. Enough. It was time she put a stop to it. After hours of soul-searching, Cynthia knew what she must do. As her nephew had said: _Anything and everything must be done to bring about the right conclusion_. God help her but she had no choice.
The Phone's eyelids flickered, then snapped open. He came to attention and nodded to her. "Ma'am," he said briskly, hoping to sound like someone who had not just been half-asleep.
Cynthia smiled at him and kept the smile in place as she turned to her husband.
"Prosper. Dear. You've been sitting there for ages. You've barely touched your lunch. Might I get you something to eat?"
"Hmm? Oh, no. I'm fine."
"Drink, then?"
"Again, fine. Don't need to fuss over me."
"I take it the Kuczinskis haven't called yet."
"Only a matter of time. Only a matter of time. The Pan-Slavic Federation's demanded that America step in and play peace-broker. That's a definite sign. They're cracking. Can't take the pressure."
"If you say so. You're sure about that drink? How about some coffee? Strong coffee? You look worn out. You need something to help keep you going."
The solicitous, ever sympathetic wife. How often had she pretended to play that role? It came to her easily now, second nature.
"Some coffee?" said Prosper. "Yes, all right. Why not? Have a servant bring some."
"Better yet," Cynthia said, "I'll make it for you and bring it myself."
**58**
THE TAXI DRIVER was tongue-tied throughout the journey to New Aldwych, repeatedly trying to formulate a sentence and failing. Frequent checks in his rearview mirror confirmed that none other than Provender Gleed was sitting in the back of his cab, but he simply could not work out a way of remarking on the fact that wouldn't come across as glib or grovelsome, nor did he feel he could opt for some innocuous comment—about the weather, say—for fear of sounding disrespectfully trite. He was torn between excitement and the desire to appear unflustered, as if driving a Family member across London was something he did every day. He knew that at the first available opportunity he would call his wife and anyone else he could think of and tell them about this, and the prospect somewhat mitigated his present state of speechlessness. In his account of this episode, he and Provender would be chatting like old pals and the Gleed heir would declare himself impressed by the taxi driver's opinions and observations on life. It wouldn't be a lie so much as an embellishment of the truth: had the driver not been dumbstruck, Provender would surely have been delighted to hear what he thought about things.
As far as Moore was concerned, the driver's silence was golden. He'd been worried that the man would talk them all to death before they reached the Notting Hill Skyway or even the Shepherd's Bush Tunnel. Provender's presence, however, was talismanic. It granted an unexpressed wish.
It did the same at the Shortborn Theatre. The building which Moore had been unable to penetrate, this seemingly impregnable fortress of Thespis, raised its portcullis and lowered its drawbridge and surrendered without a siege. All that was needed was for Provender to enter the lobby, and within seconds there were members of the front-of-house staff rushing around madly, and the manager appeared, and there was much hand-wringing and kowtowing, and the three visitors—Provender, Moore, the girl called Is—were given free rein to venture anywhere they wanted. Provender asked the manager where he might find his cousin, and was told, "On stage." It transpired that an unscheduled extra rehearsal was going on, the show's star dissatisfied with the previous night's performance and wanting to give the play that last little extra polish to make it just so.
"A consummate perfectionist, our leading man," said the manager.
"A complete pain in the arse, more like," Provender muttered. "So we can go into the auditorium, then? Have a look at what's happening?"
"But of course," said the manager with an unctuous writhe. "Allow me to escort you."
"No. If you don't mind, I'd prefer it if we slipped quietly in. So as not to cause a fuss."
"Very well." The manager bit his lip with disappointment. "Perhaps later, though, I could take you on a tour of the theatre. The Shortborn is one of London's most historic venues, substantially rebuilt after the war with funds from the Bannerjee Foundation, but still retaining—"
"Yes, maybe." Provender turned to Moore and Is. "Public place. Lots of witnesses around to see. This should be good."
Rubbing his hands, he headed for the doors that led from the lobby to the stalls. Moore and Is filed after him.
OUTSIDE, AT A bus stop across the street from the theatre, a figure who had been lying in wait made his move.
Damien had been standing at the bus stop for nigh on an hour. Buses had come and gone, passengers had stepped on and off, and Damien had stayed put, making it look each time as if the bus he was waiting for wasn't this one but the next. His air of long-suffering, barely-contained impatience was readily recognisable to anyone with experience of the vagaries of London's public transport system. His huffs and grimaces were taken by others to mean he was being badly let down by the RLA and its inability to run a bus service which was even on nodding acquaintance with the word efficiency.
It wasn't completely an act, but the real source of Damien's discontent was not, of course, buses. Every minute he spent at the stop had been a minute in which it seemed even more implausible that Provender Gleed and Is were going to turn up at the theatre. As long shots went, this one was inordinately, inconceivably long. It was, however, his only shot. He had no alternative, other than to sit at home and stew in his own frustration. Which he couldn't anyway do because there was the small matter of the body of a dead detective cluttering up his flat. His only option had been to come here and hope.
Hope that the detective had not lied.
Hope that Is had conferred with Provender and told him that Damien had collaborated with a Family insider.
Hope that Provender put two and two together and came to the same conclusion as the dead detective's partner.
Hope that Provender would choose to visit the Shortborn Theatre and confront his cousin.
A ragged patchwork quilt of hopes, threadbare and full of holes, but it was all Damien had to draw around him and take comfort from. Where else could he go to look for Provender? What other chance did he have of getting his hands on his hostage again? Circumstances forced him to be at the theatre. His choices were narrowed down to this tiny, mote-like, infinitesimal scrap of possibility.
And he had been close to giving up, on the point of going back to his parked Dragon Wind and driving dismally back to Needle Grove, when remarkably, astonishingly, his against-all-odds gamble paid off. A taxi pulled up in front of the theatre and three passengers disembarked from it: Provender Gleed, then Is, then a little man Damien did not recognise but, were he to hazard a guess, would have said was Merlin Milner's partner-in-crimebusting.
There was no time for Damien to catch them in the few seconds it took them to cross the pavement and disappear into the theatre lobby. The traffic was flowing thick and fast in the roadway and he wasn't able to reach the other side of the street for a full minute. When he got there, a glance through the lobby's glassed doors showed Provender surrounded by people and speaking to someone who was obviously the theatre manager. Damien considered barging in, but the lobby was too public a place. What with all the theatre employees, there were too many eyewitnesses, too many potential have-a-go heroes who could make his life difficult. Then Provender left the lobby, heading deeper into the building, and Damien knew he would have to find another way into the theatre.
Easily done. All theatres had stage doors, and the Shortborn's wasn't difficult to find. It was situated down an alley at the side. Damien walked up to it and jabbed the buzzer-button marked ENQUIRIES.
The person who answered the buzzer was not some wispy theatrical type as Damien had anticipated, but rather a stocky, thick-necked, short-back-and-sided individual whose bad suit and matching attitude said, unmistakably, bouncer. Which made sense, what with a Gleed in the play's cast.
Damien was unfazed. Not pausing, he shunted the man backwards with an outstretched hand, unsheathing his knife with the other hand. The bouncer, taken by surprise, staggered and collided with a plastic chair, sending it and the nudie mag that was lying on it skidding across the floor. He recovered his balance expertly and came back at Damien, adopting a boxer's stance, weight on the rear foot, fists loosely clasped at jaw height. The knife was still concealed behind Damien's back, so the bouncer had no reason not to feel confident that the fight would be his. This bloke who had pushed him was big but not that big, and a venue-security professional feared no one. A venue-security professional was trained for moments like this, _lived_ for moments like this.
He swung. Damien parried. Huge equalled slow. The bouncer might as well have stopped and told him when the punch was coming and where he intended it to land.
He swung again, another hefty, lumbering roundhouse. Damien ducked in under it and brought the knife into play, whipping it in from the side and sinking it hilt-deep into the bouncer's flank.
By rights the knife-thrust ought to have settled the scuffle then and there. It was a mortal blow and the shock alone should have toppled the bouncer. Damien gave the deerhorn handle an extra twist, further ruining whichever vital organs the blade was embedded in, then stepped back, as if inviting his opponent to do the decent thing now and fall.
The bouncer teetered, looking down, exploring the knife handle with inquisitive fingers, feeling the shape of it, fathoming what it meant to have this thing protruding from his abdomen, this wetness leaking out. Then, to Damien's surprise, instead of having the good grace to keel over, he grunted and lunged, arms spread wide.
The strength with which the arms pincered around Damien's chest and began to squeeze was, literally, breathtaking. Damien's ribcage constricted; he all but heard bones creak. His lungs were suddenly straining for air but he could get none into them. Meanwhile the bouncer's own breath was gusting in his face, a series of rapid, meaty-smelling exhalations that added to the torture of being suffocated: even if he could inhale, there was nothing to inhale but _this_. Damien writhed and gasped but could not wrestle free. The pressure of the bouncer's bearhug intensified. Damien's head woozed. His backbone groaned. Something, surely, was on the point of snapping.
Then, at last, the knife-wound took effect. The bearhug relaxed. The bouncer seemed to crumble away. Suddenly he was supine on the floor. His heels were kicking the linoleum. His teeth were bared in a rictus of anguish and dismay. He started to choke, gagging gutturally.
Damien, reeling somewhat, bent down and yanked out the knife. He raised it and plunged it into the bouncer's chest, doing this much as he would have if the man had been a suffering animal—matter-of-factly, out of necessity, putting the creature out of its misery. The bouncer shuddered, spasmed, and went still. His eyes rolled and settled. A croak escaped his slack, gaping mouth. Gone.
Damien swabbed the blade clean on the bouncer's trouser-leg, then re-sheathed the knife. He stood up carefully. His chest throbbed, tender to the touch, and his head was swimmy, but otherwise he was unharmed.
He took stock of his surroundings. He was in a short corridor which terminated in a pair of swing doors inset with frosted-glass panes. A notice drew attention to the fact that no unauthorised persons were permitted beyond this point.
Damien barged both doors open and strode past dressing rooms, into the Shortborn's backstage area.
**59**
ARTHUR HAD NOT only demanded the additional rehearsal, he had insisted on it being conducted in full costume, props and all, with the lighting and sound technicians on hand to supply the necessary effects, the stagehands at work behind the scenes... basically the entire cast and crew giving up their afternoon to put on a matinée to an empty house, for no extra pay.
Naturally there was disgruntlement, mutinous mutterings backstage, threats to sabotage the proceedings, but none of it amounted to anything. The scenery humpers and the follow-spot jockeys knew better than to put their jobs at risk by offending a Gleed. As for the actors, they were too jealous of Arthur's fame and renown to mind, truly, doing as he asked. Besides, if he remembered this favour, he might be inclined to invite them to take part in some future production. In the acting world you always had to think about your next job, and open resentment of somebody higher up the ladder than you was never a wise career move. Cross Arthur Gleed, and it would be a lifetime of amateur dramatics from hereon after. _Another_ rehearsal? Well, if Arthur wanted it... And come to think of it, last night's show hadn't been _that_ great.
The director, Sean Lockwood, was trapped somewhere between these two categories, as cowed as the backstage people and as career-covetous as the people onstage. He wasn't happy about the rehearsal, but what could he do? Lockwood, in fact, had all but surrendered control of the production to his leading man and was feeling much as the captain of a pirated ship must do, watching helpless as his vessel was steered on a course he never plotted.
And it had all started so well.
At the outset Lockwood and Arthur had been of one mind: this would be a traditional _Hamlet_ , a _Hamlet_ Shakespeare himself would not have been surprised to see. Period dress and setting? Absolutely. None of your needless updating. And no gratuitous nudity or excessive bloodletting either, nothing like that, nothing that would bait the critics and earn shock-value kudos. A classic, conventional production, free of tricks and shenanigans.
How that had changed. First of all, a fortnight into rehearsals, Arthur suggested they cut the text by a quarter, in particular trimming Hamlet's soliloquies, which he said were very long and difficult to memorise. Lockwood nearly asked why Arthur wanted to play Hamlet if he didn't fancy handling the soliloquies, but he held his tongue and did as requested.
It was the compromise which paved the way for a hundred further compromises. Most of them were relatively minor, but one wasn't, namely Arthur's sudden decision that the original Ophelia should be sacked. He had had a brief, torrid fling with her, it had got messy, he had broken her heart and now was running scared of her. You couldn't have a Hamlet who was afraid to look his Ophelia in the eye. Reluctantly Lockwood did the deed, braved a flood of weeping from the distraught actress, and then endured several long late-night phone calls from her as she tried to come to terms with the emotional and professional rejection. The new Ophelia was not as right for the part as the old one but had the advantage of being a lesbian and therefore immune to Arthur's amorous approaches.
Through it all Lockwood thought of just one thing: Gleed patronage. He was young, 22, and this was only his second professional directing gig. If it did well, the Gleeds would look kindly on him, put their name behind him, and he would be set up for life.
Then came the biggest blow of all. With the sets designed, scale models constructed, parts of Elsinore Castle already built, not to mention the costumes measured for and in the process of being sewn, Arthur had a change of heart. He came to Lockwood and said he had decided he didn't want a traditional _Hamlet_ any more, he wanted a bold one, a groundbreaking one, a _Hamlet_ that would startle (but still please) the Bard and would enliven modern audiences who were jaded, he felt, by stuffy old renditions of Shakespeare and were seeking something different, something that was exciting and spoke directly to the modern-day theatregoer. He had roughed out some drawings of how he wanted Elsinore and the dramatis personae to look. Lockwood stared at the drawings, and stared at them some more, and calculated how much it would cost to abandon the existing designs and begin afresh, and came the closest he had ever got to punching someone. This thoughtless, this _arrogant_ little fuckwit...! How dare he turn up with a few clumsy ballpoint sketches and expect the set designer, the costumier, the property master, _everyone_ to scrap everything they'd already done—work they had sweated over—and start again from scratch.
But, as ever, Lockwood capitulated. _Gleed patronage_ , he told himself. _Gleed patronage, Gleed patronage, Gleed patronage_. He tried to talk Arthur into sticking with the original concept but Arthur's mind was made up and no amount of friendly persuasion could get him to budge. There was a near-riot as Lockwood announced the change of plan to the assembled design crew. For some reason not wishing to make Arthur a scapegoat, he took half of the responsibility onto himself, claiming it was a joint decision by the pair of them. He also promised to meet any overtime costs out of his own salary, an offer which meant that by the end of the play's run Lockwood would have earned a grand total of nothing, his income as director entirely eliminated by the expense of implementing Arthur's alterations.
It was around this time that Lockwood developed insomnia and, on his GP's advice, went on a course of antidepressants. Ever since, he had stopped caring about the production nearly as much and was even content to let Arthur assume some of his directorial duties. Arthur made suggestions about blocking and stage business which Lockwood rarely disagreed with. If he objected strongly, all he would do was say yes and then later have a private word with the players concerned and tell them to keep to the original way of doing the scene. They ignored him, invariably going along with Arthur's idea instead, but at least Lockwood had made the effort to look like he was still in charge. Nor was he in a position to be upset now if the reviews castigated the style and quality of the production, as some of them this morning had. He wasn't to blame. He had tried his best. He could do no more.
Arthur's re-envisioning of the play had turned it into something Lockwood barely recognised any more. The setting was now not a thirteenth-century Danish castle but a latterday English mansion, expensively decorated and furnished. The characters were kitted out in the latest fashions and had been advised by Arthur to declaim their lines in a free-form manner, ignoring the rhythms of Shakespeare's iambic pentameter. The play-within-a-play in Act II, scene ii, had been supplanted by a film-within-a-play, a prerecorded one-reeler projected onto a backdrop screen while Hamlet and family sat in cinema seats and, would you believe it, munched popcorn. The arras behind which Polonius meets his doom in IV, iii, had become a tinted-glass picture window, and Polonius himself was wheelchair-bound, though no less crotchety an old codger for that. There was no Ghost. Arthur preferred a modern psychological interpretation of the spectre—it was all in Hamlet's mind, a subjective manifestation of Oedipal leanings and madness—and so he taped Hamlet's Father's lines himself and had them played over the sound system. As a consequence, any of the other characters who see the Ghost in the course of the play were expected only to _pretend_ to see it, as if humouring Hamlet, even if Hamlet didn't happen to be onstage at the time. It was absurd, but it was what Arthur wanted, and what Arthur wanted Arthur got.
Then there was Arthur's performance itself. He had chosen to essay the role naturalistically and with a set of tics and mannerisms clearly modelled on a real person, perhaps someone he knew or had once met. This lent it the air of an in-joke, but one so obscure that possibly only Arthur himself got it. Certainly Lockwood, as he observed the rehearsal at a dispassionate distance from the back row of the stalls, had no idea who Arthur was aping with those hesitancies of his, those inhibited gestures, those improvisational ums and ers, that whole peculiar blend of realistic underplaying and relentless mugging. Not forgetting that wig which was not a wig—a fine-furred latex cap which fit snugly over Arthur's own slicked-down hair and gave the impression of a close-shaven, downy scalp.
Provender, on the other hand, understood who it was straight away.
And was at first thunderstruck, then indignant beyond belief.
WHEN PROVENDER ENTERED the auditorium, with Is and Moore not far behind him, the play was halfway done. Hamlet had just killed the figure lurking behind the arras—or rather the picture window, which he had shattered to spun-sugar smithereens by hurling a heavy potted shrub through it—and discovered that his victim, whose skull had been crushed by the pot plant, was not his uncle but Polonius. Gertrude was now soundly berating him, as well she might, and Hamlet was defending his actions at some length, though not, of course, at the length Shakespeare originally envisaged.
"Nay," said Arthur, "but to live / In the rank sweat of an enseamed bed, / Stew'd in corruption, honeying and making love / Over the nasty sty!"
"O, speak to me no more!" replied the actress playing his mother. "These words like daggers enter in my ears. / No more, sweet Hamlet!"
"A murtherer and a villain!" Arthur exclaimed.
"You bastard," Provender hissed, almost simultaneously. His voice did not carry far but it did reach the ears of Sean Lockwood, who swivelled in his seat to see who had spoken. In the dimmed auditorium light he failed to identify Provender Gleed, but something about the person was naggingly familiar. The way he held himself. His cropped hair.
"You absolute and utter bastard," Provender hissed again as, onstage, Arthur began a conversation with the unquiet spirit of his father. Much like a lunatic hearing voices in his head, Arthur twitched and twisted and frowned while he interpolated his own lines with the Ghost's booming taped tannoy pronouncements.
What Provender was looking at, however, was not acting. It was rank satire.
Is, standing at his shoulder, came to the same realisation. In a low whisper she said, "He's doing you, isn't he?"
Provender hadn't needed it confirmed but to hear it from someone else was heartening. It meant he wasn't imagining things, this wasn't an instance of misplaced vanity; his cousin really was playing Hamlet in the guise of Provender Gleed, or perhaps Provender Gleed in the guise of Hamlet.
And the more Provender looked, the more grotesque and insulting it all became.
The set—it was highly reminiscent of Dashlands House. The décor, the furnishings. The slain Polonius was lying next to an overturned wheelchair and, although Provender didn't have a clear view of the actor's sprawled body, what he could see of him made him think of Great. As for Gertrude, the actress playing her did not physically resemble his own mother but she was smartly turned out, beautiful, coiffed, shapely, stately. The similarities were there.
Rage boiled up within him, so vast and fierce and all-consuming that he could barely think straight. Laying hands on Arthur was his one overriding imperative. Wringing his cousin's scrawny little neck. He scanned the auditorium to see how he might get up onstage. The Shortborn, being an old-fashioned theatre, had an orchestra pit between stalls and footlights. It wasn't a gap that could be easily leapt (it was wider, indeed, than the gap between the closer pairs of adjacent balconies on a tower block in Needle Grove). As he cast around for some other means of reaching the stage, he noticed a man sitting in the back row. The man was staring at him in that manner Provender was fast becoming weary of: the I-know-you look. As their gazes met, the man got sharply to his feet.
"Sean Lockwood," he said. "Director. This is an honour, Mr Gleed. I'm sorry, it took me a moment to place you. Arthur mentioned some of his Family might be coming along at some point but I didn't expect—"
"There," Provender snapped, pointing at the stage. "How do I get there?"
"But the rehearsal is—"
"How?"
Lockwood collected himself. "You can get backstage if you use that exit." He indicated a door close to the stage, with a green sign glowing above it. "Turn right, there's another door beyond which connects to the wings. It's locked during proper performances but I don't think it will be at the moment. You can..."
His voice trailed away. Provender was already off and running—running with the determination of a man who had business to finish and didn't care if he finished it with help or alone.
**60**
BACKSTAGE WAS TRADITIONALLY a place of hush and caution, but the need to be discreet and avoid causing a disturbance was not, it must be said, uppermost in Provender's mind as he thrust open the door at the end of the passageway that ran alongside the auditorium. The only circumspection he showed was a brief pause, as the door swung shut behind him, to allow his eyes to adapt to the sudden gloom he found himself in. Gradually shapes made themselves apparent. He was on the side known as Opposite Prompt. Facing him was a short flight of steps, which you had to surmount in order to get level with the stage. Up there, in the wings, he could see a handful of motionless figures, various bulky props either waiting to be carried on or just recently taken off, black dropcloths hanging in swathes, and rows of sandbag-weighted ropes tethered to a complicated arrays of pulleys—people and objects in a state of suspension, all dimly limned by the light that filtered in sidelong from the stage.
No sooner had he got the lie of the land than he made for the steps, bounding up them two at a time. Heads turned. You weren't supposed to thump around like that back here. Move slowly, tread softly. Provender ignored their scowls. One man—big brawny chap, had to be a stagehand—did a double-take, evidently recognising him. Provender was by now heartily sick of being recognised by strangers. He was also, at this moment, too incensed by Arthur to care much about anything else. He breezed past the man, drawn towards the stage lights. Between two flies he caught a slivered glimpse of the set. There was Arthur-as-Hamlet, revealing to Gertrude his knowledge of Laertes's plot against him and his plans for foiling it:
Let it work,
For 'tis the sport to have the enginer
Hoist with his own petar, an't shall go hard
But I will delve one yard below their mines,
And blow them to the moon.
By the time it took Arthur to deliver these lines, Provender was just a step away from entering stage right. His foot was inches from the white gaffer tape on the floor that marked the sightline.
Then he heard a heavy huff of breath behind him. Then hands seized him, one clutching his chest, the other clamping over his mouth.
O, 'tis most sweet
When in one line two crafts directly meet
The sense of déjà vu was sickening. Provender knew, in an instant, who had grabbed him. He knew these arms, their strength. _Him_. He was here. Damien Scrase. Is's accomplice. No, _Arthur's_ accomplice.
This man shall set me packing;
Immediately, he writhed. He struggled. He fought as he had before at the party but this time with even greater force and viciousness, with an absolute refusal to be taken captive again. Damien hauled him backwards...
I'll lug his guts into the neighbour room
...but Provender continued to resist, jabbing behind him with both elbows, left, right, kicking with both heels, right, left. When that didn't work he thrust his head back, hoping to smash Damien's nose with a reverse head-butt. It didn't work either, but he did manage to dislodge his face partially from the other man's grip...
Mother, good night indeed.
...so that now his mouth was level with the top of Damien's hand, his lips pressing against the ball of the thumb.
Nothing else for it. Provender opened wide and sank his teeth in. No squeamishness, no hesitation. Biting as hard as if he was tucking into a succulent chicken drumstick.
A gush of blood over his lips. The ghastly sensation of skin splitting, flesh parting. His incisors cleaving down into gristle and knucklebone.
Come, sir, to draw toward an end with you.
And, from Damien, a scream. A shrill, unbridled howl of agony. Deliciously, deliriously wonderful to hear.
Everything onstage stopped. Backstage, pandemonium broke out. Shouts, cries from the stagehands and actors. Shh! What was this? What was going on?
The hands let go of Provender, Damien rearing back. Provender spun round, spitting out blood, spitting, spitting, and thinking he would never be able to forget the taste, never to his dying day forget how it felt to bite through the flesh of a living being. A retch reflex brought bile to the back of his throat. He spat that out too.
He looked at Damien. Damien was clutching his wounded hand under the other arm, pressing it against his ribs, and he was stamping, hissing, seething, like a stove kettle on the brink of boiling. His face was contorted, as ugly in this state as Provender had imagined it would be. His eyes, in the stage-light glow, were a pair of fireballs.
Then he had a knife. Damien's uninjured hand, his right hand, was holding a knife. The knife Is had mentioned. The sheath knife he knew how to use like an expert.
"I'm," Damien said, and a fresh wave of pain hit him and he winced. "I'm," he said again, "going to do humanity a favour. Fuck the money. Fuck Needle Grove. You"—a clench of teeth, a gasp—"are going to pay for everything you've done. Everything your Family has done. All the Families have done. And I'm going to be a hero. The nation will thank me, the world will thank me. It starts now. The British Uprising. This is the first blow. Freedom begins today."
The knife came up, quivering. Damien poised himself to attack. Provender knew he needed to run, or defend himself somehow, but he was overcome with the terrible certainty that it wouldn't make any difference. Whether he fled, whether he stood and fought, he would not win. The man had a knife. The man had vowed to kill him. The man was going to let nothing get in the way of achieving that goal. Provender had arrived at the last moments of his life, and he wished there wasn't this sense of impotence, of inevitability. He wished fear had not rendered him so pathetically helpless.
Then Damien let out yet another sharp yelp of pain, his face briefly creasing up. A look of curiosity crept over him, closely followed by a look of bewilderment. He half turned, groping behind his back with his empty hand, the bitten one. Fumbling exploration located something near the base of his spine, in the muscle above his hip. He plucked the foreign object out. His hand came round and it was holding a small transparent plastic tube, needle-tipped, empty. Damien peered at the tube, perplexed, trying to make sense of it. A hypodermic syringe. What was _that_ doing stuck into his back?
The answer came to him at much the same time that it came to Provender.
"Is," said Provender.
"Is?" said Damien.
Is was behind Damien, just out of his immediate reach. Her arm was still extended with the fingers of her hand loosely configured for depressing the syringe plunger, thumb behind middle and index. Her face showed fear, regret, determination, defiance, all at once.
"Shouldn't talk so much, Damien," she said hoarsely. "That's your trouble. Too much in love with the sound of your own voice."
"Bitch!" Damien yelled, and turned and charged at her.
Provender, at the same time, charged at _him_.
Whether Damien would actually have reached Is was a moot point. Already the Comaphase was racing around his system, shutting faculties down like a janitor switching off lights in an office block. His legs were sluggish, his thoughts were slurred, and his blood was moving like molasses in his veins. After only one step he teetered, and then Provender collided with him in a rugby tackle and Damien fell. Floorboards rushed up to greet him. The last sensation he was aware of was his face smacking into wood and his nose breaking. He did not even feel Provender on top of him. There was a skull-shivering crunch, a burst of agony, and then the emptiness of the void—pure, pain-free, weightless oblivion.
Provender, for his part, felt it wise to remain on Damien's back, pressing him down, until he was 100% certain that the drug had taken effect. He had the presence of mind to bat the knife away from Damien's limp hand, sending it slithering across the floor. Thereafter, simply lying atop his fallen enemy was about all he could do. Even if he had wanted to get up, his trembling body didn't seem ready yet to accept the command to do so.
Finally he mustered the strength to raise his head. He looked for Is. He wanted to see her acknowledge what he had done, see her smile at him. When the threat had been to himself he had been paralysed, incapable of reacting, but the moment Is had been in danger he had known exactly what to do.
Just as his eyes met hers, however, an angry figure stepped in the way, obstructing his view.
"Provender?" exclaimed Arthur, glaring down, fists on hips. "What in hell's name are you doing here?"
**61**
"NONSENSE." THE DENIAL was punctuated with a head-shake and a snort. "I can't possibly be in league with that man. I've never seen him before in my life."
"Never _seen_ him, maybe, but you've talked with him on the phone."
"Not that either." Arthur nodded emphatically to where the prone, unconscious form of Damien Scrase lay in the wings. Two burly stagehands had wrapped Scrase up in gaffer tape, all but mummifying him, and were standing watch over him self-consciously, like a pair of bit-part players—First and Second Guard. The hand Provender had bitten was wrapped in a towel, through which blood was already starting to seep darkly. "I do not know him. I have no idea who he is. And as to conspiring with him to kidnap you, Provender... Now we're in the realm of utter bonkersness. Why, for God's sake? What could I hope to gain?"
"Disruption of my life, of my Family, which you could take advantage of. An opportunity to, well, upstage me. Usurp me. Who knows, it could be you even planned to come to my 'rescue' at some point, finding out where I was and dramatically freeing me from my captors. The whole thing was an elaborate set-up designed so that you could play the hero and raise your standing in my Family's eyes."
"Pah!"
"He said 'Pah!'," Is said sidelong to Moore. "I didn't know people actually said 'Pah!'."
"Apparently they do," Moore replied.
"Do you have any idea how far-fetched this sounds?" Arthur went on. "As if I'd want to upset my relatives. Especially not Aunt Cynthia—who's worried sick about you, by the way."
"I believe you'd risk upsetting them for a short while if it meant you could be saviour of the day later on. In fact, they more upset they were, the better it'd be for you. They'd be so relieved when you brought me back, they'd give you anything you asked. Your own room at Dashlands, even."
"I don't want a room at Dashlands. All right, I'd take one if it was offered, but I don't want it _that_ badly. And yes, I wouldn't mind a bit more acceptance from you lot, but I'd never go about getting it through something as contrived as a kidnap plot. That's too much like... I was going to say hard work but that's not what I mean. Too much like... a real thing. A thing that might happen."
"I thought if it was all a sham, a pretend kidnap, that'd be right up your street. Like this." Provender waved, indicating the stage set. By this point the house lights were up and the play's cast had gathered in the auditorium to view the unscripted events that were unfolding up there on the boards. The interruption to the performance had brought everyone out from the greenroom, so that now there was an inversion of the usual order of things, an audience of actors watching a group of people being themselves onstage. Nobody was quite sure what Arthur and Provender were arguing about or who the two supporting characters with them were, or for that matter who the unconscious man in the wings was. It was all, nevertheless, fascinating stuff and, like the best kind of entertainment, had them glued to their seats.
"This?" said Arthur. "This is a whole different matter."
"Is it?" said Provender. "What is it anyway? What's it all for? Some kind of joke, I can see. But what's the point of it?"
Arthur scratched an itch beneath his velvety skullcap abstractly. Most of his fellow-troupers had been in on the game: Arthur, with this production, was gently guying his own Family. Few of them had realised, however, how explicitly his Hamlet parodied a certain member of the Gleeds till now, as Arthur and his cousin faced each other, dressed similarly, hairstyled alike. Arthur, they saw, had borrowed heavily from Provender for his rendition of the lead role and it was clear that this to no small extent accounted for Provender's unhappy mood.
"The point..." Arthur said. "Are you accepting, first of all, that I wasn't responsible for your kidnapping? I wasn't the evil-genius mastermind behind it?"
"No, I'm not."
"Because I cannot stress enough that I wasn't. Apart from anything else, for the past three months I've been busy as hell putting this damn play together. I haven't had a moment's spare time, so there's no way I could have organised anything as complex as a kidnapping. No way."
"For what it's worth," Moore whispered to Is, "I believe him."
"Me too. I think Provender's beginning to as well, but if I know him he'll take his time admitting it."
"And," said Arthur, with a flicker of irritation, "don't you see? Can't you tell? This play—that's why I was so keen for all of you to come and see it."
"So we could watch you laughing at us."
"No. I wanted you to watch yourselves. I wanted to 'hold, as 'twere, the mirror up to nature'. I was trying, in my way, to get the Gleeds to look outside themselves for once, see themselves as others see them."
"With a play."
"'The play's the thing'," Arthur said, "'Wherein I'll catch the conscience of my kin.'"
"He's practised that line," Is muttered.
Moore concurred. "Hours of work to come up with that misquotation."
Arthur rounded on them and snapped, "Would you two please stop with the asides! We're trying to settle some important stuff here and it's not easy with you two yammering on in the background. Why don't you go and do something useful? Has anyone called the police, for example? That flat-on-his-face person just tried to kill a Gleed. I think he should be put under arrest, don't you?"
Is and Moore exchanged looks, then Moore shrugged. "I'll go and find a phone. Provender? May I just say, the PLAY-ACTOR seems like he's being authentically PLACATORY. You might want to consider his innocence."
"I'll be the judge of that," came the frosty reply.
"Just saying." Hands patting the air, Moore exited stage left.
"And you?" Arthur said to Is.
"What about me?"
"Can you find something to do?"
"I'm staying put. You can't order me around."
"I can."
"No, you can't." Is plumped herself down on a suede-sheathed ottoman that sat at an angle, close to the proscenium arch. "Carry on."
Arthur glared at her, then sighed and turned back to Provender. "So, yes, I staged this _Hamlet_ for your benefit. I didn't realise at first that there were parallels. All I knew was I wanted to play the Dane because every actor does. It's the peak, the Everest of theatrical roles. I had to do it, a challenge to myself, to prove I had what it takes, I had the chops. Once we began rehearsing, though, and I got more and more familiar with the text, I began to see that the play was about a powerful family, a Family, with all sorts of tensions within, and that Hamlet himself bore similarities to, well..."
"Me."
"You. He doesn't quite know what to do with himself. He can't quite commit to any course of action. He procrastinates. He prevaricates."
"You don't know me that well. I'm not like that at all."
"Perhaps not, but that's how you appear. That's how you appeared to me when I first came south, when I was more of an outsider to the Family than I am now. I thought you a particularly ungrateful, snobbish sort of person."
"Oh thanks."
"Because you have so much going for you, Provender. You're privileged, fortunate beyond most people's wildest dreams, and what do you do with yourself? Nothing. You're miserable. You gloom around all day, your own private storm cloud hanging over your head. You can't even manage the one simple duty that's expected of you: finding a wife, carrying on the line."
"It may seem simple to you."
"It _is_. Others have done it. Your mother plonks these perfectly agreeable girls in front of you and you turn them down without even considering them. You claim you want to find someone under your own steam but you can't even be bothered to do that. You never make a decision, Provender. You live in your own world. You can't step out of it and engage with anyone else. It's just ridiculous!"
"And so you had me kidnapped—"
"No!" Arthur exclaimed, stamping his foot in exasperation. "No, I told you, I staged a fucking play! I made it this way, I arranged it to be highly reminiscent of the Gleeds, I reorganised the whole production with one specific aim: so that you would see it. I hoped the Family would see it too and that they would understand what I was getting at even if a dunderhead like you couldn't. This was all, basically, for you, Provender. I was..." His voice lowered. "In my way I was trying to help. To tell you a few home truths. To show you _you_."
Provender was stalwartly keeping up a sceptical front but his eyes had begun to betray him. They had softened, no longer hard and angry and righteous. They were the eyes of someone who, in spite of himself, was starting to acknowledge that he might have been wrong.
"And why shouldn't I?" his cousin said. "It's not as if you and I are close or anything. I'd have nothing to lose by being the one who got you to finally face up to your responsibilities. We could hardly fall out if we'd never been _in_ to be begin with. Really, it couldn't be anyone but me. My duty as a Gleed was to make you accept _your_ duty as a Gleed, and I was doing that how I thought best. Maybe if you'd seen the play the whole way through... Hamlet's pretty dynamic in the final scene when he's lobbing 'envenom'd' swords around. Maybe if you'd seen that bit you'd realise I was trying to be fair."
"As I recall, Hamlet dies at the end."
"So? Everyone dies at the end. It's a tragedy."
"He also goes mad."
"No, Ophelia goes mad, Hamlet only pretends to. Look, it wasn't intended to be some kind of direct metaphor. The resemblance isn't perfect. After all, Shakespeare didn't look into a crystal ball and see the Gleeds four centuries in the future and write a play that was exactly about them. I took a play that was written four centuries ago and saw how I could adapt it to fit what I wanted to say about you. A reasonably close match but not an absolute one."
"Fine, but..."
"But what, Prov? I shouldn't have? How dare I? How could I have the nerve? Come on, out with it. I'm barely even proper Family, isn't that right? Wrong side of the blanket, possibly illegitimate. Only proper Family can criticise Family." He shook his head. "That wouldn't seem to work, though, would it? Not with the Gleeds. No one in your immediate Family is prepared to confront anyone about anything. Oh, you bicker, there are sideswipes across the dinner table, you think you're sorting things out, but you're not. All you're doing is dusting off a problem before sticking it into the back of the wardrobe again."
Provender jerked a thumb towards the auditorium and lowered his voice. "I don't think it's appropriate to talk like this in front of strangers."
"Precisely!" said Arthur, shrill with triumph. "Precisely! Don't talk. Don't mention anything. Keep it in the Family, or not even there if possible. Hide. Bury. Disguise. Deny."
"Arthur..."
Arthur, who had puffed himself up like a bantam cock, deflated, relenting. "All right. Fine. But I've made my point, haven't I?"
"Amply."
"And you now know I didn't have anything to do with the kidnapping."
Provender pondered, making it look as if he was only just coming to that conclusion. "Probably you didn't. On balance, no. You can understand, though. I mean, the evidence was pretty incriminating."
"Not me," Arthur said, arms spread out. "I'm guilty of machinations but not those ones."
"Right then," Is said, jumping to her feet. "Now that that's all been established, it's time you kept your promise, Provender."
"Promise?"
"To speak to your father and tell him you're OK."
"I didn't promise that."
"Yes, you did. You asked for an hour to confront Arthur here and then you'd call home. You've confronted Arthur, so..."
"It wasn't a promise as such."
"As good as."
"But we still don't know who the insider is."
"Well, what are we going to do? Ask Damien?"
"When he wakes up, yes. Good idea."
"You'll never get a straight answer out of him."
"Maybe I won't, but the cops will, I'm sure, when they come."
"It could take a while. He'll be groggy when he comes round. Remember how you were? Could barely string a sentence together."
"So we just leave it, is that what you're saying?"
"One phone call, Provender."
Arthur had been following the conversation like a spectator at a tennis match, eyes flicking back and forth. Now, with a wry grin, he said, "Provender, have you managed to pick yourself up a girlfriend by any chance?"
Provender blushed, flushed, blustered, was flustered. "No. I don't... We just... She..."
"Because she's talking to you a lot like a girlfriend would."
"We've been through a lot together, that's all."
"Well, whatever. But she has a point. I've been to Dashlands. I was there today. The place is a volcano, ready to erupt. Your dad is sitting like God on the eve of Judgement Day. Your mum is at her wits" end. War's brewing out there, and we all know why. You need to get in touch and defuse the situation. I'm amazed you haven't done already."
"There've been other... Oh, all right. Have it your way. The theatre manager's office. There'll be a phone there, right?"
"I imagine so."
Provender strode offstage; Is, though not invited to, went with him; and Arthur was left alone, in the full glare of the house and stage lights. Like someone waking from a dream, he blinked, remembering himself—what he was, where he was. Out there in the auditorium was an audience. A small one, to be sure, and made up entirely of people he knew, fellow-thespians, but an audience all the same, and he could see them, they weren't lost in amorphous darkness beyond footlight dazzle, they were visible, each and every one, scattered among the raked, red-velvet tiers of seats, faces upturned and expectant, ready for the dénouement.
He could think of only one thing to say:
I cannot live to hear the news from England,
But I do prophesy th" election lights
On Fortinbras, he has my dying voice.
So tell him, with th" occurrents more and less
Which have solicited—the rest is silence.
His voice cracked in the middle of the final line, as rehearsed, as it should. Then he flopped forward from the waist in a classic curtain-call bow, arms limp, head down, and the thirty-odd occupants of the auditorium set up such a tumult of clapping and cheering you would have thought them a full house. The applause echoed to the theatre's gilded ceiling, and Arthur remembered, as he always did when he heard this sound, why he loved his job.
**62**
MOORE WAS JUST replacing the phone receiver when the theatre manager ushered Provender and Is in.
"Police are on their way," he said, stepping back from the desk. "I took the liberty of dropping the Gleed name, just to speed things along."
Provender seated himself at the desk, and Is took up position at his elbow. He twisted round in the chair, frowning up at her. "I'm going to do it, all right? You don't have to stand guard over me."
Is, relenting, moved one pace back.
Provender _tsk_ ed, picked up the receiver, and dialled the main private number for Dashlands House. As he listened to the ring tone, he surveyed the manager's office: a small room painted tobacco-brown, with framed posters, playbills and review cuttings on the walls and a pair of ungenerously-proportioned windows whose panes were browned with decades of London air-grime. The manager himself was hovering in the doorway, uncertain whether he should stay or leave. Provender invited him in with an inclusive gesture.
Then there was a click on the line and a deep, threnodic bass-baritone voice said, "Dashlands House."
"Carver? It's me."
"Master Provender."
"Yes."
"Master Provender, what a relief. How good to hear you. Where are you? How are you?"
"I'm as well as can be expected, and I'm at the Shortborn Theatre on New Aldwych, of all places."
"May I enquire how you came to be there?"
"Long story. Another time."
"But you're not being held hostage."
"Not any longer."
"That's news indeed. You're safe. Out of danger."
"Completely."
"I shall alert the household."
"Do that. My father specifically. Tell him the Kuczinskis aren't to blame. They've had nothing to do with this. Tell him to call off the dogs. I'm OK, everything's OK, let's not have a war. Is that clear?"
"Uncontestably."
"I'm heading home right now. Should be there in an hour or so if the trams behave."
"Your arrival will be eagerly awaited."
"And Carver? That detective you hired to find me. Excellent choice. He did some brilliant work."
"He found you? I am most impressed."
"I'll tell him you said that. It'll make his day."
Provender replaced the receiver and looked at Is, then Moore. "Right, who's coming back to my place with me?"
Is looked doubtful, Moore flabbergasted.
"My Family'll be breaking out the champagne. I really think we all deserve a celebration. And it is still, officially, my birthday. More than one good excuse for a party, wouldn't you say?"
Is shook her head, while Moore was too astonished to do what he wanted, which was nod.
"Oh go on, Is. What harm will it do? Please?"
"We should stay till the police get here," Is said. "Someone should."
"What for? It's open-and-shut. There's the bad guy lying on the floor, dead to the world. We've got eyewitnesses galore who'll say that he attacked me. And you can bet, with Mr Moore having mentioned my name to the cops, there'll be reporters and photographers on their way here too. This'll go berserk, and I'd rather not be around when it does. Look, soon as I get home I'll send Carver back here to deal with everything. In the meantime, I'm sure our friend"—he indicated the theatre manager—"can handle the situation."
The theatre manager professed himself only too happy to do so.
"There we are," Provender said. "I need to get back to Dashlands. I need to see everyone. I've had three days of hell and I just want to go home, and I want you two to come with me. What do you say?"
If he had spoken an ounce more commandingly, a smidgeon less imploringly, Is would have dug her heels in and refused. As it was, he gauged his appeal just right. To judge by her expression she had reservations but, with effort, she managed to set them aside. "OK," she said.
As for Moore, what else could he do but splutter out _yes_?
**63**
AND SO ROMEO Moore, Anagrammatic Detective, wound up aboard a Family tram, sipping at a nip of Family brandy, on the afternoon of a day which without question was the most remarkable of his life.
They took the taxi to the tram stop, Moore tipped the driver, and soon they were trundling westward in a tram and Moore was urging himself to take this all in, remember it, savour it, record every detail in his memory because surely nothing like this would ever happen to him again. Dashlands! He was going to Dashlands House, for heaven's sake!
If there was a fleck on the lens of this moment, a wart besmirching its beauty, it was that Milner wasn't there to share it with him. Now that the case was solved, Moore felt somewhat guilty that he had won their bet and Milner hadn't. Milner did not like losing and would like it even less because the bet had been his idea. It would have been nice, too, for Milner to be here with him right now so that Moore could be magnanimous in victory. If the roles were reversed, Moore had no doubt his partner would have crowed and preened and taken every opportunity to rub his nose in his defeat. This would have been Moore's chance to set an example, show how a winner ought to behave: with dignity and quiet satisfaction. Well, that would come later.
Or would it? Within Moore there was a nagging, wormy sense of concern that would not go away. Where _was_ Milner anyway? Having contacted the police from the theatre manager's office, Moore had then phoned work to see if his partner was there. This was the call he had been finishing when Provender, Is and the theatre manager walked in. No one had picked up, so he could only assume his partner was still out in the field pursuing his investigations. Which was all well and fine, but Moore now knew, from things gleaned over the past hour, all about Damien Scrase, the knife-wielding thug who had held Provender captive in Needle Grove and who would have killed him at the theatre if not for Is's timely intervention with the syringe full of sedative; and the unsettling thought that hunkered at the back of his mind was that Milner might have encountered the selfsame individual in the course of his enquiries and fallen foul of him. Nothing anyone had said had given Moore cause to believe his supposition had any grounding in fact, but the anxiety nonetheless remained. Had Milner gone to Needle Grove? If only he hadn't been so cagey and had revealed _something_ about his line of approach to the case. Then Moore would have genuine reason to be fretful, or alternatively no reason at all, either of which would have been better than the nameless, nebulous unease he was feeling.
Thus, Moore's joy was not entirely unalloyed. It was sufficient, still, to fill him with a warm glow inside, which he nurtured and stoked with the brandy. As the tram raced on he thought of the money that would now, thanks to him, be coming the detective agency's way, and soon he was daydreaming again about the secretary he and Milner were going to employ. She would have to love words, of course. In fact she would, perforce, require a vocabulary far more extensive than most people's if she was going to cope with _their_ paperwork. She would be pretty, presentable, demure, with nice legs—Moore liked a well-turned lady's leg as much as he liked a well-turned phrase—and with, perhaps, a soft spot for a softly-spoken man who would happily compose flattering anagrams of her name, pen pangrams for her filled with bouquet-bursts of consonants such as _waltz_ and _nymph_ , offer her acrostics that capitally expressed his liking of verbal engagement and his laudably orderly esteem for her...
...AND WHILE AT one end of the tram car a quiet, reflective Moore entertained this fantasy of the future, at the other end Provender and Is found themselves all too uncomfortably in the present moment, neither talking when both felt they ought to. The tram was almost at Heathrow before one of them spoke, and then it was only Provender saying, banally, "I'm starving. I just realised. When we get to Dashlands, first thing I'm going to do is get someone to rustle me up a huge sandwich. Roast beef with pickle and horseradish. How about you? Sound good?"
Is nodded noncommittally. "It's a nice world where you can say the word sandwich and a moment later one appears."
"It's not the only world, I realise that, Is. God, I realise that more than ever now."
"Doesn't it worry you?"
"Does what worry me? The unfairness of life? You know the answer to that."
"No, does it worry you that there's still a snake in this paradise of yours? That somebody in your household wanted you gone for some reason?"
Provender thought about it. "Right now, no. Right now simply getting back there is all I'm concerned about. The rest I'll take care of in due course. Whoever it is will become clear pretty quickly, I reckon. I'm keen to know why they did it, what they've got against me, and when the time's right I'll find out and I'll respond accordingly. There will be payback. There will be. I just don't know at the moment what form it'll take. What I do know is that I'm not going to be intimidated. I feel, now, that I can face anything. I feel that there's nothing so bad it can't be tackled head-on. Rather like I tackled Damien."
Is laughed. "After I'd pumped him full of sedative."
"Well, yeah, but when he turned on you and attacked you..."
"Full of sedative. With about five seconds of consciousness left in him."
"But he still attacked you, and I barrelled into him and he went down..."
Is understood what he was after from her and, feeling generous, gave it to him. "Thank you, Provender. And thank you, too, for when we were on the balcony and you got me to make the jump. And for when we were surrounded by the Changelings and you got us out of there."
He was pleased. "It was nothing. Thank _you_ for all you did for me."
There was a brief, genial lull, then Is said, "And now you're taking me to meet the Family."
She tried not to chuckle at the way he squirmed in his seat. "It's not like that."
"Of course not. Anyway, I've met them already, haven't I?"
"Yes. You have. But not properly." He added, as if as an afterthought, "I think you and my mother will get on."
There was no easy response to that, and Is pretended something out there in the passing countryside had distracted her, permitting her to turn away from him. It so happened that the only eye-catching thing on view was a pair of swans who were afloat on a pond by the trackside, nuzzling bills and forming a heart shape with their necks. Drat nature! Where was a gloomy omen when you needed one? Is stared at the birds anyway, and sniffed, as if unimpressed.
From then onward till arrival at Dashlands the awkward silence was back between her and Provender and neither of them could figure out a way of breaking it again, least of all Is, who sensed, with heart-sinking certainty, that at some point later today Provender was going to say something to her she didn't want to hear and she was going to have to say something back that _he_ didn't want to hear. And Provender, she felt, sensed this too.
**64**
ONE OF THE kitchen staff had to show Cynthia where the coffee beans were stored and how the grinder worked. The staff member, a sous-chef, offered to make the coffee for her but she would have none of it. "I really ought to be able to do this sort of thing for myself," she said with an airy laugh, sounding just as a doyenne of Dashlands should, ashamed by but not apologising for her lack of practicality. "I've never fixed coffee for my husband before. It strikes me it's about time I learned."
The sous-chef looked on as she ground the beans, boiled the water, filled the cafétière, found cups and saucers and a milk jug and a sugar bowl and spoons, all with a halting determination, a keenness to get the procedure exactly right first time, and he didn't know whether to feel admiration or pity, but settled on admiration, for who could not, in the end, admire Cynthia Gleed?
She carried the tray with the coffee on it through the house, a six-minute journey that took her past Triumph. In the statue's shadow she paused, glanced about to make sure she was unobserved, set the tray down, and swiftly and deftly introduced Oneirodam pills into one of the cups. She tapped out a dozen of them all told, then returned the small brown bottle to her pocket and resumed walking. The pills were so tiny they didn't cover even half of the cup's bottom. They were potent, though. One alone was enough to ensure a deep night's sleep.
Entering the television room, she laid the tray on a teak chiffonier which was out of Prosper's direct line of sight and high enough that, as long as he remained seated, he could not see into the cups. She then turned to the Phone and told him to leave the room; she wished some privacy with her husband. As the Phone exited, Cynthia heard the far-off trilling of another phone, one of the house's standard landlines. Someone would get it, Carver most likely. It didn't matter. What was important now? Nothing. Nothing except what she was about to do.
She poured out the coffee, making sure she knew which cup was which. It was simple: Prosper took his white with sugar, she took hers black. She stirred the one with the pills thoroughly until she was sure they had dissolved. Would the taste of the Oneirodam be detectable? She thought not. She had made the coffee strong, and, from experience, the pills had only the merest flavour, a faint acrid tang which you were aware of, if at all, after rather than while swallowing them. They would slip down unnoticed.
She brought the two coffees over to the sofa, handed Prosper his, then sat down in an armchair cater-corner to her husband. She reached for the cabinet into which was set the control panel that operated everything in the room—curtains, lights, television—and rotated the TV volume dial down to zero. In silence, she waited for Prosper to look round at her. Eventually he did.
"What?" he demanded. He looked haggard, irritable, old, uncharming.
"Do you love me?" she asked.
"That's an extraordinary question."
"Well?"
"Yes. Of course. What do you think?"
"I still mean something to you, even after all this time, even after all your... strayings."
"Is that another question?"
"It is."
"Same answer. Of course. You're my wife. It would be ridiculous if you didn't mean something to me."
"You're sure about that?"
He stared at her levelly, sincerely, and said, "I'm sure."
Cynthia believed him. The eyes did not lie. Whatever feelings Prosper had for other women, they were fleeting, whereas what he felt for her was a constant in his life, a guy-rope which kept him tethered and which he could always count on. It was love. It wasn't passionate love, or lustful love, but a well-aged, weathered emotion he was so accustomed to and comfortable with he barely realised it was there any more. She had reminded him of it now. In the midst of all these tribulations, he knew once again where his heart and hope and health lay. His expression became almost fond. Years eased from his face.
"What's this about, Cynthia?"
"Nothing. I just wanted to hear it from you. Drink your coffee."
"It's the strain, isn't it? I thought you'd stopped feeling it but I was wrong. Oh Lord, Cynthia, I love you, my daughters, my son, the whole of my Family. I may not show it as readily as you, but I do. You have to trust me on that. All the time, beneath it all, it's you. You I care about." He was bordering on tears. Cynthia could not recall when she had last seen him that way. "You want confirmation of it? Here it is. I'm saying so now. It's you."
"Thank you, Prosper. Drink up."
"Silly creature," he said affectionately.
"It'll get cold."
Prosper, smiling lifted the cup to his lips and took a sip. Cynthia, mirroring him, sipped too.
**PART VI**
**65**
IS WAS ON edge from the moment she stepped off the tram. Returning to Dashlands was in effect revisiting the scene of the crime, and although she was confident there would be no reprisals from the Gleeds, she suspected they would not take to her. Provender had assured her he would tout her as a heroine, the woman he owed his life to, but his life would never have been endangered in the first place had he not been kidnapped, and she had played a part in that, and his Family would learn that fact soon enough, and why would they not resent her then? All she had done for him after the kidnapping did not, in her mind, atone for the original offence.
That she cared at all what the Gleeds thought of her struck her as odd. She intended to stay at Dashlands for, what, a couple of hours? Enough time to join in the celebrations, drink a bit of the promised champagne, keep Provender company as he had asked—then she would demand a ride home. If she had to call a cab to come and take her back to London, so be it. Hang the expense. She didn't think she could cope with more than a couple of hours at the house, and setting herself a time limit was a sensible tactic. If things got uncomfortable for her, all she had to do was count the minutes till she could leave. The Gleeds could hate her if they wanted—they were welcome to—but they had only a fixed period in which to do so. Two hours, then she was gone.
The tram stop at Dashlands was roughly a mile from the house and set in a wooded glade where leaf shadows rippled and birdsong blared. As the tram car rolled away, Provender inhaled a deep, bracing breath—the sweet, sweet air of home—then struck off along an asphalted road that curved through a trunk-ribbed tunnel of deciduous forest. Is and Moore, of course, had no choice but to follow, and soon all three of them were out in the open, in the simmering flare of a summer afternoon, passing through the bowl of a shallow valley with parkland rising on either side: swathes of grass just starting to turn sere, dotted with oaks and chestnuts of venerable ancientness. Other than the drowse of insects, there was nothing but silence in the air. Moore encapsulated in two words what both he and Is, and perhaps Provender too, were feeling:
"Another world."
"It is, isn't it," she said.
"May I ask you something?"
"Go ahead."
"Your full name."
"Isis. Why?"
"And surname."
"Necker."
Provender glanced over his shoulder. "I didn't know that."
"Why should you? I never told you."
"Isis Necker," Provender said, trying it out.
"ISIS NECKER," said Moore, and hummed. "Oh yes."
"Oh yes what?"
"Well, as you know, I anagrammatise. It's what I do. The truth of a person is encoded in their name. And yours came out as..."
"Oh God, I dread to think."
"...NICE KISSER."
"That's it? That's my truth?"
"If we take 'kisser' in the American slang sense of 'face', I would say yes, unquestionably."
"Thanks. I think."
"Not pleased?"
"I suppose I was hoping for something a bit more spectacular."
"Well, give me time, I might be able to come up with another."
"If you ask me, it's spot-on," said Provender. "And maybe you're a nice kisser in another sense, who knows?" He had one eyebrow raised. His gaze was hopeful.
"What about Provender?" Is said, laughing in order that her changing of the subject would not seem quite so obvious.
"Ah, Provender is a man of many anagrams," said Moore. "Believe me, my partner and I deciphered dozens. The one that hit me hardest was, in fact, the one I can least explain. I took his full name, including middle name, which is—"
"Stop right there," said Provender, groaning. "Don't. It's too embarrassing."
"Go on," said Is.
"I beg you, please."
"It's not as if it's a state secret, Provender. I could easily look it up in Burke's Family Almanac."
"Mr Moore, I will give you anything you ask, anything at all, just do not tell her."
They were all laughing now, and Provender kept cajoling, offering Moore wilder and wilder bribes in return for his silence, and Is matched him by threatening Moore in increasingly elaborate ways, bidding against Provender's wealth with promises of violence, until the Anagrammatic Detective eventually blurted out "Oregano", saying that he feared permanent physical disfigurement far more than he craved material goods, and Is began hooting hysterically and repeating the word Oregano over and over, and nothing Provender could say, no amount of feigned stroppiness, could get her to stop.
This happy scene was brought to a halt by the arrival of a three-strong welcoming committee from the house. Gratitude, Extravagance and Uncle Fortune appeared on the road, and no sooner did the two sisters catch sight of their brother than they broke into a run and fell on him in a flurry of shrieks and hugs and kisses. Extravagance gripped him so hard he had to push her arms off him in order to draw breath. When Fortune caught up, he too embraced Provender, then leaned back to examine him from top to toe.
"Intact. A bit rough around the edges but otherwise good as new."
"I've been lucky," Provender said. He submitted to another gratefully extravagant, extravagantly grateful display of affection from his sisters, then made introductions.
Is felt the weight of the Gleed sisters" gazes on her and saw the wary calculation in their eyes. Women always assessed one another on first meeting, but usually from a position of equality. There was no equality here. Gratitude and Extravagance scrutinised her from a viewpoint of implicit superiority, and saw that her clothes were inexpensive, her hair was simply and cheaply styled, her figure was not as diet-gaunt as theirs, and her looks and attitude nowhere near as refined as theirs. She refused to give them the satisfaction of looking cowed, though that was how she felt. She held her head high and, even when they frowned at her bruised cheek and puffy eye, didn't allow that to make her self-conscious. _You're no better than me_. She radiated nonchalance until, in the end, the sisters had their fill of looking and turned away. Possibly they had come to the conclusion that she was haughty, even impertinent. Is was not bothered. Let them think what they liked.
"Where's Mum?" Provender asked.
"Somewhere," said Gratitude. "Carver found us three first to tell us you were on your way home. He said he was going to look for Mum and for Dad. I bet they're not far behind us."
"Now then, nephew," said Fortune, "I think you should tell us all about where you've been and what happened to you."
"Can it wait till we get back to the house? I'm sorry but I haven't eaten since this morning and I'm..."
Provender's voice trailed off as he spied a figure hurrying along the road towards them. It was Carver, moving at a brisk jog-trot, fast as he could go, which was considerably faster than you would think likely for a man his age. In long, loping strides he reached the group, then braced his hands on his knees while he got his wind back. Finally, raising his head, he gasped, "Quick. You must. Come quick. The house. Something's wrong. Mrs Gleed."
**66**
IN THE TELEVISION room, by the bright flicker of images of impending war, Prosper Gleed was in anguish. Medics were on their way. Carver had summoned them by using the emergency hotline in Great's apartment. But how long would they take? How soon could they get here? Soon enough?
He blamed himself. He should have noticed. His attention had been elsewhere. Cynthia had gone quiet and he thought she had simply drifted off to sleep. He had been sitting there, TV-absorbed, not realising—not even having an inkling—that something was wrong with his wife, until Carver walked in. Carver, clearing his throat, had been about to make an announcement of some sort, but one look at Cynthia and that was that. He had hurried over to her, felt for a pulse, tapped her cheek, asked how long she had been like this, then run off to the Granny Flat. Prosper had been alone with her ever since, alternately kneeling beside her and pacing the floor in circles. Her face was terrifyingly pale. When he touched her skin, she was cold. Her breaths were so shallow as to be all but imperceptible. To the casual observer she might have appeared to be asleep, but no one sleeping was quite so slumped, so slack-limbed, so motionless. Like a becalmed yacht, sails drooping, inert. How could he not have realised? It had happened right next to him, whatever it was. This silent, catastrophic collapse. Stroke? Heart failure? He had no idea. How could he have been so idiotically oblivious? His wife, slowly dying beside him! What kind of heedless moron was he?
And where the hell were those medics?
A commotion outside in the corridor brought Prosper's head snapping round and surge of hope to his heart. Here they were. At last.
But it wasn't a team of white-garbed ambulancemen who entered the television room. It was...
"Mum!"
Prosper's jaw dropped as first Provender, then a girl he faintly recognised, then Gratitude, burst in through the door. They were followed by a couple of other people but Prosper was too shocked at the sight of his son to register them. He stammered out Provender's name, but Provender scarcely spared him a glance. He rushed over to his mother with an awful keening wail. The girl was close behind him, and no sooner had she reached Cynthia's side than she began examining her, rather as Carver had but much more methodically. First the neck, two fingers pressed to it. Then lifting one eyelid, checking the eye, doing the same with the other one. Back of the hand to the forehead. The whole procedure was brisk and deft and unhesitating, and Prosper could not understand why he recognised her, but by God, what did it matter? She clearly had medical training. She knew what she was about.
"Poisoning of some kind," the girl said.
"Poisoning?" said Provender. "No. God, surely not."
"Were you here when it happened? Mr Gleed?"
Prosper realised he was being spoken to. "No. Yes. I mean, I was but I didn't see. She came in with coffee and we..."
"Coffee." The girl looked around and saw the tray, the cafétière, the drained cups. She snatched up one of the cups, then the other. Something about the dregs in the second cup caused her to frown, then nod. "OK. Provender, give me a hand. We're going to lift her and lay her out on the floor. Come on, move!"
When Cynthia was supine on the floor, the girl knelt, slipped Cynthia's nearside hand under one hip and began to pull her over. Cynthia was on her side when her body was wracked by a sudden convulsion. Dark vomit spurted from her mouth onto the girl's lap. The girl, without missing a beat, rolled her fully over while the vomit continued to pour. Someone, Gratitude probably, let out a piteous moan.
"No, it's good," the girl said to nobody and everybody. "Getting it out of her system."
When the vomiting had run its course, she inserted a forefinger into Cynthia's mouth and wiped around inside, clearing out blobs of regurgitated matter. She began arranging Cynthia's limbs into the full Recovery Position, then halted. Something was not right. Swiftly she pushed Cynthia onto her back again.
"Not breathing," she said.
Provender, kneeling the other side of his mother's body, gaped at the girl. "What did you say?"
"I said she's stopped breathing. We're going to have to resuscitate."
"We?"
"Yes, we. Works best if there's two of us." She tilted Cynthia's head back, then placed both hands on her breastbone, ready to start compression. "Put your mouth over hers and pinch her nose. When I tell you to blow, blow."
"But she just—"
"Your mother, Provender. Do it!"
Provender winced. "I can't."
"Yes you bloody well can. It's only puke. It won't kill you."
"I'll do the chest pumping thing."
"You have to know how. Do you?"
He shook his head.
"Then you're on Kiss of Life. Quickly!"
Provender lowered his head and, with a brief creasing of face, brought his lips to his mother's.
The girl bore down on Cynthia's chest five times, then said, "Blow."
Provender blew.
Five times. "Blow."
He blew.
Five times. "Blow."
Blew.
Five. "Blow."
Blew.
Five. "Blow."
Blew.
EXACTLY EIGHT MINUTES later an ambulance skidded to a halt outside Dashlands House with a spray of driveway gravel. Carver was waiting to greet it and hurried the ambulancemen indoors and through the house to the television room. There, the ambulancemen found Cynthia Gleed sitting up on the floor, supported on one side by her son and on the other by a girl who informed them that she was a nurse and that Mrs Gleed had taken an overdose of an unknown sedative or tranquilliser. She had vomited and had had to be given CPR. Her breathing had normalised but she remained listless and unreactive.
The ambulancemen unfolded their stretcher, declaring that Mrs Gleed required immediate hospitalisation. They were overruled by her husband, who told them point-blank that it was out of the question. Family did not go to hospital. Hospital, if anything, came to Family.
The ambulancemen objected but Prosper Gleed was adamant, and so in the end they had no choice. They stretchered the patient up to the master bedroom. Items of medical equipment were commandeered from the Granny Flat, most importantly Great's emergency oxygen cylinder and mask. Further equipment was brought over from Reading General, along with a couple of doctors. Cynthia Gleed was made comfortable, put on a saline drip, and hooked up to an ECG monitor, and the doctors then began giving her a blood transfusion using plasma from the exclusive, Family-donated blood reservoir which was kept at the hospital. Her condition was officially designated serious but stable. The next hour was, the Family were told, crucial. If she survived the next hour, then the prognosis was good. During that time it would also be possible to begin to establish whether any lasting damage had been done to her system. There was a possibility that organs such as the liver and kidneys could suffer failure as a result of the overdose. If that happened, the doctors said, she was going to hospital whether Prosper Gleed liked it or not.
A bedside vigil commenced. Prosper and his daughters kept watch over Cynthia, taking it in turns to hold her hand and trying not to get in the doctors" way. Fort, meanwhile, constantly harassed the medical professionals in order to make sure his sister-in-law was getting the very best attention and care. It was unlikely that the doctors would be neglectful when it came to looking after a critically ill Gleed, but Fort, at least, felt better for chasing them around. As for Provender, he wafted in and out of the room, never staying for long. He couldn't bear to see his mother lying there so weak and pallid, but more than that, he couldn't stand to be in the presence of his father, who he knew was the reason his mother had taken the overdose. It was obvious she had set out to prove a point to him, to shock him out of his belligerent stance against the Kuczinskis. In that respect she had succeeded, but if she were to die now... She was still enough of a Roman Catholic to believe that suicide was a mortal sin. If she were to die now, she had damned herself. For her husband's sake she was risking eternal hellfire. The disgust Provender felt for his father then meant he could barely look at the man. His sole consolation was that, to judge by his father's distraught manner, Prosper Gleed loathed himself almost as much.
It was while Cynthia Gleed hovered between life and death, surrounded by her Family, that the first shots were fired in what looked like becoming the Third European War.
**67**
NEITHER SIDE, IN hindsight, could say with any accuracy who started it. Arguably, neither side did. What had been simmering all day finally reached boiling point and seethed over into conflict. It was, in that sense, spontaneous, an inevitable outcome that the politicians couldn't have prevented even if they had tried. At a certain stage, events took over. The build-up to war, which had been achieved so speedily, just kept accelerating until it started helter-skeltering out of control. Men were involved—from nervous footsoldiers in the theatre of combat to calculating field marshals and rear admirals in their strategy rooms—and men could make mistakes, and did; but really war itself was to blame. War, one might say, was an organism. Once conceived, given a glimmering of existence, like any organism it wanted to survive, and thrive, and be strong, and spawn, and proliferate. Offered a chance to live, it took it.
Initial contact occurred in the Bohemian Forest, that section of the German/Czechoslovakian border where the dividing line was blurred, one country shading coniferously into the other. There, an advance detachment of Western Alliance troops encountered an advance detachment of Pan-Slavic Federation troops. Encountered? Stumbled upon would be closer to the truth, for the Federals were in a clearing, sitting on cushions of heaped pine needles, brewing themselves tea, and were as startled as the Allies were to find themselves all at once face-to-face with the enemy. There was a limited exchange of fire, before both detachments beat a retreat and radioed news of the skirmish to headquarters.
War twitched and stirred.
At approximately the same time, out in the Baltic there was a brief naval engagement, when a Swedish frigate dropped depth charges on a Federation submarine, or what it thought was a Federation submarine. Sonar had picked up a large moving object which could just as easily have been a grey whale, but the captain of the frigate was new to his command, lacking in experience and also in caution. Better to attack the thing, he felt, just to be on the safe side. If it was a submarine, then he would have done well in defending his ship against possible torpedo attack. If a whale—well, what was one less cetacean in the world? The depth charging proved nothing conclusively either way. The moving object went into a steep dive, hastening out of detection range. The captain dutifully reported in to his base at Karlskrona, ship-shaped models were shunted around on a table map of Europe, and support vessels were despatched to his location.
War flicked open its eyes and drew breath.
In the skies above north-eastern Germany, over the canal-fretted lowlands of Uckermark, a feinting sortie by six Luftwaffe fighters ended in disaster. Instrument failure in the group captain's aircraft, or possibly a misinterpretation of the dial readings, resulted in him leading his wingmen over the border into Polish airspace. By the time anyone realised the error, it was too late—a larger group of Polish fighters was zeroing in on them, guns blazing. The dogfight was nasty, brutish and short. One and one alone of the Luftwaffe pilots escaped, limping back across the border with his engine smoking and his tail rudder shot to pieces. He had to bail out over the Oder river, but alas his parachute failed and he hit the ground simultaneously with his plane and only slightly less explosively. The Polish pilots returned to base triumphant, and word flashed to Warsaw. An incursion. Roundly repulsed, but an incursion nonetheless.
War flexed its limbs and started to rise.
And so the news began zinging along the wires, journalists speaking, looking and sounding properly anxious, electronic footage and phoned-in reportage whirling through the ether to transmitters, to receivers, being pumped out again by the TV and radio stations, finding its way down aerials into homes and workplaces, the truth, the knowledge, the information, unfurling with deadly earnest now in million upon million of living rooms and office rec rooms, crisis becoming event, potential becoming fact, and nothing, it seemed, could halt the process, nothing could kill the nascent beast that was crawling out of the belly of the continent to spread carnage everywhere.
**68**
THE NAME OF the Gleeds' Phone, for he did have one, was Neville Quigley.
As a rule, Quigley enjoyed his job. It was an important job, perhaps the most important in the entire household. It had a cachet which elevated Quigley above the other domestic staff. He didn't flaunt that, he never put on airs and graces, but he knew it and they knew it: at Dashlands, Phone outranked butler, cook, housemaid, chauffeur... everyone except Carver. Phone sat in on Family meetings other staff members were excluded from. Phone was privy to Family secrets other staff members could only guess at. Sometimes Quigley wondered if he was, in fact, even more essential to the running of the Gleeds" daily lives than Carver. But no, that was not possible. It was madness even to think it.
To be a Phone demanded a knack for remembering numbers, a tolerance for standing still for long stretches of time, and discretion. Discretion was the real watchword. As a Phone you listened in on intimate, inter-Familial conversations. Admittedly you only got one side of them, but that was enough. The revelations Quigley had overheard, the details he had eavesdropped on... He could tell you a story or two. Only he wouldn't.
Some Families employed deaf-mutes as Phones for just that reason. What couldn't be heard or repeated remained safely within the Families. However, there were problems with the use of deaf-mutes, mainly the difficulty of summoning them when required and communicating your wishes to them, but also the fact that they couldn't necessarily detect when there was an incoming call, although that had been remedied by fitting their backpacks with a vibrating buzzer or even, unpopularly, with a node that emitted a mild electric jolt. A hearing-unimpaired Phone was better on all fronts, on condition that he was not a blabbermouth.
Quigley was not. Nor was he one to interfere in Family affairs. Ever. That was simply not his place. While he had his backpack on he was a Phone, a living implement, a technical device with legs on. He hung in the background till asked for. He did not speak unless spoken to and never spoke while his employers were speaking _into_ him. He did nothing, when on duty, that a machine would not do. Often, indeed, during interminable periods of inactivity, Quigley fantasised that he actually was a machine, a telephone who dreamed he was a man. Circuits for veins, electricity for blood. It passed the time.
This afternoon, in the wake of the dreadful incident in the television room, Quigley was in a quandary. Prosper Gleed, being occupied with other matters, had not dismissed him from duty, but neither was there any call for a Phone to be loitering around upstairs, near his master, while Mrs Gleed lay in her sickbed. Quigley couldn't intrude on the Family's distress, not unless a call came in and perhaps not even then.
What he did was re-enter the television room and resume his position in the corner. It was sensible to be in the last place Mr Gleed had seen him, in case Mr Gleed should come looking for him.
As he stood there, however, watching the TV, he realised that the game of brinkmanship Prosper Gleed was playing with the Kuczinskis was edging out of control. Even with the sound down, it was clear that war was breaking out. Provender was back at Dashlands, which meant his father ought to have contacted the Kuczinskis and defused the situation. He had not done so, of course, and it appeared that Quigley was the only person in the house who had any idea what was happening out there in the rest of the world. The Family was worried about Mrs Gleed's wellbeing, and rightly so, but at the same time there was an equally if not more pressing emergency they should be concerned about.
What to do? Quigley was in two minds. On the one hand, someone in the Family must be informed that conflict had begun. On the other hand, it couldn't be him—he was only a Phone.
The solution was to find Carver, and Quigley set out from the television room with a view to doing just that. Carver was the interface between Family and staff. Carver would be able to decide if and how to carry the news to Prosper Gleed.
Not knowing where Carver was in the building, Quigley began his search in the vicinity of the master bedroom, reasoning that the Gleeds" major domo was likely to want to be close at hand for the Family. In the event, Carver was not there, but Quigley did come across Provender instead, who was in a corridor, morosely tracing with one finger the dimples in the glass bricks which were inset into a section of the wall.
Quigley wavered, then made a decision which, had the circumstances not been so exceptional, he would have otherwise balked at.
"Sir?"
Provender either did not hear or refused to acknowledge that he was being addressed.
Undeterred, Quigley said, "Sir?", more loudly this time, and added, "Master Provender?"
"What?" said Provender. "What do you want?"
Quigley quickly explained.
"If," he said, by way of conclusion, "you could somehow convey to your father the need for—"
"Dial," said Provender.
Quigley gaped.
"Dial the Kuczinskis."
"Master Provender, I can't do that. You know I can't. A Phone is for the exclusive use of the head of the Family."
"The head of the Family is indisposed. The head of the Family can't come to the Phone right now. I'm the _de facto_ head of the Family. Dial."
"It's simply not—"
Provender grabbed Quigley by the shoulders, swung him round and snatched the handset off his back.
"Dial," he said, with such firmness and finality that Quigley knew he had no alternative.
He flipped open the central section of his chestplate so that the rotary dial was exposed.
_This isn't my fault_ , he thought. _I can't be held accountable. I'm just a machine_.
A machine, however, would not have got itself into such a dilemma in the first place. Nor would a machine's index finger have trembled as it began spooling in the digits of the Kuczinskis" Phone number.
**69**
" _S ŁUCHAM_. STANISLAW KUCZINSKI."
"Mr Kuczinski, this is Provender Gleed."
"Excuse me? There must be some interference on the line. I could have sworn you just said _Provender_ Gleed."
"I did."
"I see. Yes, that would account, I suppose, for the Mr before my name. But your father, then... Has something unfortunate occurred?"
"It has, but not what you're thinking." Hoping for, if Kuczinski's tone was anything to go by. "Listen, Mr Kuczinski, I won't fanny about. We need to—"
"What is this 'fanny about'? I don't know this phrase."
"I won't waste time. We need to stop this thing immediately, while we can, before it gets any worse."
"You're referring to..."
"You know what I'm referring to."
"Provender, I'm not sure it can be stopped, not now. But look on the bright side. We all stand to make a bit of profit out of it."
"People will get killed, Mr Kuczinski. You or I could get killed."
"I doubt it. You live in the countryside. My castle has a bunker. A Family would never survive without a heightened sense of self-preservation, and that certainly is true of yours and mine. So sit back, Provender. Have fun. Enjoy the show. And may the best Family win. By the way, I may be wrong, but aren't you supposed to be my prisoner?"
"Yes, I know. Problem there. I'm trying to think of a good word for it. A misapprehension on my father's part."
"A misapprehension."
"He blundered, I'll admit it. Leapt to the wrong conclusion."
"And did so in the most insulting fashion. Do you know what he said to me and my sister?"
"I don't, I'm afraid."
"I'll tell you. He called us inbred. There were many other things he called us but that was far and away the worst. Inbred."
"I'm sorry that he did."
"You shouldn't be apologising to me. My sister was the one who truly took offence. Stasha has been cursing your father's name ever since."
"I'm sorry to her too, then."
"It would be better to hear it from your father than from you."
"That's not possible at the moment. My father has other things to attend to. A Family crisis."
"I see. You have assumed the duties of Family head, then."
"Evidently."
"Interesting. Does that, I wonder, give you the authority to speak for all of the Gleeds?"
"Under the circumstances, I'd say yes."
"Hmm. I'm curious to know what those circumstances are."
"Maybe another time. Let's stick to the matter at hand."
"Ah, still keen not to 'fanny about'. Well then, Provender Gleed, son of my great enemy, tell me why exactly I should back down now. Especially when, as the fact that we're having this conversation at all proves, I am not and never was your kidnapper. Why should I, the wronged party in all of this, be the one to surrender?"
"I'm not asking you to. I'm conceding defeat."
"Excuse me?"
"You win. You and my father were eye to eye. On his behalf, I'm saying he has blinked. You have successfully called his bluff. You are the victor."
"I can't believe I'm hearing this. Are you sure you're a Gleed? You aren't some hoaxer who has tapped into the Family Phone network?"
"I'm a Gleed through and through. Just not the same kind of Gleed as my dad."
"That would seem to be so. Undoubtedly you sound like him, your voice is just like his, though that is hardly surprising. But the words you're saying—they are completely different."
"My father is a proud man, Mr Kuczinski, and for all his faults he feels the weight of history heavily. The feud between the Gleeds and the Kuczinskis is important to him. He defines his Family role, I think, by it. It is—has been—his one main way of feeling that he's doing right by his Family. Whereas me? I'm not sure I care. I mean, the feud is so old. It's been going on so long. It hasn't got anyone anywhere and it's brought so much misery generally. If it were up to me, I'd say just forget it. It isn't up to me, of course, but if it were..."
"Something so longstanding, so ingrained, cannot simply be swept away at a wish."
"No, I agree. It's woven into our Families" lives. It can't be undone overnight."
"But your implication is that we could make a start."
"Possibly."
"At least try."
"Yes."
Kuczinski said nothing for a while, but the sound of relay chatter and crackling atmospherics on the line was the sound of thoughts turning over.
"I would expect some concessions," he said.
"What sort of concessions?"
"A gesture. A token of goodwill."
"Money?"
"I was thinking a factory, maybe, or some other business concern. That's all. It doesn't even have to be an important one. A paper mill, a shipping contract. I'm not fussy. Something simply handed over freely, of your own will. It would be a show of... what's the word? Earnest?"
"Earnest, yes."
"You would consider that?"
"I'm sure it could be arranged. I can't promise it because it would require my father's authorisation... but I could talk to him. Talk him into it. Is that really it? Is that all you want?"
"I would like a formal apology from your father, before a quorum of the Congress, but I realise I'm never going to get one."
Provender half chuckled. "You're right there. I can promise you almost anything but that."
"Then a business concern will have to do."
"You hear me when I say I can't guarantee it?"
"I do. But do you know what? Surprised though I am to say this, I trust you. I trust you to try."
"I appreciate that trust. Very much."
"And of course, if you fail, it wouldn't take much to put the wheels of war back into motion if I had to."
"I don't want that. You can tell from my voice how much I don't want that."
"Indeed I can. To be honest with you, I have had no stomach for this particular fight. My sister... Well, just be thankful she is not head of the Family, that's all I can say." Kuczinski chuckled. "Provender, it has been unusual and refreshing to talk with you like this. I feel strangely optimistic in my heart—and yes, I have one, whatever your father might have told you. I do not believe that the Gleeds and the Kuczinskis are going to settle all of their differences as of this moment, and anyway, what is wrong with a bit of healthy competition between Families? It adds savour to our lives. We might become dull and jaded otherwise. I do believe, however, that something has at last shifted. I could be wrong. I could be being foolish. Stasha will doubtless tell me that I am. But if what has happened today means that our Families are no longer butting heads quite so forcefully, that is surely a good thing. Perhaps, before long, you and I will be meeting in person?"
"You mean at the Congress table? My father's still got plenty of years left in him. I don't think I'm going to be Family head just yet."
"Perhaps so. Nevertheless, you might go along as his second in place of your uncle? You are of an age when, as firstborn son, you should."
"I don't know. It remains to be seen."
"Well, whatever. I should look forward to it, though, if it were to happen. And now I must go. Calls to make. Politicians to persuade. I think I shall even be speaking to your country's prime minister. I suspect, once he gets over the shock of hearing from a Kuczinski, he will prove as biddable as the rest of them are. It's wonderful, don't you think, how those in government, who give out orders so readily, are also so eager to take them?"
"It's... it has it uses," Provender conceded. "Mr Kuczinski, many thanks for this."
"Stanislaw, Provender. Please, I insist. Call me Stanislaw."
**70**
_D IPLOMATIC BREAKTHROUGH_.
Somehow, miraculously, within a couple of hours of the pendulum starting to swing towards war, all at once it lurched in the opposite direction. When all seemed lost, a resolution was found. Governments—impelled, it seemed, by the direness of Europe's predicament—redoubled their efforts, exhorted their ambassadors to try that bit harder, composed fresh formulae for peace, and even offered to stand down their forces unconditionally if that might convince the other side to do the same. One final, last-ditch round of negotiation seemed to produce a workable solution to the crisis. All of a sudden the grim high-ranking faces that had been a fixture of TV screens for the past few hours became relieved high-ranking faces. There was even, here and there, the odd hint of a smile.
Planes were recalled. Ships about-turned and cruised back to port. Soldiers decamped and marched back to base. City-Smashers vented hydrogen and commenced the long cumbersome descent to their hangars.
A continent sighed.
War, slain in infancy, died a swift and painless death.
**71**
_A MAN COULD get lost in a house this size_, thought Moore, before promptly doing just that.
It was late afternoon, edging into evening, and Moore wasn't sure if anyone even knew he was still there. He had been left behind in the rush of events, a piece of débris stranded after a dam-burst. Upstairs the Gleeds clustered and fussed around their stricken _materfamilias_. Even Is was up there, helping. Moore, however, was no use in such a situation; he had no pertinent skills to offer. All he could do was hang around downstairs and wait for developments, and the longer he did that, the more he started to feel he had outstayed his welcome. He was unwilling to slope off without saying goodbye, but increasingly, as time went on, that looked like being his only option. It was a disappointing outcome, a far cry from the hearty congratulation, the lavishment of praise, the acclaim he had been looking forward to. He understood entirely that Cynthia Gleed had to be the focus of the Family's attention for now, he was nothing compared to her in terms of importance... but still it would have been nice, wouldn't it, to have received just a little of the recognition he was due.
No, that was a selfish way to think, and Moore cursed himself for the lapse in empathy. If only there had been something he could do, some contribution he could make to ease the Gleeds" distress. But there wasn't.
Before departing, he decided to explore. After all, he remained a guest in the house until someone told him he wasn't, and that gave him the right to roam the premises, and when was he going to get an opportunity like this again? When was he next going to be an invited visitor to Dashlands, implicitly permitted the run of the house? Never, that was when. If someone asked him later to describe what Dashlands was like inside, he would be ashamed if he could tell them about a couple of rooms at most.
So he set off wandering, room to room, corridor to corridor, passing through lounge and library and hallway and gallery, pausing every so often when some _objet_ or unusually opulent specimen of décor caught his eye. He lingered for some time in a windowless, humidity-controlled chamber whose sole purpose was to display oil portraits of every head of the Family going all the way back to Rufus Gleed. It was like a snapshot of three centuries of history of art, from murky Old Master to lurid, broad-brush Modernism and all points in-between. The styles changed, the frames grew simpler, but the features of the subjects stayed consistent throughout. Really what Moore found himself surrounded by was a dozen-plus studies of a nose. Wherever he looked, whichever way he turned, the prominent Gleed proboscis poked out at him from the walls. It, rather than any of the pairs of eyes in the portraits, was what followed him around the room. None of the artists had attempted to flatter or disguise the nose. Rather, they celebrated it, and the room itself seemed a shrine to it, and to heredity, and longevity. A monument to the nose's size and staying power, and also the Family's.
Moving on, Moore encountered a pair of servants who were going around switching on lamps. He avoided their stares, which subtly challenged him to account for his presence in the house, and continued his stroll. It was shortly after this that he realised he had roamed so far, he no longer had any clear sense of where he had set out from and how to get back there. He was the inexpert swimmer who had carelessly floated out of sight of land. Immediately, he about-faced and headed back to the spot where he had come across the two servants, but they were gone. He followed the trail of lit lamps, which by rights should have led him to them but somehow didn't. It petered out, and he was left cleaving his way through labyrinthine gloom.
Further meandering brought a by now slightly fretful Moore into the wing of the house which contained the Granny Flat, although he of course did not know this. What he did know was that all at once he could hear a voice—a profoundly deep voice that he recognised as Carver's. It muttered only a few words, but this was sufficient to enable him to pinpoint where it was coming from. Within moments he was face to face with the Gleeds" major domo, and also with the fabled Great, whom Carver was pushing along in his wheelchair.
Moore could not believe how glad he was to see Carver. It was unclear whether the feeling was mutual, but Carver at least tried to soften his expression so that it looked marginally less unwelcoming than normal.
"Mr Moore," he said. "I assumed you left a long time ago."
"I planned to. I've sort of been trying to. It's just... This place is very hard to find your way around in, let alone out of."
The ring on Great's left hand rapped out a brief, agitated tattoo on the frame of the wheelchair. Great's moist blue eyes were fixed on Moore.
"You haven't met the senior member of the Family, have you," Carver said.
"I haven't had that pleasure."
Carver bent down, bringing his mouth near to Great's ear. "This, sir, is one of the gentlemen I told you about. One of the detectives whom I hired to locate Master Provender and who, it would appear, succeeded beyond my wildest dreams."
Moore nodded respectfully to Great. "An honour."
"The honour," Carver replied, "is all ours. Is that not so, sir?"
As if in response, Great's hand started tapping again.
"Great would, I'm sure, wish to extend his warmest thanks to you, Mr Moore. You have performed a remarkable service. Speaking for myself, I can scarcely express how gratified I am that I chose to employ you and your colleague. Where, by the way, is Mr Milner?"
"I'm not sure. Frankly, I wish I knew."
"Oh well. The glory is all yours. It does strike me as almost uncanny how you knew where to look for Master Provender."
"It was luck. Well, no, skill played a big part. The anagrams guided me to where I needed to be, even if the reason I was there wasn't the reason I _thought_ I was there. If that makes any sense. SHORTBORN THEATRE, which I anagrammatised as BROTHER SON THREAT, I see now didn't actually refer to Arthur Gleed, at least not directly. It referred to his role as Hamlet, Claudius's brother's son, the nephew who opposes his uncle and ultimately proves his undoing. Which, however, got me to Arthur's house, which in turn brought me to Provender, or should I say Provender to me, and then—"
A sudden sharp rap from Great's signet ring shut him up as effectively as any words would have. Moore had to believe the timing was coincidental. He knew Great had no control over the only part of him that moved. All the same, it was hard not to feel he had been commanded to silence, and the balefulness of Great's gaze did nothing to vitiate that impression.
"Yes, yes," said Carver, "your methodology, most intriguing. But perhaps you can tell us about it some other time, when there are less pressing matters weighing on all our minds."
"Of course. I'm sorry."
"No need to be. I just happen to be conveying Great to pay a visit to Mrs Gleed. Come with us and I will direct you to a room where you can wait until such time as I can arrange transportation for you back to London. That young lady who was with you and Master Provender—I trust she would wish to return home too?"
"I have no idea. I expect so."
"Very good. This way, then."
They walked, the three of them, or rather one of them walked while one of them walked-and-pushed and one of them was pushed, and Moore was in a subdued mood, thinking again about how this hadn't turned out as he had hoped. Carver, for all that he had said complimentary things about Moore's work, didn't seem unduly impressed or full of admiration. That might simply be down to the way he was—Moore thought it would take a lot to impress Carver—but equally there was an inescapable sense that he was annoyed somehow.
Or was that just Moore's insecurity? His heightened sense of self-criticism getting the better of him?
As they journeyed onward, the only sound was that of the wheelchair tyres rumbling and the tapping of Great's signet ring, which was intermittent but unrelenting. Moore remained sunk in thought but not so deep that he didn't find the continual clack of gold against steel just that bit distracting, and after a while aggravating. How did Carver put up with it? No doubt over the years he had learned to tune it out. Didn't even notice it any more.
There was something about its arrhythmic insistence, though.
Something that demanded attention.
That would not be ignored.
If it had been just that bit less repetitive, just that bit more random...
Random? Moore was puzzled. The tapping was quite clearly random. Why would he have thought it was anything else?
He began listening to it, as opposed to simply hearing it, and yes, he could detect no obvious pattern. There were sequences of impacts, some louder than others, which came in clusters with short and sometimes long intervals between. Nothing regular about it other than that it kept happening. Random.
_Some louder than others_.
And Moore listened more closely to it, and then even more closely, and oh God, it couldn't be, it wasn't what he thought, it surely could not be...
And the pattern became apparent.
There _was_ consistency.
"Great's real name," he said, needing confirmation, "his first name—what is it?"
"Why do you ask?"
Moore tried to sound casual. "Uh, curiosity. Nothing else."
Carver seemed to think there was no harm in telling him. "It's Coriander."
CORIANDER GLEED...
The letters whirled like wind-blown leaves, then settled again.
And Moore said, because he couldn't help blurting it out:
"Morse."
And Carver halted, and swivelled his head, and pinned the Anagrammatic Detective with his gaze, and said, "I beg your pardon?"
And Moore said again, because that gaze of Carver's brooked no lies or evasion:
"Morse."
And Carver said, "Ah." And then said, "Oh." And then said, "What a shame."
"You didn't know," said Moore. Hopefully.
"Know?" Carver replied. Evenly.
"You did," said Moore. "Of course. You communicate. Army. You understand him. He can ask for things. Give you orders..."
With that, Moore's voice trailed off into silence.
He saw it.
Saw everything.
Provender's insider. The brains behind the abduction.
Insiders, plural.
Why else was Carver glaring at him now? Why else was Moore not supposed to have spotted that the tapping was not as uncontrolled as it was claimed to be? It was obviously a secret shared by only Carver and Great. And why else would it be a secret if it wasn't being used for some kind of subterfuge?
With that revelation, the wider picture began to open up. Why had Carver hired Moore and Milner if it was against his own interests? Why else unless...
"Yes, a shame," Carver said, nodding. "I mean it sincerely. And I'm being just as sincere when I say that you're good at your job, Mr Moore. Exceedingly so. Far too good, indeed, for your own good."
"We weren't supposed to find him," Moore said, meekly, weakly. "We were meant to fail."
"With the greatest of respect: _Anagrammatic_ Detectives? Jumbling up words in order to solve crimes? It's just plain silly. There's no earthly reason for it to work."
"But it does."
"It did. Or you just got lucky. You've just got lucky in every one of your few successful cases. Who knows?"
"But you took us on, threw money at us—"
"—so that I could be seen to be doing something. Within the remit I had, you were perfect. Private investigators, not police. Detectives but not, as far as I could see, especially effective ones. You'd tackle the case but had little chance of cracking it. Provender would remain a captive as long as was necessary."
"Which was how long? What were you hoping to achieve?"
"You'll never understand," Carver said. "It's not your place to, anyway."
Great had begun tapping furiously, and the difference between the dots and dashes was all too apparent now, soft for short, loud for long, and Moore knew the individual letters of the Morse alphabet but Great was going too fast for him to keep up. Words were pouring out. The wheelchair frame rang with speech.
"And," Carver continued, "I regret to say I cannot allow you to share this discovery of yours with anyone. Damage limitation is now my goal. Given the latest turn of events, Mrs Gleed's act of self-harm. it would reflect badly on Great and myself were we implicated in Master Provender's kidnap. I cannot allow that to happen."
"Can't allow it?" said Moore, dry-mouthed. "Or are you being told not to allow it?"
Carver appeared to smile. His scar, at any rate, puckered more deeply at the bottom and became curved like a hook.
"It amounts to the same thing," he said, and lunged.
**72**
"IT'S A SNUG fit," said Extravagance.
"Tight, you mean," said Is, struggling with the zip at the side of the skirt. "Do you have anything even a little bit looser?"
"That's the biggest-size thing I've got. I'm not sure why I bought it. Moment of madness. Perhaps I was a couple of pounds overweight that day. I've never worn it, anyway, because it hangs off me like a tent. I thought it would be fine on you, but..."
"But I have hips."
"You're rounded."
"And my bum is twice as large as yours."
"Rounded."
Is fought with the zip for a while longer, Extravagance assisting, but eventually both accepted that it was going up only so far and no further. An inch-long V of unmeshed teeth remained above the fastener. The skirt, however, stayed on, and when Is tugged the hem of her jumper down, the gap in the waistband was hidden. She did a couple of turns in front of Extravagance's dressing-room mirror. It was a lovely skirt, Italian silk screenprinted with a floral pattern and trimmed with lace which slithered pleasingly around her calves. Not the sort of item she herself would have bought, even if she could have afforded it. Too feminine-looking, too impractically delicate. But as a one-time-only deal, a substitute for the skirt Mrs Gleed had been sick over, she was happy to wear it.
"I'll get it back to you as soon as I can."
"Oh God, no. It's yours. Keep it."
"But I can barely breathe in it."
"Well, I don't want it. Think of it as a thank-you gift."
"Thank you for..."
"For Mum, of course. What you did."
"I didn't do much."
"You saved her life!"
"But—"
"Is, none of us had a clue how to help her. We all stood around like prunes, whereas you got straight in there and did all that chest-pushing and whatnot."
"Provender pitched in."
"Only because you told him to. You were amazing. A miracle-worker. A saint."
Is could not look her in the eye. Extravagance didn't know yet about her role in the kidnapping. No one in the household did, apart from Provender.
Is felt she was still a long way from redeeming herself.
"Will she be all right, do you think?" Extravagance asked as she and Is left her room.
"I can't say. A full recovery is perfectly possible. Then again, worse comes to worst, she might lapse into a coma." Seeing Extravagance's face fall, Is hurried on, "But that's unlikely. On balance, if she's otherwise healthy, your mother ought to be fine. We got there reasonably soon after she took the pills, and she threw up, which helps."
"I still have a hard time believing it. It's just not like Mum to do something so... extreme."
"The circumstances were extreme. People respond unpredictably to pressure." Is had offered such soothing bromides to patients" relatives in the past, but never before with an underlying sense of guilt. The guilt was starting to feel constricting—or maybe that was just Extravagance's skirt. Either way, getting away from Dashlands was now more imperative than ever as far as she was concerned. Worse than the Gleeds" enmity, she was finding their gratefulness hard to bear.
"Look, Extravagance..." She stumbled over the name. It was quite a mouthful.
"'Strav," said Extravagance. "It's simpler."
"'Strav. I really think I should be getting back home."
"Oh, you can't go! Mum—"
"—is in very good hands."
"But then there's Provender."
"What about Provender?"
"Well, don't you at least want to say goodbye to him?"
"Maybe another time. When he hasn't got so much else to worry about."
"How did you and he meet anyway? There's still a lot I don't understand about all this. Come on, at least stay till tomorrow. We've plenty of spare rooms. You can even have the official guest suite. You'd love the guest suite. It has a Jacuzzi, a four-poster, a hell of a view... Normally only Family heads get to sleep there but I could swing it for you I'm sure. And in return, you can fill me in on what's been going on and you can tell me why my brother looks at you in that way."
"He looks at me in a way?"
"Don't be daft, you know he does. When we were out there on the road to the tram stop, and even when you were bossing him about in the television room..."
"He doesn't look at me in a way."
"Trust me, he does. He's smitten. You can see it a mile off."
"Please, 'Strav, he doesn't."
"You may not want him to but that's not the same thing. It's nothing to get alarmed about. I mean, you're not Family, but at this stage, frankly, we're past caring about that. It's just a relief that he's considering anyone at all."
"'Considering'."
"Yes."
"Implying _I_ don't have any say in the matter."
"Is," said Extravagance, sweeping an enthusiastic arm around, "what choice is there to make?"
They had arrived at the head of the staircase that curved down around the perimeter of the cylindrical atrium where Triumph stood, and Is had to admit that, if what you were after was a life lived amid splendour, Dashlands House was unquestionably the place for it. Extravagance's gesture took in the statue itself, the apexed glass roof, the staircase's ornate wrought-iron banister, and by implication the whole of the rest of the house. She was offering Is, in effect, a future as glittering as Triumph's gold accents.
Before Is could respond, there was a commotion down below, quickly followed by the appearance of Romeo Moore in the atrium, fleeing, and Carver, in hot pursuit. Moore took to the stairs, and Carver was right behind him, arm out, inches away from grabbing hold. Halfway up, Moore missed his footing and stumbled. Carver seized him by the jacket collar. Moore writhed, wriggled free from his jacket, and resumed running up the stairs. Carver tossed the item of clothing aside and carried on after. His face was set in a ferocious leer. Moore's expression was pure terror.
Near the top of the stairs Moore caught sight of Is and Extravagance and faltered. The pause was brief but enough to allow Carver to catch up with him again. This time he took a firm hold of the Anagrammatic Detective, swung him around with appalling ease, as if he weighed next to nothing, and slammed him against the banister. The air was driven from Moore's lungs. Carver then proceeded to bend him backwards over the banister's handrail, fist locked against the base of his throat. Moore's head was canted directly over Triumph's upraised left hand; her fingertips daggered up approximately four yards below the back of his skull. He grunted, he grimaced. Carver's contorted face, looming over his, was surely the worst thing anyone would want to see when in a position like this, and Moore's bulging eyes said exactly that.
"Carver!"
Extravagance's sharp cry had little effect on the manservant. He pushed Moore further over, until the detective was touching the stairs with just his toecaps.
"Carver, what are you doing? What is the meaning of this?"
"It doesn't concern you, Miss Extravagance," Carver said from the side of his mouth. "You should leave. You too," he added, meaning Is. "This is between me and this... thief."
"Thief?"
"I caught him attempting to pilfer some small trinkets. Great and I both witnessed him getting ready to stuff his pockets with Family valuables. Naturally, when we came upon him _in flagrante_ , he ran, and naturally I gave chase."
Moore was whipping his head from side to side and would have denied the accusation out loud had Carver's knuckles not been sunk into his windpipe.
"You're hurting him," said Extravagance. "Let him go."
"I can't do that, Miss Extravagance. Not without risk to yourself. He's a desperate, dangerous man."
"He's half your size," said Is, "and from what I know of him he's no danger to anyone."
"Nobody asked _your_ opinion," Carver growled.
"Let him go," Extravagance said again. "That's an order."
Carver did not obey, nor did he openly disobey. What he did was shove Moore fully onto the banister, so that all that was supporting Moore and keeping him from falling was the banister itself and Carver. Moore's arms flailed and his eyes rolled, panic-stricken. The drop beneath him, assuming he missed Triumph on the way down, was far enough to kill a man.
Is took a step towards Carver, and at that same moment the banister groaned. A shudder ran through it from top to bottom and from somewhere along its length there came a resonant metallic _snap_. Moore let out a strangulated moan. Is took three more steps. Carver turned his head and shot her a look that would have scorched paint. The scar was a livid lightning flash against the thundercloud of his face. His lips were pulled back and Is could see that several back teeth were missing on the same side as the scar, presumably knocked out when the injury was inflicted.
"Do not interfere, girl," he said, reverberantly low. "Stand back or I will mess you up so badly your life will not be worth living."
"You don't scare me," Is said.
"I should and I do."
"No, you don't." She meant it, too. "This man hasn't tried to steal anything. You're lying about that and I think I know why. He's rumbled you, hasn't he? And you want him out of the way, you want to silence him. I know who you are, Mr Carver. I know what you've done."
"You know nothing."
" _You're_ Damien's insider."
"Shut your mouth. You're talking nonsense."
"Is, what do you mean?" said Extravagance. "Who's Damien? What's going on here?"
"Gleeds not paying you enough, Mr Carver? Oh no, wait, all the money was going to Damien. So what was your angle? What were you after? Do you not like Provender much?"
"I have never," Carver said, "ever done anything to the detriment of the Gleeds, any of them, and never would. I have served this Family immaculately all my years. I am loyal to them to my core. You're speaking of things you have no way of understanding, girl. I reiterate: shut your mouth."
"Will someone explain this to me immediately!" Extravagance shouted.
Is said, "Put him down, Mr Carver. We'll sort it out without hurting anybody."
The banister gave another groan and wobbled slightly beneath Moore's back. Moore yelped and clutched Carver's sleeve in fright.
"No one has to die over this," she said. "There's no point in killing the detective because I know your secret now and so does 'Strav."
"I do not," said Extravagance. "Do I?"
"Carver masterminded the kidnapping. He's behind it all."
"Carver? This can't be true. Is this true?"
"An abject falsehood, Miss Extravagance."
Extravagance looked puzzled. "Why don't I believe you?"
"Probably because he's holding a man suspended over a thirty-foot drop," said Is. "That puts a bit of a dent in his credibility."
"But what's my brother ever done to you?" Extravagance wanted to know.
"And what about the war?" said Is. The truth was unfurling in her head like a roll of carpet. "I bet you didn't count on that. And Mrs Gleed. Surely you didn't intend her to come to harm, did you? It was a consequence you just didn't foresee."
Carver looked down. Oh so briefly, but the action was a giveaway nonetheless. It spoke of a conscience pricked—remorse felt, however fleetingly.
The banister gave a lurch.
Moore squawked.
Carver raised his head again and looked Is squarely in the eye.
"I only caught a glimpse of you at the ball," he said, "otherwise I'd have recognised you straight away when you came back today. I didn't even make the connection when you attended to Mrs Gleed, which was remiss of me. I thought you were an associate of his." He nodded at Moore, who flinched in the mistaken belief that he was about to be head-butted. "Had I been thinking more clearly at the time, I would have put two and two together. It came to me shortly afterwards. The nurse. Damien's helper. But of course I wasn't going to say anything even then, and thereby incriminate myself. I'd pay no attention to you, and then you'd leave and no one would be any the wiser."
"Except it didn't work out that way. You realise, don't you, that Damien would—will—identify you as his accomplice."
"Will he I wonder. And even if he does, I'll have protection. You really don't know as much about this as you think you do, young lady."
"Maybe not. Still, we're discussing it rationally, it's out in the open—so perhaps, please, you can pull Mr Moore back. He doesn't need to be hanging over the edge like that now. He's not a threat to you any more."
"I'm not accustomed to taking orders from a non-Family member."
"Tell him, 'Strav," Is said, turning. "I don't like the sounds that banister's making. Tell him to—"
The sound the banister made next was like nothing Is had heard before. There was a long raspy shriek, punctuated by a series of deep pizzicato _plunks_ as though some giant harpist was running her fingers along the uprights. Then came a warping, grinding _sprunnng_ noise, and Is spun round in time to see the upper end of the banister detach itself from the staircase and twist outwards as fluidly as though it were cotton ribbon. It went flat, and Moore and Carver went flat with it, sprawling one on top of the other. The banister kept them there, suspended, for an instant of infinity. Then, with a squeal, it gave way.
Is threw herself forwards headlong, hand outstretched. She grabbed blindly, and more by instinct than aim seized hold of a forearm.
She hoped, she prayed, it was Moore's and not Carver's.
The banister peeled away, unspooling downward until its upper end hit the atrium floor with a clang. In the echoes of the impact Is heard a cry of pain followed by gurgling distress and then a sharp sigh. Her eyes were closed. She was lying prone on the stairs, with one arm hanging over the edge and supporting the weight of a grown man. Something had torn in her shoulder—a muscle wrench rather than a dislocation, she thought, but still it hurt like hell. She could not move. Dared not. She was gripping whoever's wrist as hard as she could. She would not let go, refused to. She was aware of Extravagance beside her. "Come on," Extravagance was saying. Not to Is. "Help us help you up. Come on. Put your foot there. Yes, that's it."
She would not let go, even after the man was safely on the stairs next to her. It took Extravagance pulling back hard on her fingers to get her to unclamp them from his wrist.
Then, at last opening her eyes, she looked and saw Romeo Moore, prone, panting frantically.
Alive.
Which meant...
She rolled her head round and looked over the edge.
It was a sight which Extravagance was trying desperately to avert her eyes from and which Moore was too traumatised to think about viewing just yet.
But Is looked. Stared. Had to see.
Triumph's upraised arm. Hand gloved to the wrist with blood. And below the hand, like some ghastly bracelet, a body. Carver. Limbs dangling. Head thrown back. Impaled through the abdomen. Twitching his last.
**73**
A GATHERING OF the Clan.
The place: the fourth largest drawing room at Dashlands House, decorated with bamboo screens, tropical ferns in urns, an elephant's foot umbrella stand, and a plethora of animal pelts, from tiger throw rug to antelope wall-hanging to leopardskin upholstery—a great white hunter's paradise.
Present, seated left to right: Provender Gleed, Isis Necker, Prosper Gleed, Fortune Gleed, Gratitude Gleed, Extravagance Gleed, and Great.
Supervising the proceedings: Anagrammatic Detective Romeo Moore...
...who was acutely aware how this scene resembled the final chapter of one of those country-house murder mystery novels he used to devour as a child, the revelatory moment when the police inspector or the private investigator unmasked the villain, who was usually the person you least suspected until after you had read widely enough in the genre, whereupon he/she became the person you suspected from the start. Moore could not help thinking he ought to say something like, "I expect you're wondering why I've called you all together." The temptation was there, but resistible. He also had to fight the desire to crack a joke about the butler having _really_ done it.
No, this was a sombre moment, not the time for clowning around. Nor was it the time for revelling in success. Moore's achievements as a detective, pleased with them as he was, meant little when he was confronted by a Family in a state of shock. The faces arrayed before him, Great's excepted, were bewildered and drawn and haggard. The Gleeds had a lot to come to terms with, and Moore's natural courtesy inclined him to downplay his role here as bringer of truth and exposer of foul play.
"I'm sorry I have to be the one to tell you what I have to tell you," he began. It helped, from the point of view of sounding tactful, that his voice was reduced to a husky croak. His throat hurt if he spoke above a certain volume. Carver's fist had bruised his larynx and Is said it would probably be sore for the next few days but the only remedies were time and not talking too much.
"I didn't even know what I was doing," he added modestly. "It all just seemed to fall into place of its own accord. I suppose it's because I'm in the habit of looking for patterns. Patterns within words, patterns in everything. If not for that, I wouldn't have—"
"Why did Carver try to kill you?" said Prosper Gleed, curtly.
Moore was thrown by the interruption. He blinked, regrouped and restarted. "Allegedly he wasn't trying to kill me. Allegedly he caught me stealing something and was tackling me as he would have any thief. But in fact I believe he _would_ have killed me if he had had the opportunity to get away with it. Then he'd have planted some piece of incriminating evidence in my pocket and come to you with the whole terrible story. And my death would have been made to look like an accident, I'm sure, or less his fault, more mine. Your manservant was keen to cover his tracks, and I, as far as he was concerned, was in every way expendable."
"But it's hard to conceive," said Gratitude. "Carver, willing to take a man's life."
"An ex-soldier? And by all accounts a fearsome warrior in his day? Not so hard to conceive, Miss Gleed."
"You weren't there, Grat," said Extravagance. "He was berserk. I think he really meant to do it."
"But why?" said Prosper. "What for?"
"To protect the Family," said Moore.
"Protect us? From...?"
"Er... Me. Or rather, what I had found out, a piece of information that was highly damaging to him."
"Come on, man, talk straight. What information?"
"I'm getting to that."
"Well, can't you hurry it up a bit?"
"Dad," said Provender. "Stop hassling him. Let him explain in his own time."
"But he's—"
" _Dad_."
Prosper fell silent, cowed by his son's forthrightness.
"Go on, Romeo," said Provender.
"Right. So. Um. What it comes down to is the fact that the whole kidnap plot was orchestrated not by some outside agency but from right here, at Dashlands."
Now it was Fortune's turn to expostulate indignantly, although he did so in a more muted manner than his brother. "That's not right. Can't be right. Why would anyone...?" Rather than complete the rhetorical question, he submerged it in a draught of gin and tonic.
"We can, I hope, get to the bottom of 'why?' shortly," Moore said, with a surreptitious glance towards Great. "I myself had an inkling from the start that it might be an inside job. What I didn't realise was that the culprit was the very person who was employing me to investigate the crime."
"Yes, why is that?" said Provender. "Why would Carver have hired you unless he thought you... Oh."
Moore nodded, with chagrin but also with a hint of vengeful satisfaction. "He told me himself shortly before he attacked me. He honestly didn't think I or my partner had a hope of cracking the case. He took us on... well, principally so that he could appear to be doing something useful, but also because of all the trees he could have barked up, ours was the wrongest one. If you see what I mean. It was almost a joke to him, I feel. 'Who's the least likely person I can find to send to look for Provender?'"
"We only have _your_ word on any of this," said Fortune. "You could be spinning us some cock-and-bull story in order to..."
"In order to what? Get myself off the hook for supposedly stealing some trinket from you? Hardly likely. Besides, I have a Family witness here who'll attest to the fact that Carver was trying to silence me, don't I, Extravagance? He all but confessed his connection to the kidnapper, Damien Scrase, in the moments before he... we..."
Moore experienced again the terror of being bent over the banister, Carver's furious features filling his vision, the sense of the drop beneath him, the hard tiles below, his utter helplessness. His fingers, reflexively, went to his throat and explored the tender flesh there. It was weird to be alive after having been so close to death. It was at once exhilarating and deflating, an emotional alp from which the only route was down.
He became aware that he had faded out and Extravagance was speaking, filling the gap he had left. She told everyone that not only had Carver clearly been intent on murder but he had recognised Is, who also had some connection with this whole messy business.
"Don't you?" she concluded, with a frosty look at the person with whom, half an hour earlier, she had been going through her wardrobe, selecting skirts to try on, all girls together.
Before Is had a chance to reply, Provender stepped in. "She was an unwilling accomplice, forced to take part against her will. She helped me escape, too, and in case you've forgotten, she saved our mother's life."
Is shifted in her seat, exquisitely uncomfortable. She opened her mouth to say something before deciding that saying nothing was the better option.
"I can vouch for her as well," said Moore. "I saw her tackle Scrase at the Shortborn, when he was threatening Provender. She's definitely on the side of the angels."
Is started gently massaging her wrenched shoulder, head down, avoiding all stares.
"But if we're looking to lay blame," Moore continued, "there is someone in this room deserving of our attention. Carver is guilty of a lot but there's someone who I'd say is even guiltier."
He let the words hang in the air, allowing the Gleeds to draw the correct inference, which, gradually, they did. Heads turned, homing in on the one person present whose head could not turn.
Great's stare remained forward-fixed as ever, his eyes stony. His hand was not tapping. His whole body was statue-still. Then, little by little, his eyes began to move, sweeping across his assembled relatives, defiant, challenging. You could read anything into the way those glittering blue orbs looked, from an admission of culpability to astonished, out-and-out refutation.
"No," said Fortune.
"Great?" said Gratitude.
"Too far," said Prosper. "You've gone too far now, Mr Detective."
Even Provender looked dubious.
"I understand your scepticism," said Moore, "and no doubt I'll only add to it when I tell you that it was his full name, his proper name, which set the seal on it for me, bearing out my suspicion that Carver was just the brawn of the outfit and someone else was the brains."
"What _is_ Great's proper name?" asked Extravagance.
"Oh really, 'Strav!" said her older sister. "You don't know?"
"I forget. No one ever calls him by it."
"Arthur does."
"Does he?
"You are _so_ unobservant sometimes. Coriander."
"Oh yes. So it is."
"Coriander," said Moore. "And CORIANDER GLEED happens to be an anagram of CODE RINGLEADER."
Fortune snorted a laugh.
"It is."
"I don't care if it is, Moore, I simply think you're taking the mickey. Anagram indeed!"
"It's what he does, uncle," said Provender, "and I hate to say it but it works. That was Carver's mistake. He thought it was ridiculous too."
"So we're expected to believe, on the strength of an _anagram_ , that a paralysed old man was capable of—"
"Forgive me," Moore interjected, "but Great is not paralysed."
"Some bloody detective! Of course he is. Look at him. He's been in that chair for, Christ, over a decade. He's not faking it. What, suddenly he's going to get up and walk and tell us it was all a big sham?"
"No, no, not at all."
"And I'll bet he speaks, too. Eh? He's just been pretending he can't all this time."
"As it happens, he can speak. Not in the conventional sense, but—"
"Pure bollocks!" Fortune exclaimed. "I can believe, I suppose, that Carver's a bad guy. Never much liked him, to be honest. But now you're telling us that the oldest member of the Family, for some reason that has yet to be established, went to the trouble of having the heir-apparent abducted and caused all this chaos. Why, for God's sake? Family doesn't harm its own. That's an unwritten law."
"His motives I hope to find out. His methods? When I said he can speak, what I meant was he can communicate."
"Oh, and how?"
"What isn't he doing right now?"
"Anything. He isn't doing anything. Because he's paralysed." Fortune said this condescendingly, as if conversing with a simpleton.
Provender said, "Tapping. He's not tapping."
"Correct," said Moore. "But when he does..."
"Code."
"Exactly."
There was a pause, a collective intake of breath, a communal click of understanding.
"It's not possible," said Gratitude. "We'd have noticed. Surely we would have."
"But we didn't," said her brother. "It happened slowly. He lost movement, he lost his speech, the tapping started... We just didn't think about it. We thought it was a symptom."
"Right under our noses," said their uncle, wonderingly.
"And Carver," said Prosper, "he knew."
"They served together in the army," said Moore. "Both would have a working knowledge of Morse code."
"Well, of course," said Fortune. "Carver always seemed to know exactly what Great wanted. We thought it was just because he was a good servant and had spent so much time in Great's company. What's that word when two different species of animal co-operate?"
"Symbiosis."
"That's the one. That was their relationship. Kind of psychic, almost."
"Only it wasn't," said Provender. "Carver knew what Great wanted all the time because Great was telling him."
"Are we idiots not to have seen it?" said Extravagance.
No one else answered, so Moore felt honour-bound to. "Not necessarily. Why would it occur to you that that's what was going on?"
" _You_ spotted it."
"Like I said, patterns. And the anagrams. It's how my brain is wired."
"But you met them and saw it straight away. We _live_ with them."
"Sometimes, when a thing's right in front of you, you adjust to it. You take it into account and don't think anything of it. It's just _there_. Also, an elderly, disabled relative tends to fade into the background, especially when, as with this Family, everyone else has such a strong personality. The elderly relative becomes, with all due respect, part of the furniture."
He anticipated protests, but there were only mute nods of assent.
Throughout the foregoing, Great's eyes flicked from speaker to speaker but his hand stayed resolutely still, denying by its very motionlessness the abilities Moore was asserting it had. Then, abruptly, it started shaking, twisting from the wrist to bring the finger with the signet ring into contact with the wheelchair armrest.
The assembled Family listened in silence, paying attention to a sound they had hitherto regarded as just so much meaningless reflex-movement drumming. Not one of them had any idea what Great was saying but they knew for the first time that he was saying _something_ , and this, in itself, lent the tapping a strange articulacy. Great, dumb for a decade, was talking again. Speech—incomprehensible but speech nonetheless—was issuing forth from him.
"Can you understand him?" Prosper asked Moore.
"I know Morse. Sort of. I know how each letter is represented. But he's going to fast for me to follow."
"Great," Prosper said, "you'll have to slow down. Mr Moore will be able to translate then."
The rate of the tapping decreased, but Moore, try though he might, still could not make head or tail of it. The louds and softs, dashes and dots, all seemed to merge into one another.
"Slower still," said Prosper.
The tapping became painstakingly protracted, Great leaving long gaps between letters and making the distinction between the dashes and dots as marked as possible. Moore was just about able to keep up now, although not without effort. He had memorised the Morse alphabet a long time ago, purely as an intellectual exercise, but he had never actually had to use it before. Adding to his difficulties was the fact that he was having to recall it under pressure. He made, therefore, several mistakes to start with, although gradually his ear attuned and his fluency improved.
"FAMILY GETTING WEAP," he interpreted. "WEAP? What's that?"
Great tapped out the last word again.
"Oh, WEAK. NEEDED SHAKING UP. BOY NEEDED... SHOCK? Is that it? SHOCK?"
Great tapped out dash-dot-dash-dash, dot, dot-dot-dot. YES.
"BOY NEEDED TO GET OFF... I'm not translating _that_ word. AND DO SOMETHING."
"Me?" said Provender.
"YES," said Moore. "USELESS LAZY... I'm sorry, could you run through that one again please?"
Dash-dot-dash-dot, dot-dot-dash, dash-dot, dash.
"SO-AND-SO." This was not, strictly speaking, the term Great had used, but Moore had no wish to offend anyone by repeating the actual profanity.
"THEREFORE KIDNAP. RUDE AWAKENING. BRING TO SENSES. GLEEDS MUST SURVIVE."
"A bit extreme, don't you think?" said Provender.
"DESPERATE TIMES DESPERATE MEASURES. IN MY DAY WAR MADE MAN OF YOU. FACE FOE FACE SELF. LEARN COURAGE AND DUTY. NO WAR NOW THEREFORE OTHER CHALLENGE NECESSARY."
"Only there nearly was a war. You didn't count on that, did you?"
"GOOD IF BOY TURNED SOLDIER."
"Yes, like _that_ was going to happen. And Mum. Another little drawback to your scheme, Great."
"SAD. WRONG. CYNTHIA ONLY DECENT GLEED. PROSPER UNGRATEFUL... No, I won't say it."
Great banged the word out again, forcefully, and Moore relented.
"All right. UNGRATEFUL BASTARD. I apologise, Mr Gleed, those aren't my sentiments of course. I'm simply the messenger."
Prosper waved it aside, looking as if he knew he deserved the censure.
"And if I'd been killed?" said Provender to Great. "Believe me, I came close. That would've scuppered you, wouldn't it? Talk about an own goal."
"ACCEPTABLE RISK."
"Oh, thanks."
"CARVER MONITORING SITUATION."
"Obviously not that closely."
"ACCEPTABLE RISK," Great reiterated, via Moore.
Provender sighed. "You're quite mad, aren't you? I'm not saying I don't understand why. Sitting in that chair all day. Stuck inside your own body. Stewing in your own thoughts. Staring out at a world you can't directly affect. Year after year of that—it's not surprising a few of your marbles have gone astray. But that's no excuse for what you did. To me. To all of us. Do you regret it now? Do you feel even the slightest remorse?"
Great's hand stayed in his lap for almost a minute, until with solemn, precise emphasis it sounded out two letters: dash-dot, dash-dash-dash.
Translation was superfluous.
"Thought not," said Provender.
"ACTED FOR FAMILY. DOING BEST FOR FAMILY. GETTING HOUSE IN ORDER. FAMILY EVERYTHING. FAMILY MUST NOT FADE. GLEEDS MUST SURVIVE. GLEEDS MUST... again, SURVIVE. GLEEDS. GLEEDS." Moore listened as Great continued to tap out the same sequence over and over. In the end the Anagrammatic Detective shrugged. "That's it. GLEEDS, GLEEDS, ad infinitum."
The tapping quickened and grew louder. It was all Great had to say now. His gaze scanned left to right and back again, taking in each and all of his relatives. The pattern of dashes and dots became insistent, hypnotic, like a peal of church bells, a phrase from a song, a complex tomtom polyrhythm, dinning itself into every skull in the room, until eventually Provender snapped to his feet, strode over, grabbed Great's hand and wrested off the signet ring. The ring came free with surprising ease, a little too large for the bony finger it encircled. Provender tossed it upwards and snatched it from the air at the start of its downward arc, stealing it from sight.
Great resumed tapping the wheelchair frame, but with his bare knuckle the sound was nowhere near as sharp and attention-getting. All he could manage was a dull, scarcely audible thud which the Gleeds could ignore without too much difficulty, and did. In a demonstration of contempt they began talking amongst themselves, huddling close, literally turning their backs on Great. Provender was asked to provide an account of his adventures of the past three days, and he duly fleshed out the sketchy details the others already knew and filled in some blanks. There were questions, prompts, interjections, and the volume of the conversation mounted until, quite deliberately, it was so loud that Great hadn't a hope of making himself heard above it. He soon gave up trying. His hand fell limply into his lap and all he could do was sit and glower, a picture of impotence and thwarted fury.
For Moore, it was hard to reconcile the frail-looking figure in the wheelchair with the force and recklessness of the scheme he had hatched, yet some clue as to the vigour of the mind trapped within that useless body lay in Great's eyes—their blue blaze radiated manic energy. Mad? Quite possibly. Bad? Not by his own reckoning. Great had been trying to save his Family. For him there was no nobler objective.
With his right-hand man gone, Great had lost his one sure link with the rest of the world, the conduit through which he channelled his wishes and desires. Moore felt little sorrow over Carver's demise, horrible though it had been. Carver would have happily visited the same fate on him, indeed had been trying to. Natural justice had in this instance been poetic justice too. Still, Great was bereft of his lifelong companion now, and it looked unlikely that the other Gleeds were going to forgive him any time soon for what he had done. If Cynthia Gleed did not recover, they might never forgive him. Moore predicted a long and frosty ostracism for the Family's senior-most member, a future in which he would be made to atone for his actions as surely as any prisoner in solitary confinement. His paralysed body would be his cell.
You could almost, Moore thought, pity the old brute.
Almost.
**74**
THE PEARL-WHITE DAGENHAM Seraph stood in the driveway, V8 engine susurrating. With its high wheelbase and pinpoint suspension the car seemed perpetually to be floating; whether in motion or stationary, its tyres seemed only just in contact the earth. Gravity-defying, it was a limousine that appeared to weigh less than a saloon car.
In the driving seat a chauffeur sat with his gloved hands resting on the steering wheel and a look of perfect impassivity on his face, professionally patient. In the back, Romeo Moore was luxuriating, stretching out his legs, swimming on the calfskin upholstery, relishing every cubic inch of limo spaciousness. One of the rear doors was open, inviting Is to join him inside. She was ready to go, but first there was a farewell to be negotiated, the awkward moment she had forgotten she had been dreading, till now.
There was still a faint glow in the sky, star-clusters pinned to a backdrop of indigo rather than pure black. Clouds of moths hovered around lawn lights, like miniature solar systems, planets orbiting suns. The Seraph's fine-tuned purr was so soft that chirruping insects in the vicinity had no trouble competing with it.
Provender waited. Provender had much to say and no idea how to begin saying it.
"So," said Is. She raised her hands and let them fall haplessly. "It's been... _something_ , hasn't it."
Numbly Provender nodded. "It has."
"Who'd have thought... I mean... I don't know what I mean. Look, it's better if I just go, I think. Get into the car and get whisked away."
"You don't have to—"
She held up a finger and darted it towards his mouth. "I have to. For one thing, they're expecting me back at work tomorrow." A small lie. The day after tomorrow. "Early shift. I've a whole life I have to pick back up. Things I have to start doing again. Back to the everyday, the routine. I need that. I need to pretend as if..."
"As if nothing ever happened?"
"Don't you think that's for the best?"
"Obviously what _I_ think doesn't count. But do _you_ think that's for the best? _Did_ nothing happen?"
She knew in what sense he meant the question but she answered as if she didn't. "Fights and dangling off balconies and wrangling a psychopathic ex-boyfriend and mixing with the Gleeds—I wouldn't call that nothing. But it's not my life. Not what I am. And I'm not sure I'd want to go back and think about it too much. It's just too out of the ordinary. I'm a very ordinary person, Provender. I like normal life, normal things. If I can just somehow push past all of it..."
"Erase it? Forget it?"
"Move on. You understand?"
His nod said yes. His eyes said no.
"I'm not saying I'm going to be the same from here on," she added. "I could hardly expect to be. But I don't want to be that different, if you see what I'm getting at."
Is's instinct, the bluntness with which she naturally dealt with life, was urging her to come right out and say it, spell it out to Provender, leave him in no doubt. But she was trying to spare his feelings. Or was she trying to spare her own? Either way, dancing around the subject seemed preferable to tackling it head-on. She couldn't bear to hurt him, but more than that, she couldn't bear to have to see him hurt and know that she was the cause.
"I hope your mother will be all right," she offered, lamely.
"Yes."
"I think her chances are good."
"If you say so."
That was it. She really could not think of anything else. It was time to leave.
She turned, then turned again and went to Provender and embraced him. Contact. Body on body. Warmth to warmth. His chin against her neck, his breath briefly in her ear. She squeezed. He squeezed back with that tiniest bit more pressure. He straightened away from her, and for a moment their faces were close, nose to nose, mirroring.
"Isn't there anything I could—" he began.
Is looked down, away. Let go of him. Headed for the car, trying not to appear to be hurrying. Stepped in. Shut the door. Did not once look round.
The chauffeur engaged gear and the Seraph glided down the drive, away from Dashlands House into the grounds of the estate, away from light into the boundless warm blue summer dark.
**75**
PROVENDER WATCHED THE car go.
The parting with Is had not gone as he might have wished. Its finality crushed him. Was that it? Was it all over? Just like that?
Peering at the Seraph's dwindling taillights, he had to fight the urge to sprint after the limo—a mad dash to catch up. He knew he would never make it, and even if he did, what would he achieve? Nothing except make himself look desperate and foolish.
He thought he had proved to Is that he was not just a Gleed; that he was so much less and at the same time so much more. He should just have come out and said it, but, tongue-tied at the crucial moment, he had fumbled and failed.
So, what now?
At the back of his mind there lurked the idea of another book, a follow-up to _The Meritocrats_ , possibly a sequel. He had been considering this for a while anyway, and perhaps if he wrote another novel, got it out into the world, spread the Family-sabotaging message a little bit further, Is would be impressed. She would see that he meant everything he said, that he sincerely wanted a better, fairer world, a world where the Families no longer held sway. This grand gesture would surely win her over.
Wouldn't it?
The flaws in the plan were many. Principally, Is hated _The Meritocrats_. It galled Provender to remember this but it was true. She couldn't stand the book, and therefore a second book might not be the ideal way to go about gaining her attention. Besides, it would take him at least a year to write, and then it would probably take another year to percolate fully through the public consciousness. Too long, too slow.
Moreover, Provender no longer believed, as he once had, that a book could change everything, or indeed anything, for the better. This view was based in part on his experiences at the hands of Damien Scrase, which was a case of the law of unintended consequences if ever there was one. Were it not for _The Meritocrats_ , would Damien have become quite the fanatic he did? Perhaps he would have, but the book had certainly added fuel to that particular fire.
Also, more relevantly, Provender surprised himself by realising that he didn't resent his Family quite as much as he used to. Was it because he was worried about his mother? Was it because he had faced the threat posed by Great (and Carver) and survived? Was it because he was simply glad to be back with them?
Maybe with time, if his mother's condition improved and he had a chance to gain perspective on things, he would lapse back into his sullen revulsion for all things Familial.
Maybe.
But he thought not.
Great was correct about one thing, at any rate. BOY NEEDED TO DO SOMETHING.
Boy had, with _The Meritocrats_. But it wasn't enough; it wasn't the best way forward.
Boy had also achieved a breakthrough with Stanislaw Kuczinski. That was a good sign for the future.
Yet, for all that, boy knew he still needed to do something else, something different, something immediate and concrete.
The Seraph turned a corner, its taillights winking out of sight. Beyond the aura of the house lights there was nothing now but a blank silhouette of trees and hillside braced against the starry sky. Provender shivered, feeling a small, lonely chill, a foretaste of night.
But he felt, too, a sudden glimmering within. A twinkling amid darkness. The precursor of an idea. A seed of thought, just starting to shoot.
_Yes_...
**PART VII**
**76**
ROUTINE WAS GOOD. At St Fiacre's there was no such thing as an average day, each day was different, each came with its own particular freight of chaos and unpredictability. At the start of a shift you had no idea what lay ahead and for the next eight hours you simply went along for the ride, dealing equally with the longueurs of boredom and the sudden frantic spurts of activity. Nevertheless, in total, one day after another, it amounted to a routine. You got up, did your shift, collapsed into bed. Is welcomed it. It was what she needed. Like the tidal beating of the waves it wore away at the memory of her time with Provender until eventually, perhaps eight or nine weeks later, she could look back on the whole episode without rancour or self-recrimination. She could safely say that it no longer meant anything to her. It was old, done with, tidied away, out of sight.
She slipped back into the swirl of life at the hospital with scarcely a ripple. Several colleagues congratulated her on having the foresight to take a week's leave just when the shit hit the fan. The day war nearly broke out had been the busiest in living memory. By noon the wards were full of panic attacks and attempted suicides, people whose fragile personalities had cracked under the strain. Then, come evening, when it became clear that peace was going to reign, Accident and Emergency had to cope with a huge influx of alcohol-related cases. The whole of London, it seemed, had gone on a bender, and St Fiacre's was where they ended up to have their stomachs pumped and their lamppost-collision wounds sutured and their brawl bruises daubed with iodine.
Everyone—nurses, interns, residents, registrars—had their war-day reminiscences and wanted to share them with Is. Those of them, however, who got round to asking her what she had been doing during those tense hours, were invariably disappointed by her reply. "Oh, not much" was hardly a fair repayment for the fraught frontline tales they had regaled her with. But she could not be pushed to say any more, and the assumption was that Is was jealous. She felt left out. She wished she could have been there to grapple with the crazies and the inebriates. Everybody else was part of a remarkable shared experience, bonded by adversity, and she was not.
During the post-Provender period, the long slow process of forgetting, Is did keep an eye on the newspapers and the TV, and every so often a reminder would pop up, some report or article that briefly brought the whole episode back. There was, for instance, a short piece in one of the Familial columns that mentioned Cynthia Gleed's recovery from a mystery illness. Though still weak, Mrs Gleed was apparently faring well and should be back to full strength in no time. The article gave no clue as to what the illness might have been, although one of the more scurrilous gossip columnists speculated that the Gleed matriarch was most likely going through the Change. A week later, photos appeared in a number of national dailies depicting a wan but smiling Cynthia accompanying her husband at some public function or other. Prosper Gleed had a solicitous hand on his wife's elbow, an arm around her waist. Every inch the caring, attentive spouse. If you knew what to look for, as Is did, you would have noticed how his eyes shone as he gazed on her. What had dwindled to embers had now been rekindled into a blaze.
Then there were the headlines that appeared when information about Damien was finally released to the press. He had been arraigned before a judge on two counts of murder and one of threat to endanger life. Is was not aware, till then, that Damien had killed anyone. All she knew about was his attempt on Provender's life. But it turned out that he had knifed to death a doorman at the Shortborn and also that a body had been discovered at his flat—the corpse of someone called Milner, likewise knifed to death. Milner, it turned out, was a private investigator. In fact, he was an associate of Romeo Moore, a fellow Anagrammatic Detective.
Her horror was great and so, too, was her fear that her involvement in the kidnapping meant she would be regarded as an accessory to murder. For several days she went around on tenterhooks, waiting for the police to come. Whenever her name was called out over the hospital's public address system, her heart would start to pound and her palms would become slick with sweat. At the back of her mind was the thought that Provender, for all his claims that he would protect her, might in a fit of pique do the exact opposite. She had rejected him. He might have no qualms about getting his own back by throwing her to the proverbial wolves. Never mind a woman scorned, what about a man?
In the event, he appeared to stay true to his word. The police did not call on Is. If anyone in officialdom connected her with Damien Scrase, for whatever reason the connection was not followed up. Gleed influence kept her in the clear. She was relieved about this, naturally, but she also felt furtively guilty. It wasn't right that she should be so utterly exonerated. It felt a bit like cheating.
A couple of her nurse friends, who knew of her one-time relationship with Damien, remarked to her about his arrest. He had always struck them as a borderline case, they said, violence lurking below the surface. In fact, they opined, they were surprised nothing like this had happened sooner. At any rate, it was a good thing Is had dumped him when she did. She was well shot of him.
Even her part in his downfall was kept out of the public domain. It was Arthur who took the credit, and he was only too happy to. In an exclusive interview on a popular TV chat show Arthur related at length how he had liberated his cousin Provender from the anti-Familial madman's clutches and then disarmed him and decked him with a single punch. It all took place in the backstage murk at the Shortborn, so there weren't any eyewitnesses who were able to disprove Arthur's claims explicitly. There was no one, even, to pass comment on the improbability of Arthur managing to bring down Damien, a man twice his size, with just one blow. So persuasive was Arthur that he made his account of the incident wholly credible. Perhaps he himself believed it was the truth. That, after all, was what good acting was about, inhabiting a role so thoroughly that you came to feel the part was really you. It was, at any rate, great publicity for his play. _Hamlet_ was now sold out for its entire run, and there was talk of taking it on a tour of the provinces and even abroad to the US and Japan.
Damien himself adopted a policy of stony silence. At the arraignment hearing he didn't utter a word, not even answering when the judge asked him to confirm his name and abode. He wore, in the words of one journalist, "a heavy armour of defeat". Pictures by court sketch artists confirmed it. In so far as such artists could be relied on for an accurate reproduction of reality, the Damien they depicted in pastel and pencil looked shrunken, hollowed, half the man he had been. He was heading for a fall and he knew it. Is believed that, once his anger had abated and he had time to reflect on the atrocities he had committed, his conscience had caught up with him. There was blood on his hands. Two innocent lives taken. Whatever his beliefs, no matter how great his faith in his cause, he had killed. There was no getting around that.
Reports of his suicide while in custody came as no surprise to Is. Damien hanged himself in his police cell on the night before his trial was due to commence, using a blanket for a rope and a light fixture for a gibbet.
Deep down she was able to find it in herself to feel sorry for him. Mostly, though, she felt that he had got what he deserved. In a sense, he had shown himself to be decent at the last. A less proud man would have tried to weasel his way out of responsibility for his deeds, blaming the Gleed Family, perhaps, rather than himself. But not Damien. Principled to the end.
She learned where and when his funeral was to be held but didn't go.
And one month became two, and two expanded into three, and Is got on with things because that was what she wanted, wasn't it? A normal life. Wasn't it?
And summer decayed into autumn, and London's few trees took on a brown tinge and there was a knowing nudge of cold in the air.
Then two letters arrived for her, both appearing on the same morning in her pigeonhole at the nurses" lodgings.
THE FIRST WAS in an ordinary-sized envelope which bulged with the several sheets of foolscap folded within.
The letter itself was videotyped and the first page was printed on a sheet of headed notepaper alerting her to the fact that it came from Romeo Moore, Anagrammatic Detective, who could now lay claim to official Gleed patronage. The Family's crest appeared alongside his name and address, motto and split-nutmeg motif stamped crisply into the paper.
For all the impressiveness of the stationery, however, the tone of the letter was anything but proud or gleeful.
_Dear Is,_
_I apologise for contacting you like this, out of the blue. Finding out where you live wasn't difficult. I am, after all, a detective. For what that's worth._
_Truth be told, these past few weeks have been very hard for me and I really need to unburden myself to someone who I know will lend a sympathetic ear, someone moreover who was there when it all happened. If you would prefer not to be that person, I will understand. I remember, in the car on the way back to London, you said you hoped to forget about it all. I don't blame you for that. If that's still the case, don't read on. Crumple this letter up and throw it away._
_I've been thinking about anagrams a lot, Is. Words have been whirling around in my brain, settling then taking off again like flocks of starlings. Words that seem to have meaning and then no meaning._
_I've been thinking about your name, for one. I feel it was unfair of me to characterise ISIS NECKER as NICE KISSER. That was a shallow and dull anagrammatic interpretation. With time and reflection I've been able to see that ISIS NECKER is also CRISIS-KEEN. You are. You were. How you dealt with things at Dashlands House that day, and also what you told me later about how you and Provender escaped from Damien Scrase... CRISIS-KEEN indeed. A remarkable, resourceful woman you are._
_Mainly, though, I've been thinking about the word RELATIVES as I sit here in my lonely office through the long hours of the day. No doubt thanks to our encounter with the Gleeds, the word has begun to obsess me. Even at night it blurs through my thoughts. Such a VERSATILE word, RELATIVES. IT REVEALS many things._
_It tells me about the VASTER LIE that was perpetrated on myself and my colleague Merlin Milner when we were hired by Carver to find Provender. He told us one lie when he praised our track record. The VASTER LIE was that he hoped we would not succeed at all. He intended us to fail in our task._
_When I didn't fail, I was exposed to the full vengeful fury of the Gleeds" manservant: a VALET'S IRE._
_But what befell me was nothing compared with what befell my partner. You probably are aware that Scrase murdered two people. What you may not have realised is that the first of his victims was my colleague, and friend, Merlin Milner, who succeeded far better than I did at locating Provender. VITAL SEER that he was, he actually tracked down Provender's captor—and was stabbed to death for his pains._
_I found out a couple of days afterwards. His corpse lay undiscovered in Scrase's flat until a neighbour noticed. I can hardly bear to think about it. Merlin, dead all that time. Somehow that's the worst part, the loneliness of it. Even dead, to be abandoned like that... And I had no idea where he was. I looked high and low for him, fretted about him, and then he turned up. I was the one who had to go to the morgue to identify his remains. Truly that period, those few days between his disappearance and his burial, was and still is the VILEST ERA I have ever had to live through._
_I attended Scrase's arraignment. I sat there in that courtroom facing my partner's murderer and I watched his deadened, faraway gaze, his VISTA LEER. (It reminded me, in its way, of the horrible resentful look in Great's eyes when Provender took his signet ring off him, that EVIL STARE of his.) I nearly cheered when a trial date was set and I did cheer when I learned that, on his TRIAL'S EVE, Scrase had killed himself. Even though, if he had gone to prison, it would have been for life—he would never LEAVE STIR—this was altogether better. I'm not by nature a sadistic or uncharitable man, but I truly hope he suffered during his final moments._
_What remains for me is to wonder about the Gleeds, whose inner strife reached out and affected ordinary existences like yours and mine, whose squabbling can have a ripple effect, shake the world, TEAR LIVES. What are we to make of people like them who can casually, inadvertently, with a selfish decision, destroy some and leave the REST ALIVE? People who have such power and wield it with such thoughtlessness?_
_I don't know. It may well be that I'm going mad. The anagrams—my trade, my craft—are closing in around me, ensnaring me. I've been too long inside my own brain and I can't seem to find a way out. Everything makes sense and nothing does._
_Maybe, with time, this will pass. Funnily enough, I feel better simply for having typed this out to you, using my brand new videotyper._
_I've been getting a lot of offers of work lately, on the strength of my new Gleed patronage. I've been turning them down, but maybe I should take them up. Maybe work is the best cure. Make myself master of the anagrams again, rather than have them be the master of me._
_I have money, Family patronage, everything I could possibly wish for. Yet I'd give it all away in a flash, if it meant I could have my friend Merlin back, sitting opposite me, annoying me, one-upping me. Really, I would._
_Yours sincerely,_
_Romeo_
_P.S. You remember, when we arrived at Dashlands by tram, I mentioned an anagram of Provender's full name which I wasn't able to account for then? I think I can now. PROVENDER OREGANO GLEED—GREEN ROAD DEVELOPER O.N.G. The O.N.G. bothered me. I don't like left-over letters. It's untidy. Then I realised, in the light of subsequent discoveries, that it might well stand for "On Needle Grove". You've seen the recent news stories about the estate, I take it. The anagrams twist and turn. They're snaky and deceptive. But in the end, they never lie._
Saddened, Is folded Moore's letter shut and tucked it back into its envelope. Poor man. Half crazy with grief. His world, even more than hers, had been churned up by Damien, and by Carver and Great, and no amount of Gleed kindness after the fact could smooth out the gouges. She resolved to phone him sometime, offer to meet up with him for a drink and a chat. It was the least she could do.
An odd thought struck her. She reopened the letter and reread the P.S. "Subsequent discoveries'? "Recent news stories'? She didn't get the reference. She would ask someone at work today what was going on at Needle Grove. If she couldn't find anyone who knew, she'd go to the local library and check back through the newspaper archives. Obviously she had missed something, but then lately she had become a lot less thorough about keeping up with current events. The outside world had ceased to impinge so directly on her, much to her delight.
Then there was the second letter. This one was in a large, card-backed manila envelope, and had apparently been hand-delivered. There was no stamp or frank. She opened it carefully, with fingertip delicacy.
Inside were maps. No covering note, just a sheaf of maps.
Architectural plans, to be precise. Copies of architectural plans...
...of Needle Grove.
Each plan detailed a section of the estate, and on most of them, though not all, there was a portion shaded in green.
Who had sent her this? She thought she knew, but she discarded the notion, not willing to acknowledge it until she had to.
Some of the shaded portions were large, some small. Each touched the edge of the page it was on. Each formed an irregular geometrical shape.
It didn't take Is long to divine that there was an over-all pattern. Cumulatively the shaded portions amounted to something greater. They were parts of a whole.
She cleared a patch of floor in her bedsit and began laying the plan copies out. Her shift was due to start soon and already she could hear other nurses in the lodgings leaving their rooms and clacking along the corridor to the sky-bridge which led across to the main part of the hospital. She was in her uniform and ready to go, but first there was this puzzle, the plan copies like jigsaw pieces demanding to assembled and solved.
On her knees, she shuffle the sheets of paper around, aligning edges, matching up shaded portion with shaded portion. The pattern grew. The geometrical shapes fell together, creating several larger, discrete geometrical shapes.
Then, all at once, she had it, and she sat back breathlessly on her haunches, staring down. The plan copies were spread out in front of her in a rough rectangle, across the middle of which were four capital letters and a punctuation mark picked out in green:
**ISIS?**
Each character was comprised of streets, roads, walkways, bridges; of plazas, squares, sections of wasteland; of numerous interlocking outdoor segments of the estate, all at different levels. Someone had taken a lot of time, expended a lot of effort, in putting this together. But for what purpose? Why contrive such an elaborate, convoluted way of writing out her name?
"And why do it anonymously?" she said aloud, adding, "Provender," as though he were in the room with her.
She peered at the plans again, and it was the question mark that snagged at her and made her think there was more to all this than met the eye. That, combined with the remarks in Moore's letter. Something was afoot. This wasn't merely some sort of declaration she was looking at, a statement of her name...
It was an invitation.
SHE GOT ONE of the other nurses to call in sick for her—stomach bug, sudden thing, sorry. She changed into civvies and sneaked out of the hospital. A bus transported her across town, the bus she always used to take when visiting Damien. She knew the route intimately, every stop and turn. Part of her felt she was wasting her time, she was blowing a sick-day for nothing, she had misread the meaning of the plans. Another part of her knew otherwise.
As she passed beneath an entrance arch and stepped onto Needle Grove soil, she flashed back to her and Provender's run-in with the Changelings and a frisson of remembered fear shivered through her. Her throat tightened and her breathing felt constricted. She nearly turned back. Then she spied a group of workmen nearby, gathered in a hard-hatted huddle, studying blueprints. Behind them stood a mechanical digger and a dump-truck whose hopper was heaped high with fresh earth. The sight restored her confidence and refreshed her curiosity. She walked past the men, close enough to overhear one of them, who looked very much like a site foreman, say something about avoiding a gas main when they began excavation. Which was reassuring to hear but not exactly a huge clue as to what was going on.
She continued walking, and was soon drawn towards an area of greenery that shimmered, mirage-like, at the base of the nearest block but one. It looked as incongruous and unreal as any desert oasis: an acre (she estimated) of newly-laid turf which stretched around the corner of the block, with mature pines and cypresses planted in it, clumps of shrubbery, some outcrops of boulder, and even a meandering manmade stream. Several of the estate's residents were out and about among the greenery, some wandering, others lolling on benches or basking on the grass. A pair of Young Moderns were perched on one of the boulder outcrops with that unmistakable air of _our patch_ about them, but somehow their cocksureness seemed tempered, as though the novelty of their location—sitting on rock, surrounded by grass—was something they were still acclimatising to.
Is ventured further into the estate, and higher, climbing an external staircase until she arrived at a tenth-storey plaza. Here, too, greening had occurred. Huge potted palms and fig trees overshadowed a square of rock garden, at the epicentre of which stood a brand new recreation area for children—swings, seesaw, a climbing frame like a scale-model skeletal city. Kids swarmed everywhere, putting the gleaming equipment to the test. They swung the swings higher than they were intended to go and they clambered like monkeys over the climbing frame and dangled precariously from the uppermost bars. One boy, Is noted, seemed to prefer the rock garden and was busy trying to kick loose a cemented-in stone with his foot. With persistence, he would no doubt prevail. Another boy, no less destructive, was picking at the bark of one of the palms, tearing off small strips.
Probably this would happen more and more, it occurred to Is. None of this new stuff would stay pristine and undamaged. That was just how people were.
But at least someone was making the effort. At least someone (Provender) was trying to brighten up the estate.
If only she could be sure it was purely for the Needle Grovers" benefit and not for his own.
Elsewhere, she came across a small jungle.
A hothouse clustered with cacti and ferns.
A building site which would, when finished, if she didn't miss her guess, be a crazy-golf course.
Another building site which was evidently on its way to becoming a yew hedge maze.
She went higher still, and higher, traversing from block to block, and each time she halted and looked out she saw another patch of the estate that was being or had been transformed, verdured, swarded. Residents she passed were already sounding blasé about the improvements being visited on their home, and several of them assumed that the Risen London Authority was responsible and that, mark their words, this meant rents would be going up, just you wait and see. Their cynicism was ingrained. They couldn't help being jaded about the widespread emeralding of the estate. But still, in their eyes, they did look just that little bit pleased.
Finally Is reached the apex of one block; she could go no higher. From this lofty vantage point she observed that the tops of a number of other blocks now sported roof gardens. She observed, too, how the introduction of lush green areas altered the look of Needle Grove. The blocks no longer crowded side by side in rigid ranks. They were softly connected, cushioned. The greenery brought untidiness, and with that untidiness, relief.
What she could not distinguish, even from so high, was the pattern of her name writ large across the estate. Only a bird flying overhead might perceive it, or the pilot of an aircraft, or God. She had the feeling, however, that because the component parts of the pattern were so disparate, so unalike, the naked eye—even God's—would not be able to make it out. Only someone who had seen the word highlighted on the plans would know it was there.
Provender.
Such a grand gesture. Such a flashy gesture.
What did he hope to achieve by it?
Is knew. She didn't like to admit it, but she knew. What she also knew but didn't like to admit was that—damn him—it was working.
BACK AT THE hospital, there was a car waiting for her. Outside the ground-floor entrance to the nurses" lodgings. A pearl-white Dagenham Seraph. Hovering on the tarmac, its idling motor like the flutter of wings.
The chauffeur stood by the rear door, which was open. He recognised Is and saluted her, nudging the peak of his cap.
Is peered into the rear of the car. It was empty—nobody on the back seat.
Empty, expecting to be filled.
She paused.
The chauffeur now fixed his gaze into the middle distance, under orders not to interfere, not to influence her in any way. Her decision and hers alone.
She continued to pause, knowing that whatever choice she made now, it was irrevocable. The offer being extended to her was, she understood, one-time only. No going back. No room for second thoughts.
The Seraph hummed.
Who was she? What had she done to deserve this?
She was Is. She was nobody.
At long last, she made up her mind.
With solid determination, and just a hint of a smile, she moved as if towards the car.
The chauffeur gently laid a hand on the rim of the door, smiling too.
And then—
**ACKNOWLEDGEMENTS**
The author wishes to extend his gratitude—in an ideal world it would be his extravagance as well—to the following:
Simon Spanton (M.S. POINTS ANON) and Gillian Redfearn (AN ELFIN DEAR GIRL) for their insightful, in-depth editing;
Ilona Jasiewicz (IN-CASE-O'-JAIL WIZ) and Krystyna Kujawinska (JINK AWAY, STRAY SKUNK) for their help with the Polish dialogue, especially the sweary bits;
Antony Harwood (A NON-WORDY OATH) and James Macdonald Lockhart (CLAN ADDS TOOL—JACKHAMMER) for being A GENT'S agents;
everyone at Arts Council South East (SALUTE COUTH COIN STARS) for their generous financial support;
and Peter Crowther (WHERE P.C. ROTTER?), Eric Brown (BROWN RICE), Adam Roberts (DR. AT SOME BAR), Roger Levy (GREY LOVER), and Chris Wooding (I OWN RICH GODS), for their generous non-financial support.
This book is fondly dedicated to my family, Lou Lovegrove (OO, LUV, LEG-OVER!) and Monty Lovegrove (ROT MY OVEN-GLOVE)... and also to my Family.
James Lovegrove
(ELSE: V. V. MAJOR EGO)
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After a series of disasterous political decisions the United Kingdom has finally fallen foul of the International Coummunity. Ostracized and bombed at random, the country has fallen apart. With the infrastructure in ruins, tiny communities struggle on relying on ancient traditions and myth for their structure and identity.
In the village of Downbourne the mayor has styled himself the Green Man. But even he is powerless to stop a raid on the village by a London based gang who kidnap a number of the village's women. One of them is the schoolmaster's wife. Their marriage was an arid disaster, but the schoolmaster feels bound to do the right thing and sets off on a journey through an England at once terrifying and magical to get her back. But does this particular damsel even want to be rescued?
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\t\t<h2>Galerie</h2>
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\t\t<h2>Ces films peuvent vous intéresser</h2>
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Oman partners with bp on multi-gigawatt renewables, green hydrogen development
January 17, 2022 Marija Maisch
The British energy giant will support the potential development of multiple gigawatts of wind, solar and green hydrogen projects in the Middle Eastern country by 2030.
Philippines clears 62 PV projects totaling 1.3GW for renewable portfolio standards
January 17, 2022 Emiliano Bellini
The list of the eligible renewable energy producers also includes 36 hydropower facilities totaling 412.8MW, 36 biomass schemes with an aggregate capacity of 264.8MW, seven wind farms with a total power of 409.9MW, and six geothermal power plants totalin...
Ecoflow launches its portable solar storage solution in Europe
January 17, 2022 Pilar Sánchez Molina and Sandra Enkhardt
The basic version of the "Delta Pro" product has a storage capacity of 3.6kWh. The weight of the battery in the basic version is 45kg and its size is 63.5x28.5x41.6 cm.
Register now & discover the most innovative PV solutions of 2021
pv magazine Webinar
The upside of TOPCon: high efficiency, low degradation in mass production
4:00 pm – 5:00 pm AEST, Sydney, Melbourne | 1:00 pm – 2:00 pm AWST, Perth
Webinar partner Jinko Solar
Analyze BESS: online diagnostics for safety, performance, and extended lifetimes
Thursday, 20. January 2022
5:00 pm – 6:00 pm CET, Berlin| 11:00 am – 12:00 pm EST, New York City | 8:00 am – 9:00 am PST, Los Angeles
Webinar partner ACCURE
Understanding and Mitigating the Dangers Posed by Hail and Wind
11:00 am – 12:00 pm EST, New York City | 8:00 am – 9:00 am PST, Los Angeles | 5:00 pm – 6:00 pm CET, Berlin
Webinar partner Nextracker
Webinar partner RETC
Reducing the environmental impact of PV mounting structures
3:00 pm – 4:00 pm CET, Berlin, Paris, Madrid | 2:00 pm – 3:00 pm GMT, London / WET, Lisbon | 4:00 pm – 5:00 pm EET, Athens
Webinar partner ArcelorMittal
Kesterite solar cell with 11.76% efficiency via aluminum oxide passivation layer
The solar cell was built with Al2O3-incorporated CZTSSe absorbers using aqueous spray pyrolysis in ambient air. It achieved an open-circuit voltage of 0.469 V, a short-circuit current of 36.96 mA cm2, and a fill factor of 67.25%.
Green hydrogen could disrupt global trade, bilateral energy relations
While there are still many uncertainties as to the way in which hydrogen trade might evolve and change economic ties and political dynamics between countries, experts agree that green hydrogen can bring winds of change to the global energy arena. Accordi...
Germany's second rooftop PV tender concludes with average price of €0.0743/kWh
January 17, 2022 Sandra Enkhardt 1
The procurement exercise's final prices ranged between €0.0570 and €0.0828 per kWh.
Toshiba launches 20Ah rechargeable lithium-ion battery
Toshiba has developed a battery that can be used with PV modules, with a design that charges and discharges at high currents. The new 20Ah-HP SCiB product has a rated capacity of 20Ah, a nominal voltage of 2.3V, and an input power of 1,900W. It measures ...
Switzerland's largest solar park planned to power refinery
The PV facility will have a capacity of 7.7MW and will rely on 19,000 of the latest generation solar modules from the Swiss Center for Electronics and Microtechnology (CSEM).
Sungrow and KarmSolar Cooperate on the Microgrid BESS Project for Cairo 3A Group
Sungrow signed a new BESS contract with KarmSolar, Egyptian largest private sector solar energy provider.
DEWA raises production capacity of the first project of the Mohammed bin Rashid Al Maktoum Solar Park's fifth phase to 330MW
HE Saeed Mohammed Al Tayer, MD&CEO of Dubai Electricity and Water Authority (DEWA), announced that the production capacity of the first project of the fifth phase of the Mohammed bin Rashid Al Maktoum Solar Park has increased from 300 megawatts (MW) to 330MW.
DEWA
TMEIC receives 100 MW order for large-scale battery energy storage systems for power grids in the UK
Toshiba Mitsubishi-Electric Industrial Systems Corporation has signed an agreement to supply large-scale battery energy storage systems for two 49. 5MW facilities aimed at power grid stability (two plants totaling approximately 100MW) with Nippon Koei Energy Europe B.
Toshiba Mitsubishi-Electric Industrial Systems Corporation
Sunseap partners NTUC Club in first solar project for lifestyle and entertainment buildin
Sunseap Group said today it is installing a rooftop solar system at Downtown East in Pasir Ris, its first clean energy project for a lifestyle and entertainment building.
Sunseap
2021 was a record-breaking year for European solar, now we must increase ambition
January 12, 2022 WALBURGA HEMETSBERGER, CEO, SOLARPOWER EUROPE
Right before the holiday season, the European Commission unveiled the latest installment of its "Fit for 55" legislative package – plans that aim to put the continent on track to reducing emissions by 55% by 2030. These additional proposals include the Hydrogen and Decarbonised Gas Package, as well as a revision to the Energy Performance of Buildings Directive (EPBDII).
EU to gut the principle of sustainable taxonomy with inclusion of nuclear and gas
January 3, 2022 FELICIA JACKSON, CENTER FOR SUSTAINABLE FINANCE OF THE SCHOOL OF ORIENTAL AND AFRICAN STUDIES, UNIVERSITY OF LONDON 1
The EU's Sustainable Taxonomy was intended to complement the Green Deal, provide investors with certainty about the sustainability of their investments, and help channel billions into sustainable, low-carbon processes and technologies. Despite input from experts and NGOs, the inclusion of gas and nuclear power just proposed by the Commission suggests that, once again, politics is trumping science.
Brazil heads for a solar installation rush
December 29, 2021 Angel Antonio Cancino, analyst, IHS Markit 2
Brazil's deployment of distributed generation PV (below 5 MWp) has exploded from a total capacity of 500 MW in 2018 to 7 GW by September of this year. The trigger for this increase, alongside rocketing electricity prices, was the 2019 proposal of law 5829, writes IHS Markit analyst Angel Antonio Cancino. The proposal is expected to pass into law at the end of this year and will gradually introduce grid-access charges for residential and commercial system owners.
A 200 GW solar year in 2022
December 27, 2021 Corrine Lin, analyst, InfoLink 2
Structural imbalances in the supply chain and the energy intensity and consumption controls that China imposed in late September have caused prices for most PV module materials and components to continue to rise. Shipping fees and PV plant construction costs also remain high. PV plants in many regions will therefore be postponed until next year, but it remains unclear when module prices will start to fall. Despite these challenges, the global race to cut carbon emissions continues, and InfoLink's Corrine Lin forecasts a bright future for PV deployments in 2022.
Europe faces 'new era of energy dependency'
December 21, 2021 Analysis by WoodMac 1
The EU has been pouring money into European battery manufacturing and recycling projects but has, as yet, been unable to address the critical question of raw materials, according to analyst WoodMac.
2021 and beyond: European solar manufacturing must shine again
December 3, 2021 WALBURGA HEMETSBERGER, CEO, SOLARPOWER EUROPE
As 2021 ends, we enter a period of reflection and preparation. The ongoing pandemic has brought supply chain disruption, while the increasingly severe effects of the climate crisis loom over us. This winter, Europeans are struggling through unprecedented energy costs, driven by extremely high global gas prices. A year of difficulties has shown that Europe, more than ever, must accelerate the deployment of renewables to provide our economy with reliable, low-cost, and clean energy.
Solar supply chain trouble to ease this year, according to analyst
January 11, 2022 Max Hall
Wood Mackenzie has predicted solar equipment cost increases will ease back after last year saw the average cost of solar electricity rise for the first time in the Asia-Pacific region.
Latvian plan to exempt big energy consumers from renewables surcharge approved by EU
December 22, 2021 Max Hall 2
The Baltic state has offered energy-intensive, international-facing industries up to an 85% discount on a surcharge levied on electricity consumers since May 2017 and made the scheme wider ranging this year, in a move approved by the European Commission.
China and India to drive record world coal demand next year
Advances in solar power and other clean energy technologies have failed to keep up with demand for electricity as economies rebound from the Covid crisis and China and India's fossil fuel appetite will ensure the world stays well short of what is needed for a net zero 2050 for at least the next three years.
Solar company's Christmas party blamed for Omicron-variant Covid outbreak in Oslo
December 6, 2021 Max Hall 1
A news article published on Friday stated 13 cases had been confirmed and a senior physician said the working hypothesis was that at least half of the 120 people who attended the event had been infected. pv magazine has contacted Scatec for an update.
'World's biggest TOPCon solar plant' begins generating
December 2, 2021 Max Hall
Solar manufacturer Jolywood, which supplied almost 500 MW of its bifacial tunnel oxide passivated contact panels for Oman's Ibri II facility, has claimed the power plant is the biggest to date to deploy the high-efficiency technology.
Solar job numbers kept on rising in 2020
October 27, 2021 Max Hall
The latest edition of a clean power jobs survey produced by IRENA and the International Labour Organization has stressed the important role which will need to be played by the public sector if the energy transition's employment benefits are to be shared equally.
What COP26 means for solar
December 8, 2021 pv magazine
COP26 was either a great success or an abject failure, depending on who you talk to. What matters for the solar industry is the extent to which decisions agreed in the Glasgow Climate Pact are going to change the direction of the energy and financial sectors.
India expands domestic content rules for open-access, net-metering PV projects
January 17, 2022 Uma Gupta
The Indian government has ruled that only solar products and companies on the Approved List of Models and Manufacturers will be eligible for open-access and net-metering projects, in addition to government-backed installations. This includes arrays set up to sell electricity to the government under Section 63 of the Electricity Act, 2003. The amendment will apply to projects that request open access or net metering from April 1, 2022.
The weekend read: V2G driving grid changes
January 15, 2022 Marija Maisch 3
The uptake of EVs in the years ahead will add up to staggering battery capacity, mostly sitting idle on driveways. The two-way flow of electricity from EV batteries, known as vehicle to grid, could not only enable power systems to rely on intermittent renewables, but could also be the trump card for network operators to respond to grid disturbances. However, there are still a few catches to be worked out, as Marija Maisch explains.
The Hydrogen Stream: Hydrogen refueling stations for automotive market
January 14, 2022 Sergio Matalucci 3
Canada's First Hydrogen and German consulting firm FEV are developing a hydrogen fueling station for remote locations where there are no electrical power grids available. Furthermore, Japan and Indonesia have started to cooperate on hydrogen and carbon capture technologies and the UK gas grid is set to start blending hydrogen around the country from next year.
Reliance Industries commits over US$75 billion for green energy projects in India
January 14, 2022 Uma Gupta 2
The Mukesh Ambani-led diversified business conglomerate has agreed to invest INR 5 lakh crore (US$67.6 billion) in building 100 GW of renewable energy capacity and green hydrogen eco-system in the state. It will also invest INR 60,000 crore (US$8.1 billion) in setting up manufacturing facilities for new and renewable energy equipment, including solar modules, electrolyzers, energy-storage batteries, and fuel cells.
Fluence, QuantumScape partner on solid-state lithium-metal energy storage
The companies will collaborate on what is believed to be a first-of-its-kind attempt to incorporate QuantumScape's solid-state lithium-metal battery technology into stationary energy storage products.
BIPV no refuge
December 8, 2021 Jonathan Gifford
Deployment in the building integrated PV segment is accelerating, and so too are the number of solar products available to architects and developers. And while BIPV had long been the segment in which an array of thin-film technologies could shine, they are now in increasingly stiff competition with crystalline silicon rivals.
Botswana issues tender for six PV power plants
The tendered solar PV plants are expected to help the Sub-Saharan country reduce its dependence on electricity imports from South Africa.
Major advances for US, Australian solar window specialists
January 17, 2022 Bella Peacock and Ryan Kennedy
Australian solar window supplier ClearVue says its products can reduce carbon emissions in buildings by as much as 90%, while California-based BIPV window coating producer Ubiquitous Energy has raised $70 million to scale up its own tech.
Micro-inverter for high-power solar panels from Hoymiles
January 14, 2022 Emiliano Bellini 2
The device has a 4-in-1 design, which means it can be connected with four solar panels with a power output of up to 625 W each, through four independent connections. The output of each panel is tracked and converted individually. According to the Chinese manufacturer, the micro-inverter can ensure savings of up to 50% due to the lower number of devices and cables needed.
Israel launches tender for 100 MW of agrivoltaics
Selected projects will be awarded a fixed tariff of ILS 0.2091 ($0.06.708)/kWh over a 23-year period.
Solar-powered battery gigafactory gets tick of approval in UK
Local planning committees have given a go-ahead to a £2.5 billion gigafactory in the English West Midlands. The facility will be powered by 100% onsite solar and storage and equipped to both manufacture new batteries and recycle used ones.
Finding faults faster
December 8, 2021 Mark Hutchins 1
PV cell and module manufacturers are increasingly turning to artificial intelligence to monitor production lines and the products coming off them in minute detail. As inline monitoring and testing equipment become more sophisticated, cell and module makers must be prepared to manage the enormous amounts of data and pull out the points that will save them time and money. pv magazine examines the software solutions backing state-of-the-art PV production.
Perovskite solar module with 21.36% efficiency via new passivation tech
Lithuanian scientists built the panel with 23.9% efficient solar cells with operational stability of over 1000 h. The module has an active area of 26 cm2.
Panasonic unveils 410 W solar panel with 22.2% efficiency
The new heterojunction module series is compatible with Panasonic's Evervolt battery and has a power output ranging from 400 to 410 W. It also features a temperature coefficient of -0.26% per degree Celsius.
NREL's online tool to assess viability of geothermal heat pumps
The research institute has upgraded its REopt web tool to include ground-source heat pump technologies. US homeowners will now be able to simulate the impact of converting conventional heating and cooling systems to geothermal heat pumps.
Chinese PV Industry Brief: JinkoSolar announces Jiangxi Jinko's IPO pricing
January 14, 2022 Max Hall 1
Jiangxi Jinko plans to issue 2 billion shares at RMB5.00 per share and expects to raise net proceeds of around RMB 10.0 million. Solar manufacturer Solargiga said it expects a 17% revenue growth for 2021.
All solar is equal, but rooftop solar is more equal
January 14, 2022 John Fitzgerald Weaver
Cornell Researchers have found that upstate New Yorkers prefer rooftop solar to community solar under 50 acres, but opinions are split 50/50 over large-scale ground mounts. The distaste for utility-scale solar is strongest when converting forests, public land and productive farmland.
All eyes upstream
December 8, 2021 pv magazine 1
The United States faces a number of compelling issues in its push to expand solar. Clean Energy Associates CEO Andy Klump recently spoke to pv magazine about supply chains, domestic manufacturing, climate change, and COP.
Perovskite ink for flexible solar panels
Developed by a Canadian start-up, Solar Ink can be used to create standalone perovskite solar modules or it can be combined with existing solar modules in a tandem configuration. It can be coated on both flexible and rigid substrates, resulting in translucent solar cells which, in turn, can be used to produce flexible and light modules for application in solar windows and vehicle-integrated photovoltaics.
Modeling method for agrivoltaics in greenhouses
Spanish researchers have developed a new modeling technique to assess the performance of semi-transparent PV systems for greenhouses. Their novel approach considers the broadband and spectral content of the irradiance, the solar cell technology and its performance metrics, and the relationship between the photosynthetic rate and the effective photon flux that falls on the crops.
Seraphim releases PV module series with 595/670W of output, up to 21.57% efficiency
Seraphim's new solar modules are available in monofacial and bifacial variants. They rely on multi-busbar technology and are built with 210 mm silicon wafers.
Work underway on Tesla's rooftop solar system in Texas
A drone pilot has discovered that Tesla is starting to install solar panels, racking and inverters on the rooftop of a manufacturing facility it is building in Texas.
Solar module tech from oldest PV system in Netherlands
A solar panel on display at a science museum in the Netherlands is one of 2,748 modules that were used for the country's oldest PV system. The module has an efficiency of around 9% and a power output of 18W. It was manufactured by Germany-based AEG-Telefunken in 1982.
Making cheaper H2
The hype surrounding green hydrogen is real, but does the cost-reduction outlook for its production technologies live up to it? Christian Roselund looks at the technology, transportation, application and enabling policies behind the promising green energy carrier.
Utility scale ocean battery, a bedfellow for floating PV
A new underwater battery storage technology is coming from Netherlands-based Ocean Grazer to address the issue of offshore long-duration storage. The company's Ocean Battery is touted as innovative yet simple, based on existing technology, and capable of enhancing marine life along the way.
US scientists explore how to compensate battery owners for grid value
January 12, 2022 William Driscoll 1
Current price signals to distributed battery owners "do not align with grid value," says a study from the Lawrence Berkeley Laboratory.
Australian energy giant submits plan for 500MW of PV, 400MWh of battery storage
January 12, 2022 Blake Matich
Woodside Energy has submitted a proposal for a 500MW solar facility to the Western Australian Environmental Protection Authority. The company wants to install up to 1 million solar panels to power industrial customers in the state, including its own Pluto LNG export facility.
Backing for solar-plus-storage mini grids in Lesotho
The 11 planned off-grid networks will offer clean power to around 20,000 people for €0.28/kWh, according to one of the EU bodies which is backing the project.
LG Energy Solution IPO attracts $80bn in bids
LG Chem's energy storage and battery division's $10.7 billion initial public offering received a staggering response from institutional investors, Reuters has reported. | {
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{"url":"https:\/\/symbol.codes\/paper","text":"# Hsin-Po Wang\n\nPhD @ UIUC\n\nFrom the newest to the oldest.\n\nAbbreviation Title\nHypotenuse19 Polar Codes\u2019 Simplicity, Random Codes\u2019 Durability\nLoglogTime19 Log-logarithmic Time Pruned Polar Coding\nLargeDevia18 Polar-like Codes and Asymptotic Tradeoff among Block Length, Code Rate, and Error Probability\nLoglogTime18 Log-logarithmic Time Pruned Polar Coding on Binary Erasure Channels\nModerDevia18 Polar Code Moderate Deviation: Recovering the Scaling Exponent\n\nModerDevia18 focuses on the moderate deviations regime (MDR) of polar coding. MDR is also called the moderate deviations principle (MDP) paradigm in some references. It discusses about the relation among block length ($N$), error probability ($P$), and code rate ($R$) in the region where $P$ is about $\\exp(-N^\\pi)$ and $R$ is about $\\text{Capacity} - N^{-\\rho}$ for some positive numbers $\\pi,\\rho$. The precise goal is to characterize the region of $(\\pi,\\rho)$ pairs that are achievable for $N\\to\\infty$.\n\nWhile ModerDevia18 deals with the classical polar codes constructed in Ar\u0131kan\u2019s original paper, LargeDevia18 extends the theory to a wide class of polar codes. We are able to predict, up to some big-$O$ notations, how codes constructed with a certain kernel $G$ will behave given the scaling exponent $\\mu$ (or its inverse $\\rho=1\/\\mu$) and the partial distances. It does not mean that such prediction is easy to make because finding the precise $\\rho$ (or $\\mu$) is difficult. That said, bounding $\\rho$ is easy, so is bounding the MDP behavior.\n\nLoglogTime18 stands on the result of ModerDevia18 and shows that, if we would like to tolerate higher $P$ and lower $R$, we can reduce the complexity of the encoding and decoding from $\\log N$ to $\\log(\\log N)$, per information bit. By higher $P$ we mean $P$ scales as $N^{-1\/5}$; By lower $R$ we mean $R$ scales as $\\text{Capacity}-N^{-1\/5}$. Thus the constructed codes still achieve capacity.\n\nWhile LoglogTime18 deals with the binary erasure channels, LoglogTime19 handles arbitrary symmetric $p$-ary channels, where $p$ is any prime. The latter result is similar: by tolerating that $P$ converge to $0$ slower and that $R$ that converge to the capacity slower, we can reduce the complexity to $\\log(\\log N)$ per information bit. In both LoglogTime18 and LoglogTime19, codes are construct with the standard kernel $[^1_1{}^0_1]$.\n\nWe later found (not included in either paper) that the conclusion generalizes to arbitrary discrete memoryless channels.\n\nHypotenuse19 shows that it is possible to construct codes whose error probabilities and code rates scale like random codes\u2019 and encoding and decoding complexities scale like polar codes\u2019. On one hand, random codes\u2019 error and rate are considered the optimal. On the other, polar codes\u2019 complexity ($\\log N$) is considered low. (Not the lowest possible complexity, as there exist $\\log(\\log N)$ constructions for general channels and $O(1)$ constructions for BEC.) This result holds for all discrete memoryless channels, the family of channels Shannon considered in 1948. This result extends a series of works done by (alphabetically) Ar\u0131kan, B\u0142asiok, Fazeli, Guruswami, Hassani, Honda, Korada, Mori, \u015ea\u015fo\u011flu, Sutter, etc.\n\nSee Table 2 at page 40 in Hypotenuse19 or the following replication.\n\nBEC BDMC $p$-ary $q$-ary finite asym.\nLLN Arikan09 Arikan09 STA09x STA09x STA09x SRDR12\nwLDP AT09 AT09 STA09x MT10c Sasoglu11 HY13\nwCLT KMTU10 HAU14 BGNRS18 by us by us by us\nwMDP GX13 GX13 BGS18 by us by us by us\nLDP KSU10 KSU10 MT10c MT10c by us by us\nCLT FHMV17 GRY19 by us by us by us by us\nMDP LargeDevia18 by us by us by us by us by us","date":"2020-02-18 10:57:54","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\": 0.8285259008407593, \"perplexity\": 2078.1894006553766}, \"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-2020-10\/segments\/1581875143646.38\/warc\/CC-MAIN-20200218085715-20200218115715-00349.warc.gz\"}"} | null | null |
Home » You're not running any free education in Ogun – NANS tells Abiodun
You're not running any free education in Ogun – NANS tells Abiodun
Gov Abiodun had in 2019 said he was committed to running free education in all public schools in Ogun State, stopping the payment of N3,700 which he had earlier approved as PTA donation to schools.
But NANS disagrees with Abiodun, stressing that what the present dispensation is masquerading under mere abolition of PTA levies did not equate free education.
According to a statement signed by the spokesperson of NANS in Ogun, Olufemi Owoeye, it was stated in clear terms that "cancellation of fees alone is not commensurate to free education."
Owoeye said "NANS Ogun JCC is against the ban placed on payment of dues" and the fact that such is being likened to free education in the State. He queried who will provide free educational materials, security, conducive environment and other indispensable facilities.
"What we're seeing is proscription of payments and nothing more," it was said.
The students further explained that school administrators in Ogun were "battling with unpaid five months running costs," thereby bringing about the inability of schools to provide basic teaching aids.
To address these challenges, NANS called for "the reintroduction of a regulated Parent-Teachers Association dues," stating that "even our parents are willing to pay.
"We urge the government to summarily lift ban on payment of Parents-Teachers Association (PTA) dues as it is traditionally a voluntary contribution of parents to offset some financial expenses on behalf of the school," Owoeye pleaded.
The levies, according to him, were used by schools to pay for security, cut grasses, repair leaking roofs and others.
He told Gov. Abiodun that the current economic realities have shown that government alone could not cater for the academic sector, asking the governor to review his policy on PTA levies in order not to "impoverish" public schools.
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Buhari Govt Reveals When Teachers Will Start Getting Increased Salaries
EKSU warns ASUU against disrespecting, maligning varsity's Governing Council | {
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Renate Potgieter, geb. Junker (* 26. März 1938 in Spremberg) ist eine ehemalige deutsche Leichtathletin, die in den Jahren um 1960 als Weitspringerin und Mehrkämpferin aktiv war.
Sie startete bis 1961 für den Rheydter Turnverein 1847 und, nach ihrer Heirat mit dem südafrikanischen Hürdenspezialisten Gert Potgieter, für den ASV Köln.
Sie belegte bei Deutschen Meisterschaften zweimal (1957 und 1962) den dritten Platz im Weitsprung und 1961 den dritten Platz im Fünfkampf. Hinzu kommt ein Meistertitel 1962, den sie mit der 4-mal-100-Meter-Staffel des ASV Kölns gewann und ein weiterer Titel aus dem gleichen Jahr mit der Fünfkampf-Mannschaft des ASV Köln.
Sie nahm an den Olympischen Sommerspielen 1960 in Rom teil. Die in der Qualifikation geforderten 5,80 m erfüllte sie mit einem Sprung von 6,00 m. Im Endkampf gelangen ihr fünf weitere Sprünge über 6 Meter, von denen der beste mit 6,19 m gemessen wurde. Damit lag sie nur sehr knapp um zwei Zentimeter hinter der Bronzemedaillengewinnerin Hildrun Claus aus der DDR.
Ihre persönliche Bestleistung beträgt 6,23 m, gesprungen am 7. August 1960 in Erfurt.
Sie ist 1,68 m groß und hatte ein Wettkampfgewicht von 62 kg.
Potgieter lebt mit ihrem Mann in Pretoria.
Weblinks
Weitspringer (Deutschland)
Olympiateilnehmer (Deutschland)
Teilnehmer der Olympischen Sommerspiele 1960
Frau
Geboren 1938
Deutscher Meister (Leichtathletik)
Sprinter (Deutschland)
Deutscher | {
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Q: Connecting PostgreSQL/PostGIS and MapGuide Maestro This is less a specific question, but hopefully more of an open question. There is little documentation regarding connecting the excellent OS web mapping software MapGuide Maestro (http://trac.osgeo.org/mapguide/wiki/maestro) with PostgreSQL/PostGIS (http://postgis.net/).
Can anyone give pointers on the connection of these two?
A: If your postgis is setup correctly, connecting to Maestro should be fairly straight forward!
Have you tried the following:
http://trac.osgeo.org/mapguide/wiki/maestro/UserGuides/RDBMSFeatureSource
| {
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Three pre-war American cars sold for more than a million dollar at the 2015 Bonhams Amelia Island classic car auction in Florida. A 1930 Cord Model L-29 Town Car achieved $1.76 million while a 1908 American Underslung sold for $1.74 million – a new record. A 1932 Stutz DV-2 Super Bearcat Convertible sold for just over a million.
Bonhams had around 80 cars on offer at its inaugural auction at the annual mid-March classic car week at Amelia Island in Florida. Bonhams earned $13.95 million with a sell-through rate of 79%.
Many of these cars were from the pre-Second World War period with Ferraris and Mercedes Benz cars from the 1950s and 1960s largely absent.
The 1930 Cord Model L-29 Town Car belonging originally to actress Delores Del Rio achieved $1,760,000 – the most expensive car sold at the first Bonham auction at Amelia Island. Only four of the L-29s were ever built and this is the only surviving short-wheel base survivor.
The 1908 American Underslung 50 HP Roadster surprised when it sold for $1,738,000 – a new world record and well above the pre-auction estimate of $1.1 – $1.2 million. The Underslung famously had its center of gravity very low with large wheels assuring sufficient ground clearance to cope with early 20th-century roads. Many consider the Underslungs to have been the first American sports cars.
Another classic American sports car, a 1932 Stutz DV-2 Super Bearcat Convertible, sold for $1,012,000 at the Bonhams Amelia Island 2015 sale. This highly original Bearcat still has its original Weyman fabric skin. Only 20 of these Bearcat Convertibles were ever built with only 8 surviving and all the others in prominent collections.
1930 Rolls Royce Phantom I Transformal Phaeton – the car formerly owned by Marlene Dietrich sold for $742,500 at the lower end of the pre-auction estimate.
1980 Ferrari 512 BB – this low-mileage, exceptionally well-preserved 512 sold for a new model record $359,700 around three times the pre-auction estimate of $100,000 – $150,000.
1981 BMW M1 Coupé – the German sports car sold for a $605,000 – a new model record and well above the pre-auction estimate of $400,000 – $450,000.
A 1934 Mercedes Benz 500K Four-Passenger Tourer attracted little interest. The highest bid of $850,000 was well below the pre-auction estimate of $1.25 – $1.5 million. A 1962 Mercedes Benz 300 SL Roadster (est. $1.6-$1.8 million) was withdrawn before the sale. However, four Mercedes Benz 300 SLs will be on offer amongst around 80 cars at the Bonhams Mercedes Benz Sale in Stuttgart on March 28, 2015. | {
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\section*{Supplementary Material}
See supplementary material for: model of T4 lysozyme L99A; MD simulations;
loss function; neighborhoodfor the loss function; minimization procedure;
adaptive biasing to a loss function minimum; classification of the
reaction pathways; biased unbinding times; software.
\begin{acknowledgments}
We thank H. Grubm\"{u}ller, W. Nowak, and M. Parrinello for useful discussions,
and Tristan Bereau and Claudio Perego for critically reading the manuscript.
This work was supported by the National Science Centre, Poland (grant
2016/20/T/ST3/00488, and 2016/23/B/ST4/01770). The MD simulations were computed
using facilities of
Interdisciplinary Centre of Modern Technologies, Nicolaus Copernicus
University, Poland.
\end{acknowledgments}
| {
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} | 106 |
7 Linux Distros to Replace CentOS on Your Servers
Looking for CentOS replacements? Plan to migrate your servers to one of these seven best CentOS replacements for your Linux server needs.
On December 8, 2020, Red Hat shocked the Linux world by announcing that it was discontinuing all CentOS investments in favor of CentOS Stream. And this is where history repeats itself. In 2004, Red Hat did the same thing by EOL'ing all "Red Hat Linux" and forcing users to Red Hat Enterprise Linux.
So, if you are currently using CentOS 8, you will have to find an alternative operating system. This is because its end-of-life cycle was cut short in December 2021. However, if you use CentOS 7, you can wait to take action, as CentOS 7 will reach its end of life on June 30, 2024.
To clarify, Red Hat will not release any new CentOS versions, only CentOS Stream. Therefore, CentOS will no longer be a stable point distribution but a rolling release one. In addition, the announcement clearly stated that CentOS Stream is not a replacement for CentOS Linux.
As expected, many CentOS users feel betrayed and seek a way out. Why? Because they found out that their "until-2029" distro had become an "until-2021" distro. Fortunately, there are several excellent options for CentOS replacements. This article closely examines each to help you make the best-informed decision for your situation and needs.
To make things even easier for you, we will divide them into two main groups. The first one includes RHEL-based Linux distributions. In other words, those that are 1:1 binary compatible with Red Hat, so migrating apps and services from CentOS to them is relatively easy and requires little effort.
The second category includes Linux distributions that have proven their reliability in the server market over the years but do not provide backward compatibility with Red Hat Enterprise Linux. Therefore, switching from CentOS to them requires you to have prior experience with the respective distribution.
With the clarification thus made, let's dive in and explore the top 7 Linux distros to replace CentOS on your servers.
Best RHEL-Based CentOS Replacements
1. AlmaLinux
When Red Hat announced that it would no longer be maintaining CentOS releases, CloudLinux, a company specializing in delivering a customized Linux-based operating system to large hosting providers and data centers, decided to create its own RHEL fork.
This initiative resulted in the emergence of AlmaLinux – an open-source, forever-free enterprise Linux distribution that intends to fill the gap left by the demise of CentOS.
As a standalone, community-driven project, AlmaLinux is a 1:1 binary-compatible fork of RHEL and enjoys $1M in annual sponsorship from CloudLinux Inc.
With ten years of experience building a hardened CentOS Linux for data centers and hosting companies, the company brings deep technical knowledge of enterprise infrastructure, kernel development, and open-source software to the project.
There are several reasons why AlmaLinux may be a suitable replacement for CentOS on your production servers. Some of the main advantages of AlmaLinux include the following:
Stability: AlmaLinux is based on the stable and well-supported RHEL, making it a reliable choice for production environments.
Compatibility: AlmaLinux is fully compatible with RHEL packages and repositories, making it easy to transition from CentOS to AlmaLinux.
Predictability: The AlmaLinux Foundation, a non-profit organization, guarantees that the distribution is entirely independent of corporate interests and AlmaLinux will stay forever free, avoiding a repeat of CentOS's fate.
Community: AlmaLinux has a strong community of users and developers who provide support and help with any issues you may encounter.
In conclusion, AlmaliLinux is a solid and reliable choice for replacing CentOS on your production servers. It offers similar features and compatibility but adds predictability and a strong community.
If you are planning to migrate your CenOS server to AlmaLinux, you will find our guides below very useful:
How to Migrate CentOS 7 to AlmaLinux 8: A Step-by-Step Guide
CentOS 8 to AlmaLinux 8: A Step-by-Step Migration Guide
2. Rocky Linux
Rocky Linux 9.1
Rocky Linux is designed as a drop-in CentsOS replacement. It was created by the same person who birthed CentOS into being, Gregory Kurtzer, and Rocky follows the same mission of offering an enterprise-ready version of Linux. The name was chosen as a tribute to early CentOS co-founder Rocky McGaugh.
As we said before, Red Hat announced it was shifting focus from downstream build CentOS to upstream build CentOS Stream on December 8, 2020. The next day, Kurtzer launched the Rocky Linux development effort on GitHub. Over 650 contributors joined in less than 24 hours.
In other words, the Rocky Linux concept got an immediate, positive community reaction. As a result, the Rocky Linux team announced the general availability of its first stable release, Rocky Linux 8.4 "Green Obsidian," on June 21, 2021.
Additionally, the project has backing from multi-billion-dollar companies, such as Microsoft, VMWare, Amazon, Google, etc.
Rocky Linux is a complete RHEL binary-compatible distro using the source code of the Red Hat Enterprise Linux operating system. It is compatible with RHEL and can run the same software and applications as RHEL.
There are several reasons to choose Rocky Linux as a replacement for CentOS. Some of the key advantages of Rocky Linux include the following:
It is a stable and reliable platform built on the foundation of RHEL, one of the world's most widely-used enterprise Linux distributions.
Rocky Linux is backed by some of the world's largest multi-billion-dollar companies. This is a strong enough guarantee of the distribution's reliability and quality.
The distribution offers full compatibility with Red Hat Enterprise Linux.
Through CIQ (Ctrl IQ), Rocky Linux provides commercial support and services for Rocky Linux to customers in research, academia, government, enterprise, partners, and everyone in between.
If you plan to migrate your CentOS server to Rocky Linux, our guide "CentOS 8 to Rocky Linux 8 Migration: A Step-by-Step Tutorial" will come in handy.
3. Oracle Linux
Oracle Linux 9.1
Oracle Linux is a free, open-source distribution developed and supported by Oracle Corporation. It is based on the source code of Red Hat Enterprise Linux (RHEL) and is designed to be fully compatible with RHEL.
One of its main advantages is that in addition to the stock RHEL kernel, Oracle Linux ships with the in-house developed UEK (Unbreakable Enterprise Kernel), which provides additional benefits over the mainline kernel.
There are several reasons to choose Oracle Linux as a replacement for CentOS. Some of them are:
Oracle Linux is completely free to download and use.
Oracle Linux is based on the Red Hat Enterprise Linux (RHEL) codebase, which means is a stable, reliable, and enterprise-grade operating system.
Oracle Linux comes with an Unbreakable Enterprise Kernel (UEK), a high-performance kernel optimized for running Oracle workloads.
Oracle Linux is backed by Oracle's world-class support team, which can assist with installation, configuration, and troubleshooting.
So, if you have any doubts about the quality of the distribution, let us dispel them. Oracle Linux uses the same codebase as Oracle's enterprise Linux clients, so it is rock-solid.
If you are planning to migrate from CentOS to Oracle Linux, the maintainers have created a script available on GitHub that allows an easy transition to Oracle Linux.
If you plan to migrate your CentOS server to Rocky Linux, our guide "CentOS 8 to Oracle Linux 8 Migration: A Step-by-Step Guide" will come in handy.
4. VzLinux
VzLinux 8
But there's another contender – VzLinux. It is also a 1:1 completely binary-compatible fork of Red Hat Enterprise Linux, just like Rocky Linux, AlmaLinux, or Oracle Linux, and it has been around for over two decades.
You've most likely never heard of this enterprise-ready Linux distribution. However, VzLinux was the foundation for OpenVz and several commercial Virtuozzo products.
In addition, VzLinux comes with extra features that cloud-native and container developers may appreciate. Those features include:
CentOS conversion dry-run.
Snapshot creation and roll-back.
Unattended mass conversion.
On top of that, VzLinux currently offers a ready-to-use utility, vzdeploy8, to convert from CentOS 8 to VzLinux without downtime.
The conversion utility allows for the smooth conversion of CentOS 8 bare-metal servers, virtual machines, and containers, effectively managing risk while minimizing negative business impact.
On the other hand, VzLinux is a less popular distribution than the others on this list because it is mostly used in virtualized environments. So, only a limited amount of documentation and articles are available to help users.
Taking note of this remark, if you are looking for a CentOS replacement, VzLinux seems like a good alternative.
Best Non-RHEL-Based CentOS Replacements
Here we enter the land of distributions that have proved their reliability as Linux servers but do not provide backward compatibility with Red Hat Enterprise Linux, as the ones listed above do.
This means that there are no ready-made tools to migrate your current CentOS system to one of them. Furthermore, their package base, as well as the services and configurations that are included with them, may differ from those in CentOS.
Therefore, to adapt them to any of the distributions listed below, you will need specific skills and knowledge for that distribution.
Debian is a free and open-source operating system composed entirely of free and open-source software. It is developed and maintained by a community of volunteers from around the world and is best known for its security, stability, and reliability.
With nearly 30 years of history, Debian is a living legend in the Linux world and is still used by countless Linux servers today.
Debian provides stable packages and a very long support window with Long Term Support (LTS) until the end of the life of its versions. It is also very conservative in upgrading Linux kernel versions and packages. This only makes your server more stable without any surprises.
The main Debian pros are:
Debian is made of free and open-source software and will always be 100% free.
Debian is known for its stability and reliability, which makes it a good choice for servers and other critical systems. Users have liked Debian's stability and reliability since 1993. The developers provide security updates for all packages over their life whenever possible.
Debian has one of the largest and richest software repositories among Linux distributions, including countless open-source applications and tools.
Debian is well known for its easy and smooth upgrades within a release cycle and the next major release.
It uses a conservative approach to updates, which means that new versions are released infrequently but are thoroughly tested and well-supported.
Debian is not just a Linux distribution. The software is co-produced by thousands of volunteers from all over the world. The distro has one of the biggest and most active communities of users and developers who contribute to the project by providing support, testing, and development.
It is hard to go wrong with Debian as your server operating system. The only main barrier to using it as a replacement for CentOS is the extra effort required to transition from an RPM-based ecosystem to a DEB-based one.
Ubuntu is another strong competitor for the niche market left by CentOS, and it needs no introduction. But just like Debian, Ubuntu has one significant drawback – it is not RHEL-based. Instead, it is from the Debian Linux family tree.
However, unlike Debian, Ubuntu is a more business-oriented operating system, and you can get paid support here. However, if we compare Debian with Ubuntu in terms of stability and reliability, we are likely to say that Debian is better.
The main arguments we can mention in favor of Ubuntu as a CentOS replacement are:
Reliable release schedule: Canonical publishes new releases of Ubuntu on a regular cadence, enabling the community, businesses, and developers to plan their roadmaps.
Long-Term Support Release: Ubuntu's LTS releases ensure five years of support with the option of extending this period. They are enterprise-grade and are utilized the most. An estimated 95% of all Ubuntu installations are LTS releases.
Stable and supported Linux OS: Ubuntu is a predictable, stable, and secure platform with commercial services and solutions provided by Canonical.
Performance and versatility: Ubuntu is certified by leading hardware OEMs, and with comprehensive deployment tools, finservs can get the most from their infrastructure deployments.
Ubuntu has a large and active community of users and developers who can support and help with any problems you may encounter.
In conclusion, Ubuntu may be a good choice as a CentOS replacement if you want an easy-to-use, feature-rich, and well-supported operating system. But, of course, the previously noted Debian considerations apply here as well.
3. openSUSE
openSUSE is a Linux distribution that often gets overlooked by individuals and businesses looking for enterprise-ready solutions but is also a good candidate for replacing CentOS.
It is a free and open-source Linux operating system developed and maintained by a community of volunteers and sponsored by SUSE, a German-based software company.
The operating system is available in two main editions: Leap, which provides a stable and reliable platform for enterprise users and server needs, and Tumbleweed, which offers the latest and most cutting-edge technology for users who want to try the latest software developments. More on this topic can be found here.
So, regarding server needs, the preferred option is Leap which is considerably more stable. Furthermore, it is based on the source code of SUSE Linux Enterprise and shares the same binaries. In other words, there is no difference between free-to-use community distribution and SUSE Linux Enterprise (SLE).
One of the main advantages of openSUSE Linux is its "Evergreen" support. Some of the chosen releases are supported for a much longer, thus named "Evergreen."
Overall, openSUSE can be a good choice for CentOS replacement for users who want a user-friendly, customizable, and secure operating system for their server needs.
Due to its stability and active community, CentOS was a popular choice for developers and system administrators. However, things have changed, and now other Linux distros will see many new users.
Here are our recommendations for the best CentOS replacement for your server needs. Choose AlmaLinux or Rocky Linux if backward compatibility and seamless migration are critical. Because both distributions are virtually identical, whichever you choose will give you a reliable and secure server operating system.
On the other hand, if you want to stay away from the RHEL-based ecosystem, we strongly recommend Debian. An operating system that has proved its reliability over the last 30 years, providing you with flexibility, predictability, security, and peace of mind.
Most users probably have already started the migration. So tell us, what is your choice?
Ubuntu Pro Subscription Is Here: What Does This Mean for Users?
Installing Caddy and PHP 8 on Rocky Linux 9 / AlmaLinux 9
5 Best Linux Distro Releases for Servers in 2022: Our Top Picks
Canonical Considering IPO in 2023: What It Means for Ubuntu Users
March 14, 2021 / 4:12 pm Reply
I'm waiting for Alma and Rocky but other viable alternatives could be:
– Springdale Linux (https://puias.math.ias.edu/), a little known RHEL clone
– openSUSE Leap (https://www.opensuse.org/#Leap), the upcoming version 15.3 will be nearly identical to SLES
the Trouble
March 15, 2021 / 10:13 am Reply
Do not forget the openSUSE.
And especially now when ooenSUSE Leap is to have exatly same software base than SUSE Enterprise. They are 100% compatible very soon.
And it is RPM distro!!
Mike Schlaffly
Yes, I agree, OpenSUSE is a better choice than all the above mentioned, we have been testing it in house for over a year and will replace all our CentOS (and Redhat) desktops & servers with Leap. OpenSUSE Leap / Tumbleweed are far more secure out of the box and so far have not had any issues with updates which I can't say for the Redhat based OS's which bork updates fairly regularly. OpenSUSE is the best enterprise grade distro available period, we will not be renewing our paid Redhat Support and will move it all over to SUSE & OpenSUSE by the middle of this year.
June 8, 2021 / 4:21 pm Reply
I don't know why the author exclude openSUSE, really stable and nearly 100% compatible with SLES, an enterprise Linux capable distro with technological upgrades that you won't find on others distros, rollback for a file or a system state with snapper, and software really up to date. Rocky Linux still a test release…. Ubuntu is a mess with the snap soft and the installer gives diferents options for different languages… Debian is really stable… but old software.
And Alma Linux… a clone of CentOS for now… but what happends when you found a bug? report to alma, alma report to red hat… redhat fix, alma fix or….. you report to alma, alma fix and the two distros begin to differ???
notta
July 10, 2021 / 8:38 pm Reply
I think you have a mistake under Debian. You wrote "The main Debian's cons are:" when I think you meant the pros.
Of course you are absolutely right! The error has been corrected.
milleja
I have used CentOS to compile when I need a version of RHEL. It was simply a means to an end. I thought RedHat already had a test bed compile all the time, so this is confusing.
I thought Fedora was the test bed and CentOS was more solid version of the Linux compiles.
Rick Lee
August 4, 2021 / 3:17 pm Reply
Oracle Linux. Its a no-brainer
Jolee
September 8, 2021 / 2:25 am Reply
if you want to sync with cpanel, then almalinux is the choice.
Mirko Rolfes
There is another Alternative: VzLinux. It is from the OpenVZ guys.
https://vzlinux.org/
Hi Mirko,
Yes, it is. We have already published an article on the subject:
https://linuxiac.com/vzlinux-8-centos-8-replacement/
Martin Ward
February 3, 2022 / 10:07 am Reply
I'm still deciding the best replacement for me to use but am surprised that OpenSUSE protagonists have not mentioned that it is not binary-compatible with CentOS. If you need to rely on CentOS or RHEL-compatible applications the OpenSUSE won't do it for you.
Don't get me wrong, I am sure it is very good at what it does, but it doesn't do this.
Oracle is not an option for me because I was at the sharp end of their open-source support previously, I won't make that mistake again.
Like Ricardo, I will be choosing between Rocky and Alma | {
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Kristína Kučová (ur. 23 maja 1990 w Bratysławie) – słowacka tenisistka, mistrzyni juniorskiego US Open w roku 2007. Tenisistka praworęczna, grająca oburęczny forhend i bekhend.
Kariera tenisowa
Kučová treningi tenisowe rozpoczęła w wieku sześciu lat. 10 września 2007 osiągnęła trzecią pozycję w klasyfikacji światowej juniorek. Występy w turniejach ITF rozpoczęła w kwietniu 2004 roku od Pucharu Słowacji, ale została pokonana już w pierwszej rundzie. W czerwcu 2005 po raz pierwszy znalazła się w finale takiej imprezy w Niemczech. Przegrała 1:6, 1:6 z Jarosławą Szwiedową. Na pierwszy juniorski tytuł czekała ponad pół roku, wygrywając w styczniu 2006 imprezę tenisową w Caracas. Wielokrotnie osiągała finały, a drugie zwycięstwo – a zarazem najważniejsze w dotychczasowej karierze sportowej – odniosła w Nowym Jorku. Okazała się najlepszą juniorką US Open, eliminując w finale Urszulę Radwańską. Wcześniej pokonała Anastasiję Pawluczenkową i Oksanę Kalasznikową.
W 2020 roku odniosła triumf w zawodach WTA 125K series w Pradze, w finale pokonując Elisabettę Cocciaretto wynikiem 6:4, 6:3.
Finały turniejów WTA
Gra pojedyncza 1 (0–1)
Finały turniejów WTA 125K series
Gra pojedyncza 1 (1–0)
Wygrane turnieje rangi ITF
Gra pojedyncza
Finały juniorskich turniejów wielkoszlemowych
Gra pojedyncza (1)
Bibliografia
Słowackie tenisistki
Triumfatorki wielkoszlemowych turniejów juniorskich
Urodzeni w 1990
Ludzie urodzeni w Bratysławie | {
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Q: How to get the first date of ISO year for the current date? GETDATE() returns the current date.
YEAR(GETDATE()) returns the current year given the current date. Appending 01-01 results in 01-01-2021.
How can I derive the start of ISO year? Expected output: 04-01-2021
A: An article on calculating the start of iso year in Excel can be found here:- https://www.microsoft.com/en-us/microsoft-365/blog/2009/09/17/calculate-the-iso-start-of-year-date/
I converted that into the SQL below. I've included the interim calculations I made as I was working through the conversion but the last column has the requested calculation.
SELECT
DATEFROMPARTS(YEAR(GETDATE()), 1 ,4) AS 'FOURTHJAN',
DATEFROMPARTS(YEAR(GETDATE()), 1 ,2) AS 'SECONDJAN',
DATEPART(weekday, DATEFROMPARTS(YEAR(GETDATE()), 1 ,2)) AS "SECONDJANDAYOFWEEK",
DATEPART(weekday, DATEFROMPARTS(YEAR(GETDATE()), 1 ,2)) % 7 AS "ADJUSTMENT",
DATEADD(day, 0 - (DATEPART(weekday, DATEFROMPARTS(YEAR(GETDATE()), 1 ,2)) % 7), DATEFROMPARTS(YEAR(GETDATE()), 1 ,4)) AS "STARTOFISOYEAR"
EDIT:-
Here's the code for a function that uses the above calculation
CREATE FUNCTION dbo.StartISOYear (@DATE datetime)
RETURNS Date
WITH EXECUTE AS CALLER
AS
BEGIN
RETURN(DATEADD(day, 0 - (DATEPART(weekday, DATEFROMPARTS(YEAR(@DATE), 1 ,2)) % 7), DATEFROMPARTS(YEAR(@DATE), 1 ,4)));
END;
GO
Which can be run using :-
SELECT dbo.StartISOYear(GETDATE())
| {
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#ifndef _READLINE_H_
#define _READLINE_H_
typedef void (*rl_vcpfunc_t)(char *c);
typedef void (*rl_compdisp_func_t)(char **c, int i, int j);
typedef char *(*rl_compentry_func_t)(const char *c, int i);
typedef char **(*rl_completion_func_t)(const char *c, int i, int j);
#define RL_STATE_DONE 0x1000000
#define RL_ISSTATE(x) (rl_readline_state & (x))
static int rl_end;
static int rl_point;
static int rl_readline_state;
static int rl_erase_empty_line;
static int rl_attempted_completion_over;
static char *rl_prompt;
static char *rl_line_buffer;
static rl_compdisp_func_t rl_completion_display_matches_hook;
static rl_completion_func_t rl_attempted_completion_function;
static inline void rl_callback_handler_install(const char *c, rl_vcpfunc_t f)
{
printf("readline not available\n");
exit(1);
}
static inline int rl_set_prompt(const char *c)
{
return -1;
}
static inline void rl_replace_line(const char *c, int i)
{
}
static inline void rl_redisplay(void)
{
}
static inline char **rl_completion_matches(const char *c, rl_compentry_func_t f)
{
return NULL;
}
static inline int rl_insert_text(const char *c)
{
return -1;
}
static inline int rl_crlf(void)
{
return -1;
}
static inline void rl_callback_read_char(void)
{
}
static inline int rl_message(const char *c, ...)
{
return -1;
}
static inline void rl_callback_handler_remove(void)
{
}
static inline char *rl_copy_text(int i, int j)
{
return NULL;
}
static inline void rl_save_prompt(void)
{
}
static inline void rl_restore_prompt(void)
{
}
static inline int rl_forced_update_display(void)
{
return -1;
}
#endif
| {
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Ein Hosianna für zwei Halunken (Originaltitel: Trinità e Sartana figli di…) ist ein Italowestern aus dem Jahr 1972, den Mario Siciliano inszenierte. Die deutschsprachige Erstaufführung war am 11. August 1972.
Handlung
Trinità (der so heißt, weil er aus Trinidad stammt) und Sartana begehen zusammen einen Bankraub. Sie sind seit langem miteinander befreundet und versuchen sich gegenseitig übers Ohr zu hauen, was regelmäßig damit endet, dass ihre Beute verschwindet oder von jemandem anderen eingestrichen wird. Diesmal suchen sie im kleinen Ort Quintana Zuflucht nach ihrem Überfall. Dort müssen sie sich bald mit dem unangenehmen Barton auseinandersetzen, der den gesamten Landstrich einheimsen möchte und dazu gegen die besitzenden Farmer nicht zimperlich vorgeht. Außerdem ist der mexikanische Bandit El Tigre in der Gegend, der ebenfalls eine Rechnung mit den beiden offen hat. Trinità und Sartana klauen zwei Millionen Pesos in Gold, aber in dem ganzen Durcheinander, das durch die verschiedenen Interessen entsteht, bleiben sie am Ende wieder mal mit leeren Taschen zurück.
Kritik
Das Lexikon des internationalen Films sah "eine liederlich inszenierte Westernparodie mit kauzigen Typen und turbulenten Prügel- und Akrobatik-Szenen, die nur bedingt Heiterkeit erzeugen.". Dem Regisseur mangelt es zwar nicht an Handwerkszeug, so Il Resto di Carlino, er "reiht hier aber nur epidemisch komische Szenen aneinander. Das hat man gesehen und nochmals gesehen – und es wird immer schlimmer." Christian Keßler attestiert dagegen dem Regisseur Siciliano die "Unfähigkeit, eine Story angemessen zu erzählen", es gehe aber ohnehin nicht um eine "Geschichte, sondern um das Aneinanderreihen mehr oder weniger fesselnder Spaßprügeleien."
Bemerkungen
Die längste der von Kritiker Keßler angesprochenen Prügelszenen dauert 7 Minuten. Der Film wurde zusammen mit dem in allen Belangen ähnlichen 100 Fäuste und ein Vaterunser gedreht.
Weblinks
Der Film bei comingsoon.it
Einzelnachweise
Filmtitel 1972
Italienischer Film
Italowestern
Filmkomödie | {
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Q: If two kets are each orthogonal to a third ket, are they also orthogonal to each other? Is there a proof for this either way?
For the normalized kets $\left|a \right\rangle, \left|b\right \rangle, \left|c\right \rangle $
If
$$
\left\langle a\middle| b \right\rangle = 0 \quad\text{and}\quad \left\langle a \middle|c \right\rangle = 0,
$$
are $\left|b\right \rangle$ and $\left|c\right \rangle$ orthogonal to each other? That is, must $\left\langle b \middle|c\right \rangle = 0$?
A: In general no. If you think of $\left|a\right>$, $\left|b\right>$ and $\left|c\right>$ as vectors $\vec{a}$, $\vec{b}$ and $\vec{c}$, you can say that $\vec{a} = \vec{b} \times \vec{c}$, so that $\vec{a}$ is orthogonal to both $\vec{b}$ and $\vec{c}$, but this doesn't imply that $\vec{b} \cdot \vec{c} = 0$.
A: No. Just let $|b\rangle = |c \rangle$.
A: (1) Answer is Yes in this example:
Consider complete set of orthonormal energy eigenfunctions of "particle in a box problem (infinite potential well)" in quantum mechanics.
Choose any 3 of them. If any one of these chosen 3 is orthogonal to remaining two, then these two are orthogonal to each other.
(2) Answer is No in the example of cross product of spatial vectors (as answered by MFH above).
| {
"redpajama_set_name": "RedPajamaStackExchange"
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import React from 'react'
import PropTypes from 'prop-types'
import classNames from 'classnames'
import PortalListDialects from 'components/PortalListDialects'
/**
* @summary ExploreLanguagesPresentation
* @component
*
* @param {object} props
*
* @returns {node} jsx markup
*/
function ExploreLanguagesPresentation({ isKids, isLoggedIn, isPublicMember, isWorkspaces, portalListProps }) {
return (
<div className="ExploreLanguages">
<div>
<div className="row">
<div className="col-xs-12">
<div className={classNames({ hidden: isKids })}>
{isLoggedIn && !isPublicMember ? <h1>Your Language Sites</h1> : <h1>Explore {portalListProps?.region} Languages</h1>}
</div>
<PortalListDialects {...portalListProps} />
{isLoggedIn && !isPublicMember && <p>To see all Publicly Visible Sites please log out.</p>}
</div>
</div>
</div>
</div>
)
}
// PROPTYPES
const { bool, object } = PropTypes
ExploreLanguagesPresentation.propTypes = {
isKids: bool,
isLoggedIn: bool,
isWorkspaces: bool,
portalListProps: object,
}
export default ExploreLanguagesPresentation
| {
"redpajama_set_name": "RedPajamaGithub"
} | 8,223 |
Q: Duct acoustic modes I have read that for a duct, the acoustic frequency is given by $$\omega = k_{lmn}=\sqrt{k_l^2+k_{mn}^2}$$ where $k_l$ and $k_{mn}$ are longitudinal and transverse wave number respectively.
Also, $k_{mn}$ can be obtained via $J_m'(k_{mn})=0$.($J_m$-Bessel function of m-th order)
Can anyone explain how is this derived or where does this come from?
A: It consists in solving the wave equation(or Hemholtz equation) which involves the wave vector k. The boundary conditions introduced at the duct boundaries impose the quantization of the wave vector components.
The most simple picture of that is a basic 1D acoustic cavity of length L where the wavelength of the wave that can be sustained must be :
\begin{equation}
m\lambda=2L ~~,~~ m\in\mathbb R
\end{equation}
where $k_m=2\pi/\lambda=m\pi/L$ . Technically $\omega$ should be related to the wave vector through the speed of the wave c $\omega = k_mc$.
In the case of a duct,it is slightly more complicated but essentially the same. Since the problem is 3D, the wave vector is quantized in 3 directions hence the presence of 3 indices.
Since the solutions of the wave equation in cylindrical coordinates are made of Bessel functions, the boundary conditions imposing the quantization of the wave vectors involves the zeros of the Bessel functions.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 1,768 |
{"url":"http:\/\/math.stackexchange.com\/questions\/260101\/writing-polar-equations-in-parametric-form","text":"# Writing Polar Equations In Parametric Form\n\nFor an example problem, in my textbook, the author wanted to demonstrate how to graph a polar function. Deeming it most convenient, my author took the polar function $r=2\\cos 3\\theta$, and re-wrote it as the parametric equations $x=2\\cos 3\\theta \\cos \\theta$ and $y=2\\cos 3\\theta \\sin \\theta$. How did the author arrive at these parametric equations?\n\n-\n\nYou can simply use the standard transformation from Cartesian coordinates to polar coordinate:\n\nGiven $r>0\\;\\text{and}\\;\\theta\\in [0,2\\pi)$\n\n$$x=r\\cos(\\theta),\\tag{x}$$ $$y=r\\sin(\\theta)\\tag{y}$$\n\nYou are given that $$r=2\\cos (3\\theta)\\tag{r}$$ So, replacing $r$ in each of the equations $(x)$ and $(y)$ with its equivalent $r = [2\\cos(3\\theta)]$, gives you:\n\n$$x=[2\\cos (3\\theta)] \\cos (\\theta)\\;\\;\\text{and}\\;\\; y=[2\\cos (3\\theta)] \\sin (\\theta).$$\n\nHere's a nice image to help make sense of the \"standard transformation\" from Cartesian to polar coordinates: The Cartesian point $(x, y)$ is the furthest point from the origin along the blue line (length $r$), so given $\\theta$ and the radius $r$, $(x, y) = (r\\cos \\theta, r \\sin\\theta)$.\n\nIt also helps to note the right triangle: $$\\cos\\theta = \\dfrac{x}{r} \\iff x = r \\cos\\theta\\;\\text{ and}\\;\\sin\\theta = \\dfrac yr \\iff y = r\\sin\\theta.$$ This image is a good reminder as to how to transform $x, y$ into polar coordinates.\n\nHint: Use this fact that there is a transformation from Cartesian coordinate to Polar coordinate: $$x=r\\cos(\\theta), y=r\\sin(\\theta),\\;\\; r>0\\;\\;\\text{and}\\;\\; \\theta\\in[0,2\\pi]$$\nGeneraly if $r(\\theta)$ is the polar function, the cartesian coordinates are given by $x(\\theta)=r(\\theta)\\cos \\theta$ and $y(\\theta)=r(\\theta)\\sin \\theta$. These are your parametric equations.","date":"2015-01-31 16:51:45","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\": 0.9695001244544983, \"perplexity\": 149.8452383706208}, \"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-2015-06\/segments\/1422122152935.2\/warc\/CC-MAIN-20150124175552-00096-ip-10-180-212-252.ec2.internal.warc.gz\"}"} | null | null |
Arques è un comune francese di 119 abitanti situato nel dipartimento dell'Aveyron nella regione dell'Occitania.
Società
Evoluzione demografica
Note
Altri progetti
Comuni dell'Aveyron | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 1,026 |
Visit Tyndale online at www.tyndale.com.
Visit Tyndale Momentum online at www.tyndalemomentum.com.
Visit Sheri Rose Shepherd at hisprincess.com.
_Tyndale Momentum_ and the Tyndale Momentum logo are registered trademarks of Tyndale House Publishers, Inc. Tyndale Momentum is an imprint of Tyndale House Publishers, Inc., Carol Stream, Illinois.
_Chocolate for Your Soul: Food, Faith, and Fun to Satisfy Your Deepest Craving_
Copyright © 2012, 2016 by Sheri Rose Shepherd. All rights reserved.
Previously published in 2012 as _If You Have a Craving, I Have a Cure_ by Tyndale House Publishers under ISBN 978-1-4143-6692-0
Cover photograph of roses copyright © Anatolii/Dollar Photo Club. All rights reserved.
Cover photograph of chocolate copyright © Danielle Wood/Getty. All rights reserved.
Designed by Jennifer Phelps
Published in association with the Loyal Arts Literacy Agency, PO Box 1414, Bend, OR 97709.
Scripture quotations are taken from the _Holy Bible_ , New Living Translation, copyright © 1996, 2004, 2015 by Tyndale House Foundation. Used by permission of Tyndale House Publishers, Inc., Carol Stream, Illinois 60188. All rights reserved.
**Library of Congress Cataloging-in-Publication Data**
Names: Shepherd, Sheri Rose, date, author.
Title: Chocolate for your soul : refreshing your relationship with God through food, faith, and fun / Sheri Rose Shepherd.
Other titles: If you have a craving, I have a cure
Description: Carol Stream, IL : Tyndale House Publishers, Inc., 2016. |
Previous edition: If you have a craving, I have a cure. Carol Stream, Ill.
: Tyndale Momentum, c2012. | Includes index.
Identifiers: LCCN 2016011147 | ISBN 9781496413499 (sc : alk. paper)
Subjects: LCSH: Food —Religious aspects —Christianity. | Dinners and dining —Religious aspects —Christianity.
Classification: LCC BR115.N87 S54 2016 | DDC 241/.68 —dc23 LC record available at http://lccn.loc.gov/2016011147
Build: 2016-05-12 12:12:20
I would like to dedicate this book to my beautiful girls . . .
My Daughter
Emmy Joy Shepherd
My Daughter-in-Love
Amanda Shepherd
My Granddaughter
Olive True Shepherd
My Spiritual Daughter
Julia Jacobo
# Contents
1. Introduction
2. Chapter 1: Craving Something Rich
3. Chapter 2: Craving Rest and Relaxation
4. Chapter 3: Craving Something Different
5. Chapter 4: Craving Zest for Life
6. Chapter 5: Craving God's Sweet Presence
7. Chapter 6: Craving Life's Celebrations
8. Chapter 7: Craving God's Best for You
9. Chapter 8: Craving Real Refreshment
10. Chapter 9: Craving Fortifying Faith
11. Chapter 10: Craving Fun and Laughter
12. Chapter 11: Craving Romance and Unconditional Love
13. Chapter 12: Craving Time with Kids
14. Chapter 13: Craving More Energy
15. Chapter 14: Craving a New Day and a New Beginning
16. Chapter 15: Craving Fresh Adventures
17. About the Author
18. Recipe Index
# Introduction
## Chocolate for Your Soul
Taste and see that the LORD is good. Oh, the joys of those who take refuge in him!
PSALM 34:8
ASK WOMEN TO NAME their guilty pleasures or biggest cravings, and chocolate is likely to be on the list. After all, most of us find its sweet, creamy texture both soothing and delicious. No wonder chocolate is a staple in our pantries and a common treat at women's gab groups. Interestingly, science has discovered that cacao, the natural base of chocolate, provides many health benefits. For instance, eating chocolate stimulates the release of endorphins, chemicals in the brain that lead to feelings of happiness and pleasure. Dark chocolate may also help lower blood pressure and improve the cardiovascular system.
This sweet treat may be good for your heart, but God invites you to indulge in blessings that are like chocolate for your soul. He offers you three amazing gifts —food, faith, and fun —to satisfy and refresh you and your loved ones. Much as we crave chocolate, He wants us to desire more of Him and His good gifts.
Life can be hard, so it is sometimes tempting to focus on what you are not allowed to do and what you should not eat, but that will leave you feeling deprived and depressed, bored and burned out. That's not how God intends for you to live. It's time to let go of guilt, grab hold of grace, recapture the life God made you for, and then . . . _live it_!
In this book I will share many of the benefits and blessings of following Christ as you discover a new kind of faith walk, one filled with joy and a refreshing perspective on life. I'm also excited to share with you some delicious, healthy recipes that helped me conquer chronic fatigue and lose over fifty pounds and keep it off. (For some delicious dishes featuring chocolate, see chapter 1. And for even more faith and food coaching via video, visit hisprincess.com.)
Together you and I will learn to embrace the life Christ wants us to live while enjoying the wholesome and amazing food our God created for us. (Please note: I am not a medical professional, so if you are looking to make lasting changes to your diet or other parts of your health regimen, be sure to check with your doctor first, particularly if you have any medical conditions.)
As the wisest man who ever ruled, King Solomon, said in Ecclesiastes 5:18:
It is good for people to eat, drink, and enjoy their work under the sun during the short life God has given them, and to accept their lot in life.
You are about to taste and see that the Lord is good and that your faith can become a fulfilling adventure. That's great for the soul!
Love,
Sheri Rose
hisprincess.com
# CHAPTER 1
## Craving Something Rich
### Chocolate Recipe Relief and Treasured Faith
I AM CONVINCED that chocolate should be in the food pyramid underneath fruits and vegetables. I often wonder if there will be unlimited chocolate fountains flowing in heaven (preferably the kind of chocolate that does not cause migraines). I believe chocolate is a gift from God, and believe me, in this chapter I think you're going to find some relief from the guilt you feel for craving it.
# Soul Food
And I will give you treasures hidden in the darkness —secret riches. I will do this so you may know that I am the LORD, the God of Israel, the one who calls you by name.
ISAIAH 45:3
God's Word tells us that wherever our treasure is, there our heart will be also. Many times we miss the secret treasures the Lord desires to give us, because our hearts are so focused on what we want. As a result, we miss the better and richer life God designed for us.
Let's look at those riches that will last forever and crave everlasting wealth. When we do, we will leave a rich legacy for all those we love and know. After all, we brought nothing into this world, and we will leave with nothing except a rich faith and treasure in heaven.
# New Life Recipes
## 1. LIVE AS ROYALTY
For you are a chosen people. You are royal priests, a holy nation, God's very own possession. . . . He called you out of the darkness into his wonderful light.
1 PETER 2:9
Live like a chosen child of the King. In other words, talk more about your riches in heaven and the blessings of being God's chosen one than about your burdens here on earth.
To remind you of your "royal status," you might frame one of your favorite Scriptures or eat rich dark chocolate while reading His Word in the evening.
## 2. INVEST IN ETERNITY
They themselves will be wealthy, and their good deeds will last forever.
PSALM 112:3
Make it your goal to do one thing a week that has eternal value. Give money to a great cause or e-mail words of encouragement to a friend. Commit to pray one day a week for our country.
## 3. COUNT THE COST
What do you benefit if you gain the whole world but are yourself lost or destroyed?
LUKE 9:25
Take a few moments to make a list of what you do with your time and energy each day. Next to this list, jot down the names of people you hang out with, what good is coming from those relationships, and what results (what the Bible calls "fruit") you are seeing from the ways you spend your time. Then pray and ask God to show you if these activities are all worth investing in.
# POWER UP WITH PRAYER
Dear friend, I hope all is well with you and that you are as healthy in body as you are strong in spirit.
3 JOHN 1:2
Dear God,
I want to live a rich life that will leave a legacy, so please give me what I need to have a rich faith. Give me as much as You want to provide for me and to help meet the needs of others, but not so much that I forget to rely on You. Amen.
# FOOD TRUTH
No food . . . is richer than becoming a reflection of His glory.
# Real Rich Recipes
Sometimes, particularly on special occasions like birthdays and anniversaries, nothing is more appropriate than chocolate or a special cake. Indulge your sweet spot with one of these delicious recipes.
## ALMOND CHOCOLATE SMOOTHIE
### Serves 2–3
### Ingredients:
1. 1 cup almond milk
2. 1 cup chocolate Rice Dream ice cream (or low-fat chocolate ice cream)
3. 1 teaspoon honey
4. 1 teaspoon almond extract
5. 1–2 cups ice
### Directions:
1. Mix all ingredients together in a blender until smooth.
2. Pour into glasses and enjoy!
### Recipe tip:
You can use real almonds instead of almond extract to make this more of a raw recipe.
## CRAVING CHOCOLATE CAKE
### Serves 12
### Ingredients:
1. 1 package Pamela's chocolate cake mix or another gluten-free cake mix
2. 1 package Pamela's dark chocolate frosting mix (optional)
3. 1 cup sour cream
4. 1 cup canola oil
5. 4 eggs
6. ½ cup warm water
7. 2 cups semisweet chocolate chips
8. Powdered sugar, if desired
9. Pint of fresh raspberries, if desired
### Directions:
1. Preheat oven to 350°.
2. In a large bowl, mix together the cake and frosting mix (if added), sour cream, oil, eggs, and water. Stir in the chocolate chips, and pour batter into a well-greased, 12-cup Bundt pan.
3. Bake for 50–55 minutes, or until a wooden toothpick inserted comes out clean.
4. Cool cake thoroughly in pan at least an hour and a half before inverting onto a plate. If desired, dust the cake with powdered sugar and place a few raspberries alongside each piece.
### Recipe tip:
After making the cake, cut it up in small slices; seal each in Tupperware and freeze so you can use individual slices as needed.
## CAROB PUDDING
### Serves 2–4
### Ingredients:
1. 2 avocados
2. 1 cup honey
3. ¼ cup carob powder or unsweetened dark cocoa powder
4. ¼ cup cocoa powder
5. 1 tablespoon raw sugar or stevia
### Directions:
1. In a blender, mix all ingredients until mixture is smooth and creamy. Add water as needed for desired consistency.
### Recipe tip:
Add semisweet chocolate chips for a chocolaty surprise in the pudding. This pudding will keep for three days in the fridge.
## CHOCOLATE DIP
### Fills a small-size bowl
### Ingredients:
1. ½ cup unsweetened dark cocoa powder
2. ½ cup honey or agave syrup
3. 1 teaspoon vanilla extract
### Directions:
1. Place all ingredients in blender and mix until smooth.
### Recipe tip:
You can heat this up if you want your chocolate dipping sauce warm. Make sure to have your favorite fruit cut and ready to dip and enjoy!
## MAKE MINE CHOCOLATE CAKE
### Serves 12
### Ingredients:
1. 1¾ cups whole-grain or gluten-free flour
2. 2 cups sugar
3. ¾ cup unsweetened dark cocoa powder
4. 2 teaspoons baking soda
5. 1 teaspoon baking powder
6. 1 teaspoon sea salt
7. 1 tablespoon instant coffee (optional)
8. 2 eggs
9. 1 cup buttermilk
10. ½ cup canola oil
11. 1 teaspoon vanilla extract
### Directions:
1. Preheat oven to 350°.
2. Grease and flour two 9-inch round cake pans or one 9 x 13-inch pan.
3. In a large bowl, combine flour, sugar, cocoa, baking soda, baking powder, salt, and instant coffee, if desired. Make a well in the center.
4. Add eggs, buttermilk, oil, and vanilla. Beat for 2 minutes on medium speed. Batter will be thin. Pour into prepared pans.
5. Bake for 30 to 40 minutes, or until toothpick inserted in center of cake comes out clean.
6. Cool for 10 minutes, then remove from pans and finish cooling on a wire rack. Layer and frost as desired.
### Recipe tip:
Use the Chocolate Dip recipe on page 7 as frosting for this cake.
## PURE FUDGE LOVE
### Serves 24
### Ingredients:
1. 9.7-ounce bar of semisweet chocolate
2. 3 cups raw sugar
3. ¾ cup unsalted butter
4. ²⁄3 cup unsweetened coconut milk
5. 7 ounces marshmallow creme
6. 2 teaspoons vanilla extract
### Directions:
1. Butter a 9 x 13-inch baking dish or line it with parchment paper.
2. Chop the chocolate bar fine, and set it aside.
3. Place the sugar, butter, and coconut milk in a thick-bottomed, medium-large saucepan. Slowly bring the mixture to an active boil, stirring constantly. Continue boiling for five minutes over medium heat. If you are using a candy thermometer, it should read about 235°.
4. Remove from heat, and stir in the chopped chocolate. Continue stirring until the chocolate is melted. Then add the marshmallow creme and vanilla.
5. Pour the fudge mixture into the prepared baking dish, and let it cool.
### Recipe tip:
You can also use this as a hot fudge chocolate dip!
## SHAKIN' ME TO PIECES SMOOTHIE
### Serves 2–3
### Ingredients:
1. ¾ cup peanut butter
2. 3 cups ice (more if needed)
3. 3 cups chocolate almond milk
4. 1 tablespoon raw sugar or stevia
5. ¼ cup semisweet chocolate chips
6. ½ cup chocolate protein powder
### Directions:
1. Place all ingredients in blender and mix for 1 to 2 minutes, until smooth. Pour and enjoy!
### Recipe tip:
If you are allergic to peanuts, try using almond or cashew butter instead.
# TASTE OF TRUTH
No amount of riches can buy you peace of mind or a home in heaven.
# CHAPTER 2
## Craving Rest and Relaxation
### Healthy Comfort Food and Recipes for Rest
WHEN MY DAUGHTER WAS A TODDLER, she never wanted to take a nap. No matter what I did to make naptime appealing, she refused to lie down without a fight.
Because nothing else seemed to work, I even tried bribing her with goodies and gifts. When you're desperate for rest, you'll do a lot of things to get it! It's not that I was a wimpy mother; it's that I was a worn-out woman.
Actually, to be honest, I can relate to my daughter because I fight my own body's cry for rest, especially if I think I am missing out on fun, food, or finishing my to-do list.
# Soul Food
God has told his people, "Here is a place of rest; let the weary rest here. This is a place of quiet rest." But they would not listen.
ISAIAH 28:12
I think there are a lot of reasons why we women struggle to be still and rest in our Lord. In our heads, we know rest is a gift from God; however, it is hard to rest when our spirits feel restless. There's always something to do, and if we haven't overcommitted ourselves, someone else needs us to get up from our place of rest and do something for him or her. We rarely allow ourselves to rest in the Lord and enjoy the gift of refreshment and relaxation.
Too many times we do not lay ourselves down until we are forced to by some sort of sickness. That's not God's plan. He wants us to rest our physical bodies, our minds, and our souls. This is not something we need to feel bad about —it does not mean we are weak. Quite the opposite, in fact: we can conquer more if we will take the time to allow the Lord to strengthen our bodies and our souls by embracing the blessing when we rest.
I invite you now to take a vacation from your problems and consider the New Life Recipes to help you get the rest and relaxation that you crave and deserve and that our Lord desires for you to have.
# New Life Recipes
## 1. BATHE YOUR BODY AND SOUL
Purify me from my sins, and I will be clean;
wash me, and I will be whiter than snow.
PSALM 51:7
There is nothing sweeter for a woman than a quiet, warm, soothing bath. One of the most famous commercials targeted to women uses the slogan, "Calgon, take me away!" This tagline is for a bubble bath, and the manufacturer promises its product will give users rest and relaxation.
As good as the marketing is behind this commercial, nothing is more relaxing than resting in the Lord. If you're craving rest and relaxation, consider drawing a bath for yourself tonight. Put on some quiet worship music and let the Lord minister to you in that warm water. To get the full benefit, be sure to let your mind rest from your worries while you soak in the water and in worship!
## 2. TAKE A VACATION FROM YOUR WORRIES
Give all your worries and cares to God, for he cares about you.
1 PETER 5:7
List all the things that make you restless so you can rest in the Lord. This, of course, is much easier said than done. Take a moment and write out a list of every burden you carry. Then take that list and hold it up toward heaven. Say these words out loud: "God, I give all of my worries to You, and in exchange I receive rest for my soul, mind, and body."
## 3. TREAT YOURSELF TO AN EARLY BEDTIME AND/OR A DAILY TWENTY-MINUTE NAP
God gives rest to his loved ones.
PSALM 127:2
If you're anything like me, once everything settles down in your home at night, you often get a burst of energy that drives you to try to get everything done into all hours of the night. Now I know there's no way you could convince me not to take advantage of those moments, and I suspect the same is true for you. If so, be sure to treat yourself to an early bedtime a few times a week. Write it on your calendar as if it were an appointment that can't be missed. If necessary, start with just one day. Once you do, you will begin to crave rest more than checking off another item on your out-of-control to-do lists.
# POWER UP WITH PRAYER
God's promise of entering his rest still stands, so we ought to tremble with fear that some of you might fail to experience it.
HEBREWS 4:1
Dear God,
I want to receive Your gift of rest and experience the amazing refreshment that You offer when I rest my body and my spirit. Help me to let go of the little things and to embrace that rest again. Show me whatever I need to let go of so I can find refreshment and relaxation once again. Amen.
# FOOD TRUTH
No food . . . is more delicious than the peace that comes from resting in the Lord.
