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The 'Disasterology' author wants us to rethink emergency management
This tech exec built a career on authenticity
How coastal cities can build climate resilience
Credit: Sébastien Thibault
To truly 'build back better,' invest in R&D, researchers say
Tracy Mayor
Roads and bridges are a start, but 21st century job creation needs federal research and development in U.S. cities with potential, these authors say.
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When Simon Johnson and Jonathan Gruber published "Jump-Starting America" in 2019, they were responding to the slowdown in U.S. productivity and loss of access to well-paying jobs that began in the 1970s and accelerated through the 2000s.
Work smart with our Thinking Forward newsletter Insights from MIT experts, delivered every Tuesday morning.
Subtitled "How Breakthrough Science Can Revive Economic Growth and the American Dream," the book proposed that the federal government jump‐start the stalled American growth engine by investing $100 billion annually to develop and commercialize innovation technologies. That investment would create 4 million good new jobs in the near term, the authors estimated.
"Almost every major innovation after World War II relied in an important way on federal government support," wrote
Johnson,
a global economics and management professor at MIT Sloan, and Gruber, an MIT economics professor. Without a similar investment, "We are at risk of falling behind and losing even more good jobs."
To close income and opportunity gaps, this federal R&D investment would be centered in 102 urban communities statistically identified by Johnson and Gruber as potential next-generation technology hubs.
"These geographically concentrated federal investments can be truly transformative: attracting companies and helping to generate more local private sector employment," they wrote.
Then COVID-19 hit, and the U.S. shut down. The economic fallout from the pandemic exacerbated the jobs gap and brought into sharper relief the racial underpinnings of economic inequality in the U.S.
Simon Johnson, MIT Sloan professor
Credit: Ed Collier
Now, a new administration is promising to "build back better," with various infrastructure, cyber defense, and innovation legislation in play. As Americans and the U.S. economy continue to navigate the pandemic, Johnson highlighted in a recent interview the ideas from "Jump-Starting America" that are more relevant than ever:
1. In an atmosphere of extreme political partisanship, a desire for good jobs cuts across party lines.
Public spending on research and development, which peaked in 1964 at nearly 2% of GDP (and is now at 0.65%), has historically been supported by both Democratic and Republican administrations. In speaking with policymakers in Washington and around the country, Johnson said he finds that support holds true today.
"The case for expanding federal support for R&D in the U.S. is very strong," Johnson said, citing the U.S. Innovation and Competition Act, which has garnered votes in the Senate from both sides of the aisle. "Everybody recognizes that you need R&D for national security and for good jobs" — which he and Gruber define as jobs that offer reasonably stable employment, a living wage, and decent benefits.
"When we talk to mayors and governors, irrespective of their party, they all say, 'We know the jobs of the future are going to be related to technology. Show us how to get there.'"
2. Federal investment is still the most effective way to redress geographic inequities.
In their book, Gruber and Johnson suggest that federal investment could help smaller cities and rural areas left behind in the innovation boom that has clustered in "superstar" U.S. regions like Silicon Valley, San Francisco, New York, Los Angeles, Seattle, the Washington, DC area, and the Boston metro region.
The case for expanding federal support for R&D in the U.S. is very strong.
Simon Johnson Professor, MIT Sloan
It's too early to tell how the pandemic-inspired work-from-home movement may change that situation, but Johnson isn't overly optimistic. Remote work tends to be an option primarily for knowledge workers, he said, and it's not yet clear how COVID-19 location disruptions will affect venture capital, which tends to cluster where innovation is already happening and there is ready access to capital.
The authors identified 102 urban communities that could be plausible next generation tech hubs, thanks to their large populations, highly educated workforces, and low costs of living. As last year's racial justice movement brought to light, these are often minority-majority metropolitan areas, such as Pittsburgh, Cleveland, or St. Louis, with higher rates of unemployment.
"We do think there's a geographic justice issue here, which is that people in small towns and smaller cities have been left behind, and various demographic groups live in those cities," Johnson said. "Our book and our work emphasize the key role of education in making sure that people can participate in this knowledge-based economy."
Johnson and Gruber champion the "spillover effect" of investing in high-tech jobs in a particular region.
"The evidence suggests that public investment in R&D creates a lot of jobs for people who don't have PhDs — in fact, for people who may not necessarily have finished college, as long as they get applicable vocational training. Each PhD job comes with three to eight non-PhD jobs, and these are generally good, well-paying jobs," Johnson said.
3. Science matters.
At the heart of Gruber and Johnson's proposal is a belief in the power of science to solve problems and create jobs — and the power of federal investment to grow those nascent technologies.
"The path the U.S. took during and after World War II was a deliberate path focused on using science and then developing more science to be useful," said Johnson.
To jump-start America, invest (a lot) in science
Jump-starting the creation of good jobs
5 bold ideas for an economic restart
The innovation that led to rapid growth after World War II was "the direct result of a fruitful partnership between the private sector, federal government, and universities," the authors write.
Post-1945, those partnerships produced developments such as jet aircraft, drugs and vaccines, microelectronics, satellites, and digital computers.
Together, the government and the private sector were able to fast-track COVID-19 vaccines.
"We have been saved by science," said Johnson, who called the rapid scale up of vaccine development and distribution "a big validation of the U.S. biopharmaceutical strategy."
Despite significant science skepticism in the U.S., Johnson remains optimistic that policymakers and the private sector can envision the benefits of scientific partnerships.
"In Washington, science is often politicized, but when I go talk to people or Zoom with people around the country now, it doesn't matter if they're left wing or right wing," Johnson said. "At the local level, they're like, 'We want more good jobs. How do we get these science-based enterprises to relocate here, remain here, and hire people here?'"
Read the policy summary
Explore 102 potential technology hubs
For more info Tracy Mayor Senior News Editor & Writer (617) 253-0065 tmayor@mit.edu
Ideas Made to Matter The 'Disasterology' author wants us to rethink emergency management
Ideas Made to Matter How coastal cities can build climate resilience
Ideas Made to Matter 2021, illustrated | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 7,145 |
Q: Obj-C enum "Incompatible Types in initialization" I'm having a problem with enum type initialization that appears to be simple to solve but I haven't figured out how to do it.
Suppose I declare the following enum type:
typedef enum NXSoundType {
NXSoundTypeNone,
NXSoundTypeEffect,
NXSoundTypeBackgroundMusic
} NXSoundType;
I declare a convenience method for returning one of the NXSoundType enum types given a NSString object like this (NOTE: NXSound is an object that contains a NXSoundType attribute named "type"):
- (NXSoundType)nxSoundTypeFromIdentifier:(NSString*)nxSoundIdentifier {
NXSoundType type = NXSoundTypeNone;
for (NXSound *nxSound in self.nxSounds) {
if ([nxSound.identifier isEqualToString:nxSoundIdentifier]) {
type = nxSound.type;
}
}
return type;
}
So far, so well. But the following call is not working:
NXSoundType type = [self nxSoundTypeFromIdentifier:@"kNXTargetGameSoundIdEffectTic"];
What's wrong?
Thank you in advance.
A: I solved the problem. Despite the compiler error message, the problem was not related to wrong enum type declaration/initialization. The problem was that the method
- (NXSoundType)nxSoundTypeFromIdentifier:(NSString*)nxSoundIdentifier;
was defined as a private method in a base-class and was been called by a sub-class. In this way, due to the Obj-C dynamic nature, it was expected to return an id which cannot be assigned to the NXSoundType enum (only to objects). A simple cast removed the problem, the solution was to change the method call to:
NXSoundType type = (NXSoundType)[self nxSoundTypeFromIdentifier:@"kNXTargetGameSoundIdEffectTic"];
Appreciate all replies and sorry for any confusion. Hope this helps somebody.
A: Try using just:
typedef enum {
NXSoundTypeNone,
NXSoundTypeEffect,
NXSoundTypeBackgroundMusic
} NXSoundType;
and see if that helps. having the typedef and name be the same might be confusing Obj-C compiler like this person's question.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 4,011 |
package eu.fraho.spring.example.starter_files;
import org.springframework.web.bind.annotation.RequestMapping;
import org.springframework.web.bind.annotation.RestController;
@RestController
public class PublicController {
@RequestMapping("/public")
public String hello() {
return "Public area";
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 3,044 |
I want to create an android app where a live camera stream captures obstacles on the ground and issues warnings to the user. This is intended as an application for the visually impaired.
I'm at a loss to understand what technologies are most suitable for this as I have no previous experience in image processing. I looked through some OpenCV examples, but they didn't provide me with much insight as to where to start the project from.
Should I learn C++, since I only know java and C#?
If you could provide me with some answers to any of the above points I'd be much grateful.
There are several sample applications and tutorials distributed with OpenCV4Android SDK. Start from Tutorial-1 application. It helps you to initialize OpenCV and get frames from camera. There are reference manual and some introduction tutorials for beginners. On Android you can use both Java and C++ API. Use Tutorial-3 app as an example of native calls. You can use any C++ functions available in desktop OpenCV except some parts of Highgui module related to window management. Video decoding and encoding are not supported also.
Most, but not all OpenCV API are wrapped to Java. So you can use Java as base language. But in some cases to achieve performance you need to use C++.
Approach for obstacle detection depends on situation. You can tries some algorithms from OpenCV Video module. There is no any tutorials for it, reference manual only. | {
"redpajama_set_name": "RedPajamaC4"
} | 1,149 |
Micron Ventures says it will invest up to USD 100 million in venture funding targeted at technology startups focused on artificial intelligence (AI), with twenty percent aimed at startups led by women and other underrepresented groups.
The US chipmaker says that it will invest up to USD 100 million in startups with a strong focus on AI and machine learning through its strategic investments entity, Micron Ventures. As companies develop more complex AI and machine learning systems and work on more advanced use cases, the hardware used to train and run those models will become increasingly important. This requires a detailed look at compute, memory and storage configurations to avoid performance and throughput bottlenecks and drive faster, better results, the company writes in a press release. "We are pleased to bring together the industry's brightest thinkers, researchers, innovators and technologists to discuss AI, machine learning and deep learning," says Micron President and CEO Sanjay Mehrotra, in the release. "These trends are at the heart of the biggest opportunities in front of us, and increasingly require memory and storage technologies to turn vast amounts of data into insights that accelerate intelligence." As part of the USD 100 million investment, Micron will target up to $20 million to fund startups led by women and other underrepresented groups. | {
"redpajama_set_name": "RedPajamaC4"
} | 4,633 |
Q: "Go up to top level" Windows 7 FTP explorer In Windows 7 you can connect to an FTP server natively.
However, in a client like FileZilla, you can click the little ".." to go up one level. But you can't do that in Windows 7, can you? You are stuck considering the "top level" as the folder the FTP server decided to start you out at, even if there are accessible folders at levels above where you started.
A: When you connect to an FTP site by mapping it (as in the linked example) to a local folder, you are stuck as it being the 'root' and you can't escape it. It's like mapping a drive letter to a shared folder with regular Windows networking, if you mapped it as "F:" you can't get to "F:.." even if you have access to the folder above the share that you mapped to.
If you need to get to the folder above, you need to map to that folder (instead, or as well).
If you need to be hopping virtual folders on an FTP site, then a full-fledged FTP client (like FileZilla, or Windows' command-line FTP) is probably your best (only?) bet.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 5,202 |
Q: Issue in Generating TestNG.xml File i try to Generate TestNG.xml through java code but it is working when i run it as java application, but it is not generating the XML File Seperately.May i know Why, Code Works Fine But can't able to Generate the Xml File Seperatly .
My Code :
package Testcases;
import java.util.ArrayList;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
import org.testng.TestListenerAdapter;
import org.testng.TestNG;
import org.testng.xml.XmlClass;
import org.testng.xml.XmlSuite;
import org.testng.xml.XmlTest;
public class GenerateTestng
{
@SuppressWarnings("deprecation")
public void runTestNGTest() {
//Create an instance on TestNG
TestNG myTestNG = new TestNG();
//Create an instance of XML Suite and assign a name for it.
XmlSuite mySuite = new XmlSuite();
mySuite.setName("MySuite");
//Create an instance of XmlTest and assign a name for it.
XmlTest myTest = new XmlTest(mySuite);
myTest.setName("Wepaythemaxx");
//Create a list which can contain the classes that you want to run.
List<XmlClass> myClasses = new ArrayList<XmlClass> ();
myClasses.add(new XmlClass("Testcases.FinalTest"));
//Assign that to the XmlTest Object created earlier.
myTest.setXmlClasses(myClasses);
//Create a list of XmlTests and add the Xmltest you created earlier to it.
List<XmlTest> myTests = new ArrayList<XmlTest>();
myTests.add(myTest);
//add the list of tests to your Suite.
mySuite.setTests(myTests);
//Add the suite to the list of suites.
List<XmlSuite> mySuites = new ArrayList<XmlSuite>();
mySuites.add(mySuite);
//Set the list of Suites to the testNG object you created earlier.
myTestNG.setXmlSuites(mySuites);
TestListenerAdapter tla = new TestListenerAdapter();
myTestNG.addListener(tla);
//invoke run() - this will run your class.
myTestNG.run();
}
public static void main(String[] args)
{
GenerateTestng dt = new GenerateTestng();
dt.runTestNGTest();
}
}
i have attached my code above, please verify, Where i done mistake i can't figure it out.
A: I created this method that will save the file:
public void createXmlFile(String saveFilePath, XmlSuite suiteName) {
File file = new File(saveFilePath);
FileWriter writer = null;
try {
writer = new FileWriter(file);
} catch (IOException e) {
// TODO Auto-generated catch block
e.printStackTrace();
}
try {
writer.write(suiteName.toXml());
} catch (IOException e) {
// TODO Auto-generated catch block
e.printStackTrace();
}
System.out.println(suiteName.toXml());
try {
writer.close();
} catch (IOException e) {
// TODO Auto-generated catch block
e.printStackTrace();
}
}
Where
*
*saveFilePath = the path where the file will be saved e.g. '.testNGxml.xml'
*suiteName = your suite name, in your case mySuite
A: Eclipse has a TestNG extension that creates the xml on its own. You can then edit the xml to change the order the tests are run on(so that you can create mock data, edit said data and delete it without getting an error for example).
I am sure most IDEs have similar approaches.
Any reason you are not using an IDE?.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 245 |
David Bennett's page-turning writing gripped me from beginning to end, and I feel sure that his perspective on what it means to give our sexuality to God is something that every Christian of our generation needs to consider.
**_—Dr. Amy Orr-Ewing,_ ** director, Oxford Centre for Christian Apologetics
This is an incredibly raw and authentic book! David paints a beautiful and compelling picture of what it looks like to desire Christ above all else. His affections for Jesus make me excited to be a Christian.
**_—Preston Sprinkle,_ ** president, Center for Faith, Sexuality, and Gender
A refreshing and powerful book. This is one of the top books I will recommend to Christians who want to know how to better love their LGBTQI friends and also to seekers—whether gay or not—who are open to considering Jesus' invitation.
**_—Sean McDowell,_ ** professor, Biola University; speaker; author, _Same-Sex Marriage_
A timely, thoughtful, and often moving story which will be hugely helpful to a lot of people. David's honesty and humanity shine through these pages, even as he handles difficult questions through the lens of his experience. This is a gift to the contemporary church.
**_—Andrew Wilson,_ ** teaching pastor, King's Church London
Here is a voice as countercultural as it is compelling, capable of engaging the whole Christian community, whether gay or straight, in a vital debate. I have no doubt that David Bennett's story is going to become an essential part in a complex jigsaw for many.
**_—Pete Greig,_ ** 24-7 Prayer International and Emmaus Rd, Guildford
Many lesbian, gay, and bisexual people feel they cannot be true to both their sexuality and the Christian faith. David demonstrates that integrity and authenticity are possible for gay Christians, sharing beautiful insights about love, friendship, and following Jesus too.
**_—Rev. Dr. Sean Doherty,_ ** Christian ethicist; author, _The Only Way Is Ethics_
This book is designed to make all of us think about our ultimate love and to work through how we should engage in a long debated area, whether inside of the church or outside of it. It is well worth the read.
**_—Darrell L. Bock,_ ** Senior Research Professor of New Testament Studies, Dallas Theological Seminary
David Bennett's book presents a particular lived Christian experience which deserves hearing. I am grateful to all who are contributing their learning, experience, study, and prayer to help us all to proclaim afresh the gospel of Jesus Christ.
**_—Sentamu Eboracensis,_ ** Archbishop of York
One of the most significant books on one of the church's most pressing subjects by one of today's most inspiring young thought leaders. David Bennett is a prophetic witness, a truth teller, a tender pastor, and a faithful follower of Jesus. This generation needs to hear this man.
**_—Rev. Simon Ponsonby,_ ** author; pastor of theology, St. Aldates Church, Oxford
This is the searingly honest story of one romanced by God against all expectations. Bennett's example of giving his whole self, including his sexual self, to the Christ who died for him is an act of Christian witness for our time.
**_—Rev. Dr. Michael P. Jensen,_ ** rector, St. Mark's Darling Point, Sydney; author, _Martyrdom and Identity_
Riveting, extraordinary—quite extraordinary! I really think I could give this book to any contact I have and they'll be fascinated. I do wonder whether it will become a Christian classic of our time.
**_—Rico Tice,_ ** All Souls Church London; author, _Christianity Explored_
I am particularly pleased to commend this book. It is an important contribution to the conversation. In a day when so often emotional story trumps thinking, David Bennett matches careful theological thinking with a truly compelling story.
**_—Charlie Cleverly,_ ** rector, St. Aldates Oxford; member, General Synod of the Church of England
ZONDERVAN
_A War of Loves_
Copyright © 2018 by David Bennett
Requests for information should be addressed to:
Zondervan, _3900 Sparks Dr. SE, Grand Rapids, Michigan 49546_
ePub Edition © October 2018: ISBN 978-0-310-53812-7
All Scripture quotations, unless otherwise indicated, are taken from The Holy Bible, New International Version®, NIV®. Copyright © 1973, 1978, 1984, 2011 by Biblica, Inc.® Used by permission of Zondervan. All rights reserved worldwide. www.Zondervan.com. The "NIV" and "New International Version" are trademarks registered in the United States Patent and Trademark Office by Biblica, Inc.®
Scripture quotations marked ESV are taken from the ESV® Bible (The Holy Bible, English Standard Version®). Copyright © 2001 by Crossway, a publishing ministry of Good News Publishers. Used by permission. All rights reserved.
Scripture quotations marked NLT are taken from the Holy Bible, New Living Translation. © 1996, 2004, 2007, 2013, 2015 by Tyndale House Foundation. Used by permission of Tyndale House Publishers, Inc., Carol Stream, Illinois 60188. All rights reserved.
Any Internet addresses (websites, blogs, etc.) and telephone numbers in this book are offered as a resource. They are not intended in any way to be or imply an endorsement by Zondervan, nor does Zondervan vouch for the content of these sites and numbers for the life of this book.
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, photocopy, recording, or any other—except for brief quotations in printed reviews, without the prior permission of the publisher.
Published in association with the literary agency of Mark Sweeney & Associates, Naples, Florida 34113.
_Cover design: Micah Kandros Design_
_Cover art: Shutterstock_
_Interior design: Kait Lamphere_
18 19 20 21 22 23 24 25 /DHV/ 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
Information about External Hyperlinks in this ebook
Please note that footnotes in this ebook may contain hyperlinks to external websites as part of bibliographic citations. These hyperlinks have not been activated by the publisher, who cannot verify the accuracy of these links beyond the date of publication.
**_To my Lord and Savior, Jesus Christ, whose love radically transformed my life in that pub almost a decade ago_**
**_And to my father, Paul, who, after a stroke that almost took his life this last year, received Jesus Christ as his Lord and Savior_**
**_And to my mother, Anne-Marie, who believed in Jesus before I did, lovingly accompanied me in my search for truth, and whose steadfast love instilled in me the hope that carried me through the harder times_**
# **CONTENTS**
_Author's Not_ e
_Foreword by N. T. Wrigh_ t
_Acknowledgment_ s
_Prefac_ e
[ **PART 1:
The Search** ](part01.xhtml#con_5)
**1.** Coming Out
**2.** Quest for Spirituality
**3.** The French Exchange
**4.** Boyfriends and Psychics
**5.** The Gay World
**6.** University and the Love Triangle
**7.** Christmas Conflicts
[ **PART 2:
The Encounter** ](part02.xhtml#con_13)
**8.** Experiencing the Love of God
**9.** The Film Festival
**10.** Providence and Prophecies
**11.** The Unrelenting Presence of Jesus
**12.** The Root of Bitterness
**13.** The Gospel of Grace
[ **PART 3:
Wrestling with God: Sense and Sexuality** ](part03.xhtml#con_20)
**14.** Living under God's Word
**15.** Marriage and the Church
**16.** Facing Facts in France
**17.** God's Greater Romance
**18.** Romance in France
[ **PART 4:
The New Identity** ](part04.xhtml#con_26)
**19.** Understanding Love and Celibacy
**20.** Bible College and Moving to Oxford
**21.** Drawing the Line: Acceptance versus Affirmation
**22.** Beloved Friendship
**23.** Living Out Now
[ **PART 5:
Reflections on Homosexuality and Christian Faithfulness** ](part05.xhtml#con_32)
**24.** Celibate, Gay, Christian: A Third Way
**25.** Speaking Truth in Love
[ **26.** Sacrifice Regained: Salvation and Holiness
](chapter31.xhtml#con_35)
_Appendix 1: What I Learned the Scriptures Really Say about Homosexualit_ y
_Appendix 2: Desiring and Imaging God: The Challenge_ s
_Note_ s
_Glossar_ y
_Recommended Resource_ s
The only thing that counts is faith expressing itself through love.
**_—The apostle Paul to the Galatians_**
# **AUTHOR'S NOTE**
**M** any of the stories I tell in this book are deeply personal, and so in most instances (except where permission has been given), to protect the privacy of those involved, I have altered names, places, and details while maintaining the storyline and events. The opinions in this book are my own and do not necessarily reflect those of the organizations, churches, people, or groups mentioned.
# **FOREWORD BY N. T. WRIGHT**
**T** his is a brave and wise book. The territory into which it leads us—in shockingly clear detail—is perhaps the most contested moral, social, and cultural issue of our times: the question of same-sex desire and practice. None of the issues is shirked here; no soft answers are on offer, no easy fudge to let us slide around the problems. David Bennett has lived for several years at the heart of the questions—or perhaps we should say that the questions have lived in his heart, like a wasps' nest buzzing angrily inside a room that ought to be a safe place. He has felt the pain of raging and unfulfilled desire, and also the pain of desire fulfilled but strangely unsatisfied. He has felt the anger of being patronized and dismissed by unthinking Christians, as well as the anger when, having discovered for himself the reality of Jesus as a living, loving, and challenging presence, he has often then been patronized and dismissed by the very people whose cause he had earlier, and loudly, advocated.
If all this sounds as though David Bennett will come across as an angry young man, nothing could be farther from the truth. David looks back not _in_ anger but _on_ anger—and sees it, names it, and deals with it. He understands and sympathizes with those who see no problem in acting upon their same-sex desires or the way of life they shape around them; he disagrees with them but is able to explain why. He understands and has learned to forgive those whose practice of Christian faith has made them simply point a finger labelled "sin" at anyone who doesn't fit their stereotypes. The real heroes of his story, though, are quite different Christians who, with no loss of integrity or biblical wisdom, continued to love him and pray for him through some dark and stormy times.
David's account of his meeting with Jesus, and the transformation that this produced in his life, his mind, his body, his imagination, and his hopes, is alone worth double the price of the book. His conversion story, like all true conversion stories, is more complex and interesting than such a phrase might suggest. I was struck, in particular, by the way that before his meeting with Jesus, David positively _hated_ the Bible. Since I have spent most of my life in love with the Bible and hoping to instill this love in others, it was and is good for me to be confronted with the sharp reminder that "that's how your stuff makes some people feel." But for those of us who engage in areas of Christian work other than frontline evangelism, his whole story is a wonderful encouragement: not that we ever supposed the gospel could no longer change lives, but that it's always good to hear fresh stories, vividly told, of how that change can happen despite the most unpromising starts.
There are, inevitably, places where we will agree to differ. David uses the language of LGBT and a few other initials as well; having lived in the world where those on the margins found a peer group with whom they could share sorrows and fears, he does not wish to turn his back on folk for whom that self-description is something of a lifeline. I have come to regard the list of initials LGBTQI as problematic, since each refers to quite different phenomena, sets of circumstances, assumptions, and challenges, and to lump them all together can, from the outside, look like a way of saying, "We're just going to live by whatever impulses we feel whenever we feel them." I stress _from the outside:_ I greatly respect David's insider viewpoint and will, I hope, continue to learn from him.