# Healthy Comfort Food Recipes
Now that we've talked about rest for our souls, let's make some healthy alternatives to the comfort foods that we all know and love, as well as foods that can help us relax from some of the stress life can create.
## NOT-REALLY-CHEESE CHEESE SAUCE!
### Serves 8
### Ingredients:
1. 2 cups raw macadamia nuts
2. 2 cups cashews
3. Juice from 1 or 2 lemons (about ¼ cup)
4. 1 clove garlic
5. ½ tablespoon Butter Buds
### Directions:
1. Place all ingredients in a blender and blend until the mixture is smooth. It will be thick! If it is too thick, you can add a little water.
2. Serve drizzled over meat, or use as a healthy cheese dip for nachos.
### Recipe tip:
Go ahead and add more garlic or lemon to make it more flavorful. Get creative! Add chopped bell peppers to make it sweet, or if you like salty cheese, add sea salt. This will keep for three to five days in the fridge.
## CAULI MAC 'N' CHEESE
### Serves 4–6
### Ingredients:
1. 1 head cauliflower
2. 2 cups whole-grain or gluten-free macaroni (elbow, bow tie, or twist noodles)
3. 6 ounces Parmesan or Monterey Jack cheese, grated
4. 1½ cups cheese sauce (use Not-Really-Cheese Cheese Sauce!; see page 17)
5. 1 teaspoon sea salt
6. 1 tablespoon onion powder
7. 1 small bunch fresh parsley, chopped fine (optional)
### Directions:
1. Slice off the stem of the cauliflower and cut or break head into small florets.
2. Cook pasta and cauliflower florets together in a large pot, according to the cooking directions for the pasta. Drain.
3. Mix Parmesan or Monterey Jack cheese with cheese sauce; add sea salt, onion powder, and parsley.
4. Mix pasta and cauliflower with cheese sauce and pour into serving bowl.
### Recipe tip:
Add chopped chicken to the mac 'n' cheese for some extra protein! The mac 'n' cheese will keep in the fridge for two to three days.
## HEALTHY MAYONNAISE*
### Makes about 2 cups
### Ingredients:
1. ½ cup water
2. ½ cup macadamia nuts
3. ¾ cup cashews
4. ¼ teaspoon sea salt
5. 1½ teaspoons apple cider vinegar
6. 1 tablespoon freshly squeezed or bottled lemon juice
7. ½ teaspoon Butter Buds
### Directions:
1. Place all ingredients in a blender and blend until smooth.
2. Thin to desired consistency with water.
### Recipe tip:
Use this recipe in tuna, egg, or potato salad —any recipe that calls for mayonnaise. Get creative with the flavor by adding different dried herbs or curry powder.
*Adapted from a recipe by Karen Knowler, The Raw Food Coach. See TheRawFoodCoach.com.
## POTATO SALAD IN THE RAW
### Serves 4–6
### Ingredients:
1. 5 large sweet potatoes, boiled and cooled
2. 1 bunch green onions, sliced (about ½ cup)
3. 1 handful chopped fresh chives
4. ½ cup chopped red onion
5. ½ cup thinly chopped red cabbage
6. ¾ cup Healthy Mayonnaise (see recipe on page 19; use more or less to taste)
### Directions:
1. Chop the sweet potatoes into bite-size pieces and place in a bowl.
2. Add green onions, chives, red onion, and red cabbage to the sweet potato pieces. Stir gently to mix.
3. Add Healthy Mayonnaise to potato mixture and stir gently to mix.
### Recipe tip:
This is a great entrée or a side dish to chicken. You can use leftovers as a snack with whole-grain or gluten-free crackers or other snack crackers for dipping.
## CORN CHOWDER
### Serves 4–6
### Ingredients:
1. 6–8 ears corn or 2 cans (15 ounces each) whole kernel corn
2. 4 cups skim or plain rice milk
3. 2 tablespoons butter
4. 1 teaspoon garlic powder
5. ½ teaspoon sea salt
6. Freshly ground pepper
7. 1 tablespoon minced fresh parsley (optional)
8. 2 tablespoons honey
### Directions:
1. If using fresh corn, cut kernels from the cobs into a large bowl. Then scrape the cobs with a spoon to extract the liquid.
2. Coat a large pot with nonstick spray and place over medium-low heat.
3. Add corn, milk, butter, garlic powder, sea salt, pepper (to taste), and parsley to the pan. Cook for about 10 minutes, stirring constantly.
4. When chowder is almost done, add the honey and stir well. Remove from heat and serve.
### Recipe tip:
The starch in the corn will have a tendency to stick and burn easily, so be sure to stir the mixture regularly while the chowder is cooking.
## HEALTHY CORN BREAD
### Serves 10–12
### Ingredients:
1. 1 cup whole-grain or gluten-free flour
2. 1 cup cornmeal
3. ¼ cup raw sugar
4. 1 teaspoon baking soda
5. ¾ teaspoon salt
6. 1 cup plain nonfat yogurt
7. 2 eggs, beaten
### Directions:
1. Preheat oven to 400° and lightly grease an 8 x 8-inch baking pan.
2. Mix flour, cornmeal, sugar, baking soda, and salt in a large bowl. Add the yogurt and eggs. Stir until well blended.
3. Pour batter into prepared pan and bake for 20 to 25 minutes, or until the center of the corn bread is springy when pressed.
### Recipe tip:
Enjoy this delicious corn bread with your favorite chili or the Corn Chowder recipe on page 21.
## SOFT-SERVE CHAMOMILE VANILLA ICE CREAM
### Serves 1–2
### Ingredients:
1. 1 cup of hot water
2. 4 chamomile tea bags
3. 2 cans (16 ounces each) coconut milk or 4 cups rice milk
4. 1 teaspoon vanilla extract
5. 1 cup honey
6. 2 cups ice
### Directions:
1. Steep tea in hot water; let cool. Make the tea about 30 minutes before you want to eat the ice cream so that it has time to cool in the fridge.
2. Put all ingredients in a blender and mix. For soft-serve, scoop into small serving dishes and enjoy. For firmer ice cream, put in freezer at least 1½ hours before serving.
### Recipe tip:
Make brownies to go along with this recipe of soft-serve ice cream, loaded with the benefits of chamomile.
# TASTE OF TRUTH
Rest is a gift to you from God Himself.
# CHAPTER 3
## Craving Something Different
### Weird, Wonderful Recipes and Becoming a Bizarre Blessing
I WAS RAISED with a very weird and wonderful father. In fact, if you often crave something different, you would have liked having my father as your best friend!
On one of my stepmother's birthdays, my dad decided to give her a different kind of birthday gift. She loved elephants; she collected and displayed them all over our home. So my wacky father decided to have Marine World/Africa USA deliver a live elephant to the door of our home!
My dad didn't stop there. He had contacted three different news stations to cover the story. Their camera crews filmed animal trainers helping my mom up on the saddle of the elephant and then parading her around our neighborhood. Although our neighbors were afraid to come out and watch, you could see their startled faces looking out the windows of every house in our cul-de-sac.
# Soul Food
God works in different ways, but it is the same God who does the work in all of us.
1 CORINTHIANS 12:6
From the day that elephant paid his house call, our neighbors never again invited us to their home for barbecues. They were somewhat distant though always pleasant —probably out of fear of what might be delivered to their door!
Sometimes I think we respond just like those neighbors. We put God in a box and forget the very different and divine ways our Lord delivers blessings to us. Rarely does He display His power or direct our lives in an ordinary way.
Think about the bizarre way He blessed many of His chosen ones in the Bible. He blessed David in front of a giant; He blessed Daniel by rescuing him from a lions' den; He blessed Moses in front of what appeared to be a sea of hopelessness but actually became the grand entrance to the Promised Land.
Too many times we crave something different from what God has planned for us, thinking it will bring us an adventure. What we're really craving, though, is a purpose-driven life filled with God adventures. Believe me, if we're prayed up, purposed, and prepared, we will find exactly what we're looking for!
When we're bored with our faith and craving something different, I believe it is because God does not want us to settle for less than what He has for us.
Deep down in the heart of every person there is a craving to make a difference, to do something that sets him or her apart. That is a God-given desire, and He has designed each of us for a very different purpose. We do not have to aspire to become Christian clones or live out our faith walk like our friends do. Yes, we learn from one another, but we are not supposed to become anything other than who God made us to be.
If you are looking for a different and divine God experience that will give you a better and bigger picture of how our weird and wonderful God works differently in each of our lives, see the following New Life Recipes.
# New Life Recipes
## 1. WATCH _IT'S A WONDERFUL LIFE_
Such knowledge is too wonderful for me,
too great for me to understand!
PSALM 139:6
This holiday classic stars Jimmy Stewart as George Bailey, a small-town banker who is never able to escape his hometown and fulfill his dream of world travel. The movie didn't do much at the box office when it was first released in 1946. Only when its copyright expired in the 1970s, making it an inexpensive program for TV stations to air, did a large number of viewers come to cherish the story of how an angel named Clarence showed the despairing George how significant his life really was.
I realize this movie is usually watched at Christmastime. However, it gives such a clear picture of how we can overlook unseen blessings that I recommend you watch it anytime you wonder whether God is really using you. You'll also be reminded how wonderful your life really is when it's lived for the greater cause of helping others.
## 2. LOOK AHEAD EXPECTANTLY
I heard a loud shout from the throne, saying, "Look, God's home is now among his people! He will live with them, and they will be his people. God himself will be with them. He will wipe every tear from their eyes, and there will be no more death or sorrow or crying or pain. All these things are gone forever."
And the one sitting on the throne said, "Look, I am making everything new!" And then he said to me, "Write this down, for what I tell you is trustworthy and true."
REVELATION 21:3-5
When you fight to find a blessing, remember and meditate on these trustworthy words above.
## 3. BECOME A BIZARRE BLESSING
Abigail wasted no time. She quickly gathered 200 loaves of bread, two wineskins full of wine, five sheep that had been slaughtered, nearly a bushel of roasted grain, 100 clusters of raisins, and 200 fig cakes. She packed them on donkeys.
1 SAMUEL 25:18
Abigail was a bizarre blessing, and she was blessed because of it. Her husband, Nabal, made David mad by refusing to feed David's army after David and his men had protected Nabal's flocks in the wilderness. As David was on his way to kill her husband, Abigail met him and, with wise and humble words, persuaded David not to harm Nabal. As a result, David changed his mind and praised God for Abigail's good sense, which had kept him from shedding blood. Not long after, when her foolish husband died, David even took Abigail as his wife!
# POWER UP WITH PRAYER
You made all the delicate, inner parts of my body and knit me together in my mother's womb. Thank you for making me so wonderfully complex! Your workmanship is marvelous —how well I know it. You watched me as I was being formed in utter seclusion, as I was woven together in the dark of the womb. You saw me before I was born. Every day of my life was recorded in your book. Every moment was laid out before a single day had passed. How precious are your thoughts about me, O God. They cannot be numbered!
PSALM 139:13-17
Heavenly Father,
Sometimes I struggle to see myself as wonderfully complex. I'm humbled when I realize how much You value me. Help me to begin seeing myself —and everyone I meet —as one of Your unique and irreplaceable creatures. In Jesus' name, amen.
# FOOD TRUTH
No food . . . will ever fill us up more than doing God's will.
# Weird and Wonderful Food Recipes
Are you tired of eating the same foods and feeling unhealthy? It's time for a recipe makeover! Here are some incredible recipes that are unique and delicious.
## GLAZED GREEN BEANS AND YAMS
### Serves 6
### Ingredients:
1. 1 cup plus 3 tablespoons water
2. 3 large yams
3. 1 pound fresh green beans
4. 1½ teaspoons butter
5. 1 tablespoon freshly squeezed or bottled lemon juice
6. 1 teaspoon gluten-free or whole-grain flour
7. 1 teaspoon grated lemon peel
8. 2 tablespoons chopped nuts (such as almonds, pecans, or cashews)
### Directions:
1. Slice yams diagonally about ¼-inch thick. This should make about 2 cups.
2. Place 1 cup water in a 10-inch skillet and bring to a boil.
3. Reduce to medium heat. Add green beans and yams to skillet. Cover and cook 5 to 8 minutes until the green beans and yams are crisp-tender, stirring occasionally. Drain and remove from skillet; keep warm.
4. Melt butter in the same skillet.
5. In a small bowl, stir together lemon juice, flour, and 3 tablespoons water. Add to the melted butter. Cook over medium heat, stirring occasionally until sauce thickens, about 2 to 3 minutes.
6. Stir in the lemon peel just before removing from heat.
7. To serve, spoon sauce over green beans and yams. Sprinkle the chopped nuts on top.
## CARROT AND ALMOND DIP
### Makes about 2 cups; serves 4
### Ingredients:
1. 2 cups almonds
2. 2 large carrots
3. ½ cup coarsely chopped red onion
4. ½ cup finely chopped fresh parsley
5. ¼ cup freshly squeezed or bottled lemon juice
6. 1 pinch sea salt
7. 1 teaspoon garlic powder
### Directions:
1. Soak almonds in a bowl of water overnight.
2. Boil carrots until soft.
3. Combine softened carrots, almonds, and the rest of the ingredients in a blender. Mix until smooth.
4. Add water for desired consistency.
5. Serve as a dip for veggies or crackers.
### Recipe tip:
You don't have to use almonds —try walnuts or even cashews instead. This recipe can also be used as a sauce for meat.
## THAT'S A WRAP!
### Serves 4
### Ingredients for wraps:
1. 8 white cabbage leaves
2. 2 avocados, sliced
3. 2 tomatoes, diced
4. 1 cup black olives, sliced
5. ¼ cup chopped cilantro
6. 1 medium zucchini, grated
### Ingredients for dip:
1. ¼ cup olive oil
2. 1 tablespoon freshly squeezed or bottled lemon juice
3. ¼ cup chopped cilantro
4. 1 tablespoon finely chopped fresh ginger
5. ¼ cup pressed garlic
6. ¼ cup water (optional)
7. 1 teaspoon onion powder
### Directions for wraps:
1. Lay open the cabbage leaves. Divide vegetables equally among cabbage leaves, placing avocado slices and tomato in the middle of each leaf, then adding black olives, 1½ teaspoons cilantro, and zucchini for each serving.
2. Fold cabbage leaves up into wraps.
### Directions for dip:
1. Pour olive oil into a small bowl. Add lemon juice and cilantro.
2. Mix the ginger with the garlic.
3. Combine olive oil mixture with the ginger and garlic, adding water if the mixture seems too oily. Mix in onion powder.
4. Use as a dipping sauce for the wraps.
### Recipe tip:
The dipping sauce is also good as a salad dressing or vegetable dip.
## SPINACH CREAM SOUP
### Serves 2–3
### Ingredients:
1. 2 teaspoons olive oil
2. 2 cups portobello mushrooms
3. 1 bag spinach
4. 3 cups water
5. 1 can (16 ounces) coconut milk
6. 2 tablespoons dried minced onion
7. 2 tablespoons butter
8. 3 tablespoons chicken bouillon powder
### Directions:
1. Warm oil in a skillet over medium heat. Add mushrooms and cook until mushrooms are softened.
2. Combine spinach and softened mushrooms in a blender until smooth. Set aside.
3. Bring water to a boil in a large saucepan. Add coconut milk, onion, butter, and bouillon.
4. Add spinach and mushroom puree to the mixture in saucepan; stir and cook on medium heat for 5 to 7 minutes or until soup thickens, stirring occasionally.
### Recipe tip:
Don't be afraid to experiment —sprinkle shredded Parmesan cheese on soup or get creative with spices to change the flavor.
## GRILLED PORTOBELLO MUSHROOM BURGERS
### Serves 4
### Ingredients:
1. 4 portobello mushroom caps
2. 1 tablespoon minced garlic
3. ¼ teaspoon sea salt
4. 2 tablespoons olive oil
5. 1 onion, sliced
6. 4 whole-grain buns
7. 1 tomato, sliced
8. 4 lettuce leaves
9. ¼ cup low-fat or Healthy Mayonnaise (see page 19), or to taste
10. ¼ teaspoon low-sodium soy sauce or Bragg Liquid Aminos
### Directions:
1. Place mushroom caps, smooth side up, in a shallow dish. In a small bowl, mix garlic and sea salt to taste. Pour over the mushrooms. Let sit at room temperature for 15 minutes.
2. Preheat grill to medium-high heat.
3. Brush grate with 1½ tablespoons oil. Place mushrooms on the grill for 5 to 8 minutes on each side, or until tender.
4. Meanwhile, sauté onion slices in 2 teaspoons olive oil in a skillet until tender.
5. Toast whole-grain buns.
6. Add cooked mushrooms to bottom halves of buns and top with tomato, onion slices, and lettuce. Mix desired amount of mayonnaise with soy sauce or Bragg Liquid Aminos. Pour mayonnaise mixture onto mushroom burgers and cover with tops of buns. Enjoy!
## ZUCCHINI PANCAKES
### Serves 2–3
### Ingredients:
1. 4 medium zucchini, shredded and drained
2. 3 medium red onions, chopped
3. 1 clove garlic, minced
4. 2 eggs, slightly beaten
5. ½ teaspoon sea salt
6. 1 pinch pepper
7. ¹⁄3 cup crumbled feta or farmer cheese
8. 2 tablespoons whole-grain or gluten-free flour
9. ½ teaspoon oregano
10. ½ teaspoon basil
### Directions:
1. Combine all ingredients and mix well.
2. Coat a nonstick skillet with cooking spray and place over medium-high heat.
3. Drop zucchini mixture one tablespoonful at a time onto the skillet to make small pancakes. Cook about one minute, then turn pancakes over to brown the other side for one more minute. Serve immediately or freeze for later.
### Recipe tip:
To cook as a casserole, pour the mixture into a greased 9 x 13-inch pan and bake at 350° for 20 minutes. Cut and serve.
## SQUASH STIR-FRY
### Serves 4–6
### Ingredients:
1. 2 medium zucchini, sliced
2. 2 medium crookneck (yellow) squash, sliced
3. ½ cup red bell pepper, julienned
4. ¼ cup diced red onion
5. ¼ teaspoon basil
6. ¼ teaspoon oregano
7. 1 teaspoon butter
8. 1 clove garlic, minced
9. Sea salt
10. Freshly ground pepper
### Directions:
1. Coat a skillet with nonstick spray and place over medium-high heat.
2. Place zucchini, squash, red bell pepper, and onion in the pan and sauté for 3 to 5 minutes.
3. Add herbs and butter, stirring for 2 to 3 minutes more.
4. Add garlic. Turn off heat and blend well. Season to taste with salt and pepper, if desired, and enjoy.
### Recipe tip:
Add diced cooked chicken breast to this recipe, and you have an easy, low-fat entrée. Yum!
# TASTE OF TRUTH
You were not created to fit in; you are divinely different to stand out.
# CHAPTER 4
## Craving Zest for Life
### Salty, Satisfying Recipes and Faith Seasonings for Life's Seasons
SEVERAL YEARS AGO while I was on a book tour, I had a craving for something salty. Unfortunately, my craving was out of control, and I ate an extra-large bag of potato chips all by myself while watching a movie.
The next day I had a television interview about a book I had just written on health. I don't eat salt very often, and when I woke up that morning, my eyes were swollen shut from the high sodium intake the night before. No amount of ice or Preparation H cream underneath my eyes could bring the swelling down. To this day, I dread seeing that interview, which is posted on YouTube. I looked as if I had been punched in both eyes. The good news, though, is that God can work even through puffy eyes and thighs!
# Soul Food
Salt is good for seasoning. But if it loses its flavor, how do you make it salty again? You must have the qualities of salt among yourselves and live in peace with each other.
MARK 9:50
Many of us have moments of weakness when we feel as if our cravings have taken us captive or left us out of control. Sometimes they leave our faith flavorless because we are craving what used to be or what we wish could be. The Bible tells us there is a season for everything, and if we don't learn to taste each season as it is served, we will end up missing special moments and those life lessons we need to draw closer to God.
I love the seasons of love and laughter, but I have discovered that the seasons of loneliness and painful places are when I learn what my faith is for. The best way to season our faith again is to become salt in others' lives when our own feels lifeless. I offer a few other ideas in the following New Life Recipes.
# New Life Recipes
## 1. TRY A NEW FLAVOR
Taste and see that the LORD is good.
Oh, the joys of those who take refuge in him!
PSALM 34:8
If you are craving more flavor in your faith walk, pick up a new Christian book to read or find a new Christian friend to hang out with.
If your church does not help you grow closer to God, don't be afraid to try a new church. The great thing about all the different ways and styles of Christian churches is that you and I have the freedom to look for the one that stimulates our faith and works best with our gifts and personality.
## 2. SING A NEW SONG
Sing a new song to the LORD! Let the whole earth sing to the LORD!
PSALM 96:1
Worship should bring joy and flavor to our faith. Find some new worship songs that fit the style of music you love to listen to. If you're craving closeness with God, sing a new song, or better yet, sit down and write a song to the Lord, putting it to your own melody.
## 3. PURIFY YOURSELF
Then he went out to the spring that supplied the town with water and threw the salt into it. And he said, "This is what the LORD says: I have purified this water. It will no longer cause death or infertility."
2 KINGS 2:21
Many times we can't taste God's goodness because we have been feeding our soul salt substitutes instead of real faith. In other words, we watch, read, and listen to things that go against everything we want to become in Christ. We lose our craving for the Word and attempt to satisfy our soul with unhealthy, man-made forms of entertainment. Just like a whole-food diet makes us crave healthier foods, a pure soul-food cleanse will get rid of the junk in our spirits so we can taste God's goodness again.
# POWER UP WITH PRAYER
Let your good deeds shine out for all to see, so that everyone will praise your heavenly Father.
MATTHEW 5:16
Dear God,
I pray that You will increase my craving for You and fill me up so full that salt and goodness will spill out onto those I love. Show me the artificial things in my life that are keeping me from tasting and becoming Your salt to this world. Amen.
# FOOD TRUTH
No food . . . is as savory as God's favor, strength, and wisdom.
# Salty and Satisfying Food Recipes
We all know salty foods aren't necessarily the best for us, so why do we crave salt so much? Instead of having a salty main dish, we should be eating healthier entrées with salty foods on the side. Here are some great recipes that are sure to satisfy your salty craving without sending your health overboard.
## OUI OUI ONION SOUP
### Serves 4
### Ingredients:
1. 1 tablespoon butter
2. 1 tablespoon olive oil
3. 3 large onions
4. ¼ teaspoon sea salt
5. 1 teaspoon raw sugar
6. 1 tablespoon whole-grain or gluten-free flour
7. ¹⁄3 cup dry cooking sherry
8. 6 cups reduced-sodium chicken broth
9. ¼ teaspoon freshly ground black pepper
10. 2 teaspoons low-sodium soy sauce or Bragg Liquid Aminos
### Directions:
1. In a heavy skillet, heat butter and olive oil. Add onions and salt. Cook 5 minutes, covered, then uncover and add sugar.
2. Cook, stirring frequently for 15 to 25 minutes or until onions are golden brown.
3. Add flour and reduce heat to medium. Cook for 1 minute.
4. Add sherry, scraping skillet frequently. Cook 1 to 2 minutes or until slightly reduced.
5. Transfer to a saucepan. Add broth and pepper and bring to a boil.
6. Reduce heat to low and simmer, covered, for 10 minutes. Add soy sauce or Bragg Liquid Aminos.
## MOTO STACK
### Serves 2–4
### Ingredients:
1. 4 ounces fresh mozzarella roll, sliced
2. 3 large ripe tomatoes, sliced into ¼-inch slices
3. 10 basil leaves (optional)
4. 3 tablespoons balsamic vinegar
5. 2 teaspoons sea salt
### Directions:
1. Place a mozzarella slice on top of each tomato slice, and then place a basil leaf on top of the mozzarella.
2. Arrange stacks on a plate, drizzle balsamic vinegar evenly over each stack, sprinkle with salt, and enjoy!
### Recipe tip:
This can also be turned into a great salad —slice cherry tomatoes in half, cut smaller mozzarella pieces, add spinach and basil leaves (if desired); use balsamic vinegar as the dressing. It is simply divine!
## MOUTHWATERING MELON BITES
### Serves 2–3
### Ingredients:
1. 2 cups sliced cantaloupe
2. 14 slices prosciutto
### Directions:
1. Wrap slices of prosciutto around individual pieces of cantaloupe.
2. Hold together with toothpicks. Serve and enjoy!
### Recipe tip:
This recipe is so simple and delicious —a great finger food for a party. Try switching out the melon for kalamata olives. Yum!
## QUESO FIESTA DIP
### Serves 3–4
### Ingredients:
1. 1 small onion, chopped
2. 1 teaspoon olive oil
3. 2 garlic cloves, minced
4. 1 package (8 ounces) low-fat cream cheese, cubed
5. 2 cups fresh diced tomatoes
6. 6 ounces shredded cheddar cheese
7. 1 teaspoon chili powder
8. ½ pound lean ground beef, cooked
9. 1 can (8 ounces) green chilies
10. 1 bag tortilla chips
### Directions:
1. In a large skillet, sauté onion in oil until tender. Add garlic and cream cheese and stir until cream cheese is melted. Add tomatoes, cheddar cheese, chili powder, ground beef, and green chilies. Mix thoroughly.
2. Stir over low heat until cheddar cheese is melted.
3. Keep warm; serve with tortilla chips.
### Recipe tip:
Add cilantro for more flavor and jalapeños for more spice!
## WRAP ME UP!
### Serves 1
### Ingredients:
1. 1 whole-grain tortilla
2. 1 Laughing Cow cheese wedge, original flavor
3. 3 or 4 lettuce leaves
4. 3 slices smoked turkey
5. 2 slices cooked turkey bacon
### Directions:
1. Spread cheese evenly on tortilla.
2. Place lettuce, turkey, and bacon on tortilla.
3. Roll up and enjoy!
### Recipe tip:
Add slices of tomato and/or olives for more saltiness.
## KALE CHIPS
### Serves 2–3
### Ingredients:
1. 1 head kale, washed and dried
2. 1 teaspoon olive oil
3. 1 teaspoon salt
### Directions:
1. Preheat oven to 350°.
2. Line a baking sheet with parchment paper.
3. Remove stems from kale; chop leaves into one-inch pieces.
4. Combine all ingredients in a bowl and mix with your hands.
5. Spread kale in a single layer on prepared baking sheet.
6. Bake for 10 to 13 minutes, until dry and crispy. Cool for 10 minutes and serve.
### Recipe tip:
Try using eggplant instead of, or along with, the kale. Slice the eggplant thin and prepare it the same way as the kale.
## PEANUT BUTTER PICKLE DELIGHT
### Serves 2–4
### Ingredients:
1. 2 whole dill pickles
2. 3 tablespoons peanut butter
3. 2 rice cakes
### Directions:
1. Slice the pickles into rounds, about six to an inch.
2. Spread peanut butter on rice cakes.
3. Place pickle slices side by side on top of the peanut butter and enjoy!
### Recipe tip:
This is seriously delicious. If you are allergic to peanuts, try using almond or cashew butter instead.
# TASTE OF TRUTH
Life will lose its flavor if it is not seasoned with faith, hope, and love.
# CHAPTER 5
## Craving God's Sweet Presence
### Real Sweet Recipes and Some Sweet Jesus Time
YEARS AGO when my husband and I were first married, we made a commitment to fast from sugar for thirty days. I have to be honest —it was the hardest thing I'd ever done, and I didn't make it. Steve was craving a breakthrough from God and fasting for the right reasons. I, on the other hand, was not fasting to draw closer to God but to impress my new husband. I was miserable without my treats.
Then I remembered that there was a frozen wedding cake in my freezer and sharp knives (wedding gifts) in my kitchen drawers. Each day when Steve would leave for work, I would grab a knife and open the freezer; then I would take out the frozen wedding cake, tip it upside down, and carve out a piece from the center. It was heavenly —until I got caught. A few weeks after I'd started my nibbling, my husband opened up the freezer and something fell onto the foiled wedding cake. With nothing left but a fragile shell of icing, it crumbled. I had eaten every ounce of cake in the center.
# Soul Food
My child, eat honey, for it is good,
and the honeycomb is sweet to the taste.
PROVERBS 24:13
I don't think there's anything wrong with eating something sweet, but I now know there is nothing better than the sweet presence of our Lord and Savior and eating the food He created for our bodies and taste buds to enjoy.
The good news is we do not have to fight our craving for sweets anymore; we just need to treat ourselves to God's goodness of natural sweeteners like honey, molasses, pure maple syrup, and stevia. I can't think of anything more satisfying than good, healthy sweets and sweet time with our Lord.
Today many health professionals advocate cutting back or eliminating white sugar from our diets altogether. If you choose to take this step, don't think of white sugar as something you have to give up; think of it as something you get to give up so you can experience sweet health benefits and the adventure of finding healthy treats to eat. Here are some sweet ideas to satisfy your soul as you discover new ways to taste and see that the Lord is good!
# New Life Recipes
## 1. SING SWEET LOVE SONGS TO JESUS
Sing praises to God, sing praises;
sing praises to our King, sing praises!
PSALM 47:6
Love songs captivate our hearts but leave us longing for love from a man that we may never find. Let's try to sing those same love songs to the one true Prince who will always give us what we are really craving. Take a moment to play your favorite love song and sing it to the Lord. You may have to alter the words a bit, but if your heart is fixed on connecting to Jesus, the words will overflow from your mouth and your heart will feel His sweet presence.
## 2. EAT SWEETS AND READ THE WORD
How sweet your words taste to me;
they are sweeter than honey.
PSALM 119:103
If you struggle with being still and spending sweet time with Jesus, then try making a healthy treat like some of the ones in this chapter. Then sit and dine with your Lord. Just as we eat popcorn and candy while watching a two-hour movie —can you imagine if a healthy snack helped you sit and savor time with your Lord? Now that would be a treat!
## 3. WRITE NOTES TO JESUS
And you must love the LORD your God with all your heart, all your soul, all your mind, and all your strength.
MARK 12:30
Keep Post-it notes by your bed, and whenever you have a craving to express love to someone, turn that love toward heaven. Write love notes to Jesus and post them on your mirror as a reminder of the love relationship you are developing with your Savior.
# POWER UP WITH PRAYER
The commandments of the LORD are right,
bringing joy to the heart. . . .
They are more desirable than gold,
even the finest gold.
They are sweeter than honey,
even honey dripping from the comb.
PSALM 19:8, 10
Dear Jesus,
Your commandments are right; let them bring joy to my heart. I want Your commands to make me wise, giving me insight for pure living and everlasting reverence. You are more desirable than gold, even the finest gold. Your Word is sweeter than honey, even honey dripping from the comb. Amen.
# FOOD TRUTH
No food . . . tastes as sweet as a fruitful day.
# "Real" Sweet Guilt-Free Recipes
I love sweets and crave them often. I can't imagine life without sweet treats! In fact, I always seem to somehow find a way to alter every sweet-tasting recipe into a healthy version. Here are some of my favorites.
## BROWN RICE CUSTARD
### Serves 2–4
### Ingredients:
1. 3 eggs, lightly beaten
2. 1 teaspoon pure vanilla extract
3. ½ cup rice, almond, or coconut milk
4. 1 teaspoon cinnamon
5. ½ teaspoon nutmeg
6. ¼ teaspoon sea salt
7. ¼ cup honey
8. 2 cups cooked brown rice
### Directions:
1. Preheat oven to 325°.
2. Combine eggs, vanilla, milk, cinnamon, nutmeg, sea salt, and honey. Mix well.
3. Stir in cooked rice.
4. Pour the mixture into a 9 x 13-inch nonstick baking pan.
5. Bake 35 to 40 minutes, or until a toothpick inserted into the center comes out clean.
6. Cool to room temperature. Scoop into dessert dishes or cut into squares.
### Recipe tip:
You could add raisins or dried cranberries to this recipe. Get creative and add your favorite fruit!
## RASPBERRY PEACH SMOOTHIE
### Serves 1
### Ingredients:
1. ½ cup warm raspberry tea, brewed strong
2. 3 tablespoons honey
3. 1 cup peaches, diced
4. ½ cup raspberries
5. ¾ cup low-fat, plain organic yogurt
6. 6 ice cubes
### Directions:
1. Dissolve honey in warm tea. Refrigerate until chilled.
2. Combine the sweetened tea, peaches, raspberries, yogurt, and ice in a blender and mix until smooth.
### Recipe tip:
This could be an incredible breakfast. You can also experiment with other fruits instead of peaches —think mangoes with raspberries!
## SWEET MINT PIE*
### Serves 12
### Ingredients for crust:
1. 2 cups ground almonds
2. ½ cup unsweetened dark cocoa powder
3. ¼ cup agave syrup or raw honey
4. 2 tablespoons coconut or grapeseed oil
5. ¼ cup semisweet chocolate chips
6. 1 pinch sea salt
### Directions for crust:
1. Pulse all ingredients together in a blender.
2. Pour into a standard 9-inch pie pan. Press with your fingers to form the pie crust.
### Ingredients for mint filling:
1. 1 cup water
2. 1 cup agave syrup or honey
3. 1 teaspoon mint extract
4. 1 tablespoon butter
5. 1 tablespoon raw sugar or agave syrup
6. 1½ cups cashew butter
### Directions for mint filling:
1. Place all ingredients in a blender and blend until smooth.
2. Pour filling into the crust.
### Ingredients for pie topping:
1. 1½ cups butter
2. ½ cup semisweet chocolate chips
3. 1 cup unsweetened dark cocoa powder
4. ¼ cup agave syrup or honey
5. 1 tablespoon coconut or grapeseed oil
6. ¼ teaspoon peppermint extract
### Directions for pie topping:
1. Melt butter.
2. Melt chocolate chips in a double boiler or in a small saucepan placed in a larger pan containing boiling water.
3. Mix with remaining ingredients.
4. Pour evenly over mint filling.
5. Keep in freezer at least one hour until ready to serve.
### Recipe tip:
This is great for parties or when you're craving a refreshing treat. The mint is oh so tasty!
*Adapted from Nina Dench's recipe for Karen Knowler, The Raw Food Coach. See TheRawFoodCoach.com.
## HEAVENLY APPLES AND BANANAS
### Serves 4–6
### Ingredients:
1. 6 very ripe bananas, sliced
2. 4 apples, sliced thin
3. 1 teaspoon cinnamon
4. ½ teaspoon nutmeg
5. 1 teaspoon vanilla extract
6. 1 tablespoon raw sugar or stevia
### Directions:
1. Coat a skillet with nonstick spray and place over medium-high heat.
2. Place bananas in skillet and stir until they begin to brown.
3. Add apples to bananas and mix. Sauté until the apples are tender when pierced with a fork.
4. Stir in cinnamon, nutmeg, and vanilla at the last minute of sautéing.
5. Turn off heat. Evenly sprinkle the raw sugar or stevia over the fruit. Spoon into dessert dishes and serve.
### Recipe tip:
Add a scoop of your favorite vanilla ice cream and you will have a spoonful of heaven! You can serve this dish warm or cold.
## BANANA BLISS PIE*
### Serves 8–10
### Ingredients for crust:
1. 3 cups oatmeal, blended to a fine powder
2. 1 cup crushed almonds
3. ¾ cup honey
4. 1 tablespoon almond or peanut butter
5. 1 pinch sea salt
6. 3 bananas
### Directions for crust:
1. Preheat oven to 350°.
2. Mix all ingredients except bananas in a large bowl.
3. Place mixture in bottom of pie dish and pat down to form a crust, using your hands or a spatula.
4. Bake for 5 to 8 minutes, until the mixture seems firm.
5. Let cool for 5 minutes. Meanwhile, cut bananas into thin slices. When crust is cool, spread banana slices to cover the bottom pie crust.
### Ingredients for toffee:
1. 1 cup almond or peanut butter
2. 1 cup maple syrup
3. 1 pinch sea salt
### Directions for toffee:
1. Mix all ingredients together until smooth.
2. Pour over bananas in crust.
### Ingredients for pie topping:
1. 5 bananas
2. 1 cup almond or peanut butter
3. ½ cup honey
4. ½ teaspoon vanilla extract
### Directions for pie topping:
1. Blend all ingredients until smooth and pour over toffee.
2. Place in fridge for an hour before serving.
*Adapted from Nina Dench's recipe for Karen Knowler, The Raw Food Coach. See TheRawFoodCoach.com.
## BASIC VANILLA SHAKE
### Serves 2
### Ingredients:
1. 2 cups vanilla Rice Dream ice cream or whole vanilla bean ice cream
2. 1 teaspoon vanilla extract
3. 1 tablespoon honey
4. 1 cup ice (more if needed)
### Directions:
1. Place all ingredients in blender.
2. Mix for 1 to 2 minutes, or until smooth. Pour and enjoy!
### Recipe tip:
Add a scoop of vanilla protein powder or oat bran to sneak in some protein!
## CHAI YUM
### Serves 1
### Ingredients:
1. 1 bag chai tea
2. 1 packet stevia
3. 1 dash coconut creamer
### Directions:
Place chai tea bag in mug filled with hot water. Add stevia and creamer.
# TASTE OF TRUTH
Nothing sweet tastes better than the Lord's presence, which satisfies the soul.
# CHAPTER 6
## Craving Life's Celebrations
### Healthy Holiday Recipes and Happy Home Memories
"OPEN HAPPINESS."
This slogan, used by the Coca-Cola Company, is one that I love —and I don't even drink Coke! Much of this slogan's appeal, I believe, stems from our desire to experience happiness.
I think one reason we don't celebrate as much as we could is because we don't believe there's anything to celebrate. In fact, the longer we live, the more we realize how hard life can be. We have to fight to find joy.
I come from a broken home, so holidays could be a painful time for me if I allowed them to be. It seems that every year I am forced to make a choice between celebrating the present or looking back on the people I lost when my parents divorced. To be honest, it is always a battle, but I have found that if I cry out to God when I'm hurting and ask Him to help me embrace those He has placed in front of me, I always find something or someone to celebrate.
# Soul Food
There is nothing better than to be happy and enjoy ourselves as long as we can.
ECCLESIASTES 3:12
Notice that the wisest king who ever lived reminds you and me that good food and good friends are meant to be enjoyed throughout our lives. Don't feel guilty for craving happiness; instead, learn how to find your joy and happiness in things that are holy, everlasting, and worth celebrating. When you read through the Bible, you see that after every trial or battle won, there was a feast and celebration.
The battles in your life are not meant to keep you down; they are meant to keep you close to God and give you a way to find joy in spite of any circumstances, knowing that your God is faithful and will fight for you. In the following New Life Recipes I have listed three ideas that I believe will help you find the happiness you're craving and new ways to celebrate!
# New Life Recipes
## 1. LOOK FOR SOMETHING TO CELEBRATE
Fix your thoughts on what is true, and honorable, and right, and pure, and lovely, and admirable. Think about things that are excellent and worthy of praise.
PHILIPPIANS 4:8
I grew up in a home that was filled with fighting, and to be honest, nothing seemed worthy of celebration. I hear from many women who describe a similar environment in their own homes. They are discouraged by the conflict that drives out any sense of peace and well-being.
I know that when life is out of control, we tend to be blind to the many blessings that come each day. Take a moment and write out one thing worthy of praise. You can even start with the little things, like a sunny day, a flower, or food to eat. Then you can build the list from there.
## 2. SPEAK OF HEAVEN OFTEN
God himself will be with them. He will wipe every tear from their eyes, and there will be no more death or sorrow or crying or pain. All these things are gone forever.
REVELATION 21:3-4
In those seasons when it seems there is nothing to celebrate, you may need to look beyond the here and now to the bigger picture. At such times, allow your heart and mind to meditate on the things of heaven. Keep in mind that we're only here for a little while, and if you're in a season in which it seems there is nothing to celebrate, remember that we will be forever celebrating in heaven. Let your mind dwell on those things.
Read the Scripture above and let your heart celebrate the day when there will be no more sickness, no more death, and no more tears. Allow yourself to breathe in His presence and dream about the Savior's return. When you do, you will find a reason to celebrate.
## 3. CREATE CELEBRATIONS
In Jerusalem, the LORD of Heaven's Armies will spread a wonderful feast for all the people of the world. It will be a delicious banquet with clear, well-aged wine and choice meat.
ISAIAH 25:6
Feasting is very much a part of creating celebrations, and you can bring this joyful mood into your home every day. Decorate your table with fresh-cut flowers or set out your pretty dishes for no reason other than to say "I love you" to those in your household. Just before you eat, turn on some soft, beautiful instrumental music. Then light a candle and seal the attitude of celebration in your home with a prayer, asking for the joy of God's presence to fill your home.
# POWER UP WITH PRAYER
Let them praise the LORD for his great love and for the wonderful things he has done for them. For he satisfies the thirsty and fills the hungry with good things.
PSALM 107:8-9
Help me, Lord, to praise You for Your great love and for the wonderful things You have done for me. Open my heart that I will be satisfied by You alone. May I thirst for You and be fulfilled with the good things You offer, now and forever. Amen.
# FOOD TRUTH
No food . . . is more delightful than celebrating a victory.
# Craving a Happy Holiday: Healthy Holiday Recipes and Holy Ways to Host Holidays
Perhaps your cherished holiday memories include scenes of your family around the table enjoying the same dishes lovingly prepared and served year after year. Fortunately, you can make healthy versions of many of these foods without sacrificing great taste. Enjoy some of the following recipes at your next holiday meal —or anytime!
## CAULI-MASHERS
### Serves 6
### Ingredients:
1. 1 head cauliflower
2. 1 tablespoon cream cheese
3. 2 pressed garlic cloves
4. 1 teaspoon fresh rosemary
5. 1 teaspoon onion powder
6. ¼ cup grated Parmesan cheese
7. ¼ cup butter
8. ¹⁄8 teaspoon chicken bouillon powder
9. 1 teaspoon sea salt, or to taste
10. ¹⁄8 teaspoon pepper, or to taste
### Directions:
1. Bring a medium pot of water to boil and cut cauliflower into small pieces. Boil until tender and drain.
2. Using a hand mixer, mash the cauliflower with the cream cheese, garlic, rosemary, onion powder, Parmesan, butter, and bouillon.
3. Once all ingredients are mashed and mixed together, add sea salt and pepper.
4. Serve and enjoy!
### Recipe tip:
This is an incredible substitute dish for mashed potatoes at Thanksgiving dinner.
## HOMEMADE CRANBERRY SAUCE
### Fills a medium-size bowl
### Ingredients:
1. 1 small (12 ounces) bag fresh or frozen cranberries
2. 1 can (16 ounces) pineapple chunks in juice, undrained (if using fresh pineapple, about 2 cups)
3. 1½ teaspoons orange zest
4. ½ cup honey, stevia, or raw sugar
### Directions:
1. Place cranberries, pineapple, pineapple juice, orange zest, and sweetener in food processor. Mix until all cranberries have been crushed.
2. If you'd like it sweeter, add one or two packets of stevia.
3. Pour mixture into bowl. Cover and chill until mealtime.
### Recipe tip:
Add walnuts or pine nuts as a garnish right before serving.
## STUFFED RED BELL PEPPER POPS
### Serves 4–6
### Ingredients:
1. 4 red bell peppers
2. 1 pound ground beef or turkey
3. ½ teaspoon chopped garlic
4. ½ cup chopped onion
5. 2 teaspoons cumin
6. 1 can (8 ounces) tomato sauce
7. 1 cup cooked brown rice or quinoa
8. ¼ cup sliced green olives
### Directions:
1. Preheat oven to 400°.
2. Halve the peppers and remove the seeds, stem, and veins. Place them in a baking dish, cut sides up. Set aside.
3. In a large skillet over medium heat, brown the meat with the garlic, onion, and cumin.
4. Add the tomato sauce and continue to cook until the mixture is heated all the way through, about 3 minutes.
5. Remove the meat mixture from heat. Stir in the rice or quinoa and sliced olives.
6. Scoop equal amounts of the meat-and-rice mixture into each pepper half.
7. Bake until the peppers are soft, approximately 25 minutes.
### Recipe tip:
Your holiday guests will love these! If you want, top them with your favorite cheese.
## CRANBERRY SWEET POTATO BREAD
### Serves 8
### Ingredients:
1. ¼ cup water
2. 2 tablespoons ground flaxseed
3. 1 medium sweet potato, diced
4. 1 cup whole-grain or gluten-free flour
5. 1 cup cornmeal
6. ¼ cup raw sugar or stevia
7. 4 teaspoons baking powder
8. 1 teaspoon sea salt
9. 1 cup rice, almond, or coconut milk
10. ¼ cup olive oil
11. ¼ cup maple syrup or agave syrup
12. ½ cup dried cranberries
### Directions:
1. Preheat oven to 425° and coat an 8 x 8-inch baking dish with nonstick cooking spray.
2. Bring the ¼ cup water to a boil in a small saucepan. Add the ground flaxseed and simmer until thickened, about 2 minutes. Set aside.
3. Place a steamer basket into a pan with water and bring to a boil. Add sweet potato. Steam until tender, approximately 15 minutes. Then remove sweet potato from pan.
4. Mash the sweet potato and set aside.
5. In a medium bowl, whisk together the flour, cornmeal, sugar or stevia, baking powder, and sea salt until fully mixed.
6. In a separate bowl, mix the wet ingredients: milk, olive oil, and maple or agave syrup. Add the ground flaxseed mixture from step 2.
7. Fold the wet ingredients into the dry ingredients, and then gently fold in the mashed sweet potato and dried cranberries to create the batter.
8. Pour the batter into the prepared baking pan and bake for 20 to 25 minutes, or until a toothpick inserted in the center comes out clean.
9. Let cool for 10 minutes.
### Recipe tip:
Try using raisins instead of dried cranberries. This is sure to be another one of your holiday guests' favorites!
## STUFF ME FULL TURKEY
### Serves 12
### Ingredients:
1. 1 turkey, 10–15 pounds
2. 4 sprigs rosemary
3. 10 apples, cored and sliced in half
4. ½ cup canola or sunflower oil
5. ½ cup balsamic vinegar
6. 1 tablespoon sea salt
7. 1 tablespoon cinnamon
### Directions:
1. To thaw a frozen turkey, place it in the refrigerator. (It takes about one day for every 4 to 5 pounds; a 15-pound bird needs 3 days.) Another method is to thaw the bird in a cold-water bath, changing the water every half hour. (This requires 30 minutes per pound —7½ hours for a 15-pound bird.)
2. When the turkey is fully thawed, preheat oven to 325°.
3. Remove the packet of giblets and the neck from the turkey's cavities.
4. Rinse the bird well (inside and outside) and pat dry with paper towels.
5. Place the turkey in a roasting pan, breast side up. Put rosemary in the large cavity of the bird, along with 2 apple halves.
6. Truss (tie legs together with string), then drizzle the bird with oil and balsamic vinegar, and sprinkle with salt and cinnamon.
7. Wedge remainder of apples around roasting pan to prop up the turkey evenly.
8. Place roasting pan in oven on lowest rack.
9. Roast 15 minutes per pound (a 15-pound turkey requires 3 hours and 45 minutes).
10. Check turkey with an instant-read thermometer to make sure it is fully cooked (the temperature should be 180° when inserted in the thickest part of the leg). Once the turkey is done, remove turkey from the oven and let it cool for 30 minutes before carving.
### Recipe tip:
Substitute oranges for apples.
## VEGGIE PIE
### Serves 4 (in individual custard dishes)
### Ingredients for pie filling:
1. 1 large sweet potato, peeled and chopped into ½-inch pieces
2. 1 large carrot, peeled and chopped
3. 1 stalk celery, chopped
4. 1 medium onion, chopped
5. ¹⁄3 cup fresh or frozen corn
6. 1 large shiitake mushroom, chopped
7. ¾ cup chopped broccoli florets
8. ½ zucchini, chopped
9. ¹⁄3 cup fresh or frozen peas
10. 4–6 garlic cloves, chopped fine
11. 1 tablespoon whole-grain or gluten-free flour
12. 2 cups vegetable broth or water
13. 1 bay leaf
14. 1 teaspoon fresh or dried oregano, or to taste
15. 1 to 2 teaspoons sea salt
16. ¹⁄8 teaspoon black pepper, or to taste
17. 1 pinch red pepper flakes
### Directions for pie filling:
1. Sauté sweet potato, carrot, celery, onion, corn, mushroom, broccoli, zucchini, peas, and garlic in a skillet until tender crisp.
2. Whisk flour into broth or water and add to pot.
3. Add bay leaf, oregano, salt, black pepper, and red pepper flakes. Heat, stirring occasionally, until sauce is thickened and bubbling.
4. Remove from heat, discard the bay leaf, and divide the mixture among four custard dishes.
### Ingredients for the top crust:
1. 1½ cups whole-grain or gluten-free flour
2. ¼ cup + 2 tablespoons butter
3. 1 egg white
4. ½ teaspoon salt
5. 3 tablespoons canola or sunflower oil
6. 3 tablespoons olive oil
7. 1½ tablespoons apple cider vinegar
8. 2½ tablespoons cold water
### Directions for top crust:
1. Preheat oven to 350°.
2. In a large bowl, stir together flour, butter, egg white, and salt.
3. Add oils, apple cider vinegar, and water. Mix with a fork or your hands, forming the dough into a ball. If dough seems too dry, you can add a little more water.
4. Place the dough ball on a clean surface, dusted with flour. With a rolling pin, roll the dough into a ¼-inch thick sheet. Cut out circles slightly larger than the baking dishes.
5. Using a spatula, transfer your dough circles onto the top of your filled serving dishes. Gently press the dough with your finger all around the edge of each dish to seal the crust.
6. Brush the tops of the crust with a thin coat of olive oil, and bake for 15 to 25 minutes, until the crust is slightly cracked and a light golden brown color.
7. Let veggie pies cool for a few minutes and enjoy!
### Recipe tip:
Try adding chicken or turkey for a more traditional potpie recipe.
## PUMPKIN, SPICE, AND EVERYTHING NICE COOKIES
### Makes about a dozen cookies
### Ingredients:
1. 8 ounces organic mashed pumpkin (canned or fresh)
2. 1 small ripe banana, chopped
3. 1½ teaspoons pumpkin pie spice
4. 3 tablespoons agave syrup or honey
5. 1 tablespoon raw sugar or stevia
6. ¼ teaspoon sea salt, finely ground
7. 2 cups organic raw whole rolled oats
8. 3 tablespoons ground flaxseed
### Directions:
1. Preheat the oven to 350°.
2. Coat a baking sheet with olive oil or canola oil cooking spray.
3. Combine pumpkin, banana, pumpkin pie spice, sweeteners, and sea salt in a large mixing bowl. Mix on high with a hand mixer until mostly smooth, about 2 minutes.
4. Using a large wooden spoon, fold in the oats and flaxseed until mixed well.
5. Form cookies using a tablespoon and bake for 12 to 16 minutes or until set.
6. Let cool 10 minutes before eating.
### Recipe tip:
If you love chocolate, this recipe is also great with semisweet chocolate chips.
# TASTE OF TRUTH
The best is yet to come —and when it does, our happiness will be everlasting.
# CHAPTER 7
## Craving God's Best for You
### Spicy Food Recipes and Spicing Up Your Faith
I ONCE READ THAT cayenne pepper was good for weight loss. I'm one of those excessively compulsive people who believe that if a little is good, a lot must be better, so I decided to take half a bottle of cayenne pepper spicy seasoning and pour it into some tomato juice. Then I chugged it, hoping to be thin by the next morning.
Within twenty minutes of my spicy culinary experiment, I was rushed to an emergency room because my face had become so flushed and my blood pressure had gone through the roof. The medical staff had to give me a tranquilizer to calm me down and Benadryl for the allergic reaction.
You may be laughing right now, wondering what kind of woman I am to do something wacky like that. However, when we are craving spice in our lives, we can do some crazy things. Sadly, some of those things may even harm us and others.
# Soul Food
"Praise the LORD your God, who delights in you and has placed you on the throne as king to rule for him. Because God loves Israel and desires this kingdom to last forever, he has made you king over them so you can rule with justice and righteousness."
Then she gave the king a gift of 9,000 pounds of gold, great quantities of spices, and precious jewels. Never before had there been spices as fine as those the queen of Sheba gave to King Solomon.
2 CHRONICLES 9:8-9
Many times when you and I crave spice in our lives, we try to season ourselves with riches, when the Creator of the universe is just waiting for us to invite Him to pour His presence, peace, and power into our lives!
The Lord is waiting to season your life with lots of flavor and His favor. Consider the three ideas in the following New Life Recipes so that you may taste and see that your Lord can satisfy your craving like nothing else.
# New Life Recipes
## 1. GIVE IN
I will give you a new heart, and I will put a new spirit in you. I will take out your stony, stubborn heart and give you a tender, responsive heart.
EZEKIEL 36:26
Many times we are so set in our ways that we cannot see God's ways. He created us to crave spice in our lives, and He wants to take our hardened hearts and help us become who we crave to be. Take an honest inventory of your deepest desires. If you discover you want anything more than you want His will for your life, try a new spice I call "Giving In to Him." Then you will taste and see that the Lord is good.
## 2. GIVE IT AWAY
Jesus took the five loaves and two fish, looked up toward heaven, and blessed them. . . . They all ate as much as they wanted, and afterward, the disciples picked up twelve baskets of leftovers!
LUKE 9:16-17
A young boy came to eat lunch and listen to Jesus. Then he got so much more when he decided to give up all he had. Jesus took what the boy willingly gave away and fed the entire crowd —about five thousand men, not to mention the many women and children! Just think about the miracle that boy could have missed being a part of if he had kept his lunch for himself out of fear he would not have enough to eat. Nothing will do more to spice up your faith than to see God multiply what you're willing to give away.
## 3. GIVE IT UP
No one can take my life from me. I sacrifice it voluntarily. For I have the authority to lay it down when I want to and also to take it up again. For this is what my Father has commanded.
JOHN 10:18
When you think about Jesus giving up His life for us, it really puts all the things we think we can't give up in perspective, doesn't it?
If you want to add spice to your life, ask the Lord what He wants you to give up for your good and His glory.
# POWER UP WITH PRAYER
Create in me a clean heart, O God.
Renew a loyal spirit within me.
Do not banish me from your presence,
and don't take your Holy Spirit from me.
PSALM 51:10-11
Dear God,
From this day forward I choose to give in to Your will and to give away whatever You ask me to, as well as whatever is getting in the way of my walk with You. I invite You now to search my heart, so that through the power of the Holy Spirit, I will see what I need to do to taste and see Your goodness again. Amen.
# FOOD TRUTH
No food . . . is more flavorful than life in Christ.
# Spicy Food Recipes
Who says healthy food needs to taste boring and bland? Add a little zip to your next meal with one of the following recipes.
## FANTASTIC FIERY CHICKEN
### Serves 4–6
### Ingredients:
1. 2 tablespoons tomato paste
2. 1½ teaspoons water
3. ½ teaspoon olive oil
4. ½ teaspoon minced garlic
5. ½ teaspoon chipotle chili powder
6. ½ teaspoon fresh oregano, chopped
7. 4 boneless chicken breasts
### Directions for marinade:
1. Blend together the tomato paste, water, and oil in a small bowl.
2. Add garlic, chili powder, and oregano. Mix well.
3. Using a brush, spread the marinade on both sides of the chicken breasts and refrigerate overnight.
### Directions for cooking chicken:
1. Prepare a charcoal or gas grill and lightly coat the grill's cooking rack or grid with nonstick cooking spray. Position it 4 to 6 inches from the heat source.
2. Place chicken on grill and cook thoroughly, about 15 to 20 minutes.
### Recipe tip:
If you really love hot spice, take some jalapeños and squeeze the juice on the chicken while it's cooking!
## HOT CABBAGE
### Serves 2–4
### Ingredients:
1. 1½ pounds red cabbage, cored, quartered, and shredded
2. 1 medium onion, chopped
3. 1 tart apple, cored and chopped
4. 1 garlic clove, crushed
5. 1 teaspoon ground cinnamon
6. ¼ teaspoon ground cloves
7. 1 teaspoon cumin seed
8. 1 tablespoon cayenne pepper
9. 2 tablespoons red wine vinegar
10. 2 teaspoons red pepper flakes
11. ½ teaspoon ground nutmeg, or to taste
12. 1 tablespoon jalapeño juice, optional
13. ½ cup water
### Directions:
1. In a large pot, stir all the ingredients together, mixing thoroughly.
2. Cover and cook over medium heat, stirring frequently until the vegetables are tender, about 1 hour.
3. Add more water as needed during the cooking process to prevent the mixture from going dry or burning.
4. Transfer to a serving bowl and serve either warm or cold.
### Recipe tip:
Serve as a side dish or add meat for a heartier entrée. This is also a great side dish to a soup!
## SPICY SQUASH
### Serves 2–4
### Ingredients:
1. 1 spaghetti squash, cut in half and seeds scraped out
2. 4 tablespoons olive oil, divided
3. Salt and pepper
4. 4 cloves garlic, minced
5. 1 zucchini, halved and sliced
6. 1 teaspoon red pepper flakes
7. Fresh chopped herbs, to taste
### Directions:
1. Preheat oven to 400°.
2. Rub about 1 tablespoon of olive oil inside each squash half, and season to taste with salt and pepper.
3. Place each piece of squash, skin side up, on a baking tray.
4. Bake for 45 minutes.
5. Remove the squash from the oven and allow it to cool slightly. Be careful, as the skin will be very hot.
6. Using a fork, pull the spaghetti-like strands of squash pulp from the skin into a mixing bowl.
7. Place 2 tablespoons of olive oil in a skillet and add the garlic, zucchini, and red pepper flakes. Heat together on medium-high heat for about 1 minute.
8. Pour the zucchini mixture over the squash and stir it in. Then add chopped fresh herbs and mix again.
### Recipe tip:
Treat this like spaghetti. Add a zesty red sauce or Parmesan to make it extra delicious.
## AREN'T WE TENDER, PORK TENDERLOIN
### Serves 4
### Ingredients:
1. ½ teaspoon freshly grated or ground ginger
2. ½ teaspoon garlic powder
3. ½ teaspoon onion powder
4. ½ teaspoon cayenne pepper
5. 1 teaspoon ground cinnamon
6. ½ teaspoon ground cloves
7. 2 teaspoons firmly packed brown sugar
8. ¾ teaspoon sea salt, divided
9. ½ teaspoon freshly ground black pepper
10. 1 pork tenderloin, about 1 pound, trimmed of fat
11. 1½ cups raw honey
12. 1 teaspoon tomato paste
13. 2 teaspoons white vinegar
14. 1 tablespoon red pepper flakes
### Directions:
1. Prepare a hot fire in a charcoal grill or heat a gas grill or oven broiler to medium-high temperature, about 400°.
2. In a small bowl, combine the ginger, garlic powder, onion powder, cayenne pepper, cinnamon, cloves, brown sugar, ½ teaspoon of the sea salt, and the black pepper to make a rub.
3. Place the meat in the bowl and rub the spice mixture over the pork. Let stand for 15 minutes.
4. In another small bowl, combine the honey, tomato paste, vinegar, red pepper flakes, and the remaining ¼ teaspoon of sea salt. Stir to blend. Set aside.
5. Place the pork on the grill rack or broiler pan. Grill or broil, turning several times, until browned, about 3 minutes on each side.
6. Move to a cooler part of the grill or reduce the heat. Continue cooking for about 14 to 16 minutes. Baste with the honey-vinegar glaze and continue cooking until the pork is slightly pink inside and an instant-read thermometer inserted into the thickest part reads 160°.
7. Move pork to a cutting board. Let stand for 5 minutes before slicing.
### Recipe tip:
This is a great recipe to make when guests come for the holidays!
## FIRE CHILI
### Serves 8
### Ingredients:
1. 1½ cups coarsely chopped onion
2. 1 cup chopped red bell pepper
3. 1 cup chopped green bell pepper
4. 3 cloves garlic, minced
5. ¾ cup chopped celery
6. ¾ cup chopped carrot
7. 3 jalapeños, sliced
8. 1 tablespoon chili powder
9. 1½ cups quartered fresh mushrooms
10. 1 cup cubed zucchini
11. 1 can (11 ounces) whole kernel corn, undrained
12. 1 tablespoon ground cumin
13. 1 can (15 ounces) chickpeas, drained and rinsed
14. 1 can (15 ounces) black beans, drained and rinsed
15. 1 can (15 ounces) diced or whole tomatoes, undrained, or 1 cup fresh diced tomatoes
16. 1½ teaspoons dried oregano
17. 1½ teaspoons dried basil
18. ½ teaspoon cayenne pepper
### Directions:
1. Coat a large saucepan with nonstick cooking spray. Add onion, red bell pepper, green bell pepper, garlic, celery, carrot, jalapeños, and chili powder. Cook over medium heat until vegetables are soft.
2. Add mushrooms and zucchini. Cook for 4 minutes.
3. Add corn, ground cumin, chickpeas, black beans, tomatoes with juice, oregano, basil, and cayenne pepper. Bring to a boil, then reduce heat to medium-low. Cover and simmer for 20 minutes, stirring occasionally.
### Recipe tip:
If this still isn't spicy enough for you, add some red pepper flakes.
## GARLIC SPICED CHICKEN
### Serves 4–6
### Ingredients:
1. 3 cloves garlic, crushed
2. 1 teaspoon fresh grated ginger
3. ½ teaspoon cayenne pepper
4. ¹⁄3 cup hoisin sauce
5. 3 tablespoons low-sodium soy sauce or Bragg Liquid Aminos
6. ¼ cup red wine vinegar
7. 1 teaspoon sesame oil
8. 12 chicken drumsticks
9. 2 teaspoons brown sugar
10. ½ teaspoon whole-grain or gluten-free flour
11. ½ teaspoon water
### Directions:
1. Combine garlic, ginger, cayenne pepper, hoisin sauce, soy sauce or Bragg Liquid Aminos, red wine vinegar, and sesame oil in a large bowl. Mix well to make a marinade.
2. Add chicken to marinade and turn to coat all sides. Cover and refrigerate for 3 hours or overnight.
3. Drain chicken, reserving marinade.
4. Heat a grill or broiler pan to medium heat, about 350°. Grill chicken until fully cooked and browned to your liking.
5. Blend brown sugar, flour, and water in a pan over medium-high heat. Stir in reserved marinade, and continue stirring until mixture boils and thickens. Serve sauce with chicken.
### Recipe tip:
This chicken dish is delicious served over brown rice.
## HOMEMADE BARBECUE SAUCE
### Makes a small bowl of sauce
### Ingredients:
1. ½ cup water
2. 1½ cups tomato sauce
3. ½ cup red wine vinegar
4. 1 tablespoon low-sodium soy sauce or Bragg Liquid Aminos
5. ½ teaspoon hot sauce
6. 1 cup agave syrup or honey
7. 2½ tablespoons dry mustard
8. 2 teaspoons paprika
9. 2 teaspoons salt
10. 1½ teaspoons black pepper
### Directions:
1. Combine water, tomato sauce, vinegar, soy sauce or Bragg Liquid Aminos, and hot sauce in a blender.
2. Season mixture with remaining ingredients; blend until smooth.
# TASTE OF TRUTH
His power displayed through you will spice up everyone else's faith.
# CHAPTER 8
## Craving Real Refreshment
### Delicious Drinks and Hydration for Your Soul
I WASN'T RAISED a Christian, and I did not give my life to the Lord until I was twenty-four. I had much time to live in the world and act like the world. During my early years, everyone I knew seemed to be driven by a desire for pleasure.
After I became a Christian, I watched most believers try to walk out their faith according to other people's expectations —almost as if they were Christian clones. Neither approach —living for pleasure as a nonbeliever or without a unique purpose as a believer —seemed to offer refreshment to me or anybody else. I assumed everyone's soul was as severely dehydrated as mine.
Today I know the Lord and understand that He created me with a distinct purpose in mind, but I still sometimes find myself seeking refreshment from things, people, or pleasure. It's not that we cannot find temporary refreshment from those three things, but they will not quench our thirst or cure the craving of our hearts and souls.
# Soul Food
Then times of refreshment will come from the presence of the Lord, and he will again send you Jesus, your appointed Messiah.
ACTS 3:20
Have you ever jumped into a lukewarm pool on a hot summer day? When you're overly warm, it's pretty disappointing to land in what feels like bathwater. No matter how many times you jump in or how long you stay in, you won't be cooled and refreshed.
Sometimes we crave refreshment because our faith feels lukewarm. We don't feel cold, and we don't feel hot. We're just going through the motions. Jesus said He came to give us life and all it has to offer. So how can we truly live the abundant life He gave His own life for? We need the real deal, and that is not easily found when we have settled for an artificial connection with God and one another.
For example, we crave refreshment in our relationships, yet texting and e-mail have become the new ways to connect. Don't get me wrong: it's not that I don't love text messaging my friends and family, but I know nothing replaces the heart-to-heart connection that comes when you spend quality time sharing your heart and looking into a friend's or family member's eyes.
We crave a breath of fresh air, but we don't allow ourselves to stop for a moment and breathe in the blessings that surround us. We crave peace for our minds, but we won't turn off the TV long enough to clear our minds of the junk we watch and simply be still before the Lord.
Refreshment is found in the simple things: a walk in a park or by a river, a good talk with a friend, a quiet afternoon, a Sunday nap in the chaise lounge or hammock in the yard. . . . Take a moment and think about the things that refresh you. Then read the three New Life Recipes that follow to help you find the refreshment you are craving.
# New Life Recipes
## 1. REFRESH OTHERS
The generous will prosper; those who refresh others will themselves be refreshed.
PROVERBS 11:25
When we're worn out and weary, how many times do we look to our loved ones to refresh us? Then, when they don't give us the refreshment we crave, we are disappointed in them.
All along God is saying, "Come to Me to get refreshment. Then go out and be My representative and refresh others." The Lord promises us in Proverbs that if we refresh others, we ourselves will be refreshed by Him. Let's refresh those we love today!
## 2. LIE DOWN
He lets me rest in green meadows;
he leads me beside peaceful streams.
PSALM 23:2
When you feel like your soul is dying of thirst and you have nothing left to give, stop everything and be still. What you're craving is to be filled up by the Holy Spirit. It's only when you sit at His feet —turning off your phone and computer, putting down your to-do list —and allow Him to pour His loving and living water over you that you will find the refreshment you crave.
Don't underestimate the power of being still in His presence.
## 3. LIVE THIS DAY
This is the day the LORD has made.
We will rejoice and be glad in it.
PSALM 118:24
We deprive ourselves of much-needed refreshment and burn out when we don't live for today. Too often our minds are in the next place we need to be or on the next thing we need to do. As a result, we don't feel satisfied; we feel frustrated. If we are not careful, we will miss those treasured moments that could refresh us.
If you're craving a breath of life, try to breathe in the moment. That means taking time to check in with whoever is standing in front of you today. As you do, you will find new refreshment.
# POWER UP WITH PRAYER
He satisfies the thirsty
and fills the hungry with good things.
PSALM 107:9
Dear God,
Your Word says that You satisfy the thirsty and fill the hungry with good things. I am thirsty for Your presence in my life, and I ask You to fill me up once again so I can fill others up. Help me be still long enough to drink in Your goodness. Amen.
# FOOD TRUTH
No food . . . refreshes like God's Word.
# Refreshing Drink Recipes
For real refreshment on a hot summer day or after a hard workout, try whipping up one of the following cool drinks.
## WATERMELON LEMONADE
### Serves 8
### Ingredients:
1. 10 to 12 pounds seedless watermelon, cut up
2. 4 tablespoons freshly squeezed lemon juice
3. 2 tablespoons raw sugar or stevia
### Directions:
1. Puree watermelon in batches in a blender. Transfer to large pitcher.
2. Mix in remaining ingredients.
3. Chill and serve for a deliciously refreshing drink!
### Recipe tip:
Great for kids or yourself on a hot summer day. You can also create healthy frozen ice pops with this recipe.
## STRAWBERRY LEMONADE
### Serves 2–4
### Ingredients:
1. 2 cups frozen strawberries
2. 2 cups peeled, seeded lemon, cut up
3. 1 peeled, seeded orange, cut up
4. 1 or 2 packets of stevia
5. 2 cups crushed ice
6. 1 to 2 cups water
7. 1 lemon, peeled, seeded, and cut into 4 slices for garnish
### Directions:
1. Place all ingredients in blender and mix for 1 to 2 minutes, until smooth.
2. Garnish each glass with a lemon slice for extra tang.
### Recipe tip:
Replace the strawberries with raspberries to make raspberry lemonade. You can also freeze the liquid and make ice pops.
## POMEGRANATE PUNCH
### Serves 2–4
### Ingredients:
1. 8 pomegranate tea bags
2. 2 cups hot water
3. 3 cups pomegranate juice
4. 1 tablespoon raw sugar or stevia
### Directions:
1. Brew pomegranate tea in hot water, according to the package directions, then let the tea cool for 15 minutes.
2. Mix pomegranate juice and sugar or stevia in pitcher.
3. Add cooled tea. Pour into glasses with ice and serve.
### Recipe tip:
You can also blend this with ice to make a smoothie, or freeze to make ice pops.
## THAT'S THE RASPBERRIES SMOOTHIE
### Serves 2–3
### Ingredients:
1. 1 cup plain nonfat yogurt
2. 1½ cups frozen raspberries
3. 1 teaspoon vanilla extract
4. ½ cup vanilla coconut milk
5. ½ cup honey
6. 1½ cups ice (more if needed)
### Directions:
1. Blend all ingredients together to desired consistency. Pour into glasses and enjoy!
### Recipe tip:
You can also freeze this into ice pops for a healthy, refreshing snack.
## FRUIT SPRITZER
### Serves 1–2
### Ingredients:
1. ½ cup naturally sweetened raspberry or cranberry juice, chilled
2. 1 cup sparkling mineral water, chilled
3. 1 lime, cut into 4 wedges
### Directions:
1. Stir the raspberry or cranberry juice and mineral water together.
2. Pour into ice-filled glasses. Before serving, add lime wedges.
### Recipe tip:
You can add any flavor packet of Emergen-C for some added vitamin C and antioxidants.
## GINGERLY PEACHY KEEN SMOOTHIE
### Serves 2–4
### Ingredients:
1. 1 cup plain low-fat yogurt
2. 1 tablespoon fresh grated ginger
3. 1 teaspoon vanilla extract
4. ½ cup fat-free cottage cheese
5. ¹⁄3 cup honey
6. 4 large peaches, sliced
### Directions:
1. Combine ingredients in blender and mix until smooth. Pour into glasses and serve.
### Recipe tip:
Try this with mangoes for another delicious smoothie.
## FROZEN HONEY COLADA SMOOTHIE
### Serves 4
### Ingredients:
1. 4 teaspoons honey
2. 1 cup pineapple
3. 2 cups coconut milk
4. 4 cups ice cubes
### Directions:
1. Combine all ingredients in blender, and mix for 30 seconds.
### Recipe tip:
If you love coconut, top off your drink with shredded coconut for some extra taste.
# TASTE OF TRUTH
Life is not measured by the number of breaths we take but by the moments that take our breath away! (Author unknown)
# CHAPTER 9
## Craving Fortifying Faith
### Raw Food Recipes and Getting Real with God
ONCE AS I WAS being interviewed live on a Christian television program, I noticed a large, very loud fly buzzing around the set of the studio. It kept landing on the bald head of the show's host, who was sitting across from me.
I did everything I could to pretend I did not see that fly —until it flew into the host's mouth. Though he continued to ignore what was real —the bug he was choking on —and went on interviewing me, I was not as good an actress as he was an actor. I finally broke out in laughter; needless to say, the show got very real at that moment.
I think sometimes we are so afraid to talk about what's really going on that we forget how freeing it is for everyone around us when we get real with one another. Of course, it's even more important that we get real with God.
# Soul Food
O LORD, how long will you forget me? Forever?
How long will you look the other way? . . .
Turn and answer me, O LORD my God!
Restore the sparkle to my eyes, or I will die.
PSALM 13:1, 3
There was nothing artificial about King David's relationship with the Lord. If you read the book of Psalms, you will see that David had a very real and authentic relationship with God. David was not perfect, but he was desperate for God and not afraid to admit it! His desperation led God to give David a very distinct description: "a man after my own heart" (Acts 13:22).
In the deepest part of every man and woman is a craving for real faith. Today, due to so many false teachings and fallen leaders, many people's faith has been fractured. But that doesn't stop our craving to find the true and living God.
Remember that man is _not_ God, so if a _man_ or _woman_ (your pastor, father, mother, boss, or friend) has sinned against God or you, please be careful not to lose your faith because of that person's actions.
That means, first of all, that we have to get real and recognize that we live in a fallen world with imperfect people. If we are ever going to find real faith, it won't be in a man —it will be in the true and living God who designed us to have a real relationship with Him.
If you're craving closeness with your heavenly Father, then I invite you to join me in finding real faith cures to connect your heart in a very real way to the one true and very real God!
# New Life Recipes
## 1. DON'T LOOK TO OTHERS
Dear friends, do not believe everyone who claims to speak by the Spirit. You must test them to see if the spirit they have comes from God. For there are many false prophets in the world.
1 JOHN 4:1
God warns us not to believe everything we see or hear from people. He tells us that not everyone who says he or she is a Christian represents God.
If you're craving a real faith relationship with the Lord, it won't be found by looking to others; it will be found by looking to God. He promises that if you seek Him with all your heart, you will find Him. If you're really craving more of God, commit yourself to praying and seeking a real relationship with Him. Then you will find the real faith your heart longs for.
## 2. DON'T PLAY FAITH GAMES
But I fear that somehow your pure and undivided devotion to Christ will be corrupted, just as Eve was deceived by the cunning ways of the serpent.
2 CORINTHIANS 11:3
God loved Eve and gave her the opportunity to be blessed in every way. However, she caved in to her curiosity, hoping it would satisfy her heart's desire to know the truth. In that moment of deception, she played a game in her own mind and allowed the enemy to convince her that God didn't really mean what He said. By acting on that craving, she sinned. Adam soon followed, and their actions were the cause of death for every one of us.
Don't make Adam and Eve's mistake. If you want a real relationship with God, you must crave obeying Him more than anything else. God is who He says He is, and He will do what He says He will do. Let's get real with Him and get our hearts right so we can receive His blessing.
## 3. DON'T LIVE BY SIGHT
For we live by believing and not by seeing.
2 CORINTHIANS 5:7
Prior to finding Christ in my midtwenties, I saw a lot of horrible things, which made it difficult for me to live by faith and not by sight. I craved real peace and a real relationship with God, yet somehow I could not understand why bad things happen to good people and why unjust things happen in the world that God created.
Today I understand that faith is all about living by what I know to be true in the Word, not by what I see around me. I now understand that I cannot control others' actions, but I can control my reactions to the world around me by the power of God.
Be real with God. Let Him know your fears and your frustrations. Tell Him when you cannot find Him, and ask Him to make Himself real to you. Then you will begin to see the invisible God become visible to you and through you.
# POWER UP WITH PRAYER
[Jesus said,] "The time is coming —indeed it's here now —when you will be scattered, each one going his own way, leaving me alone. Yet I am not alone because the Father is with me. I have told you all this so that you may have peace in me. Here on earth you will have many trials and sorrows. But take heart, because I have overcome the world."
JOHN 16:32-33
Dear God,
It is hard to find You in a world that is filled with pain, problems, and persecution. I am getting real with You and letting You know that I need You to reveal Yourself to me in a personal way today. I love You, and I want and crave more of You. Amen.
# FOOD TRUTH
No food . . . can control you without your permission.
# Raw Food Recipes
The benefits of going raw are extensive, particularly since so many of our foods are pumped with preservatives and additives. Going raw eliminates the need to wonder and worry about what you are really eating. Raw food is delicious, and eating it will make you feel amazing.
## RAW FOOD RANCH DRESSING
### Serves 2–4
### Ingredients:
1. ¼–½ cup almonds, soaked in water overnight
2. 2 cloves garlic, minced
3. Juice of 1 lemon
4. ¾ cup canola or sunflower oil
5. ¼ teaspoon kelp granules or sea salt
6. A touch of honey
### Directions:
1. Drain and rinse the almonds.
2. In blender, add almonds to all other ingredients and mix thoroughly. The dressing should be nice and thick.
### Recipe tip:
Almond skins will turn the dressing brown. If you want the dressing to be white, you can blanch the almonds by putting them in boiling water for 30 seconds. After 30 seconds, slowly add cool water until the water is warm. Peel off the almond skins with your fingers. This is a great dip for any fresh veggies.
## MUSHROOM SOUP
### Serves 4–6
### Ingredients:
1. 2 tablespoons olive oil
2. 1½ cups sliced fresh mushrooms
3. 1 red onion, diced
4. 2 carrots, grated
5. 1 tablespoon minced garlic
6. 8 cups vegetable broth
7. 3 cups cooked pearl barley
8. 1 teaspoon sea salt
### Directions:
1. Heat olive oil in a large soup pot and add mushrooms, onion, carrots, and garlic. Cook for 5 minutes.
2. Add vegetable broth, barley, and sea salt. Simmer for about 40 minutes over low heat.
3. Serve in bowls and enjoy.
### Recipe tip:
Feel free to add any other vegetables that you love to this recipe —celery leaves or kale would be fantastic!
## TASTY RAW FOOD TACOS
### Serves 4–6
### Ingredients:
1. 8 ounces salsa
2. 1 cup cashews
3. 1 cup sunflower seeds
4. 8–12 corn or gluten-free tortillas
5. 1½ cups diced cooked chicken
6. ½ red onion, diced
7. 1 cup cooked black beans
8. 2 ripe tomatoes, diced
9. 1 avocado, diced
10. 1 mango, diced
### Directions:
1. Blend together salsa, cashews, and sunflower seeds to a pastelike consistency.
2. Lay tortillas flat and spread with the salsa/cashew/sunflower seed mixture. Top with the chicken, onion, black beans, tomatoes, avocado, and mango. Fold over like a taco, and enjoy!
### Recipe tip:
Dress up your tacos with organic lettuce, or if you're feeling really brave, substitute cabbage leaves for the corn tortillas for an all-raw meal!
## GOOD-FOR-YOU GREENS SOUP
### Serves 2–4
### Ingredients:
1. 1 cup fresh diced tomato
2. ½ cup water
3. 2 cups spinach
4. ½ avocado
5. ½ cup chopped broccoli
6. 1 teaspoon fresh minced garlic or garlic powder
7. 2 tablespoons freshly squeezed or bottled lemon juice
8. 1 tablespoon olive oil
### Directions:
1. Place all the ingredients in a blender, and mix until smooth.
2. Pour mixture into a saucepan, and heat 5 to 10 minutes, stirring as needed. Taste to make sure it has the flavor you want. You can add water if soup is too thick.
### Recipe tip:
A great side dish to this soup would be sweet potato fries, made fresh in your oven!
## RAW MANGO PUDDING
### Serves 2–4
### Ingredients:
1. 4 cups frozen mango chunks
2. 1 fresh peach or nectarine
3. 1 ripe banana
4. 2 dates
5. 1 passion fruit
6. 1 tablespoon raw sugar or stevia
7. 4 strawberries
### Directions:
1. Chop all of the fruit.
2. Mix chopped fruit in the blender until smooth. Add ice if pudding is too thin.
### Recipe tip:
This is a great party recipe, and it's also great for kids. Take some to work in a Tupperware container for a fun snack. It will keep in the fridge for up to three days.
## FRESH CORN SALAD
### Serves 2–4
### Ingredients for salad:
1. 2 cups fresh corn, cut from the cob
2. ½ red onion, diced
3. ¾ cup diced red, orange, and/or yellow bell peppers
4. 1 avocado, diced
5. 1 tomato, diced
6. 1 cup cooked black beans
7. ½ cup diced mild green chilies
### Ingredients for dressing:
1. Juice of 1 lemon (about ¼ cup)
2. Juice of 1 lime (about ¼ cup)
3. 1–2 garlic cloves, minced
4. ½ bunch cilantro, chopped fine
5. 4 ounces salsa
### Directions:
1. Mix all salad ingredients together.
2. Mix all dressing ingredients together.
3. Mix salad with dressing and serve.
### Recipe tip:
Add raw honey or agave syrup to the dressing mix for a sweeter taste to this salad.
## MINT PEAR SALAD
### Serves 2–4
### Ingredients for salad:
1. 1 head romaine lettuce
2. 1 avocado, diced
3. 2 pears, diced
4. ½ cup slivered almonds
5. ½ cup dried cranberries
### Ingredients for mint dressing:
1. 1 small bunch fresh mint
2. 1½ tablespoons honey
3. Juice of 1 lemon
4. ¾ cup low-fat or Healthy Mayonnaise (see page 19)
### Directions:
1. Mix salad ingredients in a large bowl.
2. Mix dressing ingredients.
3. Mix dressing with salad, serve, and enjoy!
### Recipe tip:
This dressing can be stored in the fridge for up to three days. The mint dressing works on any of your favorite salads or as a dip for fresh fruit. If you don't want to eat this completely raw, add diced cooked chicken breast for protein.
# TASTE OF TRUTH
Get real with God, and He will become real to you.
# CHAPTER 10
## Craving Fun and Laughter
### Fun Party Food and Fun Faith Ideas
WHEN I WAS IN HIGH SCHOOL, my friends referred to me as the life of the party —so much so that they told me they could not go through a weekend without me to entertain them.
Unfortunately for them, I was one of those teenagers who never cleaned her room —the only way my parents could motivate me to clean was to ground me until my room was tidy again. Many times I opted to stay home in my dirty room. Believe it or not, since I was their entertainment, my friends would often come to my home and clean my room for me so I could go out and have fun with them.
Looking back, that probably wasn't the best training for me as a young woman. Even today, though I love having a clean house, I would prefer to have someone else clean for me. My point is not about cleaning or getting others to do things for us; it is that while God does want us to have fun, He is a faithful Father who loves us so much that He wants our hearts to crave clean fun so we don't have to live with regrets. In other words, He wants us to recognize that a moment of pleasure is not worth a lifetime of pain.
# Soul Food
Whether you eat or drink, or whatever you do, do it all for the glory of God.
1 CORINTHIANS 10:31
All my life I have loved making people laugh. After I became a Christian, I didn't realize that God would use that gift to bring people closer to Him. Like many people, I had bought into the lie that to walk by faith means we cannot have fun and that craving fun is somehow a sin. Yet the Bible says that a merry heart makes the body healthy and that laughter can be medicine to our souls.
Fun can be a good thing when we crave it in a way that draws us closer to God and offers true joy to others. It's time for us to show the world that faith is a good thing that brings much peace, power, and pleasure into our lives.
If you're craving some fun, I invite you to try the following New Life Recipes, which I believe will bring some real joy back into your life.
# New Life Recipes
## 1. WATCH CHRISTIAN OR CLEAN COMEDY
A cheerful heart is good medicine, but a broken spirit saps a person's strength.
PROVERBS 17:22
Laughter is a gift from God, and a cheerful heart is medicine to the soul. We don't have to watch inappropriate things to laugh; there are many amazing comedians who know how to help us laugh at life and ourselves without dishonoring God.
May I suggest a few sources of good, clean laughter: Anita Renfroe, Chonda Pierce, Brian Regan, Mark Lowry, and Bill Cosby.
For other ideas, use Google to search for "Christian comedians." Go on —allow yourself to laugh again.
## 2. READ A HUMOROUS CHRISTIAN BOOK OR BLOG
For the despondent, every day brings trouble; for the happy heart, life is a continual feast.
PROVERBS 15:15
Fun may be lacking in your life because of what you read. I invite you to look at the variety of amazing Christian books and blogs available that will bring you joy and laughter. They will also offer you some great life lessons that will draw you closer to God. Jonathan Acuff, Charlene Ann Baumbich, Jen Hatmaker, and Matt Mikalatos are just a few of the Christian authors who will keep you laughing.
I know that what we read truly impacts the way we think and feel, so treat yourself by reading and feeding your mind with the goodness of God found in His Word and through His people who write about the Good News.
## 3. HOST A "HIS PRINCESS" PARTY
You are royal priests, a holy nation, God's very own possession. As a result, you can show others the goodness of God, for he called you out of the darkness into his wonderful light.
1 PETER 2:9
Consider hosting a princess party for grown-ups. Personalize the invitation with a Scripture about being a daughter of the King. Have the women dress in purple. Give each one of your guests a crown and a ribbon to wear across her body, perhaps a banner that says "daughter of the King." You can also have the women bring clothes they no longer wear and do a clothing exchange. Play upbeat Christian praise music and serve some of the great party food found in this chapter. It will be a great witness and a wonderful time!
# POWER UP WITH PRAYER
You will show me the way of life,
granting me the joy of your presence
and the pleasures of living with you forever.
PSALM 16:11
Dear God,
I am fighting to find joy in my life; I want my faith walk to reflect Your glory and joy. Please help me to laugh again and to embrace life in a whole new way! Show me a clean kind of fun that brings honor to You and joy to others. I want a merry heart that will become medicine to my soul. Amen.
# FOOD TRUTH
No food . . . brings as much fun as glorifying God with your body.
# Party Food Recipes
If you are planning to serve fun and festive finger foods and dips at your next get-together, try one or more of the following recipes.
## ISLAND SNACK
### Serves 2
### Ingredients:
1. 2 large ripe bananas
2. 2 tablespoons natural cocoa powder
3. 2 tablespoons shredded coconut
### Directions:
1. Peel bananas and cut them in half, roll each half in cocoa powder, and sprinkle with shredded coconut.
### Recipe tip:
What a great recipe for when you're having a party and want some fun finger foods! Cut the bananas into bite-size pieces before rolling them in cocoa powder and coconut. These will keep for one day in the fridge but are best the day they are made.
## CREAMY FRUIT SALAD
### Serves 1–2
### Ingredients for salad:
1. Whatever fruits you choose
### Directions for salad:
1. Wash or peel fruits and cut into bite-size pieces.
2. Mix fruits in large bowl.
### Ingredients for cream:
1. 1 can (13–16 ounces) unsweetened coconut milk
2. ¼ cup agave syrup
3. ½ teaspoon vanilla extract
### Directions for cream:
1. In blender, mix ingredients until thick and smooth. If there is not enough cream for the amount of people you are serving, simply keep doubling the recipe until you have enough.
2. Drizzle cream on top of each salad portion and serve.
### Recipe tip:
Try the cream in a fruit smoothie or as a dip with pretzels for a salty-sweet snack. This recipe will keep for two to three days in the fridge.
## MUSHROOM DIP
### Serves 4–6
### Ingredients:
1. 5 cups mushrooms
2. 3 tablespoons butter
3. ½ cup coconut milk
4. 1 teaspoon onion powder
5. 1 pinch sea salt
### Directions:
1. Cook mushrooms and butter in skillet until tender.
2. In blender, mix all ingredients until thick and smooth.
3. Spoon into bowl and serve.
### Recipe tip:
Great with pita chips, tortilla chips, or as a side dip for meats at any of your parties. Your guests will absolutely love this dip!
## HUMMUS WITH ROASTED RED PEPPER AND TOMATO
### Fills a medium-size bowl
### Ingredients:
1. 2 (15.5 ounces) cans low-sodium garbanzo beans or 2 cups almonds, soaked in water overnight
2. ½ cup tahini
3. 1 large garlic clove, minced
4. 3 tablespoons freshly squeezed or bottled lemon juice
5. ½ teaspoon sea salt
6. ½ cup chopped red bell peppers
7. ¼ cup chopped sun-dried tomatoes
### Directions:
1. If using almonds, grind nuts using a blender or hand mixer. (It helps to chop the almonds first.) Set chopped almonds aside in bowl.
2. Add all other ingredients into the blender and mix until smooth. Add almonds or garbanzo beans. Add water if needed to get the consistency you desire.
3. Place in bowl and serve to guests.
### Recipe tip:
Serve with whole-grain or gluten-free crackers or pita chips.
## VEGETABLE SLAW
### Serves 8
### Ingredients:
1. ¼ teaspoon sea salt
2. ¼ teaspoon coarsely ground pepper
3. 1 tablespoon prepared horseradish
4. 2 teaspoons celery seed
5. ½ cup low-fat or Healthy Mayonnaise (see page 19)
6. ½ cup low-fat sour cream
7. 1 cup diced celery
8. 1 medium green onion, diced fine
9. 1 small head green cabbage, shredded (about 2 cups)
10. 1 small jicama, shredded
11. 1 small head red cabbage, shredded
12. Cilantro, to taste
### Directions:
1. Combine sea salt, pepper, horseradish, celery seed, mayonnaise, and sour cream in a small bowl.
2. Mix remaining ingredients in a large bowl, pour dressing over the vegetables, and toss gently to mix. Serve immediately.
### Recipe tip:
This is such a delicious party salad and a great side dish for any meat. Consider using Vegenaise instead of mayonnaise if you want a slaw lower in fat.
## ROLLOVER TURKEY
### Serves approximately 12 to 15
### Ingredients:
1. 1 pound smoked turkey, sliced thick
2. 1 tub soft cream cheese
3. 1 jar pickle spears
### Directions:
1. Take a turkey slice, spread cream cheese thinly on one side, place pickle spear on an edge of the turkey slice, and roll the turkey around the pickle.
2. Cut the turkey rolls in halves or thirds, and stick a toothpick through each piece to secure it.
3. Repeat with each turkey slice until you have enough.
### Recipe tip:
Try using miso-flavored mayonnaise instead of cream cheese for some extra-flavorful rolls!
## HONEY-BAKED ALMOND BRITTLE
### Serves 4
### Ingredients:
1. ¼ cup honey
2. 1 cup almonds
3. Dash sea salt
### Directions:
1. Preheat oven to 350°.
2. Heat honey in microwave for 30 seconds.
3. In a bowl, pour honey over the almonds and mix evenly so every almond is coated.
4. Coat cookie sheet with nonstick spray, spread almonds on cookie sheet, and sprinkle with sea salt.
5. Bake at 350° for 15 minutes. Let cool, and enjoy!
### Recipe tip:
This is a great topping for chocolate or vanilla ice cream. Your guests will love this unique brittle!
# TASTE OF TRUTH
Fun happens when our faith becomes bigger than our fears and frustration.
# CHAPTER 11
## Craving Romance and Unconditional Love
### Romantic Recipes for Two and Marinating Your Marriage
I LOVE CHICK FLICKS. I love the romance and the heart connection seen on the big screen between a man and a woman. Too many times we are told that a Christian marriage does not need romance, and we are made to feel guilty for craving it. However, never before has an upcoming generation so needed to see love expressed romantically between a husband and wife.
Our heavenly Father understands a woman's desire to feel loved and romanced by her man. He also knows the passion that burns inside a man for a woman. After all, He created that kind of love!
# Soul Food
You are beautiful, my darling,
beautiful beyond words.
Your eyes are like doves
behind your veil.
Your hair falls in waves. . . .
Your lips are like scarlet ribbon;
your mouth is inviting.
Your cheeks are like rosy pomegranates
behind your veil.
SONG OF SONGS 4:1, 3
The passage above is just one small section from the Song of Songs, which records an extremely expressive and romantic conversation between a man and a woman who are married. And yes, it is recorded in the bestselling book of all time . . . the Bible.
I am convinced after reading the Song of Songs that romantic expressions of love between a man and woman do not simply hold them together. Just as important, they speak to a world that is watching how we love one another. Nothing brings more glory to God than when a husband and a wife love each other in the way God intended. If you're ready to marinate your marriage with mutual devotion, join me as I offer a few suggestions in the following New Life Recipes.
# New Life Recipes
## 1. FLIRT WITH YOUR HUSBAND
You are so handsome, my love,
pleasing beyond words!
The soft grass is our bed;
fragrant cedar branches are the beams of our house,
and pleasant smelling firs are the rafters.
SONG OF SONGS 1:16-17
Okay, I know it may sound crazy to suggest that you flirt with your husband. But you probably flirted with him to get his attention, so why did you ever stop? Flirting with each other will stimulate your love and attraction. And it will keep you thinking about each other when someone else tries to flirt with either one of you.
Write little love notes, talk about fun things you can do together, and laugh at your husband's jokes (even if you don't think they're funny). Humor is a great way to flirt with one another, and it will bring joy and laughter to your relationship.
## 2. RELAX WITH CANDLES AND CONVERSATION
Tell me, my love, where are you leading your flock today?
Where will you rest your sheep at noon?
SONG OF SONGS 1:7
Take time to set the dinner table for two, get a babysitter for the kids if you have children, and maybe even set up a dinner table in your bedroom with candles and good relaxing music or love songs playing.
As you enjoy a meal together, don't talk about your challenges or the frustrating things that happened that day. Instead, focus on your husband. Ask about his day and be a good, loving listener. As you do, you will begin to see him in a whole new way.
## 3. CONNECT THROUGH TOUCH AND TENDERNESS
Place me like a seal over your heart,
like a seal on your arm.
For love is as strong as death,
its jealousy as enduring as the grave.
Love flashes like fire,
the brightest kind of flame.
SONG OF SONGS 8:6
I once heard a marriage counselor say that a ten-second kiss and hug can begin to heal a marriage. Yet once we're married, we rarely hold our husband's hand while walking or take a moment to look into his eyes and say I love you.
It's time to redefine marriage for ourselves and our children. Take a chance and express your love once again to your man. Even if he doesn't respond at first, continue to love him unconditionally, the way God loves you.
# POWER UP WITH PRAYER
Oh, how beautiful you are! How pleasing, my love, how full of delights! . . . I am my lover's, and he claims me as his own.
SONG OF SONGS 7:6, 10
Dear Lord,
Please renew the love and romance in my marriage.
Help me to let go of the little things that keep me from expressing love to the man I married. Help me never to take him for granted and to treat him with love, honor, and respect. Give him a heart for You, and help him to express his love to me in a way that draws us closer together. I pray that we would experience the kind of love that is expressed in Your Word in the Song of Songs. I pray that You would use the good and the bad to draw us close to You and close to each other. Amen.
# FOOD TRUTH
No food . . . is as satisfying as God's love for you.
# Romantic Meal Recipes for Two
Tell your husband that you love to watch him grill and that flirting in the kitchen is fun and that . . .
## SAUCY SALMON
### Serves 2
### Ingredients:
1. ¼ teaspoon cinnamon
2. 2 teaspoons honey
3. 2 tablespoons low-sodium soy sauce or Bragg Liquid Aminos
4. 2 tablespoons orange juice
5. 2 salmon fillets (cut thick, about ¾ to 1½ inches)
6. 1 cup cranberry juice cocktail
7. ¾ cup dried cranberries
8. ¼ cup finely chopped onion
9. 1 tablespoon brown sugar
10. 1 teaspoon orange zest
### Directions:
1. Soak a cedar grilling plank in water for 3–4 hours.
2. Combine cinnamon, honey, soy sauce or Bragg Liquid Aminos, and orange juice in a shallow dish. Let salmon marinate in mixture for 30 minutes, turning occasionally.
3. Meanwhile, combine cranberry juice cocktail, dried cranberries, onion, brown sugar, and orange zest in medium saucepan. Cook over medium to high heat until the mixture boils, then reduce heat and simmer for 10 minutes. Onions should be tender. Remove sauce from heat and set aside.
4. Heat the grill medium-high for indirect heat. Place the soaked plank on the grill for 3 to 4 minutes or until the plank starts to spit and crackle.
5. Place the salmon skin side down on the hot plank, and place the plank on or under the grill rack. Cook for 20 to 30 minutes, continually basting the salmon with the excess marinade.
6. Place the cooked salmon on plates and drizzle with the cranberry juice cocktail sauce.
7. Have a candlelit dinner with your honey and enjoy some time together!
### Recipe tip:
If you and your man like spicier foods, add red pepper flakes to the sauce.
## MIDNIGHT CHOCOLATE TRUFFLES
### Serves 2
### Ingredients:
1. ½ cup heavy whipping cream
2. 8 ounces dark chocolate baking bar, broken into pieces
3. ½ cup finely chopped nuts (optional)
4. ½ cup shredded coconut (optional)
5. Cocoa powder (optional)
### Directions:
1. Line a baking sheet with parchment or wax paper. Heat cream to a gentle boil in a medium-size heavy saucepan. Remove from heat and add the chocolate.
2. Stir until mixture is smooth and chocolate is melted. Refrigerate for 15 to 20 minutes or until slightly thickened.
3. Drop chocolate mixture by rounded measuring teaspoon onto the prepared baking sheet. Refrigerate for 20 minutes.
4. Shape or roll into balls. Coat each chocolate ball with nuts, coconut, or cocoa, if desired.
5. Store in an airtight container in the refrigerator.
### Recipe tip:
If the two of you cook these together and feed them to each other, you'll decide that chocolate has never tasted so good!
## SWEET BALSAMIC CHICKEN DELIGHT
### Serves 2
### Ingredients:
1. 2 chicken breasts
2. ½ cup olive oil
3. ½ cup balsamic vinegar
4. Sea salt and pepper
5. 1 teaspoon ground rosemary
6. 2 cups whole-grain or gluten-free pasta
7. 2 tablespoons olive oil
8. 1½ garlic cloves, chopped
9. 1½ tablespoons butter
10. 2 to 4 tablespoons balsamic vinegar
11. 1½ teaspoons dried parsley
12. 1 tablespoon onion powder
13. 1 teaspoon raw sugar (optional)
14. Salt and pepper
### Directions:
1. Marinate the chicken breasts in olive oil and balsamic vinegar. Sprinkle with sea salt, pepper, and rosemary. Let rest 10 to 15 minutes.
2. In a large saucepan, bring water to a boil and cook pasta according to the package directions. Once it is cooked, drain and set aside.
3. In a nonstick skillet, heat 2 tablespoons olive oil over medium-high heat and add garlic. Cook the chicken breasts until they're done.
4. In the saucepan you used to cook the pasta, melt butter over medium-high heat. Let it cook until it is a nice brown color. Add the pasta and toss to coat. Sprinkle with balsamic vinegar and cook over medium heat for 1 minute. Then add parsley, onion powder, sugar, and salt and pepper to taste. Serve with chicken.
### Recipe tip:
There are as many variations of this as there are varieties of pasta.
## NOT YOUR MAMA'S MEAT LOAF
### Serves 2
### Ingredients:
1. ½ medium onion, chopped
2. 1 large garlic clove, minced
3. ½ pound lean ground turkey
4. ½ pound pork sausage
5. 1 tablespoon onion powder
6. ¼ cup brown sugar
7. 1 large egg
8. ¼ cup almond or rice milk
### Directions:
1. Preheat oven to 350° and coat a bread loaf pan with nonstick cooking spray.
2. Cook onion over medium heat. Once it is tender, add garlic and cook for 1 to 2 minutes more. Set aside.
3. With your hands, mix the two meats together in a medium bowl. (Do this step with your husband for some kitchen-time flirting!)
4. Add onion powder, brown sugar, egg, and milk to the meat mixture.
5. Add cooked onion and garlic to the mixture.
6. Place meat mixture in the bread pan.
7. Bake uncovered for 1 hour and 15 minutes, and serve.
### Recipe tip:
This is delicious with chopped mushrooms added to the mixture!
## BEEFY AND LEAFY POCKETS
### Serves 2
### Ingredients:
1. ½ pound lean ground beef
2. 1½ garlic cloves, minced
3. ½ cup chopped onion
4. 1½ cups chopped fresh spinach
5. ¼ teaspoon ground cumin
6. ¹⁄8 teaspoon salt
7. 6 fresh spinach leaves
8. 1 whole-grain pita bread, halved
9. 2 tablespoons cream cheese, softened
10. ¹⁄8 teaspoon curry powder
### Directions:
1. In large nonstick skillet, combine the ground beef, garlic, and onions. Cook over medium heat until mixture is browned, stirring to crumble the beef.
2. Drain off fat, and remove beef mixture from skillet. Clean the skillet, and put beef mixture back in.
3. Add chopped spinach, cumin, and salt. Stir well. Cover and cook over medium heat 3 minutes. Remove from heat.
4. Line each pita half with whole spinach leaves, and spoon ½ cup beef mixture into each.
5. Mix cream cheese with curry powder. Top beef with cream cheese mixture.
### Recipe tip:
This is also great with mushrooms! Frying the meat mixture in a little bit of olive oil makes for a crunchier meal.
## SWEET CHOCOLATE FONDUE
### Serves 2
### Ingredients:
1. 8 ounces heavy cream
2. 1 pinch brown sugar
3. 12 ounces dark chocolate, broken into pieces
4. ½ teaspoon vanilla extract
5. 1 pinch sea salt
6. Strawberries, pineapple, and banana or other fruit of your choice, washed and cut into bite-size pieces
### Directions:
1. Warm cream over medium heat until it starts to bubble. Then add brown sugar, dark chocolate, vanilla, and sea salt. Mix until chocolate is melted completely.
2. Pour into heated fondue pot.
3. Using skewers, dip fruit into chocolate and feed bites to each other.
### Recipe tip:
This is a very romantic dessert! Get creative with the dipping foods —try pretzels and marshmallows.
## OYSTER DELIGHT SOUP WITH ANGEL-HAIR PASTA
### Serves 2
### Ingredients:
1. 1½ cups whole-grain or gluten-free angel hair pasta
2. 2 green onions, chopped
3. 2 tablespoons melted butter
4. 1 can (16 ounces) unsweetened coconut milk
5. ½ teaspoon red pepper flakes
6. 1 teaspoon sea salt
7. 12-ounce container fresh oysters, undrained
8. 1 tablespoon freshly squeezed or bottled lemon juice
### Directions:
1. Cook angel-hair pasta in boiling water, drain, and set aside.
2. In a large pot on medium-high heat, cook green onions in butter.
3. Add coconut milk, red pepper flakes, sea salt, and oysters with liquid to onions and butter. Cook until boiling.
4. Add angel-hair pasta to boiling soup; reduce heat and simmer for 5 minutes. Squeeze lemon juice over soup just before serving.
### Recipe tip:
This is really wonderful when you add sliced zucchini, mushrooms, or shrimp! You and your man will love this subtly spicy soup.
# TASTE OF TRUTH
Romantic expressions of love are the perfect gift exchange between a husband and wife.
# CHAPTER 12
## Craving Time with Kids
### Healthy Recipes for Kids and Faith Made Real at a Meal
MY SON, JAKE, is now married and has his own little girl, Olive True, our first grandbaby. When I was raising my son, I wanted him to have real faith, but I feared I would not be able to pass that faith on to him. I realize now that faith is not something that can be given away; it is something that, when we live it out, our children will come to crave.
I used to feel guilty for what I considered my shortcomings as a mother; now I realize that God entrusts us with children, and He will cover us when we cannot cover ourselves. He will be faithful to our children even when we fail them. If you're craving to find a way to instill faith in your children, let me first say this to you as a spiritual mom: don't put pressure on yourself; instead, pray and ask God to give your children a heart for Him.
# Soul Food
We will not hide these truths from our children; we will tell the next generation about the glorious deeds of the LORD, about his power and his mighty wonders.
PSALM 78:4
I always told Jake the truth: while I would let him down, God never would. I am imperfect, but God is perfect. I would not always be there, but God always would be there for him. Today my son knows and loves the Lord in a very real way, not because of my perfection but because of my honesty.
I pray that the following three creative ideas will take the pressure off you and give you joy as you begin to share the love of God with your children.
# New Life Recipes
## 1. READ A BIBLE STORY AT THE TABLE AFTER A MEAL
You must love the LORD your God with all your heart, all your soul, and all your strength. And you must commit yourselves wholeheartedly to these commands that I am giving you today. Repeat them again and again to your children. Talk about them when you are at home and when you are on the road, when you are going to bed and when you are getting up.
DEUTERONOMY 6:5-7
Food and faith talk are about as good as it gets when it comes to satisfying both our bodies and souls at mealtime. God talk around the table builds memories and keeps stress levels down.
Keep Bible storybooks in a kitchen cabinet so kids can reach them. Rotate who picks the story to read each night. Once you have read the story, sit for a moment and let your kids share what they learned.
## 2. WORSHIP IN THE KITCHEN WHILE CLEANING UP
Praise the LORD with melodies on the lyre;
make music for him on the ten-stringed harp.
PSALM 33:2
The Lord wants us to serve one another, yet getting our children to be joyful about cleaning up often becomes more of a chore than the cleaning itself.
Still, you can set the tone and make cleanup more fun. Once you're done with dinner and story time, turn on some upbeat kids' worship songs and turn cleaning into a time of worship. It's hard to complain when worship music is being played, so turn up the volume and watch what happens in your home and in your kids' hearts.
## 3. LET YOUR CHILDREN PRAY
But Jesus said, "Let the children come to me. Don't stop them! For the Kingdom of Heaven belongs to those who are like these children."
MATTHEW 19:14
Since Jesus wants little children to come to Him, let's teach our precious ones to talk to their heavenly Father in prayer. If they are toddlers, say a prayer one line at a time and let them repeat it after you. Encourage them to talk with God about everything. When prayers they prayed are answered, talk about that with them so they can celebrate God's goodness with you.
# POWER UP WITH PRAYER
You are always the same; you will live forever. The children of your people will live in security. Their children's children will thrive in your presence.
PSALM 102:27-28
Dear God,
I lift up my children before You, and I pray that they would crave You more than anything else. Help me teach them about You and Your love. Help me not to waste the teachable moments You give me to share real faith.
I dedicate our mealtimes to nourishing my family's bodies and souls while we sit and eat together. Help me begin creative conversations that will draw my children closer to You and give them hearts to hear who You are. Amen.
# FOOD TRUTH
No food . . . is as enjoyable as being healthy feels.
# Recipes for Healthy, Happy Kids
While mealtimes offer an ideal setting to provide soul nourishment to your kids, the kitchen table is also the perfect place to introduce them to great-tasting, healthy foods like the following recipes.
## FRUIT POP POPS
### Serves 6
### Ingredients:
1. ½ cup hulled strawberries
2. 1 banana, cut up
3. 1 mango, cut up
4. 1 cup orange juice
5. 2 apples, peeled, cored, and cut up
6. 2 tablespoons honey, raw sugar, or stevia
### Directions:
1. In blender, mix strawberries with banana, and pour mixture into the bottom of each ice pop mold.
2. Blend together the mango and orange juice. Add to the ice pop mold for the second layer.
3. Blend the apples with honey or sugar. Pour into ice pop mold to make the last layer.
4. Put sticks in the molds and place in freezer overnight.
### Recipe tip:
Try using pineapple juice instead of orange juice.
## PRETTY PUDDING
### Serves 4
### Ingredients:
1. 3 cups frozen raspberries
2. 2 passion fruits
3. 1 mango
4. 2 dates
5. 1 cup unsweetened applesauce
6. 1 tablespoon canola or sunflower oil
7. 1 tablespoon honey or agave syrup
### Directions:
1. In blender, mix together the fruits until smooth.
2. Add applesauce, oil, and sweetener.
3. Blend until smooth and thick. Serve!
### Recipe tip:
If your kids love coconut, mix in some shredded coconut after blending for extra texture and flavor.
## COCO CRAZY SMOOTHIE
### Serves 2
### Ingredients:
1. 3 cups coconut milk
2. 1 tablespoon vanilla extract
3. 4 dates or ¹⁄3 cup date sugar or raw sugar
4. 1 tablespoon coconut or grapeseed oil
5. 1½ mangoes
### Directions:
1. In blender, mix together all ingredients.
2. Pour and serve.
### Recipe tip:
You can substitute banana or pineapple for the mango, depending on what your kids like.
## CHOCO SAUCE
### Serves 2–4
### Ingredients:
1. 2 cups unsweetened applesauce
2. ½ teaspoon vanilla extract
3. 1 tablespoon dark unsweetened cocoa powder
4. ½ cup semisweet chocolate chips
### Directions:
1. In blender, mix all ingredients together until smooth.
2. Serve and let your kids enjoy!
### Recipe tip:
For extra fun, sprinkle shredded coconut or sliced almonds on top, depending on your kids' preferences.
## YUM-YUM NACHOS
### Serves 6
### Ingredients:
1. 1 cup canned low-fat black beans, drained
2. 1 cooked chicken breast, diced
3. 2 teaspoons freshly squeezed or bottled lime juice
4. 1 clove garlic, minced
5. 1 teaspoon onion powder
6. 7 ounces baked tortilla chips
7. ½ cup shredded cheddar cheese
8. 1 cup low-fat sour cream
### Directions:
1. Heat beans in saucepan. Add chicken, lime juice, garlic, and onion powder.
2. Arrange chips on individual plates; spoon beans and chicken mixture over chips. Sprinkle cheese on top, put some sour cream on the side, and serve.
### Recipe tip:
You could substitute ground beef or turkey for the chicken. Instead of sour cream, you could add fresh guacamole or salsa on the side.
## HEALTHY CHILI CHEESE FRIES
### Serves 6
### Ingredients:
1. 5 sweet potatoes
2. Sea salt
3. Olive oil to drizzle
4. 1 can (15 ounces) red kidney beans, drained and rinsed
5. 1 cup tomato-based chili sauce
6. 2 teaspoons ground cumin
7. 3 cloves garlic, minced
8. ¼ teaspoon black pepper
9. 1 tablespoon Dijon mustard
10. 1½ tablespoons chili powder
11. 1½ cups chicken broth
12. 3 cups chopped cooked chicken breast (about 1¼ pounds)
13. 1 cup shredded cheddar cheese
### Directions:
1. Preheat oven to 350°.
2. Slice sweet potatoes into strips like french fries. Sprinkle with sea salt and olive oil. Bake at 350° for 15 to 20 minutes or until crispy.
3. Meanwhile, coat a large saucepan with nonstick cooking spray.
4. Combine kidney beans and chili sauce in the saucepan and heat.
5. Add cumin, garlic, pepper, Dijon mustard, chili powder, chicken broth, and chicken. Simmer for 10 minutes.
6. Once sweet potato fries and chili are cooked, ladle chili into bowls. Sprinkle cheese on top, and add fries on the side. Dip fries into chili for healthy chili cheese fries!
### Recipe tip:
This can be a great recipe for adults to enjoy as well. To give it a spicier kick, add cayenne pepper, green chilies, and jalapeños.
## PIZZA NIGHT
### Serves 4–6
### Ingredients for pizza crust:
1. 1 teaspoon raw sugar
2. 1½ cups warm water
3. 1 tablespoon active dry yeast
4. 1 tablespoon olive oil
5. 1 teaspoon sea salt
6. 3 cups whole-grain or gluten-free flour, plus additional for kneading
### Directions for pizza crust:
1. Dissolve sugar in warm water in large mixing bowl. Sprinkle yeast over the top. Let stand until foamy, about 10 minutes.
2. Stir olive oil and salt into the yeast mixture. Add 3 cups flour.
3. Place dough on lightly floured surface and knead for about 10 minutes. Once ball of dough is smooth, place it in an oiled bowl, turning the dough until it is evenly coated with oil. Cover with a towel and place in a warm place for about 1 hour, until dough doubles in size.
4. Place dough onto a lightly floured surface and form into a tight ball. Let rise for about 45 minutes, until doubled again. (You can divide dough into two smaller balls for two thin-crust pizzas or use large ball for one thick-crust pizza.)
5. Preheat oven to 425°. Roll out ball of dough with a rolling pin until it won't stretch further. As you shape dough into a circle, gently pull the edges outward and rotate the crust. Once crust is the desired size, place on a well-oiled pizza pan.
### Ingredients for pizza sauce:
1. 1 can (6 ounces) tomato paste
2. ¾ cup warm water
3. 2 tablespoons honey
4. 3 tablespoons grated Parmesan cheese
5. 1 teaspoon minced garlic
6. ¾ teaspoon onion powder
7. ¼ teaspoon dried oregano
8. ¼ teaspoon dried thyme
9. ¼ teaspoon dried basil
10. ¼ teaspoon ground black pepper
11. ¼ teaspoon fennel seed
12. ¹⁄8 teaspoon salt (to taste)
### Directions for pizza sauce:
1. In a small bowl, mix together all ingredients. Be sure to break up any clumps of cheese.
2. Let sauce sit for 30 minutes to allow flavors to blend.
3. Spread evenly over pizza crust.
### Directions for pizza:
1. Once pizza dough has been placed on pizza pan, top with sauce. Then add your choice of cheese, vegetables, and meats.
2. Bake 16 to 20 minutes (depending on thickness) in preheated oven, until the edge of the crust is crisp and golden, and cheese is melted.
### Recipe tip:
This will be such fun for your kids! Play restaurant with them, and allow them to get creative with their toppings.
# TASTE OF TRUTH
As we teach our children about God, they will begin to teach us through their childlike faith.
# CHAPTER 13
## Craving More Energy
### Energizing Food and Faith Recipes
WHEN I WAS about to turn forty, I took a personal inventory of all the things I was investing my time in. I then prayed and purposed to delete anything that was draining my strength and energy. Just when I thought I had it all figured out, God gave me and my husband a surprise: I became pregnant with a baby girl.
Now, don't get me wrong, I was excited, but it had been eleven years since I'd had a baby, and at the time I barely had enough energy to make it through each day. Then the reality hit me: when I would be going through menopause, my daughter would be entering her teen years. I looked up toward God and asked, _Where am I going to find the energy to run a ministry and raise a daughter at the same time?_
If I was craving more energy before I discovered I was pregnant, I wondered how I would manage my responsibilities now.
# Soul Food
For I can do everything through Christ, who gives me strength.
PHILIPPIANS 4:13
If we can do all things through Christ, why are we so often exhausted?
To be honest, I think the two things that wear us out most are, first, trying to live in our own strength and, second, attempting to play the junior Holy Spirit. By that I mean we try to control everything in our lives and the lives of those we love. God has wired us to notice situations requiring change and needs that should be met. When He is truly guiding us to take action, He provides the energy and the grace we need to do what we could never do in our own strength. At times, though, we take on burdens He never meant for us to carry.
The truth is, as long as we try to control everything around us, we will feel out of control and overwhelmed. So the first step to gaining energy is to take a deep breath right now and speak these energizing words: "He is God. . . . I am not!" or "I surrender to You, God. Take control and lead me!" God has not called us to burn ourselves out; in fact, one of the things I've learned in my life is that if the devil can't make us bad, his next trick is to make us busy so he can burn us out.
Today my daughter, Emily, is a teenager, and, yes, I do have hot flashes. I find myself desperate every day for more energy and more of God's grace in my life. Maybe you're in a place where you, too, are living out one of God's surprises. Perhaps you're being forced to live a life you never asked for, or maybe you're just sick and tired of being sick and tired. In any event, if you're ready for an energy breakthrough, I encourage you to try three simple practices that have helped give me more energy and renewed passion and joy in spite of the stresses of everyday life.
# New Life Recipes
## 1. EXERCISE
Physical training is good, but training for godliness is much better, promising benefits in this life and in the life to come.
1 TIMOTHY 4:8
For years, no matter how many times I was told how good exercise was for me, I dreaded it. I needed an exercise breakthrough. Finally, I decided to make exercise an act of worship. My walks became my worship time and a sacrifice to the Lord. In this way, the Holy Spirit could use my body to do His work through me. Sometimes I put on worship music and danced in my bedroom, just as David danced before the Lord. (Second Samuel 6:14 says David danced in his linen ephod, or priestly garment; I dance with my workout clothes on.) I noticed that as soon as I wasn't exercising for my looks but for my Lord, I began to enjoy exercise for the first time.
How can you find renewed energy through exercise? Make a playlist of your favorite worship songs and choose the type of exercise you enjoy. Instead of thinking of exercise as something you have to do, get up in the morning and praise God that you can move your body and exercise for His glory.
Maybe you have a beautiful place where you can go walking or a friend who will become a prayer partner so you can do prayer walks together. You'll discover that something almost miraculous can happen when all that you do is done for God's glory and not your own!
## 2. HYDRATE YOUR BODY AND SOUL
But those who drink the water I give will never be thirsty again. It becomes a fresh, bubbling spring within them, giving them eternal life.
JOHN 4:14
We all want to drink the water Jesus talks about in John 4:14.
He promises that if we drink from His water, we will never thirst again. Many of us are exhausted, I believe, because we are not soaking in the Word that waters our soul. In an attempt to water our thirsty souls, we try artificial faith fixes, which leave us dissatisfied.
Our bodies may also become dehydrated when we don't drink pure water but instead fill ourselves with drinks containing sugar or artificial sweeteners.
Let's try something new. For the next seven mornings, drink a large glass of purified water as you read a short paragraph of Scripture. See how pure water and the Word energize you in a whole new way.
## 3. ELIMINATE EXCESS IN YOUR LIFE
Therefore, since we are surrounded by such a huge crowd of witnesses to the life of faith, let us strip off every weight that slows us down, especially the sin that so easily trips us up. And let us run with endurance the race God has set before us.
HEBREWS 12:1
For many years, I have spoken at women's conferences. A few years ago, I realized that, the older I got, the more stuff I thought I needed to feel comfortable while on the road. However, every time I came back from a trip my neck and back were out of whack because I dragged heavy luggage through an airport and into a hotel room. Even worse, I never really needed —or used —many of the items I brought!
Many of us have excess activity and busyness that are sucking the life out of us. If you're feeling weighed down, I invite you to take a personal inventory of what you have on your calendar and in your life. Then pray and ask God what He would like you to let go of. Lay that down at His feet and let Him deal with it. If you do this, I believe you will find new strength and the simpler life you crave.
# POWER UP WITH PRAYER
But those who trust in the LORD will find new strength. They will soar high on wings like eagles. They will run and not grow weary. They will walk and not faint.
ISAIAH 40:31
Let's make the Word personal and put it into action by praying Isaiah 40:31:
Dear God,
Help me to trust in You, and as I do, give me renewed strength. Give me eyes to soar above my circumstances and give me a renewed passion to run in Your strength and not my own. I pray from this day forward that I will not grow faint but finish strong. Amen.
# FOOD TRUTH
No food . . . is as satisfying as the energy to enjoy life.
# Seven Energizing Food Recipes
Now that we've talked about energizing our faith, let's energize our bodies with some delicious meals. I have created seven energizing recipes to help defeat the battle of fatigue once and for all.
Protein is essential to maintaining a healthy body and is an important source of energy. Salad is not only a great way to sneak in our fruit and veggies for the day, but it also helps boost our bodies' antioxidants. The recipes on the following pages are packed full of creative, protein-filled salads or meat entrées that are sure to give you that boost of energy you crave. And they taste amazing!
## STEAK SUPREME SALAD
### Serves 4
### Ingredients for salad:
1. 5 ounces lean steak
2. 2 teaspoons olive oil
3. 1 pinch sea salt
4. 3 to 4 cups spinach, washed and dried
5. 1 cup sliced cucumber
6. 8 to 12 strawberries, sliced
7. 1 avocado, peeled and sliced (optional)
### Ingredients for vinaigrette dressing:
1. 3 tablespoons sherry or red wine vinegar
2. 1 tablespoon Dijon mustard
3. 1 tablespoon honey
4. 2 tablespoons olive oil
5. 1 pinch ground black pepper
### Directions:
1. Slice steak into thin strips. Broil or panfry in 2 teaspoons oil; cook meat to your liking. Add sea salt and set meat aside.
2. Combine spinach, cucumber, and strawberries in a salad bowl and toss gently.
3. To make vinaigrette dressing, whisk together sherry or red wine vinegar, Dijon mustard, honey, olive oil, and black pepper in a small bowl.
4. Gently toss the spinach, cucumber, and strawberries with the vinaigrette.
5. Place spinach mixture on individual serving plates. Top with the steak and avocado slices, and serve.
### Recipe tip:
Use the vinaigrette dressing for any of your favorite salads. It is always better to make your own than to use a bottled dressing.
## FRUIT FIESTA CHICKEN SALAD
### Serves 4
### Ingredients:
1. 1 head romaine lettuce, torn into bite-size pieces
2. 4 ounces feta or goat cheese, crumbled
3. 1 cup pistachios
4. ¼ cup dried cranberries
5. 1 green apple, peeled, cored, and diced
6. 1 pear, cored and sliced
7. 3 cooked chicken breasts, diced
8. Freshly squeezed or bottled lemon juice, to taste
9. ¼ cup coconut (optional)
### Directions:
1. In a large serving bowl, toss together the romaine lettuce, cheese, pistachios, cranberries, apple, pear, and chicken.
2. Dress the salad with freshly squeezed lemon juice and, if desired, coconut.
## CAJUN JUMBO SHRIMP KEBABS
### Serves 6
### Ingredients for dry rub:
1. 1 teaspoon cinnamon
2. 1 pinch sea salt
3. ½ teaspoon cumin
4. ½ teaspoon ground turmeric
5. ¼ teaspoon paprika
6. ¼ teaspoon pepper
7. ¹⁄8 teaspoon ground cloves
8. ¹⁄8 teaspoon nutmeg
9. 2 teaspoons raw sugar or honey
10. ¼ teaspoon ground ginger (optional)
### Ingredients for kebabs:
1. 2 pounds jumbo shrimp, uncooked and cleaned
2. 2 small red onions, peeled and cut into 1-inch wedges
3. 2 red or yellow bell peppers, cleaned and cut into 1-inch squares
4. ¼ cup olive oil
5. ½ teaspoon sea salt
6. 1 pinch black pepper
7. 12 bamboo skewers
### Directions:
1. Soak bamboo skewers in water for 30 minutes.
2. Combine the dry rub ingredients in a small bowl, mixing well.
3. Place shrimp into a gallon-size ziplock plastic bag; add the rub mix. Seal the bag and shake it until the shrimp is evenly coated.
4. Place the onions and bell peppers in another gallon-size ziplock plastic bag. Add the olive oil, sea salt, and pepper. Seal the bag and shake to coat the vegetables well.
5. Alternate skewering shrimp and pieces of onion and bell pepper on bamboo skewers.
6. Prepare a charcoal fire or set a gas grill to medium-high, close the lid, and heat until hot —about 10 to 15 minutes.
7. Grill the kebabs about 8 to 10 minutes. Turn them once halfway through cooking time.
## ASIAN CABBAGE CRUNCH SALAD
### Serves 6
### Ingredients for salad:
1. 1 head red cabbage, cut into bite-size pieces
2. 1 head white cabbage, cut into bite-size pieces
3. 2 tablespoons diced cilantro
4. 2 tablespoons green onion
5. 1½ cups diced cooked chicken breast
6. ½ cup sliced almonds
### Ingredients for dressing:
1. 1 cup apple cider vinegar
2. 1 cup low-sodium soy sauce or Bragg Liquid Aminos
3. ½ cup honey
### Directions:
1. Combine both types of cabbage, cilantro, and green onion.
2. Add chicken and sliced almonds.
3. Mix together the vinegar, soy sauce or Bragg Liquid Aminos, and honey for the dressing.
4. Pour dressing over cabbage and chicken mixture and toss gently.
### Recipe tip:
This healthy Asian dressing is a great dip for carrots, celery, or broccoli. You can also use it on any salad you like —get creative!
## SUMMERTIME SALAD
### Serves 6
### Ingredients for salad:
1. 1 seeded and diced cucumber (cut as explained in directions)
2. 7 cups romaine lettuce
3. 1 orange, peeled and sectioned
4. 1 cup thinly sliced radishes
5. ¼ cup shredded raw sweet potato
6. ¼ cup shredded raw beet
7. ¼ cup green onion, thinly sliced
### Ingredients for dressing:
1. 2 tablespoons rice or white wine vinegar
2. 2 tablespoons orange juice
3. 1 tablespoon sesame oil
4. ¼ teaspoon sea salt
5. ¹⁄8 teaspoon black pepper
### Directions:
1. Cut cucumber into four strips (so that each is in the shape of a dill pickle spear); remove seeds. Dice cucumber strips.
2. Combine the cucumber, lettuce, orange sections, radishes, sweet potato, beet, and green onion in a large bowl.
3. In a smaller bowl, mix vinegar, orange juice, sesame oil, sea salt, and black pepper. Whisk until blended. Pour over salad, tossing gently to coat. Serve immediately.
### Recipe tip:
If you prefer fruit to raw sweet potato and beet, you can add diced kiwi, strawberries, and/or blueberries instead.
## TUNA ZEST
### Serves 1–2
### Ingredients:
1. 1 can white albacore tuna in water, drained
2. ½ avocado, smashed
3. 2 teaspoons freshly squeezed or bottled lemon juice, or to taste
4. Pepper, to taste
5. ¼ cup fresh basil (optional)
### Directions:
Mix all ingredients. Eat as is or serve on a slice of whole-grain bread or over a bed of lettuce or spinach.
### Recipe tip:
You can also enjoy this tuna dish with whole-grain or gluten-free rice crackers. Served this way, it makes a great dish for your kids!
## APPLE CINNAMON CHICKEN AND RICE
### Serves 4
### Ingredients:
1. 2 cups brown rice
2. 1 tablespoon olive oil
3. 4 skinless, boneless chicken breast halves
4. Freshly squeezed or bottled lemon juice (optional)
5. 1 tablespoon raw sugar or honey
6. 1 cup unsweetened applesauce
7. Dash cinnamon
8. Salt and pepper
### Directions:
1. Preheat oven to 350°.
2. Prepare brown rice according to package directions.
3. Warm oil in skillet over medium heat. Add chicken breasts, browning lightly on both sides. (If desired, squeeze lemon juice over chicken as it browns for extra flavor.)
4. Mix the honey into the unsweetened applesauce. Place the browned chicken in a casserole dish, and top evenly with the applesauce and cinnamon. Add pinch of salt and pepper to taste; cover and bake for 35 minutes.
5. Serve with steamed brown rice.
### Recipe tip:
This makes a great dinner for the whole family. If you don't want the chicken to be sweet, simply omit the raw sugar or honey.
# TASTE OF TRUTH
You will never regret making time to renew your strength.
# CHAPTER 14
## Craving a New Day and a New Beginning
### Breakfast Recipes and Blessings to Start Your Day
ONE OF MY FAMILY'S favorite traditions is one of our only consistent rituals. What is it? We have breakfast for dinner once a week. Given our busy schedule, this seems to be the one thing that we can stick to.
There is something so comforting about pancakes and eggs at the dinner hour. We've done it for so many years that even though our grown son is living out of state, his single friends still like to come over and have breakfast for dinner with us old folks.
While this is a fun, long-standing tradition, this chapter centers on the joy that comes from knowing we are offered a new day every morning.
# Soul Food
This is the day the LORD has made.
We will rejoice and be glad in it.
PSALM 118:24
The greatest thing about a new day is that it offers a new beginning. In that first waking moment, we can decide to worry about tomorrow, live in the regrets of yesterday, or embrace the start of a new beginning.
When you look at each morning as a second chance to live for the Lord and love others well instead of just another day, it will change the way you think and feel. Of course, I know that's easier said than done, especially if you fell asleep the night before feeling regret or pain from your past. With that in mind, here are three New Life Recipes that have helped me break free from starting my day the wrong way. I pray that you, too, will embrace a new way of living . . . one that requires checking into the present day because it's all you have.
# New Life Recipes
## 1. START YOUR DAY WITH PRAISE
It is good to give thanks to the LORD,
to sing praises to the Most High.
It is good to proclaim your unfailing love in the morning,
your faithfulness in the evening.
PSALM 92:1-2
Make a playlist of your favorite praise music, preferably upbeat worship songs that inspire you to live for God. Sing a love song to the Lord on your way to work, or make up your own praise song.
## 2. START YOUR DAY WITH PRAYER
Pray in the Spirit at all times and on every occasion. Stay alert and be persistent in your prayers for all believers everywhere.
EPHESIANS 6:18
Turn whatever thoughts are on your heart first thing in the morning into a prayer. Your heavenly Father wants to hear from you, and He cares about everything you care about. Don't miss taking the first moments in the morning to connect your heart to His and to bring your concerns and requests to the only one who can do anything about them —God Himself.
## 3. START YOUR DAY THANKFUL
Fix your thoughts on what is true, and honorable, and right, and pure, and lovely, and admirable. Think about things that are excellent and worthy of praise.
PHILIPPIANS 4:8
As hard as it is to be thankful for a hard day in front of you, let your mind think about anything worthy of praise and any good thing that is coming out of a challenging situation. If you can't find anything worthy of praise, just praise God that He is with you and fighting for you. If you're in a battle, be thankful that you are not alone.
# POWER UP WITH PRAYER
Listen to my cry for help, my King and my God,
for I pray to no one but you.
Listen to my voice in the morning, LORD.
Each morning I bring my requests to you and wait expectantly.
PSALM 5:2-3
Dear God,
I need the joy You offer on this new day. Give me Your eyes today; give me Your heart for others. Give me a new perspective on this day that I may not waste it on worry or regret. Go before me, Lord, and pave my way today. Amen!
# FOOD TRUTH
No food . . . tastes as good as living out God's plan for your day.
# Amazing Breakfast Recipes
The way you start your day may very well determine the outcome of the entire day. We often hear that breakfast is the most important meal of the day —and that's true! I have compiled my absolute favorite breakfast recipes to help you start your day off right.
## CHOCOLATE CHIP PANCAKES
### Serves 4–6
### Ingredients:
1. 2 eggs
2. 1 teaspoon vanilla extract
3. 1 cup pancake mix
4. ¾ cup water
5. 1 tablespoon canola or sunflower oil
6. 1 tablespoon cocoa powder
7. 1 tablespoon raw sugar or stevia
8. ½ cup semisweet chocolate chips
### Directions:
1. Coat a skillet with nonstick cooking spray and place over low to medium heat.
2. In a medium bowl, mix all ingredients except the chocolate chips until smooth.
3. Pour a half cup of batter into a skillet to form a circle. Sprinkle a small handful of chocolate chips onto the pancake, and let it cook on one side. Then flip.
4. Repeat step 3 until all the batter has been cooked.
5. Serve and enjoy!
### Recipe tip:
This also makes a great dessert. Just spread a thin layer of marshmallow creme on top.
## BREAKFAST DATE SMOOTHIE
### Serves 2–3
### Ingredients:
1. 2 cups frozen berries (strawberries, raspberries, and/or blueberries)
2. 1–2 dates
3. 2–3 cups of organic spinach and/or kale
4. 2 tablespoons protein powder
5. 1 cup ice (more if needed)
### Directions:
1. Place all ingredients together in blender and mix until smooth.
2. Pour and serve!
### Recipe tip:
If you're making this for your kids, don't tell them about the spinach. They won't even taste it, and they will be getting their veggies for the day. If the smoothie doesn't taste sweet enough for you, add some raw sugar or stevia.
## MAKEOVER MUFFINS
### Serves 8–12
### Ingredients:
1. 2 cups whole-grain or gluten-free flour
2. 1 cup flaxseed meal
3. 1 cup oat bran
4. ½ cup molasses
5. ½ cup raw sugar or stevia
6. 2 teaspoons baking soda
7. 1 teaspoon baking powder
8. 1 teaspoon sea salt
9. 2 teaspoons cinnamon
10. ¾ cup rice, almond, or coconut milk
11. 4 eggs, beaten
12. 1 teaspoon vanilla extract
13. 2 tablespoons canola or sunflower oil
14. 1½ cups shredded carrots
15. 2 apples, shredded
16. 1 cup dried blueberries
17. 1 cup pecans, crushed
### Directions:
1. Preheat oven to 350° and coat muffin tin with nonstick spray or use paper baking cups.
2. In large bowl, mix together all ingredients (except carrots, fruit, and nuts) until smooth.
3. Add carrots, fruit, and nuts to mixed ingredients.
4. Spoon batter into muffin cups, filling each about halfway full. Bake for 20 to 25 minutes or until golden brown.
### Recipe tip:
Take a muffin to work for an afternoon snack or pack some in your kids' lunches. Use decorative paper muffin cups for extra fun!
## POACHED PEARS
### Serves 4
### Ingredients:
1. ½ cup water
2. 4 pears, halved and cored
3. 1 tablespoon freshly squeezed or bottled lime juice
4. 3 tablespoons honey
5. 1½ cups plain nonfat yogurt
### Directions:
1. Heat water in skillet and add pears. Cover and cook for 5 to 7 minutes.
2. Remove from heat and add lime juice and honey.
3. Place pears over yogurt and enjoy!
### Recipe tip:
For something different, substitute fat-free cottage cheese or oatmeal for the yogurt.
## BROCCOLI BACON FRITTATA
### Serves 6
### Ingredients:
1. 1 cup diced broccoli
2. ¼ cup butter
3. 1 cup sliced fresh mushrooms
4. 1 medium onion, chopped
5. 6 eggs
6. 8 slices turkey bacon, cooked and crumbled
7. 1 small tomato, sliced
8. 4 ounces grated low-fat cheddar cheese
### Directions:
1. Place broccoli in a nonstick 10-inch skillet, adding enough water to cover. Bring to a full boil. Cook over medium heat until crisp-tender, 3 to 5 minutes. Drain and place broccoli on a small plate.
2. Melt butter in same skillet. Add mushrooms and onion. Cook over medium heat until tender, about 3 to 4 minutes.
3. Beat eggs together in a bowl until frothy. Add bacon. Pour into skillet and stir gently. Cook on medium heat for 3 to 4 minutes.
4. As eggs set, lift up sides to allow uncooked egg to flow underneath. Arrange broccoli and tomato slices on top. Cover and let cook until eggs are completely set, about 4 to 5 minutes.
5. Sprinkle with cheese and cut into pizzalike wedges. Serve and enjoy!
### Recipe tip:
Add chopped spinach for extra greens. You can also replace the turkey bacon with organic ground beef and serve as a dinner casserole.
## CINNAMON APPLE MUFFINS
### Serves 8–10
### Ingredients:
1. 6 tablespoons canola or sunflower oil
2. 1 teaspoon butter
3. 1 cup honey
4. 2 eggs
5. 1½ teaspoons vanilla extract
6. 2 cups whole-grain or gluten-free flour
7. 1 teaspoon cinnamon
8. ½ teaspoon baking soda
9. ½ teaspoon baking powder
10. ½ teaspoon sea salt
11. ¹⁄3 cup unsweetened applesauce
12. ²⁄3 cup low-fat sour cream
13. 1 Granny Smith apple, peeled, cored, and cut into thin slices
14. 2–4 teaspoons chopped pecans
15. Honey, for glazing
### Directions:
1. Preheat oven to 350° and coat muffin tin with nonstick spray or use paper baking cups.
2. Beat together the oil, butter, and honey with mixer on high speed until mixture is fluffy.
3. Decrease speed and add eggs and vanilla.
4. In a separate bowl, mix the dry ingredients together. Mix half the dry ingredients into the egg mixture; add applesauce and sour cream; then add the rest of the dry ingredients.
5. Spoon batter into muffin cups, filling each about halfway full. Top each cup with apple slices. Sprinkle ¼–½ teaspoon of pecans on each muffin; glaze with honey.
6. Bake on center rack until muffins are golden brown and springy to the touch, about 30 to 35 minutes.
### Recipe tip:
This is a great snack or dessert to pack in a lunch box too.
## ORIENTAL EGGS
### Serves 6
### Ingredients:
1. 8 eggs
2. 3 teaspoons low-sodium soy sauce or Bragg Liquid Aminos
3. 1 clove garlic, minced
4. ½ teaspoon toasted sesame oil
5. ½ teaspoon white pepper
6. ½ cup chopped snow peas
7. ½ cup chopped green onion
8. 1½ cups bean sprouts
### Directions:
1. Mix eggs, soy sauce or Bragg Liquid Aminos, garlic, sesame oil, and white pepper into a large bowl. Set aside.
2. Coat frying pan with nonstick spray. Cook snow peas and green onion for 2 minutes.
3. Add bean sprouts and cook for 1 minute more.
4. Add egg mixture and cook until firm.
### Recipe tip:
You can turn this into a stir-fry for lunch or dinner by adding in 3 cups of cooked brown rice and a meat of your choice.
# TASTE OF TRUTH
Every new day is God's gift of a new beginning.
# CHAPTER 15
## Craving Fresh Adventures
### Healthy Food to Go and God Time on the Road
I'VE BEEN ON a lot of airplanes in my life, but one particular flight will forever be engraved on my heart. I remember it as one of my greatest God adventures in the air.
I had been scheduled to be in first class, but the airline had given away my designated seat and put me in the last row by the bathroom. I was assigned to the middle seat between two very large men for the five-hour cross-country flight. As the plane took off, all I could think about was the loss of my first-class seat and how physically exhausted I felt. (They say Jesus can turn water into wine, but He can't turn our whining into anything.) I had such a bad attitude that I decided to try to get some sleep.
But as I started to doze off, I felt the Lord prompting me to ask the man to my left about his daughter. I opened my eyes and looked at the man, thinking, _What if this man doesn't have a daughter?_
I took a chance and asked the man about his girl. When I did, tears welled up in his eyes and he told me how his daughter had gone off to college, only to be raped and become pregnant. He was on his way to get her and take her to get an abortion. As I listened, tears began to flow down my cheeks as well. Still I went ahead and asked a very hard question: "Do you feel that this baby your daughter is carrying deserves a chance at life?" At the time he was in too much pain to answer.
I offered to pray for him and his daughter, even though I had no idea how her situation would turn out. When the plane landed, we said our good-byes. Two years later I was speaking at a conference when a young woman walked up to me holding a little boy. She told me that because of the divine appointment between me and her father on an airplane, she and her dad had talked and prayed, and in the end she'd decided to keep the baby she was holding.
I cried tears of joy and tears of terror as I feared what would have happened if I had allowed my discomfort to keep me from the divine intervention and adventure of faith God wanted me, this man, and his daughter to experience.
# Soul Food
The Lord went ahead of them. He guided them during the day with a pillar of cloud, and he provided light at night with a pillar of fire. This allowed them to travel by day or by night.
EXODUS 13:21
God put a craving for adventure in the heart of every man and woman. If we don't fulfill our need for adventure with our Lord, we will seek it in the world. His ways and our days need to become one in order for our desire for a faith adventure to be accomplished. Even if we don't have the right attitude, we can be open when the Lord interrupts a disappointing day. When we do, our God will supply the adventure we crave, and daily tasks will become divine appointments.
If you are ready for a God adventure, I invite you to try the buffet of choices below. I am hoping you will taste and see for yourself that the Lord is not only good, He is exciting!
# New Life Recipes
## 1. PRAY FOR DIVINE INTERRUPTIONS
Jesus called out to them, "Come, follow me, and I will show you how to fish for people!"
MATTHEW 4:19
One day, Peter started off as a fisherman and ended that same day as one of Jesus' disciples. Look (and pray) for ways to go fishing for a divine interruption today, and you'll find the adventure you're craving!
## 2. TAKE A JOYRIDE WITH JESUS
You will live in joy and peace. The mountains and hills will burst into song, and the trees of the field will clap their hands!
ISAIAH 55:12
Go for a drive with only one intention: to draw close to the Lord. Pack your Bible, start the praise music, and then stop at a beautiful park. Once you find a quiet place to meet with Him, ask the Lord to become real to you as you read His Word.
## 3. FUEL YOURSELF WITH THE WORD
In the beginning the Word already existed. The Word was with God, and the Word was God.
JOHN 1:1
A great way to fuel your soul and soothe the frustration caused by traffic jams and time crunches is by listening to Christian books or messages on tape while you drive. Think of long commutes as more time to be inspired by the Word.
# POWER UP WITH PRAYER
For God has not given us a spirit of fear and timidity, but of power, love, and self-discipline.
2 TIMOTHY 1:7
Dear God,
From this day forward I want to live out my faith as a daily adventure. Please help me not to miss out on time with You. I love You and want more of You every day. Amen.
# FOOD TRUTH
No food . . . is as satisfying as finishing strong.
# Food Recipes to Go
The drive-through is not your only (or usually the best) option when you hit the road or plan lunch on workdays. Not only are the following recipes delicious, they will provide you with the fuel you need all afternoon long.
## PATTY CAKES
### Serves 4
### Ingredients:
1. 1½ cups cooked brown rice
2. 2 eggs, beaten
3. 2 tablespoons water
4. 2 teaspoons onion powder
5. ¼ cup shredded sharp cheddar cheese
6. 2 tablespoons olive oil
### Directions:
1. Mix all ingredients except olive oil and form into patties.
2. Fry in olive oil in a skillet over medium heat, cooking each patty about 2 to 3 minutes per side.
### Recipe tip:
These are perfect to take on a picnic or to the office because they can be eaten hot or cold! You can also add shredded carrots and zucchini to the patties.
## YO YO ON THE GO
### Serves 1
### Ingredients:
1. ¹⁄3 cup almonds
2. 1 cup Greek yogurt
3. 2 teaspoons honey
### Directions:
1. Crush the almonds and put them in a to-go bag.
2. When you're ready to eat, sprinkle the almonds over the yogurt and drizzle honey on top.
3. Eat and enjoy!
### Recipe tip:
When you're on the go, this handy treat is perfect for an afternoon snack.
## BACON-APPLE BITES
### Serves 2
### Ingredients:
1. 4 turkey bacon strips, cooked
2. Cheddar cheese slices, cut in 2-inch squares
3. 1 apple, cored and sliced
### Directions:
1. Put half a bacon strip and a cheddar cheese square onto an apple slice.
2. Put a toothpick through each stack.
3. Take them with you wherever you go!
### Recipe tip:
This is also great with pears. It's the perfect snack to take along on a picnic or pack in a school lunch.
## EGGLICIOUS EGG SALAD
### Serves 2
### Ingredients:
1. 4 eggs, hard boiled and peeled
2. 1½ tablespoons low-fat or Healthy Mayonnaise (see page 19)
3. 1 teaspoon onion powder
4. 1 teaspoon garlic powder
### Directions:
1. Mash eggs with a fork.
2. Add mayonnaise, onion powder, and garlic powder. Stir well.
3. This is good served with whole-grain or gluten-free crackers or tortilla chips.
### Recipe tip:
This salad will keep in the fridge for three days. Add chopped red onion and bell peppers for color and taste.
## MINI ZUCCHINI PIES
### Serves 4
### Ingredients:
1. 1 tablespoon olive oil
2. 1 onion, chopped
3. 8–12 turkey bacon strips
4. 1 large carrot, grated
5. 1 large zucchini, grated
6. 3 eggs
7. ½ cup cheddar cheese, grated
8. ¼ cup cream cheese
9. Salt and pepper, to taste
10. ½ cup whole-grain flour
### Directions:
1. Preheat oven to 350°.
2. Grease and flour 12 mini muffin tins.
3. Heat the oil in a large pan and sauté the onion. Add the turkey bacon strips and fry to desired crispness. When done, remove bacon from the pan to cool.
4. Add carrot and zucchini to the same pan and cook for about 2 more minutes.
5. Transfer mixture to a bowl to cool. Break up cooled bacon and add to onion, carrot, and zucchini mixture.
6. In another bowl, beat the eggs, cheese, and cream cheese together. Season with salt and pepper as desired.
7. Stir the egg mixture into the cooled onion, carrot, and zucchini mixture. Now stir in the flour.
8. Spoon the mixture into the prepared tins.
9. Bake for 15 to 20 minutes.
### Recipe tip:
Perfect for school lunches or a picnic. These muffins can be served hot or cold.
## COLD PEA SALAD
### Serves 12
### Ingredients:
1. 1 bunch green onions, chopped
2. 1 red bell pepper, chopped
3. 5 (12 ounces) cans chickpeas, drained and rinsed
4. 1 bag frozen peas
5. ¼ cup fresh cilantro, chopped
6. 1¼ cups low-fat or Healthy Mayonnaise (see page 19)
7. 1¼ cups plain nonfat yogurt
8. 3 teaspoons ground cumin
9. 3 teaspoons curry powder
10. 1 dash pepper
11. 1 dash onion powder
### Directions:
1. Mix onions, bell pepper, chickpeas, peas, and cilantro in a large bowl.
2. Combine mayonnaise, yogurt, cumin, curry powder, pepper, and onion powder in a separate bowl. Mix well and add to vegetables.
3. Serve and enjoy!
### Recipe tip:
This is delicious with feta cheese. It's great to take to the office for lunch or send with your kids to school.
## SAUTÉED BROCCOLI
### Serves 2–3
### Ingredients:
1. 1 broccoli head, washed and cut into bite-size pieces
2. 1 cup sliced portobello mushrooms
3. 2 garlic cloves, pressed
4. 1 tablespoon butter
### Directions:
1. Place all ingredients in a skillet over low to medium heat. Cook for 10 minutes or until broccoli is tender.
2. Chill and eat.
### Recipe tip:
This is another great recipe for lunches or the office. It is best cold but also delicious heated. If you're making this at home for a meal, add chicken for a tasty entrée.
# TASTE OF TRUTH
The real adventure is found in the unexpected.
# About the Author
SHERI ROSE SHEPHERD is an award-winning author, Bible life coach, and humorist with over one million books sold. Her life experiences help her identify with almost any woman's battle. She grew up in a broken home and was severely overweight as a teen; she also experienced depression, dyslexia, and an eating disorder. Through God's strength, Sheri Rose has become a bestselling author and popular speaker at events nationwide, including Women of Joy and Extraordinary Women. Her weekly video devotions are featured on Bible Gateway. Visit her online at hisprincess.com.
# Recipe Index
BEVERAGES AND SMOOTHIES
Almond Chocolate Smoothie,
Basic Vanilla Shake,
Breakfast Date Smoothie,
Chai Yum,
CoCo Crazy Smoothie,
Frozen Honey Colada Smoothie,
Fruit Spritzer,
Gingerly Peachy Keen Smoothie,
Pomegranate Punch,
Raspberry Peach Smoothie,
Shakin' Me to Pieces Smoothie,
Strawberry Lemonade,
That's the Raspberries Smoothie,
Watermelon Lemonade,
BREAKFASTS
Chocolate Chip Pancakes,
Broccoli Bacon Frittata,
Cinnamon Apple Muffins,
Cranberry Sweet Potato Bread,
Makeover Muffins,
Oriental Eggs,
Poached Pears,
CONDIMENTS, DIPS, AND EXTRAS
Carrot and Almond Dip,
Chocolate Dip,
Healthy Mayonnaise,
Homemade Barbeque Sauce,
Hummus with Roasted Red Pepper and Tomato,
Mushroom Dip,
Not-Really-Cheese Cheese Sauce!,
Queso Fiesta Dip,
Raw Food Ranch Dressing,
DESSERTS
Banana Bliss Pie,
Brown Rice Custard,
Carob Pudding,
Choco Sauce,
Craving Chocolate Cake,
Heavenly Apples and Bananas,
Honey-Baked Almond Brittle,
Make Mine Chocolate Cake,
Midnight Chocolate Truffles,
Pretty Pudding,
Pumpkin, Spice, and Everything Nice Cookies,
Pure Fudge Love,
Raw Mango Pudding,
Soft-Serve Chamomile Vanilla Ice Cream,
Sweet Chocolate Fondue,
Sweet Mint Pie,
MAIN DISHES
Apple Cinnamon Chicken and Rice,
Aren't We Tender, Pork Tenderloin,
Beefy and Leafy Pockets,
Cajun Jumbo Shrimp Kebabs,
Fantastic Fiery Chicken,
Garlic Spiced Chicken,
Grilled Portobello Mushroom Burgers,
Not Your Mama's Meat Loaf,
Pizza Night,
Saucy Salmon,
Stuff Me Full Turkey,
Stuffed Red Bell Pepper Pops,
Sweet Balsamic Chicken Delight,
Tasty Raw Food Tacos,
Veggie Pie,
SALADS AND SOUPS
Asian Cabbage Crunch Salad,
Cold Pea Salad,
Corn Chowder,
Creamy Fruit Salad,
Egglicious Egg Salad,
Fire Chili,
Fresh Corn Salad,
Fruit Fiesta Chicken Salad,
Good-for-You Greens Soup,
Mint Pear Salad,
Mushroom Soup,
Oui Oui Onion Soup,
Oyster Delight Soup with Angel-Hair Pasta,
Potato Salad in the Raw,
Spinach Cream Soup,
Steak Supreme Salad,
Summertime Salad,
Vegetable Slaw,
SIDE DISHES
Cauli Mac 'n' Cheese,
Cauli-Mashers,
Glazed Green Beans and Yams,
Healthy Chili Cheese Fries,
Healthy Corn Bread,
Homemade Cranberry Sauce,
Hot Cabbage,
Spicy Squash,
Squash Stir-Fry,
Sautéed Broccoli,
Zucchini Pancakes,
SNACKS
Bacon-Apple Bites,
Fruit Pop Pops,
Island Snack,
Kale Chips,
Mini Zucchini Pies,
Moto Stack,
Mouthwatering Melon Bites,
Patty Cakes,
Peanut Butter Pickle Delight,
Rollover Turkey,
That's a Wrap!,
Tuna Zest,
Wrap Me Up!,
Yo Yo on the Go,
Yum-Yum Nachos,
Sheri Rose can relate to almost any woman. In spite of her painful past, a struggle with dyslexia, and an English teacer telling her she was born to lose, Sheri has sold more than one million books, lost over 50 pounds, and conquered chronic fatigue and an eating disorder—God's way!
Today she inspires millions of women through her books, conferences, and online coaching.
www.hisprincess.com
| {
"redpajama_set_name": "RedPajamaBook"
} | 1,981 |
\section*{Introduction}
The concept of a fuzzy set was introduced in 1965 by Zadeh \cite{Z65} and independently, as is pointed out by \v{S}ostak \cite{S96}, by
Salij \cite{Sa65}.
A fuzzy subset of a set $X$ is a function $f : X \to I$ where $I = [0,1]$ is
the unit interval in $\R$. For a point $x \in X$ the value $f(x)$ is understood as the degree of membership
of $x$ in the fuzzy set. An ordinary subset $A$ of $X$ corresponds to its characteristic function $\chi_A$
which is $1$ on $A$ and $0$ on its complement.
The set $I^X$ of functions from $X$ to $I$, i.e. the set of fuzzy subsets, is a complete lattice.
For any family $\{ f_i \in I^X : i \in K \}$ the
pointwise supremum $\bigvee_{i \in K} \ f_i$ and pointwise infimum $\bigwedge_{i \in K} \ f_i$ lie in $I^X$.
The association $A \mapsto \chi_A$ includes the lattice of subsets of $X$ into the lattice $I^X$.
The concept of a fuzzy topology was defined by Chang \cite{Ch68} as a collection $\d$ of fuzzy sets which satisfies
axioms strictly analogous to the axioms for a topology. The constants $0, 1$ are in $\d$ and $\d$ is closed under arbitrary
supremum and finite infimum.
Fuzzy topological spaces quickly became the object of study
by a number of authors. Of particular interest is a series of beautiful papers by Lowen, \cite{L76}, \cite{L77}, \cite{L78}, and \cite{L81}.
The subject has grown immensely. The current state is summarized in detail in Palaniappan's book \cite{P02}.
The magisterial survey by \v{S}ostak \cite{S96} covers not only fuzzy topological spaces, but also the broader theory, initiated by Goguen \cite{G67}
(and Salij \cite{Sa65}) where the fuzzy objects take values in a general complete, distributive lattice instead of $I$.
From the beginning there has been some dispute about how broad the definition of a fuzzy topology should be. In \cite{L76} Lowen introduced among the
axioms a simple additional condition, that the constants $k$ be elements of $\d$ for all $k \in I$.
He provided a number of justifications for his view that the concept of
fuzzy topological space should be restricted to include this strengthened axiom. These arguments were vigorously extended in \cite{LW88}.
Thus, Lowen and Wuyts use the label quasi-fuzzy topology for the original Chang axioms, reserving fuzzy topology for those which include constants.
On the other hand, \v{S}ostak retains the original Chang definition and uses the term laminated fuzzy topology for one which includes constants.
He argues,\cite{S96} page 671:
\begin{quote} R. Lowen and P. Wuyts insist on restricting the subject of fuzzy topology
entirely to laminated spaces. However, at present, the attitude of
most workers in fuzzy topology towards the property of laminatedness can be compared with
the attitude of general topologists towards the axiom, say, of
Hausdorffness or complete regularity: One may certainly accept it when it is really needed,
but it is not reasonable to include axiom $T_2$ or $T_{3.5}$ as part of the general definition
of a topological space. Thus the standard framework for most specialists working in fuzzy topology is the category
of Chang Fuzzy Topological Spaces, but when it is indeed necessary, they impose the additional
condition of laminatedness on the considered spaces. \end{quote}
I tend to agree with Lowen and Wuyts. In fact, I believe that the subject should be further restricted by the introduction of what I call
affine invariance. However, to avoid confusion, I will follow \v{S}ostak's terminology.
In the early paper \cite{L76} Lowen introduced functors between topological spaces and fuzzy topological spaces.
He pointed out that for a topological space $(X,\t)$ the set of lower
semicontinuous functions in $I^X$ is a laminated fuzzy topology $\om(\t)$. On the other hand, given a
fuzzy topology $\d$ we can associate to it the coarsest topology $\i(\d)$ on $X$ with respect to which the
the functions in $\d$ are lower semicontinuous, that is, the topology with subbase $\{ f^{-1}(c,\infty) :
c \in I $ and $ f \in \d \}$. Lowen also introduced the appropriate notion of compactness for fuzzy
subsets of a space with a laminated fuzzy topology. Not every fuzzy topology, not even every laminated fuzzy topology,
is of the form $\om(\t)$ for some topology $\t$. The fuzzy topologies of this form are said to be topologically induced or simply
induced fuzzy topologies.
We will say that a fuzzy topology $\d$ is affine invariant if for all $m, k \in \R$ with $m > 0$, and all $f \in \d$ such that
$m \cdot f + k \in I^X$, i.e. $m \cdot f(x) + k \in I$ for all $x \in X$, the affine adjustment $m \cdot f + k $ is an element of $ \d$. That is,
we assume that $\d$ is closed under appropriate positive affine transformations.
Clearly, the set of lower semicontinuous functions on a topological space is affine invariant. We show, conversely, that
the induced fuzzy topologies are exactly the affine invariant fuzzy topologies.
Finally, we illustrate the utility of the restriction by considering the meaning of compactness in the context of affine invariant fuzzy topologies.
The work here was inspired by a reading of the lovely survey, \cite{C08}. Although my intent is to
contract the range of fuzzy topology, I nonetheless appreciate Carlson's more expansive exposition.
After reading Carlson's paper several summers ago, I had some lunchtime conversations with
Jack Feldman from which this work is the belated fruit.
I dedicate it to his memory.
\vspace{1cm}
\section{Affine Invariance}
Let $(X, \t)$ be a topological space. A function $f : X \to \R$ is \emph{lower semicontinuous}
(hereafter \emph{lsc}) if for every $c \in \R$ the set $f^{-1}(c,\infty) \in \t$, i.e. it is open in $X$.
We will be using this sort of set so often that we introduce the notation:
\begin{equation}\label{01}
f_{(c} \ =_{def} \ f^{-1}(c,\infty) \qquad \mbox{and} \qquad f_{[c} \ =_{def} \ f^{-1}[c,\infty),
\end{equation}
for any $c \in \R$.
If $U$ is a subset of $X$ then the characteristic function $\chi_U$ of $U$ is lsc if and only if $U \in \t$. Recall
that $\chi_U(x) = 1$ if $x \in U$ and $= 0$ otherwise.
For any $L \subset \R$ we will denote by $L^X$ the set of all functions from $X$ to $L$.
\begin{df}\label{defa01} For a set $X$ let $\d \subset I^X$. We call $\d$ a \emph{fuzzy topology }
if it satisfies the conditions:
\begin{itemize}
\item[(i)] The constant functions $0, 1$ are in $\d$.
\item[(ii)] If $\{ f_i : i \in K \}$ is any indexed family of members of $\d$ then
$\bigvee_{i \in K} \ f_i \ \in \ \d$.
\item[(iii)] If $\{ f_i : i \in K \}$ is any indexed family of members of $\d$ with $K$ finite then
$\bigwedge_{i \in K} \ f_i \ \in \ \d$.
\end{itemize}
A pair $(X,\d)$ where $X$ is a set and $\d$ is a fuzzy topology on $X$ will be called a \emph{fuzzy topological space}.
We call $\d$ a \emph{laminated fuzzy topology } (or we say that $(X, \d)$ is a \emph{laminated fuzzy topological space })
when (ii) and (iii) hold and (i) is strengthened to:
\begin{itemize}
\item[(i')] The constant functions $k $ are in $\d$ for all $k \in I$.
\end{itemize}
We call $\d$ an \emph{affine invariant fuzzy topology} (or we say that the fuzzy topological space
$(X, \d)$ is \emph{affine invariant})
when (ii) and (iii) hold and (i) is replaced by:
\begin{itemize}
\item[(i'')] The constant function $0$ is in $ \d$ and $\d$ is closed under suitable positive affine transformations, i.e.
if $f \in \d$, $m,k \in \R$ with $m > 0$ and $g = m \cdot f + k$ satisfies $g(x) \in I$ for all $x \in X$
then $g \in \d$.
\end{itemize}
\end{df}
\vspace{.5cm}
For an indexed family we will always assume that the index set $K$ is nonempty.
Clearly, these are successively stronger conditions. In particular, (i'') implies (i') [Let $f = 0$].
The concept of fuzzy topology is due to Chang \cite{Ch68}. Lowen introduced the sharper condition (i') in
\cite{L76}. We adopt the term \emph{lamination} following \cite{S96}.
As with topologies, the intersection of arbitrary families of fuzzy topologies on $X$ is a fuzzy topology on $X$.
Conditions (i') and (i'') are preserved by intersection as well. Hence, for any $\A \subset I^X$ we can obtain
the smallest fuzzy topology on $X$ which contains $\A$, or the \emph{fuzzy topology generated by $\A$}, by intersecting
all fuzzy topologies which contain $\A$. Notice that $I^X$ is itself an affine invariant fuzzy topology.
It is called the \emph{discrete fuzzy topology}.
Following \cite{W75} and \cite{L76} we introduce constructions relating topologies and fuzzy topologies. We let $\R_r$ denote $\R$ equipped with
the \emph{lower topology} whose non-empty open sets are $\{ (c,\infty) : c \in \R \}$ and we let $I_r$ denote set $I$ with the
relative topology induced from $\R_r$. Thus,
a function $f : X \to \R_r$ is continuous exactly when it is a lower semicontinuous real-valued (hereafter, lsc) function.
\begin{df}\label{defa02} For $(X, \t)$ any topological space let $\om(\t)$ denote the set of all continuous functions from $X$ to $I_r$, or, equivalently,
the set of lsc functions from $X$ to $I$.
That is, $f \in \om(\t)$ if and only if $f \in I^X$ with $f_{(c} \in \t$ for all $c \in I$.
For $(X,\d)$ any fuzzy topological space let $\i(\d)$ denote the coarsest topology on $X$ so that every $f \in \d$ is continuous
from $X$ to $I_r$. That is, $\i(\d)$ has subbase
$\{ f_{(c} : \ c \in I \ $ and $ \ f \in \d \ \}$.
If $\d$ is a fuzzy topology on $X$ we will say that $\d$ is \emph{induced from the topology $\t$} on $X$ when $\d = \om(\t)$.
We will say that $\d$ is an \emph{induced fuzzy topology} or a \emph{topological fuzzy topology} when it is induced from
some topology on $X$.
\end{df}
\vspace{.5cm}
\begin{theo}\label{theoa03} If $\t$ is a topology on $X$, then $\om(\t)$ is an affine invariant fuzzy topology and
$ \i(\om(\t)) \ = \ \t$. Thus, if $\d$ is the fuzzy topology induced from $\t$, then $\t = \i(\d)$.
\end{theo}
{\bfseries Proof:} It is easy to check that the set of lsc functions satisfies (ii)and (iii). In general, a continuous
function $\phi : \R_r \to \R_r$ is a non-decreasing function on $\R$ which is continuous from the left. For example,
if $\phi(t) = m \cdot t + b$ with $m \geq 0$ then $\phi$ is such a function. If $f : X \to I_r$ is continuous and
$\phi : \R_r \to \R_r$ is continuous with $\phi(f(X)) \subset I$ then $\phi \circ f : X \to I_r$ is continuous. Thus,
$f \in \om(\t)$ implies that $\phi \circ f \in \om(\t)$. Hence,
$\om(\t)$ is an affine invariant fuzzy topology.
By definition if $f$ is lsc on $(X,\t)$ then each $f_{(c}$ is in $\t$ and so
the inclusion $\i(\om(\t)) \subset \t$ is clear. On the other hand, if $U \in \t$ then $\chi_U \in \om(\t)$ and
so $U \in \i(\om(\t))$.
Thus, if $\d = \om(\t)$ then $\i(\d) = \i(\om(\t)) \ = \ \t$.
$\Box$ \vspace{.5cm}
\begin{theo}\label{theoa04} If $\d$ is a fuzzy topology on $X$, then $\i(\d)$ is a topology on $X$ such that $\d \subset \om(\i(\d))$ with
equality if and only if $\d$ is affine invariant. Thus, if $\t = \i(\d)$, then $\d \subset \om(\t)$.
\end{theo}
{\bfseries Proof:} By definition of $\i(\d)$ every $f \in \d$ is a continuous map from $(X,\i(\d))$ to $I_r$. Hence, $\d \subset \om(\i(\d))$.
Thus, if $\t = \i(\d)$, then $\d \subset \om(\i(\d)) = \om(\t)$.
From Theorem \ref{theoa03} $\om(\t)$ is affine invariant for any topology $\t$ and so $\d = \om(\i(\d))$ implies that $\d$ is
affine invariant.
For the converse we prove a more precise result.
\begin{theo}\label{theoa05}If $\d$ is a fuzzy topology on $X$, then the
following conditions are equivalent.
\begin{enumerate}
\item[(a)] $\d$ is affine invariant.
\item[(b)] $\d$ is laminated and if $x \in U$ and $ U \in \i(\d)$, then there exists
$f \in \d $ such that $f(x) = 1$ and $f|(X \setminus U) = 0$.
\item[(c)] $\d$ is laminated and if $ U \in \i(\d)$, then $\chi_U \in \d$
where $\chi_U$ is the characteristic function of $U$.
\item[(d)] $\d = \om(\i(\d))$.
\item[(e)] $\d$ is topological, i.e. $\d$ is induced from some topology $\t$ on $X$.
\end{enumerate}
\end{theo}
{\bfseries Proof:} (a) $\Rightarrow$ (b): If $U \in \i(\d)$ and $x \in U$, then by
definition of a subbase there exists a finite index set $K$, elements
$\{ g_i \in \d : i \in K \}$ and $\{ a_i \in I : i \in K \}$ such that
\begin{equation}\label{02}
x \ \in \ \bigcap_{i \in K} \ (g_i)_{(a_i} \ \subset \ U.
\end{equation}
By (a) condition (i'') holds for $\d$ and so, in particular, (i') holds as well, i.e. $\d$ is laminated.
Let $b_i = g_i(x)$ so that $0 \leq a_i < b_i \leq 1$. By (i'),(ii) and (iii)
$h_i =_{def} a_i \vee ( b_i \wedge g_i) \in \d$ and maps $X$ to the interval
$[a_i,b_i]$. By (i'')
$f_i = (h_i - a_i)/(b_i - a_i)$ is in $\d$.
Furthermore, $f_i(x) = 1$ for all $i \in K$ and $\bigcap_{i \in K} (f_i)_{(0} \subset U$.
Finally, (iii) implies that $f = \wedge_{i \in K} \ f_i \ \in \ \d$. Clearly, $f(x) = 1$ and $f|(X \setminus U) = 0$.
(b) $\Rightarrow$ (c): For each $x \in U$, (b) implies there exists $f_x \in \d$ such that $f_x(x) = 1$ and
$f_x|(X \setminus U) = 0$. By (ii) $\chi_U = \bigvee_{x \in U} f_x$ is in $\d$.
(c) $\Rightarrow$ (d): Assume that $f : X \to I$ is lsc with respect to $\i(\d)$. We must show that
$f \in \d$.
For each $c \in I$ the set $U_c = f_{(c}$ is open, i.e. lies in $\i(\d)$,
because $f$ is lsc. Hence, by (c),
the characteristic function $\chi_{U_c} \in \d$. Let $f_c = c \wedge \chi_{U_c}$ which lies in $\d$ by
(i') and (iii). Since $f$ maps to $I, \ f \geq f_c$. Hence,
\begin{equation}\label{03}
f \ \geq \ \hat{f} \ =_{def} \ \bigvee_{c \in I} \ f_c.
\end{equation}
By (ii) $\hat{f} \in \d$.
If $f(x) = 0 $ then of course $ \hat{f}(x) \geq f(x)$.
Now assume that $f(x) > 0$ and let $\ep > 0$. Choose $c \in I$ such that $f(x) > c > f(x) - \ep$.
Since $f(x) > c, \ x \in U_c$ and so $f_c(x) = c$. Hence, $\hat{f}(x) \geq f_c(x) > f(x) - \ep$.
As $\ep$ was arbitrary we have $\hat{f}(x) \geq f(x)$.
Thus, $f = \hat{f}$ and so $f \in \d$ as required.
(d) $\Rightarrow$ (e): Obvious.
(e) $\Rightarrow$ (a): By Theorem \ref{theoa03} an induced fuzzy topology is affine invariant.
$\Box$ \vspace{.5cm}
{\bfseries Remark:} Notice that in the proof of (a) $\Rightarrow$ (b) we did not need the full strength
of the affine invariance assumption. We needed that $\d$ be laminated and if
$f \in \d$ has image $f(X) \subset [a,b]$ with $0 \leq a < b \leq 1$, then
$(f - a)/(b - a)$ is in $\d$.
\vspace{.5cm}
Following Martin \cite{M80} we define for a fuzzy topology $\d$ on $X$ the topology $\chi^*(\d) = \{ U \subset X : \chi_U \in \d \}$ on $X$.
Since $U = (\chi_U)_{(0}$ it follows that $\chi^*(\d) \subset \i(\d)$. For a topology $\t$ we define the fuzzy topology
$\chi(\t) = \{ \chi_U : U \in \t \}$. Clearly, $\chi(\t) \subset \om(\t)$ and $\t = \i(\chi(\t))$.
\begin{df}\label{defa07} We call a fuzzy topology $\d$ a \emph{weakly induced fuzzy topology} when it satisfies the
equivalent conditions
\begin{enumerate}
\item[(a)]$\chi^*(\d) = \i(\d)$.
\item[(b)]$\d \supset \chi(\i(\d))$.
\item[(c)] $\d \subset \om(\chi^*(\d))$.
\item[(d)] If $U = f_{(c}$ for $f \in \d$, then $\chi_U \in \d$.
\end{enumerate}
\end{df}
\vspace{.5cm}
Observe that condition (d) is just a restatement of conditions (a), (b) and (c).
Martin calls $\d$ an induced fuzzy topology when $\d = \om(\chi^*(\d))$. We show that this definition
agrees with the one given in Definition \ref{defa02}.
\begin{prop}\label{propa06}If $\d$ is a fuzzy topology on $X$, then the
following conditions are equivalent.
\begin{enumerate}
\item[(a)] $\d = \om(\chi^*(\d))$.
\item[(b)] $\d$ is laminated and weakly induced.
\item[(c)] $\d = \om(\i(\d))$.
\item[(d)] $\d$ is topological, i.e. $\d$ is induced from some topology $\t$ on $X$.
\item[(e)] $\d$ is affine invariant.
\end{enumerate}
\end{prop}
{\bfseries Proof:} (a) $\Rightarrow$ (b): By Theorem \ref{theoa03} $\d = \om(\chi^*(\d))$ implies $\d$ is
laminated and $\chi^*(\d)= \i(\d)$. Hence, $\d$ is weakly induced.
(b)$\Leftrightarrow$ (c): Conditions (b) and (c) are exactly conditions (c) and (d) of Theorem \ref{theoa05} and so the equivalence follows
from that theorem.
(c)$\Leftrightarrow$ (d)$\Leftrightarrow$ (e): These are restatements of parts of Theorem \ref{theoa05}.
(c) $\Rightarrow$ (a): We have seen that (c) $\Rightarrow$ (b). Hence, $\d = \om(\i(\d))$ implies that $\chi^*(\d) = \i(\d)$
and so that $\d = \om(\chi^*(\d))$.
$\Box$ \vspace{.5cm}
\begin{theo}\label{theoa09} Let $\t$ be a topology on $X$.
\begin{enumerate}
\item[(a)] The affine invariant fuzzy topology $\om(\t)$ is generated by \\
$\{ k : k \in I \} \cup \chi(\t) = \{ k : k \in I \} \cup \{ \chi_U : U \in \t \}.$
\item[(b)] If $\t$ is completely regular, then $\om(\t)$ is generated by the continuous functions in $I^X$.
\end{enumerate}
\end{theo}
{\bfseries Proof:} (a): Let $\d$ be the fuzzy topology generated by $\{ k : k \in I \} \cup \chi(\t)$. Since
the generators are lsc, it follows that $\d \subset \om(\t)$. Hence, $\i(\d) \subset \i(\om(\t)) = \t$. Clearly, $U \in \i(\d)$
for all $U \in \t$ and so $\i(\d) = \t$. Hence, $\d$ satisfies condition (c) of Theorem \ref{theoa05}. From the theorem it follows
that $\d = \om(\i(\d)) = \om(\t)$.
(b): Let $\d$ be the fuzzy topology generated by the continuous functions in $I^X$. Again, $\d \subset \om(\t)$ and $\i(\d) \subset \i(\om(\t)) = \t$.
Because $\t$ is completely regular, the collection $\{ f_{(c} \}$ with $c \in I$ and $f : X \to I$ continuous form a basis for $\t$ and
so $\t \subset \i(\d)$. Thus, $\t = \i(\d)$. By complete regularity $\d$ satisfies condition (b) of Theorem \ref{theoa05}. From the theorem it follows
that $\d = \om(\i(\d)) = \om(\t)$.
$\Box$ \vspace{.5cm}
If $H : X_1 \to X_2$ then for any $L \subset \R$ we define $H^* : L^{X_2} \to L^{X_1}$ by $H^*(f) = f \circ H$.
If $(X_1,\d_1)$ and $(X_2,\d_2)$ are fuzzy topological spaces then $H $ is defined to be \emph{fuzzy continuous}
when $H^*(\d_2) \subset \d_1$. We thus obtain the category of fuzzy topological spaces $FTOP$ and the full subcategories of
laminated fuzzy topological spaces $FLTOP$ and affine invariant fuzzy topological spaces $FATOP$.
A map $H : (X_1,\t_1) \to (X_2,\t_2)$ between topological spaces is a \emph{quotient map} when $U \in \t_2$ if and only if $H^{-1}(U) \in \t_1$.
A map $H : (X_1,\d_1) \to (X_2,\d_2)$ between fuzzy topological spaces is a \emph{fuzzy quotient map} when $f \in \t_2$ if and only if $H^*(f) \in \d_1$.
We review the proof of the following well-known result.
\begin{theo}\label{theoa10} For $ i = 1,2$ let $\t_i$ and $\d_i$ be a topology and a fuzzy topology on a set $X_i$.
Let $H : X_1 \to X_2$ be a set map.
(a) If $H : (X_1,\d_1) \to (X_2,\d_2)$ is fuzzy continuous, then $H : (X_1,\i(\d_1)) \to (X_2,\i(\d_2))$
is continuous.
(b) $H : (X_1,\t_1) \to (X_2,\t_2)$ is continuous if and only if $H : (X_1,\om(\t_1)) \to (X_2,\om(\t_2))$ is fuzzy
continuous. $H : (X_1,\t_1) \to (X_2,\t_2)$ is a quotient map if and only if $H : (X_1,\om(\t_1)) \to (X_2,\om(\t_2))$ is fuzzy
quotient map.
(c) If $\t_1$ is affine invariant, then $H : (X_1,\d_1) \to (X_2,\d_2)$ is fuzzy continuous if and only if
$H : (X_1,\i(\d_1)) \to (X_2,\i(\d_2))$.
\end{theo}
{\bfseries Proof:} If $f \in I^{X_2}$ and $c \in I$, then
\begin{equation}\label{04}
H^*(f)_{(c} \quad = \quad H^{-1}(f_{(c}).
\end{equation}
(a): If $H$ is fuzzy continuous, then $f \in \d_2$ implies $H^*(f) \in \d_1$ and so equation (\ref{04}) says that
$H$ pulls the elements of the defining subbase for $\i(\d_2)$ back into $\i(\d_1)$. Hence, $H$ is
continuous.
(b): If $H$ is continuous and $f$ is lsc, then $H^*(f) = f \circ H$ is lsc by equation (\ref{04}) and if $H$ is a quotient map,
then the converse is true as well. Hence,
$H^*$ maps $\om(\t_2)$ to $\om(\t_1)$ and so $H$ is fuzzy continuous and $H$ is a fuzzy quotient map if it is a quotient map. If $H$ is fuzzy continuous,
then by (a) $H : (X_1,\i(\om(\t_1))) \to (X_2,\i(\om(\t_2)))$ is continuous and so, $H$ is continuous by
Theorem \ref{theoa03}. Now assume that $H$ is a fuzzy quotient map and $U \subset X_2$ with $H^{-1}(U) \in \t_1$. Thus,
$H^*(\chi_U) = \chi_{H^{-1}(U)} \in \om(\t_1)$. Because $H$ is a fuzzy quotient map, $\chi_U \in \om(\t_2)$, i.e. it is lsc with respect to $\t_2$.
Hence, $U \in \t_2$.
(c): If $H$ is continuous, then by (b) $H : (X_1,\om(\i(\d_1))) \to (X_2,\om(\i(\d_2)))$ is fuzzy
continuous. If $\d_1$ is affine invariant, then by Theorem \ref{theoa04}
$\d_2 \subset \om(\i(\d_2))$ and $\d_1 = \om(\i(\d_1))$. Thus, $H$ is fuzzy continuous.
$\Box$ \vspace{.5cm}
We thus have functors $\tilde \i : FTOP \to TOP$ and $\tilde \om : TOP \to FTOP$ with $\tilde \i \circ \tilde \om$ the
identity on $TOP$ and $\tilde \om \circ \tilde i$ a retraction from $FTOP$ onto $FATOP$.
\begin{prop}\label{propa10a} For the unit interval $I_r$ equipped with the lower topology $\t_r$,
let $\d_r = \om(\t_r)$ be the induced fuzzy topology.
Let $(X,\d)$ be a fuzzy topological space. If $f : (X,\d) \to (I_r,\d_r)$ is fuzzy continuous then $f \in \d$. The fuzzy topology $\d$
is affine invariant if and only if $f : (X,\d) \to (I_r,\d_r)$ is fuzzy continuous for all $f \in \d$. \end{prop}
{\bfseries Proof:} The identity map $1_I$ is a continuous function on $I_r$ and so $1_I \in \d_r$.
Hence, if $f :(X,\d) \to (I_r,\d_r)$ is fuzzy continuous, then $f^*(1_I) = f \in \d$.
If $m, k \in \R$ with $m > 0$, let
\begin{equation}\label{04a}
\phi_{m,k}(t) \ = \ \max(0,\min(1, m \cdot t + k)).
\end{equation}
Clearly, $\phi_{m,k} : I \to I$ is continuous and non-decreasing and so $\phi_{m,k} : (I_r,\t_r) \to (I_r,\t_r)$ is continuous.
Hence, $\phi_{m,k} \in \d_r$.
So if $f :(X,\d) \to (I_r,\d_r)$ is fuzzy continuous then $f^*(\phi_{m,k}) = \phi_{m,k} \circ f \in \d$. Thus, if
every $f \in \d$ is fuzzy continuous then $\d$ is affine invariant.
If $\d$ is affine invariant, then with $\t = \i(\d), \d = \om(\t)$. So if $f \in \d$ then $f$ is lsc with respect to $\t$, i.e.
$f : (X,\t) \to (I_r,\t_r)$ is continuous and so by Theorem \ref{theoa10} (b), $f : (X,\d) \to (I_r,\d_r)$ is fuzzy continuous.
$\Box$ \vspace{.5cm}
{\bfseries Remark:} The identity from $\R$ to $\R_r$ is continuous and so is fuzzy continuous. Hence, if $f : (X,\d) \to (I,\d_I)$
is fuzzy continuous with $\d_I$ the fuzzy topology induced from the usual topology $\t_I$ on $I$
then $f : (X,\d) \to (I_r,\d_r)$ is fuzzy continuous.
\vspace{.5cm}
Let $Y \subset X$. If $\t$ is a topology on $X$, then the \emph{relative topology} $\t|Y$ on $Y$ is $\{ U \cap Y : U \in \t \}$.
For $f \in I^X$, let $f|Y$ denote the restriction of $f$ to $Y$ so that $f|Y \in I^Y$. If $\d$ is a fuzzy topology on $X$,
then the \emph{relative fuzzy topology} $\d|Y$ on $Y$ is $\{ f|Y : f \in \d \}$.
\begin{prop}\label{propa10b} Let $\t$ and $\d$ be a topology and a fuzzy topology on $X$ and let $Y \subset X$.
\begin{equation}\label{04b}
\i(\d|Y) \ = \ (\i(\d))|Y \qquad \text{and} \qquad \om(\t|Y) \ = \ (\om(\t))|Y
\end{equation}
If $\d$ is laminated or affine invariant then $\d|Y$ satisfies the corresponding property.
\end{prop}
{\bfseries Proof:} It is clear that $\d|Y$ is a fuzzy topology which is laminated if $\d$ is. Let $f \in \d$ and
$m, k \in \R$ so that with $\phi(t) = m \cdot t + k$, $\phi(f(y)) \in I$ for all $y \in Y$. Since $\phi$ is continuous and
increasing $\phi^{-1}(I)$ is a closed interval in $\R$. If $b = \sup f(Y), a = \inf f(Y)$, then $\phi([a,b]) \subset I$.
If $\bar f = a \vee (b \wedge f)$ then $\bar f|Y = f|Y$ and $\phi(f(x)) \in I$ for all $x \in X$. If $\d$ is affine invariant,
then $\bar f \in \d$ and $\phi \circ \bar f \in \d$ and so that $ \phi \circ (f|Y) = (\phi \circ \bar f)|Y \in \d|Y$. That is, $\d$ is affine invariant.
Since $f_{(c} \cap Y = (f|Y)_{(c}$ and $A \mapsto A \cap Y$ commutes with unions and intersections, it follows that
$\i(\d|Y) = (\i(\d))|Y$.
Since $(\om(\t))|Y$ is affine invariant, Theorems \ref{theoa04} and \ref{theoa03} imply
\begin{equation}\label{04c}
(\om(\t))|Y \ = \ \om(\i[(\om(\t))|Y]) \ = \ \om([\i(\om(\t))]|Y) \ = \ \om(\t|Y).
\end{equation}
$\Box$ \vspace{.5cm}
{\bfseries Remark:} In particular, this shows that any bounded lsc function on $Y$ extends to an lsc function on $X$.
\vspace{.5cm}
For $ \{ X_i : i \in K \}$ an indexed family of sets let $\prod_{i \in K} \ X_i$ denote the product with projections
$\pi_j : \prod_{i \in K} \ X_j \to X_j$ for all $j \in K$.
If $\t_i$ is a topology on $X_i$ then we denote by
$\prod_{i \in K} \ \t_i$ the product topology on $\prod_{i \in K} \ X_i$. If $\d_i$ is a fuzzy topology on $X_i$ then
we denote by $\prod_{i \in K} \ \d_i $ the fuzzy topology on $\prod_{i \in K} \ X_i$
generated by $\bigcup_{i \in K} \ \pi_i^*(\d_i)$. This is the coarsest fuzzy topology on the product so that
the projection maps $\pi_i$ are fuzzy continuous.
\begin{prop}\label{propa11} If $\{ (X_i, \d_i) : i \in K \}$ is an indexed family of fuzzy topological spaces, then we have
\begin{equation}\label{05}
\i(\prod_{i \in K} \ \d_i) \ = \ \prod_{i \in K} \ \i(\d_i).
\end{equation}
If $\d_i$ is laminated for some $i \in K$ then $\prod_{i \in K} \ \d_i $ is laminated.
If $\d_i$ is affine invariant for all $i \in K$ then $\prod_{i \in K} \ \d_i$ is affine invariant.
\end{prop}
{\bfseries Proof:} If $f \in \d_i$ and $c \in I$ then
$\pi_i^{-1}(f_{(c}) = (\pi_i^*(f))_{(c} \in \i(\prod_{i \in K} \ \d_i)$. Hence,
$\prod_{i \in K} \ \i(\d_i) \subset \i(\prod_{i \in K} \ \d_i)$.
On the other hand, the set of lsc functions $\om(\prod_{i \in K} \ \i(\d_i))$ is a fuzzy topology
which clearly contains $\bigcup_{i \in K} \ \pi_i^*(\d_i)$ and so contains $\prod_{i \in K} \ \d_i$.
So Theorem \ref{theoa03} implies
\begin{equation}\label{06}
\prod_{i \in K} \ \i(\d_i) \ = \ \i(\om(\prod_{i \in K} \ \i(\d_i))) \ \supset \ \i(\prod_{i \in K} \ \d_i).
\end{equation}
If $\d_j$ is laminated then the constant functions from $\prod_{i \in K} \ X_i$ to $I$
are contained in $\pi_j^*(\d_j)$.
If all the $\d_i$'s are affine invariant then they all laminated
and so we can apply Theorem \ref{theoa05} to $\prod_{i \in K} \ \d_i$
and check that the product fuzzy topology satisfies condition (b) of Theorem \ref{theoa05}.
If $x \in U$ and $U$ is open in the product topology then there is a
finite subset $\hat{K}$ of $K$ and open sets $\{ U_i : i \in \hat{K} \}$
so that $x \in \hat{U} =_{def} \bigcap_{i \in \hat{K}} \pi_i^{-1}(U_i) \subset U$.
By Theorem \ref{theoa05} condition (c), each $\chi_{U_i} \in \d_i$.
Hence,
\begin{equation}\label{07}
f \ =_{def} \ \chi_{\hat{U}} \ = \ \bigwedge_{i \in \hat{K}} \ \pi_i^*(\chi_{U_i}) \ \in \prod_{i \in K} \ \d_i.
\end{equation}
Clearly, $f(x) = 1$ and $f|(X \setminus U) = 0$.
$\Box$ \vspace{.5cm}
The coproduct $\coprod_{i \in K} \ X_i$ is defined to be the disjoint union of
the indexed sets $X_i$ so that each $X_i$ can be
regarded as a subset of $\coprod_{i \in K} \ X_i$. If $\t_i$ is a topology on
$X_i$ then the topology $\coprod_{i \in K} \ \t_i$ is the collection of subsets $U$
such that $U \cap X_i \in \t_i$ for all $i \in K$.
If $\d_i$ is a fuzzy topology on $X_i$ then the fuzzy topology $\coprod_{i \in K} \ \d_i $
is the set of functions $f$ such that
$f|X_i \in \d_i$ for all $i \in K$. In each case the required axioms are easy to check.
We leave the easy proof of the following analogue of
Proposition \ref{propa11} to the reader.
\begin{prop}\label{propa12} If $\{ (X_i, \d_i) : i \in K \}$ is an indexed family of fuzzy topological spaces, then
\begin{equation}\label{08}
\i(\coprod_{i \in K} \ \d_i) \ = \ \coprod_{i \in K} \ \i(\d_i).
\end{equation}
If $\d_i$ is laminated for all $i \in K$ or is affine invariant for all
$i \in K$ then $\coprod_{i \in K} \ \d_i$ satisfies the corresponding property.
\end{prop}
$\Box$ \vspace{1cm}
\begin{cor}\label{cora13} If $\{ (X_i, \t_i) : i \in K \}$ is an indexed family of topological spaces and $\d_i = \om(\t_i)$ is
the induced fuzzy topology on $X_i$, then
\begin{align}\label{09}
\begin{split}
\prod_{i \in K} \d_i \ = \ &\om(\prod_{i \in K} \t_i), \\
\coprod_{i \in K} \d_i \ = \ &\om(\coprod_{i \in K} \t_i),
\end{split}
\end{align}
are the induced fuzzy topologies on the product and coproduct.
\end{cor}
{\bfseries Proof:} By Theorem \ref{theoa03} $\t_i = \i(\d_i)$. By Proposition \ref{propa11} the product
fuzzy topology is affine invariant. Hence, from (\ref{05}) and Theorem \ref{theoa04} we have that
\begin{align}\label{10}
\begin{split}
\prod_{i \in K} \ \d_i \ = \ &\om(\i(\prod_{i \in K} \ \d_i)) \ = \\
\om(\prod_{i \in K} \ \i(\d_i)) \ &= \ \om(\prod_{i \in K} \ \t_i),
\end{split}
\end{align}
as required.
The proof for the coproduct is similar using Proposition \ref{propa12} and (\ref{08}).
$\Box$ \vspace{.5cm}
We conclude by illustrating some pathologies that can occur without lamination or affine invariance.
\vspace{.5cm}
{\bfseries Examples:} (A) For any topological space $(X, \t)$ the set of
characteristic functions of the open sets is the fuzzy topology $\chi(\t)$
which is not laminated, i.e. does not satisfy (i'). In fact,
Let $L$ be a proper subset of $I$ which contains $0$ and $1$. Call $L$ \emph{sup-closed} if $\sup A \in L$ whenever
$A$ is a nonempty subset of $L$. If $L$ is closed, then, of course, it is sup-closed. For any fuzzy topology $\d$ the
set of $k \in I$ such that the constant $k \in \d$ is sup-closed.
If $L$ is a proper, sup-closed subset of $I$ which contains $0$ and $1$.
then $\om_L(\t) =_{def} L^X \ \cap \ \om(\t)$, the set of lsc
functions with image in $L$, is a fuzzy topology which is not laminated. Only the constants $k$ with $k \in L$
are in $\d$. Clearly, each
$\d = \om_L(\t)$ satisfies $\t = \i(\d)$ and is weakly induced, but is not, of course, induced. We sketch the proof of
the following extension of Proposition \ref{propa06} and Theorem \ref{theoa09} (a).
\begin{prop}\label{propa14} (a) Let $\d$ be a fuzzy topology and $L$ be the set of constants $k \in \d$.
If $\d$ is weakly induced, then $\d \cap L^X = \om_L(\i(\d))$.
(b) If $\t$ is a topology and $L$ is a sup-closed subset which contains $0$ and $1$ then $\om_L(\t)$ is generated
by $L \cup \chi(\t)$.
\end{prop}
{\bfseries Proof:} (a): Since $\d \subset \om(\i(\d))$ it is clear that $\d \cap L^X \subset \om_L(\i(\d))$.
Now adapt the Theorem \ref{theoa05} proof of (c) $\Rightarrow$ (d). Let $f \in L^X$ be lsc
with respect to $\i(\d)$. Call $c \in L$ a right endpoint if
$L \cap (c - \ep,c) = \emptyset$ for some $\ep > 0$, i.e. $c$ is a right endpoint of one of the maximum open subintervals of
$I \setminus L$. In that case, $f_{[c} \in \i(\d)$. For $c$ a right endpoint in $L$
let $f_c = c \wedge \chi_{f_{[c}}$. For the remaining $c \in L$ let $f_c = c \wedge \chi_{f_{(c}}$. As before,
$f = \bigvee_{c \in L} \ f_c \in \d$.
(b): The proof is the obvious analogue of that of Theorem \ref{theoa09} (a) using part (a) here in place of Theorem \ref{theoa05}.
$\Box$ \vspace{.5cm}
If $Y$ is a proper open subset of $X$ then we can extend any lsc function $f : Y \to I$ to an lsc function on
$X$ by letting $f(x) = 0$ for $x \in X \setminus Y$. Thus, we can include $\om(\t|Y) \subset \om(\t)$. If
$\d$ is the fuzzy topology on $X$ generated by $\om(\t|Y) \cup \chi(\t)$ then $\d = \{ f \vee \chi_U :
f \in \om(\t|Y), U \in \t \}$. Thus, $\d$ is a weakly induced fuzzy topology with $\t = \i(\d)$ and with
no constants other than $0$ and $1$.
(B) We say that a subinterval $J$ of $I$ is \emph{non-trivial} when it has positive length.
We say that two subintervals $J, L$ of $I$ are
\emph{non-overlapping} when their interiors are disjoint. When
$J$ and $L$ are non-overlapping then either $J \leq L$, meaning
$s \leq t$ for all $s \in J$ and $t \in L$, or else $L \leq J$.
Notice that if $J \leq L$ then for all $f \in J^X, g \in L^X$
\begin{equation}\label{11}
f \wedge g \ = \ f \qquad \mbox{and} \qquad f \vee g \ = \ g.
\end{equation}
Let $\J = \{ J_1, J_2,... \}$ be a finite or infinite sequence of
nontrivial, closed subintervals of $I$ with any two non-overlapping. For a set $X$
let
\begin{equation}\label{12}
\d_{\J} \ =_{def} \ I \ \cup \ \bigcup_{i = 1,2,...} \ J_i^X \ \subset \ I^X.
\end{equation}
where the $I$ in the union denotes the set of constants in $I$. From (\ref{11}) it follows that
$\d_{\J}$ is a fuzzy topology.
For example, if $\J = \{ I \}$ then $\d_{\J}(X) = I^X$.
For a topological space $(X,\t)$ let
\begin{equation}\label{13}
\om_{\J}(\t) \quad =_{def} \quad \d_{\J} \cap \om(\t).
\end{equation}
It is clear that any $\om_{\J}(\t)$ is
a laminated fuzzy topology. Furthermore, if $a, b \in J_1$ with $a < b$ then
for any $U \in \t, \ f = a \vee(b \wedge \chi_U) $
has image in $J_1$ and so lies in $\om_{\J}(\t)$. Also, $U = f_{(a}$. Thus, $\t = \i(\om_{\J}(\t))$.
If $\J $ is not $\{ I \}$, then $\om_{\J}(\t)$ is a proper subset of $\om(\t)$. In fact, for $U \in \t$,
$\chi_U \not\in \om_{\J}(\t)$ unless $U = X$ or $\emptyset$ in which case $\chi_U$ is constant.
Thus, $\chi^*(\om_{\J}(\t)) = \{ \emptyset, X \}$.
Furthermore, if $(X, \t) = \coprod_{k \in K} \ (X_k, \t_k)$ then we can choose a separate
sequence $\J_k$ for each $k \in K$ and define a laminated fuzzy topology on $X$ by using
$\coprod_{k \in K} \ \om_{\J_k}(\t_k)$.
Thus, we
obtain many examples of laminated fuzzy topologies each of which generates
$\t$ but which are not affine invariant.
(C) The real pathologies occur with products. Suppose $(X_1, \t_1)$ and $(X_2, \t_2)$ are topological spaces
and $(X, \t) = (X_1 \times X_2, \t_1 \times \t_2)$. On $X_1$ let $\d_1 = \om_{\{[0,1/2] \} }(\t_1)$ and on
$X_2$ let $\d_2 = \om_{\{ [1/2,1] \} }(\t_2)$. Using equation (\ref{11}) again it is easy to check that the union
\begin{equation}\label{14}
\d \ =_{def} \ \pi_1^* \d_1 \ \cup \ \pi_2^* \d_2
\end{equation}
already satisfies conditions (i'),(ii) and (iii) of Definition \ref{defa01}
and so is the product fuzzy topology.
By Proposition \ref{propa11}, $\i(\d)$ is the product topology $\t$. However, each element of $\d$ is a function depending on
either the first or the second variable alone. That is, each fuzzy set is horizontal or vertical.
(D) Finally, let $(X,\t)$ be a second countable topological space with $\B$ any countable subbase for $\t$.
Let $\J$ be a countably infinite set of nontrivial, closed subintervals of $I$ with any two non-overlapping,
e.g the closures of the components of the complement of the Cantor set. Let $\rho : \B \to \J$ be a
bijection. For $U \in \B $ we will write $ \rho(U) = [a(U),b(U)] $ so that $0 \leq a(U) < b(U) \leq 1$. Let
\begin{equation}\label{15}
\d_{\rho} \ =_{def} \ \{ c \vee (d \wedge \chi_U) : U \in \B \ \& \ a(U) \leq c < d \leq b(U) \} \cup I.
\end{equation}
Now $\d_{\rho}$ is a laminated fuzzy topology with $ \t = \i(\d_{\rho})$ but nonetheless
every element of $\d_{\rho}$ is just an affine adjustment of the characteristic function of a set in $\B$.
Hence,
\begin{equation}\label{16}
\{ f_{(c} : f \in \d_{\rho}, \ c \in I \} \ = \ \B \cup \{ X, \emptyset \}.
\end{equation}
If, in addition, $(X,\t)$ is connected then the constants are the only elements of $\d_{\rho}$ which are
continuous. Let $I$ be equipped with the usual topology $\t_I$
and the induced fuzzy topology $\d_I$. By Proposition \ref{propa10b} and the Remark thereafter,
if $H :(X,\d_{\rho}) \to (I,\d_I)$ is fuzzy continuous, then $H \in \d_{\rho}$. Furthermore, Theorem \ref{theoa10}(a)
implies that $H :(X,\t) \to (I,\t_I)$ is continuous.
Hence, the constant functions are the only fuzzy continuous maps from
$(X,\d_{\rho})$ to $(I,\d_I)$ when $(X,\t)$ is connected.
(E) Assume that $(X_1, \d_1)$ and $(X_2, \d_2)$ are fuzzy topological spaces and that
$\d_2$ is laminated.
Every constant $k \in \d_2$.
If $H : X_1 \to X_2$ is any fuzzy continuous function
then $k = H^*k \in \d_1$ and so $\d_1$ is laminated
as well. Thus, if $\d_1$ is not laminated, then there is no fuzzy continuous function from $(X_1,\d_1)$
to $(X_2,\d_2)$.
\vspace{1cm}
\section{Compactness}
From now on for topological spaces $X, Y$ etc, we suppress explicit labeling of the topology,
and equip each with the induced fuzzy topology, i.e. for $X$ with topology $\t$ we use the fuzzy topology
$\d = \om(\t)$, the set of lsc functions in $I^X$. We will call these the fuzzy open sets. Thus, $f$ is a fuzzy open
set if and only if $f_{(c}$ is open for every $c \in I$. On the other hand, $f$ is fuzzy closed when its complement $1 - f$ is fuzzy
open and so when
$f$ is usc. Thus, $f$ is a fuzzy closed set when
$f_{[c}$ is closed for every $c \in I$.
We turn now to compactness. Since we are not - yet - assuming the spaces are Hausdorff, a compact set
need not be closed though a closed subset of a compact set is compact.
Among the possible definitions for fuzzy compactness, we follow Weiss \cite{W75}
\begin{df}\label{defc01} Let $X$ be a topological space with the induced fuzzy
topology and let $f$ be a fuzzy set, i.e. $f \in I^X$.
\begin{enumerate}
\item[(a)] We say that $f$ is \emph{fuzzy compact} when $f_{[c}$ is compact for all $ c \in (0,1]$.
\item[(b)] We say that $f$ satisfies \emph{ Condition L} if whenever $\{ g_i : i \in K \}$ is an indexed
family of fuzzy open sets such that $\bigvee_{i \in K} \ g_i \geq f$ and $\ep > 0$ there
exists a finite $\hat{K} \subset K$ such that $\bigvee_{i \in \hat{K}} \ g_i \geq f - \ep$.
\end{enumerate}
\end{df}
\vspace{.5cm}
In the definition of fuzzy compactness we do not assume that $ f_{[0}$, which is all of
$X$, is compact. In particular, if $f$ is fuzzy closed and has compact support, i.e. the closure of $f_{(0}$
is compact, then $f$ is fuzzy compact. Thus, the value $0$ plays a special role and fuzzy compactness need not
be preserved by affine adjustments.
Condition L was introduced in Lowen \cite{L76} as a definition of compactness in the context of
general laminated fuzzy topologies.
\begin{lem}\label{lemc02} Let $f $ be a fuzzy subset of a topological space $X$. If for every
$c \in (0,1)$ the set $f_{[c}$ is compact, then $f$ satisfies
condition L. Furthermore, if $g$ is fuzzy closed and $g \leq f$, then $g$ is fuzzy compact.
\end{lem}
{\bfseries Proof:} To verify Condition L we begin with a family $\{ g_i : i \in K \}$ of fuzzy open
sets with $\bigvee_{i \in K} \ g_i \ \geq \ f$ and an arbitrary $\ep > 0$.
Let $1 = c_0 > c_1 > ... > c_{n} = 0$ be a decreasing sequence
in $I$ with $ c_{k-1} - c_k < \ep/2$ for $k = 1,.., n$.
The set $\{ (g_i)_{(c_k} : i \in K \}$ is an open cover of the compact set $f_{[c_{k-1}}$
for $k = 2,..., n$. Choose $K_k \subset K$ finite so the $\{ (g_i)_{(c_k} : i \in K_k \}$
is a subcover.
Let $\hat{K} = \bigcup_{k = 2,..,n} K_k$.
If for some $k = 2,...,n \ f(x) \in [c_{k-2},c_{k-1}] $ then $g_i(x) > c_k \geq f(x) - \ep $ for some $i \in K_k$.
If $f(x) \in (c_{n-1},c_n] $ then $f(x) - \ep < 0 \leq g_i(x)$ for any $i$.
Thus, as required $\bigvee_{i \in \hat{K}} \ g_i \geq f - \ep$.
Now if $g \leq f$ and $g$ is fuzzy closed, let $c \in (0,1]$. Choose $a$ so that $0 < a < c$. Observe that
$g_{[c}$ is a closed subset of $f_{[a}$ which is compact by assumption (since $a < 1$). Hence, $g_{[c}$ is compact.
$\Box$ \vspace{.5cm}
\begin{theo}\label{theoc03} Let $X$ be a topological space and let $f $ be a fuzzy subset of $X$.
\begin{enumerate}
\item[(a)] If $f$ is fuzzy compact then $f$ satisfies Condition L.
\item[(b)] If $f$ is fuzzy closed and satisfies Condition L then $f$ is fuzzy compact.
\end{enumerate}
\end{theo}
{\bfseries Proof:} (a): This follows from Lemma \ref{lemc02}.
(b): Assume that $f$ is fuzzy closed and satisfies Condition L.
Let $c \in (0,1]$ and choose $\ep \in (0,c)$.
Assume $\{ U_i : i \in K \}$ is an open cover of $f_{[c}$. Let $V = X \setminus f_{[c}$
which is open because $f$ is usc. Apply Condition L to $\{ \chi_V \} \cup \{ \chi_{U_i} : i \in K \}$ and $f$.
We obtain the finite set $\hat{K} \subset \{ V \} \cup K$. If $x \in f_{[c}$ then $\chi_V(x) = 0 < c - \ep \leq f(x) - \ep$. Hence, there
exists $i \in \hat K \setminus \{ V \}$ such that $ \chi_{U_i}(x) > f(x) - \ep \geq c - \ep > 0$. That is, $x \in U_i$. Hence,
$\{ U_i : i \in \hat{K} \} $ is a finite subcover of $f_{[c}$.
$\Box$ \vspace{.5cm}
In particular we have the following, due to Lowen, \cite{L76}.
\begin{cor}\label{corc04} For a topological space $X$ the following are equivalent.
\begin{itemize}
\item[(i)] X is compact.
\item[(ii)] The constant function $1$ is fuzzy compact.
\item[(iii)] Every fuzzy closed set is fuzzy compact.
\item[(iv)] There exists $k \in (0,1]$ such that the
constant function $k$ satisfies Condition L.
\end{itemize}
\end{cor}
{\bfseries Proof:} (i) $\Leftrightarrow$ (ii): Obvious
(ii) $\Rightarrow$ (iii): Any fuzzy closed set $f$ satisfies $f \leq 1$ and
so $f$ is fuzzy compact when $1$ is by Lemma \ref{lemc02}.
(iii) $\Rightarrow$ (iv): Every constant function $k$ is fuzzy closed and
so by (iii) it is fuzzy compact. Condition L follows from Theorem \ref{theoc03} (a).
(iv) $\Rightarrow$ (i): If $k$ satisfies Condition L then by Theorem \ref{theoc03} (b) it
is fuzzy compact and $X = k_{[k}$ is compact.
$\Box$ \vspace{.5cm}
\begin{cor}\label{corc05} Assume $X$ is a Hausdorff topological space and let $f \in I^X$.
If $f$ is fuzzy compact then
it is fuzzy closed. Furthermore, $f$ is fuzzy compact if and only if it satisfies Condition L.
If $X$ is compact Hausdorff then $f$ is fuzzy compact if and only if it is fuzzy closed.
\end{cor}
{\bfseries Proof}: If $f$ is fuzzy compact then for each $c > 0$, $f_{[c}$ is compact and
so is closed because $X$ is Hausdorff. $f_{[0} = X$ is always closed. Hence, $f$ is
fuzzy closed. In addition, Theorem \ref{theoc03}(a) implies that $f$ satisfies condition L. For the converse
it suffices by Theorem \ref{theoc03}(b) to show that if $f$ satisfies condition L then it is fuzzy closed.
We prove the contrapositive,
adapting the usual proof that a compact subset of a Hausdorff space is closed.
Suppose that $f(x) = a < c$ but that $x$ is in the closure $A$ of $f_{[c}$.
For each $z \in A' =_{def} A \setminus \{ x \}$ choose disjoint open sets $U_z, W_z$ with $z \in U_z$ and
$x \in W_z$. Let $V$ be the open set $X \setminus A$. Define :
\begin{equation}\label{17}
\begin{split}
\G_{in} \ =_{def} \ \{ \chi_{U_z} : z \in A' \ \} \hspace{4cm}\\
g_{in} = \bigvee \{ g \in \G_{in} \} \quad \mbox{and} \quad g_{out} = a \vee \chi_V. \quad \hspace{2cm}
\end{split}
\end{equation}
Choose $\ep < c - a$. Observe that $g_{out}$ and the elements of $\G_{in}$ are
fuzzy open. Furthermore, if $z \not= x$ then $(g_{out} \vee g_{in})(z) = 1$ and so $ g_{out} \vee g_{in} \geq f$.
On the other hand for every
$z \in f_{[c}$, we have $f(z) - \ep \geq c - \ep > a = g_{out}(z) $. So if
Condition L were true of $f$ then applying it to $\G_{in} \cup \{ g_{out} \}$ would yield
a finite subset $\hat{A} \subset A'$ such that
$\{ U_z : z \in \hat{A} \}$ covers $f_{[c}$. But for any finite
$\hat{A} \subset A', \ \bigcup \{ U_z : z \in \hat{A} \}$ is disjoint
from $\bigcap \{ W_z : z \in \hat{A} \}$ which is a neighborhood of $x$ and so contains points of
$f_{[c}$. Hence, $\{ U_z : z \in \hat{A} \}$ does not cover $f_{[c}$ and so Condition L fails.
Finally, if $X$ is compact then any fuzzy closed set is fuzzy compact by Corollary \ref{corc04}.
$\Box$ \vspace{.5cm}
The fuzzy Tychonoff Theorem now follows from the usual Tychonoff Theorem.
\begin{theo}\label{theoc06} Let $\{ X_i : i \in K \}$ be an indexed family of topological spaces with
product space $X = \prod_{i \in K} \ X_i$. Let $f_i$ be a fuzzy subset of $X_i$ for each $i \in K$
and define $f = \bigwedge_{i \in K} \ f_i \circ \pi_i$. If each $f_i$ is fuzzy compact, then
$f$ is fuzzy compact.
\end{theo}
{\bfseries Proof:} For each $c \in (0,1]$
\begin{equation}\label{18}
f_{[c} \quad = \quad \prod_{i \in K} \ (f_i)_{[c}. \hspace{3cm}
\end{equation}
That is, for $x \in X \ f(x) \ = \ inf_{i \in K} \ f_i(x_i) \ \geq \ c$ if and only if $f_i(x_i) \geq c$ for all $i \in K$.
As the product of compact spaces, $f_{[c}$ is compact.
$\Box$ \vspace{.5cm}
Clearly a fuzzy closed set with compact support is fuzzy compact. For $X = \R$
with the usual topology and induced fuzzy topology let $f(t) = exp(-t^2)$. The element $f$ is fuzzy compact
but does not have compact support.
For a locally compact, Hausdorff space $X$ let $X^* = X \cup \{ p \}$ denote the one-point compactification
so that $U \subset X^*$ is open if and only if $U \cap X$ is open and, in addition, $p \not\in U$ or
$X \setminus U$ is compact. $X^*$ is a compact Hausdorff space.
For $f \in I^X$ let $f^* \in I^{X^*}$ be the extension of $f$ with $f^*(p) = 0$. The following
is then obvious.
\begin{prop}\label{propc07} For a locally compact, Hausdorff space $X$ with one-point compactification $X^*$ a fuzzy set
$f \in I^X$ is a fuzzy compact set in $X$ if and only if the extension $f^* \in I^{X^*}$ is a fuzzy closed set in $X^*$.
\end{prop}
$\Box$ \vspace{.5cm}
{\bfseries Example:} (F) Let $X$ be the disjoint union of $(0,1]$ and a countable set $A$. Define a $T_1$, but not
Hausdorff, topology $\t$ on $X$
so that $U \in \t$ when $U \cap (0,1]$ is open and, in addition, either $U \cap A = \emptyset$ or else
$U \cap A$ is cofinite (i.e. has finite complement in $A$) and, in addition,
$(0,a) \subset U \cap (0,1]$ for some $a > 0$.
If $Y = B \cup (0,1] \subset X$ with $B \subset A$
then $Y$ is compact if and only if $B \not= \emptyset$. Choose $\{ B_n \}$ a strictly decreasing sequence of
cofinite subsets of $A$ with $B_0 = A$ and with empty intersection.
We obtain a decreasing sequence $Y_n = B_n \cup (0,1]$
of compact sets with intersection $Y = (0,1]$ noncompact. If $f(x) = 1 - 2^{-n}$ for $x \in B_n \setminus B_{n+1}$
and $f(x) = 1$ for $x \in (0,1]$, then $f$ is a fuzzy open set (not fuzzy closed), and for every $c \in (0,1), f_{[c}$ is compact. By Lemma \ref{lemc02}, Condition L holds, but $f$ is not compact because $f_{[1}$ is not compact.
$\Box$ \vspace{1cm}
\bibliographystyle{amsplain}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 88 |
Sorry for the lack of posts!! Our family has been traveling and we are finally settling down. I have some great boxes to review so I will be playing catch up in the next couple days. Please note that I will start fresh with this month.
For those who find my blog; my hope is you find these reviews useful. I welcome your comments! My goal is to make this blog into a useful source! | {
"redpajama_set_name": "RedPajamaC4"
} | 3,044 |
Q: R ggplot double y-axis, log10 and continuous This question was closed for no reason, the provided link to a similar question does NOT provide an answer for this specific problem.
How can I have two different plots in one graph, with two separate y-axis, and with different scales?
df <- data.frame(x=3:22,
y1=c(3, 4, 5, 7, 9, 13, 15, 19, 23, 24, 29,
38, 40, 50, 56, 59, 70, 89, 104, 130),
y2=c(1,2,3,4,4,5,5,6,6,7,6,5,5,5,4,4,3,3,2,1))
ylim.prim <- c(min(df$y1), max(df$y1))
ylim.sec <- c(min(df$y2), max(df$y2))
b <- diff(ylim.prim)/diff(ylim.sec)
a <- ylim.prim[1] - b*ylim.sec[1]
ggplot(df, aes(x=x)) +
geom_line(aes(y=y1))+
geom_line(aes(y = a + y2*b))+
scale_y_continuous(sec.axis = sec_axis(~ (. - a)/b))
So with this, I can plot a double y-axis, but I would like either the left or the right one to be in log-scale. Does anyone have an idea how to do that? I would like to highlight, that each axis belongs to one of the two geom_lines.
exemplary real data:
df<-structure(list(x = c(0.3499125, 8.347913, 16.34591, 24.34391,
32.34191, 40.33992, 48.33792, 56.33592, 64.33392, 72.33192, 80.32992,
88.32792, 96.32592, 104.3239, 112.3219, 120.3199, 128.3179, 136.3159,
144.3139, 152.3119, 160.3099, 168.3079, 176.3059, 184.3039, 192.3019,
200.2999, 208.2979, 216.2959, 224.2939, 232.2919, 240.2899, 248.2879,
256.2859, 264.2839, 272.2819, 280.2799, 288.2779, 296.2759, 304.2739,
312.2719, 320.2699, 328.2679, 336.2659, 344.2639, 352.2619, 360.2599,
368.2579, 376.2559, 384.2539, 392.2519, 400.2451, 408.0882, 415.9314,
423.7745, 431.7164, 439.6766, 447.6368, 455.597, 463.5572, 471.5174,
479.4776, 487.4378, 495.398, 503.3582, 511.3184, 519.2786, 527.2465,
535.234, 543.2215, 551.209, 559.1966, 567.1841, 575.1716, 583.1591,
591.1466, 599.1342, 607.1217, 615.1092, 623.0967, 631.0842, 639.0718,
647.0593, 655.0468, 663.0343, 671.0218, 679.0094, 686.9969, 694.9844,
702.9719, 710.9594, 718.947, 726.9345, 734.922, 742.9095, 750.897,
758.8846, 766.8721, 774.8596, 782.8471, 790.8346, 798.8222, 806.8097,
814.7972, 822.7847, 830.7722, 838.7598, 846.7413, 854.7015, 862.6617,
870.6219, 878.5821, 886.5423, 894.5025, 902.4627, 910.4229, 918.3831,
926.3433, 934.3035, 942.2637, 949.9737, 957.7313, 965.6915, 973.6517,
981.6119, 989.5721, 997.5323, 1005.493, 1013.453, 1021.413, 1029.373,
1037.333, 1045.294, 1053.254, 1060.905, 1068.657, 1076.5, 1084.343,
1092.245, 1100.232, 1108.22, 1116.207, 1124.195, 1132.183, 1140.17,
1148.158, 1156.145, 1164.133, 1172.12, 1180.108, 1188.095, 1196.083,
1204.07, 1212.058, 1220.045, 1228.033, 1236.02, 1244.008, 1251.995,
1259.983, 1267.97, 1275.958, 1283.945, 1291.933, 1299.92, 1307.908,
1315.895, 1323.883, 1331.871, 1339.858, 1347.846, 1355.833, 1363.821,
1371.808, 1379.796, 1387.783, 1395.771, 1403.758, 1411.683, 1419.488,
1427.293, 1435.234, 1443.214, 1451.195, 1459.175, 1467.155, 1475.135,
1483.115, 1491.095, 1499.075, 1507.055, 1515.035, 1523.015, 1530.995,
1538.975, 1546.955, 1554.935, 1562.915, 1570.895, 1578.875, 1586.855,
1594.835, 1602.815, 1610.796, 1618.776, 1626.756), y2 = c(2.27,
2.27, 2.27, 2.27, 2.27, 2.27, 2.27, 2.27, 2.27, 2.27, 2.27, 2.27,
2.27, 2.27, 2.27, 2.27, 2.27, 2.27, 2.27, 2.27, 2.27, 2.27, 2.27,
2.27, 2.27, 2.27, 2.27, 2.27, 2.27, 2.27, 2.27, 2.27, 2.27, 2.27,
2.27, 2.27, 2.27, 2.27, 2.27, 2.27, 2.27, 2.27, 2.27, 2.27, 2.27,
2.27, 2.27, 2.27, 2.27, 2.27, 2.300344, 2.300344, 2.300344, 2.300344,
2.356774, 2.356774, 2.356774, 2.356774, 2.356774, 2.356774, 2.356774,
2.356774, 2.356774, 2.356774, 2.356774, 2.356774, 2.35672, 2.35672,
2.35672, 2.35672, 2.35672, 2.35672, 2.35672, 2.35672, 2.35672,
2.35672, 2.35672, 2.35672, 2.35672, 2.35672, 2.35672, 2.35672,
2.35672, 2.35672, 2.35672, 2.35672, 2.35672, 2.35672, 2.35672,
2.35672, 2.35672, 2.35672, 2.35672, 2.35672, 2.35672, 2.35672,
2.35672, 2.35672, 2.35672, 2.35672, 2.35672, 2.35672, 2.35672,
2.35672, 2.35672, 2.35672, 2.436441, 2.436441, 2.436441, 2.436441,
2.436441, 2.436441, 2.436441, 2.436441, 2.436441, 2.436441, 2.436441,
2.436441, 2.436441, 2.593907, 2.436372, 2.436372, 2.436372, 2.436372,
2.436372, 2.436372, 2.436372, 2.436372, 2.436372, 2.436372, 2.436372,
2.436372, 2.436372, 2.32186, 2.362217, 2.362217, 2.362217, 2.356666,
2.356666, 2.356666, 2.356666, 2.356666, 2.356666, 2.356666, 2.356666,
2.356666, 2.356666, 2.356666, 2.356666, 2.356666, 2.356666, 2.356666,
2.356666, 2.356666, 2.356666, 2.356666, 2.356666, 2.356666, 2.356666,
2.356666, 2.356666, 2.356666, 2.356666, 2.356666, 2.356666, 2.356666,
2.356666, 2.356666, 2.356666, 2.356666, 2.356666, 2.356666, 2.356666,
2.356666, 2.356666, 2.356666, 2.356666, 2.6, 2.6, 2.6, 1.38,
1.38, 1.38, 1.38, 1.38, 1.38, 1.38, 1.38, 1.38, 1.38, 1.38, 1.38,
1.38, 1.38, 1.38, 1.38, 1.38, 1.38, 1.38, 1.38, 1.38, 1.38, 1.38,
1.38, 1.38), y1 = c(1.0121711505181e-12, 1.36703949435522e-12,
1.84632494858934e-12, 2.49364868526704e-12, 3.36792573591631e-12,
4.54872499912722e-12, 6.14351261535188e-12, 8.29743536886833e-12,
1.12065270336094e-11, 1.5135549574501e-11, 2.04420900737953e-11,
2.76091094527446e-11, 3.7288908764166e-11, 5.03624430409839e-11,
6.80195634790675e-11, 9.1867308143082e-11, 1.24076096081818e-10,
1.67577290537946e-10, 2.26330068874485e-10, 3.05681854075198e-10,
4.12854243103824e-10, 5.57601379152127e-10, 7.53097024416113e-10,
1.01713383727135e-09, 1.37374208059794e-09, 1.85537854367786e-09,
2.50587585968424e-09, 3.38443865549292e-09, 4.57102650080046e-09,
6.17363418887535e-09, 8.33811836170825e-09, 1.12614720154805e-08,
1.52097587979964e-08, 2.05423179929812e-08, 2.77444811472099e-08,
3.74717262176886e-08, 5.06093638045714e-08, 6.83530636095683e-08,
9.23177269923811e-08, 1.24684445803943e-07, 1.68399029805712e-07,
2.2743990730289e-07, 3.07180534936803e-07, 4.14878418164378e-07,
5.60335245682253e-07, 7.56789448222779e-07, 1.02212079550612e-06,
1.38047758295943e-06, 1.86447536195262e-06, 2.51816121915984e-06,
3.40041627253216e-06, 4.54641422109325e-06, 6.03834395349185e-06,
7.97982308417383e-06, 1.04817057864209e-05, 1.35489394526282e-05,
1.72865813618296e-05, 2.18309175451225e-05, 2.73477089217644e-05,
3.40380929265256e-05, 4.21460976943755e-05, 5.1967369819244e-05,
6.38600965206997e-05, 7.82579725998248e-05, 9.56860600237062e-05,
0.000116779922497502, 0.000142335963852117, 0.000173355233081032,
0.000210921169220437, 0.00025641423771755, 0.000311506843394084,
0.000378223660039666, 0.000459016772258694, 0.000556855446703318,
0.000675335852469291, 0.000818812559327979, 0.000992558463515475,
0.00120295979079978, 0.00145774933544351, 0.00176629223196222,
0.00213992675332361, 0.00259238540452746, 0.00314030080012767,
0.00380380663276417, 0.00460729241649197, 0.00558028623723877,
0.00675855195676351, 0.00818539089553454, 0.00991324940277193,
0.0120056289887936, 0.0145394320140841, 0.0176077795085524, 0.0213234607142798,
0.0258230276512022, 0.0312718588796218, 0.0378702107462816, 0.0458605985746323,
0.0555366906666179, 0.0672541473478419, 0.0814435879234418, 0.0986265500083953,
0.119434540978074, 0.144632361864515, 0.175146169178876, 0.212097172372404,
0.256843809691636, 0.310804466617569, 0.369842684226363, 0.431179045399307,
0.493945429064933, 0.557253598745863, 0.620207670785615, 0.681916748818428,
0.741507890725135, 0.7981374131588, 0.85100435722966, 0.899360296843544,
0.942521141956581, 0.979876115698495, 0.999812477868897, 0.972735811573507,
0.932054481163834, 0.885815978946983, 0.834672310063189, 0.779345135479752,
0.720614966194481, 0.659310357439126, 0.596295772938628, 0.532460446628508,
0.468704750726898, 0.405928059993783, 0.345016117261179, 0.286827900234236,
0.237623456225718, 0.19790417419609, 0.164452220923679, 0.136482929335078,
0.112955983834528, 0.0932654285994524, 0.0770066613579728, 0.0635815895825471,
0.0524963384973958, 0.0433430973402779, 0.0357851408660264, 0.0295444442412585,
0.0243914258497928, 0.0201365021470287, 0.0166231553258446, 0.0137221430720713,
0.0113267390267136, 0.00934882441245559, 0.00771563465768068,
0.00636709119593569, 0.00525358045912998, 0.00433414349100376,
0.00357495316102798, 0.00294808230359634, 0.00243046968641578,
0.00200307217108402, 0.00165016998349207, 0.00135877837976224,
0.00111817834219132, 0.000919518759694046, 0.000755491588934199,
0.000620062540625639, 0.000508249477581297, 0.000415939214900695,
0.000339735906332031, 0.000276836029518111, 0.000224925814050528,
0.000182095460069257, 0.000146769499059896, 0.000117648326182113,
9.36606547647744e-05, 7.39240003391358e-05, 5.77123463706654e-05,
4.44292627620613e-05, 3.35069132161542e-05, 2.30948965054054e-05,
1.35498521268301e-05, 6.6480335943903e-06, 3.22817353776792e-06,
1.56754636933548e-06, 7.6117394173847e-07, 3.69613102610182e-07,
1.79477797412926e-07, 8.71511930430619e-08, 4.23189904393637e-08,
2.05492170784783e-08, 9.97819224010812e-09, 4.84507812590914e-09,
2.3525233197402e-09, 1.1421808424864e-09, 5.54459053511967e-10,
2.69071150351853e-10, 1.30491713616467e-10, 6.32000285938001e-11,
3.05246463595271e-11, 1.46586964219514e-11, 6.95585084010912e-12,
3.218335275606e-12, 1.40934851021314e-12, 5.43057275709068e-13,
1.47366028903012e-13, 6.63775977550542e-15)), class = c("tbl_df",
"tbl", "data.frame"), row.names = c(NA, -205L))
plot:
ylim.prim <- c(min(df$y1), max(df$y1))
ylim.sec <- c(min(df$y2), max(df$y2))
b <- diff(ylim.prim)/diff(ylim.sec)
a <- ylim.prim[1] - b*ylim.sec[1]
ggplot(df, aes(x=x)) +
geom_line(aes(y=y1, color = "y1"))+
geom_line(aes(y = 10^(a+ y2*b), color = "y2")) +
scale_y_log10(sec.axis = sec_axis(~ (log(., 10.0) - a)/b,
breaks = 1:6 * 0.5, name = "y2")) +
coord_cartesian(
xlim = c(),
ylim=c(1e-10,3))+
scale_color_brewer(palette = "Set1", name = NULL) +
theme_minimal(base_size = 16) +
theme(axis.line.y.left = element_line(color = "#E41A1C"),
axis.line.y.right = element_line(color = "#377EB8"),
axis.line.x.bottom = element_line("gray"),
axis.text.y.left = element_text(color = "#E41A1C"),
axis.text.y.right = element_text(color = "#377EB8"))
A: Showing which line belongs to which axis is simple enough by using colored theme elements and mapping each line to a color aesthetic.
The y1 series is approximately linear if we switch to scale_y_log10, which is also easy to do.
The difficult part is trying to get the second series mapped to a linear continuous axis when the primary axis is log scaled. To do this, we need to use the value of the second series as an exponent of some small number, chosen so that the scales of the two lines are approximately equal on your plot. We then need to take the log to the same base as part of our transformation in the secondary axis. In your case, 1.03 gives reasonable results:
ggplot(df, aes(x=x)) +
geom_line(aes(y=y1, color = "y1"))+
geom_line(aes(y = 1.05^(a + y2*b), color = "y2")) +
scale_y_log10(sec.axis = sec_axis(~ (log(., 1.03) - a)/b,
breaks = 1:4 * 2.5, name = "y2")) +
scale_color_brewer(palette = "Set1", name = NULL) +
theme_minimal(base_size = 16) +
theme(axis.line.y.left = element_line(color = "#E41A1C"),
axis.line.y.right = element_line(color = "#377EB8"),
axis.line.x.bottom = element_line("gray"),
axis.text.y.left = element_text(color = "#E41A1C"),
axis.text.y.right = element_text(color = "#377EB8"))
You can see that y1 is plotted on a log axis, but y2 is on a normal continuous axis.
As a caveat here, secondary axes are often frowned upon in data visualization, and having one axis on a log scale with the other being non-log is likely to make the plot very difficult for your audience to interpret.
Edit
A more general approach would be to log transform the series on the primary axis and transform its labels too. This allows using a continuous axis rather than log axis:
a <- range(log10(df$y1))
b <- range(df$y2)
ggplot(df, aes(x=x)) +
geom_line(aes(y=(log10(y1) - a[1])/diff(a), color = "y1"))+
geom_line(aes(y = (y2 - b[1])/diff(b) , color = "y2")) +
scale_y_continuous(
labels = ~ 10^(. * diff(a) + a[1]),
breaks = (pretty(log10(df$y1)) - a[1])/diff(a), name = "y1",
sec.axis = sec_axis(~ diff(b) * . + b[1], name = "y2")) +
scale_color_brewer(palette = "Set1", name = NULL) +
theme_minimal(base_size = 16) +
theme(axis.line.y.left = element_line(color = "#E41A1C"),
axis.line.y.right = element_line(color = "#377EB8"),
axis.line.x.bottom = element_line("gray"),
axis.text.y.left = element_text(color = "#E41A1C"),
axis.text.y.right = element_text(color = "#377EB8"))
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 119 |
PROJECT ?= cthulhu666/docker-rbenv
TAG ?= latest
ifdef REGISTRY
IMAGE=$(REGISTRY)/$(PROJECT):$(TAG)
else
IMAGE=$(PROJECT):$(TAG)
endif
build: Dockerfile
docker build -t $(IMAGE) .
| {
"redpajama_set_name": "RedPajamaGithub"
} | 39 |
\section{Introduction}
We study a scheduling problem
where a set $ J = \{1,\ldots,n\} $ of $n$
jobs with processing time~\mbox{\(p_j\in \mathbb{N}\setminus\{0\}\)} for each \(j \in J \)
needs to be processed by a set \(M = \{1,\ldots,m\} \) of $m$ identical parallel machines
without pre-emption.
The problem is to find an assignment of jobs to machines and a sequence
of the jobs on each machine such that some objective function \(\sum_{j \in
J}f_{j}(C_{j})\) is minimized, where $C_j$ is the completion time of $j\in J$.
We focus on parallel machine scheduling with a \textit{regular} objective function, i.e., for which \(f_{j}\) is non-decreasing for all \(j
\in J\). Moreover, we require that there exists an optimal solution without idle
time between the jobs on each machine. Scheduling with weighted completion-time objective
\(Pm||\sum w_j C_j \) is such a problem, where each job~$j$ has a weight \(w_{j}\). For this objective
the sequencing on each machine is easy (there exists a canonical sequence that can be followed),
so that the difficulty only resides in finding
an optimal division of the jobs over
the machines. Another common scheduling objective
is the weighted tardiness,
where each job \(j\) also has a due date~\(d_{j}\) and
the cost \(f_{j}(C_{j})\) associated with job \(j\) is \(w_{j}T_{j}\)
with \(T_{j} = \max \{0,C_{j} - d_{j}\} \). Since the one-machine case $1|| \sum w_j T_j $ is strongly NP-hard \citep{lawler1977pseudopolynomial}, unless \mbox{P = NP} there is no canonical order of jobs on a machine such that the
weighted-tardiness scheduling problem could reduce to partitioning jobs over the machines, and a different approach is needed.
In the remainder of the paper, we only consider
this weighted-tardiness objective, but the developed method will be generic and other regular objective functions without idle time can
be treated analogously.
The main goal of this paper is to introduce a new flow-based formulation
for \(Pm||\sum w_j T_j \).
We
first discuss some related work in Section~\ref{sec:def}.