Above all, I respect and salute David's resolute affirmation of _chastity:_ of sexual fidelity in heterosexual marriage and sexual abstinence outside it. C. S. Lewis once remarked that when Charles Williams was lecturing in Oxford, the undergraduates were shocked because, having long supposed that the old rules about chastity were outdated, they were confronted with an author, literary critic, and lecturer who knew his texts like the back of his hand and was able to bring them gloriously to life, _and who passionately believed in chastity_. Hitherto they had supposed that anyone advocating sexual abstinence must have something wrong with them; now, suddenly, they discovered that the boot might be on the other foot. David Bennett's compassionate intelligence, his forthright tell-it-like-it-is memoir, and his rich theological understanding mean that when he advocates chastity, as he does in this book, nobody will be able to dismiss him in the way they might dismiss elderly theologians like the present writer.
Of course, if people prefer to work out their morality having checked in their brains at the door—a charge that applies equally to the unthinking Christian and to the unthinking secularist—then David Bennett's book will be a wake-up call. This is about _thinking through_ what sexuality is really all about and what a wise and mature Christian reading of the Bible has got to do with it. If we can put thinking itself back on the agenda for these discussions, and then use that thinking to address in fresh ways the many-sided questions that force themselves upon us, we just might get somewhere. David Bennett's book will help at every stage of that urgently necessary process.
# **ACKNOWLEDGMENTS**
**I** am profoundly grateful for the support of the Oxford Centre for Christian Apologetics (OCCA). The centre has become both my family and my professional community. Especially among them are Nancy Gifford, Amy and Frog Orr-Ewing, Mo Anderson, Michael Ramsden, Sanj and Kay Kalra, Sarah Davis, Karen and Joe Coffey, and Michael Suderman. Other friends I'd like to thank are my professor N. T. Wright, Dominic Steele, Hazel Thompson, Merrie Goddard, Anna Yearwood, Lauren Bolton, Ron Belgau, Simon Wenham, Coggin Galbreath, and Peter Hartwig, all of whom contributed to _A War of Loves_ in different and important ways. I also credit so much to my aunt Helen, who helped me navigate church and so richly discipled me through this journey of faith. Finally, I would like to thank Wesley Hill, whose story was so pivotal to my story. I thank God for the vast multitude of often-hidden gay or same-sex-attracted Christians who faithfully follow Christ in this current climate. You are all an inspiration to me, and I hope this book will not just encourage you but also help to change the prejudices and pressures with which you bravely live.
# **PREFACE**
**A** s a nineteen-year-old atheist gay activist who felt rejected by Christianity, I had very little reason to believe in God. Then I encountered Jesus in a pub in the gay quarter of Sydney, Australia, and my life changed forever.
I wrote this book partly to help others navigate the tricky terrain of homosexuality and the Christian faith. However, my main reason for writing was simply to share how God's love has impacted my life. Rather than attempt to answer every question about homosexuality, I hoped to provide in this book's pages a clear picture of how I was reconciled to God. The gay and Christian communities are often seen as polar opposites: one a progressive, inclusive community, the other a community of oppressive, archaic laws. Having stood on both sides, I know the reality is far more complex.
My late colleague Nabeel Qureshi, author of the _New York Times_ bestseller _Seeking Allah, Finding Jesus_ , inspired me to write. Nabeel was diagnosed with stomach cancer when I began this book, and passed away in mid-2017. One evening in Oxford, just down the road from the famous Eagle and Child pub, Nabeel turned to me and said, "David, you will bless more people through a book than you ever will through speaking. It's time to write your story." Soon after, I met a prominent Christian evangelist, who agreed. "David," he told me, "you are called for a time such as this." I am grateful to them both for encouraging me forward.
_A War of Loves_ is the story of how I met Jesus Christ, directly opposing the lie that God does not love gay or same-sex-attracted people, or any of us for that matter. I do three things in these pages.
1. Describe my personal quest for truth as someone from the gay community who became a Christian.
2. Provide insight into two worlds that often misunderstand each other.
3. Discuss the universal questions of love that both communities—indeed, all people—ask.
My prayer is that this book will be a resource not only on sexuality but also on how to know and experience God's love. None of us are below or beyond that love. I wish a book like this had existed when I first wrestled with the questions that prompted it. Within the book's limitations, I can't offer a systematic doctrinal solution to the questions that arise regarding same-sex desire. Yet I do attempt to point below the surface to share hard-fought truths I've discovered.
You have probably noticed that I call myself gay or same-sex attracted (SSA). By using these terms, I stand with the thousands of LGBTQI people around the world who suffer threats, hate crimes, imprisonment, internment or refugee camps, or even capital punishment. These terms are not an ultimate identity but a part of my personal reality preresurrection. I remember those who have deeply struggled or even committed suicide because they felt unable to reconcile their faith and sexuality. I stand too with my same-sex-attracted or gay Christian brothers and sisters who are living faithfully before Christ.
I call myself gay to remind broader groups that what I choose to do with my sexuality as a Christian is caught up in my worship of God, and that the fundamental human desire for intimacy is ultimately fulfilled in a relationship with Jesus and what he accomplished on the cross for us all.
I call myself celibate because I have chosen, by God's grace, to give my sexuality to Jesus Christ. The scriptural teaching on sex is reasonably clear, but there is so much more to the experience of being a gay or same-sex-attracted person than language-games, prohibitions, or information.
This book is not essentially about being gay. It is about finding a greater identity in Jesus Christ and becoming a son of God. My ultimate identity is found in Jesus Christ, but the reality of my same-sex desires is an important part of that story. Amid all the confusion around issues of faith and sexuality, I feel much like C. S. Lewis in _Shadowlands:_ "I have no answers anymore . . . only the life I have lived." In the following pages, I invite you to consider the message of the glorious gospel that has impacted my life through this, my story.
# [ ** PART 1
THE SEARCH ** ](contents.xhtml#conn_5)
# [ ** CHAPTER 1
COMING OUT ** ](contents.xhtml#conn_6)
> You, LORD, brought me up from the realm of the dead; you spared me from going down to the pit.
**_—Psalm 30:3_**
**I** t was the first Friday evening since moving to the Sydney harborside, and a day after my fourteenth birthday. From a high sandstone outcrop bordering the water, I watched the sun set over a small mooring of boats. The chiming of their sails rang out from the cove and over the peninsula. A blush of ochre tinted the sky. Sydney Harbour Bridge was hidden behind the eucalyptus trees, but the cityscape was in view on the horizon, iridescent with skyscrapers.
Such beauty made me ache for someone to share it with—another young man. Standing in my untucked school uniform, I peered over the ledge, where water lapped at oyster-laden rocks down below. The ferry glided on the incoming tide with its monotone growl. Tears welled up from what I knew was true. _I feel light enough to jump over the edge._ The crushing ocean seemed lighter than my unwanted desires, and my feet dared me to step over the edge of the cliff. I pulled back in sudden horror. My heart raced as I ran home and the dusk fell.
Not long after, I found myself at school. The recess bell rang throughout the school grounds, and the summer sun shone over the brick buildings. More than a thousand boys, each in the traditional uniform of red-lined navy blazers, white shirt, grey woolen trousers, black shoes, and a navy blue tie, poured through the grounds to the entrances of the Anglican chapel. It was a chaotic sight that somehow always managed to become orderly in minutes as everyone lined up to enter. We resembled an army regiment at attention, with just a few naughty soldiers out of formation.
Soon the sound of hundreds of adolescent boys singing awkwardly from hymnbooks filled the chapel. As I took my place among the pews, my vision blurred. I had fond memories of singing solos in the boys' choir before my voice broke, and of my favorite soprano solo: Howard Goodall's "The Lord Is My Shepherd." But today I was silent, repulsed by the thought of singing to a God I knew didn't exist, since his only response to my unspoken questions had been a deafening silence.
My hardworking agnostic parents had attained an upper middle class lifestyle. Life was good, but I was often unhappy and lonely, surrounded by the boredom and beauty of the suburbs. I dreamed about escaping to the city, which offered the liberty and sophistication I craved.
Our extended family had a wide range of religious beliefs and convictions. With my Christian relatives, I often heard strange terms used to describe homosexuality. Either it was a kind of spiritual oppression that needed to be prayed away, or it was a result of sexual abuse that required serious healing. None of these pseudotheories fit me.
For other Christians, homosexuality was the worst of sins and homosexuals were God's enemies. This rhetoric missed the reality of what I was going through and closed me down to the honest confession and self-acceptance I deeply desired ever since I awoke at the onset of puberty to my attraction to men. The widely variant views of why people are homosexual—genetics? abuse? father issues? something else entirely?—bombarded me. I felt so confused.
On top of this, coming to terms with my attractions at the age of fourteen meant entering an ugly, polarized culture war that spanned the globe. All I wanted was a place where I could be honest. All I wanted was to find a boyfriend and escape the monotony, and ignorance I perceived in the people around me. Then I could finally be accepted and move on with my life.
One night I cried out, "Take these attractions away!" Nothing changed, and the silence drove me farther away from Christianity. The attractions I'd felt since age nine weren't about a lifestyle I'd chosen. They were about who I was.
Since a young age, I'd understood that a person's romantic attractions shape their humanity. Love makes us human, and without it, life is not worth living. I wanted all that life had to offer, so I knew I had to keep my distance from those Christians who were getting in my way. Still, the message that God didn't approve of people like me gnawed at my conscience.
For a year, I tried to think of the opposite sex the way my peers did. Then I dismissed such thoughts as ridiculous. I didn't believe in God, so why worry anymore? My growing interest in men's bodies had only increased, and the nervousness I experienced around certain members of the same sex brought me to a place where I knew I was attracted exclusively to men. I even wrote a poetry anthology about my inner secret.
As the chapel service ended, I concluded I could no longer put off the reality of my attractions. The more I denied them, the more miserable I became.
## **SEARCHING THROUGH SCIENCE**
Why was I gay? Shows like _Queer as Folk_ or _Will and Grace_ simply told me I was made or born this way. That wasn't particularly specific.
I began searching for an answer. I read through nature versus nurture arguments in studies. I googled everything I could find.
Simon LeVay's research in 1991 showed there was a substantial difference between the brains of gay and straight men in the hypothalamus. Other studies found that gay men responded to the pheromones of men, not women. Studies on identical twins showed a genetic contribution to sexual orientation, but not a genetic determination. More recent studies had shown the potential influence of the hormonal environment of the womb. Sigmund Freud's psychoanalytic theory for homosexual behavior linked same-sex attraction to parental relationships. Environment? Biology? Genetics? Nurture? Hormones? Conditioning? Nothing was conclusive. Little was clear or known about the why of it. And that almost crushed me. Understanding myself seemed completely out of reach.
A war developed in me about how to understand this part of my identity. The belief that we're all born this way wasn't the whole story. I was more confused than ever.
## **READING THROUGH RELIGION**
Since science couldn't tell me why I was gay, I decided to try religion—and didn't make it far.
Even if there was a Christian God, I felt disqualified from a relationship with him because of who I wanted to love. Yet I longed for intimacy of the spirit as much as that of the body—perhaps more.
Why did the relationship between Christianity and homosexuality have to be so complex? I read different Christian perspectives, progressive to traditional. Eventually I accepted the view that the apostle Paul was obviously unaware of any faithful, monogamous relationships between two members of the same sex. I decided his writing was a cultural artifact that didn't hold the authority orthodox Christians gave it.
Throughout my schooling, I had been exposed to Christianity through camps, youth groups, and church activities. I always felt unable to belong, especially when I heard their teachings on homosexuality. Being gay was explained as rooted in a bad relationship with my father or other masculine figures. Whenever I heard this explanation used to dismiss the gay community, my stomach twisted. I, like many others I spoke to online, had a great relationship with my father. I had never been abused. My Greek father was an ambitious software executive and a generous man. We were different from each other, but I always knew he loved me. Our relationship was quite good; the father-figure story didn't fit, and there were many gay people who had great relationships with their same-sex parent.
I felt like Christians were explaining me away, not entering into my experience. That was bad enough, but their explanation wasn't even any good! I found it frustratingly hypocritical that Christians, who worshiped a savior of transparency and truth, couldn't deal with my being honest about my humanity. Their obvious prejudice toward gay people only pushed me farther away. I perceived that perhaps homosexuality unearthed deeper problems in the church, especially an obsession with sexual desire.
All I knew was that I was gay, that I didn't choose it, and that the God represented by many Christians could not be an all-loving, all-powerful creator. How could he allow my fundamental human desire for romantic companionship to be directed toward the same sex and then reject me because of it? My unchosen desire was incompatible with the term righteous, so I was hopelessly stuck in the "sinful" category.
Without knowing exactly why I was gay, I found it hard to summon the courage to come out. I was in awe of others I read about online who had come out to their families, schools, or faith communities. I wanted to take this step for the other gay kids at my school whose lives might be significantly improved by my action. But how to start? At school, insecure boys used _gay_ as a casual insult.
Most of my school friends were agnostics or atheists and were more in touch than the Christian kids. To us, Christianity seemed like a club with narrow, oppressive political values. We aspired to the real freedoms we knew existed beyond it. Privately, I was still captured by what I knew of Jesus and reasoned that he had been the greatest human being in history. But he'd been lost in a human-invented religion that tried to make him into a god. I pictured this human-invented religion like the pencil sketches in my Good News Bible, portraying a cookie-cutter Jesus who made me gay (that would explain it!), then cruelly condemned me for it.
Yet I had a persistent inkling that maybe there was a deeper answer in those pages.
## **THE GRACE OF A GIRLFRIEND**
As I was struggling with all of this, I started seeing a girlfriend, Liz, from our sister school. She made me laugh and had a kindness and warmth that attracted me to her. She liked me because I was different—I danced better than most at our school dances, and I didn't stare at her midsection when we talked, like most of the other adolescent boys.
One afternoon we went to a film. _Planet of the Apes_ was the only one showing. After I bought our tickets, we both burst out laughing when she said that all told, I won the award for the most unromantic boyfriend ever.
We enjoyed the hammy moments of the film and she held my hand for the first time, but I was preoccupied. By the time the credits rolled, I'd decided to tell her my secret. I knew she was a safe person, trustworthy and mature. I also knew my secret meant the end of our relationship, and I felt the weight of something like guilt in the pit of my stomach.
As we walked out of the cinema, she glanced at me. "I'm sorry this was such a bad third date!" I said.
She took my hand. "David, why does it seem like you never want to kiss me or be close?"
"That's a hard question. I'm not really sure why I'm like this," I said, looking away.
"Like what?" she asked gently.
"I've wanted to tell you for a long while," I said, swallowing. "Remember my favorite park I showed you a few weeks ago? I've never had a suicidal thought in my life, but when I was there a while back, I wanted to jump off the cliff's edge, and just about did it. I was petrified.
"I have to tell you, Liz—I've been attracted to guys since I can remember. I need to finally face it. I didn't choose it, and it isn't going away."
As I spoke, relief came. And with it apprehension for what I had just voiced into the world.
Liz looked away, quiet. After a long silence, she bounced back with her usual direct but affectionate manner. "You need to come out, David. Need to. Tell your parents, okay? Promise?"
She hugged me, and I heard both sadness and concern in her voice. "It's important you be honest about who you are. You can't live with that eating away at you."
## **TELLING MY MOTHER**
I came out to my group of close school friends later that week. It felt amazing to be myself, fully accepted by them. But they weren't my biggest hurdle. By that Saturday, I couldn't keep the truth from my mother any longer. (I usually told her everything.)
I didn't expect negativity. I knew Mum had many gay friends, and she had raised me to love and respect gay people. Her friends, Chris and Tim, a couple from her university days, were our good friends. They had taken me to see musicals when I was a toddler. I felt a deep affinity with them that I later understood was related to their being an openly gay couple, committed to each other for more than forty years, even when discrimination toward gay people was far worse. But I still felt unbelievably sensitive about broaching this with her. How would she respond when it was a son?
I thought about all this as we drove to a friend's birthday party. When we pulled up to the house, she smiled at me with her kind hazel eyes and kissed me goodbye.
I looked out the window of her blue Volvo, my hand hesitating on the door handle.
"Bye, David!"
There was a pause. "Mum, before I go, I have to tell you something."
"What, darling?" she said, her tone changing to concern when she saw my pained expression.
It had come to the moment, and it was too much. Why? I looked away. "I don't think I can actually say it."
"Have you got someone pregnant?"
I shook my head, fighting the urge to laugh. Would teenage fatherhood be preferable to this?
"Are you gay?" she said as the summer humidity began to fog the windows.
"Yes, Mum," I said. Those two words felt impossibly heavy.
She reached over, wrapped me in her arms, and wept. I'll never forget the feeling of the leather seats, her wet tears on my clothing. And in that moment, I felt peace—real peace—for the first time in years, for the first time since I'd discovered I was gay. And I somehow knew that her tears weren't about her at all; they were about me. She knew how much harder my life would be as a gay man. "I'm just sad that you'll have to live with the difficulties so many gay people do," my mother said. "But we love you no matter what, David. We are with you."
By the time I got home from the party, my mother had told my father. He was fully accepting too, even if his vision of my marrying and having a family had been shattered. He proudly told me he looked forward to one day meeting my partner.
Conversations continued in the following weeks about whether this was a stage. But I knew it wasn't. Mum took me to visit a psychiatrist who was an expert in sexual health. He kindly helped me accept myself. He told me my attractions were just like having a different hair or eye color and should be a source of pride.
Coming out was deeply difficult, but it was liberating. Finally, I could be completely real with my parents.
And for a little while, I felt a respite from the war within.
# [ ** CHAPTER 2
QUEST FOR SPIRITUALITY ** ](contents.xhtml#conn_7)
> I am the LORD, and there is no other; apart from me there is no God. I will strengthen you, though you have not acknowledged me.
**_—Isaiah 45:5_**
**N** ow that I was being honest with my parents about this significant part of who I was, I wanted to reexamine the rift between homosexuality and religion. Were they really incompatible? Or was there some truth beyond traditional Christianity, which, I was convinced, stood in the way of LGBTQI people's rights? I wondered, still unable to shake that sense of something _real_ about Jesus.
I asked Mum to drive me to an affirming (of gay marriage) church on the other side of town.
We pulled up to the dull-red-brick building, adorned with rainbow flags and a big "Welcome" sign. As we entered late, we saw they were having a Communion service. The congregation was split between two groups of people—one of which, I would later learn, didn't believe in Jesus' physical resurrection.
The paradox of this church intrigued me, and I was amazed to see LGBTQI people together believing in Jesus. Yet it was the ideal of marriage, not faith, that attracted me to this church. I wanted desperately to be married. I pictured myself beside a creatively gifted, intellectually bright, and handsome husband. We'd live in an apartment in Paris, adopt an orphan, take in a poodle.
Gay marriage seemed an essential right. It harmed no one. I had no idea why the majority of Christians, who held moral sway in society, were obsessed with what others did in their bedrooms. But after attending this church for some time, something felt missing. Deep down, it seemed wrong that they were separated from the rest of the church. I also thought the arguments I read by Bishop John Shelby Spong, their favorite theologian, didn't make honest sense of the Scriptures or reconcile with traditional Christian beliefs, like the resurrection. Mum felt the same way. I didn't believe in it, sure, but I couldn't make sense of the incoherences either. We decided to leave.
Christianity continued to haunt me and my mother, though. In following months, as I came out to Christian members of my extended family, there were difficult conversations about faith and sexuality. "David, you can't accept Satan!" one of my cousins said. " _He_ gave you these desires. You just need God to help you change." Well, that explained a lot—the devil made me do it, apparently.
That was it. I stopped trying to reconcile my homosexuality with Christianity and determined to find fulfillment through some other spiritual path.
## **LOOKING FOR SPIRITUALITY**
As the years of high school passed, I caught the train to downtown Sydney often. I spent countless hours at Adyar, then the largest new age bookstore in the southern hemisphere. The store and its regulars were my oasis in a boring suburban existence of Saturday sports and my all-boys school.
I developed a crush on one of the front counter cashiers, whom I often observed behind the labyrinth of bookshelves. His dark curly hair and broad smile revealed a peace and security I'd never seen in another gay man. I found out he was a witch; he wore a pentagram, a five-pointed star used by the Wiccan religion, visibly under his shirt. "The four points represent the four elements—water, wind, fire, and earth—and the fifth is spirit," he explained.
He didn't fit the diabolical picture of witches I'd been given by Christians. He seemed a deeply spiritual person who accepted his sexuality and welcomed me with ease. I wanted that calm confidence he had.
I asked him for books on Wicca and tried to learn everything I could about "the craft." I was desperate to find a universal power or mystical reality, and Wicca allowed me to shape my own worship. I enjoyed the honesty and comradery of the neo-pagan community and even tried to start a half-hearted coven at my school.
Learning about the church's historical treatment of witches and people who practiced other spiritualties confirmed to me that Christianity was a grave, hypocritical evil, responsible for so much pain in the world. As I got to know others, it was clear many LGBTQI people became Wiccans directly because of how the church had treated them. Christianity was the enemy. Not only its people but the worldview it espoused.
But rejecting it also left an intellectual and philosophical void. For all its attraction, Wicca was impossible to test rationally, and I saw it was a too-easy projection of how I wanted the divine to be. I felt like I was bottoming out. _If the gods we worship are_ _exactly like us,_ I wondered, _are we just creating divinity to be like us or in our own image?_ I decided it was no longer for me and saw no further hope in it than what I already had.
So on I went, and on, always further on. Truth seemed to slip farther away the more I grasped at it. Eventually I read up on Theravada Buddhism, becoming enthralled by the person and teaching of Siddhartha Buddha, and decided to become a Buddhist. Buddhism seemed like a peaceful belief system with a certain logic to it that could be compatible with the more demonstrable parts of my worldview, while happily ignoring the issue of sexuality.
For most of 2005, I followed the teachings of the Dalai Lama, who argued that the center of the human problem was desire itself. Through meditative practices and self-denial, we could reach nirvana, a state of perfect consciousness. I attempted to move through the different levels of attainment by ridding myself of desire, even the desire for romantic love.
But eventually I became disillusioned with Buddhism too. Its negative view of human desire and its notion of dharma condemned humanity to an eternal cycle of self-justification and reincarnation. Didn't our desires _matter?_ Weren't they part of what made us human? And if so, didn't they point to something outside us, something we long for and were made to experience?
_My quest for love must have a reason behind it,_ I thought.
## **AN OFFER OF GRACE**
I'd become known around school for my opinions and desperately wanted to see a protective policy for LGBTQI students. Eric seemed to respect me for it. His reaction was different from those of the other Christian friends I had in my classes. He didn't annoy me as much as the other Christians, who, I was convinced, believed just because of their upbringing.
But still, no matter how I tried, I couldn't escape the influence of Christianity, at home or at school. It irked me. Whether in class or in casual conversations, it seemed like Jesus would not stay tidily out of my life.
My friend Eric caught up with me one day as we came out of choir practice. "David, do you know what grace is?"
The question was so out of the blue, I was taken aback. "I don't know if there's any of that for LGBTQI people from your ridiculous God," I replied.
"I just think it's important for you to know that God accepts you and GLBTQI people," he said.
"Eric, it's L-G-B-T-Q-I—lesbian, gay, bisexual, transgender, queer, intersex," I snapped.
He looked hurt, and sure, I had spoken harshly. But he asked for it, right? _Do I know what grace is? Who does he think he is?_ But, apparently unable to take a hint, he continued walking with me on our way to our Christian studies class.
"I still don't understand why this school makes Christian classes mandatory," I grumbled, trying to change the subject.
"Jesus is the greatest figure in history. Don't you think we should learn about him?"
I tensed. My mother had surprised me recently, saying she was considering becoming a Christian—like, really believing, not just attending services. I responded to Eric with pent-up anger. "Hey, my mother's been talking about actually believing in your imaginary God. I just told her she needs to choose between the delusion in her head and her real son right in front of her."
He seemed excited by the prospect of my mum believing. "I don't need this from you too, man," I continued. "Come on. You really think she should pick an immaterial delusion over her flesh-and-bone son? She's even saying stuff like by loving God, maybe she'll love me better. I told her she has to choose. Him or me. I hope she picks the one who, you know, actually exists."