Our formulation is based on a time
discretization of the planning horizon that was introduced
by~\cite{baptiste2009scheduling}, which we summarize in Section~\ref{sec:timehorizon}.
To the best of our knowledge, we are the first to apply a formulation with a coarser time discretization than the classical time-indexed
formulation (TIF) to a parallel machine scheduling problem.
The formulation itself is presented in
Section~\ref{sec:form}, and is derived from a binary decision diagram (BDD) that represents all the possible job
sequences on a machine. We show that the LP relaxation of this new integer
linear formulation yields a stronger lower bound than the TIF.
Our new formulation has many variables and
constraints, which renders
the computation of the
LP bound inefficient; we apply a Dantzig-Wolfe (DW)
decomposition to resolve this issue. This reformulation is discussed in Section~\ref{sec:DW}.
We also need to overcome some
convergence problems in the column generation (CG) phase,
which is achieved using the stabilization technique of~\cite{wentges1997weighted} and by variable fixing by reduced cost
as described in~\cite{pessoa2010exact}.
The running times of the CG phase for the new formulation are
much lower than
those for the arc-time-indexed formulation (ATIF),
which was introduced independently
by \cite{sourd2009new}, \cite{pessoa2010exact}, and \cite{tanaka2009exact}. At the same time, we find the quality of
the lower bounds from the new formulation to be very similar to that of the ATIF in our experiments.
In Section~\ref{sec:strongbranching} we develop a branch-and-price (B\&P) algorithm to find optimal integer solutions,
in which we use an aggressive
strong branching strategy to establish optimality of primal solutions.
We report on a series of computational experiments
in Section~\ref{sec:compexp}, including a comparison with the current state-of-the-art procedure of \cite{oliveira2020improved}.
We conclude the paper in Section~\ref{sec:conclusion}.
\section{Related work}\label{sec:def}
The most popular exact methods for single and parallel machine scheduling use Dynamic Programming (DP), Branch-and-Bound (B\&B)
including Mixed-Integer Programming (MIP) formulations that are
solved by a solver, or a mix of those two techniques.
The most popular MIP formulations in the literature are based
on completion variables, (arc-) time-indexed variables, linear ordering
variables, and positional and assignment variables. Below, we discuss
formulations with time-indexed and arc-time-indexed variables.
For an
extensive introduction to other formulations, we refer
to~\cite{queyranne1994polyhedral}.
\subsection{Time-indexed formulation TIF}
The TIF has been thorougly studied
by, among others, \cite{dyer1990formulating}, \cite{sousa1992time}, and \cite{van1999polyhedral}. With integer
processing times \(p_j\), a sufficiently large
planning horizon \(T\) can be discretized into periods of unit length. Binary
variables \(y_{jt}\) are defined for each job \(j \in J\) and each period \(t
\in \{1,\ldots,T\} \) to decide whether job~\(j\) starts at the beginning of
period \(t\) or not, where period \(t\) starts at time~\(t - 1\) and ends at~\(t\).
The model can be used to represent many different single and parallel
machine scheduling problems (esp.\ with min-sum objective) by adjusting the
cost parameters
\(\widetilde{c}_{jt}\).
\begin{subequations}\label{eq:TIform}
\begin{align}
\text{minimize } & \sum_{j \in J}\sum_{t = 1}^{T - p_{j} + 1} \widetilde{c}_{jt}y_{jt} \label{eq:objTI} \\
\text{subject to } & \sum_{t = 1}^{T - p_{j} + 1} y_{jt} = 1 & \, & \forall j \in J \label{eq:assTI} \\
& \sum_{j \in J}\sum_{s = \max\{ 1, t - p_{j} + 1\}}^{t} y_{js} \le m & \, & \forall t \in \{1,\ldots,T\} \label{eq:TInummachines} \\
& y_{jt} \in \{0,1\} & \, & \forall j \in J,\, t\in \{1,\ldots,T\} \label{eq:TIvar}
\end{align}
\end{subequations}
With Constraints~\eqref{eq:assTI} we ensure that every job starts exactly once, while
Constraints~\eqref{eq:TInummachines} impose that at most \(m\) jobs
can be processed in any period. Extra constraints such as release times \(r_{j}\) for
each job \(j \in J\) can be easily modeled by deleting the variables for which
\(t \in \{1,\ldots,r_{j}\} \).
Solutions to Equations~(\ref{eq:TInummachines}) and~(\ref{eq:TIvar})
can be represented as a flow in a directed acyclic graph (DAG) where the nodes are
associated to the starting period~\(t\) of the jobs and the edges \((t, t +
p_{j})\) are associated to a job \(j\) that starts in period \(t\) and ends in
period \(t + p_{j}-1\). A unit flow from the root node (first period) to the terminal
node (last period) is called a \emph{pseudo-schedule}. A flow satisfies the last
two equations of Formulation~(\ref{eq:TIform}) but not necessarily the
assignment constraints~\eqref{eq:assTI} and hence there can be pseudo-schedules where two or more edges associated to the same job are
chosen.~In~Figure~\ref{fig:TI} we provide an
optimal integral solution to an instance with \(n = 4\) and \(m = 2\), and with the job data given in Table~\ref{table:instancebdd}. For problem
\(Pm||\sum w_{j}T_{j}\) the time horizon~\(T\) can be chosen as
\(\lceil (\sum_{j \in J} p_{j} - p_{\max})/m \rceil + p_{\max}\) without
losing all optimal solutions, where \(p_{\max}\) is the maximum processing time
\citep[see, for instance,][]{pessoa2010exact}. In this way we obtain
\(T = 11\) as a safe upper bound for the time horizon of the instance.
\begin{figure}[t]
\begin{center}
\includegraphics[width=0.8\textwidth]{figures/TIexample-new.tex}
\caption{An integral solution to the TIF represented
as two paths in the DAG}\label{fig:TI}
\end{center}
\end{figure}
\begin{table}[t]
\centering
\caption{Job data for the example instance
\label{table:instancebdd}}{
\pgfplotstabletypeset[
col sep=comma,
display columns/0/.style={column name={job \(j\)},string type},
display columns/1/.style={column name=\(p_{j} \)},
display columns/2/.style={column name=\(d_{j} \)},
display columns/3/.style={column name=\(w_{j} \)},
every head row/.style={before row={\toprule}, after row={\midrule}},
every last row/.style={after row=\bottomrule},
]{data/instancebdd.csv}
}{}
\end{table}
The TIF is known to have a strong LP bound \citep{dyer1990formulating}, but this strength comes at a cost:
the length of the planning horizon
is pseudo-polynomial in the size of the instance input, i.e., the number of
constraints and variables depends on the number of jobs and on the processing
times. Hence, the TIF is less applicable for instances with many jobs and large processing times,
and one cannot always compute the LP relaxation in a
reasonable amount of time. Many specialized techniques have been developed to
overcome this issue; \cite{van2000time}, for instance, use CG to compute the LP relaxation of the TIF\@. Even using CG, solving the LP relaxation can be slow,
because the CG phase can suffer from the heading-in effect (when the first iterations of the CG produce irrelevant columns and bad dual
bounds because of the bad dual information), and extreme degeneracy (multiple optimal solutions in the dual and hence the solution of the
restricted master remains constant over several iterations). To cope with this
problem, various approaches were proposed; we refer to \cite{bigras2008time}, \cite{pan2007equivalence}, \cite{sadykov2013column}, and \cite{pessoa2018automation}.
We also note that the TIF can still leave a large duality
gap and hence exact algorithms may need to explore a large B\&B tree. Many polyhedral studies of the TIF were therefore performed, see for
instance \cite{crama1996scheduling}, \cite{sousa1992time}, and \cite{van1999polyhedral}.
\subsection{Arc-time-indexed formulation ATIF}
The ATIF can be seen as an
extended formulation of the TIF\@. The number of variables is a
factor of \(n\) larger than in TIF\@.
Let \(x_{ij}^{t} \in \{0,1\}\) be variables for
each pair of jobs \(i,j \in J_{+}\), with \(i \neq j\), \(J_{+} =
\{0,1,\ldots,n\} \) and \(p_{0} = 0\), and each \(t \in \{0,\ldots,T\} \). The
variables \(x_{ij}^{t}\) indicate whether or not job \(i\) completes and job \(j\) starts
at time \(t\) on some machine. Let \( \overline{c}_{jt}\) be the cost of starting job \(j\) at time~\(t\) (so $\overline{c}_{jt} = \widetilde{c}_{j,t+1}$).
\begin{subequations}\label{eq:aTIform}
\begin{align}
\text{minimize } & \sum_{i \in J_{+}} \sum_{j \in J\setminus \{i\}} \sum_{t = p_{i}}^{T - p_{j}} \overline{c}_{jt}x_{ij}^{t} \label{eq:objaTI} & & \\
\text{subject to } & \sum_{i \in J_{+}\setminus \{j\}}\sum_{t = p_{i}}^{T - p_{j}} x_{ij}^{t} = 1 & \, & \forall j \in J \label{eq:assaTI} \\
& \sum_{\substack{j \in J_{+}\setminus \{i\} \\ t - p_{j} \ge 0}}x_{ji}^{t} - \sum_{\substack{j \in J_{+}\setminus \{i\} \\ t + p_{i} + p_{j} \le T}} x_{ij}^{t + p_{i}} = 0 & \, & \forall i \in J,\,t \in \{0,\ldots,T - p_{i}\} \label{eq:aTIflow} \\
& \sum_{\substack{j \in J_{+} \\ t - p_{j} \ge 0}}x_{j0}^{t} - \sum_{\substack{j \in J_{+}\\ t + p_{j} + 1 \le T}} x_{0j}^{t + 1} = 0 & \, & \forall t \in \{0,\ldots,T - 1\} \label{eq:aTIidle}\\
& \sum_{j \in J_{+}} x_{0j}^{0} = m & \, & \label{eq:aTIcap} \\
& x_{ij}^{t} \in \mathbb{N} & \, & \forall i \in J_{+},\, j\in J_{+}\setminus \{i\},\nonumber \\
& & & t\in \{p_{i},\ldots,T - p_{j}\} \label{eq:aTIvar} \\
& x_{00}^{t} \in \mathbb{N} & \, & \forall t\in \{0,\ldots,T - 1\} \label{eq:aTIvar0}
\end{align}
\end{subequations}
Equations~\eqref{eq:aTIflow},~\eqref{eq:aTIidle}, and~\eqref{eq:aTIcap} together with the redundant equation
\begin{equation}
\sum_{i \in J_{+}} x_{i0}^{T} = m
\end{equation}
model a network flow of \(m\) units over a layered DAG\@.
Since each flow over this network has the same source and destination node, we
can decompose any integral solution into a set of \(m\) paths that correspond to
peudo-schedules.
Constraint~\eqref{eq:aTIidle} models the possibility of idle time in the
solution. With Constraint~\eqref{eq:assaTI} we impose that each job has to be
visited by exactly one path and as a result, each job is assigned to
exactly one machine. \cite{sourd2009new}, \cite{tanaka2009exact}, and \cite{pessoa2010exact}
proposed this formulation independently. \cite{pessoa2010exact} develop a branch-cut-and-price algorithm
to solve the ATIF, so as to handle the
large number of variables, and point out that the ATIF is almost isomorphic to the arc-capacity formulation for the Vehicle
Routing Problem and hence many inequalities for the latter formulation
could be transposed.
\citeauthor{pessoa2010exact} show that these valid
inequalities can close the gap between a heuristic solution and the LP
bound provided by the relaxation of the ATIF\@.
They also show that the ATIF is
stronger than the TIF, which mainly stems from the fact that direct
repetitions of jobs are forbidden by excluding variables \(x_{jj}^{t}\). One can easily project every solution \(\bar{x}\) of the linear
relaxation of~\eqref{eq:aTIform} onto a solution \(\bar{y}\) of the linear
relaxation of~\eqref{eq:TIform} by setting \(\bar{y}_{jt} = \sum_{i \in
J_{+}\setminus \{j\} } \bar{x}_{ij}^{t-1}\) for \(j \in J\) and \(t \in \{1,\dots,T - p_{j}+1\} \).
Moreover, simple dominance rules can be applied to the DAG by
omitting the variables \(x_{ij}^{t}\) if permuting jobs \(i\) and~\(j\) at
time~\(t\) decreases the overall cost.
\cite{oliveira2020improved} continued and refined the work of \cite{pessoa2010exact}, and their procedure constitutes the current state-of-the-art benchmark for \(Pm||\sum w_j T_j \).
An example of the network for the ATIF corresponding to the instance
described in Table~\ref{table:instancebdd} is given in Figure~\ref{fig:arcTI}.
The paths in this solution correspond to schedules \((2,1,0,0,0)\) and
\((4,3,0,0,0)\) on one machine, where each $0$ stands for a unit of idle time. In terms of the variables \(x_{ij}^{t}\) of formulation~\eqref{eq:aTIform},
this solution corresponds with
\(x_{02}^{0}=x_{04}^{0}=x_{43}^{4}=x_{21}^{6}=x_{10}^{8}=x_{30}^{8}=1\),
\(x_{00}^{9} = x_{00}^{10} = x_{00}^{11} = 2\), and the other variables
equal \(0\).
\begin{figure}[t]
\includegraphics[width=0.8\textwidth]{figures/arcTIexample.tex}
\caption{Example of an integral solution of the ATIF represented
as paths in the DAG, where each edge from job \(i\)
to job \(j\) that arrives in column \(t\) corresponds to variable
\(x_{ij}^{t}\)}\label{fig:arcTI}
\end{figure}
\section{Discretization of the time horizon}\label{sec:timehorizon}
To cope with the large number of variables in formulations based on a discretization of the time horizon as encountered by TIF and ATIF,
one can resort to a coarser discretization of time.
This is the underlying idea behind the models that were proposed
by~\cite{baptiste2009scheduling} and \cite{boland2016bucket} for single machine
scheduling.
~\cite{boland2016bucket} introduced the bucket-indexed formulation (BIF)\@. Like the TIF, this
formulation partitions the planning horizon into periods of equal lengths but the length of the periods in the BIF is a
parameter, and can be as long as the
processing time of the shortest job. The BIF is equivalent to the TIF if the length of the shortest job is one, but the number
of variables can reduce significantly if the length is larger than \(1\). For a good comparison between the BIF and TIF for single machine scheduling, we refer
to~\cite{boland2016bucket}.
Another formulation that uses a coarser time discretization is the
\textit{interval-indexed model}, which was introduced for single machine scheduling
by~\cite{baptiste2009scheduling}, who partition the planning horizon into time
intervals
that are defined by a proper
superset of the release dates, due dates, and deadlines of all jobs. \citeauthor{baptiste2009scheduling} show that
there exists an optimal schedule
where the jobs assigned to a time interval are sequenced according to a modified
weighted shortest-processing-time rule.
We first need the following definition: a \emph{partition} \(\mathcal{I}\) of order~\(q\) of the time horizon is a set of time
intervals \(I_{r}\) given by \(\interval[open left]{e_{r - 1}}{e_{r}}\) with
\(e_{0} = 0\), \(e_{q} = T\), and \(r \in Q = \{1,\ldots,q\} \). We say that a
partition is based on due dates if every \(d_{j}\) equals some~\(e_{r}\),
i.e., \( \{d_{1},\ldots,d_{n}\} \subseteq {\{ e_{r}\}}_{r \in Q} \). A job \(j\) is
assigned to interval \(I_{r}\) if its completion time \(C_{j}\) is
in~\(I_{r}\). A job \(j\) is on time in interval \(I_{r}\) if \(d_{j} \ge
e_{r}\) and late if \(d_{j} \le e_{r - 1}\).
Next we define for each interval \(I_{r}\) of \(\mathcal{I}\) a permutation
\(\sigma_{r}\) of \( \{1,\ldots,n\} \), and \(\sigma \) is the set of all
permutations \(\sigma_{r}\) with \(r \in Q\). We say that \(\sigma \) is an \emph{appropriate} set of
permutations for \(\mathcal{I}\) if there exists an optimal schedule in which,
for any interval \(I_{r} \in \mathcal{I}\) and any two jobs \(i,j \in J\)
assigned to the same machine and the same interval~\(I_{r} \), job \(i\) is sequenced
before job~\(j\) when \(\sigma_{r}(i) < \sigma_{r}(j)\).
For the problem \(Pm||\sum
w_j C_j \), for example, there exists a partition of
order~\(1\) with \(I_{1} = \interval[open left]{0}{T}\), where the appropriate
permutation \(\sigma_{1}\) corresponds to Smith's rule, i.e., the jobs are
sequenced in non-increasing order of the ratios \(\frac{w_{j}}{p_{j}}\). Other
problems with a similar priority rule are \(Pm||\sum w_j U_j \) and
\(Pm||\sum w_j V_j \), where function~\(U_{j}\) indicates whether job~\(j\) is late
or not, while \(V_{j} = \min \{p_{j}, \max \{0,C_{j} - d_{j}\} \} \) represents
the portion of work of job~\(j\) that is performed after its due date
\citep[see][]{van1999parallel}.
We say that a partition \(\mathcal{I}\) is \emph{appropriate} if it is possible to
compute an appropriate set of permutations for the partition
in polynomial time.~\cite{baptiste2009scheduling} show how to find an
appropriate partition for a large number of single machine
problems, and the same approach can be applied to parallel machines
because we need canonical sequences on each machine
separately. We follow \cite{baptiste2009scheduling}
for the construction of an appropriate partition of the time
horizon. Since we consider \(Pm||\sum w_j T_j \), our partition is based on
the due dates \(d_{j}\). Denote by \(\sigma \) a set of permutations for such
a partition; \(\sigma \)~will satisfy an adaptation of
the Weighted Shortest Processing Time (WSPT) and Longest Processing Time (LPT)
rule:
first all the late jobs are processed
following WSPT (Smith's) rule and then all the on-time jobs are processed
according to the LPT rule. We also demand that all the late jobs with the
same WSPT ratio be ordered according to the LPT rule. We will make a
distinction between \emph{long} and \emph{short} jobs of an interval \(I_{r}\). A job \(j\)
is long in interval \(I_{r}\) if \(p_{j} \ge e_{r} - e_{r - 1}\), and short
if \(p_{j} < e_{r} - e_{r - 1}\). We demand that all long
jobs of interval \(I_{r}\) appear first in \(\sigma_{r}\), meaning
that if \(p_{i} \ge e_{r} - e_{r - 1}\) and \(p_{j} < e_{r} - e_{r- 1}\) then
\(\sigma_{r}(i) < \sigma_{r}(j)\); note that at most one long job can effectively be assigned to $I_r$. For each pair of short jobs \(i,j\) of
interval \(I_{r}\) we require:
\begin{itemize}
\item if job \(i\) is late in \(I_{r}\) and job \(j\) is on time in \(I_{r}\) then \(\sigma_{r}(i) < \sigma_{r}(j)\),
\item if jobs \(i\) and \(j\) are on time and \(p_{i} > p_{j}\) then \(\sigma_{r}(i) < \sigma_{r}(j)\),
\item if jobs \(i\) and \(j\) are late and \(\frac{p_{i}}{w_{i}} < \frac{p_{j}}{w_{j}}\) then \(\sigma_{r}(i) < \sigma_{r}(j)\),
\item if jobs \(i\) and \(j\) are late, \(\frac{p_{i}}{w_{i}} = \frac{p_{j}}{w_{j}}\), and \(p_{i} > p_{j}\) then \(\sigma_{r}(i) < \sigma_{r}(j)\).
\end{itemize}
This set of rules was devised in~\cite{baptiste2009scheduling}. The LPT rule is merely
a tie-breaker. These rules for each partition are ``almost''
enough to be an appropriate set of permutations for a partition based on due
dates:
there is
always an optimal solution that satisfies the rules in \(I_{r}\) for each \(r
\in \{1,\ldots,q\} \) except for maybe one job \(j\), and this exception takes
place only if the job \(j\) is late in \(I_{r}\) and is completed first in
\(I_{r}\).
Based on this observation, the following theorem was derived:
\begin{theorem}[\citealp{baptiste2009scheduling}]\label{th:bapsad}
A partition \(\mathcal{I} = {\left \{I_{r} \right \}}_{r \in Q}\) is \emph{appropriate} if, for each \(r \in Q\) and each pair of jobs \(i,j \in J\) such that \(\sigma_{r}(i) < \sigma_{r}(j)\), at least one of the following conditions holds:
\begin{align}
e_{r} & \le e_{r - 1} + p_{j}\label{eq:bapsad1} \\
e_{r - 1} & \ge d_{i} + \left\lceil \frac{w_{j}p_{i}}{w_{i}}\right\rceil - p_{i}\label{eq:bapsad2}
\end{align}
\end{theorem}
We can start with a partition \(\mathcal{I}\) for which
\( \{d_{1},\ldots,d_{n}\} = \{e_{1},\ldots,e_{q}\} \), i.e., a partition based on
due dates with the smallest number of intervals. By dividing some
intervals, we can obtain a partition that satisfies the conditions of
Theorem~\ref{th:bapsad}. \cite{baptiste2009scheduling} construct an algorithm
that finds such a partition
for single machine problems.
\cite{clement2015mixed} later showed that the algorithm provided in \cite{baptiste2009scheduling} provides an appropriate partition but not always a partition with a minimum number of intervals. \cite{clement2015mixed} presents a method to construct an appropriate partition with a minimum number of intervals; we use his procedure in our implementation.
For the instance in Table~\ref{table:instancebdd},
an appropriate partition
is given by \( I_{1} =
\interval[open left]{0}{4}\), \(I_{2} = \interval[open left]{4}{6}\), \(I_{3} =
\interval[open left]{6}{8}\), and \(I_{4} = \interval[open left]{8}{11}\). The set of
permutations \(\sigma~\) is \(\sigma_{1} = (2,3,4,1)\), \( \sigma_{2} =
(2,3,4,1)\), \( \sigma_{3} = (2,3,4,1)\), and \(\sigma_{4} = (4,2,3,1)\). Clearly, none of the intervals contains a ``special'' pair of jobs, i.e., a pair that does not satisfy the requirements of Theorem~\ref{th:bapsad}.
\section{BDD-based formulation for parallel machine scheduling}\label{sec:form}
\cite{baptiste2009scheduling} present a MIP formulation for single machine problems based on
the ideas in the previous section, with binary variables for the assignment of jobs to intervals, which might also be generalized to parallel machines. In this work we follow a different approach: we will
use the partition of the time horizon described by \citeauthor{baptiste2009scheduling} to develop a new network-flow-based
formulation.
We will construct a binary decision diagram (BDD) over
which at most \(m\) units of flow are pushed; each unit flow from the root node to the
terminal node will represent a pseudo-schedule.
\subsection{Introduction to BDDs}
BDDs are data structures that allow to represent and manipulate families of
sets that can be linearly ordered. BDDs were introduced
in~\cite{lee1959representation} and~\cite{akers1978binary} as DAGs that are obtained by reducing binary decision trees that
represent
a Boolean
function. Recently, decision diagrams have also been used to
solve discrete optimization problems.
\cite{bergman2016discrete}, for instance, introduce a generic B\&B algorithm for discrete optimization,
where relaxed BDDs are used to compute
relaxation bounds and restricted BDDs are used to find feasible solutions.
Another relevant example is \cite{cire2013multivalued}, who use multi-valued decision diagrams to
solve single machine scheduling problems. We refer to \cite{CastroCireBecksurvey} for a survey of recent advances in the use of decision diagrams for
discrete optimization.
Concretely, a BDD \(B\) is a DAG that has two terminal nodes called
\(\mathbf{1}\) and \(\mathbf{0}\). Every non-terminal node \(i\) is
associated to an element v\((i)\) (the label of node \(i\)) of a set and has two
outgoing edges: the high edge, which points to the high child node hi\((i)\),
and the low edge, pointing to the low child node lo\((i)\). There is also
exactly one node that is not a child of any other node in the DAG\@; this node
is the "highest" node in the topological ordering of the DAG and is called the root
\(\mathbf{r}\). The size of the BDD can be reduced by removing every node whose high
edge points to the terminal node \(\boldsymbol{0}\) and the incoming edges of
the deleted node are connected to the end node of the low edge.
We describe how a subset \(S\) of a ground set \(V\) induces a path \(P_{S}\) from the root
node to \(\boldsymbol{1}\) in a BDD \(B\). We start at the root node of \(B\)
and iteratively choose the next node in the path as follows: if \(a\) is the
current node on the path, then the next node on the path is hi\((a)\) if
v\((a)\) \(\in S\) and lo\((a)\) otherwise. We call the last node along the path
\(P_{S}\) the output of \(S\) on~\(B\), which is denoted by \(B(S)\); clearly
\(B(S)\) is equal to \(\boldsymbol{1}\) or \(\boldsymbol{0}\). We say that \(B\)
accepts \(S\) if \(B(S) = \boldsymbol{1}\), otherwise we say that \(B\) rejects \(S\). A BDD
\(B\) characterizes a family \( \mathcal{F} \subset 2^{V}\) if \(B\) accepts all
the sets in the family \(\mathcal{F}\) and rejects all the sets not in
\(\mathcal{F}\).
Since we are only interested in paths from the root node to
the terminal node \(\boldsymbol{1}\), without loss of generality, we can
represent the BDDs without terminal node \(\boldsymbol{0}\).
One can construct a BDD
associated to a family of subsets in
different ways. In this work we use the efficient and generic recursive framework
of~\cite{iwashita2013efficient}.
Below we show how to define a
restricted family of pseudo-schedules, which is recursively constructed, based on
the interval-indexed model
of~\cite{baptiste2009scheduling}.
\subsection{Constructing a BDD that contains all feasible sequences} \label{sec:constructBDD}
Let \(\mathcal{I} = \{I_{1},\ldots,I_{q}\} \) be an appropriate partition of the
time horizon and \(\sigma = \{\sigma_{1},\ldots,\sigma_{q}\} \) the set of
permutations associated to \(\mathcal{I}\). Each \(\sigma_{r}\) imposes an
ordering \(\prec_{r} \) of the jobs in interval~\(I_{r}\), and we write this as follows:
\( j_{r}^{1}\prec_{r} \ldots \prec_{r} j_{r}^{n} \),
meaning that if job \(j_{r}^{1}\) is assigned to interval \(I_{r}\) then it is
also the first job in interval \(I_{r}\), otherwise the next job that can be
assigned to interval \(I_{r}\) is job \(j_{r}^{2}\), and so on. This leads to an
ordering \(\prec \) over the entire time horizon: \( j_{1}^{1} \prec j_{1}^{2}
\prec \ldots \prec j_{1}^{n} \prec j_{2}^{1}, \ldots \prec j_{2}^{n} \prec
\ldots,j_{q}^{1} \prec \ldots \prec j_{q}^{n} \). Obviously, for
each \(j \in J\) and \(r\in Q\) there is only one \(i \in
\{1,\ldots,n\} \) such that \(j_{r}^{i} = j\).
For a feasible schedule we need to choose for each job \(j \in J\) exactly one of
its representations (in one of the intervals). We model this using a BDD
to represent suitable subsets of the set
\( \{j_{1}^{1},j_{1}^{2},\ldots,j_{1}^{n},j_{2}^{1},
\ldots,j_{2}^{n},\ldots,j_{q}^{1},\ldots,j_{q}^{n}\} \), while ensuring that
each representation \(j_{r}^{i}\) is
completed in the corresponding interval.
\begin{figure}[t]
\centering
\caption{A BDD representing all sequences for the instance described in Table \protect\ref{table:instancebdd}. Solid lines represent high edges, while dotted lines represent low edges.}\label{fig:instancebdd}
\includegraphics{figures/bddtw-mail19-8.tex}
\end{figure}
The BDD will follow the same ordering $\prec$. A configuration
\((j_{r}^{i},t) \) of a non-terminal node is a pair consisting of a
representation \(j_{r}^{i}\) of a job \(j\) that can only be completed in
interval~\(I_{r}\) and the total processing time \(t \) of all the
job representations
that were chosen before~\(j_{r}^{i}\), so \(t
\) is the starting time of job \(j_{r}^{i} \).
Each node \((j_{r}^{i},t) \) in the BDD apart from the terminal nodes has
two
child nodes. The high edge, representing inclusion of representation~\(j_{r}^{i}
\), leads to \((j_{r'}^{i'},t + p_j) \), where \(p_{j} \) is the processing time
of the job \(j = j_{r}^{i}\) and \(j_{r'}^{i'}\) is the representation of the
next job \(j'\) that is different from job \(j\) for which \(t + p_j + p_{j'}
\in I_{r'} \). If no such representation~\(j_{r'}^{i'} \) exists, the high edge points to the \mbox{\textbf{1}-node} if
\(t + p_j \in I_{r} \) and to the \textbf{0}-node otherwise.
For the low edge (exclusion of representation \(j_{r}^{i} \)), the same holds but based on the value of \(t \) instead of \(t + p_j \).
An algorithmic description of the generation procedure of the BDD
is provided in Algorithm~\ref{alg:childBBTW} in Appendix~\ref{app:BDD}.
Figure~\ref{fig:instancebdd} shows the BDD
for the instance given in Table~\ref{table:instancebdd}.
In this instance, representation \(j_{1}^{1}\) can never be
chosen because job \(2\) cannot finish in interval~\(I_{1}\). It can also be seen that the low edge emanating from $(j^1_2, 0)$, corresponding with the non-selection of job~2 at starting time~0,
immediately leads to the terminal node, because possible next jobs would end too early to complete in intervals $I_2$, $I_3$, or $I_4$, since we do not allow for idle time in the pseudo-schedules.
\subsection{A new flow-based formulation for parallel machine scheduling}
Let \(B = (N, A)\) be the DAG that represents the constructed
BDD\@.
Each node \(v\) of the graph is associated to a configuration
\((j_{r}^{i},t)\)
and has two outgoing edges: high edge
\(e_{v}^{1}\) and low edge \(e_{v}^{0}\). The high edge \(e_{v}^{1}\)
has a cost \(c_{e_{v}^{1}} = w_{j}\max \{0,t + p_{j} - d_j\} \) with $j=j_r^i$, while the cost of low edge \(e_{v}^{0}\) is \(0\). The set of all incoming edges of node \(v\) is
given by \(\sigma^{-}(v)\). Let \(A^{0}\) and \(A^{1}\) be the set
of all low and high edges of \(B\), respectively. Let \(p_{B}:A\rightarrow J\) be a map that
projects each edge \(e\) of \(B\) onto the job associated to the head node of
\(e\).
A formulation for \(Pm||\sum w_j T_j \) can now be constructed using
a binary variable \(x_{e}\) for each \(e \in A^{1}\) to indicate that
the edge $e$ is chosen, which means that job \(j = p_B(e)\) is completed in interval \(I_{r}\) with completion time \(C_{j} = t +
p_{j}\), where the head node of $e$ has configuration $(p_B(e),t)$.
For each \(e \in A^{0}\) we define a continuous variable \(x_{e}\) to allow all sequencing decisions to be
represented by a flow from the root node of the BDD to the terminal node
\textbf{1}. The formulation can now be stated as follows:
\begin{subequations}\label{eq:BDDform}
\begin{align}
\text{minimize } & \sum_{e \in A^{1}} c_{e}x_{e} \label{eq:objBDDform} \\
\text{subject to } & \sum_{e \in A^{1}: p_{B}(e) = j} x_{e} = 1 & \, & \forall j \in J \label{eq:assBDDform} \\
& x_{e_{v}^{1}} + x_{e_{v}^{0}} = \sum_{e \in \sigma^{-}(v)} x_{e} & \, & \forall v \in N \setminus \{\textbf{r},\textbf{1}\} \label{eq:flowBDDform} \\
& \sum_{e \in \sigma^{-}(\textbf{1})} x_{e} = m & \, & \label{eq:nmachBDDform} \\
& x_{e} \in \{0,1\} & \, &\forall e \in A^{1}\, \label{eq:var1BDDform} \\
& x_{e} \ge 0 & \, & \forall e \in A^{0}\, \label{eq:var2BDDform}
\end{align}
\end{subequations}
Equations~\eqref{eq:flowBDDform} and \eqref{eq:nmachBDDform} together with
the redundant equation
\begin{equation} x_{e_{\textbf{r}}^{0}} +
x_{e_{\textbf{r}}^{1}} = m
\end{equation}
can be interpreted as a network flow
of \(m\) units through the BDD from the root node \textbf{r} to the terminal node
\textbf{1}.
Constraints~\eqref{eq:assBDDform} enforce that for each \(j \in J\) we must
choose exactly one edge \(e \in A^{1}\) such that \(p_{B}(e) = j\), meaning that
we choose exactly one representation of each job across the intervals.
In what follows, we call the new formulation~\eqref{eq:BDDform} the BDD-based formulation BDDF.
We now show that this formulation will yield better bounds than the TIF~\eqref{eq:TIform}. We show that every solution \(\overline{x}\) of
the LP relaxation of~\eqref{eq:BDDform} can be transformed into a
solution \(\overline{y}\) of the LP relaxation of~\eqref{eq:TIform}.
Consider for this the map \(q_{B}:A^{1} \rightarrow \{1,\ldots,T\}\) that
projects each high edge of the BDD onto the starting period of its head node.
Let \(\overline{y}_{jt} = \sum_{\substack{e
\in A^{1}:p_{B}(e) = j\\q_{B}(e) = t}}\overline{x}_{e}\) for \(j\in J\) and
\(t \in \{1,\ldots,T - p_{j}+1\}~\). Since \(\overline{x}\) satisfies the assignment
constraints~\eqref{eq:assBDDform}, it follows that \(\overline{y}\) also satisfies the assignment
constraints~\eqref{eq:assTI}, and accordingly
Constraints~\eqref{eq:flowBDDform} and~\eqref{eq:nmachBDDform} for
\(\overline{x}\) imply Constraint~\eqref{eq:TInummachines} for
\(\overline{y}\).
We now show that the BDDF can be
strictly better than the TIF for \(Pm||\sum w_j T_j \). Consider the instance described in Table~\ref{table:instancebdd}. An
optimal solution for this instance has cost~\(4\) with the job sequences \((1,4,3)\) and \((2)\) on the two
machines; this integral solution is also an optimal solution to the linear relaxation of the BDDF\@. An optimal solution \(\overline{y}\) of the
LP relaxation of the TIF is \(\overline{y}_{11} =
\overline{y}_{13} = \overline{y}_{31} = \overline{y}_{37} = 0.5 \),
\(\overline{y}_{21} = \overline{y}_{45} = 1.0\), and all the other variables
equal to~\(0\). Clearly, this solution to the LP
relaxation of the TIF~\eqref{eq:TIform} cannot be a solution of the
LP relaxation of the BDDF~\eqref{eq:BDDform}, because the
structure of the BDD diagram in Figure~\ref{fig:instancebdd} implies that job
\(1\) can not be assigned to the interval \(I_{1}\) twice. With $\widetilde{c}_{11} = \widetilde{c}_{13} = \widetilde{c}_{21} = \widetilde{c}_{31} = \widetilde{c}_{45} = 0$ and $\widetilde{c}_{37} = 4$, the corresponding objective value equals $2$.
We thus obtain:
\begin{prop}
The BDDF dominates the TIF.
\end{prop}
The ATIF and the new BDDF are not comparable, however; the LP bound of ATIF can be either higher or lower than that of BDDF (see Appendix~\ref{app:notcomparable} for an illustration).
\section{Solving the LP}\label{sec:DW}
\subsection{Dantzig-Wolfe decomposition} \label{subsec:DW}
Formulation~\eqref{eq:BDDform} can have many variables and constraints, which makes a
direct application restrictive. Following~\cite{van2000time}
and~\cite{pessoa2010exact}, we apply a DW decomposition
to the LP relaxation of Formulation~\eqref{eq:BDDform} (i.e., when all
variables \(x_{e}\) are non-negative reals). This will reduce the number of
constraints from \(|N| + n - 1\) to \(n + 1\), where \(|N|\) is the number of
nodes in the BDD\@. We keep the
assignment constraints~\eqref{eq:assBDDform} and the bounding
constraint~\eqref{eq:nmachBDDform} in the formulation, but we recognize that the
extreme points of the polytope formed by the flow
constraints~\eqref{eq:flowBDDform} are the paths in the BDD
from the root node to the terminal \textbf{1}. Denote the set of all these paths by
\(\mathcal{P}\), and let \(z_{e}^{p}\) be a parameter that is one if edge \(e\) belongs to
path \(p\) and zero otherwise.
We introduce a new variable
\(\lambda_{p}\) for each \(p\in \mathcal{P}\), with which the LP relaxation of Formulation~\eqref{eq:BDDform} can be re-stated as follows:
\begin{subequations}\label{eq:BDDformlambda}
\begin{align}
\text{minimize } & \sum_{e \in A^{1}} c_{e}x_{e} \label{eq:objBDDformlambda} \\
\text{subject to } & \sum_{e \in A^{1}: p_{B}(e) = j} x_{e} = 1 & \, & \forall j \in J \label{eq:assBDDformlambda} \\
& \sum_{p \in \mathcal{P}} z_{e}^{p}\lambda_{p} = x_{e} & \, & \forall e \in A \\
& \sum_{e \in \sigma^{-}(\textbf{1})} x_{e} = m & \, & \label{eq:nmachBDDformlambda} \\
& x_{e} \ge 0 & \, & \forall e \in A\, \label{eq:var2BDDformlambda} \\
& \lambda_{p} \ge 0 & \, & \forall p \in \mathcal{P}
\end{align}
\end{subequations}
Eliminating the variables \(x_{e}\) from
the model, we obtain:
\begin{subequations}\label{eq:BDDLP}
\begin{align}
\text{minimize } & \sum_{p \in \mathcal{P}}\left(\sum_{e \in A^{1}}c_{e}z_{e}^{p}\right)\lambda_{p} \label{eq:objBDDLP} \\
\text{subject to }& \sum_{p\in \mathcal{P}} \left(\sum_{e \in A^{1}: p_{B}(e) = j}z_{e}^{p}\right)\lambda_{p} = 1 &\, & \forall j \in J \label{eq:assBDDLP} \\
& \sum_{p\in\mathcal{P}} \left( \sum_{e \in \sigma^{-}(\textbf{1})}z_{e}^{p}\right)\lambda_{p} = \sum_{p\in \mathcal{P}}\lambda_{p} = m & \, & \label{eq:nmachBDDLP} \\
& \lambda_{p} \ge 0 &\, & \forall p \in \mathcal{P}
\end{align}
\end{subequations}
\subsection{Column generation} \label{subsec:CG}
We solve Formulation~\eqref{eq:BDDLP} with CG, which implies the iterative solution of a \textit{restricted master problem} (RMP), which contains a limited set of columns, and a \textit{pricing
problem}, which checks whether there exists a column with negative reduced
cost. If we assign dual variables \(\pi_{j}\) for \(j \in J\) with
Constraints~\eqref{eq:assBDDLP} and dual variable \(\pi_{0}\) with Constraint~\eqref{eq:nmachBDDLP}, the dual of the LP~\eqref{eq:BDDLP} is given by:
\begin{subequations}\label{eq:BDDdual}
\begin{align}
\text{maximize } & \sum_{j \in J}\pi_{j} + m\pi_{0} \label{eq:BDDobjdual} \\
\text{subject to } & \sum_{j\in J}\left(\sum_{e \in A^1:p_{B}(e) = j}z_{e}^p\right)\pi_{j} + \pi_{0} \leq \sum_{e\in A^1} c_{e}z_{e}^{p} & \, & \forall p \in \mathcal{P}\label{eq:BDDdualpath} \\
& \pi_{j} \in \mathbb{R} & \, & \forall j \in J \\
& \pi_{0} \in \mathbb{R} & \, &
\end{align}
\end{subequations}
At each iteration of the CG algorithm we check if one of the
constraints~\eqref{eq:BDDdualpath} is violated, meaning that the reduced cost
of the associated column is negative. Recall that a column is a path from the root node to the terminal~\textbf{1} in the BDD that was presented in Section~\ref{sec:timehorizon}.
The pricing problem is then as follows:
given current dual prices \(\overline{\pi}\), can
we find a path \(p \in \mathcal{P}\) such that
\begin{equation}\label{eq:reducedcostBDD}
\sum_{e\in A^1}
c_{e}z_{e}^{p} - \sum_{j \in J}\left(\sum_{e \in A^{1}:p_{B}(e) =
j}z_{e}^p\right)\overline{\pi}_{j} - \overline{\pi}_{0} < 0?
\end{equation}
Inequality~\eqref{eq:reducedcostBDD} can be rewritten as
\begin{equation}
\left(\sum_{e \in A^1 \cap p}\overline{c}_{e}\right) - \overline{\pi}_{0} < 0,
\end{equation}
where \(\overline{c}_{e}\) is equal to \(c_{e} - \overline{\pi}_{p_{B}(e)}\),
which is the reduced cost of high edge \(e\).
A CG algorithm typically needs fewer iterations if one considers constraints
that are strongly violated and hence we will identify paths with the lowest
reduced cost. In this way the pricing problem becomes a
shortest path problem in the BDD, where the length of the high edges \(e\) is
\(\overline{c}_{e}\), and the length of the low edges is zero.
Since the graph is acyclic and has only two
outgoing arcs per node, the running time of a
labeling algorithm for pricing will be linear in the number of nodes in the BDD \citep{ahuja1993network}.
\subsection{Labeling algorithm} \label{sec:labeling}
In our initial computational experiments we noticed that the pricing algorithm often
generates paths from the root node to the terminal for which the associated
pseudo-schedules contain jobs that are repeated in consecutive positions. The consequence of this
is that the lower bound will tend to be weaker than the
bound from the ATIF (but of course still stronger
than the bound from the TIF\@). In Figure~\ref{fig:instancebdd}, for example, the path corresponding to the pseudo-schedule \((j_{1}^{4}, j_{2}^{2} , j_{4}^{1} ) =
( 1 , 3 , 3)\) is allowed, where the path includes the low edge of $(j_3^4,6)$. In Section ~\ref{sec:constructBDD} we mentioned that we avoid two consecutive high edges for the same job, but this does not yet avoid repeated jobs via intermediate low edges.
In principle, one can impose the condition that no job can be visited by a path more than
once: we can compute the intersection of the family of pseudo-schedules and
the family of paths where each job is visited at most once (see \cite{minato1993zero} for
a generic intersection operation on BDDs).
In this way, we obtain a BDD that contains exactly all possible schedules. It would be overly time-consuming to construct such a BDD, however, and the pricing problem would also become much harder to
solve because of the number of nodes in the resulting BDD\@.
It is easier to restrict the pseudo-schedules such that all pairs of consecutive
jobs are different. Note that two jobs assigned to the same time interval will
always be different, so if two successive tasks in a pseudo-schedule
are the same then they are assigned to different intervals. Thus, one might say that the BDDF only ``remembers'' what happens in the same interval. This
implicit memory mechanism is the most fundamental reason why the flow-based formulation
is stronger than the TIF\@.
We therefore devise a labeling algorithm for pricing that
takes into account that two consecutive jobs in the pseudo-schedule cannot be
the same. This restriction will have a significant
impact on the quality of the lower bound, and the running time of the
algorithm will still be linear in the number of nodes in the
BDD\@.
To avoid that two consecutive jobs in the pseudo-schedule are the same, we
need to know the previous job in the optimal path to avoid that the
same job is scheduled consecutively. We therefore maintain a bucket with two entries
at each node in the BDD: each entry contains a distance label and the identification of the
previously selected job to achieve that distance label. The first entry is the lowest cost to reach
the node, and the second entry is the lowest cost while not passing via the same predecessor job
as the first entry. This modified labeling algorithm can be implemented in a forward or backward fashion.
We have observed in preliminary experiments that the forward
labeling algorithm is more time-consuming than the backward variant because the number of label updates is
higher in that case. In the forward labeling algorithm, we may
have to update the labels more often because the in-degree (the number of
incoming edges) of each node can be higher than the out-degree (the number of
outgoing edges), which is at most two. Hence, in our
computational experiments, we use the backward labeling algorithm to find
paths with minimal reduced cost. The forward labeling algorithm is used
to remove nodes from the BDD \((N, A)\) by reduced cost fixing. A more detailed description of the forward and backward algorithm
is provided in Appendix~\ref{app:label}.
\subsection{Stabilization}
The convergence of the CG algorithm can be slow because of primal
degeneracy. This problem can be circumvented by applying stabilization methods for CG\@.
We apply a smoothing method that was developed by~\cite{wentges1997weighted}, in which we correct the optimal solution of the dual problem of the RMP based on information from the previous iterations
before plugging it into the
pricing problem. For details of this technique and of stabilization in general, we refer to~\cite{pessoa2018automation}.
\subsection{Reduced cost fixing}
Another method to improve the convergence of the CG is that of
fixing edges of the BDD\@.
We can fix the flow on edge \(e\in A^1\) to \(0\) (so remove the high edge from the graph) if
\begin{equation} LB + (m - 1)\overline{c} +
\overline{c}_{e} \geq UB,
\end{equation}
where \(\overline{c}_{e}\) is the best reduced cost of a path from the
root node to the terminal node \textbf{1} that traverses the edge
\(e\), \(\overline{c}\) is the reduced cost of the shortest path from
the root node to node~\textbf{1}, \(LB\) is the current
lower bound of the RMP of~\eqref{eq:BDDLP}, and \(UB\) is the best known upper
bound of the optimal cost. In this way, we only remove arcs that will not improve the current best solution.
The computation of \(\overline{c}_{e}\) uses the forward and backward distance labels discussed in Section~\ref{sec:labeling}.~
Fixing edges by
reduced cost not only has a beneficial effect on the running time of the pricing
algorithm, but can also speed up the B\&B procedure for solving the integer formulation by making the BDD smaller (as a pre-solving step) and via better lower bounds \citep[see][]{irnich2010path,pessoa2010exact}.
Computationally, we find that applying variable fixing each time a number of CG iterations has past, performs better than only doing this at the end of the CG\@.
\section{Branch and price} \label{sec:strongbranching}
In order to find optimal integer solutions for the BDDF, we embed the CG into a B\&B search tree, leading to a B\&P procedure.
In this work we will branch on Generalized Upper Bound (GUB) constraints of the
form \(\sum_{i \in V} x_{i} = 1 \) for some set \(V \) of binaries. The assignment constraints~\eqref{eq:assBDDform} in the BDDF, which
require the selection of one high edge for each \(j \in J\), are clearly of this form.
Branching is based on a subset \(V' \subsetneq V\) for which the solution of
the LP relaxation at a node satisfies \(0 < \sum_{i \in V'} x_{i} < 1\), where we enforce constraint \(\sum_{i \in V'}
x_{i} = 0\) in one child node and constraint \(\sum_{i \in V \setminus V'}
x_{i} = 0\) in the other child node. This branching scheme is sometimes also called GUB Dichotomy.
A clear advantage of
branching over GUB constraints instead of branching over individual variables is
that the tree can be more balanced.
In some cases there exists a logical
ordering of the variables in set \(V\) and then the branching method is called SOS\@
branching. For Constraints~\eqref{eq:assBDDform}, for each \(j \in J\), we can order the edges in
$A_j = \{ e \in A^{1}: p_{B}(e) = j\}$ in non-decreasing order of the starting time~\(q(e)\).
In the case of SOS branching, an approach to finding an appropriate subset \(V ' \)
was formulated in~\cite{linderoth1999computational} using the concept of ``reference
rows.'' Suppose that \(a_{1} \leq \cdots \leq a_{|V|} \) are
coefficients in a reference row, then a good set for branching is
\[
V' = \{j \in V\,|\, a_{j} \leq \sum_{\ell \in V} a_{\ell} x_{\ell}^{*}\},
\]
where \(x^{*}\) is a solution of the linear relaxation. In our case we can set
\(a_{e}\) to \(q(e)\) for \(e \in A_{j}\) for every \(j \in J\). Another
possibility is to choose \(a_{e}\) as \(c_{e}\), because the weighted tardiness
objective is a regular function.
There can still remain multiple branching choices, namely for
every \(j \in J\) we can branch if the
corresponding high edges in \(A_{j}\) are not integral. We apply strong
branching to make good branching decisions. We take a small set of
branching candidates and evaluate the child nodes heuristically by performing a
small number of CG iterations. This first phase produces a ranking, and in this order we fully evaluate the child nodes.
If for a number of consecutive full evaluations of the child nodes we do not find better bounds, we terminate the full evaluations and branch on the best candidate.
\section{Computational experiments}\label{sec:compexp}
\subsection{Implementation details and instances}
All algorithms have been implemented in the C++ programming language and
compiled with \textsf{gcc} version 11.2.0 with full optimization pack
\textsf{-O3}. We have used and adjusted the
implementation of~\cite{iwashita2013efficient} that can be found on
Github\footnote{\url{https://github.com/kunisura/TdZdd}} to construct the BDDs\@. All computational experiments were performed
on one core of a server with Intel Xeon
E5--4610 at 2.4GHz processors and 64 GB of RAM under a Linux OS\@. All LPs are
solved with Gurobi 9.1.2 using default settings and only one core. The source code of the procedures can be retrieved from the KU Leuven Gitlab repository.\footnote{\url{https://gitlab.kuleuven.be/u0056096/parallel-machine-bdd}}
We use the same instances from
the OR-library as \cite{pessoa2010exact} and~\cite{oliveira2020improved}.
These instances were generated for the single machine problem with weighted
tardiness objective in~\cite{potts1985branch}. There are \(125\)
instances for each \(n \in \{40,50,100\} \). The processing time \(p_{j}\)
for each \(j \in \{1,\ldots,n\} \) was generated from the discrete uniform distribution on the integers in
\(\interval{1}{100}\) and the weight~\(w_{j}\) was generated similarly from \(\interval{1}{10}\). It was observed that the difficulty of
\(1||\sum w_j T_j \) depends on two
parameters, namely the relative range of due dates \(RDD\), and
the tardiness factor \(TF \). The due dates are generated from the discrete uniform
distribution on \(\interval{\frac{P(1 - TF - RDD)}{2}}{\frac{P(1 - TF +
RDD)}{2}}\), where \(P = \sum_{j \in J}p_{j}\) and \(TF,\,RDD \in
\{0.2,0.4,0.6,0.8,1.0\} \). For each \(n \in \{40,50,100\} \) and each pair
\((RDD,TF)\), five instances were constructed. In order to obtain reasonable instances for parallel machine scheduling, \cite{pessoa2010exact} transformed the instances
of~\cite{potts1985branch} by dividing the due dates by the number of machines \(m\). The processing times \(p_{j}\) and weights
\(w_{j}\) are kept the same for each \(j \in J\).
For each pair \((RDD,TF)\) they only retain the first instance; thus there are \(25\) instances for each \(n
\in \{40,50,100\} \) and each \(m \in \{2,4\} \).
\subsection{Comparison of the LP bounds} \label{subsec:LPresults}
In this section, we will
present computational results of CG for the LP bound computation of
the TIF~\eqref{eq:TIform}, the ATIF~\eqref{eq:aTIform}, and our new formulation BDDF~\eqref{eq:BDDform}. We have implemented a CG algorithm
for each of these three formulations, with the same enhancements such as stabilization and reduced cost fixing for all three models. We also incorporate
the pairwise-interchange-based preprocessing derived from Proposition 2 (and 3) of \cite{pessoa2010exact} in the ATIF; a similar interchange argument is implicitly embedded in the BDDF
only within each interval, while this can benefit the ATIF over the entire time horizon. In this section, ``BDDF'' refers to the formulation with a standard labeling algorithm in the CG phase,
which can generate consecutive repeated jobs, while ``BDDF$_r$'' stands for CG with the labeling refinement described in Section~\ref{sec:labeling} that avoids identical jobs in consecutive positions
in a pseudo-schedule.
\begin{table}[t]
\centering
\footnotesize \caption{Size of the graph for TIF, ATIF, BDDF$_r$, and BDDF \label{tbl:sizetw}}{
\pgfplotstabletypeset[
columns={n,m,first_size_graph_mean_TimeIndexed,first_size_graph_amax_TimeIndexed,reduction_mean_TimeIndexed,first_size_graph_mean_ArcTimeIndexed,first_size_graph_amax_ArcTimeIndexed,reduction_mean_ArcTimeIndexed,first_size_graph_mean_BddBackwardCycle,first_size_graph_amax_BddBackwardCycle,reduction_mean_BddBackwardCycle,reduction_mean_BddBackward},
every head row/.style={
before row={%
\toprule
\multicolumn{2}{c}{}& \multicolumn{3}{c}{TIF}& \multicolumn{3}{c}{ATIF} & \multicolumn{3}{c}{BDDF$_r$}& \multicolumn{1}{c}{BDDF}\\
\cmidrule(lr){3-5}\cmidrule(lr){6-8}\cmidrule(lr){9-11}\cmidrule(lr){12-12}
},
after row={\midrule},
},
every last row/.style={after row=\bottomrule},
columns/n/.style={column type=r,int detect,column name=\textit{n}},
columns/m/.style={column type=r,int detect,column name=\textit{m}},
columns/first_size_graph_mean_TimeIndexed/.style={column type=r,fixed,precision=1,zerofill,column name=\emph{avg size}},
columns/first_size_graph_amax_TimeIndexed/.style={column type=r,fixed,column name=\emph{max size}},
columns/reduction_mean_TimeIndexed/.style={multiply with=100,column type=r,precision=1,zerofill,fixed,postproc cell content/.append style={ /pgfplots/table/@cell content/.add={}{\%},} ,column name=\emph{avg red}},
columns/first_size_graph_mean_ArcTimeIndexed/.style={column type=r,precision=1,zerofill,fixed,column name=\emph{avg size}},
columns/first_size_graph_amax_ArcTimeIndexed/.style={column type=r,fixed,column name=\emph{max size}},
columns/reduction_mean_ArcTimeIndexed/.style={multiply with=100,column type=r,precision=1,zerofill,fixed,postproc cell content/.append style={ /pgfplots/table/@cell content/.add={}{\%},} ,column name=\emph{avg red}},
columns/first_size_graph_mean_BddBackward/.style={multiply with=2,column type=r,precision=1,zerofill,fixed,column name=\emph{avg size}},
columns/first_size_graph_amax_BddBackward/.style={multiply with=2,column type=r,precision=0,fixed,column name=\emph{max size}},
columns/reduction_mean_BddBackward/.style={multiply with=100,column type=r,precision=1,zerofill,fixed,postproc cell content/.append style={ /pgfplots/table/@cell content/.add={}{\%},} ,column name=\emph{avg red}},
columns/first_size_graph_mean_BddBackwardCycle/.style={multiply with=2,column type=r,precision=1,zerofill,fixed,column name=\emph{avg size}},
columns/first_size_graph_amax_BddBackwardCycle/.style={multiply with=2,column type=r,precision=0,fixed,column name=\emph{max size}},
columns/reduction_mean_BddBackwardCycle/.style={multiply with=100,column type=r,precision=1,zerofill,fixed,postproc cell content/.append style={ /pgfplots/table/@cell content/.add={}{\%},} ,column name=\emph{avg red}}
]\summary{}
}{}
\end{table}
The graphs that represent the ATIF and the
BDDF are much larger than those for the TIF\@. The number of edges for ATIF is \(O(n^{2}T)\),
while this number is \(O(nT)\) for the TIF\@. Table~\ref{tbl:sizetw} provides some empirical
evidence for this by comparing the average (\emph{avg size}) and maximum
(\emph{max size}) number of edges in all formulations. The graphs for BDDF$_r$ and BDDF are obviously the same, so those columns are not duplicated.
We see that the number of edges in the graph that represents
the~BDDF falls in between the numbers for the other two formulations.
The column \emph{avg red} presents the average percentage of edges that were removed via
reduced cost fixing by the end of the CG procedure. We observe that the ATIF benefits the most
from this variable fixing, with around $90\%$ of the high edges removed for all instance classes, followed by the BDDF, and
finally the TIF has the lowest average reduction, but this still amounts to $76.6\%$ at least across the instance classes.
Model BDDF$_r$ is a bit more restrictive than BDDF and benefits slightly more from variable fixing, but the differences are not very large.
In Tables~\ref{tbl:summarytw1} and~\ref{tbl:summarytw2} we report the runtimes
of the CG algorithms for TIF, ATIF, BDDF$_r$, and BDDF\@.
The columns \emph{avg time}, \emph{max time}, and \# \emph{opt} contain the average and the maximum CPU time of the algorithms (in seconds), and the number
of instances solved at the root node (out of 25), respectively.
An instance is said to be solved at the root node when the linear relaxation can confirm optimality
of an initial heuristic solution. The heuristic in our case is a rudimentary iterated local search mechanism that changes the position of jobs or groups of jobs, or changes their machine allocation.
This heuristic will also produce the starting solution for our B\&P in Section~\ref{subsec:exactresults}.
We find that the average running time of the CG
for computing the lower bound with BDDF is significantly less than with ATIF, and also that the time needed for TIF, in turn, is
a lot lower than with BDDF\@. These observations are completely in line with the size of the graphs in which the pricing procedures
are executed, which was reported in Table~\ref{tbl:sizetw}. Avoiding consecutive identical jobs via labeling is beneficial: BDDF$_r$ is consistently faster than BDDF\@.
\begin{table}[t]
\centering
\caption{Computation time (in seconds) and number of instances solved at the root for the LP relaxation of TIF and ATIF\label{tbl:summarytw1}}{
\pgfplotstabletypeset[
columns={n,m,tot_lb_mean_TimeIndexed,tot_lb_amax_TimeIndexed,opt_sum_TimeIndexed,tot_lb_mean_ArcTimeIndexed,tot_lb_amax_ArcTimeIndexed,opt_sum_ArcTimeIndexed},
every head row/.style={
before row={%
\toprule
\multicolumn{2}{c}{}& \multicolumn{3}{c}{TIF}& \multicolumn{3}{c}{ATIF}\\
\cmidrule(lr){3-5}\cmidrule(lr){6-8}
},
after row={\midrule},
},
every last row/.style={after row=\bottomrule},
columns/n/.style={column type=r,int detect,column name=\textit{n}},
columns/m/.style={column type=r,int detect,column name=\textit{m}},
columns/tot_lb_mean_TimeIndexed/.style={column type=r,fixed,precision=2,zerofill,column name=\emph{avg time}},
columns/tot_lb_amax_TimeIndexed/.style={column type=r,precision=2,zerofill,column name=\emph{max time}},
columns/opt_sum_TimeIndexed/.style={column type=r,fixed,column name=\emph{\# opt}},
columns/tot_lb_mean_ArcTimeIndexed/.style={column type=r,precision=2,zerofill,fixed,column name=\emph{avg time}},
columns/tot_lb_amax_ArcTimeIndexed/.style={column type=r,precision=2,zerofill,fixed,column name=\emph{max time}},
columns/opt_sum_ArcTimeIndexed/.style={column type=r,fixed,column name=\emph{\# opt}}
]\summary{}
}{}
\end{table}
\begin{table}[t]
\centering
\caption{Computation time (in seconds) and number of instances solved at the root for the LP relaxation of BDDF$_r$ and BDDF\label{tbl:summarytw2}}{
\pgfplotstabletypeset[
columns={n,m,tot_lb_mean_BddBackwardCycle,tot_lb_amax_BddBackwardCycle,opt_sum_BddBackwardCycle,tot_lb_mean_BddBackward,tot_lb_amax_BddBackward,opt_sum_BddBackward},
every head row/.style={
before row={%
\toprule
\multicolumn{2}{c}{}& \multicolumn{3}{c}{BDDF$_r$} & \multicolumn{3}{c}{BDDF}\\
\cmidrule(lr){3-5}\cmidrule(lr){6-8}
},
after row={\midrule},
},
every last row/.style={after row=\bottomrule},
columns/n/.style={column type=r,int detect,column name=\textit{n}},
columns/m/.style={column type=r,int detect,column name=\textit{m}},
columns/tot_lb_mean_BddBackward/.style={column type=r,precision=2,zerofill,fixed,column name=\emph{avg time}},
columns/tot_lb_amax_BddBackward/.style={column type=r,precision=2,zerofill,fixed,column name=\emph{max time}},
columns/opt_sum_BddBackward/.style={column type=r,fixed,column name=\emph{\# opt}},
columns/tot_lb_mean_BddBackwardCycle/.style={column type=r,precision=2,zerofill,fixed,column name=\emph{avg time}},
columns/tot_lb_amax_BddBackwardCycle/.style={column type=r,precision=2,zerofill,fixed,column name=\emph{max time}},
columns/opt_sum_BddBackwardCycle/.style={column type=r,fixed,column name=\emph{\# opt}}
]\summary{}
}{}
\end{table}
The gap between the starting solution and the LP bound
of the different formulations is given in Table~\ref{tbl:summarytw3}.
The pattern that arises here is not as clear-cut as in the previous two tables: we see from Table~\ref{tbl:summarytw3} that,
despite the smaller graphs and the lower runtimes than the ATIF, the BDDF still yields LP bounds that are quite tight, and
very close on average to the ones produced by ATIF\@. We conclude that while the BDDF is a formulation
that is positioned between the TIF and the ATIF in terms of runtimes and graph size for CG, the LP bounds produced by the BDDF are of rather similar quality as the ATIF, which makes the formulation promising
for finding optimal integer solutions.
\begin{table}[t]
\centering
\caption{Gap from the starting solution for the formulations TIF, ATIF, BDDF$_r$, and BDDF\label{tbl:summarytw3}}{
\pgfplotstabletypeset[
columns={n,m,gap_mean_TimeIndexed,gap_amax_TimeIndexed,gap_mean_ArcTimeIndexed,gap_amax_ArcTimeIndexed,gap_mean_BddBackwardCycle,gap_amax_BddBackwardCycle,gap_mean_BddBackward,gap_amax_BddBackward},
every head row/.style={
before row={%
\toprule
\multicolumn{2}{c}{}& \multicolumn{2}{c}{TIF}& \multicolumn{2}{c}{ATIF} & \multicolumn{2}{c}{BDDF$_r$} & \multicolumn{2}{c}{BDDF}\\
\cmidrule(lr){3-4}\cmidrule(lr){5-6}\cmidrule(lr){7-8}\cmidrule(lr){9-10}
},
after row={\midrule},
},
every last row/.style={after row=\bottomrule},
columns/n/.style={column type=r,int detect,column name=\textit{n}},
columns/m/.style={column type=r,int detect,column name=\textit{m}},
columns/gap_mean_TimeIndexed/.style={multiply with=100,column type=r,precision=2,zerofill,postproc cell content/.append style={ /pgfplots/table/@cell content/.add={}{\%},}, column name=\emph{avg}},
columns/gap_amax_TimeIndexed/.style={multiply with=100,column type=r,precision=2,zerofill,postproc cell content/.append style={ /pgfplots/table/@cell content/.add={}{\%},}, column name=\emph{max}},
columns/gap_mean_ArcTimeIndexed/.style={multiply with=100,column type=r,precision=2,zerofill,postproc cell content/.append style={ /pgfplots/table/@cell content/.add={}{\%},}, fixed,column name=\emph{avg}},
columns/gap_amax_ArcTimeIndexed/.style={multiply with=100,column type=r,precision=2,zerofill,postproc cell content/.append style={ /pgfplots/table/@cell content/.add={}{\%},}, fixed,column name=\emph{max}},
columns/gap_mean_BddBackward/.style={multiply with=100,column type=r,precision=2,zerofill,fixed,postproc cell content/.append style={ /pgfplots/table/@cell content/.add={}{\%},}, column name=\emph{avg}},
columns/gap_amax_BddBackward/.style={multiply with=100,column type=r,precision=2,zerofill,fixed,postproc cell content/.append style={ /pgfplots/table/@cell content/.add={}{\%},}, column name=\emph{max}},
columns/gap_mean_BddBackwardCycle/.style={multiply with=100,column type=r,precision=2,zerofill,fixed,postproc cell content/.append style={ /pgfplots/table/@cell content/.add={}{\%},}, column name=\emph{avg}},
columns/gap_amax_BddBackwardCycle/.style={multiply with=100,column type=r,precision=2,zerofill,fixed,postproc cell content/.append style={ /pgfplots/table/@cell content/.add={}{\%},}, column name=\emph{max}}
]\summary{}
}{}
\end{table}
\subsection{Comparison of exact procedures} \label{subsec:exactresults}
In this section we present the computational results of the overall B\&P algorithm
based on the BDDF formulation. We compare our algorithm with the currently most competitive procedure in the literature, which is the one by~\cite{oliveira2020improved}.
In what follows we refer to our new B\&P procedure based on the BDDF simply as ``BDDF,'' and to the algorithm devised by~\cite{oliveira2020improved} and which is based on ATIF as ``ATIF.''
We incorporate the labeling refinement described in Section~\ref{sec:labeling} (which was previously referred to as BDDF$_r$) into BDDF\@.
\cite{oliveira2020improved} feed the solutions found by the heuristic of \cite{DBLP:journals/corr/KramerS15} into their procedure as initial primal bounds, while
BDDF computes an initial solution using the local search procedure mentioned in Section~\ref{subsec:LPresults}.
The processors in our hardware are clearly slower than those used by \cite{oliveira2020improved}: the CPU in \cite{oliveira2020improved} has around 30\%
higher clock speed (according to benchmarking websites\footnote{See, for instance, \url{https://www.cpubenchmark.net/} for a comparison of the CPUs.}). Hence, we transform the results of our
algorithm accordingly, namely we multiply our results by factor~\(0.7\). The time
limit per instance is set to 7200 seconds for our computations (without rescaling).
As a tool for comparing the computational performance of the two procedures, we will use \textit{performance profiles},
which were proposed as a tool for benchmarking optimization software in \cite{dolan2002benchmarking}.
The idea is to compare the methods by the ratio of each method's runtime to the best runtime, per instance. Let $r_{p,s}$ be this ratio
for method~$s$ on instance~$p$, and let $\rho_s(\tau)$ be the probability for method $s$ that a performance ratio~$r_{p,s}$ for a given instance $p$ is within
a factor $\tau \in \mathbb{R}$ of the best possible ratio. The function $\rho_s$ is then a performance profile, which can be seen as the (cumulative) distribution
function for the performance ratio over all tested instances. In other words, considering \(\tau \) as the time needed by an
algorithm normalized with respect to the best algorithm, for each value
of~\(\tau \) a performance profile curve reports the fraction of the data set
for which the algorithm is at most \(\tau \) times slower than the best
algorithm. For a more detailed description of performance profile curves
we refer to~\cite{dolan2002benchmarking}.
In Figure~\ref{fig:overallpc} we plot the performance profiles for BDDF and ATIF for all integer
$\tau = 1,2,3,\ldots$ based on all the instances that were
solved by both methods. Note that \cite{oliveira2020improved} only provide
detailed computational results for instances that
were not ``trivial,'' i.e., not solved in the root node by merely calculating the LP relaxation of the formulation
without additional cuts. BDDF comes out rather favorably in this plot: from Figure~\ref{fig:overallpc} we can deduce that BDDF is the fastest
algorithm for approximately 65\% of the instances, while this is the case for only almost 40\% for ATIF (this can be read for the entry $\tau =1$ on the horizontal
axis, which is where the plot starts). Algorithm BDDF can solve
approximately 90\% of the instances within a computing time not exceeding five
times the time for ATIF\@.
Since the details for the trivial instances are not presented
in~\cite{oliveira2020improved}, we do not fully see the effect of the faster CG
phase of BDDF here.
\begin{figure}[t]
\caption{Performance profiles over all the instances solved to optimality by both algorithms ($s = $ BDDF, ATIF)}\label{fig:overallpc}
\centering\includegraphics{figures/profile_curve_overall_2021_07_12.tex}
\end{figure}
In Figure~\ref{fig:per_instance_pc} we present performance profiles per instance
class, i.e., per combination \((n, m)\). Clearly, BDDF outperforms ATIF for all instance sets with $m=4$ machines (the three plots on the right side).
Conversely, for instances with two machines (the left plots) ATIF wins the comparison, although the
difference in performance is slightly less pronounced than for the case with four machines.
\begin{figure}[t]
\centering
\caption{Performance profiles per instance class ($s = $ BDDF, ATIF)}\label{fig:per_instance_pc}
\foreach \i/\j in {2/40, 4/40, 2/50, 4/50,2/100,4/100}{
\subcaptionbox{\footnotesize{} \(\displaystyle m = \i \) and \(\displaystyle n = \j \)}{\resizebox*{0.45\textwidth}{!}{\includegraphics{figures/profile_curve_\j_\i_2021_07_12.tex}}}
}
\end{figure}
In Table~\ref{tbl:summarybb} we summarize the results of the two algorithms. Columns \emph{avg time} contain the average running time
over all solved non-trivial instances (in seconds), under \emph{solved} we report the number
of solved instances (out of 25), and in the column \emph{avg time all} we display the
average time over all solved instances (only for BDDF; in seconds). Algorithm ATIF solves more
instances to optimality; the runtime limit imposed is not clear, however: some of the instances have taken more than
one day to run in \cite{oliveira2020improved}. Consequently, a perfect comparison between the two methods is not possible based on this
table. Nevertheless, the overall pattern that was observed in Figure~\ref{fig:per_instance_pc} also occurs here: the runtimes of ATIF
are significantly higher than BDDF for $m=4$, while the differences are not that clear-cut for $m=2$; only for $n=50$ ATIF really dominates BDDF for $m=2$.
We conjecture that the cuts that are used by \cite{oliveira2020improved} are particularly helpful in tightening the formulation especially for instances with few machines.
Overall, for BDDF our strong branching mechanism can close the gap relatively quickly for $n=40$ and $50$, while this is not the case anymore for
instances with \(100\) jobs. In Appendix~\ref{app:details} we present the detailed
computational results of the B\&P procedure based on the formulation BDDF for every instance. We can also report
the optimal solution of three previously unsolved instances in the instance class with \(n = 100\) and
\(m = 4\), namely those with ID number 16, 31, and 56. The only remaining unsolved instance in the data set is the one with ID number~91 for $n=100$ and $m=2$.
\begin{table}[t]
\centering
\caption{Summary of the results for the exact procedures\label{tbl:summarybb}}{
\pgfplotstabletypeset[
columns={n,m,opt_TimeOliveira_mean_opt_func,OptFound_sum,opt_found_tot_bb_mean_opt_func,opt_sum,opt_tot_bb_mean_opt_func},
every head row/.style={
before row={%
\toprule
\multicolumn{2}{c}{}& \multicolumn{2}{c}{ATIF}& \multicolumn{3}{c}{BDDF}\\
\cmidrule(lr){3-4}\cmidrule(lr){5-7}
},
after row={\midrule},
},
every last row/.style={after row=\bottomrule},
columns/n/.style={column type=r,int detect,column name=\textit{n}},
columns/m/.style={column type=r,int detect,column name=\textit{m}},
columns/opt_TimeOliveira_mean_opt_func/.style={column type=r,precision=2,zerofill,column name=\emph{avg time}},
columns/OptFound_sum/.style={column type=r,column name=\emph{solved}},
columns/opt_found_tot_bb_mean_opt_func/.style={column type=r,precision=2,zerofill,fixed,column name=\emph{avg time}},
columns/opt_sum/.style={column type=r,fixed,column name=\emph{solved}},
columns/opt_tot_bb_mean_opt_func/.style={column type=r,precision=2,zerofill,fixed,column name=\emph{avg time all}},
]\summaryopt{}
}{}
\end{table}
\section{Conclusion and further research} \label{sec:conclusion}
In this work we have introduced a new formulation for \(Pm||\sum w_j T_j \)
based on binary decision diagrams, which are built using a time discretization
from \cite{baptiste2009scheduling}. We show theoretically and experimentally
that this formulation is stronger than the classical time-indexed informulation, and show
experimentally that this formulation is sometimes weaker and sometimes stronger than the arc-time-indexed formulation. The computation time of the LP lower bound
of the new formulation with column generation is lower than for the bound computation of the arc-time-indexed model. The reason for this is mainly the size of the
graphs that represent the different formulations.
We have also developed a branch-and-price procedure based on the new formulation; this procedure can solve
many instances faster than before,
thanks to strong branching together with the improved running time of the column generation. Compared with
the state-of-the-art procedure of \cite{oliveira2020improved}, our new procedure seems to perform better especially
with a larger number of machines.
As a prime avenue for further research, one can examine several techniques from the rich
vehicle routing literature to construct a branch-cut-and-price algorithm for the
new flow-based formulation. Further closing the gap without branching but rather by introducing cuts
seems to be a logical next step for rendering the resulting algorithm more competitive. \cite{pessoa2010exact} considered such a plan of attack for
the arc-time-indexed formulation for single and parallel machine scheduling, and derived
robust cuts \citep[which do not destroy the structure of the
pricing problem; see also][]{de2003integer}. A similar approach for scheduling on one machine was followed by \cite{van2000time} for the time-indexed formulation. Potentially, separation for the new formulation could be faster than for the arc-time-indexed model due to its lower number of variables.
A different interesting alternative for continuing this work is to develop a variant of the enumeration algorithm devised in~\cite{baldacci2008exact} for vehicle routing. The algorithm would iterate over all the paths from the
root node to the terminal node in the decision diagram with a reduced cost that is
less than the duality gap. One can then construct a set-partitioning
formulation containing all these paths and hand the resulting formulation to a general
MIP solver. In this case, it may be possible to add non-robust cuts to the formulation and to do the pricing by inspection if the number of retained schedules is low enough.
As a final opportunity for further work, one can try to extend the new
flow-based formulation to parallel machine scheduling problems with other
constraints and objective functions. It would be interesting to examine, for
example, whether the formulation can be adapted to the parallel machine
scheduling problem with earliness-tardiness objective, and whether idle time can be incorporated.
\bibliographystyle{ijocv081}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 7,719 |
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_The Mail on Sunday_
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«Un estudio brillantemente original, estimulante e importante sobre hacia dónde se dirige la humanidad.»
_Evening Standard_
**21 lecciones
para el siglo XXI**
## **YUVAL NOAH HARARI**
Traducción de
Joandomènec Ros
SÍGUENOS EN
@megustaleerebooks
@debatelibros
@megustaleer
_A mi marido, Itzik; a mi madre, Pnina, y a mi abuela, Fanny, por su amor y apoyo a lo largo de muchos años_
### Introducción
En un mundo inundado de información irrelevante, la claridad es poder. En teoría, cualquiera puede intervenir en el debate acerca del futuro de la humanidad, pero es muy difícil mantener una visión clara. Con frecuencia, ni siquiera nos damos cuenta de que se produce un debate, o de cuáles son las cuestiones clave. Somos miles de millones las personas que apenas podemos permitirnos el lujo de indagar en estos asuntos, porque tenemos cosas más acuciantes que hacer: ir a trabajar, cuidar de los niños u ocuparnos de unos padres ya ancianos. Lamentablemente, la historia no hace concesiones. Si el futuro de la humanidad se decide en nuestra ausencia, porque estamos demasiado ocupados dando de comer y vistiendo a nuestros hijos, ni ellos ni nosotros nos libraremos de las consecuencias. Esto es muy injusto, pero ¿quién dijo que la historia es justa?
Como historiador, no puedo proporcionar a la gente comida ni ropa, pero sí intentar ofrecer cierta claridad, y de este modo contribuir a nivelar el terreno de juego global. Si esto empodera aunque solo sea a un puñado de personas para que se incorporen al debate sobre el futuro de nuestra especie, habré hecho mi trabajo.
Mi primer libro, _Sapiens_ , revisaba el pasado humano y analizaba cómo un simio insignificante acabó rigiendo el planeta Tierra.
_Homo Deus_ , mi segundo libro, exploraba el futuro de la vida a largo plazo, contemplaba cómo los humanos podrían terminar convirtiéndose en dioses, y cuál podría ser el destino último de la inteligencia y la conciencia.
En este libro quiero centrarme en el aquí y el ahora. Para ello voy a abordar los asuntos actuales y el futuro inmediato de las sociedades humanas. ¿Qué está ocurriendo ahora mismo? ¿Cuáles son los mayores retos y opciones de hoy en día? ¿A qué debemos prestar atención? ¿Qué tenemos que enseñar a nuestros hijos?
Desde luego, 7.000 millones de personas tienen 7.000 millones de prioridades, y, como ya hemos dicho, pensar en el panorama global es un lujo relativamente escaso. Una madre soltera que intenta criar a dos niños en un suburbio de Bombay se centra en la siguiente comida; los refugiados que se encuentran en una barca en medio del Mediterráneo otean el horizonte en busca de algún indicio de tierra, y un hombre moribundo que yace en un hospital atestado de Londres reúne las fuerzas que le quedan para respirar una vez más. Todos ellos tienen problemas mucho más acuciantes que el calentamiento global o la crisis de la democracia liberal. No hay libro que pueda hacer justicia a todo ello, y no tengo lecciones que enseñar a personas que se hallen en tales situaciones. Solo puedo esperar aprender de ellas.
En esta obra mi plan es global. Observo las principales fuerzas que modelan las sociedades en el mundo, y que es probable que influyan en el futuro de nuestro planeta como un todo. El cambio climático quizá esté muy lejos de las preocupaciones de la gente que se encuentra en una emergencia de vida o muerte, pero puede que al final haga que los suburbios de Bombay sean inhabitables, que envíe nuevas y enormes oleadas de refugiados a través del Mediterráneo, y que conduzca a una crisis mundial de la atención sanitaria.
La realidad está compuesta de muchas hebras, y este libro intenta abarcar distintos aspectos de nuestro dilema global, sin pretender ser exhaustivo. A diferencia de _Sapiens_ y _Homo Deus_ , esta obra no está pensada como una narrativa histórica, sino como una selección de lecciones. Dichas lecciones no concluyen con respuestas simples. Su objetivo es fomentar más reflexión y ayudar a los lectores a participar en algunos de los principales debates de nuestra época.
En realidad, estas páginas se escribieron en conversación con el público. Muchos de los capítulos se compusieron en respuesta a preguntas que me formularon lectores, periodistas y colegas. Versiones previas de algunas partes se publicaron ya en formas diferentes, lo que me dio la oportunidad de recibir comentarios y pulir mis argumentos. Algunas secciones se centran en la tecnología, otras en la política, otras en la religión y otras en el arte. Determinados capítulos celebran la sabiduría humana, otros destacan el papel central de la estupidez humana. Pero la cuestión general sigue siendo la misma: ¿qué está ocurriendo hoy en el mundo y cuál es el significado profundo de los acontecimientos?
¿Qué implica el ascenso de Donald Trump? ¿Qué podemos hacer con la epidemia de noticias falsas? ¿Por qué está en crisis la democracia liberal? ¿Ha vuelto Dios? ¿Se aproxima una nueva guerra mundial? ¿Qué civilización domina el mundo: Occidente, China, el islam? ¿Tendría Europa que abrir sus puertas a los inmigrantes? ¿Puede el nacionalismo resolver los problemas de la desigualdad y del cambio climático? ¿Qué debemos hacer con respecto al terrorismo?
Aunque este libro adopta una perspectiva global, en él no descuido el plano personal. Por el contrario, quiero destacar las conexiones existentes entre las grandes revoluciones de nuestra era y la vida interior de los individuos. Por ejemplo, el terrorismo es a la vez un problema político global y un mecanismo psicológico interno. El terrorismo opera pulsando a fondo el botón del miedo en nuestra mente y secuestrando la imaginación individual de millones de personas. De forma similar, la crisis de la democracia liberal se desarrolla no solo en los parlamentos y los colegios electorales, sino también en las neuronas y las sinapsis. Es un tópico señalar que lo personal es lo político. Pero en una era en la que científicos, compañías y gobiernos aprenden a acceder ilegalmente al cerebro humano, este estereotipo resulta más siniestro que nunca. En consecuencia, el libro ofrece observaciones acerca de la conducta de los individuos, así como de las sociedades enteras.
Un mundo global ejerce una presión sin precedentes sobre nuestra conducta personal y nuestros valores. Cada uno de nosotros está atrapado por numerosas telarañas que lo abarcan todo, que por un lado restringen nuestros movimientos pero que al mismo tiempo transmiten nuestras más minúsculas sacudidas a destinos muy alejados. Nuestra rutina cotidiana influye en la vida de personas y animales que se hallan a medio mundo de distancia, y algunos gestos personales pueden incendiar el mundo entero, como ocurrió con la autoinmolación de Mohamed Bouazizi en Túnez, que desató la Primavera Árabe, y con las mujeres que compartieron sus experiencias de acoso sexual y desencadenaron el movimiento #MeToo.
Esta dimensión global de nuestra vida personal significa que es más importante que nunca poner al descubierto nuestros prejuicios religiosos y políticos, nuestros privilegios raciales y de género, y nuestra complicidad involuntaria con la opresión institucional. Pero ¿es esta una empresa realista? ¿Cómo puedo encontrar un terreno ético firme en un mundo que se extiende mucho más allá de mis horizontes, que gira completamente fuera del control humano y que considera sospechosos a todos los dioses y todas las ideologías?
El libro empieza con la revisión de la problemática política y tecnológica actual. Al finalizar el siglo XX parecía que las grandes batallas ideológicas entre el fascismo, el comunismo y el liberalismo daban como resultado la victoria abrumadora del liberalismo. La política democrática, los derechos humanos y el capitalismo de libre mercado parecían destinados a conquistar el mundo. Pero, como es habitual, la historia dio un giro inesperado, y ahora, tras el hundimiento del fascismo y el comunismo, el liberalismo se halla en apuros. Así pues, ¿hacia dónde nos dirigimos?
Esta pregunta resulta particularmente turbadora, porque el liberalismo está perdiendo credibilidad justo cuando las revoluciones paralelas en la tecnología de la información y en la biotecnología nos enfrentan a los mayores retos que nuestra especie ha encontrado nunca. La fusión de la infotecnología y la biotecnología puede hacer que muy pronto miles de millones de humanos queden fuera del mercado de trabajo y socavar tanto la libertad como la igualdad. Los algoritmos de macrodatos pueden crear dictaduras digitales en las que todo el poder esté concentrado en las manos de una élite minúscula al tiempo que la mayor parte de la gente padezca no ya explotación, sino algo muchísimo peor: irrelevancia.
Comenté extensamente la fusión de la infotecnología y la biotecnología en mi libro anterior, _Homo Deus_. Pero mientras que aquel libro se centraba en las expectativas a largo plazo y adoptaba la perspectiva de siglos e incluso de milenios, este se concentra en las crisis social, económica y política más inmediatas. Aquí mi interés no estriba tanto en la creación eventual de vida inorgánica como en la amenaza al estado del bienestar y a instituciones concretas, como la Unión Europea.
El libro no pretende abarcar todos los impactos de las nuevas tecnologías. En particular, aunque la tecnología encierra muchas promesas maravillosas, aquí mi intención es destacar principalmente las amenazas y los peligros. Puesto que las empresas y los emprendedores que encabezan la revolución tecnológica tienden naturalmente a cantar las alabanzas de sus creaciones, les toca a sociólogos, filósofos e historiadores como yo hacer saltar la alarma y explicar todas las maneras en que las cosas pueden ir terriblemente mal.
Después de esbozar los retos a los que nos enfrentamos, en la segunda parte del libro analizamos una amplia gama de respuestas potenciales. ¿Pueden los ingenieros de Facebook utilizar la inteligencia artificial (IA) para crear una comunidad global que salvaguarde la libertad y la igualdad humanas? ¿Quizá la respuesta sea invertir el proceso de globalización y volver a empoderar el estado nación? ¿Quizá tengamos que retroceder todavía más en el tiempo, y extraer esperanza y sabiduría de los manantiales de las antiguas tradiciones religiosas?
En la tercera parte del libro vemos que, aunque los retos tecnológicos no tienen precedentes y los desacuerdos políticos son grandes, la humanidad puede aprovechar la ocasión si controlamos nuestros temores y somos un poco más humildes respecto a nuestras ideas. En esa parte se investiga lo que puede hacerse ante la amenaza del terrorismo, ante el peligro de la guerra global y ante los prejuicios y los odios que desencadenan dichos conflictos.
La cuarta parte está dedicada a la noción de la posverdad, y pregunta hasta qué punto podemos comprender los acontecimientos globales y distinguir entre las fechorías y la justicia. ¿Es capaz _Homo sapiens_ de dar sentido al mundo que ha creado? ¿Existe todavía una frontera clara que separe la realidad de la ficción?
En la quinta y última parte reúno las diferentes hebras y adopto una mirada más general sobre la vida en una época de desconcierto, cuando los relatos antiguos se han desplomado y, de momento, no ha surgido uno nuevo para sustituirlos. ¿Quiénes somos? ¿Qué debemos hacer en la vida? ¿Qué tipo de talentos necesitamos? Dado todo lo que sabemos y no sabemos acerca de la ciencia, acerca de Dios, acerca de la política y la religión, ¿qué podemos decir acerca del significado de la vida en la actualidad?
Esto puede parecer sumamente ambicioso, pero _Homo sapiens_ no puede esperar. A la filosofía, a la religión y a la ciencia se les está acabando el tiempo. Durante miles de años se ha debatido sobre el significado de la vida. No podemos prolongar este debate de manera indefinida. La inminente crisis ecológica, la creciente amenaza de las armas de destrucción masiva y el auge de las nuevas tecnologías disruptivas no lo permitirá. Y quizá, lo que es más importante, la inteligencia artificial y la biotecnología están ofreciendo a la humanidad el poder de remodelar y rediseñar la vida. Muy pronto alguien tendrá que decidir cómo utilizar este poder, sobre la base de algún relato implícito o explícito acerca del significado de la vida. Los filósofos son personas muy pacientes, pero los ingenieros no lo son en la misma medida, y los inversores lo son aún menos. Si no sabemos qué hacer con el poder para diseñar vida, las fuerzas del mercado no esperarán mil años para que demos con una respuesta. La mano invisible del mercado nos obligará con su propia y ciega respuesta. A menos que nos contentemos con confiar el futuro de la vida a la merced de informes trimestrales de ingresos, necesitamos una idea clara sobre el sentido de la vida.
En el último capítulo me permito unas cuantas observaciones personales, y hablo como un sapiens lo haría a otro justo antes de que el telón caiga sobre nuestra especie y se inicie un drama de todo punto diferente.
Antes de embarcarme en este viaje intelectual, me gustaría destacar un aspecto crucial. Buena parte del libro cuestiona los defectos de la visión liberal del mundo y del sistema democrático. Lo hago no porque crea que la democracia liberal es singularmente problemática, sino más bien porque pienso que es el modelo político más versátil y de mayor éxito que los humanos han desarrollado hasta ahora para afrontar los retos del mundo moderno. Aunque quizá no sea apropiado para todas las sociedades en todas las fases del desarrollo, ha demostrado su valor en más sociedades y en más situaciones que ninguna de sus alternativas. Por tanto, cuando examinemos los nuevos retos que se nos presenten, será necesario comprender las limitaciones de la democracia liberal, y pensar cómo podemos adaptar y mejorar sus instituciones actuales.
Por desgracia, en el clima político actual cualquier pensamiento crítico sobre el liberalismo y la democracia podría acabar secuestrado por autócratas y diversos movimientos iliberales, cuyo único interés es desacreditar la democracia liberal en lugar de dedicarse a un debate abierto acerca del futuro de la humanidad. Si bien están más que dispuestos a debatir los problemas de la democracia liberal, casi no tienen tolerancia frente a cualquier crítica que se les dirija.
Como autor, por consiguiente, se me exigía que hiciera una elección difícil: ¿tenía que hablar con franqueza, arriesgándome a que mis palabras se interpretaran fuera de contexto y se usaran para justificar autocracias en expansión, o bien debía autocensurarme? Una característica de los regímenes iliberales es que dificultan más la libertad de expresión incluso fuera de sus fronteras. Debido a la expansión de tales regímenes, está resultando cada vez más peligroso pensar con actitud crítica en el futuro de nuestra especie.
Después de cierta introspección, elegí la discusión libre frente a la autocensura. Sin criticar el modelo liberal no podemos reparar sus faltas ni ir más allá de él. Pero advierta por favor el lector que este libro solo podía escribirse si la gente era todavía relativamente libre de pensar lo que quiere y de expresarse como quiere. Si el lector valora este libro, debería valorar también la libertad de expresión.
# Parte I
El desafío tecnológico
_La humanidad está perdiendo la fe en el relato liberal que ha dominado la política global en las últimas décadas, exactamente cuando la fusión de la biotecnología y la infotecnología nos enfrenta a los mayores desafíos que la humanidad ha conocido._
### 1
Decepción
####
#### El final de la historia se ha pospuesto
Los humanos pensamos más en relatos que en hechos, números o ecuaciones, y cuanto más sencillo es el relato, mejor. Cada persona, grupo y nación tiene sus propias fábulas y mitos. Pero durante el siglo XX las élites globales en Nueva York, Londres, Berlín y Moscú formularon tres grandes relatos que pretendían explicar todo el pasado y predecir el futuro del mundo: el relato fascista, el relato comunista y el relato liberal. La Segunda Guerra Mundial dejó fuera de combate el relato fascista, y desde finales de la década de 1940 hasta finales de la de 1980 el mundo se convirtió en un campo de batalla entre solo dos relatos: el comunista y el liberal. Después, el relato comunista se vino abajo, y el liberal siguió siendo la guía dominante para el pasado humano y el manual indispensable para el futuro del planeta, o eso es lo que le parecía a la élite global.
El relato liberal celebra el valor y el poder de la libertad. Afirma que durante miles de años la humanidad vivió bajo regímenes opresores que otorgaban al pueblo pocos derechos políticos, pocas oportunidades económicas o pocas libertades personales, y que restringían sobremanera los movimientos de individuos, ideas y bienes. Pero el pueblo luchó por su libertad, y paso a paso esta fue ganando terreno. Regímenes democráticos reemplazaron a dictaduras brutales. La libre empresa superó las restricciones económicas. Las personas aprendieron a pensar por sí mismas y a seguir su corazón, en lugar de obedecer ciegamente a sacerdotes intolerantes a y a tradiciones rígidas. Carreteras abiertas, puentes resistentes y aeropuertos atestados sustituyeron muros, fosos y vallas de alambre de espino.
El relato liberal reconoce que no todo va bien en el mundo, y que todavía quedan muchos obstáculos por superar. Gran parte de nuestro planeta está dominado por tiranos, e incluso en los países más liberales muchos ciudadanos padecen pobreza, violencia y opresión. Pero al menos sabemos qué tenemos que hacer a fin de superar estos problemas: conceder más libertad a la gente. Necesitamos proteger los derechos humanos, conceder el voto a todo el mundo, establecer mercados libres y permitir que individuos, ideas y bienes se muevan por todo el planeta con la mayor facilidad posible. Según esta panacea liberal (que, con variaciones mínimas, aceptaron tanto George W. Bush como Barack Obama), si continuamos liberalizando y globalizando nuestros sistemas políticos y económicos, generaremos paz y prosperidad para todos.[1]
Los países que se apunten a esta marcha imparable del progreso se verán recompensados muy pronto con la paz y la prosperidad. Los países que intenten resistirse a lo inevitable sufrirán las consecuencias, hasta que también ellos vean la luz, abran sus fronteras y liberalicen sus sociedades, su política y sus mercados. Puede que tome tiempo, pero al final incluso Corea del Norte, Irak y El Salvador se parecerán a Dinamarca o a Iowa.
En las décadas de 1990 y 2000 este relato se convirtió en un mantra global. Muchos gobiernos, desde Brasil hasta la India, adoptaron fórmulas liberales en un intento de incorporarse a la marcha inexorable de la historia. Los que no lo consiguieron parecían fósiles de una época obsoleta. En 1997, el presidente de Estados Unidos, Bill Clinton, reprendió confidencialmente al gobierno chino diciéndole que su negativa a liberalizar su política lo situaba «en el lado equivocado de la historia».[2]
Sin embargo, desde la crisis financiera global de 2008, personas de todo el mundo se sienten cada vez más decepcionadas del relato liberal. Los muros y las barras de control de acceso vuelven a estar de moda. La resistencia a la inmigración y a los acuerdos comerciales aumenta. Gobiernos en apariencia democráticos socavan la independencia del sistema judicial, restringen la libertad de prensa y califican de traición cualquier tipo de oposición. Los caudillos de países como Turquía y Rusia experimentan con nuevos tipos de democracia intolerante y dictadura absoluta. Hoy en día son pocos los que declararían de forma confidencial que el Partido Comunista chino se halla en el lado equivocado de la historia.
El año 2016, marcado sin duda por la votación sobre el Brexit en Gran Bretaña y el acceso de Donald Trump a la presidencia de Estados Unidos, fue el momento en que esta marea de desencanto alcanzó los estados liberales básicos de Europa occidental y de Norteamérica. Mientras que hace unos pocos años norteamericanos y europeos seguían intentando aún liberalizar Irak y Libia a punta de pistola, muchas personas en Kentucky y Yorkshire han terminado por considerar que la visión liberal es o bien indeseable o bien inalcanzable. Algunas han descubierto que les gusta el antiguo mundo jerárquico y, simplemente, no quieren renunciar a sus privilegios raciales, nacionales o de género. Otras han llegado a la conclusión (correcta o no) de que la liberalización y la globalización son un enorme chanchullo que empodera a una minúscula élite a costa de las masas.
En 1938 a los humanos se les ofrecían tres relatos globales entre los que elegir, en 1968 solo dos y en 1998 parecía que se imponía un único relato; en 2018 hemos bajado a cero. No es extraño que las élites liberales, que dominaron gran parte del mundo en décadas recientes, se hayan sumido en un estado de conmoción y desorientación. Tener un relato es la situación más tranquilizadora. Todo está perfectamente claro. Que de repente nos quedemos sin ninguno resulta terrorífico. Nada tiene sentido. Un poco a la manera de la élite soviética en la década de 1980, los liberales no comprenden cómo la historia se desvió de su ruta predestinada, y carecen de un prisma alternativo para interpretar la realidad. La desorientación los lleva a pensar en términos apocalípticos, como si el fracaso de la historia para llegar a su previsto final feliz solo pudiera significar que se precipita hacia el Armagedón. Incapaz de realizar una verificación de la realidad, la mente se aferra a situaciones hipotéticas catastróficas. Al igual que una persona que imagine que un fuerte dolor de cabeza implica un tumor cerebral terminal, muchos liberales temen que el Brexit y el ascenso de Donald Trump presagien el fin de la civilización humana.
##### DE MATAR MOSQUITOS A MATAR PENSAMIENTOS
La sensación de desorientación y de fatalidad inminente se agrava por el ritmo acelerado de la disrupción tecnológica. Durante la era industrial, el sistema político liberal se moldeó para gestionar un mundo de motores de vapor, refinerías de petróleo y televisores. Le cuesta tratar con las revoluciones en curso en la tecnología de la información y la biotecnología.
Tanto los políticos como los votantes apenas pueden comprender las nuevas tecnologías, y no digamos ya regular su potencial explosivo. Desde la década de 1990, internet ha cambiado el mundo probablemente más que ningún otro factor, pero la revolución internáutica la han dirigido ingenieros más que partidos políticos. ¿Acaso el lector votó sobre internet? El sistema democrático todavía está esforzándose para comprender qué le ha golpeado, y apenas está capacitado para habérselas con los trastornos que se avecinan, como el auge de la IA y la revolución de la cadena de bloques.
Ya en la actualidad, los ordenadores han hecho que el sistema financiero sea tan complicado que pocos humanos pueden entenderlo. A medida que la IA mejore, puede que pronto alcancemos un punto en el que ningún humano logre comprender ya las finanzas. ¿Qué consecuencias tendrá para el proceso político? ¿Puede el lector imaginar un gobierno que espere sumiso a que un algoritmo apruebe sus presupuestos o su nueva reforma tributaria? Mientras tanto, redes de cadenas de bloques entre iguales y criptomonedas como el bitcóin pueden renovar por completo el sistema monetario, de modo que las reformas tributarias radicales sean inevitables. Por ejemplo, podría acabar siendo imposible o irrelevante gravar los dólares, porque la mayoría de las transacciones no implicarán un intercambio claro de moneda nacional, o de ninguna moneda en absoluto. Por tanto, quizá los gobiernos necesiten inventar impuestos totalmente nuevos, tal vez un impuesto sobre la información (que será, al mismo tiempo, el activo más importante en la economía y la única cosa que se intercambie en numerosas transacciones). ¿Conseguirá el sistema político lidiar con la crisis antes de quedarse sin dinero?
Más importante todavía es el hecho de que las revoluciones paralelas en la infotecnología y la biotecnología podrían reestructurar no solo las economías y las sociedades, sino también nuestros mismos cuerpo y mente. En el pasado, los humanos aprendimos a controlar el mundo exterior a nosotros, pero teníamos muy poco control sobre nuestro mundo interior. Sabíamos cómo construir una presa y detener la corriente de un río, pero no cómo conseguir que el cuerpo dejara de envejecer. Sabíamos diseñar un sistema de irrigación, pero no teníamos ni idea de cómo diseñar un cerebro. Si los mosquitos nos zumbaban en los oídos y perturbaban nuestro sueño, sabíamos cómo matarlos; pero si un pensamiento zumbaba en nuestra mente y nos mantenía despiertos de noche, la mayoría no sabíamos cómo acabar con él.
Las revoluciones en la biotecnología y la infotecnología nos proporcionarán el control de nuestro mundo interior y nos permitirán proyectar y producir vida. Aprenderemos a diseñar cerebros, a alargar la vida y a acabar con pensamientos a nuestra discreción. Nadie sabe cuáles serán las consecuencias. Los humanos siempre han sido mucho más duchos en inventar herramientas que en usarlas sabiamente. Es más fácil reconducir un río mediante la construcción de una presa que predecir las complejas consecuencias que ello tendrá para el sistema ecológico de la región. De modo parecido, será más fácil redirigir el flujo de nuestra mente que adivinar cómo repercutirá esto en nuestra psicología individual o en nuestros sistemas sociales.
En el pasado conseguimos el poder para manipular el mundo que nos rodeaba y remodelar el planeta entero, pero debido a que no comprendíamos la complejidad de la ecología global, los cambios que hicimos involuntariamente alteraron todo el sistema ecológico, y ahora nos enfrentamos a un colapso ecológico. En el siglo que viene, la biotecnología y la infotecnología nos proporcionarán el poder de manipular nuestro mundo interior y remodelarnos, pero debido a que no comprendemos la complejidad de nuestra propia mente, los cambios que hagamos podrían alterar nuestro sistema mental hasta tal extremo que también este podría descomponerse.
Las revoluciones en la biotecnología y la infotecnología las llevan a cabo los ingenieros, los emprendedores y los científicos, que apenas son conscientes de las implicaciones políticas de sus decisiones, y que ciertamente no representan a nadie. ¿Pueden los parlamentos y los partidos tomar las riendas? Por el momento, no lo parece. La disrupción tecnológica no constituye siquiera un punto importante en los programas políticos. Así, durante la campaña presidencial de 2016 en Estados Unidos, la principal referencia a la tecnología disruptiva fue la debacle de los correos electrónicos de Hillary Clinton,[3] y a pesar de los discursos sobre la pérdida de empleos, ningún candidato abordó el impacto potencial de la automatización. Donald Trump advirtió a los votantes que mexicanos y chinos les quitarían el trabajo, y que por tanto tenían que erigir un muro en la frontera mexicana.[4] Nunca advirtió a los votantes que los algoritmos les quitarán el trabajo, ni sugirió que se construyera un cortafuegos en la frontera con California.
Esta podría ser una de las razones (aunque no la única) por las que incluso los votantes de los feudos del Occidente liberal pierdan su fe en el relato liberal y en el proceso democrático. Las personas de a pie quizá no comprendan la inteligencia artificial ni la biotecnología, pero pueden percibir que el futuro no las tiene en cuenta. En 1938, las condiciones del ciudadano de a pie en la Unión Soviética, Alemania o Estados Unidos tal vez fueran muy difíciles, pero constantemente se le decía que era la cosa más importante del mundo, y que era el futuro (siempre que, desde luego, se tratara de una «persona normal» y no un judío o un africano). Miraba los carteles de la propaganda (que solían presentar a mineros del carbón, operarios de acerías y amas de casa en actitudes heroicas) y se veía a sí mismo en ellos: «¡Estoy en este cartel! ¡Soy el héroe del futuro!».[5]
En 2018, el ciudadano de a pie se siente cada vez más irrelevante. En las charlas TED, en los comités de expertos del gobierno, en las conferencias sobre alta tecnología se difunden de forma entusiasta gran cantidad de conceptos misteriosos (globalización, cadenas de bloques, ingeniería genética, inteligencia artificial, _machine_ _learning_ o aprendizaje automático), y la gente de a pie puede sospechar con razón que ninguno tiene que ver con ella. El relato liberal era el de la gente de a pie. ¿Cómo puede seguir siendo relevante en un mundo de cíborgs y de algoritmos conectados en red?
En el siglo XX, las masas se rebelaron contra la explotación y trataron de convertir su papel vital en la economía en poder político. Ahora las masas temen la irrelevancia, y quieren usar frenéticamente el poder político que les resta antes de que sea demasiado tarde. El Brexit y el ascenso de Trump muestran así una trayectoria opuesta a la de las revoluciones socialistas tradicionales. Las revoluciones rusa, china y cubana las llevaron a cabo personas que eran vitales para la economía, pero que carecían de poder político; en 2016, Trump y el Brexit recibieron el apoyo de muchas personas que todavía gozaban de poder político pero que temían estar perdiendo su valor económico. Quizá en el siglo XXI las revueltas populistas se organicen no contra una élite económica que explota a la gente, sino contra una élite económica que ya no la necesita.[6] Esta bien pudiera ser una batalla perdida. Es mucho más difícil luchar contra la irrelevancia que contra la explotación.
##### EL FÉNIX LIBERAL
No es esta la primera vez que el relato liberal se ha enfrentado a una crisis de confianza. Incluso desde el momento en que dicho relato consiguió influir en la esfera global, en la segunda mitad del siglo XX, ha experimentado crisis periódicas. La primera era de globalización y liberalización terminó con el baño de sangre de la Primera Guerra Mundial, cuando la política del poder imperial cortó de raíz la marcha del progreso. En los días que siguieron al asesinato del archiduque Francisco Fernando en Sarajevo, las grandes potencias creyeron mucho más en el imperialismo que en el liberalismo y, en lugar de unir el mundo mediante el comercio libre y pacífico, se dedicaron a conquistar una tajada mayor del globo mediante la fuerza bruta. Pero el liberalismo sobrevivió a ese momento de Francisco Fernando y surgió de la vorágine fortalecido, y prometió que aquella sería «la guerra que terminaría con todas las guerras». En teoría, aquella carnicería sin precedentes había enseñado a la humanidad el precio terrible del imperialismo, y la humanidad se hallaba por fin preparada para crear un nuevo orden mundial basado en los principios de la libertad y la paz.
A continuación llegó el momento de Hitler, cuando, en la década de 1930 y principios de la de 1940, el fascismo pareció por un breve período arrollador. La victoria sobre esta amenaza no hizo más que abrir paso a la siguiente. En el momento del Che Guevara, entre la década de 1950 y la de 1970, de nuevo daba la impresión de que el liberalismo se hallaba en las últimas, y que el futuro pertenecía al comunismo. Al final fue el comunismo el que se derrumbó. El supermercado demostró ser mucho más fuerte que el gulag. Y lo que es más importante: el relato liberal demostró ser mucho más flexible y dinámico que ninguno de sus oponentes. Triunfó sobre el imperialismo, el fascismo y el comunismo al adoptar algunas de las mejores ideas y prácticas de estos. En particular, el relato liberal aprendió del comunismo a ampliar el círculo de la empatía y a valorar la igualdad junto con la libertad.
Al principio, el relato liberal se centró sobre todo en las libertades y los privilegios de los hombres europeos de clase media, y parecía ciego a los apuros de la clase trabajadora, las mujeres, las minorías y los no occidentales. Cuando en 1918 la Gran Bretaña y la Francia victoriosas hablaban con entusiasmo de libertad, no pensaban en los súbditos de sus imperios mundiales. Por ejemplo, ante las demandas indias de autodeterminación se respondió con la masacre de Amritsar de 1919, en la que el ejército británico acabó con cientos de manifestantes desarmados.
Incluso después de la Segunda Guerra Mundial, a los liberales occidentales aún les costó mucho aplicar sus valores en teoría universales a personas no occidentales. Así, cuando en 1945 los holandeses se liberaron de cinco años de brutal ocupación nazi, casi lo primero que hicieron fue organizar un ejército y mandarlo a medio mundo de distancia para que volviera a ocupar su antigua colonia de Indonesia. Mientras que en 1940 los holandeses habían renunciado a su independencia tras poco más de cuatro días de lucha, combatieron durante más de cuatro largos y amargos años para acabar con la independencia de Indonesia. No es extraño que muchos movimientos de liberación nacional de todo el mundo pusieran sus esperanzas en las comunistas Moscú y Pekín y no en los sedicentes adalides de la libertad en Occidente.
Sin embargo, el relato liberal amplió poco a poco sus horizontes y, al menos en teoría, acabó valorando las libertades y los derechos de todos los seres humanos sin excepción. A medida que el círculo de libertad se expandía, el relato liberal terminó por reconocer la importancia de los programas de bienestar de estilo comunista. La libertad no vale mucho a menos que esté vinculada a algún tipo de sistema de seguridad social. Los estados socialdemócratas de bienestar combinaron la democracia y los derechos humanos con la educación y la atención sanitaria sufragadas por el Estado. Incluso Estados Unidos, ultracapitalista, se ha dado cuenta de que la protección de la libertad requiere al menos algunos servicios de bienestar facilitados por el gobierno. Los niños hambrientos no tienen libertades.
En los primeros años de la década de 1990, tanto pensadores como políticos saludaron «el fin de la historia» y afirmaron confiados que todas las cuestiones políticas y económicas ya habían sido zanjadas, y que el paquete liberal renovado de democracia, derechos humanos, mercados libres y prestaciones de bienestar gubernamentales seguía siendo la única alternativa. Dicho paquete parecía destinado a extenderse por el planeta, a vencer todos los obstáculos, a borrar todas las fronteras nacionales y a transformar a la humanidad en una comunidad global libre.[7]
Pero la historia no ha terminado, y después del momento de Francisco Fernando, del de Hitler y del del Che Guevara, ahora estamos en el momento de Trump. Sin embargo, esta vez el relato liberal no se enfrenta a un oponente ideológico coherente como el imperialismo, el fascismo o el comunismo. El momento Trump es mucho más nihilista.
Mientras que la visión de los principales movimientos del siglo XX abarcaba a toda la especie humana (ya se tratara de dominación global, de revolución o de liberación), no es esto lo que ofrece Donald Trump: es justo lo contrario. Su mensaje principal es que no es tarea de Estados Unidos formular y promover ninguna visión global. De manera similar, los brexiteros británicos apenas tienen un plan para el futuro del Reino Desunido: el futuro de Europa y del mundo queda mucho más allá de su horizonte. La mayoría de las personas que votaron a favor de Trump y del Brexit no rechazaron en su totalidad el paquete liberal: perdieron la fe sobre todo en su parte globalizadora. Todavía creen en la democracia, los mercados libres, los derechos humanos y la responsabilidad social, pero piensan que estas ideas magníficas pueden detenerse en la frontera. Es más: creen que con el objetivo de preservar la libertad y la prosperidad en Yorkshire o Kentucky lo mejor es construir un muro en la frontera y adoptar políticas intolerantes para con los extranjeros.
La superpotencia china en auge presenta una imagen casi especular. Recela de liberalizar su política doméstica, pero ha adoptado un enfoque mucho más liberal hacia el resto del mundo. De hecho, en lo que se refiere a libre comercio y cooperación internacional, Xi Jinping parece el sucesor real de Obama. Después de haber dejado en segundo plano el marxismo-leninismo, China parece encontrarse a gusto con el orden liberal internacional.
La Rusia renaciente se ve a sí misma como un rival mucho más contundente del orden liberal global, pero, aunque ha reconstituido su poder militar, desde el punto de vista ideológico está acabada. Vladímir Putin es sin duda popular tanto en Rusia como entre varios movimientos de extrema derecha de todo el mundo, pero carece de una visión global del mundo que pueda atraer a los españoles desempleados, a los brasileños insatisfechos o a los estudiantes soñadores de Cambridge.
Rusia sí ofrece un modelo alternativo a la democracia liberal, pero dicho modelo no es una ideología política coherente. Es más bien una práctica política en la que varios oligarcas monopolizan la mayor parte de las riquezas y el poder del país, y después utilizan su control sobre los medios de comunicación para ocultar sus actividades y afianzar su gobierno. La democracia se basa en el principio de Abraham Lincoln de que «puedes engañar a toda la gente en algún momento, y a algunas personas todo el tiempo, pero no puedes engañar a toda la gente todo el tiempo». Si un gobierno es corrupto y no consigue mejorar la vida de la gente, un número suficiente de ciudadanos acabarán por darse cuenta de ello y lo sustituirán. Pero el control gubernamental de los medios de comunicación socava la lógica de Lincoln, pues impide que los ciudadanos se den cuenta de la verdad. Mediante su monopolio sobre los medios, la oligarquía gobernante puede acusar repetidamente de sus fracasos a otros y desviar la atención hacia amenazas externas, ya sean reales o imaginarias.
Cuando se vive bajo una oligarquía de este tipo, siempre surge alguna crisis que tiene prioridad sobre asuntos aburridos como la atención sanitaria y la contaminación. Si la nación se enfrenta a una invasión externa o a una subversión diabólica, ¿quién tiene tiempo de preocuparse por los hospitales abarrotados o los ríos contaminados? Creando un torrente interminable de crisis, una oligarquía corrupta puede prolongar su poder indefinidamente.[8]
Pero, aunque resiste en la práctica, este modelo oligárquico no atrae a nadie. A diferencia de otras ideologías que exponen con orgullo su visión, las oligarquías dominantes no están orgullosas de sus prácticas, y tienden a usar otras ideologías como cortina de humo. Así, Rusia pretende ser una democracia, y su liderazgo proclama lealtad a los valores del nacionalismo ruso y del cristianismo ortodoxo, y no a la oligarquía. Los extremistas de derechas en Francia y Gran Bretaña pueden basarse en la ayuda rusa y expresar admiración por Putin, pero ni siquiera a sus votantes les gustaría vivir en un país que copiara de verdad el modelo ruso: un país con corrupción endémica, servicios que no funcionan, sin imperio de la ley y una desigualdad abrumadora. Según determinados parámetros, Rusia es uno de los países con mayor desigualdad del mundo, donde el 87 por ciento de la riqueza se halla en manos del 10 por ciento de los más ricos.[9] ¿Cuántos votantes de clase trabajadora del Frente Nacional quieren copiar en Francia esta pauta de distribución de la riqueza?
Los humanos votan con los pies. En mis viajes por el mundo he encontrado a numerosas personas en muchos países que quieren emigrar a Estados Unidos, a Alemania, a Canadá o a Australia. He conocido a algunas que desean desplazarse a China o a Japón. Pero todavía no he encontrado a una sola que sueñe con emigrar a Rusia.
En cuanto al «islamismo global», atrae sobre todo a quienes nacieron en su seno. Aunque puede resultar atractivo para algunas personas en Siria e Irak, e incluso para jóvenes musulmanes alienados en Alemania y Gran Bretaña, cuesta pensar que Grecia o Sudáfrica, por no mencionar Canadá o Corea del Sur, se unan a un califato global como remedio para sus problemas. También en este caso la gente vota con los pies. Por cada joven musulmán de Alemania que viajó a Oriente Próximo para vivir bajo una teocracia musulmana, probablemente a cien jóvenes de Oriente Próximo les hubiera gustado hacer el viaje opuesto y empezar una nueva vida en la liberal Alemania.
Esto podría implicar que la crisis de fe actual sea menos grave que sus predecesoras. Cualquier liberal que se vea abocado a la desesperanza por los acontecimientos de los últimos años no tiene más que recordar que en 19188 o 1968 las cosas se veían mucho peor. Al final del día, la humanidad no abandonará el relato liberal, porque no tiene ninguna alternativa. La gente puede asestar al sistema un rabioso puñetazo en el estómago, pero, al no tener ningún otro lugar al que ir, acabará por volver a él.
Alternativamente, la gente puede decidir renunciar por completo a un relato global de cualquier tipo, y en cambio refugiarse en los relatos nacionalistas y religiosos locales. En el siglo XX, los movimientos nacionalistas fueron una pieza clave política, pero carecían de una visión coherente para el futuro del mundo, como no fuera apoyar la división del planeta en estados nación independientes. Así, los nacionalistas indonesios lucharon contra la dominación holandesa y los nacionalistas vietnamitas querían un Vietnam libre, pero no había un relato indonesio ni vietnamita pensado y válido para la humanidad como un todo. Cuando llegó el momento de explicar de qué manera Indonesia, Vietnam y las demás naciones libres debían relacionarse entre sí, y cómo debían enfrentarse los humanos a problemas globales tales como la amenaza de la guerra nuclear, los nacionalistas recurrieron invariablemente a las ideas liberales o comunistas.
Pero si tanto el liberalismo como el comunismo están ahora desacreditados, quizá los humanos deban renunciar a la idea misma de un único relato global. Después de todo, ¿no fueron todos estos relatos globales (incluso el comunismo) producto del imperialismo occidental? ¿Por qué habrían de depositar su fe los campesinos vietnamitas en la ocurrencia de un alemán de Trier y de un industrial de Manchester? Quizá cada país debería adoptar una senda idiosincrásica diferente, definida por sus propias y antiguas tradiciones. Tal vez incluso los occidentales deberían tomarse un descanso en su intento de gobernar el mundo y centrarse en sus propios asuntos, para variar.
Puede decirse que esto es lo que ocurre en todo el planeta, cuando el vacío creado por la descomposición del liberalismo está llenándose provisionalmente de fantasías nostálgicas acerca de algún pasado glorioso local. Donald Trump unió sus llamadas al aislacionismo estadounidense a la promesa de «hacer que América sea grande de nuevo»..., como si los Estados Unidos de las décadas de 1980 o 1950 fueran una sociedad perfecta que los estadounidenses tuvieran que recrear de alguna manera en el siglo XXI. Los brexiteros sueñan con convertir Gran Bretaña en una potencia independiente, como si aún vivieran en los tiempos de la reina Victoria y como si el «aislamiento glorioso» fuera una política viable en la era de internet y del calentamiento global. Las élites chinas han redescubierto sus herencias imperiales y confucianas nativas, como suplemento o incluso sustituto de la dudosa ideología marxista que importaron de Occidente. En Rusia, la visión oficial de Putin no es crear una oligarquía corrupta, sino resucitar el antiguo Imperio zarista. Un siglo después de la Revolución bolchevique, promete un retorno a las antiguas glorias zaristas con un gobierno autocrático mantenido a flote por el nacionalismo ruso y la piedad ortodoxa, que extienda su poderío desde el Báltico al Cáucaso.
Sueños nostálgicos parecidos que mezclan vínculos nacionalistas con tradiciones religiosas apuntalan los regímenes en la India, Polonia, Turquía y numerosos países más. En ningún lugar son estas fantasías más extremas que en Oriente Próximo, donde los islamistas quieren copiar el sistema establecido por el profeta Mahoma en la ciudad de Medina hace mil cuatrocientos años, mientras que los judíos fundamentalistas en Israel superan incluso a los islamistas y sueñan con retroceder dos mil quinientos años, a los tiempos bíblicos. Los miembros de la coalición de gobierno que gobierna en Israel hablan sin tapujos de su esperanza de expandir las fronteras del Israel moderno hasta que coincidan a la perfección con las del Israel bíblico, de reinstaurar la ley bíblica e incluso de reconstruir el antiguo Templo de Yahvé en Jerusalén en lugar de la mezquita de Al-Aqsa.[10]
Las élites liberales contemplan horrorizadas estas situaciones, y esperan que la humanidad retorne a la senda liberal a tiempo de evitar el desastre. En su discurso de despedida ante las Naciones Unidas, en septiembre de 2016, el presidente Obama desaconsejó a la audiencia que se volviera «a un mundo fuertemente dividido, y en último término en conflicto, a lo largo de antiguas líneas de nación y tribu, de raza y religión». En cambio, dijo, «los principios de mercados abiertos y gobierno responsable, de democracia y derechos humanos y ley internacional ...] siguen siendo los cimientos más firmes para el progreso humano en este siglo».[[11]
Obama ha señalado con acierto que, a pesar de los numerosos defectos del paquete liberal, este tiene un historial mucho mejor que cualquiera de sus alternativas. La mayoría de los humanos nunca han disfrutado de mayor paz o prosperidad que durante la tutela del orden liberal de principios del siglo XXI. Por primera vez en la historia, las enfermedades infecciosas matan a menos personas que la vejez, el hambre mata a menos personas que la obesidad y la violencia mata a menos personas que los accidentes.
Pero el liberalismo no tiene respuestas obvias a los mayores problemas a los que nos enfrentamos: el colapso ecológico y la disrupción tecnológica. Tradicionalmente, el liberalismo se basaba en el crecimiento económico para resolver como por arte de magia los conflictos sociales y políticos difíciles. El liberalismo reconciliaba al proletariado con la burguesía, a los fieles con los ateos, a los nativos con los inmigrantes y a los europeos con los asiáticos, al prometer a todos una porción mayor del pastel. Con un pastel que crecía sin parar, esto era posible. Sin embargo, el crecimiento económico no salvará al ecosistema global; justo lo contrario, porque es la causa de la crisis ecológica. Y el crecimiento económico no resolverá la disrupción tecnológica: esta se afirma en la invención de tecnologías cada vez más disruptivas.
El relato liberal y la lógica del capitalismo de mercado libre estimulan a la gente para que albergue grandes expectativas. Durante las últimas décadas del siglo XX, cada generación (ya fuera en Houston, Shangai, Estambul o São Paulo) disfrutó de una educación mejor, una atención sanitaria superior y unos ingresos más cuantiosos que la que la precedió. Sin embargo, en las décadas que vienen, debido a una combinación de disrupción tecnológica y colapso ecológico, la generación más joven podrá sentirse afortunada si al menos consigue subsistir.
En consecuencia, nos queda la tarea de crear un relato actualizado para el mundo. De la misma manera que los grandes cambios generados por la revolución industrial dieron origen a las nuevas ideologías del siglo XX, es probable que las revoluciones venideras en biotecnología y tecnología de la información requieran perspectivas nuevas. Por tanto, las próximas décadas podrían estar caracterizadas por grandes búsquedas espirituales y por la formulación de nuevos modelos sociales y políticos. ¿Podría reinventarse de nuevo el liberalismo, como hizo a raíz de las crisis de las décadas de 1930 y 1960, y renacer más atractivo que antes? ¿Podrían la religión y el nacionalismo tradicionales proporcionar las respuestas que se les escapan a los liberales, y usar la sabiduría antigua para crear una visión del mundo actualizada? ¿O quizá haya llegado el momento de cortar para siempre con el pasado y elaborar un relato completamente nuevo que vaya más allá no solo de los antiguos dioses y las antiguas naciones, sino incluso de la esencia de los valores modernos de la libertad y la igualdad?
En la actualidad, la humanidad está lejos de alcanzar un consenso sobre estas cuestiones. Nos hallamos todavía en el momento nihilista de la desilusión y la indignación, después de que la gente haya perdido la fe en los relatos antiguos, pero antes de que haya adoptado uno nuevo. Y entonces ¿qué hay que hacer? El primer paso es bajar el tono de las profecías del desastre, y pasar del modo de pánico al de perplejidad. El pánico es una forma de arrogancia. Proviene de la sensación petulante de que uno sabe exactamente hacia dónde se dirige el mundo: cuesta abajo. La perplejidad es más humilde y, por tanto, más perspicaz. Si el lector tiene ganas de correr por la calle gritando: «¡Se nos viene encima el apocalipsis!», pruebe a decirse: «No, no es eso. Lo cierto es que no entiendo lo que está ocurriendo en el mundo».
En los capítulos que siguen se intentará clarificar algunas de las perspectivas nuevas y desconcertantes a las que nos enfrentamos, y cómo deberíamos proceder a partir de ahí. Pero antes de explorar soluciones potenciales para los problemas de la humanidad, necesitamos comprender mejor el desafío que plantea la tecnología. Las revoluciones en la tecnología de la información y en la biotecnología se hallan todavía en una fase temprana, y es discutible hasta qué punto son en verdad responsables de la crisis actual del liberalismo. La mayoría de los habitantes de Birmingham, Estambul, San Petersburgo y Bombay solo son un poco conscientes, si acaso lo son, del incremento de la inteligencia artificial y de su impacto potencial sobre su vida. Sin embargo, es indudable que las revoluciones tecnológicas se acelerarán en las próximas décadas, y plantearán a la humanidad las mayores dificultades a las que nos hayamos enfrentado nunca. Cualquier relato que trate de ganarse a la humanidad será puesto a prueba, por encima de todo, por su capacidad para afrontar las revoluciones paralelas en la infotecnología y la biotecnología. Si el liberalismo, el nacionalismo, el islamismo o cualquier credo nuevo desea modelar el mundo de 2050, no solo necesitará dar sentido a la inteligencia artificial, a los algoritmos de macrodatos y a la bioingeniería: también tendrá que incorporarlos en una nueva narrativa que tenga significado.
Para entender la naturaleza de este desafío tecnológico, quizá sea mejor empezar por el mercado laboral. Desde 2015 he viajado por todo el mundo y he hablado con funcionarios gubernamentales, empresarios, activistas sociales y escolares acerca del atolladero humano. Siempre que se impacientan o se aburren con la cháchara sobre inteligencia artificial, algoritmos de macrodatos y bioingeniería, por lo general solo tengo que mencionar tres palabras mágicas para que presten atención inmediatamente: puestos de trabajo. Quizá la revolución tecnológica eche pronto del mercado de trabajo a miles de millones de humanos y cree una nueva y enorme clase inútil, que lleve a revueltas sociales y políticas que ninguna ideología existente sabrá cómo manejar. Todos los debates sobre tecnología e ideología pueden parecer muy abstractos y lejanos, pero la perspectiva muy real del desempleo masivo (o del desempleo personal) no deja indiferente a nadie.
### 2
Trabajo
#### Cuando te hagas mayor, puede que no tengas un empleo
No tenemos idea alguna de cómo será el mercado laboral en 2050. Por lo general, se está de acuerdo en que el aprendizaje automático cambiará casi todos los tipos de trabajo, desde la producción de yogures hasta la enseñanza del yoga. Sin embargo, hay opiniones contradictorias acerca de la naturaleza del cambio y de su inminencia. Algunos creen que apenas dentro de una o dos décadas miles de millones de personas se volverán innecesarias desde el punto de vista económico. Otros creen que, incluso a largo plazo, la automatización seguirá generando nuevos empleos y mayor prosperidad para todos.
Así pues, ¿nos hallamos a las puertas de un período convulso y terrible, o tales predicciones son solo otro ejemplo de histeria ludita infundada? Es difícil decirlo. Los temores de que la automatización genere un desempleo masivo se remontan al siglo XIX, y hasta ahora nunca se han materializado. Desde el inicio de la revolución industrial, para cada empleo que se perdía debido a una máquina se creó al menos uno nuevo, y el nivel de vida medio ha aumentado de manera espectacular.[1] Pero hay buenas razones para pensar que esta vez será diferente y que el aprendizaje automático conllevará un cambio real en las reglas del juego.
Los humanos tienen dos tipos de capacidades: la física y la cognitiva. En el pasado, las máquinas competían con los humanos principalmente en las capacidades físicas en bruto, mientras que estos tenían una enorme ventaja sobre las máquinas en cuanto a cognición. De ahí que cuando los trabajos manuales en la agricultura y la industria se automatizaron, aparecieron nuevos empleos de servicios que requerían capacidades cognitivas que solo los humanos poseían: aprender, analizar, comunicar y, por encima de todo, comprender las emociones humanas. Sin embargo, la IA está empezando ahora a superar a los humanos cada vez en más de estas capacidades, entre ellas la comprensión de las emociones humanas.[2] No conocemos un tercer campo de actividad (más allá del físico y el cognitivo) en el que los humanos se hallen siempre en situación de ventaja.
Es fundamental darse cuenta de que la revolución de la IA no tiene que ver solo con que los ordenadores sean cada vez más rápidos y listos. Está impulsada asimismo por descubrimientos en las ciencias de la vida y las ciencias sociales. Cuanto mejor comprendamos los mecanismos bioquímicos que subyacen a las emociones, los deseos y las elecciones humanas, mejores serán los ordenadores a la hora de analizar el comportamiento humano, de predecir las decisiones de los humanos y de sustituir a los conductores, banqueros y abogados humanos.
En las últimas décadas, la investigación en áreas tales como la neurociencia y la economía conductual ha permitido a los científicos acceder a los humanos, y en particular comprender mucho mejor cómo toman las decisiones. Se ha descubierto que todas las elecciones que hacemos, escoger desde la comida hasta la pareja, son resultado no de algún misterioso libre albedrío, sino del trabajo de miles de millones de neuronas que calculan probabilidades en una fracción de segundo. La tan cacareada «intuición humana» es en realidad «reconocimiento de patrones».[3] Los buenos conductores, banqueros y abogados no tienen intuiciones mágicas acerca del tráfico, la inversión o la negociación; lo que ocurre es que, al reconocer patrones recurrentes, divisan e intentan evitar a peatones despistados, a prestatarios ineptos y a delincuentes deshonestos. También se ha visto que los algoritmos bioquímicos del cerebro humano están lejos de ser perfectos. Se basan en el ensayo y el error, atajos y circuitos anticuados adaptados a la sabana africana y no a la jungla urbana. No es extraño que incluso los buenos conductores, banqueros y abogados cometan a veces errores tontos.
Esto significa que la IA puede superar a los humanos incluso en tareas que en teoría exigen «intuición». Si el lector cree que la IA debe competir con el alma humana en términos de corazonadas místicas, eso parece imposible. Pero si la IA debe competir con redes neurales en el cálculo de probabilidades y el reconocimiento de patrones, eso parece mucho menos abrumador.
En particular, la IA puede ser mejor en tareas que requieren intuiciones acerca de otras personas. Muchos tipos de trabajo, como conducir un vehículo en una calle atestada de peatones, prestar dinero a desconocidos o negociar un acuerdo comercial, exigen la capacidad de evaluar correctamente las emociones y los deseos de otras personas. ¿Está ese chico a punto de saltar a la carretera? ¿Acaso ese hombre del traje intenta quitarme el dinero y desaparecer? ¿Actuará ese abogado según las amenazas que profiere, o solo va de farol? Cuando se creía que tales emociones y deseos los generaba un espíritu inmaterial, parecía evidente que los ordenadores nunca serían capaces de sustituir a los conductores, banqueros y abogados humanos. Porque ¿cómo va a ser capaz un ordenador de comprender el espíritu humano, creado divinamente? Pero si tales emociones y deseos son en realidad poca cosa más que algoritmos bioquímicos, no hay razón alguna por la que los ordenadores no puedan descifrar dichos algoritmos y hacerlo mucho mejor que cualquier _Homo sapiens_.
Un conductor que predice las intenciones de un peatón, un banquero que evalúa la credibilidad de un prestatario potencial y un abogado que calibra el estado de ánimo en la mesa de negociación no hacen uso de la brujería. Por el contrario, y aunque no lo sepan, el cerebro de cada uno de ellos reconoce patrones bioquímicos al analizar expresiones faciales, tonos de voz, gestos de las manos e incluso olores corporales. Una IA equipada con los sensores adecuados podría hacer todo eso de manera mucho más precisa y fiable que un humano.
De ahí que la amenaza de pérdida de puestos de trabajo no sea simplemente el resultado del auge de la infotecnología. Es el resultado de la confluencia de la infotecnología con la biotecnología. El camino que va de la imagen por resonancia magnética funcional al mercado laboral es largo y tortuoso, pero todavía puede recorrerse en cuestión de pocas décadas. Lo que los científicos están descubriendo en la actualidad acerca de la amígdala y el cerebelo podría llevar a que los ordenadores superaran a los psiquiatras y guardaespaldas en 2050.
La IA no solo está a punto de suplantar a los humanos y de superarlos en lo que hasta ahora eran habilidades únicamente humanas. También posee capacidades exclusivamente no humanas, lo que hace que la diferencia entre una IA y un trabajador humano sea también de tipo, no simplemente de grado. Dos capacidades no humanas importantes de la IA son la conectividad y la capacidad de actualización.
Puesto que los humanos somos individuos, es difícil conectarnos entre nosotros para garantizar que todos nos mantengamos actualizados. En cambio, los ordenadores no son individuos, y resulta fácil integrarlos en una única red flexible. De ahí que a lo que nos enfrentamos no sea a la sustitución de millones de trabajadores humanos individuales por millones de robots y ordenadores individuales. Más bien es probable que los individuos humanos seamos sustituidos por una red integrada. Por tanto, cuando se piensa en la automatización, es erróneo comparar las capacidades de un único conductor humano con las de un único coche autónomo sin conductor, o las de un único médico humano con las de una única IA médica. Deberíamos comparar las capacidades de un conjunto de individuos humanos con las capacidades de una red integrada.
Por ejemplo, muchos conductores no están familiarizados con todas las normas de tráfico cambiantes y a menudo las incumplen. Además, dado que cada vehículo es una entidad autónoma, cuando dos vehículos se acercan al mismo cruce al mismo tiempo, los conductores podrían comunicar erróneamente sus intenciones y chocar. En cambio, todos los coches sin conductor pueden estar conectados entre sí. Cuando dos de esos vehículos se acercan al mismo cruce, no son en realidad dos entidades separadas: forman parte de un único algoritmo. Por ello las probabilidades de que se comuniquen mal y colisionen son mucho menores. Y si el Ministerio de Transporte decide modificar alguna norma de tráfico, todos los vehículos sin conductor podrán ponerse fácilmente al día justo en el mismo instante y, a menos que el programa esté afectado por algún virus, todos cumplirán la misma norma al pie de la letra.[4]
De forma parecida, si la Organización Mundial de la Salud identifica una nueva enfermedad o si un laboratorio produce un nuevo medicamento, es casi imposible que todos los médicos humanos del mundo se pongan al día acerca de esas novedades. En cambio, aunque tengamos 10.000 millones de IA médicas en el mundo y cada una de ellas supervise la salud de un único humano, aún es posible actualizarlas todas en una fracción de segundo, y todas pueden comunicarse entre sí sus impresiones acerca de la nueva enfermedad o el nuevo medicamento. Estas ventajas potenciales de la conectividad y de la capacidad de actualización son tan enormes que al menos en algunas profesiones podría tener sentido sustituir a todos los humanos por ordenadores, aunque de forma individual algunos humanos todavía hagan una tarea mejor que las máquinas.
El lector puede objetar que al pasar de los humanos individuales a una red de ordenadores perderemos las ventajas de la individualidad. Por ejemplo, si un médico humano comete un error en su diagnóstico, no mata a todos los pacientes del mundo, ni bloquea en su totalidad el desarrollo de todos los nuevos medicamentos. En cambio, si todos los médicos son realmente un único sistema y dicho sistema comete un error, los resultados podrían ser catastróficos. Sin embargo, lo cierto es que un sistema de ordenadores integrado es capaz de maximizar las ventajas de la conectividad sin perder los beneficios de la individualidad. Es posible ejecutar muchos algoritmos alternativos en la misma red, de modo que una paciente en una remota aldea de la jungla pueda acceder a través de su teléfono inteligente no solo a un único médico acreditado, sino en realidad a cien IA médicas diferentes, cuyo desempeño relativo se está comparando constantemente. ¿No le gusta lo que el médico de IBM le dijo? No pasa nada. Aunque se encuentre usted inmovilizado en algún lugar de las laderas del Kilimanjaro, podrá contactar fácilmente con el médico de Baidu, el motor de búsqueda chino, para tener una segunda opinión.
Es probable que los beneficios para la sociedad humana sean inmensos. Las IA médicas podrían proporcionar una atención sanitaria mucho mejor y más barata a miles de millones de personas, en particular a las que normalmente no reciben ningún tipo de atención sanitaria. Gracias a algoritmos de aprendizaje y a sensores biométricos, un campesino pobre de un país subdesarrollado podría llegar a gozar de una atención sanitaria mucho mejor mediante su teléfono inteligente que la que la persona más rica del mundo obtiene en la actualidad del hospital urbano más avanzado.[5]
De forma similar, los coches autónomos pueden proporcionar a las personas unos servicios de transporte mucho mejores, y en concreto reducir la mortalidad causada por accidentes de automóvil. Hoy en día, cerca de 1,25 millones de personas mueren al año en accidentes de tráfico (el doble de las que mueren por guerras, crímenes y terrorismo sumados).[6] Más del 90 por ciento de estos accidentes se deben a errores muy humanos: alguien que bebe alcohol y conduce, alguien que escribe un mensaje mientras conduce, alguien que se queda dormido al volante, alguien que sueña despierto en lugar de estar atento a la carretera. En 2012, la Administración Nacional de Seguridad del Tráfico en las Carreteras de Estados Unidos estimó que el 31 por ciento de los choques fatales en el país estaba relacionado con el abuso de alcohol, el 30 por ciento con la velocidad excesiva y el 21 por ciento con la distracción de los conductores.[7] Los vehículos autónomos nunca harán ninguna de estas cosas. Aunque tienen sus propios problemas y limitaciones, y aunque algunos accidentes son inevitables, se espera que sustituir a todos los conductores humanos por ordenadores reduzca las muertes y las lesiones en carretera en aproximadamente un 90 por ciento.[8] En otras palabras, es probable que pasar a los vehículos autónomos salve la vida de un millón de personas al año.
De ahí que sea una locura la idea de bloquear la automatización en campos tales como el transporte y la atención sanitaria con el único fin de salvaguardar los empleos humanos. Después de todo, lo que deberíamos proteger en último término es a los humanos, no los puestos de trabajo. Los conductores y médicos que sean innecesarios tendrán que encontrar otra cosa que hacer.
#####
##### MOZART EN LA MÁQUINA
Al menos a corto plazo, es improbable que la IA y la robótica acaben con industrias enteras. Los empleos que requieran especialización en una estrecha gama de actividades rutinizadas se automatizarán. Pero será mucho más difícil sustituir a los humanos por máquinas en tareas menos rutinarias que exijan el uso simultáneo de un amplio espectro de habilidades, y que impliquen tener que afrontar situaciones imprevistas. Pensemos en la atención sanitaria, por ejemplo. Muchos médicos se ocupan de manera casi exclusiva a procesar información: recaban datos médicos, los analizan y emiten un diagnóstico. Las enfermeras, en cambio, necesitan también buenas habilidades motrices y emocionales a fin de administrar una inyección dolorosa, cambiar un vendaje o contener a un paciente agresivo. De ahí que quizá tengamos una IA médico de cabecera en nuestro teléfono inteligente décadas antes de que tengamos un robot enfermera fiable.[9] Es probable que la industria de los cuidados a personas (que se ocupa de los enfermos, los niños y los ancianos) siga siendo un bastión humano durante mucho tiempo. De hecho, dado que las personas viven más y tienen menos hijos, el cuidado de los ancianos será probablemente uno de los sectores del mercado de trabajo humano que más deprisa crezcan.
Junto con el cuidado a las personas, la creatividad plantea también obstáculos particularmente difíciles para la automatización. Ya no necesitamos a humanos que nos vendan música: podemos bajarla directamente del almacén de iTunes; pero los compositores, músicos, cantantes y DJ son todavía de carne y hueso. Recurrimos a su creatividad no solo para crear música completamente nueva, sino también para elegir entre una gama alucinante de posibilidades a nuestra disposición.
No obstante, a la larga ningún puesto de trabajo se librará por completo de la automatización. Incluso los artistas deben estar prevenidos. En el mundo moderno, el arte suele asociarse a las emociones humanas. Tendemos a pensar que los artistas canalizan fuerzas psicológicas internas, y que el objetivo general del arte es conectarnos con nuestras emociones o inspirar en nosotros algún sentimiento nuevo. En consecuencia, cuando nos decidimos a evaluar el arte, tendemos a juzgarlo por el impacto emocional que genera en la audiencia. Pero si el arte se define por las emociones humanas, ¿qué podría ocurrir una vez que algoritmos externos sean capaces de comprender y manipular las emociones humanas mejor que Shakespeare, Frida Kahlo o Beyoncé?
Al fin y al cabo, las emociones no son un fenómeno místico: son el resultado de un proceso bioquímico. De ahí que, en un futuro no muy lejano, un algoritmo de aprendizaje automático quizá analice los datos biométricos que surjan de sensores situados sobre y dentro de nuestro cuerpo, determine nuestro tipo de personalidad y nuestros humores cambiantes y calcule el impacto emocional que es probable que una canción concreta (incluso un tono musical determinado) pueda tener en nosotros.[10]
De todas las formas de arte, la música probablemente sea la más susceptible al análisis de macrodatos, porque tanto las entradas como las salidas se prestan a una caracterización matemática precisa. Las entradas son los patrones matemáticos de las ondas sonoras, y las salidas, los patrones electroquímicos de las tormentas neurales. En pocas décadas, un algoritmo que analice millones de experiencias musicales podría aprender a predecir de qué manera determinadas entradas producen determinadas salidas.[11]
Supongamos que acabamos de tener una desagradable discusión con nuestro novio. El algoritmo encargado de nuestro sistema de sonido discernirá de inmediato nuestra confusión emocional interna y, sobre la base de lo que conoce de nosotros personalmente y de la psicología humana en general, reproducirá canciones a medida para que resuenen con nuestra tristeza y se hagan eco de nuestra aflicción. Quizá tales canciones no funcionen bien con otros individuos, pero son perfectas para nuestra personalidad. Después de ayudarnos a entrar en contacto con las profundidades de nuestra tristeza, a continuación el algoritmo reproduciría la única canción del mundo que es probable que nos levante el ánimo, quizá porque nuestro subconsciente la relaciona con un recuerdo feliz de la infancia del que ni siquiera somos conscientes. Ningún DJ humano puede esperar igualar las habilidades de semejante IA.
El lector puede objetar que de esta manera la IA acabaría con la serendipia y nos encerraría en un estrecho capullo musical, tejido por nuestras preferencias y aversiones previas. ¿Y qué hay de explorar nuevos gustos y estilos musicales? Ningún problema. Podríamos ajustar con facilidad el algoritmo para que hiciera sus selecciones completamente al azar, de manera que nos emitiera de forma inesperada una grabación de un conjunto indonesio de gamelán, una ópera de Rossini o el último éxito de K-pop. Con el tiempo, al repasar nuestras reacciones, la IA podría determinar incluso el nivel ideal de aleatoriedad que optimizara la búsqueda al tiempo que evitara el fastidio, quizá reduciendo su nivel de serendipia al 3 por ciento o aumentándolo al 8 por ciento.
Otra posible objeción es que no está claro cómo pueda establecer el algoritmo su objetivo emocional. Si solo nos peleamos con nuestro novio, ¿debería pretender el algoritmo ponernos tristes o alegres? ¿Debería seguir a ciegas una rígida escala de emociones «buenas» y «malas»? ¿Quizá haya momentos en la vida en los que sea bueno sentirse triste? Desde luego, la misma pregunta podría formularse a músicos y DJ humanos. Pero en el caso de un algoritmo hay muchas soluciones interesantes a este acertijo.
Una opción es dejarlo sin más a la libre elección del cliente. Podemos evaluar nuestras emociones como queramos, y el algoritmo seguirá nuestros dictados. Ya deseemos regodearnos en la autocompasión o bien saltar de alegría, el algoritmo seguirá servilmente nuestro ejemplo. De hecho, podrá aprender a reconocer nuestros deseos incluso sin que seamos conscientes de ellos de forma explícita.
Alternativamente, si no confiamos en nosotros, podemos instruir al algoritmo para que siga las recomendaciones de cualquier psicólogo eminente en el que confiemos. Si nuestro novio acaba por dejarnos plantados, el algoritmo podrá llevarnos a pasar por las cinco fases del duelo, primero ayudándonos a negar lo que ocurrió reproduciendo la canción de Bobby McFerrin «Don't Worry, Be Happy», después avivando nuestro enfado con «You Oughta Know», de Alanis Morissette, luego animándonos a negociar con «Ne me quitte pas», de Jacques Brel, y «Come Back and Stay», de Paul Young, después dejándonos caer en el pozo de la depresión con «Someone Like You» __ y __ «Hello», de Adele, y, por último, ayudándonos a aceptar la situación con «I Will Survive», de Gloria Gaynor.
El paso siguiente es que el algoritmo empiece a trastear con las propias canciones y melodías, cambiándolas un poco para que se ajusten a nuestras peculiaridades. Quizá nos desagrada un pasaje concreto en una canción, por otro lado excelente. El algoritmo lo sabe porque nuestro corazón omite un latido y nuestros niveles de oxitocina descienden ligeramente siempre que oímos esa parte que no nos gusta. El algoritmo podría reescribir o eliminar las notas irritantes.
A la larga, los algoritmos quizá aprendan a componer canciones enteras, jugando con las emociones humanas como si estas fueran el teclado de un piano. Utilizando nuestros datos biométricos, podrían producir incluso melodías personalizadas que solo nosotros, en todo el universo, apreciaríamos.
A menudo se dice que las personas conectan con el arte porque se encuentran en él. Esto podría llevar a resultados sorprendentes y algo siniestros en el caso de que, por ejemplo, Facebook empezara a crear arte personalizado basado en cuanto sabe de nosotros. Si nuestro novio nos abandona, Facebook nos agasajará con una canción personalizada sobre ese cabrón concreto en lugar de sobre la persona desconocida que rompió el corazón de Adele o de Alanis Morissette. La canción nos recordará incidentes reales de nuestra relación, que nadie más en el mundo conoce.
Desde luego, podría ocurrir que el arte personalizado jamás arraigara, porque la gente continúe prefiriendo éxitos comunes que gustan a todo el mundo. ¿Cómo puede uno cantar una canción o bailar a su son si nadie más que nosotros la conoce? Pero tal vez los algoritmos podrían ser incluso más propensos a producir éxitos globales que rarezas personalizadas. Utilizando bases de datos biométricos masivos obtenidos de millones de personas, el algoritmo podría saber qué botones bioquímicos pulsar a fin de producir un éxito global que hiciera que todos se lanzaran como locos a las pistas de baile. Si el arte trata en verdad de inspirar (o manipular) las emociones humanas, pocos músicos humanos, o ninguno, tendrían la posibilidad de competir con un algoritmo de este tipo, porque no serían capaces de igualarlo a la hora de comprender el principal instrumento con el que están operando: el sistema bioquímico humano.
¿Resultará todo esto en un arte excepcional? Eso depende de la definición de arte. Si la belleza está verdaderamente en los oídos del oyente, y si el cliente siempre tiene razón, entonces los algoritmos biométricos disponen de la oportunidad de producir el mejor arte de la historia. Si el arte es algo más profundo que las emociones humanas y debe expresar una verdad más allá de nuestras vibraciones bioquímicas, los algoritmos biométricos no serán muy buenos artistas. Pero tampoco lo son la mayoría de los humanos. Para entrar en el mercado del arte y desplazar a muchos compositores y músicos humanos, los algoritmos no tendrán que empezar superando directamente a Chaikovski: bastará con que lo hagan mejor que Britney Spears.
##### ¿NUEVOS EMPLEOS?
La pérdida de muchos puestos de trabajo en todos los ámbitos, desde el arte a la atención sanitaria, se verá compensada en parte por la creación de nuevos empleos humanos. Los médicos de cabecera que se ocupan de diagnosticar enfermedades conocidas y de administrar tratamientos comunes serán sustituidos probablemente por IA médicas. Pero justo por eso, habrá mucho más dinero para pagar a médicos humanos y a ayudantes de laboratorio a fin de que realicen investigaciones punteras y desarrollen nuevos medicamentos o procedimientos quirúrgicos.[12]
La IA podrá colaborar en la creación de empleos humanos de otra manera. En lugar de que los humanos compitan con la IA, podrían centrarse en su mantenimiento y en su uso. Por ejemplo, la sustitución de pilotos humanos por drones ha acabado con algunos empleos, pero ha creado muchos puestos en mantenimiento, control remoto, análisis de datos y ciberseguridad. Las fuerzas armadas de Estados Unidos necesitan a treinta personas para operar cada dron Predator o Reaper no tripulado que sobrevuela Siria, mientras que analizar la cantidad de información resultante ocupa al menos a ochenta personas más. En 2015, la aviación de Estados Unidos carecía de suficientes humanos adiestrados para ocupar todos estos puestos de trabajo y, por tanto, irónicamente se enfrentó a una crisis cuando tuvo que a dedicar personal a sus vehículos aéreos no tripulados.[13]
Si es así, bien podría ocurrir que el mercado laboral de 2050 estuviera caracterizado por la cooperación humano-IA en lugar de por la competición entre uno y otra. En ámbitos que van desde la vigilancia hasta las operaciones bancarias, equipos de humanos-más-IA tal vez superen tanto a los humanos como a los ordenadores. Después de que el programa de ajedrez Deep Blue de IBM derrotara a Garri Kaspárov en 1997, los humanos no dejaron de jugar al ajedrez. En cambio, gracias a IA entrenadoras, los maestros de ajedrez humanos se hicieron mejores que nunca, y, al menos durante un tiempo, equipos de humanos-IA conocidos como «centauros» ganaron tanto a humanos como a ordenadores al ajedrez. De manera parecida, la IA podría ayudar a preparar a los mejores detectives, banqueros y soldados de la historia.[14]
Sin embargo, el problema de estos nuevos empleos es que probablemente exigirán un gran nivel de pericia y, por tanto, no resolverán los problemas de los trabajadores no cualificados sin empleo. Crear nuevos trabajos humanos podría resultar más fácil que volver a adiestrar a humanos para que ocuparan realmente dichos puestos. Durante los períodos de automatización anteriores, por lo general las personas podían pasar de un empleo rutinario que exigía poca pericia a otro. En 1920, un obrero agrícola al que echaban a raíz de la mecanización de la agricultura podía encontrar un nuevo empleo en una fábrica de tractores. En 1980, un obrero de una fábrica que se quedara en el paro podía empezar trabajando como cajero en un supermercado. Estos cambios ocupacionales eran posibles porque el paso de la granja a la fábrica y de la fábrica al supermercado solo requería un readiestramiento limitado.
Sin embargo, en 2050 podría ser difícil que un cajero o un obrero del sector textil que perdiera su trabajo debido a un robot empezara a trabajar como investigador del cáncer, como operador de drones o como parte de un equipo de banca humano-IA. No dispondrán de la pericia necesaria. En la Primera Guerra Mundial tenía sentido enviar a millones de reclutas bisoños a que cargaran con ametralladoras y murieran por millares. Sus habilidades individuales importaban poco. Hoy en día, a pesar de la escasez de operadores de drones, en las fuerzas aéreas de Estados Unidos son reacios a ocupar los puestos vacantes con personas despedidas de Walmart. A nadie le gustaría que un recluta sin experiencia confundiera una fiesta de boda afgana con una reunión de talibanes de alto rango.
En consecuencia, a pesar de la posibilidad de que aparecieran muchos nuevos empleos humanos, quizá presenciaríamos el surgimiento de una nueva clase «inútil». De hecho, podríamos tener lo peor de ambos mundos, y padecer a la vez unas tasas de desempleo elevadas y escasez de mano de obra especializada. Muchas personas no compartirían el destino de los conductores de carros del siglo XIX, que pasaron a conducir taxis, sino el de los caballos del siglo XIX, a los que se apartó poco a poco del mercado laboral hasta que desaparecieron de él por completo.[15]
Además, ningún empleo humano que quede estará jamás a salvo de la amenaza de la automatización futura, porque el aprendizaje automático y la robótica continuarán mejorando. Una cajera de Walmart de cuarenta años que se quede sin empleo y que con esfuerzos sobrehumanos consiga reinventarse como piloto de drones podría tener que reinventarse de nuevo diez años después, porque entonces quizá el vuelo de los drones también se habrá automatizado. Semejante inestabilidad hará asimismo que sea más difícil organizar sindicatos o conseguir derechos laborales. Ya en la actualidad, muchos empleos nuevos en economías avanzadas implican trabajo temporal no protegido, trabajadores autónomos y trabajo ocasional.[16] ¿Cómo se sindicaliza una profesión que surge de pronto y desaparece al cabo de una década?
De manera parecida, es probable que los equipos centauros de humanos y ordenadores se caractericen por un tira y afloja constante entre unos y otros, en lugar de establecerse como una empresa para toda la vida. Los equipos constituidos solo por humanos (como Sherlock Holmes y el doctor Watson) suelen desarrollar jerarquías y rutinas permanentes que duran décadas. Pero un detective humano que haga equipo con el sistema informático Watson de IBM (que se hizo famoso después de ganar el concurso televisivo estadounidense _Jeopardy!_ en 2011) se topará con que cada rutina es una invitación a la interrupción, y cada jerarquía, una invitación a la revolución. El compinche de ayer podría transformarse en el comisario de mañana, y todos los protocolos y manuales tendrán que reescribirse anualmente.[17]
Una mirada más atenta al mundo del ajedrez podría indicar hacia dónde irán las cosas a largo plazo. Es cierto que durante varios años después de que Deep Blue venciera a Kaspárov, la cooperación humano-ordenador floreció en el ajedrez. Pero en los últimos años, los ordenadores son tan buenos jugadores de ajedrez que sus colaboradores humanos han perdido su valor, y pronto podrían ser de todo punto irrelevantes.
El 7 de diciembre de 2017 se alcanzó un hito crítico no cuando un ordenador ganó a un humano al ajedrez (esto ya no es noticia), sino cuando el programa AlphaZero de Google derrotó al programa Stockfish 8. Stockfish 8 fue el campeón mundial de ajedrez en 2016. Tenía acceso a siglos de experiencia humana acumulada en ajedrez, así como a décadas de experiencia de ordenador. Podía calcular 70 millones de posiciones en el tablero por segundo. En cambio, AlphaZero solo realizaba 80.000 de tales cálculos por segundo, y sus creadores humanos nunca le enseñaron ninguna estrategia ajedrecística, ni siquiera aperturas estándar. En cambio, AlphaZero se sirvió de los últimos principios de aprendizaje automático para autoenseñarse ajedrez al jugar contra sí mismo. No obstante, de cien partidas que el novicio AlphaZero jugó contra Stockfish, AlphaZero ganó veintiocho y quedaron en tablas en setenta y dos. No perdió ni una sola vez. Puesto que AlphaZero no aprendió nada de ningún humano, muchos de sus movimientos y estrategias vencedoras parecían poco convencionales a los ojos humanos. Bien pudiera considerárselos creativos, si no geniales.
¿Adivina el lector cuánto tiempo le llevó a AlphaZero aprender ajedrez, prepararse para las partidas contra Stockfish y desarrollar sus intuiciones geniales? Cuatro horas. No se trata de ninguna errata. Durante siglos se ha considerado el ajedrez uno de los mayores logros de la inteligencia humana. AlphaZero pasó de la ignorancia más absoluta a la maestría creativa en cuatro horas, sin ayuda de ningún guía humano.[18]
AlphaZero no es el único programa imaginativo que existe. Hoy en día, muchos programas superan de manera rutinaria a jugadores humanos de ajedrez, no solo en cálculos simples, sino incluso en «creatividad». En los campeonatos de ajedrez exclusivos para humanos, los árbitros están vigilando en todo momento por si hay jugadores que intentan hacer trampa sirviéndose secretamente de la ayuda de ordenadores. Una de las maneras de descubrir a los que hacen trampas es supervisar el nivel de originalidad que muestran los jugadores. Si efectúan un movimiento excepcionalmente creativo, los árbitros sospecharán a menudo que no puede tratarse de un movimiento humano: ha de ser de ordenador. Al menos en el ajedrez, ¡la creatividad ya es propia de los ordenadores y no de los humanos! Así pues, si el ajedrez es nuestro canario en la mina, ya estamos bien avisados de que el canario se está muriendo. Lo que ahora ocurre a los equipos de ajedrez humanos-IA puede ocurrirles también a los equipos de humanos-IA en vigilancia, medicina y operaciones bancarias.[19]
En consecuencia, crear nuevos empleos y volver a formar a personas para que los ocupen no será el único esfuerzo. La revolución de IA no será un único punto de inflexión crucial después del cual el mercado laboral alcanzará un nuevo equilibrio. Más bien será una cascada de disrupciones cada vez mayores. Hoy ya son pocos los empleados que esperan ocupar el mismo empleo toda la vida.[20] En 2050, no solo la idea de «un trabajo para toda la vida», sino también la idea misma de «una profesión para toda la vida» podrían parecer antediluvianas.
Incluso si fuéramos capaces de inventar constantemente empleos nuevos y de volver a formar la fuerza laboral, ¿tendría el humano medio la resistencia emocional necesaria para llevar una vida de tantos y tan incesantes trastornos? El cambio es siempre estresante, y el mundo frenético de principios del siglo XXI ha producido una epidemia global de estrés.[21] A medida que aumente la volatilidad del mercado laboral y de las carreras individuales, ¿será capaz la gente de sobrellevarlo? Probablemente necesitaremos técnicas de reducción del estrés más efectivas (desde los fármacos a la meditación, pasando por la neurorretroalimentación) para impedir que la mente de los sapiens se quiebre. Hacia 2050 podría surgir una clase «inútil» debido no simplemente a una falta absoluta de trabajo o a una falta de educación pertinente, sino también a una resistencia mental insuficiente.
Como es evidente, la mayor parte de lo dicho son solo especulaciones. En el momento de escribir esto (principios de 2018), la automatización ha perturbado muchas industrias, pero no ha desembocado en un desempleo masivo. En realidad, en muchos países, como Estados Unidos, el paro se encuentra en un nivel bajo histórico. Nadie puede saber con seguridad qué tipo de impacto tendrán el aprendizaje automático y la automatización en las diferentes profesiones del futuro, y es muy difícil evaluar el calendario de los acontecimientos relevantes, sobre todo porque dependen tanto de decisiones políticas y de tradiciones culturales como de descubrimientos puramente tecnológicos. Así, incluso después de que los vehículos autónomos demuestren ser más seguros y baratos que los conductores humanos, los políticos y consumidores podrían no obstante impedir el cambio durante años, quizá décadas.
Sin embargo, no podemos permitirnos darnos por satisfechos. Es peligroso suponer simplemente que surgirán empleos nuevos suficientes para compensar las pérdidas. El hecho de que esto haya ocurrido en períodos anteriores de automatización no es en absoluto garantía de que ocurra de nuevo en las condiciones muy diferentes del siglo XXI. Las disrupciones sociales y políticas potenciales son tan alarmantes que incluso si la probabilidad de desempleo sistémico y masivo es baja, estamos obligados a tomárnosla muy en serio.
En el siglo XIX, la revolución industrial generó nuevas condiciones y problemas que ninguno de los modelos sociales, económicos y políticos existentes podía resolver. El feudalismo, la monarquía y las religiones tradicionales no estaban preparados para gestionar las metrópolis industriales, a los millones de obreros desarraigados o la naturaleza siempre cambiante de la economía moderna. En consecuencia, la humanidad tuvo que desarrollar modelos del todo nuevos (democracias liberales, dictaduras comunistas y regímenes fascistas), e hizo falta más de un siglo de guerras y revoluciones terribles para probar estos modelos, separar el grano de la paja y poner en marcha las mejores soluciones. El trabajo infantil en las minas de carbón dickensianas, la Primera Guerra Mundial y la Gran Hambruna ucraniana de 19323 solo fueron una pequeña parte de la cuota de matrícula que la humanidad pagó.
El reto que la infotecnología y la biotecnología plantean a la humanidad en el siglo XXI es sin duda alguna mucho mayor que el que en épocas anteriores supusieron las máquinas de vapor, los ferrocarriles y la electricidad. Y dado el inmenso poder destructor de nuestra civilización, no podemos permitirnos más modelos fallidos, guerras mundiales ni revoluciones sangrientas. Esta vez, los modelos fallidos podrían acabar en guerras nucleares, monstruosidades diseñadas genéticamente y un colapso completo de la biosfera. En consecuencia, tenemos que hacerlo mejor de lo que lo hicimos cuando nos enfrentamos a la revolución industrial.
##### DE LA EXPLOTACIÓN A LA IRRELEVANCIA
Las soluciones posibles corresponden a tres categorías principales: qué hacer para evitar que se pierdan empleos, qué hacer para crear suficientes puestos de trabajo nuevos, y qué hacer si, a pesar de todos nuestros esfuerzos, la pérdida de empleo supera con mucho la creación.
Evitar la pérdida general de puestos de trabajo es una estrategia poco interesante y probablemente insostenible, porque supone abandonar el inmenso potencial positivo de la IA y la robótica. No obstante, tal vez los gobiernos reduzcan de manera deliberada el ritmo de la automatización, a fin de reducir los impactos que se deriven de aquella y dar tiempo a los reajustes. La tecnología nunca es determinista, y el hecho de que algo pueda hacerse no significa que tenga que hacerse. Las normativas gubernamentales pueden cerrar efectivamente el paso a las nuevas tecnologías aunque sean viables desde el punto de vista comercial y lucrativas desde el económico. Por ejemplo, durante décadas hemos dispuesto de la tecnología para crear un mercado de órganos humanos completo con «granjas de cuerpos» humanos en países subdesarrollados y una demanda casi insaciable de compradores ricos y desesperados. Tales granjas de cuerpos bien pudieran valer cientos de miles de millones de dólares. Pero las leyes han impedido el libre comercio de partes del cuerpo humano, y aunque existe un mercado negro de dichos órganos, es mucho menor y se halla más circunscrito de lo que cabría esperar.[22]
Reducir el ritmo del cambio quizá nos proporcionaría tiempo para crear suficientes puestos de trabajo que sustituyeran a la mayoría de los que se perderán. Pero, como se ha dicho, el espíritu emprendedor económico tendrá que ir acompañado de una revolución en la educación y la psicología. Suponiendo que los nuevos empleos no sean solo sinecuras gubernamentales, probablemente exigirán una gran pericia, y a medida que la IA continúe mejorando, los empleados humanos deberán aprender sin parar nuevas habilidades y cambiar de profesión. Los gobiernos tendrán que intervenir, tanto para subsidiar un sector educativo durante toda la vida como para proporcionar una red de seguridad durante los inevitables períodos de transición. Si una expiloto de drones de cuarenta años necesita tres para reinventarse como diseñadora de mundos virtuales, es muy probable que precise de mucha ayuda gubernamental para mantenerse y mantener a su familia durante dicho tiempo. (En la actualidad, este tipo de proyectos está empezando a ponerse en marcha en Escandinavia, donde los gobiernos siguen el lema «proteger a los obreros, no los empleos».)
Pero incluso si se dispone de ayuda suficiente del gobierno, ni mucho menos se da por descontado que miles de millones de personas sean capaces de reinventarse una y otra vez sin poner en riesgo su equilibrio mental. De ahí que, si a pesar de todos nuestros esfuerzos, hay un porcentaje significativo de la humanidad que resulta expulsada del mercado laboral, tendremos que buscar nuevos modelos para las sociedades, las economías y las políticas poslaborales. El primer paso es reconocer con honestidad que los modelos sociales, económicos y políticos que hemos heredado del pasado son inadecuados para afrontar este reto.
Pensemos, por ejemplo, en el comunismo. A medida que la automatización amenace con sacudir el sistema capitalista hasta sus cimientos, cabría suponer que el comunismo podría reaparecer. Pero el comunismo no se generó para explotar este tipo de crisis. El comunismo del siglo XX daba por sentado que la clase obrera era vital para la economía, y los pensadores comunistas intentaron enseñar al proletariado cómo convertir su inmenso poder económico en influencia política. El plan político comunista exigía una revolución de la clase trabajadora. ¿Cuán relevantes serán estas enseñanzas si las masas pierden su valor económico y, por tanto, necesitan luchar contra la irrelevancia en lugar de hacerlo contra la explotación? ¿Cómo se inicia una revolución de la clase obrera sin una clase obrera?
Algunos podrían aducir que los humanos nunca llegarán a ser irrelevantes desde el punto de vista económico, porque aun cuando no puedan competir con la IA en el puesto de trabajo siempre se los necesitará como consumidores. Sin embargo, no está en absoluto asegurado que la economía futura nos necesite siquiera como consumidores. Las máquinas y los ordenadores podrían serlo también. En teoría, podría existir una economía en la que una compañía minera produzca y venda hierro a una compañía robótica, la compañía robótica produzca y venda robots a la compañía minera, que de ese modo extraerá más hierro, que se usará para producir más robots, y así sucesivamente. Estas compañías podrían crecer y expandirse hasta los confines más remotos de la galaxia, y cuanto necesitarán será robots y ordenadores: no requerirán humanos ni siquiera para comprar sus productos.
De hecho, ya hoy en día ordenadores y algoritmos están empezando a funcionar como clientes además de como productores. En la Bolsa de valores, por ejemplo, los algoritmos se están convirtiendo en los compradores más importantes de bonos, acciones y mercancías. De forma parecida, en el negocio de la publicidad el cliente más importante de todos es un algoritmo: el algoritmo de búsqueda de Google. Cuando la gente diseña páginas web, a menudo satisface el gusto del algoritmo de búsqueda de Google en lugar del gusto de un ser humano.
Evidentemente, los algoritmos no tienen conciencia, de modo que, a diferencia de los consumidores humanos, no pueden disfrutar de lo que compran, y sus decisiones no están condicionadas por sensaciones y emociones. El algoritmo de búsqueda de Google no puede saborear los helados. Sin embargo, los algoritmos seleccionan cosas a partir de sus cálculos internos y de sus preferencias incorporadas, y dichas preferencias modelan nuestro mundo de manera creciente. El algoritmo de búsqueda de Google tiene un gusto muy refinado cuando se trata de ordenar las páginas web de vendedores de helados, y entre estos, los que más éxito tienen en el mundo son los que el algoritmo de Google sitúa en los primeros puestos, no los que hacen los helados más deliciosos.
Esto lo sé por experiencia propia. Cuando publico un libro, los editores me piden que escriba una descripción breve, que usan para la publicidad en línea. Pero cuentan con un experto especial, que adapta lo que yo escribo al gusto del algoritmo de Google. El experto lee mi texto y dice: «No uses esta palabra; usa esta otra en su lugar. De esta manera, el algoritmo de Google nos prestará más atención». Sabemos que si somos capaces de captar la atención del algoritmo, podemos dar por sentado que captaremos la de los humanos.
De modo que si los humanos no se necesitan como productores ni como consumidores, ¿qué amparará su supervivencia física y su bienestar psicológico? No debemos esperar a que la crisis irrumpa con toda su fuerza para ponernos a buscar respuestas. Entonces ya sería demasiado tarde. A fin de enfrentarnos a las disrupciones tecnológicas y económicas del siglo XXI, necesitamos desarrollar nuevos modelos sociales y económicos tan pronto como sea posible. Dichos modelos deberían guiarse por el principio de proteger a los humanos y no los empleos. Muchos trabajos resultan fastidiosos y aburridos, y no vale la pena conservarlos. Nadie sueña con convertirse en un cajero. En lo que tenemos que centrarnos es en satisfacer las necesidades básicas de la gente y en proteger su nivel social y su autoestima.
Un nuevo modelo, que despierta cada vez más interés, es la renta básica universal. La RBU propone que los gobiernos graven a los multimillonarios y a las empresas que controlan los algoritmos y los robots, y que utilicen el dinero para pagar a cada persona un salario generoso que cubra sus necesidades básicas. Esto atenuaría la pérdida de empleo de los pobres y sus problemas económicos, al tiempo que protegería a los ricos de la ira popular.[23]
Una idea relacionada propone ampliar la gama de actividades humanas que se consideran «empleos». En la actualidad, miles de millones de progenitores cuidan de sus hijos, los vecinos se ayudan mutuamente y los ciudadanos organizan comunidades, sin que ninguna de estas actividades valiosas se considere un empleo. Quizá sea necesario que accionemos un interruptor en nuestra mente y nos demos cuenta de que cuidar de un niño es, sin duda, la tarea más importante y exigente del mundo. Si es así, no habrá escasez de trabajo aunque los ordenadores y los robots sustituyan a todos los conductores, banqueros y abogados. La pregunta, desde luego, es: ¿quién evaluará y pagará estos empleos acabados de reconocer? Dando por hecho que los bebés de seis meses no pagarán un salario a sus mamás, probablemente el gobierno tenga que encargarse de ello. Dando por hecho, también, que querremos que dichos salarios cubran todas las necesidades básicas de una familia, acabaremos en algo que no diferirá mucho de la renta básica universal.
Alternativamente, los gobiernos podrían subvencionar servicios básicos universales en lugar de salarios. En lugar de dar dinero a las personas, que después comprarán todo lo que quieran, podrían subvencionar la educación gratuita, la atención sanitaria gratuita, el transporte gratuito, etcétera. En realidad, esta es la visión utópica del comunismo. Aunque el proyecto comunista de iniciar una revolución de la clase obrera podría estar ya anticuado, quizá todavía seríamos capaces de alcanzar el objetivo comunista por otros medios.
Es discutible si es mejor proporcionar a las personas una renta básica universal (el paraíso capitalista) o servicios básicos universales (el paraíso comunista). Ambas opciones tienen ventajas e inconvenientes. Pero, con independencia del paraíso que escojamos, el problema real es definir qué significan en realidad «universal» y «básico».
##### ¿QUÉ ES UNIVERSAL?
Cuando la gente habla de una ayuda básica universal (ya sea en forma de renta o de servicios), generalmente se refiere a una ayuda básica nacional. Hasta la fecha, todas las iniciativas de RBU han sido estrictamente nacionales o municipales. En enero de 2017, Finlandia inició un experimento de dos años proporcionando a 2.000 finlandeses desempleados 560 euros al mes, con independencia de si encontraban trabajo o no. Experimentos similares están en marcha en la provincia canadiense de Ontario, en la ciudad italiana de Livorno y en varias ciudades holandesas.[24] (En 2016, Suiza celebró un referéndum sobre si se instituía un plan de renta básica nacional, pero los votantes rechazaron la idea.)[25]
Sin embargo, el problema de estos planes nacionales y municipales es que las principales víctimas de la automatización quizá no vivan en Finlandia, Ontario, Livorno o Amsterdam. Debido a la globalización, la población de un país depende por completo de mercados de otros países, pero la automatización podría desenredar grandes partes de esta red comercial global con consecuencias desastrosas para los eslabones más débiles. En el siglo XX, los países en vías de desarrollo que carecían de recursos naturales progresaron en el plano económico sobre todo vendiendo el trabajo barato de sus obreros no cualificados. Hoy en día, millones de bangladesíes se ganan la vida fabricando camisas y vendiéndolas a clientes de Estados Unidos, mientras que en Bangalore lo hacen en los servicios telefónicos de atención al cliente que tramitan las quejas de los clientes norteamericanos.[26]
Pero con el auge de la IA, los robots y las impresoras 3-D, el trabajo barato y no cualificado será mucho menos importante. En lugar de fabricar una camisa en Daca y enviarla a Estados Unidos, podremos comprar en línea en Amazon el código de la camisa e imprimirla en Nueva York. Las tiendas de Zara y Prada de la Quinta Avenida podrían ser sustituidas por centros de impresión 3-D en Brooklyn, y algunas personas incluso podrían tener una impresora en casa. Al mismo tiempo, en lugar de llamar al servicio de atención al cliente de Bangalore para quejarnos de nuestra impresora, tal vez habláramos con un representante de la IA en la nube de Google (cuyo acento y tono estarán ajustados a nuestras preferencias). Los obreros y operadores de los centros de atención al cliente que perderán su empleo en Daca y Bangalore carecen de la educación necesaria para ponerse a diseñar camisas de moda o programas informáticos; así pues, ¿cómo sobrevivirán?
Si la IA y las impresoras 3-D acaban relevando a bangladesíes y bangaloreses, los ingresos que antes fluían hacia el Sudeste Asiático llenarán las arcas de unos pocos gigantes tecnológicos en California. En lugar de que el crecimiento económico mejore las condiciones en todo el mundo, habrá riquezas nuevas e inmensas creadas en los centros de alta tecnología, como Silicon Valley, mientras que muchos países en vías de desarrollo se desmoronarán.
Desde luego, algunas economías emergentes (entre ellas, la India y Bangladesh) podrían avanzar lo bastante deprisa para incorporarse al equipo ganador. Si se les da el tiempo suficiente, los hijos o los nietos de los obreros textiles y de los operadores de los centros de atención al cliente podrían muy bien convertirse en los ingenieros y emprendedores que construyan y posean los ordenadores y las impresoras 3-D. Pero el tiempo para efectuar dicha transición se acaba. En el pasado, el trabajo barato y no cualificado ha servido de puente seguro para salvar la brecha económica global, e incluso si un país avanzaba despacio, podía esperar alcanzar finalmente la seguridad. Dar los pasos adecuados era más importante que hacer avances rápidos. Pero ahora el puente se tambalea, y podría derrumbarse pronto. Quienes ya lo han cruzado (progresando del trabajo barato a las industrias de alta especialización) estarán probablemente bien. Pero los que se demoren podrían encontrarse inmovilizados en el lado equivocado de la brecha, sin posibilidad alguna de cruzarla. ¿Qué hace uno cuando nadie necesita a sus obreros baratos y no cualificados, y carece de los recursos para construir un buen sistema de educación y enseñarles nuevas capacidades?[27]
¿Cuál será entonces la suerte de los rezagados? Cabe la posibilidad de que los votantes norteamericanos acordaran que los impuestos que pagan Amazon y Google por sus negocios en Estados Unidos se usaran para proporcionar salarios o servicios gratuitos a los mineros desempleados de Pensilvania y a los taxistas en paro de Nueva York. Sin embargo, ¿estarían también de acuerdo los votantes norteamericanos en que esos impuestos se enviaran para sostener a las personas desempleadas en lugares que el presidente Trump definió como «países de mierda»?[28] Si el lector lo cree, para el caso también podría creer que Santa Claus y el Conejito de Pascua resolverán el problema.
##### ¿QUÉ ES BÁSICO?
La ayuda básica universal pretende satisfacer necesidades humanas básicas, pero no hay una definición aceptada al respecto. Desde una perspectiva puramente biológica, un sapiens necesita solo 1.500-2.500 calorías diarias para sobrevivir. Lo que pase de esta cantidad es lujo. Pero, además de este límite de pobreza biológica, todas las culturas en la historia han definido necesidades adicionales como «básicas». En la Europa medieval, el acceso a los servicios religiosos se consideraba incluso más importante que el alimento, porque cuidaban de nuestra alma eterna y no de nuestro cuerpo efímero. En la Europa actual se considera que unos servicios decentes de educación y de asistencia sanitaria son necesidades humanas básicas, y algunos aducen que incluso el acceso a internet es ahora esencial para todo hombre, mujer y niño. Si en 2050 el Gobierno Mundial Unido acuerda cobrar impuestos a Google, Amazon, Baidu y Tencent a fin de proporcionar el sustento básico a todos los seres humanos de la Tierra (tanto en Daca como en Detroit), ¿cómo definirá «básico»?
Por ejemplo, ¿qué incluye la educación básica: solo leer y escribir, o también diseñar programas informáticos y tocar el violín? ¿Solo seis años de escuela elemental, o lo necesario hasta obtener un doctorado? ¿Y qué hay de la asistencia sanitaria? Si hacia 2050 los avances médicos hacen posible demorar los procesos de envejecimiento y alargar de manera significativa la duración de la vida, ¿estarán los nuevos tratamientos disponibles para los 10.000 millones de humanos del planeta, o solo para algunos multimillonarios? Si la biotecnología permite que los padres mejoren a sus hijos, ¿se considerará esto una necesidad humana básica, o veremos que la humanidad se divide en diferentes castas biológicas, con superhumanos ricos que gozarán de capacidades que sobrepasarán con mucho las de los _Homo sapiens_ pobres?
Sea cual sea la manera en que se definan las «necesidades humanas básicas», una vez que se proporcionen a todo el mundo libres de cargos, se darán por supuestas, y entonces las duras competiciones sociales y las luchas políticas se centrarán en lujos no básicos, ya sean los vehículos autónomos de moda, el acceso a los parques de realidad virtual o el cuerpo mejorado mediante bioingeniería. Pero si las masas de desempleados no obtienen recursos económicos, es difícil pensar de qué manera pueden esperar disfrutar de tales lujos. En consecuencia, la brecha entre ricos (los gestores de Tencent y los accionistas de Google) y pobres (los que dependan de la renta básica universal) puede hacerse no simplemente mayor, sino en verdad infranqueable.
De ahí que aun cuando algún plan universal de ayuda proporcionara a los pobres en 2050 una atención sanitaria y una educación mucho mejores que en la actualidad, podrían seguir muy enfadados por la desigualdad global y por la falta de movilidad social. La gente sentirá que el sistema está manipulado en su contra, que el gobierno sirve solo a los superricos y que el futuro será todavía peor para ellos y sus hijos.[29]
_Homo sapiens_ no está hecho para la satisfacción. La felicidad humana depende menos de condiciones objetivas que de nuestras propias expectativas. Sin embargo, las expectativas tienden a adaptarse a las condiciones, incluidas las condiciones de otras __ personas. Cuando las cosas mejoran, las expectativas aumentan, y en consecuencia incluso mejoras espectaculares en las condiciones pueden dejarnos tan insatisfechos como antes. Si la ayuda básica universal se enfoca a mejorar las condiciones objetivas de una persona media en 2050, tiene una buena probabilidad de lograr éxito. Pero si pretende que la gente esté subjetivamente más satisfecha con lo que tiene y evitar el descontento social, es probable que fracase.
Para conseguir realmente sus objetivos, la ayuda básica universal tendrá que llevar el complemento de algunas actividades plenas, que vayan de los deportes a la religión. Quizá el experimento que más éxito haya tenido hasta la fecha sobre cómo llevar una vida satisfactoria en un mundo postrabajo se haya realizado en Israel. Allí, alrededor del 50 por ciento de los hombres judíos ultraortodoxos no trabajan. Dedican su vida a estudiar las sagradas escrituras y a cumplir con rituales religiosos. Ellos y sus familias no pasan hambre debido en parte a que sus esposas suelen trabajar, y en parte a que el gobierno les proporciona subsidios generosos y servicios gratuitos, lo que cubre las necesidades básicas de la vida. Esto es una ayuda básica universal _avant la lettre_.[30]
A pesar de que son pobres y están sin empleo, en todas las encuestas estos hombres judíos ultraortodoxos dan cuenta de niveles de satisfacción superiores a los de cualquier otro sector de la sociedad israelí. Ello se debe a la fuerza de sus vínculos con la comunidad, así como a la profunda realización que hallan en el estudio de las escrituras y en el cumplimiento de los rituales. Una pequeña sala llena de hombres judíos que debaten el Talmud podría muy bien generar más alegría, compromiso y entendimiento que una enorme fábrica textil llena de obreros que realizan un trabajo duro. En las encuestas globales de satisfacción vital, Israel suele situarse en alguno de los primeros lugares, gracias en parte a estas personas pobres y sin trabajo.[31]
Los israelíes seglares suelen quejarse amargamente de que los ultraortodoxos no contribuyen lo suficiente a la sociedad y viven aislados del duro trabajo de las otras personas. Los israelíes seglares también suelen argumentar que el modo de vida ultraortodoxo es insostenible, en especial porque las familias ultraortodoxas tienen un promedio de siete hijos.[32] Tarde o temprano, el Estado ya no podrá sustentar a tantas personas sin empleo, y los ultraortodoxos se verán obligados a trabajar. Pero podría muy bien ocurrir lo contrario. A medida que los robots y la IA vayan echando a los humanos del mercado laboral, los judíos ultraortodoxos quizá sean considerados el modelo del futuro en lugar de fósiles del pasado. No es que todo el mundo vaya a convertirse en judíos ultraortodoxos y se encierren en las yeshivás a estudiar el Talmud. Pero en la vida de todas las personas, la búsqueda de plenitud y de comunidad podría eclipsar la búsqueda de un puesto de trabajo.
Si conseguimos combinar una red de seguridad económica universal con comunidades fuertes y la búsqueda de una vida plena, perder nuestros puestos de trabajo frente a los algoritmos podría ser en verdad una bendición. Sin embargo, perder el control de nuestra existencia es una situación hipotética mucho más temible. A pesar del peligro del desempleo masivo, aquello que debería preocuparnos mucho más es el paso de la autoridad de los humanos a la de los algoritmos, lo que podría acabar con la poca fe que queda en el relato liberal y abrir el camino a la aparición de dictaduras digitales.
### 3
Libertad
#### Los macrodatos están observándote
El relato liberal considera la libertad humana el valor más importante. Aduce que toda autoridad surge en último término del libre albedrío de los individuos humanos, que se expresa en sus sentimientos, deseos y opciones. En política, el liberalismo cree que el votante sabe lo que le conviene. Por tanto, defiende las elecciones democráticas. En economía, el liberalismo mantiene que el cliente siempre tiene la razón. Por tanto, da la bienvenida a los principios del mercado libre. En cuestiones personales, el liberalismo anima a las personas a que se escuchen a sí mismas, a que sean fieles a sí mismas y a que sigan los dictados de su corazón, siempre y cuando no vulneren las libertades de los demás. Esta libertad personal queda consagrada en los derechos humanos.
En el discurso político occidental el término «liberal» se usa a veces hoy en día en un sentido partidista mucho más estricto, para denotar a los que apoyan causas específicas como el matrimonio gay, el control de las armas y el aborto. Pero la mayoría de los llamados conservadores también defienden la amplia visión liberal del mundo. Sobre todo en Estados Unidos, tanto republicanos como demócratas deberían tomarse de vez en cuando un respiro de sus acaloradas disputas para recordarse que todos están de acuerdo en cuestiones fundamentales como las elecciones libres, la judicatura independiente y los derechos humanos.
En particular, es vital recordar que héroes de la derecha, como Ronald Reagan y Margaret Thatcher, fueron grandes adalides no solo de las libertades económicas, sino también de las individuales. En una famosa entrevista de 1987, Thatcher dijo: «No existe tal cosa como la sociedad. Existe un tapiz vivo de hombres y mujeres, ...] y la calidad de nuestra vida depende de lo mucho que cada uno esté preparado para responsabilizarse de sí mismo».[[1]
Los herederos de Thatcher en el Partido Conservador estaban totalmente de acuerdo con el Partido Laborista en que la autoridad política procede de los sentimientos, las opciones y el libre albedrío de los votantes individuales. Así, cuando Gran Bretaña necesitó decidir si debía abandonar la Unión Europea, el primer ministro David Cameron no pidió a la reina Isabel II, al arzobispo de Canterbury ni a los rectores de Oxford y Cambridge que resolvieran la cuestión. Ni siquiera a los miembros del Parlamento. En cambio, convocó un referéndum en que a todos y a cada uno de los británicos se les preguntó: «¿Qué opina sobre la cuestión?».
El lector podría objetar que a la gente se le tenía que haber preguntado: «¿Qué piensa?» en lugar de: «¿Qué opina?», pero este es un error común. Los referéndums y las elecciones tienen siempre que ver con los sentimientos humanos, no con la racionalidad humana. Si la democracia fuera un asunto de toma de decisiones racionales, no habría ninguna razón para conceder a todas las personas los mismos derechos de voto o quizá ningún derecho de voto. Existe evidencia sobrada de que algunas personas están más informadas y son más racionales que otras, y en especial cuando se trata de cuestiones económicas y políticas específicas.[2] Después de la votación sobre el Brexit, el eminente biólogo Richard Dawkins protestó diciendo que nunca se le hubiera debido pedir a la inmensa mayoría de la opinión pública británica (él incluido) que votara en referéndum, porque carecían de los conocimientos suficientes de economía y ciencia política. «Por la misma razón podría convocarse un plebiscito nacional para decidir si Einstein hizo correctamente sus cálculos algebraicos, o dejar que los pasajeros de un avión votaran en qué pista debería aterrizar el piloto.»[3]
Sin embargo, para lo bueno y para lo malo, las elecciones y los referéndums no tratan de lo que pensamos. Tratan de lo que sentimos. Y cuando la cosa va de sentimientos, Einstein y Dawkins no son mejores que cualquier hijo de vecino. La democracia da por sentado que los sentimientos humanos reflejan un «libre albedrío» misterioso y profundo, que este «libre albedrío» es el origen último de la autoridad, y que mientras que algunas personas son más inteligentes que otras, todos los humanos son igualmente libres. Como Einstein y Dawkins, una sirvienta analfabeta también tiene libre albedrío, de modo que el día de las elecciones sus sentimientos (representados por su voto) cuentan tanto como los de cualquier otra persona.
Los sentimientos guían no solo a los votantes, sino también a los líderes. En el referéndum sobre el Brexit de 2016, la campaña del _Leave_ estaba encabezada a la vez por Boris Johnson y Michael Gove. Tras la dimisión de David Cameron, Gove apoyó inicialmente a Johnson para el puesto de primer ministro, pero en el último minuto Gove declaró que Johnson era inadecuado para el cargo y anunció su propia intención de presentarse para el puesto. La acción de Gove, que acabó con las opciones de Johnson, se describió como un asesinato político maquiavélico.[4] Pero Gove defendió su conducta recurriendo a sus sentimientos, al explicar: «En cada fase de mi vida política me he hecho una misma pregunta: "¿Qué es lo correcto? ¿Qué me dice el corazón?"».[5] Esta es la razón por la que, según Gove, luchó con tanto ahínco por el Brexit, y por la que se sintió obligado a traicionar a su antiguo aliado Boris Johnson y a competir él mismo por la posición de macho alfa: porque su corazón le dijo que lo hiciera.
Esta confianza en el corazón puede ser el talón de Aquiles de la democracia liberal. Porque una vez que alguien (ya sea en Pekín o en San Francisco) disponga de la capacidad tecnológica de acceder al corazón humano y manipularlo, la política democrática se transformará en un espectáculo de títeres emocional.
##### ESCUCHA EL ALGORITMO
La creencia liberal en los sentimientos y las opciones libres de los individuos no es natural ni muy antigua. Durante miles de años la gente creyó que la autoridad procedía de leyes divinas y no del corazón humano, y que por tanto debíamos santificar la palabra de Dios y no la libertad humana. Solo en los últimos siglos el origen de la autoridad pasó de las deidades celestiales a los humanos de carne y hueso.
La autoridad puede cambiar de nuevo pronto: de los humanos a los algoritmos. De la misma manera que la autoridad divina estaba legitimada por mitologías religiosas y la autoridad humana estaba justificada por el relato liberal, así la revolución tecnológica que se avecina podría establecer la autoridad de los algoritmos de macrodatos, al tiempo que socavaría la idea misma de la libertad individual.
Tal como hemos indicado en el capítulo anterior, los descubrimientos científicos sobre la manera en que nuestro cerebro y nuestro cuerpo funcionan sugerirían que nuestros sentimientos no son una cualidad espiritual exclusivamente humana y que no reflejan ningún tipo de «libre albedrío». Por el contrario, los sentimientos son mecanismos bioquímicos que todos los mamíferos y aves emplean para calcular rápidamente probabilidades de supervivencia y de reproducción. Los sentimientos no están basados en la intuición, la inspiración o la libertad; están basados en el cálculo.
Cuando un mono, un ratón o un humano ve una serpiente, el miedo aflora porque millones de neuronas calculan muy deprisa en el cerebro los datos relevantes y concluyen que la probabilidad de muerte es elevada. Los sentimientos de atracción sexual surgen cuando otros algoritmos bioquímicos calculan que un individuo cercano ofrece una probabilidad elevada de apareamiento exitoso, de vinculación social o de otro objetivo ansiado. Los sentimientos morales, como la indignación, el remordimiento o el perdón, se derivan de mecanismos neurales que surgieron por evolución para permitir la cooperación en grupo. Todos estos algoritmos bioquímicos se perfeccionaron a lo largo de millones de años de evolución. Si los sentimientos de algún antiguo antepasado cometieron una equivocación, los genes que los modelaron no pasaron a la siguiente generación. Así, los sentimientos no son lo opuesto a la racionalidad: encarnan la racionalidad evolutiva.
Por lo general no nos damos cuenta de que los sentimientos son en realidad cálculos, porque el rápido proceso del cálculo tiene lugar muy por debajo de nuestro umbral de la conciencia. No sentimos los millones de neuronas en el cerebro que computan probabilidades de supervivencia y reproducción, de modo que creemos erróneamente que nuestro miedo a las serpientes, nuestra elección de pareja sexual o nuestras opiniones sobre la Unión Europea son el resultado de algún misterioso «libre albedrío».
No obstante, aunque el liberalismo se equivoca al pensar que nuestros sentimientos reflejan un libre albedrío, hasta el día de hoy todavía tenía un buen sentido práctico. Porque aunque no había nada mágico o libre en nuestros sentimientos, eran el mejor método en el universo para decidir qué estudiar, con quién casarse y a qué partido votar. Y ningún sistema externo podía esperar comprender mis sentimientos mejor que yo. Aun cuando la Inquisición española o el KGB soviético me espiaran cada minuto del día, carecían del conocimiento biológico y la capacidad de cómputo necesarios para acceder subrepticiamente a los procesos bioquímicos que modelan mis deseos y opciones. A efectos prácticos, era razonable argumentar que poseía libre albedrío, porque mi deseo estaba conformado principalmente por la interacción de fuerzas internas, que nadie externo a mí podía ver. Puedo gozar de la ilusión de que controlo mi liza interna y secreta, mientras que los extraños jamás podrán comprender en verdad lo que ocurre en mí y cómo tomo las decisiones.
En consecuencia, el liberalismo estaba en lo cierto al aconsejar a la gente que siguiera los dictados de su corazón en lugar de los de algún sacerdote o de algún _apparatchik_ del partido. Sin embargo, pronto los algoritmos informáticos podrán aconsejarnos mejor que los sentimientos humanos. A medida que la Inquisición española y el KGB dejan paso a Google y a Baidu, es probable que el «libre albedrío» quede desenmascarado como un mito, y el liberalismo pueda perder sus ventajas prácticas.
Porque ahora nos hallamos en la confluencia de dos revoluciones inmensas. Por un lado, los biólogos están descifrando los misterios del cuerpo humano, y en particular del cerebro y los sentimientos. Al mismo tiempo, los informáticos nos proporcionan un poder de procesamiento de datos sin precedentes. Cuando la revolución de la biotecnología se fusione con la revolución de la infotecnología, producirá algoritmos de macrodatos que supervisarán y comprenderán mis sentimientos mucho mejor que yo, y entonces la autoridad pasará probablemente de los humanos a los ordenadores. Es posible que mi ilusión del libre albedrío se desintegre a medida que me tope diariamente con instituciones, compañías y organismos gubernamentales que comprendan y manipulen lo que hasta la fecha era mi fuero interno inaccesible.
Esto ya está ocurriendo en el campo de la medicina. Las decisiones médicas más importantes de nuestra vida no dependen de nuestras sensaciones de enfermedad o bienestar, ni siquiera de las predicciones informadas de nuestro médico, sino de los cálculos de ordenadores que comprenden nuestro cuerpo mucho mejor que nosotros. Dentro de unas pocas décadas, algoritmos de macrodatos alimentados por un flujo constante de datos biométricos podrán controlar nuestra salud a todas horas y todos los días de la semana. Podrán detectar el inicio mismo de la gripe, de un cáncer o del Alzheimer mucho antes de que notemos que algo va mal en nosotros. Entonces podrán recomendar tratamientos, dietas y regímenes diarios apropiados, hechos a medida para nuestro físico, nuestro ADN y nuestra personalidad únicos.
La gente gozará de la mejor atención sanitaria de la historia, pero justo por eso es probable que esté enferma todo el tiempo. Siempre hay algo que está mal en algún lugar del cuerpo. Siempre hay algo que puede mejorarse. En el pasado, nos sentíamos perfectamente sanos mientras no sufriésemos dolor o no padeciéramos una discapacidad aparente como una cojera. Pero en 2050, gracias a sensores biométricos y algoritmos de macrodatos, podrán diagnosticarse y tratarse las enfermedades mucho antes de que generen dolor o produzcan discapacidad. Como resultado, siempre nos encontraremos padeciendo alguna «enfermedad» y siguiendo esta o aquella recomendación algorítmica. Si nos negamos, quizá nuestro seguro sanitario quede invalidado, o nuestro jefe nos despida: ¿por qué habrían de pagar ellos el precio de nuestra testarudez?
Una cosa es seguir fumando a pesar de las estadísticas generales que relacionan el tabaco con el cáncer de pulmón, y otra muy distinta es continuar fumando a pesar de una advertencia concreta de un sensor biométrico que acaba de detectar diecisiete células cancerosas en la parte superior de nuestro pulmón izquierdo. Y si estamos dispuestos a desafiar al sensor, ¿qué haremos cuando el sensor transmita la advertencia a nuestra agencia de seguros, a nuestro jefe o a nuestra madre?
¿Quién dispondrá del tiempo y la energía para ocuparse de todas estas enfermedades? Con toda probabilidad, podremos sencillamente instruir a nuestro algoritmo de salud para que se ocupe de la mayoría de estos problemas como considere conveniente. En el mejor de los casos, enviará actualizaciones periódicas a nuestros teléfonos inteligentes, y nos dirá que «se detectaron y se destruyeron diecisiete células cancerosas». Los hipocondríacos quizá lean con responsabilidad esas actualizaciones, pero la mayoría seguramente las pasaremos por alto de la misma manera que hacemos caso omiso de esos avisos tan fastidiosos del antivirus en nuestros ordenadores.
##### EL DRAMA DE LA TOMA DE DECISIONES
Es probable que lo que ya está empezando a ocurrir en medicina ocurra cada vez en más ámbitos. La invención clave es el sensor biométrico, que la gente puede llevar sobre su cuerpo o dentro del mismo, y que convierte procesos biológicos en información electrónica que los ordenadores pueden almacenar y analizar. Dados los suficientes datos biométricos y la suficiente potencia de cómputo, los sistemas externos de procesamiento de datos pueden acceder a todos nuestros deseos, decisiones y opiniones. Son capaces de saber con exactitud quiénes somos.
La mayoría de la gente no se conoce muy bien a sí misma. Cuando yo tenía veintiún años, comprendí de una vez por todas que era gay, después de varios años de negarme a aceptarlo. Esto no es nada excepcional. Muchos hombres gais pasan toda su adolescencia inseguros sobre su sexualidad. Imagine ahora el lector la situación en 2050, cuando un algoritmo pueda decirle exactamente a un quinceañero en qué lugar se encuentra en un espectro de gais a heterosexuales (e incluso lo flexible que es dicha posición). Quizá el algoritmo nos muestre imágenes o vídeos de hombres y mujeres atractivos, siga los movimientos de nuestros ojos, la presión sanguínea y la actividad cerebral, y en cuestión de cinco minutos produzca un número en la escala de Kinsey.[6] Esto podría haberme ahorrado años de frustración. Quizá el lector no quiera realizar dicha prueba de forma individual, pero imagínese que se encuentra con un grupo de amigos en la aburrida fiesta de aniversario de Michelle, y que alguien sugiere que todos nos sometamos por turnos a este algoritmo nuevo y genial (y que todos estén alrededor observando los resultados y comentándolos). ¿Acaso el lector se marcharía?
Incluso en el caso de que lo hiciera, y aunque se escondiera de sí mismo y sus compañeros de clase, no podría esconderse de Amazon, Alibaba o la policía secreta. Mientras el lector navega por la web, mira algo en YouTube o lee las noticias de su red social, los algoritmos lo supervisarán y analizarán discretamente, y le dirán a Coca-Cola que si quiere venderle algún refresco, será mejor que en los anuncios utilice al chico descamisado antes que a la chica sin blusa. El lector ni siquiera lo sabrá. Pero ellos sí lo sabrán, y esta información valdrá miles de millones.
Y además, quizá todo esto se haga de manera abierta y la gente comparta su información a fin de obtener mejores recomendaciones, y al final para hacer que el algoritmo tome decisiones por ella. Se empieza por cosas sencillas, como decidir qué película ver. Mientras nos sentamos con un grupo de amigos para pasar una agradable tarde frente al televisor, primero hemos de elegir qué vamos a ver. Hace cincuenta años no teníamos opción, pero hoy en día, con el auge de los servicios de películas a la carta, existen miles de títulos disponibles. Llegar a un acuerdo puede ser bastante difícil, porque mientras que al lector le gustan las películas de ciencia ficción y suspense, Jack prefiere las comedias románticas y Jill vota por pretenciosos filmes franceses. Podría muy bien ocurrir que terminarais aviniéndoos a ver alguna película mediocre de serie B que os decepcione a todos.
Un algoritmo podría ayudar. Podríamos decirle qué películas anteriores nos han gustado de verdad a cada uno y, en función de su base de datos estadística masiva, el algoritmo encontraría entonces la combinación perfecta para el grupo. Por desgracia, es fácil que un algoritmo tan tosco esté mal informado, en particular porque es evidente que los informes personales suelen ser un indicador muy poco fiable de las verdaderas preferencias de la gente. Suele ocurrir que oímos a muchas personas elogiar una determinada película como una obra maestra, nos sentimos obligados a verla y, aunque nos quedamos dormidos a la mitad, no queremos parecer ignorantes, de modo que decimos a todo el mundo que fue una experiencia increíble.[7]
Sin embargo, estos problemas pueden resolverse si simplemente dejamos que el algoritmo recopile datos en tiempo real sobre nosotros mientras vemos los filmes, en lugar de basarnos en nuestros informes personales y dudosos. Para empezar, el algoritmo puede supervisar qué películas vimos enteras y cuáles dejamos a medio ver. Incluso si le decimos a todo el mundo que _Lo que el viento se llevó_ es la mejor película jamás rodada, el algoritmo sabrá que nunca pasamos de la primera media hora y nunca vimos en verdad cómo se incendiaba Atlanta.
Pero el algoritmo incluso puede ir mucho más allá. Hoy en día algunos ingenieros están desarrollando programas informáticos capaces de detectar las emociones humanas sobre la base del movimiento de nuestros ojos y músculos faciales.[8] Añadamos una buena cámara a la televisión y ese programa sabrá qué escenas nos hicieron reír, qué escenas nos entristecieron y qué escenas nos aburrieron. A continuación, conectemos el algoritmo a sensores biométricos, y sabrá de qué modo cada fotograma ha influido en nuestro ritmo cardíaco, nuestra tensión sanguínea y nuestra actividad cerebral. Mientras vemos, pongamos por caso, _Pulp Fiction_ , de Tarantino, el algoritmo puede advertir que la escena de la violación nos causó un asomo apenas perceptible de excitación sexual, que cuando Vincent disparó por accidente a la cara de Marvin nos hizo reír de forma culpable y que no captamos el chiste sobre la Gran Hamburguesa Kahuna, pero aun así nos reímos, para no parecer estúpidos. Cuando uno se obliga a reír, emplea circuitos cerebrales y músculos distintos que cuando nos reímos porque algo es realmente divertido. Los humanos no suelen detectar la diferencia. Pero un sensor biométrico podría hacerlo.[9]
La palabra «televisor» procede del griego _tele_ , que significa «lejos», y del latín _visio_ , «visión». Originalmente se concibió como un artilugio que nos permite ver desde lejos. Pero pronto nos permitirá que seamos vistos desde lejos. Tal como George Orwell imaginó en _1984_ , la televisión nos estará observando mientras la vemos. Una vez hayamos visto toda la filmografía de Tarantino, quizá podamos olvidar la mayor parte de ella. Pero Netflix o Amazon o quienquiera que posea el algoritmo de la televisión conocerá nuestro tipo de personalidad y cómo pulsar nuestros botones emocionales. Estos datos pueden permitir a Netflix y a Amazon elegir filmes para nosotros con precisión asombrosa, pero también puede permitirles que tomen por nosotros las decisiones más importantes de nuestra vida, como qué estudiar, dónde trabajar y con quién casarnos.
Por supuesto, Amazon no acertará siempre. Eso es imposible. Los algoritmos cometerán errores repetidamente debido a datos insuficientes, a programación defectuosa, a definiciones confusas de los objetivos y a la naturaleza caótica de la vida.[10] Pero Amazon no tiene que ser perfecto. Solo necesita ser, de media, mejor que nosotros, los humanos. Y eso no es muy difícil, porque la mayoría de las personas no se conocen muy bien a sí mismas, y la mayoría de las personas suelen cometer terribles equivocaciones en las decisiones más importantes de su vida. Más incluso que los algoritmos, los humanos adolecen de insuficiencia de datos, de programación (genética y cultural) defectuosa, de definiciones confusas y del caos de la vida.
El lector podría hacer la lista de los muchos problemas que afectan a los algoritmos, y llegar a la conclusión de que las personas nunca confiarán en ellos. Pero eso es un poco como catalogar todos los inconvenientes de la democracia y concluir que ninguna persona en sus cabales elegiría nunca defender un sistema de este tipo. Es sabido que Winston Churchill dijo que la democracia es el peor sistema político del mundo, con excepción de todos los demás. Acertadamente o no, la gente podría llegar a las mismas conclusiones acerca de los macrodatos: tienen muchísimas trabas, pero carecemos de una alternativa mejor.
A medida que los científicos conozcan cada vez mejor la manera en que los humanos toman decisiones, es probable que la tentación de basarse en algoritmos aumente. Acceder a la toma de decisiones de los humanos no solo hará que los algoritmos de macrodatos sean más fiables, sino que los sentimientos humanos sean menos fiables. A medida que gobiernos y empresas consigan acceder al sistema operativo humano, estaremos expuestos a una andanada de manipulación, publicidad y propaganda dirigidos con precisión. Nuestras opiniones y emociones podrían resultar tan fáciles de manipular que nos viéramos obligados a fiarnos de los algoritmos de la misma manera que un piloto que sufre un ataque de vértigo no ha de hacer caso de lo que sus propios sentidos le dicen y debe depositar toda su confianza en la maquinaria.
En algunos países y en determinadas situaciones, quizá a la gente no se le dé ninguna opción, y esta se vea obligada a obedecer las decisiones de los algoritmos de macrodatos. Pero incluso en sociedades supuestamente libres, los algoritmos pueden ir ganando autoridad debido a que aprenderemos por experiencia a confiar en ellos en cada vez más cuestiones, y poco a poco perderemos nuestra capacidad para tomar decisiones por nosotros mismos. Piense simplemente el lector en la manera en que, en las dos últimas décadas, miles de millones de personas han llegado a confiar al algoritmo de búsqueda de Google una de las tareas más importantes de todas: buscar información relevante y fidedigna. Ya no buscamos información. En lugar de ello, «googleamos». Y a medida que confiamos cada vez más en Google para hallar respuestas, nuestra capacidad para buscar información por nosotros mismos disminuye. Ya hoy en día, la «verdad» viene definida por los primeros resultados de la búsqueda de Google.[11]
Esto ha ido ocurriendo también con las capacidades físicas, como el espacio para orientarse y navegar. La gente pide a Google que la guíe cuando conduce. Cuando llega a una intersección, su instinto puede decirle: «Gira a la izquierda», pero Google Maps le dice: «Gire a la derecha». Al principio hacen caso a su instinto, giran a la izquierda, quedan atascados en un embotellamiento de tráfico y no llegan a tiempo a una reunión importante. La próxima vez harán caso a Google, girarán a la derecha y llegarán a tiempo. Aprenden por experiencia a confiar en Google. Al cabo de uno o dos años, se basan a ciegas en lo que les dice Google Maps, y si el teléfono inteligente falla, se encuentran completamente perdidos.
En marzo de 2012, tres turistas japoneses que viajaban por Australia decidieron realizar una excursión de un día a una pequeña isla situada lejos de la costa, y acabaron con su coche dentro del océano Pacífico. La conductora, Yuzu Noda, de veintiún años, dijo después que no había hecho más que seguir las instrucciones del GPS: «Nos dijo que podríamos conducir hasta allí. No dejaba de decir que nos llevaría a una carretera. Quedamos atrapados».[12] En varios incidentes parecidos, los conductores acabaron dentro de un lago, o cayeron desde lo alto de un puente demolido, aparentemente por haber seguido las instrucciones del GPS.[13] La capacidad de orientarse es como un músculo: o lo usas o lo pierdes.[14] Lo mismo puede decirse de la capacidad de elegir cónyuge o profesión.
Todos los años, millones de jóvenes necesitan decidir qué estudiar en la universidad. Esta es una decisión muy importante y difícil. Los jóvenes se encuentran sometidos a la presión de sus padres, sus amigos y sus profesores, que tienen intereses y opiniones diferentes. Los jóvenes deben también enfrentarse a sus propios temores y fantasías. Su juicio está ofuscado y manipulado por éxitos de taquilla de Hollywood, malas novelas y refinadas campañas publicitarias. Es particularmente difícil tomar una decisión sensata porque los interesados no saben en realidad qué hace falta para medrar con éxito en las diferentes profesiones y tampoco tienen necesariamente una imagen realista de sus propias fortalezas y debilidades. ¿Qué se necesita para triunfar como abogado? ¿Cómo me comportaré bajo presión? ¿Sabré trabajar bien en equipo?
Una estudiante puede empezar la carrera de Derecho porque posee una imagen inexacta de sus propias capacidades, y una visión todavía más distorsionada de lo que implica en verdad ser abogado (no se sueltan discursos espectaculares ni se grita «¡Protesto, señoría!» a todas horas). Mientras tanto, su amiga decide cumplir un sueño de la infancia y estudiar ballet de manera profesional, aunque carece de la estructura ósea y la disciplina necesarias. Años más tarde, ambas lamentan mucho su elección. En el futuro, confiaremos en que Google tome estas decisiones por nosotros. Google podrá decirme que perderé el tiempo en la Facultad de Derecho o en la academia de ballet, pero que podré ser una excelente (y muy feliz) psicóloga o fontanera.[15]
Una vez que la IA decida mejor que nosotros las carreras e incluso las relaciones, nuestro concepto de la humanidad y de la vida tendrá que cambiar. Los humanos están acostumbrados a pensar en la existencia como un drama de toma de decisiones. La democracia liberal y el capitalismo de libre mercado ven al individuo como un agente autónomo que no para de tomar decisiones sobre el mundo. Las obras de arte (ya sean las piezas teatrales de Shakespeare, las novelas de Jane Austen o las chabacanas comedias de Hollywood) suelen centrarse en que el o la protagonista ha de tomar alguna decisión particularmente crucial. ¿Ser o no ser? ¿Hacer caso a mi mujer y matar al rey Duncan, o hacer caso a mi conciencia y perdonarlo? ¿Casarme con el señor Collins o con el señor Darcy? Las teologías cristiana y musulmana se centran de manera parecida en el drama de la toma de decisiones, y aducen que la salvación o la condena eternas dependen de haber tomado la decisión correcta.
¿Qué pasará con esta forma de entender la vida si cada vez confiamos más en la IA para que tome las decisiones por nosotros? En la actualidad nos fiamos de Netflix para que nos recomiende películas y de Google Maps para elegir si giramos a la derecha o a la izquierda. Pero una vez que empecemos a contar con la IA para decidir qué estudiar, dónde trabajar y con quién casarnos, la vida humana dejará de ser un drama de toma de decisiones. Las elecciones democráticas y los mercados libres tendrán poco sentido. Lo mismo ocurrirá con la mayoría de las religiones y de las obras de arte. Imagine el lector a Anna Karénina sacando su teléfono inteligente y preguntándole al algoritmo de Facebook si debe seguir casada con Karenin o fugarse con el conde Vronsky. O imagine el lector su obra teatral favorita de Shakespeare con todas las decisiones cruciales tomadas por el algoritmo de Google. Hamlet y Macbeth llevarían una vida mucho más confortable, pero ¿qué tipo de vida sería, exactamente? ¿Tenemos modelos para dar sentido a una existencia de este tipo?
Cuando la autoridad se transfiera de los humanos a los algoritmos, quizá ya no veamos el mundo como el patio de juegos de individuos autónomos que se esfuerzan para tomar las decisiones correctas. En lugar de ello, podríamos percibir todo el universo como un flujo de datos, concebir los organismos como poco más que algoritmos bioquímicos y creer que la vocación cósmica de la humanidad es crear un sistema de procesamiento de datos que todo lo abarque y después fusionarnos con él. Hoy en día ya nos estamos convirtiendo en minúsculos chips dentro de un gigantesco sistema de procesamiento de datos que nadie entiende en realidad. A diario absorbo innumerables bits de datos mediante correos electrónicos, tuits y artículos. No sé exactamente dónde encajo yo en el gran esquema de las cosas, ni cómo mis bits de datos se conectan con los bits producidos por miles de millones de otros humanos y de ordenadores. No tengo tiempo de descubrirlo, porque estoy demasiado ocupado contestando a todos estos correos electrónicos.
##### EL COCHE FILOSÓFICO
La gente tal vez objetará que los algoritmos nunca podrán tomar decisiones importantes por nosotros, porque las decisiones importantes suelen implicar una dimensión ética, y los algoritmos no entienden de ética. Pero no hay ninguna razón para suponer que no serán capaces de superar al humano medio incluso en ética. Ya hoy en día, cuando dispositivos como los teléfonos inteligentes y los vehículos autónomos toman decisiones que solían ser monopolio humano, empiezan a habérselas con el mismo tipo de problemas éticos que han atormentado a los humanos durante milenios.
Por ejemplo, supongamos que dos chicos que persiguen una pelota saltan delante de un automóvil autónomo. Basándose en sus cálculos instantáneos, el algoritmo que conduce el coche concluye que la única manera de evitar atropellar a los chicos es virar bruscamente al carril opuesto, y arriesgarse a colisionar con un camión que viene en sentido contrario. El algoritmo calcula que en tal caso existe un 70 por ciento de probabilidades de que el propietario del coche (que está profundamente dormido en el asiento posterior) muera en el impacto. ¿Qué debería hacer el algoritmo?[16]
Los filósofos llevan milenios debatiendo sobre estos «problemas del tranvía» (se llaman «problemas del tranvía» porque los ejemplos de manual en los debates filosóficos modernos se refieren a un tranvía fuera de control que se precipita por las vías, en lugar de a un automóvil autónomo).[17] Hasta ahora, resulta vergonzoso que estos debates hayan tenido poquísima influencia sobre el comportamiento real, porque en épocas de crisis los humanos suelen olvidar con demasiada frecuencia sus opiniones filosóficas y en cambio siguen sus emociones e instintos viscerales.
Uno de los experimentos más desagradables en la historia de las ciencias sociales se realizó en diciembre de 1970 con un grupo de estudiantes del Seminario Teológico de Princeton, que se estaban preparando para convertirse en ministros de la Iglesia presbiteriana. A cada estudiante se le pidió que se dirigiera apresuradamente a un aula alejada, y que allí diera una charla sobre la parábola del Buen Samaritano, que cuenta que un judío que viajaba de Jerusalén a Jericó fue asaltado y robado por criminales, que lo dejaron moribundo junto al camino. Después de algún tiempo, un sacerdote y un levita pasaron cerca, pero ninguno de ellos hizo caso del hombre. En cambio, un samaritano (un miembro de una secta muy despreciada por los judíos) se detuvo cuando vio a la víctima, cuidó de ella y le salvó la vida. La moraleja de la parábola es que el mérito de la gente ha de juzgarse por su comportamiento real y no por su filiación religiosa ni por sus opiniones filosóficas.
Los jóvenes e impacientes seminaristas corrieron al aula, mientras en el trayecto iban pensando cómo explicar mejor la parábola del Buen Samaritano. Pero los investigadores dispusieron en su ruta a una persona vestida con andrajos, que estaba sentada despatarrada en un portal, con la cabeza gacha y los ojos cerrados. Cada vez que un incauto seminarista pasaba rápidamente por su lado, la «víctima» tosía y gemía de forma lastimosa. La mayoría de los seminaristas ni siquiera se detuvieron para preguntar al hombre qué le pasaba, y mucho menos le ofrecieron ayuda. El estrés emocional generado por la necesidad de correr hasta el aula superó a su obligación moral de ayudar a un desconocido en apuros.[18]
Las emociones humanas superan a las teorías filosóficas en muchas otras situaciones. Esto hace que la historia ética y filosófica del mundo sea un relato bastante deprimente de ideas maravillosas y de comportamientos menos que ideales. ¿Cuántos cristianos ofrecen ahora la otra mejilla, cuántos budistas se elevan en realidad por encima de las obsesiones egoístas y cuántos judíos aman realmente a sus vecinos como a sí mismos? Esta es justo la manera como la selección natural ha modelado a _Homo sapiens_. Al igual que todos los mamíferos, _Homo sapiens_ emplea las emociones para tomar rápidas decisiones de vida o muerte. Hemos heredado nuestra ira, nuestro miedo y nuestro deseo de millones de antepasados, los cuales pasaron los controles de calidad más rigurosos de la selección natural.
Por desgracia, lo que era bueno para la supervivencia y la reproducción en la sabana africana hace un millón de años no tiene por qué dar lugar necesariamente a un comportamiento responsable en las carreteras del siglo XXI. Todos los años, conductores humanos distraídos, enfadados y ansiosos matan a más de un millón de personas en accidentes de tráfico. Podemos enviar a todos nuestros filósofos, profetas y sacerdotes a que prediquen ética a dichos conductores, pero en la carretera seguirán predominando las emociones propias de los mamíferos y los instintos de la sabana. En consecuencia, los seminaristas apresurados no prestarán atención a personas en apuros y los conductores en un momento crítico atropellarán a infortunados peatones.
Esta disyunción entre el seminario y la carretera es uno de los mayores problemas prácticos en la ética. Immanuel Kant, John Stuart Mill y John Rawls ya pueden acomodarse en alguna acogedora aula universitaria y discutir durante días problemas teóricos de ética, pero ¿en verdad los conductores estresados aplicarán sus conclusiones en plena emergencia y en una fracción de segundo? Quizá Michael Schumacher (el campeón de Fórmula Uno del que a veces se ha dicho que ha sido el mejor conductor de la historia) tenía la capacidad de pensar en filosofía mientras conducía su coche, pero la mayoría no somos Schumacher.
De todos modos, los algoritmos informáticos no han sido conformados por la selección natural, y no tienen emociones ni instintos viscerales. De ahí que, en momentos críticos, puedan seguir directrices éticas mucho mejor que los humanos, siempre que encontremos una manera de codificar la ética en números y estadísticas precisos. Si enseñáramos a Kant, Mill y Rawls a escribir programas informáticos, podrían programar el automóvil autónomo en su confortable laboratorio, y estar seguros de que el coche seguiría sus órdenes en la autopista. En efecto, cada coche será conducido por Michael Schumacher e Immanuel Kant unidos en una única entidad.
Así, si programamos un automóvil autónomo para que se detenga y ayude a extraños en apuros, lo hará contra viento y marea (a menos, desde luego, que insertemos una cláusula de excepción para situaciones de vendavales y marejadas). De manera parecida, si nuestro automóvil autónomo se halla programado para pasar al otro carril a fin de esquivar a dos chicos situados en su trayectoria, podemos apostar la vida a que será justo esto lo que hará. Lo que significa que cuando diseñen su automóvil autónomo, Toyota o Tesla transformarán un problema teórico de la filosofía de la ética en un problema práctico de ingeniería.
Sin duda, los algoritmos filosóficos nunca serán perfectos. Todavía habrá errores, que acarrearán heridos, muertos y pleitos complicadísimos. (Por primera vez en la historia, podremos demandar a un filósofo por las desafortunadas consecuencias de sus teorías, porque por primera vez en la historia podremos demostrar una conexión causal directa entre ideas filosóficas y acontecimientos de la vida real.) Sin embargo, para ocupar el lugar de los conductores humanos, los algoritmos no tienen que ser perfectos. Solo mejor que los humanos. Dado que los conductores humanos matan al año a más de un millón de personas, no es pedir demasiado. A fin de cuentas, ¿preferirá el lector que el coche que está junto al suyo lo conduzca un adolescente ebrio o el equipo Schumacher-Kant?[19]
La misma lógica puede aplicarse no solo a la conducción de automóviles, sino a muchas otras situaciones. Pongamos como ejemplo la solicitud de empleo. En el siglo XXI, la decisión de contratar o no a alguien para un puesto de trabajo la tomarán cada vez más los algoritmos. No podemos basarnos en la máquina para establecer criterios éticos relevantes: será necesario que esto sigan haciéndolo los humanos. Pero una vez que hayamos decidido acerca de un criterio ético en el mercado laboral (por ejemplo, que está mal discriminar a los negros y a las mujeres), podemos confiar en las máquinas para que implementen y mantengan ese criterio mejor que los humanos.[20]
Un gestor humano puede saber e incluso estar de acuerdo en que no es ético discriminar a los negros y a las mujeres, pero cuando una mujer negra solicita un empleo, el gestor la discrimina de forma inconsciente, y decide no contratarla. Si permitimos que un ordenador evalúe solicitudes de empleo y lo programamos para que no tenga en absoluto en cuenta raza ni género, no cabe duda de que el ordenador en verdad pasará por alto estos factores, porque los ordenadores no tienen subconsciente. Desde luego, no será fácil diseñar un programa para evaluar solicitudes de empleo, y siempre existirá el peligro de que los ingenieros introduzcan de alguna manera sus propios prejuicios inconscientes en el programa.[21] Pero una vez que hayamos descubierto tales errores, seguramente será mucho más fácil corregir el programa que librar a los humanos de sus prejuicios racistas y misóginos.
Hemos visto que el auge de la inteligencia artificial podría expulsar a la mayoría de los humanos del mercado laboral, entre ellos a conductores y policía de tráfico (cuando los humanos pendencieros sean sustituidos por algoritmos obedientes, la policía de tráfico no será necesaria). Sin embargo, podría haber algunas nuevas vacantes para los filósofos, porque sus habilidades (que hasta ahora carecen de mucho valor de mercado) de repente serán muy demandadas. Así, si queremos estudiar algo que garantice un buen empleo en el futuro, quizá la filosofía no sea una mala apuesta.
Desde luego, los filósofos rara vez se ponen de acuerdo en el procedimiento adecuado. Pocos «problemas del tranvía» se han resuelto a gusto de todos los filósofos, y pensadores consecuencialistas como John Stuart Mill (que juzga las acciones por sus consecuencias) sostienen opiniones muy diferentes a los deontologistas como Immanuel Kant (que juzga las acciones mediante reglas absolutas). ¿Tendría que posicionarse realmente Tesla respecto a estos asuntos tan enrevesados para producir un automóvil?
Bueno, quizá Tesla simplemente deje esta cuestión al mercado. Fabricará dos modelos de automóvil autónomo: el Tesla Altruista y el Tesla Egoísta. En una emergencia, el Altruista sacrifica a su dueño por un bien mayor, mientras que el Egoísta hace cuanto está en su mano para salvar a su dueño, incluso si ello significa matar a los dos chicos. Entonces los clientes podrán comprar el coche que mejor se adapte a su opinión filosófica favorita. Si hay más personas que compran el Tesla Egoísta, no podremos culpar a Tesla. Al fin y al cabo, el cliente siempre tiene razón.
No es un chiste. En un estudio pionero de 2015, a unas personas se les presentó una situación hipotética en la que un automóvil autónomo estaba a punto de atropellar a varios peatones. La mayoría dijeron que en este caso el coche tenía que salvar a los peatones aun a costa de matar a su dueño. Cuando después se les preguntó si ellos comprarían un automóvil programado para sacrificar a su dueño por un bien mayor, la mayoría contestaron que no. Para ellos, preferirían el Tesla Egoísta.[22]
Imagine la lectora la situación: ha comprado un coche nuevo, pero antes de empezar a usarlo, ha de meterse en el menú de configuración y elegir una de varias opciones. En caso de un accidente, ¿quiere que el automóvil sacrifique su vida o que mate a la familia del otro vehículo? ¿Es esta una elección que desearía hacer? Piense solo en las discusiones que habrá de tener con su marido acerca de qué opción elegir.
¿Acaso el Estado debería intervenir para regular el mercado e imponer un código ético para todos los automóviles autónomos? Algunos legisladores estarían sin duda entusiasmados con la oportunidad de promulgar por fin leyes que siempre se cumplan al pie de la letra. Otros legisladores podrían sentirse alarmados por semejante responsabilidad totalitaria y sin precedentes. Después de todo, a lo largo de la historia las limitaciones del cumplimiento de las leyes han sido un freno bien acogido a los prejuicios, errores y excesos de los legisladores. Fue una gran fortuna que leyes contra la homosexualidad y contra la blasfemia se hicieran cumplir solo parcialmente. ¿De verdad queremos un sistema en que las decisiones de políticos falibles se conviertan en algo tan inexorable como la fuerza de la gravedad?
##### DICTADURAS DIGITALES
La IA suele asustar a la gente porque esta no cree que vaya a ser siempre obediente. Hemos visto demasiadas películas de ciencia ficción sobre robots que se rebelan contra sus amos humanos, que corren descontrolados por las calles matando a todo el mundo. Pero el problema real con los robots es justo el contrario. Debemos temerlos porque probablemente obedecerán siempre a sus amos y nunca se rebelarán.
No hay nada malo en la obediencia ciega, desde luego, mientras los robots sirvan a amos benignos. Incluso en la guerra, basarse en robots asesinos puede asegurar que, por primera vez en la historia, las leyes de la guerra se respeten de verdad en el campo de batalla. A veces los soldados humanos se dejan llevar por sus emociones y asesinan, saquean y violan, transgrediendo así las leyes de la guerra. Solemos asociar las emociones con la compasión, el amor y la empatía, pero en tiempos de guerra, las emociones que predominan son con demasiada frecuencia el miedo, el odio y la crueldad. Puesto que los robots carecen de emociones, puede confiarse en que siempre cumplirán al pie de la letra el código militar, y que nunca se dejarán influir por temores y odios personales.[23]
El 16 de marzo de 1968, en la aldea sudvietnamita de My Lai, los soldados norteamericanos de un regimiento se volvieron locos y aniquilaron a unos 400 civiles. Este crimen de guerra fue el resultado de la iniciativa local de hombres que habían estado combatiendo durante varios meses en una guerra de guerrillas en la jungla. No tuvo ninguna finalidad estratégica, y contravino tanto el código legal como la política militar estadounidenses. Se debió a emociones humanas.[24] Si Estados Unidos hubiera hecho uso de robots asesinos en Vietnam, la masacre de My Lai jamás se hubiera producido.
No obstante, antes de que nos apresuremos a desarrollar y a usar robots asesinos, debemos recordar que los robots siempre reflejan y amplifican las cualidades de su programa. Si el programa es mesurado y benévolo, los robots serán probablemente una mejora enorme respecto al soldado humano medio. Pero si el programa es despiadado y cruel, los resultados serán catastróficos. El problema real de los robots no es su propia inteligencia artificial, sino más bien la estupidez y crueldad naturales de sus amos humanos.
En julio de 1995, tropas serbobosnias mataron a más de 8.000 musulmanes bosnios en los alrededores de la ciudad de Srebrenica. A diferencia de la masacre caótica de My Lai, los asesinatos de Srebrenica fueron una operación prolongada y bien organizada que reflejaba la política de los serbobosnios de «limpiar étnicamente» Bosnia de musulmanes.[25] Si los serbobosnios hubieran tenido robots asesinos en 1995, es probable que la atrocidad hubiera sido aún mayor. Ningún robot hubiera dudado ni un momento en cumplir las órdenes que se le hubieran dado, y no hubiera escatimado la vida de un solo niño musulmán por sentimientos de compasión, repulsión o simple letargia.
Un dictador despiadado armado con estos robots asesinos nunca debería temer que sus soldados se volvieran en su contra, con independencia de lo desalmadas y locas que fueran sus órdenes. Un ejército de robots habría sin duda estrangulado en su cuna a la Revolución francesa en 1789, y si en 2011 Hosni Mubarak hubiera dispuesto de un contingente de robots asesinos, habría podido desplegarlos contra el populacho sin temor a su defección. De forma parecida, un gobierno imperialista que se basara en un ejército de robots podría librar guerras impopulares sin preocuparse de si los robots pierden la motivación, o de si sus familias organizan protestas. Si Estados Unidos hubiera dispuesto de robots asesinos en la guerra de Vietnam, la masacre de My Lai podría haberse evitado, pero la contienda misma tal vez habría durado muchos más años, porque el gobierno estadounidense no hubiera tenido tantos problemas con soldados desmoralizados, manifestaciones multitudinarias contra la contienda o un movimiento de «robots veteranos contra la guerra» (algunos ciudadanos norteamericanos quizá aún se habrían opuesto a la guerra, pero sin el temor a ser reclutados, sin el recuerdo de haber cometido atrocidades personalmente y sin la dolorosa pérdida de un familiar querido, los manifestantes habrían sido probablemente menos numerosos y habrían estado menos motivados).[26]
Estos tipos de problemas son mucho menos relevantes para los vehículos civiles autónomos, porque ningún fabricante de coches programaría de forma malévola sus vehículos para que se dirigieran hacia las personas y las mataran. Pero los sistemas de armas autónomas suponen una catástrofe en ciernes, porque hay demasiados gobiernos que tienden a ser éticamente corruptos o directamente malvados.
El peligro no se limita a las máquinas asesinas. Los sistemas de vigilancia pueden ser igualmente peligrosos. En manos de un gobierno benévolo, los algoritmos de vigilancia potentes quizá sean lo mejor que le haya ocurrido nunca a la humanidad. Pero esos algoritmos de macrodatos podrían asimismo empoderar a un futuro Gran Hermano, de modo que termináramos sometidos a un régimen de vigilancia orwelliana en el que cada uno de los individuos fuera controlado todo el tiempo.[27]
De hecho, podríamos acabar de una manera que ni siquiera Orwell hubiera imaginado: con un régimen de vigilancia global que haga el seguimiento no solo de todas nuestras actividades y nuestras manifestaciones externas, sino que también logre incluso metérsenos bajo la piel para conocer nuestras experiencias internas. Considérese por ejemplo lo que el régimen de Kim en Corea del Norte sería capaz de hacer con la nueva tecnología. En el futuro, a cada ciudadano norcoreano se le podría exigir que llevara un brazalete biométrico que supervisara cuanto hiciera y dijera, así como su tensión sanguínea y su actividad cerebral. Mediante el uso de nuestro conocimiento creciente del cerebro humano, y empleando los inmensos poderes del aprendizaje automático, el régimen norcoreano podría, por primera vez en la historia, evaluar lo que todos y cada uno de los ciudadanos está pensando en cualquier momento. Si miramos una fotografía de Kim Jong-un y los sensores biométricos captan las señales que delatan la ira (aumento de la tensión sanguínea, actividad acrecentada en la amígdala), podríamos vernos en el gulag la mañana siguiente.
Por supuesto, debido a su aislamiento, al régimen de Corea del Norte le costaría desarrollar por sí mismo la tecnología necesaria. Sin embargo, dicha tecnología podría iniciarse en naciones más avanzadas técnicamente, y luego ser copiada o comprada por los norcoreanos y otras dictaduras atrasadas. Tanto China como Rusia están mejorando sin cesar sus instrumentos de vigilancia, como varios países democráticos más, desde Estados Unidos hasta mi patria, Israel. Llamada la «nación emprendedora», Israel tiene un sector de alta tecnología muy dinámico y una industria puntera de ciberseguridad. Al mismo tiempo, está también enzarzada en un conflicto letal con los palestinos, y al menos algunos de sus dirigentes, generales y ciudadanos se pondrían muy contentos si se creara un régimen de vigilancia total en Cisjordania tan pronto como se disponga de la tecnología necesaria.
Ya hoy en día, siempre que los palestinos realizan una llamada telefónica, publican algo en Facebook o viajan de una ciudad a otra, es probable que se los vigile con micrófonos, cámaras, drones o programas espía israelíes. Los datos obtenidos se analizan después mediante algoritmos de macrodatos. Esto ayuda a las fuerzas de seguridad israelíes a precisar y a neutralizar amenazas potenciales sin tener que desplazar demasiados efectivos sobre el terreno. Los palestinos pueden administrar algunas ciudades y pueblos en Cisjordania, pero los israelíes controlan el cielo, las ondas de radio y el ciberespacio. Por tanto, son necesarios muy pocos soldados israelíes para controlar de manera efectiva a alrededor de 2,5 millones de palestinos en Cisjordania.[28]
En un incidente tragicómico acaecido en octubre de 2017, un peón palestino publicó en Facebook una fotografía de sí mismo en su lugar de trabajo, al lado de un buldócer. Junto a la imagen escribió: «¡Buenos días!». Un algoritmo automático cometió un pequeño error cuando transliteró las letras arábigas. En lugar de «Ysabechhum!» (que significa «¡Buenos días!»), el algoritmo identificó las letras como «Ydbachhum!» (que significa «¡Mátalos!»). Al sospechar que el hombre podía ser un terrorista que intentaba utilizar un buldócer para atropellar a gente, las fuerzas de seguridad israelíes lo detuvieron de inmediato. Quedó en libertad cuando se dieron cuenta de que el algoritmo había cometido un error. No obstante, el post ofensivo se eliminó de Facebook. Nunca se es demasiado prudente.[29] Lo que los palestinos están viviendo hoy en día en Cisjordania podría ser simplemente un burdo anticipo de lo que miles de millones de personas acabarán por experimentar en todo el planeta.