Entering the classroom, we picked up red imitation leather Bibles and sat down. I rolled my eyes at Eric. The reverend at our school had given us all diaries in which to write our thoughts, questions, and objections as part of our final mark for the class. I would often tap my shoe as the reverend spoke, largely unconvinced by his answers to student questions that cropped up as we read.
That day we started our reading in Luke 16. Jesus was telling a parable about the afterlife, and as we read, I felt ready to explode. Was I the only one seeing through this farce? It seemed so fake.
My hand shot up at question time. "Sir, I don't understand how you can believe in God or this book. We know so much about the universe and science, and we're still talking about fairy tales? Not just harmless ones either; church history is a history of oppression. It's delusional or worse to believe that without Jesus Christ someone's going to hell for things that aren't even their fault."
The reverend smiled kindly. "David, Jesus welcomes any questions we have. There's freedom in belief, not just a history of oppression."
"But why are we wasting our time reading a dead book?" I was getting closer to the real question, the one I'd been dancing around since my hand shot up. "And what about your view on gay marriage?"
Everyone stared, like I'd stepped over a line. Not that they were surprised, surely, with the question coming from me.
"I'm gay," I continued. "So what about people like me? Are we loved by God, as you claim, or are we unable to enter the kingdom of God, like Paul says in 1 Corinthians?"
That was one way to quiet down a room of high schoolers. But our teacher seemed unfazed. "Let's talk after class," he said. "You're asking an important question. It requires a much longer answer than I can give without delaying the class."
At the end of class, as students stood and chattered, filing out the door, the reverend caught me before I could leave. I was still fuming. He handed me a black notebook. "Write it all down," he said, "all your questions and objections. I promise to respond." I took it and nodded, thinking that the poor man had no idea what he'd just signed up for.
I wrote and wrote and wrote. I worked to organize my questions, from the most pressing and concrete to the more abstract, and every week he would respond to one. It was obvious that he was taking time, really engaging, with a kind of intellectual honesty that disturbed me. It was easier to dismiss believers as ignorant, cruel, or numb to real issues. But he didn't let me dismiss him. It was too evident that he cared.
It was the first time I'd felt loved by a Christian. He took each question seriously and wrote back with his opinion. We covered gay marriage and the Bible's stance on homosexuality. We covered the historical accuracy of events in Genesis; the trustworthiness of the Gospels; Paul's view of women; evolution; the problem of suffering; and the question of salvation and other religions.
But I remained unconvinced. Homosexuality was my stumbling block. He talked about God's love for gay people, but I still couldn't comprehend how, if I were to become a Christian, my homosexuality was reconcilable with Scripture. I just didn't see it.
Around this time, I was also close to fully embracing atheism. I'd met with my English teacher, also willing to give my unusual questions extra attention, and my interests started to turn to postmodernism. I was attracted by the agnosticism of existentialists like Jean-Paul Sartre, Albert Camus, and Simone de Beauvoir and had decided to take extra units in French to better understand their work.
It felt like my mind was being stretched between two points that were quickly moving apart. I would have to choose one or the other or snap clean in two. Christianity seemed impossible to embrace with intellectual or personal honesty. And yet the atheists brought with them a profound sense of emptiness. For all my anger at the church, for all my objections, for all the oppression, there was meaning there. Disagree, sure, but I could not fully dismiss it.
Christians? _Hypocrites, of course,_ I thought. _All of them._ But were the secular atheists any better? Their problems ran just as deep, it seemed; they were just different. There was a hypocrisy about atheistic existentialism, a fundamental self-contradiction. Try as I might, I could not make it add up. If I took moral responsibility for my own actions, the consequences would outweigh my capacity to repair them. I would be condemned to always be like Sisyphus, rolling the boulder of my choices up and down the mountain of life. And was that it? Was that constant torment of consciousness what it really meant to be human? Was helplessness the result of rationality?
I'd abandoned what I thought was an absurd world of the spirit, whether ensconced in high-church hymns or enshrouded in adolescent witches' covens. But would existentialism leave me just as empty?
De Beauvoir's heart had been crushed by Sartre. They had it all figured out but couldn't even live well with each other. There had to be something better, but I felt farther away from it than ever as the weeks went by.
I eventually resumed wrestling with that hated book I could not shake off. One night I opened the Bible and read all six passages dealing with homosexuality. By the end, I threw it down, determined to never read it again.
The Bible was a dangerous book. It taught, I thought, that simply by being who I was, I was the worst of sinners, unable to inherit the kingdom of God and unacceptable to the very one who made me. What kind of God makes a person with one hand and condemns him with the other? What kind of good news is that? No good news at all. I saw it with a terrible finality that, for the moment, ended all my questions.
The Christian faith was bad news. For everyone. It was especially terrible news for gay people. I had no love for this cruel, imaginary God and never would. To love him would be the ultimate betrayal of myself.
I decided that night, with my Bible open and a seething fury in my heart, that I was going to dedicate my life to stopping the Christian faith.
# [ ** CHAPTER 3
THE FRENCH EXCHANGE ** ](contents.xhtml#conn_8)
> The LORD appeared to us in the past, saying: "I have loved you with an everlasting love; I have drawn you with unfailing kindness."
**_—Jeremiah 31:3_**
**H** ow adult I felt then! Wrestling with the foundational questions of existence has a way of growing you up. But really I was still a young teen.
When I was fifteen, I found myself at the end of a two-month student exchange in France. One evening, my host family and I had returned from a holiday in Ardèche, and as I unpacked in my room in their apartment, with its beautiful parquet floor and high roof, I looked out again at a tiny café where a regular always sat smoking a cigarette, reading the newspaper, and sipping his coffee. That winter, I had mimicked him by reading or writing letters by my window, coffee in hand. Often the sound of organ music serenaded me as my French dad practiced for Mass.
I found the godlessness of France attractive, and its staunch separation of church and state, called _laïcité,_ comfortable. During my stay, I had attempted to read _Existentialism Is a Humanism_ by Jean-Paul Sartre, using my high school French skills. I finally deciphered Sartre's thesis: unlike Søren Kierkegaard or Fyodor Dostoevsky, he didn't believe God was necessary to be an existentialist. I too didn't need a belief in God for meaning and significance. I could happily invent that myself.
"Existentialism is not atheist in the sense that it would exhaust itself in demonstrations of the non-existence of God," Sartre wrote. "It declares, rather, that even if God existed that would make no difference . . . what man needs is to find himself again and to understand that nothing can save him from himself, not even a valid proof of the existence of God."
France represented my freedom from all those fundamentalists with their talk of a judgmental God. As an agnostic atheist, I also now identified as an existentialist in Sartre's line.
Before long, I said my goodbyes to my host family _._ My French dad accompanied me to the _Lyon-Part Dieu_ station and placed a CD in my hand on which he had stored a short film he had made with footage from my trip. On it was a quote from my favorite French film, _Amélie_. He hugged me and gave me two big _bisous_ on my cheek.
All the Australian students staying in France met for a reunion in Paris before heading home. As we huddled at the train station and ordered espressos to go, we were abuzz with the delight of our experiences. Later that night, I felt a deep liberation as I sat in my parquet-floored hostel room.
But I was also sad. A secret internet love interest had sent his last letter weeks before, breaking off our relationship. As I explored Paris with my friends and found myself in the center of Paris's lively gay community in the Marais district, my heart ached to find love. Surveying the cafés, Jewish delis, and clubs concentrated in what seemed a cosmopolitan utopia, I wished I could stay there forever. Yet in this free, secular space, I sensed an open wound in my heart. My search for God had waned, and a painful desire for romantic love had replaced it.
## **IMPOSSIBLE SPIRES**
As I waved goodbye to my friends in France, I boarded a plane for London to see some of the United Kingdom with my mother's ex-colleague, Daniel, before returning home to Australia. He was a kind man and an ardent atheist. We were fond of each other. He knew I had rejected the Christian faith after coming out a year before, and we shared a similar disdain for religion.
Daniel collected me from London's Heathrow Airport in his blue Ford. We were soon out in the English countryside, and I sat quietly, taking in the lush green landscape for the first time. Daniel had blond hair, thinning on top, and a charming gap in his teeth when he smiled. As we drove, thatched houses, sheep, tall birch trees, and flat pastures blooming with spring flowers dazzled me after the long French winter.
After settling in at Daniel's lovely Cotswolds cottage just outside Strafford-upon-Avon, we decided over tea to see Oxford the next day. We mapped out each site, with our final evening stop at Christ Church Meadow. My image of Oxford was rather grand. It was an idea to me, the place of an intellectual golden age, the enchanting domain of masters of the imagination like Lewis and Tolkien. It was the university of people who made history.
The next morning was blue and beautiful. Passing for an hour through verdant fields, we finally entered Oxfordshire. After touring colleges and visiting the Ashmolean Museum, Daniel insisted we stop at the famous Blackwell's bookstore. He said he'd buy me a book of my choosing and select one for me as a gift. As we searched the enormous underground selection of books, he came back to me, smiling.
"I think this will really help you. Your mother has told me you've been on a spiritual quest to find some kind of faith," he said as he passed me _The Selfish Gene_ by Richard Dawkins. "Also, with your interest in Sartre, Dawkins will help you with the freedom of realizing there is no God. We can all get on with our lives!"
I was charmed by the intensity of Daniel's tone. As we walked, he explained how evolution alone explained our search for love and transcendence. He reiterated how we had to rise above blind faith to regain a human ethic of generosity, even if we were born selfish animals bent on our own fear-based survival.
The conversation turned to my future as we passed into a huge meadow where college rugby teams were training. We paused, watching the players. My breath caught at this stunning vista of Christ Church and Corpus Christi colleges, with the setting sun reflecting off the millennium-old sandstone buildings. _I will never study here. I'll never be good enough,_ I thought. I would remember these thoughts and words of self-doubt years later when I returned to Oxford.
My time in France and the UK brought me great freedom. But the future remained unclear, and my desire to find love was greater than ever. I wondered if I would ever find the belonging and intimacy that I longed for with every atom of my being.
# [ ** CHAPTER 4
BOYFRIENDS AND PSYCHICS ** ](contents.xhtml#conn_9)
> Now, this is what the LORD says—he who created you, Jacob, he who formed you, Israel: "Do not fear, for I have redeemed you; I have summoned you by name; you are mine."
**_—Isaiah 43:1_**
**R** omantic relationships and sex were everywhere and in everything I talked about with my teenage friends. Frankly, I was exhausted by my sexuality being just a theory.
It was almost the school year, and I decided to have my three best friends over to celebrate. My parents had gone away for the evening, and I ordered pizza for a movie night and slumber party. We could enjoy our newfound teenage freedom and stay up as late as we liked.
My three friends were all so different. But one of them stood out. Really stood out. Andrew, who joined us from the more rebellious group of boys at school, was deeply perceptive and had a quick intelligence I found appealing. We were in the same English class, and an emotional chemistry and friendly rivalry had grown between us as we discussed books, especially French writers and Shakespeare. We loved the same bands and planned to buy tickets to the same concerts. We had so much in common.
I sat next to Andrew on the old green leather couch and pulled up a big woolen blanket for us to ward off the early autumn chill. As we started the final film, I felt Andrew's hand slide next to me under the blanket. I was shocked. Nothing like this had happened before. My heart rate doubled—or at least it felt like it did.
The intensity of my fifteen-year-old reaction was hard to handle. All the pent-up excitement from years of watching gay sitcoms flooded through me. I reached my hand over to reciprocate. _Is Andrew gay?_
Andrew looked over and smiled, and my heart thudded as I processed his advance. I gestured to go upstairs to my bed, leaving the others to the film. He looked straight back at me. _This is it,_ I thought. _This is the moment I've waited for._ My desires were about to be more than theoretical. I couldn't wait to get to my room.
But as we both lay heatedly back on the bed, Andrew suddenly pushed me away. "Oh, God, no! I'm not gay. I can't believe this has happened! What was I thinking?" Sitting up, he hit his hand against his forehead.
"Andrew, it's okay. There's nothing wrong with being gay," I said, trying to comfort him.
"Get away from me!"
"Let's at least chat this through . . . or we could just hold each other?" I said, realizing he was slipping away.
"You're the one who did this to me!" he said with a scowl.
"Andrew, you need to accept yourself. Don't take this out on me," I whispered, afraid of waking the others.
"I'm not gay, David. I'm not interested in you, and I don't find you in _any_ way attractive. This whole thing is over," he said. He moved off the bed and hit his head hard against the wall. I tried to stop him, but he pulled away and slammed the door behind him.
My heart dropped. My first sexual encounter was over before it had really begun. I felt lonelier than ever.
As I stared out my window that night, the universe remained indifferent and the stars glinted coldly. It felt as if there was nothing but an infinite, cruel void. Perhaps loneliness was my fate, no matter how hard I tried.
Eventually I pulled up the covers, wrapped my arms around myself, and wept for hours. The next morning, I awoke to blue but chilly skies. I told my mother what had happened, and she called in late to work.
I'd lost not only a friendship but also my virginity. I hadn't wanted it to be like this; I wanted a loving boyfriend who would be there for me and vice-versa. If only I could find a partner like me, one who was free and open, I would be complete and loved.
I didn't go to school for weeks. The shame in Andrew's reaction was, for me, exactly why things had to change in our society, and why I would become an activist.
## **THE AMBER CROSS**
In time, the initial sting of my experience with Andrew numbed. But the deep, gnawing desire for connection didn't. Months later I met Vlad through a chat room for gay teenagers. He attended my neighboring school, and we began a relationship. Vlad was unique, with a sensitivity and maturity beyond his age. He had been a ballet dancer and always stood with perfect, confident posture.
One day of our time together is engrained in my memory forever. My train to meet him slowed at the station platform with its habitual clunk. The doors flung wide, and the smell of burnt rubber hit me, and the cries of schoolboys rushing to take their seats filled my ears. The blue and red of their jerseys blurred as I peered through the crowd, where Vladimir was waiting at the end of the platform. As I ran up the last few stairs, I could see him waving at me to hurry. I just made it. We got on together just as the train doors closed.
I was relieved to finally be done with the school term, and excited for time alone with Vlad. As we filed to the end of the train, we decided to get off at the next station, near our favorite hangout spot. This area of the suburbs had leafy parks where we could escape from view. I had to keep reminding myself that Vlad, my first real boyfriend, hadn't come out yet.
"This weekend I'm seeing my father," Vlad explained. "He wants to take me to the Orthodox church. We have a feast day, and my grandmother's going to cook Russian dumplings."
"That's nice, but isn't your dad a complete homophobe? I thought you weren't seeing him since your parents divorced."
"My father is just _Russian_ about homosexuality," he said quietly as some boys from our brother schools rushed past us. "It's like something he's allergic to." He brushed his hand against mine, and his blue eyes shone as we walked.
"How can you go to a church that hates you? I would be so angry with my dad if he were a Christian," I said as we made it up the station stairs. The spring sun shone over the park, and the scent of freesias and freshly cut grass was on the breeze.
"Being Russian is more complex than that, David. Church is a part of our identity. I don't agree with my dad, but I love him," Vlad said.
I shook my head. "I don't like anything traditional like that, Vlad. Christians are bigoted. I mean, I'm spiritual but the Bible's just horrible. I can't stand how ignorance can shroud itself in religious ceremony. Why would a supposed God of love create us with these desires and then punish us for them? Even if Jesus never said anything about homosexuality, God made it pretty clear. I really think it comes back to Paul, who clearly had issues with women and gay people . . ." I trailed off, realizing I'd lost Vlad's attention and that he had found a place to sit down.
After looking to see if the coast was clear, he pressed his finger to my lips and then kissed me. "I have a gift for you," he said, pulling a small pouch from his duffle bag. He dropped it in my hand and smiled proudly. Opening it, I discovered a fine silver-chain necklace with a small amber cross. I held it up and watched as the amber's golden flecks glinted in the sun. It was a mysterious but beautiful symbol.
"My father gave it to me when I was a child. I've been thinking about giving it to you for a long while," Vlad said. "It's just a little token of faith, something to carry on you."
I pulled him in to kiss me. I had met an equal, a true companion, someone who wasn't going to run off, who wasn't afraid of deeper things. Something about him fit, even if I thought his faith naive and misplaced. As we kissed, a sense of security filled me.
Suddenly a weight thudded against my rib cage, knocking me sideways. Pain pulsed through my right side. In my peripheral vision, I saw something land at my feet in the grass. I looked down, stunned.
It was a large rock.
Vlad's face went red with shock. Wincing at the pain, I looked behind me and saw a man with a white helmet. He flicked his visor down over his face and mounted his motorcycle. As the low growl of his throttle pierced the air, tears of both rage and sadness streamed down my face.
Instinctively I touched the amber cross still hanging around my neck and over my white oxford shirt. Somehow it both confused and comforted me.
## **GRACE FORETOLD**
One of the cafés I liked the most was nestled in the heart of one of Sydney's inner city suburbs, Newtown. The walls were covered with organized sections of books, poetry being my favorite. Posters littered the notice board, including three for a marriage equality march.
It wasn't that long after that day in the park with Vlad. I was meeting up with my best friend, Emma. As I entered the café and ordered my usual soy chai, I looked around but barely recognized her. Her hair had been dyed black. "Hey! What have you done to your hair?"
Emma put down her book. It was my favorite biography of Jean-Paul Sartre and Simone de Beauvoir, one I'd picked up at a writer's festival. "I'm sick of being valued just for my blond hair. It's my statement for the cause of women!" she said enthusiastically.
I smiled and sat down. "Love it. So _you're_ the token feminist and _I'm_ the token gay activist. Is that how this is gonna play out?" We laughed.
"I actually just dyed it for fun; the protest is secondary," she said with a flourish of conscience. "Also, I'm doing a part for a theatre piece, and it fits with the character."
She leaned toward me. "So, you know how yesterday we were talking about getting in touch with our spiritual side? I saw a sign for psychic readings down the road. Have you ever had your cards read? I'm kind of curious. Want to go?"
I thought of my past obsessions with Wicca and new age religion. I now considered myself an atheist, but I figured there was no harm in a simple reading. We walked down to the health food store, and as we entered, the pungent smell of vitamin tablets, dietary supplements, and patchouli oil filled our senses.
I strode up to the counter, where a woman with dreadlocks tied up in a bun was sitting, filing through the day's receipts. "Could we please have our tarot read?"
She looked at the clock. "Sorry, there's only one reading left for today. I can arrange it for one of you in about fifteen minutes. It's twenty dollars for thirty minutes."
Emma was happy to go another day, so we waited for my reading. I was filled with nervous excitement. When it was time, I passed through the beaded strands that hung in the doorway, clicking exotically together.
A rosy-cheeked woman with dark hair and a large, purple velvet coat greeted me. Sandalwood incense filled the room; aromatic candles flickered in the background. The fragrance was effusive and intense but pleasant.
"Nice to meet you, David. I'm Rose," she said. "Let's begin." We sat down at the table. She looked into my eyes for a moment, then pulled out her deck. Shuffling it, she placed the deck face-down on the table, and then drew tarot cards from the top, placing them faceup in front of me until a full reading had been laid out. I was skeptical, almost amused by the spectacle. _People believe in this stuff? I mean, it's fun, but . . . seriously?_
Rose inspected my cards. She seemed to be consulting a spirit guide in the form of a Native American sketched on a paper next to her. Suddenly, she looked at me in amazement.
"Incredible! You are very blessed! I need to tell you this now. You are a child of the light, destined to be with the greatest mediator in the spiritual realms, Jesus Christ. He has chosen you!"
I was a bit glazed for the rest of my reading, not really listening to her half hour of babbling about the various cards laid before me. _Jesus Christ?_
Back at the café, I fumed. "Emma, I think that medium is actually an undercover Christian evangelist."
She sipped her latte and cackled. "Uhhh . . . _what?_ "
"She said I was destined to be with _Jesus_. I don't think she knew who she was talking to!"
"Maybe she's right, David," Emma said matter-of-factly.
I made a face. "What do you mean? There's no way I'd ever become a Christian. Mark my words. She's a con artist."
"I used to be a Christian," she said. "Maybe it's true, Dave?"
I shook my head furiously. "I hate Christianity."
The next week, Emma returned to have her cards read. Rose never mentioned anything to her about Jesus.
The God who I thought hated me still haunted me, even through a fortune teller's words. And it wouldn't be the last time I wanted God to leave me right alone.
# [ ** CHAPTER 5
THE GAY WORLD ** ](contents.xhtml#conn_10)
> There is a way that appears to be right, but in the end it leads to death.
**_—Proverbs 14:12_**
**M** y teenage years passed, and at last I could put the all-boys school behind me. I often had moments of realization that I was finally free. My university years stretched out ahead, full of possibility. I immersed myself in this new world of student politics and activism, delighted to find a community I could fully belong to.
University felt like safe territory as an open and out gay man. At this time, I began calling myself queer after studying queer theory, which at its heart was about representing the voices not heard in mainstream culture or on the margins.
The political party I was involved with organized a huge rally for marriage equality, and we marched across the Sydney Harbour Bridge. Bedecked with glitter, I held a placard with the words "All love is equal" in one hand and a megaphone in the other. Shouting, "Shame!" at the small group of Christians holding homophobic signs thrilled and empowered me, and my friends and I snickered as we paraded victoriously past those "ignorant idiots." It was one of the greatest moments I'd had since coming out.
My student political faction had also been working nonstop to support a new bill that would legalize and recognize same-sex unions in the Australian Capital Territory and pave the way for nationwide gay marriage. This would mean full legal equality, and eventually societal acceptance, for our relationships. Predictably, Christian political groups were actively blocking this legislation. They had their rights. Why couldn't we have our own?
Weeks before our impending victory, I found out my mother was closer to becoming a Christian. Again I told her she had to choose between the God who hated me and her son. Was my own mother going to sacrifice her love for me to become a conservative?
When Christian people told me they were against same-sex marriage, it enraged me. I believed the Christian God was a moral monster who had punished his son on the cross as an act of divine child abuse. He had become a weapon in the hands of homophobes, used to deprive LGBTQI people of their rights.
Every time a Christian mentioned traditional marriage or even commented on homosexuality, all I heard was hate. The words "homosexuality is a sin" meant we couldn't have a relationship with God or a romantic companion, the two sources of human meaning and happiness. It was as if we were being stripped of dignity and deleted from existence. Anyone who thwarted our access to full acceptance was our enemy.
At last the bill went through. The LGBTQI community was known for having exhilarating parties, and the party to celebrate our victory, held at my friend's terrace house, was no exception. All different types of people from the gay political world were present, from young clerks working for inner-city ministers, to partisan hacks who spent their time constructing the next political stunt, to affluent professionals who used politics as a dating service, to queer activists who often came from less privileged backgrounds.
That night, one of the partisan leaders expressed interest in me. I didn't reciprocate, but his advance gave me the kind of power I desired within the party. Even as I told him off, I was repulsed by the power-hungry person I was becoming. There was something harsh and hard and foreign creeping into my heart. Was this really who I wanted to be?
## **MARDI GRAS: PARTIES AND PARADES**
Pushing doubts aside, I continued to embrace my growing role in the gay activist community. When I turned eighteen, as a rite of passage, my queer friends signed me up to be a Mardi Gras parade official. This was the night our community took over Sydney and celebrated the freedoms we'd won. We sent the clear message, "We're queer, and we're here to stay!"
This event also honored LGBTQI people who had been horrifically treated throughout Australia's history, and those around the world who had been treated as criminals, abused, locked in shame and darkness, or even executed. (Today, in seventy-four countries around the world, homosexuality is still illegal, and in twelve of them it is punishable by death.) But one day we wouldn't have to live in fear.
I counted the days until the parade. A journalist I had been chatting with online told me he'd be waiting at the after-party, and I hoped I might find both emotional connection and an intellectual equal. On nights like these—celebrations of the right to love who we loved—I always planned a romantic conquest.
Lately, I often stayed at different guys' places on weekends, though most of the time I didn't want sex. I didn't like to sleep around, considering what I'd learned about HIV/AIDS and the tragedy it wreaked in our community. To me, promiscuity had nothing to do with being gay. I craved company and intimacy. I believed that one day my search would lead to the committed, monogamous relationship I dreamed of and so fervently wanted.
The day of the parade, I was given a huge water pistol to ward off crowd members who attempted to climb the railing and join the floats. I watched the first float, "Dykes on Bikes," move into place to inaugurate the parade. The sound of cheering and official whistles filled the air as the lesbians led off. To my right, a gaggle of drag queens tried to jump the barriers and join the next float. I blasted them with the water pistol I had been given, washing them down as they laughed and shouted obscenities, mascara streaking their faces. _I'll never forget this,_ I thought, laughing hilariously.
The onlookers' cheers were electric as they thanked us for keeping the parade safe. This smooth operation was proof that gay people were no different from the rest of the world. We were human too, a colorful explosion of diversity, and capable of peacefully celebrating our humanity with all its faults, strengths, beauty, and ugliness.
Marching down the street, I was filled with joy, as if a weight had fallen off my eighteen-year-old shoulders. I felt free from all those years of constant questioning. I was gay and proud of it. I had accepted myself.
When the parade ended and the after-party was about to begin, I suddenly remembered that journalist. He'd texted me, saying he was waiting for me in the dance hall. I entered the huge warehouse, lit up with strobe lights and pulsating with chest-thumping house music. Thousands of gay men with gym bodies were dancing shirtless, a sea of exuberance. At first I was gleeful, but as I watched this moving mass of bodies and saw men locked in lustful embraces, I felt on the outside somehow. _Are these my people?_ I asked myself. _Is this what it means to be gay?_
This was the tension I always felt when I was in settings like this. Was being gay just about having a sexual thrill or casual fling, or was there a deeper meaning? To me, being gay wasn't just about sex; it was about a common experience within a community. And this party somehow felt disconnected and impersonal, without the personal acceptance that being gay meant to me. This didn't feel like what I wanted.
I pushed back these thoughts and pressed through the sweaty crowd, still looking for the journalist. The strobe lights flashed, blotching my eyes. I just wanted to get out of there.
I looked and looked. Finally, after an hour, I spotted him, kissing a man with muscles like those of a Greek statue. He saw me staring at him, then turned away, locking eyes with the other man. I left, stung, with doubts I hadn't had when I walked in.
The joy of the parade was soured by a deep pang of ambivalence. _There has to be more to being gay than this._
## **"WHAT IS LOVE?"**
That doubt would rise and fall like the tides in Sydney Harbour. My search for a deeper love took me to even more adventurous places. Not long after Mardi Gras, I found myself in the heart of Sydney's gay and alternative scene, at one of its most celebrated clubs on Oxford Street. All of Sydney's intellectuals, fine arts students, and writers were there. The guest list was exclusive. I recognized some of the faces from political meetings on campus. One person I knew, an actor I'd dated for a while, avoided eye contact.
A small bar served cocktails named after literary figures, and the sound of the band next door filled the room. Everyone's eccentric clothes—ranging from period costumes to rockabilly outfits to casual drag—blended with the music as people danced.
I used to carry a small journal with me for occasions like these. I would write a philosophical question or the stanza of a poem and pass it around to see the response. Never a dull moment with that journal circulating in a room like that! The question I had tonight was horribly cliché, but one I genuinely wanted an answer to: "What is love?"
The music drew me to dance in the middle of the crowd. I watched as my journal circulated the large sidebar space where everyone was either sitting with a cocktail or enjoying the beats. After hours of dancing, I took my journal back from a girl with a white-powdered face who was dressed like Virginia Woolf. I sat on a couch to regain my breath. Opening the Moleskine journal, I saw a myriad of responses in every kind of handwriting imaginable. Most were superficial or humorous, some deliciously explicit, others deeply jaded—to the point of heartbreak. Many people had sarcastically scrawled, "Baby, don't hurt me." A few were philosophical and flowery, including a quote from Proust and one from Plato. But no one had a real answer. Not really. It was a simple question. Was that room as lost as I felt? Those pages showed nothing but an empty abyss, and I wondered if anyone really had an answer that would satisfy.
As the bass thudded and the crowd laughed and danced, I felt a cry of indignation rise within me. In all our films, songs, and art, we worshiped love, but no one could define it. _Really? This is it?_ Maybe no one did know. Maybe no one could know. Maybe in the end, we _were_ just slaves to our biological impulses, cultural aspirations, and desires for fame, attention, and company. Maybe love _was_ just a game of illusions in a reality of "blind, pitiless indifference."
Years later I would read C. S. Lewis's words that describe what I experienced: "If I find in myself desires which nothing in this world can satisfy, the only logical explanation is that I was made for another world." But that night those words were not there for me. The world around me seemed completely vain.
I started to sense that there _had_ to be a higher love that corresponded to my desire for intimacy. Leaving the club, I felt the facade begin to crack. I was losing my faith in the secular world. The war to find love still raged within me, but I knew there had to be more than my incessant search for intimacy in relationships. It just didn't satisfy any longer.
# [ ** CHAPTER 6
UNIVERSITY AND THE LOVE TRIANGLE ** ](contents.xhtml#conn_11)
> Come, let's drink deeply of love till morning; let's enjoy ourselves with love!
**_—Proverbs 7:18_**
**A** utumn leaves skittered across the pavement as I strode through the concrete corridors. They felt like canyons in the urban jungle of my university campus where buildings rose like old-growth rain forest petrified into gray stone. I was returning from an editor's meeting for the student newspaper, where we had decided to feature the gay marriage march I was helping to organize.
My blue shirt read, "We Demand a Better Future" across the chest. Though my bag was heavy with research books and posters, my heart was light. I was grateful to be part of the growing equity and diversity board which ensured the LGBTQI community's safety on campus. The meaning I found in that community and in activity on its behalf overshadowed the nagging doubts I'd felt a few weeks before.
But as I walked past the student commons, I stopped. The Christian Union had plastered their posters over others on the university's main notice board. Just that week, I had read about the mental health of LGBTQI youth from religious backgrounds. I grabbed a staple gun and my stack of marriage march posters, which I had picked up as a leader of the campus Queer Collective. I covered every pastel blue Christian poster I could find. When I finished, I looked over the new rainbow additions to the campus bulletin boards and felt a sense of justice. It was as if I had erected a sign for passersby, declaring LGBTQI liberation from Christian oppression. These little acts of activism, I was convinced, would eventually erode away homophobia and irrational religion. _It's the little things that count, right?_ I thought sarcastically.
I frequently made it clear that evangelical or conservative Christians were my enemies, and I avoided them in classes or at parties. Whenever I saw Christians handing out free food on campus or huddled in their pathetic Bible study groups, my skin crawled. I hated their constant effort to indoctrinate me with the deluded notion of living forever with a first-century Jewish carpenter.
But today I had happier thoughts to consider. When I returned to the main campus building, the glass doors swung wide and I saw my friend Michael, whom I'd met through an LGBTQI community website. We had become good friends and intellectual companions, often discussing our views on atheism and philosophy.
Michael's boyfriend of three years, Samuel, was a fashion designer in training. All three of us had become close, and I would often stay over at their pad in the inner city, playing late-night basketball at the park near their house. This particular weekend, Samuel had invited us to his mother's cottage in the Blue Mountains for an escape from the fast pace of Sydney life.
"Ready for the mountains?" I asked Michael, excited. He was wearing his denim jacket and desert boots and had his bag packed.
He smiled. "Definitely! Great news—Sam is coming with us on the train." I smiled widely. I couldn't wait to get away, just the three of us.
## **ESCAPE TO THE MOUNTAINS**
A canopy of mist hung over the gum trees and shrouded us as I got off the train with my two friends. Samuel was wearing a sheepskin jacket, and his blond hair was set in a curled coif; Michael's light brown hair was shaved short. They held hands, sharing a peck on the lips. Michael laughed as Samuel did one of his spot-on celebrity impressions. I laughed too. These guys were the _best_. I hardly felt like a third wheel at all.
Clouds enveloped us as we climbed down the hill from the station to a wooden cottage affectionately named Bunny Hollow. The house, hidden between gum and wattle trees, sat on a slope with open views of the valley's blue vistas. Samuel showed me the guest room and introduced me to his mother, who greeted me with a warm smile.
"David, it's so wonderful to meet you!" she said, beckoning us into the kitchen for some tea. "Samuel tells me you're going to France next year?"
"Yes. I'm doing the same program Michael did in Italy."
"Where?" she asked as Michael left for the veranda with his tea.
"Strasbourg. To study political science," I said. I couldn't _wait_ to leave Australia. We chatted pleasantly about Europe and travel.
Finally, I looked around. "Where'd Michael go?" I said to Samuel as his mum left the kitchen.
"He's not feeling very well." Samuel sighed. "He gets in these dark moods. There's nothing I can do." Then he abruptly changed the subject. "I always wanted to ask, could you teach me French?"
I smiled at him. _"Oui!"_
As we talked and joked, he sipped his tea. I studied him. Sam was handsome, with a strong nose and unruly hair. There was a curl to his lip that gave a certain symmetry to his face. His stubbly beard was well kept, and he always dressed stylishly, revealing his creativity.
"Before that, I have something to show you down at my mum's art studio," Samuel said. "I've been keeping it a secret from everyone but her."
I should have gone to check on Michael, but I chose to follow Samuel. Ahead of me, he strode down the grassy hill in his brown Chelsea boots. We stopped at a small shack with a corrugated iron exterior. Entering, I saw that in the back were large glass windows that looked out over the mountainous valley. I turned to my right, and my eyes met an array of drawings and designs of couture. I knew Samuel had been to Hong Kong weeks before to collect fabrics, but never did I expect that his new line would be ready so quickly.
Every design was dazzling, sweeping vividly, with staggering contrasts between sharp oriental lines and organic curves. It was like a symphony for the eyes. As I observed each design pinned on the wall, I spotted a line from one of my poems that I'd shown Samuel last term. He'd written it in large letters on his design board! I was flattered.
"David," he said, turning to face me, "you're the most fascinating person I've ever met. I love everything you say and write." He paused. "I made this collection for you." He hesitated, then fingered some of the designs. "You were my inspiration. There's such an energy between us. It's driven so much of what I've designed since we met."
His collection was the most beautiful thing anyone had ever made for me. I was speechless. He hugged me, and I thanked him for showing me.
But as we made our way back to the cottage, the air seemed to grow chilly, the valley turning darker somehow. _He's in love with me,_ I realized with a jolt.
The table was prepared for dinner, and Michael was stoking the fire next to it. I sat down as Samuel's mother brought out a piping-hot casserole. The fire crackled, and I opened a bottle of peppery Shiraz to pour myself a drink. Watching the deep red wine run down the side of the glass, I knew a war was waging in my heart. My conscience told me that allowing feelings to develop toward my best friend's boyfriend was wrong, but my heart told me to go for what I wanted. And I wanted Samuel.
As I put my glass down, I felt Samuel's foot touch mine under the table. Michael was quietly sitting next to him. I was thrilled with excitement but filled with deep shame. I needed to leave, and quickly, before anything further happened.
But somehow it didn't matter. In our hearts, it had been done. I knew I cared more about my desire for Samuel than I did for Michael, even as every rational impulse was telling me to flee. Still, I summoned all my resolve, packed my bags for Sydney, and departed on the train the next morning, leaving behind some half-hearted excuse by way of explanation.
## **SEEING THROUGH "LOVE"**
A war between conscience and heart continued to rage within me for the next month.
As I wrote a screenplay for my performance classes at university, my dreams were filled with longings for Samuel. I imagined myself sitting with him at fashion shows, traveling the world as I wrote and he designed. _This is so wrong, David,_ I thought.
One balmy summer's night, Samuel sent me a message asking me to meet him at Hyde Park. He had news to share.
After I spotted him by the fountain, he told me he'd broken up with Michael and the coast was clear. We kissed. I felt an incredible freedom after a month of being unable to stop thinking about him. Under the fig trees, we lay for hours in each other's arms, staring up at the skyscrapers above us and the blue-grey sky beyond.
As we lay there, the beat of his heart almost lulled me to sleep. Still, I sensed a paranoia in him that made me suspect that things weren't what he told me. To cover it over, he explained why he had broken it off with Michael. _Surely, it's fine,_ I thought. _They're no longer together._
I guessed then, and later found out, that Michael blamed me for the breakdown of their relationship. In reality, I was the catalyst, but not the sole cause, of their breakup. It didn't matter, though. I'd drunk from a cup that was not mine, and even if I didn't want to acknowledge it, it felt as if I'd betrayed Michael.
Weeks passed. One night, as I sat on my balcony, looking back over that view of the floating city, a message appeared on my phone: "I need to see you."
Samuel waited for me in the Italian quarter of Sydney. I jumped out of the cab to meet him at a small art house cinema, where I convinced him to watch a new film by Woody Allen, who was fast becoming my favorite screenwriter. The whole premise of _Vicky Cristina Barcelona_ was a love triangle, centered on two holidaying American women who spend a summer in Barcelona and meet a Spanish artist, Juan Antonio, who becomes their mutual love interest. It was uncannily similar to our scenario.
_Abandon yourself to the momentary happiness of romantic love, no matter the cost,_ seemed to be the film's message. At one point in the film, Juan Antonio muses, "Life is short, life is dull, life is full of pain, and this is the chance for something special." _The universe or fate is speaking to me,_ I said to myself. _I just need to give in and enjoy what I've found with Samuel._ It was time to throw off my moral bridle. Michael and Samuel weren't together anymore. So why did I feel as if I were betraying one of my closest friends?
Samuel kissed me behind the cinema in the summer heat. "Want to come to my place?" he asked as thunder sounded in the distance.
"Yes," I said, taking his hand.
We turned the corner past the eucalyptus trees above the old park where the three of us used to play basketball. Their branches swayed in the gust, and then cracked when the wind grew stronger. We hurried, and as we reached the door to Samuel's corner terrace, the summer rain fell torrentially, pushing us into his flat, where we kissed under the sound of it.
I woke the next morning in Samuel's arms. It was cold. I reached for my phone. It was 6:00 a.m., and the sun had barely started to rise. I silently pulled together my clothes and possessions, then glanced back at Samuel. He was lying peacefully, his arms and hands splayed open where I had been. As I looked at him, something broke inside me. I knew something about this wasn't real.
Since coming out at fourteen, I had been looking for value in romantic love. I was weary of the search. With what I had done to Michael, I knew I could never see Samuel again, at least not this way. My guilt consumed me. All I could think of was that I had gotten exactly what I thought I wanted, and the price was a friend. For a moment, I just stood there. Samuel's designs lay strewn around the floor of his studio. Then I turned and left, closing the door we had opened the night before.
The ride home in the back of a cab felt like forever. As I watched the light rain hit the window, a deep exhaustion came over me, accompanied by suffocating frustration and tears. After countless relationships—some faithful and loving, others broken by unfaithfulness—I was tired. I knew my own weakness. My self-made ethics were powerless against my heart and its desires.
I was starving for intimacy, and yet no matter the situation or person, I couldn't fulfill my need. I thought of all those who turned to drugs or casual sex or other vices, and for the first time I understood why.
The pain in my heart was drawing me back to what I termed spirituality. Looking back, I realize my orphan heart was crying out for the love of its Father. But right then, all I knew was I needed to find some source of higher meaning.
# [ ** CHAPTER 7
CHRISTMAS CONFLICTS ** ](contents.xhtml#conn_12)
> Then you will know the truth, and the truth will set you free.
**_—John 8:32_**
> We should note this curious mark of our own age: the only absolute allowed is the absolute insistence that there is no absolute.
**_—Francis Schaeffer_**
**T** he hot summer weather woke me early on Christmas day. Stretching my arms, I paused to look out from my balcony at the harbor before getting ready for Christmas lunch. Even though getting through the day's festivities would likely be a chore, I felt optimistic. Memories of Samuel, and my second year of university, were now behind me.
Gatherings were a big affair on both sides of my family, but always more raucous on my father's Greek side. Inevitably, the topic of religion would come up. We were, after all, an anglicized family with none of the Greek customs but all of the stereotypical traits, including passionate debate over politics, philosophy, and religion.
I arrived slightly late and was ushered to the long dining table to find a place among the platters of turkey, prawns, and smoked salmon. My short Greek grandfather and my grandmother were also still chatting with others near a Christmas tree covered in tinsel. They wrapped up their conversation to take their seats. To my dismay, the only spot left at the table was across from my Christian relatives.
I felt a pang of dread. Aunt Helen and Uncle Brendan had minded me from a young age with my parents at work, but I resented their family because of their strongly held Christian faith. I hadn't been to their place in years.
I still vividly remembered my phone conversation with Aunt Helen when she said, "I want to explain why homosexuality isn't a God-ordained lifestyle choice for you, David. I accept you and love you as a person and a family member, but I have to tell you what's true."
Her words felt like a dagger. They were ignorant of the fact that being gay is not a lifestyle choice but an important aspect of who someone is. I had exploded back with a fury that shocked me afterward. "You mad bigot! People like _you_ are responsible for the suicide of thousands of gay youth!"
Years later I came to understand that like many Christians, my aunt had used the wrong words to communicate both her stance and her concern for me. My uncle Brendan also deeply cared for gay people. But in my mind, he and Helen were still bigots. Anyone who disagreed with me or had a different vision of marriage was automatically a bigot. No qualification needed.
But on this Christmas day, I took my seat, trying to rise above their hatred. _I'll just ignore them,_ I thought.
As we ate, I talked with my cousin next to me. Suddenly I overheard Uncle Brendan mention God and something about truth. _Truth_ was a dangerous word. Through my university lectures, I had adopted the key doctrine of the postmodern worldview: there are no absolutes. Such "truths" are just ways to control other people.
"Are you kidding me? There's no absolute truth and certainly no God," I proclaimed, breaking up the conversation around me. All my relatives stared at me, and the whole room went silent. Out of the corner of my eye, I saw Aunt Helen recoil at my assertion.
"I've studied postmodern philosophy. I can tell you there is _no_ absolute truth," I told my uncle. "You can't even communicate truth with language, so please don't try to talk to me about God. It's ridiculous, a delusion. You can't have an exclusive claim to know God. I have many atheist, Hindu, and Muslim friends. Do you _really_ think they're all going to hell because they don't know your Jesus?"
"David, there are a few issues with what you are saying," Brendan said, cutting through my exasperation.
"Like what?" I asked irascibly.
"You say, 'There is no absolute truth' as if it is an absolute truth, and you also used language to communicate that. You just doubly contradicted yourself," he said.
He glanced at my aunt. "For me and your aunt, the truth is a Person we know, not just a concept in our heads. He's someone we have a real relationship with." He turned back to me. "Just because our understanding of him isn't always perfect doesn't change that he's the absolute truth. It's his perfect grace, not 'perfect' knowledge of God, that saves us, David."
I pushed my plate away. "But what about all the evil the church has done to LGBTQI people? Do you really think I'd believe you after all of that?" I shook my head. "I can't believe 'God' would create us this way and then punish us for it. And what about all of the other religions? You haven't answered me. Do you really think half of humanity is destined to hell because they haven't heard of Jesus?" I stood up to leave.
My aunt and uncle also left soon afterward. Years later I learned that on the way home, they talked about my response.
"When David was talking, I saw the Holy Spirit over him. He's going to be saved and baptized with the Spirit in three months' time," Brendan told my aunt confidently.
Aunt Helen stared at him, incredulous. "Are you sure? Didn't you see his reaction?"
He nodded. My uncle wasn't one to push things like prophecy. He was reserved about making extraordinary claims, and yet this time he was _adamant_.
God's grace was reaching out to me in my deepest anger. He had started through my uncle's apologetic witness.
And Brendan was right. One hundred percent.
I had only three months of atheism left.
# [ ** PART 2
THE ENCOUNTER ** ](contents.xhtml#conn_13)
# [ ** CHAPTER 8
EXPERIENCING THE LOVE OF GOD ** ](contents.xhtml#conn_14)
> I have raised up a young man from among the people. I have found David my servant; with my sacred oil I have anointed him.
**_—Psalm 89:19–20_**
> God waits to be wanted.
**_—A. W. Tozer_**
**I** t was a busy Friday night, just weeks after my nineteenth birthday. The bridge across Sydney Harbour was packed with cars. From the back of my cab, I looked out over the water and spotted the iconic white sails of the Opera House. Then I lay my head back, relieved to have a break from the monotony of life.
I was worn out from political conferences and late nights spent editing the university student magazine. Instead of the more raucous options available for my night, I decided to go to a small pub to celebrate a writer friend's birthday. It was late March.
As I got out of the cab, the streets were filled with the buzz of Sydney's nightlife. A rainbow flag flew above a building just doors down. I was only a street over from Oxford Street, Sydney's famous gay quarter, which held fond memories of Mardi Gras parades, nights out, and coffee dates with friends.
I walked up the pub stairs and scanned the room. Not many people I knew had arrived yet, but I did spot a friend of a friend holding a drink and sitting alone.
Madeline was a finalist in one of the largest short film competitions in the world, a huge accomplishment for a young creative. Everyone was talking about her in my screenwriting class, and I wanted to interview her for the student magazine. It would easily make the best feature article.
Unlike a lot of my peers, whose creative projects centered on them, Madeline was using her gifts to raise awareness for those often misunderstood or forgotten—people with disabilities. Having a disabled uncle, I found her work inspiring.
As I approached, her brown eyes warmed in recognition, and we said hello. Her hair was cut short, and she wore red lipstick and a black dress. Right away I launched into the question I wanted to ask.
"How did you become a finalist? You just graduated!"
"That depends," she said. "Do you want the _real_ answer or the _interview_ answer?"
I laughed, unprepared for what would follow. "The real answer, of course!"
"God led me to make the film."
Madeline must have seen the shock on my face. I remembered the conversation with my aunt and uncle over Christmas lunch. _Please don't mention Jesus,_ I thought. I couldn't see how Christianity had anything to do with her work. How could a faith that oppressed me and so many others motivate her to do such good?
"So, which God?" I asked, with a hint of sarcasm. "We talking, like, Vishnu here?"
"Jesus," she said.
A thousand objections flooded me as I thought of this God who stood in the way of my community's progress in society. And yet . . . Madeline wasn't like the other moralizing, intolerant, anti-intellectual, homophobic, anti-feminist Christians I'd met.
She explained that she too struggled with Christian stereotypes and the small-mindedness found in parts of the Christian community. The key word in John 3:16, she said, was _whoever:_ "God so loved the world that he gave his one and only Son, that whoever believes in him shall not perish but have eternal life." I realized Madeline didn't see my homosexuality as a hindrance to knowing God. She clearly wanted my community to find the same love she had discovered.
Madeline paused. I knew she had seen that my reaction to her faith wasn't positive. Only my admiration for her work prevented what otherwise would have been a very rude response.
"Do you think there's a God?" she asked. Not a hint of ulterior motive or trying to convert me. Just an open question.
"Well, I'm basically an atheist, but I believe there's a _Something,_ I guess. I'm a spiritual person, and I think you have to be blind to believe there's absolutely nothing behind life," I said, looking down at my drink. "I just don't like organized religion. I'm gay, so I know this Christian God isn't an option for me. I've never understood how if he existed, he'd give me these desires, then condemn me."
I expected her to quibble or awkwardly change the subject, like many of my Christian friends. But Madeline didn't hesitate. "David, have you ever experienced the love of God?"
"What do you even mean? No." My only impression of him was that of an angry, distant deity.
"God loves everyone right where they are," Madeline said. I wanted to recoil at her words, yet something drew me deeper.
Suddenly her eyes widened. "David, I can feel God's presence so strongly right now." She paused. "He loves you so incredibly much. I'd never usually ask this, but . . . can I pray for you?"
Instantly I had an internal war over how to respond. _Should I say yes or no?_
A voice in my mind whispered, _You're a good agnostic; you have to be open to prayer, because you don't know if there's a God. Any other response is intellectually dishonest and closed-minded._
Another thought, this one louder, came on its heels: _Get away from this crazy fundamentalist! She's brainwashed like those Christians you read about in the newspaper!_
The gentler voice won. "Yes, you can pray for me," I said finally. "But I don't think anything is going to happen."
As Madeline laid her hands on me and prayed, the bustle of the pub faded away. I entered into a stillness, a peace. Soon I felt a soft tingling on the crown of my head that slowly intensified, as if someone were pouring oil over me. The warm sensation ran down my entire body like a current of water. It was unlike anything I'd ever felt before.
In a moment, in that experience so totally from outside me, so totally unasked for, everything turned upside down in my mind. All my searching in religion, in relationships, in atheism—none of it compared with this love coursing through me like electricity. For the first time, I knew God was real and that he loved me. _This changes everything,_ I realized.