A finales del siglo XX, las democracias superaban por lo general a las dictaduras porque aquellas eran mejores procesando los datos. La democracia difunde el poder para procesar información y la toma de decisiones se hace entre muchas personas e instituciones, mientras que la dictadura concentra la información y el poder en un punto. Dada la tecnología del siglo XX, era ineficiente concentrar demasiada información y poder en un punto. Nadie tenía la capacidad de procesar toda la información con suficiente rapidez y de tomar las decisiones adecuadas. Esa es una parte de la razón por la que la Unión Soviética tomó decisiones mucho peores que Estados Unidos, y por la que la economía soviética se hallaba muy por detrás de la norteamericana.
Sin embargo, puede que la inteligencia artificial haga que el péndulo se mueva en la dirección opuesta. La IA hace posible procesar cantidades enormes de información de manera centralizada. De hecho, podría lograr que los sistemas centralizados fueran mucho más eficientes que los sistemas difusos, porque el aprendizaje automático funciona mejor cuando es capaz de analizar mucha información. Si concentramos toda la información relacionada con mil millones de personas en una única base de datos, sin tener en cuenta los problemas de privacidad, podemos preparar algoritmos mucho mejores que si respetamos la intimidad individual y en nuestra base de datos solo disponemos de información parcial sobre un millón de personas. Por ejemplo, si un gobierno autoritario ordenara a todos sus ciudadanos que analizaran su ADN y que compartieran sus datos médicos con alguna autoridad central, obtendría una ventaja inmensa en genética e investigación médica con respecto a sociedades en que los datos médicos son estrictamente privados. La principal desventaja de los regímenes autoritarios en el siglo XX (el intento de concentrar toda la información en un punto) podría convertirse en su ventaja decisiva en el siglo XXI.
Cuando los algoritmos lleguen a conocernos tan bien, los gobiernos autoritarios se harán con un control absoluto sobre sus ciudadanos, más incluso que en la Alemania nazi, y la resistencia a tales regímenes podría ser de todo punto imposible. El régimen no solo sabrá exactamente cómo sentimos: podrá hacer que sintamos lo que quiera. El dictador tal vez no sea capaz de proporcionar a los ciudadanos asistencia sanitaria o igualdad, pero podrá hacer que lo amen y que odien a sus oponentes. En su forma actual, la democracia no sobrevivirá a la fusión de la biotecnología y la infotecnología. O bien se reinventa a sí misma con éxito y de una forma radicalmente nueva, o bien los humanos acabarán viviendo en «dictaduras digitales».
Esto no implicará un retorno a la época de Hitler y Stalin. Las dictaduras digitales serán tan diferentes de la Alemania nazi como la Alemania nazi lo era de la Francia del _ancien régime_. Luis XIV fue un autócrata centralizador, pero carecía de la tecnología necesaria para erigir un Estado totalitario moderno. Su reinado no sufrió ninguna oposición, pero en ausencia de radios, teléfonos y trenes, ejercía poco control sobre la vida cotidiana de los campesinos de las remotas aldeas bretonas, o incluso de los ciudadanos del centro de París. No tenía la voluntad ni la capacidad para establecer un partido de masas, un movimiento juvenil que abarcara a todo el país o un sistema de educación nacional.[30] Fueron las nuevas tecnologías del siglo XX las que proporcionaron a Hitler la motivación y el poder para hacer estas cosas. No podemos predecir cuáles serán las motivaciones ni la fuerza de las dictaduras digitales en 2084, pero es muy poco probable que se limiten a copiar a Hitler y a Stalin. Aquellos que se preparen para volver a librar las batallas de la década de 1930 podrían ser objeto de un ataque por sorpresa procedente de una dirección por completo distinta.
Incluso si la democracia consigue adaptarse y sobrevivir, las personas podrían ser víctimas de nuevos tipos de opresión y discriminación. En la actualidad, hay cada vez más bancos, empresas e instituciones que emplean algoritmos para analizar datos y tomar decisiones sobre nosotros. Cuando solicitamos un préstamo al banco, es probable que nuestra solicitud sea procesada por un algoritmo y no por un humano. El algoritmo analiza muchísimos datos sobre nosotros y estadísticas acerca de millones de otras personas, y decide si somos lo bastante solventes para concedernos el préstamo. A menudo, el trabajo que realiza el algoritmo es mejor que el de un banquero humano. Pero el problema radica en que si el algoritmo discrimina injustamente a algunas personas, es difícil saberlo. Si el banco se niega a concedernos el préstamo y preguntamos: «¿Por qué?», el banco contesta: «El algoritmo dijo que no». Y entonces preguntamos: «¿Y por qué dijo que no el algoritmo? ¿Qué problema hay?», y el banco responde: «No lo sabemos. No hay ningún humano que entienda este algoritmo, porque se basa en aprendizaje automático avanzado. Pero confiamos en nuestro algoritmo, de modo que no le concederemos el préstamo».[31]
Cuando la discriminación se dirige a grupos enteros, como mujeres o negros, estos grupos pueden organizarse y protestar contra su discriminación colectiva. Pero ahora un algoritmo es capaz de discriminarnos a nosotros de forma individual, y no tenemos ni idea de por qué. Quizá el algoritmo encontró algo en nuestro ADN, nuestra historia personal o nuestra cuenta de Facebook que no le gusta. El algoritmo nos discrimina no porque seamos una mujer o un afroamericano, sino porque somos nosotros. Hay algo específico en nosotros que no le gusta. No sabemos qué es, y aunque lo supiéramos no podríamos organizarnos con otras personas para protestar, porque no hay otras personas que padezcan el mismo prejuicio exacto. Solo nosotros. En lugar de simplemente discriminación colectiva, en el siglo XXI podríamos enfrentarnos a un problema creciente de discriminación individual.[32]
En las más altas esferas de la autoridad, probablemente seguirá habiendo hombres de paja humanos, que nos generarán la ilusión de que los algoritmos solo son consejeros y que la autoridad última se halla todavía en manos humanas. No designaremos una IA como el canciller de Alemania o el director ejecutivo de Google. Sin embargo, las decisiones que tomen el canciller y el director ejecutivo estarán determinadas por la IA. El canciller podrá elegir todavía entre varias opciones, pero todas serán el resultado del análisis de macrodatos y reflejarán más la manera como la IA entiende el mundo que la manera como lo entienden los humanos.
Por poner un ejemplo análogo: en la actualidad los políticos de todo el mundo pueden elegir entre varias políticas económicas diferentes, pero en casi todos los casos las diversas políticas que se ofrecen reflejan una perspectiva capitalista de la economía. Los políticos creen que están eligiendo, pero las decisiones realmente importantes ya las han tomado mucho antes los economistas, banqueros y empresarios que modelaron las diferentes opciones en el menú. Dentro de un par de décadas, los políticos podrían encontrarse eligiendo de un menú escrito por la IA.
##### INTELIGENCIA ARTIFICIAL Y ESTUPIDEZ NATURAL
Una buena noticia es que al menos en las próximas décadas no tendremos que habérnoslas con la elaborada pesadilla de la ciencia ficción en la que la IA adquiera conciencia y decida esclavizar o aniquilar a la humanidad. Cada vez nos basaremos más en los algoritmos para que tomen decisiones por nosotros, pero es improbable que estos empiecen conscientemente a manipularnos. No tendrán ninguna conciencia.
La ciencia ficción suele confundir la inteligencia con la conciencia, y supone que para equipararse a la inteligencia humana o superarla, los ordenadores tendrán que desarrollar conciencia. El argumento básico de casi todas las películas y novelas sobre IA gira en torno al instante mágico en el que un ordenador o un robot adquieren conciencia. Una vez ocurre, o bien el héroe humano se enamora del robot, o bien el robot intenta matar a todos los humanos, o bien suceden ambas cosas a la vez.
Pero en realidad no hay razón para suponer que la inteligencia artificial adquiera conciencia, porque inteligencia y conciencia son cosas muy distintas. La inteligencia es la capacidad de resolver problemas. La conciencia es la capacidad de sentir dolor, alegría, amor e ira. Tendemos a confundir ambas cosas porque en los humanos y otros mamíferos la inteligencia va de la mano de la conciencia. Los mamíferos resuelven la mayoría de los problemas mediante los sentimientos. Sin embargo, los ordenadores los resuelven de una manera diferente.
Simplemente, hay caminos distintos que conducen a una inteligencia elevada, y solo algunos de dichos caminos implican obtener conciencia. De la misma manera que los aviones vuelan más rápidos que las aves sin desarrollar plumas, así los ordenadores pueden llegar a resolver problemas mucho mejor que los mamíferos sin desarrollar sentimientos. Es cierto que la IA tendrá que analizar con exactitud los sentimientos humanos para tratar enfermedades humanas, identificar a terroristas humanos, recomendar a parejas humanas y circular por una calle llena de peatones humanos. Pero podrá hacerlo sin experimentar ningún sentimiento propio. Un algoritmo no necesita sentir alegría, ira o miedo para reconocer los diferentes patrones bioquímicos de simios alegres, contrariados o asustados.
Desde luego, no es del todo imposible que la IA desarrolle sentimientos propios. Todavía no sabemos bastante de la conciencia para estar seguros de ello. En general, hay tres opciones que es necesario considerar:
1.La conciencia está relacionada de algún modo con la bioquímica orgánica, de tal manera que nunca será posible crear la conciencia en sistemas no orgánicos.
2.La conciencia no está relacionada con la bioquímica orgánica, pero sí con la inteligencia, de tal manera que los ordenadores podrían desarrollar conciencia y los ordenadores tendrán que hacerlo si deben superar un determinado umbral de inteligencia.
3.No existen conexiones esenciales entre la conciencia y la bioquímica orgánica o la inteligencia superior. Por tanto, los ordenadores podrían desarrollar conciencia, pero no necesariamente; podrían llegar a ser superinteligentes al tiempo que siguieran sin tener conciencia.
En nuestro estado actual de conocimiento, no podemos descartar ninguna de estas alternativas. Pero precisamente porque sabemos tan pocas cosas de la conciencia, parece improbable que seamos capaces de programar muy pronto ordenadores conscientes. De ahí que a pesar del inmenso poder de la inteligencia artificial, por ahora su uso continuará dependiendo en cierta medida de la conciencia humana.
El peligro es que, si invertimos demasiado en desarrollar la IA y demasiado poco en desarrollar la conciencia humana, la inteligencia artificial muy sofisticada de los ordenadores solo servirá para fortalecer la estupidez natural de los humanos. Es improbable que nos enfrentemos a una rebelión de robots en las décadas venideras, pero podríamos tener que habérnoslas con multitud de bots que saben cómo pulsar nuestros botones emocionales mejor que nuestra madre, y utilizar esta asombrosa capacidad para intentar vendernos cosas, ya sea un automóvil, a un político o una ideología completa. Los bots podrían identificar nuestros temores, odios y antojos más profundos, y utilizar esta ventaja contra nosotros. Ya se nos ha dado una muestra de esto en elecciones y referéndums en todo el mundo, cuando los piratas informáticos han descubierto cómo manipular a los votantes individuales analizando los datos sobre ellos y explotando sus prejuicios.[33] Aunque las novelas y películas de ciencia ficción acaban en espectaculares apocalipsis de fuego y humo, en realidad podríamos enfrentarnos a un apocalipsis banal al pulsar una tecla.
Para evitar tales resultados, por cada dólar y cada minuto que invertimos en mejorar la inteligencia artificial sería sensato invertir un dólar y un minuto en promover la conciencia humana. Por desgracia, en la actualidad no hacemos mucho para investigarla y desarrollarla. Estamos investigando y desarrollando capacidades humanas sobre todo según las necesidades inmediatas del sistema económico y político, y no según nuestras propias necesidades a largo plazo como seres conscientes. Mi jefe quiere que conteste los mensajes electrónicos tan rápidamente como sea posible, pero le interesa poco mi capacidad para saborear y apreciar los manjares que como. En consecuencia, reviso los mensajes electrónicos incluso durante las comidas, al tiempo que pierdo mi capacidad de prestar atención a mis propias sensaciones. El sistema económico me presiona para que expanda y diversifique mi cartera de valores, pero me da cero incentivos para expandir y diversificar mi compasión. De modo que me esfuerzo para entender los misterios de la Bolsa de valores, al tiempo que dedico mucho menos esfuerzo a entender las causas profundas del sufrimiento.
En esto, los humanos nos asemejamos a otros animales domésticos. Hemos criado vacas dóciles que producen cantidades enormes de leche, pero que en otros aspectos son muy inferiores a sus antepasados salvajes. Son menos ágiles, menos curiosas y menos habilidosas.[34] Ahora estamos creando humanos mansos que generan cantidades enormes de datos y funcionan como chips muy eficientes en un enorme mecanismo de procesamiento de datos, pero estos datos-vacas en absoluto maximizan el potencial humano. De hecho, no tenemos ni idea de cuál es el potencial humano completo, porque sabemos poquísimo de la mente humana. Y sin embargo, apenas invertimos en la investigación de la mente humana y en cambio nos centramos en aumentar la velocidad de nuestras conexiones a internet y la eficiencia de nuestros algoritmos de macrodatos. Si no somos prudentes, terminaremos con humanos degradados que usarán mal ordenadores mejorados y que provocarán el caos en sí mismos y en el mundo.
Las dictaduras digitales no son el único peligro que nos espera. Junto a la libertad, el orden liberal depositó también muchas esperanzas en el valor de la igualdad. El liberalismo siempre valoró la igualdad política, y gradualmente llegó al convencimiento de que la igualdad económica tiene casi la misma importancia. Porque sin un sistema de seguridad social y una igualdad económica mínima, la libertad no tiene sentido. Pero de la misma manera que los algoritmos de macrodatos podrían acabar con la libertad, podrían al mismo tiempo crear las sociedades más desiguales que jamás hayan existido. Toda la riqueza y todo el poder podrían estar concentrados en manos de una élite minúscula, mientras que la mayoría de la gente sufriría no la explotación, sino algo mucho peor: la irrelevancia.
### 4
Igualdad
#### Quienes poseen los datos poseen el futuro
En las últimas décadas, a la gente de todo el planeta se le ha ido diciendo que la humanidad se halla en la senda hacia la igualdad, y que la globalización y las nuevas tecnologías nos ayudarán a llegar pronto a ella. En realidad, en el siglo XXI podrían surgir las sociedades más desiguales de la historia. Aunque la globalización e internet salvan la distancia entre países, amenazan con agrandar la brecha entre clases, y cuando parece que la humanidad está a punto de conseguir la unificación global, la propia especie podría dividirse en diferentes castas biológicas.
La desigualdad se remonta a la Edad de Piedra. Hace 30.000 años, las bandas de cazadores-recolectores enterraban a algunos de sus miembros en tumbas suntuosas repletas de miles de cuentas de marfil, brazaletes, joyas y objetos de arte, mientras que otros miembros tenían que conformarse con un simple agujero en el suelo. No obstante, las antiguas bandas de cazadores-recolectores eran todavía más igualitarias que cualquier sociedad humana posterior, porque tenían muy pocas propiedades. La propiedad es un prerrequisito para la desigualdad a largo plazo.
Tras la revolución agrícola, la propiedad se multiplicó, y con ella la desigualdad. A medida que los humanos se hacían con la propiedad de la tierra, de animales, de plantas y utensilios, surgieron rígidas sociedades jerárquicas, en que pequeñas élites monopolizaron la mayor parte de las riquezas y el poder de generación en generación. Los humanos acabaron por aceptar esta organización como algo natural e incluso ordenado por la divinidad. La jerarquía no era solo la norma, sino también el ideal. ¿Cómo puede haber orden sin una clara jerarquía entre los aristócratas y los plebeyos, entre hombres y mujeres, o entre padres e hijos? Sacerdotes, filósofos y poetas en todo el mundo explicaban con paciencia que de la misma manera que en el cuerpo humano no todos los miembros son iguales (los pies han de obedecer a la cabeza), así en la sociedad humana la igualdad no acarrearía más que caos.
Sin embargo, a finales de la era moderna la igualdad se convirtió en un ideal en casi todas las sociedades humanas. Ello se debió en parte al auge de las nuevas ideologías del comunismo y el liberalismo. Pero se debió también a la revolución industrial, que hizo que las masas fueran más importantes de lo que nunca habían sido. Las economías industriales se basaban en masas de obreros comunes, mientras que los ejércitos industriales se basaban en masas de soldados comunes. Los gobiernos tanto de las democracias como de las dictaduras invertían mucho en la salud, la educación y el bienestar de las masas, porque necesitaban millones de obreros sanos que trabajaran en las líneas de producción y millones de soldados leales que lucharan en las trincheras.
En consecuencia, la historia del siglo XX se centró en gran medida en la reducción de la desigualdad entre clases, razas y géneros. Aunque el mundo del año 2000 tenía todavía su cuota de jerarquías, era un lugar mucho más igualitario que el mundo de 1900. En los primeros años del siglo XXI, la gente esperaba que el proceso igualitario continuara e incluso se acelerara. En particular, esperaban que la globalización llevara la prosperidad económica por todo el planeta, y que como resultado en la India y en Egipto la gente llegara a disfrutar de las mismas oportunidades y los mismos privilegios que en Finlandia y Canadá. Toda una generación creció con esta promesa.
Ahora parece que esta promesa podría no cumplirse. Ciertamente, la globalización ha beneficiado a grandes segmentos de la humanidad, pero hay indicios de una desigualdad creciente tanto entre las sociedades como en el interior de las mismas. Algunos grupos monopolizan de forma creciente los frutos de la globalización, al tiempo que miles de millones de personas se quedan atrás. Ya hoy en día, el 1 por ciento más rico posee la mitad de las riquezas del mundo. Y lo que es aún más alarmante: las 100 personas más ricas poseen más en su conjunto que los 4.000 millones de personas más pobres.[1]
Esto aún podría empeorar mucho. Como se ha visto en capítulos anteriores, el auge de la IA podría eliminar el valor económico y político de la mayoría de los humanos. Al mismo tiempo, las mejoras en biotecnología tal vez posibiliten que la desigualdad económica se traduzca en desigualdad biológica. Los superricos tendrán por fin algo que hacer que valga de verdad la pena con su extraordinaria riqueza. Mientras que hasta ahora podían comprar poco más que símbolos de estatus, pronto podrán comprar la vida misma. Si los nuevos tratamientos para alargar la vida y mejorar las condiciones físicas y cognitivas acaban siendo caros, la humanidad podría dividirse en castas biológicas. A lo largo de la historia, los ricos y la aristocracia siempre pensaron que sus capacidades eran superiores a las de todos los demás, y por ese motivo tenían el control. Por lo que sabemos, eso no era cierto. El duque medio no estaba más dotado que el campesino medio, sino que debía su superioridad solo a una discriminación legal y económica injusta. Sin embargo, hacia 2100 los ricos podrían estar realmente más dotados, ser más creativos y más inteligentes que la gente que habita en los suburbios. Una vez que se abra una brecha real en la capacidad entre los ricos y los pobres, resultará casi imposible salvarla. Si los ricos emplean sus capacidades superiores para enriquecerse todavía más, y si con más dinero pueden comprarse un cuerpo y un cerebro mejorados, con el tiempo la brecha no hará más que agrandarse. Hacia 2100, el 1 por ciento más rico podría poseer no solo la mayor parte de las riquezas del mundo, sino también la mayor parte de la belleza, la creatividad y la salud del mundo.
Los dos procesos juntos, la bioingeniería unida al auge de la IA, podrían por tanto acabar separando a la humanidad en una pequeña clase de superhumanos y una subclase enorme de _Homo sapiens_ inútiles. Para empeorar todavía más una situación agorera, al perder las masas su importancia económica y su poder político, el Estado podría a su vez perder al menos algunos de los incentivos para invertir en su salud, su educación y su bienestar. Es muy peligroso no ser necesario. Así pues, el futuro de las masas dependerá de la buena voluntad de una pequeña élite. Quizá haya buena voluntad durante unas cuantas décadas. Pero en una época de crisis (como una catástrofe climática) resultará muy tentador y fácil echar por la borda a la gente no necesaria.
En países como Francia y Nueva Zelanda, con una larga tradición de creencias liberales y prácticas de estado del bienestar, quizá la élite siga haciéndose cargo de las masas aunque no las necesite. Sin embargo, en Estados Unidos, más capitalista, la élite podría usar la primera ocasión que se le presente para desmantelar lo que quede del estado del bienestar. Un problema todavía mayor acecha en grandes países en vías de desarrollo, como la India, China, Sudáfrica y Brasil. Allí, una vez que la gente de a pie pierda su valor económico, la desigualdad podría dispararse.
En consecuencia, la globalización, en vez de generar la unidad global, podría llevar a una «especiación»: la división de la humanidad en diferentes castas biológicas o incluso diferentes especies. La globalización unirá al mundo horizontalmente al borrar las fronteras nacionales, pero de manera simultánea dividirá a la humanidad verticalmente. Las oligarquías dominantes en países tan diversos como Estados Unidos y Rusia podrían fusionarse y hacer causa común contra la masa de sapiens ordinarios. Desde esta perspectiva, el resentimiento populista actual hacia «las élites» está bien fundado. Si no vamos con cuidado, los nietos de los magnates de Silicon Valley y de los multimillonarios de Moscú podrían convertirse en una especie superior para los nietos de los palurdos de Appalachia y los campesinos siberianos.
A la larga, una situación hipotética de este tipo sería capaz incluso de desglobalizar el mundo, pues la casta superior podría congregarse dentro de una autoproclamada «civilización» y construir muros y fosos que la separaran de las hordas de «bárbaros» del exterior. En el siglo XX, la civilización industrial dependía de los «bárbaros» para el trabajo barato, las materias primeras y los mercados. Por tanto, los conquistó y absorbió. Pero en el siglo XXI, una civilización postindustrial que se base en la IA, la bioingeniería y la nanotecnología podría ser mucho más independiente y autosuficiente. No solo clases enteras, sino países y continentes enteros podrían resultar irrelevantes. Fortificaciones custodiadas por drones y robots podrían separar la zona autoproclamada civilizada, en la que los cíborgs lucharan entre sí con bombas lógicas, de las tierras bárbaras en que los humanos asilvestrados lucharan entre sí con machetes y kaláshnikovs.
A lo largo de este libro suelo usar la primera persona del plural para hablar del futuro de la humanidad. Digo lo que «nosotros» necesitamos hacer acerca de «nuestros» problemas. Pero quizá no haya «nosotros». Quizá uno de «nuestros» mayores problemas sea que diferentes grupos humanos tengan futuros completamente distintos. Quizá en algunas partes del mundo se deba enseñar a los niños a diseñar programas informáticos, mientras que en otros sea mejor enseñarles a desenfundar deprisa y a disparar de inmediato.
##### ¿QUIÉN POSEE LOS DATOS?
Si queremos evitar la concentración de toda la riqueza y el poder en manos de una pequeña élite, la clave es regular la propiedad de los datos. En tiempos antiguos, la tierra era el bien más importante del mundo, la política era una lucha para controlar la tierra y evitar que se concentrara demasiada en unas pocas manos, la sociedad se dividía en aristócratas y plebeyos. En la época moderna, las máquinas y fábricas resultaron más importantes que la tierra, y las luchas políticas se centraron en controlar estos medios vitales de producción. Si demasiadas máquinas se concentraban en unas pocas manos, la sociedad se dividía en capitalistas y proletarios. En el siglo XXI, sin embargo, los datos eclipsarán a la vez la tierra y la maquinaria como los bienes más importantes, y la política será una lucha para controlar el flujo de datos. Si los datos se concentran en unas pocas manos, la humanidad se dividirá en diferentes especies.
La carrera para poseer los datos ya ha empezado, encabezada por gigantes de los datos como Google, Facebook, Baidu y Tencent. Hasta ahora, muchos de estos gigantes parecen haber adoptado el modelo de negocio de los «mercaderes de la atención».[2] Captan nuestra atención al proporcionarnos de forma gratuita información, servicios y diversión, y después revenden nuestra atención a los anunciantes. Pero las miras de los gigantes de los datos apuntan probablemente mucho más allá que cualquier mercader de la atención que haya existido. Su verdadero negocio no es en absoluto vender anuncios. Más bien, al captar nuestra atención consiguen acumular cantidades inmensas de datos sobre nosotros, que valen más que cualquier ingreso publicitario. No somos sus clientes: somos su producto.
A medio plazo, esta acumulación de datos abre el camino para un modelo de negocio radicalmente diferente cuya primera víctima será la misma industria de publicidad. El nuevo modelo se basa en transferir la autoridad de los humanos a los algoritmos, incluida la autoridad para elegir y comprar cosas. Una vez que los algoritmos elijan y compren cosas por nosotros, la industria tradicional de la publicidad quebrará. Pensemos en Google. Google quiere llegar a un punto en que podamos preguntarle cualquier __ cosa y conseguir la mejor respuesta del mundo. ¿Qué ocurrirá cuando podamos preguntar a Google: «¡Hola, Google! Basándote en todo lo que sabes de coches y en todo lo que sabes de mí (incluidas mis necesidades, mis costumbres, mis opiniones sobre el calentamiento global así como mis opiniones sobre la política en Oriente Próximo), ¿cuál es el mejor coche para mí?». Si Google puede darnos una buena respuesta, y si aprendemos por experiencia a confiar en la sabiduría de Google en lugar de en nuestros propios sentimientos, fácilmente manipulables, ¿qué utilidad tendrían los anuncios de automóviles?[3]
A largo plazo, al unir suficientes datos y suficiente poder de cómputo, los gigantes de los datos podrían acceder a los secretos más profundos de la vida, y después usar tal conocimiento no solo para elegir por nosotros o manipularnos, sino también para remodelar la vida orgánica y crear formas de vida inorgánicas. Vender anuncios puede ser necesario para sostener a los gigantes a corto plazo, pero a menudo estos valoran apps, productos y empresas según los datos que recogen más que según el dinero que generan. Una aplicación popular puede carecer de modelo de negocio e incluso perder dinero a corto plazo, pero mientras absorba datos podría valer miles de millones.[4] Incluso si no sabemos cómo sacar partido de los datos hoy en día, vale la pena mantenerla porque tal vez posea la clave para controlar y determinar la vida en el futuro. No tengo la certeza de que los gigantes de los datos piensen de forma explícita en estos términos, pero sus acciones indican que valoran la acumulación de datos más que los meros dólares y centavos.
A los humanos de a pie puede costarles mucho resistirse a este proceso. En la actualidad, a la gente le encanta revelar su bien más preciado (sus datos personales) a cambio de servicios gratuitos de correo electrónico y de divertidos vídeos de gatos. Es un poco como las tribus africanas y americanas nativas que sin darse cuenta vendieron países enteros a los imperialistas europeos a cambio de cuentas de colores y abalorios baratos. Si, más adelante, la gente común decidiera intentar bloquear el flujo de datos, quizá se daría cuenta de que cada vez resulta más difícil, en especial porque podría acabar dependiendo de la red para todas las decisiones que tomara, e incluso para el cuidado de su salud y su supervivencia física.
Humanos y máquinas podrían fusionarse de una manera tan completa que los humanos quizá no lograran sobrevivir si se desconectaran de la red. Estarían conectados desde el seno materno, y si más adelante eligiéramos desconectarnos, las agencias de seguros podrían rechazar asegurarnos, los patronos rehusar contratarnos y los servicios de asistencia sanitaria negarse a cuidar de nosotros. En la gran batalla entre la salud y la privacidad, es probable que gane la salud sin despeinarse.
A medida que cada vez más y más datos fluyan de nuestro cuerpo y cerebro a las máquinas inteligentes a través de los sensores biométricos, más fácil les resultará a las empresas y a los organismos gubernamentales conocernos, manipularnos y tomar decisiones en nuestro nombre. Y lo que es aún más importante: podrán descifrar los mecanismos íntimos de todos los cuerpos y cerebros, y de esta manera obtener el poder para diseñar la vida. Si queremos impedir que una reducida élite monopolice estos poderes cuasidivinos y evitar que la humanidad se divida en castas biológicas, la pregunta clave es: ¿quién posee los datos? Los datos sobre mi ADN, mi cerebro y mi vida, ¿me pertenecen a mí?, ¿pertenecen al gobierno?, ¿a una empresa?, ¿al colectivo humano?
Permitir a los gobiernos que nacionalicen los datos refrenará probablemente el poder de las grandes empresas, pero también podría desembocar en espeluznantes dictaduras digitales. Los políticos son un poco como los músicos, y los instrumentos que tocan son el sistema emocional y bioquímico humano. Sueltan un discurso, y una oleada de temor recorre el país. Tuitean, y se produce un conato de odio. No creo que debamos dar a estos músicos un instrumento más refinado para que lo toquen. Una vez que los políticos puedan pulsar nuestros botones emocionales directamente, generando ansiedad, odio, alegría y aburrimiento a voluntad, la política se convertirá en un mero circo emocional. Aunque hemos de temer mucho el poder de las grandes empresas, la historia sugiere que no estaremos necesariamente mejor en manos de gobiernos superpoderosos. En marzo de 2018, yo preferiría dar mis datos a Mark Zuckerberg que a Vladímir Putin (aunque el escándalo de Cambridge Analytica reveló que quizá no tengamos mucha elección, pues cualquier dato que confiemos a Zuckerberg bien podría acabar llegando a Putin).
La propiedad de nuestros datos puede resultar más atractiva que ninguna de estas dos opciones, pero no está claro qué significa eso en realidad. Tenemos miles de años de experiencia en la regulación de la propiedad de la tierra. Sabemos cómo construir una cerca alrededor de un campo, situar un guarda en la puerta y controlar quién entra. A lo largo de los dos últimos siglos hemos extremado en grado sumo la complejidad en la regulación de la propiedad de la industria; así, hoy en día puedo poseer un pedazo de General Motors y una pizca de Toyota si compro sus acciones. Pero no tenemos mucha experiencia en regular la propiedad de los datos, que es en sí misma una tarea mucho más difícil, porque a diferencia de la tierra y las máquinas, los datos están por todas partes y en ningún lugar al mismo tiempo, pueden desplazarse a la velocidad de la luz y podemos crear tantas copias de ellos como queramos.
De modo que lo mejor que podemos hacer es recurrir a nuestros abogados, políticos, filósofos e incluso poetas para que se centren en este misterio: ¿cómo regulamos la propiedad de los datos? Podría muy bien ser que esta fuera la pregunta más importante de nuestra era. Si no somos capaces de dar una respuesta pronto, nuestro sistema sociopolítico puede venirse abajo. La gente ya está notando el cataclismo que se avecina. Quizá por eso ciudadanos de todo el mundo estén perdiendo la fe en el relato liberal, que hace solo una década parecía convincente.
Así pues, ¿de qué manera avanzamos desde aquí y cómo nos enfrentamos a los inmensos retos de las revoluciones de la biotecnología y la infotecnología? ¿Quizá los mismísimos científicos y emprendedores que fueron los primeros en trastocar el mundo serían capaces de diseñar alguna solución tecnológica? Por ejemplo, ¿algoritmos conectados en red podrían formar el andamiaje para una comunidad humana global que pudiera poseer de manera colectiva todos los datos y supervisar el desarrollo futuro de la vida? Mientras la desigualdad global y las tensiones sociales aumentan en todo el mundo, quizá Mark Zuckerberg podría recurrir a sus 2.000 millones de amigos para que sumaran fuerzas e hicieran algo juntos.
# Parte II
El desafío político
_La fusión de la infotecnología y la biotecnología es una amenaza para los valores modernos fundamentales de la libertad y la igualdad. Cualquier solución al reto tecnológico tiene que pasar por la_ _cooperación global. Pero el nacionalismo, la religión y la cultura_ _dividen a la humanidad en campos hostiles y hacen muy difícil cooperar globalmente._
### 5
Comunidad
#### Los humanos tenemos cuerpo
California está acostumbrada a los terremotos, pero aun así el temblor político de las elecciones de 2016 en Estados Unidos fue un duro golpe para Silicon Valley. Al darse cuenta de que podrían ser parte del problema, los magos de la informática reaccionaron haciendo lo que mejor hacen los ingenieros: buscaron una solución técnica. En ningún lugar fue más contundente la reacción que en la sede central de Facebook en Menlo Park. Es comprensible: dado que el negocio de Facebook es la interconexión social, es extremadamente sensible a las perturbaciones sociales.
Después de tres meses de búsqueda introspectiva, el 16 de febrero de 2017 Mark Zuckerberg publicó un audaz manifiesto sobre la necesidad de construir una comunidad global y sobre el papel de Facebook en dicho proyecto.[1] En un discurso complementario en el acto inaugural de la Cumbre de las Comunidades, el 22 de junio de 2017, Zuckerberg explicó que los trastornos sociopolíticos de nuestra época (desde el consumo de drogas descontrolado hasta los regímenes totalitarios asesinos) son el resultado en gran medida de la desintegración de las comunidades humanas. Lamentó el hecho de que «durante décadas, la afiliación a todo tipo de grupos se ha reducido hasta una cuarta parte. Son muchísimas las personas que ahora necesitan encontrar un propósito y apoyo en algún otro lugar».[2] Prometió que Facebook lideraría la tarea de reconstruir estas comunidades y que sus ingenieros recogerían la carga que los párrocos habían desechado. «Empezaremos a introducir algunas herramientas para hacer más fácil la creación de comunidades», dijo.
Después siguió explicando: «Iniciamos un proyecto para ver si podríamos hacerlo mejor a la hora de sugerir grupos que fueran importantes para ustedes. Empezamos a crear inteligencia artificial a tal fin. Y funciona. En los primeros seis meses, ayudamos a un 50 por ciento más de personas a unirse a comunidades que merecen la pena». Su objetivo último es «ayudar a mil millones de personas a unirse a comunidades que merecen la pena. ...] Si podemos hacerlo, no solo se invertirá por completo la reducción en la afiliación a comunidades de que hemos sido testigos durante décadas, sino que además empezará a fortalecerse nuestro tejido social y el mundo estará más unido». Es este un objetivo tan importante que Zuckerberg prometió «cambiar toda la misión de Facebook para encargarse del mismo».[[3] Zuckerberg tiene razón al lamentarse de la descomposición de las comunidades humanas. Pero algunos meses después de que hiciera esta promesa, y justo mientras este libro entraba en imprenta, el escándalo de Cambridge Analytica reveló que los datos que se confiaban a Facebook eran recogidos por terceras partes y usados para manipular las elecciones en todo el mundo. Esto convirtió en una burla las idealistas promesas de Zuckerberg e hizo añicos la confianza pública en Facebook. Solo cabe esperar que antes de emprender la creación de nuevas comunidades humanas, Facebook se comprometa a proteger la privacidad y la seguridad de las ya existentes.
No obstante, vale la pena considerar a fondo la visión comunitaria de Facebook y analizar si una vez que se haya fortalecido la seguridad, las redes sociales en línea pueden ayudar a la creación de una comunidad humana global. Aunque en el siglo XXI los humanos podrían ser mejorados en dioses, en 2018 seguimos siendo animales de la Edad de Piedra. Para prosperar aún necesitamos fundamentarnos en comunidades íntimas. Durante millones de años nos hemos adaptado a vivir en pequeñas bandas de no más de unas pocas docenas de personas. Incluso hoy en día a la mayoría nos parece imposible conocer a más de ciento cincuenta individuos, con independencia de que alardeemos de tener un elevado número de amigos en Facebook.[4] Fuera de estos grupos, los humanos se sienten solos y alienados.
Por desgracia, a lo largo de los dos últimos siglos las comunidades íntimas han ido desintegrándose. El intento de sustituir grupos pequeños de personas que de verdad se conocen entre sí con comunidades imaginadas de naciones y partidos políticos nunca será un éxito rotundo. Nuestros millones de hermanos en la familia nacional y nuestros millones de camaradas en el Partido Comunista no pueden proporcionarnos la cálida intimidad que un único hermano o amigo reales sí pueden. En consecuencia, la gente lleva vidas cada vez más solitarias en un planeta cada vez más conectado. El origen de muchas de las perturbaciones sociales y políticas de nuestra época puede rastrearse hasta este malestar general.[5]
Por lo tanto, el proyecto de Zuckerberg de volver a conectar a los humanos entre sí es oportuno. Pero las palabras son más baratas que los actos, y a fin de poner en marcha dicho proyecto, Facebook tendría que cambiar por completo su modelo de negocio. Difícilmente puede constituirse una comunidad global cuando se gana dinero a fuerza de captar la atención de la gente y vendérsela a los anunciantes. A pesar de ello, la disposición de Zuckerberg de al menos formular tal proyecto merece nuestro elogio. La mayoría de las empresas creen que tendrían que centrarse en ganar dinero, que los gobiernos deberían intervenir lo menos posible y que la humanidad debería confiar en que las fuerzas del mercado tomaran por nosotros las decisiones que de verdad son importantes.[6] De ahí que si Facebook pretende adoptar un compromiso ideológico real para crear comunidades humanas, los que teman su poder no deberían hacerla retroceder hasta la capa protectora empresarial a gritos de «¡Gran Hermano!». En cambio, deberíamos animar a otras empresas, instituciones y gobiernos a que compitan con Facebook adoptando sus propios compromisos ideológicos.
Desde luego, no escasean las organizaciones que lamentan la descomposición de las comunidades humanas y se esfuerzan por reconstruirlas. Todo el mundo, desde las activistas feministas hasta los fundamentalistas islámicos, está en el negocio de la creación de comunidades, y en capítulos posteriores analizaremos algunos de estos esfuerzos. Lo que hace que la maniobra de Facebook sea única es su ámbito global, su respaldo empresarial y su profunda fe en la tecnología. Zuckerberg parece estar convencido de que la nueva IA de Facebook puede no solo identificar «comunidades que merecen la pena», sino también «fortalecer nuestro tejido social y hacer que el mundo esté más unido». Eso es mucho más ambicioso que utilizar la IA para conducir un automóvil o diagnosticar el cáncer.
La visión de la comunidad de Facebook es quizá el primer intento explícito de usar la IA para la ingeniería social planificada centralmente a escala global. Por tanto, constituye un caso crucial que puede sentar precedente. Si tiene éxito, es probable que presenciemos muchos más intentos de este tipo, y se reconocerán los algoritmos como los nuevos líderes de las redes sociales humanas. Si fracasa, pondrá en evidencia las limitaciones de las nuevas tecnologías: los algoritmos pueden servir para la circulación de vehículos y la cura de enfermedades, pero cuando se trate de resolver problemas sociales, tendremos que seguir confiando en políticos y sacerdotes.
__
##### EN LÍNEA VERSUS FUERA DE LÍNEA
En los últimos años, el éxito de Facebook ha sido asombroso, y en la actualidad cuenta con más de 2.000 millones de usuarios activos en línea. Pero para poner en marcha su nuevo proyecto tendrá que salvar la brecha entre estar en línea, conectado, y fuera de línea, desconectado. Una comunidad quizá empiece como una reunión en línea, pero para fortalecerse de verdad también tendrá que echar raíces en el mundo fuera de línea. Si un día un dictador prohíbe Facebook en su país o cierra el grifo de internet, ¿se evaporarán las comunidades, o bien se reagruparán y contraatacarán? ¿Serán capaces de organizar una manifestación sin comunicación en línea?
Zuckerberg explicó en su manifiesto de febrero de 2017 que las comunidades conectadas ayudan a promover a las desconectadas. Esto es verdad a veces. Pero en muchos casos la conexión se produce a expensas de la desconexión, y hay una diferencia fundamental entre las dos. Las comunidades físicas tienen una profundidad que las comunidades virtuales no pueden igualar, al menos no en un futuro inmediato. Si me encuentro enfermo en Israel, mis amigos de California en línea pueden hablarme, pero no pueden traerme una sopa o una taza de té.
Los humanos tienen cuerpo. Durante el último siglo, la tecnología ha estado distanciándonos de nuestro cuerpo. Hemos ido perdiendo nuestra capacidad de prestar atención a lo que olemos y saboreamos. En lugar de ello, nos absorben nuestros teléfonos inteligentes y ordenadores. Estamos más interesados en lo que ocurre en el ciberespacio que en lo que está pasando en la calle. Es más fácil que nunca hablar con mi primo en Suiza, pero más difícil hablar con mi marido durante el desayuno, porque está todo el rato pendiente de su teléfono inteligente en lugar de estarlo de mí.[7]
En el pasado, los humanos no podían permitirse tal indiferencia. Los antiguos recolectores siempre estaban alerta y vigilantes. Mientras se desplazaban por el bosque en busca de setas, observaban el terreno, atentos a cualquier protuberancia reveladora. Percibían el menor movimiento en la hierba para descubrir si allí podría haber una serpiente al acecho. Cuando encontraban una seta comestible, la comían con suma atención para distinguirla de sus parientes venenosas. Los miembros de las sociedades pudientes actuales no necesitan esa percepción tan aguda. Podemos pasearnos entre las estanterías del supermercado mientras escribimos mensajes, y comprar cualquiera de un millar de productos alimenticios, todos ellos supervisados por las autoridades sanitarias. Pero escojamos lo que escojamos, podemos terminar comiéndolo apresuradamente frente a una pantalla mientras leemos los correos electrónicos o vemos la televisión, sin que apenas prestemos atención al gusto real de lo que comemos.
Zuckerberg dice que Facebook se ha comprometido «a continuar mejorando nuestras herramientas para proporcionarnos el poder de compartir nuestra experiencia» con los demás.[8] Pero lo que la gente podría necesitar en realidad son las herramientas para conectarse a sus propias experiencias. En nombre de «compartir experiencias», se anima a la gente a entender lo que les ocurre en términos de cómo lo ven los demás. Si sucede algo emocionante, el instinto visceral de los usuarios de Facebook es sacar sus teléfonos inteligentes, hacer una foto, publicarla en línea y esperar los «Me gusta». En el proceso, apenas se dan cuenta de lo que han sentido ellos. De hecho, lo que sienten está determinado cada vez más por las reacciones en línea.
Es probable que las personas separadas de su cuerpo, sentidos y ambiente físico se sientan alienadas y desorientadas. Los expertos suelen atribuir estos sentidos de alienación a la reducción de los vínculos religiosos y nacionales, pero perder el contacto con el propio cuerpo probablemente sea más importante. Los humanos han vivido millones de años sin religiones ni naciones; es probable que también puedan vivir felices sin ellas en el siglo XXI. Pero no pueden vivir felices si están desconectados de su cuerpo. Si uno no se siente cómodo en su cuerpo, nunca se sentirá cómodo en el mundo.
Hasta ahora, el modelo de negocio de Facebook animaba a la gente a pasar cada vez más tiempo en línea, aunque esto supusiera disponer de menos tiempo y energía para dedicar a las actividades fuera de línea. ¿Podrá adoptar un nuevo modelo que anime a la gente a conectarse solo cuando es realmente necesario y a dedicar mayor atención a su ambiente y a su propio cuerpo y sentidos? ¿Qué pensarían los accionistas de tal modelo? (Hace poco, Tristan Harris, un exgooglero y tecnofilósofo que ha dado con una nueva métrica del «tiempo bien invertido», ha sugerido un programa de dicho modelo alternativo.)[9]
Las limitaciones de las relaciones en línea también socavan la solución de Zuckerberg a la polarización social. Este empresario señala con acierto que solo conectar a las personas y exponerlas a diferentes opiniones no salvará las brechas sociales porque «mostrar a la gente un artículo acerca de la perspectiva opuesta, ahonda en realidad la polarización al enmarcar las demás perspectivas como extrañas». En lugar de ello, Zuckerberg sugiere que «las soluciones óptimas para mejorar el discurso pueden proceder de conocer a los demás como personas completas en lugar de hacerlo solo como opiniones, algo que Facebook puede estar muy preparado para hacer. Si conectamos con las personas respecto a lo que tenemos en común (equipos deportivos, espectáculos televisivos, intereses), es más fácil dialogar sobre aquello en lo que no estamos de acuerdo».[10]
Pero es muy difícil conocerse mutuamente como personas «completas». Ello exige mucho tiempo y una interacción física directa. Como ya se ha señalado, el _Homo sapiens_ medio probablemente sea incapaz de conocer de manera íntima a más de 150 individuos. En un plano ideal, crear comunidades no debería ser un juego de suma cero. Los humanos pueden sentirse leales a diferentes grupos al mismo tiempo. Por desgracia, las relaciones íntimas posiblemente sean un juego de suma cero. Más allá de un punto determinado, el tiempo y la energía que invertimos para llegar a conocer a nuestros amigos en línea de Irán o Nigeria serán a expensas de nuestra capacidad para conocer a nuestros vecinos de al lado.
La prueba crucial de Facebook llegará cuando un ingeniero invente un nuevo instrumento que haga que la gente pase menos tiempo comprando en línea y más tiempo en actividades significativas fuera de línea con los amigos. ¿Adoptará o suprimirá Facebook un instrumento de este tipo? ¿Dará Facebook un verdadero voto de confianza y favorecerá las preocupaciones sociales por encima de los intereses financieros? Si lo hace y consigue evitar la quiebra, será una transformación trascendental.
Dedicar más tiempo al mundo desconectado que a sus informes trimestrales también es relevante para las políticas tributarias de Facebook. Al igual que Amazon, Google, Apple y otros gigantes tecnológicos, Facebook ha sido acusado repetidas veces de evasión fiscal.[11] Las dificultades inherentes a gravar las actividades en línea facilitan que estas empresas globales se dediquen a todo tipo de contabilidad creativa. Si pensamos que la gente vive principalmente en línea, conectada, y que les proporcionamos todos los instrumentos necesarios para su existencia en línea, podemos considerarnos un servicio social benéfico, aunque evitemos pagar impuestos a los gobiernos fuera de línea, desconectados. Pero una vez que recordamos que los humanos tienen cuerpo y que, por tanto, necesitan carreteras, hospitales y sistemas de alcantarillado, se hace mucho más difícil justificar la evasión fiscal. ¿Cómo pueden elogiarse las virtudes de la comunidad al tiempo que se rehúsa mantener económicamente los servicios comunitarios más importantes?
Solo cabe esperar que Facebook pueda cambiar su modelo de negocio, adoptar una política de impuestos más reconciliada con las actividades desconectadas, ayudar a unir el mundo... y seguir siendo rentable. Pero no debemos abrigar expectativas poco realistas acerca de su capacidad para llevar a cabo su proyecto de una comunidad global. Históricamente, las empresas no han sido el vehículo ideal para encabezar las revoluciones sociales y políticas. Una revolución real exige, tarde o temprano, sacrificios que las empresas, sus empleados y sus accionistas no están dispuestos a hacer. Esta es la razón por la que los revolucionarios fundan iglesias, partidos políticos y ejércitos. Las denominadas revoluciones de Facebook y Twitter en el mundo árabe se iniciaron en optimistas comunidades en línea, pero una vez que aparecieron en el caótico mundo fuera de línea, se las apropiaron fanáticos religiosos y juntas militares. Si ahora Facebook pretende instigar una revolución global, tendrá que cumplir una tarea mucho mejor a la hora de salvar la brecha entre lo conectado y lo desconectado. Facebook y los demás gigantes en línea suelen considerar que los humanos son animales audiovisuales: un par de ojos y un par de oídos conectados a diez dedos, una pantalla y una tarjeta de crédito. Un paso crucial hacia la unificación de la humanidad es apreciar que los humanos tienen cuerpo.
Desde luego, esta apreciación tiene su aspecto negativo. Darse cuenta de las limitaciones de los algoritmos en línea podría provocar únicamente que los gigantes tecnológicos expandieran más todavía su alcance. Dispositivos como Google Glass y juegos como Pokémon Go están diseñados para borrar la distinción entre en línea y fuera de línea, al fusionarlas en una única realidad aumentada. A un nivel todavía más profundo, los sensores biométricos y las interfaces directas cerebro-ordenador pretenden erosionar la frontera entre las máquinas electrónicas y los cuerpos orgánicos, y meterse literalmente bajo nuestra piel. Una vez que los gigantes tecnológicos lleguen a un acuerdo con el cuerpo humano, podrían acabar manipulándolo por completo igual que suelen manipular nuestros ojos, dedos y tarjetas de crédito. Podríamos llegar a echar en falta aquellos buenos y viejos tiempos en que lo en línea estaba separado de lo fuera de línea.
### 6
Civilización
#### Solo existe una civilización en el mundo
Mientras Mark Zuckerberg sueña con unir a la humanidad en línea, acontecimientos recientes en el mundo fuera de línea parecen insuflar nueva vida a la tesis del «choque de civilizaciones». Muchos expertos, políticos y ciudadanos corrientes creen que la guerra civil en Siria, el auge de Estado Islámico, el caos del Brexit y la inestabilidad de la Unión Europea son resultado de un enfrentamiento entre la «civilización occidental» y la «civilización islámica». Los intentos occidentales de imponer la democracia y los derechos humanos en las naciones musulmanas han provocado una violenta respuesta islámica, y una oleada de inmigración musulmana junto a ataques terroristas islamistas han hecho que los votantes europeos abandonen los sueños multiculturales en favor de identidades culturales xenófobas.
Según esta tesis, la humanidad ha estado dividida siempre en varias civilizaciones cuyos miembros entienden el mundo de maneras irreconciliables. Estas visiones incompatibles hacen que los conflictos entre civilizaciones sean inevitables. De la misma manera que en la naturaleza las diferentes especies luchan por la supervivencia según las leyes implacables de la selección natural, a lo largo de la historia las civilizaciones se han enfrentado repetidas veces y solo las más adaptadas han sobrevivido para contarlo. Los que pasan por alto este desagradable hecho, ya se trate de políticos liberales o de ingenieros que están en las nubes, lo hacen asumiendo su propio riesgo.[1]
La tesis del «choque de civilizaciones» tiene implicaciones políticas trascendentales. Sus defensores sostienen que cualquier intento de reconciliar «Occidente» con el «mundo musulmán» está destinado al fracaso. Los países musulmanes jamás adoptarán los valores occidentales y los países occidentales nunca podrán absorber con éxito a las minorías musulmanas. En consecuencia, Estados Unidos no debe admitir a inmigrantes de Siria o Irak, y la Unión Europea debe renunciar a su falacia multicultural en favor de una identidad occidental inmutable. A la larga, solo una civilización puede sobrevivir a las pruebas implacables de la selección natural, y si los burócratas de Bruselas rehúsan salvar a Occidente del peligro islámico, entonces será mejor que Gran Bretaña, Dinamarca o Francia vayan por su cuenta.
Aunque está muy generalizada, esta tesis es engañosa. Sin duda, el fundamentalismo islámico puede suponer un reto radical, pero la «civilización» a la que desafía es una civilización global y no un fenómeno únicamente occidental. No es casualidad que Estado Islámico consiguiera unir en su contra a Irán y a Estados Unidos. E incluso los fundamentalistas islámicos, con todas sus fantasías medievales, se basan mucho más en la cultura contemporánea global que en la Arabia del siglo VII. Se nutren de los miedos y las esperanzas de la juventud moderna y alienada más que de los de campesinos y mercaderes medievales. Como han planteado de manera convincente Pankaj Mishra y Christopher de Bellaigue, los islamistas radicales han estado influidos tanto por Marx y Foucault como por Mahoma, y heredan tanto el legado de los anarquistas europeos del siglo XIX como el de los califas omeyas y abasíes.[2] Por tanto, es mucho más exacto considerar que Estado Islámico es un brote descarriado de la cultura global que todos compartimos y no una rama de algún misterioso árbol foráneo.
Más importante todavía es que la analogía entre la historia y la biología que respalda la tesis del «choque de civilizaciones» es falsa. Los grupos humanos, desde las tribus pequeñas a las civilizaciones enormes, son fundamentalmente diferentes de las especies animales, y los conflictos históricos difieren muchísimo de los procesos de selección natural. Las especies animales poseen identidades objetivas que se mantienen durante miles y miles de generaciones. El que uno sea un chimpancé o un gorila depende de sus genes, no de sus creencias, y genes diferentes dictan comportamientos sociales distintos. Los chimpancés viven en grupos mixtos de machos y hembras. Compiten por el poder forjando coaliciones de adeptos de ambos sexos. Entre los gorilas, en cambio, un único macho dominante establece un harén de hembras, y por lo general expulsa a cualquier macho adulto que pueda poner en peligro su posición. Los chimpancés no son capaces de adoptar disposiciones sociales del tipo de la de los gorilas; los gorilas no son capaces de empezar a organizarse como los chimpancés, y, por lo que sabemos, justo los mismos sistemas sociales han caracterizado a chimpancés y a gorilas no solo en décadas recientes, sino a lo largo de cientos de miles de años.
No encontramos nada parecido entre los humanos. Sí, los grupos humanos pueden tener sistemas sociales distintos, pero no están determinados por la genética, y rara vez duran más de unos pocos siglos. Piénsese en los alemanes del siglo XX, por ejemplo. En menos de cien años, los alemanes se organizaron en seis sistemas muy diferentes: el Imperio Hohenzollern, la República de Weimar, el Tercer Reich, la República Democrática Alemana (es decir, la Alemania Oriental, comunista), la República Federal de Alemania (es decir, la Alemania Occidental) y por último la Alemania reunida y democrática. Desde luego, los alemanes conservan su idioma y su amor por la cerveza y el _bratwurst_. Pero ¿existe alguna esencia alemana única que los distinga de las demás naciones y que haya permanecido inalterable desde Guillermo II hasta Angela Merkel? Y si el lector encuentra alguna, ¿estaba también ahí hace mil o cinco mil años?
El Preámbulo de la Constitución Europea (no ratificado) empieza declarando que se inspira en «la herencia cultural, religiosa y humanista de Europa, a partir de la cual se han desarrollado los valores universales de los derechos inviolables e inalienables de la persona humana, la democracia, la igualdad, la libertad y el Estado de Derecho».[3] Así, fácilmente podría dar la impresión de que la civilización europea se define por los valores de los derechos humanos, la democracia, la igualdad y la libertad. Innumerables discursos y documentos trazan una línea directa que va de la antigua democracia ateniense a la Unión Europea actual, celebrando de ese modo 2.500 años de libertad y democracia europeas. Esto recuerda al proverbial ciego que palpa la cola de un elefante y llega a la conclusión de que un elefante es una especie de brocha. Sí, las ideas democráticas han formado parte de la cultura europea durante siglos, pero nunca en su totalidad. A pesar de su prestigio e influencia, la democracia ateniense fue un experimento tímido que sobrevivió apenas doscientos años en un pequeño rincón de los Balcanes. Si la civilización europea en los últimos veinticinco siglos ha estado definida por la democracia y los derechos humanos, ¿qué decir entonces de Esparta y Julio César, de los cruzados y los conquistadores, de la Inquisición y del tráfico de esclavos, de Luis XIV y de Napoleón, de Hitler y Stalin? ¿Fueron todos ellos intrusos procedentes de alguna civilización extranjera?
Lo cierto es que la civilización europea es cuanto los europeos quieran que sea, del mismo modo que el cristianismo es cuanto los cristianos quieren que sea, el islamismo cuanto los musulmanes quieren que sea y el judaísmo cuanto los judíos quieren que sea. Y han querido que fueran cosas notablemente diferentes a lo largo de los siglos. Los grupos humanos se definen más por los cambios que experimentan que por ninguna continuidad, pero no obstante consiguen crearse identidades antiguas gracias a sus habilidades narrativas. No importa qué revoluciones vivan, por lo general pueden entretejer lo antiguo y lo nuevo en un único relato.
Incluso un individuo puede fusionar cambios personales revolucionarios en una historia vital coherente e intensa: «Soy una persona que antaño fue socialista, pero que después me hice capitalista; nací en Francia, y ahora vivo en Estados Unidos; estuve casado, y luego me divorcié; tuve un cáncer, y después me curé». De forma parecida, un grupo humano como los alemanes puede llegar a definirse por los mismos cambios que experimentó: «Antaño fuimos nazis, pero hemos aprendido la lección, y ahora somos pacíficos demócratas». No tenemos que buscar una única esencia alemana que se manifestara primero en Guillermo II, después en Hitler y finalmente en Merkel. Estas transformaciones radicales son justo lo que define la identidad alemana. Ser alemán en 2018 significa habérselas con la difícil herencia del nazismo al tiempo que se defienden valores liberales y democráticos. ¿Quién sabe lo que esto significará en 2050?
La gente suele negarse a reconocer estos cambios, sobre todo cuando se trata de valores políticos y religiosos fundamentales. Insistimos en que nuestros valores son una herencia preciosa de antiguos antepasados. Pero eso solo podemos decirlo porque nuestros antepasados hace mucho que murieron y no pueden hablar por sí mismos. Piénsese, por ejemplo, en las actitudes de los judíos hacia las mujeres. En la actualidad, los judíos ultraortodoxos prohíben las imágenes de mujeres en la esfera pública. Las vallas publicitarias y los anuncios dirigidos a los judíos ultraortodoxos suelen presentar solo hombres y chicos, nunca mujeres ni chicas.[4]
En 2011 se desató un escándalo cuando el diario ultraortodoxo de Brooklyn _Di Tzeitung_ publicó una foto de unos funcionarios norteamericanos que contemplaban la incursión en el recinto de Osama bin Laden, de la que se había borrado digitalmente a todas las mujeres, incluida la secretaria de Estado, Hillary Clinton. El diario explicaba que se había visto obligado a hacerlo debido a las «leyes del recato» judías. Estalló un escándalo similar cuando el diario _HaMevaser_ eliminó a Angela Merkel de una fotografía correspondiente a una manifestación en contra de la masacre de _Charlie Hebdo_ , no fuera que su imagen provocara pensamientos lujuriosos en las mentes de los devotos lectores. El editor de un tercer diario ultraortodoxo, _Hamodia_ , defendía esta política al explicar que «nos respaldan miles de años de tradición judía».[5]
En ningún lugar es más estricta la prohibición de ver a mujeres que en la sinagoga. En las sinagogas ortodoxas se las segrega minuciosamente de los hombres y son confinadas a una zona restringida donde están ocultas tras una cortina, de modo que ningún hombre pueda ver por casualidad la forma de una mujer mientras reza sus plegarias o lee las escrituras. Pero si todo esto lo respaldan miles de años de tradición judía y de leyes divinas inmutables, ¿cómo explicar que cuando los arqueólogos excavaron sinagogas antiguas en Israel, que databan de la época de la Mishná y el Talmud, no encontraran señal alguna de segregación por género, y en cambio descubrieran suelos con bellos mosaicos y pinturas en las paredes que representaban a mujeres, algunas de ellas bastante ligeras de ropa? Los rabinos que escribieron la Mishná y el Talmud solían rezar y estudiar en aquellas sinagogas, pero los judíos ortodoxos actuales lo considerarían una blasfema profanación de las antiguas tradiciones.[6]
Distorsiones similares de las tradiciones antiguas caracterizan todas las religiones. Estado Islámico se jacta de haber vuelto a la versión pura y original del islamismo, pero lo cierto es que su interpretación del islam es nueva. Sí, citan muchos textos venerables, pero eligen con sumo criterio qué textos citar y cuáles no, y cómo interpretarlos. En realidad, su actitud de «yo me lo guiso» a la hora de interpretar los textos sagrados es en sí misma muy moderna. Tradicionalmente, la interpretación era una prerrogativa de los doctos ulemas, eruditos que estudiaban la ley y la teología musulmanas en instituciones respetadas, como la escuela de Al-Azhar de El Cairo. Pocos dirigentes de Estado Islámico poseen tales credenciales, y los ulemas más respetados han despreciado a Abu Bakr al-Baghdadi y a los de su clase por criminales ignorantes.[7]
Eso no significa que Estado Islámico haya sido «no islámico» o «antiislámico», como algunos dicen. Resulta bastante irónico que líderes cristianos como Barack Obama tengan la temeridad de decir a los que se proclaman musulmanes, como Abu Bakr al-Baghdadi, qué significa ser musulmán.[8] La acalorada discusión acerca de la verdadera esencia del islam es, simplemente, inútil. El islam no tiene un ADN fijo. El islam es lo que los musulmanes quieren que sea.[9]
##### ALEMANES Y GORILAS
Una diferencia todavía más fundamental distingue a los grupos humanos de las especies animales. Las especies a menudo se dividen, pero nunca se fusionan. Hace unos siete millones de años, chimpancés y gorilas tenían antepasados comunes. Esta única especie ancestral se dividió en dos poblaciones que al final siguieron caminos evolutivos separados. Una vez que ocurrió esto, no había manera de volver atrás. Puesto que los individuos pertenecientes a especies diferentes no pueden tener descendientes fértiles, las especies nunca pueden fusionarse. Los gorilas no pueden fusionarse con los chimpancés, las jirafas no pueden fusionarse con los elefantes y los perros no pueden fusionarse con los gatos.
En cambio, las tribus humanas tendieron a unirse con el tiempo en grupos cada vez más grandes. Los alemanes modernos surgieron a partir de la fusión de sajones, prusianos, suabos y bávaros, que hasta no hace mucho se profesaban poco cariño entre sí. Se sabe que Otto von Bismarck dijo (después de haber leído _El origen de las especies_ de Darwin) que el bávaro es el eslabón perdido entre el austríaco y el humano.[10] Los franceses se crearon por la unificación de francos, normandos, bretones, gascones y provenzales. Mientras tanto, al otro lado del Canal, ingleses, escoceses, galeses e irlandeses fueron uniéndose poco a poco (de forma voluntaria o no) para dar lugar a los británicos. En un futuro no muy lejano, alemanes, franceses y británicos podrían todavía unirse para formar europeos.
Las fusiones no siempre duran, como estos días saben muy bien los habitantes de Londres, Edimburgo y Bruselas. El Brexit podría iniciar la descomposición simultánea tanto del Reino Unido como de la Unión Europea. Pero a la larga, la dirección de la historia es clara. Hace diez mil años la humanidad estaba dividida en incontables tribus aisladas. Con cada milenio que pasaba, estas tribus se fusionaron en grupos cada vez mayores, creando cada vez menos civilizaciones diferentes. En las generaciones recientes, las pocas civilizaciones que perduraban han estado uniéndose en una única civilización global. Las divisiones políticas, étnicas, culturales y económicas resisten, pero no socavan la unidad fundamental. De hecho, algunas divisiones solo son posibles por una estructura común dominante. Por ejemplo, en economía la división del trabajo no puede funcionar a menos que todos compartan un mismo mercado. Un país no puede especializarse en producir automóviles o petróleo a menos que pueda comprar alimentos a otros países que cultivan trigo y arroz.
El proceso de unificación humana ha adoptado dos formas: establecer vínculos entre grupos distintos y homogenizar prácticas en los distintos grupos. Pueden formarse vínculos incluso entre grupos que continúan comportándose de manera muy diferente. De hecho, se establecen vínculos incluso entre enemigos declarados. La propia guerra puede generar algunos de los vínculos humanos más fuertes. Los historiadores suelen aducir que la globalización alcanzó su primer punto culminante en 1913, después experimentó una larga disminución durante la época de las guerras mundiales y la Guerra Fría, y solo se recuperó a partir de 1989.[11] Esto tal vez sea cierto respecto a la globalización económica, pero pasa por alto la dinámica, diferente aunque igual de importante, de la globalización militar. La guerra difunde ideas, tecnologías y personas mucho más deprisa que el comercio. En 1918, Estados Unidos estaba más estrechamente conectado con Europa que en 1913; ambos fueron separándose en los años de entreguerras, para acabar con sus destinos inextricablemente mezclados por la Segunda Guerra Mundial y la Guerra Fría.
La guerra también hace que las personas se interesen mucho más las unas por las otras. Estados Unidos nunca tuvo un contacto tan estrecho con Rusia como durante la Guerra Fría, cuando cada tos en un pasillo de Moscú hacía que algunas personas corrieran por las escaleras de Washington. La gente se preocupa mucho más por sus enemigos que por sus socios comerciales. Por cada película americana sobre Taiwán, probablemente haya cincuenta sobre Vietnam.
##### LAS OLIMPIADAS MEDIEVALES
El mundo de principios del siglo XXI ha ido mucho más allá de formar vínculos entre grupos diferentes. En todo el globo, las personas no solo están en contacto entre sí, sino que comparten cada vez más creencias y prácticas idénticas. Hace mil años, el planeta Tierra era terreno fértil para docenas de modelos políticos diferentes. En Europa podían encontrarse principados feudales que rivalizaban con ciudades estado independientes y con teocracias minúsculas. El mundo musulmán poseía su califato, que afirmaba tener soberanía universal, pero también contaba con reinos, sultanatos y emiratos. Los imperios chinos creían ser la única entidad política legítima, mientras que al norte y al oeste confederaciones tribales luchaban con júbilo entre sí. La India y el Sudeste Asiático eran un calidoscopio de regímenes, mientras que las organizaciones políticas en América, África y Australasia iban desde minúsculas bandas de cazadores-recolectores a extensos imperios. No es extraño que incluso a grupos humanos vecinos les costara ponerse de acuerdo en procedimientos diplomáticos comunes, por no mencionar en leyes internacionales. Cada sociedad se regía por su propio paradigma político, y encontraba difícil entender y respetar los conceptos políticos ajenos.
Hoy en día, en cambio, un único paradigma político es aceptado en todas partes. El planeta está dividido en unos 200 estados soberanos, que por lo general están de acuerdo en los mismos protocolos diplomáticos y en leyes internacionales comunes. En nuestros atlas, Suecia, Nigeria, Tailandia y Brasil están marcados con el mismo tipo de formas coloreadas; todos son miembros de las Naciones Unidas, y a pesar de múltiples diferencias, son reconocidos como estados soberanos que gozan de derechos y privilegios similares. De hecho, comparten muchas más ideas y prácticas políticas, que incluyen al menos una creencia testimonial en cuerpos representativos, partidos políticos, sufragio universal y derechos humanos. Hay parlamentos en Teherán, Moscú, Ciudad del Cabo y Nueva Delhi, así como en Londres y París. Cuando israelíes y palestinos, rusos y ucranianos, kurdos y turcos compiten por los favores de la opinión pública global, todos emplean el mismo discurso de derechos humanos, soberanía estatal y ley internacional.
El mundo puede estar salpicado de varios tipos de «estados fracasados», pero solo conoce un paradigma para un Estado con éxito. Así, la política global sigue el principio de Anna Karénina: todos los estados exitosos son iguales, pero cada Estado fracasado fracasa a su manera, al faltarle tal o cual ingrediente de la oferta política dominante. Recientemente, Estado Islámico destacaba por su rechazo total a esa oferta y por su intento de establecer un tipo de entidad política de todo punto diferente: un califato universal. Pero justo por eso ha fracasado. Numerosas fuerzas guerrilleras y organizaciones terroristas han conseguido establecer nuevos países o conquistar países ya existentes. Pero siempre lo han hecho aceptando los principios fundamentales del orden político global. Incluso los talibanes buscaron el reconocimiento internacional como el gobierno legítimo del país soberano de Afganistán. Ningún grupo que niegue los principios de la política global ha conseguido hasta ahora ejercer un control duradero de ningún territorio importante.
Quizá pueda apreciarse mejor la fuerza del paradigma político global si no analizamos duras cuestiones políticas de guerra y diplomacia, sino algo como los Juegos Olímpicos de 2016 en Río de Janeiro. Dediquemos un momento a reflexionar sobre la manera como se organizaron las Olimpiadas. Los 11.000 atletas se agruparon en delegaciones por su nacionalidad y no por su religión, clase o idioma. No había una delegación budista, una delegación proletaria, una delegación anglófona. Excepto en unos pocos casos (en particular, en los de Taiwán y Palestina), determinar la nacionalidad de los atletas fue sencillo.
En la ceremonia inaugural, el 5 de agosto de 2016, los atletas desfilaron en grupos, y cada grupo hacía ondear su bandera nacional. Cada vez que Michael Phelps ganaba otra medalla de oro, la bandera de las barras y estrellas se alzaba al son del «Star-Spangled Banner». Cuando Émilie Andéol consiguió la medalla de oro en judo, se alzó la bandera tricolor francesa y se interpretó «La Marsellesa».
Oportunamente, cada país del mundo tiene un himno que se ajusta al mismo modelo universal. Casi todos los himnos son fragmentos orquestales de unos pocos minutos de duración, en lugar de un cántico de veinte que solo puede ser ejecutado por una casta especial de sacerdotes ancestrales. Incluso países como Arabia Saudí, Pakistán y el Congo han adoptado para sus himnos convenciones musicales occidentales. La mayoría suenan como algo que hubiera compuesto Beethoven. (Se puede pasar una tarde con los amigos reproduciendo los distintos himnos que hay en YouTube e intentando adivinar cuál es cuál.) Incluso la letra es casi la misma en todo el mundo, lo que indica concepciones comunes de la política y la lealtad de grupo. Por ejemplo, ¿a qué nación piensa el lector que pertenece el siguiente himno? (solo he cambiado el nombre del país por el genérico «mi país»):
_Mi país, mi patria,_
_la tierra en la que he vertido mi sangre,_
_aquí es donde estoy de pie,_
_para ser el guardián de mi tierra natal._
_Mi país, mi nación,_
_mi gente y mi patria,_
_proclamemos:_
_«¡Mi país, unámonos!»._
_Larga vida a mi país, larga vida a mi Estado,_
_mi nación, mi patria, en su totalidad._
_Construye su alma, despierta su cuerpo,_
_¡por mi gran país!_
_Mi gran país, independiente y libre_
_mi hogar y mi país, a los que quiero._
_Mi gran país, independiente y libre,_
_¡larga vida a mi gran país!_
La respuesta es Indonesia. Pero ¿se habría sorprendido el lector si le hubiera dicho que la respuesta era en realidad Polonia, Nigeria o Brasil?
Las banderas nacionales exhiben la misma monótona conformidad. Con una única excepción, todas las banderas son piezas de tela rectangulares que se caracterizan por un repertorio muy limitado de colores, bandas y formas geométricas. Nepal es el país anómalo, pues su bandera está compuesta por dos triángulos. (Pero nunca ha ganado una medalla olímpica.) La bandera indonesia consiste en una banda roja sobre una blanca. La polaca muestra una banda blanca sobre una roja. La bandera de Mónaco es idéntica a la de Indonesia. A una persona daltónica le costaría señalar la diferencia entre las banderas de Bélgica, El Chad, Costa de Marfil, Francia, Guinea, Irlanda, Italia, Mali y Rumanía: todas tienen tres bandas verticales de diversos colores.
Algunos de estos países han estado enzarzados unos contra otros en guerras implacables, pero durante el tumultuoso siglo XX solo se cancelaron tres olimpiadas debido a la guerra (en 19160 y 1944). En 1980, Estados Unidos y algunos de sus aliados boicotearon las Olimpiadas de Moscú, en 1984 el bloque soviético boicoteó las de Los Ángeles, y en otras varias ocasiones los Juegos Olímpicos se encontraron en el centro de una tormenta política (en especial en 1936, cuando el Berlín nazi fue el anfitrión de las Olimpiadas, y en 1972, cuando terroristas palestinos masacraron a la delegación israelí en las de Múnich). Pero, en su conjunto, las controversias políticas no han desbaratado el proyecto olímpico.
Remontémonos ahora mil años. Suponga el lector que quiere celebrar los Juegos Olímpicos Medievales en Río en 1016. Olvide por un momento que Río era entonces una pequeña aldea de indios tupí,[12] y que asiáticos, africanos y europeos ni siquiera eran conscientes de la existencia de América. Olvide los problemas logísticos de hacer llegar a los principales atletas del mundo a Río sin contar con aviones. Olvide también que pocos deportes eran compartidos en todo el mundo, e incluso que, aunque todos los humanos pueden correr, no todos podrían ponerse de acuerdo en las mismas reglas para una competición de carrera. Pregúntese simplemente el lector cómo agrupar a las delegaciones que competirían. En la actualidad, el Comité Olímpico Internacional invierte muchísimas horas discutiendo la cuestión de Taiwán y la de Palestina. Multiplique esto por 10.000 para estimar el número de horas que tendría que invertir en la política de la Olimpiada Medieval.
Para empezar, en 1016 el Imperio chino Song no reconocía a ninguna entidad política en la Tierra como su igual. Por tanto, sería una humillación inconcebible conceder a su delegación olímpica la misma categoría que se diera a las delegaciones del reino Koryo de Corea o al reino vietnamita de Dai Co Viet, por no mencionar las delegaciones de los primitivos bárbaros de allende los mares.
El califa de Bagdad afirmaba asimismo su hegemonía universal, y la mayoría de los musulmanes suníes lo reconocían como su jefe supremo. Sin embargo, en términos prácticos el califa apenas gobernaba la ciudad de Bagdad. Así, ¿querrían formar parte todos los atletas suníes de una única delegación del califato, o querrían separarse en las docenas de delegaciones de los numerosos emiratos y sultanatos del mundo suní? Pero ¿por qué quedarse en los emiratos y sultanatos? El desierto Arábigo estaba lleno de tribus de beduinos libres, que no reconocían a ningún jefe supremo salvo a Alá. ¿Tendría derecho cada una de ellas a enviar una delegación independiente para competir en tiro con arco o carreras de camellos? Europa daría al lector un número parecido de quebraderos de cabeza. Un atleta de la aldea normanda de Ivry, ¿competiría bajo el estandarte del conde de Ivry local, de su señor el duque de Normandía o quizá del débil rey de Francia?
Muchas de estas entidades políticas aparecieron y desaparecieron en cuestión de años. Cuando el lector estuviera preparándose para los Juegos Olímpicos de 1016, no podría saber de antemano qué delegaciones acudirían, porque nadie estaría seguro de qué entidades políticas seguirían existiendo al año siguiente. Si el reino de Inglaterra hubiera enviado una delegación a la Olimpiada de 1016, cuando los atletas hubieran retornado al hogar con sus medallas habrían descubierto que los daneses acababan de tomar Londres y que Inglaterra estaba siendo absorbida en el Imperio del mar del Norte del rey Canuto el Grande, junto con Dinamarca, Noruega y partes de Suecia. En cuestión de otras dos décadas aquel imperio se desintegró, pero treinta años más tarde Inglaterra fue conquistada de nuevo, por el duque de Normandía.
Ni que decir tiene que la inmensa mayoría de estas entidades políticas efímeras no disponían de himno que interpretar ni de bandera que enarbolar. Los símbolos políticos eran de suma importancia, desde luego, pero el lenguaje simbólico de la política europea era muy distinto de los lenguajes simbólicos de las políticas indonesia, china o tupí. Ponerse de acuerdo en un protocolo común para señalar la victoria habría sido casi imposible.
Así, cuando el lector vea los Juegos Olímpicos de Tokio en 2020, recuerde que la aparente competición entre naciones supone en realidad un asombroso acuerdo global. Aun con todo el orgullo nacional que la gente siente cuando su delegación gana una medalla de oro y se iza su bandera, hay muchísima más razón para sentir orgullo porque la humanidad sea capaz de organizar un acontecimiento de este tipo.
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##### UN DÓLAR PARA GOBERNARLOS A TODOS
En la época premoderna, los humanos probaron no solo diversos sistemas políticos, sino también una variedad abrumadora de modelos económicos. Los boyardos rusos, los marajás hindúes, los mandarines chinos y los jefes tribales amerindios tenían ideas muy diferentes acerca del dinero, el comercio, los impuestos y el empleo. En la actualidad, en cambio, casi todo el mundo cree, con variaciones un poco distintas, en el mismo tema capitalista, y todos somos piezas de una única línea de producción global. Ya vivamos en el Congo o en Mongolia, en Nueva Zelanda o en Bolivia, nuestras rutinas cotidianas y nuestras riquezas económicas dependen de las mismas teorías económicas, las mismas compañías y bancos y los mismos flujos de capital. Si los ministros de Finanzas de Israel e Irán tuvieran que encontrarse para almorzar, compartirían un lenguaje económico y podrían fácilmente comprender las tribulaciones de cada uno y empatizar con ellas.
Cuando Estado Islámico conquistó gran parte de Siria e Irak, asesinó a decenas de miles de personas, demolió yacimientos arqueológicos, derribó estatuas y destruyó de manera sistemática los símbolos de los regímenes previos y de la influencia cultural occidental.[13] Pero cuando los combatientes de Estado Islámico entraron en los bancos locales y encontraron allí montones de dólares estadounidenses con las caras de presidentes estadounidenses y con lemas en inglés que ensalzaban los ideales políticos y religiosos americanos, no quemaron estos símbolos del imperialismo estadounidense. Porque los billetes de dólar son venerados universalmente a través de las separaciones políticas y religiosas. Aunque no tiene un valor intrínseco (no podemos comernos ni bebernos un billete), la confianza en el dólar y en la sensatez de la Reserva Federal es tan sólida que incluso la comparten los fundamentalistas islámicos, los señores de la droga mexicanos y los tiranos norcoreanos.
Pero la homogeneidad de la humanidad contemporánea es más aparente si consideramos nuestra visión del mundo natural y del cuerpo humano. Si uno enfermaba hace mil años, era muy importante dónde vivía. En Europa, el sacerdote del lugar le diría probablemente que había hecho enfadar a Dios y que para recuperar la salud tenía que dar algo a la iglesia, realizar una peregrinación a un lugar sagrado y rezar fervientemente por el perdón divino. O la bruja de la aldea le explicaría que lo había poseído un demonio al que podía expulsar mediante canciones, bailes y la sangre de un gallo joven negro.
En Oriente Próximo, los médicos formados en las tradiciones clásicas podrían decirle al enfermo que sus humores corporales estaban desequilibrados y que tenía que armonizarlos con una dieta adecuada y lociones malolientes. En la India, los expertos ayurvédicos ofrecerían sus propias teorías en relación con el equilibrio entre los tres elementos corporales conocidos como _doshas_ , y recomendarían un tratamiento de hierbas, masajes y posturas de yoga. Los médicos chinos, los chamanes siberianos, los brujos africanos, los curanderos amerindios, cada imperio, reino y tribu contaban con sus propias tradiciones y expertos, cada uno de los cuales tenía ideas distintas del cuerpo humano y la naturaleza de la enfermedad, y cada uno de los cuales ofrecía su propio cuerno de la abundancia de rituales, brebajes y curas. Algunos de estos funcionaban increíblemente bien, mientras que otros casi suponían una sentencia de muerte. Lo único que unía las prácticas médicas europeas, chinas, africanas y americanas era que al menos un tercio de los niños morían antes de alcanzar la edad adulta y que la esperanza de vida media se hallaba muy por debajo de los cincuenta años.[14]
Hoy en día, si nos ponemos enfermos es mucho menos importante dónde vivamos. En Toronto, Tokio, Teherán o Tel Aviv se nos trasladará a hospitales de aspecto similar, donde encontraremos a médicos con bata blanca que aprendieron las mismas teorías científicas en las mismas facultades de Medicina. Seguirán idénticos protocolos y usarán idénticas pruebas para emitir diagnósticos muy similares. Después dispensarán las mismas medicinas producidas por las mismas empresas farmacéuticas internacionales. Sigue habiendo algunas diferencias culturales menores, pero los médicos canadienses, japoneses, iraníes e israelíes tienen opiniones muy parecidas del cuerpo humano y las enfermedades. Después de que Estado Islámico tomara Al Raqa y Mosul, no derribó los hospitales locales; en cambio, emitió un llamamiento a médicos y a enfermeras musulmanes de todo el mundo para que de forma voluntaria prestaran sus servicios allí.[15] Se supone que incluso los médicos y las enfermeras islamistas creen que el cuerpo está constituido por células, que las enfermedades las causan agentes patógenos y que los antibióticos matan las bacterias.
¿Y qué constituye estas células y bacterias? Y, de hecho, ¿qué constituye el mundo entero? Hace mil años, cada cultura tenía su propio relato del universo y de los ingredientes fundamentales del caldo cósmico. En la actualidad, las personas cultas de todo el mundo creen exactamente las mismas cosas sobre la materia, la energía, el tiempo y el espacio. Pongamos el ejemplo de los programas nucleares de Irán y Corea del Norte. Todo el problema reside en que iraníes y norcoreanos tienen exactamente el mismo parecer sobre la física que israelíes y estadounidenses. Si iraníes y norcoreanos creyeran que _E = mc_ 4, a Israel y a Estados Unidos les importarían un comino sus programas nucleares.
La gente tiene todavía diferentes religiones e identidades nacionales. Pero cuando se trata de asuntos prácticos (cómo construir un estado, una economía, un hospital o una bomba), casi todos pertenecemos a la misma civilización. Existen discrepancias, sin duda, pero todas las civilizaciones tienen sus disputas internas. En realidad, tales disputas las definen. Cuando intentan describir su identidad, las personas suelen hacer una lista de la compra con rasgos comunes. Es un error. Les iría mucho mejor si hicieran una lista de conflictos y dilemas comunes. Por ejemplo, en 1618 Europa carecía de una sola identidad religiosa: estaba definida por el conflicto religioso. Ser europeo en 1618 significaba obsesionarse con diferencias doctrinales minúsculas entre católicos y protestantes o entre calvinistas y luteranos, y con estar dispuesto a matar o que te mataran debido a estas diferencias. Si en 1618 a un humano no le preocupaban estos conflictos, dicha persona sería quizá un turco o un hindú, pero sin duda no un europeo.
De forma similar, en 1940 Gran Bretaña y Alemania tenían valores políticos muy distintos, pero ambas formaban parte integral de la «civilización europea». Hitler no era menos europeo que Churchill. Más bien, la misma lucha entre ambos definió lo que era ser europeo en aquella coyuntura concreta de la historia. En contraste, en 1940 un cazador-recolector !kung no era europeo porque la confrontación europea interna acerca de la raza y el imperio habrían tenido poco sentido para él.
Las personas con quienes nos peleamos más a menudo son los miembros de nuestra propia familia. La identidad se define más por conflictos y dilemas que por acuerdos. ¿Qué significa ser europeo en 2018? No significa tener la piel blanca, creer en Jesucristo o defender la libertad. En cambio, significa debatir apasionadamente acerca de la inmigración, la Unión Europea y los límites del capitalismo, y también preguntarnos de manera obsesiva: «¿Qué define mi identidad?», así como preocuparnos por la población envejecida, el consumismo desbocado y el calentamiento global. En sus conflictos y dilemas, los europeos del siglo XXI son diferentes de sus antepasados de 1618 y 1940, pero son cada vez más parecidos a sus socios comerciales chinos e indios.
Cualesquiera que sean los cambios que nos aguardan en el futuro, es probable que impliquen una lucha fraterna en el seno de una única civilización en lugar de una confrontación entre civilizaciones extrañas. Los grandes desafíos del siglo XXI serán de naturaleza global. ¿Qué ocurrirá cuando el cambio climático desencadene catástrofes ecológicas? ¿Qué ocurrirá cuando los ordenadores superen a los humanos cada vez en más tareas y los sustituyan en un número creciente de empleos? ¿Qué ocurrirá cuando la biotecnología nos permita mejorar a los humanos y alargar la duración de la vida? Sin duda, tendremos grandes debates y amargos conflictos sobre estas cuestiones. Pero es improbable que dichos debates y conflictos nos aíslen a unos de otros. Justo lo contrario. Nos harán todavía más interdependientes. Aunque la humanidad está muy lejos de constituir una comunidad armoniosa, todos somos miembros de una única y revoltosa civilización global.
¿Cómo explicar, pues, la oleada nacionalista que se extiende por gran parte del mundo? Quizá en nuestro entusiasmo por la globalización hayamos despachado con demasiada celeridad a las buenas y antiguas naciones. El retorno al nacionalismo tradicional, ¿podría ser la solución para nuestras desesperadas crisis globales? Si la globalización conlleva tantos problemas, ¿por qué no abandonarla, simplemente?
### 7
Nacionalismo
#### Los problemas globales necesitan respuestas globales
Puesto que toda la humanidad constituye en la actualidad una única civilización, y toda la gente comparte retos y oportunidades comunes, ¿por qué británicos, norteamericanos, rusos y otros numerosos grupos se encaminan hacia el aislamiento nacionalista? ¿Acaso un retorno al nacionalismo ofrece soluciones reales a los problemas sin precedentes de nuestro mundo global, o se trata de un lujo escapista que puede condenar al desastre a la humanidad y a toda la biosfera?
A fin de responder a esta pregunta, primero hemos de disipar un mito muy extendido. Al contrario de lo que suele creerse, el nacionalismo no es una parte natural y eterna de la psique humana, y no está basado en la biología humana. Sin duda, los humanos son animales sociales de los pies a la cabeza y llevan la lealtad al grupo impresa en sus genes. Sin embargo, durante cientos de miles de años, _Homo sapiens_ y sus antepasados homínidos vivían en pequeñas comunidades íntimas de no más de unas pocas docenas de personas. Los humanos desarrollan fácilmente lealtad a grupos pequeños e íntimos, como una tribu, una compañía de infantería o un negocio familiar, pero no es en absoluto natural para ellos ser leales a millones de completos desconocidos. Tales lealtades en masa han aparecido solo en los últimos miles de años (ayer por la mañana, en términos evolutivos) y requieren inmensos esfuerzos de construcción social.
La gente se impuso la dificultad de crear colectivos nacionales porque se enfrentaba a retos que una sola tribu no podía resolver. Pensemos, por ejemplo, en las antiguas tribus que vivían a lo largo del Nilo hace miles de años. El río era su elemento vital: irrigaba sus campos y transportaba su comercio. Pero era un aliado impredecible. Demasiada poca lluvia, y la gente se moría de hambre; demasiada lluvia, y las aguas se desbordaban de sus orillas y destruían aldeas enteras. Ninguna tribu podía resolver este problema por sí sola, porque cada una de ellas controlaba una pequeña sección del río y tan solo podía movilizar a unos cuantos cientos de obreros. Únicamente con un esfuerzo común para construir presas enormes y excavar cientos de kilómetros de canales se podía esperar contener y domeñar el poderoso río. Esta fue una de las razones por las que las tribus se fusionaron poco a poco en una única nación que tenía el poder de construir presas y canales, regular el flujo del río, acumular reservas de grano para los años de vacas flacas y establecer un sistema de transporte y comunicación en todo el país.
A pesar de tales ventajas, transformar tribus y clanes en una nación única nunca fue fácil, ni en épocas antiguas ni en la actualidad. Para darse cuenta de lo difícil que es identificarse con una nación de este tipo solo tenemos que preguntarnos: «¿Conozco a esta gente?». Puedo nombrar a mis dos hermanas y once primos y pasar todo un día hablando de sus personalidades, peculiaridades y relaciones. No puedo nombrar a los ocho millones de personas que comparten mi ciudadanía israelí, nunca he conocido a la mayoría de ellos y es muy improbable que llegue a conocerlos en el futuro. Mi capacidad, no obstante, para sentir lealtad hacia esa nebulosa masa no es una herencia de mis antepasados cazadores-recolectores, sino un milagro de la historia reciente. Un biólogo marciano que estuviera familiarizado únicamente con la anatomía y la evolución de _Homo sapiens_ jamás podría adivinar que dichos simios fueran capaces de desarrollar vínculos comunitarios con millones de extraños. A fin de convencerme de ser leal a «Israel» y a sus ocho millones de habitantes, el movimiento sionista y el Estado israelí tuvieron que crear un gigantesco aparato de educación, propaganda y ondeo de banderas, así como sistemas nacionales de seguridad, sanidad y bienestar.
Eso no significa que haya algo malo en los vínculos nacionales. Los sistemas enormes no pueden funcionar sin lealtades en masa, y expandir el círculo de la empatía humana tiene sin duda sus méritos. Las formas más moderadas de patriotismo figuran entre las creaciones humanas más benignas. Creer que mi nación es única, que merece mi lealtad y que tengo obligaciones especiales para con sus miembros me impulsa a cuidar a otros y hacer sacrificios en su nombre. Es un error peligroso imaginar que sin nacionalismo todos viviríamos en un paraíso liberal. Es más probable que viviéramos en un caos tribal. Países pacíficos, prósperos y liberales como Suecia, Alemania y Suiza poseen un marcado sentido de nacionalismo. La lista de países que carecen de vínculos nacionales sólidos incluye Afganistán, Somalia, el Congo y la mayoría de los demás estados fracasados.[1]
El problema empieza cuando el patriotismo benigno se metamorfosea en ultranacionalismo patriotero. En lugar de creer que mi nación es única (lo que es cierto para todas las naciones), puedo comenzar a sentir que mi nación es suprema, que le debo toda mi lealtad y que no tengo obligaciones importantes para con nadie más. Este es terreno fértil para los conflictos violentos. Durante generaciones, la crítica más básica del nacionalismo era que conducía a la guerra. Pero la conexión entre nacionalismo y violencia no refrenó los excesos nacionalistas, en particular porque cada nación justificaba su propia expansión militar por la necesidad de protegerse de las maquinaciones de sus vecinos. Mientras la nación proporcionara a la mayoría de sus ciudadanos niveles inauditos de seguridad y prosperidad, estos se hallaban dispuestos a pagar el precio en sangre. En el siglo XIX y principios del XX, el acuerdo nacionalista parecía todavía muy atractivo. Aunque el nacionalismo conducía a conflictos horrendos a una escala sin precedentes, los estados nación modernos también creaban enormes sistemas de asistencia sanitaria, educación y bienestar. Gracias a los servicios nacionales de salud, parecía que Passchendaele y Verdún hubieran valido la pena.
Todo cambió en 1945. La invención de las armas nucleares alteró considerablemente las condiciones del acuerdo nacionalista. Después de Hiroshima, la gente ya no temía que el nacionalismo condujera a la simple guerra: empezó a temer que llevara a la guerra nuclear. La aniquilación total es capaz de aguzar la mente de la gente, y, gracias en no poca medida a la bomba atómica, ocurrió lo imposible y el genio nacionalista fue introducido en la lámpara, al menos la mitad del genio. De la misma manera que los antiguos aldeanos de la cuenca del Nilo redirigieron parte de su lealtad desde los clanes locales a un reino mucho mayor capaz de contener el peligroso río, en la era nuclear se desarrolló entre las diversas naciones una comunidad global, porque solo una comunidad así podría contener el demonio nuclear.
En la campaña presidencial de 1964 en Estados Unidos, Lyndon B. Johnson difundió el famoso «anuncio de la margarita», uno de los mayores éxitos de la propaganda en los anales de la televisión. El anuncio se inicia con una niñita que arranca y cuenta los pétalos de una margarita, pero cuando llega a diez, se oye una voz masculina y metálica que cuenta en sentido inverso de diez a cero, como en la cuenta atrás del lanzamiento de misiles. Al llegar a cero, el brillante destello de una explosión nuclear llena la pantalla, y el candidato Johnson se dirige al público norteamericano y dice: «Esto es lo que está en juego. Construir un mundo donde todos los niños de Dios puedan vivir, o dirigirse hacia la oscuridad. O hemos de amarnos los unos a los otros, o hemos de morir».[2] Solemos asociar el lema «Haz el amor, no la guerra» con la contracultura de finales de la década de 1960, pero en realidad ya en 1964 era algo aceptado incluso entre políticos duros como Johnson.
En consecuencia, durante la Guerra Fría el nacionalismo adoptó un papel secundario frente a una perspectiva más global de la política internacional, y cuando la Guerra Fría terminó, la globalización parecía ser la tendencia arrolladora del futuro. Se esperaba que la humanidad dejaría atrás las políticas nacionalistas, como una reliquia de épocas más primitivas que a lo sumo quizá atrajeran a los habitantes mal informados de unos pocos países subdesarrollados. Sin embargo, los acontecimientos de años recientes han demostrado que el nacionalismo tiene todavía un arraigo profundo incluso en los ciudadanos de Europa y Estados Unidos, por no mencionar Rusia, la India y China. Alienada por las fuerzas impersonales del capitalismo global y temiendo por el futuro de los sistemas nacionales de salud, educación y bienestar, la gente de todo el mundo busca seguridad y sentido en el regazo de la nación.
Pero la disyuntiva que planteó Johnson en el «anuncio de la margarita» es incluso más pertinente hoy de lo que era en 1964. ¿Crearemos un mundo donde todos los humanos puedan vivir juntos, o nos dirigiremos hacia la oscuridad? ¿Están salvando el mundo Donald Trump, Theresa May, Vladímir Putin, Narendra Modi y sus colegas al avivar nuestros sentimientos nacionales, o la actual avalancha nacionalista es una forma de escapismo ante los inextricables problemas globales a que nos enfrentamos?
##### EL RETO NUCLEAR
Empecemos con la némesis común del género humano: la guerra nuclear. Cuando en 1964 se emitió el «anuncio de la margarita», dos años después de la crisis de los misiles cubanos, la aniquilación nuclear era una amenaza palpable. Expertos y profanos temían por igual que la humanidad no tuviera la sensatez de evitar la destrucción y creían que solo era cuestión de tiempo que la Guerra Fría se volviera caliente y abrasadora. En realidad, la humanidad se enfrentó con éxito al reto nuclear. Norteamericanos, soviéticos, europeos y chinos cambiaron la manera como se ha realizado la geopolítica durante milenios, de forma que la Guerra Fría llegó a su fin con poco derramamiento de sangre, y un nuevo mundo internacional promovió una era de paz sin precedentes. No solo se evitó la guerra nuclear, sino que las contiendas de todo tipo se redujeron. Es sorprendente que desde 1945 muy pocas fronteras se hayan redibujado a raíz de una agresión brutal, y la mayoría de los países han dejado de utilizar la guerra como una herramienta política estándar. En 2016, a pesar de las guerras en Siria, Ucrania y varios otros puntos calientes, morían menos personas debido a la violencia humana que a la obesidad, los accidentes de tráfico o el suicidio.[3] Este podría muy bien haber sido el mayor logro político y moral de nuestra época.
Por desgracia, estamos ya tan acostumbrados a este logro que lo damos por hecho. Esta es en parte la razón por la que la gente se permite jugar con fuego. Rusia y Estados Unidos se han embarcado recientemente en una nueva carrera de armas nucleares y han desarrollado nuevos artilugios del fin del mundo que amenazan con destruir los logros tan duramente ganados de las últimas décadas, y volvernos a llevar al borde de la aniquilación nuclear.[4] Mientras tanto, la opinión pública ha aprendido a dejar de preocuparse y a amar a la bomba (tal como sugería _¿Teléfono rojo? Volamos hacia Moscú_ ), o simplemente ha olvidado su existencia.
Así, el debate sobre el Brexit en Gran Bretaña (una potencia nuclear importante) versó principalmente sobre cuestiones de economía e inmigración, mientras que la contribución vital de la Unión Europea a la paz europea y a la paz global se pasó en gran parte por alto. Después de siglos de matanzas terribles, franceses, alemanes, italianos y británicos han creado al final un mecanismo que asegura la armonía continental, solo para que el pueblo británico haya lanzado una llave inglesa dentro de la máquina milagrosa.
Fue extremadamente difícil construir el régimen internacionalista que evitó la guerra nuclear y salvaguardó la paz en el planeta. Sin duda necesitamos adaptar este régimen a las condiciones cambiantes del mundo, por ejemplo, dependiendo menos de Estados Unidos y confiriendo un papel más decisivo a potencias no occidentales como China y la India.[5] Pero abandonar por completo este régimen y retornar a la política del poder nacionalista sería una apuesta irresponsable. Cierto, en el siglo XIX los países jugaron al juego nacionalista sin destruir la civilización humana, pero ocurrió en la era pre-Hiroshima. Desde entonces, las armas nucleares han hecho subir la apuesta y cambiado la naturaleza fundamental de la guerra y la política. Mientras los humanos sepan cómo enriquecer el uranio y el plutonio, su supervivencia dependerá de preferir la prevención de la guerra nuclear frente a los intereses de cualquier nación concreta. Los nacionalistas entusiastas que gritan: «¡Primero nuestro país!» deberían preguntarse si su país, por sí solo, sin un sistema sólido de cooperación internacional, puede proteger al mundo (o incluso protegerse a sí mismo) de la destrucción nuclear.
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##### EL RETO ECOLÓGICO
Además de la guerra nuclear, en las décadas venideras la humanidad se enfrentará a una nueva amenaza existencial que apenas se registraba en los radares políticos en 1964: el colapso ecológico. Los humanos están desestabilizando la biosfera global en múltiples frentes. Cada vez tomamos más recursos del entorno, al tiempo que vertemos en él cantidades ingentes de desechos y venenos, lo que provoca cambios en la composición del suelo, del agua y de la atmósfera.
Apenas somos conscientes siquiera de las múltiples maneras en que alteramos el delicado equilibrio ecológico formado a lo largo de millones de años. Considérese, por ejemplo, el uso del fósforo como fertilizante. En pequeñas cantidades es un nutriente esencial para el crecimiento de las plantas. Pero en cantidades excesivas se vuelve tóxico. La agricultura industrial moderna se basa en la fertilización artificial de los campos con grandes cantidades de fósforo, pero la escorrentía cargada de fósforo procedente de los campos de cultivo envenena después ríos, lagos y océanos, y tiene un impacto devastador sobre la vida marina. Un agricultor que cultive maíz en Iowa podría, sin saberlo, estar matando peces en el golfo de México.
Debido a estas actividades, los hábitats se degradan, animales y plantas se extinguen y ecosistemas enteros, como la Gran Barrera de Coral australiana y la pluviselva amazónica, podrían acabar destruidos. Durante miles de años, _Homo sapiens_ se ha comportado como un asesino ecológico en serie; ahora está transformándose en un asesino ecológico en masa. Si continuamos con esta trayectoria, no solo se llegará a aniquilar un gran porcentaje de todos los seres vivos, sino que también podrían debilitarse los cimientos de la civilización humana.[6]
Lo más preocupante de todo es la perspectiva del cambio climático. Los humanos llevan aquí cientos de miles de años y han sobrevivido a numerosas edades de hielo y períodos cálidos. Sin embargo, la agricultura, las ciudades y las sociedades complejas existen desde hace no más de diez mil años. Durante este período, conocido como Holoceno, el clima del planeta ha sido relativamente estable. Cualquier desviación de los patrones del Holoceno planteará a las sociedades humanas actuales problemas enormes que nunca han conocido. Será como realizar un experimento con final abierto con miles de millones de cobayas. Y aunque la civilización humana acabara por adaptarse a las nuevas condiciones, ¡quién sabe cuántas víctimas podrían perecer en el proceso de adaptación!
Este experimento terrorífico ya se ha puesto en marcha. A diferencia de la guerra nuclear, que es un futuro potencial, el cambio climático es una realidad actual. Los científicos están de acuerdo en que las actividades humanas, en particular la emisión de gases de efecto invernadero como el dióxido de carbono, hacen que el clima de la Tierra cambie a un ritmo alarmante.[7] Nadie sabe exactamente cuánto dióxido de carbono podemos continuar bombeando a la atmósfera sin desencadenar un cataclismo irreversible. Pero nuestras estimaciones científicas más optimistas indican que a menos que reduzcamos de forma drástica la emisión de gases de efecto invernadero en los próximos veinte años, las temperaturas medias globales aumentarán más de 2 ºC,[8] lo que provocará la expansión de los desiertos, la desaparición de los casquetes polares, el aumento del nivel de los océanos y una mayor incidencia de acontecimientos meteorológicos extremos, como huracanes y tifones. Estos cambios alterarán a su vez la producción agrícola, inundarán ciudades, harán que gran parte del mundo se vuelva inhabitable y que cientos de millones de refugiados busquen nuevos hogares.[9]
Además, estamos acercándonos rápidamente a varios puntos de inflexión, más allá de los cuales incluso una reducción espectacular de las emisiones de gases de efecto invernadero no bastará para invertir la tendencia y evitar una tragedia mundial. Por ejemplo, a medida que el calentamiento global funde las capas de hielo polares, se refleja menos luz solar desde nuestro planeta al espacio exterior. Ello significa que la Tierra absorbe más calor, que las temperaturas aumentan todavía más y que el hielo se funde con mayor rapidez. Una vez que este bucle retroactivo traspase un umbral crítico alcanzará un impulso irrefrenable, y todo el hielo de las regiones polares se derretirá aunque los humanos dejen de quemar carbón, petróleo y gas. De ahí que no sea suficiente que reconozcamos el peligro al que nos enfrentamos. Es fundamental que realmente hagamos algo al respecto ahora.
Por desgracia, en 2018, en lugar de haberse reducido las emisiones de gases de efecto invernadero, la tasa de emisión global sigue aumentando. A la humanidad le queda muy poco tiempo para desengancharse de los combustibles fósiles. Es necesario que iniciemos la rehabilitación hoy mismo. No el año próximo o el mes próximo, sino hoy. «Hola, soy _Homo sapiens_ y soy adicto a los combustibles fósiles.»
¿Dónde encaja el nacionalismo en este panorama alarmante? ¿Existe una respuesta nacionalista a la amenaza ecológica? ¿Puede una nación, por poderosa que sea, frenar el calentamiento global por sí sola? Sin duda, los países pueden adoptar a título individual toda una serie de políticas verdes, muchas de las cuales tienen gran sentido tanto ambiental como económico. Los gobiernos pueden cobrar impuestos a las emisiones de carbono, añadir el costo de las externalidades al precio del petróleo y el gas, promulgar leyes ambientales más restrictivas, recortar los subsidios a las industrias contaminantes e incentivar el cambio a energías renovables. También pueden invertir más dinero en investigar y desarrollar tecnologías respetuosas con el medio ambiente, en una especie de Proyecto Manhattan ecológico. Hay que agradecer al motor de combustión interna muchos de los avances de los últimos ciento cincuenta años, pero si hemos de mantener un ambiente físico y económico estable habrá que retirarlo ya y sustituirlo por nuevas tecnologías que no quemen combustibles fósiles.[10]
Los avances tecnológicos pueden ayudar en otros muchos ámbitos además de la energía. Considérese, por ejemplo, el potencial de desarrollar «carne limpia». En la actualidad, la industria de la carne no solo inflige un dolor incalculable a miles de millones de seres dotados de sensibilidad, sino que también es una de las principales causas del calentamiento global, una de las principales consumidoras de antibióticos y venenos, y una de las mayores contaminadoras de aire, tierra y agua. Según un informe de 2013 de la Institución de Ingenieros Mecánicos, hacen falta 15.000 litros de agua para producir un kilogramo de carne de res, en comparación con 287 litros de agua para un kilogramo de patatas.[11]
Es probable que la presión ambiental empeore a medida que el aumento de la prosperidad en países como China y Brasil permita a cientos de millones de personas más pasar de comer patatas a comer carne de manera regular. Sería difícil convencer a chinos y a brasileños (por no mencionar a estadounidenses y a alemanes) para que dejaran de comer bistecs, hamburguesas y salchichas. Pero ¿qué ocurriría si los ingenieros pudieran encontrar una manera de generar carne a partir de células? Si usted quiere una hamburguesa, simplemente cultívela, en lugar de criar y sacrificar una vaca entera (y transportar el cuerpo a miles de kilómetros).
Esto podría parecer ciencia ficción, pero la primera hamburguesa limpia del mundo se generó a partir de células (y después fue comida) en 2013. Costó 330.000 dólares. Cuatro años de investigación y desarrollo hicieron bajar el precio a 11 dólares la unidad, y se espera que al cabo de otra década la carne limpia sea más barata que la procedente de animales sacrificados. Este desarrollo tecnológico podría ahorrarles a miles de millones de animales una vida de dolor abyecto, podría alimentar a miles de millones de humanos desnutridos y, a la vez, ayudar a evitar el colapso ecológico.[12]
Así que hay muchas cosas que los gobiernos, empresas e individuos pueden hacer para evitar el cambio climático. Pero para ser efectivas, tienen que emprenderse a un nivel global. Cuando se trata del clima, los países ya no son soberanos. Se encuentran a merced de acciones que otras personas efectúan en la otra punta del planeta. La república de Kiribati (una nación insular en el océano Pacífico) podría reducir sus emisiones de gases a cero y no obstante verse sumergida bajo el oleaje creciente si otros países no hacen lo mismo. El Chad podría instalar un panel solar en cada tejado del país y sin embargo convertirse en un desierto yermo debido a las políticas ambientales irresponsables de extranjeros lejanos. Ni siquiera países poderosos como China y Japón son soberanos desde el punto de vista ecológico. Para proteger Shangai, Hong Kong y Tokio de inundaciones y tifones destructivos, los chinos y los japoneses tendrán que convencer a los gobiernos estadounidense y ruso de que abandonen su estrategia de «hacer lo de siempre».
El aislacionismo nacionalista probablemente sea incluso más peligroso en el contexto del cambio climático que en el de la guerra nuclear. Una guerra nuclear total amenaza con destruir a todas las naciones, de modo que todas las naciones tienen el mismo interés en evitarla. En cambio, el calentamiento global tendrá probablemente un impacto diferente en función de cada nación. Algunos países, y de manera notable Rusia, podrían en verdad beneficiarse de ello. Rusia tiene relativamente pocos recursos costeros, de manera que está mucho menos preocupada que China o Kiribati por el aumento del nivel del mar. Y mientras que las temperaturas más altas es probable que transformen El Chad en un desierto, al mismo tiempo podrían transformar Siberia en el granero del mundo. Además, a medida que el hielo se funda en el lejano norte, las vías marítimas árticas, dominadas por Rusia, podrían convertirse en la arteria del comercio global, y Kamchatka tal vez sustituyera a Singapur como encrucijada del mundo.[13]
De manera similar, es probable que la idea de sustituir los combustibles fósiles por fuentes de energía renovable resulte más interesante a algunos países que a otros. China, Japón y Corea del Sur dependen de la importación de enormes cantidades de petróleo y gas; estarían encantadas de librarse de esta carga. Rusia, Irán y Arabia Saudí dependen de la exportación de petróleo y gas; sus economías se desplomarían si el petróleo y el gas dejan paso de repente a la energía solar y la eólica.
En consecuencia, mientras que quizá algunas naciones como China, Japón y Kiribati se impliquen mucho en la reducción de las emisiones globales de carbono tan pronto como sea posible, otras naciones como Rusia e Irán podrían mostrarse mucho menos entusiastas. Incluso en países en que es evidente que perderán mucho debido al calentamiento global, como Estados Unidos, los nacionalistas podrían ser tan miopes y estar tan satisfechos de sí mismos para no apreciar el peligro. Un prueba de ello, nimia pero reveladora, se dio en enero de 2018, cuando Estados Unidos impuso un arancel del 30 por ciento a los paneles solares y a los equipos solares fabricados en el extranjero, pues preferían respaldar a los productores solares norteamericanos incluso al precio de ralentizar el paso a las energías renovables.[14]
Una bomba atómica es una amenaza tan evidente e inmediata que nadie puede pasarla por alto. En cambio, el calentamiento global es una amenaza más vaga y demorada en el tiempo. De ahí que siempre que las consideraciones ambientales a largo plazo exijan algún sacrificio doloroso a corto plazo, los nacionalistas podrían verse tentados a anteponer los intereses nacionales inmediatos y a tranquilizarse diciendo que ya se preocuparán más adelante del medioambiente, o bien dejar que lo haga la gente de otros sitios. O podrían sencillamente negar el problema. No es casual que el escepticismo respecto al cambio climático tienda a ser terreno de la derecha nacionalista. Rara vez se ve a los socialistas de izquierdas tuitear que «el cambio climático es un timo chino». Ya que no hay una respuesta nacional al problema del calentamiento global, algunos políticos nacionalistas prefieren creer que el problema no existe.[15]
##### EL RETO TECNOLÓGICO
Es presumible que la misma dinámica dé al traste con cualquier antídoto nacionalista para la tercera amenaza existencial del siglo XXI: la disrupción tecnológica. Como hemos visto en capítulos anteriores, la fusión de la infotecnología y la biotecnología abre la puerta a un sinfín de situaciones hipotéticas sobre el tema del fin del mundo, que van de las dictaduras digitales a la creación de una clase inútil global. ¿Cuál es la respuesta nacionalista a estas amenazas?
No hay respuesta nacionalista. Con la disrupción tecnológica ocurre lo mismo que con el cambio climático: el estado nación es simplemente el marco equivocado para enfrentarse a esa amenaza. Puesto que la investigación y el desarrollo no son monopolio de ningún país, ni siquiera una superpotencia como Estados Unidos es capaz de limitarlos por sí sola. Si el gobierno estadounidense prohíbe manipular genéticamente embriones humanos, esto no impide que científicos chinos lo hagan. Y si los progresos resultantes confieren a China alguna ventaja económica o militar, Estados Unidos se sentirá tentado a incumplir su propia prohibición. En particular en un mundo xenófobo y de competición salvaje, aunque un solo país eligiera seguir la senda tecnológica de alto riesgo pero elevados beneficios, otros países se verían obligados a hacer lo mismo, porque nadie puede permitirse quedarse rezagado. Para evitar esta carrera hacia el abismo, probablemente la humanidad necesite algún tipo de identidad y de lealtad globales.
Además, mientras que la guerra nuclear y el cambio climático amenazan solo la supervivencia física de la humanidad, las tecnologías disruptivas podrían cambiar la naturaleza misma del género humano y, por tanto, están mezcladas con las creencias éticas y religiosas más profundas de las personas. Aunque esté de acuerdo con que se debería evitar la guerra nuclear y el desastre ecológico, la gente tiene opiniones muy diferentes acerca del uso de la bioingeniería y la IA para mejorar a los humanos y crear nuevas formas de vida. Si la humanidad no consigue concebir e impartir globalmente reglas éticas generales y aceptadas, se abrirá la veda del doctor Frankenstein.
Cuando se trata de formular estas reglas éticas generales, el nacionalismo adolece por encima de todo de falta de imaginación. Los nacionalistas piensan en términos de conflictos territoriales que duran siglos, mientras que las revoluciones tecnológicas del siglo XXI deberían entenderse en realidad en términos cósmicos. Después de 4.000 millones de años de vida orgánica que ha evolucionado mediante la selección natural, la ciencia da lugar a la era de la vida inorgánica modelada por el diseño inteligente.
En el proceso, es probable que el propio _Homo sapiens_ desaparezca. En la actualidad somos todavía simios de la familia de los homínidos. Aún compartimos con neandertales y chimpancés la mayoría de nuestras estructuras corporales, capacidades físicas y facultades mentales. No solo nuestras manos, ojos y cerebro son claramente homínidos, sino también nuestro deseo sexual, nuestro amor, nuestra ira y nuestros vínculos sociales. Dentro de un siglo o dos, la combinación de la biotecnología y la IA podría resultar en características corporales, físicas y mentales que se liberen por completo del molde homínido. Hay quien cree incluso que la conciencia podría separarse de cualquier estructura orgánica y surfear por el ciberespacio, libre de toda limitación biológica y física. Por otra parte, podríamos asistir a la desvinculación completa de la inteligencia y la conciencia, y el desarrollo de la IA quizá diera como resultado un mundo dominado por entidades superinteligentes pero absolutamente no conscientes.
¿Qué opinan de ello el nacionalismo israelí, ruso o francés? Con el fin de tomar decisiones sensatas sobre el futuro de la vida necesitamos ir mucho más allá del punto de vista nacionalista y considerar las cosas desde una perspectiva global o incluso cósmica.
##### LA NAVE ESPACIAL _T_ IERRA
Cada uno de estos problemas (la guerra nuclear, el colapso ecológico y la disrupción tecnológica) basta para amenazar el futuro de la civilización humana. Pero en su conjunto constituyen una crisis existencial sin precedentes, en especial porque es probable que se refuercen y se agraven mutuamente.
Por ejemplo, aunque la crisis ecológica amenaza la supervivencia de la civilización humana como la hemos conocido, es improbable que frene el desarrollo de la IA y de la bioingeniería. Si el lector cuenta con que el aumento del nivel de los océanos, la reducción de los recursos alimenticios y las migraciones en masa distraerán nuestra atención de algoritmos y genes, piénselo de nuevo. A medida que la crisis ecológica se intensifique, probablemente el desarrollo de tecnologías de elevado riesgo y de elevados beneficios no hará más que acelerarse.
En realidad, podría muy bien ocurrir que el cambio climático llegue a cumplir la misma función que las dos contiendas mundiales. Entre 1914 y 1918, y de nuevo entre 1939 y 1945, el ritmo del desarrollo tecnológico se disparó, porque las naciones enzarzadas en la guerra total abandonaran la prudencia y el ahorro, e invirtieron enormes recursos en todo tipo de proyectos audaces y fantásticos. Muchos de tales proyectos fracasaron, pero algunos acabaron en tanques, el radar, gases venenosos, aviones supersónicos, misiles intercontinentales y bombas nucleares. De forma parecida, las naciones que se enfrentan a un cataclismo climático podrían verse tentadas a depositar sus esperanzas en jugadas tecnológicas desesperadas. La humanidad tiene muchas preocupaciones justificadas respecto a la IA y a la bioingeniería, pero en épocas de crisis la gente hace cosas arriesgadas. Cualquiera que sea la opinión del lector ante la reglamentación de las tecnologías disruptivas, pregúntese si es probable que estas reglas se mantengan incluso si el cambio climático causa carestías alimentarias globales, si acaba por inundar ciudades en todo el mundo y si envía a cientos de millones de refugiados allende las fronteras.
A su vez, las disrupciones tecnológicas podrían aumentar el riesgo de que estallasen guerras apocalípticas, no solo al incrementar las tensiones globales, sino también al desestabilizar el equilibrio de poderes nucleares. Desde la década de 1950, las superpotencias han evitado los conflictos debido a que todas sabían que la guerra significaba una destrucción mutua asegurada. Pero al aparecer nuevos tipos de armas ofensivas y defensivas, una superpotencia tecnológica en auge podría llegar a la conclusión de que es capaz de destruir impunemente a sus enemigos. Y al revés: una potencia que se hallara en horas bajas podría temer que sus armas nucleares tradicionales quedaran pronto obsoletas y que sería mejor usarlas antes de perderlas. Tradicionalmente, las confrontaciones nucleares parecían una partida de ajedrez hiperracional. ¿Qué ocurrirá cuando los jugadores puedan usar ciberataques para arrebatar el control de las piezas de un rival, cuando terceras partes anónimas logren mover un peón sin que nadie sepa quién está haciendo el movimiento, o cuando AlphaZero deje atrás su dominio del ajedrez ordinario y se gradúe en ajedrez nuclear?
De la misma manera que es probable que los diferentes retos se agraven unos a otros, también la buena voluntad necesaria para enfrentarse a un reto puede acabar debilitada por problemas en otros frentes. Es improbable que los países enzarzados en una competición armada estén de acuerdo en restringir el desarrollo de la IA, y a los países que se esfuerzan por superar los logros tecnológicos de sus rivales les costará mucho acceder a un plan común para frenar el cambio climático. Mientras el mundo siga dividido en naciones rivales, será muy difícil superar a la vez los tres retos, y el fracaso incluso en un único frente podría resultar catastrófico.
Para concluir, la oleada nacionalista que recorre el mundo no puede hacer retroceder el reloj a 1939 o 1914. La tecnología lo ha cambiado todo al crear un conjunto de amenazas existenciales globales que ninguna nación puede resolver por sí sola. Un enemigo común es el mejor catalizador para forjar una identidad común, y ahora la humanidad tiene al menos tres de esos enemigos: la guerra nuclear, el cambio climático y la disrupción tecnológica. Si a pesar de estas amenazas comunes los humanos deciden anteponer sus lealtades nacionales particulares a lo demás, las consecuencias pueden ser mucho peores que en 1914 y 1939.
Un camino mucho mejor es el que se esboza en la Constitución de la Unión Europea, que afirma que «los pueblos de Europa, sin dejar de sentirse orgullosos de su identidad y su historia nacional, están decididos a superar sus antiguas divisiones y, cada vez más estrechamente unidos, a forjar un destino común».[16] Esto no significa abolir todas las identidades nacionales, abandonar cada una de las tradiciones locales y transformar a la humanidad en un menjunje gris homogéneo. Como tampoco denigrar toda expresión de patriotismo. De hecho, al proporcionar una cubierta protectora continental, militar y económica, puede decirse que la Unión Europea ha promovido el patriotismo local en Flandes, Lombardía, Cataluña y Escocia. La idea de establecer una Escocia independiente o una Cataluña independiente parece más interesante cuando no se teme una invasión alemana y cuando puede contarse con un frente común europeo contra el calentamiento global y las empresas globales.
Por tanto, los nacionalistas europeos se toman las cosas con calma. A pesar de toda la cháchara de retorno de la nación, pocos europeos están en verdad dispuestos a matar o morir por ello. Cuando los escoceses quisieron separarse del control de Londres, tuvieron que organizar un ejército para hacerlo. En cambio, ni una sola persona murió durante el referéndum escocés de 2014, y si en la próxima ocasión los escoceses votan por la independencia, es muy improbable que deban volver a librar la batalla de Bannockburn. El intento catalán de separarse de España ha generado más violencia, pero mucha menos que la carnicería que Barcelona vivió en 1939 o en 1714.
Cabe esperar, pues, que el resto del mundo aprenda del ejemplo europeo. Incluso en un planeta unido habrá mucho espacio para ese patriotismo que celebra la singularidad de mi nación y destaca mis obligaciones especiales hacia ella. Pero si queremos sobrevivir y prosperar, la humanidad no tiene otra elección que completar estas lealtades locales con obligaciones sustanciales hacia una comunidad global. Una persona puede y debe ser leal simultáneamente a su familia, sus vecinos, su profesión y su nación, ¿por qué no añadir a la humanidad y el planeta Tierra a dicha lista? Es cierto que cuando se tienen lealtades múltiples, a veces los conflictos son inevitables. Pero ¿quién dijo que la vida es sencilla? Lidiemos con ella.
En siglos anteriores las identidades nacionales se forjaron porque los humanos se enfrentaban a problemas y posibilidades que se hallaban mucho más allá del ámbito de las tribus locales, y que solo la cooperación a la escala de todo el país podía esperar gestionar. En el siglo XXI, las naciones se encuentran en la misma situación que las antiguas tribus: ya no son el marco adecuado para afrontar los retos más importantes de la época. Necesitamos una nueva identidad global porque las instituciones nacionales son incapaces de gestionar un conjunto de dilemas globales sin precedentes. Ahora tenemos una ecología global, una economía global y una ciencia global, pero todavía estamos empantanados en políticas solo nacionales. Esta falta de encaje impide que el sistema político se enfrente de manera efectiva a nuestros principales problemas. Para que la política sea efectiva hemos de hacer una de dos cosas: desglobalizar la ecología, la economía y la ciencia, o globalizar nuestra política. Ya que es imposible desglobalizar la ecología y el progreso de la ciencia, y ya que el coste de desglobalizar la economía seguramente sería prohibitivo, la única solución real es globalizar la política. Esto no significa establecer un «gobierno global», una visión dudosa e irrealista, sino más bien que las dinámicas políticas internas de los países e incluso de las ciudades den mucha más relevancia a los problemas y los intereses globales. En la tarea, es improbable que los sentimientos nacionalistas ayuden mucho. Así pues, ¿quizá podamos confiar en que las tradiciones religiosas universales de la humanidad ayudarán a unir el mundo? Hace cientos de años, religiones como el cristianismo y el islamismo ya pensaban en términos globales en lugar de locales, y se mostraban muy interesadas en las grandes cuestiones de la vida en lugar de solo en las luchas políticas de esta o aquella nación. Pero ¿siguen siendo relevantes las religiones tradicionales? ¿Conservan el poder para dar forma al mundo, o son solo reliquias inertes de nuestro pasado, lanzadas aquí y allá por las poderosas fuerzas de los estados, las economías y las tecnologías modernos?
### 8
Religión
#### Dios sirve ahora a la nación
Hasta ahora, las ideologías modernas, los científicos expertos y los gobiernos nacionales no han conseguido dar forma a una perspectiva viable para el futuro de la humanidad. ¿Puede obtenerse tal visión de los profundos pozos de las tradiciones religiosas humanas? Quizá la respuesta ha estado esperándonos todo este tiempo entre las páginas de la Biblia, el Corán o los Vedas.
Es probable que los seglares reaccionen ante esta idea con menosprecio o aprensión. Las Sagradas Escrituras quizá fueran relevantes en la Edad Media, pero ¿cómo van a guiarnos en la era de la inteligencia artificial, la bioingeniería, el calentamiento global y la ciberguerra? Sin embargo, los seglares son una minoría. Miles de millones de humanos profesan todavía más fe en el Corán y en la Biblia que en la teoría de la evolución; los movimientos religiosos determinan la política de países tan diversos como la India, Turquía y Estados Unidos, y las hostilidades religiosas impulsan conflictos desde Nigeria hasta Filipinas.
Así pues, ¿cuán relevantes son religiones tales como el cristianismo, el islamismo y el hinduismo? ¿Pueden ayudarnos a resolver los principales problemas a que nos enfrentamos? Para comprender el papel de las religiones tradicionales en el mundo del siglo XXI, necesitamos distinguir entre tres tipos de problemas:
1.Problemas técnicos. Por ejemplo, ¿cómo pueden los agricultores de países áridos habérselas con sequías severas debidas al calentamiento global?
2.Problemas políticos. Por ejemplo, ¿qué medidas han de adoptar los gobiernos para evitar el calentamiento global en primer lugar?
3.Problemas de identidad. Por ejemplo, ¿debo preocuparme incluso de los problemas de los agricultores del otro lado del mundo, o solo de los problemas de la gente de mi propia tribu y mi propio país?
Como veremos en las páginas que siguen, las religiones tradicionales resultan en gran parte irrelevantes a la hora de enfrentarnos a los problemas técnicos y políticos. En cambio, son muy relevantes respecto a los de identidad, pero en la mayoría de los casos constituyen una parte importante del problema más que de una solución potencial.
##### PROBLEMAS TÉCNICOS: LA AGRICULTURA CRISTIANA
En tiempos premodernos, las religiones eran responsables de solucionar una amplia gama de problemas técnicos en ámbitos tan prosaicos como la agricultura. Calendarios divinos determinaban cuándo plantar y cosechar, mientras que rituales en el templo aseguraban la lluvia y protegían contra las plagas. Si se presentaba una crisis agrícola debido a una sequía o una plaga de langostas, los agricultores se dirigían a los sacerdotes para que intercedieran con los dioses. También la medicina fue víctima del ámbito religioso. Casi todos los profetas, gurús y chamanes hacían además de curanderos. Así, Jesús dedicó gran parte de su tiempo a curar a los enfermos, haciendo que los ciegos vieran, que los mudos hablaran y que los locos sanaran. Ya viviera uno en el antiguo Egipto o en la Europa medieval, si se encontraba enfermo era más probable que se dirigiera al santero que al médico y que peregrinara a un templo famoso más que a un hospital.
En épocas más recientes, biólogos y cirujanos han relevado a sacerdotes y milagreros. Si ahora una plaga de langostas amenaza Egipto, podría muy bien ocurrir que los egipcios soliciten la ayuda de Alá (¿por qué no?), pero no se olvidarán de llamar a los químicos, entomólogos y genetistas para que desarrollen plaguicidas más potentes y cepas de trigo resistentes a los insectos. Si el hijo de un hindú devoto padece un caso grave de sarampión, el padre dirigirá una plegaria a Dhanvantari y ofrecerá flores y dulces al templo local, pero solo después de haber llevado de urgencia al pequeño al hospital más cercano y haberlo confiado al cuidado de sus médicos. Incluso la enfermedad mental (el último bastión de los curanderos religiosos) está pasando poco a poco a manos de los científicos, al sustituir la neurología a la demonología y al suplantar el Prozac al exorcismo.
El triunfo de la ciencia ha sido tan rotundo que nuestra idea misma de la religión ha cambiado. Ya no asociamos la religión a la agricultura y a la medicina. Incluso muchos fanáticos padecen ahora amnesia colectiva y prefieren olvidar que las religiones tradicionales siempre reclamaban para sí estos ámbitos. «¿Y qué pasa si acudimos a los ingenieros y los médicos? —dicen los fanáticos—. Eso no demuestra nada. Para empezar, ¿qué tiene que ver la religión con la agricultura y la medicina?»
Las religiones tradicionales han perdido mucho terreno porque, para ser francos, simplemente no lo hacían muy bien en agricultura ni en atención sanitaria. La verdadera pericia de sacerdotes y gurús nunca fue atraer la lluvia, curar, profetizar o hacer magia. En cambio, siempre ha sido la interpretación. Un sacerdote no es alguien que sabe cómo bailar la danza de la lluvia y acabar con la sequía. Un sacerdote es alguien que sabe cómo justificar por qué la danza de la lluvia no funcionó y por qué hemos de seguir creyendo en nuestro dios, aunque parezca sordo a nuestras plegarias.
Pero es precisamente su talento para la interpretación lo que sitúa a los líderes religiosos en desventaja cuando compiten contra los científicos. Los científicos también saben tomar atajos y distorsionar la evidencia, pero al final, el signo de la ciencia es la disposición a admitir el fracaso y a intentar una aproximación diferente. Por eso los científicos aprenden poco a poco a producir mejores cosechas y a elaborar medicamentos mejores, mientras que sacerdotes y gurús solo aprenden a pergeñar excusas mejores. A lo largo de los siglos, incluso los verdaderos creyentes han notado esa diferencia, razón por la que la autoridad religiosa ha estado reduciéndose en cada vez más campos técnicos. Y es también la razón por la que todo el mundo se ha convertido cada vez más en una única civilización. Cuando las cosas funcionan de verdad, todos las adoptan.
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##### PROBLEMAS POLÍTICOS: LA ECONOMÍA MUSULMANA
La ciencia nos da respuestas claras a las cuestiones técnicas, como curar el sarampión, pero entre los científicos existe un considerable desacuerdo sobre las cuestiones políticas. Casi todos los científicos están de acuerdo en que el calentamiento global es un hecho, pero no existe consenso con relación a la reacción económica más conveniente ante tal amenaza. Eso no significa, sin embargo, que las religiones tradicionales puedan ayudarnos a resolver la cuestión. Las antiguas escrituras no son una buena guía para la economía moderna, y las principales brechas (por ejemplo, entre capitalistas y socialistas) no se corresponden con las divisiones entre las religiones tradicionales.
Es cierto que en países como Israel e Irán los rabinos y ayatolás tienen voz y voto directos en la política económica del gobierno, e incluso en países más seglares como Estados Unidos y Brasil, los líderes religiosos influyen sobre la opinión pública en cuestiones que van desde los impuestos hasta las normativas ambientales. Pero un análisis más detallado revela que en la mayoría de estos casos las religiones tradicionales desempeñan en realidad un papel secundario en relación con las teorías científicas modernas. Cuando el ayatolá Jamenei debe tomar una decisión crucial acerca de la economía iraní, no puede hallar la respuesta necesaria en el Corán, porque los árabes del siglo VII sabían muy poco de los problemas y las posibilidades de las economías industriales modernas y los mercados financieros globales. De modo que él, o sus ayudantes, han de acudir a Karl Marx, Milton Friedman, Friedrich Hayek y a la moderna ciencia de la economía para encontrar respuestas. Después de haberse convencido de aumentar las tasas de interés, reducir los impuestos, privatizar los monopolios del gobierno o firmar un acuerdo arancelario internacional, Jamenei puede entonces usar su conocimiento religioso y su autoridad para envolver la respuesta científica en los ropajes de tal o cual versículo del Corán, y presentarlo a las masas como la voluntad de Alá. Pero los ropajes poco importan. Cuando comparamos las políticas económicas del Irán chií, de la Arabia Saudí suní, del Israel judío, de la India hindú y de la América cristiana, sencillamente no vemos tanta diferencia.
Durante los siglos XIX y XX, los pensadores musulmanes, judíos, hindúes y cristianos despotricaron contra el materialismo moderno, contra el capitalismo desalmado y contra los excesos del estado burocrático. Prometieron que solo con que se les diera una oportunidad, resolverían todos los males de la modernidad y establecerían un sistema socioeconómico muy diferente, basado en los valores espirituales eternos de su fe. Bien, se les han dado unas cuantas oportunidades, y el único cambio perceptible que han hecho al edificio de las economías modernas es pintarlo de nuevo y colocar una enorme media luna, una cruz, una estrella de David o un «om» en el tejado.
Al igual que en el caso de propiciar la lluvia, cuando se trata de la economía, es la experiencia de los eruditos religiosos a la hora de reinterpretar textos, perfeccionada durante largo tiempo, la que vuelve la religión irrelevante. Da igual la política económica que elija Jamenei, siempre podrá adecuarla al Corán. De ahí que el Corán sea degradado de una fuente de verdadero conocimiento a una fuente de mera autoridad. Cuando uno se enfrenta a un dilema económico difícil, lee a Marx y a Hayek detenidamente, y ellos lo ayudan a entender mejor el sistema económico, a ver las cosas desde un nuevo ángulo y a pensar en soluciones posibles. Después de haber formulado una respuesta, entonces uno se dirige al Corán y lo lee con atención en busca de alguna sura que, interpretada con la suficiente imaginación, pueda justificar la solución que se obtuvo de Hayek o Marx. Con independencia de qué solución se encontró allí, si uno es un buen erudito en el Corán, siempre podrá justificarla.
Lo mismo vale para el cristianismo. Un cristiano puede ser tanto capitalista como socialista, y aunque algunas de las cosas que dijo Jesús suenan a comunismo total, durante la Guerra Fría buenos capitalistas norteamericanos seguían leyendo el Sermón de la Montaña sin apenas darse cuenta. Sencillamente, no existe una «economía cristiana», una «economía musulmana» o una «economía hindú».
Y no es que no haya ninguna idea económica en la Biblia, el Corán o los Vedas; lo que ocurre es que estas ideas no están actualizadas. La lectura que Mahatma Gandhi hizo de los Vedas llevó a que imaginara una India independiente como un conjunto de comunidades agrarias autosuficientes, cada una de las cuales tejía sus propias telas de _khadi_ , exportaba poco e importaba todavía menos. La fotografía más famosa de Gandhi lo muestra hilando algodón con sus propias manos: él hizo de la humilde rueca el símbolo del movimiento nacionalista indio.[1] Pero esta visión arcádica era sencillamente incompatible con las realidades de la economía moderna, razón por la cual no ha quedado mucho de ello, excepto la radiante imagen de Gandhi en miles de millones de billetes de rupias.
Las teorías económicas modernas son mucho más relevantes que los dogmas tradicionales, al punto de que es común interpretar conflictos claramente religiosos en términos económicos, mientras que nadie piensa en hacer lo contrario. Por ejemplo, hay quien aduce que los _Troubles_ en Irlanda del Norte entre católicos y protestantes surgieron en gran parte por los conflictos de clase. Debido a varios accidentes históricos, en Irlanda del Norte las clases altas eran principalmente protestantes y las clases bajas, principalmente católicas. De ahí que lo que a primera vista parece haber sido un conflicto teológico sobre la naturaleza de Cristo fuera en realidad una lucha típica entre pudientes y necesitados. En cambio, muy pocas personas afirmarían que los conflictos entre las guerrillas comunistas y los terratenientes capitalistas en Sudamérica en la década de 1970 no eran en realidad más que un pretexto para un desacuerdo mucho más profundo sobre la teología cristiana.
Así pues, ¿qué diferencia supondría la religión a la hora de enfrentarse a las grandes cuestiones del siglo XXI? Pongamos como ejemplo la cuestión de si conceder a la IA la autoridad para tomar decisiones acerca de la vida de la gente: que elija por nosotros qué estudiar, dónde trabajar y con quién casarnos. ¿Cuál es la posición musulmana sobre esta cuestión? ¿Cuál es la posición judía? Aquí no hay posiciones «musulmana» o «judía». Es probable que la humanidad se divida en dos bandos principales: los que estén a favor de conceder a la IA una autoridad importante y los que se opongan. Es probable que haya musulmanes y judíos en ambos, y que justifiquen la posición que adoptan con imaginativas interpretaciones del Corán y el Talmud.
Desde luego, los grupos religiosos podrían endurecer sus puntos de vista sobre temas concretos, y transformarlos en dogmas supuestamente sagrados y eternos. En la década de 1970, algunos teólogos latinoamericanos inventaron la teología de la liberación, que hizo que Jesús se pareciera un poco al Che Guevara. De forma similar, es fácil reclutar a Jesús para el debate sobre el cambio climático y hacer que las posiciones políticas actuales parezcan principios religiosos eternos.
Esto ya está empezando a suceder. La oposición a las normativas ambientales se incorpora a los sermones de fuego y alcrebite de algunos pastores evangélicos norteamericanos, mientras que el papa Francisco encabeza la carga contra el calentamiento global en nombre de Cristo (como atestigua su segunda encíclica, «Laudato si»).[2] De modo que quizá en 2070 con relación a las cuestiones ambientales supondrá una gran diferencia que uno sea evangélico o católico. Ni que decir tiene que los evangélicos pondrán objeciones a cualquier limitación a las emisiones de carbono, mientras que los católicos creerán que Jesús predicó que debemos proteger el medio ambiente.
Podremos apreciar las diferencias incluso en los coches que usarán. Los evangélicos conducirán enormes SUV trasegadores de gasolina, mientras que los católicos devotos se desplazarán en impecables coches eléctricos con un adhesivo en el parachoques que rezará: «¡Quema el planeta y quémate en el Infierno!». Sin embargo, aunque pueden citar varios pasajes bíblicos en defensa de sus posiciones, el origen real de su diferencia estará en las teorías científicas y en los movimientos políticos modernos, no en la Biblia. Desde esta perspectiva, la religión no puede en realidad contribuir mucho a los grandes debates políticos de nuestra época. Tal como dijo Karl Marx, es solo una fachada.
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##### PROBLEMAS DE IDENTIDAD: LAS LÍNEAS EN LA ARENA
Pero Marx exageraba cuando rechazaba la religión como una mera superestructura que ocultaba poderosas fuerzas tecnológicas y económicas. Aunque el islamismo, el hinduismo y el cristianismo sean decoraciones de vivos colores sobre una estructura económica moderna, la gente suele identificarse con el decorado, y las identidades de la gente constituyen una fuerza histórica crucial. El poder humano depende de la cooperación de las masas, la cooperación de las masas depende de fabricar identidades de las masas, y todas las identidades de las masas se basan en relatos de ficción, no en hechos científicos, ni siquiera en necesidades económicas. En el siglo XXI, la división de los humanos en judíos y musulmanes o en rusos y polacos depende todavía de mitos religiosos. Los intentos de los nazis y los comunistas para determinar de manera científica las identidades humanas de raza y clase demostraron ser una pseudociencia peligrosa, y desde entonces los científicos han sido muy reacios a colaborar en la definición de cualesquiera identidades «naturales» respecto a los seres humanos.
De modo que en el siglo XXI las religiones no atraen la lluvia, no curan enfermedades, no fabrican bombas, pero sí determinan quiénes somos «nosotros» y quiénes son «ellos», a quién debemos curar y a quién bombardear. Como se ha indicado ya, en términos prácticos hay poquísimas diferencias entre el Irán chií, la Arabia Saudí suní y el Israel judío. Todos son estados nación burocráticos, todos siguen políticas más o menos capitalistas, todos vacunan a los niños contra la poliomielitis, y todos confían en químicos y físicos para la fabricación de bombas. No existe una burocracia chií, un capitalismo suní o una física judía. Así pues, ¿cómo hacer que la gente se sienta única, y sea leal a una tribu humana y hostil a otra?
A fin de trazar líneas firmes en las arenas cambiantes de la humanidad, la religión usa ritos, rituales y ceremonias. Chiíes, suníes y judíos ortodoxos llevan ropas diferentes, cantan plegarias diferentes y observan tabúes diferentes. Estas tradiciones religiosas diversas suelen llenar la cotidianidad con belleza y animan a la gente a comportarse de manera más amable y caritativa. Cinco veces al día, la voz melodiosa del almuédano se eleva sobre el ruido de bazares, oficinas y fábricas, y llama a los musulmanes a que hagan una pausa del ajetreo de las actividades mundanas e intenten conectar con una verdad eterna. Sus vecinos hindúes pueden alcanzar el mismo objetivo con ayuda de puyás diarias y recitado de mantras. Todas las semanas, los viernes por la noche, las familias judías se sientan a la mesa para disfrutar de una comida especial de alegría, acción de gracias y solidaridad. Dos días después, el domingo por la mañana, los coros cristianos de góspel aportan esperanza a la vida de millones de personas, con lo que ayudan a forjar vínculos comunitarios de confianza y afecto.
Otras tradiciones religiosas llenan el mundo de enorme fealdad y hacen que la gente se comporte de manera miserable y cruel. Por ejemplo, poco hay que decir en favor de la misoginia o de la discriminación de castas, inspiradas por la religión. Pero ya sean hermosas o feas, todas estas tradiciones religiosas unen a determinadas personas al tiempo que las diferencian de sus vecinos. Vistas desde fuera, las tradiciones religiosas que dividen a la gente suelen parecer insignificantes, y Freud ridiculizó la obsesión que las personas tienen sobre estas cuestiones llamándola «el narcisismo de las pequeñas diferencias».[3] Pero en historia y en política, las pequeñas diferencias pueden tener un recorrido muy largo. Así, el hecho de ser gay o lesbiana supone literalmente una cuestión de vida o muerte si uno vive en Israel, Irán o Arabia Saudí. En Israel, la comunidad LGBT goza de la protección de la ley, e incluso hay algunos rabinos que bendecirían el matrimonio entre dos mujeres. En Irán, gais y lesbianas son perseguidos de forma sistemática y en ocasiones incluso ejecutados. En Arabia Saudí, una lesbiana ni siquiera podía conducir un automóvil hasta 2018 solo por ser una mujer, no importaba que fuera lesbiana.
Quizá el mejor ejemplo del poder y la importancia continuados de las religiones tradicionales en el mundo moderno proceda de Japón. En 1853, una flota norteamericana obligó a Japón a abrirse al mundo moderno. En respuesta, el Estado japonés se embarcó en un proceso rápido y muy exitoso de modernización. Al cabo de pocas décadas, se convirtió en un poderoso Estado burocrático que se basó en la ciencia, el capitalismo y la tecnología militar más puntera para derrotar a China y a Rusia, ocupar Taiwán y Corea, y por último hundir la flota estadounidense en Pearl Harbor y destruir los imperios europeos del Lejano Oriente. Pero Japón no copió a ciegas el programa occidental. Estaba rotundamente decidido a proteger su identidad única y a asegurar que los japoneses modernos fueran leales a Japón y no a la ciencia, a la modernidad o a alguna nebulosa comunidad global.
A tal fin mantuvo la religión nativa del sintoísmo como piedra angular de la identidad japonesa. En realidad, el Estado japonés reinventó el sintoísmo. El sintoísmo tradicional era una mezcla de creencias animistas en diversas deidades, espíritus y fantasmas, y cada aldea y templo tenía sus propios espíritus favoritos y costumbres locales. A finales del siglo XIX y principios del XX, Japón creó una versión oficial del sintoísmo, mientras disuadía a sus súbditos de seguir muchas tradiciones locales. Este «sintoísmo de Estado» se fusionó con ideas muy modernas de nacionalidad y raza, que la élite tomó prestadas de los imperialistas europeos. Cualquier elemento en el budismo, el confucianismo y los valores feudales de los samuráis que pudiera ayudar a cimentar la lealtad al país se añadió a la mezcla. Para rematarlo, el sintoísmo de Estado consagró como su principio supremo la adoración al emperador japonés, considerado descendiente directo de la diosa solar Amaterasu, y él mismo no menos que un dios viviente.[4]
A simple vista, este extraño brebaje de lo viejo y lo nuevo parecía una elección muy inapropiada para un Estado que se embarcaba en un curso acelerado de modernización. ¿Un dios viviente? ¿Espíritus animistas? ¿Valores feudales? Sonaba más a un caciquismo neolítico que a una moderna potencia industrial.
Pero funcionó como por arte de magia. Los japoneses se modernizaron a un ritmo impresionante al tiempo que desarrollaron una lealtad fanática a su país. El símbolo mejor conocido del éxito del sintoísmo de Estado es el hecho de que Japón fue la primera potencia en desarrollar y usar misiles guiados con precisión. Décadas antes de que Estados Unidos sacara la bomba inteligente, y en una época en que la Alemania nazi estaba empezando apenas a desplegar los tontos cohetes V-2, Japón hundió docenas de buques aliados con misiles guiados con precisión. Conocemos estos misiles como «kamikazes». Mientras que en las municiones guiadas con precisión actuales la guía la dan los ordenadores, los kamikazes eran aviones ordinarios cargados de explosivos y guiados por pilotos humanos que deseaban participar en misiones de solo ida. Esta disposición era el producto del espíritu de sacrificio que desafiaba a la muerte cultivado por el sintoísmo de Estado. Así, los kamikazes se basaban en la combinación de la tecnología más avanzada con el adoctrinamiento religioso más avanzado.[5]
A sabiendas o no, en la actualidad numerosos gobiernos siguen el ejemplo japonés. Adoptan las herramientas y estructuras universales de modernidad al tiempo que se basan en religiones tradicionales para preservar una identidad nacional única. El papel del sintoísmo de Estado en Japón lo cumplen en un grado mayor o menor el cristianismo ortodoxo en Rusia, el catolicismo en Polonia, el islamismo chií en Irán, el wahabismo en Arabia Saudí y el judaísmo en Israel. Da igual lo arcaica que una religión parezca: con un poco de imaginación y reinterpretación casi siempre puede casarse con los últimos artilugios tecnológicos y las instituciones modernas más sofisticadas.
En algunos casos, los estados podrían crear una religión completamente nueva para reafirmar su identidad única. El ejemplo más extremo lo tenemos en la actualidad en Corea del Norte, antigua colonia de Japón. El régimen norcoreano adoctrina a sus súbditos con una religión de Estado fanática denominada «juche». Consiste en una mezcla de marxismo-leninismo, algunas tradiciones coreanas antiguas, una creencia racista en la pureza única de la raza coreana y la deificación del linaje familiar de Kim Il-sung. Aunque nadie afirma que los Kim sean descendientes de una diosa solar, son venerados con más fervor que casi cualquier dios en la historia. Quizá, a sabiendas de cómo el Imperio japonés acabó siendo derrotado, el juche norcoreano insistió también durante mucho tiempo en añadir armas nucleares a la mezcla, representando su desarrollo como un deber sagrado digno de sacrificios supremos.[6]
##### LA SIRVIENTA DEL NACIONALISMO
De ahí que, comoquiera que se desarrolle la tecnología, cabe esperar que los debates acerca de las identidades y los rituales religiosos continúen influyendo en el uso de las nuevas tecnologías, y que vayan a seguir teniendo el poder de incendiar el mundo. Los misiles nucleares más modernos y las ciberbombas podrían emplearse para zanjar una discusión doctrinal acerca de textos medievales. Religiones, ritos y rituales continuarán siendo importantes mientras el poder de la humanidad resida en la cooperación de las masas y mientras la cooperación de las masas resida en la creencia en ficciones compartidas.
Por desgracia, todo esto hace en realidad que las religiones tradicionales sean parte del problema de la humanidad, no del remedio. Las religiones ejercen todavía un gran poder político, puesto que pueden cimentar identidades nacionales e incluso desatar la Tercera Guerra Mundial. Pero cuando se trata de resolver los problemas globales del siglo XXI, y no de avivarlos, no parecen aportar mucho. Aunque numerosas religiones tradicionales promueven valores universales y afirman una validez cósmica, en la actualidad se usan sobre todo a modo de sirvienta del nacionalismo moderno, ya sea en Corea del Norte, en Rusia, Irán o Israel. Por tanto, hacen que sea todavía más difícil trascender las diferencias nacionales y encontrar una solución global a las amenazas de la guerra nuclear, el colapso ecológico y la alteración o disrupción tecnológica.
Así, cuando tratan del calentamiento global o de la proliferación nuclear, los clérigos chiíes animan a los iraníes a ver tales problemas desde una perspectiva iraní estricta, los rabinos israelíes inspiran a los israelíes a preocuparse sobre todo de lo que es bueno para Israel, y los sacerdotes ortodoxos instan a los rusos a anteponer los intereses rusos. Al fin y al cabo, somos la nación elegida por Dios, de manera que lo que es bueno para nuestra nación también es satisfactoria para Dios. Sin duda, hay sabios religiosos que rechazan los excesos nacionalistas y adoptan visiones mucho más universales. Lamentablemente, tales sabios no ostentan en la actualidad un gran poder político.
Así pues, estamos atrapados entre la espada y la pared. La humanidad constituye en la actualidad una única civilización, y problemas como la guerra nuclear, el colapso ecológico y la disrupción tecnológica solo pueden resolverse a nivel global. Por otro lado, el nacionalismo y la religión dividen todavía a nuestra civilización humana en campos diferentes y a menudo hostiles. Esta colisión entre problemas globales e identidades locales se manifiesta en la crisis actual que está sufriendo el mayor experimento multicultural del mundo: la Unión Europea. Erigida sobre la promesa de valores liberales universales, la Unión Europea se tambalea al borde de la desintegración debido a las dificultades de la integración y la inmigración.
### 9
Inmigración
#### Algunas culturas podrían ser mejores que otras
Aunque la globalización ha reducido muchísimo las diferencias culturales en todo el planeta, a la vez ha hecho que sea más fácil toparse con extranjeros y que nos sintamos molestos por sus rarezas. La diferencia entre la Inglaterra anglosajona y el Imperio Pala indio era mucho mayor que la diferencia entre la moderna Gran Bretaña y la India moderna, pero British Airways no ofrecía vuelos directos entre Delhi y Londres en los días del rey Alfredo el Grande.
A medida que cada vez más humanos cruzan cada vez más fronteras en busca de trabajo, seguridad y un futuro mejor, la necesidad de enfrentarse, de asimilar o de expulsar a extranjeros pone en tensión los sistemas políticos y las identidades colectivas que se crearon en épocas menos fluidas. En ningún lugar es más agudo el problema que en Europa. La Unión Europea se construyó sobre la promesa de trascender las diferencias culturales entre franceses, alemanes, españoles y griegos. Podría desmoronarse debido a su incapacidad para contener las diferencias culturales entre europeos y emigrantes de África y Oriente Próximo. Irónicamente, el gran éxito de Europa en la creación de un sistema multicultural próspero es lo que ha atraído a tantos emigrantes en primer lugar. Los sirios prefieren emigrar a Alemania antes que a Arabia Saudí, Irán, Rusia o Japón, no porque Alemania esté más cerca o sea más rica que los demás destinos potenciales, sino porque Alemania tiene un historial mucho mejor a la hora de recibir de buena manera y asimilar a los inmigrantes.
La creciente oleada de refugiados e inmigrantes produce reacciones contradictorias en los europeos y provoca ásperos debates sobre la identidad y el futuro de Europa. Algunos europeos exigen que Europa cierre de golpe sus puertas: ¿están traicionando los ideales multiculturales y tolerantes de Europa, o simplemente dando los pasos sensatos para evitar el desastre? Otros claman para que se abran más las puertas: ¿son fieles a los valores europeos fundamentales, o son culpables de endilgar al proyecto europeo expectativas imposibles? Esta discusión sobre la inmigración suele degenerar en una pelea a gritos en la que ninguna parte escucha a la otra. Para clarificar las cosas, quizá ayude contemplar la inmigración como un pacto con tres condiciones o términos básicos:
TÉRMINO 1.El país anfitrión permite la entrada de inmigrantes en su territorio.
TÉRMINO 2.A cambio, los inmigrantes deben adoptar al menos las normas y los valores fundamentales del país anfitrión, aunque ello implique abandonar algunas de sus normas y valores tradicionales.
TÉRMINO 3.Si los inmigrantes se asimilan hasta cierto grado, con el tiempo se convierten en miembros iguales y completos del país anfitrión. «Ellos» se transforman en «nosotros».
Estos tres términos dan origen a tres debates sobre el significado exacto de cada término. Un cuarto debate concierne al cumplimiento de los términos. Cuando la gente habla de inmigración, suele confundir los cuatro debates, de modo que nadie entiende de qué va en verdad la discusión. Por tanto, es mejor considerar cada uno de dichos debates por separado.
DEBATE 1. La primera cláusula del pacto de inmigración reza simplemente que el país anfitrión permite la entrada de inmigrantes. Pero ¿debe esto considerarse un deber o un favor? ¿Está obligado el país anfitrión a abrir sus puertas a todo el mundo, o tiene el derecho de seleccionar, e incluso de detener totalmente la inmigración? Los proinmigracionistas parecen pensar que los países tienen el deber moral de aceptar no solo a refugiados, sino también a personas de países azotados por la pobreza que buscan trabajo y un futuro mejor. En especial en un mundo globalizado, todos los humanos tienen obligaciones morales hacia los demás humanos, y quienes las eluden son egoístas o incluso racistas.
Además, muchos proinmigracionistas señalan que es imposible frenar completamente la inmigración, y que no importa cuántos muros y vallas erijamos, pues la gente desesperada siempre encontrará una manera de entrar. De modo que es mejor legalizar la inmigración y tratar con ella abiertamente que crear un enorme submundo de tráfico humano, trabajadores ilegales y niños sin papeles.
Los antiinmigracionistas replican que, usando la fuerza suficiente, puede detenerse por completo la inmigración, y excepto quizá en el caso de refugiados que huyen de una persecución brutal en un país vecino, no estamos obligados a abrir nuestras puertas. Turquía puede tener el deber moral de permitir que los desesperados refugiados sirios crucen su frontera. Pero si después dichos refugiados intentan desplazarse a Suecia, los suecos no están obligados a aceptarlos. En cuanto a los migrantes que buscan trabajo y beneficios sociales, depende totalmente del país anfitrión decidir si los quiere o no, y en qué condiciones.
Los antiinmigracionistas destacan que uno de los derechos más básicos de cada colectivo humano es defenderse contra la invasión, en forma ya sea de ejércitos, ya sea de migrantes. Los suecos han trabajado con mucho ahínco y han hecho numerosos sacrificios para crear una democracia liberal próspera, y si los sirios no han conseguido hacer lo mismo, no es culpa de los suecos. Si los votantes suecos no quieren que entren más inmigrantes sirios en su país, por la razón que sea, están en su derecho de negarles la entrada. Y si aceptan a algunos inmigrantes, debería quedar muy claro que es un favor que Suecia ofrece y no una obligación que cumple. Lo que significa que los inmigrantes a quienes se permita entrar en Suecia tienen que sentirse muy agradecidos por aquello que obtengan, en lugar de llegar con una lista de peticiones como si fueran los dueños del lugar.
Además, dicen los antiinmigracionistas, un país puede tener la política de inmigración que quiera, y evaluar a los inmigrantes no solo por sus antecedentes penales o talentos profesionales, sino incluso por cosas como la religión. Tal vez parezca desagradable que un país como Israel solo quiera permitir la entrada en él de judíos y uno como Polonia solo acceda a asumir refugiados de Oriente Próximo a condición de que sean cristianos, pero está perfectamente en consonancia con los derechos de los votantes israelíes y polacos.
Lo que complica las cosas es que en muchos casos la gente quiere nadar y guardar la ropa. Numerosos países hacen la vista gorda ante la inmigración ilegal, o incluso aceptan a trabajadores extranjeros por un tiempo, porque quieren beneficiarse de la energía, el talento y el trabajo barato de estos. Sin embargo, los países rehúsan después legalizar las condiciones de estas personas, alegando que no quieren la inmigración. A la larga, esto podría crear sociedades jerárquicas en las que una clase alta de ciudadanos con pleno derecho explota a una subclase de extranjeros impotentes, como ocurre en la actualidad en Catar y en otros estados del golfo Pérsico.
Mientras este debate no se zanje, es dificilísimo responder a todas las preguntas que conlleva la inmigración. Puesto que los proinmigracionistas piensan que la gente tiene derecho a inmigrar a otro país si así lo desea y los países anfitriones el deber de acogerlos, reaccionan con indignación moral cuando se viola el derecho de la gente a inmigrar y cuando hay países que no consiguen cumplir con su deber de acogida. Los antiinmigracionistas se quedan anonadados ante estas ideas. Consideran que la inmigración es un privilegio, y la acogida un favor. ¿Por qué acusar a la gente de ser racistas o fascistas solo porque rechacen la entrada en su propio país?
Desde luego, incluso si permitir la entrada de inmigrantes es un favor y no un deber, una vez que los inmigrantes se establecen, el país anfitrión contrae poco a poco numerosos deberes para con ellos y sus descendientes. Así, no podemos justificar el antisemitismo en el Estados Unidos actual aduciendo que «le hicimos un favor a tu bisabuela dejándola entrar en este país en 1910, de manera que ahora podemos trataros como nos plazca».
DEBATE 2. La segunda cláusula del pacto de la inmigración dice que si se les deja entrar, los inmigrantes tienen la obligación de integrarse en la cultura local. Pero ¿hasta dónde ha de llegar la integración? Si los inmigrantes pasan de una sociedad patriarcal a una liberal, ¿tienen que hacerse feministas? Si proceden de una sociedad profundamente religiosa, ¿es necesario que adopten una visión laica del mundo? ¿Deberían abandonar sus códigos tradicionales de vestimenta y sus tabúes alimentarios? Los antiinmigracionistas tienden a situar el listón alto, mientras que los proinmigracionistas lo colocan mucho más bajo.
Los proinmigracionistas aducen que la misma Europa es muy diversa, y que sus poblaciones nativas cuentan con un amplio espectro de opiniones, hábitos y valores. Esto es precisamente lo que hace que Europa sea dinámica y fuerte. ¿Por qué habría de obligarse a los inmigrantes a plegarse a alguna identidad europea imaginaria respecto a la cual pocos europeos están realmente a la altura? ¿Acaso quiere obligarse a los inmigrantes musulmanes del Reino Unido a convertirse en cristianos, cuando muchos ciudadanos británicos apenas pisan la iglesia? ¿Queremos pedir a los inmigrantes del Punjab que abandonen su curry y su masala en favor de la fritura de pescado con patatas y del pudin de Yorkshire? Si Europa posee algunos valores fundamentales reales, son los valores liberales de la tolerancia y la libertad, que implican que los europeos deben mostrar tolerancia también hacia los inmigrantes, y concederles tanta libertad como sea posible para que sigan sus propias tradiciones, siempre que estas no perjudiquen las libertades y los derechos de otras personas.
Los antiinmigracionistas están de acuerdo en que la tolerancia y la libertad son los valores europeos más importantes, y acusan a muchos grupos inmigrantes, sobre todo procedentes de países musulmanes, de intolerancia, misoginia, homofobia y antisemitismo. Justo porque Europa valora la tolerancia, no puede permitir demasiadas personas intolerantes en su seno. Mientras que una sociedad tolerante puede gestionar pequeñas minorías iliberales, si el número de tales extremistas excede un determinado umbral, la naturaleza de la sociedad al completo cambia. Si Europa admite la entrada de demasiados inmigrantes de Oriente Próximo, terminará pareciendo Oriente Próximo.
Otros antiinmigracionistas van mucho más allá. Afirman que una comunidad nacional es mucho más que un conjunto de personas que se toleran mutuamente. De ahí que no baste con que los inmigrantes se adhieran a los estándares europeos de tolerancia. Tienen que adoptar también muchas de las características únicas de la cultura británica, alemana o sueca, cualesquiera que sean estas. Al permitirles entrar, la cultura local asume un gran riesgo y un gasto enorme. No hay razón para que también se destruya. Al final brinda una igualdad completa, de modo que exige una integración completa. Si los inmigrantes tienen algún problema con determinadas peculiaridades de la cultura británica, alemana o sueca, se verá con buenos ojos que se vayan a otra parte.
Las dos cuestiones clave de este debate son la discrepancia acerca de la intolerancia de los inmigrantes y la discrepancia acerca de la identidad europea. Si los inmigrantes son en realidad culpables de una intolerancia incurable, muchos europeos liberales que ahora están a favor de la inmigración tarde o temprano se opondrán a ella de manera vehemente. Y, al contrario, si la mayoría de los inmigrantes demuestran ser liberales y tolerantes en su actitud hacia la religión, el género y la política, esto dará al traste con algunos de los argumentos más efectivos contra la inmigración.
Sin embargo, todavía dejará abierta la cuestión de las identidades nacionales únicas de Europa. La tolerancia es un valor universal. ¿Acaso existen normas y valores franceses únicos que debería aceptar quien inmigrara a Francia, y acaso hay normas y valores daneses únicos que los inmigrantes a Dinamarca han de adoptar? Mientras los europeos estén irreconciliablemente divididos respecto a esta cuestión, apenas tendrán una política clara de la inmigración. Y al revés, una vez que los europeos sepan quienes son millones de europeos no deberían tener ninguna dificultad en acoger a varios millones de refugiados... o en prohibirles la entrada.
DEBATE 3. La tercera cláusula del pacto de la inmigración dice que si los inmigrantes hacen de verdad un esfuerzo sincero por integrarse (y en particular por adoptar el valor de la tolerancia), el país anfitrión está obligado a tratarlos como ciudadanos de primera. Pero ¿cuánto tiempo ha de pasar antes de que los inmigrantes se conviertan en miembros de pleno derecho de la sociedad? ¿Deben sentirse agraviados los inmigrantes de primera generación procedentes de Argelia si todavía no se les ve del todo como franceses después de veinte años en el país? ¿Y qué hay de los inmigrantes de tercera generación cuyos abuelos llegaron a Francia en la década de 1970?
Los proinmigracionistas suelen pedir una pronta aceptación, mientras que los antiinmigracionistas quieren un período probatorio mucho más prolongado. Para los proinmigracionistas, si los inmigrantes de tercera generación no son vistos y tratados como ciudadanos iguales, esto significa que el país anfitrión no está cumpliendo sus obligaciones, y si ello provoca tensiones, hostilidad e incluso violencia, el país anfitrión no puede culpar a nadie de su propia intolerancia. Para los antiinmigracionistas, estas expectativas excesivas constituyen una parte fundamental del problema. Los inmigrantes han de ser pacientes. Si tus abuelos llegaron aquí hace solo cuarenta años y ahora tú estás participando en algaradas callejeras porque piensas que no se te trata como a un nativo, entonces no has superado la prueba.
La cuestión clave de este debate se refiere a la brecha entre la escala temporal personal y la escala temporal colectiva. Desde el punto de vista de los colectivos humanos, cuarenta años es un período corto. No puede esperarse que la sociedad asimile completamente a grupos extranjeros en cuestión de unas pocas décadas. En las civilizaciones del pasado que asimilaron a extranjeros y los hicieron ciudadanos de pleno derecho (como la Roma Imperial, el califato musulmán, los imperios chinos y Estados Unidos), se tardó siglos y no décadas en conseguir la transformación.
Pero desde un punto de vista personal, cuarenta años pueden ser una eternidad. Para una adolescente nacida en Francia veinte años después de que sus abuelos inmigraran allí, el viaje desde Argel a Marsella es historia antigua. Ella nació aquí, todos sus amigos nacieron aquí, habla francés en lugar de árabe y nunca ha estado en Argelia. Francia es el único hogar que ha conocido. ¿Y ahora la gente le dice que Francia no es su hogar y que tiene que «volver» a un lugar donde nunca vivió?
Es como si tomáramos una semilla de un eucalipto de Australia y la plantáramos en Francia. Desde una perspectiva ecológica, los eucaliptos son una especie invasora, y pasarán generaciones antes de que los botánicos los reclasifiquen como plantas europeas nativas. Pero desde el punto de vista del árbol individual, es francés. Si no se lo riega con agua francesa, morirá. Si se intenta desarraigarlo, se descubrirá que ha arraigado profundamente en suelo francés, igual que las encinas y los pinos locales.
DEBATE 4. Además de estos desacuerdos en relación con la definición exacta del pacto de inmigración, la pregunta clave es si el pacto funciona de verdad. ¿Están ambas partes a la altura de sus obligaciones?
Los antiinmigracionistas suelen aducir que los inmigrantes no cumplen el término 2. No hacen un esfuerzo sincero por integrarse y muchos de ellos siguen aferrados a visiones del mundo intolerantes y prejuiciosas. De ahí que el país anfitrión no tenga motivo para cumplir el término 3 (tratarlos como ciudadanos de primera) y sí tenga todos los motivos para reconsiderar el término 1 (permitirles la entrada). Si personas de una determinada cultura han demostrado de manera fehaciente que están poco dispuestos a cumplir el pacto de la inmigración, ¿por qué permitir que entren más de ellas y crear un problema todavía mayor?
Los proinmigracionistas replican que es el país anfitrión el que no cumple con su parte del pacto. A pesar de los esfuerzos honestos de la enorme mayoría de los inmigrantes para integrarse, los anfitriones les dificultan conseguirlo y, peor todavía, aquellos inmigrantes que se integran con éxito siguen siendo tratados como ciudadanos de segunda, incluso en la segunda y la tercera generaciones. Desde luego, es posible que ambas partes no estén a la altura de sus compromisos, con lo que promueven las sospechas y los resentimientos de la otra parte en lo que se convierte en un círculo vicioso creciente.
Este cuarto debate no puede resolverse antes de dar la definición exacta de los tres términos. Mientras no sepamos si la integración es un deber o un favor, qué nivel de integración se exige a los inmigrantes y con qué rapidez los países anfitriones deben tratarlos como ciudadanos de pleno derecho, no podremos juzgar si las dos partes cumplen con sus obligaciones. Hay un problema adicional en la contabilidad. Cuando se evalúa el pacto de inmigración, ambas partes conceden mucho más peso a las infracciones que al cumplimiento. Si un millón de inmigrantes son ciudadanos respetuosos de las leyes, pero cien se unen a grupos terroristas y atacan al país anfitrión, ¿significa eso que en su conjunto los inmigrantes cumplen los términos del acuerdo o que los violan? Si una inmigrante de tercera generación pasea por la calle mil veces sin que se la moleste, pero en alguna ocasión algún racista la insulta a gritos, ¿significa eso que la población nativa acepta o rechaza a los inmigrantes?
Pero subyacente a todos estos debates acecha una cuestión mucho más fundamental, que concierne a nuestra visión de la cultura humana. ¿Participamos en el debate de la inmigración desde el supuesto de que todas las culturas son intrínsecamente iguales, o pensamos que algunas culturas podrían ser superiores a otras? Cuando los alemanes discuten acerca de asimilar a un millón de refugiados sirios, ¿se los puede justificar porque piensen que la cultura alemana es en algún aspecto mejor que la siria?
##### DEL RACISMO AL CULTURISMO(1)
Hace un siglo, los europeos daban por sentado que algunas razas (en especial, la raza blanca) eran intrínsecamente superiores a otras. Después de 1945, estas ideas se convirtieron cada vez más en anatema. El racismo se veía no solo como algo pésimo desde el punto de vista moral, sino que también estaba desacreditado desde el científico. Los científicos de la vida, y en particular los genetistas, han dado pruebas científicas muy sólidas de que las diferencias biológicas entre europeos, africanos, chinos y norteamericanos nativos son nimias.
Sin embargo, al mismo tiempo, antropólogos, sociólogos, historiadores, economistas del comportamiento e incluso neurocientíficos han acumulado gran cantidad de datos de la existencia de diferencias importantes entre las culturas humanas. De hecho, si todas las culturas humanas fueran en esencia la misma, ¿por qué necesitaríamos a antropólogos y a historiadores? ¿Por qué invertir recursos en el estudio de las diferencias triviales? Como mínimo, tendríamos que dejar de financiar todas estas costosas expediciones de campo al Pacífico Sur y al desierto del Kalahari, y contentarnos con estudiar a la gente de Oxford o Boston. Si las diferencias culturales son insignificantes, entonces aquello que descubramos acerca de los estudiantes de Harvard también tiene que ser cierto para los cazadores-recolectores del Kalahari.
Cuando reflexiona, la mayoría de la gente admite la existencia de al menos algunas diferencias importantes entre las culturas humanas, en aspectos que van desde las costumbres sexuales hasta los hábitos políticos. ¿Cómo abordar entonces tales diferencias? Los relativistas culturales dicen que la diferencia no implica jerarquía, y que nunca hemos de preferir una cultura a otra. Los humanos pueden pensar y comportarse de maneras diversas, pero debemos celebrar dicha diversidad y conceder igual valor a todas las creencias y prácticas. Por desgracia, estas actitudes abiertas de miras no soportan el peso de la realidad. La diversidad humana puede ser grande en lo que a la cocina y a la poesía se refiere, pero pocos considerarán la quema de brujas, el infanticidio o la esclavitud como idiosincrasias humanas fascinantes que deban protegerse de las intrusiones del capitalismo global y del coca-colonialismo.
O bien pensemos en la manera en que las diferentes culturas se relacionan con los extranjeros, los inmigrantes y los refugiados. No todas las culturas se caracterizan por el mismo nivel de aceptación. La cultura alemana a principios del siglo XXI es más tolerante con los extranjeros y está más dispuesta a acoger a inmigrantes que la cultura saudí. Es mucho más fácil para un musulmán inmigrar en Alemania que para un cristiano inmigrar en Arabia Saudí. De hecho, incluso a un refugiado musulmán procedente de Siria probablemente le sea más fácil inmigrar en Alemania que en Arabia Saudí, y desde 2011 Alemania ha acogido a más refugiados sirios de los que han sido aceptados por Arabia Saudí.[1] De manera similar, el peso de la evidencia sugiere que la cultura de California a principios del siglo XXI es más favorable para los inmigrantes que la cultura de Japón. De ahí que si el lector cree que es bueno tolerar a los extranjeros y dar la bienvenida a inmigrantes, ¿debería pensar también que, al menos en este aspecto, la cultura alemana es superior a la saudí y la cultura californiana es mejor que la japonesa?
Además, aunque dos normas culturales sean igualmente válidas en la teoría, en el contexto práctico de la inmigración todavía podría estar justificado pensar que la cultura anfitriona es mejor. Las normas y los valores que sirven en un país simplemente no funcionan bien en circunstancias diferentes. Observemos con detenimiento un ejemplo concreto. A fin de no ser presa de los prejuicios bien arraigados, imaginemos dos países ficticios: Friolandia y Calidostán. Los dos países tienen muchas diferencias culturales, entre las cuales figura su actitud hacia las relaciones humanas y el conflicto interpersonal. A los friolandeses los educan desde la infancia para que si entran en conflicto con alguien en la escuela, el trabajo o incluso la propia familia, lo mejor es que se contengan. Hay que evitar gritar, expresar rabia o enfrentarse a la otra persona: los arrebatos de ira no hacen más que empeorar las cosas. Es mejor trabajarse los propios sentimientos, al tiempo que se deja que las cosas se calmen. Mientras tanto, debe limitarse el contacto con la persona en cuestión, y si el contacto es inevitable, hay que ser lacónico pero educado, y evitar cuestiones candentes.
A los calidostanos, en cambio, los educan desde la infancia para que externalicen los conflictos. Si nos hallamos en un conflicto, no hay que dejar que se acumule ni reprimir nada. Hay que aprovechar la primera oportunidad para ventilar abiertamente nuestras emociones. Está bien enfadarse, gritar y decirle a la otra persona exactamente cómo nos sentimos. Es la única manera de resolver a la vez las cosas, de forma honesta y directa. Con un día de gritos puede resolverse un conflicto que, de otro modo, tal vez se encone durante años y aunque la confrontación directa nunca es agradable, después todos nos sentiremos mucho mejor.
Ambos métodos tienen sus pros y sus contras, y es difícil decir cuál es mejor. ¿Qué puede ocurrir, sin embargo, cuando un calidostano inmigra en Friolandia y consigue trabajo en una empresa friolandesa?
Cada vez que surge un conflicto con un compañero de trabajo, el calidostano da un puñetazo en la mesa y grita a voz en cuello, esperando que esto centre la atención en el problema y ayude a resolverlo enseguida. Varios años más tarde queda vacante un puesto importante. Aunque el calidostano reúne todas las cualificaciones necesarias, la jefa prefiere promover a un empleado friolandés. Cuando se le pregunta la razón, la jefa explica: «Sí, el calidostano tiene muchas cualidades, pero también un grave problema con las relaciones humanas. Es exaltado, crea tensiones innecesarias a su alrededor y perturba nuestra cultura empresarial». La misma suerte corren otros inmigrantes calidostanos en Friolandia. La mayoría de ellos permanecen en puestos secundarios o no consiguen encontrar trabajo, porque los gerentes presuponen que si son calidostanos, probablemente serían empleados de temperamento sanguíneo y problemáticos. Puesto que los calidostanos nunca llegan a ocupar puestos de responsabilidad, es difícil que cambien la cultura empresarial friolandesa.
Les ocurre algo muy parecido a los friolandeses que inmigran a Calidostán. Un friolandés que empiece a trabajar en una empresa calidostana adquiere pronto la reputación de arrogante o antipático, y hace pocos amigos, o ninguno. La gente piensa que no es sincero, o que carece de las habilidades básicas para las relaciones humanas. Nunca progresa hasta ocupar puestos de responsabilidad y, por tanto, jamás tiene la oportunidad de cambiar la cultura empresarial. Los directores calidostanos concluyen que la mayoría de los friolandeses son ariscos o tímidos, y prefieren no contratarlos para trabajos que requieran el contacto con los clientes o la cooperación estrecha con otros empleados.
Ambos podrían parecer casos de racismo. Pero, en realidad, no son hechos racistas. Son «culturistas». La gente continúa llevando a cabo una heroica lucha contra el racismo tradicional sin darse cuenta de que el frente de batalla ha cambiado. El racismo tradicional está menguando, pero ahora el mundo está lleno de «culturistas».
El racismo tradicional estaba firmemente asentado sobre teorías biológicas. En las décadas de 1890 o 1930 se creía de manera general, por ejemplo en Gran Bretaña, Australia y Estados Unidos, que algún rasgo biológico hereditario hace que los africanos y los chinos sean de manera innata menos inteligentes, menos emprendedores y menos morales que los europeos. El problema residía en su sangre. Tales opiniones gozaban de respetabilidad política, así como de un amplio soporte científico. Hoy en día, en cambio, aunque muchos individuos realizan todavía este tipo de aseveraciones racistas, estas han perdido todo su respaldo científico y la mayor parte de su respetabilidad política, a menos que se replanteen en términos culturales. Decir que las personas negras suelen cometer crímenes porque tienen genes de calidad inferior no está de moda; decir que suelen cometer crímenes porque provienen de culturas disfuncionales está muy de moda.
En Estados Unidos, por ejemplo, algunos partidos y dirigentes apoyan abiertamente políticas discriminatorias y suelen hacer observaciones denigrantes de los afroamericanos, los latinos y los musulmanes; pero rara vez, o nunca, dicen que haya algo erróneo en su ADN. Se pretende que el problema radique en su cultura. Así, cuando el presidente Trump describió a Haití, el Salvador y algunas partes de África como «países de mierda», en teoría planteaba a la opinión pública una reflexión sobre la cultura de estos lugares y no sobre su constitución genética.[2] En otra ocasión dijo de los inmigrantes mexicanos a Estados Unidos que «cuando México envía a su gente, no manda a los mejores. Envía a gente que tiene muchos problemas y ellos traen esos problemas. Traen drogas, traen crímenes. Son violadores y algunos, supongo, son buena gente». Esta es una afirmación muy ofensiva, pero desde el punto de vista sociológico, no desde el biológico. Trump no está diciendo que la sangre mexicana sea un impedimento para la bondad; solo que los buenos mexicanos suelen quedarse al sur del río Grande.[3]
El cuerpo humano (el cuerpo latino, el cuerpo africano, el cuerpo chino) sigue todavía en el centro del debate. El color de la piel importa mucho. Andar por una calle de Nueva York con una piel con mucha melanina significa que, a donde sea que nos dirijamos, la policía podría mirarnos con un recelo añadido. Pero personas como el presidente Trump y el presidente Obama explicarán la importancia del color de la piel en términos culturales e históricos. La policía considera sospechoso el tono de nuestra piel no debido a ninguna razón biológica, sino más bien a la historia. Presumiblemente, los simpatizantes de Obama explicarán que este prejuicio de la policía es una herencia desafortunada de crímenes históricos como el esclavismo, mientras que los de la órbita de Trump explicarán que la criminalidad negra es una herencia desafortunada de errores históricos cometidos por liberales blancos y comunidades negras. En cualquier caso, incluso si uno es en realidad un turista de Nueva Delhi que no sabe nada acerca de la historia americana, tendrá que apechugar con las consecuencias de dicha historia.
El paso de la biología a la cultura no es solo un cambio de jerga y ya está. Es un cambio profundo con consecuencias prácticas trascendentales, algunas buenas, otras malas. En primer lugar, la cultura es más maleable que la biología. Esto significa, por un lado, que los culturistas de hoy en día podrían ser más tolerantes que los racistas tradicionales: si los «otros» adoptan nuestra cultura, los aceptaremos como nuestros iguales. Asimismo, podría dar pie a presiones mucho más fuertes en los «otros» para que se integren y una crítica mucho más severa si no lo consiguen.
No puede acusarse a una persona de piel oscura de no blanquear su piel, pero la gente puede acusar, y lo hace, a africanos y musulmanes de no adoptar las normas y los valores de la cultura occidental. Lo que no significa que dichas acusaciones estén necesariamente justificadas. En muchos casos, hay pocas razones para adoptar la cultura dominante y en muchos otros se trata de una misión casi imposible. Los afroamericanos de un suburbio azotado por la pobreza que intenten con honestidad encajar en la cultura norteamericana hegemónica para empezar podrían hallar su camino bloqueado por la discriminación institucional, solo para ser acusados después de que no hicieron el esfuerzo suficiente y de que, por tanto, solo deben culparse a sí mismos de sus problemas.
Una segunda diferencia clave entre hablar de biología y hablar de cultura es que, a diferencia de la intolerancia racista tradicional, los argumentos culturistas podrían en ocasiones tener sentido, como en el caso de Calidostán y Friolandia. Calidostanos y friolandeses tienen en verdad culturas diferentes, caracterizadas por distintos estilos de relaciones humanas. Puesto que las relaciones humanas son fundamentales para algunos empleos, ¿es poco ético que una empresa calidostana penalice a los friolandeses por comportarse según su herencia cultural?
Antropólogos, sociólogos e historiadores se sienten muy incómodos con esta cuestión. Por un lado, todo ello parece rozar peligrosamente el racismo. Por otro, el culturismo tiene una base científica mucho más firme que el racismo, y en particular los expertos en humanidades y ciencias sociales no pueden negar la existencia y la importancia de las diferencias culturales.
Desde luego, aunque aceptemos la validez de algunas afirmaciones culturistas, no tenemos que aceptarlas todas. Muchas adolecen de tres errores comunes. Primero, los culturistas suelen confundir la superioridad local con la superioridad objetiva. Así, en el contexto de Calidostán, el método calidostano de resolución de conflictos podría muy bien ser superior al método friolandés, en cuyo caso una empresa calidostana que opere en Calidostán tiene una buena razón para discriminar a los empleados introvertidos (lo que penalizará de manera desproporcionada a los inmigrantes friolandeses). Sin embargo, esto no significa que el método calidostano sea objetivamente mejor. Los calidostanos podrían quizá aprender un par de cosas de los friolandeses, y si las circunstancias cambian (por ejemplo, si la empresa calidostana se hace global y abre sucursales en muchos países), la diversidad podría convertirse de repente en un activo.
En segundo lugar, cuando se define con claridad un criterio, una época y un lugar, las declaraciones culturistas bien pueden ser sensatas desde el punto de vista empírico. Pero con demasiada frecuencia la gente adopta afirmaciones culturistas muy generales, lo que tiene poco sentido. Así, decir que «la cultura friolandesa es menos tolerante con los arrebatos públicos de cólera que la cultura calidostana» es una afirmación razonable, pero resulta mucho menos razonable decir que «la cultura musulmana es muy intolerante». Esta última afirmación es sumamente vaga. ¿Qué queremos decir con «intolerante»? ¿Intolerante con quién o con qué? Una cultura puede ser intolerante con las minorías religiosas y las opiniones políticas insólitas, mientras que a la vez puede ser muy tolerante con las personas obesas o los ancianos. ¿Y qué queremos decir con «cultura musulmana»? ¿Estamos hablando de la península Arábiga en el siglo VII? ¿Del Imperio otomano en el siglo XVI? ¿De Pakistán a principios del siglo XXI? Por último, ¿cuál es el estándar de comparación? Si nos ocupamos de la tolerancia hacia las minorías religiosas y comparamos el Imperio otomano en el siglo XVI con Europa occidental en el siglo XVI, podemos llegar a la conclusión de que la cultura musulmana es muy tolerante. Si comparamos el Afganistán de los talibanes con la Dinamarca contemporánea, llegaremos a una conclusión muy diferente.
Pero el peor problema de las afirmaciones culturistas es que, a pesar de su naturaleza estadística, suelen utilizarse demasiado a menudo para prejuzgar a individuos. Cuando un nativo calidostano y un inmigrante friolandés solicitan el mismo puesto en una empresa calidostana, el gerente puede preferir contratar al calidostano porque «los friolandeses son fríos e insociables». Incluso si eso es cierto estadísticamente, quizá ese friolandés concreto sea en realidad mucho más cálido y extravertido que ese calidostano en concreto. Aunque la cultura es importante, las personas son también modeladas por sus genes y su historia personal única. Los individuos desafían a menudo los estereotipos estadísticos. Tiene sentido que una empresa prefiera a empleados sociables y no a impávidos, pero no lo tiene preferir antes a calidostanos que a friolandeses.
Sin embargo, todo esto modifica las aseveraciones culturistas concretas sin desacreditar al culturismo en su conjunto. A diferencia del racismo, que es un prejuicio acientífico, los argumentos culturistas a veces resultan muy fiables. Si consultamos las estadísticas y descubrimos que las empresas calidostanas tienen a pocos friolandeses en puestos importantes, esto puede ser el resultado no de una discriminación racista, sino de decisiones acertadas. ¿Tendrían que albergar los inmigrantes friolandeses resentimiento ante esta situación, y afirmar que Calidostán reniega del pacto de inmigración? ¿Tendríamos que obligar a las empresas calidostanas a contratar a más gerentes friolandeses mediante medidas a favor de las minorías con la esperanza de enfriar la cultura empresarial exaltada de Calidostán? ¿O quizá el problema radique en los inmigrantes friolandeses que no consiguen integrarse en la cultura local y, por tanto, deberíamos hacer un esfuerzo mayor y más enérgico para inculcar a los niños friolandeses las normas y valores calidostanos?
Volviendo del ámbito de la ficción al de los hechos, vemos que el debate europeo sobre la inmigración está lejos de ser una batalla bien delimitada entre el bien y el mal. Sería erróneo considerar a todos los antiinmigracionistas «fascistas», del mismo modo que lo sería presentar a todos los proinmigracionistas como personas comprometidas con el «suicidio cultural». Por tanto, el debate sobre la inmigración no debiera desarrollarse como una lucha sin cuartel acerca de algún imperativo moral no negociable. Se trata de una discusión entre dos posiciones políticas legítimas, que habrá que dilucidar mediante procedimientos democráticos estándar.
En la actualidad no está en absoluto claro si Europa encontrará una vía intermedia que le permita mantener las puertas abiertas a los extranjeros sin que se vea desestabilizada por gente que no comparte sus valores. Si Europa consigue encontrar dicha vía, quizá su fórmula pueda copiarse al nivel global. Sin embargo, si el proyecto europeo fracasara, implicaría que la creencia en los valores liberales de la libertad y la tolerancia no bastan para resolver los conflictos culturales del mundo y para unir a la humanidad ante la guerra nuclear, el colapso ecológico y la disrupción tecnológica. Si griegos y alemanes no logran ponerse de acuerdo sobre un destino común, y si 500 millones de europeos ricos no son capaces de acoger a unos pocos millones de refugiados pobres, ¿qué probabilidades tiene la humanidad de superar los conflictos de mucha más enjundia que acosan a nuestra civilización global?
Algo que puede ayudar a Europa y al mundo en su conjunto a integrar mejor y a mantener abiertas las fronteras y las mentes es restar importancia a la histeria en relación con el terrorismo. Sería muy lamentable que el experimento europeo de libertad y tolerancia se desintegrara debido a un temor exagerado a los terroristas. Esto no solo cumpliría los objetivos de los propios terroristas, sino que también concedería a ese puñado de locos una influencia demasiado grande sobre el futuro de la humanidad. El terrorismo es el arma de un segmento marginal y débil de la humanidad. ¿Cómo ha llegado a dominar la política global?
# Parte III
Desesperación y esperanza
_Aunque los retos no tienen precedentes, y aunque los desacuerdos son enormes, la humanidad puede dar la talla si mantenemos nuestros temores bajo control y somos un poco más humildes respecto a nuestras opiniones._
### 10
Terrorismo
#### No nos asustemos
Los terroristas son maestros en el control de las mentes. Matan a muy pocas personas, pero aun así consiguen aterrorizar a miles de millones y sacudir enormes estructuras políticas como la Unión Europea o Estados Unidos. Desde el 11 de septiembre de 2001, los terroristas han matado anualmente a unas 50 personas en la Unión Europea y a unas 10 en Estados Unidos, a unas 7 en China y a hasta 25.000 en todo el mundo (la mayoría en Irak, Afganistán, Pakistán, Nigeria y Siria).[1] En comparación, los accidentes de tráfico matan anualmente a unos 80.000 europeos, a 40.000 norteamericanos, a 270.000 chinos y a 1,25 millones de personas en todo el mundo.[2] La diabetes y los niveles elevados de azúcar matan al año a hasta 3,5 millones de personas, mientras que la contaminación atmosférica, a alrededor de 7 millones.[3] Así, ¿por qué tememos más al terrorismo que al azúcar, y por qué hay gobiernos que pierden elecciones debido a esporádicos ataques terroristas, pero no debido a la contaminación atmosférica crónica?
Como indica el significado literal del término, el terrorismo es una estrategia militar que espera cambiar la situación política extendiendo el terror en lugar de causar daños materiales. Esta estrategia la adoptan casi siempre grupos muy débiles que no pueden infligir mucho daño material a sus enemigos. Desde luego, toda acción militar desata miedo. Pero en la guerra convencional, el miedo no es más que un subproducto de las pérdidas materiales, y por lo general es proporcional a la fuerza que causa las pérdidas. En el terrorismo, el miedo es el argumento principal, y existe una desproporción asombrosa entre la fuerza real de los terroristas y el miedo que consiguen inspirar.
No siempre es fácil cambiar la situación política mediante la violencia. El primer día de la batalla del Somme, el 1 de julio de 1916, murieron 19.000 soldados británicos y otros 40.000 resultaron heridos. Para cuando la batalla terminó, en noviembre, ambos bandos habían sufrido en conjunto más de un millón de bajas, entre ellas 300.000 muertos.[4] Pero esta terrible carnicería apenas alteró el equilibrio del poder en Europa. Hicieron falta otros dos años y millones de bajas más para que al final ocurriera algo.
Comparado con la ofensiva del Somme, el terrorismo es algo nimio. Los ataques en París de noviembre de 2015 mataron a 130 personas; las bombas de Bruselas de marzo de 2016, a 32, y las bombas en el Manchester Arena de mayo de 2017, a 22. En 2002, en el momento culminante de la campaña terrorista palestina contra Israel, cuando a diario se colocaban bombas en autobuses y restaurantes, la lista de bajas anual alcanzó los 451 israelíes.[5] En el mismo año israelíes murieron en accidentes de tráfico.[6] Unos pocos ataques terroristas, como la bomba en el vuelo 103 de Pan Am sobre Lockerbie en 1988, acabaron con la vida de cientos de personas.[7] Los ataques del 11-S supusieron un nuevo récord, al matar casi a 3.000.[8] Pero incluso estas cifras parecen insignificantes en comparación con el precio de la guerra convencional. Si se suman todas las personas muertas y heridas en Europa por ataques terroristas desde 1945, incluidas las víctimas de grupos nacionalistas, religiosos, de izquierdas y de derechas, el total sigue siendo muy inferior al de las bajas de cualquiera de las batallas poco conocidas de la Primera Guerra Mundial, como la tercera batalla del Aisne (250.000) o la décima batalla de Isonzo (225.000).[9]
Entonces ¿cómo es que los terroristas esperan lograr algo? Después de un acto de terrorismo, el enemigo continúa teniendo el mismo número de soldados, tanques y buques que antes. La red de comunicación, las carreteras y los ferrocarriles del enemigo están en gran parte intactos. Sus fábricas, puertos y bases apenas han sido tocados. Sin embargo, los terroristas esperan que aunque apenas pueden hacer mella en el poder material del enemigo, el miedo y la confusión provoquen que haga un uso incorrecto de su fuerza intacta y reaccione de manera desproporcionada. Los terroristas calculan que cuando el enemigo enfurecido use su enorme poder contra ellos, generará una tormenta militar y política mucho más violenta que la que los propios terroristas podían haber provocado. En cada tormenta ocurren muchas cosas no previstas: se cometen errores y atrocidades, la opinión pública titubea, los neutrales cambian de postura y el equilibrio de poder se desplaza.
De ahí que los terroristas se parezcan a una mosca que intenta destruir una cristalería. La mosca es tan débil que ni siquiera es capaz de mover una simple taza de té. Así pues, ¿cómo destruye una cristalería? Encuentra un toro, se introduce en su oreja y empieza a zumbar. El toro enloquece de miedo e ira, y destruye la cristalería. Eso ocurrió después del 11-S, cuando los fundamentalistas islámicos incitaron al toro norteamericano a destruir la cristalería de Oriente Próximo. Ahora medran entre los escombros. Y en el mundo no escasean los toros con malas pulgas.
##### VOLVIENDO A BARAJAR LAS CARTAS
El terrorismo es una estrategia militar muy poco interesante, porque deja todas las decisiones importantes en manos del enemigo. Ya que todas las opciones que el enemigo tenía antes de un ataque terrorista siguen estando a su disposición después de este, goza de completa libertad para escoger entre ellas. Por lo general, los ejércitos intentan evitar tales situaciones a toda costa. Cuando atacan, no quieren desplegar un espectáculo aterrador que enojaría al enemigo y daría lugar a que devolviera el golpe. En cambio, buscan infligirle daños materiales importantes y reducir su capacidad para contraatacar. En particular, tratan de eliminar sus armas y opciones más poderosas.
Esto es, por ejemplo, lo que hizo Japón en diciembre de 1941, cuando lanzó un ataque sorpresa sobre Estados Unidos y hundió la flota estadounidense del Pacífico en Pearl Harbor. No fue terrorismo. Era guerra. Los japoneses no podían saber qué represalias tomarían los estadounidenses ante el ataque, pero sí tenían una certeza: con independencia de lo que los norteamericanos decidieran hacer, no podrían enviar una flota a Filipinas o a Hong Kong en 1942.
Provocar al enemigo para que actúe, sin eliminar ninguna de sus armas u opciones, es un acto de desesperación que se adopta solo cuando no existe ninguna otra opción. Siempre que es posible ocasionar graves daños materiales, nadie renuncia a esta opción en favor del mero terrorismo. Si en diciembre de 1941 los japoneses hubieran torpedeado un buque civil de pasajeros para provocar a Estados Unidos mientras dejaban intacta la flota del Pacífico en Pearl Harbor, habría sido una locura.
Pero los terroristas tienen poca elección. Son tan débiles que no pueden librar una guerra. De modo que optan, en su lugar, por generar un espectáculo teatral con la esperanza de que provocará al enemigo y lo hará reaccionar de manera desproporcionada. Los terroristas montan un espectáculo aterrador de violencia que se apodera de nuestra imaginación y la vuelve contra nosotros. Al matar a unas cuantas personas, los terroristas consiguen que millones de ellas teman por su vida. Para apaciguar ese temor, los gobiernos reaccionan ante el teatro del terror con un espectáculo de seguridad, orquestando inmensas exhibiciones de fuerza, como la persecución de poblaciones enteras o la invasión de países extranjeros. En la mayoría de los casos, esta reacción exagerada al terrorismo genera una amenaza mucho mayor a nuestra seguridad que los propios terroristas.
De ahí que los terroristas no piensen como generales del ejército. En cambio, piensan como productores teatrales. El recuerdo de la opinión pública de los ataques del 11-S atestigua que todos entendemos esto intuitivamente. Si se pregunta a la gente qué ocurrió el 11-S, es probable que digan que Al Qaeda derribó las torres gemelas del World Trade Center. Pero no fue solo un ataque a las torres, sino que hubo otras dos acciones, en particular un ataque con éxito al Pentágono. ¿Cómo es que lo recuerdan tan pocas personas?
Si la operación del 11-S hubiera sido una campaña militar convencional, el ataque al Pentágono habría recibido la máxima atención. Con él, Al Qaeda consiguió destruir parte del cuartel general del enemigo, matando e hiriendo a jefes y a analistas importantes. ¿Por qué la memoria colectiva concede mucha más importancia a la destrucción de dos edificios civiles y al asesinato de corredores de Bolsa, contables y administrativos?
Pues porque el Pentágono es un edificio relativamente plano y sencillo, mientras que el World Trade Center era un alto tótem fálico cuyo desmoronamiento ocasionó un inmenso impacto audiovisual. Nadie que viera las imágenes de su derrumbe las olvidará nunca. Puesto que de forma intuitiva entendemos que el terrorismo es teatro, lo juzgamos más por su impacto emocional que por el material.
Al igual que los terroristas, los que combaten el terrorismo deben pensar también más como productores teatrales y menos como generales del ejército. Por encima de todo, si queremos combatir de manera efectiva el terrorismo, hemos de ser conscientes de que nada que los terroristas hagan podrá derrotarnos. Somos los únicos que podemos derrotarnos, si reaccionamos de manera excesiva y equivocada a las provocaciones terroristas.
Los terroristas emprenden una misión imposible: cambiar el equilibrio político del poder mediante la violencia, a pesar de no disponer de un ejército. Para conseguir su objetivo, plantean al Estado un reto imposible por sí mismo: demostrar que puede proteger a sus ciudadanos de la violencia política, en cualquier lugar y en cualquier momento. Los terroristas esperan que cuando el Estado intente realizar esta misión imposible, volverá a barajar las cartas políticas y les repartirá algún as imprevisto.
Es verdad que cuando el Estado está a la altura del desafío, por lo general logra aplastar a los terroristas. En las últimas décadas, diversos estados han eliminado cientos de organizaciones terroristas. En 20024, Israel demostró que incluso es posible acabar con las campañas de terror más feroces mediante la fuerza bruta.[10] Los terroristas saben muy bien que en estas confrontaciones las probabilidades están en su contra. Pero puesto que son muy débiles y carecen de otra opción militar, no tienen nada que perder y sí mucho que ganar. De vez en cuando, la tormenta política creada por las campañas antiterroristas beneficia a los terroristas, lo que da sentido a la apuesta. Un terrorista es como un jugador con una mano especialmente mala que intenta convencer a sus rivales para que vuelvan a repartir las cartas. No puede perder nada y sí ganarlo todo.
__
##### UNA PEQUEÑA MONEDA EN UN GRAN FRASCO VACÍO
¿Por qué tendría que aceptar el Estado volver a barajar las cartas? Puesto que el daño material causado por el terrorismo es nimio, en teoría el Estado podría no hacer nada al respecto, o tomar medidas contundentes pero discretas lejos de cámaras y micrófonos. De hecho, los estados suelen hacer justo esto. Pero de vez en cuando pierden los estribos y reaccionan de una manera demasiado vehemente y pública, con lo que caen en el juego de los terroristas. ¿Por qué son tan sensibles los estados a las provocaciones terroristas?
La respuesta es que les cuesta soportar estas provocaciones porque la legitimidad del Estado moderno se basa en su promesa de mantener la esfera pública libre de violencia política. Un régimen puede soportar catástrofes terribles, e incluso ignorarlas, siempre y cuando su legitimidad no se base en evitarlas. Por otro lado, un régimen puede desmoronarse debido a un problema menor, si se considera que socava su legitimidad. En el siglo XIV, la peste negra eliminó a entre la cuarta parte y la mitad de las poblaciones europeas, pero a raíz de ello ningún rey perdió su trono y tampoco ningún rey hizo ningún gran esfuerzo para erradicar la peste. Por aquel entonces, nadie pensaba que evitar pestes fuera una de las tareas reales. En cambio, los gobernantes que permitieron que herejías religiosas se extendieran por sus dominios se arriesgaban a perder la corona, e incluso la cabeza.
Hoy en día, un gobierno puede adoptar una perspectiva más indulgente frente a la violencia doméstica y sexual que frente al terrorismo, porque a pesar de movimientos como #MeToo, la violación no socava la legitimidad gubernamental. En Francia, por ejemplo, se informa a las autoridades de más de 10.000 casos de violación al año y probablemente haya decenas de miles de casos más de los que no se informa.[11] Sin embargo, los violadores y maridos maltratadores no se ven como una amenaza existencial al Estado francés, porque históricamente este no se construyó sobre la promesa de eliminar la violencia sexual. En cambio, los casos muchísimo más raros de terrorismo se consideran una amenaza letal para la República francesa, porque a lo largo de los últimos siglos los estados occidentales modernos han ido basando gradualmente su legitimidad sobre la promesa explícita de no tolerar la violencia política dentro de sus fronteras.
En la Edad Media, la esfera pública rebosaba de violencia política. De hecho, la capacidad de usar la violencia era el pasaje de entrada al juego político, y quien carecía de esta capacidad no tenía voz política. Numerosas familias nobles poseían fuerzas armadas, como las poseían pueblos, gremios, iglesias y monasterios. Cuando moría un abad y surgía una disputa acerca de su sucesión, las facciones rivales (constituidas por monjes, dirigentes locales y vecinos preocupados) solían emplear la fuerza armada para dirimir la cuestión.
El terrorismo no tenía lugar en aquel mundo. Quien no fuera lo bastante fuerte para causar daños materiales importantes no contaba. Si en 1150 unos cuantos musulmanes fanáticos hubieran asesinado a algunos civiles en Jerusalén, exigiendo que los cruzados abandonaran Tierra Santa, la reacción habría sido de desprecio más que de terror. Si uno quería que se le tomara en serio, al menos tenía que haber conseguido conquistar uno o dos castillos fortificados. El terrorismo no preocupaba a nuestros antepasados medievales, porque tenían problemas mucho mayores de que ocuparse.
Durante la era moderna, los estados centralizados redujeron gradualmente el nivel de violencia política dentro de sus territorios, y en las últimas décadas los países occidentales han conseguido erradicarla casi por entero. Los ciudadanos de Francia, Gran Bretaña o Estados Unidos pueden luchar por el control de ciudades, empresas, organizaciones e incluso el propio gobierno sin ninguna necesidad de una fuerza armada. El control de billones de dólares, millones de soldados y miles de buques, aviones y misiles nucleares pasa de un grupo de políticos a otro sin que se dispare un solo tiro. La gente se acostumbró pronto a esto, y lo considera un derecho natural. En consecuencia, incluso actos esporádicos de violencia política que matan a algunas docenas de personas se ven como una amenaza letal a la legitimidad e incluso a la supervivencia del Estado. Una pequeña moneda agitada dentro de un gran frasco vacío hace mucho ruido.
Por ese motivo tiene tanto éxito el teatro del terrorismo. El Estado ha creado un espacio enorme, vacío de violencia política, que ahora funciona como una caja de resonancia y amplifica el impacto de cualquier ataque armado, por pequeño que sea. Cuanta menos violencia política hay en un Estado concreto, mayor es la conmoción pública ante un acto de terrorismo. Matar a unas pocas personas en Bélgica atrae mucha más atención que matar a cientos de ellas en Nigeria o Irak. Paradójicamente, pues, el mismo éxito de los estados modernos a la hora de evitar la violencia política los hace vulnerables en particular al terrorismo.
El Estado ha insistido muchas veces en que no tolerará violencia política dentro de sus fronteras. Los ciudadanos, por su parte, se han acostumbrado a una violencia política cero. De ahí que el teatro del terror genere temores viscerales de anarquía, que llevan a la gente a sentirse como si el orden social estuviera a punto de derrumbarse. Después de siglos de luchas sangrientas hemos salido arrastrándonos del agujero negro de la violencia, pero notamos que el agujero negro sigue ahí, esperando con paciencia el momento de volver a engullirnos. Unas pocas atrocidades espantosas, e imaginamos que ya estamos cayendo de nuevo en él.
Para aplacar estos temores, el Estado se ve impelido a responder al teatro del terror con su propio teatro de la seguridad. La respuesta más eficiente al terrorismo podría ser un buen servicio de inteligencia y acciones clandestinas contra las redes financieras que lo alimentan. Pero eso los ciudadanos no pueden verlo por televisión. Los ciudadanos han sido testigos del teatro terrorista del derrumbamiento del World Trade Center. El Estado necesita representar un contraespectáculo igualmente llamativo, incluso con más fuego y más humo. De modo que, en lugar de actuar de manera silenciosa y eficiente, desencadena una poderosa tormenta, que no es infrecuente que satisfaga los sueños más preciados de los terroristas.
Así pues, ¿cómo debería el Estado lidiar con el terrorismo? Para que una lucha antiterrorista tenga éxito debe emprenderse en tres frentes. Primero, los gobiernos han de centrarse en acciones clandestinas contra las redes terroristas. Segundo, los medios de comunicación han de mantener el asunto en perspectiva y evitar la histeria. El teatro del terror no puede tener éxito sin publicidad. Por desgracia, con demasiada frecuencia los medios ofrecen dicha publicidad gratis. Informan obsesivamente de los ataques terroristas y aumentan mucho su peligro, porque las noticias sobre terrorismo hacen que los periódicos se vendan mucho más que las que tratan de la diabetes o la contaminación atmosférica.
El tercer frente es la imaginación de cada uno. Los terroristas tienen cautiva nuestra imaginación y la usan contra nosotros. Una y otra vez volvemos a representar el ataque terrorista en el escenario de nuestra mente, recordando el 11-S o los últimos suicidas con bombas. Los terroristas matan a cien personas y hacen que cien millones imaginen que hay un asesino acechando detrás de cada árbol. Es responsabilidad de cada ciudadano liberar su imaginación de los terroristas y ser consciente de las verdaderas dimensiones de esta amenaza. Es nuestro propio terror interior lo que hace que los medios se obsesionen con el terrorismo y los gobiernos reaccionen de manera desproporcionada.
El éxito o el fracaso del terrorismo depende, pues, de nosotros. Si permitimos que nuestra imaginación caiga presa de los terroristas y después reaccionamos de manera exagerada ante nuestros propios temores, el terrorismo triunfará. Si liberamos nuestra imaginación de los terroristas y reaccionamos de una manera equilibrada y fría, el terrorismo fracasará.
##### EL TERRORISMO SE HACE NUCLEAR
Este análisis vale para el terrorismo según lo hemos conocido en los dos últimos siglos y aún se manifiesta en la actualidad en las calles de Nueva York, Londres, París y Tel Aviv. Sin embargo, si los terroristas adquieren armas de destrucción masiva, la naturaleza no solo del terrorismo, sino también del Estado y de la política global, cambiará de manera radical. Si organizaciones minúsculas que representan a unos pocos fanáticos pueden destruir ciudades enteras y matar a millones de personas, ya no habrá una esfera pública libre de violencia política.
De ahí que mientras que el terrorismo actual es en gran parte teatro, el futuro terrorismo nuclear, el ciberterrorismo o el bioterrorismo plantearía una amenaza mucho más seria, y exigiría una reacción mucho más drástica de los gobiernos. Justo debido a ello, hemos de ir con mucho cuidado para diferenciar estos escenarios hipotéticos futuros de los ataques terroristas reales que hasta ahora hemos presenciado. El temor de que los terroristas puedan un día hacerse con una bomba nuclear y destruir Nueva York o Londres no justifica una reacción histérica desproporcionada ante un terrorista que mata a una docena de transeúntes con un rifle automático o un camión fuera de control. Los estados deberían ser más cuidadosos incluso para no empezar a perseguir a todos los grupos disidentes dando por hecho que un día podrían intentar hacerse con armas nucleares, o que podrían apoderarse de nuestros automóviles inteligentes y transformarlos en una flota de robots asesinos.
Asimismo, aunque no hay duda de que los gobiernos deben vigilar a los grupos radicales y emprender acciones para evitar que se hagan con el control de armas de destrucción masiva, necesitan mantener el equilibrio entre el temor al terrorismo nuclear y otras situaciones amenazadoras. En las dos últimas décadas, Estados Unidos ha malgastado billones de dólares y mucho capital político en su guerra contra el terror. George W. Bush, Tony Blair, Barack Obama y sus gabinetes pueden aducir, con cierta justificación, que persiguiendo a los terroristas los obligaron a pensar más en la supervivencia que en adquirir bombas nucleares. De esa manera podrían haber salvado al mundo de un 11-S nuclear. Puesto que se trata de una afirmación contrafactual («Si no hubiéramos lanzado la guerra contra el terror, Al Qaeda habría adquirido armas nucleares»), es difícil juzgar si es cierta o no.
Sin embargo, no cabe duda de que al dedicarse a la guerra contra el terror, los norteamericanos y sus aliados no solo han provocado una destrucción inmensa por todo el planeta, sino que también han incurrido en lo que los economistas denominan «costes de oportunidad». El dinero, el tiempo y el capital político invertido en luchar contra el terrorismo no se han invertido en luchar contra el calentamiento global, el sida y la pobreza; en aportar paz y prosperidad al África subsahariana, o en forjar mejores vínculos con Rusia y China. Si Nueva York o Londres acaban hundiéndose bajo un océano Atlántico cuyo nivel va en ascenso, o si las tensiones con Rusia estallan en una guerra abierta, la gente bien podría acusar a Bush, Blair y Obama de haberse centrado en el frente equivocado.
Es difícil establecer prioridades en tiempo real, a la vez que es demasiado fácil anticipar prioridades en retrospectiva. Acusamos a los líderes de no haber prevenido las catástrofes que ocurrieron, pero a la vez permanecemos felizmente ignorantes de los desastres que nunca se materializaron. Así, la gente piensa en retrospectiva en el gobierno de Clinton en la década de 1990 y lo acusa de pasar por alto la amenaza de Al Qaeda. Pero en la década de 1990, pocas personas imaginaban que los terroristas islámicos pudieran desencadenar un conflicto global al estrellar aviones de pasajeros contra los rascacielos de Nueva York. En cambio, muchos temían que Rusia pudiera desmoronarse por completo y perdiera el control no solo de su vasto territorio, sino también de miles de bombas nucleares y biológicas. Una preocupación añadida fue que las sangrientas guerras en la antigua Yugoslavia pudieran extenderse a otras partes de Europa oriental, y provocar conflictos entre Hungría y Rumanía, entre Bulgaria y Turquía, o entre Polonia y Ucrania.
A muchos incluso los inquietaba más la reunificación de Alemania. Solo cuatro décadas y media después de la caída del Tercer Reich, muchísima gente albergaba todavía temores viscerales frente al poder alemán. Libre de la amenaza soviética, ¿no se convertiría Alemania en una superpotencia que dominara el continente europeo? ¿Y qué pasaría con China? Alarmada por el hundimiento del bloque soviético, China podría abandonar sus reformas, volver a las políticas maoístas duras y terminar como una versión mayor de Corea del Norte.
Hoy en día podemos mofarnos de estos siniestros escenarios, porque sabemos que no se materializaron. La situación en Rusia se estabilizó, la mayor parte de Europa oriental se integró pacíficamente en la Unión Europea, la Alemania reunificada es considerada en la actualidad líder del mundo libre y China se ha convertido en el motor económico del planeta. Todo esto se consiguió, al menos en parte, gracias a políticas constructivas de Estados Unidos y la Unión Europea. ¿Habría sido más sensato que Estados Unidos y la Unión Europea se hubieran centrado en la década de 1990 en los extremistas islámicos y no en la situación del antiguo bloque soviético o en China?
Simplemente, no podemos prepararnos para todas las eventualidades. En consecuencia, aunque no cabe duda de que hemos de evitar el terrorismo nuclear, este no puede ocupar el punto número uno en el programa de la humanidad. Y, por supuesto, no debemos usar la amenaza teórica del terrorismo nuclear como justificación para reaccionar de manera desproporcionada ante el terrorismo común. Se trata de problemas diferentes que exigen soluciones diferentes.
Si a pesar de nuestros esfuerzos los grupos terroristas acaban por hacerse con armas de destrucción masiva, es difícil predecir cómo se llevarán a cabo las luchas políticas, pero serán muy diferentes de las campañas de terrorismo y antiterrorismo de principios del siglo XXI. Si en 2050 el mundo está lleno de terroristas nucleares y bioterroristas, sus víctimas mirarán hacia atrás, al mundo de 2018, con una nostalgia teñida de incredulidad: ¿cómo pudo gente que vivía una vida tan segura haberse sentido aun así tan amenazada?
Desde luego, la sensación actual de peligro que experimentamos no se debe solo al terrorismo. Muchísimos expertos y gente de a pie temen que la Tercera Guerra Mundial se halle solo a la vuelta de la esquina, como si ya hubiéramos visto esta película hace un siglo. Al igual que en 1914, en 2018 las crecientes tensiones entre las grandes potencias junto a problemas globales inextricables parecen arrastrarnos hacia una guerra global. ¿Está dicha ansiedad más justificada que nuestro temor sobredimensionado del terrorismo?
### 11
Guerra
#### Jamás subestimemos la estupidez humana
Las últimas décadas han sido las más pacíficas de la historia de la humanidad. Mientras que en las primeras sociedades agrícolas la violencia de los humanos causaba hasta el 15 por ciento de todas las muertes humanas, y en el siglo XX causó el 5 por ciento, en la actualidad es responsable de solo el 1 por ciento.[1] Pero dado que desde la crisis financiera global de 2008 la situación internacional está deteriorándose muy deprisa, el belicismo vuelve a estar de moda, y el gasto militar aumenta sobremanera.[2] Tanto los ciudadanos de a pie como los expertos temen que, del mismo modo que en 1914 el asesinato de un archiduque austríaco provocó la Primera Guerra Mundial, en 2018 algún incidente en el desierto sirio o algún movimiento imprudente en la península de Corea pueda prender la mecha de un conflicto global.
Dadas las tensiones crecientes en el mundo y la personalidad de los líderes en Washington, Pionyang y otros lugares más, desde luego no faltan motivos para preocuparse. Pero hay varias diferencias clave entre 2018 y 1914. En particular, la guerra de 1914 tuvo un gran atractivo para las élites de todo el mundo porque disponían de muchos ejemplos concretos de cómo las guerras exitosas contribuían a la prosperidad económica y al poder político. En cambio, en 2018 las guerras exitosas parecen ser una especie amenazada.
Desde la época de los asirios y los qin, los grandes imperios solían crearse mediante la conquista violenta. También en 1914 las principales potencias debían su condición a guerras coronadas con éxito. Por ejemplo, el Japón Imperial se convirtió en una potencia regional debido a sus victorias sobre China y Rusia; Alemania se convirtió en el mandamás de Europa después de sus triunfos sobre Austria-Hungría y Francia, y Gran Bretaña creó el mayor y más próspero imperio del mundo mediante una serie de guerras reducidas y gloriosas por todo el planeta. Así, en 1882 Gran Bretaña invadió y ocupó Egipto, y apenas perdió unos 57 soldados en la decisiva batalla de Tel el-Kebir.[3] Mientras que hoy en día la ocupación de un país musulmán es la esencia de las pesadillas occidentales, después de Tel el-Kebir los británicos encontraron poca resistencia armada, y durante más de seis décadas controlaron el valle del Nilo y el decisivo canal de Suez. Otras potencias europeas emularon a los británicos, y cada vez que los gobiernos en París, Roma o Bruselas se planteaban enviar tropas Vietnam, Libia o el Congo, su único temor era que alguna otra potencia llegara allí antes.
Incluso Estados Unidos debía su condición de gran potencia a la acción militar y no solo a las empresas económicas. En 1846 invadió México y conquistó California, Nevada, Utah, Arizona, Nuevo México y partes de Colorado, Kansas, Wyoming y Oklahoma. El tratado de paz confirmó asimismo la anexión previa de Texas por Estados Unidos. Unos 13.000 soldados norteamericanos murieron en la guerra, que añadió 2,3 millones de kilómetros cuadrados a Estados Unidos (más territorio que Francia, Gran Bretaña, Alemania, España e Italia juntos).[4] Fue la ganga del milenio.
De ahí que en 1914 las élites de Washington, Londres y Berlín supieran exactamente cómo era una guerra con éxito, y lo mucho que se podía ganar con ella. En cambio, en 2018 las élites globales tienen buenas razones para sospechar que este tipo de guerra podría haberse extinguido. Aunque algunos dictadores del Tercer Mundo y actores no estatales consiguen todavía medrar a costa de la guerra, por lo visto las principales potencias ya no saben cómo hacerlo.
La mayor victoria de los últimos tiempos (la de Estados Unidos frente a la Unión Soviética) se obtuvo sin ninguna confrontación militar importante. Luego, Estados Unidos saboreó fugazmente la gloria militar chapada a la antigua en la primera guerra del Golfo, pero esto solo lo tentó para malgastar billones de dólares en humillantes fracasos militares en Irak y Afganistán. China, la potencia en auge de principios del siglo XXI, ha evitado con tesón todos los conflictos armados desde su fracasada invasión de Vietnam en 1979, y debe su ascenso a factores estrictamente económicos. En esto ha emulado no a los imperios japonés, alemán e italiano de la era anterior a 1914, sino a los imperios japonés, alemán e italiano de la era posterior a 1945. En todos estos casos, prosperidad económica e influencia geopolítica se consiguieron sin disparar un solo tiro.
Incluso en Oriente Próximo (el ring del mundo), las potencias regionales no saben cómo enzarzarse en guerras victoriosas. Irán no ganó nada con el prolongado baño de sangre de la guerra contra Irak, y luego evitó todas las confrontaciones militares directas. Los iraníes financian y arman movimientos locales desde Irak hasta Yemen, y han enviado a sus Guardianes de la Revolución para que ayuden a sus aliados en Siria y el Líbano, pero por el momento se han mostrado comedidos y no han invadido ningún país. Recientemente, Irán se ha convertido en la potencia regional hegemónica no a fuerza de alguna brillante victoria en el campo de batalla, sino más bien por defecto. Sus dos principales enemigos (Estados Unidos e Irak) se enzarzaron en una guerra que acabó con Irak y el apetito norteamericano por los embrollos en Oriente Próximo, con lo que dejaron a Irán disfrutando del botín.
De Israel puede decirse algo muy parecido. Su última guerra victoriosa se libró en 1967. Desde entonces, el país ha prosperado a pesar de sus muchas guerras, no gracias a ellas. La mayoría de sus territorios ocupados le suponen pesadas cargas económicas y obligaciones políticas que lo perjudican. De manera parecida a Irán, Israel ha mejorado últimamente su posición geopolítica no por haber librado guerras victoriosas, sino por haber evitado aventuras militares. Mientras que la guerra ha devastado a sus antiguos enemigos en Irak, Siria y Libia, Israel ha permanecido apartado. No haber acabado absorbido por la guerra civil en Siria ha sido sin duda el mayor logro político de Netanyahu (al menos hasta marzo de 2018). Si hubieran querido, las Fuerzas de Defensa de Israel podrían haber tomado Damasco en cuestión de una semana, pero ¿qué habrían ganado con ello? Habría sido incluso más fácil para las FDI conquistar Gaza y derrocar el régimen de Hamás, pero Israel se ha negado repetidas veces a hacerlo. A pesar del coraje militar y la retórica militarista de los políticos israelíes, Israel sabe que hay poco que ganar con la guerra. Al igual que Estados Unidos, China, Alemania, Japón e Irán, parece comprender que en el siglo XXI la estrategia de mayor éxito es sentarse a esperar y dejar que otros luchen por uno.
##### LA PERSPECTIVA DEL KREMLIN
Hasta ahora, la única invasión exitosa llevada a cabo por una potencia importante en el siglo XXI ha sido la conquista rusa de Crimea. En febrero de 2014, fuerzas rusas invadieron la vecina Ucrania y ocuparon la península de Crimea, que luego quedó anexionada a Rusia. Sin apenas luchar, Rusia consiguió un territorio vital desde el punto de vista estratégico, atemorizó a sus vecinos y volvió a establecerse como potencia mundial. Sin embargo, la conquista triunfó debido a un conjunto extraordinario de circunstancias. Ni el ejército ucraniano ni la población local opusieron mucha resistencia a los rusos, mientras que otras potencias se abstuvieron de intervenir directamente en la crisis. Tales circunstancias serán difíciles de reproducir en otros lugares del mundo. Si la condición previa para una guerra victoriosa es la ausencia de enemigos que estén dispuestos a resistir al agresor, las oportunidades quedarán seriamente limitadas.
De hecho, cuando Rusia intentó reproducir su éxito en Crimea en otras partes de Ucrania, se enfrentó a una oposición sustancialmente más firme, y la guerra en Ucrania oriental se empantanó en un punto muerto improductivo. Peor, incluso (desde la perspectiva de Moscú), pues la guerra ha avivado sentimientos antirrusos en Ucrania y el país ha pasado de ser aliado a enemigo declarado. De la misma manera en que el éxito en la primera guerra del Golfo tentó a Estados Unidos para extralimitarse en Irak, el éxito en Crimea pudo haber tentado a Rusia para extralimitarse en Ucrania.
Analizadas en su conjunto, las guerras de Rusia en el Cáucaso y Ucrania a principios del siglo XXI difícilmente pueden considerarse muy exitosas. Aunque han impulsado el prestigio de Rusia como gran potencia, también han hecho que aumentara la desconfianza y la animosidad hacia Rusia, y en términos económicos han sido una empresa con pérdidas. Las instalaciones turísticas en Crimea y las destartaladas fábricas de la era soviética en Lugansk y Donetsk apenas compensan lo que ha costado financiar la guerra, y ciertamente no contrarrestan los costes de la fuga de capitales y de sanciones internacionales. Para darse cuenta de las limitaciones de la política rusa, solo hay que comparar el inmenso progreso económico de la pacífica China en los últimos veinte años con el estancamiento de la «victoriosa» Rusia en el mismo período.[5]
A pesar del discurso triunfalista de Moscú, la élite rusa es probablemente muy consciente de los costes y los beneficios reales de sus aventuras militares, razón por la cual hasta ahora ha tenido mucho cuidado en no incrementarlas. Rusia ha estado comportándose como el abusón de un patio de colegio: «Elige al niño más débil, y no le pegues mucho, no sea que el maestro intervenga». Si Putin hubiera dirigido sus guerras con el espíritu de Stalin, Pedro el Grande o Gengis Kan, entonces haría ya mucho que los tanques rusos se habrían dirigido rápidamente a Tiflis y Kiev, si no a Varsovia y a Berlín. Pero Putin no es Gengis Kan ni Stalin. Parece saber mejor que nadie que en el siglo XXI el poder militar no puede ir muy lejos, y que enzarzarse en una guerra victoriosa significa enzarzarse en una guerra limitada. Incluso en Siria, a pesar de la crueldad de los bombardeos aéreos rusos, Putin ha tenido cuidado en minimizar la intervención rusa, en dejar a otros entablar la lucha seria y en evitar que la guerra se desborde hacia los países vecinos.
De hecho, desde la perspectiva rusa, todos los movimientos recientes supuestamente agresivos no fueron las maniobras abiertas de una nueva guerra global, sino más bien un intento de apoyar defensas expuestas. Los rusos pueden señalar justificadamente que después de sus retiradas pacíficas a finales de la década de 1980 y principios de la de 1990 los trataron como a un enemigo derrotado. Estados Unidos y la OTAN se aprovecharon de la debilidad rusa y, a pesar de las promesas en sentido contrario, expandieron la OTAN por Europa oriental e incluso a algunas antiguas repúblicas soviéticas. Occidente siguió pasando por alto los intereses de Rusia en Oriente Próximo, invadió Serbia e Irak con pretextos dudosos y, en general, dejó muy claro a Rusia que podía contar únicamente con su propio poderío militar para proteger su esfera de influencia de las incursiones de Occidente. Desde esta perspectiva, los responsables de las jugadas militares rusas recientes pueden ser tanto Bill Clinton y George W. Bush como Vladímir Putin.
Desde luego, las acciones militares rusas en Georgia, Ucrania y Siria bien pudieran ser al final las salvas iniciales de un impulso imperial mucho más atrevido. Incluso si hasta ahora Putin no ha albergado planes serios de conquistas globales, los éxitos pueden alentar sus ambiciones. Sin embargo, también estaría bien recordar que la Rusia de Putin es mucho más débil que la Unión de Repúblicas Socialistas Soviéticas de Stalin, y a menos que se le unan otros países como China, no puede sostener una nueva Guerra Fría, por no hablar de una guerra mundial total. Rusia tiene una población de 150 millones de personas y un PIB de 4 billones de dólares. Tanto en población como en producción queda muy por debajo de Estados Unidos (325 millones de personas y 19 billones de dólares) y de la Unión Europea (500 millones de personas y 21 billones de dólares).[6] En total, Estados Unidos y la Unión Europea tienen 5 veces más población que Rusia y 10 veces más dólares.
Los avances tecnológicos recientes han hecho que esta brecha sea todavía mayor de lo que parece. La Unión Soviética alcanzó su apogeo a mediados del siglo XX, cuando la industria pesada era la locomotora de la economía global, y el sistema centralizado soviético destacaba en la producción en masa de tractores, camiones, tanques y misiles intercontinentales. En la actualidad, la tecnología de la información y la biotecnología son más importantes que la industria pesada, pero Rusia no sobresale en ninguna de estas. Aunque tiene unas capacidades de ciberguerra impresionantes, carece del sector civil de las tecnologías de la información (TI), y su economía se basa de manera unánime en los recursos naturales, en particular petróleo y gas. Esto puede ser bastante beneficioso para enriquecer a unos pocos oligarcas y mantener a Putin en el poder, pero no es suficiente para vencer en una carrera armamentística digital o biotecnológica.
Y lo que es aún más importante: la Rusia de Putin carece de una ideología universal. Durante la Guerra Fría, la Unión Soviética se basaba en el atractivo global del comunismo tanto como en el alcance global del Ejército Rojo. El putinismo, en cambio, tiene poco que ofrecer a cubanos, vietnamitas o intelectuales franceses. El nacionalismo autoritario podría estar extendiéndose por el mundo, pero por su propia naturaleza no contribuye al establecimiento de bloques internacionales cohesionados. Mientras que el comunismo polaco y el ruso estaban comprometidos, al menos en teoría, con los intereses universales de una clase obrera internacional, el nacionalismo polaco y el ruso están comprometidos, por definición, con intereses opuestos. Al generar el auge de Putin un incremento notable del nacionalismo polaco, esto solo hará que Polonia sea más antirrusa que antes.
De ahí que aunque Rusia se haya embarcado en una campaña global de desinformación y subversión que pretende dividir la OTAN y la Unión Europea, no parece probable que esté decidida a embarcarse en una campaña global de conquista física. Cabe esperar, con cierta justificación, que la anexión de Crimea y las incursiones rusas en Georgia y Ucrania oriental sigan siendo ejemplos aislados más que heraldos de una nueva era de guerra.
##### EL ARTE PERDIDO DE GANAR LAS GUERRAS
¿Por qué les resulta tan difícil a las grandes potencias emprender guerras con éxito en el siglo XXI? Una razón es el cambio en la naturaleza de la economía. En el pasado, los activos económicos eran sobre todo materiales, por lo que resultaba bastante fácil enriquecerse mediante la conquista. Si se derrotaba a los enemigos en el campo de batalla, podía sacarse tajada saqueando sus ciudades, vendiendo a sus civiles en los mercados de esclavos y ocupando valiosos trigales y minas de oro. Los romanos prosperaron vendiendo a griegos y a galos cautivos, y los norteamericanos del siglo XIX medraron ocupando las minas de oro de California y los ranchos ganaderos de Texas.
Pero en el siglo XXI, de este modo solo pueden obtenerse beneficios exiguos. Hoy en día, los principales activos económicos consisten en el conocimiento técnico e institucional más que en los trigales, las minas de oro o incluso los campos petrolíferos, y el conocimiento no se conquista mediante la guerra. Una organización como Estado Islámico puede medrar aún saqueando ciudades y pozos petrolíferos en Oriente Próximo (se apoderaron de más de 500 millones de dólares de los bancos iraquíes y en 2015 consiguieron otros 500 con la venta de petróleo),[7] pero para una gran potencia como China o Estados Unidos dichas sumas son insignificantes. Con un PIB anual de más de 20 billones de dólares, es improbable que China inicie una guerra por unos irrisorios 1.000 millones. En cuanto a gastar billones de dólares en un enfrentamiento contra Estados Unidos, ¿cómo podría China devolver esos gastos y equilibrar todos los daños producidos por la guerra y las oportunidades comerciales perdidas? ¿Acaso el victorioso Ejército Popular de Liberación saquearía Silicon Valley? Es verdad que empresas como Apple, Facebook y Google valen cientos de miles de millones de dólares, pero esas fortunas no se pueden conseguir por la fuerza. No hay minas de silicio en Silicon Valley.
Una guerra con éxito en teoría todavía podría producir beneficios enormes si permitiera al vencedor redistribuir a su favor el sistema de comercio global, como hizo Gran Bretaña después de su victoria sobre Napoleón y como hizo Estados Unidos tras su victoria sobre Hitler. Sin embargo, los cambios en la tecnología militar dificultan repetir esta hazaña en el siglo XXI. La bomba atómica ha convertido en un suicidio colectivo la victoria en una guerra mundial. No es casual que desde Hiroshima las superpotencias nunca hayan luchado directamente entre sí, y se hayan enzarzado solo en lo que (para ellas) eran conflictos en los que se jugaban poco, en los que la tentación de utilizar armas nucleares para evitar la derrota era pequeña. De hecho, incluso atacar a una potencia nuclear de segunda categoría como Corea del Norte es una propuesta muy poco atractiva. Asusta pensar lo que la familia Kim podría hacer si se enfrentara a la derrota militar.
La ciberguerra hace que las cosas sean todavía peores para los imperialistas en potencia. En los buenos y viejos tiempos de la reina Victoria y de la ametralladora Maxim, el ejército británico podía masacrar a los _fuzzy-wuzzies_(2) en algún desierto lejano sin que peligrara la paz en Manchester y Birmingham. Incluso en los días de George W. Bush, Estados Unidos podía sembrar el caos en Bagdad y Faluya mientras que los iraquíes no tenían manera de contraatacar en San Francisco o Chicago. Pero si ahora Estados Unidos ataca a un país con capacidades para la ciberguerra, incluso moderadas, la contienda podría trasladarse a California o Illinois en cuestión de minutos. Programas malignos y bombas lógicas podrían interrumpir el tráfico aéreo en Dallas, hacer que chocaran trenes en Filadelfia y provocar la caída de la red eléctrica en Michigan.
En la gran época de los conquistadores, la guerra era un asunto de daños reducidos y grandes beneficios. En la batalla de Hastings, en 1066, Guillermo el Conquistador se hizo con toda Inglaterra en un solo día al precio de apenas unos pocos miles de muertos. Por el contrario, las armas nucleares y la ciberguerra son tecnologías de daños elevados y pocos beneficios. Se pueden emplear estas herramientas para destruir países enteros, pero en absoluto para construir imperios rentables.
De ahí que en un mundo que está llenándose de ruido de sables y de malas vibraciones, quizá la mejor garantía de paz que tenemos sea que las principales potencias no estén familiarizadas con ejemplos recientes de guerras victoriosas. Aunque Gengis Kan y Julio César podían invadir un país extranjero a las primeras de cambio, los líderes nacionalistas de la actualidad, como Erdogan, Modi y Netanyahu, que no se reprimen al hablar, son sin embargo muy cuidadosos a la hora de emprender una guerra. Desde luego, si alguien encuentra una fórmula para desencadenar una guerra victoriosa dadas las condiciones del siglo XXI, las puertas del infierno podrían abrirse de golpe. Por eso el éxito ruso en Crimea es un presagio particularmente alarmante. Esperemos que siga siendo una excepción.