As my eyes filled with tears, I heard a voice in my head say, softly at first, _Do you want me?_ It cut to my core, to a deeper place I never knew existed. It grew in intensity. _Do you want me?_
I'd never heard a voice like this, and I was scared. I didn't know who this was. It felt like there was a dark veil around me, trying to stop me from responding. But I was so stunned by what was happening, and so desirous of real love. I answered the voice, _Is that you, God, Creator of the universe?_
Then again: _Do you want me?_ The question was direct and immediate, from outside my own cognition.
A fourth time I heard the voice, this time even louder and more pressing: _Do you want me?_
And I did. I was so exhausted from my loveless world that I reached out for what was offered.
_If you are really there, then yes,_ I said, to my own surprise.
As soon as I did, a laser-like pinprick of light pierced the darkness over my heart and entered that mysterious place deep inside me. I was later to find out that Jesus speaks of this place in John 7:38 as the innermost being, from which rivers of living water, God's Spirit, flow for those who believe in him.
Then I felt a wind, like someone breathing on me, filling me with life. It was as if I were taking my first breath.
"Madeline!" I said, both frightened and exhilarated, "I'm breathing without taking a breath! What's happening?"
"David, that's the Holy Spirit filling you. He loves you," she said, unaware of my internal dialogue.
As she kept praying, I heard the voice ask, _Will you accept my Son, Jesus, as your Lord and Savior?_
Immediately I was offended by the Christian nature of the question. Once again the war inside raged like a tug-of-war over my soul. I heard two voices. The first said, _What you're feeling is a psychological reaction. It's just wish fulfillment! Get away from here!_
A calmer, quieter voice followed it: _I am calling you, David. This is real and true. You've never experienced anything like this in all your searching._ This internal struggle felt like the longest moment of my life. Then the most reluctant of words came from my mouth: "Yes, I accept your Son, Jesus, as my Lord and Savior."
As I surrendered myself, something like hot fire coursed throughout my body. I knew I had become a Christian, and I began to weep.
But these tears were different. They were tears of freedom and healing.
After excusing myself from the friends now celebrating at the pub, I left with Madeline to catch a ride home to my parents' house. In the cab, she attempted to explain what had happened inside my heart, but my mind just couldn't grasp it.
I was dumbfounded. I was an atheist gay activist, perhaps the least likely of anyone to ever find Jesus. But in that moment, I knew I had become a new person.
As I opened the door to my parents' house, I could see the light was on. My mother was up later than usual. When I entered the living room, she saw my face and knew something had happened. "David? Is everything okay?"
I couldn't say it. It was as if admitting what had happened meant I had to eat my words and objections to my mother's faith.
"Mum, tonight . . . I . . . uh . . . think I've become . . . uh . . . a Christian," I said sheepishly. For a minute she stared at me, awestruck.
The moment my news sunk in, she jumped up and hugged me. My mother's reactions always had a hint of drama about them—she had been an opera singer in her younger years. "David, I prayed that if he was truly the God of the impossible, God would save you, because you were so impossible to save! Now I know he can do anything!" she said, wiping away tears.
She told me Aunt Helen had been praying for eleven years that I would come to know Jesus. She also told me about Uncle Brendan's prophecy after Christmas lunch. I quickly did the math and realized that day was exactly three months ago. My salvation had been foretold more than once, it seemed.
I began to see I was the object of a benevolent divine conspiracy to reveal the love of God to me.
# [ ** CHAPTER 9
THE FILM FESTIVAL ** ](contents.xhtml#conn_15)
> When Paul placed his hands on them, the Holy Spirit came on them, and they spoke in tongues and prophesied.
**_—Acts 19:6_**
> These signs will accompany those who believe: . . . they will speak in new tongues.
**_—Mark 16:17_**
**T** he night after I met with Madeline, peace washed over me as I slept. It was as if I were dreaming yet somehow aware in semiconsciousness of the Holy Spirit cleansing me, filling me, restoring me from the inside.
As the sensation grew stronger, gushing over me like a torrent, I felt the dead shell around my heart being carried away. Out of nowhere, I began speaking in an unknown language. This otherworldly speech poured out so forcefully that it woke me.
I opened my eyes, realizing I was speaking in tongues. I had read that speaking in tongues was a common brainwashing technique, especially in megachurches. My personal theory was that it helped churches financially exploit people and subdue their rational faculties.
"I'm part of a cult!" I screamed, waking my parents.
"Shhhhhhh!" I heard my father say from down the hallway. He sounded grumpy from being woken. My mother got up to check on me.
"Darling, what's wrong?" she asked, peering around the door.
"Mum," I gasped, trying to slow my breathing, "I think I've become part of a cult!"
"Calm down! What happened?"
I told her what I had experienced while I slept and what awoke me. "Isn't that what cults do?"
She sat down on the bed and rubbed my back. "There's nothing cultish about speaking in tongues. It's pure spirit-to-spirit communication with God. Let me get a Bible so I can show you."
As she left, I thought, _I'm okay with God and Jesus and even the Holy Spirit, but I_ hate _the Bible!_ It was a book that condemned me and had caused me immense pain. I was deeply skeptical about its composition and historical accuracy. How could it be inspired by the God of love I'd met that night?
When she slipped back through my doorway, I shook my head. "I don't want to read the Bible."
"Wait, let me show you." She opened her well-worn leather Bible and pointed to the page. "It's 1 Corinthians 14:2. Paul explains that 'anyone who speaks in a tongue does not speak to people but to God. Indeed, no one understands them; they utter mysteries by the Spirit.' "
"I hate Paul, Mum! He's anti-gay and anti-women. According to him, you need to be quiet and not teach me anything!"
"Darling, I don't think that's a sound interpretation. And you know, the Bible doesn't just talk about sexuality. It's God's love letter to us." She studied me. "The washing you experienced is described by Jesus. He says in John that for all those who believe in him, living waters will flow from within them."
I couldn't believe my mother knew the Scriptures so well. As she sat next to me on the bed and leafed through her Bible, I was filled with anger. I grabbed it and threw it against the wall.
"I hate that book!"
"David, I'm just trying to help you understand!"
"I'm going back to sleep," I said, turning over.
But even in sleep, I couldn't escape this mysterious presence of God.
Over the next three weeks, everywhere I went, I felt it—him—with me. Whether I was riding on public transport, sitting on a park bench, or attending classes, the same living water flowed through me. Sometimes it was as if a wind unexpectedly blew over and through me.
Strange as it was, I loved this intimate presence. Words could not fully describe the Spirit. Unlike pleasures of this world, there was no adverse effect. Experiencing the Spirit was entirely safe.
I even started sharing the little I'd read about the grace of God with my gay and atheist friends. I just told them what I knew: God offers a free relationship with him through Jesus' death on the cross. He loves absolutely everyone and is desperate for them to return home to him, and it's only in that love that we truly repent.
Christians were amazed by what I knew, even though I'd barely read the Bible since school. My skeptical friends asked me questions I had no answers for, but many were privately interested.
Their questions made me curious about what the Bible said. Cautiously I read portions of it, still avoiding the Old Testament or anything written by Paul. What I did read explained many of my experiences. Gradually I began to see its trustworthiness and value.
But even with all these experiences and my growing openness to the Bible, I struggled to rationally accept God's existence. There was a war between my heart and my mind; my heart knew what had happened inside me, but my mind wasn't convinced. The horrific things the church had done and the pain the Bible had caused the LGBTQI community stood in my way. How could Christians treat gay people that way and yet claim to know the Source of the love I'd encountered? How could God allow hurtful words to be written about gay people and still be good?
I felt myself torn between two worlds: this new Christian world and the gay world that allowed me to be honest about who I was and what I desired. My heart's love for God was growing, but my old loves were still stronger.
Little did I know that God would soon prove himself again in a dramatic way.
## **A REPLY FROM GOD**
The night of the film competition, I set out a picnic blanket near the festival stage. I couldn't wait to see if Madeline's film had won. The atmosphere was electric. A crowd of tens of thousands was gathered around the four big screens in the center of the Sydney city park.
I watched as the orange sky faded into midnight blue, and stars and planets appeared, including Venus, blinking at me from the expanse. Scanning the cosmos, I prayed, _God, if you're really there, I can't just have these experiences. I need a sign, a reply of some kind._
Soon the competition began. Each film was played, but Madeline's clearly stood out. Its honesty and artistry spoke to me, and judging by the enraptured faces around me, her film spoke to many others as well.
Finally, it was time to announce the winner. Numbers counted down and the suspense grew. The crowd roared with appreciation when Madeline's film won. As the judges hugged her and handed over her trophy, she glowed with joy.
When she stepped off the stage, the press swarmed around her. I ran down to the red carpet, where my favorite Australian actors, Geoffrey Rush and Cate Blanchett, had just walked past. But tonight I didn't care. "Madeline!" I called from the barricades.
She turned and waved her trophy at me. "David, this event is for God's glory. I'm just his servant!" Her face suddenly became serious, and she leaned closer as she shouted, "I need to tell you something! All night, I couldn't shake it. God wants me to tell you he really exists. He's there for you!"
I froze, amazed. The living God had provided a direct reply to my prayer! Perhaps faith really was evidence-based trust in response to real communication from God.
In an instant, I was reassured that God was real, and my heart and my mind were at peace.
"David, I have to go, but come to church with me this Sunday," Madeline called. "I'll give you that interview you've been wanting!"
## **DIVINE CONSPIRACY**
Madeline, I found out, attended the same church movement as my mum and my aunt and uncle. This detail astounded me. When I entered the church with her, the same presence I experienced in the pub flooded back, stronger than before. During the worship time, I stared as people lifted their hands in adoration. I'd never seen anything like it. The Holy Spirit's loving presence emanated out of everyone.
I too lifted my hands. I found it strange and yet natural, as if I were created for it. Floods of power and love flowed over me, and I wept. Jesus' grace had found me in a church—the last place I wanted to be, not long ago.
In his sermon, the pastor quoted Matthew 10:32, where Jesus says, "Whoever acknowledges me before others, I will also acknowledge before my Father in heaven." He followed with a simple gospel message: Jesus died on the cross for our sins to make us right with God, and confirmed it through his resurrection.
The pastor then invited people to accept Jesus as their Lord and Savior. My hand went up straight away, and I walked down the aisle to give my life to him as an outward sign of what had happened to me. As the pastor prayed for me, I repented, turning away from my old life. Even though church culture was still alien to me, I knew I'd come home—to my Father's house.
I basked in God's love and acceptance. But I had questions. _Why did you save me?_ I asked Jesus. _Why did you come into my life, when so many others don't know you?_
God was about to reveal his answers to me.
# [ ** CHAPTER 10
PROVIDENCE AND PROPHECIES ** ](contents.xhtml#conn_16)
> Today I appoint you to stand up against nations and kingdoms. Some you must uproot and tear down, destroy and overthrow. Others you must build up and plant.
**_—Jeremiah 1:10 NLT_**
**O** ver the next several weeks, the Holy Spirit did a profound work in my heart as I attended my new church. Incredible as it sounds, some Sundays I saw visions of what I later realized were the heavenly realms.
In one service, I found myself singing, "Holy, holy, holy" entirely out of sync with the rest of the music. Other times, at my first Christian conferences, I began singing songs, sometimes in angelic tongues pouring from my mouth. They were completely different from what was playing, and they were supernaturally beautiful. It seemed unbelievable this was happening to me, but I couldn't dismiss it. I was afraid those around me were going to think I was crazy or something.
Even deeper changes were taking place too. I started to fall in love with God and told everyone about Jesus. Homeless gentlemen received the gospel message along with fresh sushi, my favorite fast food, on my walk to the station. As I sat next to people on public transport, I felt prompted to speak to them about Jesus' love. I even shared about Christ with some of my toughest atheist and agnostic friends at university. I had no fear.
I read the gospel of John for the first time since my conversion and found I hungered for God's Word. Scriptures began coming to my mind that I didn't even know were in the Bible, and people showed me where they were.
My desires started to change. I no longer felt like hitting up the gay clubs, and my desire for a boyfriend lessened. I felt a deeper desire for fellowship with Christians. Many university classes weren't as interesting to me, and I was frustrated by the anti-theistic tone of most of my professors. The editorial team at the student magazine found my God talk offensive. Many of the members started to withdraw their friendship.
I was a different human being, and it showed. But to my political and gay friends, I was a cultural traitor. I experienced more severe hatred from many of my secular friends than I did before from Christians for being gay. My secular friends assumed things about me that were just as prejudiced, if not more so. Many mocked me. But I knew that before I met Christ, I would have done exactly the same. I could point no finger. I had become the very person I once hated.
Yet despite my longing for fellowship, I was also lonely among Christians. Most of the people around me had no idea what had happened in my life, and those who did were unsure about my still-vocal views on gay marriage.
This Christian culture felt very foreign. As pastors preached, even as I loved what they said about Jesus, I was upset by insensitive things they said about the gay community or by their offhand remarks about political and social affairs. My church was only blocks away from one of the world's largest LGBTQI populations, yet no one expressed any empathy for LGBTQI people or a heart to reach them with the gospel. They seemed to act like they didn't exist, which somehow was more hurtful than vilifying them.
I struggled with bringing friends to church, especially when terms like sin were mentioned flippantly, or when people spoke about how "our values" were under threat, never suspecting that someone with other convictions might be listening. I knew they were talking about people like me, yet there I was, right at the center of this church, by God's own providence.
I often left church distressed, angry, or confused. How was I supposed to be a gay or same-sex-attracted Christian? There were no answers. It felt like I was living a dual existence—my faith on one side, my sexuality on the other.
Yet I knew God understood. I thought, _He who knows all things_ must _know how difficult it is for me to belong in the church._ He showed me grace and gave me reminders of his continual, faithful presence. Every Sunday, words and concepts I had been thinking about the previous week seemed to uncannily appear in the sermon, as if the Holy Spirit were saying, _Look, I'm here too. Bear with the church. I'm with you._
It was the Spirit who kept me there. Each time I attended Sunday services or weekday prayer meetings, his presence filled me like a fire. One Sunday, God's voice was clear: _David, don't worry about the question of your sexuality. Enjoy me. Love me and practice my royal law: love your neighbor as yourself. Your sexuality seems like a mountain to you. It is a grain of sand to me._
I made a decision to be single for a year to give God time to show me his intention in the Scriptures. _I need to let God be God,_ I thought. _After all, if he thinks exactly like me, is he really God, or am I just making him in my own image?_ I knew the Bible was clear that God was holy—set apart and different from me, even though I was made in his image.
One Sunday after service, my new friend Sarah and I had a picnic in Hyde Park, at a spot not far from where I'd kissed Samuel just one year before. We spent some time praying for one another. As we sat on the lawn with our Bibles open, it felt like the Holy Spirit came and joined us. When Sarah prayed, she told me she had received a word from God for me. At first, I didn't know what that meant, but I was moved by her care. It was obvious this presence was more than a feeling. He was a person who wanted to speak to us.
There was weight to the words that came next. "David," she said, "you're like a golden chisel in God's hand. You're made to both tear down and build up, like the prophet Jeremiah. Through you, Jesus is going to tear down walls of division in the church and reach many people with the gospel. He's going to take you across the earth to share his love for all people. He's anointed you to do this."
She then read me Isaiah 61:1, which was the chapter Jesus read out loud from at the start of his ministry: "The Spirit of the Sovereign LORD is on me, because the LORD has anointed me to proclaim good news to the poor." Suddenly the sensation of oil being poured over my head in that pub months before made more sense. I understood it more now.
The next week at university, I met with two friends from campus, Stephen and James, a couple planning to be married at their church. I told them what had happened in the preceding weeks, and they invited me to their campus Bible study. Everyone in the study was similar to me intellectually and politically, and many were humanities students. I instantly felt at home. They knew exactly what I was going through, and their affirmation of me as a gay Christian was healing.
We discussed our view that Paul was not aware of the monogamous homosexual relationships exhibited in gay marriages today. I was so relieved and excited by these arguments that I felt a premature reconciliation between my faith and sexuality. It was so encouraging to find friends wrestling like I was. I didn't question what they said, because I trusted their earnest faith and intellectual gifts.
Still, I stood by my commitment to remain single. I was convinced I needed time to let Jesus make his will clear to me.
_After all,_ I considered, _if I'm anointed, he must have something mysteriously great in store for me._
# [ ** CHAPTER 11
THE UNRELENTING PRESENCE OF JESUS ** ](contents.xhtml#conn_17)
> The LORD your God is with you, the Mighty Warrior who saves. He will take great delight in you; in his love he will no longer rebuke you, but will rejoice over you with singing.
**_—Zephaniah 3:17_**
**F** or my first years as a Christian, I was stuck. There's no other word for it. I felt wedged right in the middle of the church's division over the gay elephant in the room. The root question _Who am I, Lord?_ was morphing into _How can I love?_ On a fundamental level, I had a practical question to answer: could I live out my Christianity as a partner in a gay, sexually active marriage, or was that in conflict with my newfound faith?
The church didn't make the dilemma easier. _Churches,_ I should say, because I attended two of them during those years. One was quite charismatic, its attention fixed on the work of God's Holy Spirit among us. The other was focused largely on social justice.
The pastor of the latter showed me theological arguments for gay marriage, encouraging me to accept this part of myself actively as a gay Christian man. He spoke about the inclusion of the Gentiles and how throughout church history, many LGBTQI people like me had received the Holy Spirit—proof of their acceptance in Jesus. He explained that I simply didn't have to live under oppressive church laws which privileged heterosexual people. To him, marriage was a bond of love between two individuals, no matter their sex or gender. This union imitated Christ's love for the church and should be offered to all, regardless of their orientation.
However, at this church, the Holy Spirit's presence was somehow _weaker_. It felt different. The same pastor jokingly called me "Jesus-is-my-boyfriend David" because of how I talked about my love for Christ and because I raised my hands during worship, as an expression of my passion and faith. No one else did that there. Most members of the church gave me a cold reaction, dismissive or even condescending, when I described my experiences with the Spirit. In this place where everything in me hoped for affirmation, they were actually affirming only one part of me—the part that was like them, the part they could easily accept.
I also felt uncomfortable with how this church understood the Bible. For them, it seemed useful only to justify their chosen social causes. Jesus was a political zealot, a radical figure who challenged the heresy of private, cheap-grace faith. The cross was a symbol of solidarity with the poor, suffering, and rejected minority groups. They laughed at the theology of the other church I attended. I hated that division and the critical spirit I saw toward members of Christ's body. I didn't see why they couldn't hold on to the best parts of their theology while also, in humility, letting themselves be truly changed by God's Word.
But don't get me wrong: there was also a wonderful side to their faith. I _loved_ the way they served the poor and took discipleship seriously in ways many other churches didn't. They did love the heart of Jesus. Just not the whole heart of Jesus, I felt. Ultimately, I realized that the intensity of the first love I'd encountered in the pub was ebbing away faster than I expected it would. And—little surprise—this church really didn't have a category for it.
When I went to the other church with my family, Jesus' presence seemed to come freely, like a flood. The auditorium was filled with loud music and expressive praise. Stage lights flashed, and the worship leaders sang to God as if no one else were in the room. The whole church of more than a thousand people lifted their hands in worship. It was an incredible feeling of joy and oneness. But they missed so much. There was no place in their worship for someone like me, unless I was committed to bottling it all up and becoming more like them, not more like who I most truly was in Jesus.
Still, for all the shortcomings, I felt old mindsets falling away, like the scales that fell from Paul's eyes after his encounter with Jesus. For the first year at my family's church, I wept at every service. I would often shout out in the service when I disagreed with what the pastors were saying, yet I felt power and grace working in me each time I went. Sitting with my mum and Aunt Helen, I was changed by God.
One weekend after the service, I had coffee with my aunt. Despite the ways I saw God moving in my heart, I was irritated with some of the things the church said about homosexuality being a sin. I wanted to tell her my thoughts.
My yearlong commitment to singleness was up. With a deep internal sigh of relief, I was dating Thomas, a handsome Italian Catholic I'd met online months earlier. He was amazed to meet a born-again Christian who was gay and open to a relationship. But the issue of whether we would be accepted at this church remained. That Sunday, I was ready to reckon with it.
I sat with my Bible open and my coffee untouched. "I can't believe a loving marriage between two members of the same sex is sinful. I'm happy to concede that sex before marriage is wrong, and that's exactly why the church needs to have gay marriages," I said to my aunt. "If I wanted to marry Thomas, where would I go? I'd have to leave this church where God meets me so profoundly." I stared intently at her, waiting for a response.
Helen met my gaze. "David," she began slowly, "I agree with what Scripture says. I believe its intent is clear. But it's _easy_ for me. I've never struggled with same-sex attraction."
She paused to sip her coffee before continuing. "All of us have a cross to bear, an ultimate issue to wrestle over with God. This is something you'll have to work out with _him_. That's faith! You have the Holy Spirit, your teacher, living in you now. You need to seek _his_ answer to your question. The voices of falsehood are loud— _so_ loud. But God's voice is a still whisper. You'll have to learn to hear him. Remember, God will never contradict his Word. Never."
She locked eyes with me. "I'm sorry if we or this church have failed to love you. No one should bear their cross alone. We're here for you. Whatever you come to believe about your sexuality, you are always welcome, and if you have a partner, you're both welcome." She reached across the table and grabbed my hand. "Yes, we have a policy that means our church will submit to what Scripture says about marriage. But, David, if we didn't have you, we would be missing an irreplaceable part of Christ's body. You are wanted."
That weekend, I got a glimpse of what real acceptance looks like. My aunt, the church, and my mother weren't going to change what God's Word said, but they _would_ love me, accept me, and embrace me no matter what. Through their responses, I peered into Jesus' acceptance of my human struggle maintaining both truth and grace. I didn't fully understand it. At all. But I knew he was there. I sensed his unrelenting presence. I concluded I would call this church home.
## **TOUCHING HIS ROBE**
As time went on, I started to desire deeper, longer worship than the fifteen-minute segments of praise on Sunday mornings. A friend invited me to a healing service, in which a small group of passionate worshipers and healing ministers from my church gathered to pray for the sick. As we sang and adored Jesus, the chapel was filled with a glorious presence, as if God had come into the room somehow. I had sensed this before during services, but never so powerfully. My heart trembled as both the power of God and the pain of my past washed over me.
I suddenly thought back to the story of the woman with the problem of blood in Luke 8:43–48. Jesus, walking through a crowd, was surrounded by people pressing to see and touch him. A woman who had suffered for almost her entire adult life pushed through, hoping to touch the hem of Jesus' garment.
This woman had not done anything to have this problem. It wasn't her fault, but it meant she was ostracized, deemed perpetually unclean by the law of Moses. While her bleeding and uncleanness was not an exact equivalent to being same-sex attracted, her suffering and predictament reflected mine and spoke to me. The lack of a solution in the Jewish religious system resonated with how I felt about church. I too didn't fit, through no fault of my own. I felt I was continually questioned, looked on with suspicion, or deemed second-class by the crowd around me. The constant feeling that I needed to explain myself exhausted me.
I recalled how with amazing faith, the woman reached out and touched Jesus' hem. Jesus felt the power go out of him in that moment of union, and she was healed. What if what I had been looking for this whole time was the healing of simply being close to Jesus? I sensed myself on the edge of a profound mystery.
The kingdom of God, I realized, is for those who, like this woman, are poor in spirit. It is this very poverty that leads them to reach out for God, longing for him. In this place of trust, we are lifted up, made whole, and brought into the compassionate embrace of Jesus. Could my same-sex attraction be not simply a barrier but actually the _means_ to seek greater grace and wholeness in him? Might it bring me close to him in ways that no other work or struggle could?
The worship continued. "Worthy is the Lamb who was slain," we sang. As we adored Jesus and shouted, "Holy, holy, holy!" I felt a presence in the middle of the room. It was overwhelming. So _real_. But I wasn't afraid. I knew it was the Spirit of Jesus. As his presence came over me, my heart opened afresh to God's grace. Tears fell from my eyes as I felt past sins being cleansed by his shed blood.
_Reach out and touch the hem of my garment._ The voice in my heart was unmistakable. As I closed my eyes, a bright light shone from above. I can't explain it, but I looked up at the dazzling sight of Jesus with his back to me, high and lifted up. _David, take hold of my presence,_ he told me. _All you have to do is hold on._
In the vision, I reached out and touched his robe. It shimmered with light yet had an otherworldly substance; it was anything but flimsy and ephemeral. Power flowed through my hand and through my body as I experienced my own union with grace. I held on.
And somehow I knew that healing had met me and was holding me.
I had so many questions and deep hurts. But in that moment, I chose to simply trust. Jesus called me to step into the unknown, and I knew he would walk with me each step on the difficult road ahead, until I reached the other side of understanding.
He would be there. No, that wasn't it. He _was_ there. And I would keep holding on.
# [ ** CHAPTER 12
THE ROOT OF BITTERNESS ** ](contents.xhtml#conn_18)
> He has sent me to bind up the brokenhearted.
**_—Isaiah 61:1_**
> See to it that no one fails to obtain the grace of God; that no "root of bitterness" springs up and causes trouble, and by it many become defiled.
**_—Hebrews 12:15 ESV_**
**A** s I slid into my seat for a language theory class, our language and philosophy professor leaned over the lectern, his face animated. "This week we'll be looking at Nietzsche's statement 'God is dead,' " he explained. To us, our professor was an intellectual giant, writing for a living and publishing academic articles on modern language theory and poetry.
I was now in my third year at the university, studying culture, writing, and journalism, and it wasn't making holding on to Jesus an easy proposition.
Throughout the lecture, our professor read from European philosophers who had come to the same conclusion Nietzsche had. "Michel Foucault argued that 'the individual, with his identity and characteristics, is the product of a relation of power exercised over bodies, multiplicities, movements, desires, forces,' " he said, pausing to peer at us over his glasses. "Foucault and Lyotard show us that there is actually no such thing as a grand narrative that can claim to be absolute truth; rather _we_ construct these narratives to control others. There is no such thing as 'meaning' without a power relationship involved."
I absorbed everything he said. While I was now a Christian, I saw that these thinkers weren't denying the reality of God, just questioning our capacity to know him. They were being intellectually honest. Could I blame them for that? Without the Spirit of Jesus' revelation and his work to communicate with us, God _was_ dead to us. Sure, the skeptics ended up in a place few would wish to go. But they were following the truth as they saw it, more honestly than many of the Christians I'd met.
This wasn't the only obstacle I had to overcome since becoming a follower of Christ. Though I didn't realize it, I also had deep bitterness because of past hurts Christianity had caused me. I could not let go of my activist past, especially when I heard of numerous young gay people committing suicide and of the hate crimes committed against LGBTQI people every week around the world. I seethed with anger, and rightly so. _Why aren't Christians standing up for these precious human beings?_ I wondered, my heart breaking. Clearly, many people saw homosexuality as something to resist at all costs, even if that cost was a life. People like me were the victims; _they_ were the aggressors. That much seemed obvious.
I struggled to forgive the church for its lack of love and understanding for the LGBTQI community. Many of the characterizations of gender I heard inside church angered me. They constantly talked about what I understood as "gender essentialism," the idea that a person's sex is fixed and their gender is in no way constructed. (This book isn't the place to fully deal with this question. For now, let's just say it's complicated.) I saw _almost no_ sensitivity for transgender or intersex people. There was no way to account for many of the complex realities of sin and the created goodness of our humanity. In the Christian mind, it seemed there was no nuance to human gender or sexuality; it was just "a boy with boy parts" or "a girl with girl parts." How did this understanding answer the question of intersex people and genetic exceptions? How about those who experience gender dysphoria? Eunuchs in the Bible? The story was much more complex, and even _one_ exception to the rule prompted honestly asking why.
I still did not understand the depths of my bitterness, but I was about to take another step in my journey to forgive. The Sunday following my class, I sat next to Aunt Helen. The church was packed, and something seemed different. Since becoming a Christian, I'd frequently heard the word revival, but I didn't really know what it meant and had never experienced it firsthand. Today I would. I sensed in others around me a hunger for God that I'd never felt in the service before. Helen swept back her long black hair and looked at me sideways. "Get ready," she said. "God is about to move!"
As the band played, the lead singer suddenly stopped the usual program. The whole church started to sing three simple words: "I exalt thee!"
I cannot claim to explain it, but again it felt like a power from outside filled the room. As it became stronger and stronger, my chest shook from within. I felt as if my heart were being cleansed. The words from Ezekiel 36 came to me: _I will sprinkle you with water and give you a heart of flesh for a heart of stone._
As in previous encounters with God's Spirit, pain quickly resurfaced from my past. As I closed my eyes and lifted my hands and voice, I saw a picture in my mind: what seemed to be a thick root, deep in my core. The memories of hurtful things people had said to me, my own anger toward the church, my past relationships and friendships—all these flitted past. _What is this?_ I asked.
_This is the root of bitterness that defiles many._ I recognized this from Hebrews 12:15. Deep inside, rejection had rooted itself as bitterness. My sorrow had grown into darkness and morphed into something strangling my soul. It was a legitimate hurt, to be sure. But it was growing into something monstrous. God needed to pull it from me before it _became_ me. All I could do was ask for the strength to surrender.
The worship music crescendoed. A liquid purity seemed to fill me, a spiritual sense of something beyond my understanding. Suddenly I felt as if I were in another dimension yet somehow still present in my body. _Perhaps this is what John referred to as being caught up in the Spirit,_ I thought.
As I looked, I saw the whole earth. It was filled with a sea of people doing all the things we know so well: backbiting, swearing, slandering, jeering at God, setting themselves up as his judges. Their hatred was palpable. They were gripped by pain yet filled with rebellion toward the God who could heal it if only they would let him. It was horrific. I felt my heart break for every person in the crowd.
Then I spotted myself among them.
I heard a voice say, _This is what you would have become._ I looked up and saw Jesus, lifted above the earth, shining in unapproachable light.
I opened my eyes and was back in the auditorium. The whole church started to sing in adoration, "Holy, holy, holy is the Lord." I had never seen a service where every single person was so focused on Christ. The contrast to the people in my vision stunned me.
As I closed my eyes and raised my hands, it happened again. I saw Jesus and the jeering crowd of people. His whole being radiated with energy. The words of Colossians 1:17 flashed through my mind like an arc of electricity: _"He is before all things, and in him all things hold together."_
I heard Jesus say, _David, my son, you are free._ He raised his hand in a gesture of authority, and dazzling light swept the face of the earth. It touched various people in the crowd, transforming them. His voice boomed: _My glory will come for them._
This light finally touched me too. I let out a bellow of anger. The music wasn't enough to mask it, and my aunt looked at me, startled. But I barely noticed. Something was happening inside.
I felt God's power come upon me. As my chest trembled, this deep root of pain was pulled out of someplace deep within me. Finally, and gloriously, I was free from past injury. My heart had been set free and softened.
Later, as we talked, my aunt saw that I'd been set free from the unforgiveness that kept me from fully following Jesus and trusting the church. Somehow I knew she was right.
The vision had marked me. My bitterness from feeling rejected by Christians and God was removed, replaced with a knowledge of just how deep God's love for this world and for me went.
Just when the path ahead seemed impossible, Jesus turned my bitterness into life-giving joy. The horizon that had felt so stifling—the authority of Christ—had widened into a vista as broad as the world. I realized that this Jesus is forever the exalted Lord of all.
# [ ** CHAPTER 13
THE GOSPEL OF GRACE ** ](contents.xhtml#conn_19)
> It is by grace you have been saved, through faith—and this is not from yourselves, it is the gift of God—not by works, so that no one can boast.
**_—Ephesians 2:8–9_**
**M** y bitterness was gone, but the other war continued in me. I wrestled more than ever with my two conflicting identities, knowing that aspects of my gay identity no longer worked with the new person I was in Christ. The battle exhausted me.
I faced two opposing temptations: one was to try to fit into the church by hiding my real life and history; the other, to make everything about my gay identity, ignoring the call to follow Jesus. I wanted to be accepted by Christians and follow the Bible's ethic, but I also felt that God called me to personal authenticity. _Following Jesus must lead me to honesty,_ I thought, _or it would not be following Jesus._ I couldn't imagine the Christ of my vision condoning hiding myself away. His light and power were so far beyond those kinds of mental and cultural games.
I was a Christian. I also was gay. What did that mean? They felt like irreconcilable realities, identities at war. But were they?
Throughout my primary school years, Christianity had seemed like a system of laws, doctrines, oppressive constraints, and social conventions created to try to get right with a God who demanded perfection but could never bring himself to say good enough. I now knew I could not work my way to God, but what did it mean to obey him, to love him with my whole self, from the heart? He had saved me, and I wanted to live a life that met his approval.
As I read Scripture, especially Paul's letters, it became clear that rules could not make me right with God. That was why Jesus Christ came to save me. If I could have become perfect by myself, why would I have needed his salvation in the first place? He was full of grace, giving it richly to all who repent, filling them with the Holy Spirit, and reconciling them with the Father.
Other things I was learning surprised me. I had never known that the gospel stood _against_ many of the social constraints or laws of its ancient context, which social groups used to condemn each other. What would this mean if it was true? Might the gospel I'd once considered my worst enemy be an unexpected ally in moving beyond condemnation and hatred?
While the New Testament upheld that the law was perfect, it also taught that the law could never produce real righteousness in us. At best it showed us God's perfection. At worst it turned us into religious fakers, whitewashed tombs. My desire to make myself worthy of God's love was actually working against his grace in my life. But how could I navigate my sexuality through this gospel of grace? The question haunted me, and more than as an abstruse question of theology. It involved my very life.
One day, sitting on my bed, I listened to a Melbourne pastor preach on freedom, looking at letters to the Galatians and Romans. "We are already declared righteous in Christ yet still experience sinful desires," he explained. When we form our Christian identity, we have to understand the difference between obedience by law and obedience by grace. He quoted Romans 4:4–5: "To the one who works, wages are not credited as a gift but as an obligation. However, to the one who does not work but trusts God who justifies the ungodly, their faith is credited as righteousness."
Something clicked when I heard that. Doing good was wonderful. But it was ultimately useless in creating true relationship: "By grace you have been saved through faith. And this is not your own doing; it is the gift of God, not a result of works, so that no one may boast" (Eph. 2:8–9 ESV). _Wait,_ I realized. _My sexual orientation has nothing to do with my righteousness before God!_ I was accepted by him because of Jesus Christ, not because of my moral performance. I didn't have to earn it. My chosen sexual _behavior_ , just like for a heterosexual person, was a different story. But my orientation? It was not a barrier. It was just part of me.
I felt I had been given back something of who I was. Identity and action separated themselves in my mind, and I caught a glimpse of a third option for my life, one I hadn't suspected until that moment.
The false gospel of striving fell like shackles, and I began to see the beauty of grace, and the real gospel of Jesus Christ. Again the truth hit me: _My sexual orientation does not separate me from God!_ My sexual orientation had nothing at all to do with this free gift of grace that had been placed in my hands.
Any attempt to obey God through my striving and effort, rather than his grace and power in me, was resisting the Spirit of God. As Paul stated in Galatians 5:1, "It is for freedom that Christ has set us free. Stand firm, then, and do not let yourselves be burdened again by a yoke of slavery."
I leapt off my bed and shouted for joy. (I know, I should probably be more demonstrative in my emotional life.) "I'm free. I'm actually free!" I felt liberated from the law's condemnation. My desires could not condemn me. _This_ was radical, beautiful grace. Suddenly my identity no longer centered on what I desired sexually; it centered on Jesus Christ and his costly and abundant grace.
## **MISSING GRACE**
As with most of my breakthroughs, though, my questions seemed like the Greek Hydra: chop the head off one with a good answer, and two more would grow in its place. If God's Word was so clear, I was confused as to why the church was so quick to emphasize obedience through the law and so slow to offer grace to LGBTQI people (or in some cases, act as if there is no law in the first place!). Rather than inviting the LGBTQI community to know God by first showing them love, churches were often guilty of doing all kinds of irresponsible things, including using the Old Testament law to condemn people's behavior in the most vicious terms. It struck me that this graceless message was deadlier than the world's unrestrained sensuality, because it hindered the _real_ good news. It was like inoculating people against the gospel: when the truth came, they would bristle, thinking, _I've heard that before, and you aren't duping me again._
Historically, the church had more often than not dealt with moral issues like homosexuality by focusing on sin management rather than emphasizing Christ's transforming grace through the Holy Spirit. This only confirmed what many in the LGBTQI community believed: that God wanted to enslave them in an oppressive obedience of hopelessness. He was a thirsty God, in so many minds, who wanted their very lives, their very identity, to appease his wrath and disgust.
And I'd been one of those people, of course. One of my big hindrances to faith was the practice of reparative therapy, for years recommended and used in the church. This outdated science saw homosexuality and same-sex desires as a pathological disease and viewed the production of heterosexual desires as the cure. Problematic on every level—theologically, psychologically, scientifically, clinically. After I met Christ, I resolved never to get involved with a reparative ministry. _If the gospel really does transform us from the inside out,_ I reasoned, _it needs no help from a man-made solution. God calls us to walk through our weaknesses in his power, not to try to change ourselves into something acceptable to him._
Reparative therapies also pointed to a deeper issue. They missed the point that God, not heterosexual marriage, was the goal of our desires. Why would someone give up their same-sex desires and their hope for romance, unless they'd found something higher? When Paul wrote in 1 Corinthians 6:13 that the body is "for the Lord, and the Lord for the body," was he not pointing to a desire even more fundamental than sex? Our deepest longing was to be spiritually intimate with God, to experience the belonging we were made for. Many people in the church, I realized, didn't even have a real, practical category for this belief. At least, they didn't act like they did.
I had committed to a year of singleness not as an act of legalistic obedience but as an act of faith, from a desire to experience satisfaction in Christ. The motivation for this decision came from trusted people who spoke truth and grace into my life. My church never compromised their views of sexuality and the priority of God's presence, even though sometimes that made me angry. I am eternally grateful. Without these clear boundaries, I would have found it far harder to find real repentance and stay on the narrow path of righteousness I now attempted to walk by the grace of Jesus.
## **A WAY ACROSS**
I sat in my car before a job interview, reading Romans 1, especially the bit about same-sex expression. It stung. Grace was making a way. But even after learning so much about it, at times I found myself exasperated. Some of my closest friends at church had either entered romantic relationships or become engaged. Simply put, I was lonely. Watching them enjoy something I was missing out on was hard, especially when everyone around seemed to revel in married bliss as the ultimate experience of human life. Even in my church, friendship seemed secondary to romantic love. It seemed like everyone had been reading Jane Austen more than the New Testament, or watching nineties rom-coms more than the work of the Spirit.
I felt guilty for judging them so quickly. But the struggle wasn't just a problem of pride. As I sat in my seat, I felt so torn between my desire for a boyfriend and God's will. _Lord, how could you allow me to have these desires?_ I asked him again.
Nothing.
Apparently, you don't get life-defining revelations on your own timetable. _God, how can you possibly allow me to go through something this hard?_ I thought. _How can you expect me to never belong? To live without a companion, without a family?_ I had no doubt that I'd be a faithful husband, a caring dad. I could see myself growing old with the husband I'd never have, raising my kids to love Jesus. For the first time since I met Jesus in that pub years before, I doubted it—doubted it all.
He could have put kind and detailed instructions for this in the Bible. Instead we got a handful of difficult passages that just seem to prompt confusion, hatred, and bickering. My anger grew. This time I yelled out loud, "Lord, if you really cared, why didn't you just tell me what to do?"
As I lowered my head against the steering wheel, I sensed his still, quiet voice. _David, I have concealed this as a mystery that I will reveal on the final day. Right now, I need you to trust me in the unknown. As you keep walking in my grace, I will show you the deeper secrets of my Word. I will not abandon you._
The Spirit of God was suddenly there with special weight. I felt his strength fill me. I was no longer sitting in the car but seemingly standing at a cliff, with no way across the expanse to the other side. _It's hopeless,_ I thought. Far from being encouraging, this was just a visualization of how stuck I was. No explanation.
The next night at a prayer meeting, I had the same experience. Again, in my mind, I stood at that cliff's edge. There was simply no way across.
But this time there was more than silence. This time God's voice whispered, _Walk on nothing. I will hold you up. Do not be afraid. Walk by faith and not by sight. Trust me. Step over._ I closed my eyes in the vision and stepped, straight over the edge. I didn't fall. My foot was held up, by what I could not see. But whatever it was, I could walk on it. Step by step, I progressed across the impossible chasm. Finally, I made it safely to the other side.
This was the precious trust of believing and not seeing everything! This was a deeper, maturing faith! I realized that God held me up when I did not know how to go forward.
I thought back to moments I had found it hard to trust God because of how different the church was from the gay world I came from. The values. The language. The politics. The culture. Yet even though this Christian world was ignorant of what I had been a part of, somehow I knew I was meant to belong here. If I had been given grace, I could show it to others. Could? No, _must_.
The vision came back twice more, each time taking me a little farther. On the other side of the divide, the land was thick with vegetation. I could not see through it. Again it seemed impossible to move ahead. Then I looked down. In my hand was a sword. I could not see the way forward, but I could cut it. _He is making a way in the wilderness,_ I realized. The sword God had placed in my hand was the sword of the Spirit. The Holy Spirit would open up the way of grace for me, through the Word of God by faith.
_David,_ God said to me, _I have called you to make a way where there is no way. Many thousands will find their way to me through you. I love you, my son._ I was flooded with a sense of his closeness, even as I pondered his words.
The last time I found myself there was months later. I was again exhausted, struggling to trust God. This time in the vision, I found myself in a pitch-black night, surrounded by thick forest. _Keep going, David,_ I heard a voice call, though I could not see who or where it came from. Taking my sword, I hacked my way through the vegetation and entered a clearing. Suddenly a blinding light shone down from a majestic mountain far off in the distance. _You will lead them here to Zion, my heavenly city,_ the voice told me.
The dazzling light from the city filled me with hope and gave me strength to keep trusting God when it felt impossible. Jesus filled me with the desire to obey through grace. This was his power in my weakness.
So much was unresolved. So much still did not make sense. While I still believed gay marriage was the way forward for my same-sex desires, I had learned not to try to earn grace but to obey out of it.
Strengthened, I was ready to take another step of faith. Where it would lead me? I had no idea.
# [ ** PART 3
WRESTLING WITH GOD: SENSE AND SEXUALITY ** ](contents.xhtml#conn_20)
# [ ** CHAPTER 14
LIVING UNDER GOD'S WORD ** ](contents.xhtml#conn_21)
> If we come to Scripture with our minds made up, expecting to hear from it an echo of our own thoughts and never the thunderclap of God's, then indeed he will not speak to us and we shall only be confirmed in our own prejudices. We must allow the Word of God to confront us, disturb our security, to undermine our complacency and to overthrow our patterns of thought and behavior.
**_—John Stott_**
> The Christian story proclaims that all the demands of Scripture are ultimately summons, calls, invitations—beckoning us to experience true, beautiful, and good humanness.
**_—Wesley Hill_**
> I delight in your decrees; I will not neglect your word.
**_—Psalm 119:16_**
**I** 'd been a Christian for three years, and the question of whether same-sex sexual expression was always sinful loomed. I had learned that grace, as Paul said, was not a license to sin. Okay. And I knew the attraction itself wasn't sinful. But what about acting on it? I was still dating Thomas, so this wasn't just a theoretical question.
I was insecure, uncertain, searching. I wanted to start by learning more about affirming theology.
Through my university, I met a new friend, Josh, who headed up a Christian media club. I admired his sharp intelligence. However, I also knew he was part of the denomination I grew up with at school, which sometimes made me defensive in our conversations.
Every week, Josh and I met at a café a few blocks from the university. As I ate my vegan nachos and he sipped his chai, we studied the Bible. Through our discussions, I gained a deeper understanding of the scandalous nature of God's grace, and how the worst sinners and the most moral citizens both equally fall short of his glory. Only Jesus could lead us into glory and reconciliation.
"Hey, David, do you want to come to a Bible conference? I'm going," Josh asked one day.
I shook my head and shifted in my chair, uncomfortable. "Not sure that's my cup of tea. I assume they're all against gay marriage. And is the worship any good?"
"I can't guarantee about the worship," Josh said. "But there's a scholar and Bible teacher coming from Canada—Don Carson. He's going to talk about the inspiration of the Bible. I think you'd find it helpful." He paused. "Actually, I already asked my church if they would pay your way. So . . ." He smiled.
I sighed but was touched. "And they said yes?"
"Yup."
What could I say?
The day of the conference came quickly. As I entered the huge hall, I spotted many old school friends in the crowd of thousands of young people. I had walked into the heart of evangelical Australian faith, and I was curious and nervous.
When Don Carson got up to preach about the Bible's place in the Christian life, I hung on his words. "We must not put ourselves _over_ Scripture," he said, "but we must live _under_ the Word of God."
For the next forty-five minutes, he poured out his heart, imploring us to treasure the Bible, God's greatest gift outside of himself. Thousands of saints, he explained, had lost their lives so we could hold it in our hands. How would we receive it?
As he spoke, the Holy Spirit convicted me that I needed to trust God's authoritative words. Tears poured down my cheeks. I realized I had sat in judgment above Scripture, never really appreciating its preciousness. I had never been willing to submit to it. I could no longer claim to love Jesus without _really_ knowing his words and choosing to live according to them.
Carson's sermon sent me on a deeper journey of exploring the Bible, especially what it said about sexuality and holiness. This was not a flippant or trivial issue for me. Celibacy still wasn't a serious option in my mind, but I felt a conviction, a tug in my heart. I sought to ignore it; I had so many friends in loving gay relationships.
How could I believe there was something wrong with seeking a monogamous, faithful, same-sex relationship that eventually led to marriage? But after hearing Don Carson, I needed to confirm whether Scripture actually supported—or at least allowed—my position. I desperately needed godly, mature believers who could face my questions and answer them using Scripture, reason, and tradition.
Now that I was uncertain about gay marriage, when I was in secular spaces that believed the church needed to affirm it, I remained quiet, feeling confused. For the first time, the secular world felt unsafe to me. I started to understand what it was like to be an orthodox Christian in a world that quickly judged people according to stereotypes and would not take the time to understand the real complexity of their situations. In a way, that was a familiar feeling, as you can imagine. But it was odd to experience it from this new vantage point.
While I saw that Scripture had lots to say about homosexuality and about marriage, my struggle was anything but simple. I wrestled with what to accept and what to reject, and it all was _achingly_ personal. This was about my life, my real life. My choices. My living situation. My hopes. My parents' hopes. All of it.
If I allowed my own biases to fade away so the text could speak for itself, what would I do if it said what I _really_ didn't want to hear? I knew I would be rejected by many friends I dearly loved for taking this incomprehensible position. And how could I blame them? By everything we'd ever held as true, I would be betraying them.
Yes, the cost just felt too high. And I didn't really have to decide anyway just yet, right?
Right.
# [ ** CHAPTER 15
MARRIAGE AND THE CHURCH ** ](contents.xhtml#conn_22)
> The real sin of marriage today is not adultery or lack of "adjustment" or "mental cruelty." It is the idolization of the family itself, the refusal to understand marriage as directed toward the Kingdom of God.
**_—Alexander Schmemann_**
> We live in a world, in fact, in which respect and support for _eros_ has acquired the hallmarks of a cult.
**_—Andrew Sullivan_**
> You shall have no other gods before me.
**_—Deuteronomy 5:7_**
**S** ince coming out at fourteen, I had searched for meaning and transcendence in romance. Now that I'd arrived in the Christian world, I was beginning to find that meaning in a deeper relationship—with God. And yet something just didn't add up.
I saw many of my Christian peers spend more of their time pondering who their future spouse might be than pursuing God. A kind of matrimonial madness seemed to have descended upon everyone—like that scene from Disney's _Bambi,_ in which the animals flounced around the springtime meadow, surrounded by pastel flower petals, utterly "twitterpated." It got ludicrous at times. Many of our pastors would occasionally tell single members of the church to stand up, look at each other, and find their future marriage partner. Sure, we all laughed. But still— _what?_
This puzzled and disturbed me. I mean, I had read up on my Christian history. Until the Reformation, most of the superstars of Christianity were single. Why had so many of our forerunners in the early church been celibate, if marriage was the golden ideal of Christian life? The way people talked, marriage was almost as big a deal as getting saved in the first place.
Reminders of it were everywhere—in the programs, in our church planting teams sent out for ministry, in the assumptions that people glibly preached and prayed. I suspect pretty much anyone single in the church today can relate. I felt discouraged.
It was as if the message to Christian singles was, "If you just get married, have kids, and buy a property, you'll be truly happy." I mean, it made sense; no one wants to pay their mortgage alone or come home with the flu to an empty apartment. But it began to ring hollow. It also felt familiar.
Both in the gay community and in the church, what seemed to matter most to people was fulfillment in a partner. Singleness was second-class. The sense of displacement I had felt at the Mardi Gras after-party wasn't that different from what I felt on Sunday. Both situations seemed idolatrous.