##### EL DESFILE DE LA LOCURA
Por desgracia, aunque las guerras sigan siendo un negocio improductivo en el siglo XXI, esto no nos da una garantía absoluta de paz. Jamás debemos subestimar la estupidez humana. Tanto en el plano personal como en el colectivo, los humanos son propensos a dedicarse a actividades autodestructivas.
En 1939, la guerra era probablemente un paso contraproducente para las potencias del Eje, pero eso no salvó al mundo. Una de las cosas sorprendentes de la Segunda Guerra Mundial es que tras la contienda las potencias derrotadas prosperaron como nunca lo habían hecho. Veinte años después de la aniquilación completa de sus ejércitos y del hundimiento absoluto de sus imperios, alemanes, italianos y japoneses gozaban de niveles de riqueza sin precedentes. Así pues, ¿por qué fueron a la guerra, para empezar? ¿Por qué infligieron una muerte y una destrucción innecesarias a innumerables millones de personas? Todo se debió a un estúpido error de cálculo. En la década de 1930, generales, almirantes, economistas y periodistas japoneses estaban de acuerdo en que, sin el control de Corea, Manchuria y la costa de China, Japón estaba condenado al estancamiento económico.[8] Todos se equivocaron. De hecho, el famoso milagro económico japonés no se inició hasta que Japón perdió todas sus conquistas en el continente.
La estupidez humana es una de las fuerzas más importantes de la historia, pero a veces tendemos a pasarla por alto. Políticos, generales y estudiosos ven el mundo como una gran partida de ajedrez, en la que cada movimiento obedece a meticulosos cálculos racionales. Esto es correcto hasta cierto punto. Pocos dirigentes en la historia han estado locos en el sentido estricto del término, y se han puesto a mover peones y caballos aleatoriamente. El general Tojo, Sadam Husein y Kim Jong-il tenían razones racionales para cada paso que dieron. El problema es que el mundo es mucho más complejo que un tablero de ajedrez, y la racionalidad humana no está a la altura del desafío de entenderlo realmente. De ahí que incluso los líderes racionales terminen con frecuencia haciendo cosas muy estúpidas.
Así, ¿cuánto hemos de temer una guerra mundial? Es mejor evitar dos extremos. Por un lado, y definitivamente, la guerra sin duda no es inevitable. El final pacífico de la Guerra Fría demuestra que cuando los humanos toman las decisiones adecuadas, incluso los conflictos entre las superpotencias pueden resolverse por la vía pacífica. Además, es muy peligroso suponer que una nueva guerra mundial sea inevitable. Sería una profecía que se cumple. Una vez que los países asumen que la guerra es inevitable, refuerzan sus ejércitos, se embarcan en una espiral de carreras armamentistas, rehúsan comprometerse en cualquier conflicto y sospechan que los gestos de buena voluntad son solo trampas. Esto garantiza el estallido de la guerra.
Por otro lado, sería ingenuo suponer que la guerra es imposible. Incluso si es catastrófica para todos, no hay dios ni ley de la naturaleza que nos proteja de la estupidez humana.
Un remedio potencial para la estupidez humana es una dosis de humildad. Las tensiones nacionales, religiosas y culturales empeoran por el sentimiento grandioso de que mi nación, mi religión y mi cultura son las más importantes del mundo; de ahí que mis intereses se hallen por encima de los intereses de cualquier otro, o de la humanidad en su conjunto. ¿Cómo podemos hacer que las naciones, las religiones y las culturas sean un poco más realistas y modestas respecto a su verdadero lugar en el mundo?
### 12
Humildad
#### No somos el centro del mundo
La mayoría de la gente suele creer que es el centro del mundo y su cultura, el eje de la historia humana. Muchos griegos creen que la historia empezó con Homero, Sófocles y Platón, y que todas las ideas e invenciones importantes nacieron en Atenas, Esparta, Alejandría o Constantinopla. Los nacionalistas chinos replican que la historia empezó en verdad con el Emperador Amarillo y las dinastías Xia y Shang, y que lo que consiguieron los occidentales, musulmanes o indios no es más que una pálida copia de los descubrimientos chinos originales.
Los nativistas hindúes rechazan tales presunciones chinas y aducen que incluso los aviones y las bombas atómicas fueron inventados por antiguos sabios en el subcontinente indio mucho antes de Confucio o Platón, por no mencionar a Einstein o a los hermanos Wright. ¿Sabía el lector, por ejemplo, que fue Maharishi Bhardwaj quien inventó los cohetes y los aviones, que Vishwamitra no solo inventó los misiles, sino que además los usó, que Acharya Kanad fue el padre de la teoría atómica, y que el _Mahabharata_ describe con todo detalle las armas nucleares?[1]
Los musulmanes piadosos consideran que toda la historia previa al profeta Mahoma es en buena medida irrelevante, y creen que la historia posterior a la revelación del Corán gira alrededor de la _umma_(3) musulmana. Las principales excepciones son los nacionalistas turcos, iraníes y egipcios, que argumentan que incluso antes de Mahoma su nación en concreto fue el manantial de cuanto resultó bueno para la humanidad, y que incluso después de la revelación del Corán fue principalmente su pueblo el que conservó la pureza del islamismo y extendió su gloria.
Ni que decir tiene que británicos, franceses, alemanes, estadounidenses, rusos, japoneses e incontables otros grupos están convencidos de manera similar de que la humanidad habría vivido en la ignorancia bárbara e inmoral de no haber sido por los espectaculares logros de su nación. A lo largo de la historia, algunas personas llegaron incluso a imaginar que sus instituciones políticas y sus prácticas religiosas eran esenciales para las leyes mismas de la física. Así, los aztecas estaban convencidos de que sin los sacrificios que efectuaban anualmente el sol no saldría y el universo al completo se desintegraría.
Todas estas afirmaciones son falsas. Combinan una terca ignorancia de la historia con más de un indicio de racismo. Ninguna de las religiones o las naciones de hoy en día existían cuando los humanos colonizaron el mundo, domesticaron plantas y animales, construyeron las primeras ciudades o inventaron la escritura y el dinero. La moral, el arte, la espiritualidad y la creatividad son capacidades humanas universales incrustadas en nuestro ADN. Su génesis tuvo lugar en el África de la Edad de Piedra. Por tanto, es de un craso egoísmo adscribirles un lugar y una época más recientes, ya sea China en la época del Emperador Amarillo, Grecia en la época de Platón o Arabia en la época de Mahoma.
Personalmente, estoy más que familiarizado con este craso egoísmo, porque los judíos, mi propio pueblo, piensan también que son lo más importante del mundo. Nómbrese cualquier logro o invención humanos, y de inmediato reclamarán el reconocimiento por ello. Y puesto que los conozco íntimamente, también sé que están convencidos de manera genuina de dichas afirmaciones. Una vez tuve un profesor de yoga en Israel que, en la clase introductoria, explicó con toda seriedad que el yoga lo inventó Abraham, ¡y que todas las posturas básicas del yoga se derivaban de la forma de las letras del alfabeto hebreo! (Así, la postura _trikonasana_ imita la forma de la letra hebrea _aleph_ , la _tuladandasana_ la letra _daled_ , etcétera.) Abraham enseñó estas posturas al hijo de una de sus concubinas, que viajó a la India y enseñó yoga a los indios. Cuando le pregunté si tenía alguna prueba de ello, el maestro citó un versículo bíblico: «A los hijos de las concubinas les hizo donaciones; pero, viviendo él todavía, los separó de su hijo Isaac, hacia oriente, a la tierra de oriente»(4) (Génesis 25, 6). ¿Qué crees que fueron esas donaciones? Como ves, incluso el yoga fue en verdad inventado por los judíos.
Considerar que Abraham inventó el yoga es una idea radical. Pero el judaísmo dominante sostiene de manera solemne que el cosmos entero existe para que los rabinos puedan estudiar sus Sagradas Escrituras y que si los judíos cesaran en esta práctica, el universo tocaría a su fin. China, la India, Australia e incluso las galaxias lejanas serían aniquiladas si en Jerusalén y en Brooklyn los rabinos no debatieran más el Talmud. Este es un artículo de fe básico de los judíos ortodoxos, y quien se atreve a dudar de él es considerado un tonto ignorante. Los judíos seglares pueden ser un poco más escépticos a propósito de esta grandilocuente afirmación, pero también creen que el pueblo judío son los héroes centrales de la historia y el manantial último de la moral, la espiritualidad y el saber humanos.
Aquello de lo que mi pueblo carece en número de personas y en influencia real lo compensa de sobra con desfachatez. Puesto que es más educado criticar a nuestra propia gente que criticar a los extranjeros, utilizaré el ejemplo del judaísmo para ilustrar lo ridículos que son estos discursos sobre la importancia propia, y dejaré que los lectores de todo el mundo pinchen los globos de aire caliente que han inflado sus propias tribus.
__
##### LA MADRE DE FREUD
Mi libro _Sapiens. De animales a dioses. Breve historia de la humanidad_ fue escrito originalmente en hebreo, para un público israelí. Tras publicarse la edición en hebreo en 2011, la pregunta que más veces me hicieron los lectores israelíes era por qué apenas mencionaba el judaísmo en mi historia de la raza humana. ¿Por qué escribía extensamente sobre el cristianismo, el islamismo y el budismo, pero solo dedicaba unas pocas palabras a la religión y al pueblo judíos? ¿Pasaba por alto deliberadamente su inmensa contribución a la historia humana? ¿Me motivaba a ello algún programa político siniestro?
Tales preguntas las formulan naturalmente los judíos israelíes, que desde la guardería son educados para pensar que el judaísmo es la superestrella de la historia humana. Los niños israelíes suelen acabar doce años de escuela sin tener ninguna imagen clara de los procesos históricos globales. Casi no se les enseña nada sobre China, la India o África, y aunque estudian el Imperio romano, la Revolución francesa y la Segunda Guerra Mundial, estas piezas de rompecabezas sueltas no constituyen ninguna narración global. En cambio, la única historia coherente que ofrece el sistema educativo israelí empieza con el Antiguo Testamento hebreo, continúa hasta la época del Segundo Templo, pasa por varias comunidades judías de la Diáspora y culmina con el auge del sionismo, el Holocausto y el establecimiento del Estado de Israel. La mayoría de los estudiantes abandonan la escuela convencidos de que ese debe de ser el principal hilo argumental de todo el relato humano. Porque incluso cuando los pupilos oyen hablar del Imperio romano o de la Revolución francesa, la discusión en clase se centra en la manera como el Imperio romano trató a los judíos o sobre la situación política de los judíos en la República francesa. A la gente alimentada con una dieta histórica de este tipo le cuesta mucho digerir la idea de que el judaísmo tuvo relativamente poco impacto en el mundo en su conjunto.
Pero lo cierto es que el judaísmo desempeñó solo un papel modesto en los anales de nuestra especie. A diferencia de religiones universales como el cristianismo, el islamismo y el budismo, el judaísmo ha sido siempre una fe tribal. Se centra en el destino de una nación pequeña y una tierra minúscula, y le interesa poco la suerte de los demás pueblos y países. Por ejemplo, le preocupan poco los acontecimientos en Japón, o la gente del subcontinente indio. No es extraño, por tanto, que su papel histórico haya sido limitado.
Es verdad que el judaísmo dio origen al cristianismo, y que influyó en el nacimiento del islamismo, dos de las religiones más importantes de la historia. Sin embargo, el reconocimiento por los logros globales del cristianismo y el islamismo, así como la culpa por sus muchos crímenes, es para los propios cristianos y musulmanes y no para los judíos. De la misma manera que sería injusto acusar a los judíos de las matanzas en masa de las cruzadas (el cristianismo es culpable al cien por cien), tampoco hay razón alguna para atribuir al judaísmo la importante idea cristiana de que todos los seres humanos son iguales ante Dios (una idea que entra en contradicción directa con la ortodoxia judía, que incluso en la actualidad sostiene que los judíos son intrínsecamente superiores a los demás humanos).
El papel del judaísmo en el relato de la humanidad es algo así como el papel de la madre de Freud en la historia occidental moderna. Para bien o para mal, Sigmund Freud ejerció una influencia inmensa sobre la ciencia, la cultura, el arte y el saber popular del Occidente moderno. También es cierto que sin la madre de Freud no hubiéramos tenido a Freud, y que es probable que la personalidad, las ambiciones y las opiniones de Freud fueran modeladas de manera importante por sus relaciones con su madre, como él sería el primero en admitir. Pero cuando se escribe la historia del Occidente moderno, nadie espera un capítulo entero dedicado a la madre de Freud. De manera parecida, sin el judaísmo no habría cristianismo, pero eso no merece conceder mucha importancia al judaísmo cuando se escribe la historia del mundo. La cuestión crucial es qué hizo el cristianismo con la herencia de su madre judía.
Ni que decir tiene que el pueblo judío es un pueblo único con una historia asombrosa (aunque esto valga para la mayoría de los pueblos). Asimismo, ni que decir tiene que la tradición judía está llena de conocimientos profundos y valores nobles (aunque también de algunas ideas discutibles, y de actitudes racistas, misóginas y homofóbicas). También es verdad que, en relación con su número, el pueblo judío ha tenido un impacto desproporcionado en la historia de los últimos dos mil años. Pero cuando se analiza el panorama general de nuestra historia como especie, desde la aparición de _Homo_ _sapiens_ hace más de cien mil años, es evidente que la contribución judía a la historia ha sido muy limitada. Los humanos se establecieron en todo el planeta, adoptaron la agricultura, construyeron las primeras ciudades e inventaron la escritura y el dinero miles de años antes de la aparición del judaísmo.
Incluso en los dos últimos milenios, si se considera la historia desde la perspectiva de los chinos o de los indios norteamericanos nativos, es difícil hallar alguna contribución judía importante excepto a través de la mediación de cristianos o musulmanes. Así, el Antiguo Testamento hebreo se convirtió al final en una piedra angular de la cultura humana global porque fue adoptado sinceramente por el cristianismo e incorporado a la Biblia. En cambio, el Talmud (cuya importancia para la cultura judía sobrepasa con mucho la del Antiguo Testamento) fue rechazado por el cristianismo, y en consecuencia siguió siendo un texto esotérico apenas conocido por los árabes, los polacos o los holandeses, por no mencionar a los japoneses y a los mayas. (Lo que es una pena, porque el Talmud es un libro muchísimo más reflexivo y compasivo que el Antiguo Testamento.)
¿Puede el lector citar una gran obra de arte inspirada por el Antiguo Testamento? ¡Oh!, es fácil: el _David_ de Miguel Ángel, _Nabucco_ de Verdi, _Los diez mandamientos_ de Cecil B. DeMille. ¿Conoce el lector alguna obra famosa inspirada por el Nuevo Testamento? Pan comido: _La última cena_ de Leonardo, la _Pasión según San Mateo_ de Bach, _La vida de Brian_ de los Monty Python. Y ahora la prueba real: ¿puede mencionar algunas obras de arte inspiradas por el Talmud?
Aunque las comunidades judías que estudiaban el Talmud se expandieron por grandes partes del mundo, no desempeñaron un papel importante en la creación de los imperios chinos, en los viajes de descubrimiento europeos, en el establecimiento del sistema democrático o en la revolución industrial. La moneda, la universidad, el parlamento, la banca, la brújula, la imprenta y la máquina de vapor fueron inventos de los gentiles.
##### ÉTICA ANTES DE LA BIBLIA
Los israelíes suelen usar la frase «las tres grandes religiones», pensando que dichas religiones son el cristianismo (2.300 millones de adeptos), el islamismo (1.800 millones) y el judaísmo (15 millones). El hinduismo, con sus 1.000 millones de creyentes, y el budismo, con sus 500 millones de seguidores (por no mencionar la religión sintoísta, con 50, y la sij, con 25), no cuentan.[2] Este concepto distorsionado de «las tres grandes religiones» implica a menudo que en la mente de los israelíes las principales religiones y las tradiciones éticas surgieran del seno del judaísmo, que fuera la primera religión que predicó normas éticas universales. Como si los humanos anteriores a los días de Abraham y Moisés hubieran vivido en un estado de naturaleza hobbesiano sin ningún compromiso moral, y como si toda la moralidad contemporánea se derivara de los Diez Mandamientos. Esta es una idea insolente e infundada, que pasa por alto muchas de las tradiciones éticas más importantes del mundo.
Las tribus de cazadores-recolectores de la Edad de Piedra poseían códigos morales decenas de miles de años antes de Abraham. Cuando los primeros colonos europeos llegaron a Australia a finales del siglo XVIII, se encontraron con tribus de aborígenes que tenían una visión ética del mundo bien desarrollada, a pesar de ser totalmente ignorantes de Moisés, Jesús y Mahoma. Sería difícil aducir que los colonos cristianos que desposeyeron de forma violenta a los nativos hicieron gala de códigos morales superiores.
Hoy en día, los científicos señalan que en realidad la moral tiene profundas raíces evolutivas anteriores en millones de años a la aparición de la humanidad. Todos los animales sociales, como lobos, delfines y monos, poseen códigos éticos, adaptados por la evolución para promover la cooperación del grupo.[3] Por ejemplo, cuando los lobeznos juegan entre sí siguen normas de «juego limpio». Si un lobezno muerde demasiado fuerte, o continúa mordiendo a un oponente que se ha tumbado sobre el lomo y se ha rendido, los demás lobeznos dejarán de jugar con él.[4]
En los grupos de chimpancés se espera que los miembros dominantes respeten los derechos de propiedad de los miembros más débiles. Si una hembra joven de chimpancé encuentra una banana, incluso el macho alfa evitará por lo general robársela para quedársela. Si rompe esta norma, es probable que pierda su posición social.[5] Los simios no solo evitan sacar ventaja de los miembros débiles del grupo, sino que a veces los ayudan de manera activa. Un macho de chimpancé pigmeo llamado Kidogo, que vivía en el zoológico municipal de Milwaukee, padecía una dolencia cardíaca grave que hacía que estuviera débil y confuso. Al ser trasladado por primera vez al zoo, no conseguía orientarse ni comprendía las instrucciones de los cuidadores. Cuando los demás chimpancés percibieron su apuro, intervinieron. A menudo cogían a Kidogo de la mano y lo llevaban a donde necesitaba ir. Si Kidogo se perdía, emitía fuertes señales de angustia, y algún simio acudía enseguida a ayudarlo.
Uno de los principales ayudantes de Kidogo era el macho de mayor rango en el grupo, Lody, que no solo guiaba a Kidogo, sino que también lo protegía. Aunque casi todos los miembros del grupo trataban con cariño a Kidogo, un macho joven llamado Murph lo incordiaba con frecuencia sin piedad. Cuando Lody advertía este comportamiento, a menudo hacía huir al abusón, o colocaba un brazo protector alrededor de Kidogo.[6]
Un caso todavía más conmovedor tuvo lugar en las junglas de Costa de Marfil. Después de que un joven chimpancé apodado Oscar perdiera a su madre, se esforzó por sobrevivir solo. Ninguna de las demás hembras estaba dispuesta a adoptarlo y a cuidarlo, porque ya tenían a su cargo a sus propias crías. Poco a poco, Oscar perdió peso, salud y vitalidad. Pero cuando todo parecía perdido, Oscar fue «adoptado» por el macho alfa del grupo, Freddy. Este se aseguraba de que Oscar comiera bien e incluso lo trasladaba cargándolo a cuestas. Las pruebas genéticas demostraron que Freddy no estaba emparentado con Oscar.[7] Solo podemos especular acerca de lo que llevó al viejo y huraño jefe a tomar a su cargo al joven huérfano, pero por lo visto los cabecillas de los simios desarrollaron la tendencia a ayudar a los pobres, necesitados y huérfanos millones de años antes de que la Biblia instruyera a los antiguos israelitas en que «no dañarás a la viuda ni al huérfano» (Éxodo 22), y antes de que el profeta Amós se quejara de las élites sociales «que oprimís a los débiles y maltratáis a los pobres» (Amós 4, 1).
Ni siquiera entre los _Homo sapiens_ que vivían en el Oriente Próximo antiguo los profetas bíblicos carecían de precedentes. «No matarás» y «No robarás» eran bien conocidos en los códigos legales y éticos de las ciudades estado sumerias, en el Egipto faraónico y en el Imperio babilónico. Días de descanso periódicos anteceden con mucho al Sabbat judío. Mil años antes de que el profeta Amós recriminara a las élites israelitas su comportamiento opresor, el rey Hammurabi de Babilonia explicaba que los grandes dioses le habían instruido «para que demostrara justicia en la tierra, destruyera el mal y la maldad, impidiera que los poderosos explotaran a los débiles».[8]
Entretanto, en Egipto (siglos antes del nacimiento de Moisés) los escribas redactaron «el relato del campesino elocuente», que cuenta la historia de un pobre campesino cuya propiedad le había robado un terrateniente codicioso. El campesino fue a ver a los funcionarios corruptos del faraón, y cuando no lo protegieron, empezó a explicarles por qué debían impartir justicia y en particular defender a los pobres ante los ricos. En una vívida alegoría, este campesino egipcio explicó que las escasas posesiones de los pobres son como el mismo aire que respiran, y que la corrupción de los funcionarios los asfixia al obturar sus orificios nasales.[9]
Muchas leyes bíblicas copian las reglas que eran aceptadas en Mesopotamia, Egipto y Canaán siglos e incluso milenios antes de la fundación de los reinos de Judá e Israel. Si el judaísmo bíblico dio a dichas leyes un giro único, fue porque las transformó de normas universales aplicables a todos los humanos en códigos tribales dirigidos sobre todo al pueblo judío. La moral judía se modeló al principio como un asunto tribal y exclusivo, y así ha permanecido en cierta medida hasta hoy en día. El Antiguo Testamento, el Talmud y muchos rabinos (aunque no todos) sostenían que la vida de un judío es más valiosa que la de un gentil, razón por la que, por ejemplo, se permite a los judíos profanar el Sabbat a fin de salvar a un judío de la muerte, pero les está prohibido hacerlo simplemente para salvar a un gentil (Talmud babilónico, Yomá 84, 2).[10]
Algunos sabios judíos han argumentado que incluso el famoso mandamiento «Amarás a tu prójimo como a ti mismo» se refiere solo a los judíos y que no existe ningún mandamiento para amar a los gentiles. De hecho, el texto original del Levítico reza: «No te vengues y no guardes rencor contra los hijos de tu pueblo. Amarás a tu prójimo como a ti mismo» (Levítico 19), que plantea la sospecha de que «tu prójimo» se refiera únicamente a los miembros de «tu pueblo». Esta sospecha está muy reforzada por el hecho de que la Biblia ordena a los judíos exterminar a determinados pueblos, como por ejemplo los amalequitas y los cananeos: «No dejarás con vida a nada de cuanto respira», decreta el libro sagrado, «darás el anatema a esos pueblos, a los heteos, amorreos, cananeos, ferezeos, heveos y jebuseos, como Yahvé, tu Dios, te lo ha mandado» (Deuteronomio 20). Este es uno de los primeros casos registrados en la historia humana en que el genocidio se presentaba como un deber religioso coercitivo.
Solo los cristianos fueron los que escogieron algunos fragmentos seleccionados del código moral judío, los transformaron en mandamientos universales y los difundieron por el mundo. De hecho, el cristianismo se separó del judaísmo justo por esa razón. Mientras que muchos judíos todavía creen que el llamado «pueblo elegido» está más cerca de Dios que otras naciones, el fundador del cristianismo (el apóstol san Pablo) estipuló en su famosa Epístola a los Gálatas que «no hay ya judío o griego, no hay siervo o libre, no hay varón o hembra, porque todos sois uno en Cristo Jesús» (Gálatas 3).
Y hemos de insistir de nuevo en que, a pesar del enorme impacto del cristianismo, esta no fue en absoluto la primera vez que un humano predicó una ética universal. La Biblia está lejos de ser la fuente exclusiva de la moral humana (y menos mal, dadas las numerosas actitudes racistas, misóginas y homofóbicas que contiene). Confucio, Lao-Tse, Buda y Mahavira establecieron códigos éticos universales mucho antes que san Pablo y Jesús, sin saber nada de la tierra de Canaán ni de los profetas de Israel. Confucio enseñó que cada persona debe amar a los demás como se ama a sí misma unos quinientos años antes de que el rabino Hillel el Viejo dijera que esa era la esencia de la Torá. Y en una época en que el judaísmo todavía exigía el sacrificio de animales y el exterminio sistemático de poblaciones humanas enteras, Buda y Mahavira ya instruían a sus seguidores para que evitaran hacer daño no solo a todos los seres humanos, sino a cualquier ser vivo, incluidos los insectos. Por tanto, no tiene en absoluto ningún sentido atribuir al judaísmo y a su descendencia cristiana y musulmana la creación de la moral humana.
##### EL NACIMIENTO DEL FANATISMO
Entonces ¿y el monoteísmo? ¿No merece al menos el judaísmo una mención especial por haber propuesto por vez primera la creencia en un único Dios, lo que no tenía ningún paralelismo en el mundo (aunque esta creencia la propagaran después por los cuatro puntos de la Tierra los cristianos y musulmanes más que los judíos)? Podemos poner alguna objeción incluso a esto, ya que la primera prueba clara de monoteísmo procede de la revolución religiosa del faraón Akenatón hacia 1350 a. C., y documentos como la Estela Mesha (erigida por el rey moabita Mesha) indican que la religión del Israel bíblico no era tan diferente de la religión de reinos vecinos, como Moab. Mesha describe a su gran dios Quemos casi de la misma manera como el Antiguo Testamento a Yahvé. Pero el verdadero problema de la idea de que el monoteísmo es una contribución del judaísmo al mundo es que no puede estar orgulloso precisamente de ello. Desde una perspectiva ética, no hay duda de que el monoteísmo fue una de las peores ideas de la historia humana.
El monoteísmo hizo poco para mejorar las normas morales de los humanos; ¿de verdad piensa el lector que los musulmanes son intrínsecamente más éticos que los hindúes, solo porque los primeros creen en un único dios mientras que los segundos creen en muchos dioses? ¿Eran los conquistadores cristianos más éticos que las tribus nativas americanas paganas? Lo que sin duda hizo el monoteísmo fue conseguir que mucha gente se volviera mucho más intolerante que antes, con lo que contribuyó a la expansión de las persecuciones religiosas y las guerras santas. Los politeístas encontraban perfectamente aceptable que diferentes personas adoraran a dioses distintos y realizaran diversos ritos y rituales. Raramente o nunca luchaban, perseguían o mataban a gente debido solo a sus creencias religiosas. Los monoteístas, en cambio, creían que su Dios era el único, y que exigía obediencia universal. En consecuencia, a medida que el cristianismo y el islamismo se extendían por el mundo, también lo hizo la incidencia de cruzadas, yihads, inquisiciones y discriminaciones religiosas.[11]
Compárese, por ejemplo, la actitud del emperador Ashoka de la India en el siglo III a. C. con la de los emperadores cristianos del Imperio romano tardío. El emperador Ashoka gobernaba un imperio que bullía de religiones, sectas y gurús. Se concedió a sí mismo el título de Amado de los Dioses y El que Contempla a Todos con Afecto. Hacia el año 250 a. C. decretó un edicto imperial de tolerancia que proclamaba:
El Amado de los Dioses, el Rey que Contempla a Todos con Afecto, honra tanto a los ascetas como a los dueños de la casa de todas las religiones ...] y valora que debe haber crecimiento en lo esencial de todas las religiones. El crecimiento en lo esencial puede hacerse de diferentes maneras, pero todas ellas tienen como base la templanza a la hora de hablar, es decir, no alabar la propia religión, o condenar la religión de otros sin buena causa. [...] Quienquiera que elogia su propia religión, debido a devoción excesiva, y condena las demás con el pensamiento «Dejadme glorificar mi propia religión», no hace más que dañar a su misma religión. Por tanto, el contacto entre religiones es bueno. Deben escucharse y respetarse las doctrinas profesadas por otros. El Amado de los Dioses, el Rey que Contempla a Todos con Afecto, desea que todo sea bien aprendido en las buenas doctrinas de otras religiones.[[12]
Quinientos años después, el Imperio romano tardío era tan múltiple como la India de Ashoka, pero cuando el cristianismo tomó el relevo, los emperadores adoptaron una estrategia muy distinta respecto a la religión. Empezando con Constantino el Grande y su hijo Constancio II, los emperadores cerraron todos los templos no cristianos y prohibieron los rituales calificados de «paganos» so pena de muerte. La persecución culminó bajo el reinado del emperador Teodosio (cuyo nombre significa «dado por Dios»), que en 391 proclamó los Decretos Teodosianos, a raíz de los cuales todas las religiones, excepto el cristianismo y el judaísmo, fueron ilegales (el judaísmo también era perseguido de muchas maneras, pero practicarlo seguía siendo legal).[13] Según las nuevas leyes, un ciudadano podía ser ejecutado incluso por adorar a Júpiter o a Mitra en la intimidad de su propia casa.[14] Como parte de su campaña para barrer del imperio toda herencia infiel, los emperadores cristianos suspendieron asimismo los Juegos Olímpicos. Tras haberse celebrado durante más de mil años, la última olimpiada antigua tuvo lugar en algún momento a finales del siglo IV o principios del V.[15]
Desde luego, no todos los gobernantes monoteístas fueron tan intolerantes como Teodosio, y muchos gobernantes rechazaron el monoteísmo sin adoptar las políticas tolerantes de Ashoka. No obstante, al insistir en que «no hay otro dios que nuestro Dios», la idea monoteísta tendió a promover el fanatismo. Los judíos harían bien en restar importancia a su participación en la diseminación de este peligroso meme, y dejar que cristianos y musulmanes carguen con esa culpa.
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##### FÍSICA JUDÍA, BIOLOGÍA CRISTIANA
Solo en los siglos XIX y XX vemos que los judíos realizan una contribución extraordinaria al conjunto de la humanidad mediante el importantísimo papel desempeñado por ellos en la ciencia moderna. Además de nombres tan conocidos como Einstein y Freud, alrededor del 20 por ciento de todos los galardonados con el Premio Nobel de Ciencia han sido judíos, aunque en total estos constituyen menos del 0,2 por ciento de la población mundial.[16] Pero debe destacarse que ha sido una contribución de judíos individuales y no del judaísmo como religión o cultura. La mayoría de los científicos judíos importantes de los últimos doscientos años trabajaron fuera de la esfera religiosa judía. De hecho, los judíos empezaron a efectuar su notable contribución a la ciencia solo cuando abandonaron las yeshivás en favor de los laboratorios.
Antes de 1800, la influencia de los judíos en la ciencia era limitada. Por supuesto, no desempeñaron ningún papel decisivo en el progreso de la ciencia en China, la India o en la civilización maya. En Europa y en Oriente Próximo algunos pensadores judíos como Maimónides ejercieron una influencia considerable en sus colegas gentiles, pero el impacto judío global fue más o menos proporcional a su peso demográfico. Durante los siglos XVI, XVII y XVIII, el judaísmo no fue decisivo para el inicio de la revolución científica. Excepto por Spinoza (que fue excomulgado por sus aspectos conflictivos por la comunidad judía), apenas puede nombrarse un solo judío que fuera fundamental para el nacimiento de la física, la química, la biología o las ciencias sociales modernas. No sabemos qué hacían los antepasados de Einstein en los días de Galileo y Newton, pero seguro que estaban más interesados en estudiar el Talmud que en estudiar la luz.
El gran cambio se produjo ya en los siglos XIX y XX, cuando la secularización y la Ilustración judía hicieron que muchos hebreos adoptaran la visión del mundo y el estilo de vida de sus vecinos gentiles. Entonces empezaron a frecuentar las universidades y los centros de investigación de Alemania, Francia y Estados Unidos. Desde los guetos y los _shtetls_ ,(5) los estudiosos judíos llevaron consigo importantes legados culturales. El valor fundamental de la educación en la cultura judía fue una de las principales razones para el éxito extraordinario de los científicos judíos. Otros factores fueron el deseo de una minoría perseguida de demostrar su valor y las barreras que impedían que judíos de talento progresaran en instituciones más antisemitas, como el ejército y la administración del Estado.
Pero mientras que los científicos judíos aportaban desde las yeshivás una disciplina férrea y una profunda fe en el valor del conocimiento, no llevaban consigo ningún equipaje útil de ideas e intuiciones concretas. Einstein era judío, pero la teoría de la relatividad no era «física judía». ¿Qué tiene que ver la fe en el carácter sagrado de la Torá con la intuición de que la energía es igual a la masa multiplicada por la velocidad de la luz al cuadrado? Puestos a comparar, Darwin era cristiano e incluso inició en Cambridge estudios que le habrían permitido convertirse en un sacerdote anglicano. ¿Implica eso que la teoría de la evolución es una teoría cristiana? Sería ridículo poner en una lista la teoría de la relatividad como contribución judía a la humanidad, de la misma manera que sería ridículo atribuir al cristianismo la teoría de la evolución.
De forma parecida, es difícil ver nada particularmente judío en la invención del proceso para sintetizar amoníaco por parte de Fritz Haber (Nobel de Química en 1918); en el descubrimiento del antibiótico estreptomicina por Selman Waksman (Nobel de Fisiología o Medicina en 1952), o en el descubrimiento de los cuasicristales por Dan Shechtman (Nobel de Química en 2011). En el caso de los estudiosos de las humanidades y las ciencias sociales (como Freud), su herencia judía tuvo probablemente mayor impacto en sus intuiciones. Pero incluso en tales casos, las discontinuidades son más patentes que los eslabones que sobreviven. Las ideas de Freud sobre la psique humana eran muy diferentes de las del rabino Joseph Caro o las del rabino Yochanan ben Zakkai, y no descubrió el complejo de Edipo al leer detenidamente la Shulhan Arukh (el código de la ley judía).
En resumen: aunque la importancia dada por los judíos a la educación probablemente constituyera un elemento decisivo en el éxito excepcional de los científicos judíos, fueron los pensadores gentiles quienes pusieron los cimientos para los logros de Einstein, Haber y Freud. La revolución científica no fue un proyecto judío, y los judíos solo encontraron su lugar en ella cuando pasaron de las yeshivás a las universidades. De hecho, la costumbre judía de buscar respuestas a todas las preguntas mediante la lectura de textos antiguos supuso un obstáculo importante para la integración judía en el mundo de la ciencia moderna, donde las respuestas proceden de observaciones y experimentos. Si algo intrínseco a la religión judía lleva necesariamente a los descubrimientos científicos, ¿por qué entre 1905 y 1933 diez judíos alemanes seglares ganaron el Premio Nobel en Química, Medicina y Física, pero en el mismo período ni un solo judío ultraortodoxo o ni un solo judío búlgaro o yemenita obtuvieron ninguno?
Para no parecer un «judío que se odia a sí mismo» o un antisemita, quisiera insistir en que no digo que el judaísmo fuera una religión particularmente malévola o ignorante. Lo único que digo es que no fue en particular importante para la historia de la humanidad. Durante muchos siglos, fue la humilde religión de una pequeña minoría perseguida que prefería leer y contemplar en lugar de conquistar países alejados y quemar a herejes en la hoguera.
Los antisemitas suelen pensar que los judíos son muy importantes. Imaginan que los judíos controlan el mundo, o el sistema bancario, o al menos los medios de comunicación, y que son los culpables de todo, desde el calentamiento global hasta los ataques del 11-S. Esta paranoia antisemita es tan ridícula como la megalomanía judía. Los judíos pueden ser un pueblo muy interesante, pero cuando se observa el panorama en su totalidad, hay que reconocer que han tenido un impacto muy limitado en el mundo.
A lo largo de la historia, los humanos han creado cientos de religiones y sectas diferentes. De ellas, unas cuantas (el cristianismo, el islamismo, el hinduismo, el confucianismo y el budismo) influyeron en miles de millones de personas (no siempre para bien). La inmensa mayoría de credos (como las religiones bon, yoruba y judía) tuvieron un impacto mucho menor. Personalmente, me gusta la idea de descender no de brutales conquistadores del mundo, sino de gente insignificante que rara vez metía la nariz en los asuntos de otras personas. Muchas religiones elogian el valor de la humildad pero después imaginan ser el centro del universo. Mezclan llamadas a la mansedumbre personal con una descarada arrogancia colectiva. Humanos de todas las creencias harían bien en tomarse más en serio la humildad.
Y entre todas las formas de humildad, quizá la más importante sea la humildad ante Dios. Cuando hablan de Dios, con gran frecuencia los humanos profesan una modestia supina, pero después usan el nombre de Dios para tratar despóticamente a sus hermanos.
### 13
Dios
#### No tomes el nombre de Dios en vano
¿Existe Dios? Eso depende del Dios que el lector tenga en mente. ¿El misterio cósmico o el legislador mundano? A veces, cuando la gente habla de Dios, se refiere a un enigma grandioso e impresionante, acerca del cual no sabemos absolutamente nada. Invocamos a ese Dios misterioso para explicar los enigmas más profundos del cosmos. ¿Por qué hay algo, en lugar de nada? ¿Qué modeló las leyes fundamentales de la física? ¿Qué es la conciencia y de dónde procede? No tenemos respuestas para estas preguntas, y damos a nuestra ignorancia el nombre grandioso de Dios. La característica fundamental de este Dios misterioso es que no podemos decir nada concreto sobre Él. Es el Dios de los filósofos, el Dios del que hablamos cuando nos sentamos alrededor de una fogata en el campo a altas horas de la noche y nos preguntamos sobre el sentido de la vida.
En otras ocasiones, la gente ve a Dios como un legislador severo y mundano, acerca del cual sabemos demasiado. Sabemos exactamente qué piensa sobre la moda, la comida, el sexo y la política, e invocamos a este Hombre Enojado en el Cielo para justificar un millón de normas, decretos y conflictos. Se molesta cuando las mujeres llevan blusas de manga corta, cuando dos hombres practican sexo entre sí o cuando los adolescentes se masturban. Algunas personas dicen que a Él no le gusta que bebamos alcohol, mientras que según otras Él exige absolutamente que bebamos vino todos los viernes por la noche o las mañanas del domingo. Se han escrito bibliotecas enteras para explicar hasta el más mínimo detalle qué es exactamente lo que Él quiere y lo que no le gusta. La característica fundamental de este legislador mundano es que podemos decir cosas muy concretas de Él. Es el Dios de los cruzados y de los yihadistas, de los inquisidores, los misóginos y los homófobos. Es el Dios del que hablamos cuando nos encontramos alrededor de una pira encendida, lanzando piedras e insultos a los herejes que están quemándose en ella.
Cuando a los creyentes se les pregunta si Dios de verdad existe, suelen empezar hablando de los misterios enigmáticos del universo y de los límites del conocimiento humano. «La ciencia no puede explicar el big bang —exclaman—, de modo que tiene que haberlo hecho Dios.» Pero, al igual que un mago que engaña al público sustituyendo de manera imperceptible una carta por otra, los creyentes sustituyen con rapidez el misterio cósmico por el legislador mundano. Después de haber dado el nombre «Dios» a los secretos desconocidos del cosmos, lo utilizan para condenar de alguna manera biquinis y divorcios. «No comprendemos el big bang; por tanto, debes cubrirte el pelo en público y votar contra el matrimonio gay.» No solo no existe ninguna conexión lógica entre ambas cosas, sino que en realidad son contradictorias. Cuanto más profundos son los misterios del universo, menos probable es que a quienquiera que sea responsable de ellos le importen un pimiento los códigos de la vestimenta femenina o el comportamiento sexual humano.
El eslabón perdido entre el misterio cósmico y el legislador mundano suele proporcionarlo algún libro sagrado. El libro está lleno de las normas más tontas, pero no obstante se atribuye al misterio cósmico. En teoría lo compuso el creador del espacio y del tiempo, pero Él se preocupó de iluminarnos sobre todo acerca de algunos arcanos rituales del templo y tabúes alimentarios. Lo cierto es que no tenemos ninguna evidencia, de ningún tipo, de que la Biblia o el Corán o el Libro de Mormón o los Vedas o cualquier otro texto sagrado fuera compuesto por la fuerza que determinó que la energía sea igual a la masa multiplicada por la velocidad de la luz al cuadrado, y que los protones sean 1.837 veces mayores que los electrones. Hasta donde llega nuestro conocimiento científico, todos estos libros sagrados fueron escritos por _Homo sapiens_ imaginativos. Solo son narraciones inventadas por nuestros antepasados con el fin de legitimar normas sociales y estructuras políticas.
Yo siempre estoy preguntándome acerca del misterio de la existencia, pero nunca he comprendido qué tiene que ver con las exasperantes leyes del judaísmo, el cristianismo o el hinduismo. Estas leyes fueron sin duda muy útiles a la hora de establecer y mantener el orden social durante miles de años. Pero en esto no son fundamentalmente diferentes de las leyes de los estados e instituciones seculares.
El tercero de los Diez Mandamientos bíblicos instruye a los humanos a no hacer nunca un uso arbitrario del nombre de Dios. Muchas personas creen en esto de una manera infantil, como una prohibición de pronunciar el nombre explícito de Dios (como en la famosa escena de los Monty Python «Si dices Jehová...»). Quizá el significado profundo de este mandamiento sea que nunca hemos de usar el nombre de Dios para justificar nuestros intereses políticos, nuestras ambiciones económicas o nuestros odios personales. La gente odia a alguien y dice: «Dios lo odia»; la gente codicia algo y dice: «Dios lo quiere». El mundo sería un lugar mejor si siguiéramos de manera más devota el tercer mandamiento. ¿Quieres emprender la guerra contra tus vecinos y robarles su tierra? Deja a Dios fuera de la cuestión y encuentra otra excusa.
A fin de cuentas, se trata de una cuestión de semántica. Cuando uso la palabra «Dios», pienso en el Dios de Estado Islámico, de las cruzadas, de la Inquisición y de las banderolas «Dios odia a los maricones». Cuando pienso en el misterio de la existencia, prefiero usar otras palabras, para evitar la confusión. Y a diferencia del Dios de Estado Islámico y de las cruzadas (al que preocupan mucho los nombres y sobre todo Su nombre más sagrado), al misterio de la existencia le importa un comino qué nombres le demos nosotros, los simios.
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##### ÉTICA IMPÍA
Por supuesto, el misterio cósmico no nos ayuda lo más mínimo a mantener el orden social. La gente suele defender que tenemos que creer en un dios que proporcionó algunas leyes muy concretas a los humanos; de lo contrario, la moral desaparecería y la sociedad se sumiría en un caos primigenio.
Es verdad que la creencia en dioses fue vital para varios órdenes sociales y que a veces tuvo consecuencias positivas. De hecho, las mismas religiones que inspiran odio y fanatismo en algunas personas inspiran amor y compasión en otras. Por ejemplo, a principios de la década de 1960, el reverendo metodista Ted McIlvenna fue consciente de la difícil situación en que se encontraba el colectivo LGBT de su comunidad. Empezó a analizar la situación de gais y lesbianas en la sociedad en general, y en mayo de 1964 convocó una reunión de tres días para fomentar el diálogo entre clérigos y activistas gais y lesbianas en el White Memorial Retreat Center en California. Luego los participantes establecieron el Consejo sobre Religión y el Homosexual, que además de a los activistas incluía a ministros metodistas, episcopalianos, luteranos y de la Iglesia Unida de Cristo. Esta fue la primera organización norteamericana que se atrevió a usar la palabra «homosexual» en su nombre oficial.
En los años siguientes, las actividades del CRH abarcaron desde organizar fiestas de disfraces hasta emprender acciones legales contra la discriminación y persecución injustas. El CRH se convirtió en la semilla del movimiento de los derechos de los gais en California. El reverendo McIlvenna y los otros hombres de Dios que se le unieron eran muy conscientes de los mandatos bíblicos contra la homosexualidad, pero pensaron que era más importante ser fieles al espíritu compasivo de Cristo que a la palabra estricta de la Biblia.[1]
Sin embargo, aunque los dioses pueden inspirarnos para que seamos compasivos, la fe religiosa no es una condición necesaria para el comportamiento moral. La idea de que necesitamos un ser sobrenatural que nos haga actuar moralmente implica que hay algo no natural en lo moral. Pero ¿por qué? La moral de algún tipo es natural. Todos los mamíferos sociales, desde los chimpancés hasta las ratas, poseen códigos éticos que ponen límites a cosas como el robo y el homicidio. Entre los humanos, la moral está presente en todas las sociedades, aunque no todas crean en el mismo dios, o no crean en ningún dios. Los cristianos actúan con caridad incluso sin creer en el panteón hindú, los musulmanes valoran la honestidad a pesar de rechazar la divinidad de Cristo, y los países seculares, como Dinamarca y la República Checa, no son más violentos que los países devotos, como Irán y Pakistán.
La moral no significa «seguir los mandatos divinos». Significa «reducir el sufrimiento». De ahí que para actuar moralmente no haga falta creer en ningún mito o relato. Solo necesitamos comprender de manera profunda el sufrimiento. Si comprendemos en verdad cómo un acto causa un sufrimiento innecesario, a nosotros mismos o a otros, nos abstendremos naturalmente de ella. No obstante, la gente asesina, viola y roba porque solo entiende de manera superficial la desgracia que ello causa. Se obsesiona en satisfacer su lujuria o su avaricia inmediatas, sin preocuparse por el impacto que causa en los demás, o incluso por el impacto a largo plazo sobre ellos mismos. Aun los inquisidores que deliberadamente infligen a su víctima tanto dolor como sea posible, suelen emplear varias técnicas insensibilizadoras y deshumanizadoras para distanciarse de lo que están haciendo.[2]
El lector podría objetar que todo humano busca de manera natural evitar sentirse desgraciado, pero ¿por qué habría de preocuparse un humano por las desgracias de los demás, a menos que algún dios lo exigiera? Una respuesta evidente es que los humanos son animales sociales, de modo que su felicidad depende en una medida muy grande de sus relaciones con los demás. Sin amor, amistad y comunidad, ¿quién puede ser feliz? Una vida egocéntrica y solitaria casi siempre es garantía de infelicidad. De modo que, como mínimo, para ser felices necesitamos preocuparnos de nuestra familia, nuestros amigos y los miembros de nuestra comunidad.
¿Y qué pasa, entonces, con quienes nos son totalmente extraños? ¿Por qué no matar a los extraños y arrebatarles sus posesiones para enriquecerme yo y enriquecer a mi tribu? Muchos pensadores han construido complicadas teorías sociales que explican que, a la larga, este comportamiento es contraproducente. No querríamos vivir en una sociedad donde a los extraños se les roba y asesina de forma rutinaria. No solo nos hallaríamos en peligro constante, sino que además no nos beneficiaríamos de cosas como el comercio, que depende de la confianza entre extraños. Los mercaderes no suelen visitar los antros de ladrones. Esta es la manera como los teóricos seculares, desde la antigua China hasta la moderna Europa, han justificado la regla de oro de «no hagas a los demás lo que no querrías que ellos te hicieran».
Pero en verdad no hacen falta teorías tan complejas y a largo plazo de este tipo para encontrar una base natural de la compasión universal. Olvidemos el comercio por un momento. En un plano mucho más inmediato, hacer daño a los demás siempre me hace daño también a mí. Cada acto violento en el mundo empieza con un deseo violento en la mente de alguien, que perturba la paz y la felicidad de dicha persona antes de perturbar la paz y la felicidad de alguna otra. Así, la gente rara vez roba a menos que primero desarrolle en su mente mucha avaricia y envidia. La gente no suele matar a menos que primero genere ira y odio. Las emociones como la avaricia, la envidia, la ira y el odio son muy desagradables. No podemos experimentar alegría y armonía si estamos llenos de odio o envidia. De modo que mucho antes de que matemos a alguien, nuestra ira ya ha matado nuestra paz de espíritu.
De hecho, podríamos sentir ira durante años sin llegar a matar realmente al objeto de nuestra ira. En cuyo caso no hemos dañado a nadie, pero sí nos hemos hecho daño a nosotros mismos. Por tanto, es nuestro propio interés natural (y no el mandamiento de un dios) lo que debería inducirnos a actuar respecto a nuestra ira. Si estuviéramos completamente libres de ira nos sentiríamos muchísimo mejor que si matáramos a un enemigo odioso.
En el caso de algunas personas, la firme creencia en un dios compasivo que nos ordena poner la otra mejilla puede ayudar a refrenar la ira. Esta ha sido una contribución enorme de la fe religiosa a la paz y la armonía del mundo. Por desgracia, en otras personas la fe religiosa aviva y justifica en realidad su ira, en especial si alguien se atreve a insultar a su dios o a no hacer caso de sus deseos. De modo que el valor del dios legislador depende en último término del comportamiento de sus devotos. Si actúan bien, pueden creer lo que quieran. De manera similar, el valor de los ritos religiosos y los lugares sagrados depende del tipo de sentimientos y comportamientos que inspiran. Si visitar un templo hace que la gente experimente paz y armonía, es maravilloso. Pero si un templo en concreto provoca violencia y conflictos, ¿para qué lo necesitamos? Es a todas luces un templo disfuncional. De la misma manera que no tiene sentido luchar por un árbol enfermo que produce espinas en lugar de frutos, también carece de sentido luchar por un templo defectuoso que genera enemistad en lugar de armonía.
No visitar ningún templo ni creer en ningún dios es también una opción viable. Como se ha demostrado en los últimos siglos, no hace falta invocar el nombre de Dios para llevar una vida moral. El laicismo puede proporcionarnos todos los valores que necesitamos.
### 14
Laicismo
#### Acepta tu sombra
¿Qué significa ser laico, secular o seglar? La laicidad se define a veces como la negación de la religión y, por tanto, a las personas laicas se las caracteriza por lo que no creen y no hacen. Según esta definición, las personas seculares no creen en dioses ni en ángeles, no van a iglesias ni a templos y no realizan ritos ni rituales. De esta manera, el mundo laico parece vacío, nihilista y amoral: una caja vacía a la espera de ser llenada con algo.
Pocas personas adoptarían una identidad tan negativa. Quienes se profesan laicos consideran el laicismo o secularismo de una manera muy diferente. Para ellos, el secularismo es una visión del mundo muy positiva y activa, que se define por un código de valores coherente y no por oposición a esta o a aquella religión. En realidad, varias tradiciones religiosas comparten muchos de los valores laicos. A diferencia de algunas sectas que insisten en que tienen el monopolio de toda la sabiduría y la bondad, una de las principales características de las personas laicas es que no reclaman dicho monopolio. No creen que la moral y la sabiduría bajen de los cielos en un lugar y momento determinados. Más bien, la moral y la sabiduría son la herencia natural de todos los humanos. De ahí que solo quepa esperar que al menos algunos valores surjan en las sociedades humanas por todo el mundo, y que sean comunes a musulmanes, cristianos, hindúes y ateos.
Los líderes religiosos suelen plantear a sus seguidores una elección rigurosa de esto o aquello: o bien eres musulmán, o bien no lo eres. Y si eres musulmán, debes rechazar las demás doctrinas. En cambio, las personas laicas están cómodas con identidades híbridas múltiples. En lo que concierne al laicismo, uno puede considerarse musulmán y continuar orando a Alá, comer comida halal y efectuar el _haj_ a La Meca, pero también ser un buen miembro de la sociedad seglar, mientras se acepte el código ético seglar. Este código ético (que, de hecho, es aceptado por millones de musulmanes, cristianos e hindúes, así como por los ateos), consagra los valores de la verdad, la compasión, la igualdad, la libertad, el valor y la responsabilidad. Constituye los cimientos de las instituciones científicas y democráticas modernas.
Como todos los códigos éticos, el código laico es un ideal al que aspirar más que una realidad social. De la misma manera que las sociedades y las instituciones cristianas se desvían a menudo del ideal cristiano, también las sociedades e instituciones seculares suelen quedarse muy lejos del ideal secular. La Francia medieval era un reino que se autoproclamó cristiano, pero hizo incursiones en todo tipo de actividades no muy cristianas (y si no, que se lo pregunten al campesinado oprimido). La Francia moderna es un Estado que se autoproclamó laico, pero desde los días de Robespierre se ha tomado algunas libertades preocupantes respecto a la definición misma de libertad (y si no, que se lo pregunten a las mujeres). Esto no significa que las personas laicas (en Francia o en algún otro lugar) carezcan de una brújula moral o de compromiso ético. Simplemente significa que no es fácil vivir a la altura de un ideal.
##### EL IDEAL LAICO
¿Qué es, pues, el ideal laico? El compromiso secular más importante es con la VERDAD, que se basa en la observación y la evidencia y no en la simple fe. Los seglares se esfuerzan para no confundir verdad con fe. Si tenemos una gran fe en algún relato, esto puede decirnos muchísimas cosas interesantes sobre nuestra psicología, sobre nuestra infancia y sobre nuestra estructura cerebral, pero no demuestra que el relato sea cierto. (A menudo se necesita una gran fe justo cuando el relato no es cierto.)
Además, los seglares no santifican ningún grupo, a ninguna persona ni ningún libro como si ellos, y solo ellos, fueran los únicos custodios de la verdad. En lugar de eso, las personas laicas santifican la verdad allá donde pueda revelarse: en antiguos huesos fosilizados, en imágenes de lejanas galaxias, en tablas de datos estadísticos o en los escritos de las diversas tradiciones humanas. Este compromiso con la verdad está en la base de la ciencia moderna, que ha permitido a la humanidad desintegrar el átomo, descifrar el genoma, seguir la huella de la evolución de la vida y comprender la historia de la humanidad misma.
El otro compromiso fundamental de las personas laicas es con la COMPASIÓN. La ética laica se basa no en la obediencia de los edictos de este o aquel dios, sino en una profunda comprensión del sufrimiento. Por ejemplo, la gente secular se abstiene del homicidio no porque algún libro antiguo lo prohíba, sino porque matar inflige un sufrimiento inmenso a seres conscientes. Hay algo hondamente preocupante y peligroso en las personas que evitan matar solo porque «Dios así lo dice». Estas personas que están motivadas por la obediencia, no por la compasión, ¿qué harán si acaban creyendo que su Dios les ordena matar a herejes, a brujas, a adúlteros o a extranjeros?
Desde luego, en ausencia de mandamientos divinos absolutos la ética secular se enfrenta a veces a dilemas difíciles. ¿Qué ocurre cuando la misma acción daña a una persona pero ayuda a otra? ¿Es ético gravar con impuestos elevados a los ricos con el fin de ayudar a los pobres? ¿Emprender una guerra sangrienta para derrocar a un dictador brutal? ¿Permitir la entrada de un número ilimitado de refugiados en nuestro país? Cuando las personas laicas se enfrentan a este tipo de dilemas, no preguntan: «¿Qué es lo que Dios ordena?». En cambio, sopesan con cuidado los sentimientos de todas las partes concernidas, analizan una amplia gama de observaciones y posibilidades, y buscan una vía intermedia que cause tan poco daño como sea posible.
Considérense, por ejemplo, las actitudes en relación con la sexualidad. ¿Cómo deciden las personas laicas si respaldar u oponerse a la violación, a la homosexualidad, a la bestialidad y al incesto? Analizando los sentimientos. La violación es obviamente inmoral, no porque vulnere algún mandamiento divino, sino porque hace daño a personas. En cambio, una relación de amor entre dos hombres no daña a nadie, de modo que no hay razón para prohibirla.
¿Y qué hay de la bestialidad? He participado en numerosos debates privados y públicos sobre el matrimonio gay, y con demasiada frecuencia algún listillo pregunta: «Si el matrimonio entre dos hombres está bien, ¿por qué no permitir el matrimonio entre un hombre y una cabra?». Desde una perspectiva seglar, la respuesta es evidente. Las relaciones saludables requieren profundidad emocional, intelectual e incluso espiritual. Un matrimonio que carezca de esta profundidad hará que estemos frustrados, solos y atrofiados psicológicamente. Mientras que dos hombres pueden satisfacer sin duda las necesidades emocionales, intelectuales y espirituales mutuas, una relación con una cabra no puede. De modo que si se considera que el matrimonio es una institución dirigida a promover el bienestar humano, como hacen las personas laicas, ni se nos ocurriría plantear esta extraña pregunta. Solo las personas que ven el matrimonio como una especie de ritual milagroso podrían formularla.
Y entonces ¿qué hay de las relaciones entre un padre y su hija? Ambos son humanos, de manera que ¿qué hay de malo en ello? Bueno, numerosos estudios psicológicos han demostrado que tales relaciones causan un daño inmenso y por lo general irreparable en la chica. Además, reflejan e intensifican las tendencias destructivas en el progenitor. La evolución ha modelado la psique de los sapiens de tal forma que los vínculos románticos no se mezclan bien con los parentales. Por tanto, no es necesario acudir a Dios o a la Biblia para oponerse al incesto; solo hay que leer los estudios psicológicos relevantes.[1]
Esta es la razón profunda de por qué las personas laicas aprecian la verdad científica: no con el fin de satisfacer su curiosidad, sino para saber cuál es la mejor manera de reducir el sufrimiento en el mundo. Sin la guía de los estudios científicos, nuestra compasión suele ser ciega.
Los compromisos hermanados con la verdad y la compasión resultan también en un compromiso con la IGUALDAD. Aunque las opiniones difieren en lo que concierne a cuestiones de igualdad económica y política, las personas laicas sospechan en esencia de todas las jerarquías apriorísticas. El sufrimiento es el sufrimiento, da igual quién lo padezca; y el saber es el saber, con independencia de quién lo descubra. Es probable que dar un trato de favor a las experiencias o los descubrimientos de una nación, una clase o un género concretos nos haga insensibles e ignorantes. Las personas seglares están sin duda orgullosas del carácter único de su nación, su país y su cultura concretos, pero no confunden «carácter único» con «superioridad». De ahí que, aunque los laicos reconocen sus deberes especiales hacia su nación y su país, no piensan que sean exclusivos, y al mismo tiempo reconocen sus deberes hacia la humanidad como un todo.
No podemos buscar la verdad y la manera de acabar con el sufrimiento sin la LIBERTAD de pensar, investigar y experimentar. De ahí que las personas laicas aprecien la libertad y eviten conceder autoridad suprema a ningún texto, institución o líder como jueces últimos de lo que es verdad y lo que está bien. Los humanos deberían conservar siempre la libertad de dudar, de volver a comprobar, de escuchar una segunda opinión, de escoger un camino distinto. Los laicos admiran a Galileo Galilei, que se atrevió a poner en cuestión que la Tierra se hallara en verdad inmóvil en el centro del universo; admiran a las masas de personas de a pie que asaltaron la Bastilla en 1789 y derrocaron el régimen despótico de Luis XVI, y admiran a Rosa Parks, que tuvo la valentía de sentarse en un asiento de autobús reservado únicamente a pasajeros blancos.
Se requiere mucha VALENTÍA para luchar contra los prejuicios y los regímenes opresivos, pero todavía se necesita más para admitir que no sabemos y aventurarnos en lo desconocido. La educación laica nos enseña que si ignoramos algo, no deberíamos tener miedo de reconocerlo ni de buscar nueva información. Incluso si creemos que sabemos algo, no deberíamos tener miedo de dudar de nuestras opiniones y de volver a comprobarlo. Muchas personas temen lo desconocido y quieren respuestas claras para cada pregunta. El miedo a lo desconocido puede paralizarnos más que cualquier tirano. A lo largo de la historia, a la gente le ha preocupado el hecho de que si no depositábamos toda nuestra fe en algún conjunto de respuestas absolutas, la sociedad humana se desmoronaría. En realidad, la historia moderna ha demostrado que una sociedad de individuos valientes dispuestos a admitir la ignorancia y a plantear preguntas difíciles suele ser no solo más próspera, sino también más pacífica que las sociedades en que todos deben aceptar sin cuestionarla una única respuesta. Las personas que temen perder su verdad tienden a mostrarse más violentas que las personas que están acostumbradas a considerar el mundo desde distintos puntos de vista. Las cuestiones a las que no podemos responder suelen ser mucho mejores para nosotros que las respuestas que no podemos cuestionar.
Por último, las personas laicas valoran la RESPONSABILIDAD. No creen en ningún poder superior que se encargue del mundo, castigue a los malos, recompense a los justos y nos proteja del hambre, la peste o la guerra. De ahí que nosotros, mortales de carne y hueso, hemos de aceptar la responsabilidad por lo que sea que hagamos o no hagamos. Si el mundo está lleno de desgracia, es nuestro deber encontrar soluciones. Los laicos se enorgullecen de los inmensos logros de las sociedades modernas, como los de curar epidemias, dar de comer a los hambrientos y llevar la paz a grandes regiones del mundo. No necesitamos atribuir a ningún protector divino estos logros: son el resultado de humanos que desarrollaron su propio saber y compasión. Pero, justo por la misma razón, debemos aceptar toda la responsabilidad por los crímenes y fracasos de la modernidad, desde los genocidios hasta la degradación ecológica. En lugar de rezar para que ocurran milagros, necesitamos preguntar qué podemos hacer nosotros para ayudar.
Estos son los principales valores del mundo laico. Como ya se ha indicado, ninguno de dichos valores es en exclusiva secular. Los judíos también valoran la verdad, los cristianos valoran la compasión, los musulmanes valoran la igualdad, los hindúes valoran la responsabilidad, etcétera. Las sociedades e instituciones laicas se complacen en reconocer estos vínculos y en recibir con los brazos abiertos a judíos, a cristianos, a musulmanes y a hindúes religiosos, siempre que cuando el código laico entre en conflicto con la doctrina religiosa, esta última ceda el paso. Por ejemplo, para ser aceptados en la sociedad laica, se espera que los judíos ortodoxos traten a los no judíos como sus iguales, que los cristianos eviten quemar a los herejes en la hoguera, que los musulmanes respeten la libertad de expresión y que los hindúes renuncien a la discriminación basada en las castas.
En cambio, no se espera que las personas religiosas renieguen de Dios ni abandonen sus ritos y rituales tradicionales. El mundo seglar juzga a la gente según su comportamiento y no sus vestidos ni ceremonias favoritos. Una persona puede seguir el código de vestir sectario más estrafalario y practicar las más extrañas ceremonias religiosas, pero comportarse mostrando un profundo compromiso hacia los valores laicos fundamentales. Hay muchísimos científicos judíos, ambientalistas cristianos, musulmanes feministas e hindúes activistas por los derechos humanos. Si son leales a la verdad científica, a la compasión, a la igualdad y a la libertad, son miembros de pleno derecho del mundo laico, y no hay en absoluto ninguna razón para pedirles que se quiten sus marmullas, sus cruces, sus hiyabs o sus tilakas.
Por razones parecidas, la educación laica no significa un adoctrinamiento negativo que enseñe a los niños a no creer en Dios y a no participar en ninguna ceremonia religiosa. Más bien, la educación laica enseña a los niños a distinguir la verdad de las creencias, a desarrollar la compasión hacia todos los seres que sufren, a apreciar la sabiduría y las experiencias de todos los moradores de la Tierra, a pensar libremente sin temer lo desconocido, y a ser responsable de sus actos y del mundo en su conjunto.
##### ¿ERA LAICO STALIN?
Por tanto, no tiene ningún fundamento criticar el laicismo por carecer de compromisos éticos o de responsabilidades sociales. En realidad, el principal problema del laicismo es justo el contrario: probablemente coloque demasiado alto el listón ético. La mayoría de la gente no puede estar a la altura de un código tan exigente, y las sociedades grandes no pueden ser gobernadas sobre la base de la búsqueda abierta de la verdad y la compasión. En especial en épocas de emergencia (como la guerra o una crisis económica), las sociedades han de actuar rápida y enérgicamente, incluso si no están seguras de cuál es la verdad y cuál es la acción más compasiva que puede emprenderse. Necesitan guías claras, consignas pegadizas y gritos de batalla inspiradores. Dado que es difícil enviar soldados a la batalla o imponer reformas económicas radicales en el nombre de conjeturas dudosas, los movimientos laicos mutan de forma repetida en credos dogmáticos.
Karl Marx, por ejemplo, empezó afirmando que todas las religiones eran engaños opresivos, y animó a sus seguidores a investigar por sí mismos la verdadera naturaleza del orden global. En las décadas que siguieron, las presiones de la revolución y la guerra endurecieron el marxismo, y en la época de Stalin la línea oficial del Partido Comunista soviético establecía que el orden global era demasiado complicado para que la gente de a pie lo comprendiera, de manera que siempre era mejor confiar en la sabiduría del partido y hacer cuanto este dijera, aunque dispusiera el encarcelamiento y el exterminio de decenas de millones de personas inocentes. Puede parecer espantoso pero, como los ideólogos del partido no se cansaban nunca de explicar, la revolución no es un pícnic, y para hacer una tortilla es necesario romper algunos huevos.
Que se considere o no a Stalin un líder laico o secular depende, por tanto, de cómo definimos el secularismo. Si empleamos la definición negativa minimalista («La gente laica no cree en Dios»), entonces Stalin era sin duda laico. Si empleamos una definición positiva («Las personas laicas rechazan todos los dogmas acientíficos y están comprometidas con la verdad, la compasión y la libertad»), entonces Marx era una luminaria secular, pero Stalin no lo era en absoluto. Era el profeta de la religión sin dios, pero totalmente dogmática, del estalinismo.
El estalinismo no es un caso aislado. En el otro extremo del espectro político, también el capitalismo empezó como una teoría científica muy amplia de miras, pero poco a poco se consolidó como un dogma. Muchos capitalistas siguen repitiendo el mantra de los mercados libres y del crecimiento económico, con independencia de las realidades sobre el terreno. Da igual las consecuencias espantosas que resulten ocasionalmente de la modernización, la industrialización o la privatización: los verdaderos creyentes en el capitalismo las rechazan como simples «dolores de crecimiento», y prometen que todo irá muy bien con un poco más de crecimiento.
Los demócratas liberales comunes y corrientes han sido más leales a la búsqueda laica de la verdad y la compasión, pero incluso ellos la abandonan a veces en favor de dogmas reconfortantes. Así, cuando se enfrentan al desorden de las dictaduras brutales y los estados fallidos, los liberales suelen poner su fe indiscutible en el ritual estupendo de las elecciones generales. Luchan en guerras y gastan miles de millones en lugares como Irak, Afganistán y el Congo con el firme convencimiento de que celebrar elecciones generales transformará por arte de magia esos sitios en versiones más soleadas de Dinamarca. Y eso a pesar de los repetidos fracasos, y a pesar del hecho de que incluso en lugares con una tradición establecida de elecciones generales tales rituales llevan ocasionalmente al poder a populistas autoritarios, y dan lugar a algo tan nefasto como dictaduras de la mayoría. Si intentamos cuestionar la supuesta sabiduría de las elecciones generales, no se nos enviará al gulag, pero es probable que recibamos una ducha muy fría de insultos dogmáticos.
Desde luego, no todos los dogmas son igual de dañinos. De la misma manera que algunas creencias religiosas han beneficiado a la humanidad, también lo han hecho algunos dogmas laicos. Esto es sobre todo cierto en la doctrina de los derechos humanos. El único lugar en que existen los derechos son los relatos que los humanos inventan y se cuentan unos a otros. Dichos relatos se consagraron como un dogma obvio durante la lucha contra el fanatismo religioso y los gobiernos autocráticos. Aunque no es cierto que los humanos posean un derecho natural a la vida o a la libertad, la fe en este relato refrenó el poder de regímenes autoritarios, protegió de daños a las minorías y amparó a millones de personas de las peores consecuencias de la pobreza y la violencia. Por tanto, quizá contribuyera más a la felicidad y al bienestar de la humanidad que cualquier otra doctrina en la historia.
Pero sigue siendo un dogma. Así, el artículo 19 de la Declaración de los Derechos Humanos de las Naciones Unidas reza: «Todo individuo tiene derecho a la libertad de opinión y de expresión». Si lo entendemos como una demanda política («Todo individuo debería tener derecho a la libertad de opinión»), esto es muy sensato. Pero si creemos que todos y cada uno de los sapiens están dotados naturalmente de un «derecho a la libertad de opinión» y que por tanto la censura viola alguna ley de la naturaleza, no entendemos la verdad de la humanidad. Mientras nos definamos como «un individuo que posee derechos naturales inalienables», no sabremos quiénes somos en realidad y no entenderemos las fuerzas naturales que modelaron nuestra sociedad y nuestra propia mente (incluida nuestra creencia en los «derechos naturales»).
Dicha ignorancia quizá tenía poca importancia en el siglo XX, cuando la gente estaba atareada luchando contra Hitler y Stalin. Pero podría resultar fatal en el siglo XXI, porque ahora la biotecnología y la inteligencia artificial tratan de cambiar el significado mismo de la humanidad. Si estamos comprometidos con el derecho a la vida, ¿acaso implica esto que deberíamos emplear la biotecnología para vencer la muerte? Si estamos comprometidos con el derecho a la libertad, ¿deberíamos empoderar algoritmos que descifren y cumplan nuestros deseos ocultos? Si todos los humanos gozan de derechos humanos iguales, ¿los superhumanos gozarán entonces de superderechos? A las personas laicas les costará enfrentarse a tales preguntas mientras estén comprometidas con una fe dogmática en los «derechos humanos».
El dogma de los derechos humanos se modeló en siglos anteriores como un arma contra la Inquisición, el _ancien régime_ , los nazis y el KKK. No está en absoluto preparado para tratar con superhumanos, cíborgs y ordenadores superinteligentes. Aunque los movimientos de derechos humanos han desarrollado un arsenal de argumentos y defensas muy impresionante contra los prejuicios religiosos y los tiranos humanos, este arsenal apenas nos protege de los excesos consumistas y las utopías tecnológicas.
__
##### RECONOCER LA SOMBRA
El laicismo no debe equipararse con el dogmatismo estalinista ni con los frutos amargos del imperialismo occidental y la industrialización desenfrenada. Pero tampoco puede eludir toda la responsabilidad respecto a estos. Los movimientos seculares y las instituciones científicas han hipnotizado a miles de millones de personas con promesas de perfeccionar a la humanidad y de utilizar la munificencia del planeta para beneficio de nuestra especie. Tales promesas han generado no solo plagas y hambrunas abrumadoras, sino también gulags y la fusión de los casquetes polares. Se podría argüir que todo eso es culpa de que la gente no entiende y distorsiona los ideales laicos fundamentales y los hechos ciertos de la ciencia. Y se tendría razón. Pero este es un problema común de todos los movimientos influyentes.
Por ejemplo, el cristianismo ha sido responsable de grandes crímenes como la Inquisición, las cruzadas, la opresión de culturas nativas en todo el mundo y el despoderamiento de las mujeres. Un cristiano podría ofenderse al oírlo y replicar que todos esos crímenes fueron el resultado de una interpretación totalmente equivocada del cristianismo. Jesús predicó solo el amor, y la Inquisición se basaba en una terrible distorsión de sus enseñanzas. Podemos comprender esta afirmación, pero sería un error dejar que el cristianismo quedara impune tan fácilmente. Los cristianos horrorizados por la Inquisición y las cruzadas no pueden lavarse las manos ante tales atrocidades; en cambio, deberían plantearse algunas preguntas muy duras. ¿De qué manera, exactamente, su «religión del amor» permitió que fuera distorsionada de tal modo, y no una vez, sino muchas? A los protestantes que intenten culpar de todo ello al fanatismo de los católicos se les puede recomendar que lean algún libro sobre el comportamiento de los colonos protestantes en Irlanda o Norteamérica. De manera similar, los marxistas pueden preguntarse qué había en los textos de Marx que allanó el camino hasta el gulag, los científicos deben considerar de qué modo el proyecto científico se prestó a desestabilizar el ecosistema global y los genetistas en particular deberían tomar nota de cómo los nazis secuestraron las teorías darwinistas.
Toda religión, toda ideología y toda fe tienen su sombra, y con independencia del credo que sigamos hemos de reconocer nuestra sombra y evitar el ingenuo consuelo de que «esto no puede pasarnos a nosotros». La ciencia laica cuenta al menos con una gran ventaja respecto a la mayoría de las religiones tradicionales: no le aterroriza su sombra, y en principio está dispuesta a admitir sus errores y sus puntos ciegos. Si uno cree en una verdad absoluta revelada por un poder trascendente, no puede permitirse admitir ningún error, porque eso anularía todo su relato. Pero si uno cree en una búsqueda de la verdad por parte de humanos falibles, admitir meteduras de pata es parte inherente del juego.
Esta es también la razón por la que los movimientos seculares no dogmáticos suelen hacer promesas bastante modestas. Conscientes de su imperfección, esperan generar pequeños cambios progresivos, aumentando el salario mínimo unos pocos dólares o reduciendo la mortalidad infantil en unos pocos puntos porcentuales. La marca de las ideologías dogmáticas es que debido a su excesiva confianza en sí mismas prometen lo imposible de forma rutinaria. Sus líderes hablan con demasiada libertad de «eternidad», «pureza» y «redención», como si al promulgar una determinada ley, construir un templo concreto o conquistar algún pedazo de territorio pudieran salvar a todo el mundo en un gesto grandioso.
A la hora de tomar las decisiones más importantes en la historia de la vida, yo personalmente confiaría más en quienes admitan su ignorancia que en los que proclamen su infalibilidad. Si alguien quiere que su religión, su ideología o su visión de la vida guíen el mundo, la primera pregunta que le haría sería: «¿Cuál es el mayor error que tu religión, tu ideología o tu visión de la vida ha cometido? ¿En qué se equivocaron?». Si no es capaz de contestarme algo serio, yo, al menos, no confiaría en él.
# Parte IV
Verdad
_Si el lector se siente abrumado y confundido por la situación global, se halla en la senda adecuada. Los procesos globales se han hecho demasiado complejos para que una persona pueda comprenderlos por sí sola. ¿De qué manera, entonces, podemos saber la verdad acerca del mundo y evitar caer víctimas de la propaganda y la desinformación?_
### 15
Ignorancia
#### Sabes menos de lo que crees
En los capítulos anteriores se ha pasado revista a algunos de los problemas y las novedades más importantes de la era actual, desde la amenaza exageradamente publicitada del terrorismo hasta la amenaza muy poco apreciada de la disrupción tecnológica. Si el lector se ha quedado con la sensación inquietante de que esto es demasiado y de que no puede procesarlo todo, tiene sin duda toda la razón. Ninguna persona puede.
En los últimos siglos, el pensamiento liberal desarrolló una confianza inmensa en el individuo racional. Representó a los humanos como agentes racionales independientes, y ha convertido a estas criaturas míticas en la base de la sociedad moderna. La democracia se fundamenta en la idea de que el votante es quien mejor lo sabe, el capitalismo de mercado libre cree que el cliente siempre tiene la razón y la educación liberal enseña a los estudiantes a pensar por sí mismos.
Sin embargo, es un error depositar tanta confianza en el individuo racional. Los pensadores poscoloniales y feministas han señalado que este «individuo racional» podría muy bien ser una fantasía occidental chovinista, que ensalza la autonomía y el poder de los hombres blancos de clase alta. Como ya se ha señalado, los expertos en economía conductual y los psicólogos evolutivos han demostrado que la mayoría de las decisiones humanas se basan en reacciones emocionales y atajos heurísticos más que en análisis racionales, y que mientras que nuestras emociones y heurística quizá fueran adecuadas para afrontar la vida en la Edad de Piedra, resultan tristemente inadecuadas en la Edad del Silicio.
No solo la racionalidad es un mito: también lo es la individualidad. Los humanos rara vez piensan por sí mismos. Más bien piensan en grupos. De la misma manera que hace falta una tribu para criar a un niño, también es necesaria una tribu para inventar un utensilio, resolver un conflicto o curar una enfermedad. Ningún individuo sabe todo lo necesario para construir una catedral, una bomba atómica o un avión. Lo que confirió a _Homo sapiens_ una ventaja sobre los demás animales y nos convirtió en los amos del planeta no fue nuestra racionalidad individual, sino nuestra capacidad sin parangón de pensar de manera conjunta en grupos numerosos.[1]
De forma individual, los humanos saben vergonzosamente poco acerca del mundo, y a medida que la historia avanza, cada vez saben menos. Un cazador-recolector de la Edad de Piedra sabía cómo confeccionar sus propios vestidos, cómo prender un fuego, cómo cazar conejos y cómo escapar de los leones. Creemos que en la actualidad sabemos muchísimo más, pero como individuos en realidad sabemos muchísimo menos. Nos basamos en la pericia de otros para casi todas nuestras necesidades. En un experimento humillante, se pidió a varias personas que evaluaran cuánto conocían sobre el funcionamiento de una cremallera corriente. La mayoría contestó con absoluta confianza que lo sabían todo al respecto; a fin de cuentas, utilizaban cremalleras a diario. Después se les pidió que describieran con el mayor detalle posible todos los pasos que implican el mecanismo y el uso de la cremallera. La mayoría no tenían ni idea.[2] Esto es lo que Steven Sloman y Philip Fernbach han denominado «la ilusión del conocimiento». Creemos que sabemos muchas cosas, aunque individualmente sabemos muy poco, porque tratamos el conocimiento que se halla en la mente de los demás como si fuera propio.
Esto no tiene por qué ser malo. Nuestra dependencia del pensamiento de grupo nos ha hecho los amos del mundo, y la ilusión del conocimiento nos permite pasar por la vida sin que sucumbamos a un esfuerzo imposible para comprenderlo todo por nosotros mismos. Desde una perspectiva evolutiva, confiar en el saber de otros ha funcionado muy bien para _Homo sapiens_.
Sin embargo, como otras muchas características humanas que tenían sentido en épocas pasadas pero que en cambio causan problemas en la época moderna, la ilusión del conocimiento tiene su aspecto negativo. El mundo está volviéndose cada vez más complejo, y la gente no se da cuenta de lo poco que sabe sobre lo que está ocurriendo. En consecuencia, personas que apenas tienen conocimientos de meteorología o biología proponen no obstante políticas relacionadas con el cambio climático y la modificación genética de las plantas, mientras que otras tienen ideas muy claras acerca de lo debería hacerse en Irak o Ucrania, aunque sean incapaces de situar estos países en un mapa. La gente rara vez se es consciente de su ignorancia, porque se encierran en una sala insonorizada de amigos que albergan ideas parecidas y de noticias que se confirman a sí mismas, donde sus creencias se ven reforzadas sin cesar y en pocas ocasiones se cuestionan.[3]
Es improbable que proporcionar más y mejor información a la gente mejore las cosas. Los científicos esperan disipar las concepciones erróneas mediante una educación científica mejor, y los especialistas confían en influir en la opinión pública en temas como el Obamacare y el calentamiento global presentando a la gente hechos precisos e informes de expertos. Tales esperanzas se basan en una idea equivocada de cómo piensan en realidad los humanos. La mayor parte de nuestras ideas están modeladas por el pensamiento grupal y no por la racionalidad individual, y nos mantenemos firmes en estas ideas debido a la lealtad de grupo. Es probable que bombardear a la gente con hechos y mostrar su ignorancia individual resulte contraproducente. A la mayoría de las personas no les gustan demasiado los hechos y tampoco parecer estúpidas. No estemos tan seguros de poder convencer a los partidarios del Tea Party de la verdad del calentamiento global enseñándoles páginas y más páginas de datos estadísticos.[4]
El poder del pensamiento grupal está tan generalizado que resulta difícil romper su preponderancia, aunque las ideas parezcan ser bastante arbitrarias. Así, en Estados Unidos los conservadores de derechas suelen preocuparse mucho menos de cosas como la contaminación y las especies amenazadas que los progresistas de izquierdas, razón por la cual Luisiana tiene normativas ambientales mucho más permisivas que Massachusetts. Estamos acostumbrados a esta situación, de modo que la damos por sentada, pero en realidad es muy sorprendente. Cabría esperar que los conservadores se preocuparan mucho más por la conservación del antiguo orden ecológico y por proteger sus tierras ancestrales, sus bosques y ríos. En cambio, cabría esperar que los progresistas estuvieran más abiertos a los cambios radicales en el campo, en especial si el objetivo es acelerar el progreso y aumentar el nivel de vida de las personas. Sin embargo, una vez que la línea del partido se ha fijado sobre estas cuestiones mediante diversas particularidades históricas, para los conservadores se ha vuelto algo de lo más natural rechazar la preocupación por los ríos contaminados y las aves en peligro de extinción, mientras que los progresistas de izquierdas suelen mostrarse temerosos ante cualquier alteración del antiguo orden ecológico.[5]
Ni siquiera los científicos son inmunes al poder de pensar en grupo. Así, los científicos que creen que los hechos pueden hacer cambiar la opinión pública tal vez sean víctimas del pensamiento científico grupal. La comunidad científica cree en la eficacia de los hechos; de ahí que los leales a dicha comunidad continúen pensando que pueden ganar los debates públicos lanzando a diestro y siniestro los hechos adecuados, a pesar de que hay gran evidencia empírica de lo contrario.
De forma parecida, puede que la creencia liberal en la racionalidad individual también sea producto del pensamiento liberal en grupo. En uno de los momentos culminantes de _La vida de Brian_ , de los Monty Python, una enorme muchedumbre de seguidores ilusos confunden a Brian con el Mesías. Brian les dice a sus discípulos: «¡No es necesario que me sigáis, no es necesario que sigáis a nadie! ¡Tenéis que pensar por vosotros mismos! ¡Todos sois individuos! ¡Todos sois diferentes!». La muchedumbre entusiasta canta entonces al unísono: «¡Sí! ¡Todos somos individuos! ¡Sí, todos somos diferentes!». Los Monty Python parodiaban la ortodoxia contracultural de la década de 1960, pero la afirmación puede aplicarse igualmente al individualismo racional en general. Las democracias modernas están llenas de muchedumbres que gritan al unísono: «¡Sí, el votante es quien mejor lo sabe! ¡Sí, el cliente siempre tiene la razón!».
##### EL AGUJERO NEGRO DEL PODER
El problema del pensamiento de grupo y de la ignorancia individual afecta no solo a los votantes y clientes comunes, sino también a presidentes y directores generales. Puede que tengan a su disposición gran cantidad de asesores y vastos servicios de inteligencia, pero no por eso las cosas son necesariamente mejores. Es muy difícil descubrir la verdad cuando se gobierna el mundo. Se está demasiado atareado. La mayoría de los dirigentes políticos y de magnates de los negocios se pasan la vida trajinando. Pero para profundizar en cualquier tema se necesita mucho tiempo, y en particular el privilegio de perder el tiempo. Es necesario experimentar con caminos improductivos, probar con callejones sin salida, dejar espacio a las dudas y al aburrimiento, y permitir que pequeñas semillas de perspicacia crezcan lentamente y florezcan. Si no podemos permitirnos perder tiempo, nunca daremos con la verdad.
Y lo que es aún peor: el poder grande distorsiona inevitablemente la verdad. El poder se dedica a cambiar la realidad en lugar de verla como es. Cuando tenemos un martillo en la mano, todo parece un clavo; y cuando tenemos un gran poder en la mano, todo parece una invitación a inmiscuirse. Incluso si de alguna manera superamos esta ansia, la gente que nos rodea nunca olvidará el martillo gigante que enarbolamos. Todos los que hablen con nosotros tendrán motivaciones secretas conscientes o inconscientes, de modo que nunca podremos confiar por completo en lo que dicen. Ningún sultán puede confiar nunca en que sus cortesanos y subordinados le digan la verdad.
Así, el gran poder actúa como un agujero negro que deforma el espacio que lo rodea. Cuanto más nos acercamos, más retorcido se torna todo. Cada palabra lleva una carga adicional cuando penetra en nuestra órbita, y cada persona que vemos intenta adularnos, calmarnos u obtener algo de nosotros. Saben que no podemos dedicarles más de un minuto o dos, y temen decir algo impropio o confuso, de modo que terminan soltando consignas hueras o los mayores tópicos posibles.
Hace un par de años fui invitado a cenar con el primer ministro israelí, Benjamin Netanyahu. Unos amigos me aconsejaron no acudir, pero no pude resistir la tentación. Pensé que por fin podría escuchar algunos grandes secretos que solo se transmiten a oídos importantes tras las puertas cerradas. ¡Qué desengaño! Había allí unas treinta personas, y cada una intentaba atraer la atención del Gran Hombre, impresionarlo con su ingenio, ganarse su favor o conseguir algo de él. Si algunos de los que estaban en la cena sabían de un gran secreto, hicieron un esfuerzo ímprobo por guardarlo para sí. Eso no era culpa de Netanyahu, ni de ninguno de los demás. Era culpa de la atracción gravitatoria del poder.
Si realmente queremos la verdad, es necesario escapar del agujero negro del poder y permitirnos la pérdida de mucho tiempo vagando por aquí y por allá en la periferia. El saber revolucionario rara vez llega hasta el centro, porque el centro está construido sobre un conocimiento ya existente. Los guardianes del antiguo orden suelen determinar quién consigue alcanzar los centros del poder y tienden a filtrar a los portadores de ideas no convencionales y perturbadoras. Desde luego, también filtran gran cantidad de basura. No ser invitado al Fórum Económico Mundial de Davos no es garantía de sabiduría. Por ello debemos invertir tanto tiempo en la periferia: quizá los guardianes del antiguo orden tengan algunas ideas brillantes y revolucionarias, pero sobre todo están llenos de conjeturas infundadas, modelos desacreditados, dogmas supersticiosos y ridículas teorías conspiratorias.
Así, los dirigentes se hallan atrapados por partida doble. Si permanecen en el centro del poder, su visión del mundo estará muy distorsionada. Si se aventuran hacia los márgenes, gastarán mucho de su preciado tiempo. Y el problema no hará más que empeorar. En las décadas venideras, el mundo se volverá más complejo aún de lo que es hoy en día. En consecuencia, los humanos (ya sean peones o reyes) sabrán menos todavía de los artilugios tecnológicos, de las corrientes económicas y de las dinámicas políticas que modelan el mundo. Como observó Sócrates hace más de dos mil años, lo mejor que podemos hacer en tales condiciones es reconocer nuestra propia ignorancia individual.
Pero ¿qué ocurre entonces con la moral y la justicia? Si no podemos entender el mundo, ¿cómo confiar en distinguir entre lo que está bien y lo que está mal, entre la justicia y la injusticia?
### 16
Justicia
#### Nuestro sentido de la justicia podría estar anticuado
Como todos nuestros demás sentidos, el de la justicia también tiene antiguas raíces evolutivas. La moral humana se formó a lo largo de millones de años de evolución, adaptándose para tratar con los dilemas sociales y éticos que surgieron en la vida de las pequeñas bandas de cazadores-recolectores. Si me fui a cazar contigo y maté un ciervo mientras que tú no capturaste nada, ¿he de compartir mi botín contigo? Si fuiste a recoger setas y volviste con la cesta llena, ¿el hecho de que yo sea más fuerte que tú me permite arrebatarte todas las setas y quedármelas? Y si sé que estás tramando matarme, ¿está bien que actúe de manera preventiva y te degüelle en plena noche?[1]
A primera vista, las cosas no han cambiado mucho desde que abandonamos la sabana africana para ir a la jungla urbana. Podría pensarse que las cuestiones a que nos enfrentamos en la actualidad (la guerra civil en Siria, la desigualdad y el calentamiento globales) no son más que las mismas de siempre, pero a gran escala. Sin embargo, esto es una ilusión. El tamaño importa, y desde el punto de vista de la justicia, como desde otros muchos puntos de vista, no estamos en absoluto adaptados al mundo en que vivimos.
El problema no es de valores. Ya sean laicos o religiosos, los ciudadanos del siglo XXI tienen muchísimos valores. El problema reside en implementar dichos valores en un mundo global complejo. Todo ello es culpa de los números. El sentido de la justicia de los recolectores estaba estructurado para enfrentarse a dilemas relacionados con la vida de unas pocas docenas de personas en un área de unas pocas docenas de kilómetros cuadrados. Cuando intentamos comprender las relaciones entre millones de personas a lo largo de continentes enteros, nuestro sentido moral queda abrumado.
La justicia exige no solo un conjunto de valores abstractos, sino también comprender las relaciones concretas de causa y efecto. Si has recolectado setas para alimentar a tus hijos y yo te arrebato ahora a la fuerza el cesto, lo que quiere decir que tu trabajo no ha servido de nada y que tus hijos se irán a dormir con hambre, eso es injusto. Es fácil entenderlo, porque es fácil ver la relación de causa y efecto. Por desgracia, una característica inherente a nuestro moderno mundo global es que sus relaciones causales están muy ramificadas y son muy complejas. Puedo vivir de manera pacífica en casa, sin levantar nunca un dedo para hacer daño a nadie, pero, según los activistas de izquierdas, soy cómplice de los males infligidos por los soldados israelíes y los colonos en Cisjordania. Según los socialistas, mi vida confortable se basa en el trabajo infantil en deplorables talleres clandestinos del Tercer Mundo. Los defensores de los derechos de los animales me recuerdan que mi vida está entretejida con uno de los crímenes más abominables de la historia: la subyugación de miles de millones de animales de granja a un brutal régimen de explotación.
¿Soy en verdad culpable de todo esto? No es fácil decirlo. Dado que dependo para mi existencia de una red alucinante de lazos económicos y políticos, y dado que las conexiones causales globales están tan enredadas, me cuesta responder incluso a las preguntas más sencillas, como de dónde viene mi almuerzo, quién elaboró los zapatos que llevo y qué está haciendo mi fondo de pensiones con mi dinero.[2]
##### ROBAR RÍOS
Una cazadora-recolectora primitiva sabía muy bien de dónde procedía su almuerzo (lo recolectaba ella misma), quién elaboraba sus mocasines (quien los elaboraba dormía a veinte metros de ella) y qué hacía su fondo de pensiones (estaba jugando en el barro: por aquel entonces, la gente solo tenía un fondo de pensiones, que se llamaba «niños»). Soy mucho más ignorante que la cazadora-recolectora. Tras años de investigación, podría descubrirse que el gobierno al que voté está vendiendo en secreto armas a un turbio dictador en la otra punta del planeta. Pero durante el tiempo que me llevara descubrir esto, podría perderme descubrimientos más importantes, como la suerte de las gallinas cuyos huevos cené.
El sistema está estructurado de tal modo que quienes no hacen ningún esfuerzo para saber pueden vivir en una dichosa ignorancia y a los que sí lo hacen les costará mucho descubrir la verdad. ¿Cómo no robar cuando el sistema económico global está robando sin cesar en mi nombre y sin que yo lo sepa? No importa si se juzgan los actos por sus consecuencias (está mal robar porque hace desgraciadas a las víctimas del robo) o si creemos en deberes categóricos que hay que respetar con independencia de las consecuencias (está mal robar porque Dios así lo dijo). El problema es que se ha vuelto complicadísimo entender qué es lo que en realidad hacemos.
El mandamiento de no robar se formuló en los días en que robar significaba tomar físicamente con nuestra propia mano algo que no nos pertenecía. Pero hoy en día, los argumentos en verdad importantes acerca del robo se refieren a situaciones de todo punto diferentes. Supongamos que invierto 10.000 dólares en acciones de una gran empresa petroquímica, que me proporciona unos intereses anuales del 5 por ciento de mi inversión. La empresa obtiene muchos beneficios porque no paga por las externalidades. Vierte residuos tóxicos en un río cercano sin preocuparse por el daño que causa al sistema regional de abastecimiento de agua, a la salud pública o a la fauna local. Emplea sus riquezas para contratar a una legión de abogados que la protegen contra cualquier demanda por compensación. También mantiene a grupos de presión que bloquean todo intento de promulgar normativas ambientales más estrictas.
¿Podemos acusar a la empresa de «robar un río»? ¿Y qué ocurre conmigo, personalmente? Nunca he entrado en casa de nadie ni cogido billetes de dólar del bolso de nadie. No soy consciente de cómo genera sus beneficios esta empresa concreta. Apenas recuerdo que una parte de mi cartera de valores está invertida en ella. Así pues, ¿soy culpable de robo? ¿Cómo podemos actuar moralmente cuando no tenemos manera de conocer todos los hechos relevantes?
Podemos intentar eludir el problema adoptando una «moral de intenciones». Lo que es importante es lo que pretendo, no lo que hago en realidad o el resultado de lo que hago. Sin embargo, en un mundo donde todo está interconectado, el imperativo moral supremo se convierte en el imperativo de saber. Los mayores crímenes de la historia moderna fueron el resultado no solo del odio y la codicia, sino mucho más de la ignorancia y la indiferencia. Encantadoras damas inglesas financiaron el tráfico de esclavos en el Atlántico al comprar acciones y bonos en la Bolsa de Londres, sin haber puesto nunca un pie ni en África ni en el Caribe. Después endulzaban su té de las cuatro con blancos terrones de azúcar producidos en plantaciones infernales, de las que ellas nada sabían.
En Alemania, a finales de la década de 1930 el gerente de la oficina de Correos local podía ser un ciudadano honesto que se preocupara por el bienestar de sus empleados y que ayudara personalmente a personas angustiadas a encontrar paquetes extraviados. Siempre era el primero en llegar y el último en marcharse, e incluso cuando había neviscas se aseguraba de que el correo llegara a tiempo. ¡Qué lástima que su eficiente y acogedora oficina de Correos fuera una célula vital del sistema nervioso del Estado nazi! Enviaba propaganda racista, órdenes de reclutamiento para la Wehrmacht y órdenes severas a la rama local de la SS. Hay algo erróneo en las intenciones de aquellos que no hacen un esfuerzo sincero por saber.
Pero ¿qué es «un esfuerzo sincero por saber»? ¿Acaso los jefes de las oficinas de Correos de cada país tendrían que abrir el correo que entregan, y dimitir o rebelarse si descubren propaganda gubernamental? Es fácil mirar atrás, a la Alemania nazi de la década de 1930, con absoluta certeza moral, porque sabemos adónde condujo la cadena de causas y efectos. Pero sin el beneficio de la mirada retrospectiva, la certeza moral podría hallarse fuera de nuestro alcance. La amarga verdad es que el planeta se ha vuelto demasiado complicado para nuestro cerebro de cazadores-recolectores.
La mayoría de las injusticias en el mundo contemporáneo surgen de sesgos estructurales a gran escala más que de prejuicios individuales, y nuestro cerebro de cazadores-recolectores no ha evolucionado para detectar sesgos estructurales. Todos somos cómplices de al menos algunos de dichos sesgos, y simplemente no tenemos ni el tiempo ni la energía para descubrirlos todos. Escribiendo este libro aprendí esta lección en un plano personal. Cuando comento cuestiones globales, siempre corro el riesgo de favorecer el punto de vista de la élite global en detrimento de varios grupos desfavorecidos. La élite global domina la conversación, de modo que es imposible no conocer su punto de vista. Los grupos desfavorecidos, en cambio, son silenciados de manera rutinaria, lo que hace que sea fácil olvidarlos, no por malicia deliberada, sino por simple ignorancia.
Por ejemplo, no sé absolutamente nada de los puntos de vista únicos y de los problemas de los aborígenes tasmanos. En realidad, sé tan poco de ellos que en un libro anterior supuse que ya no existían, porque habían sido exterminados por los colonos europeos. De hecho, hay miles de personas vivas en la actualidad cuyo abolengo se remonta a la población original de Tasmania, y se enfrentan a muchos problemas únicos, uno de los cuales es que su existencia misma sea negada con frecuencia, en particular por académicos y estudiosos.
Aunque uno pertenezca a un grupo desfavorecido y, por tanto, posea un conocimiento profundo y de primera mano de su punto de vista, eso no significa que comprenda el punto de vista de otros grupos también desfavorecidos, porque cada grupo y subgrupo se enfrenta a un laberinto diferente de barreras laborales, dobles raseros, insultos codificados y discriminación institucional. Un afroamericano de treinta años cuenta con treinta años de experiencia de lo que supone ser un hombre afroamericano. Pero carece de toda experiencia de lo que significa ser una mujer afroamericana, un gitano búlgaro, un ruso ciego o una joven lesbiana china.
A lo largo de su vida, este hombre afroamericano ha sido repetidamente detenido y registrado por la policía sin razón aparente, algo que la lesbiana china nunca ha tenido que padecer. En cambio, haber nacido en una familia afroamericana en un barrio afroamericano significó que ha estado rodeado de gente como él que le enseñó lo que necesitaba saber para sobrevivir y prosperar como un hombre afroamericano. La lesbiana china no nació en una familia lesbiana de un barrio lesbiano, y quizá no haya tenido a nadie en el mundo que le enseñara sus lecciones fundamentales. Así que crecer como negro en Baltimore no facilita en absoluto comprender la lucha de crecer como lesbiana en Hangzhou.
En épocas anteriores esto importaba menos, porque raramente éramos responsables del sufrimiento de la gente situada en la otra punta del planeta. Por lo general, ya era bastante si hacíamos un esfuerzo para empatizar con nuestros vecinos menos afortunados. Pero hoy en día, los principales debates globales acerca de temas como el cambio climático y la inteligencia artificial tienen un impacto sobre todos, ya sea en Tasmania, Hangzhou o Baltimore, de modo que hemos de tener en cuenta todos los puntos de vista. Pero ¿cómo puede alguien lograrlo? ¿Cómo puede alguien entender la red de relaciones entre miles de grupos que se entrecruzan en todo el mundo?[3]
##### ¿REDUCIR O NEGAR?
Aunque de verdad lo deseemos, la mayoría ya no somos capaces de comprender los principales problemas morales del mundo. La gente puede entender las relaciones entre dos recolectores, entre veinte recolectores o entre dos clanes vecinos. Está mal preparada para comprender las relaciones entre varios millones de sirios, entre 500 millones de europeos o entre todos los grupos y subgrupos del planeta que interactúan.
Al intentar entender y juzgar los dilemas morales a esta escala, la gente suele recurrir a uno de cuatro métodos. El primero es minimizar la cuestión: comprender la guerra civil siria como si se diera entre dos recolectores; imaginar el régimen de Assad como una sola persona y a los rebeldes como otra, una mala y la otra buena. La complejidad histórica del conflicto es sustituida por una trama simple y clara.[4]
El segundo es centrarse en una historia humana conmovedora, que presumiblemente representa todo el conflicto. Cuando se intenta explicar la verdadera complejidad del conflicto mediante estadísticas y datos precisos, la gente se pierde; pero un relato personal sobre la suerte de un niño activa los conductos lagrimales, provoca que hierva la sangre y genera una falsa certeza moral.[5] Esto ya hace mucho tiempo que lo saben numerosas organizaciones benéficas. En un importante experimento se pedía a la gente que donara dinero para ayudar a una pobre niña de siete años de Malí llamada Rokia. Muchos se emocionaron con su relato, y abrieron su corazón y sus monederos. Sin embargo, cuando además de la historia personal de Rokia los investigadores mostraron también las estadísticas sobre el problema más amplio de la pobreza en África, de repente los encuestados estaban menos dispuestos a ayudar. En otro estudio, los investigadores solicitaron donaciones para ayudar a un único niño enfermo o a ocho niños enfermos. La gente dio más dinero al niño solitario que al grupo de ocho.[6]
El tercer método para habérselas con los dilemas morales a gran escala es pergeñar teorías conspiratorias. ¿Cómo funciona la economía global, y es buena o mala? Eso es demasiado complicado para entenderlo. Es mucho más fácil imaginar que hay veinte multimillonarios que mueven los hilos detrás del escenario, que controlan los medios de comunicación y que fomentan guerras para enriquecerse. Casi siempre, esto es una fantasía sin fundamento. El mundo contemporáneo es demasiado complicado no solo para nuestro sentido de la justicia, sino también para nuestras capacidades de gestión. Nadie (y esto incluye a los multimillonarios, a la CIA, a los francmasones y a los Sabios de Sión) comprende bien lo que ocurre en el planeta. De modo que nadie es capaz de mover efectivamente los hilos.[7]
Estos tres métodos intentan negar la verdadera complejidad del mundo. El cuarto y último método es crear un dogma, depositar nuestra confianza en alguna supuesta teoría, institución o jefe omniscientes y seguirlos allá adonde nos conduzcan. Los dogmas religiosos e ideológicos tienen gran poder de atracción en nuestra época científica justo porque nos ofrecen un refugio seguro frente a la frustrante complejidad de la realidad. Como se ha indicado antes, los movimientos laicos no han estado exentos de este peligro. Incluso si se empieza rechazando todos los dogmas religiosos y con un firme compromiso respecto a la verdad científica, más tarde o más temprano la complejidad de la realidad se vuelve tan irritante que nos vemos impelidos a imaginar una doctrina que no pueda cuestionarse. Aunque tales doctrinas ofrezcan comodidad intelectual y certeza moral a la gente, es discutible que proporcionen justicia.
Y entonces ¿qué hemos de hacer? ¿Debemos adoptar el dogma liberal y confiar en el colectivo de votantes y clientes individuales? ¿O quizá hemos de rechazar el enfoque individualista y, como otras muchas culturas previas en la historia, empoderar a las comunidades para que encuentren juntas el sentido al mundo? Sin embargo, una solución de este tipo solo nos lleva del fuego de la ignorancia individual a las brasas del pensamiento de grupo sesgado. Los grupos de cazadores-recolectores, las comunidades rurales e incluso los barrios de las ciudades podían pensar juntos acerca de los problemas comunes a que se enfrentaban. Pero ahora padecemos problemas globales, sin tener una comunidad global. Ni Facebook, ni el nacionalismo ni la religión están cerca de crear dicha comunidad. Todas las tribus humanas existentes se hallan absortas en promover sus intereses particulares y no en entender la verdad global. Ni los norteamericanos, ni los chinos, ni los musulmanes ni los hindúes constituyen la «comunidad global», de modo que su interpretación de la realidad no puede ser digna de confianza.
Así pues, debemos darnos por vencidos, y declarar que la búsqueda humana para comprender la verdad y encontrar justicia ha fracasado? ¿Hemos entrado oficialmente en la era de la posverdad?
### 17
Posverdad
#### Algunas noticias falsas duran para siempre
Estos días se nos dice repetidamente que vivimos en una era nueva y espantosa de «posverdad», y que estamos rodeados de mentiras y ficciones. No es difícil encontrar ejemplos. Así, a finales de febrero de 2014, unidades rusas especiales que no llevaban ninguna insignia militar invadieron Ucrania y ocuparon instalaciones clave en Crimea. El gobierno ruso y el presidente Putin en persona negaron una y otra vez que se tratara de tropas rusas y las describieron como «grupos de autodefensa» espontáneos que podían haber adquirido equipamiento de apariencia rusa en tiendas locales.[1] Mientras hacían esta ridícula afirmación, Putin y sus ayudantes sabían muy bien que estaban mintiendo.
Los nacionalistas rusos pueden excusar esta mentira aduciendo que servía a una verdad superior. Rusia estaba enzarzada en una guerra justa, y si está bien matar por una causa justa, ¿no es evidente que también está bien mentir? La causa superior que en teoría justificaba la invasión de Ucrania era la preservación de la sacrosanta nación rusa. Según los mitos nacionales rusos, Rusia es una entidad sagrada que ha resistido mil años a pesar de repetidos intentos por parte de rabiosos enemigos de invadirla y desmembrarla. Después de los mongoles, los polacos, los suecos, la Grande Armée de Napoleón y la Wehrmacht de Hitler, en la década de 1990 fueron la OTAN, Estados Unidos y la Unión Europea los que intentaron destruir Rusia al separar partes de su cuerpo y convertirlas en «países falsos», como Ucrania. Para muchos nacionalistas rusos, la idea de que Ucrania es una nación distinta de Rusia constituye una mentira mucho mayor que nada de lo que dijera el presidente Putin durante su sagrada misión de reintegrar la nación rusa.
Los ciudadanos ucranianos, además de los observadores y los historiadores profesionales, podrían sentirse ofendidos por esta explicación, y considerarla una especie de «mentira atómica» del arsenal ruso del engaño. Afirmar que Ucrania no existe como nación ni como país independiente supone desconocer una larga lista de hechos históricos; por ejemplo, que de los mil años de supuesta unidad rusa, Kiev y Moscú formaron parte del mismo país solamente unos trescientos. También viola numerosas leyes y tratados internacionales que Rusia aceptó con anterioridad y que han salvaguardado la soberanía y las fronteras de la Ucrania independiente. Y lo que es todavía más importante: pasa por alto lo que millones de ucranianos piensan de sí mismos. ¿Es que no tienen nada que decir a propósito de quiénes son?
Sin duda, los nacionalistas ucranianos estarían de acuerdo con los nacionalistas rusos en que existen algunos países falsos. Pero Ucrania no es uno de ellos. Más bien, estos países falsos son la «República Popular de Lugansk» y la «República Popular de Donetsk» que Rusia ha dispuesto para enmascarar su invasión no provocada de Ucrania.[2]
Sea cual sea el bando que respaldemos, parece que en realidad estamos viviendo en una terrible era de posverdad cuando no solo incidentes particulares concretos, sino historias y naciones enteras pueden falsificarse. Pero si esta es la era de la posverdad, ¿cuándo, exactamente, tuvo lugar la era dorada de la verdad? ¿En la década de 1980? ¿En la de 1950? ¿En la de 1930? ¿Y qué desencadenó nuestra transición a la de la posverdad? ¿Internet? ¿Las redes sociales? ¿El advenimiento de Putin y Trump?
Un rápido vistazo a la historia nos muestra que la propaganda y la desinformación no son nada nuevo, e incluso el hábito de negar naciones enteras y de crear países falsos cuenta con un largo pedigrí. En 1931, el ejército japonés escenificó ataques simulados sobre sí mismo para justificar su invasión de China, y después creó el país falso de Manchukuo para legitimar sus conquistas. La misma China niega desde hace tiempo que el Tíbet haya existido nunca como país independiente. El asentamiento británico en Australia se justificó por la doctrina legal de _terra nullius_ («tierra de nadie»), que borró de un plumazo 50.000 años de historia aborigen.
A principios del siglo XX, uno de los eslóganes favoritos de los sionistas hablaba del retorno de «un pueblo sin tierra [los judíos] a una tierra sin pueblo [Palestina]». La existencia de la población árabe local se pasó por alto a conveniencia. En 1969, la primera ministra israelí Golda Meir pronunció la célebre frase de que el pueblo palestino no existe y nunca existió. Estas ideas son muy comunes en Israel incluso en la actualidad, a pesar de décadas de conflictos armados contra algo que no existe. Por ejemplo, en febrero de 2016 la diputada Anat Berko pronunció un discurso en el Parlamento israelí en el que dudaba de la realidad y la historia del pueblo palestino. ¿Su prueba? La letra «p» ni siquiera existe en árabe, de modo que, ¿cómo puede haber un pueblo palestino? (En árabe, la «f» representa a la «p», y el nombre árabe de Palestina es Falastin.)
__
##### LA ESPECIE DE LA POSVERDAD
En realidad, los humanos siempre han vivido en la era de la posverdad. _Homo sapiens_ es una especie de la posverdad, cuyo poder depende de crear ficciones y creer en ellas. Ya desde la Edad de Piedra, los mitos que se refuerzan a sí mismos han servido para unir a los colectivos humanos. De hecho, _Homo sapiens_ conquistó este planeta gracias sobre todo a la capacidad distintivamente humana de crear y difundir ficciones. Somos los únicos mamíferos que podemos cooperar con numerosos extraños porque solo nosotros podemos inventar relatos de ficción, difundirlos y convencer a millones de personas para que crean en ellos. Mientras todos creamos en las mismas ficciones, todos obedeceremos las mismas leyes y, por tanto, podremos cooperar de manera eficaz.
De modo que si el lector quiere culpar a Facebook, Trump o Putin por inaugurar una era nueva y espantosa, recuerde que hace muchos siglos millones de cristianos se encerraron en una burbuja mitológica que se refuerza a sí misma, sin atreverse nunca a cuestionar la veracidad de los hechos narrados en la Biblia, mientras que millones de musulmanes depositaron su fe inquebrantable en el Corán. Durante milenios, muchas de las cosas que pasaban por «noticias» y «hechos» en las redes sociales humanas eran relatos de milagros, ángeles, demonios y brujas, con valientes periodistas que informaban en vivo y en directo desde los pozos más profundos del inframundo. Carecemos de toda prueba empírica de que Eva fuera tentada por la Serpiente, de que las almas de los infieles ardan en el infierno después de morir o de que al creador del universo no le guste que un brahmán se case con una intocable; pero millones de personas han creído en estos relatos durante miles de años. Algunas noticias falsas duran para siempre.
Soy consciente de que a mucha gente le molestará que equipare la religión con las noticias falsas, pero este es exactamente el objetivo. Cuando mil personas creen durante un mes algún cuento inventado, esto es una noticia falsa. Cuando mil millones de personas lo creen durante mil años, es una religión, y se nos advierte que no lo llamemos «noticia falsa» para no herir los sentimientos de los fieles (o provocar su ira). Adviértase, sin embargo, que no niego la efectividad ni la benevolencia potencial de la religión. Justo lo contrario. Para bien o para mal, la ficción figura entre las herramientas más eficaces de la caja de herramientas de la humanidad. Al unir a la gente, los credos religiosos hacen posible la cooperación entre personas a gran escala. Inspiran a la gente para que construya hospitales, escuelas y puentes, además de ejércitos y prisiones. Adán y Eva nunca existieron, pero la catedral de Chartres sigue siendo hermosa. Gran parte de la Biblia puede ser ficción, pero continúa haciendo feliz a miles de millones de personas y todavía puede motivar a los humanos para que sean compasivos, valientes y creativos, al igual que otras grandes obras de ficción, como _Don Quijote de la Mancha_ , _Guerra y paz_ y _Harry Potter_.
De nuevo, algunas personas tal vez se ofendan porque compare la Biblia con _Harry Potter._ Si el lector es un cristiano de mente científica, podría justificar todos los errores y mitos de la Biblia aduciendo que el libro sagrado nunca se pensó para que se leyera como una narración basada en los hechos, sino como un relato metafórico que contiene una profunda sabiduría. Pero ¿esto no vale también para _Harry Potter_?
Si el lector es un cristiano fundamentalista, es muy probable que insista en que todas y cada una de las palabras de la Biblia son literalmente ciertas. Supongamos por un momento que tiene razón, y que la Biblia es en efecto la palabra infalible del único Dios verdadero. Así pues, ¿qué hacemos con el Corán, el Talmud, el Libro de Mormón, los Vedas, el Avesta y el Libro de los Muertos egipcio? ¿No le tienta decir que dichos textos son ficciones complejas creadas por humanos de carne y hueso (o quizá por demonios)? ¿Y cómo considera el lector la divinidad de emperadores romanos como Augusto y Claudio? El Senado romano afirmaba tener el poder de convertir a los hombres en dioses, y después esperaba que los súbditos del imperio adoraran a estos dioses. ¿No era esto una ficción? De hecho, tenemos al menos un ejemplo en la historia de un falso dios que admitió la ficción por su propia boca. Como se ha indicado anteriormente, el militarismo japonés en la década de 1930 y principios de la de 1940 se basaba en la fe fanática en la divinidad del emperador Hirohito. Tras la derrota de Japón, Hirohito proclamó públicamente que tal divinidad no era cierta, y que después de todo él no era un dios.
De modo que, aunque estemos de acuerdo en que la Biblia es la verdadera palabra de Dios, todavía tenemos a miles de millones de devotos hindúes, musulmanes, judíos, egipcios, romanos y japoneses que durante miles de años depositaron su confianza en ficciones. De nuevo, esto no significa que estas ficciones sean necesariamente inútiles o perjudiciales. Aún pueden ser hermosas e inspiradoras.
Desde luego, no todos los mitos religiosos han sido igual de beneficiosos. El 29 de agosto de 1255 se encontró en un pozo de la ciudad de Lincoln el cuerpo de un niño inglés de nueve años llamado Hugh. Aunque no hubiera Facebook ni Twitter, rápidamente se propagó el rumor de que Hugh había sido sacrificado por los judíos locales en un ritual. El rumor no hizo más que crecer a medida que se contaba, y uno de los cronistas ingleses de más renombre de la época, Mateo de París, dio una descripción detallada y sangrienta de cómo judíos prominentes de toda Inglaterra se habían reunido en Lincoln para engordar, torturar y finalmente crucificar al niño secuestrado. Se juzgó a diecinueve judíos y se los ejecutó por presunto asesinato. Libelos sangrientos similares se hicieron populares en otras ciudades inglesas, lo que condujo a una serie de pogromos en los que se masacró a comunidades enteras. Al final, en 1290, se expulsó a toda la población judía de Inglaterra.[3]
La historia no terminó aquí. Un siglo después de la expulsión de los judíos de Inglaterra, Geoffrey Chaucer (el padre de la literatura inglesa) incluyó un libelo sangriento fundamentado en el relato de Hugh de Lincoln en _Los cuentos de Canterbury_ («El cuento de la Priora»). El cuento termina con los judíos ahorcados. Libelos sangrientos parecidos se convirtieron luego en parte esencial de todo movimiento antisemita, desde la España medieval tardía hasta la Rusia moderna. Un eco distante pudo oírse incluso en el relato de «noticias falsas» de 2016 según el cual Hillary Clinton encabezaba una red de tráfico infantil que retenía a niños como esclavos sexuales en el sótano de una popular pizzería. El cuento lo creyeron los suficientes norteamericanos para que perjudicara la campaña electoral de Clinton, y una persona incluso fue a la pizzería armada con un fusil y exigió ver el sótano (resultó que el local no tenía sótano).[4]
En cuanto a Hugh de Lincoln, nadie sabe cómo encontró en verdad la muerte, pero lo enterraron en la catedral de Lincoln y lo veneraron como santo. Se le atribuyeron varios milagros, y su tumba continuó atrayendo a peregrinos incluso siglos después de la expulsión de todos los judíos de Inglaterra.[5] No fue hasta 1955 (diez años después del Holocausto) cuando la catedral de Lincoln repudió el libelo de sangre, y colocó una placa cerca de la tumba de Hugh que reza así:
Relatos falseados de «asesinatos rituales» de muchachos cristianos por parte de comunidades judías proliferaron en toda Europa durante la Edad Media e incluso mucho más tarde. Estas ficciones costaron la vida a muchos judíos inocentes. Lincoln tuvo su propia leyenda y la supuesta víctima fue enterrada en la catedral en 1255. Tales relatos no redundan beneficio del cristianismo.[6]
Bueno, algunas noticias falsas solo duran setecientos años.
##### UNA VEZ UNA MENTIRA, SIEMPRE LA VERDAD
Las religiones antiguas no han sido las únicas que se sirvieron de la ficción para consolidar la cooperación. En épocas más recientes, cada nación ha creado su propia mitología nacional, mientras que movimientos como el comunismo, el fascismo y el liberalismo pergeñaron complicados credos que se reforzaban a sí mismos. Según se dice, Joseph Goebbels, el maestro de la propaganda nazi y quizá el más completo mago de los medios de comunicación de la era moderna, explicó sucintamente su método al afirmar que «una mentira contada una vez sigue siendo una mentira, pero contada mil veces se convierte en una verdad».[7] En _Mein Kampf_ , Hitler escribió que «la más brillante técnica de propaganda no producirá ningún éxito a menos que siempre se tenga presente un principio fundamental: debe limitarse a unos pocos puntos y debe repetirlos una y otra vez».[8] ¿Acaso puede un vendedor ambulante actual de noticias falsas mejorarlo?
La máquina de propaganda soviética fue igualmente flexible con la verdad, y reescribió la historia de todo, desde guerras enteras a fotografías concretas. El 29 de junio de 1936, el diario oficial _Pravda_ (cabecera que significa «verdad») presentaba en su página inicial una fotografía de un sonriente Iósif Stalin abrazando a Gelya Markizova, una niña de siete años. La imagen se convirtió en un icono estalinista, que consagró a Stalin como Padre de la Nación e idealizó a la Feliz Infancia Soviética. Imprentas y fábricas de todo el país empezaron a producir en masa millones de carteles, esculturas y mosaicos de la escena, que se exhibieron en instituciones públicas de un extremo al otro de la Unión Soviética. De la misma manera que ninguna iglesia ortodoxa rusa estaba completa sin un icono de la Virgen María con el niño Jesús en brazos, ninguna escuela soviética podía estar sin un icono de Papá Stalin abrazando a la pequeña Gelya.
Por desgracia, en el imperio de Stalin la fama solía ser una invitación al desastre. En cosa de un año, el padre de Gelya fue arrestado bajo falsas acusaciones de que era un espía japonés y un terrorista trotskista. En 1938 fue ejecutado; una más de los millones de víctimas del terror estalinista. Gelya y su madre fueron desterradas a Kazajistán, donde la madre murió pronto en misteriosas circunstancias. ¿Qué hacer ahora con los incontables iconos que presentaban al Padre de la Nación con la hija de un «enemigo del pueblo» convicto? Sin problemas. A partir de aquel momento, Gelya Markizova se esfumó, y la Feliz Niña Soviética de la imagen ubicua fue identificada como Mamlakat Nakhangova, una muchacha tayika de trece años que ganó la Orden de Lenin por haber recolectado de manera diligente gran cantidad de algodón en los campos (si alguien pensó que la niña de la fotografía no parecía tener trece años, fue lo bastante sensato para no expresar en voz alta esa herejía contrarrevolucionaria).[9]
La máquina propagandística soviética era tan eficiente que consiguió ocultar atrocidades monstruosas en casa, al tiempo que proyectaba una visión utópica hacia el exterior. Hoy en día, los ucranianos se quejan de que Putin ha conseguido engañar a muchos medios de comunicación occidentales respecto a las acciones de Rusia en Crimea y Donbas. Pero en el arte del engaño Putin no puede estar a la altura de Stalin. A principios de la década de 1930, los periodistas e intelectuales occidentales de izquierdas elogiaban la Unión Soviética como una sociedad ideal en una época en que los ucranianos y otros ciudadanos soviéticos morían por millones debido a la hambruna artificial que Stalin orquestó. Aunque en la época de Facebook y Twitter a veces es difícil decidir qué versión de los acontecimientos creer, al menos ya no es posible que un régimen mate a millones de ciudadanos sin que el mundo lo sepa.
Además de las religiones y las ideologías, las marcas comerciales también se basan en la ficción y las noticias falsas. La creación de marcas y de su valor suele implicar contar una y otra vez el mismo relato ficticio hasta que la gente se convence de que es la verdad. ¿Qué imágenes le vienen a la mente al lector cuando piensa en Coca-Cola? ¿Las de jóvenes sanos que se dedican al deporte y que se lo pasan bien juntos? ¿O las de pacientes con diabetes y sobrepeso tumbados en la cama de un hospital? Beber mucha Coca-Cola no nos hará jóvenes, no nos hará sanos y no nos hará atléticos; más bien, aumenta las probabilidades de padecer obesidad y diabetes. Pero durante décadas, Coca-Cola ha invertido miles de millones de dólares para que se la asociara a la juventud, a la salud y a los deportes..., y miles de millones de humanos creen de manera inconsciente en dicha relación.
Lo cierto es que la verdad no estuvo nunca situada muy arriba en el orden del día de _Homo sapiens_. Muchas personas piensan que si una religión o ideología concretas tergiversan la realidad, sus partidarios acabarán por descubrirlo tarde o temprano, porque no podrán competir con rivales más perspicaces. Bueno, eso es solo otro mito tranquilizador. En la práctica, el poder de la cooperación humana depende de un equilibrio delicado entre verdad y ficción.
Si distorsionamos demasiado la realidad, nos debilitaremos, porque obraremos de maneras poco realistas. Por ejemplo, en 1905 un médium de África Oriental llamado Kinjikitile Ngwale afirmó estar poseído por Hongo, el espíritu serpiente. El nuevo profeta tenía un mensaje revolucionario para los habitantes de la colonia alemana de África Oriental: uníos y expulsad a los alemanes. Para que el mensaje fuera más atractivo, Ngwale proporcionó a sus seguidores medicina mágica que supuestamente convertiría las balas alemanas en agua ( _maji_ en suajili). Así empezó la rebelión Maji Maji. Fracasó. Porque en el campo de batalla las balas alemanas no se transformaban en agua; por el contrario, desgarraban sin piedad los cuerpos de los mal armados rebeldes.[10] Dos mil años antes, la Gran Revolución Judía contra los romanos estuvo inspirada de forma similar por una ardiente creencia en que Dios lucharía por los judíos y los ayudaría a derrotar al aparentemente invencible Imperio romano. También esta revolución fracasó, lo que llevó a la destrucción de Jerusalén y al exilio de los judíos.
Por otra parte, no puede organizarse de manera efectiva a las masas sin tener una base en alguna mitología. Si nos ceñimos a la realidad sincera, pocas personas nos seguirán. Sin mitos, habría sido imposible organizar no solo las fracasadas revoluciones Maji Maji y judía, sino también las rebeliones mucho más exitosas del Mahdi y los Macabeos.
De hecho, las historias falsas tienen una ventaja intrínseca frente a la verdad cuando se trata de unir a la gente. Si pretendemos evaluar la lealtad de grupo, hacer que la gente crea en un absurdo es una prueba mucho mejor que pedirle que crea la verdad. Si un gran jefe dice «El Sol sale por el este y se pone por el oeste», no se requiere lealtad al jefe para ovacionarlo. Pero si el jefe dice «El Sol sale por el oeste y se pone por el este», solo los verdaderos leales batirán palmas. De forma parecida, si todos los vecinos creen el mismo cuento extravagante, podemos contar con ellos para que estén unidos en tiempos de crisis. Si solo están dispuestos a creer hechos acreditados, ¿qué demuestra eso?
Podría aducirse que, al menos en algunos casos, es posible organizar a la gente de manera efectiva mediante acuerdos de consenso en lugar de mediante ficciones y mitos. Así, en la esfera económica el dinero y las empresas unen a la gente de modo mucho más efectivo que ningún dios o libro sagrado, aunque todo el mundo sabe que se trata solo de una convención humana. En el caso de un libro sagrado, un verdadero creyente diría: «Creo que el libro es sagrado», mientras que en el caso del dólar, un verdadero creyente diría: «Creo que otra gente cree que el dólar es valioso». Es evidente que el dólar es solo una creación humana, pero la población de todo el mundo lo respeta. Si es así, ¿por qué no abandonan los humanos todos los mitos y ficciones, y se organizan fundamentándose en convenciones de consenso, como el dólar?
Sin embargo, dichas convenciones no son tan distintas de la ficción. La diferencia entre los libros sagrados y el dinero, por ejemplo, es mucho más pequeña de lo que pueda parecer a simple vista. Cuando la mayoría de la gente ve un billete de dólar, olvida que se trata solo de una convención humana. Cuando ve el pedazo de papel verde con la imagen del hombre blanco ya fallecido, lo ve como algo valioso en y por sí mismo. Casi nunca se dice: «En realidad, esto es un pedazo de papel sin valor, pero debido a que otra gente lo considera valioso, puedo usarlo». Si se observa un cerebro humano en un escáner de resonancia magnética funcional, se ve que cuando se le enseña a alguien una maleta llena de billetes de cien dólares, las partes del cerebro que empiezan a animarse frenéticamente no son las partes escépticas («Otra gente cree que esto es valioso»), sino las partes codiciosas («¡Mierda! ¡Lo quiero!»). Y al revés: en la inmensa mayoría de los casos la gente solo empieza a santificar la Biblia, o los Vedas o el Libro de Mormón después de una exposición prolongada y repetida a otras personas que los consideran sagrados. Aprendemos a respetar los libros sagrados justo de la misma manera en que aprendemos a respetar los billetes de dinero.
De ahí que, en la práctica, no haya una división estricta entre «saber que algo es solo una convención humana» y «creer que algo es intrínsecamente valioso». En muchos casos, la gente es ambigua u olvidadiza con respecto a esta división. Para poner otro ejemplo, si el lector tomara asiento y mantuviera una profunda discusión filosófica a este respecto, casi todo el mundo estaría de acuerdo en que las empresas son relatos ficticios creados por los seres humanos. Microsoft no es el edificio que posee ni la gente a la que emplea ni los accionistas a los que sirve; es, más bien, una intrincada ficción legal tejida por legisladores y abogados. Pero durante el 99 por ciento del tiempo no nos dedicamos a profundas discusiones filosóficas, y tratamos a las empresas como si fueran entidades reales en el mundo, igual que los tigres o los humanos.
Difuminar la línea entre la ficción y la realidad puede hacerse con muchos fines, empezando por «divertirse» y siguiendo luego el camino hasta la «supervivencia». No se puede jugar a juegos o leer novelas a no ser que suspendamos la incredulidad al menos por un instante. Para gozar realmente del fútbol hemos de aceptar las reglas del juego y olvidar al menos durante noventa minutos que son simplemente invenciones humanas. Si no, pensaremos que es absolutamente ridículo que veintidós personas corran tras un balón. El fútbol puede empezar solo como diversión, pero después puede convertirse en algo mucho más serio, como atestiguará cualquier vándalo inglés o cualquier nacionalista argentino. El fútbol puede ayudar a formular identidades personales, consolidar comunidades a gran escala e incluso proporcionar razones para la violencia. Las naciones y las religiones son clubes de fútbol que han tomado esteroides.
Los humanos tienen esta notable capacidad de saber y de no saber al mismo tiempo. O mejor dicho, pueden saber algo cuando piensan de verdad en ello, pero la mayor parte del tiempo no piensan en ello, de modo que no lo saben. Si nos centramos de verdad, nos damos cuenta de que el dinero es ficción. Sin embargo, por lo general no nos centramos. Si se nos pregunta acerca del fútbol, sabemos que es una invención humana. Pero en el ardor del partido, nadie nos pregunta por ello. Si dedicamos tiempo y energía, podemos descubrir que las naciones son cuentos complicados. Pero en plena guerra no tenemos tiempo ni energía. Si queremos conocer la verdad última, nos damos cuenta de que el relato de Adán y Eva es un mito. Pero ¿con qué frecuencia queremos conocer la verdad última?
La verdad y el poder pueden viajar juntos solo durante un trecho. Más tarde o más temprano, seguirán por sendas separadas. Si queremos poder, en algún momento tendremos que difundir ficciones. Si queremos saber la verdad sobre el mundo, en algún punto tendremos que renunciar al poder. Deberemos admitir cosas —por ejemplo, sobre los orígenes de nuestro poder— que enojarán a nuestros seguidores o socavarán la armonía social. No hay nada místico en esta brecha entre la verdad y el poder. Si quiere comprobarlo el lector, encuentre simplemente a un típico WASP norteamericano y plantéele la cuestión de la raza, localice a un israelí del montón y saque a colación la Ocupación, o intente hablarle a un tipo corriente sobre el patriarcado.
A lo largo de la historia, los eruditos se han enfrentado reiteradamente a este dilema: ¿están al servicio del poder o de la verdad? ¿Debería ser su objetivo unir a la gente asegurándose de que todo el mundo crea en la misma historia, o deberían dejar que la gente sepa la verdad incluso al precio de la desunión? Los estamentos más poderosos de la erudición —ya sean los sacerdotes cristianos, los mandarines confucianos o los ideólogos comunistas— situaron la unidad por encima de la verdad. Y eso explica que fueran tan poderosos.
Como especie, los humanos prefieren el poder a la verdad. Invertimos mucho más tiempo y esfuerzo en intentar controlar el mundo que en intentar entenderlo, e incluso cuando tratamos de entenderlo, por lo general lo hacemos con la esperanza de que comprenderlo hará más fácil controlarlo. De manera que si el lector sueña con una sociedad en que la verdad reine de manera suprema y no se haga caso a los mitos, tiene poco que esperar de _Homo sapiens_. Será mejor que pruebe suerte con los chimpancés.
##### SALIR DE LA MÁQUINA DE LAVAR CEREBROS
Todo esto no significa que las noticias falsas no sean un problema grave, o que políticos y sacerdotes tengan licencia para mentir con malicia. También sería completamente erróneo llegar a la conclusión de que todo son noticias falsas, que cualquier intento de descubrir la verdad está condenado al fracaso y que no hay ningún tipo de diferencia entre el periodismo serio y la propaganda. A todas las noticias falsas subyacen hechos reales y sufrimiento real. En Ucrania, por ejemplo, los soldados rusos están luchando de verdad, miles de personas han muerto de verdad y cientos de miles han perdido de verdad su casa. El sufrimiento humano suele generarse por creer en la ficción, pero el propio sufrimiento sigue siendo real.
Por tanto, en lugar de aceptar las noticias falsas como la norma, debemos reconocerlas como un problema mucho más difícil de lo que acostumbramos suponer, y hemos de esforzarnos todavía más para distinguir la realidad de la ficción. No esperemos la perfección. Una de las mayores ficciones de todas es negar la complejidad del mundo, y pensar en términos absolutos de pureza prístina frente al mal satánico. No hay ningún político que cuente toda la verdad y nada más que la verdad, pero aun así algunos políticos son mucho mejores que otros. Si pudiera escoger, confiaría mucho más en Churchill que en Stalin, aunque el primer ministro británico no dejaba de adornar la verdad cuando le convenía. De manera similar, no hay periódico que se halle libre de prejuicios y errores, pero algunos periódicos hacen un esfuerzo honesto para encontrar la verdad, mientras que otros son una máquina de lavar cerebros. Si yo hubiera vivido en la década de 1930, confío en que habría tenido el buen juicio de creer al _The_ _New York Times_ más que al _Pravda_ y al _Der Stürmer_.
Es responsabilidad de todos dedicar tiempo y esfuerzo a descubrir nuestros prejuicios y a verificar nuestras fuentes de información. Como se ha señalado en capítulos anteriores, no podemos investigarlo todo nosotros. Pero precisamente por ello, necesitamos al menos investigar detenidamente nuestras fuentes de información favoritas, ya se trate de un diario, de una página web, de una cadena de televisión o de una persona. En el capítulo 20 veremos con mayor profundidad cómo evitar el lavado de cerebro y cómo distinguir la realidad de la ficción. Aquí me gustaría proponer dos sencillas reglas generales.
Primera: si el lector quiere información fidedigna, pague un buen dinero por ella. Si el lector consigue las noticias gratis, podría muy bien ser él el producto. Suponga que un multimillonario sospechoso le ofreciera el siguiente acuerdo: «Te pagaré 30 dólares al mes y a cambio me permitirás que te lave el cerebro una hora al día, y que instale en tu mente todos los prejuicios políticos y comerciales que quiera». ¿Aceptaría el lector el trato? Pocas personas en su sano juicio lo harían. De modo que el multimillonario sospechoso ofrece un acuerdo algo distinto: «Me permitirás que te lave el cerebro durante una hora al día, y a cambio no te cobraré nada por ese servicio». Ahora, de repente, el trato les parece tentador a cientos de millones de personas. No siga el lector su ejemplo.
La segunda regla general es que si alguna cuestión le parece de importancia excepcional, haga el esfuerzo para leer la literatura científica relevante. Y por literatura científica me refiero a artículos revisados por pares, libros publicados por editores académicos bien conocidos y aquellos escritos por profesores de instituciones respetables. Sin duda, la ciencia tiene sus limitaciones, y en el pasado ha hecho muchas cosas mal. No obstante, la comunidad científica ha sido nuestra fuente más fiable de conocimiento durante siglos. Si el lector cree que la comunidad científica se equivoca en algún tema, sin duda eso es posible, pero conozca al menos las teorías científicas que está rechazando y proporcione alguna evidencia empírica en apoyo de su afirmación.
Los científicos, por su parte, deben implicarse mucho más en los debates públicos actuales. No han de tener miedo de hacer oír su voz cuando el debate cae dentro de su campo de conocimiento, ya sea este la medicina o la historia. El silencio no es neutralidad: es apoyar el _statu quo_. Desde luego, es muy importante seguir haciendo investigación académica y publicar los resultados en revistas científicas que solo leen algunos expertos. Pero es igual de importante comunicar las últimas teorías científicas al público general mediante libros de divulgación científica, e incluso mediante el uso hábil de arte y ficción.
¿Significa esto que los científicos deben empezar a escribir ciencia ficción? En realidad, no es una mala idea. El arte desempeña un papel clave en dar forma a la visión que la gente tiene del mundo, y en el siglo XXI puede asegurarse que la ciencia ficción es el género más importante de todos, porque da forma a cómo entiende la mayoría de la gente asuntos como la IA, la bioingeniería y el cambio climático. Sin duda, necesitamos buena ciencia, pero desde una perspectiva política, una buena película de ciencia ficción vale mucho más que un artículo en _Science_ o _Nature_.
### 18
Ciencia ficción
#### El futuro no es lo que vemos en las películas
Los humanos controlan el mundo porque pueden cooperar mejor que ningún otro animal, y pueden cooperar tan bien porque creen en las ficciones. Poetas, pintores y dramaturgos son, por tanto, tan importantes al menos como los soldados y los ingenieros. La gente va a la guerra y construye catedrales porque cree en Dios, y cree en Dios porque ha leído poemas sobre Dios, porque ha visto cuadros de Dios y porque ha quedado hipnotizada por las obras teatrales sobre Dios. De modo similar, nuestra creencia en la mitología moderna del capitalismo está respaldada por las creaciones artísticas de Hollywood y la industria del pop. Creemos que comprar más nos hará felices, porque vemos el paraíso capitalista con nuestros propios ojos en la televisión.
En los primeros años del siglo XXI, el género artístico más importante quizá sea la ciencia ficción. Muy poca gente lee los últimos artículos publicados sobre el aprendizaje automático o la ingeniería genética. En cambio, películas como _Matrix_ y _Her_ y series de televisión como _Westworld_ y _Black Mirror_ modelan la idea de la gente sobre las cuestiones tecnológicas, sociales y económicas más importantes de nuestra época. Esto significa también que la ciencia ficción ha de ser mucho más responsable en la manera como representa las realidades científicas, pues de otro modo podría imbuir en la gente ideas equivocadas o hacer que centrara su atención en los problemas equivocados.
Como se ha señalado en un capítulo anterior, quizá el peor pecado de la ciencia ficción actual es que tiende a confundir inteligencia con conciencia. Como resultado, se preocupa en demasía por una guerra potencial entre robots y humanos, cuando en realidad lo que hay que temer es un conflicto entre una pequeña élite de superhumanos empoderada por algoritmos y una enorme subclase de _Homo sapiens_ despoderados. Cuando se piensa en el futuro de la IA, Karl Marx sigue siendo mejor guía que Steven Spielberg.
En efecto, muchos filmes sobre inteligencia artificial están tan alejados de la realidad científica que cabe sospechar que son simplemente alegorías de preocupaciones completamente diferentes. Así, la película _Ex Machina_ , de 2015, parece tratar de un experto en IA que se enamora de una mujer robot solo para ser embaucado y manipulado por ella. Pero en realidad esta película no versa sobre el miedo humano hacia los robots inteligentes, sino sobre el miedo de los hombres hacia las mujeres inteligentes, y en particular sobre el miedo a que la liberación femenina pueda conducir a la dominación femenina. Siempre que el lector vea una película sobre una IA en la que la IA es una mujer y el científico es un hombre, probablemente se trate de un filme sobre feminismo y no sobre cibernética. Pues ¿por qué demonios tendría que tener una IA una identidad sexual o de género? El sexo es una característica de los seres orgánicos multicelulares. ¿Qué puede significar para un ser cibernético no orgánico?
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##### VIVIR EN UNA CAJA
Un tema que la ciencia ficción ha explorado con una intuición mucho más aguda se refiere al peligro de que se use la tecnología para manipular y controlar a los seres humanos. _Matrix_ presenta un mundo donde casi todos los seres humanos se hallan presos en el ciberespacio, y todo lo que experimentan está creado por un algoritmo maestro. _El show de Truman_ se centra en un único individuo que es la estrella involuntaria de un _reality show_. Sin que él lo sepa, todos sus amigos y conocidos (incluidos su madre, su esposa y su mejor amigo) son actores; todo lo que le sucede sigue un guion bien estructurado, y cuanto dice y hace es registrado por cámaras ocultas y es seguido ávidamente por millones de fanáticos.
Sin embargo, las dos películas, aunque son muy buenas, no acaban de desarrollar todas las implicaciones de su argumento. Suponen que los humanos atrapados dentro de la matriz poseen un yo auténtico, que no ha sido tocado por las manipulaciones tecnológicas, y que más allá de la matriz aguarda una realidad auténtica, a la que los héroes pueden acceder si lo intentan esforzándose lo suficiente. La matriz no es más que una barrera artificial que separa nuestro yo interior auténtico del mundo exterior auténtico. Después de muchas dificultades y tribulaciones, Neo en _Matrix_ y Truman en _El show de Tru_ _man_ , consiguen trascender la red de manipulaciones y escapar de ella, descubrir su yo auténtico y alcanzar la tierra prometida auténtica.
Resulta muy curioso que esta tierra prometida auténtica sea idéntica en todos los aspectos importantes a la matriz inventada. Cuando Truman se escapa del estudio de televisión, trata de encontrarse con su amor del instituto, a quien el director del show televisivo había expulsado. Pero si Truman satisface esta fantasía romántica, su vida será justo como el perfecto sueño hollywoodiense que _El show de Truman_ vendió a millones de espectadores de todo el mundo: más vacaciones en Fiyi. La película no nos ofrece ni un atisbo de qué tipo de vida alternativa puede encontrar el protagonista en el mundo real.
De manera parecida, cuando Neo se evade de la matriz al tragarse la famosa píldora roja, descubre que el mundo exterior no es diferente del interior. Tanto fuera como dentro hay violentos conflictos y personas que actúan movidas por miedo, deseo, amor y envidia. La película tendría que haber terminado informando a Neo de que la realidad a la que ha accedido es solo una matriz mayor, y que si quiere huir al «verdadero mundo real», debe elegir de nuevo entre la píldora azul y la roja.
La revolución tecnológica y científica actual no implica que individuos auténticos y realidades auténticas puedan ser manipuladas por algoritmos y cámaras de televisión, sino más bien que la autenticidad es un mito. A la gente la asusta estar atrapada dentro de una caja, pero no se da cuenta de que ya está encerrada en el interior de una caja (su cerebro), que a su vez está encerrado dentro de una caja mayor: la sociedad humana con su infinidad de ficciones. Cuando escapamos de la matriz, lo único que descubrimos es una matriz mayor. Cuando los campesinos y los obreros se rebelaron contra el zar en 1917, terminaron en manos de Stalin; y cuando empezamos a analizar las múltiples maneras en que el mundo nos manipula, al final nos damos cuenta de que nuestra identidad fundamental es una ilusión compleja creada por redes neurales.
La gente teme que al estar atrapada dentro de una caja se perderá todas las maravillas del mundo. Mientras Neo permanezca encerrado en la matriz y Truman en el estudio de televisión, nunca visitarán Fiyi, o París o Machu Picchu. Pero, en realidad, cuanto experimentamos en la vida se halla dentro de nuestro propio cuerpo y nuestra propia mente. Escapar de la matriz o viajar hasta Fiyi no supondrá ninguna diferencia. No es que en algún lugar de nuestra mente haya un cofre de hierro con una gran inscripción en rojo que diga «¡Ábrase únicamente en Fiyi!», y que cuando finalmente viajemos al Pacífico Sur y abramos el cofre, de él vayan a salir todo tipo de emociones y sentimientos especiales que solo podremos experimentar en Fiyi. Y que si nunca visitamos Fiyi, nos perderemos estos sentimientos especiales para siempre. No. Sea lo que sea que podamos vivir en Fiyi, podemos sentirlo en cualquier lugar del mundo, incluso dentro de la matriz.
Quizá todos vivamos dentro de una gran simulación informática, al estilo de _Matrix_. Esto contradeciría nuestros relatos nacionales, religiosos e ideológicos. Pero nuestras experiencias mentales seguirían siendo reales. Sería muy embarazoso para Karl Marx y para Estado Islámico que al final la historia humana fuera una compleja simulación que tiene lugar en un superordenador accionado por científicos ratas del planeta Zircón. Pero estos científicos ratas seguirían sin tener respuesta para el genocidio armenio y para Auschwitz. ¿Cómo consiguieron que algo así pasara por el comité de ética de la Universidad de Zircón? Incluso si las cámaras de gas no fueron más que señales eléctricas en chips de silicio, las experiencias de dolor, miedo y desesperación no fueron por ello ni un ápice menos atroces.
El dolor es dolor, el miedo es miedo y el amor es amor, incluso en la matriz. Da igual si el miedo que sentimos lo inspira un conjunto de átomos en el mundo exterior o las señales eléctricas manipuladas por un ordenador: el miedo sigue siendo real. De modo que si queremos conocer la realidad de nuestra mente, podemos hacerlo tanto dentro de la matriz como fuera de ella.
La mayoría de las películas de ciencia ficción cuentan en verdad una narración muy antigua: la victoria de la mente sobre la materia. Hace treinta mil años, la narración era: «Mente imagina cuchillo de piedra - mano crea cuchillo - humano mata mamut». Pero lo cierto es que los humanos consiguieron el control del mundo no tanto por inventar cuchillos y matar mamuts como por manipular mentes humanas. La mente no es el sujeto que modela libremente acciones históricas y realidades biológicas: la mente es un objeto que está modelado por la historia y la biología. Incluso nuestros ideales más queridos (libertad, amor, creatividad) son como un cuchillo de piedra que alguien que no somos nosotros creó para matar algún mamut. Según las teorías científicas más reputadas y las herramientas tecnológicas más avanzadas, la mente nunca está libre de manipulación. No existe un yo auténtico a la espera de ser liberado de la cáscara manipuladora.
¿Tiene el lector alguna idea de cuántas películas, novelas y poemas ha consumido a lo largo de los años, y de cómo estos artefactos han esculpido y modelado su idea del amor? Las comedias románticas son al amor lo que la pornografía al sexo y Rambo a la guerra. Y si el lector cree que puede pulsar alguna tecla de borrar y eliminar toda traza de Hollywood de su subconsciente y su sistema límbico, se engaña.
Nos gusta la idea de elaborar cuchillos de piedra, pero no nos gusta la idea de ser cuchillos de piedra nosotros mismos. De manera que la variación de matriz de la antigua narración del mamut reza más o menos así: «Mente imagina robot - mano crea robot - robot mata a terroristas pero también intenta controlar mente - mente mata robot». Pero esta narración es falsa. El problema no es que la mente no podrá matar al robot. El problema, para empezar, es que la mente que imaginó el robot ya era el producto de manipulaciones muy anteriores. De ahí que matar al robot no nos liberará.
__
##### DISNEY PIERDE LA FE EN EL LIBRE ALBEDRÍO
En 2015, Pixar Studios y Walt Disney Pictures lanzaron una saga de animación mucho más realista y preocupante sobre la condición humana, que pronto se convirtió en un gran éxito tanto para los niños como para los adultos. _Del revés (Inside Out)_ narra la historia de una niña de once años, Riley Andersen, que se traslada con sus padres de Minnesota a San Francisco. Al echar de menos a sus amigos y su ciudad natal, Riley tiene dificultades para adaptarse a su nueva vida, e intenta huir y volver a Minnesota. Pero sin que Riley lo sepa, al mismo tiempo está teniendo lugar un drama mucho mayor. Riley no es la estrella inconsciente de un _reality show_ ni está atrapada en la matriz. Más bien, ella misma es la matriz y hay algo atrapado en su interior.
Disney ha erigido su imperio a fuerza de contar una y otra vez el mismo mito. En incontables películas de Disney, los héroes se enfrentan a dificultades y peligros, pero al final triunfan al encontrar su auténtico yo y seguir su libre albedrío. _Del revés_ desmantela brutalmente este mito. Adopta las últimas ideas neurobiológicas sobre los humanos y conduce a los espectadores en un viaje al interior del cerebro de Riley solo para descubrir que ella no tiene un auténtico yo y que nunca realiza ninguna elección libremente. Riley es, en realidad, un robot enorme gestionado por una serie de mecanismos bioquímicos en conflicto, que el filme caracteriza como adorables personajes de dibujos animados: Alegría, amarilla y alegre; Tristeza, azul y taciturna; Ira, roja y de malas pulgas, etcétera. Al manipular un conjunto de botones y palancas en la Sede Central, mientras observan todos los movimientos de Riley en una enorme pantalla de televisión, estos personajes controlan el conjunto de humores, decisiones y actos de la niña.
El fracaso de Riley para adaptarse a su nueva vida en San Francisco es el resultado de una metedura de pata en la Sede Central que amenaza con desequilibrar por completo el cerebro de Riley. Para arreglar el entuerto, Alegría y Tristeza efectúan un viaje épico por el cerebro de la niña, montadas en un tren de pensamientos, explorando la prisión inconsciente y visitando el estudio interior donde un equipo de neuronas artísticas está atareado produciendo sueños. Mientras seguimos a estos mecanismos bioquímicos personificados en las profundidades del cerebro de Riley, en ningún momento encontramos un alma, un auténtico yo ni un libre albedrío. De hecho, el instante de revelación sobre el que gira todo el argumento no tiene lugar cuando Riley descubre su único y auténtico yo, sino cuando resulta evidente que no puede ser identificada con ningún núcleo único y que su bienestar depende de la interacción de muchos mecanismos diferentes.
Al principio, a los espectadores se los induce a identificar a Riley con el personaje principal, la amarilla y alegre Alegría. Pero al final resulta que ese fue el error crítico que amenazó con arruinar la vida de la niña. Al pensar que solo ella es la auténtica esencia de Riley, Alegría intimida a los demás personajes internos, con lo que altera el delicado equilibrio del cerebro de Riley. La catarsis se produce cuando Alegría comprende su error, y comprende (junto con los espectadores) que Riley no es Alegría, ni Tristeza ni ninguno de los demás personajes. Riley es un relato complejo producido por los conflictos y las colaboraciones de todos los personajes bioquímicos juntos.
Lo realmente sorprendente no es que Disney se atreviera a comercializar una película con un mensaje tan radical, sino que se convirtiera en un éxito mundial. Quizá tuvo tanto éxito porque _Del revés_ es una comedia con final feliz, y la mayoría de los espectadores tal vez no hayan captado tanto su significado neurológico como sus siniestras implicaciones.
No puede decirse lo mismo del más profético de los libros de ciencia ficción del siglo XX. No puede pasarse por alto su naturaleza siniestra. Fue escrito hace casi un siglo, pero resulta más relevante con cada año que pasa. Aldous Huxley escribió _Un mundo feliz_ en 1931, con el comunismo y el fascismo afianzados en Rusia e Italia, el nazismo en auge en Alemania, el Japón militarista embarcándose en su guerra de conquista en China y todo el mundo atenazado por la Gran Depresión. Pero Huxley consiguió ver a través de esas oscuras nubes e imaginó una sociedad futura sin guerras, hambrunas ni plagas, que gozaba de una paz, prosperidad y salud ininterrumpidas. Es un mundo consumista, que da rienda suelta completa al sexo, a las drogas y al rock and roll, y cuyo valor supremo es la felicidad. La tesis subyacente al libro es que los humanos son algoritmos bioquímicos, que la ciencia puede piratear el algoritmo humano y que entonces puede usarse la tecnología para manipularlo.
En este mundo nuevo y valiente,(6) el Gobierno Mundial emplea biotecnología e ingeniería social avanzadas para asegurarse de que todos estén siempre contentos y nadie tenga ningún motivo para rebelarse. Es como si Alegría, Tristeza y los demás personajes que habitan en el cerebro de Riley se hubieran transformado en leales agentes gubernamentales. Por tanto, no hay necesidad de una policía secreta, ni de campos de concentración ni de un Ministerio del Amor al estilo del de _1984_ de Orwell. De hecho, el genio de Huxley consiste en demostrar que es posible controlar a la gente con mucha mayor seguridad mediante el amor y el placer que mediante el miedo y la violencia.
Cuando la gente lee _1984_ , se le hace evidente que Orwell está describiendo un mundo de pesadilla estremecedora, y la única pregunta que se plantea es: «¿Cómo evitamos llegar a un estado tan terrible?». Leer _Un mundo feliz_ es una experiencia mucho más desconcertante y desafiante, porque nos resulta muy difícil señalar lo que hace que este mundo sea exactamente distópico. Es pacífico y próspero, y todos están muy satisfechos todo el tiempo. ¿Qué es lo que hay de malo en ello?
Huxley plantea esta pregunta directamente en el momento culminante de la novela: el diálogo entre Mustafá Mond, el Interventor Mundial para la Europa occidental, y John el Salvaje, que ha vivido toda su vida en una reserva nativa en Nuevo México, y que es la única otra persona en Londres que todavía sabe algo acerca de Shakespeare o Dios.
Cuando John el Salvaje intenta incitar a la gente de Londres para que se rebele contra el sistema que los controla, todos reaccionan con una apatía absoluta a su llamada, pero la policía lo arresta y lo lleva ante Mustafá Mond. El Interventor Mundial mantiene una agradable charla con John, y le explica que si insiste en ser antisocial debería simplemente irse a algún lugar apartado y vivir como un ermitaño. Entonces John pone en cuestión las ideas que subyacen al orden global, y acusa al Gobierno Mundial porque en su búsqueda de la felicidad ha eliminado no solo la verdad y la belleza, sino todo lo que es noble y heroico en la vida:
—Mi joven y querido amigo —dijo Mustafá Mond—, la civilización no tiene en absoluto necesidad de nobleza ni de heroísmo. Tales cosas son síntomas de ineficacia política. En una sociedad bien organizada como la nuestra, nadie tendrá ocasión de ser noble y heroico. Es preciso que las circunstancias se hagan fundamentalmente inestables para que tal ocasión pueda surgir. Donde hay guerras, donde hay juramentos de fidelidad, donde hay tentaciones que resistir, donde hay objetos de amor por los que luchar o a los que defender, allí, naturalmente, nobleza y heroísmo tienen una explicación. Pero hoy ya no hay guerras. Se tiene el mayor cuidado en evitar que se ame demasiado a alguien. No hay una fidelidad dividida; está uno acondicionado de tal suerte que no puede dejar de hacer lo que tiene que hacer. Y lo que tiene que hacer es, en conjunto, tan agradable, a tantos impulsos naturales se les permite que se manifiesten libremente que no hay en realidad tentaciones que resistir. Y si, por una desgraciada casualidad, sucediera de alguna manera algo desagradable, bueno, siempre queda [la droga] _soma_ para permitir evadirse de la realidad. Y siempre hay _soma_ para calmar su cólera, para reconciliarle a uno con sus enemigos, para volverle paciente y sufrido. Antaño, estas cosas solo podían lograrse realizando un gran esfuerzo y tras muchos años de dura disciplina moral. Ahora, uno se traga dos o tres tabletas de medio gramo, y ya está. Todos pueden ser virtuosos ahora. Pueden llevar consigo, en un frasquito, la mitad cuando menos de su moralidad. Cristianismo sin lágrimas, esto es lo que es el _soma_.
—Pero las lágrimas son necesarias. ¿No recuerda lo que dijo Otelo? «Si tras cada tempestad vienen tales calmas, ¡que soplen los vientos hasta que despierten a la muerte!» Uno de los viejos indios solía contarnos un relato, el de la doncella de Mátsaki. Los jóvenes que querían casarse con ella tenían que pasar una mañana cavando en su jardín. Parecía fácil, pero había moscas y mosquitos, moscas y mosquitos mágicos. La mayoría de los jóvenes no podían resistir las mordeduras y picaduras. Pero el único que pudo, aquel obtuvo la chica.
—¡Encantador! Pero en los países civilizados —dijo el Interventor— se pueden tener muchachas sin cavar para ellas, y no hay moscas ni mosquitos que le piquen. Hace ya siglos que nos libramos de ellos.
El Salvaje asintió, frunciendo el ceño.
—Se han librado de ellos. Sí, eso es muy propio. Librarse de todo lo desagradable en vez de aprender a soportarlo. Pero es más noble sufrir en el alma los golpes y saetas de la suerte, o tomando las armas contra un piélago de desgracias, triunfar de ellas al fin. [...] Pero ustedes no hacen ni lo uno ni lo otro. Ni sufren ni luchan. Solo han abolido hondas y saetas. Es demasiado fácil. [...] Lo que les hace falta —prosiguió el Salvaje— es algo que cueste lágrimas. [...] ¿Acaso no vale nada vivir peligrosamente?
—¡Muchísimo! —replicó el Interventor—. Hombres y mujeres necesitan que se les estimule de vez en cuando las glándulas suprarrenales. [...] Es una de las condiciones de la salud perfecta. Por esto hemos hecho que los tratamientos de SPV sean obligatorios.
—¿SPV?
—Sucedáneo de Pasión Violenta. Regularmente, una vez al mes. Inundamos todo el organismo con adrenalina. Es el equivalente fisiológico completo del miedo y la cólera. Todos los efectos tónicos de asesinar a Desdémona y de ser asesinada por Otelo, sin ninguno de los inconvenientes.
—Pero a mí me gustan los inconvenientes.
—A nosotros no —dijo el Interventor—. Preferimos hacer las cosas cómodamente.
—Pero yo no quiero la comodidad. Quiero a Dios, quiero la poesía, quiero el peligro verdadero, quiero la libertad, quiero la bondad. Quiero el pecado.
—De hecho —dijo Mustafá Mond—, usted reclama el derecho a ser desgraciado.
—Muy bien, pues —dijo desafiante el Salvaje—, reclamo el derecho a ser desgraciado.
—Por no mencionar el derecho a envejecer y a volverse feo e impotente, el derecho a tener sífilis y cáncer, el derecho a tener muy poco que comer, el derecho a ser piojoso, el derecho a vivir en la constante inquietud de lo que pueda ocurrir mañana, el derecho a contraer la fiebre tifoidea, el derecho a ser atormentado por indecibles dolores de todo tipo.
Hubo un largo silencio.
—Los reclamo todos —dijo finalmente el Salvaje.
Mustafá Mond se encogió de hombros.
—Concedido —dijo.[1]
John el Salvaje se retira a un desierto deshabitado, donde vive como un ermitaño. Los años de existencia en una reserva india y de lavado de cerebro a manos de Shakespeare y la religión lo han condicionado para rechazar todas las bendiciones de la modernidad. Pero las noticias de un tipo tan insólito y excitante se extienden rápidamente, la gente acude en masa para observarlo y registrar cuanto hace, y muy pronto se convierte en una celebridad. Muy deprimido por toda esta atención no deseada, el Salvaje escapa de la matriz civilizada no tragándose una píldora roja, sino ahorcándose.
A diferencia de los creadores de _Matrix_ y de _El show de Truman_ , Huxley dudaba de la posibilidad de escapar, porque cuestionaba que hubiera alguien que quisiera darse a la fuga. Puesto que nuestro cerebro y nuestro «yo» son parte de la matriz, para escapar de esta hay que escapar del yo. La matriz, sin embargo, es una posibilidad que vale la pena explorar. Escapar de la reducida definición del yo podría muy bien convertirse en una habilidad de supervivencia necesaria en el siglo XXI.
# Parte V
Resiliencia
_¿Cómo se vive en una época de desconcierto cuando los relatos antiguos se han desmoronado y todavía no ha surgido un relato nuevo que los sustituya?_ __
### 19
Educación
#### El cambio es la única constante
La humanidad se enfrenta a revoluciones sin precedentes, todos nuestros relatos antiguos se desmoronan y hasta el momento no ha surgido ningún relato nuevo para sustituirlos. ¿Cómo prepararnos y preparar a nuestros hijos para un mundo de transformaciones sin precedentes y de incertidumbres radicales? Un recién nacido ahora tendrá treinta y tantos años en 2050. Si todo va bien, ese bebé todavía estará vivo hacia 2100, e incluso podría ser un ciudadano activo en el siglo XXII. ¿Qué hemos de enseñarle a ese niño o esa niña que le ayude a sobrevivir y a prosperar en el mundo de 2050 o del siglo XXII? ¿Qué tipo de habilidades necesitará para conseguir trabajo, comprender lo que ocurre a su alrededor y orientarse en el laberinto de la vida?
Por desgracia, puesto que nadie sabe cómo será el mundo en 2050 (por no mencionar el de 2100), no tenemos respuesta a estas preguntas. Desde luego, los humanos nunca pudieron predecir el futuro con exactitud. Pero hoy es más difícil de lo que ha sido jamás, porque una vez que la tecnología nos permita modificar cuerpos, cerebros y mentes, ya no podremos estar seguros de nada, ni siquiera de aquello que parecía fijo y eterno.
Hace mil años, en 1018, la gente no sabía muchas cosas acerca del futuro, pero no obstante estaba convencida de que las características básicas de la sociedad humana no cambiarían. Si hubiéramos vivido en China en 1018, sabríamos que hacia 1050 el Imperio Song podría desmoronarse, que los kitanos podrían invadir desde el norte y que la peste podría matar a millones de personas. Sin embargo, tendríamos claro que incluso en 1050 la mayoría de la gente seguiría trabajando como agricultores y tejedores, que los gobernantes todavía confiarían en que los humanos dotaran de personal a sus ejércitos y burocracias, que los hombres todavía dominarían a las mujeres, que la esperanza de vida seguiría siendo de unos cuarenta años y que el cuerpo humano sería exactamente el mismo. De modo que en 1018, los padres chinos pobres enseñaban a sus hijos a plantar arroz o a tejer seda, y los padres más ricos enseñaban a sus hijos a leer los clásicos confucianos, a escribir caligrafía o a luchar a caballo, y a sus hijas a ser amas de casa modestas y obedientes. Era evidente que tales habilidades todavía se necesitarían en 1050.
Por el contrario, hoy en día no tenemos ni idea de cómo será China o el resto del mundo en 2050. No sabemos qué hará la gente para ganarse la vida, no sabemos cómo funcionarán los ejércitos ni las burocracias y no sabemos cómo serán las relaciones de género. Probablemente, algunas personas vivirán mucho más que en la actualidad, y el cuerpo humano podría experimentar una revolución sin precedentes gracias a la bioingeniería y a interfaces directas cerebro-ordenador. De ahí que muchas de las cosas que los chicos aprenden hoy en día serán irrelevantes en 2050.
En la actualidad, demasiadas escuelas se centran en que se aprenda de memoria la información. En el pasado esto tenía sentido, porque esta escaseaba, e incluso el lento goteo de la información existente era repetidamente bloqueado por la censura. Si uno vivía, pongamos por caso, en un pequeño pueblo de México en 1800, difícilmente sabría muchas cosas sobre el resto del mundo. No había radio, ni televisión, ni periódicos diarios ni bibliotecas públicas.[1] Y aun en el caso de que uno fuera culto y tuviera acceso a una biblioteca privada, no había mucho que leer, aparte de novelas y tratados religiosos. El Imperio español censuraba con dureza todos los textos impresos localmente, y solo permitía importar desde el extranjero un goteo de publicaciones revisadas.[2] La cosa era muy parecida si se vivía en alguna ciudad de provincias de Rusia, la India, Turquía o China. Cuando aparecieron las escuelas modernas, que enseñaron a todos los niños a leer y a escribir y a les impartieron los datos básicos de geografía, historia y biología, supusieron una mejora inmensa.
En cambio, en el siglo XXI estamos inundados de una cantidad enorme de información, y ni siquiera los censores intentan impedirla. En cambio, están atareados difundiendo desinformación o distrayéndonos con cosas sin importancia. Si vivimos en algún pueblo mexicano de provincias y disponemos de un teléfono inteligente, podemos pasar muchas vidas enteras solo leyendo la Wikipedia, mirando charlas TED y haciendo cursos gratuitos en línea. Ningún gobierno puede pensar en ocultar toda la información que no le gusta. Por otro lado, es alarmante lo fácil que resulta inundar a la gente con informes conflictivos y pistas falsas. Personas de todo el mundo están solo a un clic de distancia de los últimos informes sobre el bombardeo de Alepo o de la fusión de los casquetes polares, pero hay tantos informes contradictorios que no sabemos qué creer. Además, hay muchísimas más cosas que también están a solo un clic de distancia, lo que hace difícil centrarse, y cuando la política o la ciencia parecen demasiado complicadas, es tentador pasar a ver algunos divertidos vídeos de gatitos, cotilleos de famosos o pornografía.
En un mundo de este tipo, lo último que un profesor tiene que proporcionar a sus alumnos es más información. Ya tienen demasiada. En cambio, la gente necesita la capacidad de dar sentido a la información, de señalar la diferencia entre lo que es y no es importante y, por encima de todo, de combinar muchos bits de información en una imagen general del mundo.
A decir verdad, ese ha sido el ideal de la educación liberal occidental durante siglos, pero hasta ahora muchas escuelas occidentales han sido bastante indolentes a la hora de darle cumplimiento. Los profesores se permitían centrarse en acumular datos al tiempo que animaban a los alumnos a «pensar por sí mismos». Debido a su temor al autoritarismo, las escuelas liberales sentían un horror particular hacia las grandes narraciones. Suponían que mientras diéramos a los estudiantes muchísimos datos y un poco de libertad, los alumnos crearían su propia imagen del mundo, e incluso si esta generación no conseguía sintetizar todos los datos en un relato del mundo significativo y coherente, habría mucho tiempo para construir una buena síntesis en el futuro. Ahora nos hemos quedado sin tiempo. Las decisiones que tomemos en las próximas décadas moldearán el futuro de la propia vida, y podemos tomar estas decisiones solo a partir de nuestra visión actual del mundo. Si esta generación carece de una concepción cabal al respecto, el futuro de la vida se decidirá al azar.
##### LA COSA ESTÁ QUE ARDE
Además de información, la mayoría de las escuelas se centran demasiado asimismo en proporcionar a los alumnos un conjunto de habilidades predeterminadas, como resolver ecuaciones diferenciales, escribir lenguaje de programación en C++, identificar sustancias químicas en un tubo de ensayo o conversar en chino. Pero dado que no tenemos ni idea de cómo serán el mundo y el mercado laboral en 2050, no sabemos qué pericias concretas necesitará la gente. Podemos hacer un gran esfuerzo para enseñar a los chicos a escribir en C++ o a hablar en chino, para acabar descubriendo que en 2050 la IA podría codificar los programas informáticos mucho mejor que los humanos y que una nueva app de Google Translate nos permitirá mantener una conversación en mandarín, cantonés o hakka casi perfectos, aunque solo sepamos decir «Ni hao».
Así pues, ¿qué tendríamos que enseñar? Muchos pedagogos expertos indican que en las escuelas deberían dedicarse a enseñar «las cuatro ces»: pensamiento crítico, comunicación, colaboración y creatividad.[3] De manera más amplia, tendrían que restar importancia a las habilidades técnicas y hacer hincapié en las habilidades de uso general para la vida. Lo más importante de todo será la capacidad de habérselas con el cambio, de aprender nuevas cosas y de mantener el equilibrio mental en situaciones con las que no estemos familiarizados. Para estar a la altura del mundo de 2050, necesitaremos no solo inventar nuevas ideas y productos: sobre todo necesitaremos reinventarnos una y otra vez.
Porque a medida que la velocidad del cambio aumente, es probable que no solo mute la economía, sino también lo que significa el «ser humano». Ya en 1848 el _Manifiesto comunista_ declaraba que «todo lo sólido se desvanece en el aire». Sin embargo, Marx y Engels pensaban principalmente en las estructuras sociales y económicas. Hacia 2048, las estructuras físicas y cognitivas también se desvanecerán en el aire o en una nube de bits de datos.
En 1848, millones de personas perdían su trabajo en las granjas rurales y se dirigían a las grandes ciudades para trabajar en las fábricas. Pero cuando llegaban a la gran ciudad, era improbable que cambiaran de género o que asumieran un sexto sentido. Y si encontraban un trabajo en alguna fábrica textil, podían esperar seguir teniendo esa profesión el resto de su vida laboral.
En 2048, la gente tendrá que habérselas con migraciones al ciberespacio, con identidades de género fluidas y con nuevas experiencias sensoriales generadas por implantes informáticos. Si encuentran tanto trabajo como sentido en diseñar la moda más vanguardista para un juego de realidad virtual en tres dimensiones, pasada una década no solo esta profesión concreta, sino todos los empleos que exijan tal nivel de creación artística podrían realizarlos inteligencias artificiales. Así, con veinticinco años de edad una persona puede meterse en una web de citas como «mujer heterosexual de veinticinco años que vive en Londres y trabaja en una tienda de moda». A los treinta y cinco, la misma persona dice que es «una persona de género no especificado que se ha sometido a un ajuste de edad, y cuya actividad neocortical tiene lugar principalmente en el mundo virtual de NewCosmos, y cuya misión en la vida es llegar a donde ningún diseñador de moda haya llegado antes». A los cuarenta y cinco años, tanto buscar citas como definirse a uno mismo son cosas completamente pasadas de moda. Solo cabe esperar que un algoritmo encuentre (o cree) la pareja perfecta para nosotros. En cuanto extraer sentido del arte de diseñar moda, los algoritmos nos han superado de manera tan irrevocable que contemplar nuestros grandes logros de la década anterior nos abochorna más que nos enorgullece. Y a los cuarenta y cinco todavía nos aguardan muchas décadas de cambios radicales.
Por favor, no interprete el lector al pie de la letra esta situación hipotética. En realidad, nadie puede predecir los cambios específicos que presenciaremos. Es probable que cualquier escenario futuro concreto se halle lejos de la verdad. Si alguien nos describe el mundo de mediados del siglo XXI y parece ciencia ficción, probablemente sea falso. Pero si entonces alguien nos describe el mundo de mediados del siglo XXI y no parece ciencia ficción, entonces es falso con toda seguridad. No podemos estar seguros de las cosas concretas, pero el propio cambio es la única certeza.
Este cambio tan profundo podría muy bien transformar la estructura básica de la vida, haciendo de la discontinuidad su característica más destacada. Desde tiempo inmemorial, la existencia se dividía en dos partes complementarias: un período de aprendizaje seguido de otro de trabajo. En la primera parte de la vida se acumulaba información, se desarrollaban habilidades, se construía una visión del mundo y una identidad estable. Incluso si a los quince años uno pasaba la mayor parte del día trabajando en el arrozal de la familia (en vez de en el colegio), lo más importante que uno hacía era aprender: cómo cultivar el arroz, cómo llevar las negociaciones con los comerciantes ricos y codiciosos de la gran ciudad, y cómo resolver conflictos sobre la tierra y el agua con los demás aldeanos. En la segunda parte de la vida uno se basaba en las capacidades acumuladas para moverse por el mundo, ganarse la vida y contribuir a la sociedad. Por supuesto, incluso a los cincuenta años uno continuaba aprendiendo más sobre el arroz, los comerciantes y los conflictos, pero se trataba de pequeñas modificaciones de capacidades ya muy perfeccionadas.
A mediados del siglo XXI, el cambio acelerado unido a una esperanza de vida más prolongada hará que este modelo tradicional quede obsoleto. La vida se descontrolará y habrá cada vez menos continuidad entre los diferentes períodos de la existencia. «¿Quién soy?» será una pregunta más urgente y complicada de lo que nunca fue.[4]
Es probable que esto conlleve niveles altísimos de estrés, porque el cambio casi siempre es estresante, y a partir de una determinada edad a la mayoría de la gente no le gusta cambiar. Cuando tenemos quince años, toda nuestra vida es cambio. Nuestro cuerpo crece, nuestra mente se desarrolla, nuestras relaciones se intensifican. Todo fluye, y todo es nuevo. Estamos atareados inventándonos. A casi todos los adolescentes les resulta aterrador, pero al mismo tiempo también es emocionante. Ante nosotros se abren nuevos horizontes, y tenemos todo un mundo por conquistar.
Cuando tenemos cincuenta, no queremos cambios, y la mayoría de las personas han desistido de conquistar el mundo. Estuve allí, hice esto, me compré una camiseta. Preferimos con mucho la estabilidad. Hemos invertido tanto en nuestras habilidades, nuestra carrera, nuestra identidad y nuestra visión del mundo que no queremos empezarlo todo de nuevo. Cuanto más hemos trabajado para construir algo, más difícil es abandonarlo y hacer sitio a algo nuevo. Quizá sigamos valorando nuevas experiencias y ajustes menores, pero la mayoría de las personas en la cincuentena no están preparadas para revisar las estructuras profundas de su identidad y su personalidad.
Hay razones neurológicas para ello. Aunque el cerebro adulto es más flexible e inestable de lo que antaño se creía, sigue siendo menos maleable que el cerebro adolescente. Reconectar neuronas y reconexionar sinapsis son tareas condenadamente difíciles.[5] Pero en el siglo XXI apenas podemos permitirnos la estabilidad. Si intentamos aferrarnos a alguna identidad, trabajo o visión del mundo estables, nos arriesgamos a quedar rezagados mientras el mundo pasa zumbando por nuestro lado. Dado que es probable que aumente la esperanza de vida, podríamos tener que permanecer al final muchas décadas como un fósil inútil. Para seguir siendo relevantes (no solo desde el punto de vista económico, sino por encima de todo desde el punto de vista social) necesitaremos la capacidad de aprender de manera constante y de reinventarnos, sin duda a una edad joven, como los cincuenta años.
A medida que lo raro se convierte en lo nuevo normal, nuestras experiencias pasadas, así como las experiencias pasadas de la humanidad entera, se convertirán en guías menos fiables. Los humanos como individuos y la humanidad como un todo tendrán que habérselas cada vez más con cosas con que nadie se topó antes, como máquinas superinteligentes, cuerpos modificados, algoritmos que puedan manipular nuestras emociones con asombrosa precisión, rápidos cataclismos climáticos causados por el hombre y la necesidad de cambiar de profesión cada década. ¿Qué es lo correcto cuando nos enfrentamos a una situación de todo punto sin precedentes? ¿Cómo actuar cuando nos vemos inundados por enormes cantidades de información y no hay ninguna manera de poder asimilarla y analizarla toda? ¿Cómo vivir en un mundo donde la incertidumbre profunda no es un error, sino una característica?
Para sobrevivir y prosperar en semejante mundo necesitaremos muchísima flexibilidad mental y grandes reservas de equilibrio emocional. Tendremos que desprendernos de manera repetida de algo de lo que mejor conocemos, y sentirnos cómodos con lo desconocido. Por desgracia, enseñar a los chicos a aceptar lo desconocido y a mantener su equilibrio mental es muchísimo más difícil que enseñarles una ecuación de física o las causas de la Primera Guerra Mundial. No podemos aprender resiliencia leyendo un libro o escuchando una conferencia. Los mismos profesores suelen carecer de la flexibilidad mental que el siglo XXI exige, porque ellos son el producto del sistema educativo antiguo.
La revolución industrial nos ha legado la teoría de la educación como una cadena de producción. En medio de la ciudad hay un gran edificio de hormigón dividido en muchas salas idénticas, cada una de ellas equipada con hileras de mesas y sillas. Al sonido de un timbre nos dirigimos a una de estas salas con otros treinta niños que nacieron el mismo año que nosotros. Cada hora entra un adulto en la sala y empieza a hablar. A todos ellos les paga el gobierno para eso. Uno de ellos nos habla de la forma de la Tierra, otro nos cuenta cosas del pasado de los humanos y un tercero nos explica aspectos del cuerpo humano. Es fácil reírse de este modelo, y casi todo el mundo está de acuerdo en que, con independencia de sus logros anteriores, ahora se halla en crisis. Pero hasta ahora no hemos creado una alternativa viable; al menos, y sin duda, no una capaz de ajustarse y que pueda ser implementada en el México rural y no solo en los lujosos barrios residenciales de California.
##### HACKEAR A HUMANOS
De modo que el mejor consejo que puedo dar a un chico o a una chica de quince años atascados en una escuela anticuada en algún lugar de México, la India o Alabama es: no confíes demasiado en los adultos. La mayoría tienen buenas intenciones, pero no acaban de entender el mundo. En el pasado, seguir a los adultos era una apuesta segura, porque conocían el mundo muy bien y el mundo cambiaba muy despacio. Pero el siglo XXI va a ser diferente. Debido a la velocidad creciente del cambio, nunca puedes estar seguro de si lo que te dicen los adultos es sabiduría intemporal o prejuicio anticuado.
Así pues, ¿en qué puedes confiar? ¿Quizá en la tecnología? Es una apuesta más arriesgada aún. La tecnología puede ayudarte mucho, pero si acaba ejerciendo un gran poder sobre tu vida, podrías convertirte en un rehén de sus planes. Hace miles de años, los humanos inventaron la agricultura, pero esta tecnología enriqueció solo a una élite minúscula, al tiempo que esclavizaba a la mayoría de sus congéneres. La mayor parte de la gente se encontró arrancando malas hierbas, acarreando agua y cosechando maíz bajo un sol abrasador desde el alba hasta el atardecer. También puede ocurrirte a ti.
La tecnología no es mala. Si sabes lo que quieres hacer en la vida, tal vez te ayude a obtenerlo. Pero si no lo sabes, a la tecnología le será facilísimo moldear tus objetivos por ti y tomar el control de tu vida. Sobre todo porque la tecnología es cada vez más sofisticada a la hora de entender a los humanos, por lo que puedes verte sirviéndola cada vez más, en lugar de que ella te sirva. ¿Has visto a esos zombis que vagan por las calles con la cara pegada a sus teléfonos inteligentes? ¿Crees que controlan la tecnología, o que esta los controla a ellos?
Entonces ¿tienes que confiar en ti mismo? Esto suena muy bien en _Barrio Sésamo_ o en una anticuada película de Disney, pero en la vida real no funciona tanto. Incluso Disney se ha dado cuenta de ello. Al igual que Riley Andersen, la mayoría de la gente apenas se conoce a sí misma, y cuando intenta «escucharse», cae fácilmente presa de manipulaciones externas. La voz que oímos en nuestra cabeza nunca fue digna de confianza, porque siempre reflejaba la propaganda del Estado, el lavado ideológico del cerebro y la publicidad comercial, por no mencionar los virus bioquímicos.
A medida que la biotecnología y el aprendizaje automático mejoren, será más fácil manipular las emociones y los deseos más íntimos de la gente, y resultará más peligroso que nunca seguir simplemente nuestro corazón. Cuando Coca-Cola, Amazon, Baidu o el gobierno sepan cómo tirar de los hilos de nuestro corazón y pulsar los botones de nuestro cerebro, ¿podrás seguir apreciando la diferencia entre tu yo y sus expertos en marketing?
Para tener éxito en una tarea tan abrumadora deberás esforzarte mucho en conocer mejor tu sistema operativo. Para saber qué eres y qué quieres de la vida. Este es, desde luego, el consejo más antiguo del libro: conócete a ti mismo. Durante miles de años, filósofos y profetas han animado a la gente a que se conociera a sí misma. Pero este consejo nunca fue más urgente que en el siglo XXI, porque, a diferencia de lo que ocurría en la época de Lao-Tse o de Sócrates, ahora tienes una competencia seria. Coca-Cola, Amazon, Baidu y el gobierno se apresuran a piratearte, a hackearte. No a hackear tu teléfono inteligente, ni tu ordenador ni tu cuenta bancaria: están inmersos en una carrera para hackearte a ti y a tu sistema operativo orgánico. Quizá hayas oído que vivimos en la época de hackear ordenadores, pero eso apenas es una parte de la verdad. En realidad, vivimos en la época de hackear a humanos.
Ahora mismo los algoritmos te están observando. Observan adónde vas, qué compras, con quién te ves. Pronto supervisarán todos tus pasos, tu respiración, los latidos de tu corazón. Para llegar a conocerte cada vez mejor, se basan en macrodatos y en el aprendizaje automático. Y cuando estos algoritmos te conozcan mejor de lo que te conoces tú, lograrán controlarte y manipularte, y tú poco podrás hacer al respecto. Vivirás en _Matrix_ , o en _El show de Truman_. Al final, se trata de una cuestión empírica sencilla: si los algoritmos entienden de verdad lo que ocurre dentro de ti mejor que tú mismo, la autoridad pasará a ellos.
Desde luego, podrías ser perfectamente feliz cediendo toda la autoridad a los algoritmos y confiando en ellos para que decidan por ti y por el resto del mundo. Si es así, limítate a relajarte y a disfrutar del viaje. No es necesario que hagas nada: los algoritmos se encargarán de todo. Si, en cambio, quieres conservar cierto control de tu existencia personal y del futuro de la vida, tendrás que correr más deprisa que los algoritmos, más que Amazon y el gobierno, y conseguir conocerte a ti mismo antes de que lo hagan ellos. Para correr deprisa, no lleves contigo mucho equipaje. Deja atrás todas tus ilusiones. Pesan mucho.
### 20
Significado
#### La vida no es un relato
¿Quién soy? ¿Qué debo hacer en la vida? ¿Cuál es el sentido de la vida? Los humanos han estado formulándose estas preguntas desde tiempo inmemorial. Cada generación necesita una respuesta nueva, porque lo que sabemos y lo que no sabemos va cambiando. Dado todo lo que sabemos y lo que no sabemos de la ciencia, de Dios, de la política y de la religión, ¿cuál es la mejor respuesta en la actualidad?
¿Qué tipo de respuesta espera la gente? En casi todos los casos, cuando la gente pregunta por el sentido de la vida, espera que se le cuente un relato. _Homo sapiens_ es un animal que cuenta relatos, que piensa en relatos más que en números o en gráficos, y que cree que su propio universo funciona como un relato, lleno de héroes y villanos, conflictos y resoluciones, momentos culminantes y finales felices. Cuando buscamos el sentido de la vida, queremos un relato que explique de qué va la realidad y cuál es mi papel concreto en el drama cósmico. Este papel me convierte en una parte de algo más grande que yo y da sentido a todas mis experiencias y elecciones.
Un relato popular, que se ha contado durante miles de años a miles de millones de humanos ansiosos, explica que todos formamos parte de un ciclo eterno que incluye y conecta a todos los seres. Cada ser cumple una función distintiva en el ciclo. Comprender el sentido de la vida significa comprender la función única de cada uno, y llevar una vida satisfactoria significa cumplir dicha función.
La epopeya hindú del Bhagavad Gita relata cómo, en mitad de una devastadora guerra civil, al gran príncipe guerrero Arjuna lo consumen las dudas. Viendo a amigos y a familiares en el ejército contrario, vacila antes de luchar contra ellos y matarlos. Empieza a preguntarse qué son el bien y el mal, quién decidió que así fuera y cuál es el propósito de la vida humana. Entonces el dios Krisna le explica a Arjuna que dentro del gran ciclo cósmico cada ser posee un _dharma_ único, el camino que debes seguir y los deberes que debes cumplir. Si realizas tu _dharma_ , por difícil que sea el camino, gozarás de paz mental y te liberarás de todas las dudas. Si rehúsas seguir tu _dharma_ e intentas seguir el camino de alguna otra persona (o vagar sin tomar ningún camino), perturbarás el equilibrio cósmico y nunca encontrarás paz ni alegría. Da igual cuál sea tu camino concreto, mientras lo sigas. Una lavandera que sigue devotamente el camino de lavandera es muy superior a un príncipe que se aparta del camino de príncipe. Al haber entendido el sentido de la vida, Arjuna se dedica a seguir su _dharma_ como guerrero. Mata a sus amigos y parientes, conduce a su ejército a la victoria, y se convierte en uno de los héroes más estimados y amados del mundo hindú.
La epopeya de 1994 de Disney _El rey león_ se reinventó este relato antiguo para audiencias modernas, donde el joven león Simba interpreta el papel de Arjuna. Cuando Simba quiere conocer el sentido de la existencia, su padre (el rey león Mufasa) le cuenta el gran Círculo de la Vida. Mufasa explica que los antílopes comen hierba, los leones se comen a los antílopes, y cuando los leones mueren, su cuerpo se descompone y alimenta a la hierba. Así es como la vida continúa de generación en generación, siempre que cada animal desempeñe su papel en el drama. Todo está conectado, y cada cual depende de los demás, de manera que si tan solo una hoja de hierba dejara de cumplir su misión, todo el Círculo de la Vida podría deshacerse. La misión de Simba, dice Mufasa, es gobernar el reino de los leones después de la muerte de Mufasa, y mantener en orden a los demás animales.
Sin embargo, cuando Mufasa muere prematuramente, asesinado por su malvado hermano Scar, el joven Simba se siente responsable de la catástrofe y, atormentado por la culpa, abandona el reino del león, rehúye su destino real y se pierde en la tierra salvaje. Allí encuentra a otros dos parias, una suricata y un facóquero, y juntos pasan unos años despreocupados fuera del camino trillado. Su filosofía antisocial implica que a cada problema responden cantando «hakuna matata»: no te preocupes.
Pero Simba no puede escapar a su _dharma_. Cuando madura, cada vez está más preocupado al no saber quién es y qué debe hacer en la vida. En el momento culminante del filme, el espíritu de Mufasa se le revela a Simba en una visión, y le recuerda el Círculo de la Vida y su identidad real. Simba también se entera de que, en su ausencia, el malvado Scar ha ocupado el trono y ha dirigido mal el reino, que ahora padece mucho debido a la discordia y a la hambruna. Simba comprende por fin quién es y qué debe hacer. Retorna al reino del león, mata a su tío, se convierte en rey y restablece la armonía y la prosperidad. La película termina con un orgulloso Simba presentando a su heredero recién nacido a los animales reunidos, lo que asegura la continuidad del gran Círculo de la Vida.
El Círculo de la Vida presenta el drama cósmico como un relato circular. Porque cuanto Simba y Arjuna saben es que los leones comen antílopes y los guerreros luchan en batallas durante incontables eones y continuarán haciéndolo por siempre jamás. La repetición eterna confiere poder al relato, pues implica que este es el devenir natural de las cosas, y que si Arjuna evita el combate o si Simba rehúsa convertirse en rey, estarán rebelándose contra las leyes mismas de la naturaleza.
Si creo en alguna versión del relato del Círculo de la Vida, esto significa que poseo una identidad fija y verdadera que determina mis deberes vitales. Durante muchos años puedo albergar dudas acerca de dicha identidad o pasarla por alto, pero algún día, en algún gran momento culminante, me será revelada, y comprenderé mi papel en el drama cósmico, y aunque luego tal vez me tope con muchas pruebas y tribulaciones, me habré liberado de las dudas y la desesperanza.
Otras religiones e ideologías creen en un drama cósmico lineal, que tiene un principio definido, una parte intermedia no muy larga y un final definitivo. Por ejemplo, según el relato musulmán, en el principio Alá creó todo el universo y estableció sus leyes. Después reveló dichas leyes a los humanos a través del Corán. Por desgracia, gentes ignorantes y malvadas se rebelaron contra Alá e intentaron quebrantar u ocultar dichas leyes, y depende de los musulmanes virtuosos y leales hacer cumplir estas leyes y propagar el conocimiento de las mismas. Finalmente, en el Día del Juicio, Alá juzgará la conducta de todos y cada uno de los individuos. Recompensará a los virtuosos con una dicha eterna en el paraíso y arrojará a los malvados a los pozos ardientes del infierno.
Esta narración grandiosa implica que mi papel en la vida, pequeño pero importante, es seguir las órdenes de Alá, difundir el conocimiento de Sus leyes y asegurar la obediencia a Sus deseos. Si me creo el relato musulmán, le encuentro sentido a rezar cinco veces al día, a donar dinero para construir una nueva mezquita y a luchar contra apóstatas e infieles. Incluso las actividades más mundanas (lavarse las manos, beber vino, practicar sexo) están impregnadas de un sentido cósmico.
También el nacionalismo mantiene un relato lineal. Así, el relato sionista comienza con las aventuras y los logros bíblicos del pueblo judío, narra dos mil años de exilio y persecución, alcanza un clímax con el Holocausto y el establecimiento del Estado de Israel, y desea que llegue el día en que Israel goce de paz y prosperidad, y se convierta en un faro moral y espiritual para el mundo. Si me creo el relato sionista, llego a la conclusión de que la misión de mi vida es promover los intereses de la nación judía protegiendo la pureza del lenguaje hebreo, luchando para recuperar el territorio judío perdido, o quizá teniendo y criando a una nueva generación de leales niños israelíes.
También en este caso, incluso los proyectos rutinarios están impregnados de significado. El Día de la Independencia, los escolares israelíes suelen entonar una canción popular hebrea que ensalza cualquier acción emprendida por el bien de la patria. Un niño canta: «He construido una casa en la tierra de Israel», otro niño canta: «He plantado un árbol en la tierra de Israel», otro interviene con: «He escrito un poema en la tierra de Israel», y así sucesivamente, hasta que al final todos se unen en un coro que canta: «Así tenemos una casa, un árbol, un poema [y cualquier otra cosa que se quiera añadir] en la tierra de Israel».
El comunismo cuenta un relato análogo, pero se centra en la clase y no en la etnicidad. El _Manifiesto comunista_ empieza proclamando:
La historia de toda sociedad hasta nuestros días no ha sido sino la historia de las luchas de clases. Hombres libres y esclavos, patricios y plebeyos, nobles y siervos, maestros y oficiales; en una palabra, opresores y oprimidos, en lucha constante, mantuvieron una guerra ininterrumpida, ya abierta, ya velada; una guerra que termina siempre, bien por una transformación revolucionaria de la sociedad, bien por la destrucción de las dos clases antagónicas.[1]
El manifiesto sigue explicando que, en la época moderna, «la sociedad en su conjunto se divide cada vez más en dos grandes campos hostiles, en dos grandes clases enemigas: la burguesía y el proletariado».[2] Su lucha terminará con la victoria del proletariado, lo que señalará el fin de la historia y el establecimiento del paraíso comunista en la Tierra, donde nadie poseerá nada y todos serán completamente libres y felices.
Si creo en este relato comunista, llego a la conclusión de que la misión de mi vida es acelerar la revolución global escribiendo feroces panfletos, organizando huelgas y manifestaciones, o quizá asesinando a capitalistas codiciosos y luchando contra sus lacayos. El relato confiere significado incluso a los gestos más nimios, como boicotear una marca que explota a los trabajadores textiles en Bangladés o discutir con el cerdo capitalista de mi suegro durante la comida de Navidad.
Cuando considero toda la gama de relatos que buscan definir mi verdadera identidad y dar sentido a mis actos, me sorprende percatarme de que la escala significa muy poco. Algunos relatos, como el Círculo de la Vida de Simba, parecen extenderse hacia la eternidad. Solo ante el telón de fondo del universo puedo saber quién soy. Otros relatos, como la mayoría de los mitos nacionalistas y tribales, son poco convincentes en comparación. El sionismo considera sagradas las aventuras de alrededor del 0,2 por ciento de la humanidad y del 0,005 por ciento de la superficie de la Tierra durante una minúscula fracción de la duración total del tiempo. El relato sionista no atribuye ningún significado a los imperios chinos, a las tribus de Nueva Guinea ni a la galaxia de Andrómeda, y tampoco a los incontables eones que transcurrieron antes de la existencia de Moisés, Abraham y la evolución de los simios.
Esta miopía puede tener repercusiones graves. Por ejemplo, uno de los mayores obstáculos para cualquier tratado de paz entre israelíes y palestinos es que los israelíes no están dispuestos a dividir la ciudad de Jerusalén. Aducen que esta ciudad es «la capital eterna del pueblo judío», y sin duda no es posible transigir en algo que es eterno.[3] ¿Qué son unas pocas personas muertas en comparación con la eternidad? Desde luego, esto es una completa estupidez. La eternidad tiene como mínimo 13.800 millones de años (la edad actual del universo). El planeta Tierra se formó hace unos 4.500 millones de años y los humanos han existido durante al menos 2 millones de años. En cambio, la ciudad de Jerusalén se estableció hace solo 5.000 años y el pueblo judío tiene, a lo sumo, 3.000 años de antigüedad, lo que difícilmente cumple los requisitos de eternidad.
En cuanto al futuro, la física nos dice que el planeta Tierra será absorbido por un Sol en expansión dentro de unos 7.500 millones de años,[4] y que nuestro universo continuará existiendo al menos 13.000 millones de años más. ¿Acaso hay alguien que crea seriamente que el pueblo judío, el Estado de Israel o la ciudad de Jerusalén seguirán existiendo dentro de 13.000 años, por no hablar ya de 13.000 millones de años? Considerando el futuro, el sionismo tiene un horizonte de no más de unos pocos siglos, pero eso basta para colmar la imaginación de la mayoría de los israelíes y de alguna manera calificarlo como «eternidad». Y la gente está dispuesta a hacer sacrificios en nombre de «la ciudad eterna», que probablemente no harían por un efímero conjunto de casas.
Cuando era un adolescente en Israel, también me cautivó inicialmente la promesa nacionalista de convertirme en algo mayor que yo mismo. Quería creer que, si daba mi vida por la nación, viviría para siempre en la nación. Pero no podía comprender lo que quería decir «vivir para siempre en la nación». La frase parecía muy profunda, pero ¿qué significaba en realidad? Recuerdo una ceremonia concreta del día de los Caídos, cuando yo tenía trece o catorce años. Mientras que en Estados Unidos el día de los Caídos se caracteriza sobre todo por ir de compras, en Israel el día de los Caídos es un acontecimiento muy solemne e importante. Ese día en las escuelas se realizan ceremonias para recordar a los soldados que han muerto en las muchas guerras de Israel. Los chicos visten de blanco, recitan poemas, cantan canciones, colocan coronas y hacen ondear banderas. De modo que allí estaba yo, vestido de blanco, durante la ceremonia de mi colegio, y entre el ondear de las banderas y el recitado de poemas pensé naturalmente que cuando creciera también me gustaría ser un soldado caído. Después de todo, si fuera un heroico soldado caído que sacrificó su vida por Israel, todos esos chicos recitarían poemas y harían ondear banderas en mi honor.
Pero entonces pensé: «Espera un momento. Si estoy muerto, ¿cómo sabré que estos chicos está en verdad recitando poemas en mi honor?». De modo que intenté imaginarme muerto. Y me vi reposando bajo alguna lápida blanca en un pulcro cementerio militar, escuchando los poemas procedentes de algo más arriba, la superficie del suelo. Pero entonces pensé: «Si estoy muerto, no puedo oír ningún poema porque no tengo oídos, y no tengo cerebro, y no puedo oír ni sentir nada. Así pues, ¿qué sentido tiene?».
Peor todavía era que a los trece años yo ya sabía que el universo tenía un par de miles de millones de años de antigüedad y que probablemente seguiría existiendo durante miles de millones de años más. ¿Era realista que esperara que Israel existiera durante un tiempo tan extenso? ¿Acaso chicos _Homo sapiens_ vestidos de blanco recitarían todavía poemas en mi honor doscientos millones de años después? En aquel asunto había algo sospechoso.
Si resulta que el lector es palestino, no se sienta ufano: es igual de improbable que exista ningún palestino dentro de unos doscientos millones de años. De hecho, con toda probabilidad para entonces no existirá ningún mamífero. Otros movimientos nacionales son igualmente estrechos de miras. Al nacionalismo serbio le importan poco los acontecimientos del período Jurásico, mientras que los nacionalistas coreanos creen que una pequeña península en la costa oriental de Asia es la única parte del cosmos que de verdad importa en el gran plan de las cosas.
Ni que decir tiene que ni siquiera Simba (a pesar de su entrega al perpetuo Círculo de la Vida) contempla nunca el hecho de que leones, antílopes y hierba no sean eternos. Simba no piensa en cómo era el universo antes de la evolución de los mamíferos, ni cuál será el destino de su amada sabana africana después de que los humanos hayan matado a todos los leones y cubierto las praderas de asfalto y hormigón. ¿Haría esto que la vida de Simba careciera de sentido?
Todos los relatos son incompletos. Pero para construir una identidad viable para mí y dar sentido a mi vida, en realidad no necesito un relato completo desprovisto de puntos ciegos y de contradicciones internas. Para dar sentido a mi vida, un relato solo tiene que satisfacer dos condiciones: primera, ha de darme a mí algún papel que desempeñar. Es improbable que el miembro de una tribu de Nueva Guinea crea en el sionismo o en el nacionalismo serbio, porque a estos relatos no les importa en absoluto Nueva Guinea ni su gente. Al igual que las estrellas de cine, a los humanos les gustan solo los guiones que les reservan un papel importante.
En segundo lugar, aunque no es necesario que un buen relato se extienda hasta el infinito, sí tiene que extenderse más allá de mis horizontes. El relato me proporciona una identidad y da sentido a mi vida al asignarme algo mayor que yo mismo. Pero siempre existe el riesgo de que pueda empezar a preguntarme qué da sentido a este «algo mayor». Si el sentido de mi vida es ayudar al proletariado o a la nación polaca, ¿qué otorga sentido exactamente al proletariado o a la nación polaca? Hay un cuento de un hombre que afirmaba que el mundo se mantiene en su lugar porque descansa sobre el lomo de un enorme elefante. Cuando se le preguntó sobre qué reposaba el elefante, contestó que sobre el caparazón de una gran tortuga. ¿Y la tortuga? Sobre el caparazón de una tortuga todavía mayor. ¿Y esa tortuga más grande? El hombre contestó apresuradamente: «No se preocupe por eso. A partir de ahí hay tortugas hasta el final».
Los relatos de mayor éxito tienen el final abierto. Nunca necesitan explicar de dónde procede en último término el sentido, porque saben captar muy bien la atención de la gente y mantenerla dentro de una zona segura. Así, cuando se explica que el mundo descansa sobre el lomo de un elefante inmenso, uno debe anticiparse a cualquier pregunta difícil describiendo con gran detalle que cuando el elefante bate sus gigantescas orejas, provoca un huracán, y cuando tiembla de cólera, un terremoto sacude la superficie de la Tierra. Si se teje un cuento lo bastante bueno, a nadie se le ocurrirá preguntar sobre qué se sostiene el elefante. De manera parecida, el nacionalismo nos seduce con relatos de heroísmo, hace que se nos salten las lágrimas al contarnos antiguos desastres y desata nuestra furia al mortificarse por las injusticias que padeció nuestra nación. Quedamos tan absortos en esta epopeya nacional que empezamos a evaluar cuanto ocurre en el mundo en función de su impacto sobre nuestra nación, y rara vez pensamos en preguntar, para empezar, qué hizo que nuestra nación fuera tan importante.
Cuando creemos un relato concreto, nos resulta interesantísimo conocer sus detalles más nimios, al tiempo que permanecemos ciegos a todo lo que queda fuera de su ámbito. Los comunistas devotos pueden pasar innumerables horas debatiendo si es permisible que se alíen con los socialdemócratas en los primeros estadios de la revolución, pero rara vez se detienen a reflexionar sobre el lugar del proletariado en la evolución de los mamíferos en el planeta Tierra, o en la expansión de la vida orgánica en el cosmos. Tales charlas ociosas se consideran un desperdicio de palabras contrarrevolucionario.
Aunque algunos relatos se toman la molestia de abarcar la totalidad del espacio y del tiempo, si son capaces de captar la atención, muchos relatos exitosos permanecen en un ámbito mucho más reducido. Una ley fundamental de la narración es que una vez que un relato consigue extenderse más allá del horizonte de la audiencia, su ámbito último importa poco. La gente puede mostrar el mismo fanatismo asesino en nombre de una nación con mil años de historia que en nombre de un dios con mil millones de años de antigüedad. A la gente, simplemente, no se le dan bien los grandes números. En la mayoría de los casos, cuesta sorprendentemente poco agotar nuestra imaginación.
Dado lo que sabemos acerca del universo, parecería absolutamente imposible que una persona sensata creyera que la verdad última de este y de la existencia humana sea el relato del nacionalismo israelí, alemán o ruso, o de hecho del nacionalismo en general. Un relato que pasa por alto casi la totalidad del tiempo, todo el espacio, el big bang, la física cuántica y la evolución de la vida es, a lo sumo, una minúscula parte de la verdad. Pero, de alguna manera, la gente consigue no ver más allá de él.
En realidad, miles de millones de personas a lo largo de la historia creyeron que para que su vida tuviera sentido ni siquiera necesitaban ser asimilados dentro de una nación o de un gran movimiento ideológico. Era suficiente con que, simplemente, «dejaran algo tras de sí», con lo que se aseguraban que su relato personal continuara más allá de su muerte. El «algo» que dejo atrás es idealmente mi alma o mi esencia personal. Si renazco en un nuevo cuerpo tras la muerte de mi cuerpo actual, entonces la muerte no es el final. Es solo el espacio entre dos capítulos, y la trama que se inició en un capítulo continuará en el siguiente. Mucha gente tiene al menos una fe vaga en una teoría de este tipo, aunque no la basen en ninguna teología específica. No necesitan un dogma complicado, únicamente el sentimiento reconfortante de que su relato continúa más allá del horizonte de la muerte.
Esta teoría de la vida como una epopeya interminable es sumamente atractiva y común, pero adolece de dos problemas principales. Primero, al alargar mi relato personal no lo hago en verdad más significativo; simplemente, lo hago más largo. De hecho, las dos grandes religiones que aceptan la idea de un ciclo interminable de nacimientos y muertes (el hinduismo y el budismo) comparten su aversión por la futilidad de todo ello. Millones y millones de veces aprendo a caminar, crezco, me peleo con mi suegra, enfermo, muero, y luego lo hago todo de nuevo. ¿Qué sentido tiene? Si yo acumulara todas las lágrimas que he vertido en cada una de mis vidas anteriores, llenarían el océano Pacífico; si reuniera todos los dientes y cabellos que he perdido, alcanzarían una altura superior a la del Himalaya. ¿Y qué he conseguido con todo eso? No es extraño que los sabios hindúes y budistas hayan dedicado gran parte de sus esfuerzos a encontrar la manera de salir de este tiovivo en lugar de perpetuarlo.
El segundo problema de esta teoría es la escasa evidencia de apoyo. ¿Qué prueba tengo de que en una vida pasada fui un campesino medieval, un cazador neandertal, un _Tyrannosaurus rex_ o una ameba (si realmente viví millones de vidas, tuve que haber sido un dinosaurio y una ameba en algún momento, porque los humanos solo han existido en los últimos 2,5 millones de años)? ¿Quién pondrá las manos en el fuego asegurando que en el futuro renacerá como un cíborg, un explorador intergaláctico o incluso una rana? Basar mi vida en esta promesa es como vender mi casa a cambio de un cheque diferido que pagará un banco situado por encima de las nubes.
Por tanto, la gente que duda de que algún tipo de alma o espíritu sobreviva en realidad a su muerte se esfuerza por dejar atrás algo un poco más tangible. Ese «algo tangible» puede tomar una de dos formas: cultural o biológica. Puedo dejar atrás un poema, pongamos por caso, o algunos de mis preciosos genes. Mi vida tiene sentido porque la gente todavía leerá mi poema dentro de cien años, o porque mis hijos y nietos estarán todavía aquí. ¿Y cuál es el sentido de sus vidas? Bueno, ese es su problema, no el mío. El sentido de la vida es de este modo un poco como jugar con una granada de mano activada: una vez que se la pasas a alguna otra persona, estás seguro.
Por desgracia, esa modesta esperanza de solo «dejar atrás algo» rara vez se cumple. La mayoría de los organismos que han existido se extinguieron sin dejar ninguna herencia genética. Casi todos los dinosaurios, por ejemplo. O una familia de neandertales cuando los sapiens los relevaron. O el clan polaco de mi abuela. En 1934, mi abuela Fanny emigró a Jerusalén con sus padres y dos hermanas, pero la mayor parte de sus familiares quedaron atrás, en las ciudades polacas de Chmielnik y Czestochowa. Unos pocos años después llegaron los nazis y los eliminaron a todos, hasta al último niño.
Los intentos de dejar atrás algún legado cultural pocas veces tienen más éxito. Nada ha quedado del clan polaco de mi abuela excepto unas pocas caras descoloridas en el álbum de fotografías familiar, y a los noventa y seis años ni siquiera mi abuela logra poner nombres a las caras. Por lo que yo sé, los miembros del clan no han dejado atrás ninguna creación cultural: ni un poema, ni un diario, ni siquiera una lista de la compra. Se podría aducir que comparten una parte de la herencia colectiva del pueblo judío o del movimiento sionista, pero es difícil que eso dé sentido a su vida individual. Además, ¿cómo sabemos que todos ellos valoraban su identidad judía o estaban de acuerdo con el movimiento sionista? Quizá uno de ellos fuera un comunista convencido y sacrificara su vida siendo espía para los soviéticos. Quizá otro no quisiera más que integrarse en la sociedad polaca, sirviera como oficial en el ejército polaco y fuera asesinado por los soviéticos en la masacre de Katyn. Quizá un tercero fuera una feminista radical que rechazaba todas las identidades tradicionales religiosas y nacionalistas. Puesto que no dejaron nada atrás, es demasiado fácil reclutarlos póstumamente para tal o cual causa, y ni siquiera pueden protestar.
Si no logramos dejar nada tangible atrás, como un gen o un poema, ¿no será suficiente con que hagamos que el mundo sea un poco mejor? Podemos ayudar a alguien, y ese alguien ayudará a continuación a alguna otra persona, y así contribuiremos a la mejora general del mundo y seremos un pequeño eslabón en la gran cadena de la bondad. Quizá seamos el profesor de un niño brillante pero difícil, que acabará siendo médico y salvará la vida de cientos de personas. Quizá ayudemos a una anciana a cruzar la calle e iluminemos una hora de su vida. Aunque tiene sus méritos, la gran cadena de la bondad es un poco como la gran cadena de las tortugas: no es en absoluto evidente de dónde procede su sentido. A un anciano sabio se le preguntó qué había aprendido acerca del sentido de la vida. «Bueno —contestó—, he aprendido que estoy aquí, en la Tierra, para ayudar a otras personas. Lo que todavía no he entendido es por qué hay aquí otras personas.»
Para quienes no confían en ninguna gran cadena, en ninguna herencia futura ni en ninguna epopeya colectiva, tal vez el relato más seguro y parsimonioso al que pueden encomendarse sea al del amor. El amor no pretende que se vaya más allá del aquí y el ahora. Como atestiguan incontables poemas amorosos, cuando se está enamorado, todo el universo se reduce al lóbulo de la oreja, a la pestaña o al pezón de nuestro amado. Cuando Romeo contempla a Julieta, que apoya la mejilla en su mano, exclama: «¡Oh! ¡Que no fuera yo un guante de esa mano para poder tocar esa mejilla!». Al conectarnos con un único cuerpo aquí y ahora, nos sentimos conectados con todo el cosmos.
Lo cierto es que nuestra amada es solo otro humano, no diferente en esencia de multitudes a las que pasamos por alto a diario en el tren y en el supermercado. Pero para nosotros, él o ella parece el infinito, y somos felices de perdernos en esta infinitud. Poetas místicos de todas las tradiciones han combinado a menudo el amor romántico con la unión cósmica y han escrito sobre Dios como si fuera un amante. Los poetas románticos han saldado la galantería al escribir sobre sus amantes como si fueran dioses. Si estamos de verdad enamorados de alguien, nunca nos preocupa el sentido de la vida.
¿Y qué ocurre si no estamos enamorados? Bueno, si creemos en el relato romántico pero no estamos enamorados, al menos sabemos cuál es el objetivo de nuestra vida: encontrar el amor verdadero. Lo hemos visto en un sinnúmero de películas y hemos leído sobre ello en un sinnúmero de libros. Sabemos que un día conoceremos a ese ser especial, veremos el infinito dentro de dos ojos centelleantes, toda nuestra vida tendrá sentido de repente y todas las preguntas que hayamos albergado se contestarán repitiendo un nombre una y otra vez. Igual que Tony en _West Side Story_ o que Romeo al ver a Julieta contemplándolo desde el balcón.
##### EL PESO DEL TECHO
Aunque un buen relato ha de otorgarme un papel y extenderse más allá de mis horizontes, no tiene por qué ser verdadero. Un relato puede ser pura ficción, y aun así darme una identidad y hacer que sienta que mi vida tiene sentido. De hecho, hasta donde llega nuestro conocimiento científico, ninguno de los miles de relatos que las diferentes culturas, religiones y tribus han inventado a lo largo de la historia es cierto. Todos son solo invenciones humanas. Si buscamos el sentido real de la vida y a cambio obtenemos un relato, debemos saber que es la respuesta equivocada. Los detalles exactos en realidad no importan. Cualquier relato es erróneo, simplemente por ser un relato. El universo no funciona como un relato.
Así pues, ¿por qué la gente cree en estas ficciones? Una razón es que su identidad personal se ha construido sobre el relato. A las personas se nos pide que creamos en el relato desde la más tierna infancia. Lo oímos por boca de nuestros padres, nuestros maestros, nuestros vecinos y de la cultura general mucho antes de que desarrollemos la independencia intelectual y emocional necesaria para poner en cuestión dicho relato y verificarlo. Para cuando nuestro intelecto madura, hemos proyectado tanto en el relato que es mucho más probable que usemos nuestro intelecto para racionalizarlo que para dudar de él. La mayoría de la gente que se dedica a la búsqueda de identidad es como los niños que van a la caza de tesoros: solo encuentra lo que sus padres han ocultado previamente para ella.
En segundo lugar, no únicamente nuestras identidades personales, sino también nuestras instituciones colectivas se han construido sobre el relato. En consecuencia, resulta muy intimidante dudar de este. En muchas sociedades, a quien intenta hacerlo se le condena al ostracismo o se le persigue. Aunque no sea así, hay que tener nervios de acero para cuestionar el tejido mismo de la sociedad. Porque si de verdad el relato es falso, entonces el mundo tal como lo conocemos no tiene sentido. Leyes estatales, normas sociales, instituciones económicas, todas podrían desmoronarse.
La mayoría de los relatos se mantienen cohesionados por el peso de su techo más que por la solidez de sus cimientos. Pensemos en el relato cristiano. Sus cimientos son los más endebles de todos. ¿Qué prueba tenemos de que el hijo del Creador del universo entero naciera como una forma de vida basada en el carbono en algún lugar de la Vía Láctea hace unos dos mil años? ¿Qué prueba tenemos de que esto ocurriera en la provincia romana de Galilea y de que Su madre fuera una virgen? Pero se han erigido enormes instituciones globales sobre dicho relato, y su peso presiona con una fuerza tan abrumadora que lo mantienen en su lugar. Se han librado guerras enteras por haber querido cambiar una sola palabra del relato. El cisma de mil años entre los cristianos occidentales y los cristianos ortodoxos orientales, que recientemente se ha manifestado en la matanza mutua de croatas y serbios, se inició a partir de la sola palabra _filioque_ («y del hijo» en latín). Los cristianos occidentales querían introducir este término en la profesión de fe cristiana, mientras que los orientales se opusieron de forma vehemente. (Las consecuencias de añadir este término son tan arcanas que sería imposible explicarlas aquí de una manera que tuviera sentido. Si el lector es curioso, pregúntele a Google.)
Una vez que identidades personales y sistemas sociales enteros se construyen sobre un relato, resulta impensable dudar del mismo, no debido a las pruebas que lo apoyan, sino porque su hundimiento desencadenaría un cataclismo personal y social. En historia, a veces el techo es más importante que los cimientos.
##### _H_ OCUS POCUS(7) Y LA INDUSTRIA DE LA FE
Todos los relatos que nos dan sentido e identidad son ficticios, pero los humanos necesitamos creer en ellos. Así, ¿cómo hacer que el relato se perciba como real? Es evidente por qué los humanos quieren creer en él, pero ¿cómo se lo creen realmente? Ya hace miles de años que sacerdotes y chamanes dieron con la respuesta: mediante rituales. Un ritual es un acto mágico que hace que lo abstracto sea concreto y lo ficticio, real. La esencia del ritual es el conjuro mágico «Hocus pocus, ¡X es Y!».[5]
¿Cómo hacer que Cristo sea real para sus devotos? En la ceremonia de la misa, el sacerdote toma un pedazo de pan y un vaso de vino, y proclama que el pan es la carne de Cristo y que el vino es la sangre de Cristo, y comiéndolos y bebiéndolos los fieles consiguen la comunión con Cristo. ¿Qué hay más real que sentir de verdad a Cristo en nuestra boca? Tradicionalmente, el sacerdote hacía estas audaces proclamaciones en latín, el lenguaje antiguo de la religión, la ley y los secretos de la vida. Frente a los asombrados ojos de los campesinos reunidos, el sacerdote mantenía en alto un pedazo de pan y exclamaba «Hoc est corpus!» («¡Este es el cuerpo!») y el pan se convertía en teoría en la carne de Cristo. En la mente de los analfabetos campesinos, que no hablaban latín, «Hoc est corpus!» se embarullaba en «¡Hocus pocus!», y así nació el potente hechizo capaz de transformar una rana en un príncipe y una calabaza en un carruaje.[6]
Mil años antes del nacimiento del cristianismo, los antiguos hindúes usaban el mismo truco. El Brihadaranyaka Upanishad interpreta el sacrificio ritual de un caballo como una realización de todo el relato del cosmos. El texto sigue la estructura del «Hocus pocus, ¡X es Y!», y dice: «La cabeza del caballo sacrificial es el alba, su ojo es el sol, su fuerza vital el aire, su boca abierta el fuego llamado Vaisvanara, y el cuerpo del caballo sacrificial es el año, ...] sus miembros son las estaciones, sus articulaciones los meses y quincenas, sus pies los días y noches, sus huesos las estrellas, y su carne las nubes, [...] su bostezo es el relámpago, el temblor de su cuerpo es el trueno, su producción de agua es la lluvia y su relincho es la voz».[[7] Y así un pobre caballo se convierte en la totalidad del cosmos.
Casi todo puede transformarse en un ritual al conferir a gestos mundanos, como encender cirios, tañer campanas o contar cuentas, un significado religioso profundo. Lo mismo cabe decir de gesticulaciones físicas, como inclinar la cabeza, postrar todo el cuerpo o juntar las palmas de las manos. Varias formas de tocados, desde el turbante sij hasta el hiyab musulmán, han estado tan cargadas de significado que durante siglos han desencadenado luchas apasionadas.
También el alimento puede estar cargado de significado espiritual mucho más allá de su valor nutritivo, ya se trate de los huevos de Pascua que simbolizan nueva vida y la resurrección de Cristo, o las hierbas amargas y el pan ácimo que los judíos han de comer en la Pascua judía para recordar su esclavitud en Egipto y su huida milagrosa. Apenas hay un plato en el mundo que no se haya interpretado como símbolo de algo. Así, el día de Año Nuevo los judíos creyentes comen miel para que el año que comienza sea dulce, cabezas de pescado para ser fecundos como los peces y desplazarse hacia delante y no hacia atrás, y granadas para que sus buenas obras se multipliquen como las muchas semillas de este fruto.
Asimismo, se han usado rituales similares para fines políticos. Durante miles de años, coronas, tronos y báculos representaron reinos e imperios enteros, y millones de personas murieron en guerras brutales que se libraron por la posesión del «trono» o de la «corona». Las cortes reales cultivaron protocolos sumamente complejos, equiparables a las más intrincadas ceremonias religiosas. En lo militar, disciplina y ritual son inseparables, y los soldados, desde la antigua Roma hasta hoy en día, pasan muchísimas horas marchando en formación, saludando a los superiores y lustrando las botas. Es bien sabido que Napoleón comentó que él podía hacer que los hombres sacrificaran su vida por un galón de colores.
Quizá nadie entendió la importancia política de los rituales mejor que Confucio, que consideró que la observancia estricta de los ritos ( _l_ _i_ ) era la clave de la armonía social y la estabilidad política. Clásicos confucianos como _El libro de los ritos_ , _Los ritos de Zhou_ y _El libro de la etiqueta y los ritos_ registraron hasta el más mínimo detalle qué ritos había que ejecutar en cada acontecimiento de Estado, desde el número de recipientes rituales usados en la ceremonia hasta el tipo de instrumentos musicales que debían tocarse y los colores de los ropajes que debían llevarse. Siempre que China se veía afectada por alguna crisis, los eruditos confucianos culpaban enseguida al abandono de los ritos, como un sargento mayor que culpa de la derrota militar a los soldados holgazanes por no abrillantar sus botas.[8]
En el Occidente moderno, la obsesión confuciana por los rituales se ha visto con frecuencia como una señal de superficialidad y arcaísmo. En realidad, es probable que dé fe de la apreciación profunda e intemporal de la naturaleza humana por parte de Confucio. Quizá no sea una coincidencia que las culturas confucianas (la primera y principal en China, pero también en las vecinas Corea, Vietnam y Japón) crearan estructuras sociales y políticas perdurables. Si queremos conocer la verdad última de la vida, ritos y rituales son un obstáculo enorme. Pero si estamos interesados (como Confucio) en la estabilidad y la armonía sociales, la verdad suele ser una carga, mientras que ritos y rituales figuran entre nuestros mejores aliados.
Esto es tan relevante en el siglo XXI como lo fue en la antigua China. El poder de _hocus pocus_ está vivito y coleando en nuestro moderno mundo industrial. En 2018, para mucha gente dos palos de madera clavados son Dios, un cartel coloreado en la pared es la revolución y un retazo de tela que ondea al viento es la nación. No podemos ver ni oír Francia, porque existe solo en nuestra imaginación, pero sin duda podemos ver la bandera tricolor y escuchar «La Marsellesa». De modo que ondeando una bandera y cantando un himno transformamos la nación, que pasa de ser un relato abstracto a una realidad tangible.
Hace miles de años, los hindúes devotos sacrificaban a preciosos caballos; hoy invierten en la producción de costosas banderas. La bandera nacional de la India es conocida como Tiranga (literalmente, «tricolor»), porque está formada por tres bandas de color azafrán, blanco y verde. El Código de la Bandera de la India de 2002 proclama: «La bandera representa las esperanzas y aspiraciones del pueblo de la India. Es el símbolo de nuestro orgullo nacional. A lo largo de las últimas cinco décadas, varias personas, entre ellas miembros de las fuerzas armadas, han sacrificado incondicionalmente su vida para hacer que la tricolor siga ondeando en todo su esplendor».[9] A continuación, el Código de la Bandera cita a Sarvepalli Radhakrishnan, el segundo presidente de la India, que explicó:
El color azafrán denota renuncia o desinterés. Nuestros dirigentes han de mostrarse indiferentes frente a las ganancias materiales y dedicarse a su trabajo. El blanco en el centro es luz, el camino de la verdad para guiar nuestra conducta. El verde muestra nuestra relación con el suelo, nuestra relación con la vida vegetal de la que depende toda otra vida. La rueda Ashoka en el centro del blanco es la rueda de la ley del _dharma_. La verdad o _satya_ , el _dharma_ o la virtud tienen que ser los principios controladores de todos los que trabajan bajo esta bandera.[10]
En 2017, el gobierno nacionalista de la India izó una de las banderas más grandes del mundo en Attari, en la frontera indopakistaní, en un gesto calculado para inspirar no renuncia ni desinterés, sino más bien la envidia pakistaní. Aquella Tiranga concreta pesaba 55 toneladas, medía 36 metros de largo y 24 metros de ancho y se izaba sobre un palo de 110 metros de alto (¿qué hubiera dicho Freud de esto?). La bandera podía divisarse desde la metrópoli pakistaní de Lahore. Por desgracia, fuertes vientos la rasgaban continuamente y el orgullo nacional requería que se la cosiera una y otra vez, con gran coste para los contribuyentes indios.[11] ¿Por qué el gobierno indio invierte sus escasos recursos en tejer banderas enormes en lugar de construir sistemas de alcantarillado en los suburbios de chabolas de Nueva Delhi? Porque la bandera hace que la India sea real de una manera que los sistemas de alcantarillado no lo consiguen.
De hecho, el coste mismo de la bandera vuelve el ritual más efectivo. De todos los rituales, el sacrificio es el más potente, porque de todas las cosas del mundo, el sufrimiento es la más real. Nunca puede pasarse por alto o dudar de él. Si queremos que la gente crea de verdad en alguna ficción, persuadámosla para que haga un sacrificio en su nombre. Una vez que sufrimos por un relato, eso suele bastar para convencernos de que el relato es real. Si ayunamos porque Dios nos ordenó que lo hiciéramos, la sensación tangible de hambre hace que Dios esté presente más que cualquier estatua o icono. Si perdemos las piernas en una guerra patriótica, nuestros muñones y la silla de ruedas hacen que la nación sea más real que cualquier poema o himno. A un nivel menos épico, si preferimos comprar pasta local en lugar de pasta italiana de calidad superior, podríamos estar realizando un pequeño sacrificio diario que hace que sintamos la nación real incluso en el supermercado.
Esto es, desde luego, una falacia lógica. Que suframos debido a nuestra fe en Dios o en la nación no demuestra que nuestras creencias sean ciertas. Quizá estemos simplemente pagando el precio de nuestra credulidad. Sin embargo, a la mayoría de la gente no le gusta admitir que es tonta. En consecuencia, cuanto más se sacrifica por una determinada creencia, más se fortalece su fe. Esta es la misteriosa alquimia del sacrificio. A fin de situarnos bajo su poder, el sacerdote sacrificador no necesita darnos nada: ni lluvia, ni dinero ni una victoria bélica. Más bien necesita quitarnos algo. En cuanto nos convence de que hagamos algún sacrificio doloroso, estamos atrapados.
Esto funciona también en el mundo comercial. Si compramos un Fiat de segunda mano por 2.000 dólares, es probable que nos quejemos de ello al que quiera oírnos. Pero si compramos un Ferrari nuevecito por 200.000 dólares, entonaremos elogios a diestro y siniestro, no porque sea un coche muy bueno, sino porque hemos pagado tanto por él que tenemos que creer que es la cosa más maravillosa del mundo. Incluso en el amor, cualquier aspirante a Romeo o Werther sabe que sin sacrificio no existe un verdadero amor. El sacrificio no es solo una manera de convencer a nuestro amante de que somos serios: es también una manera de convencernos de que estamos realmente enamorados. ¿Por qué cree el lector que las mujeres piden a sus amantes que les regalen anillos de diamantes? Una vez que el amante hace un sacrificio económico tan grande, debe convencerse a sí mismo de que fue por una causa digna.
El sacrificio personal es muy persuasivo no solo para los propios mártires, sino también para los espectadores. Pocos dioses, naciones o revoluciones pueden sostenerse sin mártires. Si nos atrevemos a poner en cuestión el drama divino, el mito nacionalista o la saga revolucionaria, se nos reprocha de inmediato: «Pero ¡los mártires benditos murieron por esto! ¿Te atreves a decir que murieron por nada? ¿Acaso crees que esos héroes eran estúpidos?».
Para los musulmanes chiíes, el drama del cosmos alcanzó su momento culminante en el día de la Ashura, que fue el décimo día del mes de muharram, sesenta y un años después de la Hégira (el 10 de octubre de 680, según el calendario cristiano). Aquel día, en Kerbala (Irak), soldados del malvado usurpador Yazid asesinaron a Husáin ibn Ali, nieto del profeta Mahoma, junto con un pequeño grupo de seguidores. Para los chiíes, el martirio de Husáin simboliza la lucha eterna del bien contra el mal y de los oprimidos contra la injusticia. De la misma manera que los cristianos representan repetidamente el drama de la crucifixión e imitan la pasión de Cristo, los chiíes representan el drama de la Ashura e imitan la pasión de Husáin. Millones de ellos acuden en masa al sagrado altar de Kerbala, que se estableció donde Husáin fue martirizado, y en el día de la Ashura chiíes de todo el mundo llevan a cabo rituales de duelo, en algunos casos flagelándose y cortándose con cuchillos y cadenas.
Pero la importancia de la Ashura no se limita a un lugar ni a un día. El ayatolá Ruhollah Jomeini y otros numerosos líderes chiíes han dicho muchas veces a sus seguidores que «todos los días son la Ashura, y todo lugar es Kerbala».[12] Así, el martirio de Husáin en Kerbala da sentido a cualquier acontecimiento, en cualquier lugar, en cualquier momento, y ha de considerarse que incluso las decisiones más prosaicas tienen un impacto en la gran lucha cósmica entre el bien y el mal. Si nos atrevemos a dudar de este relato, enseguida se nos recordará Kerbala, y dudar del martirio de Husáin o burlarnos del mismo es la peor ofensa que puede cometerse.
Alternativamente, si los mártires escasean y la gente no desea sacrificarse, el sacerdote sacrificador puede hacer que sacrifiquen a algún otro. Podemos sacrificar a un humano a Baal, el dios vengativo, quemar a un hereje en la hoguera para la mayor gloria de Jesucristo, ejecutar a mujeres adúlteras porque Alá así lo dijo, o enviar a los enemigos de clase al gulag. Una vez que lo hacemos, una alquimia del sacrificio ligeramente distinta empieza a operar su magia en nosotros. Cuando nos infligimos sufrimiento a nosotros mismos en el nombre de algún relato, esto nos plantea una disyuntiva: «O bien el relato es cierto, o yo soy un tonto crédulo». Cuando infligimos sufrimiento a los demás, también se nos plantea: «O bien el relato es cierto, o yo soy un villano cruel». Y de la misma manera que no queremos admitir que somos tontos, tampoco queremos admitir que somos villanos, de forma que preferimos creer que el relato es cierto.
En marzo de 1839, en la ciudad iraní de Mashhad, un matasanos local le dijo a una mujer judía que padecía una enfermedad de la piel, y que si mataba a un perro y lavaba las manos en su sangre, se curaría. Mashhad es una ciudad chií sagrada, y sucedió que la mujer comenzó la macabra terapia en el día sagrado de la Ashura. Algunos chiíes, al verla, creyeron (o afirmaron creer) que la mujer mató al perro para burlarse del martirio de Kerbala. Por las calles de Mashhad enseguida corrió la voz de este sacrilegio impensable. Alentada por el imán local, una muchedumbre enfurecida irrumpió en el barrio judío, incendió la sinagoga y asesinó a treinta y seis judíos. A los judíos supervivientes de Mashhad se les ofreció después una elección rigurosa: convertirse al islamismo inmediatamente o la muerte. El sórdido episodio apenas dañó la reputación de Mashhad como «capital espiritual de Irán».[13]
Cuando pensamos en sacrificios humanos, por lo general nos vienen a la mente rituales horripilantes en templos cananeos o aztecas, y suele argumentarse que el monoteísmo puso fin a esta práctica terrible. En realidad, los monoteístas practicaron el sacrificio humano a una escala mucho mayor que la mayoría de los cultos politeístas. El cristianismo y el islamismo mataron a mucha más gente en nombre de Dios que los seguidores de Baal o de Huitzilopochtli. En una época en que los conquistadores españoles pusieron fin a todos los sacrificios humanos a los dioses aztecas e incas, en España la Inquisición quemaba a herejes a carretadas.
Los sacrificios pueden darse en todas las formas y envergaduras. No siempre implican a sacerdotes armados con cuchillos o pogromos sangrientos. El judaísmo, por ejemplo, prohíbe trabajar o viajar en el día sagrado del Sabbat (el significado literal de la palabra Sabbat es «estarse quieto» o «descansar»). El Sabbat empieza con la puesta de sol del viernes y dura hasta la puesta del sol del sábado, y entretanto los judíos ortodoxos se abstienen de hacer casi cualquier tipo de trabajo, incluso cortar papel higiénico del rollo del lavabo. (Tras cierto debate sobre el tema entre los rabinos más doctos, se llegó a la conclusión de que cortar el papel higiénico violaría el tabú del Sabbat, y en consecuencia los judíos devotos que quieran limpiarse el trasero durante el Sabbat han de preparar una reserva de papel higiénico cortado previamente.)[14]
En Israel, los judíos religiosos suelen obligar a los judíos seglares e incluso a ateos consumados a observar esos tabúes. Puesto que el equilibrio del poder en la política israelí suele depender de los partidos ortodoxos, a lo largo de los años han conseguido que se aprobaran leyes que prohíben todo tipo de actividad durante el Sabbat. Aunque no han logrado ilegalizar el uso de vehículos privados durante el Sabbat, sí han podido conseguir que se prohibiera el transporte público. Este sacrificio religioso a escala nacional afecta sobre todo a los sectores más débiles de la sociedad, en especial porque el sábado es el único día de la semana en que las personas trabajadoras están libres para viajar y visitar a familiares y a amigos lejanos y acudir a atracciones turísticas. Una abuela rica no tiene ningún problema en conducir su coche nuevo para visitar a sus nietos en otra ciudad, pero una abuela pobre no puede hacerlo, porque no hay autobuses ni trenes.
Al causar tales dificultades a cientos de miles de ciudadanos, los partidos religiosos demuestran y fortalecen su fe inquebrantable en el judaísmo. Aunque no se vierta sangre, sí se sacrifica el bienestar de muchas personas. Si el judaísmo solo es un relato ficticio, entonces es algo cruel y desalmado impedir que una abuela visite a sus nietos o impedir que un estudiante sin blanca vaya a divertirse un poco a la playa. Cuando, a pesar de todo, esto se hace, los partidos religiosos están diciéndole al mundo (y a sí mismos) que creen de verdad en el relato judío. ¿Acaso piensa el lector que disfrutan perjudicando a la gente si no hay una buena razón, sea esta la que fuere?
El sacrificio no solo fortalece nuestra fe en el relato, sino que a menudo es un sustituto de todas las demás obligaciones para con este. La mayoría de los grandes relatos de la humanidad han establecido ideales que la mayor parte de la gente no puede cumplir. ¿Cuántos cristianos observan realmente los Diez Mandamientos al pie de la letra, y no dan falsos testimonios ni codician bienes ajenos nunca? ¿Cuántos budistas han alcanzado hasta ahora la fase de ausencia del ego? ¿Cuántos socialistas trabajan al máximo posible de su capacidad al tiempo que no toman más de lo que en realidad necesitan?
Incapaz de estar a la altura del ideal, la gente se dedica al sacrificio como una solución. Un hindú puede cometer fraudes en los impuestos, visitar ocasionalmente a una prostituta y maltratar a sus ancianos padres, pero después se convence de que es una persona muy piadosa, porque ha respaldado la destrucción de la mezquita de Babri Masjid en Ayodhya e incluso ha donado dinero para construir un templo hindú en su lugar. En el siglo XXI ocurre lo mismo que en los tiempos antiguos: la búsqueda humana del sentido de la vida acaba muy a menudo con una sucesión de sacrificios.
##### LA CARTERA DE LA IDENTIDAD
Los antiguos egipcios, cananeos y griegos se aseguraban los sacrificios. Tenían muchos dioses, y si uno fallaba, esperaban que acabara apareciendo otro, de modo que hacían sacrificios al dios Sol por la mañana, a la diosa Tierra al mediodía y a un grupo diverso de hadas y demonios por la tarde. Esto tampoco ha cambiado mucho. Todos los relatos y dioses en que cree la gente en la actualidad (ya se trate de Yahvé, del Becerro de oro, la Nación o la Revolución) son incompletos, están llenos de agujeros y plagados de contradicciones. Por tanto, la gente rara vez deposita toda su fe en un único relato. En cambio, mantiene una cartera de varios relatos y diversas identidades, y pasan de uno a otro según sus necesidades. Estas disonancias cognitivas son inherentes a casi todas las sociedades y los movimientos.
Piense el lector en un típico simpatizante del Tea Party que de alguna manera armoniza una fe ardiente en Jesucristo con una firme objeción a las políticas de bienestar gubernamentales y un apoyo a ultranza a la Asociación Nacional del Rifle. ¿No era Jesús algo más aficionado a ayudar a los pobres que a armarse hasta los dientes? Podría parecer algo incompatible, pero el cerebro humano tiene muchos cajones y compartimentos, y algunas neuronas, simplemente, no se hablan entre sí. De manera similar, podemos encontrar a muchos defensores de Bernie Sanders que tienen una fe vaga en alguna revolución futura, mientras que también creen en la importancia de invertir su dinero de forma sensata. Pueden pasar con toda facilidad de debatir sobre la injusta distribución de la riqueza en el mundo a debatir cómo van sus inversiones en Wall Street.
Casi nadie tiene una sola identidad. Nadie es solo musulmán, o solo italiano o solo capitalista. Pero de vez en cuando aparece un credo fanático e insiste en que la gente debe creer únicamente un relato y tener solo una identidad. En generaciones recientes, el más fanático de dichos credos fue el fascismo. El fascismo insistía en que la gente no tenía que creer ningún relato excepto el relato nacional y no había de tener ninguna identidad excepto la identidad nacional. No todos los nacionalistas son fascistas. La mayoría de los nacionalistas sienten una gran fe en el relato de su nación, y hacen hincapié en los méritos únicos de su nación y las obligaciones únicas que tienen para con su nación; no obstante, reconocen que en el mundo hay más cosas aparte de su nación. Yo puedo ser un italiano leal con obligaciones especiales con la nación italiana, y aun así tener otras identidades. Puedo ser un socialista, un católico, un marido, un padre, un científico y un vegetariano, y cada una de estas identidades conlleva obligaciones añadidas. A veces, varias de mis identidades me impulsan en direcciones diferentes y algunas de mis obligaciones entran en conflicto entre sí. Pero, bueno, ¿quién dijo que la vida es fácil?
El fascismo surge cuando el nacionalismo quiere hacer que la vida sea demasiado fácil para sí, negando todas las demás identidades y obligaciones. Últimamente ha habido mucha confusión sobre el significado exacto de «fascismo». La gente tilda de «fascistas» a todos aquellos que no le gustan. La palabra corre el riesgo de degenerar en un insulto que valga para cualquier cosa. Así pues, ¿qué significa realmente? En resumen, mientras que el nacionalismo me enseña que mi nación es única y que tengo obligaciones especiales para con ella, el fascismo dice que mi nación es suprema y que debo a mi nación obligaciones exclusivas. Nunca antepondré los intereses de ningún grupo o individuo a los intereses de mi nación, con independencia de las circunstancias. Aunque mi nación se dedique a causar muchas desgracias a millones de extranjeros en un país lejano y a cambio de ello consiga un beneficio irrisorio, no he de tener ningún escrúpulo en apoyarla. Si no lo hago, soy un traidor despreciable. Si mi nación me exige que mate a millones de personas, debo matarlas. Si mi nación me exige que traicione la verdad y la belleza, debo traicionarlas.
¿Cómo valora el arte un fascista? ¿Cómo sabe si una película es buena? Muy sencillo. Solo existe una vara de medir. Si el filme sirve a los intereses nacionales, es bueno. Si el filme no sirve a los intereses nacionales, es malo. ¿Y cómo decide un fascista qué enseñar a los niños en la escuela? Usa la misma vara de medir. Enseña a los niños aquello que sirva a los intereses de la nación; la verdad no importa.[15]
Esta veneración por la nación resulta muy atractiva no solo porque simplifica muchos dilemas difíciles, sino también porque hace que la gente piense que pertenece a lo más importante y hermoso del mundo: su nación. Los horrores de la Segunda Guerra Mundial y del Holocausto demuestran las consecuencias terribles de esta línea de pensamiento. Por desgracia, cuando la gente habla de los males del fascismo suele hacerlo a medias, porque tiende a presentar al fascismo como un monstruo horrible al tiempo que no consigue explicar qué tiene de tan fascinante. Por esta razón, en la actualidad hay personas que a veces adoptan ideas fascistas sin darse cuenta. La gente piensa: «Me enseñaron que el fascismo es feo, y cuando me miro en el espejo veo algo muy hermoso, de modo que no puedo ser un fascista».
Es algo parecido al error que cometen las películas de Hollywood cuando presentan a los malos (lord Voldemort, lord Sauron, Darth Vader) como feos y malvados. Por lo general, son crueles y despreciables incluso para con sus más leales partidarios. Al ver estos filmes, nunca he entendido por qué alguien querría seguir a un tipo tan repugnante como Voldemort.
El problema de la maldad radica en que en la vida real no es necesariamente fea. Puede parecer muy hermosa. El cristianismo lo sabía mejor que Hollywood, razón por la cual el arte cristiano tradicional solía presentar a Satanás como un galán bellísimo. Por ese motivo es tan difícil resistirse a las tentaciones de Satanás. Y también por ese motivo es difícil habérselas con el fascismo. Cuando se mira en el espejo fascista, lo que se ve no es feo en absoluto. Cuando los alemanes miraron en el espejo fascista en la década de 1930, vieron Alemania como lo más bello del mundo. Si hoy en día los rusos miran en el espejo fascista, verán Rusia como lo más bello del mundo. Y si los israelíes miran en el espejo fascista, verán Israel como lo más bello del mundo. Entonces desearán perderse dentro de este hermoso colectivo.
El término «fascismo» proviene del latín _fascis_ , que significa «haz de varas». Más bien parece un símbolo poco glamuroso para una de las ideologías más feroces y letales en la historia del mundo. Pero tiene un significado profundo y siniestro. Una única vara es muy endeble y se la puede partir fácilmente en dos. Sin embargo, cuando se atan diversas varas juntas en un _fascis_ , resulta casi imposible romperlas. Esto implica que el individuo es algo sin importancia, pero mientras el colectivo permanezca unido, es muy poderoso.[16] Por tanto, los fascistas creen en favorecer los intereses del colectivo por encima de los de cualquier individuo, y exigen que ni una sola vara se atreva jamás a romper la unidad del haz.
Desde luego, nunca está claro dónde termina un «haz de varas» humano y empieza otro. ¿Por qué tengo que considerar Italia el haz de varas al que pertenezco? ¿Por qué no mi familia, o la ciudad de Florencia, o la provincia de la Toscana, o el continente europeo o la especie humana en su conjunto? Las formas más leves de nacionalismo me dirán que, en efecto, tengo obligaciones para con mi familia, Florencia, Europa y la humanidad entera, así como obligaciones especiales para con Italia. En cambio, los fascistas italianos exigirán lealtad absoluta únicamente a Italia.
A pesar de todos los esfuerzos de Mussolini y su partido fascista, la mayoría de los italianos se mantuvieron bastante indiferentes a eso de poner Italia por delante de su _famiglia_. En Alemania, la propaganda nazi realizó una tarea mucho más concienzuda, pero ni siquiera Hitler consiguió que la gente se olvidara de los relatos alternativos. Incluso en los días más oscuros de la época nazi, la gente siempre mantuvo algunos relatos en reserva que se sumaban al oficial. Como resultó evidente y claro en 1945. Cabía pensar que después de doce años de lavado de cerebro por parte de los nazis, muchos alemanes serían de todo punto incapaces de dar sentido a sus vidas en la posguerra. Habiendo puesto toda su fe en un gran relato, ¿qué hacer cuando dicho relato saltó por los aires? Pero la mayoría de los alemanes se recobraron a una velocidad asombrosa. En algún lugar de su mente conservaron otros relatos acerca del mundo, y apenas Hitler se había disparado una bala en la sien, los habitantes de Berlín, Hamburgo y Múnich adoptaron nuevas identidades y dieron un renovado sentido a sus vidas.
Es cierto que alrededor del 20 por ciento de los _Gauleiters_ (los dirigentes regionales del partido) nazis se suicidaron, como hizo alrededor del 10 por ciento de los generales.[17] Pero eso significa que el 80 por ciento de los _Gauleiters_ y el 90 por ciento de los generales estuvieron muy contentos de seguir viviendo. La inmensa mayoría de los nazis con carnet e incluso de las bases de la SS nunca se volvieron locos ni se mataron. Acabaron siendo productivos agricultores, profesores, médicos y agentes de seguros.
De hecho, ni siquiera el suicido demuestra un compromiso absoluto con un único relato. El 13 de noviembre de 2015, Estado Islámico organizó varios ataques suicidas en París que costaron la vida a 130 personas. El grupo extremista explicó que lo hicieron en venganza por el bombardeo a activistas de Estado Islámico en Siria e Irak por parte de la aviación francesa, y con la esperanza de disuadir a Francia de seguir llevando a cabo esos bombardeos en el futuro.[18] Al mismo tiempo, Estado Islámico declaró que todos los musulmanes que habían muerto por causa de la aviación francesa eran mártires que ahora gozaban de felicidad eterna en el cielo.
Aquí hay algo que no tiene sentido. Si en efecto los mártires que habían muerto por causa de la aviación francesa están ahora en el cielo, ¿por qué habría nadie de buscar venganza? ¿Venganza por qué, exactamente? ¿Por enviar gente al cielo? Si el lector acabara de oír que su querido hermano ha ganado un millón de dólares en la lotería, ¿empezaría a hacer volar por los aires todas las administraciones de lotería como venganza? Así pues, ¿por qué causar el caos en París solo porque la aviación francesa dio a algunos de sus hermanos un billete de ida al paraíso? Sería aún peor si de hecho se consiguiera disuadir a los franceses de efectuar más bombardeos en Siria. Porque en este caso irían al cielo menos musulmanes.
Podríamos vernos tentados de llegar a la conclusión de que los activistas de Estado Islámico en realidad no creen que los mártires vayan al cielo. Por ese motivo se encolerizan cuando los bombardean y matan. Pero si es así, ¿por qué algunos de ellos se colocan cinturones explosivos y voluntariamente se inmolan y quedan hechos pedazos? Con toda probabilidad, la respuesta es que se aferran a dos relatos contradictorios, sin pensar demasiado en las incoherencias. Como ya se ha dicho, algunas neuronas no se hablan con otras.
Ocho siglos antes de que la aviación francesa bombardeara los baluartes de Estado Islámico en Siria e Irak, otro ejército francés invadió Oriente Próximo, en lo que es conocido por la posteridad como la Séptima Cruzada. Bajo el mando del rey santo Luis IX, los cruzados esperaban conquistar el valle del Nilo y convertir Egipto en un bastión cristiano. Sin embargo, fueron derrotados en la batalla de Mansura, y la mayoría de los cruzados acabaron prisioneros. Un caballero cruzado, Jean de Joinville, escribió en sus memorias que cuando la batalla estaba perdida y decidieron rendirse, uno de sus hombres dijo: «No puedo estar de acuerdo con esta decisión. Lo que aconsejo es que dejemos que nos maten, porque así iremos al paraíso». Joinville comenta escuetamente que «ninguno hicimos caso de su consejo».[19]
Joinville no explica por qué lo rechazaron. Al fin y al cabo, se trataba de hombres que habían abandonado sus confortables _chateaux_ en Francia para embarcarse en una aventura prolongada y peligrosa en Oriente Próximo, sobre todo porque creían en la promesa de la salvación eterna. Entonces ¿por qué cuando solo se hallaban a un instante de distancia de la felicidad eterna del paraíso prefirieron la cautividad musulmana? Por lo visto, aunque los cruzados creían fervientemente en la salvación y en el paraíso, en el momento de la verdad optaron por ir sobre seguro.
##### EL SUPERMERCADO DE ELSINORE
A lo largo de la historia, casi todos los humanos han creído en varios relatos al mismo tiempo, y nunca han estado absolutamente convencidos de la verdad de ninguno de ellos. Esta incertidumbre ha inquietado a la mayoría de las religiones, que por ello consideraron que la fe era una virtud cardinal y la duda, uno de los peores pecados posibles. Como si hubiera algo intrínsecamente bueno en creer en las cosas sin pruebas. Sin embargo, con el auge de la cultura moderna, la situación cambió. La fe se consideró cada vez más una esclavitud mental, mientras que la duda acabó viéndose como una condición previa a la libertad.
En algún momento entre 1599 y 1602, William Shakespeare escribió su versión de _El rey león_ , más conocida como _Hamlet_. Pero, a diferencia de Simba, Hamlet no completa el Círculo de la Vida. Permanece escéptico e indeciso hasta el final mismo, sin descubrir jamás el sentido de la vida y sin acabar nunca de decidir si es mejor ser o no ser. En esto, Hamlet es el héroe moderno paradigmático. La modernidad no rechaza la plétora de relatos que ha heredado del pasado. En cambio, abre un supermercado para ellos. El humano moderno es libre de probarlos todos, eligiendo y combinando lo que más se acomode a su gusto.
Algunas personas no pueden soportar tanta libertad e incertidumbre. Los movimientos totalitarios modernos como el fascismo reaccionaron de forma violenta al supermercado de ideas dudosas, y superaron incluso a las religiones tradicionales en exigir una fe absoluta en un relato único. Sin embargo, a la mayoría de las personas modernas les gustó el supermercado. ¿Qué se hace cuando no se conoce el sentido de la vida y en qué relato creer? Se santifica la capacidad misma de elegir. Nos quedamos quietos para siempre en el pasillo del supermercado, con el poder y la libertad de elegir lo que nos plaza, de examinar los productos que tenemos delante y..., congela este fotograma, corta, fin. Que pasen los créditos.
Según la mitología liberal, si nos quedamos el tiempo suficiente en este gran supermercado, tarde o temprano experimentaremos la epifanía liberal, y nos percataremos del verdadero sentido de la vida. Todos los relatos de las estanterías del supermercado son falsos. El sentido de la vida no es un producto prefabricado. No hay un guion divino, y nada externo a mí puede dar sentido a mi vida. Soy yo quien lo impregno todo de significado mediante mi libre albedrío y a través de mis propios sentimientos.
En la película de fantasía _Willow_ (un cuento de hadas típico, de George Lucas), el héroe epónimo es un enano normal y corriente que sueña con convertirse en un gran hechicero y dominar los secretos de la existencia. Un día, un hechicero de este tipo pasa por la aldea del enano en busca de un aprendiz. Willow y otros dos enanos candidatos se presentan al hechicero, que plantea a los aspirantes una prueba sencilla. Extiende la mano derecha, despliega sus dedos y pregunta con un tono parecido al de Yoda: «El poder de controlar el mundo, ¿en qué dedo está?». Cada uno de los tres enanos elige un dedo, pero todos eligen el equivocado. No obstante, el hechicero percibe algo en Willow, y después le pregunta: «Cuándo os mostré los dedos, ¿cuál fue tu primer impulso?». «Bueno, fue algo estúpido —contesta Willow, turbado—: elegir mi propio dedo.» «¡Ajá! —exclama el hechicero exultante—. ¡Esa era la respuesta correcta! ¡Te falta fe en ti mismo!» La mitología liberal nunca se cansa de repetir esta lección.
Fueron nuestros propios dedos humanos los que escribieron la Biblia, el Corán y los Vedas, y es nuestra mente la que confiere poder a tales relatos. Son, sin duda, relatos bellos, pero su belleza reside estrictamente en los ojos del espectador. Jerusalén, La Meca, Benarés y Bodh Gaya son lugares sagrados, pero solo debido a lo que sienten los humanos cuando van allí. En sí mismo, el universo es solo un revoltijo sin sentido de átomos. Nada es hermoso, sagrado o sexy, pero los sentimientos humanos así hacen que sea. Solo los sentimientos humanos hacen que una manzana roja sea apetitosa y un zurullo, repugnante. Si eliminamos los sentimientos humanos, nos quedamos con un montón de moléculas.
Esperamos encontrar sentido al encajar nosotros mismos en algún relato prefabricado sobre el universo, pero, según la interpretación liberal del mundo, la verdad es justo lo contrario. El universo no me da sentido. Yo doy sentido al universo. Esta es mi vocación cósmica. No tengo un destino fijado o un _dharma_. Si me encontrara en la piel de Simba o Arjuna, podría elegir luchar por la corona de un reino, pero no tengo por qué hacerlo. Quizá podría unirme a un circo ambulante, ir a Broadway para cantar en un musical o desplazarme a Silicon Valley y lanzar una nueva empresa. Soy libre de crear mi propio _dharma_.
Así, como todos los demás relatos cósmicos, el relato liberal empieza con una narración creacionista. Afirma que la creación tiene lugar en cada momento y que yo soy el creador. ¿Cuál es, pues, el objetivo de mi vida? Crear sentido mediante los sentimientos, los pensamientos, los deseos y las invenciones. Cualquier cosa que limite la libertad humana para sentir, pensar, desear o inventar, limita el sentido del universo. De ahí que la libertad frente a tales limitaciones sea el ideal supremo.
En términos prácticos, los que creen en el relato liberal viven a la luz de dos mandamientos: crea y lucha por la libertad. La creatividad puede manifestarse en escribir un poema, explorar nuestra sexualidad, inventar una nueva app o descubrir una sustancia química desconocida. Luchar por la libertad incluye cualquier cosa que libere a las personas de las limitaciones sociales, biológicas y físicas, ya sea manifestarse contra dictadores brutales, enseñar a niñas a leer, encontrar una cura para el cáncer o construir una nave espacial. El panteón liberal de los héroes alberga a Rosa Parks y a Pablo Picasso junto a Louis Pasteur y a los hermanos Wright.
Esto parece muy emocionante y profundo en la teoría. Por desgracia, la libertad y la creatividad humanas no son lo que el relato liberal imagina. Hasta donde alcanza nuestro conocimiento científico, no hay magia tras nuestras elecciones y creaciones. Son el producto de miles de millones de neuronas que intercambian señales bioquímicas, e incluso si liberamos a humanos del yugo de la Iglesia católica y de la Unión Soviética, sus elecciones seguirán estando dictadas por algoritmos bioquímicos tan despiadados como la Inquisición y el KGB.
El relato liberal nos instruye en buscar libertad para expresarnos y realizarnos. Pero tanto «nosotros» como la libertad son quimeras mitológicas tomadas prestadas de los cuentos de hadas de tiempos antiguos. El liberalismo tiene una idea particularmente confusa del «libre albedrío». Evidentemente, los humanos tenemos libre albedrío, tenemos deseos y a veces somos libres para cumplirlos. Si por «libre albedrío» entendemos la libertad para hacer lo que deseamos, entonces sí, los humanos tenemos libre albedrío. Pero si por «libre albedrío» entendemos la libertad para escoger qué desear..., entonces no, los humanos no tenemos libre albedrío.
Si me atraen sexualmente los hombres, puedo ser libre para realizar mis fantasías, pero no para sentir, en cambio, atracción por las mujeres. En algunos casos quizá decida refrenar mis ansias sexuales o incluso probar una terapia de «conversión sexual», pero el deseo mismo de cambiar mi orientación sexual es algo que mis neuronas me obligan a hacer, tal vez alentadas por prejuicios culturales y religiosos. ¿Por qué una persona se siente avergonzada de su sexualidad e intenta cambiarla mientras que otra celebra los mismos deseos sexuales sin rastro ninguno de culpa? Podría decirse que los sentimientos religiosos de la primera tal vez sean más fuertes que los de la segunda. Pero ¿acaso la gente elige libremente albergar sentimientos religiosos fuertes o débiles? Asimismo, una persona puede decidir ir a la iglesia todos los domingos en un esfuerzo consciente para reforzar sus débiles sentimientos religiosos; pero ¿por qué una persona aspira a ser más religiosa mientras que otra está muy feliz de seguir siendo atea? Esto puede ser el resultado de un número cualquiera de disposiciones culturales y genéticas, pero nunca del «libre albedrío».
Lo que vale para el deseo sexual vale para todos los deseos, y de hecho para todos los sentimientos y pensamientos. Considere simplemente el lector el próximo pensamiento que aflore en su mente. ¿De dónde procede? ¿Ha elegido el lector pensarlo libremente, y solo entonces lo ha pensado? Claro que no. El proceso de autoexploración empieza con cosas sencillas, y cada vez se torna más difícil. Al principio nos damos cuenta de que no controlamos el mundo exterior a nosotros. Yo no decido cuándo llueve. Después nos damos cuenta de que no controlamos lo que ocurre dentro de nuestro propio cuerpo. Yo no controlo mi tensión sanguínea. A continuación comprendemos que no gobernamos siquiera nuestro cerebro. Yo no les digo a las neuronas cuándo disparar. Al final hemos de darnos cuenta de que no controlamos nuestros deseos, ni siquiera nuestras reacciones a tales deseos.
Percatarnos de esto puede ayudarnos a ser menos obsesivos con nuestras opiniones, nuestros sentimientos y nuestros deseos. No tenemos libre albedrío, pero podemos ser un poco más libres de la tiranía de nuestro albedrío. Por lo general, los humanos damos tanta importancia a nuestros deseos que intentamos controlar y modelar el mundo entero según dichos deseos. Al perseguir nuestros antojos, los humanos volamos a la Luna, nos enzarzamos en guerras mundiales y desestabilizamos todo el ecosistema. Si comprendemos que nuestros deseos no son las manifestaciones mágicas de la libre elección, sino que por el contrario son el producto de procesos bioquímicos (influidos por factores culturales que también se hallan fuera de nuestro control), nos preocuparíamos menos de ellos. Es preferible entendernos a nosotros, nuestra mente y nuestros deseos que intentar alcanzar cualquier fantasía que surja de nuestra cabeza.
Y a fin de conocernos, un paso fundamental es reconocer que el «yo» es un relato ficticio que los mecanismos intrincados de nuestra mente construyen, ponen al día y reescriben sin cesar. En mi mente hay un narrador que explica quién soy, de dónde vengo, hacia dónde me dirijo y qué está ocurriendo ahora mismo. Como los expertos manipuladores del gobierno que explican (y maquillan) las últimas turbulencias políticas, el narrador interno se equivoca en muchas ocasiones, pero rara vez, o nunca, lo admite. Y de la misma forma que el gobierno construye un mito nacional con banderas, iconos y desfiles, mi máquina de propaganda interna construye un mito personal con recuerdos estimados y traumas apreciados que suelen guardar muy poco parecido con la verdad.
En la época de Facebook e Instagram, este proceso de creación de mitos puede observarse mejor que nunca, porque parte del mismo se ha externalizado desde la mente al ordenador. Resulta a la vez fascinante y espantoso ver que hay personas que pasan incontables horas construyendo y embelleciendo un yo perfecto en línea, que quedan prendadas de su propia creación y que la confunden con la verdad sobre ellas mismas.[20] Así es como unas vacaciones familiares repletas de atascos de tráfico, riñas insignificantes y silencios tensos se convierte en una colección de bellos paisajes, cenas perfectas y caras sonrientes; el 99 por ciento de lo que experimentamos nunca forma parte del relato del yo.
Resulta particularmente digno de atención que nuestro yo de fantasía suela ser muy visual, mientras que nuestras experiencias reales son corpóreas. En la fantasía, observamos una escena en el ojo de nuestra mente o en la pantalla del ordenador. Nos vemos de pie en una playa tropical, el mar azul detrás de nosotros, una amplia sonrisa en nuestra cara, con una copa de cóctel en una mano y con el otro brazo rodeando la cintura de nuestro amante. El paraíso. Lo que la fotografía no muestra es la molesta mosca que nos muerde la pierna, la fastidiosa sensación en nuestro estómago por haber comido aquella horrible sopa de pescado, la tensión en la mandíbula mientras fingimos una amplia sonrisa y la fea pelea que esa feliz pareja ha tenido hace cinco minutos. ¡Si pudiéramos sentir lo que siente la gente de las fotografías al tiempo que las hacemos!
De ahí que si de verdad queremos comprendernos, no hemos de identificarnos con nuestra cuenta de Facebook o con el relato interno del yo. En cambio, hemos de observar el flujo real de cuerpo y mente. Veremos aparecer y desaparecer pensamientos, emociones y deseos sin mucha razón y sin ninguna orden por nuestra parte, de la misma manera que vientos diferentes soplan desde esta o aquella dirección y nos despeinan. Y de la misma manera que no somos los vientos, tampoco somos el batiburrillo de pensamientos, emociones y deseos que experimentamos, y sin duda no somos el relato expurgado que contamos de ellos en retrospectiva. Los experimentamos todos, pero no los controlamos, no los poseemos y no somos ellos. La gente pregunta: «¿Quién soy?», y espera que se le cuente un relato. Lo primero que hemos de saber de nosotros es que no somos un relato.
##### NINGÚN RELATO
El liberalismo dio un paso radical al negar todos los dramas cósmicos, pero después recreó el drama dentro del ser humano: el universo no tiene guion, de manera que nos corresponde a los humanos escribirlo, y esa es nuestra vocación y el sentido de nuestras vidas. Miles de años antes de nuestra época liberal, el antiguo budismo fue más allá al negar no solo todos los dramas cósmicos, sino incluso el drama interno de la creación humana. El universo no tiene sentido, y los sentimientos humanos tampoco tienen sentido alguno. No son parte de un gran relato cósmico: son solo vibraciones efímeras que aparecen y desaparecen sin propósito concreto. Esta es la verdad. Piénsalo, lector.
El Brihadaranyaka Upanishad nos dice que «la cabeza del caballo sacrificial es el alba, su ojo es el sol, ...] sus miembros son las estaciones, sus articulaciones los meses y quincenas, sus pies los días y noches, sus huesos las estrellas, y su carne las nubes». En cambio, el Mahasatipatthana Sutta, un texto budista fundamental, explica que cuando un humano medita, él o ella observa su cuerpo con detenimiento, advirtiendo que «en este cuerpo hay cabellos en la cabeza, pelos en la piel, uñas, dientes, piel, carne, tendones, huesos, médula, riñones, corazón, [...] saliva, moco nasal, fluido sinovial y orina. Así sigue observando el cuerpo. [...] Ahora se ha producido su comprensión: "¡Esto es el cuerpo!"».[[21] Los cabellos, huesos y orina no significan nada más. Solo son lo que son.
Fragmento tras fragmento, el texto sigue explicando que da igual lo que la persona que medita observe en el cuerpo o en la mente: él o ella sencillamente lo entienden. Así, cuando quien medita respira, «al inspirar una gran bocanada de aire, el monje lo entiende adecuadamente: "Estoy inspirando una gran bocanada". Al inspirar una bocanada pequeña, lo entiende perfectamente: "Inspiro una bocanada pequeña"».[22] La bocanada grande no representa las estaciones ni la bocanada pequeña los días. Son solo vibraciones en el cuerpo.
Buda enseñó que las tres realidades básicas del universo son que todo cambia sin cesar, que nada tiene ninguna esencia perdurable y que nada es completamente satisfactorio. Podemos explorar las regiones más alejadas de la galaxia, o nuestro cuerpo o nuestra mente, pero nunca encontraremos algo que no cambie, que tenga una esencia eterna y que nos satisfaga por completo.
El sufrimiento surge porque la gente no tiene en cuenta esto. Cree que en algún lugar existe alguna esencia eterna, y que si pudiera encontrarla y conectarse a ella, estaría completamente satisfecha. A veces, a esta esencia eterna se la denomina Dios, a veces nación, a veces alma, a veces el auténtico yo y a veces amor verdadero; y cuántas más personas están conectadas a ella, más desengañadas y desgraciadas se sienten debido a su incapacidad de encontrarla. Peor todavía: cuanto mayor es dicha conexión, mayor es el odio que esta gente desarrolla hacia cualquier persona, grupo o institución que parezca situarse entre ellos y su objetivo anhelado.
Así pues, según Buda la vida no tiene sentido, y la gente no necesita crear ningún sentido. Solo tiene que darse cuenta de que no existe sentido, y así se librará del sufrimiento causado por nuestras conexiones y nuestra identificación con fenómenos hueros. «¿Qué debo hacer?», pregunta la gente, y Buda aconseja: «No hagas nada. Absolutamente nada». Todo el problema radica en que no paramos de hacer cosas. No necesariamente en el plano físico: podemos estar sentados inmóviles y con los ojos cerrados durante horas, pero en el plano mental estamos muy atareados creando relatos e identidades, luchando en batallas y obteniendo victorias. No hacer nada en realidad significa que la mente tampoco hace nada ni crea nada.
Por desgracia, también esto se transforma muy fácilmente en una epopeya heroica. Incluso mientras permanecemos sentados con los ojos cerrados y percibimos el aire que entra y sale por nuestros orificios nasales, podríamos empezar a construir relatos al respecto. «Mi respiración es un poco forzada, y si respiro más despacio, estaré más sano», o «Si sigo observando mi respiración y no hago nada, accederé a la iluminación y seré la persona más sabia y feliz del mundo». Entonces la epopeya empieza a expandirse, y la gente se embarca en una búsqueda no solo para liberarse de sus propias conexiones, sino también para convencer a otros de que lo hagan. Después de aceptar que la vida no tiene sentido, encuentro el sentido al explicar esto a los demás, debatiendo con los incrédulos, dando discursos a los escépticos, donando dinero para construir monasterios, etcétera. «Ningún relato» puede convertirse demasiado fácilmente en otro relato.
La historia del budismo proporciona mil ejemplos de cómo personas que creen en la transitoriedad y la futilidad de todos los fenómenos, y en la importancia de no tener conexiones, pueden discutir y luchar por gobernar un país, por poseer un edificio o incluso por el significado de una palabra. Pelearse con otras personas porque creemos en la gloria de un Dios eterno es lamentable pero comprensible; pelearse con otras personas porque creemos en la futilidad de todos los fenómenos es realmente extraño, pero muy humano.
En el siglo XVIII, las dinastías reales de Birmania y del vecino Siam se enorgullecían de su devoción a Buda, y ganaron legitimidad al proteger la fe budista. Los reyes dotaban monasterios, erigían pagodas y escuchaban semanalmente a monjes sabios que predicaban elocuentes sermones sobre los cinco compromisos morales básicos de todo ser humano: abstenerse de matar, robar, maltratar sexualmente, engañar y embriagarse. No obstante, los dos reinos no paraban de luchar entre sí. El 7 de abril de 1767, tras un prolongado asedio, el ejército del rey birmano Hsinbyushin atacó la capital de Siam. Las tropas victoriosas mataron, saquearon, violaron e incluso se embriagaron por doquier. Después incendiaron gran parte de la ciudad, con sus palacios, monasterios y pagodas, y se llevaron a casa a miles de esclavos y carretas rebosantes de oro y joyas.
Y no es que el rey Hsinbyushin se tomara su budismo a la ligera. Siete años después de su gran victoria, efectuó una procesión real a lo largo del gran río Irawadi, rindiendo culto en las pagodas importantes del camino y rogando a Buda para que bendijera a sus ejércitos con más victorias. Cuando Hsinbyushin llegó a Rangún, reconstruyó y amplió el edificio más sagrado de toda Birmania, la pagoda de Shwedagon. Después lo recubrió con el oro equivalente al peso del edificio y erigió un chapitel también de oro sobre la pagoda que engastó con piedras preciosas (quizá las del saqueo en Siam). También aprovechó la ocasión para ejecutar al rey cautivo de Pegu, a su hermano y a su hijo.[23]
En el Japón de la década de 1930, la gente incluso encontró maneras imaginativas de combinar las doctrinas budistas con el nacionalismo, el militarismo y el fascismo. Pensadores budistas radicales, como Nissho Inoue, Ikki Kita y Tanaka Chigaku, adujeron que para disolver las conexiones egoístas propias, la gente debía entregarse por completo al emperador, eliminar todo pensamiento personal y observar una lealtad completa a la nación. Estas ideas inspiraron varias organizaciones ultranacionalistas, entre ellas un grupo militar fanático que pretendía derrocar el sistema político conservador de Japón mediante una campaña de asesinatos. Mataron al antiguo ministro de Finanzas, al director general de la compañía Mitsui y al final al primer ministro Inukai Tsuyoshi. De este modo aceleraron la transformación de Japón en una dictadura militar. Cuando más tarde los militares se embarcaron en la guerra, los sacerdotes budistas y los maestros de meditación zen predicaron la obediencia abnegada a la autoridad del Estado y recomendaron el sacrifico personal para el esfuerzo de la guerra. En cambio, las enseñanzas budistas sobre la compasión y la no violencia se olvidaron de alguna forma, y no ejercieron ninguna influencia perceptible en el comportamiento de las tropas japonesas en Nanjing, Manila o Seúl.[24]
Hoy en día, el historial de derechos humanos de la budista Myanmar figura entre los peores del mundo, y un monje budista, Ashin Wirathu, encabeza el movimiento antimusulmán en el país. Afirma que solo quiere proteger Myanmar y el budismo contra las conspiraciones musulmanas de la yihad, pero sus sermones y artículos son tan incendiarios que en febrero de 2018 Facebook eliminó su página, aludiendo a la prohibición en Facebook de los discursos de odio. En 2017, durante una entrevista para _The_ _Guardian_ , el monje predicó la compasión hacia un mosquito que pasaba, pero cuando se le presentaron alegaciones de que mujeres musulmanas habían sido violadas por militares de Myanmar, se rio y dijo: «Imposible. Su cuerpo es demasiado repugnante».[25]
Hay muy pocas probabilidades de que se alcance la paz mundial y la armonía global cuando 8.000 millones de humanos se pongan a meditar de manera regular. ¡Es tan difícil observar la verdad sobre nosotros mismos! Incluso si de alguna manera conseguimos que la mayoría de los humanos lo intenten, muchos de nosotros distorsionaremos enseguida la verdad que descubramos para convertirla en algún relato con héroes, villanos y enemigos, y encontraremos excusas realmente buenas para ir a la guerra.
##### LA PRUEBA DE LA REALIDAD
Aunque todos estos grandes relatos son ficciones generadas por nuestra propia mente, no hay motivos para desesperar. La realidad sigue estando ahí. No podemos interpretar un papel en ningún drama fantástico, pero ¿por qué querríamos hacerlo, para empezar? La gran pregunta a la que se enfrentan los seres humanos no es: «¿Cuál es el sentido de la vida?», sino: «¿Cómo podemos librarnos del sufrimiento?». Cuando abandonemos todos los relatos ficticios, estaremos en condiciones de observar la realidad con mucha más claridad que antes, y si sabemos realmente la verdad sobre nosotros y sobre el mundo, nada podrá hacernos desgraciados. Pero, desde luego, esto es mucho más fácil de decir que de hacer.
Los humanos hemos conquistado el mundo gracias a nuestra capacidad de crear relatos ficticios y de creérnoslos. Por tanto, somos bastante torpes a la hora de conocer la diferencia entre la ficción y la realidad. Pasar por alto esta diferencia ha sido cuestión de supervivencia. Si, no obstante, queremos conocer la diferencia entre una y otra, hay que empezar desde el sufrimiento. Porque la cosa más real en el mundo es el sufrimiento.
Cuando nos enfrentemos a algún gran relato y deseemos saber si es real o imaginario, una de las preguntas clave que habrá que plantear es si el héroe central de la narración puede sufrir. Por ejemplo, si alguien nos cuenta el relato de la nación polaca, dediquemos un momento a reflexionar si Polonia puede sufrir. Es bien sabido que Adam Mickiewicz, el gran poeta romántico y padre del moderno nacionalismo polaco, denominó a Polonia «el Cristo de las naciones». Al escribir en 1832, décadas después de que Polonia fuera repartida entre Rusia, Prusia y Austria, y poco después de que la rebelión polaca de 1830 fuera brutalmente aplastada por los rusos, Mickiewicz explicó que el horrendo sufrimiento de Polonia fue un sacrificio en nombre de toda la humanidad, comparable al sacrificio de Cristo, y que igual que Cristo, Polonia se alzaría de entre los muertos.
En un pasaje famoso, Mickiewicz escribió:
Polonia dijo al pueblo de Europa]: «Quienquiera que venga a mí será libre e igual, porque yo soy la LIBERTAD». Pero los reyes, cuando lo oyeron, amedrentándose sus corazones, crucificaron a la nación polaca y la tendieron en su tumba, gritando: «Hemos matado y enterrado a la Libertad». Pero gritaron neciamente. [...] Porque la nación polaca no murió. [...] Al tercer día, el alma retornará al cuerpo y la nación se levantará y librará de la esclavitud a todos los pueblos de Europa.[[26]
¿Puede sufrir en verdad una nación? ¿Tiene una nación ojos, manos, sentidos, afectos y pasiones? Si se la pincha, ¿sangrará? Claro que no. Si es vencida en la guerra, pierde una provincia o incluso renuncia a su independencia, pero no puede experimentar dolor, tristeza ni ningún otro tipo de desgracia porque no tiene cuerpo, ni mente, ni ningún tipo de sentimiento. Lo cierto es que se trata solamente de una metáfora. Solamente en la imaginación de determinados humanos es Polonia una entidad real capaz de sufrir. Polonia resiste porque esos humanos le prestan su cuerpo, no solo sirviendo como soldados en el ejército polaco, sino por encarnar en su carne las alegrías y penas de la nación. Cuando en mayo de 1831 llegaron a Varsovia las noticias de la derrota polaca en la batalla de Ostrołęka, los estómagos humanos se revolvieron angustiados, los pechos humanos jadearon apenados, los ojos humanos se llenaron de lágrimas.
Nada de esto justifica la invasión rusa, por descontado, ni socava el derecho de los polacos a establecer un país independiente y a decidir sus propias leyes y costumbres. Pero sí significa que, en último término, la realidad no puede ser el relato de la nación polaca, porque la existencia misma de Polonia depende de imágenes de las mentes humanas.
En comparación, considérese el destino de una mujer de Varsovia a la que las tropas invasoras rusas robaron y violaron. A diferencia del sufrimiento metafórico de la nación polaca, el sufrimiento de aquella mujer fue muy real. Podría muy bien haber sido causado por las creencias humanas depositadas en varias ficciones, como el nacionalismo ruso, el cristianismo ortodoxo y el heroísmo machista, todos los cuales inspiraban a muchos de los estadistas y soldados rusos. Sin embargo, el sufrimiento resultante seguía siendo cien por cien real.
Cuando los políticos empiezan a hablar en términos místicos, ¡cuidado! Podrían intentar disfrazar y justificar el sufrimiento real envolviéndolo en palabras altisonantes e incomprensibles. Sea el lector especialmente prudente a propósito de las cuatro palabras siguientes: sacrificio, eternidad, pureza, redención. Si oye alguno de estos términos, haga sonar la alarma. Y si resulta que vive en un país cuyo dirigente dice de forma rutinaria cosas como «Su sacrificio redimirá la pureza de nuestra nación eterna», sepa que tiene un problema grave. Para conservar la cordura, intente siempre traducir esta monserga en términos reales: un soldado que grita agonizante, una mujer que es apaleada y vejada, un niño que tiembla de miedo.
De modo que si el lector quiere saber la verdad acerca del universo, del sentido de la vida y de su propia identidad, lo mejor para empezar es observar el sufrimiento y analizar lo que es.
La respuesta no es un relato.
### 21
Meditación
#### Simplemente, observemos
Después de haber criticado tantos relatos, religiones e ideologías, no deja de ser justo que también yo me sitúe en la línea de fuego, y explique cómo alguien tan escéptico es capaz todavía de despertar alegre por las mañanas. Dudo en hacerlo, en parte por temor a la autocomplacencia y en parte porque no quiero dar la impresión equivocada de que lo que funciona para mí funciona para todo el mundo. Soy bien consciente de que los caprichos de mis genes, neuronas, historia personal y _dharma_ no los comparten todos. Pero quizá sea bueno que los lectores sepan qué matices colorean las gafas a través de las cuales veo el mundo y distorsionan mi visión y mi escritura.
De adolescente era una persona inquieta y llena de problemas. El mundo no tenía sentido para mí y no hallaba respuestas a las grandes preguntas que me formulaba acerca de la vida. En particular, no comprendía por qué había tanto sufrimiento en el mundo y en mi propia existencia, y qué podía hacerse al respecto. Todo lo que obtuve de la gente que me rodeaba y de los libros que leía eran ficciones complicadas: mitos religiosos sobre dioses y cielos, mitos nacionalistas sobre la patria y de su misión histórica, mitos románticos sobre el amor y la aventura, o mitos capitalistas sobre el crecimiento económico, y sobre cómo comprar y consumir cosas me haría feliz. Yo tenía juicio suficiente para darme cuenta de que probablemente todos estos mitos eran ficciones, pero no tenía idea de cómo encontrar la verdad.
Cuando empecé a estudiar en la universidad, pensé que sería el lugar ideal para dar con las respuestas. Pero me llevé un desengaño. El mundo académico me proporcionó herramientas potentes para deconstruir los mitos que los humanos han forjado, pero no respuestas satisfactorias a las grandes preguntas de la vida. Por el contrario, me animaba a centrarme en preguntas cada vez más reducidas. Acabé escribiendo una tesis doctoral en la Universidad de Oxford sobre textos autobiográficos de soldados medievales. Como pasatiempo complementario leí muchísimos libros de filosofía y mantuve numerosos debates filosóficos, pero, aunque esto me proporcionaba un entretenimiento intelectual infinito, apenas aportaba un conocimiento real. Resultaba muy frustrante.
Finalmente, mi buen amigo Ron me sugirió que, al menos por unos días, dejara de lado todos los libros y discusiones intelectuales y probara con un curso de meditación Vipassana. ( _Vipassana_ significa «introspección» en el lenguaje pali de la antigua India.) Pensé que se trataba de alguna monserga new age, y puesto que no tenía ningún interés en escuchar otra mitología más, rehusé ir. Pero después de un año de paciente insistencia, en abril de 2000 mi amigo me llevó a un retiro Vipassana de diez días.[1]
Por entonces yo sabía muy poco de la meditación, y suponía que debía implicar todo tipo de complicadas teorías místicas. De modo que me sorprendió lo práctica que resultó ser la enseñanza. El profesor del curso, S. N. Goenka, instruía a los alumnos a sentarse con las piernas cruzadas y los ojos cerrados, y a centrar toda su atención en el aire que entraba y salía por sus orificios nasales al respirar. «No hagáis nada —repetía una y otra vez—, no intentéis controlar la respiración ni respirar de una manera determinada. Simplemente observad la realidad del momento presente, sea la que sea. Cuando el aire entra solo sois conscientes de que ahora el aire está entrando. Y cuando perdéis vuestra concentración y vuestra mente empieza a vagar por recuerdos y fantasías, solo sois conscientes de que ahora vuestra mente se ha alejado de la respiración.» Fue lo más importante que nadie me había dicho nunca.
Cuando las personas formulan las grandes preguntas de la vida, por lo general no tienen el menor interés en saber cuándo entra el aire por sus orificios nasales y cuándo sale. Lo que desean es saber cosas tales como qué ocurre cuando nos morimos. Pero el enigma real de la vida no es qué ocurre cuando nos morimos, sino qué ocurre antes. Si queremos comprender la muerte, necesitamos comprender la vida.
La gente pregunta: «Cuando muera, ¿desapareceré simplemente por completo? ¿Iré al cielo? ¿Renaceré en un nuevo cuerpo?». Estas preguntas se basan en la suposición de que existe un «yo» que dura desde el nacimiento hasta la muerte, y la pregunta es: «¿Qué le ocurrirá a este yo al morir?». Pero ¿qué perdura desde el nacimiento hasta la muerte? El cuerpo cambia a cada momento, el cerebro cambia a cada momento, la mente cambia a cada momento. Cuanto más detenidamente nos observamos, más evidente resulta que nada perdura, ni siquiera de un instante al siguiente. Así pues, ¿qué mantiene unida toda una vida? Si no conocemos la respuesta a esta pregunta, no comprendemos la vida, y ciertamente no tenemos oportunidad de comprender la muerte. Si alguna vez descubrimos lo que mantiene unida la vida, la respuesta a la gran pregunta sobre la muerte se hará también evidente.
La gente dice: «El alma dura desde el nacimiento a la muerte y, por tanto, mantiene unida la vida»; pero eso es solo un cuento. ¿Ha observado el lector alguna vez un alma? Eso puede estudiarse en cualquier momento, no solo en el de la muerte. Si podemos entender qué nos ocurre cuando termina un momento y otro momento empieza, también entenderemos qué nos ocurrirá en el instante de la muerte. Si somos capaces de observarnos de verdad durante el tiempo que dura una única respiración, lo entenderemos todo.
Lo primero que aprendí al observar mi respiración fue que, a pesar de todos los libros que había leído y todas las clases a las que había asistido en la universidad, no sabía casi nada sobre mi mente y tenía muy poco control sobre ella. Aunque me esforzaba mucho, no lograba contemplar la realidad del aire de mi respiración al entrar por mis orificios nasales y al salir de ellos durante más de diez segundos sin que mi mente empezara a vagar. Durante años viví con la impresión de que era el dueño de mi vida y el director general de mi propia marca personal. Pero unas pocas horas de meditación bastaron para mostrarme que apenas tenía ningún control sobre mí mismo. Yo no era el director general, casi ni era el portero. Se me pidió que me situara en el portal de mi cuerpo (los orificios nasales) y simplemente observara lo que entraba o salía. Pero a los pocos instantes perdí la concentración y abandoné el puesto. Fue una experiencia reveladora.
A medida que el curso avanzaba, a los alumnos se nos enseñó a observar no solo nuestra respiración, sino sensaciones a través de todo nuestro cuerpo. No sensaciones especiales de arrobamiento o éxtasis, sino las sensaciones más prosaicas y ordinarias: calor, presión, dolor, etcétera. La técnica del Vipassana se basa en la intuición de que el flujo de la mente se halla estrechamente interconectado con las sensaciones corporales. Entre yo y el mundo siempre hay sensaciones corporales. Nunca reacciono a los acontecimientos del mundo exterior: siempre reacciono a las sensaciones de mi propio cuerpo. Cuando la sensación es desagradable, reacciono con aversión. Cuando la sensación es placentera, con ganas de tener más. Incluso cuando pensamos que reaccionamos a lo que otra persona ha hecho, al último tuit del presidente Trump o a un lejano recuerdo de la infancia, lo cierto es que siempre reaccionamos a nuestras sensaciones corporales inmediatas. Si nos ofendemos porque alguien ha insultado a nuestra nación o a nuestro dios, lo que hace que el insulto resulte insoportable son las sensaciones ardientes en la boca del estómago y la franja de dolor que atenaza nuestro corazón. Nuestra nación no nota nada, pero nuestro cuerpo está realmente dolido.
¿Quiere saber el lector lo que es la ira? Bueno, pues observe simplemente las sensaciones que surgen en su cuerpo y que lo atraviesan cuando está enfadado. Yo tenía veinticuatro años cuando fui a este retiro, y antes había estado enfadado probablemente diez mil veces, pero nunca me había preocupado de observar cómo se siente en realidad la ira. Siempre que había estado enojado, me centraba en el objeto de mi enfado (algo que alguien había hecho o dicho) y no en la realidad sensorial del enfado.
Creo que aprendí más cosas sobre mí mismo y los humanos en general observando mis sensaciones durante aquellos diez días que lo que había aprendido en toda mi vida hasta ese momento. Y para ello no tuve que aceptar ningún cuento, teoría o mitología. Solo tuve que observar la realidad tal como es. Lo más importante de lo que me di cuenta es que el origen profundo de mi sufrimiento se halla en las pautas de mi propia mente. Cuando quiero algo y no ocurre, mi mente reacciona generando sufrimiento. El sufrimiento no es una condición objetiva en el mundo exterior. Es una reacción mental generada por mi propia mente. Aprender esto es el primer paso para dejar de generar más sufrimiento.
A partir de aquel primer curso en 2000, empecé a meditar durante dos horas diarias y todos los años realizo un largo retiro de meditación de un par de meses. No es una huida de la realidad. Es entrar en contacto con la realidad. Al menos durante dos horas diarias observo de verdad la realidad como es, mientras que a lo largo de las otras veintidós horas me abruman los mensajes de correo electrónico y los tuits y los vídeos de cachorros encantadores. Sin la concentración y la claridad que proporciona esta práctica, no podría haber escrito _Sapiens_ ni _Homo Deus_. Al menos para mí, la meditación nunca ha entrado en conflicto con la investigación científica. Al contrario: ha sido otro instrumento valioso en la caja de herramientas científica, sobre todo cuando he intentado entender la mente humana.
##### CAVAR DESDE AMBOS LADOS
A la ciencia le resulta difícil descifrar los misterios de la mente en gran parte porque carecemos de herramientas eficientes. Muchas personas, incluidos muchos científicos, tienden a confundir la mente con el cerebro, pero en realidad son cosas muy diferentes. El cerebro es una red material de neuronas, sinapsis y sustancias bioquímicas. La mente es un flujo de experiencias subjetivas, como dolor, placer, ira y amor. Los biólogos suponen que el cerebro produce de alguna manera la mente, y que reacciones bioquímicas en miles de millones de neuronas generan de algún modo experiencias como dolor y amor. Sin embargo, hasta el momento no tenemos ninguna explicación en absoluto de cómo la mente surge del cerebro. ¿Cómo es que cuando miles de millones de neuronas disparan señales eléctricas en un determinado patrón, yo siento dolor, y cuando las disparan siguiendo una pauta diferente, siento amor? No tenemos ni idea. De ahí que incluso si la mente surge realmente del cerebro, al menos por ahora estudiar la mente es una empresa diferente de estudiar el cerebro.
La investigación del cerebro está avanzando deprisa gracias a la ayuda de microscopios, escáneres cerebrales y potentes ordenadores. Pero no podemos ver la mente en un microscopio o en un escáner cerebral. Estos dispositivos nos permiten detectar cambios en las actividades bioquímicas y eléctricas del cerebro, pero no nos dan ningún acceso a las experiencias subjetivas asociadas a dichas actividades. En 2018, la única mente a la que puedo acceder directamente es la mía. Si quiero saber qué están experimentando otros seres sintientes, solo puedo lograrlo basándome en informes de segunda mano, que como es obvio adolecen de numerosas distorsiones y limitaciones.
Desde luego, podríamos recoger muchos informes de segunda mano procedentes de varias personas y utilizar estadísticas para identificar patrones recurrentes. Tales métodos han permitido a psicólogos y neurocientíficos no solo comprender mucho mejor la mente, sino también mejorar la vida, e incluso salvarla, de millones de personas. Sin embargo, es difícil ir más allá de un determinado punto empleando solo informes de segunda mano. En ciencia, cuando se investiga un fenómeno concreto, es mejor observarlo de manera directa. Los antropólogos, por ejemplo, hacen un uso exhaustivo de las fuentes secundarias, pero si uno quiere comprender en verdad la cultura samoana, más tarde o más temprano tendrá que hacer las maletas y visitar Samoa.
Por supuesto, con visitar no basta. Un blog escrito por un mochilero que viaje por Samoa no se consideraría un estudio antropológico científico, porque la mayoría de los mochileros carecen de los instrumentos y la preparación necesarios. Sus observaciones son demasiado aleatorias y sesgadas. Para convertirnos en antropólogos dignos de confianza, hemos de aprender cómo observar las culturas humanas de manera metódica y objetiva, libre de ideas preconcebidas y prejuicios. Eso es lo que se estudia en los departamentos de Antropología y es lo que permitió a los antropólogos desempeñar un papel tan fundamental a la hora de acercar posiciones entre diferentes culturas.
El estudio científico de la mente rara vez sigue este modelo antropológico. Mientras que los antropólogos suelen informar de sus visitas a islas distantes y países misteriosos, los estudiosos de la conciencia no suelen emprender viajes personales de este tipo a los ámbitos de la mente. Porque la única mente que puedo observar de forma directa es la mía, y por difícil que sea observar la cultura samoana sin sesgos ni prejuicios, más difícil aún es observar con objetividad mi propia mente. Después de más de un siglo de trabajo duro, en la actualidad los antropólogos disponen de poderosos procedimientos para la observación objetiva. En cambio, aunque los estudiosos de la mente desarrollaron muchas herramientas para acopiar y analizar informes de segunda mano, en lo que respecta a observar nuestra propia mente apenas hemos arañado la superficie.
En ausencia de métodos modernos para la observación directa de la mente, podemos intentar utilizar algunas de las herramientas desarrolladas por las culturas premodernas. Varias culturas antiguas prestaron mucha atención al estudio de la mente, y no se basaron en reunir informes de segunda mano, sino en adiestrar a personas para que observaran de manera sistemática su propia mente. Los métodos que desarrollaron están agrupados bajo el término genérico de «meditación». Hoy en día, dicho término suele asociarse a religión y a misticismo, pero en principio la meditación es cualquier método de observación directa de nuestra propia mente. En efecto, muchas religiones han hecho un uso exhaustivo de varias técnicas de meditación, pero eso no significa que la meditación sea necesariamente religiosa. Muchas religiones han hecho también un gran uso de los libros, y eso no significa que servirse de los libros sea una práctica religiosa.
A lo largo de milenios, los humanos han desarrollado cientos de técnicas de meditación que difieren en sus principios y eficacia. Yo solo he tenido experiencia con una técnica, la Vipassana, de modo que es la única de la que puedo hablar con cierta autoridad. Al igual que otras técnicas de meditación, se dice que la Vipassana la descubrió Buda en la India. A lo largo de los siglos se han atribuido a Buda muchas teorías y relatos, a menudo sin contar con ninguna prueba al respecto. Pero para meditar no es necesario creerse ninguno de ellos. El maestro del que yo aprendí Vipassana, Goenka, era un tipo de guía muy práctico. Instruía repetidamente a los alumnos que cuando observaran la mente debían dejar de lado todas las descripciones de segunda mano, dogmas religiosos y conjeturas filosóficas, y centrarse en su propia experiencia y en cualquier realidad que encontraran de verdad. Numerosos alumnos acudían a diario a su habitación para buscar consejo y plantear preguntas. En la puerta había un cartel que rezaba: «Evitad por favor las discusiones teóricas y filosóficas, y centrad vuestras preguntas en asuntos relacionados con vuestra práctica real».
La práctica real significa observar las sensaciones corporales y las reacciones mentales a las sensaciones de manera metódica, continua y objetiva, descubriendo así las pautas básicas de la mente. A veces la gente convierte la meditación en una búsqueda de experiencias especiales de arrobamiento y éxtasis. Pero la verdad es que la conciencia es el mayor misterio del universo, y las sensaciones prosaicas de calor y comezón son tan misteriosas como las de embeleso o unidad cósmica. A los que meditan con Vipassana se les advierte de que no se embarquen en una búsqueda de experiencias especiales, sino que se concentren en comprender la realidad de su mente, sea cual sea dicha realidad.
En años recientes, los estudiosos de la mente y el cerebro han mostrado un interés creciente en dichas técnicas de meditación, pero hasta ahora la mayoría de los investigadores han usado esta herramienta solo de manera indirecta.[2] El científico típico no practica en verdad la meditación. Lo que hace es invitar a meditadores experimentados a su laboratorio, cubre sus cabezas con electrodos, les pide que mediten y observa las actividades cerebrales resultantes. Esto puede enseñarnos muchas cosas interesantes acerca del cerebro, pero si el objetivo es entender la mente, nos estamos perdiendo algunas de las percepciones más importantes. Es como alguien que intentara comprender la estructura de la materia observando una piedra con una lupa. Nos acercamos a dicha persona, le damos un microscopio y le decimos: «Pruebe con esto. Lo verá mucho mejor». Dicha persona toma el microscopio, lo pone bajo la lupa en la que confía y observa con cuidado a través de ella la materia de la que está hecho el microscopio. La meditación es un instrumento para observar directamente la mente. Si en lugar de meditar nosotros hacemos el seguimiento de las actividades eléctricas en el cerebro de algún otro meditador, nos perderemos la mayor parte de su potencial.
No estoy sugiriendo en absoluto que se abandonen los instrumentos y las prácticas actuales de investigación del cerebro. La meditación no los sustituye, pero podría complementarlos. Es algo así como unos ingenieros que excavan un túnel a través de una montaña enorme. ¿Por qué excavar únicamente desde un lado? Es mejor excavar a la vez desde ambos lados. Si mente y cerebro son de verdad una única cosa, los dos túneles acabarán por encontrarse. ¿Y si el cerebro y la mente no son la misma cosa? Entonces todavía es más importante excavar en la mente, y no solo en el cerebro.
Algunas universidades y laboratorios han empezado, en efecto, a usar la meditación como instrumento de investigación en lugar de solo como un mero objeto para los estudios del cerebro. Pero este proceso se halla aún en sus albores, en parte porque requiere una inversión extraordinaria de los investigadores. La meditación seria exige una disciplina tremenda. Si intentamos observar de manera objetiva nuestras sensaciones, lo primero que advertiremos es lo salvaje e impaciente que es la mente. Incluso si nos centramos en observar una sensación distinta, como el aire que entra y sale de nuestros orificios nasales, nuestra mente puede hacerlo por lo general durante solo unos pocos segundos antes de perder la concentración y empezar a vagar entre pensamientos, recuerdos y ensoñaciones.
Cuando un microscopio se desenfoca, solo necesitamos girar una pequeña manecilla. Si la manecilla está rota, podemos llamar a un técnico para que la repare. Pero si la mente se desenfoca, no podemos repararla tan fácilmente. Por lo general hace falta mucho entrenamiento para calmarnos y concentrar la mente, de manera que sea capaz de empezar a observarse a sí misma de forma metódica y objetiva. Quizá en el futuro podremos tomarnos una píldora y conseguir la concentración instantánea. Pero puesto que la meditación pretende explorar la mente en lugar de solo centrarla, este atajo podría resultar contraproducente. La píldora quizá haga que estemos muy alerta y centrados, pero al mismo tiempo podría impedirnos explorar todo el espectro de la mente. Al fin y al cabo, incluso hoy en día podemos concentrar fácilmente la mente al ver una buena película de suspense en la televisión, pero la mente está tan centrada en el filme que no puede observar su propia dinámica.
Sin embargo, aunque no podamos fiarnos de estos artefactos tecnológicos, no hemos de desistir. Los antropólogos, zoólogos y astronautas pueden servirnos de inspiración. Los antropólogos y zoólogos pasaron años en islas remotas, expuestos a una plétora de males y peligros. Los astronautas dedican muchos años a difíciles regímenes de adiestramiento como preparación para sus arriesgadas excursiones al espacio exterior. Si estamos dispuestos a hacer tales esfuerzos para entender culturas extrañas, especies desconocidas y planetas lejanos, valdría la pena trabajar con el mismo empeño a fin de comprender nuestra propia mente. Y es mejor que comprendamos nuestra mente antes de que los algoritmos lo hagan por nosotros.
La observación de uno mismo nunca ha sido fácil, pero con el tiempo podría resultar aún más difícil. A medida que la historia se desplegaba, los humanos fueron generando relatos cada vez más complejos sobre sí mismos que hicieron que cada vez resultara más difícil saber quiénes somos en verdad. Esos relatos tuvieron como objetivo unir a grandes cantidades de personas, acumular poder y preservar la armonía social. Fueron cruciales para alimentar a miles de millones de individuos hambrientos y garantizar que no se degollaran los unos a los otros. Cuando la gente intentaba observarse, lo que solía encontrar eran esos relatos prefabricados. La exploración libre y abierta resultaba demasiado peligrosa: amenazaba con socavar el orden social.
Con la mejora en la tecnología ocurrieron dos cosas. En primer lugar, mientras los cuchillos de sílex evolucionaron gradualmente hacia los misiles nucleares, se volvió más peligroso desestabilizar el orden social. En segundo lugar, mientras las pinturas rupestres evolucionaron gradualmente hacia las emisiones televisivas, se volvió más fácil engañar a la gente. En el futuro cercano, los algoritmos podrían completar este proceso, haciendo imposible que la gente observe la realidad sobre sí misma. Serán los algoritmos los que decidan por nosotros quiénes somos y lo que deberíamos saber sobre nosotros.
Durante unos cuantos años o décadas más, aún tendremos la posibilidad de elegir. Si hacemos el esfuerzo, todavía podemos investigar quiénes somos en realidad. Pero si queremos aprovechar de verdad esta oportunidad, será mejor que lo hagamos ahora.
### Agradecimientos
Quisiera dar las gracias a todos los que me ayudaron a escribir, y también a borrar:
A Michal Shavit, mi editor en Penguin Random House en el Reino Unido, que fue quien me dio la idea para este libro y quien me guio durante el largo proceso de escribirlo; y también a todo el equipo de Penguin Random House, por su duro trabajo y su apoyo.
A David Milner, quien, como de costumbre, hizo un magnífico trabajo al editar el texto original. A veces yo solo tenía que pensar qué diría David para trabajar más a fondo el texto.
A Suzanne Dean, mi directora creativa en Penguin Random House, que es el genio que hay detrás de la cubierta del libro.
A Preena Gadher y sus colegas en Riot Communications, por haber orquestado una campaña brillante de relaciones públicas.
A Cindy Spiegel, de Spiegel & Grau, por sus comentarios y por cuidarse de las cosas al otro lado del Atlántico.
A todos mis otros editores en todos los continentes del mundo (excepto en la Antártida), por su confianza, dedicación y trabajo profesional.
A mi ayudante de investigación, Idan Sherer, por comprobarlo todo, desde los datos de las sinagogas antiguas hasta los de la inteligencia artificial.
A Shmuel Rosner, por su apoyo continuo y sus buenos consejos.
A Yigal Borochovsky y Sarai Aharoni, que leyeron el original y dedicaron mucho tiempo y esfuerzo a corregir mis errores, y me ayudaron a ver las cosas desde otras perspectivas.
A Danny Orbach, Uri Sabach, Yoram Yovell y Ron Merom, por su conocimiento de los kamikazes, la vigilancia, la psicología y los algoritmos.
A mi fiel equipo (Ido Ayal, Maya Orbach, Naama Wartenburg y Eilona Ariel), que ha pasado muchos días pendiente del correo electrónico por mi causa.
A todos mis amigos y a los miembros de mi familia, por su paciencia y amor.
A mi madre, Pnina, y a mi suegra, Hannah, por dedicarme su tiempo y experiencia.
A mi esposo y agente, Itzik, sin el cual nada de esto habría ocurrido. Yo solo sé cómo escribir libros. Él hace todo lo demás.
Y, por último, a todos mis lectores por su interés, tiempo y comentarios. Si un libro se halla en una estantería y nadie lo lee, ¿acaso tiene algún efecto?
Como se indicó en la introducción, este libro se ha escrito en conversación con el público. Muchos de sus capítulos se compusieron en respuesta a preguntas que me dirigieron lectores, periodistas y colegas. Algunas versiones originales de algunas partes se publicaron previamente como ensayos y artículos, lo que me dio la oportunidad de recibir comentarios y perfeccionar mis argumentos. Dichas versiones incluyen los siguientes ensayos y artículos:
«If We Know Meat Is Murder, Why Is It So Hard For Us to Change and Become Moral?», _Haaretz_ de junio de 2012.
«The Theatre of Terror», _The Guardian_ de enero de 2015.
«Judaism Is Not a Major Player in the History of Humankind», _Haaretz_ de julio de 2016.
«Yuval Noah Harari on Big Data, Google and the End of Free Will», FT.com de agosto de 2016. __
«Isis is as much an offshoot of our global civilisation as Google», _The Guardian_ , 9 de septiembre de 2016.
«Salvation by Algorithm: God, Technology and New 21st Century Religion», _New Statesman_ , __ 9 de septiembre de 2016.
«Does Trump's Rise Mean Liberalism's End?», _The New Yorker_ , 7 de octubre de 2016.
«Yuval Noah Harari Challenges the Future According to Facebook», _Financial Times_ de marzo de 2017.
«Humankind: The Post-Truth Species», Bloomberg.com de abril de 2017.
«People Have Limited Knowledge. What's the Remedy? Nobody Knows», _The New York Times_ de abril de 2017.
«The Meaning of Life in a World Without Work», _The Guardian_ , 8 de mayo de 2017.
«In Big Data vs. Bach, Computers Might Win», _Bloomberg View_ de mayo de 2017.
«Are We About to Witness the Most Unequal Societies in History?», _The Guardian_ de mayo de 2017.
«Universal Basic Income is Neither Universal Nor Basic», _Bloomberg View_ , 4 de junio de 2017.
«Why It's No Longer Possible For Any Country to Win a War», Time.com de junio de 2017.
«The Age of Disorder: Why Technology is the Greatest Threat to Humankind», _New Statesman_ de julio de 2017.
«Reboot for the AI Revolution», _Nature News_ de octubre de 2017.
### Índice alfabético
aborígenes tasmanos
Abraham
acoso sexual de las mujeres
actualización, capacidad de
Administración Nacional de Seguridad del Tráfico en las Carreteras de Estados Unidos
ADN, algoritmos y
Afganistán
guerra en
nacionalismo en
talibanes en
terrorismo en
agricultura
cristiana
mecanización de la
trabajo manual en la
aislacionismo nacionalista
ajedrez
«centauros», equipos de IA-humanos
creatividad no humana en
programa AlphaZero de Google
programa Deep Blue
Akenatón, faraón
alemanes modernos, origen de los
Alemania
después de la guerra
inmigración en
llegada de refugiados sirios
musulmanes en
nacionalismo en
reunificación de
sistemas políticos de
Alemania nazi
Alepo, bombardeo de
Ali, Husáin ibn
algoritmo
bioquímicos
Bolsa de valores y
de aprendizaje
de búsqueda de Google
de macrodatos
de vigilancia potentes
en bancos y empresas
en la toma de decisiones
filosóficos
observados por los
AlphaZero de Google, programa de ajedrez
Amaterasu, diosa solar
Amazon
amoníaco, sintetizador del
Amós, profeta
Amritsar, masacre de (1919)
Andéol, Emilie
Andrómeda, galaxia de
antiinmigracionistas
antisemitismo
Apple
aprendizaje automático
Arabia Saudí
exportación de petróleo y gas
inmigración a
lesbianas en
wahabismo en
armas nucleares
armenio, genocidio
arte
definición de
emociones humanas y
Ashoka, emperador de la India
Ashura, drama de la
Asociación Nacional del Rifle
Assad, Bashar al-
atención sanitaria
crisis mundial de la
gratuita
las IA médicas
religiones tradicionales y
Augusto, emperador
Auschwitz, campo de concentración
Austen, Jane
Australia, aborígenes de
autocráticos, regímenes
automatización
desempleo masivo y
ayuda básica universal
aztecas, sacrificios de los
Baal, dios
babilónico, Imperio
Bach, Johann Sebastian: la _Pasión según San Mateo_
Baghdadi, Abu Bakr al-
Baidu
Balcanes, guerra de los
banderas nacionales
Bangladesh
Barrio Sésamo
Beethoven, Ludwig van
Bellaigue, Christopher de
Benarés, como lugar sagrado
Berko, Anat
Beyoncé
Bhagavad Gita, epopeya hindú
Bhardwaj, Maharishi
Biblia
Amós
Deuteronomio
Éxodo
Gálatas
Génesis
Levítico
obras inspiradas en el Antiguo Testamento
big bang, explicación del
Bin Laden, Osama
bioingeniería
unida al auge de la IA
bioquímica orgánica
biotecnología
combinación con la IA
fusión con la infotecnología
revolución en
Birmania, dinastía real de
Bismarck, Otto von
bitcóin, criptomoneda
Blair, Tony
Bodh Gaya, como lugar sagrado
bomba atómica
Bosnia, limpieza étnica de
Bouazizi, Mohamed, autoinmolación de
Brasil
aumento de la propiedad en
desigualdades en
liberalismo en
líderes religiosos en
Brihadaranyaka Upanishad
Buda
budismo
budistas
Buen Samaritano, parábola del
Bush, George W.
calentamiento global
Chad, El, en
Chaikovski, Piotr Ilich
California, elecciones de 2016 y
cambio climático
Cambridge Analytica, escándalo de
Cameron, David
capacidades físicas
capitalismo de libre mercado
carne, industria de la
«carne limpia», desarrollo de la
Caro, Joseph, rabino
casquetes polares, desaparición de los
castas biológicas, distinción en
Cataluña, intento de independencia en
catolicismo
cazadores-recolectores
de la Edad de Piedra
del Kalahari
!kung
César, Julio
Charlie Hebdo, masacre de
Chaucer, Geoffrey
Chigaku, Tanaka
chiíes, musulmanes
China
aumento de la propiedad en
combustibles fósiles en
como motor económico
desigualdades en
evitación de conflictos armados
imperial
instrumentos de vigilancia
liberalismo en
progreso económico
terrorismo en
«choque de civilizaciones», tesis del
Churchill, Winston
ciberguerra
ciencia ficción
novelas y películas de
científicos, divulgación de los
Cisjordania
palestinos en
clase obrera
Claudio, emperador
Clinton, Bill
liberalismo y
Clinton, Hillary
correos electrónicos de
noticias falsas sobre
Coca-Cola
cognitivas, capacidades
colapso ecológico
combustibles fósiles, sustitución de
Comité Olímpico Internacional (COI)
compasión, compromiso secular con la
comunidades, creación de
comunismo
automatización y
comunistas
igualdad y
renta básica universal y
conciencia humana
concepto de
investigación y desarrollo de la
conectividad, capacidad de la IA
confucianismo
Confucio
Congo
nacionalismo en
Consejo sobre Religión y el Homosexual
Constancio II, emperador
Constantino el Grande, emperador
Constitución Europea
Preámbulo de la
Corán
Corea del Norte
programa nuclear de
religión de Estado juche
Corea del Sur, combustibles fósiles en
crecimiento económico
cremallera ordinaria, experimento del funcionamiento de la
Crimea, anexión rusa de
crisis financiera de 2008
cristianismo
como responsable de grandes crímenes
_véanse también_ cruzadas; Inquisición española
cristianismo ortodoxo
cristianos
Cristo, realidad para sus devotos
cruzadas, matanzas de las
cuasicristales, descubrimiento de los
Cuba, crisis de los misiles
cultura musulmana
culturas nativas, opresión de
Darwin, Charles
_El origen de las especies_
datos, propiedad de los
Davos, Fórum Económico Mundial de
Dawkins, Richard
decisiones, toma de
Declaración de los Derechos Humanos
Decretos Teodosianos
Deep Blue, programa de ajedrez
_Del revés (Inside Out)_ , película de animación
DeMille, Cecil B.: _Los diez mandamientos_
democracia liberal
deontologistas
derechos humanos
libertad personal y
política de
derechos laborales, automatización y descenso de los
desempleo masivo, perspectiva de
desiertos, expansión de los
desigualdad
orígenes de la
propiedad y
_dharma_
_Di Tzeitung_ , diario ultraortodoxo
dictaduras digitales
Diez Mandamientos
Dinamarca
Dios
dióxido de carbono, en la atmósfera
disrupción tecnológica
crecimiento económico y
duelo, cinco fases del
música y
ecología global
ecológico, reto
economía conductual
economía musulmana
educación
Egipto
faraónico
invasión británica de
nacionalistas de
Einstein, Albert
elecciones humanas, papel de las neuronas en las
emociones humanas
arte y
y las teorías filosóficas
empleos humanos, creación de nuevos
energía renovable, fuentes de
Engels, Friedrich: _Manifiesto comunista_
Erdogan, Recep Tayyip
Escocia, referéndum de 2014 en
escuelas modernas, aparición de las
español, Imperio, y la educación
especies, fusión imposible de
espíritu humano
Estado Islámico
ataques suicidas en París
auge del
califato universal y
médicos y enfermeras musulmanas y
estado-nación: empoderamiento del
Estados Unidos
aislacionismo de
antisemitismo en
«anuncio de la margarita» en las presidenciales de 1964
atentados del 11 de septiembre de 2001
calentamiento global y
carrera de armas nucleares
economía de
élite en
fuerzas armadas de
guerra con México y conquistas territoriales
instrumentos de vigilancia
movimientos religiosos en
niveles de paro
oligarquía en
población y PIB
estreptomicina, antibiótico
estrés, reducción del
estupidez humana
ética
impía
problemas teóricos y prácticos en
Europa
conflictos religiosos en 1618 en
enfermos en
_véase también_ Unión Europea
Europa Oriental, expansión de la OTAN por
evolución, teoría de la
existencia, misterio de la
extrema derecha, movimientos de
Facebook
inteligencia artificial (IA) y
revolución de
sede central en Menlo Park
fanatismo, nacimiento del
fascismo
Segunda Guerra Mundial y
fe, industria de la
Fernbach, Philip
fertilización artificial
ficción
distinción entre realidad y
equilibrio entre verdad y
Filipinas, conflictos religiosos en
Finlandia, ayuda básica nacional en
física judía
Flandes, patriotismo en
Foucault, Michel
Francia
_ancien régime_ en
ataques suicidas de Estado Islámico
élite en
extrema derecha en
inmigración en
laicidad de
medieval
violencia sexual en
Francisco, papa
Francisco Fernando, archiduque, asesinato de
Frente Nacional de Francia
Freud, Sigmund
influencia sobre la humanidad
sobre las tradiciones religiosas
Friedman, Milton
fundamentalistas islámicos
Galileo Galilei
Gandhi, Mahatma
gases de efecto invernadero
Gaza
Gengis Kan
Georgia, incursión rusa en
globalización
invertir el proceso de
problemas de la
respuestas globales a los problemas de la
Goebbels, Joseph
Goenka, S. N.
Golfo, primera guerra del
Google
Glass
Maps
nube de
Translate
góspel, coros cristianos de
Gove, Michael
Gran Bretaña, _véase_ Reino Unido
Grecia antigua
guerra contra el terror
Guerra Fría
Guerra Mundial, Primera
Guerra Mundial, Segunda
Guerra Mundial, Tercera, peligro de una
guerra nuclear
total
Guevara, Ernesto Che
Guillermo II, emperador
Haber, Fritz
Hamás, régimen de
Hambruna ucraniana, Gran
_HaMevaser_ , diario ultraortodoxo
Hammurabi, rey de Babilonia
_Hamodia_ , diario ultraortodoxo
Harari, Yuval Noah
_Homo Deus_
_Sapiens. De animales a dioses_
Harris, Tristan
Hastings, batalla de (1066)
Hayek, Friedrich
Hillel el Viejo, rabino
himnos nacionales
hinduismo
Hirohito, emperador
Hiroshima, bomba atómica de
Hitler, Adolf
_Mein Kampf_
Holanda, ocupación nazi de
Holocausto
Holoceno, período
Homero
_Homo sapiens_
como asesino ecológico en serie
inútiles, subclase de
que cuenta y piensa en relatos
selección natural y
Hsinbyushin, rey birmano
Hugh de Lincoln
humano-IA, cooperación
humildad, valor de la
Husein, Sadam
Huxley, Aldous: _Un mundo feliz_
IA, _véase_ inteligencia artificial
identidad, cartera de la
identidades nacionales
Iglesia católica
Iglesia Unida de Cristo
ignorancia
individual
igualdad
como un ideal
compromiso secular con la
económica
«ilusión del conocimiento»
imperialismo
impresoras 3-D
impuestos, creación de nuevos
India
independencia de la
demandas de autodeterminación
bandera nacional
Código de la Bandera de la
enfermos en
movimientos religiosos en
desigualdades en
liberalismo en
individualidad
beneficios de la
individuo racional
Indonesia
como colonia holandesa
industria, trabajo manual en la
infotecnología
fusión con la biotecnología
revolución en
Inglaterra, expulsión de la población judía de
inmigración, cláusulas del pacto de la
inmigrantes
intolerancia de los
llegada a Europa de
_véase también_ antiinmigracionistas
Inoue, Nissho
Inquisición española
inteligencia artificial (IA)
análisis de sentimientos humanos
auge de la
bioingeniería unida a la
capacidades no humanas de la
combinación con la biotecnología
competencia con redes neurales humanas
creación de empleos humanos y la
diferencia con un trabajador humano
en la toma de decisiones
en programas de ajedrez
Facebook y la
futuro de la
médica
películas alejadas de la realidad científica sobre
posible desarrollo de sentimientos propios de la
revolución de la
sistemas centralizados de información y
inteligencia, concepto de
internet, revolución de
intuición humana
invernadero, efecto
ira, sentimiento de la
Irak
Estado Islámico en
guerra con Irán
guerra de
islamismo global y
terrorismo en
Irán
ayatolás en
economía de
Estado Islámico en
exportación de petróleo y gas
Guardianes de la Revolución
guerra con Irak
islamismo chií en
nacionalistas de
persecución de gais y lesbianas
programa nuclear de
Irlanda del Norte
Isabel II, reina del Reino Unido
islam, interpretaciones del
islamismo
chií
global
Israel
creación del sentimiento de Estado
día de los Caídos en
establecimiento del Estado de
Fuerzas de Defensa de
industria de ciberseguridad
inmigración en
israelíes seglares
judíos ultraortodoxos en
protección de la comunidad LGTB
rabinos en
reino de
Israel, reino de
Italia fascista
Jamenei, ayatolá
Japón
ataque a Pearl Harbor
combustibles fósiles en
Imperial
kamikazes
milagro económico
poder del sintoísmo de Estado en
Jean de Joinville
_Jeopardy!_ , concurso televisivo
Jerusalén
antiguo Templo de Yahvé en
como lugar sagrado
establecimiento de
Johnson, Lyndon B., «anuncio de la margarita» en la campaña de 1964
Jomeini, ayatolá Ruhollah
Joyhnson, Boris
juche, religión norcoreana
Judá, reino de
judaísmo
día sagrado del Sabbat
judíos
leyes del recato
premios Nobel en ciencia
ultraortodoxos
Juegos Olímpicos
cancelaciones y boicots de
de 2016 en Río de Janeiro
Medievales en Rio en 1016
justicia
Kahlo, Frida
kamikazes
Kanad, Acharya
Kant, Immanuel
Kaspárov, Garri
Katyn, masacre de polacos en
KGB soviético
Kim Il-sung
Kim Jong-un, régimen norcoreano de
Kinsey, escala de
Kiribati, república de
Kita, Ikki
laicismo
definición
ideal laico
Lao-Tse
_Leave_ , campaña en el Reino Unido
Leonardo da Vinci: _La última cena_
liberación nacional, movimientos de
liberal, término
liberalismo
concepto de
creencia en los sentimientos
descomposición del
fénix liberal
igualdad y
igualdad económica y
negación de los dramas cósmicos
liberalización
libertad
compromiso secular con la
humana, como valor más importante
protección de la
libertad de expresión
Libia
libre albedrío
_libro de la etiqueta y los ritos, El_
Libro de los Muertos egipcio
_libro de los ritos, El_
Libro de Mormón
limpieza étnica en los Balcanes
Lincoln, Abraham
Livorno, ayuda básica nacional en
Lombardía, patriotismo en
Lucas, George
Luis IX, rey de Francia
Luis XIV, rey de Francia
Luis XVI, rey de Francia
Mahabharata
Mahasatipatthana Sutta, texto budista
Mahavira
Mahoma, profeta
Maimónides
Maji Maji, rebelión
Mansura, batalla de
máquinas, competencia con los humanos
Markizova, Gelya, la Feliz Niña Soviética
mártires
Marx, Karl
_Manifiesto comunista_
marxismo-liberalismo
masas, rebelión de las
Mashhad, en Irán
Mateo de París
_Matrix_ , película
May, Theresa
McIlvenna, Ted
Meca, La
como lugar sagrado
efectuar el _haj_ a
médicas, prácticas
meditación
como instrumento de investigación
Meir, Golda
mercado laboral, nuevo equilibrio del
Merkel, Angela
Mesha, rey moabita
Mesopotamia
#MeToo, movimiento
Mickiewicz, Adam
Miguel Ángel: _David_
Mill, John Stuart
Mishná
Mishra, Pankaj
mitos, proceso de creación de
Moab, reino de
Modi, Narendra
Moisés
monoteísmo
Monty Python
_La vida de Brian_
moral de intenciones
mortalidad infantil
Mubarak, Hosni
mujeres, judíos ultraortodoxos y las
mundo global
música
análisis de macrodatos y
cinco fases del duelo y
Mussolini, Benito
My Lai, masacre en
Myanmar, derechos humanos en
nacionalismo
orígenes del
respuesta a la amenaza ecológica
reto ecológico
reto nuclear
reto tecnológico
nacionalistas
movimientos
Naciones Unidas, Organización de
nanotecnología
Napoleón Bonaparte
_Nature_ , revista
nazis
teorías darwinistas y
_véase también_ Alemania nazi
nazismo, herencia del
Nepal
Netanyahu, Benjamin
Netflix
neurociencia
_New York Times_
Newton, Isaac
Nigeria
conflictos religiosos en
terrorismo en
noticias falsas
Nueva Guinea, tribus de
Nueva Zelanda, élite en
Obama, Barack
discurso en Naciones Unidas
Obamacare
océanos, subida del nivel de los
oligarquía gobernante
Ontario, ayuda básica nacional en
ordenadores, revolución de la IA y
pérdida de la individualidad y
Organización del Tratado del Atlántico Norte (OTAN)
Organización Mundial de la Salud (OMS)
órganos humanos, mercado de
Oriente Próximo
conflictos en
enfermos en el
Orwell, George
1984
otomano, Imperio
Pablo, apóstol san
paganismo, persecución del
países falsos
Pakistán
Palestina
cuestión de
palestinos, vigilancia israelí sobre los
Parks, Rosa
Partido Comunista chino
Partido Comunista soviético
Partido Conservador británico
Partido Laborista británico
Passchendaele, batalla de
Pasteur, Louis
patrones recurrentes, reconocimiento de
Pedro el Grande, zar
Pegu, rey de
peste negra, epidemia de
Phelps, Michael
Picasso, Pablo
piratas informáticos
Pixar Studios
Platón
poder, agujero negro del
Pokémon Go
politeísmo
Polonia
catolicismo en
inmigrantes en
invasión nazi de
sufrimiento de
posverdad
especie de la
_Pravda_ , diario soviético
Primavera Árabe, en Túnez
propiedad, como prerrequisito de la desigualdad
Putin, Vladímir
Qaeda, Al
Qatar, subclase de extranjeros en
racionalidad evolutiva
racionalidad individual
racismo tradicional
Radhakrishnan, Sarvepalli
Rawls, John
RBU, _véase_ renta básica universal
Reagan, Ronald
realidad, prueba de la
reconocimiento de patrones
refugiados, llegada a Europa de
Reino Unido
Brexit en
extrema derecha en
inmigrantes musulmanes del
relatos
comunista
fascista
liberal
religiones tradicionales, papel de las
renta básica universal (RBU)
Reserva Federal
resiliencia
responsabilidad social
responsabilidad, compromiso secular con la
revolución agrícola, propiedad y
Revolución bolchevique
revolución científica, judaísmo y la
Revolución francesa
revolución industrial
_ritos de Zhou, Los_
Robespierre, Maximilien de
robótica
robots
asesinos
romano, Imperio
Rusia
calentamiento global y
carrera de armas nucleares
como rival del orden liberal global
conquista de Crimea
cristianismo ortodoxo
desigualdades económicas en
exportación de petróleo y gas
instrumentos de vigilancia
oligarquía en
población y PIB de
poder militar de
sacrificios personales, véase mártires
Salvador, El
Sanders, Berni
Schumacher, Michael
_Science_ , revista
secularismo
actitudes con la sexualidad
definición
seculares, personas
valores del
selección natural
sensores biométricos
señores de la droga mexicanos
Serbia, nacionalismo de
serendipia, nivel de
Shakespeare, William
_Hamlet_
Shang, dinastía
_show de Truman, El_ , película
Shulhan Arukh, código de la ley judía
Siam, dinastía real de
sij, religión
Silicon Valley
sinagoga, prohibición de mujeres en la
sintoísmo
sionismo, movimiento
auge del
Siria
Estado Islámico en
guerra civil en
islamismo global y
terrorismo en
Sloman, Steven
socialdemócratas, estados
Sócrates
Sófocles
Somalia, nacionalismo en
Somme, batalla del
Spears, Britney
Spielberg, Steven
Spinoza, Baruch
Srebrenica, matanza de musulmanes bosnios en
Stalin, Iósiv V. D.
propaganda soviética y
Stockfish 8, programa de ajedrez
_Stürmer, Der_
Sudáfrica, desigualdades en
Suecia
inmigrantes en
nacionalismo en
sufragio universal
Suiza
nacionalismo en
renta básica nacional y
sumerias, ciudades estado
suníes
Tailandia
Taiwán
cuestión de
talibanes
Talmud
Tasmania, aborígenes de
Tea Party
tecnología
tecnología de la información
tecnológico, reto
TED, charlas
Tel el-Kebir, batalla de
teléfonos inteligentes
Tencent
teocracia musulmana
Teodosio, emperador
teología de la liberación
terrorismo
amenaza del
atentados en Europa
con armas nucleares
lucha del Estado contra el
reacción exagerada al
temor al
víctimas del
terroristas
objetivo de los
Tesla, automóviles autónomos de
Thatcher, Margaret
Tierra, cambio climático de la
Tojo, general
Torá
Toyota, automóvil autónomo de
trabajo infantil
«tranvía, problemas del»
Trump, Donald
aislacionismo de Estados Unidos y
ascenso de
muro en la frontera mexicana y
sobre la inmigración mexicana
Tsuyoshi, Inukai
Túnez, Primavera Árabe en
Turquía
movimientos religiosos en
nacionalistas de
Twitter, revolución de
Ucrania oriental, invasión rusa de
Unión Europea
Brexit del Reino Unido
diferencias culturales en la
inestabilidad de la
población y PIB
terrorismo en la
Unión Soviética
economía de la
Ejército Rojo
máquina propagandística de la
valentía, compromiso secular con la
Vedas
vehículos autónomos
verdad, compromiso secular con la
Verdi, Giuseppe: _Nabucco_
Verdún, batalla de
Victoria, reina de Inglaterra
Vietnam, guerra del
Vietnam, nacionalismo en
Vipassana, curso de meditación
Vishwamitra
wahabismo
Waksman, Selman
Wall Street
Walt Disney Pictures
Wikipedia
_Willow_ , película
Wirathu, Ashin
Wright, hermanos
Xi Jinping, liberalismo chino y
Xia, dinastía
Yazid, usurpador
Yemen
yihad
yihadistas
Zakkai, Yochanan ben, rabino
zarista, Imperio
Zuckerberg, Mark
### Notas
1. DECEPCIÓN
[1] Véase por ejemplo el discurso inaugural de George W. Bush en 2005, en el que dijo: «Los acontecimientos y el sentido común nos llevan a una conclusión: la supervivencia de la libertad en nuestro país depende cada vez más del éxito de la libertad en otros países. La mejor esperanza para la paz en nuestro mundo es la expansión de la libertad en todo el mundo». («Bush Pledges to Spread Democracy», _CNN_ , 20 de enero de 2005, http://edition.cnn.com/2005/ _ALLPOLITICS_ /01/20/bush.speech, consultado el 7 de enero de 2018.) Para Obama, véase por ejemplo su discurso final en las Naciones Unidas: Katie Reilly, «Read Barack Obama's Final Speech to the _UN_ as President», _Time_ , 20 de septiembre de 2016, <http://time.com/4501910/president-obama-united-nations-speech-transcript,> consultado el 3 de diciembre de 2017.
[2] William Neikirk y David S. Cloud, «Clinton: Abuses Put China "On Wrong Side of History"», _Chicago Tribune_ , 30 de octubre de 1997, <http://articles.chicagotribune.com/1997->10-30/news/9710300304_1_human-rights-jiang-zemin-chinese-leader, consultado el 3 de diciembre de 2017.
[3] Eric Bradner, «Hillary Clinton's Email Controversy, Explained», _CNN_ , 28 de octubre de 2016, <http://edition.cnn.com/2015/09/03/politics/hillary-clinton-email-controversy-explained-2016/index.html>, consultado el 3 de diciembre de 2017.
[4] Chris Graham y Robert Midgley, «Mexico Border Wall: What is Donald Trump Planning, How Much Will It Cost and Who Will Pay for It?», _The Telegraph_ , 23 de agosto de 2017, <http://www.telegraph.co.uk/news/0/mexico-border-wall-donald-trump-planning-much-will-cost-will>, consultado el 3 de diciembre de 2017; Michael Schuman, «Is China Stealing Jobs? It May Be Losing Them, Instead», _The New York_ _Times_ , 22 de julio de 2016, https://www.nytimes.com/2016/07/23business/international/china-jobs-donald-trump.html, consultado el 3 de diciembre de 2017.
[5] Para diversos ejemplos del siglo XIX y principios del XX, véanse Evgeny Dobrenko y Eric Naiman (eds.), _The Landscape of Stalinism:_ _The Art and Ideology of Soviet Space_ , Seattle, University of Washington Press, 2003; W. L. Guttsman, _Art for the Workers: Ideology and the Visual Arts in Weimar Germany_ , Nueva York, Manchester University Press, 1997. Para una discusión general, véase por ejemplo Nicholas John Cull, _Propaganda and Mass Persuasion:_ _A Historical Encyclopedia, 1500 to the Present_ , Santa Bárbara, _ABC_ - _CLIO_ , 2003.
[6] Para esta interpretación, véanse Ishaan Tharoor, «Brexit: A modern-day Peasants' Revolt?», _The Washington Post_ , 25 de junio de 2016, <https://www.washingtonpost.com/news/worldviews/wp/2016/06/25/the-brexit-a-modern-day-peasants-revolt/?utm_term=.9b8e81bd5306>; John Curtice, « _US_ election 2016: The Trump-Brexit voter revolt», _BBC_ , 11 de noviembre de 2016, <http://www.bbc.com/news/election-us-2016-37943072>.
[7] De ellos, el más famoso sigue siendo, desde luego, Francis Fukuyama, _The End of History and the Last Man_ , Londres, Penguin, 1992 [hay trad. cast.: _El fin de la historia y el último hombre_ , Barcelona, Planeta De Agostini, 1994].
[8] Karen Dawisha, _Putin's Kleptocracy_ , Nueva York, Simon & Schuster, 2014; Timothy Snyder, _The Road to Unfreedom: Russia, Europe, America_ , Nueva York, Tim Duggan Books, 2018; Anne Garrels, _Putin Country: A Journey Into the Real Russia_ , Nueva York, Farrar, Straus & Giroux, 2016; Steven Lee Myers, _The New Tsar: The Rise and Reign of Vladímir Putin_ , Nueva York, Knopf Doubleday, 2016.
[9] Credit Suisse, _Global Wealth Report 2015_ , p. 53, <https://publications.credit-suisse.com/tasks/render/file/?fileID=F2425415-DCA7-80B8-EAD989AF9341D47E>, consultado el 12 de marzo de 2018; Filip Novokmet, Thomas Piketty y Gabriel Zucman, «From Soviets to Oligarchs: Inequality and Property in Russia 1905-2016», julio de 2017, _World Wealth and Income Database_ , http://www.piketty.pse.ens.fr/files/ _NPZ_ 2017 _WID_ world.pdf, consultado el 12 de marzo de 2018; Shaun Walker, «Unequal Russia», _The Guardian_ , 25 de abril de 2017, <https://www.theguardian.com/inequality/2017/apr/25/unequal-russia-is-anger-stirring-in-the-global-capital-of-inequality>, consultado el 12 de marzo de 2018.
[10] Ayelet Shani, «The Israelis Who Take Rebuilding the Third Temple Very Seriously», _Haaretz_ , 10 de agosto de 2017, https://www.haaretz.com/israel-news/.premium-1.805977, consultado en enero de 2018; «Israeli Minister: We Should Rebuild Jerusalem Temple», _Israel Today_ , 7 de julio de 2013, http://www.israeltoday.co.il/Default.aspx?tabid=178&nid=23964, consultado el 7 de enero de 2018; Yuri Yanover, «Dep. Minister Hotovely: The Solution Is Greater Israel without Gaza», _Jewish Press_ , 25 de agosto de 2013, <http://www.jewishpress.com/news/breaking-news/dep-minister-hotovely-the-solution-is-greater-israel-without-gaza/2013/08/25>, consultado el 7 de enero de 2018; «Israeli Minister: The Bible Says West Bank Is Ours», _Al Jazeera_ , 24 de febrero de 2017, <http://www.aljazeera.com/programmes/upfront/2017/02/israeli-minister-bible-west-bank-170224082827910.html>, consultado el 29 de enero de 2018.
[11] Katie Reilly, «Read Barack Obama's Final Speech to the United Nations as President», _Time_ , 20 de septiembre de 2016, <http://time.com/4501910/president-obama-united-nations-speech-transcript>, consultado el 3 de diciembre de 2017.
2. TRABAJO
[1] Gregory R. Woirol, _The Technological Unemployment and Structural Unemployment Debates_ , Westport, Greenwood Press, 1996, pp. 18-20; Amy Sue Bix, _Inventing Ourselves out of Jobs? America's Debate over Technological_ _Unemployment, 1929-1981_ , Baltimore, Johns Hopkins University Press, 2000, pp. 1-8; Joel Mokyr, Chris Vickers y Nicolas L. Ziebarth, «The History of Technological Anxiety and the Future of Economic Growth: Is This Time Different?», _Journal of Economic Perspectives_ , 29, 3 (2015), pp. 33-42; Joe Mokyr, _The Gifts of Athena: Historical Origins of the Knowledge Economy_ , Princeton, Oxford, Princeton University Press, 2002, pp. 255-257; David H. Autor, «Why Are There Still So Many Jobs? The History and the Future of Workplace Automation», _Journal of Economic Perspectives_ , 29, 3 (2015), pp. 3-30; Melanie Arntz, Terry Gregory y Ulrich Zierahn, «The Risk of Automation for Jobs in _OECD_ Countries», _OECD Social, Employment and Migration Working Papers_ 89 (2016); Mariacristina Piva y Marco Vivarelli, «Technological Change and Employment: Were Ricardo and Marx Right?», _IZA Institute of Labor Economics, Discussion Paper No.10471_ (2017).
[2] Véase, por ejemplo, que la _IA_ se desempeña mejor que los humanos en el vuelo, y especialmente en simulaciones de vuelo de combate: Nicholas Ernest _et al_., «Genetic Fuzzy based Artificial Intelligence for Unmanned Combat Aerial Vehicle Control in Simulated Air Combat Missions», _Journal of Defense Management_ , 6, 1 (2016), pp. 1-7; sistemas inteligentes de tutoría y enseñanza: Kurt VanLehn, «The Relative Effectiveness of Human Tutoring, Intelligent Tutoring Systems, and Other Tutoring Systems», _Educational Psychologist_ , 46, 4 (2011), pp. 197-221; comercio algorítmico: Giuseppe Nuti _et al_., «Algorithmic Trading», _Computer_ , 44, 11 (2011), pp. 61-69; planificación financiera, gestión de carteras de valores, etcétera: Arash Baharammirzaee, «A comparative Survey of Artificial Intelligence Applications in Finance: Artificial Neural Networks, Expert System and Hybrid Intelligent Systems», _Neural Computing and Applications_ , 19, 8 (2010), pp. 1165-1195; análisis de datos complejos en sistemas médicos y producción de diagnóstico y tratamiento: Marjorie Glass Zauderer _et al_., «Piloting IBM Watson Oncology within Memorial Sloan Kettering's Regional Network», _Journal of Clinical Oncology_ , 32, 15 (2014), p. e17653; creación de textos originales en lenguaje natural a partir de cantidades enormes de datos: Jean-Sébastien Vayre _et al_., «Communication Mediated through Natural Language Generation in Big Data Environments: The Case of Nomao», _Journal of Computer and Communication_ , 5 (2017), pp. 125-148; reconocimiento facial: Florian Schroff, Dmitry Kalenichenko y James Philbin, «FaceNet: A Unified Embedding for Face Recognition and Clustering», _The IEEE Conference on Computer Vision and Pattern Recognition (CVPR)_ (2015), pp. 815-823; y conducción de vehículos: Cristiano Premebida, «A Lidar and Vision-based Approach for Pedestrian and Vehicle Detection and Tracking», _2007 IEEE Intelligent Transportation Systems Conference_ (2007).
[3] Daniel Kahneman, _Thinking, Fast and Slow_ , Nueva York, Farrar, Straus & Giroux, 2011 [hay trad. cast.: _Pensar rápido, pensar despacio_ , Barcelona, Debate, 2012]; Dan Ariely, _Predictably Irrational_ , Nueva York, Harper, 2009 [hay trad. cast.: _Las trampas del deseo. Cómo controlar los impulsos irra_ _cionales que nos llevan al error_ , Barcelona, Ariel, 2008]; Brian D. Ripley, _Pattern Recognition and Neural Networks_ , Cambridge University Press, 2007; Christopher M. Bishop, _Pattern Recognition and Machine Learning_ , Springer, 2007.
[4] Seyed Azimi _et al_., «Vehicular Networks for Collision Avoidance at Intersections», _SAE International Journal of Passenger Cars – Mechanical Systems_ , 4 (2011); pp. 406-416; Swarun Kumar _et al_., «CarSpeak: A Content-Centric Network for Autonomous Driving», _SIGCOM Computer Communication Review_ , 42 (2012), pp. 259-270; Mihail L. Sichitiu y Maria Kihl, «Inter-Vehicle Communication Systems: A Survey», _IEEE Communications Surveys & Tutorials _(2008), p. 10; Mario Gerla, Eun-Kyu Lee y Giovanni Pau, «Internet of Vehicles: From Intelligent Grid to Autonomous Cars and Vehicular Clouds», _2014 IEEE World Forum on Internet of Things (WF-IoT)_ (2014), pp. 241-246.
[5] David D. Luxton _et al_., «mHealth for Mental Health: Integrating Smartphone Technology in Behavioural Healthcare», _Professional Psychology: Research and Practice_ , 42, 6 (2011), pp. 505-512; Abu Saleh Mohammad Mosa, Illhoi Yoo y Lincoln Sheets, «A Systematic Review of Healthcare Application for Smartphones», _BMC Medical Informatics and Decision Making_ , 12, 1 (2012), p. 67; Karl Frederick Braekkan Payne, Heather Wharrad y Kim Watts, «Smartphone and Medical Related App Use among Medical Students and Junior Doctors in the United Kingdom (UK): A Regional Survey», _BMC Medical Informatics and Decision Making_ , 12, 1 (2012), p. 121; Sandeep Kumar Vashist, E. Marion Schneider y John H.T. Loung, «Commercial Smartphone-Based Devices and Smart Applications for Personalised Healthcare Monitoring and Management», _Diagnostics_ , 4, 3 (2014), pp. 104-128; Maged N. Kamel Bouls _et al_., «How Smartphones Are Changing the Face of Mobile and Participatory Healthcare: An Overview, with Example from e _CAALYX_ », _BioMedical Engineering OnLine_ , 10, 24 (2011), <https://doi.org/10.1186/1475-925X-10-24>, consultado el 30 de julio de 2017; Paul J. F. White, Blake W. Podaima y Marcia R. Friesen, «Algorithms for Smartphone and Tablet Image Analysis for Healthcare Applications», _IEEE Access_ 2 (2014), pp. 831-840.
[6] Organización Mundial de la Salud, _Global status report on road safety 2015_ (2016); «Estimates for 2000-2015, Cause-Specific Mortality», <http://www.who.int/healthinfo/global_burden_disease/estimates/en/index1.html>, consultado el 6 de septiembre de 2017.
[7] Para un análisis de las causas de accidentes de automóvil en Estados Unidos, véase Daniel J. Fagnant y Kara Kockelman, «Preparing a Nation for Autonomous Vehicles: Opportunities, Barriers and Policy Recommendations», _Transportation Research Part A: Policy and Practice_ , 77 (2015), pp. 167-181; para un análisis mundial general, véase, por ejemplo _OECD/ITF,_ _Road Safety Annual Report 2016_ , París, OECD Publishing, 2016, <http://dx.doi.org/10.1787/irtad-2016-en>.
[8] Kristofer D. Kusano y Hampton C. Gabler, «Safety Benefits of Forward Collision Warning, Brake Assist, and Autonomous Braking Systems in Rear-End Collisions», _IEEE Transactions on Intelligent Transportation Systems_ , 13, 4 (2012), pp. 1546-1555; James M. Anderson _et al_., _Autonomous Vehicle Technology: A Guide for Policymakers_ , Santa Mónica, _RAND_ Corporation, 2014, esp. pp. 13-15; Daniel J. Fagnant y Kara Kockelman, «Preparing a Nation for Autonomous Vehicles: Opportunities, Barriers and Policy Recommendations», _Transportation Research Part A: Policy and Practice_ , 77 (2015), pp. 167-181; Jean-François Bonnefon, Azim Shariff e Iyad Rahwan, «Autonomous Vehicles Need Experimental Ethics: Are We Ready for Utilitarian Cars?», _arXiv_ (2015), pp. 1-15. Para sugerencias para que las redes entre vehículos prevengan colisiones, véanse Seyed R. Azimi _et al_., «Vehicular Networks for Collision Avoidance at Intersections», _SAE International Journal of Passenger Cars – Mechanical Systems_ , 4, 1 (2011), pp. 406-416; Swarun Kumar _et al_., «CarSpeak: A Content-Centric Network for Autonomous Driving», _SIGCOM Computer Communication Review_ , 42, 4 (2012), pp. 259-270; Mihail L. Sichitiu y Maria Kihl, «Inter-Vehicle Communication Systems: A Survey», _IEEE Communications Surveys & Tutorials_, 10, 2 (2008); Mario Gerla _et al_., «Internet of Vehicles: From Intelligent Grid to Autonomous Cars and Vehicular Clouds», _2014 IEEE World Forum on Internet of_ _Things (WF-IoT)_ (2014), pp. 241-246.
[9] Michael Chui, James Manyika y Mehdi Miremadi, «Where Machines Could Replace Humans _–_ and Where They Can't (Yet)», _McKinsey_ _Quarterly_ (2016), <http://www.mckinsey.com/business-functions/digital-mckinsey/our-insights/where-machines-could-replace-humans-and-where-they-cant-yet>, consultado el 1 de marzo de 2018.
[10] Wu Youyou, Michal Kosinski y David Stillwell, «Computer-based personality judgments are more accurate than those made by humans», _PANS_ , California, vol. 112 (2014), pp. 1036-1138.
[11] Stuart Dredge, «AI and music: will we be slaves to the algorithm?», _The Guardian_ , 6 de agosto de 2017, https://www.theguardian.com/technology/2017/aug/06/artificial-intelligence-and-will-we-be-slaves-to-the-algorithm, consultado el 15 de octubre de 2017. Para una revisión general de métodos, véase José David Fernández y Francisco Vico, «AI Methods in Algorithmic Composition: A Comprehensive Survey», _Journal of Artificial Intelligence Research_ , 48 (2013), pp. 513-582.
[12] Eric Topol, _The Patient Will See You Now: The Future of Medicine is in Your Hands_ , Basic Books, 2015; Robert Wachter, _The Digital Doctor: Hope, Hype and Harm at the Dawn of Medicine's Computer Age_ , Nueva York, McGraw-Hill Education, 2015; Simon Parkin, «The Artificially Intelligent Doctor Will Hear You Now». _MIT Technology Review_ (2016), https://www.technologyreview.com/s/600868/the-artificially-intelligent-doctor-will-hear-you-now/; James Gallagher, «Artificial intelligence "as good as cancer doctors"», BBC, 26 de enero de 2017, http://www.bbc.com/news/health-38717928.
[13] Kate Brannen, «Air Force's lack of drone pilots reaching "crisis" levels», _Foreign Policy_ , 15 de enero de 2015, <http://foreignpolicy.com/2015/01/15/air-forces-lack-of-drone-pilots-reaching-crisis-levels>.
[14] Tyler Cowen, _Average is Over: Powering America Beyond the Age of_ _the Great Stagnation_ , Nueva York, Dutton, 2013; Brad Bush, «How combined human and computer intelligence will redefine Jobs», _TechCrunch_ (2016), <https://techcrunch.com/2016/11/01/how-combined-human-and-computer-intelligence-will-redefine-jobs>.
[15] Ulrich Raulff, _Farewell to the Horse: The Final Century of Our Relationship_ , Londres, Allen Lane, 2017; Gregory Clark, _A Farewell to Alms: A Brief Economic History of the World_ , Princeton, Princeton University Press, 2008, p. 286 [hay trad. cast.: _Adiós a la sopa de pan, hola al sushi. Breve historia económica mundial_ , Valencia, Universitat de València, 2014]; Margo DeMello, _Animals and Society: An Introduction to Human-Animal Studies_ , Nueva York, Columbia University Press, 2012, p. 197; Clay McShane y Joel Tarr, «The Decline of the Urban Horse in American Cities», _The Journal of Transport History_ , 24, 2 (2003), pp. 177-198.
[16] Lawrence F. Katz y Alan B. Krueger, «The Rise and Nature of Alternative Work Arrangements in the United States, 1995-2015», _National Bureau of Economic Research_ (2016); Peter H. Cappelli y J. R. Keller, «A Study of the Extent and Potential Causes of Alternative Employment Arrangements», _ILR Review_ , 66, 4 (2013), pp. 874-901; Gretchen M. Spreitzer, Lindsey Cameron y Lyndon Garrett, «Alternative Work Arrangements: Two Images of the New World of Work», _Annual Review of Organizational Psychology and Organizational Behavior_ , 4 (2017), pp. 473-499; Sarah A. Donovan, David H. Bradley y Jon O. Shimabukuru, «What Does the Gig Economy Mean for Workers?», Washington DC: Congressional Research Service (2016), https://fas.org/sgp/crs/misc/R44365.pdf, consultado el 11 de febrero de 2018; «More Workers Are in Alternative Employment Arrangements», Pew Research Center, 28 de septiembre de 2016, <http://www.pewsocialtrends.org/2016/10/06/the-state-of-american-jobs/st_2016-10-06_jobs-26>, consultado el 11 de febrero de 2018.
[17] David Ferrucci _et al_., «Watson: Beyond _Jeopardy_!», _Artificial Intelligence_ , 199-200 (2013), pp. 93-105.
[18] «Google's AlphaZero Destroys Stockfish in 100-Game Match», Chess.com, 6 de diciembre de 2017, <https://www.chess.com/news/view/google-s-alphazero-destroys-stockfish-in-100-game-match>, consultado el 11 de febrero de 2018; David Silver _et al_., «Mastering Chess and Shogi by Self-Play with a General Reinforcement Learning Algorithm», _arXiv_ (2017), <https://arxiv.org/pdf/1712.01815.pdf>, consultado el 2 de febrero de 2018; véase también Sarah Knapton, «Entire Human Chess Knowledge Learned and Surpassed by DeepMind's AlphaZero in Four Hours», _Telegra_ _ph_ , 6 de diciembre de 2017, <http://www.telegraph.co.uk/science/2017/12/06/entire-human-chess-knowledge-learned-surpassed-deepminds-alphazero/>, consultado el 11 de febrero de 2018.
[19] Tyler Cowen, _Average is Over: Powering America Beyond the Age of the Great Stagnation_ , Nueva York, Dutton, 2013; Tyler Cowen, «What are humans still good for? The turning point in freestyle chess may be approaching» (2013), <http://marginalrevolution.com/marginalrevolution/2013/11/what-are-humans-still-good-for-the-turning-point-in-freestyle-chess-may-be-approaching.html>.
[20] Maddalaine Ansell, «Jobs for Life Are a Thing of the Past. Bring On Lifelong Learning», _The Guardian_ , 31 de mayo de 2016, <https://www.theguardian.com/higher-education-network/2016/may/31/jobs-for-life-are-a-thing-of-the-past-bring-on-lifelong-learning>.
[21] Alex Williams, «Prozac Nation Is Now the United States of Xanax», _The New York Times_ , 10 de junio de 2017, <https://www.nytimes.com/2017/06/10/style/anxiety-is-the-new-depression-xanax.html>.
[22] Simon Rippon, «Imposing Options on People in Poverty: The Harm of a Live Donor Organ Market», _Journal of Medical Ethics_ , 40 (2014), pp. 145-150; I. Glenn Cohen, «Regulating the Organ Market: Normative Foundations for Market Regulation», _Law and Contemporary Problems_ , 77 (2014); Alexandra K. Glazier, «The Principles of Gift Law and the Regulation of Organ Donation», _Transplant International_ , 24 (2011), pp. 368-372; Megan McAndrews y Walter E. Block, «Legalizing Saving Lives: A Proposition for the Organ Market», _Insights to A Changing World Journal_ , 2015, pp. 1-17.
[23] James J. Hughes, «A Strategic Opening for a Basic Income Guarantee in the Global Crisis Being Created by AI, Robots, Desktop Manufacturing and BioMedicine», _Journal of Evolution & Technology_, 24 (2014), pp. 45-61; Alan Cottey, «Technologies, Culture, Work, Basic Income and Maximum Income», _AI & Society_, 29 (2014), pp. 249-257. __
[24] Jon Henley, «Finland Trials Basic Income for Unemployed», _The Guardian_ , 3 de enero de 2017, <https://www.theguardian.com/world/2017/jan/03/finland-trials-basic-income-for-unemployed>, consultado el 1 de marzo de 2018.
[25] «Swiss Voters Reject Proposal to Give Basic Income to Every Adult and Child», _The Guardian_ , 5 de junio de 2017, <https://www.theguardian.com/world/2016/jun/05/swiss-vote-give-basic-income-every-adult-child-marxist-dream>.
[26] Isabel Hunter, «Crammed into squalid factories to produce clothes for the West on just 20p a day, the children forced to work in horrific unregulated workshops of Bangladesh», _Daily Mail_ , 1 de diciembre de 2015, http://www.dailymail.co.uk/news/article-3339578/Crammed-squalid-factories-produce-clothes-West-just-20p-day-children-forced-work-horrific-unregulated-workshops-Bangladesh.html, consultado el 15 de octubre de 2017; Chris Walker y Morgan Hartley, «The Culture Shock of India's Call Centers», _Forbes_ , 16 de diciembre de 2012, <https://www.forbes.com/sites/morganhartley/2012/12/16/the-culture-shock-of-indias-call-centres/#17bb61d372f5>, consultado el 15 de octubre de 2017.
[27] Klaus Schwab y Nicholas Davis, _Shaping the Fourth Industrial Revolution_ , World Economic Forum, 2018, p. 54. Sobre estrategias de desarrollo a largo plazo, véase Ha-Joon Chang, _Kicking Away the Ladder: Development Strategy in Historical Perspective_ , Londres, Anthem Press, 2003 [hay trad. cast.: _Retirar la escalera. La estrategia del desarrollo en perspectiva histórica_ , Madrid, Los Libros de la Catarata, 2004].
[28] Lauren Gambini, «Trump Pans Immigration Proposal as Bringing People from "Shithole Countries"», _The Guardian_ , 12 de enero de 2018, <https://www.theguardian.com/us-news/2018/jan/11/trump-pans-immigration-proposal-as-bringing-people-from-shithole-countries>, consultado el 11 de febrero de 2018.
[29] Para la idea de que una mejora absoluta en las condiciones tendría que ir acompañada de un aumento de la inequidad relativa, véase en particular Thomas Piketty, _Capital in the 21st Century_ , Cambridge, _MA_ , Harvard University Press, 2013 [hay trad. cast.: _El capital en el siglo_ XXI _,_ Madrid, Fondo de Cultura Económica, 2014].
[30] «2017 Statistical Report on Ultra-Orthodox Society in Israel», _The Israel Democracy Institute_ y _Jerusalem Institute for Israel Studies_ (2017), <https://en.idi.org.il/articles/20439>, consultado el 1 de enero de 2018; Melanie Lidman, «As ultra-Orthodox women bring home the bacon, don't say the F-word», _The Times of Israel_ , 1 de enero de 2016, <https://www.timesofisrael.com/as-ultra-orthodox-women-bring-home-the-bacon-dont-say-the-f-word/>, consultado el 15 de octubre de 2017.
[31] Melanie Lidman, «As ultra-Orthodox women bring home the bacon, don't say the F- Word», _The Times of Israel_ , 1 de enero de 2016, <https://www.timesofisrael.com/as-ultra-Orthodox-women-bring-home-the-bacon-dont-say-the-f-word/>, consultado el 15 de octubre de 2017; «Statistical Report on Ultra-Orthodox Society in Israel», _The Israel Democracy Institute_ y _Jerusalem Institute for Israel Studies_ (2016), p. 18, https://en.idi.org.il/media/4240/shnaton-e_8-9-16_web.pdf, consultado el 15 de octubre de 2017. En cuanto a la felicidad, Israel se hallaba recientemente en el puesto undécimo de un total de treinta y ocho países en satisfacción vital, según la _OCDE_ : «Life Satisfaction», _OECD_ Better Life Index, http://www.oecdbetterlifeindex.org/topics/life-satisfaction, consultado el 15 de octubre de 2017.
[32] «2017 Statistical Report on Ultra-Orthodox Society in Israel», _The Israel Democracy Institute_ y _Jerusalem Institute for Israel Studies_ (2017), https://en.idi.org.il/articles/20439, consultado el 1 de enero de 2018.
3. LIBERTAD
[1] Margaret Thatcher, «Interview for _Woman's Own_ ("no such thing as society")», _Margaret Thatcher Foundation_ , 23 de septiembre de 1987, https://www.margaretthatcher.org/document/106689, consultado el 7 de enero de 2018.
[2] Keith Stanovich, _Who Is Rational? Studies of Individual Differences in Reasoning_ , Nueva York, Londres, Psychology Press, 1999.
[3] Richard Dawkins, «Richard Dawkins: We Need a New Party _–_ the European Party», _NewStatesman_ , 29 de marzo de 2017, <https://www.newstatesman.com/politics/uk/2017/03/richard-dawkins-we-need-new-party-european-party>, consultado el 1 de marzo de 2018.
[4] Steven Swinford, «Boris Johnson's allies accuse Michael Gove of "systematic and calculated plot" to destroy his leadership hopes», _The Telegraph_ , 30 de junio de 2016, <http://www.telegraph.co.uk/news/2016/06/30boris-johnsons-allies-accuse-michael-gove-of-systematic-and-calc>, consultado el 3 de septiembre de 2017; Rowena Mason y Heather Stewart, «Gove's thunderbolt and Boris's breaking point: a shocking Tory morning», _The Guardian_ , 30 de junio de 2016, <https://www.theguardian.com/politics/2016/jun/30/goves-thunderbolt-boris-johnson-tory-morning>, consultado el 3 de septiembre de 2017.
[5] James Tapsfield, «Gove presents himself as the integrity candidate for Downing Street job but sticks the knife into Boris _AGAIN_ », _Daily Mail_ , 1 de julio de 2016, <http://www.dailymail.co.uk/news/article-3669702/I-m-not-great-heart-s-right-place-Gove-makes-bizarre-pitch-Downing-Street-admitting-no-charisma-doesn-t-really-want-job.html>, consultado el 3 de septiembre de 2017.
[6] En 2017, un equipo de Stanford produjo un algoritmo que supuestamente puede detectar si uno es gay o no con una precisión del 91 por ciento, basándose únicamente en el análisis de unas pocas fotografías faciales del sujeto (<https://osf.io/zn79k/>). Sin embargo, puesto que el algoritmo se desarrolló sobre la base de fotografías que las personas seleccionaron para colgar en páginas web de citas, puede ser que el algoritmo identifique en realidad diferencias en los ideales culturales. No es que los rasgos faciales de las personas homosexuales sean necesariamente diferentes de los de las personas heterosexuales. Más bien, los hombres homosexuales que cuelgan fotos en páginas web de citas homosexuales intentan ajustarse a ideales culturales diferentes de los de los hombres heterosexuales que cuelgan fotos en páginas web de citas heterosexuales.
[7] David Chan, «So Why Ask Me? Are Self-Report Data Really That Bad?», en Charles E. Lance y Robert J. Vandenberg (eds.), _Statistical and_ _Methodological Myths and Urban Legends_ , Nueva York, Londres, Routledge, 2009, pp. 309-336; Delroy L. Paulhus y Simine Vazire, «The Self-Report Method», en Richard W. Robins, R. Chris Farley y Robert F. Krueger (eds.), _Handbook of Research Methods in Personality Psychology_ , Londres, Nueva York, The Guilford Press, 2007, pp. 228-233.
[8] Elizabeth Dwoskin y Evelyn M. Rusli, «The Technology that Unmasks Your Hidden Emotions», _The Wall Street Journal_ , 28 de enero de 2015, https://www.wsj.com/articles/startups-see-your-face-unmask-your-emotions-1422472398, consultado el 6 de septiembre de 2017.
[9] Norberto Andrade, «Computers Are Getting Better Than Humans at Facial Recognition», _The Atlantic_ , 9 de junio de 2014, <https://www.theatlantic.com/technology/archive/2014/06/bad-news-computers-are-getting-better-than-we-are-at-facial-recognition/372377>, consultado el 10 de diciembre de 2017; Elizabeth Dwoskin y Evelyn M. Rusli, «The Technology That Unmasks Your Hidden Emotions», _The Wall Street Journal_ , 28 de junio de 2015, <https://www.wsj.com/articles/startups-see-your-face-unmask-your-emotions-1422472398>, consultado el 10 de diciembre de 2017; Sophie K. Scott, Nadine Lavan, Sinead Chen y Carolyn McGettigan, «The Social Life of Laughter», _Trends in Cognitive Sciences_ , 18, 12 (2014), pp. 618-620.
[10] Daniel First, «Will big data algorithms dismantle the foundations of liberalism?», _AI & Soc_, 10.1007/s00146-017-0733-4.
[11] Carole Cadwalladr, «Google, Democracy and the Truth about Internet Search», _The Guardian_ , 4 de diciembre de 2016, <https://www.theguardian.com/technology/2016/dec/04/google-democracy-truth-internet-search-facebook>, consultado el 6 de septiembre de 2017.
[12] Jeff Freak y Shannon Holloway, «How Not to Get to Straddie», _Red Land City Bulletin_ , 15 de marzo de 2012, <http://www.redlandcitybulletin.com.au/story/104929/how-not-to-get-to-straddie.>
[13] Michelle McQuigge, «Woman Follows GPS; Ends Up in Ontario Lake», _Toronto Sun_ , 13 de mayo de 2016, <http://torontosun.com/2016/05/13/woman-follows-gps-ends-up-in-ontario-lake/wcm/fddda6d6-6b6e-41c7-88e8-aecc501faaa5>, consultado el 1 de marzo de 2018; «Woman Follows GPS into Lake», News. com. au, 16 de mayo de 2016, <http://www.news.com.au/technology/gadgets/woman-follows-gps-into-lake/news-story/a7d362dfc4634fd094651afc63f853a1>, consultado el 1 de marzo de 2018.
[14] Henry Grabar, «Navigation Apps Are Killing Our Sense of Direction. What if They Could Help Us Remember Places Instead?», _Slate_ , <http://www.slate.com/blogs/moneybox/2017/07/10/google_and_waze_are_killing_out_sense_of_direction_what_if_they_could_help.html>, consultado el 6 de septiembre de 2017.
[15] Joel Delman, «Are Amazon, Netflix, Google Making Too Many Decisions For Us?», _Forbes_ , 24 de noviembre de 2010, <https://www.forbes.com/2010/11/24/amazon-netflix-google-technology-cio-network-decisions.html>, consultado el 6 de septiembre de 2017; Cecilia Mazanec, «Will Algorithms Erode Our Decision-Making Skills?», _NPR_ , 8 de febrero de 2017, <http://www.npr.org/sections/alltechconsidered/2017/02/08/514120713/will-algorithms-erode-our-decision-making-skills>, consultado el 6 de septiembre de 2017.
[16] Jean-François Bonnefon, Azim Shariff e Iyad Rawhan, «The Social Dilemma of Autonomous Vehicles», _Science_ , 352, 6293 (2016), pp. 1573-1576.
[17] Christopher W. Bauman _et al_., «Revisiting External Validity: Concerns about Trolley Problems and Other Sacrificial Dilemmas in Moral Psychology», _Social and Personality Psychology Compass_ , 8, 9 (2014), pp. 536-554.
[18] John M. Darley y Daniel C. Batson, «"From Jerusalem to Jericho": A Study of Situational and Dispositional Variables in Helping Behavior», _Journal of Personality and Social Psychology_ , 27, 1 (1973), pp. 100-108.
[19] Kristofer D. Kusano y Hampton C. Gabler, «Safety Benefits of Forward Collision Warning, Brake Assist, and Autonomous Braking Systems in Rear-End Collisions», _IEEE Transactions on Intelligent Transportation Systems_ , 13, 4 (2012), pp. 1546-5155; James M. Anderson _et al_., _Autonomous Vehicle Technology: A Guide for Policymakers_ , Santa Mónica, RAND Corporation, 2014, esp. pp. 13-15; Daniel J. Fagnant y Kara Kockelman, «Preparing a Nation for Autonomous Vehicles: Opportunities, Barriers and Policy Recommendations», _Transportation Research Part A: Policy and Practice_ , 77 (2015), pp. 167-181. __
[20] Tim Adams, «Job Hunting Is a Matter of Big Data, Not How You Perform at an Interview», _The Guardian_ , 10 de mayo de 2014, https://www.theguardian.com/technology/2014/may/10/job-hunting-big-data-interview-algorithms-employees, consultado el 6 de septiembre de 2017.
[21] Para un tratamiento muy esclarecedor, véase Cathy O'Neil, _Weapons of Math Destruction: How Big Data Increases Inequality and Threatens Democracy_ , Nueva York, Crown, 2016. Este libro es realmente de lectura obligatoria para quien esté interesado en los efectos potenciales de los algoritmos en la sociedad y la política.
[22] Bonnefon, Shariff y Rahwan, «Social Dilemma of Autonomous Vehicles».
[23] Vincent C. Müller y Thomas W. Simpson, _Autonomous Killer Robots Are Probably Good News_ , memorándum político de la Universidad de Oxford, Blavatnik School of Government, noviembre de 2014. Ronald Arkin, _Governing Lethal Behaviour: Embedding Ethics in a Hybrid Deliberative/Reactive Robot Architecture_ , Georgia Institute of Technology, Mobile Robot lab, 2007, pp. 1-13.
[24] Bernd Grainer, _War without Fronts: The USA in Vietnam_ , trad. Anne Wyburd y Victoria Fern, Cambridge, MA, Harvard University Press, 2009, p. 16. Para al menos una referencia del estado emocional de los soldados, véase Herbert Kelman y V. Lee Hamilton, «The My Lai Massacre: A Military Crime of Obedience», en Jodi O'Brien y David M. Newman (eds.), _Sociology: Exploring the Architecture of Everyday Life Reading_ , Los Ángeles, Pine Forge Press, 2010, pp. 13-25.
[25] Robert J. Donia _, Radovan Karadzic: Architect of the Bosnian Genocide_ , Cambridge, Cambridge University Press, 2015. Véase también Isabella Delpla, Xavier Bougarel y Jean-Louis Fournel _, Investigating Srebrenica: Institutions, Facts, and Responsibilities_ , Nueva York, Oxford, Berghahn Books, 2012.
[26] Noel E. Sharkey, «The Evitability of Autonomous Robot Warfare», _International Rev. Red Cross_ , 94 (886), 2012, pp. 787-799.
[27] Ben Schiller, «Algorithms Control Our Lives: Are They Benevolent Rulers or Evil Dictators?», _Fast Company_ , 21 de febrero de 2017, <https://www.fastcompany.com/3068167/algorithms-control-our-lives-are-they-benevolent-rulers-or-evil-dictators>, consultado el 17 de septiembre de 2017.
[28] Elia Zureik, David Lyon y Yasmeen Abu-Laban (eds.), _Surveillance_ _and Control in Israel/Palestine: Population, Territory and Power_ , Londres, Routledge, 2011; Elia Zureik, _Israel's Colonial Project in Palestine_ , Londres, Routledge, 2015; Torin Monahan (ed.), _Surveillance and Security: Technological Politics and Power in Everyday Life_ , Londres, Routledge, 2006; Nadera Shalhoub-Kevorkian, «E-Resistance and Technological In/Security in Everyday Life: The Palestinian case», _The British Journal of Criminology_ , 52, 1 (2012), pp. 55-72; Or Hirschauge y Hagar Sheizaf, «Targeted Prevention: Exposing the New System for Dealing with Individual Terrorism», _Haaretz_ , 26 de mayo de 2017, https://www.haaretz.co.il/magazine/.premium-1.4124379, consultado el 17 de septiembre de 2017; Amos Harel, «The IDF Accelerates the Crisscrossing of the West Bank with Cameras and Plans to Surveille all Junctions», _Haaretz,_ 18 de junio de 2017, https://www.haaretz.co.il/news/politics/.premium-1.4179886, consultado el 17 de septiembre de 2017; Neta Alexander, «This is How Israel Controls the Digital and Cellular Space in the Territories», 31 de marzo de 2016, https://www.haaretz.co.il/magazine/.premium- _MAGAZINE_ -1.2899665, consultado el 12 de enero de 2018; Amos Harel, «Israel Arrested Hundreds of Palestinians as Suspected Terrorists Due to Publications on the Internet», _Haaretz_ , 16 de abril de 2017, <https://www.haaretz.co.il/news/politics/.premium-1.4024578>, consultado el 15 de enero de 2018; Alex Fishman, «The Argaman Era», _Yediot Aharonot, Weekend Supplement,_ 28 de abril de 2017, p. 6.
[29] Yotam Berger, «Police Arrested a Palestinian Based on an Erroneous Translation of "Good Morning" in His Facebook Page», _Haaretz_ , 22 de octubre de 2017, https://www.haaretz.co.il/.premium-1.4528980, consultado el 12 de enero de 2018.
[30] William Beik, _Louis XIV and Absolutism: A Brief Study with Documents_ , Boston, MA, Bedford/St. Martin's, 2000.
[31] O'Neil, _Weapons of Math Destruction_ , _op. cit._ ; Penny Crosman, «Can AI Be Programmed to Make Fair Lending Decisions?», _American Banker_ , 27 de septiembre de 2016, <https://www.americanbanker.com/news/can-ai-be-programmed-to-make-fair-lending-decisions>, consultado el 17 de septiembre de 2017.
[32] Matt Reynolds, «Bias Test to Prevent Algorithms Discriminating Unfairly», _New Scientist_ , 29 de mayo de 2017, <https://www.newscientist.com/article/mg23431195-300-bias-test-to-prevent-algorithms-discriminating-unfairly>, consultado el 17 de septiembre de 2017; Claire Cain Miller, «When Algorithms Discriminate», _The New York Times_ , 9 de julio de 2015, https://www.nytimes.com/2015/07/10/upshot/when-algorithms-discriminate.html, consultado el 17 de septiembre de 2017; Hannah Devlin, «Discrimination by Algorithm: Scientists Devise Test to Detect AI Bias», _The Guardian_ , 19 de diciembre de 2016, <https://www.theguardian.com/technology/2016/dec/19/discrimination-by-algorithm-scientists-devise-test-to-detect-ai-bias>, consultado el 17 de septiembre de 2017.
[33] Snyder, _Road to Unfreedom_ , _op. cit._
[34] Anna Lisa Peterson, _Being Animal: Beasts and Boundaries in Nature_ _Ethics_ , Nueva York, Columbia University Press, 2013, p. 100.
4.I GUALDAD
[1] «Richest 1 Percent Bagged 82 Percent of Wealth Created Last Year – Poorest Half of Humanity Got Nothing», _Oxfam_ , 22 de enero de 2018, <https://www.oxfam.org/en/pressroom/pressreleases/2018-01-22/richest-1-percent-bagged-82-percent-wealth-created-last-year>, consultado el 28 de febrero de 2018; Josh Lowe, «The 1 Percent Now Have Half the World's Wealth», _Newsweek_ , 14 de noviembre de 2017, <http://www.newsweek.com/1-wealth-money-half-world-global-710714>, consultado el 28 de febrero de 2018; Adam Withnall, «All the World's Most Unequal Countries Revealed in One Chart», _The Independent_ , 23 de noviembre de 2016, <http://www.independent.co.uk/news/world/politics/credit-suisse-global-wealth-world-most-unequal-countries-revealed-a7434431.html>, consultado el 11 de marzo de 2018.
[2] Tim Wu, _The Attention Merchants_ , Nueva York, Alfred A. Knopf, 2016.
[3] Cara McGoogan, «How to See All the Terrifying Things Google Knows about You», _Telegraph_ , 18 de agosto de 2017, <http://www.telegraph.co.uk/technology/0/see-terrifying-things-google-knows>, consultado el 19 de octubre de 2017; Caitlin Dewey, «Everything Google Knows about You (and How It Knows It)», _The Washington Post_ , 19 de noviembre de 2014, <https://www.washingtonpost.com/news/the-intersect/wp/2014/11/19/everything-google-knows-about-you-and-how-it-knows-it/?utm_term=.b81c3ce3ddd6>, consultado el 19 de octubre de 2017.
[4] Dan Bates, «YouTube Is Losing Money Even Though It Has More Than 1 Billion Viewers», _Daily Mail_ , 26 de febrero de 2015, http://www.dailymail.co.uk/news/article-2970777/YouTube-roughly-breaking-nine-years-purchased-Google-billion-viewers.html, consultado el 19 de octubre de 2017; Olivia Solon, «Google's Bad Week: YouTube Loses Millions As Advertising Row Reaches US», _The Guardian_ , 25 de marzo de 2017, <https://www.theguardian.com/technology/2017/mar/25/google-youtube-advertising-extremist-content-att-verizon>, consultado el 19 de octubre de 2017; Seth Fiegerman, «Twitter Is Now Losing Users in the U.S.», _CNN_ , 27 de julio de 2017, http://money.cnn.com/2017/07/27/technology/business/twitter-earnings/index.html, consultado el 19 de octubre de 2017.
5. COMUNIDAD
[1] Mark Zuckerberg, «Building Global Community», 16 de febrero de 2017, <https://www.facebook.com/notes/mark-zuckerberg/building-global-community/10154544292806634>, consultado el 20 de agosto de 2017.
[2] John Shinal, «Mark Zuckerberg: Facebook can play a role that churches and Little League once filled», _CNBC_ , 26 de junio de 2017, <https://www.cnbc.com/2017/06/26/mark-zuckerberg-compares-facebook-to-church-little-league.html>, consultado el 20 de agosto de 2017.
[3] <https://www.cnbc.com/2017/06/26/mark-zuckerberg-compares-facebook-to-church-little-league.html>; <https://www.cnbc.com/2017/06/22/facebook-has-a-new-mission-following-fake-news-crisis-zuckerberg-says.html>.
[4] Robin Dunbar, _Grooming, Gossip, and the Evolution of Language_ , Cambridge, _MA_ , Harvard University Press, 1998.
[5] Véase, por ejemplo, Pankaj Mishra, _Age of Anger: A History of the Present_ , Londres, Penguin, 2017 [hay trad. cast.: _La edad de la ira. Una historia del presente_ , Barcelona, Galaxia Gutenberg, 2017].
[6] Para una revisión general y una crítica, véase Derek Y. Darves y Michael C. Dreiling, _Agents of Neoliberal Globalization: Corporate Networks, State Structures and Trade Policy_ , Cambridge, Cambridge University Press, 2016.
[7] Lisa Eadicicco, «Americans Check Their Phones 8 Billion Times a Day», _Time_ , 15 de diciembre de 2015, http://time.com/4147614/smartphone-usage-us-2015, consultado el 20 de agosto de 2017; Julie Beck, «Ignoring People for Phones Is the New Normal», _The Atlantic_ , 14 de junio de 2016, <https://www.theatlantic.com/technology/archive/2016/06/ignoring-people-for-phones-is-the-new-normal-phubbing-study/486845>, consultado el 20 de agosto de 2017.
[8] Zuckerberg, «Building Global Community», _op. cit_.
[9] _Time Well Spent_ , http://www.timewellspent.io, consultado el 3 de septiembre de 2017.
[10] Zuckerberg, «Building Global Community», _op. cit_.
[11] https://www.theguardian.com/technology/2017/oct/04/facebook-uk-corporation-tax-profit; https://www.theguardian.com/business/2017/sep/21/tech-firms-tax-eu-turnover-google-amazon-apple; <http://www.wired.co.uk/article/facebook-apple-tax-loopholes-deals>.
6. CIVILIZACIÓN
[1] Samuel P. Huntington, _The Clash of Civilizations and the Remaking of World Order_ , Nueva York, Simon & Schuster, 1996 hay trad. cast.: _El choque de civilizaciones y la reconfiguración del orden mundial_ , Barcelona, Paidós, 1997]; David Lauter y Brian Bennett, «Trump Frames Anti-Terrorism Fight As a Clash of Civilizations, Defending Western Culture against Enemies», _Los Angeles Times_ , 6 de julio de 2017, <http://www.latimes.com/politics/la-na-pol-trump-clash-20170706-story.html>, consultado el 29 de enero de 2018; Naomi O'Leary, «The Man Who Invented Trumpism: Geert Wilders' Radical Path to the Pinnacle of Dutch Politics», _Politico_ , 23 de febrero de 2017, https://[www.politico.eu/article/the-man-who-invented-trumpism-geert-wilders-netherlands-pvv-vvd-populist, consultado el 31 de enero de 2018.
[2] Pankaj Mishra, _From the Ruins of Empire: The Revolt Against the West_ _and the Remaking of Asia_ , Londres, Penguin 2013 [hay trad. cast.: _De las ruinas_ _de los imperios: la rebelión contra Occidente y la metamorfosis de Asia_ , Barcelona, Galaxia Gutenberg - Círculo de Lectores, 2014]; Pankaj Mishra, _Age of Anger: A History of the Present_ , _op. cit_.; Christopher de Bellaigue, _The Muslim Enlightenment. The Modern Struggle Between Faith and Reason_ , Londres, The Bodley Head, 2017.
[3] «Treaty Establishing A Constitution for Europe», _European Union_ , <https://europa.eu/european-union/sites/europaeu/files/docs/body/treaty_establishing_a_constitution_for_europe_es.pdf>, consultado el 18 de octubre de 2017.
[4] Phoebe Greenwood, «Jerusalem Mayor Battles Ultra-Orthodox Groups over Women-Free Billboards», _The Guardian_ , 15 de noviembre de 2011, <https://www.theguardian.com/world/2011/nov/15/jerusalem-mayor-battle-orthodox-billboards>, consultado el 7 de enero de 2018.
[5] <http://nypost.com/2015/10/01/orthodox-publications-wont-show-hillary-clintons-photo.>
[6] Simon Schama, _The Story of the Jews: Finding the Words 1000 BC – 1492 AD_ , Nueva York, Ecco, 2014, pp. 190-197 hay trad. cast.: _La historia de los judíos_ , Barcelona, Debate, 2015]; Hannah Wortzman, «Jewish Women in Ancient Synagogues: Archaeological Reality vs. Rabbinical Legislation», _Women in Judaism_ , 5, 2 (2008), [http://wjudaism.library.utoronto.ca/index.php/wjudaism/article/view/3537, consultado el 29 de enero de 2018; Ross S. Kraemer, «Jewish Women in the Diaspora World of Late Antiquity», en Judith R. Baskin (ed.), _Jewish Women in Historical Perspective_ , Detroit, Wayne State University Press, 1991, esp. p. 49; Hachlili Rachel, _Ancient Synagogues – Archaeology and Art: New Discoveries and Current Research_ , Leiden, Brill, 2014, pp. 578-581; Zeev Weiss, «The Sepphoris Synagogue Mosaic: Abraham, the Temple and the Sun God-They're All in There», _Biblical Archeology Society_ 26, 5 (2000), pp. 48-61; David Milson, _Art and Architecture of the Synagogue in Late Antique Palestine_ , Leiden, Brill, 2007, p. 48.
[7] Ivan Watson y Pamela Boykoff, «World's Largest Muslim Group Denounces Islamist Extremism», CNN, 10 de mayo de 2016, http://edition.cnn.com/2016/05/10/asia/indonesia-extremism/index.html, consultado el 8 de enero de 2018; Lauren Markoe, «Muslim Scholars Release Open Letter To Islamic State Meticulously Blasting Its Ideology», _Huffington Post_ , 25 de septiembre de 2014, <https://www.huffingtonpost.com/2014/09/24/muslim-scholars-islamic-state_n_5878038.html>, consultado el 8 de enero de 2018; para la carta, véase «Open Letter to Al-Baghdadi», http://www.lettertobaghdadi.com, consultado el 8 de enero de 2018.
[8] Chris Perez, «Obama Defends the "True Peaceful Nature of Islam"», _New York Post_ , 18 de febrero de 2015, <http://nypost.com/2015/02/18/obama-defends-the-true-peaceful-nature-of-islam>, consultado el 17 de octubre de 2017; Dave Boyer, «Obama Says Terrorists Not Motivated By True Islam», _The Washington Times_ , 1 de febrero de 2015, <http://www.washingtontimes.com/news/2015/feb/1/obama-says-terrorists-not-motivated-true-islam>, consultado el 18 de octubre de 2017.
[9] Christopher de Bellaigue, _The Islamic Enlightenment, op. cit_.
[10] Christopher McIntosh, _The Swan King: Ludwig II of Bavaria_ , Londres, I.B. Tauris, 2012, p. 100.
[11] Robert Mitchell Stern, _Globalization and International Trade Policies_ , Hackensack, NJ, World Scientific, 2009, p. 23.
[12] John K. Thornton, _A Cultural History of the Atlantic World, 1250-1820_ , Cambridge, Cambridge University Press, 2012, p. 110.
[13] Susannah Cullinane, Hamdi Alkhshali y Mohammed Tawfeeq, «Tracking a Trail of Historical Obliteration: ISIS Trumpets Destruction of Nimrud», CNN, 14 de abril de 2015, http://edition.cnn.com/2015/03/09/world/iraq-isis-heritage/index.html, consultado el 18 de octubre de 2017.
[14] Kenneth Pomeranz, _The Great Divergence: China, Europe and the Making of the Modern World Economy_ , Princeton, Oxford, Princeton University Press, 2001, pp. 36-38.
[15] «ISIS Leader Calls for Muslims to Help Build Islamic State in Iraq», _CBCNEWS_ , 1 de julio de 2014, <http://www.cbc.ca/news/world/isis-leader-calls-for-muslims-to-help-build-islamic-state-in-iraq-1.2693353>, consultado el 18 de octubre de 2017; Mark Townsend, «What Happened to the British Medics Who Went to Work for ISIS?», _The Guardian_ , 12 de julio de 2015, https://www.theguardian.com/world/2015/jul/12/british-medics-isis-turkey-islamic-, consultado el 18 de octubre de 2017.
7. NACIONALISMO
[1] Francis Fukuyama, _Political Order and Political Decay: From the Industrial Revolution to the Globalization of Democracy_ , Nueva York, Farrar, Straus & Giroux, 2014 [hay trad. cast.: _Orden y decadencia de la política: desde la revolución industrial a la globalización de la democracia_ , Barcelona, Deusto, 2016].
[2] Ashley Killough, «Lyndon Johnson's "Daisy" Ad, Which Changed the World of Politics, Turns 50», CNN, 8 de septiembre de 2014, <http://edition.cnn.com/2014/09/07/politics/daisy-ad-turns-50/index.html>, consultado el 19 de octubre de 2017.
[3] «Cause-Specific Mortality: Estimates for 2000-2015», _World Health Organization_ , http://www.who.int/healthinfo/global_burden_disease/estimates/en/index1.html, consultado el 19 de octubre de 2017.
[4] David E. Sanger y William J. Broad, «To counter Russia, U.S. signals nuclear arms are back in a big way», _The_ _New York Times_ , 4 de febrero de 2018, https://www.nytimes.com/2018/02/04/us/politics/trump-nuclear-russia.html, consultado el 6 de febrero de 2018; Departamento de Defensa de los Estados Unidos, «Nuclear Posture Review 2018», <https://www.defense.gov/News/Special-Reports/0218_npr,> consultado el 6 de febrero de 2018; Jennifer Hansler, «Trump Says He Wants Nuclear Arsenal in "Tip-Top Shape", Denies Desire to Increase Stockpile», CNN, 12 de octubre de 2017, http://edition.cnn.com/2017/10/11/politics/nuclear-arsenal-trump/index.html, consultado el 19 de octubre de 2017; Jim Garamone, «DoD Official: National Defense Strategy Will Enhance Deterrence», _Department of Defense News, Defense Media Activity_ , 19 de enero de 2018, <https://www.defense.gov/News/Article/Article/1419045/dod-official-national-defense-strategy-will-rebuild-dominance-enhance-deterrence>, consultado el 28 de enero de 2018.
[5] Michael Mandelbaum, _Mission Failure: America and the World in the Post-Cold War Era_ , Nueva York, Oxford University Press, 2016.
[6] Elizabeth Kolbert, _Field Notes from a Catastrophe_ , Londres, Bloomsbury, 2006 [hay trad. cast.: _La catástrofe que viene. Apuntes desde el frente del cambio climático_ , Barcelona, Planeta, 2008]; Elizabeth Kolbert, _The Sixth Extinction_ , Londres, Bloomsbury, 2004 [hay trad. cast.: _La sexta extinción. Una historia nada natural_ , Barcelona, Crítica, 2015]; Will Steffen _et al_., «Planetary Boundaries: Guiding Human Development on a Changing Planet», _Science_ , 347, 6223, 13 de febrero de 2015, DOI: 10.1126/science.1259855.
[7] John Cook _et al_., «Quantifying the Consensus on Anthropogenic Global Warming in the Scientific Literature», _Environmental Research Letters_ 8, 2 (2013); John Cook _et al_., «Consensus on Consensus: A Synthesis of Consensus Estimates on Human-Caused Global Warming», _Environmental Research Letters_ 11, 4 (2016); Andrew Griffin, «15,000 Scientists Give Catastrophic Warning about the Fate of the World in New "Letter to Humanity"», _The Independent_ , 13 de noviembre de 2017, <http://www.independent.co.uk/environment/letter-to-humanity-warning-climate-change-global-warming-scientists-union-concerned-a8052481.html>, consultado el 8 de enero de 2018; Justin Worland, «Climate Change Is Already Wreaking Havoc on Our Weather, Scientists Find», _Time_ , 15 de diciembre de 2017, http://time.com/5064577/climate-change-arctic, consultado el 8 de enero de 2018.
[8] Richard J. Millar _et al_., «Emission budgets and pathways consistent with limiting warming to 1.5 C», _Nature Geoscience_ , 10 (2017), pp. 741-747; Joeri Rogelj _et al_., «Differences between carbon budget estimates unravelled», _Nature Climate Change_ , 6 (2016), pp. 245-252; Akshat Rathi, «Did We Just Buy Decades More Time to Hit Climate Goals», _Quartz_ , 21 de septiembre de 2017, <https://qz.com/1080883/the-breathtaking-new-climate-change-study-hasnt-changed-the-urgency-with-which-we-must-reduce-emissions>, consultado el 11 de febrero de 2018; Roz Pidcock, «Carbon Briefing: Making Sense of the IPCC's New Carbon Budget», _Carbon Brief_ , 23 de octubre de 2013, <https://www.carbonbrief.org/carbon-briefing-making-sense-of-the-ipccs-new-carbon-budget>, consultado el 11 de febrero de 2018.
[9] Jianping Huang _et al_., «Accelerated Dryland Expansion under Climate Change», _Nature Climate Change_ 6 (2016), pp. 166-171; Thomas R. Knutson, «Tropical Cyclones and Climate Change», _Nature Geoscience,_ 3 (2010), pp. 157-163; Edward Hanna _et al_., «Ice-Sheet Mass Balance and Climate Change», _Nature_ , 498 (2013), pp. 51-59; Tim Wheeler y Joachim von Braun, «Climate Change Impacts on Global Food Security», _Science_ , 341, 6145 (2013), pp. 508-513; A. J. Challinor _et al_., «A Meta-Analysis of Crop Yield under Climate Change and Adaptation», _Nature Climate Change_ , 4 (2014), pp. 287-291; Elisabeth Lingren _et al_., «Monitoring EU Emerging Infectious Disease Risk Due to Climate Change», _Science,_ 336, 6080 (2012), pp. 418-419; Frank Biermann e Ingrid Boas, «Preparing for a Warmer World: Towards a Global Governance System to Protect Climate Change», _Global Environmental Politics,_ 10, 1 (2010), pp. 60-88; Jeff Goodell, _The Water Will Come: Rising Seas, Sinking Cities and the Remaking of the Civilized World_ , Nueva York, Little, Brown and Company, 2017; Mark Lynas, _Six Degrees: Our Future on a Hotter Planet_ , Washington, National Geographic, 2008; Naomi Klein, _This Changes Everything: Capitalism vs. Climate_ , Nueva York, Simon & Schuster, 2014 [hay trad. cast.: _Esto lo cambia todo. El capitalismo contra el clima_ , Barcelona, Paidós, 2015]; Kolbert, _The Sixth Extinction_ , _op. cit_.
[10] Johan Rockström _et al_., «A Roadmap for Rapid Decarbonization», _Science_ , 355, 6331, 23 de marzo de 2017, DOI, 10.1126/science.aah3443.
[11] Institution of Mechanical Engineers, _Global Food: Waste Not, Want Not_ , Londres, Institution of Mechanical Engineers, 2013, p. 12.
[12] Paul Shapiro, _Clean Meat: How Growing Meat Without Animals Will Revolutionize Dinner and the World_ , Nueva York, Gallery Books, 2018.
[13] «Russia's Putin Says Climate Change in Arctic Good for Economy», CBS News, 30 de marzo de 2017, <http://www.cbc.ca/news/technology/russia-putin-climate-change-beneficial-economy-1.4048430>, consultado el 1 de marzo de 2018; Neela Banerjee, «Russia and the US Could be Partners in Climate Change Inaction», _Inside Climate News_ , 7 de febrero de 2017, https://insideclimatenews.org/news/06022017/russia-Vladímir-putin-donald-trump-climate-change-paris-climate-agreement, consultado el 1 de marzo de 2018; Noah Smith, «Russia Wins in a Retreat on Climate Change», _Bloomberg View_ , 15 de diciembre de 2016, <https://www.bloomberg.com/view/articles/2016-12-15/russia-wins-in-a-retreat-on-climate-change>, consultado el 1 de marzo de 2018; Gregg Easterbrook, «Global Warming: Who Loses-and Who Wins?», _Atlantic_ (abril de 2007), <https://www.theatlantic.com/magazine/archive/2007/04/global-warming-who-loses-and-who-wins/305698/>, consultado el 1 de marzo de 2018; Quentin Buckholz, «Russia and Climate Change: A Looming Threat», _Diplomat_ , 4 de febrero de 2016, https://thediplomat.com/2016/02/russia-and-climate-change-a-looming-threat, consultado el 1 de marzo de 2018.
[14] Brian Eckhouse, Ari Natter y Christopher Martin, «President Trump slaps tariffs on solar panels in major blow to renewable energy», 22 de enero de 2018, http://time.com/5113472/donald-trump-solar-panel-tariff, consultado el 30 de enero de 2018.
[15]. Miranda Green y Rene Marsh, «Trump Administration Doesn't Want to Talk about Climate Change», _CNN_ , 13 de septiembre de 2017, <http://edition.cnn.com/2017/09/12/politics/trump-climate-change-silence/index.html>, consultado el 22 de octubre de 2017; Lydia Smith, «Trump Administration Deletes Mention of "Climate Change" from Environmental Protection Agency's Website», _The Independent_ , 22 de octubre de 2017, <http://www.independent.co.uk/news/world/americas/us-politics/donald-trump-administration-climate-change-deleted-environmental-protection-agency-website-a8012581.html>, consultado el 22 de octubre de 2017; Alana Abramson, «No, Trump Still Hasn't Changed His Mind About Climate Change After Hurricane Irma and Harvey», _Time_ , 11 de septiembre de 2017, <http://time.com/4936507/donald-trump-climate-change-hurricane-irma-hurricane-harvey>, consultado el 22 de octubre de 2017.
[16] «Treaty Establishing A Constitution for Europe», _European Union_ , <https://europa.eu/european-union/sites/europaeu/files/docs/body/treaty_establishing_a_constitution_for_europe_en.pdf>, consultado el 23 de octubre de 2017.
8. RELIGIÓN
[1] Bernard S. Cohn, _Colonialism and Its Forms of Knowledge: The British in India_ , Princeton, Princeton University Press, 1996, p. 148.
[2] «Encyclical Letter "Laudato Si" of the Holy Father Francis on Care for Our Common Home», _The Holy See_ , <http://w2.vatican.va/content/francesco/en/encyclicals/documents/papa-francesco_20150524_enciclica-laudato-si.html>, consultado el 3 de diciembre de 2017.
[3] Freud lo introdujo por primera vez en su tratado de 1930 «Civilization and Its Discontents»: Sigmund Freud, _Civilization and Its Discontents_ , trad. de James Strachey, Nueva York, W. W. Norton, 1961, p. 61.
[4] Ian Buruma, _Inventing Japan, 1853-1964_ , Nueva York, Modern Library, 2003 [hay trad. cast.: _La creación de Japón, 1853-1964_ , Barcelona, Mondadori, 2003].
[5] Robert Axell, _Kamikaze: Japan's Suicide Gods_ , Londres, Longman, 2002.
[6] Charles K. Armstrong, «Familism, Socialism and Political Religion in North Korea», _Totalitarian Movements and Political Religions_ , 6, 3 (2005), pp. 383-394; Daniel Byman y Jennifer Lind, «Pyongyang's Survival Strategy. Tools of Authoritarian Control in North Korea», _International_ _Security_ , 35, 1 (2010), pp. 44-74; Paul French, _North Korea: The Paranoid Peninsula,_ 2.ª ed., Londres, Nueva York, Zed Books, 2007; Andrei Lankov, _The Real North Korea: Life and Politics in the Failed Stalinist Utopia_ , Oxford, Oxford University Press, 2015; Young Whan Kihl, «Staying Power of the Socialist "Hermit Kingdom"», en Hong Nack Kim y Young Whan Kihl (eds.), _North Korea: The Politics of Regime Survival_ , Nueva York, Routledge, 2006, pp. 3-36.
9. INMIGRACIÓN
[1] «Global Trends: Forced Displacement in 2016», UNHCR, http://www.unhcr.org/5943e8a34.pdf, consultado el 11 de enero de 2018.
[2] Lauren Gambini, «Trump Pans Immigration Proposal as Bringing People from "Shithole Countries"», _The Guardian_ , 12 de enero de 2018, <https://www.theguardian.com/us-news/2018/jan/11/trump-pans-immigration-proposal-as-bringing-people-from-shithole-countries>, consultado el 11 de febrero de 2018.
[3] Tal Kopan, «What Donald Trump Has Said about Mexico and Vice Versa», CNN, 31 de agosto de 2016, <https://edition.cnn.com/2016/08/31/politics/donald-trump-mexico-statements/index.html>, consultado el 28 de febrero de 2018.
10. TERRORISMO
[1] http://www.telegraph.co.uk/news/0/many-people-killed-terrorist-attacks-uk; National Consortium for the Study of Terrorism and Responses to Terrorism (START) (2016), Global Terrorism Database [archivo de datos], consultado en <https://www.start.umd.edu/gtd;> <http://www.cnsnews.com/news/article/susan-jones/11774-number-terror-attacks-worldwide-dropped-13-2015>; <http://www.datagraver.com/case/people-killed-by-terrorism-per-year-in-western-europe-1970-2015>; <http://www.jewishvirtuallibrary.org/statistics-on-incidents-of-terrorism-worldwide>; Gary LaFree, Laura Dugan y Erin Miller, _Putting Terrorism in Context: Lessons from the Global Terrorism Database_ , Londres, Routledge, 2015; Gary LaFree, «Using open source data to counter common myths about terrorism», en Brian Forst, Jack Greene y Jim Lynch (eds.), _Criminologists on Terrorism and Homeland Security_ , Cambridge, Cambridge University Press, 2011, pp. 411-442; Gary LaFree, «The Global Terrorism Database: Accomplishments and challenges», _Perspectives on Terrorism_ , 4 (2010), pp. 24-46; Gary LaFree y Laura Dugan, «Research on terrorism and countering terrorism», en M. Tonry (ed.), _Crime and Justice:_ _A Review of Research_ , Chicago, University of Chicago Press, 2009, 38, pp. 413-477; Gary LaFree y Laura Dugan, «Introducing the global terrorism data base», _Political Violence and Terrorism_ , 19 (2007), pp. 181-204.
[2] «Deaths on the roads: Based on the WHO Global Status Report on Road Safety 2015», Organización Mundial de la Salud, consultado el 26 de enero de 2016; https://wonder.cdc.gov/mcd-icd10.html; «Global status report on road safety 2013», World Health Organisation; <http://gamapserver.who.int/gho/interactive_charts/road_safety/road_traffic_deaths/atlas.html>; http://www.who.int/violence_injury_prevention/road_safety_status/2013/en; <http://www.newsweek.com/2015-brought-biggest-us-traffic-death-increase-50-years-427759>.
[3] <http://www.euro.who.int/en/health-topics/noncommunicable-diseases/diabetes/data-and-statistics>; http://apps.who.int/iris/bitstream/10665/204871/1/9789241565257_eng.pdf?ua=1; https://www.theguardian.com/environment/2016/sep/27/more-than-million-died-due-air-pollution-china-one-year.
[4] Para la batalla, véase Gary Sheffield, _Forgotten Victory: The First World War. Myths and Reality_ , Londres, Headline, 2001, pp. 137-164.
[5] «Victims of Palestinian Violence and Terrorism since September 2000», Israel Ministry of Foreign Affairs, <http://mfa.gov.il/MFA/ForeignPolicy/Terrorism/Palestinian/Pages/Victims%20of%20Palestinian%20Violence%20and%20Terrorism%20sinc.aspx>, consultado el 23 de octubre de 2017.
[6] «Car Accidents with Casualties, 2002», _Central Bureau of Statistics_ (en hebreo), http://www.cbs.gov.il/www/publications/acci02/acci02h.pdf, consultado el 23 de octubre de 2017.
[7] «Pan Am Flight 103 Fast Facts», _CNN_ , 16 de diciembre de 2016, http://edition.cnn.com/2013/09/26/world/pan-am-flight-103-fast-facts/index.html, consultado el 23 de octubre de 2017.
[8] Tom Templeton y Tom Lumley, «9/11 in Numbers», _The Guardian_ , 18 de agosto de 2002, https://www.theguardian.com/world/2002/aug/18/usa.terrorism, consultado el 23 de octubre de 2017.
[9] Ian Westwell y Dennis Cove (eds.), _History of World War I,_ vol. 2, Nueva York, Marshall Cavendish, 2002, p. 431. Para Isonzo, véase John R. Schindler, _Isonzo: The Forgotten Sacrifice of the Great War_ , Westport, Praeger, 2001, pp. 217-218.
[10] Sergio Catignani, _Israeli Counter-Insurgency and the Intifadas: Dilemmas of a Conventional Army_ , Londres, Routledge, 2008.
[11] «Reported Rapes in France Jump 18% in Five Years», France 24, 11 de agosto de 2015, http://www.france24.com/en/20150811-reported-rapes-france-jump-18-five-years, consultado el 11 de enero de 2018.
11. GUERRA
[1] Yuval Noah Harari, _Homo Deus: A Brief History of Tomorrow_ , Nueva York, HarperCollins, 2017, pp. 14-19 hay trad. cast.: _Homo Deus. Breve historia del mañana_ , Barcelona, Debate, 2016]; «Global Health Observatory Data Repository, 2012», World Health Organization, <http://apps.who.int/gho/data/node.main.RCODWORLD?lang=en>, consultado el 16 de agosto de 2015; «Global Study on Homicide, 2013», _UNDOC_ , <http://www.unodc.org/documents/gsh/pdfs/2014_GLOBAL_HOMICIDE_BOOK_web.pdf>; consultado el 16 de agosto de 2015; [http://www.who.int/healthinfo/global_burden_disease/estimates/en/index1.html.
[2] «World Military Spending: Increases in the _USA_ and Europe, Decreases in Oil-Exporting Countries», _Stockholm International Peace Research_ _Institute_ , 24 de abril de 2017, <https://www.sipri.org/media/press-release/2017/world-military-spending-increases-usa-and-europe>, consultado el 23 de octubre de 2017.
[3] <http://www.nationalarchives.gov.uk/battles/egypt/popup/telel4.htm>.
[4] Spencer C. Tucker (ed.), _The Encyclopedia of the Mexican-American War: A Political, Social and Military History_ , Santa Bárbara, _ABC_ - _CLIO_ , 2013, p. 131.
[5] Ivana Kottasova, «Putin Meets Xi: Two Economies, Only One to Envy», _CNN_ , 2 de julio de 2017, <http://money.cnn.com/2017/07/02/news/economy/china-russia-putin-xi-meeting/index.html>, consultado el 23 de octubre de 2017.
[6] El _PIB_ , según las estadísticas del _FMI_ , se calcula sobre la base de paridad en el poder adquisitivo: Fondo Monetario Internacional, «Report for Selected Countries and Subjects, 2017», <https://www.imf.org/external/pubs/ft/weo/2017/02/weodata/index.aspx>, consultado el 27 de febrero de 2018.
[7] [http://www.businessinsider.com/isis-making-50-million-a-month-
from-oil-sales-2015-10](http://www.businessinsider.com/isis-making-50-million-a-month-from-oil-sales-2015-10).
[8] Ian Buruma, _Inventing Japan_ , Londres, Weidenfeld & Nicolson, 2003 [hay trad. cast.: _La creación de Japón, 1853-1964_ , Barcelona, Mondadori, 2003]; Eri Hotta, _Japan 1941: Countdown to Infamy_ , Londres, Vintage, 2014 [hay trad. cast.: _Japón 1941: el camino a la infamia_ , Barcelona, Galaxia Gutenberg, 2015].
12. HUMILDAD
[1] <http://www.ancientpages.com/2015/10/19/10-remarkable-ancient-indian-sages-familiar->with-advanced-technology-science-long-before-modern-era; https://www.hindujagruti.org/articles/31.html; <http://mcknowledge.info/about-vedas/what-is-vedic-science>.
[2] Estas cifras y la proporción pueden verse claramente en el gráfico siguiente: Conrad Hackett y David McClendon, «Christians Remain World's Largest Religious Group, but They Are Declining in Europe», _Pew Research Center_ , 5 de abril de 2017, <http://www.pewresearch.org/fact-tank/2017/04/05/christians-remain-worlds-largest-religious-group-but-they-are-declining-in-europe>, consultado el 13 de noviembre de 2017.
[3] Jonathan Haidt, _The Righteous Mind: Why Good People Are Divided by Politics and Religion_ , Nueva York, Pantheon, 2012; Joshua Greene, _Moral Tribes: Emotion, Reason, and the Gap Between Us and Them_ , Nueva York, Penguin Books, 2013.
[4] Marc Bekoff y Jessica Pierce, «Wild Justice – Honor and Fairness among Beasts at Play», _American Journal of Play_ , 1, 4 (2009), pp. 451-475.
[5] Frans de Waal, _Our Inner Ape_ , Londres, Granta, 2005, cap. 5 [hay trad. cast.: _El mono que llevamos dentro_ , Barcelona, Tusquets, 2007].
[6] Frans de Waal, _Bonobo: The Forgotten Ape_ , Berkeley, University of California Press, 1997, p. 157 [hay trad. cast.: _El bonobo y los diez mandamientos_ , Barcelona, Tusquets, 2014].
[7] El relato se convirtió en el tema de un documental titulado _Chimpanzee_ , que en 2010 emitió Disneynature.
[8] M. E. J. Richardson, _Hammurabi's Laws_ , Londres, Nueva York, T&T Clark International, 2000, pp. 29-31.
[9] Loren R. Fisher, _The Eloquent Peasant_ , 2.ª ed., Eugene, Wipf and Stock Publishers, 2015.
[10] Algunos rabinos permitieron que se profanara el Sabbat con el fin de salvar a un gentil, basándose en el típico ingenio del Talmud. Argumentaron que si los judíos se abstenían de salvar a gentiles, esto indignaría a los gentiles y haría que estos atacaran y mataran a judíos. De modo que, salvando al gentil, indirectamente se podía salvar a un judío. Pero incluso este argumento destaca el valor diferente que se atribuye a la vida de gentiles y judíos.
[11] Catherine Nixey, _The Darkening Age: The Christian Destruction of the Classical World_ , Nueva York, Macmillan, 2017 [hay trad. cast.: _La edad de la penumbra_ , Barcelona, Taurus, 2018].
[12] Charles Allen, _Ashoka: The Search for India's Lost Emperor_ , Londres, Little, Brown, 2012, pp. 412-413.
[13] Clyde Pharr _et al_. (eds.), _The Theodosian Code and Novels, and the_ _Sirmondian Constitutions_ , Princeton, Princeton University Press, 1952, pp. 440, 467-471.
[14] _Ibid_., esp. pp. 472-473.
[15] Sofie Remijsen, _The End of Greek Athletics in Late Antiquity_ , Cambridge, Cambridge University Press, 2015, pp. 45-51.
[16] Ruth Schuster, «Why Do Jews Win So Many Nobels?», _Haaretz_ , 9 de octubre de 2013, <https://www.haaretz.com/jewish/news/1.551520>, consultado el 13 de noviembre de 2017.
13. DIOS
[1] Lillian Faderman, _The Gay Revolution: The Story of the Struggle_ , Nueva York, Simon & Schuster, 2015.
[2] Elaine Scarry, _The Body in Pain: The Making and Unmaking of the World_ , Nueva York, Oxford University Press, 1985.
14. LAICISMO
[1] Jonathan H. Turner, _Incest: Origins of the Taboo_ , Boulder, Paradigm Publishers, 2005; Robert J. Kelly _et al_., «Effects of Mother-Son Incest and Positive Perceptions of Sexual Abuse Experiences on the Psychosocial Adjustment of Clinic-Referred Men», _Child Abuse & Neglect_, 26, 4 (2002), pp. 425-441; Mireille Cyr _et al_., «Intrafamilial Sexual Abuse: Brother-Sister Incest Does Not Differ from Father-Daughter and Stepfather-Stepdaughter Incest», _Child Abuse & Neglect_, 26, 9 (2002), pp. 957-973; Sandra S. Stroebel, «Father-Daughter Incest: Data from an Anonymous Computerized Survey», _Journal of Child Sexual Abuse_ , 21, 2 (2010), pp. 176-199.
15. IGNORANCIA
[1] Steven A. Sloman y Philip Fernbach, _The Knowledge Illusion: Why We Never Think Alone_ , Nueva York, Riverhead Books, 2017; Greene, _Moral Tribes_ , _op. cit_.
[2] Sloman y Fernbach, _The Knowledge Illusion_ , _op. cit_., p. 20.
[3] Eli Pariser, _The Filter Bubble_ , Londres, Penguin Books, 2012; Greene, _Moral Tribes_ , _op. cit_.
[4] Greene, _Moral Tribes_ , _op. cit_.; Dan M. Kahan, «The Polarizing Impact of Science Literacy and Numeracy on Perceived Climate Change Risks», _Nature Climate Change_ , 2 (2012), pp. 732-735. Pero para una opinión contraria, véase Sophie Guy _et al_., «Investigating the Effects of Knowledge and Ideology on Climate Change Beliefs», _European Journal of Social Psychology_ , 44, 5 (2014), pp. 421-429.
[5] Arlie Russell Hochschild, _Strangers in Their Own Land: Anger and Mourning on the American Right_ , Nueva York, The New Press, 2016.
16. JUSTICIA
[1] Greene, _Moral Tribes_ , _op. cit_.; Robert Wright, _The Moral Animal_ , Nueva York, Pantheon, 1994.
[2] Kelsey Timmerman, _Where Am I Wearing?: A Global Tour of the Countries, Factories, and People That Make Our Clothes_ , Wiley, 2012; Kelsey Timmerman, _Where Am I Eating?: An Adventure Through the Global Food Economy_ , Hobolcen Wiley, 2013.
[3] Reni Eddo-Lodge, _Why I Am No Longer Talking to White People_ _About Race_ , Londres, Bloomsbury, 2017; Ta-Nehisi Coates, _Between the World_ _and Me_ , Melbourne, Text Publishing Company, 2015.
[4] Josie Ensor, «"Everyone in Syria Is Bad Now", Says UN War Crimes Prosecutor as She Quits Post», _The_ _New_ _York_ _Times_ , 17 de agosto de 2017, <http://www.telegraph.co.uk/news/2017/08/07/everyone-syria-bad-now-says-un-war-crimes-prosecutor-quits-post>, consultado el 18 de octubre de 2017.
[5] Por ejemplo, Helena Smith, «Shocking Images of Drowned Syrian Boy Show Tragic Plight of Refugees», _The Guardian_ , 2 de septiembre de 2015, <https://www.theguardian.com/world/2015/sep/02/shocking-image-of-drowned-syrian-boy-shows-tragic-plight-of-refugees>, consultado el 18 de octubre de 2017.
[6] T. Kogut e I. Ritov, «The singularity effect of identified victims in separate and joint evaluations», _Organizational Behavior and Human Decision Processes_ , 97, 2 (2005), pp. 106-116; D. A. Small y G. Loewenstein, «Helping a victim or helping the victim: Altruism and identifiability», _Journal of Risk and Uncertainty_ , 26, 1 (2003), pp. 5-16; Greene, _Moral Tribes_ , _op. cit_., p. 264.
[7] Russ Alan Prince, «Who Rules the World?», _Forbes_ , 22 de julio de 2013, <https://www.forbes.com/sites/russalanprince/2013/07/22/who-rules-the-world/#63c9e31d7625>, consultado el 18 de octubre de 2017.
17. POSVERDAD
[1] Julian Borger, «Putin Offers Ukraine Olive Branches Delivered by Russian Tanks», _The Guardian_ , 4 de marzo de 2014, <https://www.theguardian.com/world/2014/mar/04/putin-ukraine-olive-branches-russian-tanks>, consultado el 11 de marzo de 2018.
[2] Serhii Plokhy, _Lost Kingdom: The Quest for Empire and the Making of the Russian Nation_ , Nueva York, Basic Books, 2017; Snyder, _The Road to Unfreedom, op. cit_.
[3] Mateo de París, _Matthew Paris' English History_ , trad. de J. A. Gyles, vol. 3, Londres, Henry G. Bohn, 1854, pp. 138-141; Patricia Healy Wasyliw _, Martyrdom, Murder and Magic: Child Saints and Their Cults in Medieval Europe_ , Nueva York, Peter Lang, 2008, pp. 123-125.
[4] Cecilia Kang y Adam Goldman, «In Washington Pizzeria Attack, Fake News Brought Real Guns», _The New York Times_ , 5 de diciembre de 2016, https://www.nytimes.com/2016/12/05/business/media/comet-ping-pong-pizza-shooting-fake-news-consequences.html, consultado el 12 de enero de 2018.
[5] Leonard B. Glick, _Abraham's Heirs: Jews and Christians in Medieval Europe_ , Siracusa, Syracuse University Press, 1999, pp. 228-229.
[6] Anthony Bale, «Afterword: Violence, Memory and the Traumatic Middle Ages», en Sarah Rees Jones y Sethina Watson (eds.), _Christians and Jews in Angevin England: The York Massacre of 1190, Narrative and Contexts_ , York, York Medieval Press, 2013, p. 297.
[7] Aunque la cita se suele atribuir a Goebbels, es adecuado indicar que ni yo ni mi leal ayudante de investigación hemos podido verificar que Goebbels la escribiera ni la dijera nunca.
[8] Hilmar Hoffman, _The Triumph of Propaganda: Film and National Socialism, 1933-1945_ , Providence, Berghahn Books, 1997, p. 140.
[9] Lee Hockstader, «From A Ruler's Embrace To A Life In Disgrace», _The Washington Post_ , 10 de marzo de 1995, consultado el 29 de enero de 2018.
[10] Thomas Pakenham, _The Scramble for Africa_ , Londres, Weidenfeld & Nicolson, 1991, pp. 616-617.
18. CIENCIA FICCIÓN
[1] Aldous Huxley, _Brave New World_ , Londres, Vintage cap. 17 [hay trad. cast.: _Un mundo feliz_ , Barcelona, Plaza & Janés, 1983].
19. EDUCACIÓN
[1] Wayne A. Wiegand y Donald G. Davis (eds.), _Encyclopedia of Library History_ , Nueva York, Londres, Garland Publishing, 1994, pp. 432-433.
[2] Verity Smith (ed.), _Concise Encyclopedia of Latin American Literature_ , Londres, Nueva York, Routledge, 2013, pp. 142, 180.
[3] Cathy N. Davidson, _The New Education: How to Revolutionize the University to Prepare Students for a World in Flux_ , Nueva York, Basic Books, 2017; Bernie Trilling, _21st Century Skills: Learning for Life in Our Times_ , San Francisco, Jossey-Bass, 2009; Charles Kivunja, «Teaching Students to Learn and to Work Well with 21st Century Skills: Unpacking the Career and Life Skills Domain of the New Learning Paradigm», _International Journal of Higher Education_ , 4, 1 (2015). Para la página web del P21, véase «P21 Partnership for 21st Century Learning», http://www.p21.org/our-work/4cs-research-series, consultado el 12 de enero de 2018. Para un ejemplo de la implementación de nuevos métodos pedagógicos, véase por ejemplo la publicación de la National Education Association de Estados Unidos: «Preparing 21st Century Students for a Global Society», NEA, http://www.nea.org/assets/docs/A-Guide-to-Four-Cs.pdf, consultado el 21 de enero de 2018.
[4] Maddalaine Ansell, «Jobs for Life Are a Thing of the Past. Bring On Lifelong Learning», _The Guardian_ , 31 de mayo de 2016, <https://www.theguardian.com/higher-education-network/2016/may/31/jobs-for-life-are-a-thing-of-the-past-bring-on-lifelong-learning>.
[5] Erik B. Bloss _et al_., «Evidence for Reduced Experience-Dependent Dendritic Spine Plasticity in the Aging Prefrontal Cortex», _The Journal of Neuroscience_ , 31, 21 (2011), pp. 7831-7839; Miriam Matamales _et al_., «Aging-Related Dysfunction of Striatal Cholinergic Interneurons Produces Conflict in Action Selection», _Neuron_ , 90, 2 (2016), pp. 362-372; Mo Costandi, «Does your brain produce new cells? A skeptical view of human adult neurogenesis», _The Guardian_ , 23 de febrero de 2012, <https://www.theguardian.com/science/neurophilosophy/2012/feb/23/brain-new-cells-adult-neurogenesis>, consultado el 17 de agosto de 2017; Gianluigi Mongillo, Simon Rumpel y Yonatan Loewenstein, «Intrinsic volatility of synaptic connections – a challenge to the synaptic trace theory of memory», _Current Opinion in Neurobiology_ , 46 (2017), pp. 7-13.
20. SIGNIFICADO
[1] Karl Marx y Friedrich Engels, _The Communist Manifesto_ , Londres, Nueva York, Verso, 2012, pp. 34-35 [hay trad. cast.: _El manifiesto comunista_ , Madrid, Turner, 2005].
[2] _Ibid_., p. 35.
[3] Raoul Wootlif, «Netanyahu Welcomes Envoy Friedman to "Jerusalem, Our Eternal Capital"», _The Times of Israel_ , 16 de mayo de 2017, <https://www.timesofisrael.com/netanyahu-welcomes-envoy-friedman-to-jerusalem-our-eternal-capital>, consultado el 12 de enero de 2018; Peter Beaumont, «Israeli Minister's Jerusalem Dress Proves Controversial in Cannes», _The Guardian_ , 18 de mayo de 2017, <https://www.theguardian.com/world/2017/may/18/israeli-minister-miri-regev-jerusalem-dress-controversial-cannes>, consultado el 12 de enero de 2018; Lahav Harkov, «New 80-Majority Jerusalem Bill Has Loophole Enabling City to Be Divided», _The Jerusalem Post_ , 2 de enero de 2018, <http://www.jpost.com/Israel-News/Right-wing-coalition-passes-law-allowing-Jerusalem-to-be-divided-522627>, consultado el 12 de enero de 2018.
[4] K. P. Schroder y Robert Connon Smith, «Distant Future of the Sun and Earth Revisited», _Monthly Notices of the Royal Astronomical Society_ , 386, 1 (2008), pp. 155-163.
[5] Véase especialmente Roy A. Rappaport, _Ritual and Religion in the Making of Humanity_ , Cambridge, Cambridge University Press, 1999 [hay trad. cast.: _Ritual y religión en la formación de la humanidad_ , Madrid, Alcalá, 2016]; Graham Harvey, _Ritual and Religious Belief: A Reader,_ Nueva York, Routledge, 2005.
[6] Esta es la interpretación más común, aunque no la única, del truco de la combinación: Leslie K. Arnovick, _Written Reliquaries_ , Amsterdam, John Benjamins Publishing Company, 2006, p. 250, n. 30.
[7] Joseph Campbell, _The Hero with a Thousand Faces_ , Londres, Fontana Press, 1993, p. 235 [hay trad. cast.: _El héroe de las mil caras. Psicoanálisis del mito_ , México, Fondo de Cultura Económica, 1959].
[8] Xinzhong Yao, _An Introduction to Confucianism_ , Cambridge, Cambridge University Press, 2000, pp. 190-199.
[9] «Flag Code of India, 2002», Press Information Bureau, Government of India, http://pib.nic.in/feature/feyr2002/fapr2002/f030420021.html, consultado el 13 de agosto de 2017.
[10] <http://pib.nic.in/feature/feyr2002/fapr2002/f030420021.html>
[11] <https://www.thenews.com.pk/latest/195493-Heres-why-Indias-tallest-flag-cannot-be-hoisted-at-Pakistan-border>.
[12] Stephen C. Poulson, S _ocial Movements in Twentieth-Century Iran: Culture, Ideology and Mobilizing Frameworks_ , Lanham, Lexington Books, 2006, p. 44.
[13] Houman Sharshar (ed.), _The Jews of Iran: The History, Religion and Culture of a Community in the Islamic World_ , Nueva York, Palgrave Macmillan, 2014, pp. 52-55; Houman M. Sarshar, _Jewish Communities of Iran_ , Nueva York, Encyclopedia Iranica Foundation, 2011, pp. 158-160.
[14] Gersion Appel, _The Concise Code of Jewish Law_ , 2.ª ed., Nueva York, KTAV Publishing House, 1991, p.191.
[15] Véase especialmente Robert O. Paxton, _The Anatomy of Fascism_ , Nueva York, Vintage Books, 2005 [hay trad. cast.: _Anatomía del fascismo_ , Barcelona, Península, 2005].
[16] Richard Griffiths, _Fascism_ , Londres, Nueva York, Continuum, 2005, p. 33.
[17] Christian Goeschel, _Suicide in the Third Reich_ , Oxford, Oxford University Press, 2009.
[18] «Paris attacks: What happened on the night», BBC, 9 de diciembre de 2015, <http://www.bbc.com/news/world-europe-34818994>, consultado el 13 de agosto de 2017; Anna Cara, «ISIS expresses fury over French airstrikes in Syria; France says they will continue», CTV News, 14 de noviembre de 2015, <http://www.ctvnews.ca/world/isis-expresses-fury-over-french-airstrikes-in-syria-france-says-they-will-continue-1.2658642>, consultado el 13 de agosto de 2017.
[19] Jean de Joinville, _The Life of Saint Louis_ , en M. R. B. Shaw (ed.), _Chronicles of the Crusades_ , Londres, Penguin, 1963, p. 243; Jean de Joinville, _Vie de saint Louis_ , ed. Jacques Monfrin, París, 1995, cap. 319, p. 157.
[20] Ray Williams, «How Facebook Can Amplify Low Self-Esteem/Narcissism/Anxiety», _Psychology Today_ , 20 de mayo de 2014, <https://www.psychologytoday.com/blog/wired-success/201405/how-facebook-can-amplify-low-self-esteemnarcissismanxiety>, consultado el 17 de agosto de 2017.
[21] _Mahasatipatthana Sutta_ , cap. 2, sec. 1, ed. Vipassana Research Institute, Igatpuri, Vipassana Research Institute, 2006, pp. 12–13.
[22] _Ibid_., 5.
[23] G. E. Harvey, _History of Burma: From the Earliest Times to 10 March 1824_ , Londres, Frank Cass & Co. Ltd., 1925, pp. 252-260.
[24] Brian Daizen Victoria, _Zen at War_ , Lanham, Rowman & Littlefield, 2006; Buruma, _Inventing Japan_ , _op. cit_.; Stephen S. Large, «Nationalist Extremism in Early Showa Japan: Inoue Nissho and the "Blood-Pledge Corps Incident", 1932», _Modern Asian Studies_ , 35, 3 (2001), pp. 533-564; W. L. King, _Zen and the Way of the Sword: Arming the Samurai Psyche_ , Nueva York, Oxford University Press, 1993; Danny Orbach, «A Japanese prophet: eschatology and epistemology in the thought of Kita Ikki», _Japan Forum_ , 23, 3 (2011), pp. 339-361.
[25] «Facebook removes Myanmar monk's page for "inflammatory posts" about Muslims», _Scroll.in_ , 27 de febrero de 2018, <https://amp.scroll.in/article/870245/facebook-removes-myanmar-monks-page-for-inflammatory-posts-about-muslims>, consultado el 4 de marzo de 2018; Marella Oppenheim, «"It only takes one terrorist": The Buddhist monk who reviles Myanmar's Muslims», _The Guardian_ , 12 de mayo de 2017, <https://www.theguardian.com/global-development/2017/may/12/only-takes-one-terrorist-buddhist-monk-reviles-myanmar-muslims-rohingya-refugees-ashin-wirathu>, consultado el 4 de marzo de 2018.
[26] Jerzy Lukowski y Hubert Zawadzki, _A Concise History of Poland_ , Cambridge, Cambridge University Press, 2001, p. 163 [hay trad. cast.: _Historia de Polonia_ , Cambridge, Cambridge University Press, 2002].
21. MEDITACIÓN
[1] www.dhamma.org.
[2] Britta K. Hölzel _et al_., «How Does Mindfulness Meditation Work? Proposing Mechanisms of Action from a Conceptual and Neural Perspective», _Perspectives on Psychological Science_ , 6, 6 (2011), pp. 537-559; Adam Moore y Peter Malinowski, «Meditation, Mindfulness and Cognitive Flexibility», _Consciousness and Cognition_ , 18, 1 (2009), pp. 176-186; Alberto Chiesa, Raffaella Calati y Alessandro Serretti, «Does Mindfulness Training Improve Cognitive Abilities? A Systematic Review of Neuropsychological Findings», _Clinical Psychology Review_ , 31, 3 (2011), pp. 449-464; Antoine Lutz _et al_., «Attention Regulation and Monitoring in Meditation», _Trends in Cognitive Sciences_ , 12, 4 (2008), pp. 163-169; Richard J. Davidson _et al_., «Alterations in Brain and Immune Function Produced by Mindfulness Meditation», _Psychosomatic Medicine_ , 65, 4 (2003), pp. 564-570; Fadel Zeidan _et al_., «Mindfulness Meditation Improves Cognition: Evidence of Brief Mental Training», _Consciousness and Cognition_ , 19, 2 (2010), pp. 597-605.
##### NOTAS EXPLICATIVAS
(1) «Culturismo» y «culturista» son neologismos del autor cuyo significado en el contexto del libro no se corresponde con sus homónimos en castellano, según el Diccionario de la RAE. _(N. del T.)_
(2) Así llamaban los británicos a los guerreros hadendoas a quienes combatieron en la guerra del Mahd, en Sudán, a finales del siglo XIX, y cuyo valor ensalzó Rudyard Kipling en el poema homónimo. _(N. del T.)_
(3) Comunidad de creyentes. _(N. del T.)_
(4) Según la versión española de la Sagrada Biblia (de E. Nácar y A. Colunga, Madrid, BAC6), de donde se han tomado también las demás citas. _(N. del T.)_
(5) Pueblos con una población mayoritariamente judía. _(N. del T.)_
(6) El título original es _Brave New World_. _(N. del T.)_
(7) «Abracadabra.» _(N. del T.)_
Sapiens es un recorrido por nuestro pasado.
Homo Deus, una mirada a nuestro futuro.
21 lecciones para el siglo XXI es una exploración de nuestro presente.
¿Cómo podemos protegernos de las guerras nucleares, los cataclismos ecológicos o las tecnologías disruptivas? ¿Qué podemos hacer contra la propagación de la posverdad o la amenaza del terrorismo? ¿Qué debemos enseñar a nuestros hijos?
Con la misma prosa inteligente, fresca y provocadora, Harari vuelve a librerías con un nuevo título, 21 lecciones para el siglo XXI, en el que examina algunas de las cuestiones más urgentes de nuestro presente. El hilo dorado que recorre este estimulante nuevo libro es el desafío de mantener nuestro enfoque colectivo e individual frente al constante y desorientador cambio que estamos viviendo.
¿Somos aún capaces de entender el mundo que hemos creado?
### Sobre el autor
**Yuval Noah Harari** (1976) es profesor de historia en la Universidad Hebrea de Jerusalén. Se especializó en historia medieval e historia militar, pero tras doctorarse en Historia por la Universidad de Oxford, pasó al campo más amplio de la historia del mundo y los procesos macrohistóricos. Sus dos libros _Sapiens. De animales a dioses_ (Debate, 2014) y _Homo Deus. Breve historia del mañana_ (Debate, 2016) siguen siendo fenómenos editoriales internacionales con más de doce millones de ejemplares vendidos en todo el mundo y se han traducido a más de cuarenta y cinco idiomas.
Título original: _21 Lessons for the 21st Century_
Edición en formato digital: agosto de 2018
© 2018, Yuval Noah Harari
© 2018, Penguin Random House Grupo Editorial, S. A. U.
Travessera de Gràcia, 47-49. 08021 Barcelona
© 2018, Joandomènec Ros i Aragonès, por la traducción
TODOS LOS DERECHOS RESERVADOS
Diseño de la cubierta: Penguin Random House Grupo Editorial basado en el diseño original de Suzanne Dean
Imagen de la cubierta: © _We Share Our Chemistry with the Stars_ , Marc Quinn, óleo sobre tela. Cortesía de Marc Quinn Studio.
Penguin Random House Grupo Editorial apoya la protección del _copyright_. El _copyright_ estimula la creatividad, defiende la diversidad en el ámbito de las ideas y el conocimiento, promueve la libre expresión y favorece una cultura viva. Gracias por comprar una edición autorizada de este libro y por respetar las leyes del _copyright_ al no reproducir ni distribuir ninguna parte de esta obra por ningún medio sin permiso. Al hacerlo está respaldando a los autores y permitiendo que PRHGE continúe publicando libros para todos los lectores. Diríjase a CEDRO (Centro Español de Derechos Reprográficos, <http://www.cedro.org>) si necesita reproducir algún fragmento de esta obra.
ISBN: 978-84-9992-877-7
Composición digital: M.I. Maquetación, S.L.
www.megustaleer.com
Índice
21 lecciones para el siglo XXI
Introducción
Parte I. El desafío tecnológico
1. Decepción. El final de la historia se ha pospuesto
2. Trabajo. Cuando te hagas mayor, puede que no tengas un empleo
3. Libertad. Los macrodatos están observándote
4. Igualdad. Quienes poseen los datos poseen el futuro
Parte II. El desafío político
5. Comunidad. Los humanos tenemos cuerpo
6. Civilización. Solo existe una civilización en el mundo
7. Nacionalismo. Los problemas globales necesitan respuestas globales
8. Religión. Dios sirve ahora a la nación
9. Inmigración. Algunas culturas podrían ser mejores que otras
Parte III. Desesperación y esperanza
10. Terrorismo. No nos asustemos
11. Guerra. Jamás subestimemos la estupidez humana
12. Humildad. No somos el centro del mundo
13. Dios. No tomes el nombre de Dios en vano
14. Laicismo. Acepta tu sombra
Parte IV. Verdad
15. Ignorancia. Sabes menos de lo que crees
16. Justicia. Nuestro sentido de la justicia podría estar anticuado
17. Posverdad. Algunas noticias falsas duran para siempre
18. Ciencia ficción. El futuro no es lo que vemos en las películas
Parte V. Resiliencia
19. Educación. El cambio es la única constante
20. Significado. La vida no es un relato
21. Meditación. Simplemente, observemos
Agradecimientos
Índice alfabético
Notas
Sobre este libro
Sobre el autor
Créditos
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//======= Copyright (c) Valve Corporation, All rights reserved. ===============
//
// Purpose: Applies spherical projection to output.
//
//=============================================================================
using UnityEngine;
namespace Valve.VR
{
[ExecuteInEditMode]
public class SteamVR_SphericalProjection : MonoBehaviour
{
static Material material;
public void Set(Vector3 N,
float phi0, float phi1, float theta0, float theta1, // in degrees
Vector3 uAxis, Vector3 uOrigin, float uScale,
Vector3 vAxis, Vector3 vOrigin, float vScale)
{
if (material == null)
material = new Material(Shader.Find("Custom/SteamVR_SphericalProjection"));
material.SetVector("_N", new Vector4(N.x, N.y, N.z));
material.SetFloat("_Phi0", phi0 * Mathf.Deg2Rad);
material.SetFloat("_Phi1", phi1 * Mathf.Deg2Rad);
material.SetFloat("_Theta0", theta0 * Mathf.Deg2Rad + Mathf.PI / 2);
material.SetFloat("_Theta1", theta1 * Mathf.Deg2Rad + Mathf.PI / 2);
material.SetVector("_UAxis", uAxis);
material.SetVector("_VAxis", vAxis);
material.SetVector("_UOrigin", uOrigin);
material.SetVector("_VOrigin", vOrigin);
material.SetFloat("_UScale", uScale);
material.SetFloat("_VScale", vScale);
}
void OnRenderImage(RenderTexture src, RenderTexture dest)
{
Graphics.Blit(src, dest, material);
}
}
} | {
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This collection contains the the literary, personal and business papers of the bestselling author and playwright, Sue Townsend (1946-2014), the creator of the Adrian Mole.
First page of the original manuscript of The Secret Diary of Adrian Mole Aged 13 3/4.
The Sue Townsend Archive contains a wealth of material documenting Sue Townsend's entire literary career, from successful early plays such as Womberang (1979) to more recent novels including Number 10 (2002), Queen Camilla (2006) and the later Mole diaries.
The literary papers consist of correspondence with publishers, agents and contemporary writers; drafts, notebooks and research material relating to her books, plays and screeplays; and material relating to her contributions to newspapers and magazines. The collection also contains personal papers including family photographs, letters and ephemera; and business papers relating to Sue Townsend Ltd, including accounts, contracts and royalty statements. | {
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<?xml version="1.0" encoding="utf-8"?>
<resources>
<string name="app_name">Skeleton Wearable App</string>
<string name="intro_text">Long press to go back home.</string>
<string name="main_activity_title_text"> Main Activity </string>
<string name="grid_activity_title_text"> Grid Activity </string>
<string name="finish_activity"> Finish Activity </string>
<string name="start_timer"> Start Timer (5 sec) </string>
<string name="show_notification"> Show Notification </string>
<string name="notification_title"> Skeleton App Notification </string>
<string name="action_launch_activity">Launch Activity</string>
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Global manufacturer Terex announces £12m investment in Derry, and 100 new jobs
You are here: Home / News / Uncategorized / Global manufacturer Terex announces £12m investment in Derry, and 100 ...
The Mayor of Derry City and Strabane District Council Cllr John Boyle has welcomed the announcement today by global manufacturer Terex to invest £12m in Campsie and create up to 100 new jobs in the region.
Speaking following the announcement made earlier this morning, the Mayor said this was a major good news story for the city and district and a substantial financial commitment and vote of confidence for the City and wider North West region.
He said: "This is a fantastic news for the city region and further evidence of our city's offering in terms of skills base and investment proposition. These are high quality jobs that reflect the commitment of Terex to the region and its confidence in the city as a good place to do business.
"Terex is a major global player in materials processing equipment and their investment in the North West is hugely significant in helping to promote the region, developing our economy and creating new jobs and opportunities for all our citizens.
"The Council is committed to working with Terex and Invest NI as well as other stakeholders to support business growth and to promote Derry City and Strabane District is to the forefront in terms of attracting foreign direct investment.
"Today's announcement will not only bring employment but also demonstrates the company's confidence in the city and region as a competitive and innovative place to do business," he added.
Kieran Hegarty, Segment President, Terex Materials Processing said: "This major investment by Terex demonstrates a long-term commitment to Northern Ireland and recognises the importance of the region as a manufacturing location for our global company. We look forward to the new facility and recruits supporting our ongoing growth and development as we seek to build on the momentum of increased demand for our products globally."
Danske Bank Academy set to open with NWRC in Derry ~ Londonderry Foreign & Commonwealth Office hears about Derry growth plans | {
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Add lentils, 3 cups purified water (or Hippocrates Soup stock) and bay leaf to a small pot and bring to a boil. Once boiling, lower to a gentle simmer and continue to cook uncovered for 30 minutes.
Combine all remaining ingredients in a small bowl. Once lentils are cooked add them, along with any liquid left in the pot, and mix well. If the mixture seems dry, add a little bit of the remaining purified water (or Hippocrates Soup stock) and mix.
Place mixture in an oven-safe dish, cover and bake for 45 minutes.
Remove the cover and bake for an additional 15 minutes, allowing the top layer to become golden brown. | {
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Q: jquery .after not working for non appeneded objects I need to create two objects separately and then add one after the other and return combined object from function. My requirement is that i have to append this object outside the function and function should return 2 created objects as one.
See code below. it only returns div .. no table ?
function html() {
var _tab = $("<table>").attr("id", "table_1")
var _div = $("<div>").attr("id", "div_1").text("test");
return _div.after(_tab);
}
$("body").append(html()); // only returns div .. no table
A: I had to use .add() for this ...Solved !!!
_div.add(_tab);
A: Actually this is quite strange behavior, jquery documentation clearly states that this should work in jquery > 1.4 (http://api.jquery.com/after/#after-content-content see section inserting disconnected nodes)
However in my fiddle it does not work in jquery 1.9.1 but does work in 1.6.4->1.8.3
http://jsfiddle.net/XSXYW/
apparantly i need code to post fiddle links
What version are you using?
A: function html() {
var _tab = $("<table>").attr("id", "table_1")
_tab.html('<tr><td>Hi all</td></tr>');
var _div = $("<div>").attr("id", "div_1").text("test");
return _div.after(_tab);
}
$("body").append(html());
Is working in a glory. The problem is there is no rows in the table.
A: return _div + _tab
as simple as this
after add an element after the object and return the object only it cannot group the 2 as they are siblings and _div has to remain _div or you imagine the mess in the dom if _div was becoming div+tab ? how you'd get to _div ?
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THE RETREATS
Royal Way Retreat Center
Royal Way Retreat Centertekmiss2020-03-11T16:55:58+00:00
"Out beyond the ideas of right thinking and wrong thinking, there is a Field. When the soul lies down in that Field, words are unnecessary, even the idea "each other" does not exist. I will meet you there." ~ Rumi
Meet us in this Field of pure awareness, the vast and spacious Love of the Universe. As we make an intention to have a quiet heart and a clear eye we naturally expand and open to That Love and Light that is always there. We entrain our hearts to each other and discover anew the ancient yet imminent Presence in which we all abide and exist, seemingly separate but essentially One.
We offer a direct experience through this RENDEZVOUS WITH LOVE.
Through a total immersion with music, meditation and creative experiences, we return to this Field that Rumi pointed to. Set your intention to join us. Commit to the Love that you are. Practice being what you are and seeing with the eyes of love.
"Love sees only love, and only love sees love." ~ Ernest Holmes
Please rendezvous with us as we return to the Source of our Being and the Heart of Love.
What is Circle of Love Gathering?
David Leonard
Inspired teacher and speaker, Dr. Rev. David Leonard, embodies heart-centered living.
As a courageous example of authentic being and co-director of the Circle of Love Gathering, he has guided thousands of students across North America on a Spirit-centered journey. Currently, he is the senior minister at the Center for Spiritual Living in Huntsville, Alabama.
Lisa Ferraro
Lisa Ferraro has been singing since the age of three.
As a child, she heard vibrations emanating from flowers and trees, symphonies ringing from the garden, and she sang constantly to express what she heard. She grew up singing in churches, where she was known as "the little redhead that could sing."
Lisa has a distinct vocal style which is soulful, powerful and warm, with a vocal range that extends over four and a half octaves. In performance, she tries to connect with the audience individually and personally. "We co-create my performances," she says, "so that no two are exactly alike."
The Retreat in March 2020 has been canceled due to travel advisories related to the corona virus. Stay tuned for upcoming dates.
Lucerne Valley, California
Visit resort website
Registered attendees, click here for directions and information
Registration will open when new dates are set.
Experience our amazing, spiritual and talented partners. More will be announced as we get closer to the retreat.
Gary Lynn Floyd
Gary Lynn Floyd is an American singer-songwriter who connects straight to the heart and lifts up a room with his inspirational lyrics and soulful style.
He sings deep and meaningful music and shares these songs like a gift to audiences across the country. His style is a mix of pop, rhythm, and blues, combining silky vocals with powerful lyrics.
It is Gary's openness to divine inspiration that fuels his endless supply of musical ideas create his heart-opening lyrics and is the light that shines through his performances. With his piano and microphone, Gary is a catalyst for positive change and raises the collective vibration not only through his music but also through his welcoming presence on stage.
Kathy Rausch
Mandala Artist, Workshop Facilitator and Public Speaker and Author of "Activate Divine Creativity: The Life-Changing Magic of the Mandala"
Kathy wrote, "Activate Divine Creativity: The Life-Changing Magic of the Mandala" to help women and men become mindful and find joy in their everyday lives.
Teaching others to doodle mandalas brings Kathy great joy and helps balance her life, she hopes others will get a sense of balance and joy from the process as well.
Kathy has been painting, drawing, doodling, and creating mandalas of all kinds since 2000. She is a guest speaker and artist at retreats and conferences around the world bringing the magic of community art and mandalas to the attendees.
All attendees will receive a copy of her book, learn to draw their own mandala and be a part of a GIANT community mandala created just for Circle of Love.
Mark Accomando
Mark is an ordained minister with the Centers for Spiritual Living, former senior minister at CSL Raleigh NC and now serves as an assistant staff minister at CSL Palm Springs. Mark is an inspiring public speaker and teacher sharing insightful messages for following the passion of the heart and cultivating a deep inner sense of peace and wholeness that leads to living a happy, productive and a fully self-expressed life.
In 2011 Mark founded Evoke Peace Now and wrote an evidenced-based curriculum called Spiritual Education in Recovery with an intended focus to work with people in early stages of recovering and healing from patterns of addiction. His curriculum includes empowering lessons with a universal approach to meditation and spirituality that supports people on the healing path through experiential workshops, simple daily practices, inspiring messages, guided meditations, and Spiritual Nature Adventure outings.
He published, "An Ancient Peace" guided peace and healing meditations CD and currently is working on his next CD "Soothing Peace, sleep and healing" which focuses on assisting sleep, pain management, and emotional regulation all backed by his beautiful Native American flute music, Piaste Gongs and Tibetan singing bowls. Mark creates a deeply healing space through guided meditations, mantra, breath work, empowering lessons and healing sound immersions (sound baths) that align the body, mind, emotions, and spirit in their natural state of wholeness.
Mark has developed a private practice of spiritual guidance and shares simple Practical Spiritual practices and principles. He currently shares his offerings throughout Palm Springs CA and the Coachella Valley.
Natalia Zukerman
Musician, painter and educator Natalia Zukerman grew up in New York City, studied art at Oberlin, started her mural business Off The Wall in San Francisco, began her songwriting career in Boston, and now resides, writes, plays, teaches and paints in Brooklyn, NY.
Having released seven independent albums on Weasel Records and her own label Talisman Records, Zukerman has toured internationally as a solo performer since 2005.
Her music can be heard on the soundtrack of several seasons of The L Word and ABC Family's Chasing Life. She also created the score for The Arch of Titus, an independent film created for Yeshiva University and a Harvard online course called Poetry in America.
In May 2018, she was the artist in residence at the cell theatre in New York City where she developed her multimedia one woman show, The Women Who Rode Away. She has since released the soundtrack and accompanying book of the show and is currently on tour throughout North America in support of that project.
Rob McDonald
Rob has been a bassist and vocalist for The Agape International Spiritual Center since 1992.
A self-taught musician, bassist and singer/songwriter, Rob McDonald, began his musical career at an early age. Growing up in a musical household, McDonald learned to play drums at the age of six. Because his three older brothers each played drums, it seemed the logical choice; however, as McDonald's talent grew, he found it harder and harder to find a full set of drums readily available. Because his brothers were always using the drums for local club gigs McDonald decided it was time to try a new instrument, a guitar. Emulating the style of legendary guitarist, Jimi Hendrix, McDonald learned to play the guitar left-handed and upside down. (not knowing Jimi's right-handed guitar was actually strung left-handed) This proved to be a difficult method for playing open cords, and that was when, at the age of 13, he picked up a bass.
Proving to be a talented musician, McDonald performed with his high school's concert and jazz bands, and upon graduation from Cooley High, moved to Los Angeles with a Detroit based band called Paradise.
Local gigs and an international tour in Japan soon followed. Honing his skills while working local clubs and in national touring productions of "Your Arms Are Too Short to Box with God" starring Jennifer Holiday, and "The Wiz" starring Grace Jones, Peabo Bryson, Tony Terry, Cece Peniston, and Howard Hewitt, McDonald began to attract the attention of other national artists including, Brenda Russell, Jeffery Osbourne, Chaka Khan, Cindy Bradley, Peter White and Rick Braun. A two-year touring engagement with Johnny "Guitar" Watson, performance opportunities with Billy Preston, legendary music icon, Tom Jones, a Tonight Show appearance with Toni Braxton, and European engagements with The Funk Bros, George Clinton and the Al McKay All-stars are among career highlights. McDonald toured 6 years with Grammy award-winning guitarist, Norman Brown, whose Summer Storm tour has included guests artists, Peabo Bryson, Richard Elliott, Marion Meadows, Eric Darius, Jeff Lorber, Chante Moore, Paul Taylor, Alex Bugnon, Phil Perry, and Mindy Abair. McDonald, counts among his early influences such greats as Larry Graham, Sly Stone, Johnny "Guitar' Watson, Bootsy Collins, Parliment Funkadelic Stanley Clark, Louis Johnson, EW&F, Louis Satterfield, is a compilation of versatility, resulting from over 30 years in the music industry.
Royal Way Spiritual Center
The March 26- 29, 2020 Retreat has been postponed due to travel advisories related to the corona virus. Stay tuned for new dates soon.
Each retreat is unique with a mixture of the spiritual warriors you see below. We work with the very best musicians, speakers, artists, poets, and workshop facilitators.
"The Circle of Love Gathering is a joyous and warm experience of friends, consciousness, music, depth, connection and freedom. There is something special and a bit hard to define that is completely nourishing to the soul."
Dr. Kathy Hearn
"Save this time to retreat, allowing all the walls and all the doing to cease. This time is designed for you simply to reveal what is already within, so you may deeply experience and recognize your True Essential Self: The Self that knows no walls and is free. This True Self arises and shines when we take the time to nurture, cultivate and celebrate it! When you return home, you naturally share the heart that has been awakened!"
Rev. Mark Accomando
"I have never been to an event that has changed me so intensely for the good. The combination of professional, spiritual music, speakers, workshops and mandala art was powerful. I left on such a spiritual high that I knew I would come back again and again. I woke up singing many of the songs I heard for months. I made friends from all over. Don't miss this opportunity to awaken your heart and deepen the love in your soul.
From Gary Lynn Floyd
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Marracash (* 22. Mai 1979 in Nicosia, Sizilien, als Fabio Bartolo Rizzo) ist ein italienischer Rapper und Musikproduzent.
Karriere
Auf Sizilien geboren, wuchs Rizzo im Mailänder Viertel Barona auf, wohin seine Eltern zum Arbeiten gezogen waren. Mit 18 Jahren machte er seine ersten Schritte in der Mailänder Hip-Hop-Szene, wobei er Marracash (Bezug auf Marrakesch) als Künstlernamen wählte, aufgrund seines südländischen Aussehens. Schließlich wurde er Teil des Rapkollektivs Dogo Gang. In diesem Umfeld begann er auch, besonders mit den drei Mitgliedern von Club Dogo (wie er Teil des Kollektivs) zusammenzuarbeiten: 2004 war er am Mixtape PMC Vs Club Dogo (mit der Porzione Massiccia Crew) beteiligt, danach an Regular (mit Don Joe und Grand Agent) sowie an Hashishinz Sound vol. 1 (Guè Pequeno und Deleterio).
Im Jahr 2005 veröffentlichte Marracash beim unabhängigen Label Area seine erste Single Popolare, die wieder von Don Joe produziert wurde. Dieser folgte das Mixtape Roccia Music vol. 1, auf dem er wieder mit einer Reihe von Rappern aus seinem Umfeld zusammenarbeitete. 2007 war er auf Struggle Music von Frank Siciliano und DJ Shocca zu hören.
Mit einem Plattenvertrag bei Universal kam für Marracash 2008 der Durchbruch. Dem selbstbetitelten Debütalbum ging die Single Badabum Cha Cha voraus. Dabei blieb er dem Kollektiv treu, Don Joe und Deleterio fungierten als Produzenten und Beatmaker. Sowohl Single als auch Album erreichten die Top 10 der Charts. 2010 reichte er das zweite Album Fino a qui tutto bene nach, für das darauf enthaltene Lied Rivincita arbeitete er mit der Sängerin Giusy Ferreri zusammen. Für das dritte Album wählte Marracash einen unkonventionellen Veröffentlichungsweg: Wöchentlich veröffentlichte er ein neues Lied auf YouTube, das Album King del rap setzte sich anschließend aus genau diesen (zehn) Liedern zusammen. Als Reaktion auf die Erdbeben in Norditalien 2012 nahm er zusammen mit Emis Killa, Club Dogo und J-Ax als Rapper per Emilia die Charity-Single Se il mondo fosse auf; mit Emis Killa arbeitete er auch im Lied Giusto un giro zusammen.
Den Anfängen treu, war Marracash 2013 auf den Soloalben Bravo ragazzo und Musica commerciale von Guè Pequeno bzw. Jake La Furia (Club Dogo) zu hören. Außerdem gründete er mit dem Produzenten Shablo das unabhängige Label Roccia Music, das wiederum als Kollektiv fungiert, und veröffentlichte mit Tayone die Single La tipa del tipo. Nach einer Zusammenarbeit mit Deleterio, Luchè und Jake La Furia 2014 kündigte Marracash mit der Single Status sein gleichnamiges Album an, das Anfang 2015 erschien. Wieder zusammen mit Guè Pequeno begann er daraufhin ein neues Projekt, das 2016 in das Kollaboalbum Santeria mit mehreren erfolgreichen Singles mündete.
Diskografie
Studioalben
Singles
Weitere Singles
S.E.N.I.C.A.R. (2011) – (50.000+)
A volte esagero (2015) – (50.000+)
XDVRMX (2015) – (25.000+)
Gastbeiträge
Weitere Gastbeiträge
2007: Puro Bogotà (Club Dogo feat. Vincenzo & Marracash, IT: )
Weblinks
Offizielle Website
Marracash bei Rockol.it
Belege
Rapper
Autor eines Beitrags beim Sanremo-Festival
Pseudonym
Italiener
Geboren 1979
Mann | {
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} | 2,344 |
\chapter{Asymptotic Safety}
\begin{abstract}
Asymptotic safety is a set of conditions,
based on the existence of a nontrivial fixed point for the renormalization group flow,
which would make a quantum field theory consistent to arbitrarily high energies.
After introducing the basic ideas of this approach, I review the present evidence
in favor of an asymptotically safe quantum field theory of gravity.
\end{abstract}
\section{Introduction}
The problems of perturbative Quantum Field Theory (QFT) in
relation to the UV behaviour of gravity
have led to widespread pessimism about the possibility of constructing
a fundamental QFT of gravity.
Instead, we have become accustomed to thinking of General Relativity
(GR) as an effective field theory, which only gives an accurate
description of gravitational physics at low energies.
The formalism of effective field theories provides a coherent framework
in which quantum calculations can be performed even if the theory is not renormalizable.
For example, quantum corrections to the gravitational potential
have been discussed by several authors; see
Bjerrum-Bohr {\it et al.}\ (2003) and references therein.
This continuum QFT description is widely expected to break down at very short
distances and to be replaced by something dramatically different
beyond the Planck scale.
There is however no proof that continuum QFT will fail, and the current situation
may just be the result of the lack of suitable technical tools.
Weinberg (1979) described a generalized, nonperturbative notion
of renormalizability called ``asymptotic safety'' and suggested that
GR may satisfy this condition, making it a consistent QFT at all energies.
The essential ingredient of this approach is the existence of a Fixed Point (FP)
in the Renormalization Group (RG) flow of gravitational couplings.
Several calculations were performed using the $\epsilon$--expansion around $d=2$
dimensions, supporting the view that gravity is asymptotically safe
(Gastmans {\it et al.}\ (1978), Christensen \& Duff (1978), Kawai \& Ninomiya (1990)).
However, the continuation to four dimensions ($\epsilon\to 2$)
was questionable and this line of research slowed down for some time.
It was revived by Reuter (1998) who calculated the gravitational
beta functions directly in $d=4$ dimensions, using a truncation of an
Exact Renormalization Group Equation (ERGE).
Matter couplings were considered by Dou \& Percacci (1998);
then Souma (1999) found that these beta functions admit a non--Gau\ss ian FP.
Further work by Lauscher \& Reuter (2002a,b), Percacci (2006), Codello \& Percacci (2006)
strongly supports the view that this FP is not a mere artifact of the approximations made.
An extensive review of this subject can be found in Niedermaier \& Reuter (2006).
In section 1.2 I introduce the general idea of asymptotic safety;
the reader is referred to Weinberg (1979) for a more detailed discussion.
In section 1.3 I describe some peculiarities of the gravitational RG,
which derive from the dual character of the metric as a dynamical field
and as definition of lengths.
Recent evidence for a FP, coming mainly from the ERGE, is reviewed in section 1.4.
Some relations to other approaches to quantum gravity
are briefly mentioned in section 1.5.
\medskip
\section{The general notion of asymptotic safety}
\smallskip
The techniques of effective QFT have been recognized as being
of great generality and are now quite pervasive in particle physics.
An effective field theory is described by an effective action $\Gamma_k$
which can be thought of as the result of having integrated out all fluctuations
of the fields with momenta larger than $k$.
We need not specify here the physical meaning of $k$:
for each application of the theory one will have to identify the
physically relevant variable acting as $k$
(in particle physics it is usually some external momentum).
One convenient definition of $\Gamma_k$ that we shall use here is as follows.
We start from a (``bare'') action $S[\phi_A]$
for multiplets of quantum fields $\phi_A$,
describing physics at an energy scale $k_0$.
We add to it a term $\Delta S_k[\phi_A]$, quadratic in the $\phi_A$,
which in Fourier space has the form:
$\Delta S_k[\phi]=\int d^d q \phi_A R_k^{AB}(q^2)\phi_B$.
The kernel $R_k^{AB}(q^2)$, henceforth called the cutoff function,
is chosen in such a way that the propagation of
field modes $\phi_A(q)$ with momenta $q<k$ is suppressed, while
field modes with momenta $k<q<k_0$ are unaffected.
We formally define a $k$--dependent generating functional of connected Green functions
$$
W_k[J^A]=-\log \int (d\phi_A) \exp\left(-S[\phi_A]-\Delta S_k[\phi_A]-\int J^A\phi_A\right)
\eqno(1.2.1)
$$
and a modified $k$--dependent Legendre transform
$$
\Gamma_k[\phi_A]=W_k[J^A]-\int J^A\phi_A -\Delta S_k[\phi_A]\ ,\eqno(1.2.2)
$$
where $\Delta S_k$ has been subtracted.
The ``classical fields'' $\frac{\delta W_k}{\delta J^A}$
are denoted again $\phi_A$ for notational simplicity.
This functional interpolates continuously between $S$, for $k=k_0$,
and the usual effective action $\Gamma[\phi_A]$,
the generating functional of one--particle irreducible Green functions, for $k=0$.
It is similar in spirit, but distinct from, the Wilsonian effective action.
In the following we will always use this definition of $\Gamma_k$,
but much of what will be said should be true also with other definitions.
In the case of gauge theories there are complications due to the fact that
the cutoff interferes with gauge invariance.
One can use a background gauge condition, which circumvents these
problems by defining a functional of two fields, the background field and the classical field;
the effective action $\Gamma_k$ is then obtained by identifying these fields.
See Pawlowski (2005), or Reuter (1998) for the case of gravity.
The effective action $\Gamma_k[\phi_A]$, used at tree level,
gives an accurate description of processes occurring at momentum scales of order $k$.
In general it will have the form
$\Gamma_k(\phi_A,g_i)=\sum_i g_i(k) {\cal O}_i(\phi_A)$,
where $g_i$ are runnning coupling constants and
${\cal O}_i$ are all possible operators constructed with the fields
$\phi_A$ and their derivatives, which are compatible
with the symmetries of the theory.
It can be thought of as a functional on ${\cal F}\times{\cal Q}\times R^+$,
where ${\cal F}$ is the configuration space of the fields, ${\cal Q}$
is an infinite dimensional manifold parametrized by the coupling constants,
and $R^+$ is the space parametrized by $k$.
The dependence of $\Gamma_k$ on $k$ is given by
$\partial_t\Gamma_k(\phi_A,g_i)=\sum_i \beta_i(k) {\cal O}_i(\phi_A)$
where $t=\log(k/k_0)$ and
$\beta_i(g_j,k)=\partial_t g_i$ are the beta functions.
Dimensional analysis implies the scaling property
$$
\Gamma_k(\phi_A,g_i)=\Gamma_{bk}(b^{d_A} \phi_A ,b^{d_i} g_i )\ ,\eqno(1.2.3)
$$
where $d_A$ is the canonical dimension of $\phi_A$,
$d_i$ is the canonical dimension of $g_i$, and $b\in R^+$
is a positive real scaling parameter
\footnote{We assume that the coordinates are dimensionless,
as is natural in curved space,
resulting in unconventional canonical dimensions.
The metric is an area.}.
One can rewrite the theory in terms of dimensionless fields
$\tilde\phi_A=\phi_A k^{-d_A}$ and dimensionless couplings $\tilde g_i=g_i k^{-d_i}$.
A transformation (1.2.3) with parameter $b=k^{-1}$ can be used to
define a functional $\tilde\Gamma$ on $({\cal F}\times{\cal Q}\times R^+)/R^+$:
$$
\tilde\Gamma(\tilde\phi_A,\tilde g_i):=
\Gamma_{1}(\tilde\phi_A ,\tilde g_i )=
\Gamma_k(\phi_A,g_i)\ .
\eqno(1.2.4)
$$
Similarly, $\beta_i(g_j,k)=k^{d_i}a_i(\tilde g_j)$
where $a_i(\tilde g_j)=\beta_i(\tilde g_j,1)$.
There follows that the beta functions of the dimensionless couplings,
$$
\tilde\beta_i(\tilde g_j)\equiv\partial_t \tilde g_i=a_i(\tilde g_j)-d_i\tilde g_i
\eqno(1.2.5)
$$
depend on $k$ only implicitly via the $\tilde g_j(t)$.
The effective actions $\Gamma_k$ and $\Gamma_{k-\delta k}$
differ essentially by a functional integral over field modes
with momenta between $k$ and $k-\delta k$.
Such integration does not lead to divergences, so the beta functions
are automatically finite.
Once calculated at a certain scale $k$, they are automatically determined
at any other scale by dimensional analysis.
Thus, the scale $k_0$ and the ``bare'' action $S$ act just as initial conditions:
when the beta functions are known,
one can start from an arbitrary initial point on ${\cal Q}$
and follow the RG trajectory in either direction.
The effective action $\Gamma_k$ at any scale $k$ can be obtained integrating the flow.
In particular, the UV behaviour can be studied by taking the limit $k\to\infty$.
It often happens that the flow cannot be integrated beyond
a certain limiting scale $\Lambda$, defining the point
at which some ``new physics'' has to make its appearance.
In this case the theory only holds
for $k<\Lambda$ and is called an ``effective'' or ``cutoff'' QFT.
It may happen, however, that the limit $t\to\infty$
can be taken; we then have a self-consistent description of a certain set
of physical phenomena which is valid for arbitrarily high energy scales
and does not need to refer to anything else outside it.
In this case the theory is said to be ``fundamental''.
The couplings appearing in the effective action can be related
to physically measurable quantities such as cross
sections and decay rates. Dimensional analysis implies that aside
from an overall power of $k$, such quantities only depend on
dimensionless kinematical variables $X$, like scattering angles and ratios
of energies, and on the dimensionless couplings $\tilde g_i$
(recall that usually $k$ is identified with one of the momentum variables).
For example, a cross section can be expressed as
$\sigma=k^{-2}\tilde\sigma(X,\tilde g_i)$.
If some of the couplings $\tilde g_i$ go to infinity
when $t\to\infty$, also the function $\tilde\sigma$ can be expected to diverge.
A sufficient condition to avoid this problem is to assume that
in the limit $t\to\infty$ the RG trajectory tends to
a FP of the RG, {\it i.e.}\ a point $\tilde g_*$
where $\tilde\beta_i(\tilde g_{*})=0$ for all $i$.
The existence of such a FP is the first requirement for asymptotic safety.
Before discussing the second requirement, we have to understand
that one needs to impose this condition only on a subset of all couplings.
The fields $\phi_A$ are integration variables, and a redefinition
of the fields does not change the physical content of the theory.
This can be seen as invariance under a group ${\cal G}$ of coordinate
transformations in ${\cal F}$.
There is a similar arbitrariness in the choice of coordinates
on ${\cal Q}$, due to the freedom of redefining the couplings $g_i$.
Since, for given $k$, $\Gamma_k$ is assumed to be the ``most general''
functional on ${\cal F}\times{\cal Q}$ (in some proper sense),
given a field redefinition $\phi'=\phi'(\phi)$
one can find new couplings $g'_i$ such that
$$
\Gamma_k(\phi'_B(\phi_A),g_i)=\Gamma_k(\phi_A,g'_i)\ .\eqno(1.2.6)
$$
At least locally, this defines an action of ${\cal G}$ on ${\cal Q}$.
We are then free to choose a coordinate system
which is adapted to these trasformations, in the sense that
a subset $\{g_{\hat \imath}\}$ of couplings transform nontrivially
and can be used as coordinates in the orbits of ${\cal G}$,
while a subset $\{g_{\bar \imath}\}$ are invariant under the action
of ${\cal G}$ and define coordinates on ${\cal Q}/{\cal G}$.
The couplings $g_{\hat \imath}$ are called redundant or inessential,
while the couplings $g_{\bar \imath}$ are called essential.
In an adapted parametrization there exists, at least locally,
a field redefinition $\bar\phi(\phi)$ such that using (1.2.6)
the couplings $g_{\hat \imath}$ can be given fixed values $(g_{\hat \imath})_0$.
We can then define a new action $\bar\Gamma$ depending only on the
essential couplings:
$$
\bar\Gamma_k(\bar\phi_A,g_{\bar \imath}):=
\Gamma_k(\bar\phi_A,g_{\bar \imath},(g_{\hat \imath})_0)
=\Gamma_k(\phi_A;g_{\bar \imath},g_{\hat \imath})\ .\eqno(1.2.7)
$$
Similarly, the values of the redundant couplings can be fixed also
in the expressions for measurable quantities,
so there is no need to constrain their RG flow in any way:
they are not required to flow towards a FP.
For example, the action of a scalar field theory in a background $g_{\mu\nu}$,
$$
\Gamma_k(\phi,g_{\mu\nu};Z_\phi,\lambda_{2i})=\int d^4x\sqrt{g}\left[
{\frac{Z_\phi}{2}}g^{\mu\nu}\partial_\mu\phi\partial_\nu\phi
+\lambda_2\phi^2+\lambda_4\phi^4+\ldots
\right]\ \eqno(1.2.8)
$$
has the scaling invariance
$$
\Gamma_k(c\phi,g_{\mu\nu};c^{-2}Z_\phi,c^{-2i}\lambda_{2i})=
\Gamma_k(\phi,g_{\mu\nu};Z_\phi,\lambda_{2i})\ ,\eqno(1.2.9)
$$
which is a special case of (1.2.6).
There exists an adapted coordinate system where $Z$ is inessential
and $\bar\lambda_{2i}=\lambda_{2i}Z_\phi^{-i}$
are the essential coordinates.
A transformation with $c=\sqrt{Z_\phi}$ then leads to $Z_\phi=1$,
leaving the essential couplings unaffected.
A comparison of (1.2.4) and (1.2.7) shows that $k$ behaves like
a redundant coupling.
In ordinary QFT's, it is generally the case that for each multiplet
of fields $\phi_A$ there is a scaling invariance like (1.2.9)
commuting with (1.2.3). One can use these invariances to eliminate
simultaneously $k$ and one other redundant coupling per field multiplet;
the conventional choice is to eliminate the wave function
renormalization $Z_A$.
No conditions have to be imposed on the RG flow of the $Z_A$'s,
and the anomalous dimensions $\eta_A=\partial_t\log Z_A$,
at a FP, can be determined by a calculation.
More generally, (1.2.3) and (1.2.6) can be used
to eliminate simultaneously the dependence of $\Gamma_k$ on $k$ and
on the inessential couplings, and to define an effective action
$\tilde\Gamma(\tilde\phi_A,\tilde g_{\bar \imath})$, depending only on the
dimensionless essential couplings
$\tilde g_{\bar \imath}=g_{\bar \imath}k^{-d_{\bar\imath}}$.
It is only on these couplings that one has to impose the FP
condition $\partial_t\tilde g_{\bar \imath}=0$.
We can now state the second requirement for asymptotic safety.
Denote $\tilde{\cal Q}=({\cal Q}\times R^+)/({\cal G}\times R^+)$
the space parametrized by the dimensionless essential couplings
$\tilde g_{\bar \imath}$.
The set ${\cal C}$ of all points in $\tilde{\cal Q}$ that flow towards the
FP in the UV limit is called the UV critical surface.
If one chooses an initial point lying on ${\cal C}$, the whole trajectory
will remain on ${\cal C}$ and will ultimately flow towards the FP
in the UV limit.
Points that lie outside ${\cal C}$ will generally flow towards infinity
(or other FP's).
Thus, demanding that the theory lies on the UV critical surface
ensures that it has a sensible UV limit.
It also has the effect of reducing the arbitrariness in the choice of the coupling constants.
In particular, if the UV critical surface is finite dimensional,
the arbitariness is reduced to a finite number of parameters,
which can be determined by a finite number of experiments.
Thus, a theory with a FP and a finite dimensional UV
critical surface has a controllable UV behaviour, and is predictive.
Such a theory is called ``asymptotically safe''.
A perturbatively renormalizable, asymptotically free field theory
such as QCD is a special case of an asymptotically safe theory.
In this case the FP is the Gau\ss ian FP, where
all couplings vanish, and the critical surface is spanned,
near the FP, by the couplings that are renormalizable in the perturbative sense
(those with dimension $d_{\bar\imath}\geq 0$).
The requirement of renormalizability played an important role
in the construction of the Standard Model (SM) of particle physics.
Given that the SM is not a complete theory, and that some of its
couplings are not asymptotically free, nowadays it is
regarded an effective QFT, whose nonrenormalizable couplings
are suppressed by some power of momentum over cutoff.
On the other hand, any theory that includes both the SM and gravity
should better be a fundamental theory.
For such a theory, the requirement of asymptotic safety will have the same
significance that renormalizability originally had for the SM.
\medskip
\section{The case of gravity}
\smallskip
We shall use a derivative expansion of $\Gamma_k$:
$$
\Gamma_k(g_{\mu\nu};g^{(n)}_i)=
\sum_{n=0}^\infty \sum_i g^{(n)}_i(k) {\cal O}^{(n)}_i(g_{\mu\nu})\ ,\eqno(1.3.1)
$$
where ${\cal O}^{(n)}_i=\int d^dx\,\sqrt{g}{\cal M}^{(n)}_i$ and ${\cal M}^{(n)}_i$
are polynomials in the curvature tensor and its derivatives
containing $2n$ derivatives of the metric; $i$ is an index that
labels different operators with the same number of derivatives.
The dimension of $g^{(n)}_i$ is $d_n=d-2n$.
The first two polynomials are just ${\cal M}^{(0)}=1$, ${\cal M}^{(1)}=R$.
The corresponding couplings are
$g^{(1)}=-Z_g=-\frac{1}{16\pi G}$,
$g^{(0)}=2 Z_g\Lambda$, $\Lambda$ being the cosmological constant.
Newton's constant $G$ appears in $Z_g$, which in linearized Einstein theory
is the wave function renormalization of the graviton.
Neglecting total derivatives, one can choose as terms with
four derivatives of the metric
${\cal M}^{(2)}_1=C^2$ (the square of the Weyl tensor) and
${\cal M}^{(2)}_2=R^2$.
We also note that the coupling constants of higher derivative gravity
are not the coefficients $g^{(2)}_i$ but rather their inverses $2\lambda=(g^{(2)}_1)^{-1}$ and
$\xi=(g^{(2)}_2)^{-1}$.
Thus,
$$
\Gamma_k^{(n\leq 2)}=\int d^dx\,\sqrt{g}\left[
2 Z_g\Lambda-Z_gR+\frac{1}{2\lambda}C^2+
\frac{1}{\xi}R^2\right]\ .\eqno(1.3.2)
$$
As in any other QFT, $Z_g$ can be eliminated from the
action by a rescaling of the field.
Under constant rescalings of $g_{\mu\nu}$, in $d$ dimensions,
$$
\Gamma_k(g_{\mu\nu};g^{(n)}_i)=
\Gamma_{bk}(b^{-2}g_{\mu\nu};b^{d-2n}g^{(n)}_i)\ .\eqno(1.3.3)
$$
This relation is the analog of (1.2.9) for the metric,
but also coincides with (1.2.3), the invariance at the basis of dimensional analysis;
fixing it amounts to a choice of unit of mass.
This is where gravity differs from any other field theory
(Percacci \& Perini (2004), Percacci (2007)).
In usual QFT's such as (1.2.8), one can exploit the two invariances (1.2.3) and (1.2.9)
to eliminate simultaneously $k$ and $Z$ from the action.
In the case of pure gravity there is only one such invariance and
one has to make a choice.