Shouldn't only God occupy our sense of purpose? Was our goal really to produce happy, debt-free, middle-class families? I mean, that's great, don't get me wrong. But is that _it?_ Then why was Jesus a man of sorrows with no place to lay his head, and single throughout his ministry?
Jesus was an unmarried, childless man in a Jewish society of family values, and a celibate in a Roman society of sexual liberation that mocked singleness. In a world of two-sided sexual obsession, Jesus invited others into pure intimacy, modeled loving friendship, and lived in life-giving singleness.
I never once heard a sermon about the friendship or singleness of Jesus Christ. Why? I wondered if we were missing the point. Jesus called us to value him above everything else, including our sexual desires _and_ our marriage relationships. Yes, marriage was God-ordained, and God had said it was not good for man to be alone. But God, not marriage, was to be our _ultimate_ desire. Period.
This overemphasis on marriage made it terribly difficult, as a gay man wrestling with my sexuality, to flourish in the young adult community at my church. When the focus was on God's kingdom, I could belong, but as soon as romantic relationships were the focus, I felt alienated. I often wanted to run out of meetings in tears.
My frustration culminated at a men's conference. We were encouraged to invite friends, and I brought two gay friends from university. Both of them sat with me, their disgust apparent at this "heteronormative" nightmare they'd been sucked into. It was _incredible_ they had even agreed to come. But I hoped that, like me, they'd discover in the messages the grace of Jesus Christ.
As I sat worshiping Jesus, I thought about how same-sex attractions are not some horrible curse but an invitation to live a radical life that brought about a far deeper faith than many aspired to live. As in the vision of the forest I had to cut through, I had to trust that God would show me the way through my struggle. He would show me what it looks like to follow Christ in my situation. As my mother had told me when I confessed I'd become a Christian, God really was the God of the impossible. Did I truly believe it?
I felt God speaking in my heart and was deeply encouraged. I did believe it. I did.
The good feeling didn't last long, though. My heart dropped as the pastor transitioned out of worship and made a passing joke related to homosexuality. One strike was all my friends could take. They signaled that they were leaving, and, ashamed and upset, I followed them out. As we made our way to the car, the Lord whispered to me, _David, I'm sorry. Remember how much grace I've had for you. Please have grace for the church, my broken bride._
The drive home was silent, awkward. I was embarrassed and angry with my church. How could people who claimed to know Christ be so insensitive and miss the entire goal of the Christian life, which is to be like Jesus? Instead of offering grace and showing people like me and my friends a vision for what it means to follow Jesus, a bunch of Christians had gathered to make jokes at the expense of people like us?
I wondered how many of the men in that room struggled with their sexual orientation. I wondered how many of them had family members, close friends, neighbors, or coworkers who were somehow barred from the heteronormative dream that church often elevated. It seemed so disconnected, so uncaring.
## **SEEING CHRIST IN AN UNLIKELY FACE**
But my own idol was about to be tested in no uncertain terms.
Because of my relationship with Thomas, I became increasingly passionate about finding biblical support for same-sex marriage. Ironically, just like the people I was so harshly critiquing, I was idolizing marriage. I wanted to marry someone like Thomas so I could have a holy and sexually pure relationship like my straight married peers. I wanted to belong.
Thomas had dark hair and green eyes. Our political views were worlds apart, but we could tease each other about controversial topics. The two of us drove around Sydney, enjoying the beaches and cafés. I often fell asleep in his arms as we sat in his car late into the evening. Thomas even came to my church a few times, though he preferred his Catholicism.
Our relationship grew. But I didn't understand why every time I was close to him, the Holy Spirit felt distant. I could just tell that something was off.
Finally, I made a commitment more than once of the kind that tend to be dangerous; God just might ask you to follow through on it. "God, please show me _directly_ what you want for my life. I don't want to be influenced by church, by politics, or by anyone else's opinion. Whatever you show me, I'll obey it."
He did answer directly, but not through a vision or revelation. My relationship with Thomas continued to gnaw at me. A deeper voice told me that my sexual desires, no matter how sincere I was in my affection for another man, would never be the best for me.
It hurt so much. But gradually I realized that I needed to love Thomas the way Jesus loved him. And in order to love him like Jesus did, I had to leave my relationship with him. What I wanted with Thomas could never be God's will for us.
I didn't want to face the reality that marriage might never be mine. It was so incredibly hard. But to follow Jesus, I had to let this dream die.
I remembered Jesus' words in Matthew 19:29: "Everyone who has left houses or brothers or sisters or father or mother or wife or children or fields for my sake will receive a hundred times as much and will inherit eternal life." I clung to the promise that he offered me _life_ , not just brokenness and heartache. When I came to this realization and was ready to own it, I went to see Thomas. But I struggled to do what I knew was right.
We sat and talked. Sensing that I was dancing around an issue, he turned to me, serious. "David, what attracted me to you in the first place was your faith. You have a passion for God. It anchors you in a way I've never seen. I struggle to believe like you."
"Thank you, Tom," I said. "But I still think gay marriage is probably fine with God! It has to be!" Even I could hear the doubt in my voice, and I knew that I had just broached the concern at the center of all this.
He shook his head. "I'm getting in the way of your faith, David. I don't want to do that."
"No, Thomas. I love you," I said, holding back tears. This was too much. It just was. I couldn't follow through with the breakup.
In the following days, he picked me up and we drove back to his apartment to cheer me up and eat my favourite sushi. After the meal, we sat on the couch. I lay with my head on his chest, looking up at his stubble, and traced the shape of his chin with my finger. I lifted my head to kiss him.
"No, David. Stop." He pulled back.
"What's wrong?" I said.
He pushed me gently off his chest. "You're a Christian. I won't let you betray who you are. If I let you do this, you'll be devastated."
He was right. By staying with him, I was betraying my own conscience.
As I sat up and looked at Thomas that last time, I realized that in the very place I shouldn't have been searching for intimacy, I had found Jesus' love. Thomas put me and my identity as a Christian above his own desires. It was as if the Lord himself were gazing back at me through his eyes. I found the fulfillment of my desire for intimacy in its very denial.
That act of love from Thomas was a glimpse of the greater love I was searching for and would really satisfy me all along.
## **WHAT'S IN A MARRIAGE?**
A year later the lesson of romantic idolatry I'd learned through my relationship with Thomas came back to me as my friend Tristan prepared for his wedding. We both ran a discipleship group and had seen the Lord do miraculous things, with many young men becoming Christians that year. We'd become close friends.
One night we realized together that it was Jesus who needed to be our first love, no matter what commitments or relationships might come our way, including Tristan's marriage. It was one of my first experiences of the incredible power of friendship to shape one's life and affections.
Finally, the couple's big day came. I sat in a pew and watched Tristan's bride, Renée, enter the chapel and walk down the aisle. She reached her bridegroom, and her father blessed them as they joined hands. When Tristan and Renée exchanged vows and kissed, tears filled my eyes. I knew in this moment that marriage was something innate to God's own image and his intention for our humanity. He had made them male and female to reflect his glory. It was beautiful.
For the first time, I didn't feel the jealousy and loneliness I sometimes felt at weddings or when I was with my married friends. Instead I was filled with incredible joy that I could witness the love of Jesus Christ pictured in the bridegroom and his bride. The minister read from Song of Songs:
Place me like a seal over your heart,
like a seal on your arm;
for love is as strong as death,
its jealousy unyielding as the grave.
It burns like blazing fire,
like a mighty flame.
Many waters cannot quench love;
rivers cannot sweep it away.
_—Song of Songs 8:6–7_
As I listened to these words, I realized that being gay did not exclude me from this kind of intense, faithful love. Like Tristan and Renée, I was part of the marriage between Jesus and his bride, the church, regardless of my sexual orientation. Marriage was that unique union in which, as Martin Luther said, "a man and wife united in the estate of matrimony are two in one flesh as God and man are united in the one person, Christ." We weren't just celebrating their individual marriage; we were anticipating the future heavenly marriage of God and his people.
It was a fitting celebration for my new season ahead. Though I was sad to leave my church and friends like Tristan and Renée, I was excited to study abroad for a year. My dream had always been to return to France. It was my teenage romantic ideal, where I had wanted to walk in the footsteps of my intellectual heroes. I still hadn't forgotten my longtime dream of that handsome husband and our dreamy apartment in Paris.
Before I flew out, I poured my heart out to God. I sensed him saying, _David, I do not want to erase your dreams or delete your desires. I made you; I know you better than you know yourself. I know the ways you are broken, and I know the ways you will flourish. I gave you the desire to go back to France, and I am going to reinvent the dream that came from that desire all those years ago. Trust me, my son._
There were lessons ahead to be learned, new dreams God wanted to give me. Was I ready to receive them?
# [ ** CHAPTER 16
FACING FACTS IN FRANCE ** ](contents.xhtml#conn_23)
> Guide me in your truth and teach me, for you are God my Savior, and my hope is in you all day long.
**_—Psalm 25:5_**
**K** osher grocers and delis lined the streets of the Jewish quarter of Strasbourg, France, where I'd moved into an antique Protestant chaplaincy building that also served as a student residence. My room, on the mid level of this grand building, was in the same building that was once home to renowned French theologian and philosopher Paul Ricoeur, whom I had studied in university classes years before. I noted that fact with a little thrill of satisfaction.
Just around the corner was the political science faculty, where I was completing the final year of my degree. Beyond that? A statue of the German poet Goethe, and only a little farther still, European Parliament.
It had been a long winter. Looking out my window, I watched the melting snow drip from the roofs. This was the first day it had been above freezing, and a white dusting still covered the city.
I longed for a thaw of my heart too. Without my Christian community in Australia, I was lonely. The European students I studied with seemed interested only in their future careers—administration and politics. I was interested in that too but longed for deeper connection.
I picked up an old journal and began reading it, remembering waypoints in my spiritual journey so far. One day, reading back in my journal, I recalled something a mentor in Sydney had told me: "Like a ship on the sea, God is going to give you a compass to navigate your way through Europe." I held on to those words.
The next week, I met another Christian at the political science faculty, and she introduced me to the Navigators student ministry. Its symbol, I discovered, was a sailing ship.
That was where I met my compass. Merrie, a Bible teacher who mentored Christian students, became my closest friend and confidant through our shared intellectual, political, and spiritual interests, and before I knew it, my heart was coming out of its freeze into a much warmer Strasbourg.
Every week I would arrive at her apartment building and ring the buzzer, eager for our time together. As the smell of fresh bread wafted up from the bakery downstairs, we talked about the gospel, philosophy, our encounters with God, the poor, and those in need. Merrie shared my love for food and cooked all kinds of French dishes during our visits. I'd never been loved so holistically by, or received this kind of hospitality from, an elder believer. Though she lived a frugal, God-dependent lifestyle and had known real poverty, she radiated warmth, wisdom, and a simple richness.
For more than thirty years, Merrie had dedicated her life to bringing the gospel to her beloved France, quietly making disciples among students and other people often left on the margins by the church. She even told me about a brief discussion in Rome her Christian friend had with none other than my onetime hero, Jean-Paul Sartre, shortly before he died. Sartre ended the conversation saying, "I'm not far from where you are with Jesus." Merrie's life inspired me.
I was also deeply encouraged by her strength and resolve as a celibate middle-aged woman. Three men had proposed marriage to her over the years, but each time she refused them because marriage did not align with her God-given calling. I filed this fact away. Such an example was new in my experience but remarkably compelling, as I felt the genuineness of being welcomed as family by this Christlike woman who'd chosen such a different life.
Merrie had an authority to speak into my life. She had truly given up everything for Jesus. She never judged me for my sexual orientation but embraced me as her own son. She told me she admired the way I had chosen to live, desiring to hear from God and follow his will. Through her example, she taught me to love and appreciate any church that believed in Jesus, from the small charismatic Lutheran church down the road to the mainline Protestant churches, as well as the conservative evangelicals, Pentecostals, and Roman Catholics who met in the cathedral.
I found in Merrie a marriage between the intellectual and existential sides of Christian faith. God knit a precious bond between us. This richer friendship, I started to see, came directly from Merrie's intimacy with Jesus. It seemed he had brought me to Strasbourg to meet her.
Months later, on Easter morning, the spires of the Strasbourg Cathedral pierced the purple sky as I walked down the _Rue des Freres_ with Merrie, her hand resting on my arm. Soon the church bells announced it was midday, and people poured out of the cathedral after Mass. The city square was crammed with market stalls, and the restaurant terraces lining the streets were packed with holiday tourists enjoying traditional Alsatian food and sipping fine white wines.
As we browsed the busy market stalls, Merrie brought up the topic of homosexuality.
"David," she said gently, "you need to face the question of whether Jesus is Lord over all of your life, and the reality that same-sex desire will only lead you into sin."
I couldn't believe what I was hearing. If it had been anyone but Merrie, I would have snapped back a reply, but she had earned my trust.
"I'm not sure about that, Merrie," I stammered, flustered.
"David, I say this only because I really do love you. I know what it will cost you. But our lives are not about sex. Our lives are about serving Jesus and his kingdom."
I left the market early, upset by Merrie's words. Deep down, I knew there wasn't a hint of homophobia in them, just pure love, accompanied by truth. She understood what it would cost me to believe them—understood even in a way I couldn't, from decades of sacrifice. Real Christian discipleship, she had told me before, had to involve moments of tough love—it was costly.
Sure, she had my best interests in mind. But that didn't mean it didn't feel like an ocean of pain. _I just wish I could revise what God said in Scripture,_ I thought as I walked home.
But her words haunted me, amplified by a whisper in my heart: _He wants all of your heart, all of your worship._
I thought back to the weeks before I left Australia, when I was devouring everything I could read by Henri Nouwen. His experience was so similar to my own. He was a same-sex-attracted Catholic priest who left his academic life at Princeton to join a community and care for mentally disabled people. Henri wrote of our never-ending struggle to overcome self-rejection and simply know that we are God's beloved children.
This divine love was what I desired more than anything, even romantic love. Almost all my past boyfriends had told me I was searching for something far greater than what they could offer me. For a little while, I'd dated a fashion writer, who, after a concert, broke off our relationship. "David," he said, hugging me goodbye, "you're too profound for me."
I struggled for weeks there in Strasbourg. One night I collapsed on my bed, exhausted by my internal dialogue. I was sick of struggling with my sexuality over three years of being a Christian.
I thought back, reviewing my life so far. All my life, I had believed that romantic love was what would make me whole. But it couldn't. Every relationship had only left me more vulnerable and in need of love.
_Perhaps,_ I thought, _I can live like Merrie, right at the center of God's kingdom, to invite people deeper into God's love. Maybe the desire for a partner was a distraction from some greater task I've been given._
Not long before, I would have greeted that idea with no uncertain language. But Merrie's love gave me the strength to really consider it.
# [ ** CHAPTER 17
GOD'S GREATER ROMANCE ** ](contents.xhtml#conn_24)
> God has bound everyone over to disobedience so that he may have mercy on them all. . . . Therefore, I urge you, brothers and sisters, in view of God's mercy, to offer your bodies as a living sacrifice, holy and pleasing to God—this is your true and proper worship.
**_—Romans 11:32; 12:1_**
**I** t was spring in Strasbourg, and I opened the large windows that overlooked the _Avenue de la Fôret Noire_ and sat down at my reading desk. One of my favorite pastimes was watching people from this vantage point, and soon I recognized everyone in the neighborhood. That Saturday morning, the sun shone over the misty street. I watched an old man cross to the bakery to buy bread, and breathed deeply. This was _France_.
Reading was another of my favorite ways to spend free time. My too-small bookcase overflowed with secondhand novels, and I was currently working through a French translation of Hemingway. His sparse style made it easier to enjoy the story and decipher bits of the French language I hadn't mastered.
I had been shopping and bought fresh chicken Kiev to serve my Swedish friends who were coming to study that evening. New friendships meant that the loneliness of the winter had abated, though I was romantically frustrated, watching so many of my friends pair off into relationships. France seemed like an impossible place to be alone. It was made to be shared.
My conversation with Merrie weeks before still bothered me. As I sat on my bed reading, I suddenly threw my book down. "God," I said out loud, "I need a direct answer from you. I can't keep living this way. Do I have a romantic future or not?"
Silence.
As I bustled about to get ready for my guests, I struggled with this. It bit at every part of my identity.
Two days before, I'd attended a book launch at Librairie Kleber, a large bookstore in town, for _Le Triangle Rose,_ the memoir of Rudolf Brazda. This stout and vivacious elderly man was the last living gay Holocaust survivor. He'd shared his incredible story of survival, and I couldn't get it out of my mind. One hundred thousand gay men and women had been persecuted by the Nazis, many of them exterminated. Brazda, the son of Czech immigrants to Germany, spent thirty-two months in the Buchenwald camp in central Germany before he was freed by American forces on April 11, 1945. The title of his book referred to the pink triangle the Nazis made him wear, identifying him, alongside thousands of others, as homosexual.
Brazda had shown us his concentration camp tattoos and talked about being beaten by Nazi guards. Once he had three teeth knocked out and was told he was going to be executed. He survived only because two guards, one of whom had feelings for Brazda, helped by getting him off hard-labor quarry duty. The possibly gay guard also gave him stolen food rations. In late March 1945, as the Allies closed in, another SS officer hid him in the camp's pig shed so he wouldn't be taken on a forced death march.
"I lay there with the pigs for fourteen days until the Americans came," he said, reading from his book. "After that I was a free man. Others died, but I came through."
I felt my soul wrestling with God as I listened to the atrocious things the Nazis did to Brazda. In a profound way, I was in awe of his strength through such horrendous evil and suffering. I had been a part of this community; in a different place and time, I too would have faced the death that looked him in the eye. As a Christian, did I have to deny the reality of my same-sex desires entirely? Was every aspect of my past—even with the strong and beautiful things about it—doomed to be erased and forgotten? As a Christian, did I have to ignore the history of LGBTQI people and the freedoms people like him had suffered so much to gain?
At one point, Brazda's eyes met mine. I felt a solidarity with him that, while different, felt something like the bond of fellowship I often felt when I first met Christians. I remembered that in the Beatitudes, Jesus says the poor in spirit are blessed, for theirs is the kingdom of God. Though Brazda and I had very different lives, there was a deep reciprocity of spirit—something like this poverty of spirit.
It was as if the harrowing dehumanization he suffered exposed a part of my felt alienation. I could no longer ignore the complexity of my soul and the life I was called to. I had deceived myself, thinking that it was easier just to run away from the reality of being SSA/gay, when actually God wanted to redeem and use it. A harder path was set calling for a true poverty of spirit. Brazda's story gave me the courage to really face the conundrum of my faith and sexuality.
I hopped onto my bicycle and headed home, knowing I would never forget that day at Librairie Kleber. Something else was on my mind too. Many Christians had encouraged me to use the term same-sex attracted to distance myself from the gay world, but somehow this just didn't work when I spoke to people outside Christian circles. Others said, "Don't call yourself gay! You're making your sexuality your identity." Such a statement, while seemingly caring, dismissed the nuanced reality of my story. There was something in our shared reality of living with these desires and bodily differences that contained a shared history, a common experience. This aspect didn't have to conflict with my choice to follow Christ or what I chose to do with my homosexuality. While it risked confusing some Christians, no term was perfect and had limitations, but I knew God was calling me to be transparent about this part of my identity.
As I weaved through the streets, I asked, _God, what's your response? Do you want me to stop identifying myself as gay altogether?_
Jesus' broken body flashed before me. _I died with them,_ his quiet voice said. _I entered into the evil of death and injustice._
God, I realized, didn't dismiss the suffering of the gay community. Rather he identified with unjust human suffering on the cross. He said it mattered.
The Suffering Servant of Isaiah 53 knew what it was like to be led to death, just like many of those gay Holocaust survivors. As God's Son, his death was able to deliver others from sorrow, injustice, pain, and sin. That meant I needed to give him my pain, not hide parts of myself. While my homosexuality was secondary to Jesus' claim on my life, it still was important to him. It was part of my broken humanity, a humanity he took on himself in order to redeem it.
After meeting Brazda, I knew I could never forget or run away from the reality of my same-sex desires, even though I knew being gay or SSA could never be my ultimate identity. It would only ever be secondary to the lordship of Jesus. Yet I had to find a faithful way to live it out. I had no idea what that would mean, but I knew it started with honesty, not running away from this aspect of my current reality. I trusted that Jesus would lead me, just as he always had.
## **GIVING GOD MY HOMOSEXUALITY**
One day, not long after the event at Librairie Kleber, I sat on my bed yet again. "God," I cried out loud once more, "I have a body. Where do you expect me to find the intimacy you created me for? I thought it was not good for man to be alone. Lord, I need an answer."
_David,_ his quiet voice whispered, _my church is meant to be that body to you._
"Really?" I was skeptical. "I haven't been able to find a church where that kind of intimacy is even possible. I need a partner."
What came next was as clear as it was odd. _I'm sending you a birthday present._
My birthday was just a few days away. When the day came, I just about ran to check the mail. Sure enough, there was a small parcel from Joshua, my friend who'd invited me to hear Don Carson. Even though he had entirely forgotten about my birthday, his package just happened to arrive on it.
I tore it open. It was a book. " _Washed and Waiting,_ " I read, "by Wesley Hill." It was a reflection on homosexuality and Christian faithfulness.
Joshua had scrawled on a little note, "A friend recommended this, and I thought it would bless you."
I devoured the book, astonished by how closely Hill's story mirrored mine. Both joy and pain filled my heart as I read. He had resolved to call himself a celibate gay (or SSA) Christian. Even if Hill was raised as a Christian, unlike myself, I'd never heard of someone doing this before, but it fit so naturally with what I'd just experienced after hearing Brazda. Hill's words reflected my own theological intuitions and my identity as a Christian as well as the reality of being a man attracted to men. The way he put Jesus Christ at the center of his life inspired me.
Hours passed, and I flew through the pages. When I finally put the book down, a storm was brewing outside. I listened to the first water droplets hit the roof, accompanied by a dramatic thunderclap. I thought again of Paul's words in Romans 12: "I urge you, brothers and sisters, in view of God's mercy, to offer your bodies as a living sacrifice, holy and pleasing to God—this is your true and proper worship" (v. 1). And another verse from Paul, this one in 1 Corinthians 6: "All other sins a person commits are outside the body, but whoever sins sexually, sins against their own body" (v. 18).
I knew beyond doubt that God was asking me to do what I had never thought I could: give him my homosexuality and choose celibacy. It was that simple. It was also that hard.
From a sort of loving, desperate surrender, I prayed. "Lord," I whispered, "you died on the cross for me. You gave me your body. How could I not give you my body in return? How could I hold back my sexuality, let alone my money, my plans, my affections, my whole self? Anything less wouldn't be true worship."
This was different from my other times of surrender. God had given me all of himself in his Son and Spirit, and it was time to give him all of myself. My gay identity had to bow to Jesus Christ, and that meant being willing to live without a partner for the remainder of my life.
His love called me to relinquish the desires warring against my repentance. I gave them over to him and was swept into his arms. This was the greater romance, the one true love that could fulfill me, far more than sex or any relationship could.
In that beautiful moment, I couldn't know that my heartfelt commitment to celibacy was about to clash with my long-held dream of finding romance in France.
# [ ** CHAPTER 18
ROMANCE IN FRANCE ** ](contents.xhtml#conn_25)
> If you let this chance pass, eventually, your heart will become as dry and brittle as my skeleton. So, go get him, for Pete's sake!
**_—The old artist "Glass Man" in_ Amélie**
> This is what the LORD says: "Cursed is the one who trusts in man, who draws strength from mere flesh and whose heart turns away from the LORD."
**_—Jeremiah 17:5_**
**S** pring had ripened into a warm summer. I sat with Merrie and friends from church, watching Bastille Day fireworks light up the July sky. The crackling fireworks and the cheering crowd reached a crescendo, and the burst of colors became a kaleidoscopic blur. _Red. White. Blue._ As I stared at them, my mind drifted, until it settled on a now-familiar face. _Jerome._ It felt like I'd just met him. I couldn't stop thinking about him.
It all started a week after my decision to surrender my sexuality to God. I was in the library with a pile of books on my desk, nose down, working. I had looked up from the stack of reading, just for a moment, and my heartbeat quickened. There was a handsome student I hadn't seen before—French, I thought. He saw me looking and smiled back. I quickly ducked behind my books, trying to act as if nothing had happened. But something had.