If we choose $k$ as unit of mass, we can define the effective action,
$$
\tilde\Gamma(\tilde g_{\mu\nu};\tilde Z_g,\tilde\Lambda,\ldots)=
\Gamma_1(\tilde g_{\mu\nu};\tilde Z_g,\tilde\Lambda,\ldots)=
\Gamma_k(g_{\mu\nu};Z_g,\Lambda,\ldots)\ ,\eqno(1.3.4)
$$
where $\tilde g_{\mu\nu}=k^{2}g_{\mu\nu}$,
$\tilde Z_g=\frac{Z_g}{k^2}=\frac{1}{16\pi \tilde G}$,
$\tilde\Lambda=\frac{\Lambda}{k^2}$, etc..
There is then no freedom left to eliminate $Z_g$.
Physically measurable quantities will depend explicitly on $\tilde Z_g$,
so by the arguments of section 1.2, we have to impose
that $\partial_t \tilde Z_g=0$, or equivalently $\partial_t \tilde G=0$, at a FP.
Alternatively, one can use (1.3.3) to set $Z_g=1$:
this amounts to working in Planck units.
Then we can define a new action
\footnote{Note that to completely eliminate $Z_g$ from the action
one has to scale the whole metric, and not just the fluctuation, as is customary in perturbation theory.}:
$$
\Gamma'_{k'}(g'_{\mu\nu};\Lambda',\ldots)=
\Gamma_{k'}(g'_{\mu\nu};\Lambda',1,\ldots)=
\Gamma_k(g_{\mu\nu};\Lambda,Z_g,\ldots)\ ,
\eqno(1.3.5)
$$
where $g'_{\mu\nu}=16\pi Z_gg_{\mu\nu}$,
$\Lambda'=\frac{1}{16\pi Z_g}\Lambda$,
$k'=\sqrt{\frac{1}{16\pi Z_g}}k$ etc.
are the metric, cosmological constant and cutoff measured in Planck units.
In this case, the dependence on $G$ disappears;
however, the beta functions and measurable quantities
will depend explicitly on $k'$.
In theories of gravity coupled to matter, the number of these scaling invariances
is equal to the number of field multiplets, so the situation is the same
as for pure gravity. (Without gravity, it is equal to the number of field
multiplets plus one, due to dimensional analysis.)
The situation can be summarized by saying that when the metric
is dynamical, $k$ should be treated as one of the couplings, and that
there exist parametrizations where $k$ is redundant or $G$
is redundant, but not both.
Scale invariance is usually thought to imply that a theory contains
only dimensionless parameters, and the presence at a FP of nonvanishing
dimensionful couplings may seem to be at odds with
the notion that the FP theory is scale--invariant.
This is the case if only the fields are scaled, and not the couplings.
In an asymptotically safe QFT, scale invariance is realized in another way:
all dimensionful couplings scale with $k$ as required by their canonical dimension.
In geometrical terms, the RG trajectories in ${\cal Q}$
lie asymptotically in an orbit of the transformations (1.2.3) and (1.2.6).
This also has another consequence.
At low momentum scales $p\ll \sqrt{Z_g}$ the couplings are not expected to run
and the terms in the action (1.3.2) with four derivatives are
suppressed relative to the term with two derivatives by a factor $p^2/Z_g$.
On the other hand in the FP regime, if we evaluate the couplings at $k=p$,
the running of $Z_g$ exactly compensates the effect
of the derivatives: both terms are of order $p^4$.
From this point of view, {\it a priori} all terms in (1.3.1) could be equally important.
From the existence of a FP for Newton's constant there would immediately follow
two striking consequences.
First, the cutoff measured in Planck units would be bounded.
This is because the cutoff in Planck units, $k'=k\sqrt{G}$, is equal to the square root of
Newton's constant in cutoff units, $\sqrt{\tilde G}$.
Since we have argued that the latter must have a finite limit at a FP,
then also the former must do so.
This seems to contradict the notion that the UV limit is defined by $k\to\infty$.
The point is that only statements about dimensionless quantities
are physically meaningful, and the statement ``$k\to\infty$'' is
meaningless until we specify the units.
In a fundamental theory one cannot refer to any
external ``absolute'' quantity as a unit, and any internal quantity
which is chosen as a unit will be subject to the RG flow.
If we start from low energy ($k'\ll 1$) and we increase $k$,
$k'$ will initially increase at the same rate, because in this regime
$\partial_t G\approx 0$; however, when $k'\approx 1$ we reach the FP regime
where $G(k)\approx\tilde G_*/k^2$ and therefore $k'$ stops growing.
The second consequence concerns the graviton anomalous dimension, which in $d$
dimensions is $\eta_g=\partial_t \log Z_g=\partial_t \log\tilde Z_g+d-2$.
Since we have argued that $\partial_t\tilde Z_g=0$ at a gravitational FP,
if $\tilde Z_{g*}\not=0$ we must have $\eta_{g*}=d-2$.
The propagator of a field with anomalous dimension $\eta$ behaves like $p^{-2-\eta}$,
so one concludes that at a nontrivial gravitational FP the graviton propagator
behaves like $p^{-d}$ rather than $p^{-2}$, as would follow from a naive
classical interpretation of the Einstein-Hilbert action.
Similar behaviour is known also in other gauge theories away from
the critical dimension, see {\it e.g.}\ Kazakov (2003).
\medskip
\section{The Gravitational Fixed Point}
\smallskip
I will now describe some of the evidence that has accumulated in favor of
a nontrivial gravitational FP.
Early attempts were made in the context of the
$\epsilon$--expansion around two dimensions ($\epsilon=d-2$), which yields
$$
\beta_{\tilde G}=\epsilon \tilde G-q \tilde G^2\ .
\eqno(1.4.1)
$$
Thus there is a UV--attractive FP at $\tilde G_*=\epsilon/q$.
The constant $q=\frac{38}{3}$ for pure gravity
(Weinberg (1979), Kawai \& Ninomiya (1990),
see Aida \& Kitazawa (1997) for two--loop results).
Unfortunately, for a while it was not clear whether one could
trust the continuation of this result to four dimensions ($\epsilon=2$).
Most of the recent progress in this approach has come from the application
to gravity of the ERGE.
It was shown by Wetterich (1993) that the effective action $\Gamma_k$
defined in (1.2.2) satisfies the equation
$$
\partial_t\Gamma_k=
\frac{1}{2}\mathrm{STr}\left(\frac{\delta^2\Gamma_k}{\delta\phi_A\delta\phi_B}+R_k^{AB}\right)^{-1}
\partial_tR_k^{BA}\ ,\eqno(1.4.2)
$$
where STr is a trace over momenta as well as over particle species
and any spacetime or internal indices,
including a sign -1 for fermionic fields and a factor 2 for complex fields.
In the case of gauge theories, the ghost fields have to be included among the $\phi_A$.
Comparing the r.h.s. of the ERGE with the $t$-derivative of (1.3.1)
one can extract the beta functions.
Note that in general the cutoff function $R_k$ may depend on the couplings and therefore
the term $\partial_t R_k$ in the r.h.s. of (1.4.2) contains the beta functions.
Thus, extracting the beta functions from the ERGE implies solving an equation
where the beta functions appear on both sides.
At one loop, the effective action $\Gamma_k$ is
${\rm Tr}\log\frac{\delta^2 (S+\Delta S_k)}{\delta\phi\delta\phi}$;
it satisfies an equation which is formally identical to (1.4.2) except that in the r.h.s.
the running couplings $g_i(k)$ are replaced everywhere by the ``bare''
couplings $g_i(k_0)$, appearing in $S$.
We will call ``one--loop beta functions'' those extracted from the ERGE
ignoring the derivatives of the couplings that may appear in the r.h.s. of (1.4.2).
It is usually impossible to get the beta functions for all couplings,
so a common procedure is to consider a truncation of the theory
where the effective action $\Gamma_k$ contains only a (finite or infinite) subset
of all possible terms.
In these calculations there is no small parameter to tell us
what terms can be safely neglected, so the choice of truncation
has to be motivated by physical insight.
On the other hand, in this way one can obtain genuine nonperturbative information.
This and other similar ERGEs have been applied to a variety of problems.
One can reproduce the universal one loop beta functions of familiar theories,
and in more advanced approximations the results are quantitatively
comparable to those obtainable by other methods.
See Bagnuls \& Bervilliers (2001), Berges {\it et al.}\ (2002), Pawlowski (2005)
for reviews.
The simplest way to arrive at a gravitational FP in four dimensions,
avoiding the technical complications of graviton propagators,
is through the contributions of matter loops
to the beta functions of the gravitational couplings.
Thus, consider gravity coupled to $n_S$ scalar fields,
$n_D$ Dirac fields, $n_M$ gauge (Maxwell) fields, all massless and minimally coupled.
A priori, nothing is assumed about the gravitational action.
For each type of field $\phi_A$ we choose the cutoff function in such a way that
$P_k(\Delta^{(A)})=\Delta^{(A)}+R_k(\Delta^{(A)})$,
where $\Delta^{(S)}=-\nabla^2$ on scalars, $\Delta^{(D)}=-\nabla^2+\frac{R}{4}$ on Dirac fields
and $\Delta^{(M)}=-\nabla^2\delta^\mu_\nu+R^\mu{}_\nu$
on Maxwell fields in the gauge $\alpha=1$.
Then, the ERGE is simply
\begin{equation*}
\partial_t\Gamma_k=\sum_{A=S,D,M}
\frac{n_A}{2}{\rm STr}_{(A)}\left(\frac{\partial_t P_k}{P_k}\right)
-{n_M}{\rm Tr}_{(S)}\left(\frac{\partial_t P_k}{P_k}\right)\ ,
\eqno(1.4.3)
\end{equation*}
where ${\rm STr}=\pm{\rm Tr}$ depending on the statistics,
and the last term comes from the ghosts.
Using integral transforms and the heat kernel expansion,
the trace of a function $f$ of $\Delta$ can be expanded as
\begin{equation*}
{\rm Tr}f(\Delta)=
\sum_{n=0}^\infty Q_{2-n}(f) B_{2n}(\Delta)
\eqno(1.4.4)
\end{equation*}
where the heat kernel coefficients $B_{2n}(\Delta)$ are linear combinations
of the ${\cal O}^{(n)}_i$, $Q_n(f)=(-1)^n f^{(n)}(0)$ for $n\leq0$
and $Q_n(f)$ are given by Mellin transforms of $f$ for $n>0$
\footnote{This technique is used also in some noncommutative geometry models,
see Chamseddine \& Connes (1996).}.
In this way one can write out explicitly the r.h.s. of (1.4.3) in terms of
the ${\cal O}^{(n)}_i$ and read off the beta functions.
When $N\to\infty$, this is the dominant contribution to the
gravitational beta functions, and graviton loops can be neglected
(Tomboulis (1977), Smolin (1982), Percacci (2005)).
The functions $a^{(n)}_i$ defined in (1.2.5)
become numbers;
with the so--called optimized cutoff function
$R_k(z)=(k^2-z)\theta(k^2-z)$, discussed in Litim (2001, 2004), they are
\begin{align*}
a^{(0)}=&\frac{n_S-4n_D+2n_M}{32\pi^2}\ ,
\qquad a^{(1)}=\frac{n_S+2n_D-4n_M}{96\pi^2}\ ,\\
a^{(2)}_1=&\frac{6 n_S+36 n_D+72 n_M}{11520\pi^2}\ ,
\qquad a^{(2)}_2=\frac{10 n_S}{11520\pi^2}\ ,
\end{align*}
while $a^{(n)}_i=0$ for $n\geq 3$.
The beta functions (1.2.5) are then
\begin{equation*}
\partial_t \tilde g^{(n)}_i=(2n-4)\tilde g^{(n)}_i+a^{(n)}_i\ .
\eqno(1.4.5)
\end{equation*}
For $n\not= 2$ this leads to a FP
$$
\tilde g^{(n)}_{i*}=\frac{a^{(n)}_i}{4-2n}\ ,
\eqno(1.4.6)
$$
in particular we get
\begin{equation*}
\tilde\Lambda_*=-\frac{3}{4}\frac{n_S-4n_D+2 n_M}{n_S+2n_D-4n_M}\ ,\ \
\tilde G_*=\frac{12\pi}{-n_S-2n_D+4n_M}\ .
\eqno(1.4.7)
\end{equation*}
For $n=2$, one gets instead
$g^{(2)}_i(k)=g^{(2)}_i(k_0)+a^{(2)}_i\ln(k/k_0)$,
implying asymptotic freedom for the couplings $\lambda$ and $\xi$ of (1.3.2).
Remarkably, with this cutoff all the higher terms are zero at the FP.
The critical exponents are equal to the canonical dimensions of the $g^{(n)}$'s,
so $\Lambda$ and $G$ are UV--relevant (attractive),
$\lambda$ and $\xi$ are marginal and all the higher terms are UV--irrelevant.
Note that in perturbation theory $G$ would be UV--irrelevant (nonrenormalizable).
At the nontrivial FP the quantum corrections conspire with the classical
dimensions of $\Lambda$ and $G$ to reconstruct the dimensions of $g^{(0)}$ and $g^{(1)}$.
This does not happen at the Gau\ss ian FP, where the transformation between
$\tilde G$ and $\tilde g^{(1)}$ is singular.
\begin{figure}
{\includegraphics{flow.eps}}
\caption{The flow in the upper $\tilde\Lambda$--$\tilde G$ plane for pure gravity with
higher derivative terms at one loop, eq.(1.4.8). All other couplings are set to zero.
The nontrivial FP at (0.221,1.389) is UV--attractive with eigenvalues $(-4,-2)$,
the one in the origin is UV--attractive along the $\tilde\Lambda$ axis with eigenvalue $-2$
and repulsive in the direction of the vector $(1/2\pi,1)$ with eigenvalue $2$.}
\end{figure}
Using the same techniques, the one loop beta functions for gravity
with the action (1.3.2) have been calculated by Codello \& Percacci (2006).
The beta functions for $\lambda$ and $\xi$ agree with those
derived in the earlier literature on higher derivative gravity
(Fradkin \& Tseytlin (1982), Avramidy \& Barvinsky (1985),
de Berredo--Peixoto \& Shapiro (2005)).
These couplings tend logarithmically to zero
with a fixed ratio $\omega=-3\lambda/\xi\to \omega_*=-0.023$.
The beta functions of $\tilde\Lambda$ and $\tilde G$
differ from the ones that were given in the earlier literature
essentially by the first two terms of the expansion (1.4.4).
In a conventional calculation of the effective action these terms
would correspond to quartic and quadratic divergences,
which are normally neglected in dimensional regularization,
but are crucial in generating a nontrivial FP.
Setting the dimensionless couplings to their FP--values, one obtains:
\begin{equation*}
\beta_{\tilde\Lambda} = 2\tilde\Lambda+\frac{2\tilde G}{\pi}-q_*\tilde G \tilde\Lambda\ ,\qquad \qquad
\beta_{\tilde G}=2\tilde G-q_* \tilde G^2\ .
\eqno(1.4.8)
\end{equation*}
where $q_*\approx 1.440$.
This flow is qualitatively identical to the flow in the $N\to\infty$ limit,
and is shown in fig.1.
In order to appreciate the full nonperturbative content of the ERGE,
let us consider pure gravity in the Einstein--Hilbert truncation,
{\it i.e.}\ neglecting terms with $n\geq 2$.
In a suitable gauge the operator
$\frac{\delta^2\Gamma_k}{\delta g_{\mu\nu}\delta g_{\rho\sigma}}$
is a function of $-\nabla^2$ only.
Then, rather than taking as $\Delta$ the whole linearized wave operator,
as we did before, we use (1.4.4) with $\Delta=-\nabla^2$.
In this way we retain explicitly the dependence on $\Lambda$ and $R$.
Using the optimized cutoff, with gauge parameter $1/\alpha=Z$, the ERGE gives
\begin{align*}
\beta_{\tilde \Lambda}=&
\frac{-2(1-2\tilde\Lambda)^2\tilde\Lambda
+\frac{36-41\tilde\Lambda+42\tilde\Lambda^2-600\tilde\Lambda^3}{72\pi}\tilde G
+\frac{467-572\tilde\Lambda}{288\pi^2}\tilde G^2}
{(1-2\tilde\Lambda)^2-\frac{29-9\tilde\Lambda}{72\pi}\tilde G}\tag{1.4.9}\\
\beta_{\tilde G}=&
\frac{2(1-2\tilde\Lambda)^2\tilde G
-\frac{373-654\tilde\Lambda+600\tilde\Lambda^2}{72\pi}\tilde G^2}
{(1-2\tilde\Lambda)^2-\frac{29-9\tilde\Lambda}{72\pi}\tilde G}\tag{1.4.10}
\end{align*}
This flow is shown in Figure 2.
\begin{figure}
{\includegraphics{flowspirals.eps}}
\caption{The flow in the Einstein--Hilbert truncation, see Eq.(1.4.9-10).
The nontrivial FP at $\tilde\Lambda=0.171$, $\tilde G=0.701$ is UV--attractive with eigenvalues $-1.69\pm 2.49i$. The Gau\ss ian FP is attractive along the $\tilde\Lambda$--axis
with eigenvalue $-2$ and repulsive in the direction $(0.04,1.00)$ with eigenvalue $2$.}
\end{figure}
Lauscher \& Reuter (2002a), Reuter \& Saueressig (2002) have studied
the gauge-- and cutoff--dependence of the FP in the Einstein--Hilbert truncation.
The dimensionless quantity $\Lambda'=\Lambda G$ (the cosmological constant
in Planck units) and the critical
exponents have a reassuringly weak dependence on these parameters.
This has been taken as a sign that the FP is not an artifact of the truncation.
Lauscher \& Reuter (2002b) have also studied the ERGE
including a term $R^2$ in the truncation.
They find that in the subspace of $\tilde{\cal Q}$ spanned by $\tilde\Lambda,\tilde G,1/\xi$,
the non--Gau\ss ian FP is very close to the one of the Einstein--Hilbert truncation,
and is UV--attractive in all three directions.
More recently, the FP has been shown to exist if the Lagrangian density is
a polynomial in $R$ of order up to six (Codello, Percacci and Rahmede (2008)).
In this truncation the UV critical surface is three dimensional.
There have been also other generalizations.
Niedermaier (2003) considered the RG flow for dimensionally reduced $d=4$
gravity, under the hypothesis of the existence of two Killing vectors.
This subsector of the theory is parametrized by infinitely many couplings,
and has been proved to be asymptotically safe.
Matter couplings have been considered by
Percacci \& Perini (2003a,b). Consider the general action
$$
\Gamma_k(g_{\mu\nu},\phi)=\int d^4x\,\sqrt{g}
\left(-\frac{1}{2}g^{\mu\nu}\partial_\mu\phi\partial_\nu\phi
-V(\phi^2)+F(\phi^2)R\right)\ ,
\eqno(1.4.11)
$$
where $V$ and $F$ are arbitrary functions of $\phi^2$, analytic at $\phi^2=0$.
This action has a so-called Gau\ss ian--Matter FP, meaning that only the coefficients
of the $\phi$-independent terms in (1.4.11) (namely $g^{(0)}$ and $g^{(1)}$) are nonzero.
The critical surface has dimension four and there are no marginal operators.
In the presence of other, minimally coupled matter fields,
the dimension of the critical surface can be larger, and
it is easy to find theories where a polynomial potential
in $\phi$ is renormalizable and asymptotically free.
Thus, gravity seems to provide a solution to the so--called triviality problem
of scalar field theory.
It is tempting to speculate with Fradkin \& Tseytlin (1982)
that in the presence of gravity
all matter interactions are asymptotically free.
One loop calculations reported in Buchbinder {\it et al.}\ (1992), Robinson \& Wilczek (2005)
indicate that this may be the case also for gauge and Yukawa interactions.
Then, in studying the FP, it would be consistent to neglect matter
interactions, as we did in the $1/N$ expansion.
If this is the case, it may become possible to show asymptotic safety
for realistic unified theories including gravity and the SM.
For the time being, the gravitational FP has been found
with a number of different approximations:
the $2+\epsilon$ expansion, the $1/N$ expansion,
polynomial truncations with a variety of cutoffs and gauges,
the two Killing vector reduction
and the most general four--derivative gravity theory at one loop.
The fact that all these methods yield broadly consistent results
should leave little doubt about the existence of a nontrivial
FP with the desired properties.
\medskip
\section{Other approaches and applications}
\smallskip
In this final section we briefly comment on the relation of asymptotic safety
to other approaches and results in quantum gravity.
Gravity with the Einstein--Hilbert action has been shown by Goroff \& Sagnotti (1986)
and van de Ven (1992) to be perturbatively nonrenormalizable at two loops.
Stelle (1977) proved that the theory with action (1.3.2) and $\Lambda=0$
is perturbatively renormalizable:
all divergences can be absorbed into redefinitions of the couplings.
In general, asymptotic safety does not imply that in the UV limit
only a finite number of terms in (1.3.1) survive:
there could be infinitely many terms, but there would be relations between their
coefficients in such a way that only a finite number of parameters would be left free.
At one loop or in the large--$N$ limit, the ERGE predicts
that the UV critical surface can be parametrized by
the four couplings $\tilde\Lambda$, $\tilde G$, $\lambda$ and $\xi$,
the first two being nonzero at the FP and UV--relevant, the latter two being
asymptotically free and marginal.
Thus, at least in some approximations, asymptotic safety implies
that near the FP quantum corrections to the action (1.3.2) will not generate
new terms when one takes the UV limit.
This is very similar to the result of Stelle.
The main difference lies therein, that the perturbative proof
holds at the Gau\ss ian FP while the statement of asymptotic safety
holds near the non--Gau\ss ian one.
According to the ERGE, the Gau\ss ian FP is unstable, and moving
by an infinitesimal amount towards positive $\tilde G$
(even with $\tilde\Lambda=0$)
would cause the system to be dragged in the direction of the repulsive
eigenvector towards the non-Gau\ss ian FP (see fig.1).
It is unclear whether in a more accurate description it will still
be possible to describe the UV limit of the theory by an action containing
finitely many terms.
We now come to other nonperturbative approaches to quantum gravity.
Monte Carlo simulations of quantum gravity
have found evidence of a phase transition which can be related
to the existence of a gravitational FP.
Hamber \& Williams (2004) review various results and arguments,
mainly from quantum Regge calculus,
supporting the claim that the mass critical exponent $\nu$ is equal to 1/3.
In a theory with a single coupling constant $\tilde G$
we have $-1/\nu=\beta'_{\tilde G}(\tilde G_*)$, so for a rough comparison we can
solve (1.4.10) with $\tilde\Lambda=0$, finding a FP at $\tilde G_*=1.21$
with $\beta'(\tilde G_*)\approx -2.37$.
The agreement is numerically not very good for a universal quantity,
but it might perhaps be improved by taking into account the flow
of the cosmological constant.
In the so--called causal dynamical triangulation approach,
recent numerical simulations have produced quantum worlds that exhibit
several features of macroscopic four--dimensional spacetimes
(see Ambj\o rn, Jurkiewicz and Loll's contribution to this volume).
In particular they have also studied diffusion processes in such quantum spacetimes
and found that the spectral dimension characterizing them
is close to two for short diffusion times and to four for long diffusion times.
This agrees with the expectation from asymptotic safety and can be seen as further
independent evidence for a gravitational FP, as we shall mention below.
The physical implications of a gravitational FP and, more generally, of the
running of gravitational couplings, are not yet well understood.
First and foremost, one would expect asymptotic safety to lead to new insight into the local,
short--distance structure of a region of spacetime.
The boundedness of the cutoff in Planck units, derived in section 1.3,
would be in accord with the widely held expectation of some kind of discrete spacetime
structure at a fundamental level.
In particular, it may help understand the connection
to theories such as loop quantum gravity, which predict that areas
and volumes have quantized values.
However, the discussion in section 1.3 should make it clear
that the issue of a minimal length in quantum gravity
may have limited physical relevance,
since the answer depends on the choice of units.
Another point that seems to emerge is that the spacetime geometry cannot be understood in
terms of a single metric: rather, there will be a different effective metric
at each momentum scale.
This had been suggested by Floreanini \& Percacci (1995a,b),
who calculated the scale dependence of the metric using an effective
potential for the conformal factor.
Such a potential will be present in the effective action $\Gamma_k$ before the
background metric is identified with the classical metric (as mentioned in section 1.2).
A scale dependence of the metric has also been postulated by Magueijo \& Smolin (2004)
in view of possible phenomenological effects.
Lauscher \& Reuter (2005) have suggested the following picture of a fractal spacetime.
Dimensional analysis implies that in the FP regime
$\langle g_{\mu\nu}\rangle_k=k^{-2}(\tilde g_0)_{\mu\nu}$, where $\tilde g_0$,
defined as in (1.3.4),
is a fiducial dimensionless metric that solves the equations of motion of $\Gamma_{k_0}$.
For example, in the Einstein--Hilbert truncation, the effective metric $\langleg_{\mu\nu}\rangle_k$
is a solution of the equation $R_{\mu\nu}=\Lambda_k g_{\mu\nu}$, so
$$
\langle g_{\mu\nu}\rangle_k=
\frac{\Lambda_{k_0}}{\Lambda_{k}}\langle g_{\mu\nu}\rangle_{k_0}
\approx \left(\frac{k_0}{k}\right)^2\langle g_{\mu\nu}\rangle_{k_0}=k^{-2}(\tilde g_0)_{\mu\nu}\ ,
\eqno(1.5.1)
$$
where $\approx$ means ``in the FP regime''.
The fractal spacetime is described by the collection of all these metrics.
A phenomenon characterized by an energy scale $k$ will ``see''
the effective metric $\langle g_{\mu\nu}\rangle_k$.
For a (generally off-shell) free particle with four--momentum $p_\mu$
it is natural to use $k\propto p$, where $p=\sqrt{(\tilde g_0)^{\mu\nu}p_\mu p_\nu}$.
Its inverse propagator is then $\langle g^{\mu\nu}\rangle_{p}p_\mu p_\nu$.
At low energy $\langle g_{\mu\nu}\rangle_k$ does not
depend on $k$ and the propagator has the usual $p^{-2}$ behaviour;
in the FP regime, (1.5.1) implies instead that it is proportional to $p^{-4}$.
Its Fourier transform has a short--distance
logarithmic behaviour which is characteristic of two dimensions,
and agrees with the aforementioned numerical results on the spectral
dimension in causal dynamical triangulations.
This agreement is encouraging, because it suggests that the two approaches are
really describing the same physics.
When applied to gravitons in four dimensions (and only in four dimensions!)
it also agrees with the general prediction, derived in the end of section 1.3,
that $\eta_g=2$ at a nontrivial gravitational FP.
The presence of higher derivative terms in the FP action
raises the old issue of unitarity:
as is well--known, the action (1.3.2) describes, besides a massless graviton,
also particles with Planck mass and negative residue (ghosts).
From a Wilsonian perspective, this is clearly not very significant:
to establish the presence of a propagator pole at the mass $m_P$ one should
consider the effective action $\Gamma_k$ for $k\approx m_P$,
which may be quite different from the FP action.
Something of this sort is known to happen in the theory of strong interactions:
at high energy they are described by a renormalizable and asymptotically free theory
(QCD), whose action near the UV (Gau\ss ian) FP describes quarks and gluons.
Still, none of these particles appears in the physical spectrum.
As in QCD, matching the UV description to low energy phenomena
may turn out to be a highly nontrivial issue.
A change of degrees of freedom could be involved.
From this point of view one should not assume {\it a priori} that the metric appearing
in the FP action is ``the same'' metric that appears in the low energy description of GR.
Aside from a field rescaling, as discussed in section 1.2,
a more complicated functional field redefinition may be necessary,
perhaps involving the matter fields, as exemplified in Tomboulis (1996).
Unless at some scale the theory was purely topological, it will always involve a metric
and from general covariance arguments it will almost unavoidably contain an
Einstein--Hilbert term.
This explains why the Einstein--Hilbert action, which describes GR at macroscopic distances,
may play an important role also in the UV limit, as the results of section 1.4 indicate.
With this in mind, one can explore the consequences
of a RG running of gravitational couplings also in other regimes.
Motivated in part by possible applications to the hierarchy problem,
Percacci (2007) considered a theory with an action of the form (1.4.11),
in the intermediate regime between the scalar mass and the Planck mass.
Working in cutoff units (1.3.4), it was shown that the warped geometry
of the Randall--Sundrum model can be seen as a geometrical
manifestation of the quadratic running of the mass.
For applications to black hole physics,
Bonanno \& Reuter (2000) have included quantum gravity effects
by substituting $G$ with $G(k)$ in the Schwarzschild metric,
where $k=1/r$ and $r$ is the proper distance from the origin.
This is a gravitational analog of the \"Uhling approximation of QED.
There is a softening of the singularity at $r=0$, and it is predicted
that the Hawking temperature goes to zero for Planck mass black holes,
so that the evaporation stops at that point.
In a cosmological context, it would be natural to identify the scale $k$
with a function of the cosmic time.
Then, in order to take into account the RG evolution of the couplings,
Newton's constant and the cosmological constant can be replaced
in Friedman's equations by the effective Newton's constant
and the effective cosmological constant calculated from the RG flow.
With the identification $k=1/t$, where $t$ is cosmic time,
Bonanno \& Reuter (2002) have applied this idea to the Planck era,
finding significant modifications to the cosmological evolution;
a more complete picture extending over all of cosmic history
has been given in Reuter \& Saueressig (2005).
It has also been suggested that an RG running of gravitational
couplings may be responsible for several astrophysical or cosmological effects.
There is clearly scope for various interesting speculations,
which may even become testable against new cosmological data.
Returning to the UV limit, it can be said that
asymptotic safety has so far received relatively little attention,
when compared to other approaches to quantum gravity.
Establishing this property is obviously only the first step:
deriving testable consequences is equally important and may prove an even
greater challenge.
Ultimately, one may hope that asymptotic safety will play a similar role
in the development of a QFT of gravity as asymptotic freedom played
in the development of QCD.
\section{Acknowledgements}
I wish to thank R. Floreanini, D. Dou, D. Perini, A. Codello and C. Rahmede
for past and present collaborations, and M. Reuter for many discussions.
\vfill
\break
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\break
\centerline{\bf Questions and answers}
\bigskip
{\bf Q}: Could an asymptotically safe theory be regarded as an
approximation to another more fundamental theory, or does it have
to be regarded as a self-contained fundamental theory?
{\bf A}: The asymptotic safety programme is very closely related to the
formalism of effective field theories and both possibilities
can be envisaged.
If a fixed point with the desired properties did exist, then mathematically
it would be possible to take the limit $k\to\infty$ and one could call this
a fundamental theory.
It would do for gravity what the Weinberg--Salam model originally did
for electroweak interactions.
However, experience shows that today's fundamental theory
may become tomorrow' effective theory.
The renormalizability of the Weinberg--Salam model was important in establishing
it as a viable theory but nowadays this model is widely regarded
as an effective theory whose nonrenormalizable couplings are suppressed
by powers of momentum over some cutoff. In a distant future, the same could
happen to an asymptotically safe theory of gravity.
To understand this point better, notice that
in order to hit the fixed point as $k\to\infty$,
one would have to place the initial point of the flow
in the critical surface with ``infinite precision''.
In the case of the standard model, where the use of
perturbative methods is justified, this corresponds to setting
all couplings with negative mass dimension {\it exactly} equal to zero.
Even assuming that the property of asymptotic safety could be firmly
established theoretically, because measurements are always imprecise,
it is hard to see how one could ever establish
experimentally that the world is described by such a theory.
One could say at most that experiments are compatible with the theory
being fundamental.
On the other hand suppose that the theory requires drastic modification
at an energy scale of, say, a billion Planck masses, perhaps because
of the existence of some presently unknown interaction.
Then at the Planck scale one would expect the dimensionless couplings
of the theory ($\tilde g_i$) to lie off the critical surface by an amount
of the order of some power of one in a billion.
Suppose we follow the flow in the direction of decreasing energies
starting from a scale which is much larger than one, and much less
than a billion Planck masses.
Since the fixed point is IR--attractive in all directions except
the ones in the critical surface, starting from a generic point in the space
of coupling constants, the theory will be drawn quickly towards the critical surface.
Going towards the infrared, the flow at sub--Planckian scales
will then look as if it had originated from the fixed point,
up to small deviations from the critical surface
which may be hard or impossible to measure.
Thus, the formalism can accommodate both effective and
fundamental theories of gravity. The most important point is that
asymptotic safety would allow us to push QFT beyond the Planck scale,
up to the next frontier, wherever that may be.
\medskip
{\bf Q}: What is your take on the issue of continuum versus discrete picture of
spacetime, coming from a renormalization group perspective? If gravity is
asymptotically safe, would it imply that a continuum description of
spacetime is applicable at all scales, or one can envisage a role of
discrete spacetime structures even in this case? How would a breakdown of
the continuum description show up in the ERG approach?
{\bf A}: First of all it should be said that the renormalization group can be
realized both in continuum and discrete formulations and is likely to play a role
in quantum gravity in either case. It should describe the transition from
physics at the ``lattice'' or UV cutoff scale down to low energies.
Then, one has to bear in mind that when one formulates a quantum field theory
in the continuum but with a cutoff $\Lambda$, it is impossible to resolve
points closer that $1/\Lambda$, so the continuum should be regarded as a
convenient kinematical framework that is devoid of physical reality.
If the asymptotic safety program could be carried through literally as described,
it would provide a consistent description of physics down to arbitrarily
short length scales, and in this sense the continuum would become, at least
theoretically, a reality.
Of course, it would be impossible to establish experimentally the continuity of spacetime
in the mathematical sense, so this is not a well--posed physical question.
What is in principle a meaningful physical question, and may become answerable
sometimes in the future, is whether spacetime is continuous down to, say,
one tenth of the Planck length.
But even then, the answer may require further qualification.
Recall that in order to define a distance one has to specify a unit of lengths.
Units can ultimately be traced to some combination of
the couplings appearing in the action. For example, in Planck units one takes
the square root of Newton's constant as a unit of length.
Because the couplings run, when the cutoff is sent to infinity the distance
between two given points could go to zero, to a finite limit or to infinity
depending on the asymptotic behaviour of the unit.
In principle it seems possible that spacetime looks discrete in certain
units and continuous in others.
Then, even if asymptotic safety was correct, it need not be in conflict
with models where spacetime is discrete.
\medskip
{\bf Q}: What differences, in formalism and results, can one expect in the ERG
approach, if one adopts a 1st order (e.g. Palatini) or BF-like (e.g.
Plebanski) description of gravity?
{\bf A}: Writing the connection as the sum of the Levi--Civita connection and
a three-index tensor $\Phi$, one can always decompose an action for independent
connection and metric into the same action written for the Levi-Civita connection,
plus terms involving $\Phi$. The effects due to $\Phi$ will be similar to those
of a matter field.
In the case when the action is linear in curvature, and possibly quadratic in torsion
and nonmetricity, up to a surface term the action for $\Phi$ is just a mass term,
implying that $\Phi$ vanishes on shell.
In this case one expects the flow to be essentially equivalent to that obtained in the
Einstein-Hilbert truncation plus some matter fields, although this has not been explicitly checked yet.
The presence of a mass for $\Phi$ of the order of the Planck mass
suggests that a decoupling theorem is at work and that $\Phi$ (or equivalently the connection)
will become propagating degrees of freedom at the Planck scale.
This is indeed the case when the action involves terms quadratic in curvature
(which can be neglected at low energies).
Then the field $\Phi$ propagates, and has quartic self-interactions.
There will be new couplings, that may influence the running of Newton's constant,
for example. But again, this should be equivalent to fourth-order
gravity plus matter.
\medskip
{\bf Q}: You mention that the results of the ERG seem to point out that spacetime
structure cannot be described in terms of a single metric for any momentum
scale. How would one notice, in the RG approach, that it cannot be described
by a metric field at all, but that a description in terms of connections or
even a non-local one would be more appropriate, say, at the Planck scale?
{\bf A}: I do in fact expect that an independent connection will manifest itself at the
Planck scale, as I have indicated in my answer to another question, though
I don't think that this will be forced upon us by the ERG.
The scale-dependence of the metric could manifest itself as violations
of the equivalence principle, or perhaps as Lorentz-invariance
violations or deformations of the Lorentz group.
There is much work to be done to understand this type of phenomenology.
Even more radically, it is possible that gravity is just the ``low energy''
manifestation of some completely different physics,
as suggested in the article by Dreyer. This would probably imply a failure
of the asymptotic safety programme, for example a failure to find a
fixed point when certain couplings are considered.
\medskip
{\bf Q}: Can you please comment on possibility of extending the ERG approach to
the Lorentzian signature or to the case of dynamical space topology?
{\bf A}: So far the ERG has been applied to gravity in conjunction with the background
field method. Calculations are often performed in a convenient background,
such as (Euclidean) de Sitter space, but the beta functions obtained in this way
are then completely general and independent of the background metric and
spacetime topology. The choice of a background is merely a calculational trick.
It is assumed that the beta functions are also independent of the signature of the
background metric, although this point may require further justification.
One should also stress in this connection that the use of the background field
method and of the background field gauge does not make this a
``background-dependent'' approach. On the contrary, when properly implemented
it guarantees that the results are background-independent.
\end{document}
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Форум свободной России (ФСР) — конференция российской оппозиции, проходящая два раза в год в Вильнюсе (Литва). Форум был основан в марте 2016 года Гарри Каспаровым и Иваном Тютриным — бывшим исполнительным директором российского демократического движения «Солидарность».
1 февраля 2023 года Генеральной прокуратурой России форум был признан нежелательной организацией на территории Российской Федерации.
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Форум ставит перед собой задачу формирования интеллектуальной альтернативы действующему в России политическому режиму. По заявлению организаторов, «любой желающий, разделяющий ценности демократии и считающий Россию неотъемлемой частью цивилизованного международного сообщества, может стать участником, спонсором и организатором Форума». По словам Ивана Тютрина, «единственным фактором, препятствующим участию, является позиция "крымнашиста"», то есть сторонника агрессии в отношении Украины. Поэтому в форуме невозможно участие таких деятелей, как Мария Баронова, Вячеслав Мальцев и Сергей Удальцов.
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Форум проходит в течение двух дней. В ходе дискуссионных панелей обсуждаются такие темы, как противодействие российской пропаганде в России и за рубежом, перспективы международного давления на путинский режим посредством санкций, экономическая ситуация, отношения между Россией и Западом, стратегия российской оппозиции в условиях действующего в стране режима.
Чтобы стать участником форума, необходимо предоставить при регистрации две рекомендации от политиков, активистов оппозиции, журналистов или правозащитников.
В разные годы в форуме участвовали Гарри Каспаров, Олег Сенцов, Сергей Гуриев, Аркадий Бабченко, Геннадий Гудков, Марат Гельман, Евгений Чичваркин, Илья Пономарёв, Ольга Романова, Альфред Кох, Леонид Невзлин, Маша Гессен, Александр Гольдфарб, Евгений Киселёв, Леонид Гозман, Роман Доброхотов, Андрей Илларионов, Владислав Иноземцев, Алексей (Профессор) Лебединский, Марк Фейгин, Андрей Солдатов, Артемий Троицкий, Мария Алёхина, Александр Морозов, Айдер Муждабаев, Валентин Наливайченко, Вигаудас Ушацкас, Андрей Пионтковский, Андрюс Кубилюс, Игорь Чубайс, Лев Пономарёв, Михаил Крутихин, Борис Райтшустер, Евгения Чирикова, Божена Рынска, Михаил Светов, Дэвид Саттер, Томас Венцлова, Александр Кынев, Елена Фанайлова, Лилия Шевцова, Константин Эггерт, Андрей Санников, Аркадий Янковский, Игорь Эйдман, Елена Лукьянова, Игорь Яковенко, Сергей Гуляев.
7-й Форум
Седьмой форум проходит 8-9 июня 2019 года в городе Тракай в 26 километрах от Вильнюса. На него съехались представители 60 регионов России. По состоянию на конец мая, на Форум записалось рекордное число участников — 442 (большинство — жители России), что говорит о подъёме оппозиционного движения.
Перед началом программы было зачитано заявление ФСР по поводу задержания специального корреспондента «Медузы» Ивана Голунова.
Основные темы 7-го Форума:
Изменение общественных настроений в России
Украина после президентских выборов и перспективы российско-украинских отношений
Русофилия или русофобия?
Информационный терроризм путинского телевизора и его жертвы
Новые формы гражданского активизма в России
Власть и общество: границы допустимого сотрудничества
Беларусь и проблемы безопасности Восточной Европы
Существует ли в российской политике «правый фланг»?
Будущее России: распад или сохранение единого государства
Члены Татарского правительства в изгнании обратились к Форуму свободной России с просьбой признать независимость республик Идель-Урала. В ответ редакционная комиссия Форума опубликовала комментарий Вадима Сидорова, в котором он подверг эту просьбу критике ввиду отсутствия выраженной воли соответствующих народов и высокой доли русского населения на указанных территориях. Сидоров предложил обсуждать этот вопрос в ходе образования обновленной федерации или иного содружества новых государств на месте нынешней РФ.
Всеобщим голосованием участников 7-го Форума было принято решение о расширении санкционного «Списка Путина» на 28 персон.
Приняты заявления в поддержу задержанного журналиста Ивана Голунова, в поддержку активистов Открытой России, в отношении которых были возбуждены уголовные дела.
Участники Форума единогласно поддержали резолюцию в поддержку инициативы общественности Торонто по наименованию улицы в парке Эрл Бейлс в честь Бориса Немцова.
8-й Форум
Прошёл 9-10 ноября 2019 года. На него собрались более трёхсот человек, из них 68 % приехали из России. В дискуссиях принимали участие в том числе Гарри Каспаров, Олег Сенцов, Лев Пономарёв, Марат Гельман и другие.
Ключевые темы: изменение и развитие репрессивного аппарата и способы противостояния репрессиям, возможные стратегии российской оппозиции применительно к участию в выборах, прошедшие выборы в Мосгордуму, экологические протесты в регионах, социально — экономическая ситуация в России, перспективы развития российско-украинского конфликта на Донбассе, перспективы и угрозы интеграции России и Беларуси.
Вначале форум почтил память недавно скончавшегося оппозиционера Владимира Буковского. Затем активисты и политики из регионов рассказали о своей деятельности и перспективах.
В честь 30-летия падения Берлинской стены участники поговорили о причинах краха коммунистических режимов.
Журналист Дмитрий Запольский презентовал свою книгу «Путинбург». В ней автор показывает, как в Петербурге создавалась система управления, существующая сейчас в России.
9-й Форум
Состоялся 20-21 ноября 2020. Из-за пандемии коронавируса и закрытых границ мероприятие было проведено в онлайн-режиме. В нём приняли участие Сергей Гуриев, Гарри Каспаров, Леонид Гозман, Михаил Крутихин, Елена Лукьянова, Геннадий Гудков, Ольга Романова, Андрей Солдатов, Александр Кынев, Андрей Пионтковский, Леонид Невзлин, Лев Пономарёв, Андрей Илларионов, Константин Эггерт, Илья Пономарёв, Владислав Иноземцев, Борис Райтшутер, Александр Морозов, Андрей Санников, Марат Гельман, Игорь Яковенко, Евгения Чирикова, Ирина Бороган, Михаил Светов и другие.
10-й Форум
Был проведён 28-29 мая 2021 в онлайн-формате. В числе новых спикеров, не участвовавших в ФСР раньше: писатель Алина Витухновская, обозреватель Борис Грозовский, историк Андрей Зубов, политолог Ариэль Коэн, политолог Николай Петров, белорусская журналистка Наталья Радина, политолог, колумнист Deutsche Welle Иван Преображенский, политолог Мария Снеговая и другие.
С приветственным словом к участникам конференции обратился Гарри Каспаров, в котором отметил, что Форум свободной России и его работа приобретают особое значение в новых условиях.
Участники 10-го Форума приняли решение о начале работы по созданию за рубежом разветвленной сети эмигрантских организаций, которые должны будут координировать свои усилия по борьбе с путинским режимом, а также приняли резолюцию в связи с принудительной посадкой воздушного судна Ryanair и задержанием Романа Протасевича.
Среди новых фигурантов Списка Путина оказались те, кто по мнению участников Форума являются нарушителями прав человека. В него вошли сотрудники государственных медиа, судьи, сотрудники силовых структур, в частности директор вещания телеканала RT на русском языке Антон Красовский, сотрудница телеканала Мария Бутина, одна из ведущих принадлежащего RT ютьюб-канала «Прекрасная Россия бу-бу-бу» Олеся Рябцева, один из ведущих того же канала Валерий Серуканов, сотрудник RT Максим Кононенко, руководитель Администрации Президента Антон Вайно, ряд судей и чиновников, ответственных по мнению участников ФСР за осуществление политических репрессий в России.
11-й Форум
Прошёл 2 и 3 декабря 2021 года в Вильнюсе. Впервые за два года очно — но из-за коронавирусных ограничений участников из России было меньше. В основном была представлена российская политэмиграция, также участвовали общественные деятели и журналисты из Украины, Литвы и других стран. Некоторые видные оппоненты режима В. Путина приняли участие в форуме впервые — среди них Михаил Ходорковский, Дмитрий Быков, Виктор Шендерович (все по видеосвязи). На форум были приглашены и сторонники Алексея Навального, многие из которых эмигрировали из России, однако, по словам ответственного секретаря форума Ивана Тютрина, они не откликнулись. Тем не менее, в форуме приняли участие поддерживающие Навального Сергей Гуриев и Евгений Чичваркин.
2-я антивоенная конференция
Состоялась 20 мая 2022 года. В ходе конференции было объявлено о создании оппозиционной коалиционной структуры «Российский комитет действия». Его представители выступили за создание Worldview ID — так называемого «паспорта хорошего русского» для тех, кто выступил против вторжения России на Украину.
3-я антивоенная конференция
30 ноября — 1 декабря 2022 года. Предыдущие встречи в этом формате получили противоречивые отзывы со стороны оппозиционно настроенных граждан России: конференцию, в частности, критикуют за отсутствие инклюзивности и ясной программы действий. Накануне очередного собрания правозащитник Лев Пономарёв предложил сосредоточиться на обозначении общих ценностей — в проекте Хартии-2022.
Постоянный комитет Форума
В 2018 году был создан Постоянный комитет Форума свободной России. В его состав были избраны Владимир Ашурков, Марат Гельман, Андрей Илларионов, Гарри Каспаров, Даниил Константинов, Леонид Невзлин, Илья Пономарев, Андрей Сидельников, Иван Тютрин, Марк Фейгин и Евгения Чирикова.
В марте 2019 года постоянный комитет Форума свободной России обратился к канцлеру Германии Ангеле Меркель с просьбой предотвратить реализацию проекта «Северный поток-2». «С "Северным потоком 2" поставки российского газа в ЕС будут опасно зависеть от двусторонних отношений между Москвой и Берлином», — говорится в открытом письме.
Постоянный комитет принимает заявления по вопросам актуальной политики. Так, в 2019 году Комитет заявил о признании Хуана Гуайдо в качестве легитимного временно исполняющего обязанности Президента Венесуэлы, поздравил народ и нового президента Украины Владимира Зеленского с успешными выборами (В. В. Путин поздравлений не направлял), осудил разгон первомайских демонстраций в нескольких городах России, разгон протестующих в Екатеринбурге (против строительства церкви) и в Архангельской области (против строительства мусорного полигона), выступил с осуждением разгона акции в поддержку независимых кандидатов от оппозиции на выборах в Московскую Городскую Думу, осудил приговоры участникам т. н. «Московского дела», назвав их неправосудными и продиктованными стремлением кремлёвского режима уничтожить в России любые очаги сопротивления электоральной диктатуре Владимира Путина.
«Список Путина»
В декабре 2017 года участниками форума был составлен «Список Путина». Документ содержал более трехсот фамилий, распределенных по 12 категориям. Он, по заявлению создателей, был призван стать основой для введения в отношении фигурантов персональных санкций странами Запада. Среди фигурантов Списка российские чиновники, крупные бизнесмены, журналисты государственных и близких к Кремлю СМИ, ответственные, по мнению составителей, в узурпации власти, нарушении прав человека, коррупции, военной агрессии, пропаганде ненависти.
В 2018 году члены Постоянного комитета форума Марк Фейгин и Иван Тютрин совершили поездку в Вашингтон для презентации Списка в ответственных ведомствах США.
В апреле 2019 года было объявлено об открытии базы данных «Списка Путина» на специальном сайте www.spisok-putina.org. Здесь представлены подробные досье с биографиями и описанием действий фигурантов, повлекших включение их в базу. В апреле 2020 года сайт был заблокирован Роскомнадзором.
Досье в базе распределены по следующим категориям (некоторые персоны указаны в нескольких категориях):
владельцы
исполнители
«праворазрушители»
агрессоры
выгодополучатели
олигархи и коррупционеры
пропагандисты
пособники
База данных регулярно пополняется новыми досье, о чём сообщается в новостях сайта. На 30.12.2019, согласно счетчику в левом верхнем углу сайта, база данных содержала информацию о 375 фигурантах.
Дополнения в Список Путина принимаются путем открытого голосования участников очных форумов. В декабре 2018 на 6-м ФСР в Список были включены 93 новых фигуранта, а в июне 2019 на 7-м форуме Список пополнился 28 персонами.
На 7-м ФСР в Список Путина был включен Олег Кашин. В качестве основания указывается его соучастие в пропаганде путинского режима, использование статуса авторитетного и популярного публициста для легитимации агрессивной неоимперской политики руководства России. В ходе обсуждения кандидатуры Кашина мнения участников форума разделились, но большинство участников поддержало включение. За внесение высказались члены Постоянного комитета ФСР Леонид Невзлин и Марк Фейгин. Против внесения активно выступил Марат Гельман.
На 8-м Форуме Список Путина пополнился 57 фигурантами. Среди новых фигурантов: телеведущий Тигран Кеосаян, дизайнер Артемий Лебедев, а также судьи и следователи по «Московскому делу».
В декабре 2019 года представители Форума свободной России Андрей Илларионов, Илья Пономарев и Иван Тютрин представили обновленный Список Путина в Конгрессе США и нескольких других американских ведомствах. Как заявил один из участников делегации Иван Тютрин, особое внимание в обновленном докладе было уделено «Московскому делу». Представители Форума планируют донести информацию об очередном политическом процессе в России, назвав поимённо людей, ответственных за силовые разгоны мирных демонстраций и фабрикацию уголовных дел против гражданских активистов.
На 10-м Форуме список был пополнен 52 фамилиями.
15 февраля 2022 года в «Список Путина» были включены инициаторы обращения к президенту РФ Путину с просьбой признать независимость ДНР и ЛНР
16 марта 2022 года в «Список Путина» внесены ректоры российских вузов, подписавших обращение Российского союза ректоров в поддержку агрессии против Украины.
19 марта 2022 года в «Список Путина» пополнен 26 персонами, поддержавшими вторжение в Украину. В основном это деятели шоу-бизнеса, в том числе Никита Михалков, Владимир Бортко и Тина Канделаки.
Реакция в России
22 февраля 2019 года Роскомнадзор заблокировал сайт Форума forumfreerussia.org на территории РФ. Решение о блокировке принял Таганский суд Москвы. В качестве основания указана статья 15.1 закона об информации — «Распространение запрещенной информации».
1 февраля 2023 года генпрокуратура РФ признала «Форум свободной России» нежелательной организацией.
Суды
Депортация съемочной группы ВГТРК из Литвы
Первый Форум свободной России, проходивший в марте 2016 года, сопровождался громким скандалом. В одном из отелей Вильнюса произошла драка с участием Божены Рынски и сотрудников государственного телеканала Россия 24, после чего все члены съёмочной группы телеканала были депортированы из Литвы с формулировкой «возможная угроза национальной безопасности». Высланным журналистам был также запрёщен въезд в страну.
На ситуацию с выдворением отреагировали в российском МИДе. Официальный представитель ведомства Мария Захарова прокомментировала ситуацию так: «В очередной раз вынуждены констатировать, что литовские власти продолжают линию на введение в стране тотальной цензуры и искоренение любого инакомыслия.»
Журналисты опротестовали решение о депортации в Европейском суде по правам человека, обвинив литовские власти в нарушении свободы слова. ЕСПЧ большинством голосов принял решение, согласно которому жалобы сотрудников телеканала «Россия-24» признаны неприемлемыми, а доводы властей Литвы — обоснованными. ЕСПЧ подчеркнул, что гарантии свободы слова распространяются на журналистов, если они действуют добросовестно в целях распространения соответствующей действительности информации, основываясь на принципах ответственной журналистики. В данном деле ЕСПЧ не признал поведение заявителей таковым.
Анатолий Шарий
2 декабря 2019 года Вильнюсский окружной суд удовлетворил иск украинского журналиста и блогера Анатолия Шария к Форуму свободной России из-за публикации клеветы в его адрес. Ему должны выплатить 3000 евро и 1200 евро судебных трат.
Позже решение было отменено в суде следующей инстанции, Шария обязали покрыть судебные расходы ответчика. В мае 2021 года Литва лишила Анатолия Шария политического убежища.
Позиция в связи с российским вторжением в Украину
24 февраля 2022 года участники ФСР выступили с заявлением, в котором осудили войну в Украине, призвали к формированию международной антипутинской коалиции и высказались за введение нефте-газового эмбарго в отношении России.
5 марта в Вильнюсе состоялась антивоенная конференция, организованная Форумом свободной России. Заявленная организаторами цель мероприятия — объединение усилий как российской оппозиции, так и европейской и американской политических элит, а также украинской и белорусской диаспор в противодействии действиям российского режима против Украины. В конференции приняли участие Гарри Каспаров, Константин Эггерт, Леонид Невзлин, Евгения Чирикова, Леонид Гозман, Илья Пономарев и другие.
8 марта участники ФСР выступили с призовом к НАТО усилить свое военное присутствие в восточноевропейском регионе. По мнению авторов обращения, следующим объектом агрессии России могут стать страны Североатлантического альянса, в частности балтийские государства.
В последующих заявлениях ФСР призывал Запад к «максимальному расширению военной помощи Украине во всех ее формах», предоставить Украине «такие вооружения, которые позволят ей эффективно отвечать на ракетные обстрелы своей территории», «отбросить колебания и перестать бояться "спровоцировать Путина на дальнейшую эскалацию"».
20 мая 2022 года Форум свободной России провел в Вильнюсе вторую антивоенную конференцию, на которой обсуждались последствия войны с Украиной и будущее России. На антивоенной конференции объявили о создании «Российского комитета действия», в который вошли Сергей Алексашенко, Дмитрий Гудков, Сергей Гуриев, Борис Зимин, Гарри Каспаров, Юлия Латынина, Иван Тютрин, Михаил Ходорковский, Евгений Чичваркин.
На конференции 20 мая впервые прозвучала идея введения миграционного документа, получившего в сетях название «Паспорт хорошего русского». Многие поняли это предложение как деление русских на «хороших» и «плохих», на уехавших и оставшихся (предлагаемый документ призван, в основном, облегчать жизнь российских граждан за рубежом), в результате в соцсетях возникла бурная полемика. Критически высказывались, прежде всего, деятели в России, например Илья Яшин. Инициаторам пришлось выступать с разъяснениями. Для реализации этой идеи был создан «Российский комитет действия», на сайте которого россияне могут заявить о своей антивоенной позиции.
См. также
Координационный совет российской оппозиции
Форум мирной России
Съезд народных депутатов
Примечания
Ссылки
Сайт Форума свободной России (заблокирован на территории РФ)
База данных «Список Путина» (сайт заблокирован на территории РФ)
Сайт Российского комитета действия
// Голос Америки — о 4-м Форуме,
// Немецкая Волна — о 5-м.
// Эхо Москвы — о 6-м.
// Радио Свобода — о 6-м.
«Мы видим агонию»: освобождение России уже началось // РИА Новости, 10 декабря 2018
Политические организации России
Политическая оппозиция
Вильнюс
Международные конференции
Форумы
Дела Европейского суда по правам человека с участием Литвы
Неправительственные организации, деятельность которых признана нежелательной на территории Российской Федерации | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 586 |
Q: Error: Arguments 'event.e' and 'subgroup' must have the same length I'm getting the above error when trying to run my R code with metabin, here's my code and error library
aa<-read.csv("C:/Users/Lizzie/Desktop/aa.csv")
aa1<-metabin(Tevent,Ttotal,Cevent,Ctotal,data=aa,sm="RR", studlab = paste(study,year), label.e = "Intervention",label.c = "Control", subgroup = "Type" )
summary(aa1)
When I run the second line of my codes, I got this error:
Error: Arguments 'event.e' and 'subgroup' must have the same length.
I really don't understand what's going on, because I'm new in R
"event.e" is number like 1, 2, 3, while "subgroup" is text like a, b, c,
Hope you guys could help me with this, thanks a lot!!
A: aa1<-metabin(Tevent,Ttotal,Cevent,Ctotal,data=aa,sm="RR", studlab = paste(study,year), label.e = "Intervention",label.c = "Control", subgroup = Type )
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 6,623 |
Browsing History HOMECase LawLake Arrowhead v. Lake Arrowhead
LAKE ARROWHEAD CHALETS TIMESHARE OWNERS v. LAKE ARROWHEAD CHALETS OWNERS
(1996) 51 Cal.App.4th 1403
[Opinion certified for partial publication. fn. * ]
Fiore, Walker, Racobs & Powers, Peter E. Racobs and Margaret G. Wangler for Plaintiffs and Appellants.
Feldsott, Lee & Feinberg, Martin L. Lee and Stanley Feldsott for Defendants and Appellants.
McKINSTER, J.
The Lake Arrowhead Chalets is a 62-unit residential condominium project. It is governed by the Lake Arrowhead Chalets Owners Association (Condominium Association). Of the 62 units, 24 are operated as time-share facilities. The time-share units are governed by the Lake Arrowhead Chalets Timeshare Owners Association (Timeshare Association).
A meeting of the members of the Condominium Association was held on February 1, 1992, to elect new members of the association's board of directors and to vote on a proposed third amendment to the association's bylaws. Mr. Dave Burdick, a member of the boards of directors of both the Condominium Association and the Timeshare Association, appeared at the meeting, purporting to be empowered to vote on behalf of the owners of the 24 time-share units. Burdick cast the votes of those 24 units against the proposed bylaws amendment, but the Condominium Association refused to recognize either his authority or the validity of his vote. Accordingly, the third amendment was declared to have been adopted by a vote of 36 to 0.
In March of 1992, the Timeshare Association and Bruce Rummer, an individual member of the Condominium Association, sued the Condominium Association and two of its officers and directors, Linda Hanneman and James Genn. As ultimately amended, that action sought (1) a declaration that the third amendment to the Condominium Association's bylaws was invalid, (2) a declaration that a prior second amendment to the bylaws was rescinded, (3) damages against Hanneman and Genn for alleged violations of fiduciary duty, and (4) a variety of injunctive relief. The Condominium Association cross-complained against the Timeshare Association in June of 1992, seeking a declaration that various provisions of the declaration of covenants, [51 Cal.App.4th 1406] conditions and restrictions under which the Timeshare Association operated were invalid.
In May of 1994, the plaintiffs represented that they had reached a settlement of their dispute with the Condominium Association and applied for a determination that the settlement was in good faith. (Code Civ. Proc., § 877.6, subd. (a)(2).) The Condominium Association contested the settlement. (Ibid.) The trial court denied the application in August of 1994.
Meanwhile, in June of 1994, the plaintiffs moved for an order (1) disqualifying defense counsel, Feldsott, Lee & Feinberg, from continuing to represent either the Condominium Association or the individual defendants, and (2) restraining the Condominium Association from continuing to pay the costs of defense of the individual defendants. Both aspects of the motion were denied.
The declaratory relief claim concerning the validity of the third amendment to the Condominium Association bylaws was bifurcated from all other issues. Trial on that issue began on August 18, 1994. At the conclusion of the plaintiffs' case-in-chief, the defendants successfully moved for judgment. (Code Civ. Proc., § 631.8.) In particular, the court determined that the third amendment was valid.
The Condominium Association then dismissed its cross-complaint. Shortly thereafter, the plaintiffs dismissed the remaining causes of action of their complaint. All claims having been resolved either through trial or dismissal, a judgment was entered in favor of the defendants.
Relying on Civil Code section 1354, subdivision (f), the defendants then moved for an award of over $200,000 in attorney's fees. Their motion was denied.
The plaintiffs appeal from the judgment against them. The defendants cross-appeal from the denial of their motion for attorney's fees.
The plaintiffs contend that the judgment should be reversed because the trial court erred in refusing to approve the settlement with the Condominium Association, refusing to disqualify defense counsel, and finding that the third amendment was valid. On the cross-appeal, the defendants contend that the trial court erred by denying their motion for attorney's fees. In addition, arguing that the plaintiffs' appeal is frivolous, the defendants have moved [51 Cal.App.4th 1407] for an award of attorney's fees on appeal, pursuant to Code of Civil Procedure section 907 and California Rules of Court, rule 26.
Discussion A. , B. fn. *** C. The Third Amendment to the Bylaws Is Invalid.
[1] The plaintiffs' principal argument is that the trial court erred on the merits of the only issue tried, i.e., the validity of the third amendment to the Condominium Association's bylaws. In particular, they contend that the amendment is invalid for three reasons: (a) the notice of the meeting at which it was adopted was inadequate; (b) there were insufficient favorable votes to adopt the amendment; and (c) the amendment was not approved by the owners of the time-share units, as required by Corporation Code section 7150, subdivision (b). Finding the last issue to be dispositive, we address it first.
Since the initial adoption of the bylaws of the Condominium Association, they have been amended three times. The first amendment increased the number of directors from five to seven. The second amendment provides that four of the seven directors shall be owners of whole condominium units, while the remaining three directors shall be owners of fractional interests in time-share units. The third amendment, which is the subject of this action, provides that "only timeshare owners/representatives may vote for the three (3) seats on the Board of Directors occupied by the timeshare owners. Only the condominium owners may vote for candidates for the remaining four (4) seats on the Board of Directors."
Subdivision (b) of Corporations Code section 7150 establishes certain restrictions on the powers of a mutual benefit corporation's members to amend its bylaws. fn. 3 In particular, it provides that some amendments, although approved by the members generally, are not effective unless they are also approved by the members of a class. (Ibid.) Among the proposed amendments requiring class approval are those which would "[a]uthorize a new [51 Cal.App.4th 1408] class of memberships" (id., subd. (b)(6)) or "[m]aterially and adversely affect the rights, privileges, preferences, restrictions or conditions of that class as to voting ... in a manner different than such action affects another class" (id., subd. (b)(1)).
The plaintiffs contend that the third amendment creates a new and disadvantaged class of members, and is therefore ineffective because it was not approved by the members of that new class. They are correct.
" 'Class' refers to those memberships which ... have the same rights with respect to voting ...." (Corp. Code, § 5041.) By specifying that the time-share owners could only vote for the directors who would constitute a minority of the board, while the whole-unit owners would select the board's majority, the third amendment created two classes of members. We cannot accept the trial court's finding to the contrary.
Not only did the third amendment divide the members into two classes, but it materially and adversely affected the voting rights of the minority time-share class. Prior to the amendment, the time-share members of the association, though owners of a minority of the units, had the chance to elect a majority of the board of directors. fn. 4 After the division of the membership into two classes, only the whole-unit owners had that opportunity. Thereafter, the time-share owners could never elect a majority of the board, regardless of how much greater their degree of organization and voter turn-out compared to the owners of the whole units.
The defendants deny that the change in voting rights was adverse to the time-share owners, arguing that in fact the change benefited the time-share owners by guaranteeing that they would always have some representation on the board. They concede, however, that another effect of the amendment would be to prevent the continuation of the practice by which a passive majority (of whole-unit) owners, through their lack of participation, allowed an active minority (the time-share owners) to control the board. Thus, we [51 Cal.App.4th 1409] cannot say as a matter of law that the effect of the amendment were entirely beneficial to the time-share owners. fn. 5 Because the amendment confers potential disadvantages as well as potential advantages, the weighing process is reserved for the members of the affected class. (Corp. Code, § 7150, subd. (b).)
Since the owners of the time-share units did not approve the third amendment, it was not validly adopted, and thus is not effective, even though it was approved by a majority of the members. Therefore, we need not decide whether the Condominium Association failed to give adequate notice at the meeting at which the amendment was purportedly approved, or whether there would have been sufficient favorable votes cast by the members to adopt the amendment in the absence of the need for separate votes by class. The judgment declaring that the amendment was validly adopted and effective must be reversed.
D. The Issue Raised in the Defendants' Cross-appeal Is Moot. fn. ***
The judgment is reversed. Having decided the invalidity of the adoption of the third amendment to the Condominium Association's bylaws as a matter of law, we direct the trial court to enter a declaratory judgment in favor of the plaintiffs.
Hollenhorst Acting P. J., and Ward J., concurred.
FN *. Pursuant to California Rules of Court, rules 976(b) and 976.1, this opinion is certified for publication with the exception of parts A, B, and D.
FN †. Judge of the San Bernardino Municipal Court, East Division, assigned by the Chief Justice pursuant to article VI, section 6 of the California Constitution.
FN *. See footnote, ante, page 1403.
FN 3. The statutory restrictions on the power of a corporation's board to amend bylaws (Corp. Code, § 7150, subd. (a)), to which the defendants refer, are irrelevant. A board may not amend the bylaws if the bylaws withhold that power. (Corp. Code, § 7150, subd. (c).) Here, the bylaws specify that the power to amend is solely in the hands of the members.
FN 4. Since the term of office of directors is only one year, all seven seats are open at the annual election. The election is held at the annual meeting. A quorum for the meeting is 51 percent of the units. Thus, under the pre-amendment bylaws, an election could be decided on just 32 votes. If all 24 time-share unit owners participated in the election and voted cumulatively for 4 candidates, each candidate would receive 42 votes (24 X 7 ö 4). If the eight whole-unit owners who attended also voted cumulatively for four candidates, each would receive only fourteen votes. Under the old system, therefore, the time-share units could (and apparently, frequently did) elect a majority of the board because they participated in the election in greater numbers and voted as a block. Under the third amendment, however, the whole-unit members would be ensured of a majority of the board, regardless of how few of them bothered to turn out and vote.
FN 5. Indeed, if the amendment were entirely beneficial to the time-share owners and adverse to the whole-unit owners, one would be hard pressed to explain why the time-share owners have spent so much time and attorney's fees to prevent the amendment from going into effect, or why the whole-unit owners have worked so long and hard to enforce it. The Condominium Association's actions speak louder than its words. | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 3,080 |
Congress Passes Nationwide Alert System For Law Enforcement Killed Or Injured In Line Of Duty
Kerry Picket Political Reporter
Congress passed the Rafael Ramos and Wenjian Liu National Blue Alert Act on Thursday, a nationwide alert system to be used when a law enforcement official is injured or killed in the line of duty. The bill is named after two New York Police Department officers who were killed in their police cruiser last December.
"Similar to Amber Alerts, Blue Alerts help distribute time-sensitive information to help quickly identify and apprehend violent criminals. The bill will soon head to the President's desk, where it is expected to be signed into law," House Speaker John Boehner's office said in a press release.
In 2014, 51 law enforcement officers were killed in the line of duty, an increase of almost 89 percent compared to the 27 officers killed in 2013, FBI statistics say.
Blue Alerts is just one of the pieces of legislation the Fraternal Order of Police (FOP) pushed for this year. FOP's president Chuck Canterbury told The Daily Caller the organization is looking toward is reforming investigations on law enforcement.
"There needs to be uniformity in the investigations conducted on police officers. Police officers need to have the same due process rights as the suspects that we arrest and currently law-enforcement officers are compelled in a lot of places to give statements without the ability to have an attorney and only in places that have a law enforcement bill of rights do officers have that kind of due process," he said. "We are going to push for national legislation. That's been a piece of our legislation for a number of years."
Tags : police
Kerry Picket | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 3,160 |
package org.objenesis.tck;
import static org.junit.Assert.*;
import java.io.ByteArrayInputStream;
import java.io.IOException;
import org.junit.Before;
import org.junit.Test;
/**
* @author Joe Walnes
*/
public class CandidateLoaderTest {
private StringBuilder recordedEvents;
private CandidateLoader candidateLoader;
@Before
public void setUp() throws Exception {
recordedEvents = new StringBuilder();
TCK tck = new TCK() {
@Override
public void registerCandidate(Class<?> candidateClass, String description) {
recordedEvents.append("registerCandidate('").append(candidateClass).append("', '")
.append(description).append("')\n");
}
};
CandidateLoader.ErrorHandler errorHandler = new CandidateLoader.ErrorHandler() {
public void classNotFound(String name) {
recordedEvents.append("classNotFound('").append(name).append("')\n");
}
};
candidateLoader = new CandidateLoader(tck, getClass().getClassLoader(), errorHandler);
}
@Test
public void testReadsClassesAndDescriptionsFromPropertiesFile() throws IOException {
String input = "" + "org.objenesis.tck.CandidateLoaderTest$A = A candidate\n" + "\n"
+ "# a comment and some whitespace\n" + "\n"
+ "org.objenesis.tck.CandidateLoaderTest$B = B candidate\n"
+ "org.objenesis.tck.CandidateLoaderTest$C = C candidate\n";
candidateLoader.loadFrom(new ByteArrayInputStream(input.getBytes()));
assertEquals(""
+ "registerCandidate('class org.objenesis.tck.CandidateLoaderTest$A', 'A candidate')\n"
+ "registerCandidate('class org.objenesis.tck.CandidateLoaderTest$B', 'B candidate')\n"
+ "registerCandidate('class org.objenesis.tck.CandidateLoaderTest$C', 'C candidate')\n",
recordedEvents.toString());
}
@Test
public void testReportsMissingClassesToErrorHandler() throws IOException {
String input = "" + "org.objenesis.tck.CandidateLoaderTest$A = A candidate\n"
+ "org.objenesis.tck.CandidateLoaderTest$NonExistant = Dodgy candidate\n"
+ "org.objenesis.tck.CandidateLoaderTest$C = C candidate\n";
candidateLoader.loadFrom(new ByteArrayInputStream(input.getBytes()));
assertEquals(""
+ "registerCandidate('class org.objenesis.tck.CandidateLoaderTest$A', 'A candidate')\n"
+ "classNotFound('org.objenesis.tck.CandidateLoaderTest$NonExistant')\n"
+ "registerCandidate('class org.objenesis.tck.CandidateLoaderTest$C', 'C candidate')\n",
recordedEvents.toString());
}
@Test
public void testLoadsFromResourceInClassPath() throws IOException {
// See CandidateLoaderTest-sample.properties.
candidateLoader.loadFromResource(getClass(), "CandidateLoaderTest-sample.properties");
assertEquals(""
+ "registerCandidate('class org.objenesis.tck.CandidateLoaderTest$A', 'A candidate')\n"
+ "registerCandidate('class org.objenesis.tck.CandidateLoaderTest$B', 'B candidate')\n",
recordedEvents.toString());
}
@Test
public void testThrowsIOExceptionIfResourceNotInClassPath() throws IOException {
try {
candidateLoader.loadFromResource(getClass(), "Blatently-Bogus.properties");
fail("Expected exception");
}
catch(IOException expectedException) {
// Good!
}
}
// Sample classes.
public static class A {
}
public static class B {
}
public static class C {
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 2,189 |
A Ballantine Book
Published by The Random House Publishing Group
Copyright © 1974 by Harry Lorayne and Jerry Lucas
All rights reserved.
Published in the United States by Ballantine Books, an imprint of The Random House Publishing Group, a division of Random House, Inc., New York, and distributed in Canada by Random House of Canada Limited, Toronto.
Ballantine and colophon are registered trademarks of Random House, Inc.
www.ballantinebooks.com
Library of Congress Catalog Card Number: 96-96797
eISBN: 978-0-307-81406-7
v3.1
# **Praise for
_The Memory Book_**
"A most unusual book about memory training... absorbing material to practice and use."
— _Los Angeles Times_
"Will enable you to remember anything from long-digit numbers to where you left your car keys."
— _Nashville Banner_
"It's easy, it's fun... it works."
— _The Columbus Dispatch_
# Contents
_Cover_
_Title Page_
_Copyright_
FOREWORD: _Jerry Lucas_
FOREWORD: _Harry Lorayne_
1 Some History of the Art
2 In the First Place: Association
3 The Link
4 Substitute Words
5 Long Words, Appointments and Errands, Shopping Lists
6 Speeches
7 Foreign and English Vocabulary
8 Names and Faces
9 Absentmindedness
10 Long-Digit Numbers
11 The Peg
12 Style Numbers, Prices, Telephone Numbers
13 Playing Cards
14 Weekly Appointments; Days of the Week
15 Anniversaries, the Zodiac, Historical Dates
16 The Alphabet and Picturing Letters
17 Start Your Children
18 Sports
19 The Stock Market
20 Politics
21 The Arts
22 Music for Beginners
23 Reading
24 The Memory Graph
25 Potpourri
26 Look, I'm a Genius
27 Finally
_Dedication_
_Other Books by This Author_
# **_FOREWORD: JERRY LUCAS_**
As a child, I had a peculiarly busy mind. I can never remember a time when my mind wasn't occupied with some sort of activity, whether it was communicating directly with someone else, or being actively involved with a mental game of my own invention.
By the time I was eight years old, I had so much nervous energy that it was hard for me to sit still. On lengthy automobile trips my constant fidgeting, tapping, and so on got on my parents' nerves. It got to the point where I became used to requests from them to "calm down a little."
Just after one such request, I remember looking at an oil company billboard and saying to myself, "What would 'SHELL' look like if the letters were arranged in alphabetical order?" I mentally rearranged it to "EHLLS," and I was hooked. Ever since then, I have memorized words alphabetically as well as normally.
Thanks to this mental habit, I could spell amazingly well as a child. If you can rearrange a word instantly and spell it in alphabetical order, you know that word very well. To give some examples: CAT becomes ACT, MEMORY becomes EMMORY, JERRY LUCAS becomes EJRRY ACLSU, and HARRY LORAYNE becomes AHRRY AELNORY! Once I've alphabetized a word, I can remember it in that form—when you read the chapter on how to remember English and foreign vocabulary, you'll understand how I do this. I apply the same system, since an alphabetized word is like a foreign word.
I soon followed this alphabetical spelling game with various other kinds of mental games. You might think I was a bit crazy if I took the time to explain all of them, so I won't, but they did require a lot of counting, cataloging, and recall on the part of a very young boy.
As I grew older, my mental games and activities became more complex. I began to develop simple memory systems to help me with my studies in school. To me, schoolwork always seemed to be at least 90 percent memory work, and I wanted to make it easier and less time-consuming for myself. These systems worked, and I began to expand and sophisticate them. They worked well for me throughout junior high school and high school, where I was practically a straight-A student.
I would like to impress upon you that all of this mental activity was of a private nature. No living human being knew that I had the ability, for example, to alphabetize any word faster than most people could spell it normally, nor did anyone know how involved I was with other mental activities and memory systems.
An important change took place when I entered college. I read one of Harry Lorayne's books and used many of his systems or ideas in areas where I thought his were better, or simpler, or easier to apply; others I adapted to my own. He became something of an idol to me, and I was soon to find out how the combination of his systems and mine would help me in my college studies.
My roommate at Ohio State University during my freshman year was John Havlicek, the great professional basketball star of the Boston Celtics. John became the first person to know about all the things that went on in my mind.
My first college class was traumatic. I entered the classroom and sat in the back row, knowing other students would be unable to see over my six-foot-eight frame. It was an American history class.
The professor spent about fifteen minutes telling us what he expected of us and how the class would be conducted. His last statement before he excused us was something to the effect that "Any athlete who expects to be in my class, sit in the back row, do nothing, and get good grades is sadly mistaken. You are excused."
I told John Havlicek what had happened and shared with him my determination to use memory systems to my best advantage in this particular class.
"What systems?" he asked me, and it all began to flow out for the first time. I told John how I had begun to spell alphabetically as a child and I demonstrated it for him.
He couldn't really believe what he was hearing. I explained, as best I could, how my mind worked and all the mental activity I was involved in. I'm sure he thought I was a little crazy, but he challenged me to spell some words of his choosing alphabetically, and when I did, he wished me well in the use of my systems.
As for my American history class, the systems worked beautifully. On the first exam, my grade was 99; the closest grade to mine was 77. Four years later, I graduated Phi Beta Kappa—having put in something like one-fourth the study time that most students used.
Many years later, after I was traded to the New York Knickerbockers basketball team, I looked up Harry Lorayne. Our first meeting lasted over eighteen hours! Obviously, we had much in common, and we later became associated in our endeavors—including this book. It is, in fact, a combination of some of our ideas, thoughts on, systems of, memory.
Believe me, if you read about these systems and actually apply them as you go, there is no limit to how great your memory can be.
JERRY LUCAS
# **_FOREWORD: HARRY LORAYNE_**
Unfortunately, I never had the opportunity to receive a formal education. I didn't complete the first year of high school. My grades, during that short time, were among the highest in my class. Why was this so? My IQ was average, and my "natural" memory was no better or worse than most people's. As a matter of fact, I originally was one of those many people who think they have the worst memory in the world.
I received good grades for one reason—I applied memory systems to my schoolwork. It's as simple as that.
Jerry has told you how he got hooked on alphabetizing words as a child. Well, as a very young boy _my_ burning interest was card magic. I suppose I drove most of my friends up the wall, asking them to "pick a card, any card."
One of the "tricks" I performed during those years wasn't really a trick at all, it was a memory stunt. It consisted of memorizing an entire shuffled deck of playing cards, in order. All the cards were called off to me once, and I would know the position of every card in the deck! I still perform this stunt today, but at the time it was the only memory trick I knew.
One day, the thought struck—if I could apply a simple system to help me remember playing cards, why couldn't I do the same to help me remember anything I wanted to? That single simple thought started me on a lifetime career.
First I compiled a bibliography of all the material available on the subject of memory training. This started me thinking about and then devising my own systems. Years later, I started to perform for groups, organizations, conventions, and so on. My performance consisted of memory feats and demonstrations only. During these early years, literally thousands of people approached me after a performance to express their interest in learning "how to remember."
That is what led me to write my first book on the subject. It eventually sold over a million hardcover copies and was translated into nine languages.
Other books and courses on the art of a trained memory followed this first book. I have cartons full of the letters I received from people whose memories improved dramatically, thanks to my systems. One of these letters was from Jerry Lucas, then a freshman at Ohio State University.
We corresponded over the years. He had devised systems of his own, and his interest in the subject knew no bounds. He manipulated some of my systems, changed some of them to fit his purposes, applied them to his schoolwork. I could not have had a better or more dedicated disciple.
I went on with my work, Jerry went on with his. I eventually founded the Harry Lorayne School of Memory; Jerry became a championship basketball player. We still corresponded. A few years ago, Jerry started to demonstrate some of his mental abilities on national television. I had been doing the same thing for twenty years, including remembering the names and faces of up to five hundred people in the studio audience. Nobody, at that time, knew of any connection between Jerry and myself.
When Jerry was traded to the Knicks, we finally met. That first meeting, as Jerry has told you, lasted very nearly around the clock.
Even with our trained memories, Jerry and I would have been hard put to remember all the things we talked about. And so, at one point, we decided to run a tape recorder as we spoke. Throughout the book, you'll be reading small portions of that dialogue. Most, but not all, of these conversations were taken from that tape of our original meeting.
This will sound immodest, but it is my true feeling—I envy you! I envy you the discoveries you're about to make, the new areas you're about to explore, the pleasure of learning and enjoying at the same time. I wish I were in your place, right now.
HARRY LORAYNE
# 1 **_SOME HISTORY OF THE ART_**
Memory systems date back to antiquity. In the ancient world, a trained memory was of vital importance. There were no handy note-taking devices, and it was memory techniques and systems that enabled bards and storytellers to remember their stories, poems, and songs.
Early Greek and Roman orators delivered lengthy speeches with unfailing accuracy because they learned the speeches, thought for thought, by applying memory systems.
What they did, basically, was associate each thought of a speech to a part of their own homes. These were called "loci," or "places." The opening thought of a speech would, perhaps, be associated to the front door, the second thought to the foyer, the third to a piece of furniture in the foyer, and so on. When the orator wanted to remember his speech, thought for thought, he actually took a mental tour through his own home. Thinking of the front door reminded him of the first thought of his speech. The second "place," the foyer, reminded him of the next thought; and so on to the end of the speech. It is from this "place" or "loci" memory technique that we get the time-worn phrase "in the first place."
Although Simonides (circa 500 B.C.) is known as the father of the art of trained memory, scraps of parchment dating back a thousand years or so before Simonides state that memory techniques were an essential part of the orator's equipment.
Cicero wrote that the memories of the lawyers and orators of his time were aided by systems and training and in _De oratore_ he described how he himself applied memory systems.
It's important to realize that oratory was an important career during those early days. "We should never have realized how great is the power [of a trained memory]," wrote the philosopher Quintilian, "nor how divine it is, but for the fact that it is memory which has brought oratory to its present position of glory."
The ancients also knew that memory training could help the thinking process itself. From a fragment dated about 400 B.C. we learn that "A great and beautiful invention is memory, always useful both for learning and for life." And Aristotle, after praising memory systems, said that "these habits too will make a man readier in reasoning."
If Simonides was the inventor of the art of trained memory, and Cicero its greatest early teacher, St. Thomas Aquinas was to become its patron saint, instrumental in making the art of trained memory a devotional and ethical art.
During the Middle Ages, monks and philosophers were virtually the only people who knew about and applied trained-memory techniques. The systems, whose use was mostly limited to religion, were basic to some religions. For example, memory systems were used to memorize Virtues and Vices, and some priests and philosophers taught that memory systems showed "how to reach Heaven and avoid Hell."
In 1491, Peter of Ravenna wrote _The Phoenix_ , which became the best known of all early memory-training books and brought the art of trained memory out into the lay world. During the fifteenth and sixteenth centuries, many other books were written on the subject.
King Francis I of France used memory systems, as did England's Henry III. Shakespeare is held to have used trained-memory systems—his Globe Theater was called the "memory theater." Philosophers of the seventeenth century taught memory systems (Francis Bacon has one in his book _The Advancement of Learning_ ), and some scholars insist that Leibniz invented calculus while searching for a memory system that would aid in memorizing numbers.
So you see, there's nothing really new about trained-memory techniques. Unfortunately, the techniques fell into disuse for centuries. Some people who did practice them were actually regarded as witches. It's true that memory systems remained in use as a source of entertainment for others—in our own century, vaudeville players used memory systems to perform "mental tricks" onstage—but they were seldom if ever used for practical purposes or serious learning. Here and there someone would try to bring the systems to the fore again, but without success.
In a book titled _Memory_ , William Stokes, a philosopher and memory teacher of the 1800's, summarizes the degree of public interest in the art of trained memory:
It is true... that notwithstanding the records of the past and the achievements, triumphs, and trophies of the present, the "educated," the intelligent masses—the world—know not and seem not to care to know its wondrous worth. The adoption of the science by a few paltry thousands cannot be regarded as anything when we consider the countless myriads peopling the earth—when we realize the fact that it is as essential to the proper exercise and full development of our intellectual existence as proper breathing is to our physical well-being; in spite of all that has been said and done, we may say comparatively—almost absolutely—that the art is a thing unknown!
There can be little doubt that before long, it will be generally recognized as an established science; and posterity will look back, and regard... this plea on behalf of memory... as an indication of the intellectual _darkness_ of this age of boasted enlightenment....
Let us hope that the day will come when it shall be considered as great a disgrace not to use memory systems as it is at present not to read!
Stokes's book was published in 1888. Nearly a century later, it is our pleasure to bring the art of trained memory back into the foreground—not only by teaching memory systems, but by bringing them to a level that the ancient (and not-so-ancient) thinkers would never have conceived as being within the realm of possibility.
# 2 **_IN THE FIRST PLACE: ASSOCIATION_**
HL: Can't you picture those ancient orators, wandering around the streets of a city looking for other buildings to use as "places"?
JL: And the search made them more knowledgeable, not just better able to remember what they needed to. Eventually, they realized that any information that was already sequential could be used as loci or things to associate with _other_ things.
HL: So when a searcher came across something like the signs of the zodiac, and realized that here he had twelve "places," he had to _learn_ them first. And much later, some people realized that parts of the Bible could be used as places, so they had to learn that first.
JL: A case of knowledge begetting knowledge, wouldn't you say?
•
All memory, whether trained or untrained, is based on association. But that's stating it too simply. You will be taught many systems of association in this book, but it goes much deeper than that. You see, when people say, "I forgot," they didn't, usually—what really happened was that they didn't remember in the first place.
How can you forget something that you didn't _remember_ , originally? Turn that around, and you have the solution to remembering—if you do remember something originally, how can you _forget_ it?
That brings you to forcing yourself to remember originally.
How can you do this? The simple systems of association you'll learn here will do it _for_ you, automatically!
One of the fundamentals of a trained memory is what we call Original Awareness. Anything of which you are Originally Aware _cannot_ be forgotten. And, applying our systems of association will _force_ Original Awareness. Observation is essential to Original Awareness—anything you wish to remember must first be observed. Using association will take care of that, too.
But how in the world do you associate something that's intangible or abstract? That question leads to another fundamental of trained memory. It is always easier to remember things that have meaning than it is to remember things that do not. You'll see, as you get a bit deeper into our methods, that _nothing_ is abstract or intangible so far as the systems are concerned. You will learn how to make any intangible thing, any abstract piece of information, tangible and meaningful in your mind. Once you've mastered that simple technique, all remembering and therefore all learning will be easier for you for the rest of your life.
We'd like to insist right here that virtually all learning is based on memory. Educators don't like to admit it, but they know it's true. And any student knows that the more he remembers, the better grades he'll get from the teacher who likes to put down "memorization." We believe that there are three basic learning skills: 1) the search for information, 2) remembering the information, and 3) applying the information. The search is up to the educators and the sources of knowledge, the application is up to you. We'll take care of step 2.
Let's begin with association. First of all, you should realize that you've used association all your life. The problem is that you've usually associated subconsciously, without recognizing the association for what it was. Anything you clearly associated, even if subconsciously, is sure to have been easily remembered. But since you have no control over your subconscious, association has been a hit-or-miss kind of thing all your life.
Here's a basic memory rule: You Can Remember Any New Piece of Information if It Is Associated to Something You Already Know or Remember.
Do you remember the lines on the music staff, the treble clef, E, G, B, D, and F? If your teacher ever told you to think of the sentence **E** very **G** ood **B** oy **D** oes **F** ine, then you _do_ remember them. Your teacher was following that basic memory rule, probably without realizing it. He or she was helping you to remember new (and abstract) information, the letters E, G, B, D, and F, by associating them to something you already knew, or at least understood—the simple sentence Every Good Boy Does Fine. Obviously, it worked.
Teachers in the early grades have been telling their students for years that it's easy to remember how to spell _piece_ if you think of the phrase "a **pie** ce of **pie**." Since most young students already know how to spell _pie_ , associating that old knowledge to the new—the spelling of " **pie** ce"—solves the problem. Again, the basic rule has been followed.
Very few people can easily remember the shape of Russia, or Greece, or any other country—except Italy, that is. That's because most people have been told, or have read, that Italy is shaped like a boot. There's that rule again—the shape of a boot was the something already known, and the shape of Italy _could not be forgotten_ once that association was made.
These are common examples of association, subconscious or conscious. And so it goes: medical students use mnemonics (a technique for improving the memory) to help themselves remember the cranial nerves; other students picture **homes** on a **great lake** to help themselves remember that the five Great Lakes are **H** uron, **O** ntario, **M** ichigan, **E** rie, and **S** uperior; others picture a quartet being stabbed ( **stab** gives you the initial letters of **s** oprano, **t** enor, **a** lto, and **b** ass) to remember the four voices in a quartet. People have remembered that Mount Fujiyama is 12,365 feet high by associating it to a calendar (12 months, 365 days in a year).
The trouble with such examples is that they work only for those specific things; they're limited. The systems of trained memory you'll learn in this book are applicable to anything. They are limited only to the extent that your willingness to use them is limited. The point is this: If you know how to _consciously_ associate anything you want to remember to something you already know, you'll have a trained memory. It's as simple as that. And you can learn to associate anything you like—quickly and naturally.
The trained-memory systems you'll be taught in this book are not unnatural in any way; they merely systematize, or patternize, a natural process. Many times during your life you've heard or seen something that caused you to snap your fingers and say, "Oh, that reminds me...." And, usually, the thing that reminded you of something had nothing to do with what it reminded you of. Somewhere back in your mind an absurd or random association had been made.
Why, when the orators of ancient times could use their own homes as "loci" to remind themselves of the thoughts of a speech, did they search for other buildings to give them more "places"? It wasn't that the same home or building couldn't be used over and over again—it could. ("The loci," said one thinker, "are like wax tablets which remain when what is written on them has been effaced and are ready to be written on again.")
No, the problem was that the "home" loci became too familiar after a while—after all, a staircase is a staircase, and a foyer is a foyer. But an important memory principle simply never occurred to the ancient orators: It isn't necessary to associate the thoughts of a speech, or anything else, to places— _the thoughts may be associated to each other_ , so that one thought will remind you of the next thought.
That simple idea is the basis of the Link system of memory. First, we'll show you how to use it to help you memorize tangible items. Later on, when you've learned how to picture thoughts or concepts, you'll see that the idea can easily be applied to intangibles.
Right now, let's apply the basic association rule to remembering ten unrelated items. But we'll change the rule, slightly, by adding one important phrase. The revised rule: In Order to Remember Any New Piece of Information, It Must Be Associated to Something You Already Know or Remember _in Some Ridiculous Way_. The addition of that simple four-word phrase accomplishes quite a few things. It will force the Original Awareness that's necessary to remember anything, it will force you to concentrate and use your imagination as you never have before, and it will force you to form associations consciously.
Assume you wanted to memorize these ten items, in sequence: airplane, tree, envelope, earring, bucket, sing, basketball, salami, star, nose. All right, picture an **airplane** in your mind. There's no way to apply our memory rule yet. But now we come to the next item: tree.
The rule can now be applied, if we make the assumption that you already know, or remember, **airplane**. The new piece of information that you want to remember is **tree**. All you need to do is to form a ridiculous picture, or image, in your mind's eye—an association between those two things.
There are two steps involved. First you need a ridiculous—impossible, crazy, illogical, absurd—picture or image to associate the two items. What you don't want is a logical or sensible picture.
An example of a logical picture might be: an airplane parked near a tree. Though unlikely, that is not ridiculous, it is possible—therefore, it probably won't work. A ridiculous or impossible picture might be: A gigantic tree is flying instead of an airplane, or an airplane is growing instead of a tree, or airplanes are growing on trees, or millions of trees (as passengers) are boarding airplanes. These are crazy, impossible pictures. Now, select one of these pictures, or one you thought of yourself, and see it in your mind's eye.
We don't, of course, mean to see the words _airplane_ and _tree_. You are to actually see the action you've selected—and most ridiculous associations between any two items will be actions, like the examples given here.
See that picture, that action, in your mind for a split second. You're not doing anything unusual; you've been seeing pictures in your mind all your life. Actually, you can't think without seeing pictures. Aristotle said it, centuries ago—one of his books opened with this sentence: "It is impossible even to think without a mental picture."
Seeing pictures, or images, in your mind is almost like having a movie screen in your head. If you read the words _husband, child, car_ , etc., you cannot think of any of those people or things without "seeing" a picture of them—even if it's only for a split second. Try _not_ to picture an elephant; _don't_ see an elephant in your mind. What happened? It became impossible not to see, or picture, an elephant!
All right, then. Choose a ridiculous association between airplane and tree, and see it in your mind's eye, right now.
Once you've tried to do that, stop thinking about it. The "trying," however, is quite important. We tell our students that even if our systems don't work, they must work! That sounds silly, but it's true. Just trying to apply the systems must improve your memory, whether or not they really work. The fact that they do work, and work beautifully, will improve your memory to an unbelievable degree.
The next item on the list is **envelope**. We'll assume that you already know, or remember, tree. The new thing to remember is envelope. Simply form a ridiculous picture, or association, in your mind between tree and envelope. You might see millions of envelopes growing on a tree, or a tree is sealing a gigantic envelope, or you're trying to seal a tree in an envelope. There are many other suggestions we could give you, but all you need is _one_ ridiculous picture. Select one of these, or one you thought of yourself, and see it in your mind's eye for an instant.
You needn't labor over seeing that picture. All it takes is a fraction of a second. It's the clarity of the picture that's important, not how long you see it. So see it, clearly, for just a second.
The next item to be remembered is **earring**. The thing you already know is envelope. Form a ridiculous association between envelope and earring. You might see yourself wearing envelopes instead of earrings, or you open an envelope and millions of earrings fly out and hit you in the face.
You're much better off, incidentally, thinking up your own pictures. When we suggest the ridiculous pictures, we're taking away some of your Original Awareness. We'll keep on giving you suggestions, but whether you use ours or your own, be sure to see the pictures _clearly_.
Select one of our associations between envelope and earring, or one you thought of yourself, and see it in your mind's eye.
**Bucket** is the new thing to remember. Associate it to earring. You might see yourself wearing buckets instead of earrings. Or a gigantic bucket is wearing gigantic earrings. See one of these pictures in your mind.
The next thing to remember is **sing**. (This is not an object, not a noun, and it's here only to show you that this doesn't matter—an association will still remind you of it.) Associate sing to the last thing you already know—bucket. If you see a gigantic bucket singing, that will do it. Or you might see yourself singing with a bucket over your head. That's not impossible, but it's certainly ridiculous. Just be sure to see your picture clearly.
The next item is **basketball**. Associate that to sing. Picture a basketball singing. Or someone is singing and millions of basketballs fly out of his mouth.
**Salami**. Picture a gigantic salami playing basketball. Or a basketball player (Jerry Lucas, who else?) is dribbling a salami instead of a basketball.
**Star**. Picture a gigantic salami twinkling in the sky. Or you're slicing a star, instead of a salami! See the picture.
**Nose**. Picture someone with a twinkling star on his face instead of a nose. Or a star has a large nose. See that picture.
If you've tried to see all the pictures, you will know all ten items. The first item is the only one you may have trouble with, because you didn't associate it to anything to remind you of it. This will be straightened out for you soon enough. If you know the item, fine. If not, it was **airplane**. Try to think of the items before you read them in the paragraphs to follow. Now, think of airplane for a moment. What does that remind you of? **Tree** , of course.
Think of tree—that reminds you of... **envelope**. Think of envelope, which should remind you of... **earring**. Think of earring, and it will remind you of **bucket**. What silly thing was the bucket doing? Singing, of course—and that reminds you of **sing**. What else was singing? A **basketball**. Thinking of basketball for a moment will remind you of... **salami**. Salami should make you think of... **star**. And, finally, star will remind you of... **nose**.
How did you do? You should have known all of them. If you had trouble with one or two, if you think you forgot any, it's probably because you read the word here before you had the chance to think of it. You didn't "forget" it at all. If you're convinced that you did, then you didn't really remember it in the first place—go back to that item and _strengthen_ your association. That is, be sure the picture is ridiculous, and, more important, be sure to really see it in your mind.
If you take paper and pencil and try it now, on your own, you'll see that you can list the ten items, in sequence, without missing any. Try it and see. Now, try it backward! Think of nose; that will make you think of... star. Star will remind you of... salami. That reminds you of... basketball. Basketball to... sing, sing to... bucket, bucket to... earring, earring to... envelope, envelope to... tree, and tree to... airplane. Try this with your own list, and you'll be proud of yourself—you'll be able to remember any list of items, in sequence, backward and forward.
# 3 **_THE LINK_**
HL: Of course, everyone knows that motivation is an important part of memory. The systems themselves can actually provide enough interest and challenge to add up to motivation.
JL: Without motivation, nobody would accomplish anything. When I was a senior in high school, I was named to the _Parade_ magazine High School All-American Team. We were brought to New York City to be on the "Steve Allen Show" along with the All-American College Team, of which Wilt Chamberlain was a member. During the rehearsal, I was with Wilt in the lobby of the theater, where there was a high ledge—it must have been about twelve feet high. Someone approached Wilt and said, "Hey, Wilt, can you jump up and touch that ledge?"
Wilt said he thought he'd just forgotten how to jump. "But I'll tell you what," he said, "I'll bet you if you throw a hundred-dollar bill up there, I'd remember how to jump _real_ quick!"
What you've learned in the preceding chapter is a tiny part of the Link system of memory. We call it the "Link" system because what you're doing when you apply it is linking one item to another, forming the links of a memory chain. One item _must_ lead you to the next, if you're associating properly.
Having applied the Link system, you can retain any list for as long as you like. It's really hypothetical at the moment. When you start applying the Link for practical reasons, you're memorizing a list of things because you intend to _use_ that list. It's the practical use that sets the retention—and provides the motivation to remember it in the first place. You'll see that this is so just as soon as you learn to apply it practically.
Although there's no reason why you should feel motivated to retain the list you memorized in the preceding chapter, you can if you want to. Simply go over it tomorrow; go over it mentally, that is, while you're driving or eating or whatever. Go over it again three days later, then go over it a week later, and you'll still know all the items in sequence. You'll know them for as long as you _want_ to know them.
The Link system is used to remember things in sequence only, and there are many things that must be remembered, or learned, in sequence. A speech is a sequence of thoughts, a formula is a sequence of components, any number with more than two digits is a sequence. (You can't apply the Link system to numbers now because you don't yet know how to _picture_ numbers. Later, you'll be using the Link to remember long-digit numbers.)
The one problem you may have in Linking, only at first, is in making your pictures ridiculous. There are four simple rules to help you do this right from the start. The easiest rule to apply is the rule of _Substitution_. That is, picture one item _instead of_ the other. In the preceding chapter, we suggested that you might see a tree flying _instead of_ an airplane. We were trying to force you to apply the rule of Substitution.
Another rule is _Out of Proportion_. Try to see the items larger than life. Check our suggestions again and you'll see that we used the word "gigantic" quite often. This was to force you to apply the rule of Out of Proportion.
Another rule is _Exaggeration_. Whenever the word "millions" was used, it was to force you to apply this rule. Try to see "millions" of an item.
And, try to get _Action_ into your pictures. Action is always easy to remember. One suggestion was to see millions (exaggeration) of earrings flying out of an envelope and hitting you in the face. Hitting you was the action.
Applying one or more of these rules to any picture will help you to make that picture ridiculous. After a short while, you won't have to think about applying them; you'll do it automatically.
It does take some imagination to form ridiculous pictures in your mind. It's unfortunate that those "wheels" of imagination, observation, curiosity, enthusiasm, etc., that turned so quickly and smoothly when we were young have slowed down by the time we're adults. Society tends to do that, somehow. _Children_ never have any problem forming silly or ridiculous pictures. They do it easily and naturally.
You'll find that our systems will start turning those wheels again; perhaps slowly at first, but turning nevertheless. Your imagination needs exercise, that's all. The important point is that simply _trying_ to apply our systems will automatically give you that exercise. Your imagination must improve, as will your powers of observation, as you keep working with the systems. In a short while, you'll find that it will be the ridiculous, illogical picture that first comes to mind whenever you think of any two items.
Making the pictures ridiculous is what enables you to really see them; a logical picture is usually too vague. Once you really see the ridiculous picture, it does register in your mind. Research carried out by the department of basic and visual science at the Southern California College of Optometry indicates that when you actually see something, an electrical impulse reaches the vision center of the brain. They've also discovered (rediscovered scientifically, really, since ancient philosophers said the same thing) that there is not much physiological difference between the electrical signals that are activated _by the mind's eye_ and ones that are activated _by the eye itself_.
So don't feel bad if, at first, you have to apply some effort in order to come up with those ridiculous pictures—at least, to come up with them quickly. That extra effort at first is good. It forces you to be Originally Aware.
We can't say it any better than it was said on parchment, in the scrolls called _Ad Herennium_ , over three thousand years ago:
... Now nature herself teaches us what to do. When we see in everyday life things that are petty, ordinary, and banal, we generally fail to remember them, because the mind is not being stirred by anything novel or marvelous. But if we see or hear something exceptionally base, dishonorable, unusual, great, unbelievable, or ridiculous, that we are likely to remember for a long time. Accordingly, things immediate to our eye or ear we commonly forget; incidents of our childhood we often remember best. Nor could this be so for any other reason than that ordinary things easily slip from the memory while the striking and the novel stay longer in the mind.
Again, the idea, or the realization, is not new; it has just been neglected, or overlooked. Be sure, then, to make all your pictures ridiculous ones. In that way, and again from _Ad Herennium_ , "Art will supplement nature." That's exactly what happens. When something assaults our senses in an unusual, great, unbelievable, or ridiculous way, it "stirs" the mind. It is usually retained without effort. It is the ordinary, everyday things that we have trouble remembering. Forming ridiculous pictures helps to make them outstanding, novel, or marvelous. The art (of trained memory) _is_ supplementing nature, and all our systems are based on this fact.
If you can apply the Link and memorize ten items, then you can use it to remember twenty or thirty items. Of course, it will take more time to remember thirty items than it will to remember ten. But that would be so whether you applied the Link system or not. There is really no limit to the number of items you can memorize this way.
We strongly suggest that before you continue to the next chapter you try a Link on your own. Have someone give you fifteen or so items, and you form the Link. Or try it on your own. Make a list of items, and then Link them. After you've practiced awhile, when you feel fairly confident, show off for a friend.
Have him call off fifteen or sixteen items, as many as you feel comfortable with. Let him write them down as he calls them. If he doesn't, he won't be able to check you later because he won't remember the items himself (unless he's read this book). Also, his writing gives you the moment you need to make your association. For the time being, don't let him call off intangibles; he's to choose concrete things, nouns or active verbs.
When he's called the fifteen or sixteen items, you call them right back to him, by memory. If you miss one or two, there's no problem. Simply ask him what they are, strengthen that particular association, and then call off the items backward!
And how will you be sure to remember the first item called? Well, once you start using the Link for practical purposes, that won't be a problem. The subject you're memorizing will _start_ your Link.
But even for now the problem is really a hypothetical one. If you think of any item near the start of your Link and work backward, you must eventually come to the first item. And, to save you even this small amount of time: When your friend calls the first item, just associate it—to _him_.
Take the list in the preceding chapter. If your friend called "airplane" as the first item, you might look at him and see an airplane on his head. That's all it takes. The next item is associated to airplane, and so on to the end of the Link.
When you're ready to call off the list of items, simply look at your friend. You'll "see" the airplane on his head, and that association will lead you through the rest of the list.
Again, we suggest that you try a few test Links before continuing. Show off for your friends, or make your own list and show off to yourself. We suggest showing off only because we know that each time you do, you'll gain confidence. You'll see that the system works!
# 4 **_SUBSTITUTE WORDS_**
HL: I've never met anyone who hasn't at times come up with a similar-sounding word or phrase when thinking of something completely different—like "can't elope" and "cantaloupe."
JL: I know one example that was even used in a song—"chicken in a car, and the car can't go—that's how you spell 'Chicago'!"
HL: My favorite is children saying the Lord's Prayer who don't understand the word "temptation." In the New York area, the phrase is likely to come out: "Lead us not into _Penn Station!_ "
•
The states of the United States can easily be memorized in alphabetical sequence. Of course, you probably couldn't care less about knowing the states in sequence. That's not the point. The point is to show you how to picture abstractions, like names. Again, once you understand how to make an intangible tangible and meaningful, it becomes easy to remember. This will be a good exercise for the Link, and it will also start you on the Substitute Word system of memory.
The Substitute Word concept can be applied to any seemingly abstract material. Basically, it's this: When you hear or see a word or phrase that seems abstract or intangible to you, think of something—anything—that sounds like, or reminds you of, the abstract material and _can be pictured_ in your mind.
Ordinarily, the name of a person, thing, or place cannot be pictured in the mind. Most names are intangible, which is why they're so difficult to remember. For example, there would seem to be no way to "picture" (or associate) Minnesota. You might, however, easily picture a **mini soda** , a small bottle of soda. Mini soda sounds like Minnesota, and must remind you of it. And you can associate mini soda to anything you like. If you were trying to memorize the states in their alphabetical order, you might associate mini soda to **Mrs. sip** ; perhaps a married lady is sipping a little soda. This would remind you that Mississippi follows Minnesota, alphabetically.
Ordinarily, you could not "picture" Maryland and Massachusetts. But you could picture a girl named **Mary** (or a bride, **marry** ) **land** ing among a **mass** of people who **chew** and **sit**. Marry land must remind you of Maryland, and mass chew sit will certainly remind you of Massachusetts. Now, you may be wondering how you'd know which of the two items in your picture comes first. Well, aside from the fact that they're alphabetical in this particular example, which comes first is a problem only because we're discussing two at a time. When you actually Link all of them, or more than two, it's no problem. That's the whole point of the Link; one item must lead you to the next.
To repeat, you do have to use a bit of imagination, and the more often you form conscious associations, the easier it will become because you will be improving your imagination as you improve your memory. As Aristotle explained in _De anima_ ,
The perceptions brought in by the five senses are first treated or worked upon by the faculty of imagination, and it is the images so formed which become the material of the intellectual faculty. Imagination is the intermediary between perception and thought.
It is the image-making part of the mind which makes the work of the higher processes of thought possible. Hence the mind never thinks without a mental picture. The thinking faculty thinks of its forms in pictures. No one could ever learn or understand anything, if he had not the faculty of perception; even when he thinks speculatively, he must have some mental picture with which to think.
Aristotle went on to say that all men can think because "it is possible to put things before our eyes, the way those who invent trained-memory techniques teach us to construct images."
_We_ are teaching you, now, how to "construct images" with intangibles. The pictures (Substitute Words, thoughts, or phrases) that you use must remind you of the intangible material. And, again, simply _trying_ to apply the idea must better your memory. Trying to find a Substitute Word for anything _forces_ you to think about it, to concentrate on it as you normally would not.
If, during any of the examples in this book, the Substitute Word does not remind you of what you wanted to remember, it's undoubtedly because you used _our_ suggestion for the Substitute Word, which didn't work for you. Usually, it will—but you're certainly better off thinking up your own Substitute Words, thoughts, or phrases. Again, our giving you suggestions does remove the necessity for you to use your own imagination, thereby diminishing your Original Awareness.
Still, we have no choice but to give you suggestions for most of the examples we'll be using. If you want to use those suggestions, fine. But be sure to form good, clear pictures in your mind.
Getting back to the states, do you see now that if you make up a Substitute Word or phrase for each state and then Link them, you can memorize them all? It's easy to do, and it's fun.
If you don't want to memorize them all in sequence, try it with some of them—just for the practice and the (imagination) exercise. Linking all of them would be excellent practice for forming Substitute Words or phrases, and forming pictures and associations for your Link
Here are all the states, listed alphabetically and numbered from 1 to 50. Later, after learning the Peg system, you can turn back to this page and try memorizing them by number. As you Link them, pause after every ten or so to review mentally the pictures you've formed up to that time.
1. Alabama
2. Alaska
3. Arizona
4. Arkansas
5. California
6. Colorado
7. Connecticut
8. Delaware
9. Florida
10. Georgia
11. Hawaii
12. Idaho
13. Illinois
14. Indiana
15. Iowa
16. Kansas
17. Kentucky
18. Louisiana
19. Maine
20. Maryland
21. Massachusetts
22. Michigan
23. Minnesota
24. Mississippi
25. Missouri
26. Montana
27. Nebraska
28. Nevada
29. New Hampshire
30. New Jersey
31. New Mexico
32. New York
33. North Carolina
34. North Dakota
35. Ohio
36. Oklahoma
37. Oregon
38. Pennsylvania
39. Rhode Island
40. South Carolina
41. South Dakota
42. Tennessee
43. Texas
44. Utah
45. Vermont
46. Virginia
47. Washington
48. West Virginia
49. Wisconsin
50. Wyoming
Trying to memorize these from the top, you start by thinking up a Substitute Word that reminds you of Alabama. **Album** will do nicely. An album can be pictured, whereas Alabama cannot. If you're old enough to remember a song called "I'm Alabamy Bound," which had to do with a train, you might have thought of that and pictured a train. For Alaska, you can picture the flaming dessert **baked Alaska** , or **I'll ask her** , or **a last car**. Now start your Link: You might picture a gigantic album serving baked Alaska to other albums.
For Arizona, you can use **air zone** as the Substitute phrase. Picture a gigantic piece of baked Alaska floating in the air, over a safety zone. For Arkansas, you might see yourself sawing an ark; associate that picture to air zone.
Please bear in mind that _anything_ can be pictured, a noun, an action, whatever. Remember, _sing_ was used in the first sample Link—and you could, and did, picture _sing_ as well as any of the other items, which were all nouns.
For Arizona and Arkansas, an **ark and a saw** floating in the **air** over a safety **zone** would do the trick. For California, how about **call a fawn** as a Substitute Word? To associate that to Arkansas, you could picture yourself calling a fawn into an ark. Whatever Substitute phrase you use, be sure to really see the pictures.
California to Colorado ( **color a toe** ). You might see that fawn painting (coloring) one of his toes.
Colorado to Connecticut ( **connect a cut** ). You cut the colored toe, then connect the two parts.
Connecticut to Delaware ( **Della wear** ). A girl named Della is wearing flowing robes as she bends over to connect a cut.
Delaware to Florida ( **flower there** ). Della throws those flowing robes to the floor and a gigantic flower grows there.
Florida to Georgia ( **George** ). The gigantic flower is named... George! Or, millions of flowers are growing in a **gorge**.
If you've made these or your own associations and have seen the pictures in your mind, you know the first ten states just as you knew the ten items in the first sample Link. There are, of course, many other Substitute Words you could have used. If you thought of the Everglades when you thought of Florida, picturing its swamps would have served the purpose for you. Remember that Linking is individual, personal—what you think of is usually best for you. And, most often, the first Substitute Word that comes to mind is the best to use.
If you want to practice some more, review the first ten states in sequence and then continue your Link with the next ten. Perhaps, George to **how are ya** ; how are ya to **Ida hoe** or **potato** ; potato to **ill noise** ; ill noise to **Indian** ; to **I owe her** ; to **can sass** ; to **can't talk** ; to **lose Anna** ; to water **main** (pipe); to **marry land**. We'll leave the associations here up to you.
Review the Link, the twenty states, then continue with the next ten, and so on. If you can provide your own Substitute Words for the remaining states, without using the suggestions that follow, all the better.
Michigan, **mix again** ; Missouri, **misery** ; Montana, **mountain** ; Nebraska, **new brass car** ; Nevada, **never there** , gambling; New Hampshire, **hamster** ; New Jersey, **Jersey** cow; New Mexico, **Mexican** sombrero; New York, **new cork, E** mpire State Building; North Carolina, **carry liner**. (Make up a "standard" for _north_ and _south_ and use them all the time. For example, you might use **snow** to represent north, and **mouth** to represent south. A picture of someone carrying a liner [ship] in a snowstorm would therefore remind you of North Carolina.)
To continue Substitute Words: North Dakota, **decoder** ; Ohio, **oh, hi!, higher!** ; Oklahoma, **homer** ; Oregon, **are gone** ; Pennsylvania, **pencil** ; Rhode Island, **rode** ; South Carolina, **carry liner** (perhaps carrying a liner in your **mouth** ); South Dakota, **decoder** ; Tennessee, **tennis (see)** ; Texas, **taxes** ; Utah, **you tear** ; Vermont, **vermin** ; Virginia, **virgin** ; Washington, **wash** ; West Virginia, **best virgin** ; Wisconsin, **wise cousin** ; Wyoming, **roaming**.
If you've gone down the list of states ten at a time, using the combination of Substitute Words and Linking, then reviewing each ten once learned, you should be able to reel off all fifty states with hardly a stumble.
Try it—and if you miss a few, simply go back and strengthen those particular associations. You'll be surprised at how easy it is to remember something most people would find difficult, if not impossible.
# 5 **_LONG WORDS,
APPOINTMENTS AND
ERRANDS, SHOPPING LISTS_**
JL: So, Simonides, who was attending a large banquet, was called out to receive a message, and the building collapsed. All the diners were killed. Simonides was able to identify every mangled body for burial purposes. When he was asked how he'd done it, he said that he'd used a memory system.
HL: The banquet may have been large, but Lucius Scipio was supposedly able to remember the names and faces of all the citizens of ancient Rome.
JL: I'll bet you've met and remembered more people than that in your career, Harry.
HL: That's true—at the last count I'd met and remembered somewhere around twenty million people. I can start my own country!
JL: During his news conferences, General George Marshall used to listen to reporters' questions without breaking the continuity of his prepared statement. When he finished the statement, he'd look at each reporter and answer his question in turn. What he did was, he associated the key word or thought of the question to the reporter's name or face. And James Farley's fantastic memory for names and faces supposedly helped elect Franklin D. Roosevelt to his first term.
HL: Did you know I met David Roth? And his fame as a memory expert goes back to the early 1900's. The last time I spoke to him, he told me that his local Rotary Club was giving a luncheon in honor of his ninety-sixth birthday. He told me, "I won't do much, Harry—I'm just going to remember everybody's telephone number." And there were two hundred people there!
JL: So maybe people with trained memories live longer. Using trained-memory systems certainly does keep a person more alert and aware. Which might have something to do with longevity.
HL: Let's hope so!
•
The famous chess player Harry Pillsbury was almost as well known for his memory as for his skill at chess. He was once challenged by two professors to memorize up to thirty words or phrases, read to him only once. Pillsbury repeated them in correct sequence, and then in reverse order. He also knew them the following day. This garnered quite a bit of publicity for Pillsbury, yet the feat is fairly easy to accomplish—if you apply the Link and the Substitute Word systems of memory.
Now, the words and phrases that were read to Pillsbury were not quite so easy to grasp as a list of everyday items or the states of the union. They were: antiphlogistine, periosteum, takadiastase, plasmon, threlkeld, streptococcus, staphylococcus, micrococcus, plasmodium, Mississippi, freiheit, Philadelphia, Cincinnati, athletics, no war, Etchenberg, American, Russian, philosophy, Piet Potgelter's Rost, salmagundi, oomisillecootsi, Schlechter's Nek, Manyinzama, theosophy, catechism, Madjescomalops.
You can remember them all, in sequence, by applying the two systems you've already learned—the Link and the Substitute Word. **Auntie flog a stein** would remind you of antiphlogistine. Associate that silly picture to, perhaps, **pear eat a steam** (periosteum). You might see your auntie (or any little old lady—whatever auntie conjures up in your mind) flogging a (beer) stein as she eats a gigantic pear that's steaming hot. Try to see that picture.
Pear eat a steam to, perhaps, **tack a dais daze**. A gigantic pear that's eating a steam (radiator) is tacking up a dais (platform); the pear is in a daze as he does it. For the next association you might see a **plastic man** (plasmon) tacking up a dais.
Now, plastic man to **thrill cold** (threlkeld), to **strap to cock** (rooster) and **ass** (donkey), to **staff ill of carcass** , to **micro cock ass** , to **place my dime** , to **Mrs. sip** , to **fry height** , to **fill a dell for ya** (or **Philadelphia** brand cream cheese), to **sin sin at tea** , to people performing **athletics, to no war** , to **etchin'** (ice) **berg** , to **a merry can** , to **Russian** roulette, to **fill a sofa** , to **pie et** (ate) **pot** (of) **gal tears rust** , to **sell my gun D** , to **ooh, my silly coat see** , to **sh, let us neck** , to **many in summer** , to **tea owes a fee** , to **cat kiss 'im** , to **Madge's comb elopes**.
This may seem like a lot of work to you. Well, it will certainly take more time and effort than, say, remembering twenty-seven simple items. But just think of how much work it would be to memorize twenty-seven words like this _without_ a system. Not only would that require an enormous amount of time and effort, but you'd probably never accomplish it. Forming Substitute Words, phrases, or thoughts, and Linking, on the other hand, is fun; it _forces_ you to use your imagination and to concentrate; and above all—it works!
Whatever any Substitute phrase conjures up in your mind is what you should use for the picture. For **sell my gun D** , you might see yourself selling your gun to a gigantic letter D. (In another chapter, you'll learn how letters of the alphabet can themselves be pictured, concretely and easily.) You might have thought of **sailor my gun die** —a sailor takes your (my) gun and kills himself with it. Whatever you think of and see will work for you.
Take a few moments to see if you can remember all the words listed above. If Pillsbury could do it, so can you! You may be surprised at the facility with which you can do it.
Linking difficult words is like swinging two bats to help you swing one better. It isn't often necessary to remember words like that. But the idea of the Link can, of course, be wonderfully practical. Later on, we'll show you how to remember specific weekly appointments, by day and hour. For now, if you need to remember simple errands and appointments during most normal days, you can use a simple Link; usually no Substitute Words are necessary.
Assume it is important that you remember to pick up a lamp you ordered. You also must remember to buy a package of typing paper. Start a Link; associate lamp to paper. Perhaps you see yourself putting a lighted lamp, instead of paper, into your typewriter. Or, a gigantic sheet of paper is on your bedside table, you pull a string—and it lights like a lamp. Select one of these pictures, or one you thought of yourself, and see it in your mind.
You don't want to forget to pick up your suit at the cleaners. Continue the Link; perhaps you're wearing sheets of typing paper instead of a suit.
You promised to call about arranging for swimming lessons for your child. See a suit, with nobody in it, swimming or diving into a pool.
For days, you've been meaning to buy some lightbulbs. Picture gigantic lightbulbs swimming.
You must remember to visit a friend at the hospital. Picture yourself putting your friend, instead of a lightbulb, into a socket.
You want to pick up a roll of stamps before the post office closes. Picture your sick friend lying on (and sticking to) a gigantic stamp instead of a hospital bed. Or you're licking your friend and sticking him on an envelope.
If you've actually visualized the silly pictures, you'll remember the things you must do. Start with **lamp** —that should remind you of the next chore or errand, and so on. When applying this idea practically, you'd form your Link the night before. Then, in the morning, you'd simply go over that Link while getting dressed or having breakfast.
If you think of something else you want to accomplish that day, tack it on to the end of your Link. It's important to go over your Link before you leave, because thinking of the chores will remind you to take whatever you need from your home in order to accomplish the errand. For example, if you need a receipt in order to get your suit from the cleaners, thinking of the suit will remind you to go to your desk and get the receipt.
During the day, go over your Link every once in a while—or while you're walking, eating, whatever. Anytime you think of an errand that you have not yet done, you'll know it; simply go and do it. As a final check, go over the Link before you prepare to go home.
This practical use of the Link will save you plenty of time and aggravation. The worst that can happen is that it won't work completely and you'll forget an errand. Well, you haven't much to lose—you've been doing _that_ all your life!
Exactly the same idea can be applied to remembering a shopping list. Granted, remembering a shopping list is not the most important thing in the world. But people who make out a shopping list on a piece of paper often either forget to take it with them, or forget to look at it until they get home again.
Simply Link the items you want to purchase. Be sure to make the pictures ridiculous—you're peeling an **orange** and there's a container of **milk** (or a cow) inside it; you're milking a cow and slices of **bread** , instead of milk, come out, etc. Once inside the supermarket, just go over your Link every once in a while. If you do this, you won't forget _any_ items.
# 6 **_SPEECHES_**
JL: After I graduated from Ohio State, I was booked to speak at a high school athletic banquet. I got plenty of applause, but just as everyone was leaving, this kid comes up to me and says, "Mr. Lucas, I enjoy watching you play basketball—but I thought that was the worst speech I ever heard in my life!"
Well, his mother was right behind him, and of course she heard. "Oh, Mr. Lucas," she said, "please pay no attention to him. He only repeats what he hears!"
HL: I got zinged by a "repeater" _before_ a speech, once. I always tell the chairman of the group how to introduce me. To save time, I make it short and simple, and I always say it in exactly the same way. This particular time, when I was the after-dinner speaker, I told the chairman to say, "Ladies and gentlemen, we have a surprise for you this evening, something different, unique, blah, blah, blah. You've seen him on TV, et cetera, et cetera." He took notes as I spoke.
We finished our meal, and the chairman went to the lectern to introduce me. He said, "Ladies and gentlemen, we have a surprise for you this evening, something different, unique, _blah... blah... blah_. You've seen him on..."!
•
Probably the worst mistake you can make is to try to memorize a speech word for word. First of all, it isn't really necessary. The assumption is that if you've been asked to deliver a speech on a particular subject, you _know_ something about that subject.
Secondly, memorizing the speech word for word will make it sound that way when you deliver it—memorized. And, finally, when you memorize a speech word for word, you're taking the chance of fumbling over one word you can't remember. Why take that chance when there are probably dozens of other words that would do?
Reading a speech doesn't work either, because you want to hold the group's attention, and reading to them is likely to put them to sleep. Even if you occasionally look up at your audience as you read, it won't help much. As a matter of fact, that's the moment when you're likely to lose your place and start hemming and hawing as you try to find it.
The best way to deliver a speech is to talk it in your own words, _thought for thought_. A speech is a _sequence_ of thoughts; if the thoughts are out of sequence, the speech won't make much sense. Now, you know how to use the Link system to remember things in sequence. The Link, plus one other idea, will help you to remember your speech thought for thought.
First, write out or type your speech, including all the things you want to say about all the ideas you think are important. Read it over to get the gist of it. Now for that "other idea": Select a Key Word from each thought that will _remind you of the entire thought_.
This is easier to do than it might seem. There is rarely a thought, whether it is to be expressed in one sentence or two paragraphs, that cannot be brought to mind by _one_ word or phrase. It is these Key Words (or Key Thoughts) that you Link—at which point you have the speech memorized thought for thought!
Here are some excerpts from a talk delivered at a convention to a group of merchants and dealers selling the same line of products. The speaker was asked to talk about a sharp drop in profits over the previous two years and to suggest ways of doing something about it.
The talk originally took thirty-five minutes to deliver. Excerpts have been culled from it to demonstrate the Key Words or Thoughts that the speaker wanted to get across.
The problem is an obvious one. We're all selling just as many of the product as we always have, but our _profit margin_ has been drastically reduced. The reasons, too, are obvious. The cost of material and manufacture has gone up, and so have our prices. The trouble is that if we raise our prices any higher, we'll lose sales. What we have to do is find ways to raise our profit margin....
We have to get more people to _walk in_ to our stores. Obviously, the more people that walk in to our stores, the more opportunities we have to make sales. Perhaps we can organize contests, etc....
An important part of each of our businesses depends on building a _good name_ in each of our local areas. There are many ways to do this; relaxing our "no return" policy....
Our products are _nationally advertised_ , but we haven't been taking advantage of that at all. At least, not to my knowledge. We've got to plan local advertising to mesh with national advertising; blowups of the national ads in our windows should be considered, and....
The _new line_ , Starbright, Holly, Baby Soft, Meteor, and Honeymoon, is really good, and should help to stir up some fresh business. It's been a long time since we had any new line of product at all....
We also must work harder to turn _bread and butter_ sales. Why should a customer walk out after buying only the item she came for? A little thought, and effort, would help toward finding ways to almost force the customer to buy at least one other item, perhaps just an accessory, to go with the one she bought. A two-for-one sale might work, or....
And how can we make customers _come back_ to the store? How many of you follow up a sale? How many of you take advantage of the names and addresses on your sales receipts that are gathering dust in your files? Use those names—send notes and notices of sales....
The Key Words have been italicized within each of the thoughts of this talk. Let us emphasize that the speaker knew what he wanted to say about each thought—that wasn't his problem. What he wanted to avoid was omitting an entire thought. Forming a Link takes care of that.
There are two ways to do this. You can either list or underline the Key Words, and then Link them; or you can Link them as you go. As you become more proficient, you'll most likely Link the Key Words as you go.
Now. The first Key Word or Thought is **profit margin**. Use a Substitute Word to remind you of it. Perhaps your **Ma** is drinking **gin** and being paid for it—she's making a **profit**. That will certainly remind you of the thought; if you were delivering this talk, either **Ma gin** or **profit** alone would suffice.
The next Key Word is **walk in**. Associate **Ma gin** and/or **profit** to that; a silly picture of your gin-drinking Ma **walking in** to a store will do it. The next Key Word is **good name**. Continue the Link; you might see a **name** (picture gigantic letters of your name, or a gigantic business card) that's **good** , walking into a store.
Good name to **nationally advertised**. You might see your good name being on the cover of a **national magazine**.
Nationally advertised to **new line**. See a ridiculous picture of a long **line** of national magazines hot off the press—they're **new**.
New line to **bread and butter**. See a long line of **bread and butter**.
Bread and butter to **come back**. Picture yourself calling a gigantic piece of bread and butter to **come back**.
Forming such a Link accomplishes two things. It forces you to concentrate on (to be Originally Aware of) the thoughts of the speech, and it will give you the sequence of thoughts. _Knowing_ that you definitely have that sequence also gives you a confidence that you wouldn't otherwise have.
Thinking of the first thought, **Ma gin** , is all you need to remind you that you want to talk about the reduction of the profit margin—so talk about it, say it in your own words. When you've said all you have to say about that, you'll automatically be reminded of **walk in**. Since you wrote the speech, you'll know just what **walk in** refers to; it will remind you of the entire thought. Just say what you want to say about getting people to walk in to the store.
If you made the ridiculous association, the Key Word **walk in** must remind you of **good name**. Talk about that; then **good name** will remind you of **nationally advertised** , at which point you say what you have to say about that thought. And so on, to the end of your speech.
You need only try this idea to see that it will work for you. You might be wondering what you'd do if you had a few facts to remember that pertained to a particular thought. For example, take the product names listed within the **new line** thought—you simply form an "offshoot" or "tangent" Link. That is, after you've formed your basic Link, go back to **new line** and form an offshoot Link of the names.
You might see a picture of a long line of **bright stars** ; bright stars are forming a **holly** wreath on your door; you're holding a holly wreath in your arms like a **baby** —it's very **soft** ; a baby is shooting across the sky like a **meteor** ; two meteors are going on a **honeymoon**.
You'll see, when you're delivering the speech, that **new line** will lead you right through the offshoot Link, reminding you of the product names. Then, you'll still be reminded of the thought you originally associated to **new line** in the basic Link— **bread and butter**. If the products have style numbers, you can Link them, too—once you've learned how to picture numbers.
If, for some reason, you want to remember the speech virtually word for word, you'll find that simply going over it a few more times will do the trick. Since you wrote the speech yourself, your own words would be the most likely ones to come to mind as you voiced each thought.
This same system—a combination of the Link and the Key Thought ideas—can be applied to reading material or lectures in almost exactly the same way. Simply Link Key Words as you read or listen. Applied to reading material, the idea forces you to read actively, with concentration; applied to lectures, it does the same thing. It's difficult to allow your mind to wander when you're listening for Key Words to remind you of thoughts. The next time you want to remember more of reading or lecture material than you usually do, try applying what you've learned here. You'll be surprised at how much you retain.
The system can also be applied to song lyrics and scripts. Apply the same idea, then go over the material a few more times. It's still necessary to remember the material thought for thought first; _then_ you worry about word for word. The language itself is a memory aid—there are certain ways to say certain things. Once you definitely know the sequence of thoughts, the words tend to take care of themselves. If you know the thought, the worst that can happen is that you'll say the line a bit differently from the way it was written; it's when you don't know the thought that you can really "go up" (have no idea what comes next).
One famous, award-winning actress has for some time applied these ideas to all her difficult-to-memorize scripts. In a letter, she wrote that the systems "make what is a usual drudgery part of the creative art!"
We'll be giving you more help in remembering reading material later on in the book. For now, you might want to apply the same basic idea to help you remember jokes and anecdotes. Two memory problems may have to be solved: remembering the joke in the first place, and remembering the idea of the joke, its premise and punchline.
To remember jokes, many professional comedians Link a Key Word or thought of one joke to the Key Word of the next, and so on. The comedian knows the jokes; he simply needs reminders of the jokes and their sequence. So, a Link of orange to politics to elephant to gas pump would be enough to remind a comedian to tell the joke about oranges, then the one about politics, and so on.
Remembering the idea and punchline of a joke is just as easy. Let's remember this old gag:
"How do you make a Venetian blind?"
"Stick a finger in his eye!"
Simply form a silly association. Picture a venetian blind with one large eye on your window—see a gigantic finger going into that eye. That's all. You'll remember the idea and the punchline of the joke.
# 7 **_FOREIGN AND ENGLISH VOCABULARY_**
JL: When I played on the United States basketball team during the 1960 Olympics in Rome, our first game was to be against the Japanese team. I asked one of the interpreters to teach me a couple of Japanese phrases, so I'd be able to say something to the Japanese players the next morning.
I had no trouble with the phrase "good morning," because it's pronounced _ohio_ in Japanese, and of course I associated it to my home state. I easily learned a few more phrases by applying the systems.
The game was scheduled for 9:30 A.M. Just before it was about to start, I looked over at my opponent and said, "Ohio, gozai mosk," which means, "Good morning, how are you?" He gave me a big smile, happy to have found somebody from America who could speak his language.
Well, he backed out of the jump circle and began to bow to me, rattling off Japanese as fast as he could. This created quite a scene, because he was so engrossed in this conversation he thought he was going to carry on with me that he forgot he was there to play a basketball game.
One referee was from Russia, the other from France, and I spoke only English. The Japanese player and the officials each spoke only their own languages. So there were the four of us trying to talk to each other—nobody knowing what the other was saying. They had to call time out, we had to go back to the sidelines, and we had to start the game later. Then the player rattled Japanese at me throughout the entire game. Of course I didn't know the Japanese words to tell him I didn't know Japanese, so I must have said "Good morning" to him dozens of times during that game! He couldn't have been more pleased.
HL: Had you had the time to apply the systems to Japanese for a week before that game, you'd have had plenty of things besides "ohio" to say to him.
JL: Sure, but then he'd have gotten so excited it might have thrown his game off!
•
Now that you've learned how to apply the Substitute Word idea to intangible words and names—and Link them—you can go a step further. Instead of associating, say, one state to the next in order to form a Link, you can associate a state to its capital city. You can also associate a word to its meaning, whether it's an English word or a foreign word.
This brings us to an important point. Most often, where memory is concerned, an entity consists of two things. Even the most complicated-seeming memory chores can usually be broken down into entities of two: a name to a face, an address to a person or company, a price or style number to an item, a telephone number to a person or company, a definition or meaning to a word, and so on. Even when forming a long Link, you're still basically working with only two items at a time.
The capital city of Maryland is Annapolis (that's right; it is not Baltimore); if you form a ridiculous association of a bride ( **marry** ) **land** ing on **an apple** , you'll find it difficult to forget. The capital of Wyoming is Cheyenne; you might picture a **shy** girl, named **Ann** , carrying a large letter **Y** and **roaming**. Michigan's capital is Lansing; associate **mix again** to **land sing**. California's is Sacramento; associate **call a fawn** to **sack cement toe**. Tennessee's is Nashville; associate **tennis** to **gnash** ing your teeth (see a tennis racket gnashing its teeth). Vermont's is Montpelier; associate **vermin** to **mount peeler**. Apply this to any state whose capital you'd like to remember, and whenever you think of the state, the capital city will surely come to mind.
The same system can be applied to Presidents and Vice-Presidents. Associate the Substitute Word for the name of the one to the Substitute Word for the name of the other. For example, President Rutherford B. Hayes's Vice-President was named Wheeler. Associate **hay** to **wheel** in order to remember that. If you picture the hay saying, " **oh, hi** ," to the wheel, you'll also be reminded of the fact that Hayes was from Ohio.
JL: I've applied the systems to Japanese, Polish, Russian, and a few other languages, but never to Portuguese—for the simple reason that I've never been to Portugal.
HL: I spent most of one summer there, and I knew even before I got there that Portuguese is a difficult language to learn. Anyway, they have terrific clams in Portugal, and I love clams. In the very first restaurant I visited, I found out that the Portuguese word for clams is _amejues_ , pronounced _ah-mezz-you-iz_. I immediately saw a picture of a gigantic clam approaching me, all drippy and dirty, and I say to it, "What a mess you is!" So before I learned how to say, "Do you have," when the waiter approached I just said "amejues" and got them.
JL: Which is all you were interested in at the moment.
HL: Exactly. People who need a doctor in a foreign country don't have to be able to say "Please call a" or "Take me to a." But they'd better know the word for doctor!
The Substitute Word idea can be applied to any word of any language. There is no word that does not sound like, or make you think of, something in your own language. To remember the meaning of a simple French word like _père_ (father), you might picture a gigantic **pear** being your father. For _pont_ (bridge), you might see yourself **punt** ing a bridge instead of a football.
The idea applies to any word, short or long. The French word for grapefruit is _pamplemousse_. Picture huge yellow **pimples** all over a **moose** ; each pimple is actually a grapefruit. If you try to see any of these silly pictures, the system must work—for reasons you already know: You're forcing yourself to be Originally Aware, you're really concentrating on the word, and you're forcing yourself to use your imagination. There just is no way to apply the Substitute Word system to a foreign word _without_ concentrating on or being Originally Aware of that word, and using some imagination. And finally, applying the system reminds you of the two things (that entity of two mentioned before) you must know: the pronunciation of the foreign word, and its English equivalent.
If you used our or your own Substitute Word and saw a ridiculous picture, the next time you hear or see _pamplemousse_ , it must make you think of a moose with grapefruit pimples. When you hear, see, or think _grapefruit_ , the same thing will happen. Students of ours do this with twenty foreign words in an evening, every evening, and remember them all easily—simply because the intangible, abstract conglomeration of sounds of the foreign word is changed to a definite, tangible picture in the mind.
Since Portuguese has been mentioned, let's use a few Portuguese words as examples. _Walnut_ in Portuguese is _noz_ , pronounced _nawsh_. Simply picture a gigantic walnut being **nauseous** , or you eat a gigantic walnut and it makes you **nauseous**. See that picture. The word for a woman's _skirt_ is **saia** , pronounced _syer_. Picture a skirt sighing—it's a **sigher**. A _peach_ is a _pêssego_ , pronounced _pess-a-goo_. See a gigantic peach asking you to **pass the goo**.
A woman's _purse_ is a _bolsa_. Picture a gigantic purse made of **balsa** wood, or a large piece of **balsa** wood carrying a purse.
The word for _dinner_ is _jantar_ , pronounced _John-tar_ (the _n_ is really a nasal sound). Picture **John** eating **tar** for dinner.
_Handkerchief_ is _lenço_ , pronounced _leng-ssoo_ (the _ng_ is a nasal sound). Picture yourself **lend** ing **Sue** your handkerchief; make the picture ridiculous; perhaps you're lending her millions of handkerchiefs or one gigantic one.
_Father_ is _pai_ , pronounced _pie_. A gigantic **pie** is your father.
A _strawberry_ is a _morango_ , pronounced _moo-ran-goo_. See a gigantic strawberry, or millions of them, eating **meringue goo**.
The word for _socks_ is _peúgas_ , pronounced _pee-oo-gesh_. You might picture a gigantic sock that has a terrible odor; you say, " **Peeyoo** , it smells like **gas**."
Bear in mind that if you were trying to really learn a particular language, you'd be aware of the basic sounds and letters. In the last example, "true" memory would tell you that _gas_ is pronounced _gesh_ , with a soft _sh_ sound. Of course, you would also be using the Substitute Word _you_ thought of—the one that would remind you of the proper pronunciation _because_ you thought of it. That's why our helping with suggestions for Substitute Words is not really helping you—you might have used **gash** instead of **gas**.
At this point, why don't you try something? Go back to the first examples of foreign words and _really_ form the associations. Then see if you know the words and their meanings by filling in these blanks. Don't worry about spelling—when you're in a foreign country, you need the pronunciations and meanings, not the spelling.
Now try it this way (without looking at the above, of course):
If you missed a few, simply go back and strengthen those particular associations. Then test yourself again. Most likely, you'll get them all.
The method is applicable under any circumstances. If the English equivalent is not tangible, you can use a Substitute Word or phrase for that English equivalent. The Siamese word for August is _singhakom_. Ordinarily, August is difficult to picture, because it's intangible. But a **gust** of wind blowing over a **singing comb** is not. See that picture, and you've got it.
The system will work even if a foreign word contains sounds that we don't often use in English (like **the soft** _sh_ in Portuguese). The word for _squirrel_ in both French and German contains unfamiliar sounds. In German, the word is _Eichhörnchen;_ the _ch_ is a back-of-the-throat, guttural sound—almost as if you're clearing your throat. We do not use that sound in English, yet the system applies. **I horn kin** might remind you of _Eichhörnchen;_ or, perhaps, **I corn kin**. Use either one for your Substitute phrase, but be sure you get a squirrel into your picture. To help you not just approximate the pronunciation but pronounce the word correctly, you might add clearing your throat to your picture.
The French word for _squirrel_ is _écureuil_. We do not have the _euil_ sound in English. But **egg cure oil** can certainly get you close to the pronunciation of that difficult word. You might picture a squirrel laying a sick egg, and it cures the egg with oil.
The Greek word for _scissors_ is _psalidi_. The _p_ is pronounced. Associate **pass a lady** to scissors, and you'll have memorized both the pronunciation of the foreign word _and_ its meaning.
The grammar of a language will usually fall into place as you learn the vocabulary, although the system is applicable to any kind of word. It is also applicable to phrases—why shouldn't it be, since phrases are made up of words? The French phrase _rien de grave_ is idiomatic for _It's nothing_ or _It's nothing serious_. Associate **ran the grave** to **It's nothing** in some ridiculous way and you've memorized it.
When you fly to a foreign country, you're usually armed with a money converter and a "conversation" booklet in that language. What you see in those booklets is the English equivalent, followed by the foreign translation. The translation is then spelled phonetically (as we did with the Portuguese examples) to give you the pronunciation.
All very well. Only, when you arrive, you end up searching through the booklet (feeling like an idiot), trying to find a word or phrase whenever you want to understand or be understood. Nowhere in these booklets does it tell you how to _remember_ the words, phrases, pronunciations, and meanings.
What we're interested in is having you spend the six-plus hours on a transatlantic flight with such a booklet, only _remembering_ enough so that when you disembark you'll be able to ask a porter to get your luggage, find you a taxi, tell the taxi driver where to go, etc. And to remember enough, during that flight, to help you through a few weeks' stay. Apply what you're learning here, and you will do just that.
Obviously, you'll learn more if you also apply the systems during your stay. And we're assuming you are neither a linguist nor are you determined to speak like a native. (The systems are extremely helpful for those people, too, but we're concerned at the moment with those who would simply like to make their way more easily during a visit to a foreign country.)
The Portuguese examples were used to teach you the idea, in a language that isn't familiar to many Americans. Here are a few examples in French—really, a mini in-flight French lesson.
If you intend to visit France, you certainly need to be familiar with the French words for many foods. In restaurants heavily patronized by tourists, you may find English translations on the menu—and food that makes you wonder what all the shouting is about when it comes to French cuisine.
In small restaurants, out-of-the-way restaurants, special restaurants, you may not find translations, nor will you find English-speaking waiters—which makes it a little difficult to find out what a word on the menu means.
We asked four volunteers who had no knowledge of the French language (but some knowledge of our systems) to apply the systems to the following words. In less than twenty minutes, they all knew the English meaning when we said the French word, and vice versa. See if you can do it in that time. The _only_ way to do it that quickly is to think of pictures for the suggestions and really see them.
Bread— _pain (pan)_. The handle of a **pan** is a loaf of French bread.
Butter— _beurre (buhr)_. A large bar of butter is full of **burrs**.
Mushrooms— _champignons (shahn-peen-yawn)_. A gigantic mushroom delivers a monstrous, **champion yawn**.
Beans— _haricots (ah-ree-koh)_. Millions of beans are wearing **hairy coats**.
Chicken— _poulet (poo-leh)_. You're **pull** ing the **leg** of a gigantic chicken.
Watermelon— _pastèque (pass-tehk)_. A gigantic watermelon **pass** es a **deck** of cards to you.
Snails— _escargots (ess-cahr-go)_. A gigantic snail is carrying a cargo of S's— **S cargo**
Ham— _jambon (zhan-bown)_. You **jam** a **bone** into a gigantic ham.
Duck— _canard (ka-nar)_. Someone throws a **can hard** , and you duck.
Lobster— _homard (oh-mar)_. Your mother is disguised as a lobster; you say, " **Oh, Ma**."
Water— _l'eau (low)_. You go under the table ( **low** ) to drink water.
Garlic— _ail (eye)_. A gigantic piece of garlic ( **smell** it) falls in your **eye**.
Cake— _gâteau (gah-toh)_. A gigantic birthday cake has **got** you by the **toe**.
Ice cream— _glace (glas)_. You're eating **glass** instead of ice cream.
Check— _l'addition (lah-dish-yawn)_. A **dish yawns** as it hands you the check.
Tip— _pourboire (poor-bwahr)_. You tip over a **poor boy**.
Look at them once again, and go over _(see)_ your associations.
Bread— _pain (pan)_
Mushrooms— _champignons (shahn-peen-yawn)_
Chicken— _poulet (poo-leh)_
Snails— _escargots (ess-cahr-go)_
Duck— _canard (ka-nar)_
Water— _l'eau (low)_
Cake— _gâteau (gah-toh)_
Check— _l'addition (lah-dish-yawn)_
Butter— _beurre (buhr)_
Beans— _haricots (ah-ree-koh)_
Watermelon— _pastèque (pass-tehk)_
Ham— _jambon (zhan-bown)_
Lobster— _homard (oh-mar)_
Garlic— _ail (eye)_
Ice cream— _glace (glas)_
Tip— _pourboire (poor-bwahr)_
Now, either test yourself or have someone else test you.
Remember to apply the system to phrases just as you do to words. The French for _How much is it?_ is _Combien est-ce?_ ( _kawn-byen-ehss_ ). You see a comb that can change and be an S ( **comb be an S** ); you want it, so you ask how much it is. " **Come be an ass'** would also do. Of course, if you only say _"Combien?"_ the merchant will know what you mean. Picture yourself asking how much it costs to **comb Ben**. When you get the answer, you may want to say, "That's too much" (or too expensive): _C'est trop cher (seh-troh-shehr)_ —you want to **sit** and **row** in a **chair** , but it's much too expensive.
_Please: s'il vous plaît (seel-voo-pleh)_. Picture a seal playing by yelling "Boo"; you ask it to please stop. **Seal boo play** will remind you of _s'il vous plaît_.
_I need: il me faut (eel-muh-foh)_. A gigantic eel is your foe ( **eel my foe** ) and coming to hurt you—you need help.
If some of the Substitute Words or thoughts used as examples seem farfetched to you, make up your own. But it doesn't matter if they're farfetched; they'll still serve as reminders. If you try to actually see the suggested pictures, you'll see that they serve quite well.
Except for _l'eau_ and _l'addition_ , we've omitted the articles, which in many languages are "masculine" or "feminine." In French, _le_ is masculine, _la_ is feminine, and _les_ is plural for either gender. All you really need is a standard for one of them. For example, you might decide to use singing ( **la, la** ) as the standard for the feminine article. Any picture that has singing in it tells you that the item is feminine; if it doesn't have singing in it, the item is masculine. Or, see a dress on any noun that takes the feminine article.
For example, take _table_ (pronounced _tabluh_ ). That's a word you won't need a Substitute for because it's spelled exactly like the English equivalent, _table_. Let's assume you _do_ want to remember whether it's masculine or feminine. If you picture a table singing to you, and singing is the standard you've chosen for feminine, you won't forget that _table_ is _la_ table, not _le_ table. On the other hand, _restaurant_ (another easy one) is masculine because the restaurant you picture _doesn't_ sing.
An English word that you never heard before is really the same as a foreign word; it's foreign to you, anyway. Apply the system in exactly the same way. The English word _peduncle_ means a flower stalk. See yourself having **paid** your **uncle** with flower stalks instead of money, and you have both a reminder of the pronunciation of the new word and its meaning.
The _omphalos_ is the navel or belly button. Omphalos sounds like **arm fell loose.** See this picture: Your arm fell loose—where did it fall? Right into your belly button, of course.
A _factotum_ is a handyman. Picture a handyman (whatever that conjures up in your mind) painting **facts** on a **totem** pole.
If you're a crossword-puzzle nut, you'd save time if you remembered that the clue "sun god" usually refers to _Ra_. Picture the sun cheering, " **rah,** " and you'll probably never have to look it up again. The clue "Chinese pagoda" usually refers to _taa_. Associate pagoda to **tar** , and you'll have your reminder.
The idea applies to any kind of terminology. To a medical student, the Substitute Word for femur could **be fee more** ; for sacrum, **sack rum** ; for patella, **pat Ella** ; hypoglossal, a **glossy hypodermic** needle; and so on.
A pharmaceutical student might picture someone putting a large **bell down** over his head as he **throws pine** trees from under it—to remember that atropine (I throw pine) comes from the belladonna (bell down) root or leaf.
As with the foreign words, if you go back a bit and really form the associations for the English words (instead of just reading passively) you should be able to fill in these blanks easily:
It might interest you to know that, as far back as the 1600's, children were taught language by means of pictures and pictures in the mind. It must have worked pretty well—think of all the people then who could speak Latin, Greek, and other languages.
There's one point that should be stressed: We have yet to find the memory problem that the systems taught in this book can't make easier to handle. You'll see that, with a slight twist or manipulation, the systems must apply. It doesn't matter how difficult the problem is; in fact, the more difficult the problem, the more valuable the systems.
When we teach students how to remember foreign language vocabulary, there's usually one who'll say, "Great, but what about languages like Chinese?" Well, what about them? Of course it's more difficult to learn Chinese or Japanese than French or Spanish—but it always will be, whether or not you use our systems. Applying the systems will still make the chore less of a chore, and take the drudgery out of what can be enjoyable.
If we show a student how to remember things in sequence, and he says, "Okay, but I have hundreds of things I must remember in sequence," his thinking is a bit inverted. It's _because_ he has hundreds of things to remember that he _needs_ the systems. If he had only four things to remember, he wouldn't need them at all.
# 8 **_NAMES AND FACES_**
JL: I had agreed to help one of Coach Woody Hayes's football players with his studies, so I went over to the player and said, "Hi, I'm Jerry Lucas—what's your name?" He didn't say anything for maybe a half a minute, just seemed to be rapidly counting on his fingers. Then he said, "Bob." I heard him, but I was curious. "I'm sorry," I said, "what did you say your name was?" He went through the same routine again, before finally saying, "Bob." Of course, I had to ask him why he did that.
"Well," he said, "I have a terrible memory—I even find it hard to remember my own name. So, what I do is sing to myself, keeping time on my fingers, 'Happy birthday to you, happy birthday to you, happy birthday, dear... _Bob!_ "
HL: That's about the best "worst memory" story I've ever heard. It reminds me of the late Richard Himber, the musician and magician, who was a good friend of mine. During the early years, when I was first starting, he was going to get me on the "Ed Sullivan Show."
He dragged me to the studio during a rehearsal and cornered Sullivan. "Ed," he said, "this guy is fantastic. He'll meet everyone in your audience. Then, during the show, he'll call each person's name. As he does, each person will stand up—until the _entire audience_ is standing!" As was often the case with Dick he had it mixed up—all the people I've met stand, then _sit down_ as I call their names.
Anyway, Sullivan looked at Dick for a moment, and said, "I can have the band play 'The Star-Spangled Banner' and get the same result!"
JL: Well, _he_ could get things mixed up too. One year I was named _Sports Illustrated_ Sportsman of the Year, and the announcement was to be made on the Sullivan show—you know, Ed was to introduce me from the audience.
So, near the end of the show, he says, "Ladeez and gentlemen, we have in our audience the _Sports Illustrated_ Sportsman of the Year. Would you please give a big welcome to Mr. Jerry... _Lewis!_ "
Most of us recognize faces (did you ever hear anyone say, "Oh, I know your name, but I don't recognize your face"?). It's the names we have trouble with. Since we do usually recognize faces, the thing to do is apply a system wherein the face _tells_ us the name. That is basically what our system accomplishes, if it is applied correctly.
The first problem is the name. Well, that one is easily solved—simply apply the Substitute Word system of memory. You won't need it for many names that already have meaning—names like Hayes, Howe, Carpenter, Fox, Paige, Coyne, Paynter, Gold, or Knott immediately create pictures in your mind.
Other names may not have meaning, but will still remind you of something tangible. For example, the names Hudson, Jordan, and Shannon will probably make you think of a river, and the name Ruth might make you think of baseball.
The vast majority of names, however, have no meaning at all. They are conglomerations of sound, just like a word in a foreign language. That's where the Substitute Word system comes in.
Before we give you some examples, you should be aware of the fact that most people don't really forget names. They just don't remember them in the first place—often, they don't really _hear_ them in the first place. Just think back and remember the many times you've been introduced to someone, when all you heard was a mumble. There's no way on earth to remember a mumble!
For some reason, people are usually embarrassed to simply say, "I'm sorry, I didn't hear your name." There's nothing to be embarrassed about. Since a person's name is one of his most prized possessions, it's flattering to make even the slightest fuss over it. Asking him to repeat it shows that you're interested enough in him to want to be sure you get his name right.
Then there are those who don't bother asking the person to repeat his name because they feel that they'll probably never meet him again, so what difference does it make? Of course, they often do meet that person again—which is why half the world seems to address the other half as Darling, Buddy, Fella', Mac, Champ, Honey, or Sweetheart. Not because "Honey" is so special to them, but because they don't know who in blazes they're talking to! Which is probably all right, because the chances are that "Honey" and "Buddy" don't know who _they're_ talking to, either!
Anyway, if you would like to remember names and faces, there are three steps involved; the first step takes care of the name, the second takes care of the face, and the third locks the two of them together. What you have to do is associate the name _to_ the face in some ridiculous way. But for now, let's talk about the first step, remembering the name.
Ordinarily, there'd be no way to picture a name like Bentavagnia (pronounced _bent-a-vane-ya_ ). But you _can_ picture, say, a bent weather vane. And **bent vane** has to remind you of Bentavagnia!
The Substitute Word system will work beautifully to help you remember names. Applying it will _force_ you to listen to, pay attention to, concentrate on that name—to be Originally Aware of it. You can't come up with a Substitute Word for a mumble. You simply _must_ be sure to hear the name, even if you have to ask the person to repeat it.
Before you learn how to attach a Substitute Word to a face, you should be convinced that there is no name, no matter how long or odd-sounding, for which you cannot find a Substitute Word, phrase, or thought. It might even be a thought you can't put into words. But you'll always be able to think of something that can be pictured, and that will remind you of the name.
The name Antesiewicz seems formidable. But it's pronounced _ante-sevage_ , and it's easy enough to picture **anti-savage** or **Auntie save itch**. Suddenly, the name seems less formidable. Pukczyva (pronounced _puk-shiva_ ) is another name that ordinarily would go in one ear and out the other because, subconsciously or consciously, you'd think, "I'll never remember that, anyway—why try?" And, of course, you'd be right; you'd never remember it. But if you picture a hockey **puck shivering** because it's on ice, you can picture that name.
For the name Barclay, you could use **bar clay** or **bark lay** ; for Smolenski, a **small lens** (camera) **skii** ng; for Caruthers, a **car** with **udders** ; for Krakowitz, **cracker wits** ; for Frankesni, **frank** (hot dog) **has knee** ; for Esposito, **expose a toe** ; for Dalrymple, **doll rumple** ; for Kolodny, **colored knee** ; for Androfkavitz, **Ann drop car witch** ; for Giordano, **jawed on O** ; for Virostek, **virile stick** ; and so on.
The Substitute Word or phrase you use needn't contain all the exact sounds of the name; cover the main sound or elements, and you'll have the reminder you need. "True" memory will fill in the rest for you.
As with most anything else, it will become easier and easier as you practice applying the idea. You'll develop standards for certain names, prefixes, suffixes, and even sounds. Here are three standards we mention to our students: For Smith, always picture a blacksmith's hammer; for Cohen, an ice cream **cone** ; for Gordon, a **garden**.
For the suffix - _son_ , you might always see a smaller version of the main thing you're picturing. For example, for Robinson, you could see **a robin** and a smaller robin—its **son**. Or, you could use the **sun** in the sky as your standard. For _Mc_ \- or _Mac_ -, you could always picture a **Mack** truck; for - _itz_ or - _witz_ , picture brains ( **wits** ); for - _berg_ , see an ice **berg** ; for - _stein_ , picture a beer **stein** ; for - _ton_ , see the item weighing a **ton** ; for a - _ger_ ending, we usually picture either a wild animal growling ( **grr** ), or a ci **gar**.
Once you use something for any name, prefix, suffix, etc., you'll probably use it automatically when you hear that sound again—it will become a standard to you.
Here's a list of nearly six hundred of the most common names in America, plus suggestions for Substitute Words or phrases for each of them. (Names that already have meaning, like Storm, Bell, Paine, Brown, Wolfe, etc., are not listed.) Take the time to go over these at least once; some standards will start forming for you. You can use the list as a drill, if you like. Cover the Substitute Word suggestions with your hand or a piece of paper, and see if you don't come up with some of the same words or phrases we've listed. It will help you become more familiar with the idea, and it's a good imagination exercise.
Aarons | run on air, air runs
---|---
Abbott | an abbott, I bought
Abrams | rams, ape rams
Abramson | ram son
Adams | fig leaf, Adam's apple, a dam
Adler | paddler, add law
Alexander | lick sand, lick sander
Allen | alley, all in
Altman | old man
Anderson | hand and son
Andrews | Ann draws, Ann drools
Anthony | hand ton, Mark Anthony
Applebaum | apple bum
Archer | archer, ah chair
Arnold | arm old
Ashburn | ash burn
Atkins | hat kin
Atkinson | hat kin son
Bailey | bale E
Baldwin | bald one, bald win
Barnett | bar net
Barry | bury, berry
Bartley | bought lay, barred lea (meadow)
Barton | bar ton
Bauer | bower
Baxter | back stir, backs tear
Beck | back, peck
Bennett | bend net, bend it, Tony
Benson | bend son
Bentley | band lay, English car
Berman | bar man (bartender)
Bernstein | burn stein
Blair | blare, lair
Blake | flake, lake
Borden | milk, boarding
Bowen | bowing
Boyd | bird
Bradley | brad lay
Brady | braid E
Brent | rent, bent
Brewster | brew stir, rooster
Brody | broad E
Bruce | ruse, bruise
Bryant | buy ant, buoyant
Buckley | buckle
Burke | berg, perk
Burton | buy ton, burr ton
Callahan | call a hand
Cameron | camera on
Campbell | soup, camp bell
Carroll | Christmas carol, carry all
Carson | car son, Johnny
Carter | car tear, cart her
Chadwick | shadow wick, chat wick
Chandler | chandelier
Chapman | chapped man, chop man
Charles | char, quarrels
Chester | chest tear, jester
Chilton | chill ton
Chisholm | chisel
Christenson | Christian son
Christopher | Christ go far
Clark | clock, clerk
Clinton | clean ton
Cochran | rooster (cock) ran
Coleman | cold man, coal man
Collier | collar, call ya'
Collins | collie, Tom Collins
Connolly | con a lay
Connor | counter, con her
Cooper | chicken coop, coo pair
Craig | crack
Crandall | ran doll, crane doll
Crawford | crawl Ford, Joan
Crawley | crawl lay, Raleigh
Crosby | cross bee, Bing
Crowley | crow lay
Cunningham | cunning ham
Curtis | curt, Tony
Daley | daily, day
Daniels | Dan yells
Davis | Davis cup (tennis)
Davison | Davis cup and son
Dawson | door son
Denton | dent ton
Deutsch | touch, German
Dixon | Dick (Tracy) son
Donahue | don a hue (color)
Donald | Duck, darn old
Donovan | don a van
Doran | door ran
Dougherty | dough in tea, dock her tea
Douglas | dug glass, dug less
Doyle | doily, toil, oil
Driscoll | drizzle
Dudley | dud lay, dead lay
Duffy | the fee
Dugan | do again, due again
Duncan | dunkin'
Dunlap | down lap, down lip
Dunn | dun, down
Dutton | button, the ton
Dwyer | wire, dryer
Eaton | eat ton, eatin'
Eberhardt | ever hard
Edelman | a dull man
Edwards | wards (off)
Egan | he can, again
Ehrlich | air lick, oil lick
Elliott | lot, L E hot
Ellis | L ass, Alice
Engle | angle, and gull
Epstein | ebb stein
Evans | heavens
Farber | far bar, far bear
Farrell | far rail, barrel
Feinberg | fine berg
Feldman | fell man
Ferguson | fur go son
Feuer | foyer, fire
Finney | fishy, fini
Flanagan | fan again
Fleming | flaming, lemming
Fletcher | fetch her, lecher
Flynn | flyin', Errol
Foley | fall E, foal
Forbes | four bees, orbs
Forman | boss, four men
Forrester | forest, forest tear
Foster | forced her
Frazer | freezer, raise her
Freedman | free man, reed man
Fried | freed
Friedlander | free land
Fuller | full, brush
Gallagher | gal
Gardner | gardener
Garrison | carry son
Gaynor | gain her
Geller | gala, gal law, kill her
Gelman | kill man
Gerber | go bare, baby food
Gibson | vodka gibson, give son
Gilbert | kill bed
Ginsberg | gin berg
Gladstone | glad stone
Gleason | glee son, Jackie
Goodwin | good win
Gorman | gore man, doorman
Graham | cracker, gray ham
Gregory | gory, Peck, gray gory
Griffin | grip fin
Griffith | grip fish
Grover | rover, grow
Gulliver | giant, gull liver
Gunther | gun tore, gunned her
Hahn | hone
Hamilton | hammer ton
Hansen | hansom cab, handsome
Harper | harp, hopper
Harrington | herring ton, her ring ton
Harris | harass, hairy
Harrison | hairy son
Hartman | heart man, hard man
Haupt | hopped, hoped
Healey | heal E
Heller | hello
Helman | hell man, held man
Henderson | hen son
Hendricks | hen tricks, hand tricks
Henry | hen
Herman | her man
Hicks | hicks, hiccups
Hirsch | Hershey bar
Hirshfeld | Hershey fell
Hobart | whole bar, hope hard
Hodges | hedges
Hoffman | huff man, half man
Hogan | hoe can, whole can
Holden | hold in, hold den
Hollis | hollers
Holt | halt, hold
Hooper | hoop
Hopkins | hop kin
Hornsby | horns bee
Horowitz | horror wits
Houlihan | hold a hand, hooligan
Houston | house ton, use ton
Howard | how hard
Hoyle | hurl, oil
Hubbard | Old Mother (Hubbard), hop hard
Hughes | hues, use, ewes
Hyman | high man
Isaacs | eye sacks, ice axe
Israel | is real, Star of David
Jackson | jack son
Jacobs | cobs, Jacob's ladder
Jaffe | café, coffee
James | aims
Jansen | Sen Sen, _jan_ itor's son
Jerome | chair roam
Johnson | john son, Lyndon, yawn son
Jones | owns, john
Kagan | K again
Kahn | can, con
Kaiser | guy sore, geyser
Kantor | cantor, can't tear
Kaufman | cough man
Keegan | key can
Keller | call her, kill her, color
Kelly | call E, kill E, green
Kennedy | can a day, can of D's
Kenny | can knee, penny
Kent | can't, canned
Kerr | car, cur
Kessler | cast law
Klein | climb, K line
Knapp | nap, knapsack
Koenig | king, K nick, coin nick
Kornfeld | corn fell
Kramer | gray Ma, creamer
Krieger | regal, cry gore
Lafferty | laugh tea
Lambert | lamb butt
Lang | long
Langer | longer, languor, linger
Larkin | lark in, lark kin
Larson | arson, larceny
Lawrence | law ants, lower ants
Lawson | law son
Lawton | law ton
Lederman | leader man, letter man
Lee | lea
Lehman | layman
Leonard | lean hard
Leslie | less lie
Lester | less tear, jester
Levine | the vine, live in
Levinson | level son, leavin' son
Levy | levee, Levi's
Lewis | lose, loose, who is
Lieberman | labor man, leave her man
Lindsey | lint sea, lindy hop
Logan | low can, low again
Loughran | lock ran
Lund | land
McCarthy | Mack cart tea
McCoy | me coy, decoy
McDonald | Mack and Duck (Donald)
McGee | my key
MacLeod | Mack loud, Mack cloud, my cloud
McMann | Mack man
Mahoney | Ma hold knee, my whole knee, my honey
Malone | alone
Manning | man ink, manning
Marcus | mark us
Marshall | marshal, Ma shall
Martin | Ma tin, mar tin
Mason | mason, my son
Maxwell | makes well, mix well
Mayer | mayor
Mead | meat, meet
Merrill | merry ill
Metcalf | met calf
Meyer | mire, my ear
Michaels | mike calls, mike kills
Middleton | middle ton
Mitchell | shell, mitt shell
Monroe | man row, Marilyn
Moore | moor, more
Moran | Ma ran, more ran
Morgan | more can
Morris | Morris chair, Ma is, more rice
Morse | moss
Morton | mutton, more ton
Muller | mulling it over
Murphy | my fee, more fee, morphine
Nash | gnash
Neill | kneel
Nelson | kneel son, wrestling hold
Nichols | nickels
Nixon | mix on, nicks on
North | storm, wind, compass
Norton | no ton
Nussbaum | nose bum, nuts bum
O'Brien | oh burn, brine
Ogden | egg den, egged on
Oliver | olive
Olsen | old son
O'Neal | kneel, O kneel
Oppenheim | open home
Owens | owes, owns
Padgett | patch it, page it
Paley | pale, pail
Palmer | palm, palm Ma
Parkington | parking ton
Patrick | pat trick
Patterson | pat a son
Paul | pull, pall
Pawley | pulley, pull E
Paxton | packs ton
Pearce | pierce
Pearson | pierce son, pear son
Perkins | perking
Perlman | pearl man
Perlmutter | pearl mutter
Perry | bury, pear
Peters | peters out, fades, P tears
Phillips | full lips
Pincus | pin cushion, pink ass, pink S
Powell | dowel, towel, power, Pa well
Quinn | win
Rafferty | rap for tea
Raleigh | roll lea, raw lea, roll E
Randall | ran doll
Rappaport | rap on port
Ratner | rat knee, rat on her
Raymond | ray on mount, rain mount
Reiss | rise, rice
Resnick | rest nick
Reynolds | ran old, rain old, rain holds
Rhodes | roads
Richards | rich
Rigney | rig knee
Riley | rye lea, rile E
Roberts | robbers
Robeson | robe son
Rogers | Buck Rogers, roger (affirmative)
Rosen | rose in
Rosenberg | rose in (ice)berg
Ross | rose, raws
Roth | wrath
Rubin | ruby
Ruppert | rope pat, rude pit
Russell | rustle, wrestle
Rutherford | rode a Ford, rudder Ford
Ryan | cryin', rind, Rhine
Samuels | some mules
Satenstein | satin stein
Sawyer | saw ya'
Saxon | sacks on
Scher | chair, share, sheer
Schmidt | blacksmith's hammer, shy mitt
Schneider | she neither
Schoenberg | shine (ice)berg, shone berg
Schultz | shields, shoots
Schuster | shoe stir, shoe store
Schwartz | warts
Scott | scotch, Scot
Sears | burns (sears), Sears Roebuck
Seiden | side in
Seward | steward, seaward
Sexton | sacks ton, sexy ton
Shaeffer | shave four, shaver, beer
Shaw | shore, pshaw
Shay | shade, say, shave
Sheehan | sheen
Shelton | shell ton, shelter
Sherman | show man, sure man
Siegel | sea gull, see gal
Simmons | simmers, see man, mattress
Simon | sigh man, Simple
Simpson | simple son, simper son
Sitron | sit run
Skidmore | skid more
Slade | slayed, slate
Sloan | loan, slow
Slocum | slow comb
Snead | need, snood, Sammy
Solomon | wise man, solo man, solemn man
Sommers | summers
Spector | spectator, ghost, inspector
Spencer | expense her, pins her, pen sore
Squire | wire, square, choir
Stacey | stay see, tasty
Sterling | silver, starling
Stern | stern (father figure)
Stevens | stevedore, steep fins
Stewart | steward
Sullivan | John L., sold a van
Sussman | shush man
Swanson | swan son
Sweeney | sweet knee
Talmadge | tall midget, tall Madge
Tate | tight, tea ate
Taub | daub, tub
Teitelbaum | titled bum
Terry | cloth (towel), tear E
Thatcher | that chair, thatcher
Thomas | tom tom, tom ask
Thompson | tom tom son, thump son
Tipton | tip ton
Tobias | toe bias, toe buy us
Todd | toddle, toddy
Tracy | trace E
Travers | travels, traverse
Treadway | tread, dread way
Trent | rent
Tucker | tuck 'er, tuck car
Tuttle | turtle
Tyler | tiler, tile her
Udall | you doll
Unger | hunger
Victor | winner, Vic tore
Vincent | win cent
Wagner | wag her, wagoner
Wallace | wall lace, wall is, wall ace
Walsh | waltz
Walters | wall tears, falters, Barbara
Warner | warn her
Warren | warring, war in
Wasserman | blood test, water man
Watkins | watt kin
Watson | watt son, what son
Watts | watts, light bulb
Waverly | wave early, waver lea
Wayne | wane, John
Weber | web, web bar
Webster | web stir, dictionary
Weeks | calendar, weak
Weiner | frankfurter, weenie
Weintraub | wine trap
Weiss | wise
Welch | grape juice, welsh (on a bet)
Wellington | well ink ton
Whalen | whalin', whale, wailing
Whitney | white knee, whittle knee
Williams | will yams, yams
Wilson | will son, whistle
Winston | wins ton, Churchill
Woolsey | wool see, we'll see
Worthington | worth ink ton
Wright | write
Young | baby
Zimmer | simmer
Zuckerman | sucker man, man with all-day sucker
If you've gone over this list even once, you'll find that many of these Substitute Words will come to mind the next time you hear some of these names. And when you come up with your own Substitute Word or phrase for a name, you're even more likely to remember it whenever you hear the name.
JL: The first time I saw you on television....
HL: I know, you were just a little boy!
JL: Well, not quite. Anyway, I knew something about memory systems, but I'd never heard of anyone remembering four hundred names. I couldn't believe it.
HL: The funny thing is that nobody else believed it—or so it seemed. My first national television exposure was on the original Jack Paar "Tonight Show." He put me on for about eight minutes near the end of the show, and I guess I must have rattled off close to four hundred names in about seven minutes.
Two days later, someone from Paar's office called me. It seems they'd received hundreds of calls, letters, and telegrams to the effect that what I'd done was impossible, no one could remember that many people in so short a time—they must have all been friends of mine!
JL: What did you say to _that_?
HL: I said, "Who the heck has four hundred friends?!"
•
Now for step two. You've just been introduced to someone and you've made up a Substitute Word for his name; what do you do with it? Well, what you have to do is look at that person's face and select what _you_ think is its outstanding feature.
You've accomplished one of the two important steps by forcing yourself to be Originally Aware of the name. Now, by searching for an outstanding feature, you're accomplishing the second important step—you're forcing yourself to look at, be interested in, concentrate on, that face!
What you select could be anything: hair or hairline; forehead (narrow, wide, or high); eyebrows (straight, arched, bushy); eyes (narrow, wide-spaced, close-set); nose (large, small, pug, ski); nostrils (flaring, pinched); high cheekbones; cheeks (full or sunken); lips (straight, arched, full, thin); chin (cleft, receding, jutting); lines, pimples, warts, dimples—anything.
First impressions are usually lasting impressions, and what is outstanding on someone's face now will, most likely, seem outstanding when you see that face again. That's important; but more important is the fact that you've really looked at that face. You're etching that face into your memory by just _trying_ to apply the system.
What you select may not be what someone else would select, but it will work for you. We all think and see differently—fine, that's as it should be. What _you_ see, what you select, is best for you.
All right; you've decided on an outstanding feature, and you already had a Substitute Word for its owner's name. Now we come to step three—you associate the Substitute Word to the outstanding feature. If you do this properly, it will almost be like having the person's name written on his face!
Even if step three didn't work (which it does), just applying steps one and two _must_ improve your memory for names and faces, because you've done what most people don't do—you've _paid attention;_ you've listened and looked.
But it is step three that gives purpose to steps one and two—it locks the name and face together for you. Form a ridiculous association between your Substitute Word and the outstanding feature of the face; that's all. And, you'll find that it's almost impossible _not_ to make the picture ridiculous; it will happen automatically.
Look, you've just met Mr. Crane. A picture of a large crane, as used by construction workers, comes to mind; or perhaps the storklike bird. You've looked at his face and decided that his high forehead is the outstanding feature. You look at that forehead, and _really_ picture many large **cranes** flying out of it; or, you can see them attacking that high forehead! Or perhaps the entire forehead is one gigantic **crane**. As with any association, you have many choices as to the kind of picture you visualize. You must be sure— _force_ it at first—to really see that picture. The next time you meet Mr. Crane, _you'll know his name!_
If Mr. Bentavagnia has a large nose, you'd see a **bent** weather **vane** where the nose should be. Mr. Pukczyva has bulging eyes; really see those **shiver** ing hockey **pucks** flying out of his eyes, hitting you in the face. Or, his eyes _are_ shivering hockey pucks. Mr. Antesiewicz has a noticeable cleft in his chin. See savages charging at you out of that cleft; you're defending yourself against them—you're **anti-savage**. Mr. Cohen has deep character lines (they used to be called "worry" lines) on his forehead. Picture those lines being dripping ice cream **cone** s; or millions of dripping ice cream cones flying out of those lines.
You've just learned the best system for remembering names and faces—and the only one that works for _any_ name. (A strong statement, but we'll stand by it!) In our classes, after learning the system, students call off the names of twenty to forty other students, whose names they've heard once—the first time they try it!
You can try it right now, using "word pictures." Five of these were just used as examples. Go back to Mr. Crane, Mr. Bentavagnia, Mr. Pukczyva, Mr. Antesiewicz, Mr. Cohen, and really see those pictures in your mind's eye. For now, since you're trying it without real people or faces, see just the features themselves and the ridiculous associations. Now, meet four more "people" (features and names) and do the same thing.
Mr. Colletti has very thick lips. Picture those lips and see millions of cups of tea or tea bags coming out of them; you're calling one of those cups or bags. Really try to visualize that silly action, and **call a tea** will remind you of Colletti. As always, you can make up your own Substitute Words and pictures. You might want to see yourself tasting the tea, spitting out a mouthful, and saying, " **Call 'at tea?** "
Miss Meisterman has very full cheeks. You might picture a man coming out of each cheek and you stir him. **Me stir man—** Meisterman. See that crazy picture.
Dr. Caruthers has very long, wide sideburns. You might see those sideburns being cars (or have cars driving out of them); the cars have udders—you're milking the cars. **Car udders**. See the picture. If you want to remember that this is _Dr._ Caruthers, put something into the picture that will _tell_ you so. Make up a standard to represent doctor—a stethoscope, perhaps. As you see yourself milking the cars, picture **stethoscopes** coming out of the udders.
Mr. Ponchatrain has deep creases (character lines) from his nostrils to the corners of his mouth. You can see trains running along those tracks (creases); you punch them. **Punch a train**.
Now, if you've really visualized each of those silly pictures, try to fill in the name for each outstanding feature listed below, without worrying about how the names are spelled. They're not listed in the order in which you "met" the people.
If you remembered to put "Dr." and "Miss" where they belonged, give yourself an extra couple of mental points.
Doing this with "word pictures" is not as easy as applying the system to real faces. Of course, you could practice with newspaper or magazine pictures. Cut out pictures of faces, make up names, and write the names on the backs of the pictures. The system will work with one-dimensional pictures.
The best way to practice, however, is by applying the system from now on, whenever you meet people. You have nothing to lose, and much to gain. The next time you're at a meeting, a cocktail party—the next time you're with a group—apply the system. You'll probably remember 50 percent more names and faces than you ever have before. And that percentage will increase every time you use the system.
When you do try it at, say, a party, be sure to review the names during the evening. If you've applied the system properly, each time you see one of the faces, the name should spring to mind. That's your review. If you look at one face and the name doesn't come to mind, think about it for a while. If it still doesn't come to you, don't be embarrassed to ask for the name again. Then strengthen your association. When you leave the party, you should be able to say good night to people by name. Try it and see for yourself.
Now, meeting people in groups and remembering their names is one thing, but what if you're in a business where, perhaps, three people a day visit your store, office, showroom—and you don't know when, or if, they'll ever come back? Of course, if they do come back, you'd like to call them by name. Many a sale has been clinched that way.
This is the only instance where we suggest that you write down information. Assume you've met three new people today, and have applied the system you just learned. Later, write those three names down on a pad you keep for just that purpose.
Writing each name is a review. You can't write the name without thinking of it, and, if you've applied the system, you can't think of the name without the face being conjured up in your mind. That's the way the system works—think of the name and you'll visualize the face; think of the face and you'll visualize the name.
The next day, read those names. Three days later, read them again, and a week later read them once more. Then forget about them. The next time one of those people comes into your place of business, you'll know that person's name!
If you meet, say, three people every business day, you may occasionally be reading (reviewing) fifteen to eighteen names at a time. It takes a few minutes. You have to make the decision—is it worth a few minutes, every once in a while, to be able to remember the names of people who may or may not visit you again? Most people think it is.
Now for some more tips on names and faces.
To remember _titles_ , come up with standards like the stethoscope in your picture for _Dr_. Caruthers. You can make up a word to represent any title; then just get it into the picture as a reminder. For judge, picture a gavel; for captain, picture a cap, and so on.
For _first_ names, make up a Substitute Word for the name and get it into your picture. Once you make one up for any name, it will become a standard for you. You might use **all in** for Alan, **robber** for Robert, **cherry** for Jerry, **floor ants** for Florence, bride ( **marry** ) for Mary, **shield** for Sheila, **hairy** for Harry, **gym** for **Jim** , and so on.
You can put anything you like into your original picture—the person's business affiliation, spouse's name, children's names, hobby, how much money he owes you—whatever. Of course, it will take longer to form the original picture or association, but it would take longer to remember all that information in any case.
Say you meet a Mr. Bill Gordon, who is a sales executive with United States Steel; his wife's name is Renée; he has a son named Jack; and he plays golf.
Bill Gordon has very bushy eyebrows. When you first meet him, you might see his eyebrows being a **garden** ; there are dollar **bills** growing there. As you talk, you find out the other bits of information. Put them into the picture. See an American flag ( **U.S.** ) that's made of **steel** growing in the garden. The flag is **sell** ing something to the flowers in the garden. The flowers start to run; they say, "Want to see me **run, eh**?" (Renée). **H** ydraulic **jacks** ( **J** ack) are also running in the garden—they're swinging **golf** clubs.
It takes time and space to explain these pictures; thinking or visualizing them takes much less time, and you do it during your initial conversation. Don't lose sight of the fact that _trying_ to form these ridiculous pictures is forcing you to be Originally Aware; you're registering that information in the first place. Also, remember that after you've used the information a few times, whether it's just the name or information about a person—it all becomes knowledge and the ridiculous pictures fade; they're no longer necessary.
Some final points: Yes, you'll be using high foreheads, big noses, bushy eyebrows, over and over again. Don't worry about it—in remembering the name of every person in an audience, we may use as many as thirty high foreheads! The system still works. It still works because, again, you've had to look at that face with interest, attention, and concentration in order to decide that the forehead is the outstanding feature. That's what really makes the system work. Similarly, it doesn't matter if you always use a blacksmith's hammer to remind you of Smith, Smythe, and Schmidt. You'll know the difference because you had to listen carefully in order to apply the system.
Occasionally, a student will tell us that he or she met someone who had no outstanding feature. That's almost impossible, particularly after you've been using the system for a while—because you'll be noticing and observing more. But if, at first, this seems to be a problem, decide on one feature to use in all such cases. Perhaps you'll always use the nose, if you find no outstanding features. The system will still work because you still have to really _look_ at that face in order to decide that it has no outstanding feature.
You might try something now. Turn back to the list of features used in the "word pictures." If you made the associations originally, you'll still know the name that goes with each outstanding feature.
# 9 **_ABSENTMINDEDNESS_**
JL: When I played basketball in high school, I had a teammate named Bob Cole—really one of the greatest shooters I've ever seen, before or since. Trouble was, Bob had a tendency to be absentminded.
He was a starter, of course, and at one game I remember we'd finished our warm-up and were all standing around the coach, ready to go out on the floor. We started to pull off our long warm-up pants; Bob pulled his off, and he had nothing on under them—I mean, _nothing!_ He'd forgotten to put on his uniform, and didn't know he was stark naked until he heard all the giggles!
HL: That's embarrassing, of course, but in most cases absentmindedness is annoying, really aggravating. And it's not a problem that has much to do with intelligence. We've all heard of the absent-minded professor who winds up the cat, puts his wife out for the night, and kisses the alarm clock good night! And he's intelligent.
JL: On the other hand, I know "idiot savants"—people with fantastic memories who are really _dumb_. Which further supports the idea that intelligence isn't necessarily a factor in memory.
HL: Misplacing something means not remembering where you placed it. When you don't know if you locked your door, you don't _remember_ whether or not you locked it—absentmindedness is basically a memory problem.
•
You are absentminded when your mind is absent; when you perform actions unconsciously, without thinking. We've discussed the difference between seeing and observing—we see with our eyes, but we observe with our minds. If your mind is "absent" when performing an action, there can be no observation; more important, there can be no Original Awareness.
Absentmindedness is probably the most widespread of minor self-annoyances. Although it plagues most of us, it seems particularly to affect the elderly. The techniques we'll discuss here have succeeded in eliminating absentmindedness for countless people, including the elderly.
To some readers, absentmindedness may seem to be a trivial problem. Perhaps they don't realize how much time, energy, and aggravation they spend on searching for items they "just put down for a moment," or on worrying about whether they have turned off the oven, locked the door, unplugged the iron, or on retrieving items they have left in trains, buses, cars, offices, and friends' homes.
The solution to the problem of absentmindedness is both simple and obvious: All you have to do is to be sure to think of what you're doing _during the moment in which you're doing it_. That's all, but obviously it's easier said than done. How can you be sure to _force_ yourself to think of a minor action at the moment you're doing it?
There's only one way, and that is by using association. Since association forces Original Awareness—and since being Originally Aware is the same as having something register in your mind in the first place, at the moment it occurs—then forming an instant association must solve the problem of absentmindedness.
You're writing at your desk and the phone rings. As you reach for the phone, you place the pencil behind your ear, or in your hair. The phone call is finished—that took only a few minutes—but now you waste time searching for the pencil that's perched behind your ear. Would you like to avoid that aggravation? All right, then; the next time the phone rings and you start to place the pencil behind your ear, make a fast mental picture in your mind. Actually "see" the pencil going _into_ your ear—all the way.
The idea may make you shudder, but when you think of that pencil, you'll know where it is. That silly association of seeing the pencil go into your ear _forced_ you to think of two things in a fraction of a second: 1) the pencil, and 2) where you were putting it. Problem solved!
Solved, that is, if you make an association each time you put down your pencil, wherever you put it. Just make it a habit. Keep the idea in mind the first few times, force yourself to form the associations, and after that it _will_ become habitual.
If you place your eyeglasses on your television set as you leave your living room, "see" the antenna of the television set going right through the eyeglass lens, shattering it. This association is made without breaking stride, as you walk. We'll guarantee that the next time you think of your glasses, you'll know where they are. For two reasons: First, you _thought_ about it when you put them down; and second, the thing that made you think about it, the association, also reminds you of where they are.
If you placed the eyeglasses on your bed, you can picture a gigantic pair of glasses sleeping in your bed. If you stuck them into a pocket, picture the lenses breaking in your pocket and tearing it. Or you're reaching in to get the glasses and your hand is badly cut. All the same idea; the association, no matter what it is, forces you to think of the action at _that_ moment. Always do it at the moment; if you put off doing it, you'll forget to form the association and you'll forget where your glasses are!
Many people are plagued by misplacing treasured items. You usually put the item in a particularly good hiding place—and then never see it again. (If you do, it's likely to be when you move, and empty all your drawers and closets.)
This problem, too, can be solved by making an instant association. Say you have an expensive fountain pen that you want to keep for a child or grandchild. You place it in a drawer beneath your good sweaters for safekeeping. _As_ you place it there, see a picture of the pen leaking ink all over those sweaters, ruining them. Be assured that the next time you think of that pen, no matter how long after you've put it away, you'll _know_ that it's under your sweaters. You need only associate an item you're putting away to its hiding place once to see that the idea works beautifully.
If you want to be sure not to leave your umbrella at your friend's house, associate umbrella to the last thing you're sure to notice when you leave. If you're wearing a coat, and it's cold outside, you know you won't forget the coat. Associate umbrella to coat; you might see yourself putting on a gigantic umbrella instead of a coat, or using a coat instead of an umbrella to protect you from the rain. The principle is the same—one thing reminds you of the other. If your picture is a clear one, and a ridiculous one, the coat must remind you of the umbrella. If you want to make extra sure, and if you're driving, associate umbrella to your car. You might picture yourself opening the car with an open umbrella instead of a key. Now, if the coat doesn't remind you to take that umbrella, the car certainly will.
Do you often leave your umbrella at the office instead of taking it home? As you arrive and put your umbrella away, associate it to the last thing you normally see or do as you're leaving the office. If you punch a time clock, see yourself placing the umbrella in the slot instead of your card. Or, if you ride an elevator, picture an umbrella operating it. You might also associate the umbrella to something you always see just outside the office building—if one association doesn't remind you to take it with you, the other will remind you to go back and get it.
Perhaps you're one of those people who write an important letter and then forget to take it out of the house and mail it. What's the last thing you do as you leave your house or apartment? Perhaps you check your doorknob to make sure the door is shut, or perhaps you lock the door with a key. Simply associate letter to either doorknob or key—or both. (If you associate letter to, say, doorknob a few times, you probably won't have to do it ever again. _Every_ time you look at that knob, it will make you think of letter, and if you've left one inside you'll go back and get it.)
You can always use a second picture as insurance. Perhaps you often take out some garbage when you leave your home. See yourself throwing millions of letters into your garbage can or incinerator.
This will help you remember to take the letter, but you may still leave it in your pocket or purse for a few weeks! One way to avoid that is to hold the letter in your hand until you see a mailbox. Another way is to associate the person or company that the letter is addressed to, to a mailbox. If it's going to someone you can picture or visualize, see that person's head coming out of a mailbox. If it's going to a company, use a Substitute thought. For example, if it's an electric bill, see electricity (lightning) shooting out of a mailbox. In either case, the next time you notice a mailbox—and sooner or later you will—you'll be reminded to take that letter out of your pocket or purse and mail it.
A woman in one of our classes told us that she often burned the roast that she put in the oven because she simply forgot about it. Well, she could avoid this by putting a smaller roast into the oven along with the regular one—when she smelled the small one burning, she'd know the other one was done! The price of meat being what it is, however, there has to be a better way.
Make this a habit— _every_ time you put something in the oven, place a small frying pan smack in the center of the kitchen floor! How can you possibly forget about the roast now? Each time you see (or trip over) that frying pan, you'll be reminded of the roast in the oven.
Upon hearing this idea one man said, "That's fine, except that when I put a roast in the oven, I usually go into another room to watch television. Then **I** can't see the reminder." The solution for him was obvious, of course—to take the frying pan along and put it on top of the television set.
Instead of a frying pan, you can use anything that looks out of place on the floor (or television set): a pot holder, a plate, a hunk of cheese. The idea is based on the standard rule of memory—one thing reminds you of another.
It's not a new idea by any means; it's similar to tying a string on your finger, wearing your watch on the wrong wrist, turning your ring to face the wrong way, or putting a crumpled dollar bill in with your coins. Each of these "out-of-place" things is supposed to remind you of something you want to remember. The problem is that too often they'll remind you that you wanted to remember "something," which isn't much help if you can't remember what the something is. The frying pan on the kitchen floor, on the other hand, must remind you of the roast in the oven because that's all you'll be using it for. If you insist on tying a string around your finger or wearing your watch on the wrong wrist, now you have a way to make it definite. Go ahead and tie the string around your finger, but at the same time be sure to associate whatever it is you want to remember to the string. Now you have the two essentials: first the reminder, then what it is you're being reminded of.
Why ruin your evening out because you spend most of it worrying about whether or not you turned off the oven, locked the door, or unplugged the iron? Form the habit of making a quick association at the moment you do these things. As you shut off the oven, picture yourself (or just your head) in the oven! Really see that picture, and you've consciously thought about the action for a split second. Later on, when you think about the oven, you'll _know_ you shut it off.
As you lock your door, see yourself locking it with your head instead of a key. When you unplug your iron, see your head coming out of the socket. The picture you choose is unimportant— _any_ picture forces you to think of the action at that moment.
**D** o you sometimes find yourself going to your refrigerator, opening the door, and then staring inside and wondering what it is you wanted? Just make an association the moment you think of what it is you want from the refrigerator. **If** you want a glass of milk, see yourself opening the refrigerator door and gallons of milk flying out and hitting you in the face! Try this idea, and you'll never stare into a refrigerator again.
That's all there is to it. It's like grabbing your mind by the scruff of the neck and forcing it to think of a specific thing at a specific moment. Force yourself to do it at first, and it will become habitual before you know it.
Forming these associations may strike you as a waste of time. You won't feel that way once you've tried using the idea. You'll see, after a short while, that the ridiculous pictures are formed in hardly any time at all. Even more important is the time that you'll be _saving_.
•
JL: The "out-of-place" idea has saved me when it comes to getting out of bed in the mornings. You see, if the alarm clock is where it belongs, I'll just reach over with my long arm, shut it off, and go right back to sleep. So I keep it across the room—and whenever I pull out the alarm-set I picture that little knob going right through my thumb, nail and all.
HL: Which forces you to think, at that exact moment, about the fact that you _are_ setting the alarm.
JL: I do this every night, and I never have to get out of bed after I'm in to check whether or not I set the clock.
HL: All right. Now, you saw that picture last night, and you'll think of the clock after you're in bed tonight. Does last night's picture ever come back to you, making you think you set the alarm when you actually didn't?
JL: Never has happened. "True" memory tells me the truth. Most important is the Original Awareness. If I _haven't_ made the silly picture on any night, I'll know I haven't set the clock.
HL: I know it can't go wrong—I've used it for years, just as I've used the "out-of-place" idea for years to remind me in the morning of something I thought of during the night.
JL: You mean when you've had that million-dollar idea—
HL: Which is usually worth $1.63 in the morning light. Still, I always felt that idea had to be immortalized. So at first I'd put on the lights, find a pad and pencil, and write it down—then, since I invariably woke up my wife, I started keeping a pad on my night table and writing down the idea in the dark.
JL: Could you read your writing in the morning?
HL: Not too well. Which was fine, because that inspired me to really solve the problem. Now, whenever I get an idea, I reach out an arm and do something that will be sure to catch my attention in the morning. Usually, I dump all my cigarettes on the floor—when I get out of bed in the morning I can't miss stepping on those cigarettes and being reminded that I had an idea during the night.
JL: Do you ever have trouble remembering _what_ the idea was?
HL: Not usually. But if I do feel I need a reminder of the thought itself—
JL: You associate the Key Word of the idea to cigarettes.
HL: Right! And if I ever manage to stop smoking, I'll reach over and turn my clock face down, or put it on the floor, or push a book off my night table.
JL: Anything that's out of place, that forces you to look at it and think, "What in the world is that doing there?" will do.
•
If you've been applying the systems, you've not only improved your memory, you've improved your sense of imagination, concentration, and _observation_.
By now, you must realize that in order to remember anything, you must pay attention to it—it must be observed. Applying our systems will automatically sharpen your observation.
Having a better sense of observation is almost like taking an "awareness pill." You'll be able to _really_ notice, and be aware of, things that ordinarily would make only a vague impression. Most people we've talked to admit that they would have taken an "awareness pill," if there were such a thing, whenever they traveled to new places. After the trip or visit, they never could clearly visualize the beautiful things they'd seen—hadn't _really_ noticed or observed them.
All the ideas in this chapter have been intended to force you to pay attention, to observe. You cannot sharpen your observation without applying some effort at first, as is the case with most of the memory systems. But observation, too, will become habit if you practice it consciously and conscientiously.
Up to now, you probably haven't had to expend much effort in learning and applying our systems. Names and faces, errands, foreign words—whatever the memory problem, the solution has largely been a matter of grasping a simple idea and using just a bit of imagination.
But nothing worthwhile comes _too_ easily. You're about to embark on some entirely new ideas. Although they remain simple, applying them will take a little more effort on your part—but only until the fundamentals are learned and absorbed.
As you move into remembering the more challenging material that follows, work to apply the systems. You may feel that applying memory systems to it seems like a lot of work. Again, that's thinking negatively. _Any_ new art or skill seems difficult and cumbersome at first—but only at first, only until you've grasped the fundamentals of the skill. It is _rote_ memory that's really a lot of work—and usually for naught, because it just doesn't work too well or too often. Applying the systems, once you've learned the basics, _must_ save you much time and work.
So be sure to take the time to learn the basics that follow. You won't regret it!
# 10 **_LONG-DIGIT NUMBERS_**
91852719521639092112
A Beautiful Naked Blond Jumps Up and Down
HL: The most difficult category to remember? It has to be numbers.
JL: No question about it. Numbers are completely intangible, they're just designs.
HL: They also happen to be the most important things some people have to remember—addresses, telephone numbers, prices, style numbers, formulas, equations, computer codes, statistics, credit card numbers, and so on.
JL: Those who most need to remember numbers like these have trouble for the same reason most people do—it seems impossible to picture them in the mind.
HL: And, of course, it's not at all impossible to learn to picture numbers, even long ones. Like, say...
JL: 91852719521639092112!
•
The problem of remembering numbers, probably the most difficult of all memory chores, can be solved by learning a simple phonetic alphabet, consisting of just ten pairs of digits and sounds. They are not at all difficult to learn, even if you use rote memory—which you won't need to do. We want to eliminate rote, not find uses for it. You'll be given a simple memory aid for each pair, and if you concentrate, you'll probably find that you know them after one reading.
First, to break down the idea for you, there are ten digits in our numerical system: 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0. There are also ten basic _consonant_ phonetic sounds. (Technically, of course, there are more than ten, but the ten basic ones will serve our purpose admirably.)
Think of the letters _t_ and _d_ for a moment. Although they are different letters, and fall in different parts of the alphabet, they make the same phonetic sound. Your vocal apparatus (tongue, teeth, lips) is in exactly the same position when making the _t_ sound as when making the _d_ sound. The _t_ sound is a bit harder than the _d_ , that's all. For our purposes, they'll be considered the same.
The rule—the vocal apparatus being in the same position—will hold true for other consonant sounds. For example, although _f_ and _v_ (and _ph_ ) are different letters, they form the same phonetic sound; again, the only difference is that one is harder than the other, and, again, your lips, tongue, and teeth are in the same position to form either one.
_P_ and _b_ are phonetically the same for our purposes. So are _j, sh, ch_ , and soft _g_ —your tongue curls the same way to sound any one of them. The hissing sounds, _s, z_ , soft _c_ , are also the same phonetic sound, and so are _k_ , hard _c_ , and hard _g_.
All right, then. There are ten of these phonetic sounds, and it is the _sounds_ we're interested in, not the letters themselves. All we've done is to pair a sound to each digit, and there are only ten pairs for you to learn. That's the phonetic alphabet. Learn it; once you do, you'll use it for the rest of your life—it will never change. Don't worry now about _how_ it will be used; just learn it. It can be useful to you in ways you couldn't imagine.
Pay attention to the memory aids; they're silly but they'll enable you to learn the phonetic alphabet in minutes. The sound that will represent number 1 will always be the sound made by the letters _t_ or _d_ , and vice versa. The memory aid, which you'll need for only a short while, is this: A typewritten _t_ has _one_ downstroke. Think of that for just a moment.
The number 2 will always be represented by the sound made by the letter _n_. The memory aid is: A typewritten small letter _n_ has _two_ downstrokes. Think of that for a moment.
Number 3 will always be represented by the sound made by the letter _m;_ 3 = _m_ and _m_ = 3. The small typewritten letter _m_ has _three_ downstrokes, or you might think of the 3M Corporation. Again, it is the sound we're interested in, not the letter.
Number 4 will always be represented by the sound made by the letter _r_. The simplest memory aid for this is that the word "fou _r_ " ends with an _r_.
Number 5 will always be represented by the sound of _l_. The memory aid: Spread the _five_ fingers of one hand, thumb straight out, and the thumb and forefinger form the letter _l_.
Number 6 will always be represented by the sounds _j, sh, ch_ , and soft _g_ (as in _gentle_ ); they all make the same phonetic sound. The memory aid: The digit 6 and a capital letter _j_ are almost mirror images .
Number 7 will always be represented by the sounds _k_ , hard _c_ (as in _cap_ ), hard _g_ (as in _glide_ ). As the memory aid, you can form a capital _k_ with two 7's, one right side up and the other upside down, like this: .
Number 8 will always be represented by the sound made by the letters _f_ or _v_ or the sound _ph_. To help you remember this quickly, an 8 and a handwritten _f_ are both made with two loops, one above the other .
Number 9 will always be represented by the sound made by the letters _p_ or _b_. The number 9 and the letter _p_ are almost exact mirror images .
And, finally, the zero (0) will be represented by the hissing sound made by the letters _z, s_ , or soft _c_ (as in _century)_. The memory aid: The first sound in the word " _z_ ero" is _z_.
If you've read the last few paragraphs with some degree of concentration, the odds are that you already know all, or most, of them. But look at this chart for a moment:
1 = _t_ or _d_. A typewritten small _t_ has _one_ downstroke.
2 = _n_. A typewritten small _n_ has _two_ downstrokes.
3 = _m_. A typewritten small _m_ has three downstrokes.
4 = _r_. The word four ends with an _r_.
5 = _l_. The _five_ fingers, thumb out, form an _l_.
6 = _j, sh, ch_ , soft _g_. A 6 and a capital _j_ are almost mirror images .
7 = _k_ , hard _c_ , hard _g_. You can make a capital with two 7's .
8 = _f, v, ph_. An 8 and a handwritten _f_ look similar .
9 = _p_ or _b_. A 9 and a _p_ are mirror images .
0 = _z, s_ , soft _c_. The first sound in the word _z_ ero is _z_.
A few rules: The vowels, _a, e, i, o, u_ , have no value whatsoever in the phonetic alphabet; they are disregarded. So are the letters _w, h_ , and _y_. The only time that _h_ is important is when it follows certain consonants, changing the sound. Also, although this is rarely used, the _th_ sound will for our purposes be the same as the _t_ sound: _th_ = 1.
Silent letters are disregarded. The word _knee_ would transpose to 2 in the phonetic alphabet, not 72. Remember, we are interested in the sound, not the letter. There is a _k_ in that word, but it is silent; it makes no sound and therefore has no value. The word _bomb_ transposes to 93, not 939; the last _b_ is silent. The beauty of this, if you'll forgive our saying so, is that it doesn't even matter whether or not you pronounce (or read) a word correctly. If you happened to speak with an accent, and pronounced that final _b_ in _bomb_ , you would transpose that word to 939. But since you'd always pronounce it that way, the system would work just as well for you.
This leads to the rule for double letters. The word _patter_ transposes to 914, _not_ 9114. Yes, there are two _t_ 's in the word, but they are pronounced as one _t_. The word _bellow_ would transpose to 95: _b_ = 9, _l_ = 5; the _ow_ has no value. The rule is simple and definite; always consider double letters as making only one sound. (Except, of course, where the two letters are obviously pronounced differently—as in "a _cc_ ident." The double _c_ here transposes to 70.)
Finally, the letter _x_ will almost never be used, but it transposes according to the way it is pronounced in a particular word. In the word _fox_ the _f_ is 8, and the _x_ is 70. (The _x_ makes the _ks_ sounds in that word.) In the word _complexion_ , however, the _x_ would transpose to 76. Pronounce _complexion_ slowly and you'll see why. As for the letter _q_ , it always makes the same sound as _k_ —so it transposes to the number 7.
The phonetic alphabet should become second nature to you. That is, whenever you hear or see the sound _r_ , you should think, 4. When you hear or see 2, you should think, _n_. You must know them quickly and out of order. Go over them mentally now; you probably already know them. Those simple little memory aids make the phonetic alphabet easy to remember. Don't continue reading until you're familiar with the ten pairs of digits and sounds and have really practiced transposing sounds ( _not_ letters) to numbers.
Now. Without turning back to the first page of this chapter, do you remember the long-digit number that is at the top of that page? If you are like most people, the answer has got to be, "Are you kidding? Of course not."
But think: Do you remember the sentence that appears right under the long-digit number? Again, if you're among the majority, you do remember that sentence: "A beautiful naked blond jumps up and down." That's easy to picture, and if you simply thought of the picture when you first read the sentence, you'd have remembered it.
Well, look at that sentence, or think of it. What is the first consonant sound? The _b_ in beautiful. What digit does _b_ represent? You should already know the answer—9. The next consonant sound is _t_ ; you know, by now, that _t_ always represents the number 1.
Use paper and pencil and put down the digits for all the consonant sounds in that sentence. You already have 91. The word _beautiful_ transposes to 9185. If you've transposed the entire sentence, you should have 91852719521639092112. Which _is_ the number at the top of the first page of this chapter. And you thought you didn't remember it!
Have we made the point? It is much, much easier to remember the tangible sentence, which makes sense, than the intangible numbers. Had the sentence been "A pretty girl is like a melody," the number would have been 941745057351.
You _don't_ , however, have to try to make the phonetic sounds of a long number form a sentence or cliché in order to remember the number—thanks to our old friend the Link.
Take this number:
941 140 494 275
The number has been broken into groups of three digits for teaching purposes only. Ordinarily you wouldn't break a number into equal groups like that. Try to think of a word that would phonetically fit 941. There are many such words; parrot, **br** e **ad** , **pr** ou **d** , a **p** a **rt** , **b** e **r** a **t** e, **p** i **r** a **t** e, **br** a **t** , **b** o **ard** , **b** o **r** e **d** , to name only a few. The first one you think of is usually the best for you to use.
Now look at the next group of three digits, 140. What word would fit those phonetically? **T** ea **rs** , **thr** ows, **thr** oes, **dr** ess, **d** u **r** e **ss**... Think of one yourself.
Now, start forming a Link; your association might be a gigantic **parrot** wearing a **dress**. Be sure to see the picture. The next three digits are 494: **r** o **bber** , **r** u **bber** , or a **rb** o **r** would fit phonetically. Continue your Link; you might picture a gigantic **dress** (just the dress; no lady in it) being a **robber**. See the picture; either the one suggested here or one you thought of yourself.
The last three digits are 275; **n** i **ck** e **l** , k **n** u **ckl** e, or a **ngl** e would fit. Select one and continue your Link; associate robber or whatever you used for 494) to nickel. You might see a gigantic **nickel** catching a **robber** , or being a robber.
You've just formed a short Link of only four words. But if you know those four words, if you know the Link, _you also know the twelve-digit number:_ that is, if you also know the sounds.
Simply think of the first word of your Link, and transpose it to digits. If you used **parrot** , parrot can _only_ break down to... 941. Think of parrot for a moment; that makes you think of—what? **Dress** , of course; and that can only transpose to... 140. Dress leads to **robber** , and robber transposes to... 494. And, finally, robber reminds you of **nickel** , and nickel can only be... 275. There are no decisions to make here; if you know the fundamentals—in this case, the sounds—any word breaks down, or transposes, to a specific group of digits.
Try it without looking at the book; see if you know the number. When you've tried it at least once, try it backward. Simply think of the last word of your Link; transpose it to digits and write, or say, those digits backward. That word will remind you of the next-to-last word, and so on. Nickel, robber, dress, parrot, _must_ tell you—572494041149.
Do you see how applying both the Link and the phonetic alphabet has enabled you to memorize a long-digit number? What we've done is show you a way to turn abstract, intangible numbers into tangibles. Now you _can_ picture numbers in your mind!
The only problem you may have had is transposing from sounds to numbers. If that slowed you down, it's because you don't know the sounds as well as you should—you haven't made them second nature. Obviously, the better you know the sounds, the faster you'll memorize numbers.
Let's try a longer one this time:
7412 3212 5390 0141 4952
Not at all impossible to remember—not now. Again, the number is broken into groups of four for teaching purposes only. Look at the first group; if you simply say the sounds to yourself, you'll almost automatically form a word. Say _k r t n;_ you may have thought of **c** u **rt** ai **n** , **c** a **rt** o **n** , **cr** e **t** i **n** , or **g** a **rd** e **n** —any one of which is perfect.
Look at 3212: _m n t n_. If you voice those sounds, you'll immediately think of something like **m** ou **nt** ai **n** or **m** ai **nt** ai **n**. If you picture a **carton** as large as a **mountain** , that's the start of your Link. Just be sure to see the picture. You needn't use our suggestions, of course; use whatever comes to mind—as long as the words fit the numbers phonetically, and your pictures are ridiculous.
Now, 5390: _l m p s_. You may have thought **lamps, limps** , or **l** u **mps**. (No, **lambs** wouldn't do. That would transpose to 530; the _b_ is silent.) Associate mountain to, say, lamps; you might see millions of **lamps** (it must be more than one lamp to remind you of the plural _s_ ) piled as high as a **mountain**. See that picture.
0141: _s t r t_. **Str** ee **t** , **st** a **rt** , or **st** o **r** e i **t** will do just fine. You might see many **lamps** walking down a **street** , or **start** ing a race. See the picture.
4952: _r p l n_. You probably thought of ai **rpl** ane, and that's as good as any. Associate street or start to airplane; perhaps a gigantic **airplane** is parked on your **street**. Be sure to see the picture in your mind.
You've Linked only five words and those five words will remind you of a _twenty-digit_ number. Try this on your own. Start with **carton** and go through your Link, to **airplane**. Transpose the consonant sounds into numbers as you go, and you'll see that you know the number!
Have you tried it? If you have, you should be pleased with yourself. Go a step further—try it backward. And, perhaps even more impressive, think of **parrot** and you'll see that you still **re** member the first (twelve-digit) number that we used as an example.
In a moment, we'll give you some numbers to practice with. **B** ut first: **T** here's no rule that says that you must use a noun to represent any group of digits; nor must you use only one word for a group of digits—a phrase is just as good. In fact, there are some groups of digits that no single word would fit, but you can _always_ find a phrase to fit. **F** or example, we couldn't find a word for 989, but **p** u **ff** u **p** , **p** ie **f** i **b** , or **b** ee **f** **p** ie will serve the purpose. And although a phrase consists of two or more words, it's as easy to picture as one word.
Once you become familiar with the idea, you might look at 01414952, the last eight digits of the last example, and think **straight airplane**. That would have made the entire number easier and faster to memorize. Linking carton to mountain to lamps to straight airplane would have done it. And straight airplane (an airplane standing straight up on its tail) is one picture in your mind, although it consists of two words.
For a four-digit number like 4312, you might use **r** aw **m** u **tt** o **n** , **ram** **t** i **n** , **r** oo **med** i **n** , **r** hyme **t** o **n** e, and so on. All can be pictured, and all fit phonetically. Even a particularly silly phrase, like **r** oo **m** **di** e **n** ow, can be pictured. Simply see a room dying now. If you thought of it, it can be pictured.
Don't lose sight of the basic idea. Aside from making numbers tangible, you're also forcing yourself to be Originally Aware of a number. Simply trying to come up with words or phrases _forces_ you to concentrate on that number as you've never done before.
There are some standards that you can start using as you keep applying the idea. For example, whenever you see a zero, simply try to pluralize what comes before it. For 975, you might use **b** u **ckl** e; if you see 9750, simply use **b** u **ckl** es. For 27, always try to use the - _ing_ ending; for 97527, use **b** u **ckl** ing. When you see a 4, you can try to use the - _er_ ending; 9754 could be **b** u **ckl** e **r**. And for 1, you can use the past tense; 9751 would be **b** u **ckl** e **d**.
For 85, always try to use the - _ful_ ending. The digits 92 might be **pain** , and 9285 would easily make you think of **p** ai **nf** u **l**. Aside from these standards, you can use anything you like to remind you of any group of digits. Always use the first thing that comes to mind and fits phonetically, no matter how many digits it includes, and Link one thing to the other.
One more example:
94301491846108732198420315
Here are only some of the ways to handle it: brooms, tripped over, jets, vacuum, knot, bufferins, metal. Pram, strip, tougher, jets off, come in, tip, frowns, my tail. Bear, master, pit, forage, toss off, commando, buffer, no summit, hill.
On your own, try your fantastic new memory for numbers on these:
839027195830274
10121650718430137
540381930136586926349
379205927153640
293846104529585736102654
619103481254027452
If you've really mastered the phonetic alphabet and practiced transposing, this formidable list isn't formidable for you. It's taken concentration, practice, and time to get to this point—well, we said at the outset that remembering numbers is the most difficult of memory chores. But again, think of the effort it would have taken (assuming you could have done it at all; few people could) to remember _one_ long-digit number without a system.
It's true that most of you won't ever _need_ to remember a twenty-digit number. Well, later we'll give you specific help with remembering the short-digit numbers you _do_ need to know. But for now, you can enjoy the fact that anyone who can remember 91852719521639092112 is unlikely to forget, say, a telephone number.
If you _haven't_ yet mastered the phonetic alphabet, you should take the time to really absorb those ten digit-sound pairs. Playing a mental game will help you do this faster: Whenever you see a number—an address, a license plate number, whatever—mentally transpose the digits into sounds. Whenever you see a word on a sign or billboard, transpose the consonant sounds to digits.
Do this for a while, and the sounds will become second nature. There are two traps to avoid: transposing according to letter instead of sound, and considering a double letter as two sounds instead of one. The _s_ in the word _envision_ transposes to 6, not 0; the _s_ makes a soft _sh_ sound. The same is true for the _t_ in the word _position;_ it transposes to 6, not 1. The word _pattern_ transposes to 9142, not 91142—a double letter makes one sound only.
Play this mental game for a while; learn the sounds really well before you go on to the next chapter. Once the sounds have become second nature, you're ready for an amazingly useful memory system—the Peg.
# 11 **_THE PEG_**
HL: The student challenged me—he thought he could remember a long-digit number faster than I could. Another student wrote down the number and timed us. Well, I beat him by just a few seconds. (I wouldn't tell the story if he had beaten me!) In discussing it, we realized that we had used pretty near the same words and phrases for the numbers. We were both faced with 0384 at one point. He said that this was where he lost the few seconds, he couldn't think of a word or phrase quickly enough. He asked me what I had used, and I said, "Somevere." He said, "Somevere!? What kind of word is _that?_ " Well, _somevere_ wouldn't mean anything to anyone else but me. When I was growing up in a tenement on the Lower East Side of Manhattan, my neighbor was a sweet old man with a heavy accent. He always pronounced the word _somewhere_ as _somevere_. This old gentleman was like a father to me, and left a lasting impression. So when I saw 0384, I thought of _somevere_ and pictured him.
JL: It's a good story, but of course you could have used _samovar_.
HL: _Now_ you tell me. And besides, I don't know what a samovar is.
•
Having memorized a list of items in sequence, using the Link, how would you know, say, the 8th item instantly? You wouldn't; you'd have to go over the Link and count, either mentally or on your fingers. There's a much easier way, using _Peg Words_ that are based on the phonetic alphabet. This is the Peg system of memory.
If you know the sounds of the phonetic alphabet, and you should by now, this won't take much time or effort. We'll start by giving you ten Peg Words, then we'll show you how to use them.
Since the number 1 is always represented by the sound _t_ or _d_ , the Peg Word for 1 must contain only that sound. Many words could fit for any number, but the ones here are easy to picture and serve the purpose as well as any.
The word for 1 will always be **tie**. The word _tie_ contains only one consonant sound, and that sound _(t)_ can only represent 1. So, a mental picture of a man's necktie will always represent 1.
The number 2 is also a single digit, so the Peg Word must contain only one consonant sound—but now, that sound must be the sound that represents 2, which is _n_. The word (name) that will always represent 2 is **Noah**. Picture whatever you like, probably a man with a long gray beard, or just the beard.
The Peg Word for 3 will always be **Ma** ; picture your mother, or a little old lady.
4: **rye**. That word could only represent 4 because it contains only one consonant sound, _r_. Picture a loaf of rye bread, or a bottle of rye whiskey.
5: **law**. Picture whatever law represents to you; we always picture a policeman.
6: **shoe**. Shoe contains only the _sh_ consonant sound, which represents 6. Picture a shoe.
7: **cow**. Picture a cow, of course.
8: **ivy**. The _v_ sound can only represent 8, therefore ivy can only represent 8. Picture ivy climbing on a wall.
9: **bee**. Picture the stinging insect.
The number 10 contains two digits, therefore the Peg Word for 10 must have the sound _t_ (or _d_ , for 1) and _s_ (for 0) in that order. The word is **toes** ; toes can only represent 10. Picture your toes.
Those are the first ten Peg Words. They are easy to remember because the phonetic sounds practically _tell_ you what the words are. Look at them again; then see if you know them. You'll know them out of order because you know the _sounds_ out of order. And they will never change; once you know them, they'll always be useful.
1. **t** ie
2. **N** oah
3. **M** a
4. **r** ye
5. **l** aw
6. **sh** oe
7. **c** ow
8. i **v** y
9. **b** ee
10. **t** oe **s**
Go over these a few times; you should be able to think of any number from 1 to 10 and know the Peg Word almost immediately. If you hear one of the Peg Words, you should, just as instantly, know the number it represents. When you know them fairly well, you're ready to learn how to use these Pegs.
Let's assume that you want to remember ten items in and out of order, by number. Let's also assume that you handle these items in a haphazard order.
You must remember that number 8 is **cracker**. There would, ordinarily, be no problem picturing a cracker, but how would you picture the 8? Well, it's easy if you learned the first ten Peg Words—the number 8 is... **ivy**. Simply associate cracker to ivy; see a ridiculous picture between those two items in your mind's eye, perhaps millions of crackers instead of ivy growing all over a brick wall.
Now. You want to remember that number 3 will be **scissors**. Associate scissors to your Peg Word for number 3, which is **Ma**. You might see yourself cutting your Ma in half with a gigantic pair of scissors. (That picture may make you shudder, but you won't forget it.) For each of these, be sure to _see_ the picture you select; we won't bother reminding you again.
Number 5 will be **fish**. Associate fish to your Peg Word for the number 5, **law**. Perhaps a policeman is arresting a gigantic fish, or a large fish is walking the beat like a cop.
Number 1 is **pen**. You might see yourself wearing a gigantic pen, instead of a **tie** (your Peg Word for the number 1), around your neck—see the ink dripping all over your shirt.
Number 10 is **teeth**. Associate teeth to your Peg Word, **toes**. Perhaps you want to picture large teeth on your feet instead of toes, or teeth are biting off your toes.
Number 4 is **telephone**. Your Peg Word is **rye** ; you might see yourself talking into a loaf of rye bread instead of a telephone, or a large bottle of rye whiskey is making a phone call.
Number 7 is **car**. Associate car to your Peg Word for the number 7, **cow**. See a cow driving a car, or you're milking a cow and cars come out instead of milk.
Number 2 is **article**. Your Peg Word for 2 is **Noah** ; you must associate article to that. This is being used here purposely. If you want to picture millions of articles falling out of a long gray beard, fine. If you feel that article is too vague to picture, use a Substitute Word to remind you of it. You might use **ah tickle** , or a newspaper article. Use whatever you like, but be sure to associate it to beard, or whatever you're using to represent Noah.
Number 9 is **pillow.** Associate that to **bee** , your Peg Word for 9. Perhaps pillows, instead of bees, are swarming all over you and stinging you; or you're sleeping on a gigantic bee instead of a pillow.
Finally, you must remember that number 6 is **balloon**. The Peg Word for 6 is **shoe**. See yourself wearing balloons instead of shoes, or you're blowing up a shoe instead of a balloon. Use one of these, or one you thought of yourself, and see it in your mind's eye.
If you've made all the associations and visualized them clearly, there's no doubt that you know the ten items. Try it. Think of the Peg Word for number 1: tie. What does tie remind you of? What were you wearing instead of a tie? A pen, of course.
Think of Noah (2). That reminds you of... article.
Think of Ma (3). That reminds you of... scissors.
Think of rye (4). That reminds you of... telephone.
Think of law (5). That reminds you of... fish.
Think of shoe (6). That reminds you of... balloon.
Think of cow (7). That reminds you of... car.
Think of ivy (8). That reminds you of... cracker.
Think of bee (9). That reminds you of... pillow.
Think of toes (10). That reminds you of... teeth.
Aside from the fact that the items were given to you in an out-of-sequence order, you haven't really accomplished too much more than you could have accomplished with the Link. But there is a difference. If you want to know what number 6 is, simply think of the Peg Word for 6 (shoe) and you'll _instantly_ know the 6th item! It's... balloon, right?
That's not all. If you think of any item, you'll instantly know its numerical position. Where was the telephone? Well, telephone makes you think rye, and rye is the Peg Word for the number 4, so telephone _has_ to be 4.
If you'd like to test yourself, see how quickly you can fill in these blanks:
(cow) 7 = _____
(Ma) 3 = _____
(toes) 10 = _____
(bee) 9 = _____
(tie) 1 = _____
(law) 5 = _____
(shoe) 6 = _____
(Noah) 2 = _____
(ivy) 8 = _____
(rye) 4 = _____
And these:
scissors is _____
telephone is _____
fish is _____
article is _____
pillow is _____
balloon is _____
cracker is _____
car is _____
teeth is _____
pen is _____
And these:
10 is _____
3 is _____
1 is _____
8 is _____
4 is _____
car is _____
fish is _____
article is _____
pillow is _____
balloon is _____
Are you impressed with yourself? You should be. Having read them only once, you've remembered ten items forward, backward, and inside out.
The Peg Words are an extension of the places or "loci" idea mentioned at the beginning of the book. You've arrived at them slowly, step by step. The simple memory aids helped you to remember the sounds of the phonetic alphabet, the sounds themselves helped you to remember the Peg Words, and the Peg Words made it easy to remember ten random items. Obviously, the better you know the Pegs, the faster you'll be able to memorize a Peg list, as you just did.
But what if you have to remember eleven items, or twelve, or twenty? No problem. Knowing the phonetic alphabet enables you to make up Peg Words for any number. You can't picture the number 11, but you _can_ picture **a tot** , a young child. And the word _tot_ can only represent the number 11, because it has the _t_ and _t_ sounds, 1 and 1.
The Peg Word for 12 is **tin** ; picture **a tin** can, or see the item at that position made of **tin**.
Then come:
13. **t** o **m** b; picture a gravestone.
14. **t** i **r** e
15. **t** owe **l**
16. **d** is **h**
17. **t** a **ck**
18. **d** o **ve**
19. **t** u **b**
20. **n** o **se**
Go over these once or twice and you'll know them. Now you can really show off. Have someone number a paper from 1 to 20 and let him call any number and any item, until each number has an item next to it. You make good strong associations, of course, of Peg Word to item. Next, call the items off from 1 to the last number. Then let your friend call any number—you tell him the item—followed by any item, whereupon you tell him the number!
A list of Peg Words up to 100 follows. They really are easy to learn, and there's no rote memory involved. Had the words been selected haphazardly, the idea would still work, but that would entail rote memory. As it is, the words all fit the pattern you've learned, and anything patternized is easier to remember. The sounds of the phonetic alphabet make it a fairly easy task.
We won't tell you that it's important for you to know them all thoroughly. You should know twenty or so perfectly however, and we do suggest that you at least become familiar with all of them. Go over them, with concentration, a few times and you will be familiar with them. And, it can't hurt you in the least to really learn them all.
After you've gone over the words a few times, you can use this list as a drill. Put your hand or a piece of paper over the words, look at the numbers, and see if the word comes to you. If you like, you can make up flash cards, but that isn't really necessary. **I** f you're stuck on a word, think of the consonant sounds, then stick vowels in there until the word comes to you. It will, sooner or later.
1. tie
2. Noah
3. Ma
4. rye
5. law
6. shoe
7. cow
8. ivy
9. bee
10. toes
11. tot
12. tin
13. tomb
14. tire
15. towel
16. dish
17. tack
18. dove
19. tub
20. nose
21. net
22. nun
23. name
24. Nero
25. nail
26. notch
27. neck
28. knife
29. knob
30. mouse
31. mat
32. moon
33. mummy
34. mower
35. mule
36. match
37. mug
38. movie
39. mop
40. rose
41. rod
42. rain
43. ram
44. rower
45. roll
46. roach
47. rock
48. roof
49. rope
50. lace
51. lot
52. lion
53. loom
54. lure
55. lily
56. leech
57. log
58. lava
59. lip
60. cheese
61. sheet
62. chain
63. chum
64. cherry
65. jail
66. choo choo
67. chalk
68. chef
69. ship
70. case
71. cot
72. coin
73. comb
74. car
75. coal
76. cage
77. coke
78. cave
79. cob
80. fuzz
81. fit
82. phone
83. foam
84. fur
85. file
86. fish
87. fog
88. fife
89. fob
90. bus
91. bat
92. bone
93. bum
94. bear
95. bell
96. beach
97. book
98. puff
99. pipe
100. disease
After you use the words for a while, you'll see that it's the picture that will come to mind when you see or hear a number, not the actual word. What happens when we see or hear, say, 36? We actually see a match, _not_ the word _match_. This will happen automatically if you use the Peg Words—and you will use them, as you continue reading.
You'll learn many uses for the Peg Words. Going back to the long-digit numbers in the preceding chapter, for instance, when you're stuck on one or two digits in a number you can simply use the Peg Word and keep right on going. It saves time. Occasionally, you'll come to the end of a long number and still have one or two digits to take care of. Use the Peg Word for that.
And incidentally, if you see a group of like digits, don't worry—usually, like digits actually make a number easier to remember. Take 000000 in the middle of a long number—well, **S** ouza's **s** i **z** e would take care of five zeros; **z** oo **s** **su** e **S** ou **z** a' **s** **sis** would take care of eight zeros. You won't even have to do that if there are digits before and after the zeros—9000000941, **p** a **ss** e **s** ( **p** o **s** e **s** , **p** o **ss** e **ss** ) **S** ou **z** a' **s** **sp** o **rt** (or **sp** i **r** i **t** ) would do it.
If you're worried about the ridiculous pictures staying with you, running around in your mind forever, don't be. One of the beauties of the systems is the fact that all of them are means to an end. Once that end is accomplished, the means fade and disappear because they are no longer necessary. When the information is used a few times, you _know_ that information—what you _won't_ remember are your original silly pictures! That's one reason you can use the same Peg Words over and over again.
•
JL: The Peg Words are the handiest things—they've helped me get rid of some hostilities without anyone knowing what I'm talking about.
HL: Do you mean the names you sometimes yell out on the basketball floor?
JL: Right. When a referee makes what I think is an unfair call, and his number is **thirty-three** , I'll yell something like, "You, you— **mummy**!" Or if a player whose number is nineteen sticks an elbow in my ribs, I might call him "You **tub** , you!"—never mind some of the _other_ names some numbers remind me of!
•
You've just learned the third of the three basic systems of memory: the Link, the Substitute Word, and now the Peg. We haven't been able to find any memory problem that could not be solved—made easier—by applying one of these three, or one in conjunction with another. It is sometimes necessary to twist or manipulate the systems somewhat, but they will still make any memory chore easier to handle.
Let's go back a bit. Earlier you learned to memorize the fifty states in alphabetical sequence; you also realized that you could associate a Substitute Word for the state to a Substitute Word for its capital city. To remember the states in sequence, you would use the Link system and the Substitute Word system. But now you can memorize them by number, in and out of order, by using the Substitute Word system and the Peg system.
You simply associate the Substitute Word or phrase for the state name to the vital Peg Word. Once you form a ridiculous picture in your mind between, say, **tie** and **album** , it will be easier to remember than to forget that the first (tie) state is Alabama (album), and vice versa.
Picture a con (prisoner) being a whiz ( **whiz con** ) with a **rope** (49), and you'll know that the 49th state, alphabetically, is Wisconsin. Picture yourself playing **tennis** (Tennessee) in the pouring **rain** (42), and you have the information you want.
A **new brass car** (Nebraska) is driving around and around your **neck** (27); millions of gigantic **pencils** (Pennsylvania) are seeing a **movie** (38); there are **peaches** (Georgia) growing between your **toes** (10); **a sassy can** (Kansas) is in a gigantic **dish** (16); a **nun** (22) is **mix** ing something **again** and again (Michigan); a bride ( **marry** ) **lands** (Maryland) on your **nose** (20); a gigantic bottle of **gin** , wearing a **west** ern ten-gallon hat (West Virginia) is jumping off a **roof** (48); an **Indian** (Indiana) is wearing a **tire** (14) as a headdress; and so on.
Now you can remember not only nouns, but anything—by number. What works for the states can be applied to the Presidents of the United States. You might want to try to memorize them all by number, just for the mental exercise. It shouldn't take more than a few minutes. Find a list of the Presidents and apply the Substitute Word and Peg systems. (Here you'll be making up a Substitute Word for a person's name rather than for a place name—no difference, really.)
Some examples: The 11th President was Polk; you see yourself **pok** ing your finger through a **tot** ; the 30th President was Coolidge, a **mouse** is **cool** on a building **ledge** ; a ( **blue** ) **cannon** (Buchanan) is firing **towels** (15) instead of cannonballs; you're **pierc** ing (Pierce) a **tire** (14); a gigantic **tub** (19) is full of **hay** , or **haze** (Hayes); you pour ink on a door **knob** (29) and the **ink** gets **hard** (Harding); and so on.
The Peg and Substitute Word systems can be applied to concepts almost as easily. Suppose you had to learn the amendments to the Constitution of the United States, by number. Select one word, phrase, or thought from the amendment—the word, phrase, or thought that you think will remind you of the entire amendment. And usually, what _you_ select _will_ remind you of the entire concept. (This is the Key Word or Thought idea that we discussed in Chapter 6.) Now, associate that Key Thought to the Peg Word. That's all you have to do. It's really the same as what you did with states and Presidents, except that here the Substitute Word—the Key Thought—will remind you of much more information.
We're assuming that if you're interested in learning the amendments, or any material, you basically understand what it is you're studying. What you need are _reminders_.
For example, the seventh amendment to the Constitution gives the citizens of the United States the right to trial by jury. Associate cow (7) to that; all you really need to do is to see yourself in a courtroom, being judged by a **jury** of **cows**.
The fourth amendment has to do with protection against unreasonable search and seizure. See a gigantic loaf of **rye** bread (or a gigantic bottle of whiskey) coming into your home to **search** it; you can't stop him because he has a warrant to do so.
Picture a **tomb** being a **slave** driver to remind you that the thirteenth amendment abolished slavery.
The sixteenth amendment is the one we'd rather forget—the one that established the income tax. See yourself paying your **taxes** with **dish** es instead of money.
The eighteenth amendment started Prohibition—picture a **dove** trying to get into a **speakeasy**.
There is, of course, no way for us to use examples that will necessarily zero in on one of your specific, personal memory problems. What we're trying to accomplish is to make you aware of the variety of ways in which the systems can be applied. By the time you're finished with the book, you should have all the necessary weapons to face, attack, and solve any memory problem.
# 12 **_STYLE NUMBERS, PRICES, TELEPHONE NUMBERS_**
HL: I imagine the first thing most people who know that you memorized the first few hundred pages of the Manhattan telephone book wonder is, "Why on earth would anyone _want_ to?"
JL: If they asked me, I'd tell them the truth—for the publicity. Actually, I memorized only the first column of every page. And the names and numbers don't start until page 22.
HL: That's still... let's see... maybe thirty thousand names and telephone numbers?
JL: At least. Anyway, I don't know them anymore. The stunt served its purpose—to publicize the systems that enable people to remember short numbers, like telephone numbers, instantly. And to keep on remembering them, as long as they want to.
•
The ability to picture numbers via the phonetic alphabet, plus the ability to use the Substitute Word system of memory is all that's necessary to help you remember style numbers, prices, and telephone numbers.
To remember a style number, associate the number to the product; it's that simple. If the style number of a typewriter is 691, associate **chopped** or **chipped** to typewriter. **If** you're in the typewriter business, then you'd have to associate the style number to the distinctive features of each machine, since you'd have many styles of typewriters. (Some style numbers include letters; you'll learn how to handle that, too.)
The same approach works for prices. Here are a few examples of different items and prices. Form the suggested ridiculous associations, or use your own, then you can test yourself and see if it works.
A lamp sells for $40.11; picture a **rested** or **roasted** lamp. See that picture.
A camera sells for $19.18; picture a gigantic camera being **tipped off** a table, or a camera taking a picture of **taped** ivy.
Television set, $142.05; see a gigantic television set riding the tracks like a train; it has a sail on it ( **train sail** = $142.05).
Toaster, $34.95; see a gigantic **marble** toasting bread, or a toaster popping up millions of marbles.
Car, $3,102.86; you might see a car taking a dose of **medicine** from a **fish**.
**If** you've tried to see these silly pictures, now try to fill in the correct prices:
When it comes to telephone numbers, there's no question that remembering them must save you a lot of time and aggravation over a long period. All you need do is calculate the minutes it takes to look up a number or dial the information operator, redial because you dialed the wrong number first, etc., to be convinced.
To remember a telephone number you simply associate a word or phrase that tells you the number (phonetically) to the person or company, or to a Substitute Word for the person or company. Eventually, the phone company will be using the ANC, _A_ ll _N_ umber _C_ ode, and there will be no exchange names. At the present time, some exchange names are still in use.
Remembering an all-digit phone number is the same as remembering any number. If your doctor's number is 940-8212, associate doctor ( **stethoscope** , perhaps) to **press fountain** , or **brass fountain** , or **price fountain**. If you'd rather, you can associate the number to his name.
If you'd like to have your electrician's number at your fingertips, associate his number to **electric**. If the number is 862-9421, you might see an electric plug **fishin** ' and drinking **brandy** , or you could use **fashion brand**. There's no rule that says your words must cover the first three digits and then the last four digits. Use any words to cover any of the digits; it doesn't matter. If a word that contains all the necessary sounds comes to mind—use it. For 720-5127, you might think of **cans looting** , which is fine, but **consulting** also would tell you the number.
As for exchange-name telephone numbers, there's a simple way to handle them. The first word in your association must tell you both the two exchange letters and the exchange number. You then use any word or phrase to tell you the remaining digits.
If the number you want to remember is RA 3-9110, the phrase **ram potatoes** would do it. The word _ram_ begins with _ra_ , and the very next consonant sound is _m_ , for 3; **RA** 3. This becomes even easier when you realize that that first word needn't contain _only_ the two letters and the one consonant sound. It must _begin_ with that—then all following sounds are disregarded. So, you could have used **ram** part **potatoes** for this number, because **ram** p **art** would still represent **RA** 3.
The word, or picture, **burn** would represent **BU** 4; **cig** arette would represent **CI 7, plan** or **plant** would represent PL 2, and so on. For exchanges like **TN and LW** (New York exchanges), with which it is impossible to form words, make up a standard. **Ton** could represent TN, and **low** could represent LW. For those, you'd know that a picture like **ton cow marked** represents TN 7-3471. Later on, when you learn how to picture individual letters of the alphabet, you'll see how that would also help to solve this problem.
The publicity offices of Stein & Day, the publisher of this book, has the number PL 3-7285; we remembered it by associating a beer **stein** shining like the sun ( **day** ) to **plum can full** ; the shining stein was pouring out enough plums to make a can full. Of course, we could have changed the exchange letters to digits, making the number 753-7285, and used **climb can full** , or **column can fall**.
This example brings us to two points. First, when you use two words for the last four digits, using the basic Peg Words, **it may** cause a slight confusion. If we had used **coin file** , how would we know, at a future time, that it was **coin file** , and not **file coin**? It doesn't matter that much—after you've dialed a number a few times, the picture you originally made isn't necessary anyway, you'll know the number. But, you can solve this minor problem by using any word _but_ a basic Peg Word for the second word. If you make a habit of doing that, you'll know that the basic **Peg Word** always comes first. So, for the four digits 5230, you wouldn't use **lion mouse** , you'd use lion **mess** , **moss** , or **moose**.
The second point is that you can eliminate the necessity for forming words to cover the exchange name by eliminating the exchange name. You can look at a telephone dial and transpose the letters to digits, and the problem is solved. Since a telephone dial isn't always handy, the best thing to do would be to memorize it. Once you've done that, you can instantly transpose any exchange name or letters to digits.
Make up a word or phrase that reminds you of the three letters at each digit on a dial, and associate that to the digit (Peg Word). Here are some suggestions; really see the pictures, and you'll have memorized the dial in no time.
2—ABC: Picture **Noah** learning his **ABC's**.
3—DEF: Picture your **Ma** being **deaf**.
4— **GHI** : See a **GI** drinking **rye** , or you're drinking **rye** and getting high.
5—JKL: Picture a **jackal** being a policeman ( **law** ).
6—MNO: Picture a **shoe** saying, " **Me? No** "; or a **shoe** being mean to an **O**.
7—PRS: See a **cow** carrying a gigantic **purse**.
8—TUV: Picture **ivy** being **tough** (enough to remind you of TUV).
9—WXY: **A bee** is **waxy**.
All that remain to be discussed are area codes. The area code simply changes a seven-digit phone number to a ten-digit number. Make up a word to represent the area code, put it into your original association, and you've got it. If Mr. Smith's telephone number is (201) 648-9470, you might see a picture of yourself smashing a **nest** (201) with a black **smith's** hammer; a **sheriff** (648) **breaks** (9470) your hammer.
Stein and Day's main offices are located in Westchester County (area code **914** ). The telephone number is 762-2151. A picture of a large slab of **butter** on a **cushion** that is **nettled** (or **not** light) would do it.
If you make many out-of-area calls, you might want to prememorize some area codes; just associate area code to place. Then you'll have them all ready when you need them. You can memorize the codes for major cities only, if you like. It's easy enough.
The area code for Manhattan is 212; that's almost readymade for you because **Indian** represents 212 phonetically, and everyone knows that we bought Manhattan from the Indians. Or, you could associate **Indian** to **man hat**.
Associate no time to **lost angels** in order to remember that the area code for Los Angeles is 213.
The area code for all of Wyoming is 307; associate **Y roaming** to **mask**.
All of Delaware is 302; associate **Della wear** to **mason**.
Nevada is 702; associate **never there** or **gambling** to cousin.
West Virginia is 304; associate a bottle of **gin** , wearing a **west** ern hat, to **misery** or **miser**.
Cleveland is 216; associate **cleave land** to no **touch**.
Chicago is 312; associate **chick (car go)** to **my tan** , **median** , or **mutton**.
Again, you'll need the silly pictures only until the numbers become knowledge. Best of all, you'll have liberated yourself from misdialed calls, telephone books, and telephone operators!
# 13 **_PLAYING CARDS_**
JL: I've seen you handle a deck of cards—I don't blame casinos for not wanting to deal blackjack to you.
HL: There are six who won't, that I know of. But, they're not being as smart as they think. Sure, I'll probably beat the house at blackjack, but then I lose that and more at the crap tables.
JL: Memory systems won't help you _there_.
HL: No, but a combination of memory systems and knowledge of the game really works for blackjack. It's actually the only casino game where you can better the odds, sometimes even the odds, or change them so that you have a bit of an edge.
JL: Is that because you can double your bet after the hand has started?
HL: Right. And remembering exactly which cards have been played is a great help in knowing when to double your bet, and when to stop or hit. I have to tell you, it's not so easy nowadays. Thanks to people who know our systems, most casinos use more than one deck—and never deal down to the end.
JL: Too bad, Harry, you'll have to work for your money!
•
Playing cards are difficult to remember because they are abstractions; they're like numbers. There's really no way most people can picture a card, so again the concept here is to make an intangible tangible. The trick is to have each card of a deck represented by a definite, concrete item—just as you did with numbers. Once that's accomplished you'll be able to picture playing cards, and then they can be associated to other things just as numbers can. There's a different, very easy way to remember cards—the "missing card" or "mutilation" idea—which we'll get to shortly.
Incidentally, you should learn the ideas in this section whether or not you play cards. You never know, you may become interested in cards in the future—but more important, trying the ideas is a great mental exercise.
The pattern used is almost obvious. The Card Word for each card (up to the 10's) will begin with either C, H, S, or D—for clubs, hearts, spades, and diamonds. The very next consonant sound in that word will be the sound that represents the _value_ of the card. So, the word **can** could represent only the 2C. That's the pattern, and once you understand it, there are no decisions or choices to make. **Can** represents the 2C because it begins with a **C** for _c_ lubs, and the next consonant sound is _n_ , for 2.
The word (or picture) **sail** must represent the 5S, because it begins with an _s_ (for spades) and is followed by the _l_ sound, for 5. The 4H is **hare** ; 6D is **dash** ; **4C** is **core** ; 8S is **safe** ; 9D is **deb** ; AD is **date** (ace is 1); 6C is **cash** ; and so on.
Be sure you fully understand these few examples before you continue reading. Then look at the Card Words on this page. As you look them all over, you'll see that the jacks, queens, and kings represent a departure from the pattern, which we'll explain momentarily.
The _s_ sound is used to represent the 10's. Since there is no zero of any suit, we might as well use that sound for the 10's. So, the pattern or system holds for all the cards from ace to 10.
Don't worry about the _ds_ in suds, for the 10S. It's really one sound— _dz_ , which represents 0. And even if you break it into two sounds, that's _d-s_ , which is 1-0. It can represent only 10.
AC—cat | AH—hat | AS—suit | AD—date
---|---|---|---
2C—can | 2H—hen | 2S—sun | 2D—dune
3C—comb | 3H—hem | 3S—sum | 3D—dam
4C—core | 4H—hare | 4S—sewer | 4D—door
5C—coal | 5H—hail | 5S—sail | 5D—doll
6C—cash | 6H—hash | 6S—sash | 6D—dash
7C—cake | 7H—hog | 7S—sock | 7D—dock
8C—cuff | 8H—hoof | 8S—safe | 8D—dive
9C—cup | 9H—hoop | 9S—soap | 9D—deb
10C—case | 10H—hose | 10S—suds | 10D—dose
JC—club | JH—heart | JS—spade | JD—diamond
QC—cream | QH—queen | QS—steam | QD—dream
KC—king | KH—hinge | KS—sing | KD—drink
Besides, the words up through the 10's fit the pattern and can be pictured, the court card words also can be pictured—so the word itself isn't that important. It's the picture the word creates in your mind that matters—after some use, you shouldn't think the word but simply see the picture it creates.
Once you've seen a picture in your mind for any word, that's the picture you should (and will) see each time. A few suggestions: For core, picture an apple core; for cuff, trousers; case, either a briefcase or a crate; hem, a dress; hash, corned-beef hash; hoof, a horseshoe; hoop, a basketball hoop; hose, nylons or a garden hose; suit, a man's suit jacket (this is to distinguish it from cuff); sum, an adding machine or a sheet of paper covered with numbers; sash, a window sash or just a window; suds, a tub full of sudsy water; date, the fruit or a calendar; dune, a sand hill; dam, Boulder Dam or a waterfall; dash, a track star running the 100-yard dash; dock, a pier; deb, a debutante; dose, a spoonful of medicine—we simply picture a spoon.
For the picture, or court, cards we could have stayed within the pattern, but it gets a little sticky to come up with words like **hated** for the JH (since jack is 11, queen is 12, and king is 13), and **cotton** for the QC. It can be done, and we'll give you a list of words that stay with the pattern, so don't decide yet which method you'll use for the court cards.
We prefer to use the Card Words as listed. For the jacks, simply use the suit words themselves; they each have meaning—a club, a heart (the organ, or a Valentine card), a spade (shovel), and a diamond. For the QH and KC, we use the words queen and king, respectively. Just be sure that you differentiate between the two pictures since they're similar, both royalty. For queen, picture a lady wearing a crown and a _gown_ on a throne; for king, picture the crown but be sure he's wearing _trousers_.
The words for the remaining queens and kings each begin with the vital suit letter, but then each word _rhymes_ as closely as possible to queen and king. They're not exact rhymes (except for **sing** ), but close enough. Don't worry about these; you'll probably remember them easily because they _are_ exceptions. For steam, picture a radiator; for dream, a bed or someone sleeping.
As was the case with Peg Words, if you go over the Card Words a few times you may be surprised at how quickly you'll know them.
Now. As promised, here are the words for the court cards that stay within the pattern. You have choices for all of them, and you'll have to decide whether you want to use these or the ones we use. Again, it doesn't really matter. We had to use phrases for three of the kings, and take a bit of license with the JH and QH, but they will work just as well because they do create a picture in the mind.
JC—cadet, coated
JH—hothead, hated, hooted, hooded
JS—steed, staid, sated
JD—dotted, doted, dead
head, dead heat, dated
QC—cotton, codeine
QH—hootin', heatin',
hatin', headin', Hayden
(Planetarium), hoe down
QS—satan, satin, sit in,
sadden, sedan
QD—detain, deaden, dotin'
KT—cute Ma, caddie me
KH—head home, high dome,
hit me, high time, hide me
KS—steam, stem
KD—dead aim, tea time (the
_t_ will still remind you of
_d_ for diamond)
Make your decision as to which method to use for the court cards, and then put in a little time learning all the words or phrases. You'll find the Card Words just as effective an aid for remembering playing cards as the Peg Words are for remembering numbers. Obviously, they can't be much help until you know them fairly well. As was true of the Peg Words, any words would serve the purpose. But because these are patternized, you eliminate rote memory. If you know the pattern and the phonetic sounds, the chore is half done.
If you like, you can easily make up a deck of flash cards. Simply write the correct Card Word on the back of each card. Shuffle them and look at them one at a time—either back or face. If you see the face, call out the Card Word, then turn the card over to see if you're right. If you see the back, the Card Word, call out the name of the card and turn it over to check. When you get to the point where you can do this with all fifty-two cards, _without hesitation_ , you know the Card Words fairly well.
All right, assuming you know the Card Words, how do you apply them? Well, now you can remember cards as easily as you remember items. You can use the Link to remember cards in sequence. A Link of a gigantic apple **core** taking a **drink** , a **doll** drinking, a gigantic **cake** rocking a doll in its arms, a cake acting as the **sail** of a sailboat, a sail(boat) shining in the sky like the sun, the sun having long ears and hopping about like a **hare** , a gigantic **cup** hopping like a hare, a large cup wearing **socks** , and a gigantic sock being a radiator ( **steam** ), would help you remember the 4C, KD, 5D, 7C, 5S, 2S, 4H, 9C, 7S, and QS—in sequence, forward and backward.
Or you can use the Peg system to remember cards by number, in and out of order. This is quite an impressive memory demonstration, because you are memorizing two abstracts, numbers and cards. You need to know two things—the Peg Words from 1 to 52, and the Card Words. You can do it with a full deck; but it's just as impressive with half the deck, or even twenty cards.
Just to show you how it works, assume a friend shuffles the cards and calls off ten of them, from the top. Make these associations or use your own pictures:
You're wearing a large horseshoe ( **hoof** ) instead of a **tie**.
A man's beard ( **Noah** ) is made up of millions of dollar bills ( **cash** ).
Your **Ma** is **sing** ing at the Metropolitan Opera.
**A hen** is laying a bottle of **rye** instead of an egg, or it's drinking from a bottle of rye.
A gigantic **comb** is wearing a uniform; it's a policeman ( **law** ).
A gigantic **shoe** is sitting on a **throne** , wearing royal robes; it's **the king**.
It's **hail** ing **cow** s instead of hailstones.
Millions of **cup** s, instead of **ivy** , are growing all over a wall; or, ivy is growing all over a gigantic cup.
You open a **safe** , and millions of **bees** fly out and sting you.
You're wearing **toes** instead of a **hat** ; or hats are growing between your **toes**.
If you've really tried to see these or your own pictures, and if you're fairly familiar with the Card Words, you'll know ten cards by number. It's quite easy. Think of the Peg Word for number 1, **tie**. What does it make you think of? It should make you think of horseshoe, or hoof. **Hoof** can represent only one card, and that's the 8H.
Try it on your own; think of each of the Peg Words up to 10. Each one should make you think of a Card Word. Transpose that to a card, and you'll have remembered the card at that position. See if you can fill in these blanks:
Card | 2 (Noah) | is the _____.
---|---|---
Card | 3 (Ma) | is the _____.
Card | 4 (rye) | is the _____.
Card | 5 (law) | is the _____.
Card | 6 (shoe) | is the _____.
Card | 7 (cow) | is the _____.
Card | 8 (ivy) | is the _____.
Card | 9 (bee) | is the _____.
Card | 10 (toes) | is the _____.
Since this is exactly the same as doing a regular Peg list, you also know the cards out of order. If you thought of **cow** (7), the picture of hailing cows should come to mind, and **hail** can only be the 5H. If your friend called the KS, you'd transpose that to its Card Word, **sing** , which should make you think of **Ma** , and that tells you that the KS is the third card. Test yourself—number or card. If you made the associations originally, you'll know the position of each card, and which card is at which position. If you didn't form the associations, go back and do so now. Otherwise, you'll never know whether or not this really works!
Knowing the Card Words makes the cards of a deck tangible and easy to picture in the mind. Once they can be pictured, they can be associated so that you can be Originally Aware of them.
Here's some more practice for you, although you can easily do it on your own. Use the Peg Words from 11 to 20 and remember the following cards. Then you'll know twenty cards by number. After you've formed the associations, test yourself.
11. 4D (tot to door)
12. JS (tin to spade)
13. 3H (tomb to hem)
14. 8D (tire to dive)
15. 10C (towel to case)
16. 6S (dish to sash)
17. 10H (tack to hose)
18. 7H (dove to hog)
19. 5D (tub to doll)
20. KH (nose to hinge)
Now that you've impressed yourself, you're ready to learn a fascinating application of the Card Words.
Neither the Link nor the Peg would come in too handy in most card games. For any "discard" game such as gin rummy, bridge, hearts, or canasta, you need the "mutilation" idea. We'll teach it to you as a stunt, and then we'll discuss its use in different card games.
Assume that a friend shuffles a full deck of cards. He removes, say, five cards, which he puts into his pocket without looking at them. Now, he calls off the remaining forty-seven cards. When he's done that, you tell him, one by one, the cards he has in his pocket—in other words, you tell him the names of the _missing_ cards.
There's no need to use the Link or the Peg in order to accomplish this; it would take much too long. The mutilation idea is faster and easier because all you need to know is your list of Card Words. You simply do this: When you hear a card called, transpose it to its Card Word and _mutilate_ that word (the picture, **really** ) in some way.
Say the KD is called, see a _spilled_ drink; the 4H is called, picture a hare _without_ ears; the 5D, see a doll with an arm or leg missing; the AC, see a cat without a tail; the 2S, see a cloud obliterating the sun, and so on. Simply mutilate the picture that represents the card in your mind, in some quick way. This will become easier and faster to do as you keep doing it, for two reasons: You'll get to know the Card Words better, and once you see a mutilation of any Card Word, you'll use that same picture all the time. It has become an instantaneous picture in your mind.
This is probably the best example of pinpointed concentration and Original Awareness that we could demonstrate. That instantaneous picture of the mutilated Card Word has forced you to be aware of that particular card at that moment, as clearly as is humanly possible. You can prove this by trying it. After you've mutilated the called forty-seven cards, all you have to do is to go over all your Card Words, mentally. Any Card Word that has _not_ been mutilated will stand out like the proverbial sore thumb!
Go over the Card Words in a specific order; we always use CHSD, which is easy to remember if you think of the word " **chased**." Perhaps you'd prefer the HSDC order—think of the phrase " **his deck**." You might want to use the bridge, or alphabetical, order of suits (CDHS), it doesn't matter. Always using the same suit order will save you the time and possible confusion of possibly going over the same suit twice. Why take the chance of going over, say, the club Card Words, calling the one or two club cards that are in your friend's pocket, then the hearts—and then not being sure which suits you've already done? Going over the suits in the same order every time eliminates that possibility.
It doesn't matter how many cards you tell your friend to take from the deck. Actually, the more cards he removes, the easier it is for you; there'll be fewer cards for you to mutilate. Five cards is a good demonstration for poker players; for gin rummy players, have someone remove ten cards. For a bridge demonstration, you can have someone shuffle and then deal out the four hands of thirteen cards each. He then takes three of the hands, shuffles, and calls them off to you a card at a time. You should be able to name all thirteen cards in the fourth hand.
To gain speed, you should first work at making the Card Words second nature; the better you know them, the faster you'll be able to do the missing-card demonstration. After you've tried it a few times at a rate and speed you find comfortable, push yourself a bit—have a friend call the cards to you at a little faster pace than you think you can handle. Tell your friend not to slow down or stop for any reason. Then you have no choice but to "see" each mutilation within that particular slot of time. We think you'll find, believe it or not, that not only will you do the stunt (you'll know the missing cards), but you'll do it _better_.
You'll be forcing yourself to see each picture quickly and clearly, and that's better than trying to think of or see each picture for too long a period. The next time, try it at an even faster pace, and so on. If you own a metronome, set it at the pace you desire and turn a card face up whenever that pendulum swings to one side.
If you haven't as yet, you should try the missing-card stunt before you continue. Take some cards out of a shuffled deck, then look through the others—mutilating as you do. Then go over the Card Words mentally and jot down the cards you think are not mutilated, or missing. Check to see if you're correct. If you want to save a little time, remove the picture cards, then you'll be working with only forty cards. After you've mutilated, you're left with only the Card Words from aces to 10's to go over.
You may be wondering how you can repeat the missing-card demonstration. Well, you _shouldn't_ repeat it immediately for the same people. Once is enough; leave them wanting more. You can repeat it, however, if you want to. If you use mutilation again, of course, it would be confusing. This brings us to playing, say, gin rummy. Obviously, if you're applying the missing-card principle, you're going to have to do it with each hand played.
All right; for the first hand, use mutilation; for the next hand, use fire. That is, see each Card Word _burning_. It's a form of mutilation, but different enough so as not to cause confusion. For the next hand, use _water;_ see each Card Word under water, or drowning. For the next hand, see each Card Word being cut with a _knife_ , and for the next hand, associate each Card Word to _yourself_. The idea is to force yourself to concentrate on each card for that one fraction of a second, and each of the above-mentioned methods will serve—yet they're all different, and definite, enough to be distinct in your mind. You need only try it to see that this is so.
By the time you've reached the associating-to-yourself method, you're ready to go back to mutilation and start the entire cycle over again. You can, however, enlarge the cycle if you like. After associating the Card Words to yourself, for the next hand of gin you can associate each Card Word to the Peg Word for 1 (tie), next hand to Noah, next to Ma, and so on. By then, you'll surely be able to start the cycle over again without confusion.
In gin rummy, it is important to know whether or not it is safe to discard any particular card. As you play, mutilate—or burn, or whatever—each card discarded by yourself and your opponent. When you want to be sure that a card is safe, you don't have to go through all your Card Words—that would take too long. All you need do is think of three or four Card Words.
Say you're about to discard the 8H. Is it safe? Think of the Card Words for the 7H and the 9H. If they haven't been mutilated, don't throw that 8H—your opponent may be holding a heart run, and waiting for the 8H. If the surrounding cards (7H and 9H) have been mutilated, don't throw the 8H yet; think of the Card Words for two other 8-spots. If they've been mutilated, you _know_ it's safe to discard the 8H.
If and when your opponent takes a discard, associate the Card Word to his, say, nose. He takes the 7S; see a **sock** hanging from his nose. Later, when you need to know what cards he took from the discard pile, you'll know the cards! Associating the Card Word to him in some silly way makes you Originally Aware of the card. You can do this during each hand, without getting confused. Try it and see for yourself.
Bridge players use this idea to great advantage. Exactly how is up to the particular player. Some are interested in knowing only the trump cards that have been played, so they mutilate only trump cards. More experienced players may want to know all the cards that are played, so they mutilate each one as it falls. Once you understand the idea, apply it as you desire, and to your best advantage.
For pinochle, which is played with a deck of forty-eight cards containing only 9's through aces, you need two Card Words for each card from the 9's on. One fast example: For the 9C, you'd use the basic Card Word ( **cup** ) and perhaps **cap** for the second 9C; the pattern is the same. When playing, you'd mutilate **cup** when the first 9C is played, and **cap** when the second one is played. Always mutilate the basic Card Word first, then the one you made up for the second like card. For the court cards, use a word (for the second card) that the basic Card Word reminds you of. For example, **drink** might remind you of **glass** , so you can use glass to represent the second KD.
Poker is not a discard game, but a memory of what's been played is certainly helpful in most games. Good poker players do know poker odds—the chances of drawing to an inside straight, or whatever. And those odds do change according to cards played. So in an open, or stud, poker game it would be foolish to keep betting because you're waiting for a 9-spot, when you know (remember) that two 9's have already been dealt to other players. Players drop out and turn their cards down—a good player will remember the cards that he's seen during the hand, and play accordingly.
Even in a game like five-card draw, where you see none of the cards, our memory systems can help you to remember the odds for bettering your hand. For example, if you have three cards of the same suit and you want to know whether or not it pays to stay in and draw for two more of the same suit (a flush), remembering that the odds are approximately 23 to 1 against drawing that flush may help you to decide not to do it!
The word **flame** , under these circumstances, would remind you of flush-three cards. The first two letters of the word ( _fl_ ) remind you of flush, and the next consonant sound reminds you of three cards. Associate **flame** to **name** (23), and you have your reminder. The odds against drawing one card (you retain four) to a flush are approximately 5 to 1. Associating **fl** a **r** e (flush, while retaining four) to **law** (5) will do it.
Many poker players will stay in the game holding a pair and a "kicker," then drawing two cards. It might help you to know that the odds against making three-of-a-kind that way are 12 to 1. Picture a sheet of **tin** (12) **kicking** a **pear** , and you'll be able to remember this easily. The odds against making two pair under these circumstances are 5 to 1; a **pear kicking** a **policeman (law)** will do it. Your knowledge of the game will tell you whether the odds pertain to three-of-a-kind or two pair; or, you can put another word into the association to tell you what it pertains to.
In bridge, the chances of drawing thirteen cards of any one suit are 1 in to love, climb, move up, poses! The chances of drawing thirteen spades are 1 in **show mule, steam, lily up, chases**! And in poker, the odds against drawing one of the four possible royal flushes are **sharp camp** to 1. Don't bet on any of these!
The odds against rolling an eleven in one roll of the dice are 17 to 1. That's why the house has the edge at the crap table when they offer 10 or 15 to 1 on eleven.
Of course, no amount of memory of odds, or cards played, will help you much if you don't really know the strategy of the game that you're playing. We don't want to mislead you into thinking that having a great memory will make you a winner; it won't unless you're a good player. We relinquish all responsibility for your losses—but you can send us 10 percent of your winnings!
# 14 **_WEEKLY APPOINTMENTS; DAYS OF THE WEEK_**
HL: Remembering the time and place of appointments is obviously important, both in business and socially.
JL: Of course, you can remember the right place and time, and still get fouled up. In Boston, one player made a date with a girl and he was to meet her outside her hotel, after the game. It was _two degrees below zero_ that night.
Some of us were going to a restaurant after the game, and we saw him waiting there. When we finished eating, we went back to the hotel, and he was still standing there! As we passed him, he asked, "Is this the front or the back of the hotel?"
•
In an earlier chapter, you learned that a Link would help you remember simple errands and appointments for the following day. That idea alone will suffice for many people. However, you may have to remember more specific appointments, by day and time, and for the following week.
It's easy enough to do; you already have the necessary knowledge. The problem is familiar to you—how do you picture a day and time? The solution is just as familiar. Set up a pattern that enables you to create a picture for any day and time; to make the intangible tangible.
In patternizing day and time, we'll consider Monday the first day of the week. Since it is the first business day of the week, this makes more sense to most people. If you'd rather consider Sunday the first day, simply do so and change everything accordingly; it won't matter once you understand the idea. Otherwise, go along with us. Monday is the first day, Tuesday is second, and so on to Sunday, the seventh day of the week.
Thursday at 7:00 can now be thought of as a two-digit number. Thursday is the fourth day, so the first digit is 4, to represent the day. The second digit represents the hour—therefore, the two-digit number is 47. Within this pattern, 47 can represent only the fourth day (Thursday), seventh hour (7:00).
Ordinarily, it would be just as difficult to picture 47 as it would be to picture Thursday at 7:00. But you have a Peg Word for 47 that can be pictured— **rock**. And so, within this pattern, **rock** must represent Thursday at 7:00.
The Peg Word **knife** could represent only Tuesday (second day) at 8:00. **Lily** must represent the fifth day (Friday) at 5:00. Even if you don't know the Peg Words, the sounds give you the necessary information. This will work much more smoothly, of course, if you _do_ know the Peg Words. Try a few yourself—mentally transpose these Peg Words to day and hour: **name, chain, knob, net, dish, Nero, coal, mower**.
There are a few minor problems remaining. How do you handle 10:00, 11:00, and 12:00? What about A.M. and P.M.? What about minutes? And, how do you _use_ the Peg Words?
Let's take care of 10:00, 11:00, and 12:00 first. Remember our discussion of playing cards—just as there is no zero of hearts, there is also no zero o'clock. So, use the _s_ sound to represent 10:00. **Mouse** will represent Wednesday at 10:00; **toes** , Monday at 10:00; **rose** , Thursday at 10:00; **nose** , Tuesday at 10:00; **case** , Sunday at 10:00; and so on.
It is necessary to make up a word for each day of the week at 11:00 and 12:00. There are two ways to handle this: the first is to stick with the pattern and use a word containing the proper sounds. The word **mitten** , for example, is Wednesday at 12:00 (312); and **rotate** (411) could represent only Thursday at 11:00.
Here is a list of words from which you can select. Make up your own, if you'd rather.
Select the words you want, and use them. After a few uses, they will be like Peg Words—for this pattern. You'll know them _because_ you've used them.
Here's another way to handle 11:00 and 12:00: Simply consider 11:00 and 12:00 as 1:00 and 2:00, but without using the basic Peg Words since you're already using them. Use any _other_ word that fits phonetically.
For example, the Peg Word **mat** represents Wednesday at 1:00, but the words **meat** or **moat** could represent Wednesday at 11:00. The Peg Word **moon** represents Wednesday at 2:00—use **man** or **moan** to represent Wednesday at 12:00. Once you select the words, they will work perfectly well. You'll know that the basic Peg Words represent 1:00 and 2:00, and that any other words that fit 1:00 and 2:00 (for any day) would represent 11:00 and 12:00.
If all your appointments were made on the hour, you'd be all set to apply the system—by associating the appointment itself to the word that represents the day and hour of the appointment. If you had to go to the library on Saturday at 1:00, you'd form a ridiculous association between library, or books, and **sheet**. That's all.
Why not make that association now? Then we'll list some more, just to show you how it works. Later, we'll get to the minutes, and to A.M. and P.M. These hypothetical appointments will be given to you haphazardly, since that's how appointments usually come up. Form the associations, because we're going to test you.
On _Tuesday at 9:00_ , you have a dental appointment. Transpose the day and hour to the Peg Word, **knob** , and associate that to dentist. Perhaps the dentist is pulling a doorknob instead of a tooth out of your mouth. Or a gigantic doorknob is your dentist. Be sure to see the picture.
_Monday at 2:00_ , you have a meeting at the bank. Associate **tin** (first day, second hour) to bank. Perhaps you're depositing sheets of tin instead of money; or the bank tellers are all large tin cans.
_Saturday at 8:00_ , you must remember to leave your car at your garage for repairs. Associate **chef** to car. You might see a gigantic chef's hat driving a car, or a car is wearing the chef's hat.
_Wednesday at 5:00_ , you have to pick up a pair of eyeglasses. Associate **mule** to glasses. The silly picture of a mule wearing gigantic eyeglasses would do it. See that picture.
_Friday at 2:00_ , you have a luncheon appointment with Mr. Vaikovitch. Associate **lion** to, perhaps, **vague witch**. See a lion about to eat a witch, only the witch starts to fade; it gets vague. Or, a lion is trying to **wake** a **witch**.
_Thursday at 10:00_ , you want to remember your karate lesson. Associate **rose** to karate. Perhaps you're giving a gigantic rose a karate chop, or a gigantic rose is using karate on you.
_Tuesday at 5:00_ , there's a meeting of the volunteer fire department. Associate **nail** to fire. Perhaps a gigantic nail is starting a fire. Be sure to see this picture.
Now try this. Go over your Peg Words for Monday— **tot, tin, tomb** , up to **toes**. (If you still don't know the Peg Words, turn back to the list and read them. Picture each one as you read.) Now, when you come to a word that has been associated to something else, you'll know it instantly! You've only got to try it to see that this is so. Just now, when you thought **tin** , that should have made you think of... bank.
After you've done Monday, go over Tuesday's words— **net, nun, name** , etc. Then Wednesday's, Thursday's, Friday's, Saturday's, and Sunday's. Think of the words up to zero (10:00) only, since there are no 11:00 and 12:00 appointments used in the example. If you do this, you'll probably remember all the appointments!
Just exactly how would you apply this idea? Well, assume it's the following Monday. In the morning, go over Monday's Peg Words; there are only twelve. You'll be reminded of the things you must do that day. During the day, while you're having lunch, walking, etc., simply go over those words. You'll have a constant reminder of your appointments. If you'd rather know what it is you have to do the _next_ day, go over Monday's words on Sunday night. That's all there is to it. No more looking for your appointment book, which you probably left at home or at the office anyway.
For the minutes, simply add one word to the Peg Word picture. If you have a plane to catch on Friday at 5:20, **lily** is the Peg Word that represents Friday at 5:00. You could make 5:20 **lily nose—nose** tells you the minutes. There's one problem here; next week, how would you know whether it's lily nose or nose lily? (If you thought it was nose lily, you'd go to the airport three days too soon!)
The problem is easily solved by _not_ using a basic Peg Word to represent minutes—use any other word that fits phonetically (just as with the idea for 11:00 and 12:00). For the above example, use noose or niece. A ridiculous picture of a gigantic lily with a noose around its neck, flying like an airplane, would do it. This solves the problem because you'd know that the basic Peg Word always represents day and hour, and any other word always represents the minutes.
Frankly, we rarely use the minute idea. Our appointments are almost never that precise. All we really need is a reminder for a quarter, a half, and three-quarters past the hour. We use a standard to represent each one. A twenty-five-cent piece always represents a **quarter** past the hour, a **half** grapefruit represents half past the hour, and a pie with one large slice gone ( **three-quarters** of a pie) represents three-quarters past the hour. Use these standards, or make up your own.
The standards work for us, because even if we want to remember, say, a 6:19 appointment (an airplane departure or a television taping), we'll consider it as 6:15. The worst (or best) that can happen is that we're a little early for the appointment. If the appointment is for 2:38, we consider it as 2:30.
The A.M.-P.M. question is really a hypothetical one. You usually know whether any particular appointment is A.M. or P.M. If you really had a luncheon appointment with Mr. Vaikovitch at 2:00, you'd hardly assume it was 2:00 A.M.! You'd also know that your 9:00 dental appointment is in the morning, unless you have a very unusual dentist.
You can, however, make the association as definite as you want to. You can use **aim** to represent A.M. Or, you can use **white** to represent day (A.M.), and **black** to represent night (P.M.). All you really **need is** one of them. To remember that an appointment is in the morning, get white into the picture; if white isn't in the picture, then you know it's a P.M. appointment.
In the example of bringing your car to the garage on Saturday at 8:00, you could have pictured the car being sparkling white, or **aiming** at something, to remind you that the appointment was at 8:00 A.M.
•
JL: Harry, the truth now—did you ever miss an engagement because you forgot about it, and just didn't show up? I've heard something to that effect.
HL: It makes a good story, but no. Years ago, I was scheduled to appear at a Rotary Club luncheon, and I had quite a drive to get there. Somebody told me that it was a two-hour drive, and it ended up a four-hour drive. When I got there, all the Rotarians had left. There was quite a story in the next day's local paper, headed, MEMORY EXPERT FORGETS TO SHOW UP!
JL: That sounds as if it might really have happened.
HL: It did. Anyway, you shouldn't bring up things like that. If you keep it up, I'll have to tell people about the time you were driving through the exact-change booth at a tunnel, threw the half-dollar, and missed the bucket!
•
In the next chapter, we'll discuss how to remember monthly appointments, birthdays and anniversaries, and historical dates. We'll even touch on a bit of astrology. But first, an idea that may make you wonder why you didn't think of it yourself.
Suppose someone you're talking to says, "I'll be away during most of March, why don't we have lunch on April ninth?" (We're using the year 1974 in these examples.) And _you_ immediately say, "Sorry, that's a Tuesday, and I play golf on Tuesdays." How did you know that April 9 falls on a Tuesday? Well, here's a method you can use to figure, almost instantly, the day of the week for any date within the current year.
Look at this twelve-digit number: 633 752 741 631. If you memorize that number, you'll be able to know the day of the week for any date in 1974. How? It's simple; those twelve digits give you the first Sunday of the month for each of the twelve months. The first Sunday in January, 1974, is the 6th of the month; the first Sunday in February is the 3rd; the first Sunday in March is the 3rd; the first Sunday in April is the 7th; and so on to December, the first Sunday of which is the 1st of the month.
By now, you should have no trouble memorizing a twelve-digit number. You might Link **shame** him to clown to cart to **jammed** , or whatever words or phrases you come up with.
Once you've memorized the number, knowing the first Sunday of the month enables you to easily calculate the day of the week of any day during that month. Let's assume you want to know the day of the week for August 21. Check the twelve-digit number: The first Sunday of August falls on the 4th. Simply add 7's to that number (because there are seven days in a week). If the first Sunday is the 4th, then adding a 7 tells you that the 11th is also a Sunday. Add 7 to 11, and you know that the 18th is a Sunday. Then the 19th is a Monday, the 20th is a Tuesday—and the 21st of August falls on Wednesday!
Of course, there's no need to add the 7's one by one. Add a multiple of 7; in the above example, you'd simply add 14 to 4 right away, and take it from there. The largest multiple of 7 you'll ever have to add is 28.
Suppose you want to know the day of the week on which Christmas Day falls. The first Sunday of December is the 1st; add 21, and you know that the 22nd of December is also a Sunday. So the 23rd is Monday, the 24th is Tuesday, and Christmas Day falls on a Wednesday.
Occasionally, you'll work backward. For example, find the day of the week for June 14. The first Sunday in June is the 2nd. Add 14, and you know that the 16th is also a Sunday. That tells you that the 15th is a Saturday, and the 14th, of course, falls on a Friday.
Now try a few on your own. Find the day of the week for these dates in 1974: April 15, November 7, January 12, May 27, March 5, October 26, February 13, and September 8.
Breaking the twelve-digit number into groups of three makes it easier for you to get to a particular month quickly. After you use the idea for a short time, whenever you think of a month you'll also think of the word or phrase that includes that month. If you don't care about that, Link the number any way you like ( **chum, mug, linger, dishmat** would do it).
When you get to 1975, it's easy enough to memorize the new twelve-digit number at the beginning of the year—but you don't have to. In the number for 1975, you'll see that each digit is one less than for 1974. Look:
1974—633 752 741 631
1975—522 641 637 527
Don't let those 7's (beneath the 1's) throw you. Since there is no zero day, when you subtract 1 from 1 the answer must be 7. What's really happening is this: You're subtracting a day from Sunday, which brings you to Saturday. So, for 1975, you can use the same number as 1974 and simply push your answer ahead one day. You'll be correct! If for any reason it would help you to know the day of the week for the current and the following year, you'd know both automatically—except for leap years. Another way is to use the same number and consider the digits to represent _Mondays_. Again, you'll be correct!
There is a way to keep using the same number into a leap year, like 1976, but we don't want to take the space to explain that here. You can work it out yourself if you study the numbers for other years that are listed below. You can simply memorize the new number each year. Or you can use the same number for three years (the third year, you'd push your answer forward _two_ days, or consider each digit to represent _Tuesdays_ ), memorize the new one for a leap year, then memorize a new one, which you can use for three more years.
Here are the numbers up to 1983.
Before leaving this idea, weekdays within years, there's another way to handle it. Make up a Substitute Word for each month, and associate that to a Peg Word that tells you the first Sunday. For January, a picture of a **janit** or might serve as the Substitute. For the year 1974, see a gigantic **shoe** being a janitor. February? **Fib** or **fob** , and associate it to **Ma**. For March, see your **Ma march** ing. You may feel that this method is faster, or more definite. The choice is yours. Here's a suggestion or two for the remaining months:
April—ape, fool (April Fool), or showers (April showers)
May—May pole
June—bride, or chewin'
July—jewel, or firecracker (July 4)
August—gust of wind
September—scepter, or sipped
October—octopus, or oboe
November—ember, new member, or turkey (Thanksgiving)
December—Christmas tree
Whatever method you use, knowing the day of the week a future date falls on is easy, and it's fun. Test yourself now—look at the twelve-digit number for 1983 and say out loud, almost instantly, the day of the week your birthday falls on in that year.
# 15 **_ANNIVERSARIES, THE ZODIAC, HISTORICAL DATES_**
The same basic idea that is used for remembering a day and hour works for remembering a month and day. Any date that falls within the first ten days of the first nine months of the year breaks down to a basic Peg Word. The date May 4 would transpose to **54** ( **lure** )—5th month, 4th day. March 8 transposes to **movie** , August 10 to **fuse** , January 6 to **dish** , September 3 to **bum** , and July 4 to **car**.
Any day past the 10th, and any month past September, transpose to a three-digit number. In most cases, what you'd do is make up a word to represent that three-digit number. For example, October 8 could transpose to toss off (10th month, 8th day); December 3 to **denim** ; and so on.
But take another look at that last example. **Denim** transposes to 123, which could represent the 12th month, 3rd day. It could also, however, represent the 1st month, 23rd day.
There are, as usual, ways to solve the problem. The one we use is simply to put a zero in front of any single-digit date. December 3, a single-digit date, is therefore represented by the digits 1203, not 123.
Now there can be no confusion; the digits 123 can represent only the 1st month (January), 23rd day. November 7 transposes to 1107, not 117, because 117 represents January 17. All you need do is think up a word or phrase for any three- or four-digit number or date.
You'll find, if you apply this idea, that the zero isn't always necessary. You could transpose May 4 to 504 ( **loser, laser** ), but since 54 could only represent May 4, you might just as well use **lure**. You'll have to decide whether to _always_ use the zero for single-digit dates, or to use that zero only in those instances where it's needed to avoid confusion.
So. Any date can be made tangible by first breaking it down to two, three, or four digits and then coming up with a word or phrase to represent those digits phonetically. Once you understand that, all you have to do in order to remember a person's birthday or wedding anniversary is to associate the word or phrase to that person.
One way to do this is to associate the word or phrase to the person _physically_. For example, picturing your wife as a piano tuner would help you to remember that her birthday is January 24. (This wouldn't confuse you into thinking that the date is December 4; that would transpose to 1204, and **dancer** could represent it phonetically.)
Or you can associate the word or phrase to a Substitute Word for the person's name. To remember that Mr. Gordon's birthday is April 3, associate **ram** to **garden**. Mr. Pukczyva's birthday is March 2—see a hockey **puck shiver** ing as it shines, instead of the **moon** , in the sky.
Once you've visualized the silly picture, whenever you think of the person, you'll be reminded of the date. (We're assuming that if you care enough about someone to want to remember the birthday or anniversary, then you do think of that person every so often.)
If you think you'll have trouble remembering whether it's a birthday or anniversary date, put something into the picture to represent the correct one. A cake with candles on it would do for a birthday.
Any dates can be remembered by using this basic idea. We'll discuss historical dates in a moment, but first we'd like to show you how to apply the idea to the signs of the zodiac. So many people are interested in astrology these days that it sometimes seems everyone is asking everyone else what sign they were born under. And many people hear a birth date and then find it difficult to remember the sign for that date. But as you'll see, dates can be associated to other information— _any_ information.
Here are the signs of the zodiac, the date spreads, and some suggestions for changing those dates into tangible pictures:
If you want to remember all the signs, simply Link them. Either make up a Substitute Word for the sign, or, if you know the meanings, use them—they all can be pictured. For Aries, you can use **arrows, air E's** , or simply picture a ram. At this point you should be able to work this out easily for yourself.
If you don't know the meanings of the signs, associate one to the other—sign to meaning. Most of them are obvious, of course; but if you had to you could, say, associate **gem** (Gemini) to **twins**.
To remember the sign _and_ date spread in each case, associate a Substitute Word for the sign, or its meaning (see Aries-ram example above), to a phrase that will give you the vital dates. For instance, a silly picture of a **ram** sucking a gigantic **mint** as it **runs** gives you both the sign and the date spread. A picture of a **corn** wearing a **cap** , or a **goat** living in your home as a **tenant** and always toting things up ( **tote up** ) tells you that Capricorns are born between December 21 and January 19.
As usual, you can put anything you like into your association. If you see a picture of a **bull** (Taurus or **tore ass** ) being a **runt** (small bull) and very **stubbornly** breaking a gigantic **lens** , you have a reminder of the sign, the date spread, and one of the characteristics of Taurus people—stubbornness.*
Now for historical dates. Again, you already have the necessary basic knowledge. All you have to do is transpose the intangible date to a tangible picture and associate that picture to the event.
We'll start with one you already know—the date of the signing of the Declaration of Independence. A **Kaiser** (if you're using the zero in front of single digits) or a **car** (7th month, 4th day, July 4) signing the Declaration and receiving plenty of **cash** ('76) for signing it will tell you the event and the date. The assumption is that you'd know the century digits, but you can put a reminder into the association if you like. **Take cash** would do it.
Usually, it isn't necessary to put the century figures into the association. You probably know that the great Chicago fire occurred in the 1800's. So a picture of a **cot** ('71) starting a great fire tells you that the date is 1871. Napoleon was crowned emperor in 1804; picture a man with his hand in his jacket (Napoleon) wearing a large crown—it's so heavy, it makes his head sore ('04). (If you like, you can picture a **dove** flying out of the crown, to remind you of 18.) The _Titanic_ sank in the year 1912. Picture a large sheet of **tin** sinking; or, if you want the century figures, see it sinking in a **tub**.
Having used the states and the Presidents as examples earlier, we'll continue using them now—you can include a picture to represent any date in any of your original associations. Perhaps you want to remember the year in which a state was admitted to the Union. Nothing could be simpler. Indiana was admitted in 1816; get **dish** or **dove dish** into your original association. You **can't talk** ( **K** entucky) because there's a **dog bone** in your throat—this picture would remind you that Kentucky was admitted to the Union in 1792.
President Grant was born on April 27, 1822. Picture a large piece of **granite** (Substitute Word for Grant, or use **rant** ) putting a **ring** (427 = April 27) on a **nun** 's ('22) finger. If you see this silly picture taking place on a **ship** , that will help you remember that President Grant was inaugurated in 1869.
William Shakespeare's baptism was recorded on April 26, 1564. See yourself **shak** ing a **spear** in a tall jar (1564) on a **ranch** (April 26). If you want to remember only the month and year, **rattle jar** , or **retail chair** (4-1564) would suffice. If you already know the century, **rasher** or **reacher** would remind you of April, '64.
The first man to step onto the moon was Neil Armstrong, and he did it on July 20, 1969. A picture of a man with a **strong arm** (or just a strong muscular arm) holding hundreds of **cans** (720, July 20) would tell you the month and day. See the man (or the arm) coming out of a ship, and you have a reminder of the year. If you want to remember the month and year only, associate the Substitute Word for Armstrong to **ketchup** (7-'69).
If you formed an association of **a stevedore** dressed in **lace** and wrestling a **bear** , it would help you remember that Robert Louis Stevenson (stevedore) was born in 1850 (lace) and died in 1894 (bear).
Now you can remember any date by changing it to a tangible picture and associating that to the person, place, or event. Again, once you've used the memorized information a few times and it has become knowledge, the system has served its purpose—the ridiculous pictures fade because you no longer need them.
*C.f. Harry Lorayne.
# 16 **_THE ALPHABET AND PICTURING LETTERS_**
HL: Arteriosclerosis!
JL: Aceeiiloorrrssst!
HL: So you've been alphabetizing words since you were eight years old—it still amazes me. What's the story, Jerry?
JL: I'm screwy. No, seriously, I basically use the Substitute Word system. When a word is alphabetized it becomes a nonsense word, so I associate a Substitute thought for the nonsense word to the regular word. "Telephone" alphabetized is "eeehlnopt," so my original picture was **eel napped** on a **telephone**. That doesn't give me all the letters, but it does give me the nonsense word. I'll know that there are three _e_ 's, and that there has to be an _h_ in there somewhere.
•
Most people don't know the alphabet as well as they think they do. Few people know the numerical positions of the letters. Not that it's of great importance, but it is interesting that people use these twenty-six letters all their lives and still don't know, instantly, the numerical position of, say, **P** or **K,** or **M**.
We're going to show you how to _picture_ letters. But first, here's a quick way of learning the numerical positions of all the letters. It's not just an exercise—knowing them can be important if you need an extra Peg list of words, or pictures. Once you know the numerical positions and can picture each letter, you'll automatically have a twenty-six-word Peg list.
We're assuming that you know the basic Peg Words from 1 to 26. Now, you need the "adjective" idea. Make up a phrase that consists of two words—the first word is an adjective that begins with the letter whose position you want to know; the second is the Peg Word that tells you that position.
Look at these phrases:
**A** wful **tie**
**B** rave **Noah**
**C** ute **Ma**
**D** elicious **rye**
Each phrase gives you the two things you need, the letter and its position. "Delicious rye" tells you that the letter D (first letter of _delicious_ ) is the fourth letter ( **rye** ) of the alphabet. You're better off making up your own adjectives, because the ones you think of will be easier for you to remember. Here are just a few suggestions: jagged **toes** , kind **tot** , plastic **dish** , vivacious **nun, X** -rayed **Nero** , zigzag **notch**.
When you've made up all the phrases, go over them once or twice. Here, it isn't necessary to form a ridiculous association—the _logical_ aspect of the phrase will be a memory aid. Before long, if you think _P_ , the phrase " **plastic dish** " will come to mind and you'll know that P is the 16th letter of the alphabet. And before much longer, you won't need the phrase—you'll simply know the numerical positions.
That's all there is to it!
Now. To visualize each letter of the alphabet—to make each letter tangible and meaningful in your mind—make up a word that sounds like the letter. This is an offshoot of the Substitute Word system. The letter A, for instance, cannot be pictured, but you can picture an **ape**. And saying the letter A out loud almost has to remind you of ape, because ape sounds like A. You can make up your own Alphabet Words, or you can use the list that follows.
1. A—ape
2. B—bean
3. C—sea
4. D—dean
5. E—eel
6. F—half, or effort
7. G—jeans, or gee
8. H—ache, age, or itch
9. I—eye
10. J—jay (bird)
11. K—cake, or cane
12. L—el (elevated train), elf
13. M—ham, hem, or emperor
14. N—hen, or end
15. O—eau (water), or old
16. P—pea
17. Q—cue (stick)
18. R—hour (clock), or art
19. S—ess curve, or ass
20. T—tea
21. U—ewe
22. V—veal
23. W—Waterloo (Napoleon)
24. X—eggs, exit, or X ray
25. Y—wine
26. Z—zebra
We used **bean** for B only because you already know **bee** as the basic Peg Word for number 9.
Being able to picture any letter is important if you ever have to memorize anything that contains letters—formulas and equations, style numbers, stock symbols, whatever. Now, if for some reason you wanted to remember a license number, say, 146A 29C 4L, you could Link **torch** to **ape** , ape to **knob** , knob to **sea** , sea to **rye** , and rye to elevated train.
If you know the numerical position of every letter _and_ the alphabet word, you also have that twenty-six-word Peg List we mentioned. If you know that N is the **14th letter** , anything associated to **hen** is the 14th item. Anything associated to **pea** is the 16th item, anything associated to **ess** curve is the 19th item, and so on.
Now you can memorize two lists of items—by number, and in and out of order—at the same time. Use the basic Peg Words for one list and the Alphabet Words for the other.
The fact that each letter can be pictured can be useful to you in many areas. If you're one of the many people who have trouble spelling the word _insurance_ because you're never sure whether it's - _ance_ or - _ence_ , picture an **ape** selling insurance and you'll always remember that _insurance_ is spelled with an _a_. The word **audible** is spelled with an _i_ (it's not "aud _a_ ble"). Form a silly picture of your **eye** making sounds—it's **audible** —to remind you of the _i_. The word _grammar_ is often misspelled "grammer." Picture an **ape** speaking with perfect grammar, and you'll remember that _a_.
There are other ways to handle letters. For example, if all the style numbers of any company's products consist of a letter followed by digits, then a word that begins with the letter solves the memory problem. For A41, use **arid** ; for B12, **button** ; for C915, **capital** ; for R92, **robin** ; and so on. Each word would then be associated, of course, to the product it represents.
Finally, a nonearthshaking piece of information: If you form a Link from **zebra** to **wine** to **eggs** to **Waterloo** , all the way to **ape** , you'll be able to recite the alphabet backward!
# 17 **_START YOUR CHILDREN_**
JL: My son and daughter—Jeff's nine, Julie's eight—can remember things in sequence and by number, quickly and easily. And they're having a ball.
HL: When my son Bobby turned five this year, I tried him on ten items, with the Link. First time out, he remembered them—no hesitation, forward and backward—and he thought it was hilarious!
Not long ago, I tried the Peg on a children's TV show—the average age of the studio audience was seven—and the kids remembered ten items in and out of order, by number.
JL: Before my daughter was aware of the systems, she had trouble telling her left hand from her right. I'd ask her, "Which is your right hand, Julie?" She'd stand up and start reciting the Pledge of Allegiance, putting her right hand over her heart. Then she'd raise that hand and say, "This one, Daddy!"
•
Very young children have no trouble using their imagination and forming ridiculous pictures. They not only do it easily, they think it's lots of fun. If you have children, acquaint them with some of the ideas in this book; you can harness that lively imagination and help them sharpen their sense of concentration—without their realizing what you're doing, of course.
Make a game out of the Link system. During an automobile trip, see who can remember a list of items faster, or who can remember the most items. It _is_ fun—and the children are learning a useful skill at the same time.
If you want to play the game of remembering items by number with a child who's too young to learn the phonetic alphabet, there's a way to teach him ten Peg Words almost instantly. They're easy to learn—they rhyme with the numbers, and most of them come from a song your children probably know.
1. one—run
2. two—shoe
3. three—tree
4. four—pour
5. five—hive (picture bees)
6. six—sticks
7. seven—heaven
8. eight—gate
9. nine—sign
10. ten—hen
Some of the words from the song have been changed to words that are easier for a child to picture. Teach the youngster to picture the item running, for 1 ( **run** ); being poured out of something, for 4 ( **pour** ); in the sky, for 7 ( **heaven** ); and so on.
The number-word rhymes make it easy for a child to learn the words in minutes. Once he has been tested on them, and knows them, he can be taught to associate (don't use that word; the children won't know what you're talking about) any item to any of these Pegs. If you mention **banana** for number 6, the child will think **sticks** and, perhaps, see a bunch of bananas tied like a bunch of sticks. Give him a suggestion or two the first few times.
Here's another way to use the Link as a game. Place eight or so items on a tray and cover them with a cloth. First remove the cloth for a short time (a minute or so), then replace it and have everyone try to list all the items. Each player receives one point for each item listed correctly; the more a player lists, the better his score.
Or you can show the items for a moment, then remove a couple of them without letting the players see which ones have been removed. You expose the tray of items again for ten seconds or so. The first player who correctly lists the missing items wins. Both these games are fun for children and teach them to start using some important mental powers—observation, memory, and concentration. They also work as incentives for the child to try to apply a simple Link.
You can also start helping the child to remember words through the Substitute Word system. When five-year-old Bobby Lorayne kept saying "caterlipper" for caterpillar, he was told to picture a **cat** chasing the crawling thing up a **pillar** (or **pillow** ). It worked!
Surely every parent has used something of this sort at one time or another. But now you can take it much further. Use Substitute Words, with the child, for English or foreign words. It's amazing how well the system works with children.
Here's another game that children enjoy. In this one, pairs of letters are called or written, and each pair is assigned a hiding place. For example, PN is called, and the hiding place is the fish tank; FX is hidden in the TV set; CP in the window; TR in the flower pot, and so on. The child who remembers the most pairs of letters wins.
Tell the child to think of a word that begins and ends with the vital letters and then associate, in a silly way, that word (or thing) to the hiding place. The child might picture a gigantic **pin** swimming in the fish tank, a fox jumping out of the TV screen, a gigantic **cup** crashing through a window, and tar overflowing from, and ruining, a flower pot.
Any word can be used that will remind the child of the letters. If the letters are BN, **bin** is fine—but **bone** would still help the child remember them. For TR, **tire** or **tree** would also do.
The game encourages the child to think of letters and words and get them right, helps his memory, and is fun to play. Children love to win; they'll learn just because they want to play and win.
You can take this particular game a step further by using two letters plus a number from 1 to 10. Use the ten rhyming Pegs for this. If you call PT and number 5, hidden in the kitchen sink, the child might see a ridiculous picture of himself turning the faucet in the kitchen sink, and millions of **pits** and bees (hive-five) coming out of it.
There's an old game in which each player adds an item to a list. The first player might say, "I'm going to Indianapolis to get a bottle." The next player says, "I'm going to Indianapolis to get a bottle and a desk." The third player says, "I'm going to Indianapolis to get a bottle, a desk, and a fish." The game can be played with any number of players, each of whom must repeat all the items correctly and add one item. If there are four players, the first person's turn comes up again after the fourth person. The first player who misses an item is "out"; the last person "in" wins. The application of the Link to this old game gives it a new dimension. With a little thought, any game can be changed or made more challenging by using such memory systems as the Link, Substitute Words, and Peg Words.
Starting young children off on some of the principles of a trained memory is one of the most useful things you can do for them. Imagine how helpful the systems can be to them for play, in school (most schoolwork is based on memory), and, later, socially and professionally.
# 18 **_SPORTS_**
JL: Not just any professional basketball player, regardless of his abilities, could play for the New York Knickerbockers. The Knicks win championships because we're a team in the true sense of the word—the five players on the floor at any given time play for the good of all and not for themselves. That's really the only way to keep winning in pro basketball.
HL: You're a smart team, too—intelligence must be a factor.
JL: Sure it is. The basic intelligence of our players, and their basketball savvy, are actually more important than most people realize. We're not an overpowering type of team, so we have to depend on other assets—like playing unselfishly, playing intelligently, and generally outthinking our opponents. In order for us to win consistently, the five men on the floor have to think and act almost as one person. This means that each player must know what his teammates are going to do in almost every situation. A good part of this is knowing the plays we'll be running—if a play is called and one or two of the players don't remember it, the results can be disastrous.
HL: How often do the plays get called?
JL: We attempt to run a basic play every time we come down the floor, unless we have an obvious breakaway situation that will lead to an easy basket. This strategy gives us much more consistency—and leaves us in better defensive balance if we miss the shot and the other team rebounds the ball.
HL: You're really saying that none of you can perform well unless you remember the plays well. I know how _you_ remember them—but what about your teammates?
JL: Fundamentally, the other players use rote memory. We all go over and over the plays throughout the year, to make sure everybody knows them. And for the Knicks, that's maybe a total of forty plays and options.
HL: How well does the method work?
JL: This may seem hard to believe, but I've never played on a basketball team at any level including the professional level without at least one player forgetting several of the plays all the way through the season. Many times, there are several players who don't remember them.
At some crucial point in a game, the coach will tell the players during a time-out what play he wants to run, why it's important that each player know exactly what his assignment is and carry it out. So. We break, we don't take three or four steps out on the floor, and a player taps me on the shoulder—he knows I remember all the plays—and says, "What are we doing? What play are we calling?" And that has happened, and does happen, over and over again.
HL: Obviously, those players aren't very aware. And just as obviously, since they turn to you when they forget, the systems work for you in basketball.
JL: I use them to remember all our plays. And any player _could_ use them to remember what he's supposed to do during any particular play.
•
For obvious reasons, we'll begin our discussion of memory in sports with basketball. First, a play we'll designate play number 6. Most plays in basketball are called out by number, and it's a simple matter to associate that play to the basic Peg Word.
The diagram on the following page shows what play number 6 might look like after a coach has explained it:
If you ignore all the arrows, dashes, and lines in the diagram, you'll see the basic positioning of a team. C is center; LF and LG are left forward and left guard; RF and RG are right forward and right guard.
Now. A dotted line ( ) is a pass made with the ball; a solid line ( ) is the direction in which the player moves; the solid short lines ( ) are picks or blocks by one of the players.
RG starts with the ball. He passes it to LG who, in turn, passes it to LF. LF then passes the ball to C. If you follow the dotted lines and arrows, you can follow the ball's progress as it is being passed.
As soon as LF passes the ball to C, he starts to move toward the middle of the court. At the same time, LG starts to move toward the _end_ of the court. Both LF and LG are also moving toward C. Now, LF momentarily stops to pick or block LG's opponent and then continues to the middle of the court where he picks RF's opponent as RF moves toward the middle of the court to join LF.
LF then turns and moves toward the basket after he picks for RF. While all this is going on, LG (if he hasn't gotten the ball from C, for a shot) circles under the basket and back toward the middle of the floor. RG moves away from the action in order to keep his opponent from interfering with the play.
C has several options during this play. The first is to pass the ball to LG when LF picks for him. The second option is to pass to RF when LF picks for him. The third is to pass the ball to LF as he moves to the basket after he has picked for RF. Finally, if none of these options is available, C can turn and shoot the ball himself.
In this one basic play, you can see that there are several options for (hopefully) good open shots during its execution. Each player has specific duties to remember:
C—Get to basic position.
Receive ball from LF.
Pass ball to LG, RF, or LF.
If play doesn't work, shoot.
LF—Receive ball from LG.
Pass ball to C.
Move toward C and pick for LG.
Move toward middle and pick for RF.
Move to basket.
LG—Receive pass from RG.
Pass to LF.
Move off LF's pick, to the basket.
If no shot develops, circle back under basket to original position.
RF—Move off the pick by LF to center of floor. Look for pass from C and shoot if open.
RG—Pass to LG.
Move away from play.
It would be a simple task for each player to Link, or associate, his duties to **shoe** (6). All he need do is make up a few standards to represent the positions. Any words containing the proper letters would do. C could be core (picture an apple core. It begins with _c_ , and also means center); LF could be leaf; RF could be roof; LG could be log; RG could be rug.
The best way to memorize the play described above is to use one picture; no Link is necessary for so short a play. C could picture a **shoe** moving to a **basic** position. (He could simply see it moving to _his_ basic position, or he could put **base, sick** , or both, into the picture.) **A leaf** throws a ball to the shoe and the shoe looks around at a **log** , a steeple ( **roof** ), and a gigantic **leaf** , trying to decide which one to throw it to. It can't decide, so it **shoots itself!**
Check back to C's duties for this play, and you'll see that this silly picture will quickly remind the center of them. When he's on the floor and a player or coach calls "Six," he'll instantly know what he has to do. (Bear in mind that this is all the players need—reminders.)
LF might picture a **shoe** receiving a ball from a **log** ; the shoe throws the ball at an apple **core** as he moves toward that core, and **picks** up a **log** and a **roof** ; he places a shoe into a **basket**. (We consider this to be one picture. A Link would work as well: shoe to log to core to pick to log to roof to shoe to basket.)
LG: a **shoe** catches a ball thrown by a **rug** and immediately throws it to a **leaf** ; it **picks** up the leaf as it moves toward a **basket in circles**.
RF: a **shoe** moves off a **pick** held by a **leaf** ; it moves to the **middle** of the floor; an apple **core** makes a **pass** at the shoe; the shoe **shoots**.
RG: a **shoe** throws a ball to a **log** , then moves out of sight.
The player would form associations or Links like these in order to originally remember all the team plays. After a few uses, the pictures will fade as usual; he'll simply _know_ the plays.
In football, the plays are more complicated because there are eleven men on a team. But a play still involves each man's remembering what he himself is supposed to do during any called play. The exception would be the quarterback, who should pretty much be aware of what each of his teammates is supposed to do, and where they're supposed to be. To help him originally memorize the play, his Links would be a bit more involved.
The same kind of associations or Links will help any player to be Originally Aware of his duties. This is what a diagram of play number 14, the "dive-option" play, might look like on a coach's blackboard:
Here are the basic duties of the three key men in this particular play:
QB (quarterback)—Open pivot, ride the FB, read first man outside tackle for handoff, option the end man on the line of scrimmage.
FB (fullback)—Dive over the guard, mesh with the QB. If ball is received, run to daylight; if not, fake through line and block.
TB (tailback)—Take counter step and run option course maintaining 7-yard relationship with QB.
Originally, each player might have formed a Link, starting either with a **dive** —if the quarterback simply called for "dive option" in the huddle—or with **tire** , if the play was called by number. A player might simply need to know that play 14 is the dive-option play. In that case, he would originally have associated tire to dive.
QB's Link could be: A tire (or dive) is **open** ing a ballet dancer's (Substitute thought for **pivot** ) costume; an empty costume is **rid** ing on a gigantic watch **fob** (FB); a gigantic fob is **read** ing a **hand** (handoff) that's throwing fishing **tackle outside** ; the hand is trying to decide ( **option** ) who is the last ( **end** ) man in a **line** (of scrimmage).
The FB's Link: A tire dives over a **guard** rail, into a mess ( **mesh** ) of **quarters** (QB); it grabs a quarter and runs toward a **light** —it drops the quarter (doesn't receive the ball) onto a **fake line** of **blocks**.
The TB's Link: A tire **steps** on a **counter** (or someone steps on a counter in order to dive) and runs **up a chin** (option) to meet his **relation** , a gigantic **cow** (7-yard relationship); the cow is giving **quarters** instead of milk.
In baseball, a batter must remember that the signal for, say, hit and run, is the coach rubbing his elbow. He'd simply picture an elbow hitting someone and running away. Each day, the player has to remember that day's "key" signal, the signal that means, "If I do this, then the next sign is really to be followed." If the coach doesn't use the "key," the player ignores any other signal. So. The player could simply associate a **key** to whatever the key signal is for that day. There might also be a "wipeout" signal, a sign that means, "Ignore the signal I just gave you." Same thing; the player would associate **wipe** or **wipeout** to the signal.
One announcer at a trotters track used the systems for years to help him call the races. He needed to know horses' names, jockeys' names, horses' numbers, and colors for every race. He associated all the information to each horse's number, starting a Link with the number. He used a standard for every color—a **bull** might represent red, an **orange** could represent orange, a **banana** could represent yellow, **grass** could represent green, a **grape** could represent purple, and so on. In this way, even colors can be pictured.
We've been using examples from the participant's point of view. But if you're a sports fan, you can apply the same ideas to whatever information or statistics you want to remember. Babe Ruth's career home-run record is 714. Picture a gigantic **baby** playing a **guitar** at **home** ; or, the home is in the **gutter**. See a **green** ice **berg** that's **maimed** , and that picture will help you remember that Hank Greenberg hit 331 homers in his career.
Who was the world's heavyweight boxing champ in 1936? You'll remember James Braddock if you associate **match** (36) to, perhaps, **haddock** or **bad dock**. Associate **mummy** to **carnival** or **car near** to remind you that Primo Carnera was the heavyweight champ in 1933. Picture a **bear** using a lawn **mower** to tell you that Max Baer was the 1934 champ.
In what year was the famous Dempsey-Firpo fight? Associate **damp sea** and **fir pole** to **name** —1923. If you want to remember the exact date, use **butter name** : 9-14-23.
As you can see, the memory systems can be applied just as easily to sports as to anything else.
# 19 **_THE STOCK MARKET_**
HL: Much of the information people in the market need to know, such as stock symbols, is purely and simply a memory problem. A student of mine once wanted to leave his menial job and obtain a position with a brokerage house. He used the Substitute Word and Alphabet Word system to memorize the symbol of _every_ stock traded on the New York Stock Exchange—about 1,600 at the time.
He applied for the job, and found he had plenty of competition. During the interview, he handed the stock exchange listings to his potential employer and asked him to call off any company or symbol. Whichever was called, he named its counterpart instantly—without missing a one.
JL: I assume he got the job.
HL: The interviewer told him, "There are people who've been working here for years, and not one of them knows all the symbols—you're hired!" Today, that former student of mine is co-owner of his own company in the put-and-call area.
JL: I'll remember that when I'm over the hill for basketball!
•
People involved in the stock market (clients and brokers) must be able to remember a great deal of information, including names of companies, their stock symbols, and, of course, prices. You should know how to handle prices now. Make up a word or phrase for the price, then associate it to the name of the stock. That's easy enough. The only additional problem involved is that of handling the fractions.
This problem is easily solved if you change all fractions to eighths, which is the common denominator of stock market price fractions. You'd be dealing, then, with: 1/8, 2/8 (¼;), 3/8, 4/8 (½;), 5/8, 6/8 (¾;), and 7/8.
The pattern you follow, basically, is to make up a word that tells you the dollars—a word whose last single consonant sound tells you the number of eighths (the fraction). For a stock selling at 29½;, picture the word **napper** or **nipper** and you've got that price. The first two consonant sounds can only represent 29, the final consonant sound **r** (4) reminds you of the number of eighths—4, in this example, and you know that 4/8 is ½;.
You may be wondering how you would know that **nipper** represents 29½;, not 294. Well, if you aren't knowledgeable enough to know that a stock that's been fluctuating around $29 can't be selling at $294 you shouldn't be in the stock market! So, your knowledge of the market plus your common sense tells you the difference. If you had associated, say, **racket** to a gigantic telephone (AT&T), you'd know that **racket** represents 47 1/8, not 471.
As usual, there are other methods you can use. If you like, you can always use a phrase to represent a price; the first word for the dollars, followed by a Peg Word to tell you the number of eighths. That way, 29½; could transpose to **knob rye** or **nip rye** , and 47⅛; to **rack tie** or **rock tie**. This method leaves you with no decisions to make.
Of course, you may not care about the fractions at all; you may only need to know the price in dollars. Just forget about the fractions and use a word to represent only dollars.
Whichever method you decide to use will work. Associate the word to the company name by using a Substitute Word or thought to represent the company— **telephone** would certainly remind you of AT&T. A car saluting a **general** might be your Substitute thought for General Motors. A tiny bottle of soda ( **mini soda** ) wearing a miners' hat could remind you of Minnesota Mining; **spare a hand** would do for Sperry Rand; **polar hurt** for Polaroid; **Mack roar E** for McCrory Corporation; and so on.
So. An association of a **Mack** truck **roar** ing at an **E** (or **eel** ) that's sitting on a **melon** would remind you that McCrory stock was selling at 35¼;.
What about remembering stock symbols? The stockbroker has a machine on his desk that will give him current prices pretty quickly— _if_ he punches the _correct_ symbol. A broker who could instantly recall any stock symbol he needed to know would have an advantage.
Now, you probably don't want or need to remember all the symbols. But if you want to remember some of them, it's easy.
Just make up a word or phrase to represent the letters of the symbol. There are two ways to do this—you can use a word that reminds you of the letters, or you can use the Alphabet Words. For example, the symbol for Pittway Corporation is PRY. You might see a gigantic **pit pry** ing its **way** out of something—the association gives you the two pieces of information you need, the name of the company and its symbol. Associating Pittway to a **pea** on a clock ( **hour** ) drinking **wine** would accomplish the same thing.
Picture a **polly** (parrot) being a **Ma** to a **plum** , and you have a reminder that the symbol for Polymer Corporation is PLM.
The symbol for Shaw Industries is SHX; you might picture millions of **eggs** (X) coming up on a **shore** —you say " **Sh** " to them. Whatever reminder you think of will work; you could have used " **shucks** " to remind you of SHX. An **ass** (S) scratching an **itch** (H) with an **exit** (X) sign would also do.
Picture **a hen** and an **eel** eating a **ham** on a **new mount** ain to help you remember that the symbol for Newmont Mining is NEM. If you really think it's necessary, include something in the picture to remind you of mining.
You can form an association that includes the name of the company, the symbol, the average price of the stock (or the price you paid), the name of the top executive of the company—whatever you like.
The point is that now you can _picture_ letters. Picturing either the Alphabet Words, or a word that begins and ends with or contains the vital letters, is tantamount to picturing the letters.
The same ideas can be used wherever you find it necessary to remember letters in conjunction with anything else.
# 20 **_POLITICS_**
JL: It's too bad we can't drop the names of some politicians who use our systems.
HL: They wouldn't allow it—and you can't blame them. They'd never be able to get by with sitting in front of a congressional or Senate committee and saying, "I don't remember"!
•
It's obvious that being able to remember names and faces is an asset to any politician, just as it is to businessmen. But a politician should be able to remember a great many other things—certainly he should have all the political information, at least for his home state, at his fingertips. Most of this information is statistical and involves names and numbers. The systems, of course, apply to both areas.
Most people do not know the names of their representatives and senators. If you're among them, simply make up a Substitute Word to represent senator— **tore** (picture tearing), **centaur** , or **century** would do.
The senators from Nevada (elected in 1970) are Bible and Cannon. See yourself **tear** ing a gigantic **bible** and getting shot by a **cannon** for your crime. That does it. If you're not from Nevada, but still want to know who its senators are, get a Substitute Word for the state into the picture. You can take it further. If you want to remember party affiliations, make up a standard to represent each major party. Obviously, you can use an elephant (R) or a donkey (D), since those are the party symbols. Or, use **dean** (D) and **hour** (R), the Alphabet Words, or **dam** for Democrat and **pub** for Republican. In this example, if you're using the Alphabet Words for your standard, you'd get whatever you picture for dean into the association with Bible and Cannon, both of whom are Democrats.
Many people have trouble remembering which symbol belongs to which party. They're reminded of the donkey and elephant symbols during national conventions, but a short time after the election they're no longer sure. (It's rather like trying to remember last year's Academy Award winners.) One fast association of, say, elephant to **pub** —and you'll always know that the elephant is the symbol of the Republican party and, of course, the donkey is the Democratic symbol.
The senators from Ohio (all these examples are as of 1970 records) are Taft and Saxbe. You might see a **daft** (Taft) **centaur** playing a saxophone. That's probably all you need to remind you of Saxbe, but if you like, you can see a **bee** coming out of the saxophone. They're both Republicans, so you can get elephant, hour, or pub into the picture for each name.
Suppose you want to remember how many representatives your state has. Using Ohio again as the example, it has 24 representatives—7 Democrats and 17 Republicans. One easy way to apply the system to such information is to always use a word that ends with a _d_ or an _r_ for Democrat and Republican—a word whose first consonant sound or sounds tell you how many Democrats and Republicans there are.
Good, goad, or cod would mean 7 Democratic representatives; **tiger, dagger** , or **ticker** would tell you that there are 17 Republican representatives. Of course, if all you want to know is the total number of representatives, just use a word that begins or ends with _r_. Once you decide where you'll place the vital letter, always use it that way and the word will work for you. The word **runner** would work for Ohio if you're placing the _r_ first. The next consonant sound or sounds gives you the number of representatives.
You'd be surprised to see how easily you can remember the number of representatives from each state this way. Once you've made up the word that tells you the number, just associate that to your Substitute Word for the state. Try a few:
New York has 41 representatives. Associate **new cork** or the Empire State Building to roared or reared.
Oklahoma has 6 representatives. Associate **homer** to **rash** or **roach**.
Alabama has 8 representatives. Associate **album** to **roof** or **rave**.
Nebraska has 3 representatives. Associate **new brass car** to **room** or **ram**.
Texas has 43 representatives. Associate **taxis** to **rearm** or **rear 'em**.
Pennsylvania has 27 representatives. Associate **pencil** to **rink** or **ring**.
Tennessee has 9 representatives. Associate **tennis** to **rope** or **ripe**.
Kentucky has 7 representatives. Associate **can't talk** to **rag** or **rug**.
Massachusetts has 12 representatives. See a **mass chew** ing something that's **rotten**.
Including Ohio ( **high** or " **oh, hi** " to **runner** ), you have ten examples. Form the associations, then test yourself—you'll probably know the number of representatives from each of those ten states.
If you're involved (or just interested) in national politics, you might find it useful to know the number of registered Democratic voters in particular states. No problem; just as you could remember the population of, say, Tennessee by associating **tennis** to **ma banner touch 'er** , or **moppin' red chair** (3,924,164), you can associate a state to the number that represents the Democratic (or Republican, or both) registered voters. If you formed an association of a **new brass car** delivering a message to a new nail, it would help you remember that there are 306,225 registered Democrats in Nebraska. Get **my love jailer** into the picture, along with either **pub, elephant** , or **hour** , and you'll know that there are 358,654 registered Republicans. If all you need to remember is the total registration, make up a phrase to represent 664,879 and associate it to Nebraska.
At this point you should have no difficulty in working out a method to help you remember the number of state senators and/or assemblymen in your state. New York State's state senate consists of 57 senators—25 Democrats and 32 Republicans. Associate **denial** (D, 25) and **Roman** (R, 32) to your Substitute Word for state senate. If you're doing this with more than one state, get your Substitute Word or phrase for New York into the picture. Associate **decked, ducat, ducked** (D, 71) and **rake up, recoup** , or **rag pie** (R, 79) to a Substitute Word for assembly, and you'll know the affiliation breakdown of assemblymen. For California: state senate, 21 Democrats ( **donut** ) and 19 Republicans ( **retap** , or **retape** ); state assembly, 43 Democrats ( **dream** or **drum** ) and 37 Republicans ( **remake** or **room key** ).
In a quick check we asked twenty-five people, from eighteen different states, if they knew how many electoral votes their home states controlled in a presidential election. Not one person knew! And a few of them were involved in politics. All that's necessary is to associate a state to a one- or two-digit number.
If you're remembering other information as well, get a word into your association or Link that tells you the two things you want to know: 1) that it's electoral votes you're remembering, 2) how many votes. Either start the word with an _e_ for electoral or end it with an _e_ , or an - _el_. Oklahoma has 8 electoral votes; **elf** or **fuel** , according to the pattern you intend to use, would give you that information.
Let's assume you decide to _start_ each word with an _e_. For some two-digit numbers, there may not be a word to fit. For example, Pennsylvania has 27 electoral votes. Finding a word that starts with _e_ and whose consonant sounds only represent 27 may be difficult if not impossible. Simply use a word like **enc** lose—as was the case when we discussed letter-exchange telephone numbers. Since you know that no state has electoral votes comprising three digits (the largest is California, with 45), you'd simply ignore the sounds that follow **enc**.
If you're familiar with our systems, you'll see when you sit down with any memory problem that you can easily patternize the problem so that one or another of the systems applies.
Associate **mix again** to **end** and you'll know that Michigan has 21 electoral votes. **Sassy can** to **egg** (Kansas, 7); **high** to **enl** arge (Ohio, 25); **whiz con** to **edit** (Wisconsin, 11); **wash** to **ebb** (Washington, 9); **potato** to **ear** (Idaho, 4); **caliph** to early (California, 45); and so on.
All the suggestions in this chapter have been just that—suggestions. The way you patternize any memory problem is up to you. And, usually, the method you select to handle any memory problem will be the best for you.
# 21 **_THE ARTS_**
By now, you should realize that the systems are applicable to just about any kind of memory problem. And, as you've learned, most memory problems basically break down to entities of two. If you'd like to gain some knowledge of art, literature, or music, you might want to learn and associate artist and period, title of painting and artist, literary work and author, or piece of music and composer.
If you wanted to remember that Marcel Duchamp was of the dadaist school of painting, you would associate a Substitute Word or phrase for Duchamp to a Substitute thought for dada. Seeing a **toe chomp** ing on a baby crying for its **da da** might do it for you. Or, you could use **two champs** or **due champs** to remind you of Duchamp.
Braque and Picasso were cubists. See yourself **break** ing with a **rock** (Braque) a gigantic **cube** with a **pickax** (Picasso).
Monet and Renoir were impressionists. You might picture old **money** (Monet) being **renew** ed (Renoir) to appear as an **impressionist** (one who does impersonations or impressions).
Of course, for each of the last two examples, you could associate one artist at a time to the school or period. You'd simply associate first Braque and then Picasso to cubism.
Rembrandt was a humanist. You might picture a **ram brand** ing a **human**.
Van Gogh and Cézanne were postimpressionists. One picture of a **van go** ing to **press** a **post** and **seize Ann** would do it. Or, use two separate associations; a van goes to press a post, and a **post** that's **press** ing clothes (ironing) **sees Ann**.
Edvard Munch (pronounced _Muhnk_ ) was an expressionist. Picture this: You're trying to **express** yourself to a **monk**.
Dali is a surrealist. Picture a **doll** that's " **sure real**." Dali is often considered to be a superrealist, so you can see that **doll** being **real** and eating **soup**.
An example of a nonobjective painter is Kandinsky. You might form a silly association of **candy ski** ing and throwing **object** s at a **nun** ; or **can did ski** to nonobjective.
Jackson Pollock's work is considered abstract-expressionist, or action painting. Picture a gigantic **pole locked** in a room where it **obstruct** s (abstract) all **expression** and **action**. Or, a **pole** with a **lock** on it is being very **active** (running) and **obstruct** ing **express** trains.
Rauschenberg is a pop artist; picture a **roach** on an ice **berg** drinking soda **pop**.
Rousseau was of the primitive school of painting. Associate a **trousseau** or **Ruth sew** to **primitive** (see Ruth sewing primitive clothes). One of Rousseau's well-known paintings is "The Dream." Get something into your picture to represent dream, and you'll be reminded of that, too.
Mondrian was a constructivist; perhaps you'd like to remember that one of his paintings is titled "Broadway Boogie-Woogie." Picture a **man dryin'** a huge **construction** as he dances the **boogie-woogie** on **Broadway**.
Picturing a lot of **blue poles** (color blue, or sad blue) that are **lock** ed up will remind you that Pollock painted "Blue Poles."
See a gigantic **doll** sitting on a **fly** ing horse ( **Pegasus** ) to remind you that Dali did "Pegasus in Flight." If you didn't know the name of the mythical winged horse, you could use a **pea** in **gay sauce** for Pegasus.
Botticelli painted the "Birth of Venus." Perhaps you'd picture the **bot** tom of a **cello** (Botticelli) giving **birth** to a lady without arms ( **Venus** ). Select your own Substitute Words, of course. **Bottle sell E, bought a cello** , or **bought jelly** would also remind you of Botticelli, and **wean us** or the planet would remind you of Venus. Botticelli also painted "Calumny." Associate your Substitute thought for Botticelli to **column knee**.
In music appreciation, the approach is basically the same. Now that you have the idea, you won't need so many examples of ways to associate composer and composition.
Schönberg's "Violin Concerto": A **con** who's stolen a **violin** bangs it against a **chair** on a **shiny** ice **berg**.
Wagner's _Tannhäuser:_ Someone crashes a **wagon** into a **townhouse**. Wagner also composed _Lohengrin_. Associate your Substitute thought for Wagner to **low and grin** or **lone grin**.
Associate **straw win ski** to **pet rush car** and a **bird** on **fire** to help you remember that Stravinsky composed "Petrouchka" and "Firebird." Get **write off spring** into the picture, and you'll also remember that he composed "Rite of Spring." You can, of course, form a Link starting with the composer and including as many of his works as you want to remember. The same method, of course, works for paintings.
Picture a **rose** growing out of your **knee** and putting a **large O** on a **totem** pole, and you'll remember that Rossini wrote "Largo al Factotum." Picture that rose getting its hair cut by a **barber** who is **civil** (or just **barber** ) to remind you that Rossini wrote _The Barber of Seville_.
Liszt wrote "La Campanella"; see a **list camp** ing **on Ella**. Picture that list being very **grand** and **march** ing with a **crow** on **a mat** to remember that he also wrote "Grande Marche Chromatique."
Grieg's _Peer Gynt:_ see yourself **peer** ing (with a **squint,** if you like) into a **creek**.
Brahms's "Hungarian Dances": Picture **brahma** bulls (or **bare arms** ) doing **Hungarian dances,** or **danc** ing even though they're **hungry**. The "Hungarian Dances" were written as piano duets; you can see the dancing being done on two pianos. Associate the bulls or bare arms to **lead, best leader** , or just **best leader** to remind you that Brahms wrote the "Liebeslieder" waltzes.
Debussy's "La Mer": You might see a **D** being **busy** (or **bossy** ) to a **llama**.
You can associate a book title to its author just as you associated artists to periods and paintings, or compositions to their composers.
_The Invisible Man_ was written by Ralph Ellison. The author's last name is usually all you need, but you can put both names into your picture if you want to. You might picture a large, **rough** (Ralph) letter L being your son ( **L is son** ), and fading (becoming **invisible** ).
For _The Magic Barrel_ , written by Bernard Malamud: See yourself **mail** ing **mud** in a **barrel** that's performing **magic** tricks. For a reminder of the first name, get **burn hard** into your picture.
For _Dangling Man_ (Saul Bellow): See yourself **bellow** ing at a **dangling man**. Or, see yourself **below** a dangling man.
For _Rabbit Run_ (John Updike): Picture a **rabbit run** ing **up** a **dike**.
For _Catcher in the Rye_ (J. D. Salinger): A baseball **catcher** is **sailin'** a **jaw** in **rye** whiskey.
For _The Power and the Glory_ (Graham Greene): Picture a **graham** cracker turning **green** as it uses all its **power** to lift an American flag (Old **Glory** ).
One of Robert Lowell's best-known poems is "Skunk Hour"; if you see a letter **L** sinking **low** and sniffing a clock ( **hour** ) that smells like a **skunk** , you shouldn't have any trouble remembering it.
To remind you that T. S. Eliot wrote "The Waste Land," you might see a gigantic cup of **tea** (T) driving an **ess** curve (S) around a huge **lot** that's a **waste land**.
Picture a **burro** eating a **naked** person for **lunch** , and you'll know that William Burroughs wrote _The Naked Lunch_.
See a gigantic fly with **gold ink** all over it being the **lord** of the other **flies** , and you won't forget that William Golding wrote _Lord of the Flies_.
And so on. The only reason we've included so many examples is for your use, if you like, as a drill or test. You can, as usual, include any information in an association: dates, names of characters, plot, theme, whatever. It doesn't matter how difficult the material seems to be; so long as you can come up with Substitute Words or phrases, you'll find it easier to remember. Where a lot of information is involved, form a Link. For example:
One of Euripides' plays is _Alcestis_. First, associate **you rip D's** to **Al says this**. The setting of the play is outside the palace at Pherae. Start a Link—associate Al says this to a **fairy** outside a **palace**. The characters are Apollo, Death, the chorus (the old men of Pherae), Alcestis, Admetus, Eumelus, Heracles, Pheres, a manservant. You might continue your Link this way: **fairy** to **apple low** to **dies** (Death) to **chorus of old men** to **Al says this** to **add my toes** to **you mail us** to **hairy keys** to **ferries** to **servant**.
How you use the systems—and what you apply them to—has to be up to you, of course. If you're interested in the arts and want to remember all sorts of information, the systems will be invaluable time-savers. If you're not that art-minded but you would like to remember certain names, titles, and periods—why not? Memorize whatever facts you like, and you'll be able to "talk" art knowledgeably.
# 22 **_MUSIC FOR BEGINNERS_**
HL: I was about to say music is Greek to me, but that's not true. I know some Greek, and I know absolutely nothing about music—I can't sing "Happy Birthday" on key. I've found it difficult to get musical memory examples for students. I ask professional musicians, and it's hard for them to bring their minds back to the beginning, when memory was important.
JL: I know what you mean, because I don't know the first thing about music either. And I'm sure it would be hard for a professional basketball player to set down the fundamentals of the game for a beginner.
HL: Right. A professional performs by instinct. If he had to stop to remember, he'd be in trouble. But at the beginning, when he's first learning the fundamentals, memory must come into play.
•
This chapter is dedicated to all those children—and adults—who never learned the fundamentals of music because learning them involved so much drudgery and boredom. Music teachers and professional musicians tell us that most beginners who give up music do so because of the memory chores—they drop out before music becomes fun. Whether you teach these memory ideas to a child or use them yourself, you'll see that they make the study of music easier _and more fun_ at the beginning. Although we'll be touching on only a few fundamentals, you'll also see that the ideas can be applied to them all.
To play a basic, three-note chord, you have to remember two notes along with the note you want to play. There are only seven _basic_ notes to remember. This may not seem like much of a problem, but it is something you must know (remember) at the beginning. Every fundamental is basically a memory problem, hence the cliché among some music teachers: At the beginning, you learn "rote to note." So, although the memory problem may never be discussed, it's there all the same.
Let's start with piano. We assume here that you're familiar with the pattern of black and white keys on the piano keyboard; that you know the keyboard is divided into octaves, each beginning and ending with C, and so on.
First, you need to know the seven basic (white) notes on the keyboard—easy to remember because they're alphabetized: CDEFGAB. But remembering where, say, F is on the keyboard is a memory problem at the beginning. It must be, or memory aids like the following one wouldn't have been devised:
All the G and A keys
Are between the black threes
And 'tween the twos are all the D's;
Then on the right side of the threes
Will be found the B's and C's;
But on the left side of the threes
Are all the F's and all the E's.
A better way would be to assign numbers to keys. Middle C is at the center of the keyboard. In this diagram, we've numbered the black keys as well but will, for the moment, use only whole (white) notes as examples.
All you have to do now is to associate a note (letter) to a number, and you'll remember which key to hit for that note. Picture **half** (Alphabet Word for F) a **shoe** , and you'll know that F is the key numbered 6 on the keyboard. Or, make up a word that starts with the note and ends with the number; **fish** for F, **dam** for D, and so on. Chords can be remembered the same way; picture the **sea** (Alphabet Word) with a gigantic **tealeaf** on it, and you'll know that playing keys 1, 5, and 8 gives you a C chord.
Try this method with the other white notes, and you'll soon _know_ them—the numbers and associations will fade from your mind.
Once you do know the position of the notes, there's an easy way to memorize chords. To play a C chord, you'd have to remember to play C, E, and G. We're going to list the most common major chords, along with suggestions to help you remember each of them. In the list, you'll notice the symbol #for sharp; F# is F-sharp. (Sharping a note makes it higher, but not as high as the next highest note—F# is higher than F, but not quite a G.) Now. To remember these chords easily, you form a ridiculous association for each—but you'll also need to add a standard to remind you of sharp. A **knife** , or **cutting** , will do.
Here are the seven basic major chords:
C—C E G | Associate ocean (sea = C) to egg (egg will remind you of EG).
---|---
D—D F# A | Dean, half (F) a knife (#), ape. (A dean, holding half a knife, fights an ape.)
E—E G# B | Eel, jeans cut by a knife, bean. Or, an **egg** (EG) being cut (#) by a bean.
F—F A C | Picture half a **face**. Or, half an ape goes into the sea.
G—G B D | See a pair of jeans going **bad**.
A—A C# E | An **ace** with a knife, cutting an eel. Or, an ape jumps into a sea full of knives to catch an eel.
B—B D# F# | A **bed** being cut by half a knife. Or, a gigantic bean is being cut by a dean with half a knife. Or, a gigantic bean is **deaf** ; it has a knife stuck into each ear.
Once you know the major chords, you almost automatically know the sharp and flat chords. In writing, a major note is flatted by adding the flat symbol (b) to it, which lowers it slightly—Bb is lower than B but not quite an A. A sharp note is flatted by simply removing the sharp symbol. A major note is sharped by adding the sharp symbol, and a sharp note is sharped by adding another sharp. The symbol for a double sharp is .
So. If you already know that a D chord is D F# A, a D-flat chord is Db F Ab (you've flatted _each_ note); a D-sharp chord is (you've sharped each note). Musicians have told us that our systems come in handy for remembering chord progressions. Once you know how to picture a chord, you can form a Link to remind you of the progression (sequence) of chords for any piece of music. Amateurs who play for their own and others' entertainment—often "by ear," or without reading music—find the systems particularly useful.
One student who played piano in a nightclub lounge years ago had an interesting gimmick. Whenever _any_ published song title was called, he'd play the song. There are many thousands of songs, and he knew them all—all he needed was a reminder of the first four or so notes. Once he played those, his fingers automatically played the rest of the melody. His memory problem—"How do I associate the title of a song to the first few notes?"—had been solved by assigning a number to each note on the staff. One glance at the following diagram will make this clear:
Once you familiarize yourself with the notes, locations, and numbers, the solution is obvious. Any four notes will transpose to a four-digit number; any seven notes will transpose to a seven-digit number. And—you already know how to memorize numbers.
The first seven notes of "Mary Had a Little Lamb," played in the key of C, are EDCDEEE. Look at the diagram, and you'll see that these notes transpose to 3212333. An association of a **lamb** on a mountain would remind you of the first four notes. If you needed a reminder of all seven, you might see that lamb on a mountain, singing " **My Mammy**." Any words that give you the proper numbers phonetically will do.
The association will remind you of the two things you need to know—the title and the first few notes. One more example: The first seven notes of "Begin the Beguine" are CDEGEDE, and they transpose to 1235323. Picture a **tin mule begin** ning something, and you have your reminder of the first four notes. ( **A bee** drinking **gin** , a **big inn** , or **beak in** would also remind you of the song title.) To remember the first seven notes, you might use **tin mule my name**.
As usual, it is the idea that's important, not the Key Word you select or the phrase you make up for the numbers. If the Key Word reminds you of the title and the word or phrase fits phonetically, the system will work.
If you're at all familiar with the music staff, knowing which number represents which note is a matter of a few moments' concentration. If you need some help, apply the systems. An association of Alphabet Word to Peg Word will do it instantly. Associate sea to tie, dean to Noah, eel to Ma, half to rye, jeans to law, ape to shoe, and bean to cow. To distinguish the octaves, you might then associate sea to hive, dean to bay, eel to tease, half to tote, and sea to ton. (You'd know that the words that are _not_ basic Peg Words represent the higher octave notes.)
If you've read up to this point, and understand how the systems apply, then you obviously know more about music than we do, and you'll be able to patternize the ideas to fit your particular problem.
On a basic beginner's (six-string) guitar there are twelve frets. While learning the fundamentals, you'd rarely go past the third fret. In playing a particular note, the basic memory problem would be to know, or remember, which finger presses which string at which fret. This diagram shows the notes for open strings (no finger pressing down on any string):
To produce a high C, you'd press your first finger on the second (B) string at the first fret. Always think in that order: finger, string, fret. An association of **sea** (C) to **tent** would give you the information. You don't really need the last digit—at the beginning, the finger and fret digits are the same—so **tin** would suffice. You'd know that the first digit tells you finger _and_ fret.
To play a high G, you'd press your third finger on the first string at the third fret; see a pair of **jeans** (G) being a door **mat**. For low C: third finger, fifth string, third fret; associate **low sea** to **mule**. For middle E: second finger, fourth string, second fret; associate **eel** to **Nero**.
As usual, there's another way to handle it; for low C, you could simply associate **sea** to **camel** ; or, you could just think **camel**. The first letter tells you the note, and the next two consonant sounds tell you finger and string. All that remains is for you to decide on a standard picture for high, low, and middle, and you're on your way. (If you know the strings by note, you can use the letter to represent the string; for high C, associate **sea** to **tub** —first finger, **B** string.)
The same idea can be applied to the violin; it's even easier because there are no frets, and there are only four strings. If you want to remember that to produce an F note you have to place your second finger on the second string (at the top of the violin neck; as your fingers move down the neck, different notes are produced), associate **half** or **effort** to **nun**. To produce a B note, the first finger is placed on the third string; associate **bean** to **tomb**. Or, as with the guitar, use one word or phrase to tell you note, finger, and string: **fine inn** or **fannin** ' for F, and **bet 'im** or **beat 'em** for B.
There's no reason why the systems shouldn't work for any instrument. For example, a beginner on the trumpet would have to remember which valves to push down for which note. Since there are only three valves, the note would be associated to a word that represents, say, 12, 13, 23, 123, etc.
Of course, any instrument becomes more complicated as you progress. With a trumpet, the proper method of blowing is also essential. What we've tried to do in this chapter is to show you how the systems can make the fundamentals easier to grasp. That way, you get to the excitement—and the fun—of playing a musical instrument sooner.
# 23 **_READING_**
The term _speed-reading_ is a common one, yet it really doesn't mean what it says—not the way it's being used today. People who say they "speed-read" are not really reading, they're "idea-culling." And when someone tells you his reading speed is, say, 1,500 words per minute, remember this: Authorities on reading have effectively demonstrated that it is physiologically impossible to read more than 800 words a minute!
The misconception goes deeper. When we've asked people who claim to be able to read thousands of words per minute whether they _remember_ what they've read, there's usually a moment of slightly embarrassed silence. And, slow reading is usually a _memory problem_.
Most often, it is _regression_ that slows you down. The very slow readers are horizontal regressors. That is, by the time they get to the end of a sentence, they've forgotten or haven't grasped what was at the beginning of that sentence—so their eyes must go back, horizontally, to the beginning. The vertical regressors are a little better off. They're the readers who will get to the third or fourth paragraph and forget what was in the first—their eyes must go back, vertically, to that first paragraph.
Don't misunderstand; there are ways to reasonably improve your reading speed. But, in our opinion, there is only one way to read better, faster, and more effectively—and that is to read at your normal rate of speed and _remember as you read_. The goal is to be able to read any material only once, and know it! Eventually, achieving this goal will also increase your "normal" reading speed. To paraphrase educator Mortimer J. Adler: When it comes to reading material, the point is not how fast you can get through the material, but how much of the material can get through to you.
You now have the necessary knowledge to remember any reading material, _as you read_. The facts in reading material are usually sequential, so you would apply, basically, the Link system of memory. Within any reading material, you may come across names, words you're not familiar with, numbers, letters, facts, concepts, whatever. None of these need hang you up, because you've learned how to memorize them. You know the Substitute Word system, which will help you remember the names, words, facts, and concepts. You are aware of the Key Word or thought idea, which, along with the Link, will help you to keep these things in sequence. You know how to picture numbers and letters, and that takes care of remembering them as you read.
All you have to do is apply the systems you've learned to reading material. Let's assume you want to remember the facts in a news item like this one:
In the history of railroading, few tracks have been laid faster than those of the Tanzam Railway in Zambia. At this moment, it is moving from the port of Dar es Salaam to Zambia's copper belt. The 1,162-mile line is being built by Chinese laborers, with the help of a $402-million loan from China. Already completed are 21 tunnels and 200 bridges. The entire line is expected to be completed about 18 months ahead of schedule.
This news item is about Zambia and its railway, so you should start the Link with a "heading" picture, a Substitute thought that will remind you of Zambia. The one we used is **zombie. Sam be here, some be here, Sam bee** , or **Sam be a** would all do as well. The one you think of yourself is usually best for you, but we'll assume you're using **zombie** to start your Link for Zambia.
Before going into the Link, we want to be sure you realize that although we need a lot of words to describe them, the silly pictures are formed as fast as thought. All right then. Picture a **zombie walking** very **fast** along a **railroad track** ; the sun is so hot that it **tans 'im**. This silly picture will remind you of the first few facts: You're reading about Zambia, the railway tracks are being laid very quickly, and the railway is the Tanzam Railway. Before you continue, be sure to see that ridiculous picture.
Now, to continue the Link: **There is salami** (Dar es Salaam) falling on the **zombie's copper belt**. See a silly picture of millions of pieces of salami falling on the zombie's copper belt. Salami is probably enough to remind you of Dar es Salaam but, if you like, you can see yourself pointing to the huge salami and saying, "There is salami." You can also put in an association for **port** —port wine would do. Most important is that you actually see the picture.
See the zombie's copper belt (or the salami, since either one can be considered as being the last thing in your mind) turning into a **taut chain** that stretches for **miles**. This picture reminds you of the next fact: **taut chain** transposes to 1,162, and the picture tells you that the railway will be 1,162 miles long. You may have thought of **dud chain, tight chin,** or **did shine** , but we'll assume you're using **taut chain**.
Continuing: You might picture many Chinese people (picture the slanted eyes, or see them with **shiny knees** ) **laboring** to hold up that taut chain. Each one is getting a gigantic **raisin** (402) from a giant Chinese man. This silly picture reminds you that Chinese laborers are building the railway with the help of a $402-million loan from China.
For the next few facts: See a gigantic raisin running through a **tunnel** as it ties a **knot** (21) or throws a **net** (again, 21) around the **bridge** of its two **noses** (200). This will remind you that 21 tunnels and 200 bridges have already been completed. See that picture. (Remember that if you think up your own silly pictures, you're more Originally Aware of the information. Just trying to form the associations is half the battle—you're concentrating on the material as you never have before.) Finally, see a gigantic **dove** (18) flying **ahead** of the raisin—the railway is expected to be completed 18 months ahead of schedule.
A fast review: That dove, which is the last thing in your mind, is flying ahead of the raisin (18 months ahead of schedule) that is running through a tunnel, tying a knot around the bridge of its noses (21 tunnels and 200 bridges have been completed); a gigantic raisin is being given or loaned to Chinese laborers by a giant Chinese man (the railway is being built by Chinese laborers with the help of a $402-million loan from China); many Chinese laborers are holding up miles of taut chain (the railway is 1,162 miles long); the taut chain comes from a zombie's copper belt upon which salami is falling (the railway runs from Dar es Salaam to Zambia's copper belt); the zombie is walking quickly along a track as the sun tans 'im (track for the Tanzam Railway in Zambia is being laid quickly).
If you've really tried to see the pictures clearly, you should be able to fill in the following blanks:
What country is being discussed? _____.
What is the name of the railway? _____.
The railway is moving from port _____ to _____'s _____ belt.
The railway will be _____ miles long.
It is being built by _____ laborers, with the help of a $_____ loan from _____.
Already completed are _____ tunnels and 200 _____.
The line is expected to be completed _____ months ahead of schedule.
Even though you've made a Link, which is used to remember things in sequence, you'll know any fact without having to go through the entire Link. Try to answer these without going over the Link in your mind:
How long will the completed railway be? _____ miles.
What is the name of Zambia's railway? _____.
How many millions did China loan Zambia? $_____.
The first few times you apply the systems to technical reading material, they will slow down your reading rate. On the other hand, you won't have to spend time going over the material again and again. And as you apply the system, you'll see that you'll eventually be reading close to your normal rate of speed—and reading the material only _once_. And as your proficiency increases, so will your "normal" reading speed.
In our example, every fact from the news item was included in the Link. Obviously, when you're doing this on your own you'll be selective—you'll Link only what you feel you need to remember.
The idea is applicable to _any_ kind of reading material—and the more technical the material, the more useful the ideas. As you read, you can remember the names, places, and events of a historical novel, the names and applications of new drugs in a medical magazine, the style numbers and prices in a business report, the names and legal precedents in a law journal. Anything!
If you wish, you can even remember the page number on which a particular fact or quote appears. Simply associate a Key Word from the fact or quote to the Peg Word that represents that page number. If you have no Peg Word for the page number, make one up—it will work just as well. This idea can be used to remember, say, biblical or Shakespearean quotes. The association will help you remember both the fact and the page number—and, if you like, the book title. You can associate chapter titles, section headings, or facts to page numbers. You can, for particular intents and purposes, effectively memorize an entire book this way!
# 24 **_THE MEMORY GRAPH_**
The Memory Graph will help you remember _locations_ , as well as other information. The idea is based on the letter/number combinations often used to help you pinpoint any location on a map. There are letters down the left side of the map, and numbers across the top; when you look at the guide for a particular city, you may see "C4" next to that city. If you look across row C and down column 4, you'll find the correct vicinity for the city.
There _is_ a way to pinpoint locations in your mind; a way to make them tangible. Although the idea may be extended to any lengths, we'll use a hundred locations as an example. Look at the graph on the next page.
Obviously, if you can picture "C4," make the location definite in your mind, that picture will always refer to that particular spot—the box that falls at C4. Anything associated to that box will belong at that location.
The way to make all the locations tangible is to patternize them: A word will represent each location; each word will begin with the vital letter, and the very next consonant sound (any sounds that follow are disregarded) will be the sound that represents the vital number. In this pattern, the word **Ate** can represent only A1—it begins with _a_ , and the following consonant sound is _t_ (1). The word **Car** could represent only location C4; it begins with a _c_ , and the _r_ sound represents 4. The word **Impale** represents I3 (the sounds after the _m_ are ignored). The _s_ sound represents 10 in every case. All the vital (location) words given below can be pictured, of course, so that they can be associated to other information. Take a look at the list.
The pattern makes these associations easy to remember. Go over them a few times, and you'll know most of them. Once you know the words, you have a handy tool with which to solve any location memory problem. All you have to do is to superimpose the information onto the Memory Graph, then associate the vital word to the information that falls into that box, or location.
One of our students, a post office employee, wanted to remember the name, approximate location, and zip code of every post office station in Manhattan! After learning the
Memory Graph idea, he memorized all that information without too much effort. Just so that you'll see how the idea is applied, here's the way he laid out the graph:
He could have extended the graph to, say, 17—but, as you can see, it isn't necessary. The way it's laid out, he knew that **H, I, J** _up to 3_ belonged to the left of the graph, and that **H, I** , J from _7 to 10_ belonged to the right of the graph. (In other words, the Trinity, Church Street, etc., stations are south of the Village and Prince stations; the Hamilton Grange and College stations are north of the Manhattanville and Morningside stations.) Some of the stations are listed in more than one box to show that they cover a more extensive area.
He also knew that every zip code in Manhattan begins with 100, so he had to remember only the last two digits. Knowing all this, you can see that a ridiculous picture of, say, a gigantic **tire** (14) that **ate** an entire **village** gives all the necessary information. **Ate** gives you the location (A1), **tire** gives you the zip code (10014), and **village** tells you the name of the station.
The picture of a **nun** (10022) eating **mush** (36th Street Station) from a gigantic **Dish** (D6) tells you all you want to know. (The reason for not using the Peg Word **match** for 36th Street is to avoid possible confusion—you might use that to represent 10036, if you were memorizing this chart.)
For A5, the student used this picture: Many clocks ( **times** ) were drinking **Ale** (A5) by the light of a gigantic **match** (10036). So you see that an association of a Substitute Word or thought for the name of the station, the vital word for the location, and the Peg Word for the zip code number are all you need. Once the associations are made, all the necessary information is at your fingertips.
Actually, this is a simplified example. The student also wanted to remember the street boundaries for some of the stations. He put them into the proper locations and included them in the association or Link. For example, the north-south boundaries of the College Station are 134th and 144th streets. He included **timer** and **tearer** in his original picture to remind him of this. The east-west boundaries are St. Nicholas and Lenox avenues; a picture of **Santa Claus** (St. Nick) or **nickels** and **lean ox** would remind you of that.
Any information can be Linked to the vital (location) word. And the entire bloc of information can be put on the graph in any way you like—the way that tells you what you want to know. For this example, the student could have listed H, I, J stations in F, G, H and kept I and J empty. It wouldn't have mattered at all. Virtually the same information could have been condensed into a 4 × 4 Memory Graph, like this:
In this case, he could have used a Link of, say, **Ate** to **train at tea** and **sash** (Trinity, 06) to **church sack** (07) to **village** and **tire** to **shell sea** and **tot** —or he could have made _separate_ associations of **Ate** to each Substitute Word. Either method will work.
_Any_ tabular material can be placed on a Memory Graph. Any schematic problem, any location problem, can be solved this way. If you want to remember the layout (location) of the vital parts of a dissected animal, write them in the proper boxes, make your associations, and you'll know the layout. All you have to do is go over your vital words—you'll know where each part belongs.
You can learn the approximate location of all the states this way. A 3 × 3 Memory Graph will tell you the northwestern (A1), western (B1), southwestern (C1), north-central (A2), central (B2), south-central (C2), northeastern (A3), eastern (B3), and southeastern (C3) states. Look at a map, list the states in the proper squares, form your Links (vital words to states)—and it's done. Of course, you could pinpoint the locations more precisely by using a larger graph.
The same idea works for cities of states, cities of countries, streets of cities, countries of continents, rivers of countries, and so on. You'd use the Memory Graph only if you wanted to know locations; otherwise, simple Links would suffice.
Many people have memorized the entire periodic table of the elements (chemistry, physics) by superimposing it onto a Memory Graph.
The Memory Graph also enables you to do a fantastic number-memory demonstration. Lay out a 10 × 10 graph and then try to think up a word that the vital word for each square would _logically_ remind you of. Use words that contain four consonant sounds, and try not to have any repeats of four-digit numbers. Some examples: **Ate** (A1) might logically make you think of **burped** (9491); an **Awn** ing (A2) is a **sunshade** (0261); you **Aim** (A3) **rifles** (4850); an **Avenue** (A8) is a **street** (0141); the **Ace** (A10) of **clubs** (7590); a **Bell** (B5) **rings** (4270); **Comb** (C3) a **bald head** (9511); a **Dish** (D6) is **cracked** (7471); an **Eddy** (E1) is a **whirlpool** (4595); **Enter** (E2) means **come on in** (7322); a **Fur (F4)-bearing** animal (9427); **Fake** (F7) means not real (2145); **Fib** (F9) and **fibbing** (8927); **Gale** (G5) and **storm** (0143); **Hill** (H5) and mountain (3212); **Huff** (H8) **and puff** (2198); **Italy** (I1) and **spag** he **tti** (0971); (y) **Ipe** (I9) and **scream** (0743); **Jet** (J1) and **airplane** (4952).
After you've done this for all the vital words, go over them a few times until each vital word _automatically_ reminds you of the secondary word. Then lay out a Memory Graph with only the proper four-digit number in each square. Now you can have someone call any letter/number combination—you will instantly (after some practice) name the four-digit number in that square! If I1 is called, that should make you think of **Italy** ; Italy makes you think of **spaghetti** , and spaghetti can only be 0971. If A3 is called, you'd think of **Aim** ; aim reminds you of **rifles,** and that tells you the number 4850. The more often you perform this feat, the easier it will be for you. After a while you won't have to think about it anymore; when you hear a letter/number you'll almost automatically know the four-digit number.
You can change any of the vital words, of course—as long as the word you select fits the pattern.
This 400-digit (100 four-digit numbers) feat is virtually impossible to do without the system. It's a tough one to top. You may feel, however, that some of the stunts you'll be learning _do_ top it.
# 25 **_POTPOURRI_**
During one of our classes, a gentleman said he had a memory problem that was driving him crazy. The entire class leaned forward to hear this problem. "I dine out quite a lot," said the man, "and whenever I'm ready to leave the restaurant, I always have to spend time searching through all my pockets for my coat check!" There were a few snickers, yet the man was serious. His search for the coat check annoyed him, embarrassed him, and wasted his time—to him it _was_ a big problem.
We mention it here only to make the point that the systems really do apply to anything. We told the man to number his pockets: number 1, left front trouser pocket; number 2, right front pocket; number 3, left rear; number 4, right rear; number 5, left outside jacket pocket; number 6, right outside jacket pocket; numbers 7 and 8, inside jacket pockets.
Now, each pocket could be pictured. We told him to form a fast association of the coat check to the Peg Word representing the correct pocket—at the moment he put the check into the pocket. If the coat check was associated to **rye** , he'd know whenever he needed the check that it was in his right rear trouser pocket.
**If** you're wondering how he'd remember that the left front trouser pocket is number 1, etc.—he'd know, since _he_ numbered them. Or, he could simply see a **tie** in the left front trouser pocket, a long gray beard ( **Noah** ) in his right front pocket, and so on.
The principle, of course, is the same one discussed in the absentmindedness chapter. The association would _force_ him to think—for a moment, _at_ that moment—about which pocket was involved. Another way to designate specific pockets would be to make up a word that tells you the pocket. For example, for trouser pockets: **leaf** ( **l** eft **f** ront), **r** oo **f** ( **r** ight **f** ront), **lure** ( **l** eft **r** ear), **r** oa **r** or **r** owe **r** ( **r** ight **r** ear). For the jacket pockets, you might use **j** ewe **l** ( **j** acket **l** eft) and **j** a **r** ( **j** acket **r** ight). There are many ways to patternize most problems.
•
HL: It's an "unimportant" problem, but it matters to _me_. I love books. I wouldn't dream of dog-earing a page to tell me where I stopped reading. And bookmarks always seem to fall out. So, I form an instant association as I close the book. I look at the page number, and if it's page 125 I'll see the book going through a **tunnel**. The next time I pick up that book, I know which page to turn to. Since I sometimes read more than one book at a time, it's even more helpful—I do it with each book, adding a picture for the title to the association.
JL: This really is unimportant—I'm always counting things and remembering them. It's screwy, but it helps keep my mind occupied. I may count the cracks on a basketball floor, or the number of people in the stands who're wearing red, the tiles on a ceiling, the number of steps on a stairway. I've even counted and remembered the painted strips of white highway lines—I'm sure you'll be thrilled to know that there are 132 broken white lines per mile on most major highways in forty-seven of the fifty states. Whenever I return to a basketball court, stairway, highway—I'll still know the number of cracks, steps, and stripes.
This symbol, , in one of the shorthand methods, means _progress_. Look at that symbol—what does it remind you of? Use a little imagination, and it looks like a hook, a cane, a candy cane, or the side view of a bobsled. Once you "see" something, associate it to **progress**. If it looked like a hook to you, see yourself pulling on a gigantic heavy hook; finally, you move it—you're making **progress**. The association gives you the two things you need, the shape of the symbol and its meaning.
The idea can be taken to any lengths. In a Chinese dialect, this is the symbol that means _dragon_ in English:
It's pronounced _lohn_ , which is pretty close to "loan." We worked out a silly picture, or story, that made it possible to visualize the characters making up the symbol: Someone asks you for a **loan** ; you're so angry at this request that you push **one-fifth** ( ) of the amount requested, using a **stick** (—), onto a **ladder** ( ). The ladder is so tall that when you climb it you see a cup of **tea** being sipped by a **zebra** on an **el** evated train—the tea spills onto the zebra . The "spilled" tea reminds you that the **T** is on its side. The zebra yells, " **Ma**!" (which reminds you of the **three** short lines). The letter L (el **train** ) is enough to remind you of
This may seem time-consuming, but try memorizing many Chinese symbols by rote—you'll recognize the silly picture story for the shortcut it really is.
•
HL: When I was a private in the U.S. Infantry, I found that at the time, 1943, the Signal Corps scheduled three months for trainees just to memorize the Morse Code symbols—another three months was allowed for sending and receiving practice. I finally talked to the colonel in charge and boasted that I could teach the trainees to remember the symbols—"in less than an hour." I was all ready to explain the simple system I knew would do the trick, but I never got the chance. "What in blazes," he asked just before he threw me out, "would we do with the men for the rest of the three months!"
•
We've touched on Chinese characters and shorthand symbols to show you that the systems apply to abstracts. Well, what could seem more abstract than dots and dashes? Yet if you patternize the problem, it's easily solved.
Here's a simple formula: R = dot (•). **T** (or D) = dash (-). Once you have that in mind, you can picture each symbol. is the symbol for **A**. There's no way to picture , but according to the formula is **RT** ; the word **RaT** can be pictured and, within this pattern, rat can represent only and nothing else.
The symbol for B is , and the word **terror** would tell you the symbol (double _r_ 's and _t_ 's _do_ count here). The symbol represents C in the Morse (or Continental) Code; the word **torture, tartar** , or **traitor** would represent the symbol.
You can make up your own words or phrases. Here are just a few suggestions for the tough ones:
Once you've made up the words and phrases, you have to associate them to their letters. One way is simply to associate the symbol word to the Alphabet Word. Picture an **ape** (A) fighting with a rat ( ), and you have the two things you need—letter and symbol. For **B** , you might picture a gigantic **bean** (B) in terror ( ).
Perhaps the simplest way is to use the adjective idea. **A** wful rat, **B** ig terror, **C** ruel torture, etc. Once you concentrate on "flat rear tire," how could you forget that is the Morse Code symbol for **F**? "Flat" is the adjective that tells you that **F** is the letter, and "rear tire" tells you the symbol.
So you see, no information is too abstract for the systems. If the material can be written or verbalized, the systems can be applied in one form or another.
At a racetrack, airport, shopping center, etc., if you forget where your car is parked you can always wait until everyone else has driven away—the car remaining is yours! Perhaps you'd prefer to associate the car's location (row number and letter, usually) to your car.
If you're parking it in the street, associate the car to the nearest address, or to the nearest cross streets. If you park near 57th Street and Seventh Avenue in New York City, see a low cake driving your car; for 23rd Street and Third Avenue, see a new mummy in your car. If you park near 401 Fifth Avenue, see your car taking a **rest** on a hill; and so on. You know the principle—you're forcing yourself to think of the location at that moment, and locking it in with the silly association.
You can remember a person's address in the same way. Just as you can associate your car to an address, associate the person (or Substitute Word for the person's name) to the address. If you wanted to remember that Harry Cooper lives at 401 Fifth Avenue, you could picture a **hairy** (chicken) **coop** taking a **rest** on **a hill** , and you'd have the address.
You can remember any formula or equation by applying the Link and using standards to represent the things that appear regularly. An American flag can represent the equal ( = ) sign (Americans are all **equal** ); a **miner** or **mynah** bird can represent the minus (-) sign; **applause** can represent the plus (+) sign, a **tree** can represent the square **root** ( ) sign, and so on.
The formula for finding the area of a regular polygon is:
Start your Link with a Substitute Word for polygon; perhaps a parrot ( **polly** ) that's **gone** (disappeared). Associate that to a **quarter** (¼;) kneelin' ( _nl 2_) on a **cot** (cotangent) near a **hen** that's being attacked from **above** (over) by **doves** (180/ _n_ ) If you wanted to, you could see the quarter that's kneelin' looking up, to remind you that the superscript 2 is written near the top of the _nl_. Of course, you could have used hen, elevated train, and Noah to represent _nl 2;_ or you could make up a standard Substitute Word for _squared_.
See a phosphorous (glowing) ham reciting a poem ( **Ham Poem** ) to help you remember that the formula for phosphorous acid is H3Po3. Associate **pyre Vic** or **pie rude Vic** to **C** ome **H** ear **S** am or **C** omb **H** air **S** ome to remind you of the formula for pyruvic acid: C3H4O3.
When you drive into a gas station to ask directions, the first thing you usually hear is, "You can't miss it." Then, you know you're in trouble! But you don't have to be—you can use the Link to remember directions. First, you need a standard for right and left. You might use a punch ( **right** uppercut) and the red Communist flag ( **left** ). Then, form a Link as you hear the directions.
If you're told to go to the 2nd light, immediately picture **Noah** (man with long beard). Make a right turn: You're punching (right) Noah in the mouth. Go to the 4th light: You're punching a gigantic bottle of **rye**. Turn left: A gigantic bottle of rye is waving a red flag (left). And so on. Try it—you won't get lost nearly as often.
Many computer codes are really simple number codes. For a particular business, the digit 1 may represent "male," the digit 2 may represent "female," the digit 3 may represent "earns over $8,000." If a computer operator punches one wrong digit, it could cost the company a lot of money to straighten out the error. An association of digit (Peg Word) to what that digit represents solves the problem. An association of **Ma** to faces Sue might be all the operator needs to remember that digit and fact.
Are you a dieter? If you are, it's easier to keep track of what you're supposed to eat if you know how many calories (or carbohydrates, or both) are contained in certain quantities of particular foods. If you associate a fried egg to **disease** , you'll always remember that a fried egg contains 100 calories. Associating mayonnaise to **bone** will remind you that a tablespoon of mayonnaise contains 92 calories, and so on.
There is no limit to the examples we could include. If the problem is one of memory, the systems apply. They can help you remember _anything_ you want to remember.
# 26 **_LOOK, I'M A GENIUS!_**
HL: Renée and I were flying to Washington, and I was tired—I'd done seven appearances in a five-day period. I said to my wife, "I hope it's a small audience." It had become a running gag with us, because I always remembered every name in the audience, and sometimes I didn't really feel like working very hard.
At our hotel, Renée went to check out the room where I'd be appearing, and I took a nap. When I woke up she told me, "Relax, Harry—it's really a small audience."
When I went to the room to start meeting the people for my performance, I saw what she meant. I was appearing for a group called "The Little People of America"—it was an association of midgets!
JL: That's a small audience, all right.
HL: There were about three hundred of them, and it's the first time in my life—I'm five feet six—that I ever felt like Gulliver.
JL: Too bad I wasn't with you—they'd have come up to my kneecap.
HL: There's a punch line to the story. They all had special stools at their tables, so they could reach the food. I met them all during dinner, and after the dessert, I was introduced. I always begin by asking the "few" people I've met to stand up. Well, they all stood up—and they all disappeared! I was staring at a roomful of white tablecloths.
JL: You mean, when they stood up they were all below table level!
HL: That's it. They started to peek over the tabletops, and we all laughed for something like five minutes. Finally, one of them called out, "You really are amazing, Mr. Lorayne. That's the first time anyone's ever made a whole audience disappear!"
•
You may not be able to make an entire audience disappear, but there are many "amazing" feats you can perform, using the systems you've learned in this book.
Take the "missing-card" stunt described in the card chapter—it actually derives from a "missing-number" stunt, which, if performed with numbers, has the same effect. Have someone number a paper from 1 to 50, or 100. Tell him to circle any five numbers. Then ask him to call all the remaining numbers and cross them out as they're called. He's to do this haphazardly, and as quickly as he likes.
You can be across the room while this is done; you don't, of course, look at the paper. When all but the circled numbers have been crossed out, you tell your friend which numbers he circled! The principle is exactly the same as for the "missing" cards; except for this you mutilate the basic Peg Word for each called number. When he's finished, go over the Peg Words mentally (from 1 to 50, or 1 to 100), and any one that's not mutilated in your mind has to be a circled number. If you know the Peg Words well, and your friend crosses out and calls the numbers quickly, this is an impressive memory demonstration.
If you know the Card Words, try this for a group of at least eight people: Let someone shuffle a deck of cards. Then spread the deck _face up_ , and, as you approach one person at a time, let each one take any two cards. As each person takes the two cards, you form a ridiculous picture between the two Card Words. For instance, one person may take the 10C and the 7S. See a silly picture of a large **case** wearing **socks**. Another person takes the 3C and the **AH** ; see yourself **comb** ing your hair with a **hat** , or you're wearing a gigantic comb instead of a hat. The idea is to do this quickly with each person's two cards.
When all the people have two cards each (you can do this stunt with up to twenty-six people, of course, but it's just as effective with ten or fifteen), ask each one to remember his or her cards and to hold them face down.
You now have a choice of effects. You can have anybody call out one of their cards—you instantly name the other one. Easy, of course; if someone calls the 10C, you think of **case**. That should make you think of **sock** (7S).
Or, you can have one member of the audience collect all the pairs of cards and shuffle them thoroughly. Now, make it look like a mind-reading stunt; spread the cards face up and let anyone take out _one_ of his cards. Ask him to think of his second card. Then, with a great show of concentration, remove it and hand it to him. Same thing; if he removes the 3C you'll immediately think of **comb** , and that makes you think of **hat**. So, you remove the **AH**.
You can take this idea to many lengths. As one final example, you can take _one_ card from each person, and mix them. Hold them face down and distribute them, haphazardly, one card to each member of your audience. Each person holds his two cards face up. Now, if you know the people by name (which you should, if you've applied what you learned in the section on names and faces), you can amaze them by rapidly giving instructions until each person again has his original pair. Something like this: "All right, Sally, give that eight of diamonds to Jim. Jim, you give your king of hearts to Al. Sally, take the four of spades from Harry and give it to Sue in exchange for her six of clubs...." Once you've associated the pairs of cards originally taken by each person, you can perform many different card-memory feats.
Another card-oriented memory stunt: Let as many people as you like take one card. Each person quickly calls his or her card, plus any silly hiding place. For example, someone may say, "The four of diamonds, under the ashtray." All you have to do is to associate the Card Word to the hiding place. In this case, you might see a gigantic ashtray being a **door**. Do this with each call. Now, if someone calls a card, you can instantly tell where it's hidden. If someone calls a hiding place, you can just as instantly tell which card is hidden there.
Letter a paper from A to Z. Ask your audience to call out any letter, followed by a three-digit number to be written next to that letter. If someone calls the letter L and the number 489, form an association of an **elf** on a **roof** flying up. The letter P is called, plus the number 541; see a gigantic **pea** being caught with a **lariat** , or a gigantic pea being **lured**. Once every letter has been given a number, if you've made good clear associations you should know the number if a letter is called, and vice versa. This is impressive because you're remembering entities that most people can't remember—letters and numbers.
You must know your Alphabet Words, and you have to be able to make up words or phrases for three-digit numbers quickly. Your basic Peg Words and the "coupling idea" can help you with this. Make up a word that can couple easily with another word, one for each digit from 0 to 9. Here's a suggestion for each: 0—hose; 1—wet; 2—on; 3—my; 4—hairy; 5—ill; 6—ashy; 7—hack; 8—wave; 9—happy.
Decide on the word, and how to picture it. Once you've done that, you can instantly remember a three-digit number: If 017 is called, you'd picture a **tack** (Peg Word for 17) wearing **hose**. If 191 is called, see a **wet bat**. Here's one example for each "coupling" word. For 236, picture yourself putting a **match on** something; for 619, **see a tub** turning to **ash** as it burns; for 752, see yourself **hack** ing a **lion** with an ax; for 847, see a gigantic **rock wav** ing at you; for 972, see a gigantic **coin** laughing ( **happy** ).
Use the same kind of picture with any Peg Word. In other words, for any three-digit number starting with 7, you'd always see the Peg Word (for the last two digits) being **hack** ed with an ax; for any number that starts with a 4, see the Peg Word covered with **hair** , and so on.
Now you see that if **L-489** is called, you can picture a **hairy** watch **fob** on an **elf** ; for P-541, you'd associate an **ill rod** (fishing or curtain, whichever you're using) to a **pea**. This letter-number stunt, incidentally, is just as impressive if done with half the alphabet, A to M.
A really impressive memory feat is to memorize the highlights of every page in an entire magazine. Simply associate the Peg Word for each page number to the outstanding stories or photographs on that page. If the magazine contains more than a hundred pages, make up Peg Words to fit.
Once you've made your associations, you should be able to rattle off the highlights for any page number called. You'll even know the positions of the photos, without making an effort to remember them. Each association will conjure up a mental picture of that entire page. It's the closest thing to a photographic memory—try it, and you'll see!
If you have a friend or relative who has learned the phonetic alphabet and who is willing to sit home at the telephone while you're out having a good time, you can perform a fascinating demonstration in "thought transference." Tell your audience that you know someone who can actually read thoughts from miles away. Give the audience the "medium's" phone number before you begin the demonstration.
Now, have someone write any three-digit number on a large piece of cardboard—"Make it difficult," you say. "Don't repeat any digits." Everyone looks at the number and concentrates on it. Ask someone to dial the telephone number you gave before the three-digit number was even thought of. As the person reaches for the phone, you say, "Oh, and ask for Mr. Jones." When the person asks to speak with Mr. Jones, Mr. Jones will tell him that he's thinking of the number 620, and he'll be correct! How? Because of the name, **Jones**! You will have made up any name that codes the three digits (via the phonetic alphabet) to your assistant!
The reason you tell your audience to "make it difficult" and not repeat any digits is because it's easier to come up with a name that way. It's easy to come up with a legitimate-sounding name in any case; "Lorayne" would code 542 and "Lucas" would code 570, but the name you use need not contain _only_ three consonant sounds.
Since your assistant knows that you'll always ask for _three_ digits, he or she will ignore any consonant sound after the first three. So, if he hears someone ask for Mr. Cooperberg, he knows that the three digits are 794—he ignores "berg." The name **Bent** avagnia codes 921. There is no three-digit number that should cause any trouble. And you have plenty of time to think of a name while everyone else is concentrating on the number.
The "medium" should not blurt out the number. It should be given hesitantly, as if he or she were really receiving the number via mental telepathy. He might give the last digit first, then the first, and finally the center digit—we'll leave the showmanship to you.
The same idea can be used with playing cards. If you tell a member of the audience to call and ask for Mr. Sanders, that codes the 2S. The first letter always tells the suit, and the next consonant sound tells the value. The name Haggett would code the 7H, Cavanaugh the 8C, and so on.
You can't, of course, repeat either of these demonstrations for the same people—you'd have to tell them to ask to speak to a different "medium," which would look suspicious. If you're asked to repeat the stunt, claim mental fatigue!
We've just shown you how to use the systems to perform a few "amazing" feats. If you've learned and applied the systems throughout the book, you must realize that there is really no limit to the feats you can perform, provided you enjoy doing them and have a willing audience. Just use your imagination to apply one system or another to whatever feat you think will seem amazing. It's fun—for you, and for those watching you!
# 27 **_FINALLY_**
We live in the era of the "information explosion." Each year, an extraordinary amount of new technical knowledge and information comes to light, and _you_ are going to have to remember some of it.
In using many examples throughout the book, we've tried to keep them general. Hopefully, some of them are things you'd like to remember right now. But it's not important whether or not any particular example helps you remember something you need to know; what's important is that you grasp the _idea_. Then you can apply the idea to the things you do need to remember.
This is not the kind of book to read like a novel. A novel is the kind of book to read like a novel! If you've simply read through the book, nodding your head in understanding but without stopping to try, learn, and apply, you should go back to the beginning, the basics. Do the things you're told to do as you read—really learn those basics. The time you spend doing it will save you enormous blocks of time in the future.
Then start applying the ideas. That's really the only way they can work for you.
**_FOR_**
**_My wife Renée and my son Robert_**
**HARRY LORAYNE**
**_My son Jeff and my daughter Julie_**
**JERRY LUCAS**
#
By Harry Lorayne
_Harry Lorayne's Page-a-Minute Memory Book_
_The Memory Book_
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{"url":"http:\/\/mathoverflow.net\/questions\/141469\/tail-bound-for-l-2-norm-of-top-k-singular-values-of-a-random-matrix","text":"# Tail bound for $L_2$ norm of top $k$ singular values of a random matrix\n\nLet $Y=X^\\top W$ , with $X, W \\in \\mathbb{R}^{d \\times d}$ are random matrices with standard normal entries. Let $\\lambda_j$ be the $j^{th}$ singular value of $Y$. Is there a way to bound the tail probability of the $L_2$ norm of the top $k$ singular values of $Y$, i.e. $P\\Big(\\sqrt{ \\lambda_1^2(Y)+ \\lambda_2^2(Y) + ... \\lambda_k^2(Y)} > t \\Big) \\leq ?$ .\n\nAs a simple first try, I used $\\sqrt{ \\lambda_1^2(Y)+ \\lambda_2^2(Y) + ... \\lambda_K^2(Y)} \\leq \\sqrt{K}\\lambda_1(Y)$ and used bounds for $\\lambda_{max}$ of a matrix of the form of $Y$. But I need more tighter bounds and was wondering if there are other ways.\n\nI would appreciate if you could let me know of any previous work done for this case that you might be aware of.\n\n-\nIn what sense is the naive bound you suggest not good enough? \u2013\u00a0ofer zeitouni Sep 8 '13 at 22:23\nI was wondering if one could do better than $\\sqrt{k}$ times the $\\lambda_{max}$ \u2013\u00a0Krishna Sep 9 '13 at 21:16\nThis is clear, but my question was, what is the relation of k and d (I assume $d$ is large)? Note that in the model you suggested, for k fixed this bound will be essentially optimal (i.e., up to $(1+o_d(1))$ from the truth) - I suspect so because I believe that the top singular value sticks to the edge of the limiting distribution of singular values. \u2013\u00a0ofer zeitouni Sep 9 '13 at 23:21\nI am interested in the regime when $d$ increases linearly in $k$ \u2013\u00a0Krishna Sep 10 '13 at 2:55\n\nIn case $d$ increases linearly in $k$, say $k=\\alpha d$, you can compute the limiting spectral measure of your matrix (you are dealing with the product of two wishart matrices, so you can compute the limit e.g. by computing moments, or better using free probability). Call the limit distribution $F$. Then the statistics you are after is $\\sqrt{\\int_{F^{-1}(\\alpha)}^\\infty x^2 dF(x)}$. If you want estimates on the error, you can use concentration inequalities for the spectral measure (since the top singular value concentrates as well).","date":"2016-04-30 15:05:34","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\": 0.9206740260124207, \"perplexity\": 168.2519322205761}, \"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-2016-18\/segments\/1461860111868.79\/warc\/CC-MAIN-20160428161511-00126-ip-10-239-7-51.ec2.internal.warc.gz\"}"} | null | null |
<?php
// @info: Presents images in a folder as an album.
$page->addCssFiles("~sys/third-party/unite_gallery/css/unite-gallery.css");
$page->addJqFiles(["JQUERY", "~sys/third-party/unite_gallery/js/unitegallery.min.js", "~sys/third-party/unite_gallery/themes/tiles/ug-theme-tiles.js"]);
$jq = <<<EOT
$('.lzy-gallery').each(function() {
$(this).unitegallery({ tiles_type:'justified', tile_enable_textpanel:true, tile_textpanel_title_text_align: 'center' });
});
EOT;
$page->addJq($jq);
require_once SYSTEM_PATH.'gallery.class.php';
$macroName = basename(__FILE__, '.php');
$this->addMacro($macroName, function () {
$macroName = basename(__FILE__, '.php');
$this->invocationCounter[$macroName] = (!isset($this->invocationCounter[$macroName])) ? 0 : ($this->invocationCounter[$macroName]+1);
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$previewImgPath = $this->getArg($macroName, 'previewImgPath', '(optional) Path to preview images (default: thumbs/)', 'thumbs/');
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package gov.samhsa.consent2share.service.provider;
import org.springframework.security.access.annotation.Secured;
/**
* The Interface ProviderSearchLookupService.
*/
@Secured({ "ROLE_USER", "ROLE_ADMIN" })
public interface ProviderSearchLookupService {
/**
* Gets the provider search url.
*
* @return the provider search url
*/
public String getProviderSearchURL();
/**
* Sets the provider search url.
*
* @param providerSearchURL
* the new provider search url
*/
public void setProviderSearchURL(String providerSearchURL);
/**
* Provider search.
*
* @param usstate
* the usstate
* @param city
* the city
* @param zipcode
* the zipcode
* @param gender
* the gender
* @param specialty
* the specialty
* @param phone
* the phone
* @param firstname
* the firstname
* @param lastname
* the lastname
* @param facilityName
* the facility name
* @param pageNumber
* the page number
* @return the string
*/
public String providerSearch(String usstate, String city, String zipcode,
String gender, String specialty, String phone, String firstname,
String lastname, String facilityName, int pageNumber);
/**
* Provider search.
*
* @param usstate
* the usstate
* @param city
* the city
* @param zipcode
* the zipcode
* @param gender
* the gender
* @param specialty
* the specialty
* @param phone
* the phone
* @param firstname
* the firstname
* @param lastnameOrFacilityName
* the lastname or facility name
* @param pageNumber
* the page number
* @return the string
*/
public String providerSearch(String usstate, String city, String zipcode,
String gender, String specialty, String phone, String firstname,
String lastnameOrFacilityName, int pageNumber);
/**
* Generate provider search url.
*
* @param usstate
* the usstate
* @param city
* the city
* @param zipcode
* the zipcode
* @param gender
* the gender
* @param specialty
* the specialty
* @param phone
* the phone
* @param firstname
* the firstname
* @param lastname
* the lastname
* @param facilityName
* the facility name
* @param pageNumber
* the page number
* @return the string
*/
public String generateProviderSearchURL(String usstate, String city,
String zipcode, String gender, String specialty, String phone,
String firstname, String lastname, String facilityName,
int pageNumber);
/**
* Generate provider search url.
*
* @param usstate
* the usstate
* @param city
* the city
* @param zipcode
* the zipcode
* @param gender
* the gender
* @param specialty
* the specialty
* @param phone
* the phone
* @param firstname
* the firstname
* @param lastnameOrFacilityName
* the lastname or facility name
* @param pageNumber
* the page number
* @return the string
*/
public String generateProviderSearchURL(String usstate, String city,
String zipcode, String gender, String specialty, String phone,
String firstname, String lastnameOrFacilityName, int pageNumber);
/**
* Call provider search.
*
* @param query
* the query
* @return the string
*/
public String callProviderSearch(String query);
/**
* Checks if is validated search.
*
* @param usstate
* the usstate
* @param city
* the city
* @param zipcode
* the zipcode
* @param gender
* the gender
* @param specialty
* the specialty
* @param phone
* the phone
* @param firstname
* the firstname
* @param lastname
* the lastname
* @param facilityName
* the facility name
* @return true, if is validated search
*/
boolean isValidatedSearch(String usstate, String city, String zipcode,
String gender, String specialty, String phone, String firstname,
String lastname, String facilityName);
/**
* Provider search by npi.
*
* @param npi
* the npi
* @return the string
*/
public String providerSearchByNpi(String npi);
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 1,768 |
\section{Introduction}
Recent analysis of a combined sample of quasar absorption line spectra obtained using UVES (the Ultraviolet and Visual Echelle Spectrograph) on the Very Large Telescope (VLT) and HIRES (the High Resolution Echelle Spectrometer) on the Keck Telescope have provided hints of a spatial variation of the fine structure constant ($\alpha$) that is well represented by an angular dipole model \cite{Webb:2010hc,King:2012id}. \mbox{Subsequently, several} authors have shown that these results could be induced by a domain wall network described by a scalar field non-minimally coupled to the electromagnetic field \cite{Olive:2010vh, Chiba:2011en, Bamba:2011nm,Olive:2012ck} (see also \cite{Menezes:2004tp} for the first discussion of the cosmological implications of varying-$\alpha$ walls).
Domain wall networks tend to dominate the energy density of the universe at late times, a property shared by all dark energy candidates. This means that, unlike cosmic strings, domain walls are not expected to lead to observable signatures on cosmic structure formation and to contribute significantly to the primary Cosmic Microwave Background (CMB) anisotropies. Although frozen domain wall networks have been proposed in the past as a dark energy candidate \cite{Bucher:1998mh}, detailed studies have since ruled out any significant contribution of domain walls to the dark energy budget \cite{PinaAvelino:2006ia,Avelino:2008ve} \mbox{(see also \cite{Sousa:2009is,Avelino:2010qf,Sousa:2011iu})}.
As is the case with other topological defects, considering that a small domain wall contribution to the energy budget cannot be eliminated by cosmological observations, domain walls may still play a significant cosmological role. In this paper, we study the potential role of a domain wall network as a source of the reported variations of $\alpha$ based on VLT/UVES and Keck/HIRES observations, and derive tight observational constraints on this scenario.
\section{Domain Wall Evolution: The Basics}
In this section, we shall briefly review the essential aspects driving the cosmological evolution of a domain wall. In a flat homogeneous and isotropic Friedmann--Robertson--Walker (FRW) background, the line element is given by
\begin{equation} ds^2=-dt^2+a^2(t)\left[dr^2+r^2\left(d\theta^2 +\sin^2 \theta d\phi^2\right)\right]\,
\end{equation} where $t$ is the physical time, $a$ is the scale factor and $(r,\theta,\phi)$ are spherical coordinates. In such a background, the dynamics of a domain wall is essentially determined by two competing factors: the acceleration caused by domain wall curvature and the Hubble damping. The evolution equation of a domain wall in FRW universe may be rigorously derived from the Nambu--Goto action (see \citep{Sousa:2011iu}). \mbox{For the} purpose of this paper, however, it is sufficient (and considerably more succinct) to study these effects individually.
Let us start by considering the case of a spherically symmetric domain wall in a Minkowski spacetime (with $a=1$). This will allow us to pinpoint the effect of curvature on domain wall dynamics. In this case, the wall has an invariant area, $S=4 \pi \gamma r^2$ (where $\gamma \equiv (1-v^2)^{-1/2}$, and $v$ is the domain wall velocity), that is proportional to its energy (this is the domain wall analogue of the invariant perimeter of a cosmic string loop, $2\pi \gamma r$). It is straightforward to show that energy conservation then leads to the following equation of motion for a spherical domain wall in a Minkowski spacetime
\begin{equation}
\frac{dv}{dt}=n(1-v^2)\frac{f_k}{r}\,
\label{v-curv}
\end{equation} where $n=2$ and $f_k$ can be equal to $1$ or $-1$ depending, respectively, on whether the curvature is accelerating ($dv/dt>0$) or decelerating ($dv/dt<0$) the domain wall. Note that this expression also applies to point particles, if one sets $n=0$, and to cosmic strings, for $n=1$.
Note however that, in an FRW universe, the motion of the domain walls will be damped as a result of the expansion of the background, and consequently domain wall energy is no longer conserved. In such a background, the wall momentum per unit comoving area should be conserved. One thus has that, for a planar wall
\begin{equation}
\frac {d(v\gamma a^{n+1})}{dt}=0\,
\end{equation} or, alternatively
\begin{equation}
\frac {dv}{dt}=-(1-v^2)(n+1)Hv\,
\label{v-Hubble}
\end{equation} with $n=0$, $1$ and $2$, for point particles, cosmic strings and domain walls, respectively. Here, \mbox{ $H=(da/dt)/a$} is the Hubble parameter.
Equations (\ref{v-curv}) and (\ref{v-Hubble}) may be combined in order to obtain the equation of motion of a spherically symmetric domain wall in an FRW background. Although this equation describes the microscopic evolution of a single spherical wall, it also captures the essential features of the large scale dynamics of domain wall networks. As a matter of fact, a close analogue has been shown to accurately describe the root-mean-square velocity of domain wall networks. The reader may visit references~\cite{PinaAvelino:2006ia,Avelino:2008ve,Sousa:2010zz,Avelino:2010qf,Avelino:2011ev,Sousa:2011ew,Sousa:2011iu} for a detailed description of the semi-analytical Velocity-dependent One-Scale (VOS) model for domain \mbox{wall networks}.
\section{The Biased Evolution of Varying-$\alpha$ Walls}
For the remainder of this paper, we shall assume that the domain walls are associated with the variation of a scalar field $\phi$ that interpolates from $\phi_-$ to $\phi_+$ (or vice versa) at the domain wall. Note that this is the simplest realisation of a domain wall network without junctions and that more complex networks with junctions may be constructed in models with more than two minima of the scalar field \mbox{potential \cite{PinaAvelino:2006ia,Avelino:2008ve}}. Let us also assume that the value of the fine structure constant $\alpha$ is a function of the scalar field $\phi$ ($\alpha=\alpha(\phi)$)---so that it takes different values on each of the wall's domains---and let $\alpha_-\equiv\alpha(\phi_-)$ and $\alpha_+\equiv\alpha(\phi_+)$ be the values of $\alpha$ on each side of the domain wall. Due to the (weak) dependence of the quark masses on $\alpha$, the baryons on opposite sides of a domain wall have slightly different masses. \mbox{The fractional} mass difference is given approximately by
\begin{equation}
\zeta \equiv \left|\frac{\Delta m}{m}\right| = \left|\xi \frac{\Delta \alpha}{\alpha}\right|
\end{equation} where $\xi$ corresponds to the fractional electromagnetic contribution to the baryon mass. Note that $\xi$ takes different values depending on the nature of the particles under consideration: $\xi=-0.0007$ and $\xi=0.00015$, for the proton and neutron respectively \cite{Gasser:1982ap}. Protons are significantly more abundant than neutrons and the absolute value of their electromagnetic contribution is considerably larger than that of neutrons. For this reason, and for the remainder of this paper, we shall assume that $\xi=-0.0007$.
The domains on opposite sides of a wall are expected to have the same average baryon number density. However, as a consequence of the difference in baryon mass, they must have different average baryon energy densities. This energy difference between the domains introduces a bias on the dynamics of the domain walls, favouring the domains with a smaller value of the baryon energy density. Biased domain walls were originally envisioned as means to evade the Zel'dovich bound \cite{ZEL}, but they have also served as the basis of the devaluation scenario that attempted (and failed) to solve the cosmological constant problem \cite{Freese:2005pu}. The dynamics of biased domain walls has been studied in detail in these contexts (see, e.g., \cite{Sikivie:1982qv,Gelmini,Larsson:1996sp,Avelino:2008qy,Avelino:2008mh}). Here, we follow closely the approach in \cite{Avelino:2008qy}.
A generic form of a Lagrangian allowing for varying-alpha domain walls would be
\begin{equation} {\mathcal L}=-\frac12 \partial_\mu \phi \partial^\mu \phi -V_{eff}(\phi)\,
\end{equation} where the effective potential for the scalar field $\phi$ is given by
\begin{equation} V_{eff}(\phi)=V(\phi)+\rho_B(\phi)\,
\end{equation} and $V(\phi)$ is a scalar field potential allowing for domain wall solutions, such as a standard quartic potential with two degenerate minima
\begin{equation} V(\phi) = V_0 \left(\frac{\phi^2}{\eta^2}-1\right)^2\,
\end{equation}
Here $\eta=|\phi_\pm|$ and $\rho_B(\phi)$ is the baryon density, which in this case is a function of the scalar field $\phi$ coupled to electromagnetism that drives the space-time variations of $\alpha$. Although the above Lagrangian does not describe in detail microscopic interactions nor takes into account thermal corrections, it provides a generic description of the macroscopic interaction between the baryons and the domain walls.
Let us denote the values of the baryon densities on each side of the domain walls by $\rho_{B-} \equiv \rho_{B}(\phi_-)$ and $\rho_{B+} \equiv \rho_{B}(\phi_+)$ and introduce a bias parameter defined by
\begin{equation}
\epsilon=\rho_{B+}-\rho_{B-}=\zeta \rho_B\,
\end{equation} where $\rho_B$ is the average baryon energy density. In order to model the effect of this bias on the dynamics of the domain wall, we start by considering a planar domain wall in a Minkowski spacetime (so as to isolate the effect of bias on the dynamics). Energy conservation implies that
\begin{equation} d(\sigma \gamma)=v\epsilon dt\,
\end{equation} or equivalently
\begin{equation}
\frac{dv}{dt}=\frac{\epsilon f_\epsilon}{\sigma \gamma^3}\equiv \frac{f_\epsilon}{R_{\epsilon}\gamma^3}\,
\label{v-bias}
\end{equation} where $\sigma$ is the domain wall tension (equal to the domain wall energy per unit area in the wall's rest frame) and $f_\epsilon$ can be equal to $1$ or $-1$ depending on whether the bias is accelerating ($dv/dt>0$) or decelerating ($dv/dt<0$) the domain wall---an alternative way to arrive at Equation (\ref{v-bias}) would be using momentum conservation: $d(\sigma \gamma v)=\epsilon dt$. When a domain wall is moving towards a region with higher baryon energy density, the wall gains momentum to balance the resulting energy loss. Therefore, the domain walls feel a pressure that favours the suppression of the regions with a larger value of the baryon energy density. This backreaction effect on the dynamics of varying-alpha walls is a direct consequence of energy-momentum conservation. In the absence of expansion, energy-momentum conservation would require the decrease (increase) of the baryon energy density to be exactly compensated by an increase (decrease) of the energy density of the domain walls. One may infer from Equation (\ref{v-bias}) that the effect of the energy difference between the domains is to accelerate the domain wall and, in that sense, $\epsilon$ acts as an effective curvature characterised by a constant length scale $R_{\epsilon}=\sigma/\epsilon$.
The effect of the bias on the dynamics of domain walls with curvature in an expanding background is determined by the interplay of the surface pressure (which is caused by curvature), the volume pressure (which results from $\epsilon$) and the damping (which is caused by Hubble expansion). Equations (\ref{v-curv}), (\ref{v-Hubble}) and (\ref{v-bias}) may be combined into the following equation
\begin{equation}
\frac{dv}{dt}=(1-v^2)\left(\frac{2f_k}{R} + \frac{f_\epsilon}{R_{\epsilon} \gamma} -3Hv\right)\,
\label{v-full}
\end{equation} where $R=ar$ is the physical radius of the domain wall. Biased domain walls may be long-lived or disappear almost immediately, depending on the relative importance of the different terms in \mbox{Equation (\ref{v-full})}. As the domain walls evolve and the physical size of the domains increases, the importance of the bias term, when compared with the curvature and damping terms, grows with cosmic time. \mbox{When the} domains become larger than the bias scale---such that $R>R_{\epsilon}$---the walls decay due to the effect of the volume pressure. As a matter of fact, it has been shown that this result also applies to domain wall networks with junctions \cite{Avelino:2008mh}:
domains with larger baryon energy density disappear exponentially fast once the characteristic length scale of $L$ becomes larger than $R_{\epsilon}$ \cite{Larsson:1996sp} ---or, equivalently, when
\begin{equation}
\frac{\sigma}{\epsilon L}=\frac{\rho_{w}}{\epsilon}=\frac{\Omega_w}{\Omega_{B}\zeta} < 1\,
\label{constraint}
\end{equation}
Here $\rho_c$ is the critical density of the universe, $\rho_w=\sigma/L$ is the average energy density of the domain wall network, $\Omega_{B}=\rho_B/\rho_c$ and $\Omega_{w}=\rho_w/\rho_c$. Varying-$\alpha$ domain walls have, thus, an additional source of instability---the bias introduced by the energy difference between domains. As we shall see in the next section, this will allow us derive a lower bound on the admissible varying-$\alpha$ domain wall energy density.
\section{Observational Constraints}
Observations of the quasar absorption spectra at high redshifts obtained using HIRES on the Keck Telescope were shown to be consistent with a fractional variation of $\alpha$ of $(0.57\pm0.11)\times 10^{-5}$ \cite{Murphy:2003hw} \mbox{(see also} \cite{Webb:1998cq,Murphy:2000pz,Webb:2000mn}). However, ensuing studies based on VLT/UVES data have indicated a much smaller value of $\Delta \alpha/\alpha$ \cite{Chand:2004ct,Quast:2003qu}. These observational constraints can be reconciled by allowing for a spatial variation of the fine structure constant. In fact, it has been shown in \cite{King:2012id} that the data from a large sample of 295 absorbers from the VLT and Keck telescopes is compatible with an angular dipole model with amplitude \cite{King:2012id} (see also \cite{Webb:2010hc})
\begin{equation}
\Delta\alpha/\alpha=0.97^{+0.22}_{-0.20}\times 10^{-5}\,
\label{daloval}
\end{equation}
Domain wall networks described by a scalar field non-minimally coupled to the electromagnetic field have been suggested as a potential source of variations of $\alpha$ \cite{Olive:2010vh, Chiba:2011en, Bamba:2011nm,Olive:2012ck} (see also \cite{Menezes:2004tp}). It has been shown that this scenario is compatible with the current data, but a detailed verification will require a new generation of high-resolution ultra-stable spectrographs such as ESPRESSO (the Echelle SPectrograph for Rocky Exoplanet and Stable Spectroscopic Observations). Note that, in a model in which spatial variations of $\alpha$ are caused by a domain wall network, the stringent laboratory constraints (see, for example, \cite{Uzan:2010pm} and references therein) are naturally evaded.
The domain wall network would have to have a characteristic scale in the order of the Hubble radius in order to be able to induce spatial variations on a cosmological scale. The redshift of the closest domain wall may be estimated by solving the equation
\begin{equation}
\Delta \eta \equiv \eta_0-\eta = \beta L/a\,
\end{equation} with $\beta \lesssim 1$, using the VOS model for domain walls to estimate the characteristic length of the network. Here $\eta$ is the conformal time (or comoving particle horizon) defined by $\eta=\int dt/a$, and the subscript ``0'' refers to the present time. Using the calibration of the VOS model given in \cite{Leite:2012vn} and assuming fractional matter and cosmological constant energy densities compatible with the Planck results \cite{Ade:2013zuv} ($\Omega_{m0}=0.315$ and $\Omega_{\Lambda 0}=1-\Omega_{m0}$, respectively), we have found that if, as indicated by the results obtained in \cite{Olive:2012ck}, the wall closest to us is at a redshift $z = $ 0.5--1, its existence would be consistent with a plausible range for the corresponding value of $\beta$:
\begin{equation}
0.3 \lesssim \beta \lesssim 0.7
\end{equation}
Results from high resolution field theory simulations have shown no significant dependence of the characteristic velocity on the properties of the network. However, the characteristic scale of the network is highly dependent on the network configuration, and its value can vary significantly: it may be smaller by a factor of up to $3$ in the case of complex domain wall networks with junctions \cite{Avelino:2008ve}, or even by a larger factor if friction is important \cite{Sousa:2011iu} or in the presence of massive junctions \cite{Sousa:2009is}. The above estimate of the value of $\beta$ appears to favour the simplest frictionless domain wall models without junctions over more complex scenarios with junctions.
A necessary requirement for a domain wall network to be able to seed the spatial variations of $\alpha$ is that the bias introduced by the interaction with the baryons does not lead to the suppression of the domain wall network prior to the present epoch. This requirement (see Equation (\ref{constraint})) yields the following lower limit on the contribution of domain walls to the cosmic energy budget
\begin{equation}
\Omega_{w0} > \Omega_{B0} \left|\xi\frac{\Delta \alpha}{\alpha}\right| \sim 3 \times 10^{-5} \left|\frac{\Delta \alpha}{\alpha}\right|\,
\label{lowerb}
\end{equation} where we have taken $\Omega_{B0}h^2=0.02205$, with $h=0.673$, as indicated by Planck data \cite{Ade:2013zuv}, \mbox{and $\xi=-0.0007$}. Assuming that the reported spatial variations of $\alpha$, based on observations from VLT/UVES and Keck/HIRES spectrographs, are due to varying-$\alpha$ walls and using the constraint on the $\alpha$-variation given by Equation (\ref{daloval}), one finds that
\begin{equation}
\Omega_{w0} > 10^{-10}\,
\label{lowerb1}
\end{equation}
On the other hand, a conservative constraint on the contribution of a domain wall network with a characteristic length in the order of the Hubble radius to the cosmic energy budget is
\begin{equation}
\Omega_{w0} < 10^{-5}\,
\label{omup}
\end{equation} in order to prevent domain walls from providing the dominant contribution to the large scale temperature anisotropies of the CMB. Note that this upper bound is conservative and that a more detailed analysis, using the current CMB constraints from Planck and the Wilkinson Microwave Anisotropy Probe (WMAP), would most certainly lead to a tighter upper bound.
Hence, we have found that the observational window for domain wall networks as a source of the reported spatial variations of $\alpha$ is narrow:
\begin{equation} 10^{-10} < \Omega_{w0} < 10^{-5}\,
\end{equation}
The scenario of domain-wall-induced spatial variations of $\alpha$ is thus tightly constrained.
\section{\label{conc}Discussion and Conclusions}
In this paper, we have considered the possibility that a domain wall network may be responsible for the reported spatial variations of $\alpha$ based on observations from VLT/UVES and Keck/HIRES spectrographs. We have shown that in order to explain these variations, the dynamics of the domain wall network needs to be essentially frictionless (so that its characteristic length scale at the present time is in the order of the Hubble radius) and its fractional energy density should be within five orders of magnitude \mbox{($10^{-10} < \Omega_{w0} < 10^{-5}$)}. The presence of a domain wall network with a characteristic scale comparable to the Hubble radius may leave a variety of other observational signatures---in particular if its fractional energy density is sufficiently close to the upper limit set in Equation (\ref{omup}). For instance, as happens in the case of cosmic strings \cite{Seljak:2006hi,Pogosian:2007gi,Bevis:2007qz,Sanidas:2012ee,Kuroyanagi:2012wm,Sousa:2013aaa,Sousa:2014gka}, as domain wall networks evolve and interact, a fraction of their energy is released in the form of vector and tensor modes \cite{Hiramatsu:2013qaa}, which may contribute to the B-mode polarisation of the CMB.
Recent results by the Background Imaging of Cosmic Extragalactic Polarization (BICEP2) experiment seem to be consistent with an excess of B-mode power on large angular scales (in the multipole range $30 < l < 150$), which has been interpreted as the first direct evidence of a primordial gravitational wave background produced at an early inflationary stage at the Grand Unified Theory\mbox{ scale \cite{Ade:2014xna}}. However, in \cite{Lizarraga:2014eaa,Moss:2014cra,Lizarraga:2014xza}, alternative and/or complementary interpretations involving cosmic strings and other cosmic defects have been proposed. For sufficiently large values of $\Omega_{w0}$ ($\sim$$10^{-6}-10^{-5}$) the domain walls are expected to provide a significant contribution to the B-mode polarisation power spectrum associated to vector and tensor perturbations, thus being a possible explanation of the B-mode polarisation signature detected by BICEP2 \cite{Ade:2014xna}. In \cite{Moss:2014cra} it was found that, in order for cosmic strings to be the dominant contributor to excess of B-mode power on large angular scales detected by BICEP2, the inter-string distance would need to be extremely large. Although this analysis does not apply directly to domain wall networks, the fact that the characteristic length of a domain wall network is significantly larger than that of local strings is interesting. Furthermore, since domain walls only become cosmologically relevant at recent times, B-mode polarisation induced by domain walls should be strongly suppressed on small scales when compared with a corresponding contribution from cosmic strings, despite the fact that it is expected to be comparable to that of strings at low $l$, for the same average defect energy density at the present time (for this reason domain walls, unlike other defect models, provide a negligible contribution to the matter power spectrum and to the primary CMB anisotropies). These facts could make domain walls a stronger contender than other defects (such as cosmic strings) to explain the excess of B-mode power detected by BICEP2 on large angular scales.
Another interesting observation is the apparent tension between the original interpretation of the BICEP2 results and the Planck upper limit on the tensor-to-scalar ratio $r$. A recent suggestion to solve this discrepancy involves a spatial variation of $r$ that could also account for the large scale anomalies in the temperature distribution of the cosmic microwave background detected by Planck and \mbox{WMAP \cite{Ade:2013zuv,Ade:2013ktc,Hinshaw:2012aka,Bennett:2012zja,Chluba:2014uba}}. A similar signature would also be expected in the case of the domain wall scenario studied in the present paper. The large characteristic length scale of the domain wall network at the present time could be naturally associated with large scale temperature and polarisation CMB power asymmetries and with a large cosmic variance that future studies will need to tackle.
The origin of the signal detected by BICEP2 is still a matter of controversy, with several authors questioning the validity of the methods used (see, e.g., \citep{Mortonson:2014bja,Flauger:2014qra}). Still, even if the cosmological origin of the signal is ruled out, stronger upper bounds on the fractional energy density of domain walls may be inferred. In either case, valuable information might be gained by performing more detailed studies of the large scale anisotropies and CMB polarisation signatures generated by varying-$\alpha$ domain walls. Such studies will require an accurate computation of the scale dependence of both vector and tensor perturbations generated by domain wall networks around the present time for a wide range of representative domain wall network models (with or without junctions), and will be the subject of \mbox{future work}.
\acknowledgments{Acknowledgments}
P.P.A. is supported by Funda{\c c}\~ao para a Ci\^encia e a Tecnologia (FCT) through the Investigador FCT contract of reference IF/00863/2012 and POPH/FSE (EC) by FEDER funding through the program ``Programa Operacional de Factores de Competitividade-COMPETE''. L.S. is supported by Funda\c{c}\~{a}o para a Ci\^{e}ncia e Tecnologia (FCT, Portugal) and by the European Social Fund (POPH/FSE) through the grant SFRH/BPD/76324/2011. This work was also partially supported by grant \mbox{PTDC/FIS/111725/2009 (FCT)}.
\authorcontributions{Author Contributions}
The authors contribute equally to this paper. All authors have read and approved the final version.
\conflictofinterests{Conflicts of Interest}
The authors declare no conflict of interest.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 5,406 |
\section{Introduction}\label{sec:intro}
Simplified models~\cite{hep-ph/0703088, 0810.3921, 1105.2838, Okawa:2011xg, 1301.2175} have become one of the standard methods
to interpret searches for physics beyond the Standard Model (BSM). They reduce full models with dozens of particles and a plethora of
parameters to subsets with just a handful of new states.
The virtue of simplified model spectra (SMS), namely that a full model decomposes into many different SMS, also defines their main challenge:
depending on the complexity of the mass and decay patterns, a full model may not be fully reconstructed by SMS.
The question that arises is to what extent full models can indeed be constrained by SMS results.
In this article, we address this question for a 19-parameter version of the minimal supersymmetric standard model, the so-called phenomenological MSSM~\cite{Djouadi:1998di}, or pMSSM for short. Our work is based on the ATLAS pMSSM study~\cite{Aad:2015baa}, in which the points from an extensive pMSSM scan were tested against the constraints from 22 ATLAS searches from LHC Run~1.
ATLAS made the SLHA spectra of the whole scan publicly available on HepDATA~\cite{ATLASpMSSMhepdata} together with information about which point is excluded by which analyses. This is extremely useful information, which we here use to test the constraining power of SMS results by means of {\sc SModelS}~\cite{Kraml:2013mwa,Ambrogi:2017neo}.
{\sc SModelS}\ is an automatised tool for interpreting simplified model results from the LHC.
It decomposes collider signatures of new physics featuring a $\mathbb{Z}_2$-like symmetry into simplified model topologies,
using a generic procedure where each SMS is defined by the vertex structure and the Standard Model (SM) final state particles;
BSM particles are described only by their masses, production cross sections and branching ratios. The weights of the various topologies,
computed as production cross section times branching ratios,
are then compared against a large database of experimental constraints.
This procedure takes advantage of the large number of simplified models already constrained by official ATLAS and CMS
results and does not require Monte Carlo event simulation, thus providing a fast way of confronting a full BSM model
with the LHC constraints.
Furthermore, ``missing'' topologies, which are not covered by any of the experimental constraints, are also identified
and provided as an output of {\sc SModelS}.
The tool can be used for testing any BSM scenario with a $\mathbb{Z}_2$-like symmetry as long as all heavier
odd particles (cascade-)decay promptly to the lightest one, which should be electrically and colour neutral.%
\footnote{The treatment of charged tracks is also possible in the context of simplified models~\cite{Heisig:2015yla} and will be available in future versions of {\sc SModelS}.}
It has been applied to a number of minimal and non-minimal supersymmetric (SUSY) models
in~\cite{Kraml:2013mwa,Belanger:2013pna,Barducci:2015zna,Arina:2015uea}
but may also be used for non-SUSY models, see e.g.~\cite{Edelhauser:2015ksa,Kraml:2016eti}.
The underlying assumption~\cite{Kraml:2013mwa} that differences in the event kinematics
({\it e.g.}\ from different production mechanisms or from the spin of the BSM particle)
do not significantly affect the signal selection efficiencies has also been investigated.
For example, the effects of alternative production channels in squark simplified models were studied in~\cite{Edelhauser:2014ena}.
The effect of a different spin structure was studied for the case of the dijet+MET final state in~\cite{Edelhauser:2015ksa},
for the dilepton+MET final state in~\cite{Arina:2015uea} and for $t\bar{t}$+MET final states in~\cite{Kraml:2016eti}.
A comprehensive study of how well a full model like the MSSM is actually covered by SMS constraints is, however, still missing.
This gap we want to fill with the present paper.
We first describe the setup of the analysis in Section~\ref{sec:setup}. Our results are presented in Section~\ref{sec:results}, where we discuss
the exclusion obtained with {\sc SModelS}\,v1.1.1\ as compared to ATLAS and how it is improved when including efficiency maps in addition to upper limit maps.
Moreover, we discuss why a certain part of the parameter space, despite being excluded by the ATLAS study, is not excluded by
(the currently available) SMS results. In particular, we analyse the importance of asymmetric decay branches and long cascade decays
to understand the potential for increasing the coverage, and we point out a number of important SMS beyond those typically considered by the experimental collaborations. Conclusions are presented in Section~\ref{sec:conclusions}.
Appendices A and B contain useful additional material on the missing topologies discussed in the paper.
\section{Setup of the analysis}\label{sec:setup}
In~\cite{Aad:2015baa} ATLAS has analysed in total more than 310k pMSSM parameter points with SUSY masses below 4 TeV and a neutralino as the lightest SUSY particle (LSP). These points from an extensive scan, based on previous phenomenological studies \cite{Berger:2008cq,CahillRowley:2012cb,CahillRowley:2012kx,Cahill-Rowley:2014twa},
satisfy constraints from previous collider searches, flavor and electroweak (EW) precision measurements, cold dark matter relic density and direct dark matter searches.
In addition, the mass of the light Higgs boson was required to be between $124$ and $128$~GeV.
These points were classified into three sets according to the nature of the LSP: bino-like (103410 points), wino-like (80233 points) and higgsino-like (126684 points).
About 40\% of all these points were excluded by at least one of the 22 ATLAS Run~1 searches.
The points excluded by ATLAS are the center of interest of our study:
our aim is to compare the exclusion coverage obtained using SMS results only to that from full event simulation. (In the following we mean by ``coverage'' the fraction of points excluded by ATLAS which is also excluded by {\sc SModelS}.)
We restrict our analysis to the sets with bino-like or higgsino-like LSP, neglecting points with a wino-like LSP, as most of them lead to a displaced vertex signature, which cannot be studied with the current version of {\sc SModelS}.
We further remove points from the bino- and higgsino-like LSP data sets if they contain any long lived sparticles---this concerns however only a small number of points.
Likewise, points which ATLAS found to be excluded only by heavy Higgs searches are also not considered here, as such searches are not
treated in {\sc SModelS}\ for the time being.
This selection leaves us with 38575 parameter points with a bino-like LSP and 45594 parameter points with a higgsino-like LSP to be tested with {\sc SModelS}.
We use the latest version of {\sc SModelS}, v1.1.1, which works with upper limit (UL) and efficiency map (EM) type results, see~\cite{Ambrogi:2017neo}.
The cross sections for all points are calculated with the {\sc SModelS}\ cross section calculator interfaced to Pythia\,8.2~\cite{Sjostrand:2006za,Sjostrand:2014zea} and NLLfast~\cite{nllfast,Beenakker:1996ch,Kulesza:2008jb,Kulesza:2009kq,Beenakker:2009ha,Beenakker:2011fu,Beenakker:1997ut,Beenakker:2010nq}. (The exception are the cross sections for slepton-pair production, for which we use Pythia\,6.4~\cite{Sjostrand:2006za} because they are not computed correctly in Pythia\,8.226.)
Electroweak cross sections are thus computed at leading order while strong productions are computed at NLO+NLL order.
Given the information on cross sections ($\sigma$) and decay branching ratios (BR) in the SLHA~\cite{Skands:2003cj} files, {\sc SModelS}\ computes $\sigma\times {\rm BR}$ for each topology that occurs. Topologies are characterised by the SM particles originating from each vertex, and the mass vector of the SUSY particles in the decays. In order to avoid dealing with a large number of irrelevant processes, {\it i.e.}\ to save CPU time, topologies for which
$\sigma\times {\rm BR}<{\tt sigmacut}$, with ${\tt sigmacut} = 0.03$~fb, are discarded.
In addition, if the mass gap between mother and daughter particles is small, the decay products will be too soft to be detected at the LHC. This is taken care of by the so-called ``mass compression'' in {\sc SModelS}, discarding any SM particle coming from a vertex for which the mass splitting of the R-odd particles is less than a certain threshold. We use the default value of 5~GeV as the minimum required mass difference for the decay products to be visible.
After the decomposition, the weights ({\it i.e.}\ $\sigma\times {\rm BR}$) of the SMS components of each point are
rescaled by the corresponding efficiencies (see~\cite{Ambrogi:2017neo} for more details) and matched with
the experimental results in the database. In case of UL maps, this is a direct comparison of individual weights and the cross section upper limit
for a given simplified model component or topology.
In case of EMs, the weights of several topologies can be combined and may contribute to a specific signal region of a given analysis;
it is then the combined signal cross section for the most sensitive signal region ({\it i.e.}\ the signal region with the best expected limit)
which is compared against the experimental limit. Hence using efficiency maps can significantly improve
the constraining power of simplified models.
See the {\sc SModelS}\,v1.1.1\ manual~\cite{Ambrogi:2017neo} for a detailed explanation of the procedure.
For a fair comparison with~\cite{Aad:2015baa}, we employ only the 8~TeV results in the v1.1.1 database.
In order to maximise the coverage by SMS, we consider however also CMS 8~TeV results, as they may give complementary constraints.
This is justified because ATLAS and CMS SUSY searches largely consider the same final states and have very similar reach.
We also note that the official ATLAS and CMS Run~1 results available in {\sc SModelS}\ were augmented with several `home-grown' EMs in the v1.1.1 database to increase the coverage, and we further extend this database with {\sc Fastlim}-1.0~\cite{Papucci:2014rja} EMs as explained in~\cite{Ambrogi:2017neo}. The complete list of analyses and results included in the v1.1.1 database can be consulted at~\cite{smodels:listofanalyses}.
A comparison of the analyses considered in \cite{Aad:2015baa} and the SMS results included in {\sc SModelS}\ v1.1.1 is given in
Table~\ref{tab:AtlasSearchesInPaper}. The analyses covered by the {\sc Fastlim}\ EMs are listed in Table~\ref{tab:FastlimAnalyses}.
Here note that in {\sc SModelS}\,v1.1.1\ efficiencies with a relative statistical uncertainty greater than 25\%
are set to zero and, moreover, zero-only EMs are discarded per default. Therefore, from the 264 EMs of {\sc Fastlim}-1.0,
which are based on 11 ATLAS conference notes, used in practice are 163 EMs from 9 conference notes.
The CMS analyses included in the v1.1.1 database are listed in Table~\ref{tab:CMSAnalyses}.
{\sc SModelS}\ reports its results in the form of $r$-values, defined as the ratio of the theory prediction over the observed 95\% confidence level (CL) upper limit, for each experimental constraint that is matched in the database. We consider as excluded all points for which at least one $r$-value equals or exceeds unity ($r_{\rm max} \ge 1$).\footnote{We note that for staying strictly at 95\%~CL, one should use only the $r$-value of the most sensitive analysis. This is however not feasible because for many UL-type results the {\em expected} limits are not publicly available.}
Points which are not excluded ($r_{\rm max} < 1$) are further studied using the {\sc SModelS}\ coverage module (see section~3.5 in \cite{Ambrogi:2017neo}).
\begin{table}\centering
\begin{tabular}{llcll}
&{\bf Analysis} & {\bf Ref.} & {\bf ~~ID} & {\bf SModelS database} \\ \hline
\parbox[t]{3mm}{\multirow{7}{*}{\rotatebox[origin=c]{90}{Inclusive}}}
&\ZeroLepton & \cite{Aad:2014wea} & SUSY-2013-02$^{\,*}$ & 6 UL, 2 EM \\
&\Multijet & \cite{Aad:2013wta} & SUSY-2013-04$^{\,*}$ & 1 UL, 10 EM \\
&\OneLeptonStrong & \cite{Aad:2015mia} & SUSY-2013-20$^{\,*}$ & 1 UL from CONF-2013-089~\cite{ATLAS-CONF-2013-089} \\
&\TauStrong & \cite{Aad:2014mra} & SUSY-2013-10 & n.i. \\
&\SSThreeLepton & \cite{Aad:2014pda} & SUSY-2013-09 & 1 UL (+5 UL, CONF-2013-007~\cite{ATLAS-CONF-2013-007})\\
&\ThreeBjets & \cite{Aad:2014lra} & SUSY-2013-18$^{\,*}$ & 2 UL, 2 EM \\
&\Monojet & \cite{Aad:2015zva} & --- & --- (but monojet stop, see below) \\ \hline
\parbox[t]{3mm}{\multirow{7}{*}{\rotatebox[origin=c]{90}{Third generation}}}
&\ZeroLeptonStop & \cite{Aad:2014bva} & SUSY-2013-16$^{\,*}$ & 1 UL, 1 EM \\
&\OneLeptonStop & \cite{Aad:2014kra} & SUSY-2013-15$^{\,*}$ & 1 UL, 1 EM \\
&\TwoLeptonStop & \cite{Aad:2014qaa} & SUSY-2013-19$^{\,*}$ & 2 UL \\
&\StopMonojet & \cite{Aad:2014nra} & SUSY-2013-21 & 4 EM \\
&\StopZ & \cite{Aad:2014mha} & SUSY-2013-08 & 1 UL \\
&\TwoBjet & \cite{Aad:2013ija} & SUSY-2013-05$^{\,*}$ & 3 UL, 1 EM \\
&\TBmet & \cite{Aad:2015pfx} & SUSY-2014-07 & --- \\ \hline
\parbox[t]{3mm}{\multirow{6}{*}{\rotatebox[origin=c]{90}{Electroweak}}}
&\OneLeptonHiggs & \cite{Aad:2015jqa} & SUSY-2013-23$^{\,*}$ & 1 UL \\
&\TwoLepton & \cite{Aad:2014vma} & SUSY-2013-11 & 4 UL, 4 EM \\
&\TwoTau & \cite{Aad:2014yka} & SUSY-2013-14 & --- \\
&\ThreeLepton & \cite{Aad:2014nua} & SUSY-2013-12 & 5 UL \\
&\FourLepton & \cite{Aad:2014iza} & SUSY-2013-13 & --- \\
&\DisappearingTrack & \cite{Aad:2013yna} & SUSY-2013-01 & n.a.\\ \hline
\parbox[t]{3mm}{\multirow{2}{*}{\rotatebox[origin=c]{90}{Other}}}
&\LLSparticles & \cite{Aad:2012pra,ATLAS:2014fka} & --- & n.a. \\
&\HiggsToTauTau & \cite{Aad:2014vgg} & --- & n.a. \\ \hline
\end{tabular}
\caption{The 22 searches considered in the ATLAS pMSSM study~\cite{Aad:2015baa} and their correspondences in the {\sc SModelS}\,v1.1.1\ database.
A superscript $^*$ with the ID means that in addition {\sc Fastlim} EMs for a preliminary version of the analysis are included, see Table~\ref{tab:FastlimAnalyses}.
The monojet results from \cite{Aad:2015zva} are not implemented in {\sc SModelS}\ because our SMS assumptions do not apply to dark matter simplified models.
The analyses \cite{Aad:2015pfx,Aad:2014yka,Aad:2014iza} do not provide useable SMS interpretations. Finally, searches for new resonances, long-lived particles, and disappearing tracks \cite{Aad:2013yna,Aad:2012pra,ATLAS:2014fka,Aad:2014vgg} currently cannot be treated in the {\sc SModelS}\ framework. }
\label{tab:AtlasSearchesInPaper}
\end{table}
\begin{table}\centering
\begin{tabular}{llcc}
&{\bf Analysis} & {\bf Ref.} & {\bf ID} \\ \hline
\parbox[t]{3mm}{\multirow{4}{*}{\rotatebox[origin=c]{90}{Incl.}}}
& \ZeroLepton & \cite{ATLAS-CONF-2013-047} & ATLAS-CONF-2013-047 \\
& \Multijet & \cite{ATLAS-CONF-2013-054} & ATLAS-CONF-2013-054 \\
& \OneLeptonStrong & \cite{ATLAS-CONF-2013-062} & ATLAS-CONF-2013-062 \\
& \ThreeBjets & \cite{ATLAS-CONF-2013-061} & ATLAS-CONF-2013-061 \\
\hline
\parbox[t]{3mm}{\multirow{4}{*}{\rotatebox[origin=c]{90}{Third gen.}}}
& \ZeroLeptonStop & \cite{ATLAS-CONF-2013-024} & ATLAS-CONF-2013-024 \\
& \OneLeptonStop & \cite{ATLAS-CONF-2013-037} & ATLAS-CONF-2013-037 \\
& \TwoLeptonStop & \cite{ATLAS-CONF-2013-048} & ATLAS-CONF-2013-048 \\
& \TwoBjet & \cite{ATLAS-CONF-2013-053} & ATLAS-CONF-2013-053 \\
\hline
\parbox[t]{3mm}{\rotatebox[origin=c]{90}{EW}}
& \OneLeptonHiggs & \cite{ATLAS-CONF-2013-093} & ATLAS-CONF-2013-093 \\
\hline
\end{tabular}
\caption{Analyses covered by the {\sc Fastlim}~\cite{Papucci:2014rja} EMs converted to the {\sc SModelS}\ format.
For each analysis, {\sc Fastlim}\ considers 24 topologies covering stop-, sbottom- and gluino-pair production
with direct or cascade decays to a higgsino LSP, inspired by the idea of ``natural SUSY''.
As explained in the text, efficiencies with uncertainties $>25\%$ are set to zero, so in practice we use 163 of the {\sc Fastlim}\ EMs.}
\label{tab:FastlimAnalyses}
\end{table}
\begin{table}\centering
\begin{tabular}{llcll}
&{\bf Analysis} & {\bf Ref.} & {\bf ~~ID} & {\bf SModelS database} \\ \hline
\parbox[t]{3mm}{\multirow{9}{*}{\rotatebox[origin=c]{90}{Gluino, Squark}}}
& jets + \ensuremath{E_{T}^{\text{miss}}}, $\alpha_T$ & \cite{Chatrchyan:1527115} & SUS-12-028 & 4 UL \\
& 3(1$b$-)jets + \ensuremath{E_{T}^{\text{miss}}} & \cite{Chatrchyan:1546693} & SUS-12-024 & 2 UL, 3 EM \\
& jet multiplicity + $H_T^{\rm miss}$ & \cite{Chatrchyan:1662652} & SUS-13-012 & 4 UL, 20 EM \\
& $\ge 2$ jets + \ensuremath{E_{T}^{\text{miss}}}, $M_{T2}$ & \cite{Khachatryan:1989788} & SUS-13-019 & 8 UL \\
& $\ge 1b$ + \ensuremath{E_{T}^{\text{miss}}}, Razor & \cite{Khachatryan:1984165} & SUS-13-004 & 5 UL \\
& 1 lepton + $\ge 2b$-jets + \ensuremath{E_{T}^{\text{miss}}} & \cite{CMS-PAS-SUS-13-007} & SUS-13-007 & 3 UL, 2 EM \\
& 2 OS lept. + $\ge$4(2$b$-)jets + \ensuremath{E_{T}^{\text{miss}}} & \cite{CMS-PAS-SUS-13-016} & PAS-SUS-13-016 & 2 UL \\
& 2 SS leptons + $b$-jets + \ensuremath{E_{T}^{\text{miss}}} & \cite{Chatrchyan:1631468} & SUS-13-013 & 4 UL, 2 EM \\
& $b$-jets + 4 $W$s + \ensuremath{E_{T}^{\text{miss}}} & \cite{Khachatryan:1976453} & SUS-14-010 & 2 UL \\
\hline
\parbox[t]{3mm}{\multirow{5}{*}{\rotatebox[origin=c]{90}{Third gen.}}}
&0 lepton + $\ge5$(1$b$-)jets + \ensuremath{E_{T}^{\text{miss}}} & \cite{CMS-PAS-SUS-13-015} & PAS-SUS-13-015 & 2 EM \\
&0 lepton + $\ge6$(1$b$-)jets + \ensuremath{E_{T}^{\text{miss}}} & \cite{CMS-PAS-SUS-13-023} & PAS-SUS-13-023 & 4 UL \\
&1 lepton + $\ge4$(1$b$-)jets + \ensuremath{E_{T}^{\text{miss}}} & \cite{Chatrchyan:1567175} & SUS-13-011 & 4 UL, 2 EM \\
& $b$-jets + \ensuremath{E_{T}^{\text{miss}}} & \cite{CMS-PAS-SUS-13-018} & PAS-SUS-13-018 & 1 UL \\
& soft leptons, few jets + \ensuremath{E_{T}^{\text{miss}}} & \cite{Khachatryan:2117955} & SUS-14-021 & 2 UL \\
\hline
\parbox[t]{3mm}{\rotatebox[origin=c]{90}{EW}}
&multi-leptons + \ensuremath{E_{T}^{\text{miss}}} & \cite{Khachatryan:1704963} & SUS-13-006 & 6 UL \\
\hline
\end{tabular}
\caption{CMS 8~TeV results included in the {\sc SModelS}\,v1.1.1\ database and used in addition to the ATLAS
results in Tables~\ref{tab:AtlasSearchesInPaper} and \ref{tab:FastlimAnalyses}.}
\label{tab:CMSAnalyses}
\end{table}
\clearpage
\section{Exclusion compared to ATLAS}\label{sec:results}
As a first overview of our results, we list in Table~\ref{tab:smodpmssmsum} the total number of points studied,
the number of points that can be excluded by {\sc SModelS}\ ($r_{\rm max}\ge1$) when using only the UL results in the database,
and the number of points that can be excluded when using the full 8~TeV database, that is including EM results.
We see that the coverage of bino-like LSP scenarios can be improved by using EMs,
increasing from 44\% (UL results only) to 55\% (full database).
Similarly, the coverage for the higgsino-like LSP scenarios is improved from 55\% to 63\%.
\begin{table}[h!]
\centering
\begin{tabular}{c | c | c}
& Bino-like LSP & Higgsino-like LSP\\
\hline
Total number of points & 38575 & 45594 \\
\hline
Number of points excluded -- UL results only & 16957 & 25024 \\
\hline
Number of points excuded -- full database & 21151 & 28669
\end{tabular}
\caption{Summary of results, listing the number of ATLAS-excluded pMSSM points tested in this study, the number of points excluded by {\sc SModelS}\ when using UL-type results only,
and the number of points excluded when using the full 8 TeV database including EM-type results.}
\label{tab:smodpmssmsum}
\end{table}
\noindent
The improvement in coverage due to EMs largely happens for light to intermediate gluino masses,
as illustrated in Figure~\ref{fig:pmssmGlu1d}. These scenarios benefit
from the fact that EMs allow us to combine the signal for all topologies contributing to the same signal region before comparing
against an overall cross section limit, hence increasing the constraining power.
Moreover, some asymmetric topologies are included in the EM-type results (from {\sc Fastlim})
but not in the UL-type results in the database.
Figure~\ref{fig:pmssmGlu1d} also shows the importance of the {\sc Fastlim}\ and our `home-grown' EMs with respect to the official ATLAS and CMS SMS results. We note that the {\sc Fastlim}\ maps are particularly relevant for constraining
gluinos in the intermediate mass range decaying to higgsino-like EW-inos, which is typical for the natural SUSY case they have been derived for.
In numbers, official UL and EM results exclude 46\% (56\%) of the bino-LSP (higgsino-LSP) points,
which improves to 50\% (57\%) when adding our `home-grown' EMs, and to the above-mentioned 55\% (63\%) when including in addition {\sc Fastlim}\ results.
In the following, we discuss in some detail why still a large fraction of points escapes exclusion by SMS results and how the coverage could be improved.
\begin{figure}[ht!]\centering
\includegraphics[width=0.5\textwidth]{PaperPlots/glu_1d_histo_Bino_split.png}%
\includegraphics[width=0.5\textwidth]{PaperPlots/glu_1d_histo_Higgsino_split.png}
\caption{Number of points excluded by {\sc SModelS}\ using only UL results (in yellow), adding official EM results (in green), adding `home-grown' EMs (in blue) and finally adding also {\sc Fastlim}\ EMs (in red). For reference the total number of ATLAS-excluded points is also shown (in grey). On the left for bino-like LSP and on the right for higgsino-like LSP.
\label{fig:pmssmGlu1d}}
\end{figure}
\subsection{Gluinos}\label{sec:gluinos}
It is striking that there are many points with light gluinos which cannot be excluded by the SMS results in the {\sc SModelS}\ database.
To understand this better we show in Figure~\ref{fig:pmssmGlu2d} the coverage in the gluino vs.\ neutralino mass plane.
For comparison with the ``naive'' SMS expectation, the exclusion line obtained in~\cite{Aad:2014wea} for a simplified model where
pair-produced gluinos decay exclusively as
$\tilde{g}\rightarrow q q \tilde{\chi}^0_1$ is also drawn in Figure~\ref{fig:pmssmGlu2d}.
We see that light gluinos escape SMS limits especially in the compressed region where monojet-type searches become important. This is in agreement with the
simplified model exclusion line.
Moreover, while the coverage is good for very light gluinos up to about 600~GeV,
it drops for intermediate gluino masses around $1$~TeV and higher,
as can also be observed in Figure~\ref{fig:pmssmGlu1d}.
This is particularly pronounced in the bino-like LSP scenario.
Concretely, the coverage of bino-like LSP scenarios is 80\% when considering only points with light gluinos ($m_{\tilde{g}} < 600$~GeV), but drops
to 60\% when considering all points with $m_{\tilde{g}} < 1400$~GeV.
Similarly the coverage of higgsino-like LSP scenarios drops from 97\% ($m_{\tilde{g}} < 600$~GeV) to 74\% ($m_{\tilde{g}} < 1400$~GeV).
Note that for bino-like LSP scenarios light gluinos are mainly found in the compressed region ($m_{\tilde{g}} - m_{\tilde{\chi}^0_1} < 100$~GeV),
where the bins contain a large number of model points. This is not the case for higgsino-like LSP scenarios.
\begin{figure}[t!]\centering
\includegraphics[width=0.5\textwidth]{PaperPlots/glu_N1_Bino_2d_histo_all.pdf}%
\includegraphics[width=0.5\textwidth]{PaperPlots/glu_N1_Higgsino_2d_histo_all.pdf}
\caption{Coverage in the gluino vs.\ neutralino mass plane, for gluino masses up to $2$~TeV, for bino-like LSP scenarios (left) and higgsino-like LSP scenarios (right).
The color code indicates the fraction of points excluded by {\sc SModelS}, the
text gives the total number of points tested in each bin.
For comparison, the 95\%~CL exclusion line for the $\tilde{g}\rightarrow q q \tilde{\chi}^0_1$ simplified model from~\cite{Aad:2014wea} is drawn in black.
\label{fig:pmssmGlu2d}}
\end{figure}
The somewhat better coverage of non-compressed sub-TeV gluinos in the higgsino-like LSP set can be understood as follows.
In the case of a bino-like LSP, unless the gluino-LSP mass difference is small,
direct decays into the LSP often have only 30\% or less branching ratio.
Decays into wino- or higgsino-like states are often more important,
leading to cascade decays into the LSP and to asymmetric branches with different final states and, possibly, different intermediate masses.%
\footnote{Asymmetric branches can occur from pair production when the two initially produced SUSY particles undergo different decays, or from associated production of two different SUSY particles.}
This reduces the fraction of gluino signatures covered by SMS results, and as the total cross section reduces with increasing gluino mass,
the fraction that can be constrained is no longer large enough to exclude the point.
For higgsino-like LSP scenarios, on the other hand,
the second neutralino $\tilde{\chi}_2^0$ as well as the lighter chargino $\tilde{\chi}_1^{\pm}$ are
nearly degenerate with the LSP, and their decay can often be mass compressed in {\sc SModelS}.
In this case, contributions from $\tilde g\to qq'\tilde\chi^\pm_1$, $qq\tilde\chi^0_2$ and $qq\tilde\chi^0_1$ can be summed up,
which explains the better coverage of light gluinos in the higgsino-LSP case already by UL results seen in Figure~\ref{fig:pmssmGlu1d}.
Moreover, gluino decays into third generation are often dominant in the higgsino-LSP case, leading to a mix of final states ($4b$, $4t$, $2b2t$, $3b1t$, $1b3t$) which can in part be covered by the {\sc Fastlim}\ EMs.
\begin{figure}[t!]\centering
\includegraphics[width=0.5\textwidth]{PaperPlots/Rmax_allowed_glu_N1_BinoLSP.png}%
\includegraphics[width=0.5\textwidth]{PaperPlots/Rmax_allowed_glu_N1_HiggsinoLSP.png}
\caption{Maximum $r$ value reported by {\sc SModelS}\ for allowed points, for gluino masses up to $2$~TeV, for bino-like LSP scenarios (left) and higgsino-like LSP scenarios (right). Points are sorted from low to high $r$-values, with the highest values of $r$ shown on top.
\label{fig:pmssmGluRval}}
\end{figure}
Another important consideration is how far the points which escape the {\sc SModelS}\ exclusion are from becoming excluded.
Uncertainties inherent to the {\sc SModelS}\ approach and the fact that we used LO cross-sections
for EW process (while ATLAS used NLO values) can reduce the
exclusion reach.
In Figure~\ref{fig:pmssmGluRval} we show the maximum $r$ values found for points escaping exclusion by {\sc SModelS}.
We see that many points, especially in the region of intermediate gluino masses and in the more compressed region, are in fact
close to the exclusion limit.
We therefore expect that the coverage can be considerably improved by adding additional EMs, thus allowing to
test a larger fraction of the total cross section.
Furthermore, we find that 10\% of bino-like LSP scenarios and 12\% of higgsino-like LSP scenarios have $0.8<r_{\rm max}<1.2$,
which allows a rough estimate of the uncertainties involved in the exclusion.
(The overall systematic uncertainty is estimated to be of the level of 20\%~\cite{Ambrogi:2017neo}.)
In turn, we find $r_{\rm max}>1.2$ for 50\% of bino-like LSP and 58\% of higgsino-like LSP scenarios.
\begin{figure}[t!]\centering
\includegraphics[width=0.5\textwidth]{PaperPlots/glu_N1_allAsym_rel_BinoLSP.png}%
\includegraphics[width=0.5\textwidth]{PaperPlots/glu_N1_allLongC_rel_BinoLSP.png}
\caption{Relative cross section in unconstrained decays with asymmetric branches (left) and long cascade decays (right), for scenarios with a
bino-like LSP. Here the total cross section $\sigma_{tot}$ refers to the full $8$~TeV SUSY cross section.
Only {\sc SModelS}-allowed points with total cross section larger than $10$~fb are considered.
\label{fig:pmssmBinoAsym}}
\end{figure}
\begin{figure}[t!]\centering
\includegraphics[width=0.5\textwidth]{PaperPlots/glu_N1_allAsym_rel_HiggsinoLSP.png}%
\includegraphics[width=0.5\textwidth]{PaperPlots/glu_N1_allLongC_rel_HiggsinoLSP.png}
\caption{Same as Figure~\ref{fig:pmssmBinoAsym} but for points with a higgsino-like LSP.
\label{fig:pmssmHiggsinoAsym}}
\end{figure}
To understand the possibilities of further improving the coverage, without going into details
about the specific missing topologies,\footnote{In {\sc SModelS}, ``missing topologies'' are defined as topologies for which no experimental result is available in the database.} we show in Figures~\ref{fig:pmssmBinoAsym} and \ref{fig:pmssmHiggsinoAsym}
the relative cross sections of {\sc SModelS}-allowed\footnote{We define ``{\sc SModelS}-allowed'' as ``excluded by ATLAS but not excluded by {\sc SModelS}''.}
points which go into missing topologies with asymmetric branches (left) or long cascade decays (right), for
bino-like LSP scenarios and higgsino-like LSP scenarios respectively.
In this classification, asymmetric branch topologies have at most one intermediate odd particle in each
branch, so that the number of new particles and mass parameters still is sufficiently small for a viable SMS interpretation.
On the other hand, as long cascade decays we define decay chains with two or more intermediate odd particles
and we no longer consider a simplified model description viable.
We see that in fact topologies with asymmetric decay branches are important for a large number of points for both bino- and higgsino-like LSP scenarios,
whereas long cascade decay topologies are dominant only in a few cases.
Therefore inclusion of additional asymmetric topologies should have a significant impact on the SMS coverage.
A particularly important missing topology with asymmetric branches arises from gluino-squark associate production, giving
a 3~jets + $E_T^{\rm miss}$ final state. This is important in particular when the light-flavor squarks are highly split and the gluino can
decay to a single on-shell squark.
The relevant process is $pp\to \tilde g\tilde q$ followed by $\tilde q\to q\tilde\chi^0_1$ on one branch and $\tilde g\to q\tilde q\to q\bar q \tilde\chi^0_1$ on the other branch
The same topology is also possible when gluinos are lighter than all squarks and decay dominantly via a loop decay to a gluon and the neutralino LSP.
In this case we have $pp\to \tilde g\tilde q$ followed by $\tilde g\to g\tilde\chi^0_1$ on one branch and $\tilde q\to q\tilde g\to qg \tilde\chi^0_1$ on the other.
Figure~\ref{fig:pmssmGluSq} shows the cross section of this
topology in the plane of gluinos mass versus mass of the lightest squark.
Note that searches for gluino-squark production are typically interpreted either in a simplified model where gluinos and squarks are (nearly) mass-degenerate, or in a minimal gluino-squark model where all production processes---gluino pairs, squark pairs, and gluino-squark associated production---are combined~\cite{Aad:2014wea}.
Such results cannot be used for reinterpretation in generic scenarios where typically the gluino mass differs from the squark masses, and
where the relative importance of the various production and decay channels will be different from the minimal gluino-squark model description.
\begin{figure}[t!]\centering
\includegraphics[width=0.5\textwidth]{PaperPlots/glu_squark_sigGluSq_BinoLSP.png}%
\includegraphics[width=0.5\textwidth]{PaperPlots/glu_squark_sigGluSq_HiggsinoLSP.png}
\caption{Cross section for the $\tilde g\tilde q\to 3$~jets + $E_T^{\rm miss}$ missing topology in the gluino vs.\ squark mass plane, for bino-like LSP (left) and higgsino-like
LSP (right). Only {\sc SModelS}-allowed points are considered.
\label{fig:pmssmGluSq}}
\end{figure}
The importance of the
3~jets + $E_T^{\rm miss}$ topology is corroborated in Figure~\ref{fig:GluMissingTopo}, which shows
the five most important missing topologies for points with light gluinos below $1.5$~TeV.%
\footnote{For this classification, we first select for each allowed point the missing topology with the highest cross section. These are then
sorted by frequency of occurrence in the mass range considered.}
The leading missing topology for both the bino- and the higgsino-LSP datasets is indeed 3~jets + $E_T^{\rm miss}$ from gluino-squark associated production as discussed above, see the yellow points in Figure~\ref{fig:GluMissingTopo} which cover a wide range of gluino and LSP masses.
Gluino-squark associated production also leads to the 5~jets + $E_T^{\rm miss}$ missing topology; in this case all squarks are heavier than the gluino and decay via $\tilde q\to q\tilde g$, and the gluino then decays further to two jets and the $\tilde\chi^0_1$. This is the dominant missing topology for compressed gluino and neutralino masses in the bino-like LSP case, see the blue points in the left panel of Figure~\ref{fig:GluMissingTopo}.
When compressing the gluino and LSP masses even further, such that the gluino decay is not visible any more, this gives jet + $E_T^{\rm miss}$ (dark green points), which is however a rather fine-tuned situation in the pMSSM and thus occurs much less often.
\begin{figure}[t!]\centering
\includegraphics[width=0.5\textwidth]{PaperPlots/MissingTopo_noMET_glu_N1_BinoLSP.png}%
\includegraphics[width=0.5\textwidth]{PaperPlots/MissingTopo_noMET_glu_N1_HiggsinoLSP.png}
\caption{Most important missing topologies for {\sc SModelS}-allowed points with light gluinos.
The legend lists, from top to bottom, the missing topologies with highest cross sections ordered by their by frequency of occurrence (points in color).
The relevant diagrams, SUSY processes and labelling in {\sc SModelS}\ notation are given in Appendix~\ref{sec:missingtopotable}.
\label{fig:GluMissingTopo}}
\end{figure}
Also noteworthy are the orange points, which denote an asymmetric 2~jets + $E_T^{\rm miss}$ topology
with the two jets on one branch and nothing on the other branch.
This can come from $\tilde\chi^0_1\tilde\chi^0_{i\not=1}$, $\tilde\chi^0_1\tilde\chi^\pm_{1,2}$ or
$\tilde\chi^0_1\tilde g$ associated production.
While EW-ino and $\tilde\chi^0_1\tilde g$ production can have comparable cross sections, the latter process is often disregarded.
(The same topology can also arise from gluino-squark associated production when $\tilde g\to q\bar q\tilde\chi^0_1$ and the $\tilde q$
decay is ``invisible'' because of mass compression with the LSP.)
Other topologies like $2b2t$+jet+$E_T^{\rm miss}$ (from $pp\to \tilde g\tilde q$, $\tilde q\to q\tilde g$, $\tilde g\to tb\chi^+_1$ in the higgsino-LSP case)
or long cascades with $4b$+jet+$E_T^{\rm miss}$ or 3~jets+$2W$+$E_T^{\rm miss}$ also show up in Figure~\ref{fig:GluMissingTopo}, but are much less often
the missing topology with highest cross section.
The corresponding diagrams, SUSY processes and labelling in {\sc SModelS}\ notation can be found in Appendix~A.
We note that all these missing topologies could be constrained from the
${\rm jets}+\ensuremath{E_{T}^{\text{miss}}}$ searches, if the appropriate SMS interpretations were available.
For instance, a limit of 40, 20, 10~fb on the 3~jets + $E_T^{\rm miss}$ missing topology cross section would exclude additional 4846, 5799, 6599
(1377, 1948, 2637) points of the bino-like (higgsino-like) LSP dataset.
We have explicitly checked a couple of representative {\sc SModelS}-allowed points with a high 3~jets + $E_T^{\rm miss}$ cross section and verified that
including the efficiencies for the relevant gluino-squark simplified model would indeed exclude these points. A specific example is provided
in Appendix~B.
\subsection{Third generation}
Apart from gluinos and squarks, which may be regarded as the primary (and easiest) targets of the SUSY searches,
searches for stops and sbottoms are of particular interest. The coverage obtained by {\sc SModelS}\ in the
stop vs.\ neutralino and sbottom vs.\ neutralino mass planes is shown in Figures~\ref{fig:stop-n1-2d} and \ref{fig:sbot-n1-2d}.
We also show the official exclusion curves for the $\tilde t_1\to t\tilde\chi^0_1$ and $\tilde b_1\to b\tilde\chi^0_1$ simplified models
from~\cite{Aad:2014bva,Aad:2014kra,Aad:2013ija}, to help identify the region expected to be excluded by stop or sbottom production only.
\begin{figure}[ht!]\centering
\includegraphics[width=0.5\textwidth]{PaperPlots/st1_N1_Bino_2d_histo_all.pdf}%
\includegraphics[width=0.5\textwidth]{PaperPlots/st1_N1_Higgsino_2d_histo_all.pdf}
\caption{Coverage in the stop vs.\ neutralino mass plane, for $\tilde t_1$ masses up to 800~GeV,
for bino-like LSP scenarios (left) and higgsino-like LSP scenarios (right).
The color code indicates the fraction of points excluded by {\sc SModelS}\ as compared to ATLAS,
while the text gives the total number of points tested in each bin.
For comparison, the black lines are the 95\%~CL exclusion curves for the $\tilde t_1\to t\tilde\chi^0_1$ simplified model
from~\cite{Aad:2014bva} (0-lepton mode, full line) and \cite{Aad:2014kra} (1-lepton mode, dashed line).
\label{fig:stop-n1-2d}}
\end{figure}
\begin{figure}[t!]\centering
\includegraphics[width=0.5\textwidth]{PaperPlots/sb1_N1_Bino_2d_histo_all.pdf}%
\includegraphics[width=0.5\textwidth]{PaperPlots/sb1_N1_Higgsino_2d_histo_all.pdf}
\caption{Coverage in the sbottom vs.\ neutralino mass plane, for $\tilde b_1$ masses up to 800~GeV,
for bino-like LSP scenarios (left) and higgsino-like LSP scenarios (right).
The color code indicates the fraction of points excluded by {\sc SModelS}\ as compared to ATLAS,
while the text gives the total number of points tested in each bin.
The black line is the 95\%~CL exclusion line for the $\tilde b_1\to b\tilde\chi^0_1$ simplified model from~\cite{Aad:2013ija}.
\label{fig:sbot-n1-2d}}
\end{figure}
For stops, we observe an excellent coverage in the higgsino-LSP case when compared to
the official exclusion curves. (A slightly stronger exclusion is obtained by the combination of the 0-lepton and 1-lepton analyses~\cite{Aad:2015pfx}, but no UL maps are available for the combination.)
Contrary to the gluino case, the stop exclusion is not driven by EM results but by the UL maps for $t\bar t+\ensuremath{E_{T}^{\text{miss}}}$ and $b\bar b+\ensuremath{E_{T}^{\text{miss}}}$ final states (mostly because not so many different EMs are available for stops and sbottoms).
Points outside the naive SMS exclusion line are excluded by other searches or because of light sbottoms which also contribute to the signal.
In the bino-LSP case, on the other hand, light stops in the 500--650~GeV mass range often escape exclusion by SMS results. This is mostly
because they share out their branching ratios in $\tilde t_1\to t\tilde\chi^0_2\to tZ\tilde\chi^0_1$ and $\tilde t_1\to b\tilde\chi^+_1\to bW\tilde\chi^0_1$
cascade decays. While we do have EMs for a so-called T6bbWW simplified model, {\it i.e.}\ a $2b2W+\ensuremath{E_{T}^{\text{miss}}}$ final state originating from both stops decaying via an intermediate chargino, the equivalent topologies for one or both stops decaying via an intermediate neutralino ({\it e.g.}, $tbWZ+\ensuremath{E_{T}^{\text{miss}}}$ and $2t2Z+\ensuremath{E_{T}^{\text{miss}}}$ final states) are missing. Including EMs for these topologies for a variety of intermediate $\tilde\chi^0_2$ and $\tilde\chi^\pm_1$ masses would certainly allow us to get closer to the ATLAS exclusion.\footnote{Note that for cascade decays via an intermediate sparticle, it is important to have several mass planes in order to be able to interpolate in all dimensions of the SMS; see also Appendix~C of \cite{Ambrogi:2017neo}.}
Notice, however, that for light stops we are dealing with small numbers of points in each bin, so large fluctuations in the coverage are easily possible.
The importance of $\tilde t_1\to t\tilde\chi^0_{i\not=1}$ decays, followed by visible $\tilde\chi^0_{i\not=1}$ decays, for {\sc SModelS}-allowed points is illustrated in the left plot in Figure~\ref{fig:stop-sbot-branchings}.
\begin{figure}[t!]\centering
\includegraphics[width=0.5\textwidth]{PaperPlots/st1_N1_st1br_anyLSP_allowedPoints}%
\includegraphics[width=0.5\textwidth]{PaperPlots/sb1_N1_sb1br_anyLSP_allowedPoints.png}
\caption{Branching ratios of stop (left) and sbottom (right) decays into heavier neutralino mass eigenstates for {\sc SModelS}-allowed points, leading to signatures for which no SMS results are currently available ($m_{\tilde\chi^0_{i\not=1}}\!\!-m_{\tilde\chi^0_1}\ge5$~GeV). Here, bino- and higgsino-like LSP scenarios are combined. Grey points have ${\rm{BR}}<10\%$ for the decays considered. The black lines are the 95\%~CL exclusion lines for the $\tilde t_1\to t\tilde\chi^0_1$ simplified model from~\cite{Aad:2014kra} (left) and the $\tilde b_1\to b\tilde\chi^0_1$ simplified model from~\cite{Aad:2013ija} (right). See text for details.
\label{fig:stop-sbot-branchings}}
\end{figure}
Turning to sbottoms, we see that the coverage is quite good for
$m_{\tilde b_1}\lesssim 450$~GeV and $m_{\tilde\chi^0_1}\lesssim 250$~GeV.
For these mass ranges, $\tilde b_1\to b\tilde\chi^0_1$ (and/or $\tilde b_1\to t\tilde\chi^-_1$ in the higgsino-LSP case) decays dominate.
Once a larger variety of decay channels becomes relevant, the exclusion drops to about 50\% of that of ATLAS.
While results for $\tilde b_1\to t\tilde\chi^-_1\to tW\tilde\chi^0_1$ are available from ATLAS~\cite{ATLAS-CONF-2013-007} and CMS~\cite{Chatrchyan:1631468},\footnote{We appreciate the fact that these are given for 3 different chargino masses.}
these are ULs for a same-sign lepton signature assuming both sbottoms decay via a chargino; they have a reach in sbottom mass of at most 500--550~GeV.
It would be useful to have in addition simplified model results for $\tilde b_1\to b\tilde\chi^0_{i\not=1}\to bZ\tilde\chi^0_1$ or $bh\tilde\chi^0_1$, best in the form of EMs for symmetric and asymmetric decay branches. The importance of these decay modes for {\sc SModelS}-allowed points is illustrated in the right plot in Figure~\ref{fig:stop-sbot-branchings}.
It is relevant to stress that the branching ratios shown in Figure~\ref{fig:stop-sbot-branchings} only
consider {\it visible} decays.
In particular the higgsino-like LSP dataset contains many points where sbottom branching ratios are shared out in $\tilde b \to b\tilde\chi^0_{i\not=1}$ and $t\tilde\chi^-$ decays (contributing to the reduced coverage for $m_{\tilde b_1}\gtrsim 500$~GeV seen in Figure~\ref{fig:sbot-n1-2d}) but the subsequent EW-ino decays are invisible because of mass compression.
This leads to the patch of grey points just below the exclusion curve in the right plot of Figure~\ref{fig:stop-sbot-branchings}. Regardless of this, the conclusion from Figure~\ref{fig:stop-sbot-branchings} is that EM results for stops and sbottoms decaying through an intermediate particle (leading to final states with additional $W$, $Z$ or $h$ bosons) would be highly desirable.
\subsection{EW production}
It is also interesting to study how well EW production is covered by simplified models.
To this end, we first show in Figure~\ref{fig:charg-neut-2d-all} the coverage in the chargino vs.\ neutralino LSP mass plane.
Here, the bino-like and higgsino-like LSP scenarios have been combined to increase the number of points.
In the plot on the left, light charginos seem to be reasonably well constrained. However, this does not come
from searches looking specifically for EW production, as is apparent from the plot on the right.
The fact that the coverage does not follow the SMS exclusion curve is no surprise, as the latter was
obtained for the best-case scenario of pure wino production. However, from the color code we see that the
constraining power of EW searches is very poorly reproduced by SMS results. One of the reasons is that
the SMS results typically assume strictly mass-degenerate $\tilde\chi^\pm_1$ and $\tilde\chi^0_2$, a condition which is
rarely satisfied in the pMSSM. Moreover, BR($\tilde\chi^0_{i\not=1}\to h\tilde\chi^0_1$) is often sizeable,
which further reduces the coverage. (The SMS limit in the $Wh+\ensuremath{E_{T}^{\text{miss}}}$ final state is effective only for very light LSP below 40 GeV and cannot be combined with the limit on the $WZ+\ensuremath{E_{T}^{\text{miss}}}$ final state.)
Finally, the 3 or 4 lepton searches in ATLAS do not have a jet veto; therefore in the ATLAS pMSSM study strong production may also feed into the EW exclusion, which is not the case in {\sc SModelS}\ for lack of the corresponding SMS results.
\begin{figure}[t!]\centering
\includegraphics[width=0.5\textwidth]{PaperPlots/C1_N1_any_2d_histo_all.pdf}%
\includegraphics[width=0.5\textwidth]{PaperPlots/C1_N1_any_2d_histo_all_EW.pdf}
\caption{Coverage in the chargino vs.\ neutralino mass plane, for $\tilde\chi^\pm_1$ masses up to 700~GeV.
Here, bino-like and higgsino-like LSP scenarios have been combined to increase the number of points.
The plot on the left considers all analyses, the plot on the right only EW analyses.
The color code indicates the fraction of points excluded by {\sc SModelS}\ as compared to ATLAS,
while the text gives the total number of points tested in each bin.
For comparison, the exclusion line from the \ThreeLepton\ analysis~\cite{Aad:2014nua} is shown in red
and from the combination paper~\cite{Aad:2015eda} is drawn in black.
\label{fig:charg-neut-2d-all}}
\end{figure}
\begin{figure}[t!]\centering
\includegraphics[width=0.5\textwidth]{PaperPlots/slep_N1_any_2d_histo_all.pdf}%
\includegraphics[width=0.5\textwidth]{PaperPlots/slep_N1_any_2d_histo_all_EW.pdf}
\caption{Coverage in the plane of lightest slepton (first two generations) vs.\ LSP mass, for $\tilde l$ masses up to 700~GeV.
Here, bino-like and higgsino-like LSP scenarios have been combined to increase the number of points.
The plot on the left considers all analyses, the plot on the right only EW analyses.
The color code indicates the fraction of points excluded by {\sc SModelS}\ as compared to ATLAS,
while the text gives the total number of points tested in each bin.
The exclusion lines for $\tilde l_R$ (red) and $\tilde l_L$ (black) are also shown for comparison.
\label{fig:slep-neut-2d}}
\end{figure}
In Figure~\ref{fig:slep-neut-2d} we show the same kind of plots for sleptons.
Here, the coverage is quite good and reproduces reasonably well the SMS exclusion line for right sleptons.
The exclusion line for left sleptons is naturally matched less well, because pMSSM points contain a mix of light left and right sleptons.
Finally, a small fraction of points with $min(m_{\tilde l})=250$--$300$~GeV and light LSP escape exclusion in {\sc SModelS}\ because the sleptons
partly undergo cascade decays via heavier EW-inos. Even if the direct decay into the LSP still dominates, the reduction in BR
can be enough to result in $r<1$.
Last but not least we recall that EW cross sections are computed at leading order in {\sc SModelS}.
Radiative corrections typically increase these cross sections by about 20\%, which slightly improves the coverage of the EW sector
but does not change the overall picture. This is illustrated in Figure~\ref{fig:EW-2d-rescaled}, which shows the coverage of EW-inos and sleptons by EW analyses when rescaling the relevant $r$ values by 20\%.
\begin{figure}[t!]\centering
\includegraphics[width=0.5\textwidth]{PaperPlots/C1_N1_any_2d_histo_all_EW_r08.pdf}%
\includegraphics[width=0.5\textwidth]{PaperPlots/slep_N1_any_2d_histo_all_EW_r08.pdf}
\caption{Coverage of EW-inos and sleptons by EW analyses analogous to the right plots of Figures~\ref{fig:charg-neut-2d-all}
and \ref{fig:slep-neut-2d} but considering points with $r_{\rm max}>0.8$ (instead of $r_{\rm max}>1$) as excluded.
\label{fig:EW-2d-rescaled}}
\end{figure}
\section{Conclusions}\label{sec:conclusions}
We studied to which extent the SUSY search results published by ATLAS and CMS in the context of SMS constraints
actually cover the more realistic scenarios of a full model, concretely the phenomenological MSSM.
To this end we analysed the exclusion obtained with {\sc SModelS}~\cite{Ambrogi:2017neo,Kraml:2013mwa} with respect to the
ATLAS pMSSM study~\cite{Aad:2015baa}. From about 84K pMSSM points excluded by ATLAS, the 8~TeV results in {\sc SModelS}\,v1.1.1\
exclude about 50K points.
Efficiency maps proved to be important for constraining scenarios with a variety of
production and/or decay modes, because they allow to combine different contributions to the same signal region.
Nonetheless, despite the plethora of SMS results available, about 40\% of the points excluded by ATLAS are not excluded by {\sc SModelS}.
These ``escaping'' points include gluinos as light as about 500~GeV, but also light stops/sbottoms or EW-inos with reasonably large cross sections.
We analysed the reasons for this limited coverage and how it might be improved.
Concretely, we found that a large part of the unconstrained cross section goes into simple but asymmetric topologies,
either because pair-produced sparticles have two or more relevant decay modes, or because of associated production
of two different sparticles. A particularly important case, for which no SMS results are currently available, is a 3-jet topology
stemming from gluino--squark associated production with non-degenerate squarks: $pp\to \tilde g\tilde q$ followed by
$\tilde g\to q\tilde q\to q\bar q \tilde\chi^0_1$ and $\tilde q\to q\tilde\chi^0_1$ when one of the squarks is lighter than the gluino,
or $\tilde g\to g\tilde\chi^0_1$ and $\tilde q\to q\tilde g\to qg \tilde\chi^0_1$ otherwise. For one third of the bino-like LSP points which
are excluded by ATLAS but not by {\sc SModelS}, this topology has a cross section $>20$~fb.
For the case that the produced SUSY particles share out their branching ratios over several different decay modes,
which need to be combined to obtain a good limit, we highlighted the example of stop and sbottom decays via heavier EW-inos,
which in turn decay visibly into the LSP.
While SMS results for stop-pair production with both stops decaying via an intermediate chargino exist, analogous results considering also
$\tilde t_1\to t\tilde\chi^0_2\to tZ\tilde\chi^0_1$, $\tilde b_1\to b\tilde\chi^0_2\to bZ\tilde\chi^0_1$ or $\tilde b_1\to t\tilde\chi^-_1\to tW\tilde\chi^0_1$
decays are missing. Efficiency maps for these cases would be highly desirable to improve the coverage of the third generation.
Regarding the EW SUSY sector, the coverage of light sleptons by SMS results is quite good. For EW-inos, however, the situation is less satisfying.
This might be improved if EMs were available for the EW-ino searches in multi-lepton channels instead of only UL-type results. Moreover, for multi-lepton
searches without jet veto, EM results applicable also to EW-inos stemming from strong production would be interesting.
The coverage in {\sc SModelS}\ may also be limited when the initially produced SUSY particles undergo a series of cascade decays
leading to long decay chains with more than one intermediate sparticles. This situation is difficult to cover by simplified models,
since it involves a large number of free parameters.
Interestingly, we find that only a small fraction of the points which escape exclusion by {\sc SModelS}\ fall into this class.
In this view it is much more useful to improve the constraining power of simple SMS (with few parameters) by providing, {\it e.g.},
additional efficiency maps and sufficient mass-vs-mass planes for a reliable interpolation in all mass dimensions,
than to present results for more complicated topologies.
Although complicated topologies (decay chains with more than 3 mass parameters) have been considered by the experimental collaborations,
these results always assume very specific mass relations to limit the number of free parameters and hence cannot be used for generic scenarios.
Overall, the SMS approach provides a powerful means to quickly test the predictions of new physics models against the constraints from a large variety of experimental searches.
However, not excluded by SMS results does not automatically mean allowed by all LHC searches; it is advisable to further test ``surviving" points with Monte Carlo event simulation, if they have sizeable cross sections. Implementations of ATLAS and CMS analyses in public recasting tools like
{\sc CheckMATE}~\cite{Drees:2013wra,Dercks:2016npn}, {\sc MadAnalysis}\,5~\cite{Conte:2014zja,Dumont:2014tja}, {\sc Rivet}~\cite{Buckley:2010ar} (v2.5 onwards) and {\sc GAMBIT}'s ColliderBit~\cite{Athron:2017ard,Balazs:2017moi} can be used to this end.
Finally, these tools may also be used to produce additional SMS results beyond those provided by the experimental collaborations.
\section*{Acknowledgements}
We thank the ATLAS and CMS SUSY groups for providing a plethora of SMS cross section upper limits and efficiency
maps in digital format. Moreover, we are particularly grateful for the detailed material on the ATLAS pMSSM study
available on HepDATA, which made the analysis presented in this paper possible.
This research was supported in part by the ANR project DMASTROLHC grant no.\ ANR-12-BS05-0006,
the IN2P3 project ``Th\'eorie -- LHCiTools'' and the CNRS-FAPESP collaboration PRC275431.
F.A.\ is supported by the Austrian FWF, project P26896-N27,
Su.K.\ by the ``New Frontiers'' program of the Austrian Academy of
Sciences, U.L.\ by the ``Investissements d'avenir, Labex ENIGMASS'', and
A.L.\ by the S\~ao Paulo Research Foundation (FAPESP), projects 2015/20570-1 and 2016/50338-6.
\clearpage
\begin{appendix}
\section{Diagrams and processes for missing topologies}
\label{sec:missingtopotable}
Here we show the explicit diagrams, SUSY processes and labelling in {\sc SModelS}\ notation for the missing
topologies of Figure~\ref{fig:GluMissingTopo}. \\[4mm]
\noindent
\begin{tabular}{ m{5cm} m{6cm} m{1cm} m{5cm}} \hline
\mbox{Short label in Fig.~\ref{fig:GluMissingTopo}}, \mbox{{\sc SModelS}\ notation} & main SUSY process(es) \hfill & & graph \\ \hline
\mbox{3~jets + $E_T^{\rm miss}$}, \mbox{[[[jet]],\,[[jet],[jet]]]} &
\mbox{$\tilde g\tilde q$, $\tilde g\to q\tilde q$, $\tilde q\to q\tilde\chi^0_1$; or} \hfill
\mbox{$\tilde g\tilde q$, $\tilde q\to q\tilde g$, $\tilde g\to g\tilde\chi^0_1$} & &
\includegraphics[width=3cm]{PaperPlots/q_qq.png} \\[5mm]
\mbox{5~jets + $E_T^{\rm miss}$}, \mbox{[[[jet],[jet,jet]],\,[[jet,jet]]]} &
$\tilde g\tilde q$, $\tilde q\to q\tilde g$, $\tilde g\to q\bar q\tilde\chi^0_1$ & &
\includegraphics[width=3cm]{PaperPlots/qqq_qq.png} \\[5mm]
\mbox{$2b2t$ + jet + $E_T^{\rm miss}$}, \mbox{[[[b,t]],[[jet],[b,t]]]} &
$\tilde g\tilde q$, $\tilde q\to q\tilde g$, $\tilde g\to bt\tilde\chi^0_1$ & &
\includegraphics[width=3cm]{PaperPlots/bt_qbt.png} \\[5mm]
\mbox{jet + $E_T^{\rm miss}$}, \hphantom{bla bla bla} \mbox{[[[],[[jet]]]} &
$\tilde g\tilde q$, $\tilde q\to q\tilde g$, ($\tilde g\to q\bar q \chi^0_1$ or $g \chi^0_1$ being invisible) & &
\includegraphics[width=2.6cm]{PaperPlots/_q.png} \\[5mm]
\mbox{2~jets + $E_T^{\rm miss}$}, \hphantom{bla bla bla} \mbox{[[[],[[jet,jet]]]} &
$\tilde\chi^0_1\tilde\chi^0_{i\not=1}$, $\tilde\chi^0_1\tilde\chi^\pm_{1,2}$,
$\tilde\chi^0_1\tilde g$ production followed by decay to $q\bar q\tilde\chi^0_1$; or
\mbox{$\tilde g\tilde q$ production} for compressed squark and LSP & &
\includegraphics[width=2.6cm]{PaperPlots/_qq.png} \\[5mm]
\end{tabular}
\noindent
\begin{tabular}{ m{5cm} m{6cm} m{1cm} m{5cm}}
\mbox{$4b$ + jet + $E_T^{\rm miss}$}, \mbox{[[[b],[b]],\,[[jet],[b],[b]]]} &
$\tilde g\tilde q$, $\tilde q\to q\tilde g$, $\tilde g\to b \tilde b \to b\bar b\tilde\chi^0_1$ & &
\includegraphics[width=3cm]{PaperPlots/bb_qbb.png} \\[5mm]
\mbox{4~jets + $E_T^{\rm miss}$}, \mbox{[[[jet]],\,[[jet],[jet,jet]]]} &
$\tilde g\tilde q$, $\tilde q\to q\tilde g$, $\tilde g\to q\bar q \tilde\chi^0_1$ or $g\tilde\chi^0_1$ with comparable BR's; or
$\tilde q \tilde q$, $\tilde q\to q \tilde\chi^0_1$ or $\tilde q\to q \tilde\chi^0_i / \tilde\chi^{\pm}_j, i \neq 1$ with comparable BR's
& &
\includegraphics[width=3cm]{PaperPlots/q_qqq.png} \\[5mm]
\mbox{3~jets + $2W$ + $E_T^{\rm miss}$}, \mbox{[[[jet],[W]],\,[[jet],[jet],[W]]]} &
$\tilde g\tilde q$, $\tilde g\to q\tilde q$, $\tilde q\to q'\tilde\chi^\pm_1 \to q'W\tilde\chi^0_1$ & &
\includegraphics[width=3cm]{PaperPlots/qW_qqW.png} \\[5mm]
\end{tabular}
\section{Example for the impact of a 3~jets + $E_T^{\rm miss}$ simplified model}
\label{sec:missingtopoexample}
In order to illustrate the importance of asymmetric topologies, we analyse here in more detail
one of the ATLAS-excluded points with a light gluino which has not been excluded by the SMS results.
The pMSSM point we consider is no.~192342466 of the bino-LSP dataset; it has light gluinos and a highly split spectrum of squarks
with light $\tilde q_L^{}$. Concretely,
\begin{equation*}
m_{\tilde{\chi}_1^0} = 666,~m_{\tilde g} = 712,~m_{\tilde u_L} = 758,~m_{\tilde d_L} = m_{\tilde s_L} = 761,~m_{\tilde d_R} = 1343,~m_{\tilde u_R} = 3968,
\end{equation*}
where all values are in GeV.
Stops and sbottoms are heavy with $m_{\tilde t_1,\tilde b_1}\approx 1.4$~TeV and $m_{\tilde t_2,\tilde b_2}\approx 3.3$~TeV.
The wino- and higgsino-like EW-inos have masses around $3.5$~TeV.
In the following we only consider production of gluinos and the squarks
$\tilde u_L,~\tilde d_L,~\tilde s_L,~\tilde d_R$, since this corresponds
to $\simeq 95\%$ of the total SUSY cross section for this point.
For simplicity we will refer to the associated and pair
production of these squarks as $\tilde g \tilde q$ and $\tilde q \tilde q$.
The NLO+NLL cross section for gluino-pair production is 322~fb, while the $\tilde g\tilde q$ production cross section is 762~fb.
The dominant gluino and squark decays are $\tilde g\to g + \tilde \chi^0_1$ (88\% BR) and $\tilde q^{}\to q\tilde g$ (99\% BR).
As a result, a large fraction of the signal goes to the 3~jets + $E_T^{\rm miss}$ final state discussed as missing topology in Section~3.1.
According to the ATLAS pMSSM study, this point is excluded by the \ZeroLepton\ search \cite{Aad:2014wea} (ATLAS-SUSY-2013-02).
This is also the analysis which gives the highest $r$ value in {\sc SModelS},
namely $r = 0.36$ for the $\tilde g \tilde g \to$ 2~jets + $E_T^{\rm miss}$ topology.
Hence this point is clearly not excluded by the SMS results.
In oder to investigate how specific topologies contribute to the
total signal yield and to the exclusion of this point,
we used the {\sc CheckMATE\,2} (v2.0.14) implementation of this analysis along with Pythia\,8.230 and Delphes\,3.4.1 for event generation and detector simulation.
We generated signal events at leading order for associated and pair production of $\tilde g$, $\tilde u_L$, $\tilde d_L$, $\tilde s_L$ and $\tilde d_R$ and then rescaled
the cross sections using the K-factors computed with {\sc NLLfast}.
For obtaining the $r$ values we used the numbers provided by {\sc CheckMATE}, including a
20\% uncertainty for the theoretical cross sections, which corresponds to the value used in {\sc SModelS}\ when computing likelihoods.
In Table~\ref{tab:CMresults} we show, for this specific pMSSM point, the main contributions to the total signal yield for the
best signal region (SR), $2jt$, in ATLAS-SUSY-2013-02.
As we can see, if we only consider the symmetric $\tilde g \tilde g \to 2$~jets + $E_T^{\rm miss}$ topology,
we obtain an $r$ value very similar to the one obtained by {\sc SModelS}\ ($r = 0.37$)
and the point is far from being excluded.
However, if we include the asymmetric $\tilde g \tilde q\to 3~{\rm jets} + E_T^{\rm miss}$ topology, the $r$ value increases
to $1.38$ and the point can be excluded. In contrast, the contribution from $\tilde q \tilde q$ production
with $\tilde q\to q\tilde g$, $\tilde g\to g\tilde\chi^0_1$ has a tiny effect.
For completeness, in the last line of Table~\ref{tab:CMresults} we
also present the inclusive result, which incorporates all possible gluino and squark decays, thus giving
a slightly higher $r$-value ($r=1.7$).
In this example we can clearly see that the asymmetric $\tilde g \tilde q$ topology is the dominant one and
essential for excluding the tested point.
This illustrates how SMS results for $\tilde g \tilde q$ topologies, with unrelated gluino and squark masses,
would help improve the coverage of the pMSSM.
Particularly useful would be efficiency maps, as they allow to combine different contributions to the same signal region
in the simplified model context.
\begin{table}\centering
\begin{tabular}{lccc}
Topology & Cross section & Contribution to $2jt$ & $r$-value \\ \hline
$\tilde g \tilde g \to 2$~jets + $E_T^{\rm miss}$ & 250~fb & 21\% & 0.37 \\
$\tilde g \tilde q \to 3$~jets + $E_T^{\rm miss}$ & 664~fb & 59\% & 1.01 \\
$\tilde q \tilde q \to 4$~jets + $E_T^{\rm miss}$ & 136~fb & 4\% & 0.08 \\ \hline
Total $\left(\tilde g \tilde g + \tilde g \tilde q + \tilde q \tilde q \right)$ & 1220~fb & 100\% & 1.70 \\
\end{tabular}
\caption{Contributions of specific signal topologies to the total exclusion for the pMSSM point no.~192342466.
The second column shows the topology cross section (production cross section times branching ratios),
while the third column shows the topology contribution to the signal yield for the $2jt$ signal
region of Ref.~\cite{Aad:2014wea}. The last column shows the $r$-values obtained using each topology individually.
The last line shows the corresponding results including all possible gluino and squarks decays, resulting in a
larger total cross section and $r$-value. See text for details.
\label{tab:CMresults}}
\end{table}
\end{appendix}
\clearpage
\input{pmssm-sms-coverage_revised.bbl}
\end{document}
| {
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} | 6,481 |
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