I continued to read and study, but my furtive glances were noticed. My friend Margarite, a law student and the reigning socialite of the class, tapped me. "David," she whispered with a smile, "I saw you looking at Jerome."
"Huh?" I said, feigning ignorance. But my face betrayed me.
"Don't be _ridiculous_." She giggled. "Jerome came over to me a while ago. He likes you. I've set up a drink for you two tomorrow night. And you're _going,_ by the way."
My heart pounded. My dream of a French romance was here. I calmed myself down and shook my head no, but before I knew it, she was over at Jerome's desk responding for me.
Jerome's dark brown eyes stared at me through broad-rimmed glasses. "Bonjour, David," he mouthed, and something in me melted.
How much could it hurt to meet and talk? We got together for drinks the following night, and over the next weeks, I found myself spending every other day with Jerome. He was charming and brilliant. We went to the cinema to watch art house films, dipped our croissants in coffee at cafés, and discussed European politics and his plans to work as a political journalist or public servant. I started to forget about celibacy. We were just friends, and then more than friends. I was falling in love.
One evening Jerome kissed me under a full moon near the Palais Universitaire. Its beautiful facade was decorated with statues of philosophers looking down on us—whether in approval or displeasure, I couldn't tell.
The battle line was drawn between my love for God and my love for Jerome. I knew I was called to love God more than I desired this romantic relationship. I knew it was not God's will for me. But right now, I simply didn't care.
"I love you, Lord, but this is my dream," I told him. "A boyfriend. A husband. A partner. A lover. A companion. Someone to share life with. You made me for this, and I want it. You allowed me to have same-sex desires, so you'll just have to deal with this. I never chose it; _you_ did." I ignored my conscience and pursued a relationship, but I didn't shut God out.
One late Saturday evening, Jerome and I went to the cinema. It was empty except for us. After the film, we wound our way through the dark cobblestone streets, hand in hand, until the cathedral came into view. As bells announced it was midnight and we turned the final street corner, I knew Jerome was going to ask me up to his apartment.
That old French dream resurrected itself in front of me. _God, I know this is not your will, but I want this anyway,_ I thought, looking briefly to heaven. _I want it more than you right now. I'm sorry._ We climbed the spiral stairs to the top floor. Outside his door, Jerome pulled me in for a kiss. His dark brown eyes stared back at me, and he smiled. Our foreheads touched for a moment. Our connection was palpable.
As we walked into the apartment, Jerome fixed me a quintessentially French _tisane,_ or herbal tea. I joined him to drink it in his room. Sitting on the bed, we began to kiss.
Psalm 139:7–8 flickered through my mind, uninvited: _"Where can I go from your Spirit? Where can I flee from your presence? If I go up to the heavens, you are there; if I make my bed in the depths, you are there."_
_David, do not try to give him the love only I can give him,_ God's voice whispered. _You are my son. Remember who you are._
The war of loves grew intense. _God or Jerome._ My physical self was choosing Jerome over God, but my new heart knew it had to choose God over Jerome. I realized that my love for God was stronger than my desire for Jerome. This had never happened before! My heart, I saw, had been too touched by grace to accept broken sexual desires over worship of my beloved, Jesus.
I stopped kissing Jerome. "I can't do this," I said in French. "I'm a Christian."
"What do you mean?" he asked, puzzled. "I'm Catholic. There's nothing wrong with this. It's love. God _is_ love. If you have issues," he said, smiling, "you can just go to confession." He tried to kiss me again.
"No, Jerome, I'm serious. I don't think you understand. Love isn't just a feeling. Love is Jesus Christ dying on the cross for us." I put my head in my hands, then looked up at him. "He is clear on homosexuality. His grace isn't a license to do what I want with my body."
His confusion melted into acceptance. Seeing my earnestness, he nodded. "I understand," he said, with the gentle intelligence I so appreciated in him.
I understood that I'd just made one of the hardest decisions of my life.
_"On peut être des amis,"_ I said, with tears in my eyes. "We can be friends."
At church that next evening, the pastor preached from 2 Samuel, focusing on the words of David: "I will not sacrifice to the LORD . . . an offering that costs me nothing" (24:24). God knew. That was it. God _knew_.
The choice to give myself completely to God was not one I made as an indifferent, unfeeling robot. My heart was tender, bleeding, human. And it was the costly sacrifice I was offering him, a sacrifice that cannot be put into words. It went against the natural forces that raged within me, but God promised me grace and resurrection strength to help in my weakness. I was becoming a real disciple.
And even as I lost something I so desired, I was given my life back, as Jesus promised, in return. It is difficult to describe the depths of intimacy I shared with Jesus Christ after that choice against Jerome as my lover. Jesus was there, as if he were in the room, even as I mourned what I had just lost.
Jesus understood my struggles and temptations: "Because he himself suffered when he was tempted, he is able to help those who are being tempted" (Heb. 2:18). He knew what total sacrifice looked like, since he had submitted all of himself to his Father to bring us the kingdom of God.
That scared me. It also opened a new horizon of possibilities, a new kingdom reality. I knew that the intimacy and love I now shared with God was worth suffering for. _This_ was entering the fellowship of Jesus' sufferings (see Phil. 3:10).
Besides Merrie, not many believers had warned me about costly sacrifice in the Christian life. In my experience, the church barely talked about what Scripture said about being living sacrifices. Instead they settled for a comfortable, easy gospel, offering what Dietrich Bonhoeffer called "cheap grace." That meant there was no need to surrender our choice sins, our closely held dreams, our deepest desires that went against God's revealed will.
I longed, so deeply, for something more than that—his will, and not my own. And I had taken my first steps toward it.
## **FEARING GOD IS LOVING GOD**
My year in Strasbourg ended, and I moved back to Sydney. Even while I missed my life in France, I was glad to be home in Australia.
After I returned, my questions about biblical interpretation resurfaced. I saw now (Don Carson's voice ringing in my mind) that much of my reading of Scripture had simply been interpreting it as saying what I _wanted_ it to say—putting myself above the text. Besides studying the context and using reason as I read God's Word, there was also a relational aspect. I needed to have a healthy respect, a fear of the Lord. That relationship would put God's view above my own.
This fear isn't a cowardly, trembling thing. It doesn't come from fear of punishment or the understanding of God as cruel. It is simply the full acknowledgment that he is Lord, the only Lord, and we are not.
I read in Isaiah 11 that the Messiah was prophesied to have "the Spirit of the knowledge and fear of the LORD" (v. 2) and that he would "delight in the fear of the LORD" (v. 3). Jesus, this Messiah, I came to understand, perfectly modeled this awe and respect for God, and he offered and imparted it to me—to all Christians—through the power of the Holy Spirit. It was not something I could cultivate on my own, no matter how I tried.
This fear is a sign we are living in real, costly grace, not in cheap grace that requires no sacrifice and never allows God's Word to challenge or change us. Sadly, many Christians I observed seemed to live a lukewarm life that lacked this awe for God.
Søren Kierkegaard faced similar challenges from the nominal Christian culture and scholarship of his day. I resonated with his words: "The matter is quite simple. The Bible is very easy to understand. But we Christians are a bunch of scheming swindlers. We pretend to be unable to understand it because we know very well that the minute we understand, we are obliged to act accordingly. . . . Christian scholarship is the church's prodigious invention to defend itself against the Bible, to ensure that we can continue to be good Christians without the Bible coming too close."
One Sunday at church, the preacher's message was on the fear of the Lord. He quoted Psalm 19, which says, "The fear of the LORD is clean" (v. 9 ESV), and talked about how "the commandment of the LORD is pure, enlightening the eyes" (v. 8 ESV). As he shared from Scripture, I was convicted of the uncleanness of my own heart. The two other churches I sometimes attended, I realized, did not fear God in this deeper way; that was the hesitation I'd felt there from the beginning! That was why the Spirit in me held back, even in the midst of some wonderful things they taught and did. The relationship with God was skewed. They simply didn't fear him in this clean, beautiful way. _If I don't have the fear of the Lord,_ I thought, _my love isn't real._
That night, I submitted my life anew to the lordship of Christ, yet another milepost on my road. I now knew I had to leave these other churches and commit to one for my heart to be clean. While that did not mean severing friendships with people I cared about, it did mean cutting the ties of official fellowship and attendance as a sign of my new commitment.
In subsequent weeks, many of the people from these churches harshly criticized my choice to be celibate. It was so hard. I loved these people! But I didn't turn back. The freedom I'd found was worth it.
# [ ** PART 4
THE NEW IDENTITY ** ](contents.xhtml#conn_26)
# [ ** CHAPTER 19
UNDERSTANDING LOVE AND CELIBACY ** ](contents.xhtml#conn_27)
> Aim at Heaven and you get Earth thrown in. Aim at Earth and you get neither.
**_—C. S. Lewis_**
> My people have committed two sins: They have forsaken me, the spring of living water, and have dug their own cisterns, broken cisterns that cannot hold water.
**_—Jeremiah 2:13_**
**A** t this point in the book, you'll have to bear with me a bit as my story shifts. My journey to calling myself a celibate gay Christian is far from over (and will continue to develop through the final chapter), but publicly committing my life to celibacy as a gay Christian was a watershed moment. What I'd like to do now is begin to shift into more specifics about what I've learned (and am still learning!), to share the convictions and principles that inform that decision. My story is a testament to God's quiet revolution in my heart. But these principles, I pray, can be used as a manifesto for a revolution in _yours_.
During my time as an activist, we frequently used the famous slogan "Love is love" while fighting the orthodox Christian definition of marriage. Love, as we defined it, was our highest ideal and our sacred entity. That, in our minds, settled the issue.
But while our slogan was popular, it was shallow at best. "Love is love" doesn't mean that much semantically, and it provides no definition of what love actually is. Nor can it differentiate between the various _kinds_ of human love and desire. Is it really all that simple? No! Love has many commonalities, but part of what makes the human experience so rich is the multiplicity of loves that we experience. A mother's love is not a friend's love. A friend's faithfulness and a total stranger's act of compassion are both touching and wonderful. But they are not the same—cannot be, should not be.
Love, I have come to learn, is not God. Flip that. God _is_ love. The God revealed in Jesus Christ is the definition of love. This difference changes everything. We are caught up in arms greater than our own, feeling the possibility of being accepted not by our mirror but _by our maker_.
The cross is where that strange and holy God most clearly reveals his love. There he gave his very self so that the whole world could know him and enjoy the intimacy we were designed for, and without which everything else breaks down. Human romance and attempts at religion can never provide lasting meaning. Only God can. In that sense, the cross is God's intimate act of self-giving, his gentle way of critiquing our love of money, sex, self, romance, fame, and, above all, power. These weaker loves, these idols we raise in our own image, could never compare with his infinitely greater love.
Jesus taught that both the worst sin and the most sacred worship originate from the same place: the heart. Think of that revolutionary concept! What does it mean? Simply, that God's love should displace all others and occupy the primary space in our hearts. It is, simply, what we were made for.
As Christians, the romance we should most celebrate is the marriage of heaven and earth, between Christ, the Bridegroom, and his bride, the church. It is the greatest of all love stories.
But notice this: the faithfulness of intentional celibacy is part of this love story. Both Christ and the bride ought to have only one lover. Practically, all lesser human loves, even the incredible intimacy of marriage, is a half shadow of that great love we were made to experience.
Let me be clear: this does _not_ mean that we are all called to celibacy or that it makes one a super-Christian. That can turn to idolatry of lifestyle as much as marriage. But the core _skills_ of celibacy—discipline, self-control, choosing a greater love at the sacrifice of a lesser—these are all key Christian skills pointing straight to the heart of Christ. No matter your calling, single or married, you must grow in them to grow in Jesus.
So why do most Christians seem far more concerned with romantic love than with God's great story? In many congregations, when an engagement or wedding is announced, there is often greater enthusiasm than when God is worshiped. In contrast, when someone commits themselves to celibacy, there is no celebration. The person is regarded as an abnormality.
Yes, biblical marriage is a beautiful expression of romantic love that glorifies God. But as Wesley Hill says, "The New Testament views the church—rather than marriage—as the primary place where human love is best expressed and experienced." For C. S. Lewis, it was not the loves in and of themselves that were bad, whether romantic or family love, but the _order_ in which they were placed in the human heart. It sounds like heresy in our culture, but romantic and sexual love are not the deepest expressions of our humanness. Unconditional love—God's love—is.
In his essay _Deus Caritas Est,_ Pope Benedict XVI distinguishes between _agape,_ that perfect, self-sacrificial love of God, and _eros,_ that passion of sexual yearning, love, or desire for life and union most of us are so familiar with. _Agape_ love, he wrote, sanctifies and transforms eros by turning it toward the worship of God—rechannelling our passions to further his kingdom.
And Pope Benedict XVI is not alone! On the other side of the cultural room, the gay Catholic writer and activist Andrew Sullivan wrote that he believes "we live in a world . . . in which respect and support for _eros_ has acquired the hallmarks of a cult." In his book _Love Undetectable,_ he states,
The great modern enemy of friendship has turned out to be love. By love, I don't mean the principle of giving and mutual regard that lies at the heart of friendship [but] love in the banal, ubiquitous, compelling, and resilient modern meaning of love: the romantic love that obliterates all other goods, the love to which every life must apparently lead, the love that is consummated in sex and celebrated in every particle of our popular culture, the love that is institutionalized in marriage and instilled as a primary and ultimate good in every Western child. I mean _eros,_ which is more than sex but is bound up with sex. I mean the longing for union with another being, the sense that such a union resolves the essential quandary of human existence, the belief that only such a union can abate the loneliness that seems to come with being human, and deter the march of time that threatens to trivialize our very existence.
Those who define themselves through _eros_ are actually seeking the transcendence of union with God. But they will never find it in human relationships. Looking there, they set themselves up for the heartbreak of a lifetime. We humans are caught in a love triangle of our own, for there are relationships between _agape_ and _eros,_ without doubt. But we have to choose _agape_ —getting _eros_ thrown in, to paraphrase Lewis.
As I look at our messy humanity, my heart breaks for God. We choose against him, nearly constantly. He is our jilted divine lover. He designed the good things of marriage and sexuality to be a means to worship him, not the object of our worship. But as the apostle Paul explains in Romans 1, we have all committed idolatry by exchanging the Creator for created things.
## **THE SACRED GIFT OF CELIBACY**
Often when Christians focus on the world's sins, we neglect to communicate the solution: the love of Jesus Christ. In failing that way, we condemn people before they've even had the chance to know God's grace and understand that he is what they are really seeking.
Hear me well: homosexuality is not an evangelistic issue. It is a discipleship issue. So we must approach it that way. But we also need to remember that without a knowledge of God's grace, the gift of the Spirit, and an understanding of God's satisfying love, discipleship kills rather than gives life, condemns rather than convicts. Celibacy is no different. Gay or same-sex-attracted celibacy must be a response to God's love, not a legalistic bottling up of our human desires. It is about the redirected affections of a transformed heart.
Once we belong to Christ, we all—no matter our orientation—need to be discipled by him in the Spirit and be willing to be purified in our desires. Churches must not leave LGBTQI people in the dark pastorally and theologically about their particular situation. If they do, the entire body suffers from the idolatrous effects of a disordered love in the whole church body.
Over the years since my conversion, I have seen many initiatives, such as Matthew Vines' Reformation Project, which promote the affirmation of same-sex marriage in the church. Matthew Vines writes, "Christians throughout history have affirmed that lifelong celibacy is a spiritual gift and calling, not a path that should be forced upon someone."
I agree that we must be careful not to present celibacy as a moral code. But what many biblical revisionists overlook is that _both_ celibacy and marriage are a calling to find our fulfillment in Christ. Celibacy is neither an easy gift nor a repressive burden. It is an opportunity—an opportunity, not that different from marriage, to trust in God's capacity to provide for our need for intimacy. _Forsaking all others . . ._ Do the words of the marriage vow ring hollow when we speak them to God? Any lack we presently experience in celibacy can be supplied with what Nouwen describes as the three qualities of God's love in us: intimacy (closeness), fecundity (fullness), and ecstasy (self-sharing). The poverty of spirit experienced in celibacy provides the opportunity for a deeper experience of divine love. This is not to dismiss the real sacrifices of the celibate life. (Trust me, I know them.) But it gives them their proper context.
In Isaiah 56, the prophet receives a word from God about the future acceptance of eunuchs, or people whose sexual orientation or gendered state is different from the norm. The fulfillment of this prophetic text was God's embrace of the Ethiopian eunuch in Acts 8 after Jesus' resurrection. This story was radical in a society that saw eunuchs, or sexually-other people, as unclean and unable to enter God's holy presence in the temple. But today, because of Jesus, LGBTQI people are welcomed into the church, the family and temple of God.
The apostle Paul, like many of the Christians after him, was also celibate in a society that expected marriage. In other places in the New Testament, the celibate life is seen as godly and a sign of dedication to Jesus. Revelation 14:4 says those who decide to remain celibate are the firstfruits of Christ's saving work: "[Those who remained celibate] follow the Lamb wherever he goes. They were purchased from among mankind and offered as firstfruits to God and the Lamb." It echoes Isaiah 56, which promises eunuchs "a name better than [having] sons and daughters" (v. 5)—the very name of Jesus Christ, who was himself single and childless. If Jesus was celibate and the ultimate example of human flourishing for all of us, gay or straight, then isn't it clear that celibacy is not an inhumane sentence for gay people like me but actually a legitimate, and even honorable, choice?
The church needs to return to a view of celibacy as a valid option and a sacred gift to give in response to Jesus' love. If the church does not recognize and value this truth, the lives of celibate gay Christians will be indescribably difficult, and the church will remain locked in idolatry.
In Christ, I discovered, my romantic status no longer defines my value, my wholeness, or my well-being. The gospel has become increasingly good news to me because in my celibacy, I am promised a name of precious worth. Much like the apostle Paul, who considered himself a spiritual father to Timothy and Titus, as a celibate gay man, I can sire spiritual children through the gospel.
_Embraced, fulfilled, loved._ I was learning that I am all of this and more, and I was eager to see how Christ would use me next to further his kingdom.
# [ ** CHAPTER 20
BIBLE COLLEGE AND MOVING TO OXFORD ** ](contents.xhtml#conn_28)
> He guides me along the right paths for his name's sake.
**_—Psalm 23:3_**
> Delight yourself in the LORD, and he will give you the desires of your heart.
**_—Psalm 37:4_**
**T** he end of my undergraduate education had come, all too quickly. I had to decide what to do next. While I saw all of my life as worship to Jesus Christ, I wanted to spend concentrated time seeking God's presence and person. So at my church's New Year's service, a time to consecrate the year ahead to God, I responded by committing to attend a one-year course at Bible college. This was, for me, a Psalm 23 moment. _Father,_ I prayed, _lead me to graze on green pastures, to be by still waters, and to spend my time in your house._
Taking a year off from pursuing a career was an expression of love for Jesus. At the time, I had doubts about how such a school could really address my deeper needs, so choosing to go was an act of deep trust. But I wanted to mature in my relationship with him.
The decision to die to my sexuality had changed me. Strangely, I was even becoming _grateful_ for my struggles. They had pointed me to God. That much was undeniable.
I still had unanswered questions. Lots of them. But I knew God's presence was with me every day. The relationship just required patience. He would not necessarily tie up every loose end or answer every question. But the faith was there. I'd seen him work. He'd work again.
In hindsight, that year at a small Bible college was the best year of my life in terms of growing closer to him. I heard his voice clearly, encountered him powerfully. One particular class had a profound impact on me. The teacher suffered from an acute respiratory disease that caused a spluttering cough between his words. It was a poignant reminder of our mortality, that our bodies, our desires, and this world are not as God ultimately intends. Between the professor's coughs, I received words of life.
## **REDEEMING THE PAST**
One day, after that year ended, I slid into my car and headed to a job interview at a Christian aid organization. Turning up my favorite worship song, I praised God for making me right with him through Jesus, lifting the pressure of death and sin from my shoulders.
As I drove, I reflected that I was convinced like never before that "neither death nor life, neither angels nor demons, neither the present nor the future, nor any powers, neither height nor depth, nor anything else in all creation, will be able to separate us from the love of God that is in Christ Jesus our Lord" (Rom. 8:38–39).
I walked into the small, open office, nervous and excited for my interview. If I got the job, perhaps my inner activist could finally find an outlet through helping communities in developing nations.
I recognized a few people, familiar faces from Christian events I'd been involved in. One stood out in particular. I stared a little. He didn't see me. _Where do I know him from?_ The subconscious confusion lasted only a split second. It was Michael. Wait, _Michael?_
Michael. My friend from that fateful love triangle at university five years ago. I couldn't believe it. Last I knew, he was an atheist. He really _disliked_ Christians. What were the chances he'd be here, on the other side of Sydney, working for a Christian organization? Yet here he was. I felt like I'd been punched in the gut. I was so ashamed to see him after what had happened between me and Samuel, his ex-boyfriend.
I turned quickly, rushing to the bathroom area to remain out of view. Needing confirmation, I pointed over to his desk. "Who's that?" I asked a staffer nearby. She smiled. "That's Michael. He volunteers here." Afraid of being spotted, I ducked into the bathroom. _God, what's going on? Why is Michael here? What are you trying to say?_
I heard Jesus' voice respond to me: _You are justified by my death and resurrection for you. Do you really believe it? Do you really believe my blood was enough?_
_I'm not sure I really do._ I was shocked at my response.
_I've freed you from the past,_ he told me. _You are no longer_ _condemned. You are a different person, my new creation. Don't be ashamed. Walk back out there._
I took a deep breath and walked out.
I got the job. As the weeks passed, I was asked to become Michael's overseer. I knew we needed to talk. I had so many questions, and something vital to say to him.
At first he didn't want to meet me for lunch outside of work. I couldn't really blame him, but we needed a private space to talk. Finally, he agreed.
Sitting across from him, I said, "Michael, I know this may seem crazy to you, but I am an entirely different person from who I was five years ago. I've been saved and transformed by Jesus Christ. I live a very different life." I looked down, then back at him. "I just want to say how sorry I am for what happened with Samuel. I was in the wrong. Will you forgive me?"
He put down his coffee. "I'm sure you're convinced of all that, David, but that simply won't do."
Michael didn't openly forgive me. But somehow I left that meal with a closure I never thought I would have. Driving home, I heard Jesus say, _David, I didn't just die for your sins. I also died to transform the_ consequences _of your sins._
Over our final months of working together, Michael's attitude toward me changed. While still avowedly agnostic, one day at a prayer meeting, he revealed that he had contracted a serious disease and his father had been diagnosed with cancer. Our community was able to be there for him. I was grateful for the opportunity to apologize to him personally, and, in the limited way that our strained relationship allowed, to be a friend in his time of need. There was not full restoration. But there was a new kind of equilibrium. A peace.
Is this not the unique power of the Christian gospel? For all the remaining messiness, for all the rough edges that result from the consequences of our actions, can anything else reconcile and restore the most broken situations and people? Oh, the hope for all of us! It is profound.
## **BECOMING AN APOLOGIST**
The Sunday after that job interview, I met my friends from Bible college at church. After the sermon, a team of ministry leaders invited people to come up for prayer. When I stepped forward, an Armenian man named Leon, whom I knew only from afar, said the oddest thing: "David, God is showing me you will study in beautiful old libraries, poring over old books, with a Bible open at the center of it all. God has called you to study, speak, and write for him."
I hadn't told anyone (except my parents) that weeks before, at the suggestion of a mentor and friend, I had applied for a course in theology at the University of Oxford. I took this message from Leon as confirmation from God that Oxford would happen.
And sure enough, it did. Six months later I had left my job at the aid organization, crossed the world, and found myself back in the beautiful streets of Oxford, preparing to study theology. As a student concurrently at the Oxford Centre for Christian Apologetics and the University of Oxford, I hoped to grow as a writer, speaker, and communicator. I was to be trained in apologetics and evangelism by greats like John Lennox and Michael Ramsden, and I was given access to those old libraries Leon had mentioned. _This is surreal,_ I thought. It felt like a dream.
As I walked down the long streets from my college, I could not believe I was here. I had been admitted to one of the world's great universities. The sound of church bells and the sight of blooming flowers covering the lawns filled me with joy, and the old buildings reminded me of one of my favorite poets, Gerard Manley Hopkins. Everywhere I looked in this city, God was speaking his love tenderly to me.
I walked past the Martyrs' Cross outside Balliol College, commemorating where the English Reformers Latimer and Cranmer were burnt at the stake for their beliefs. Before his death, Latimer wrote, "We shall this day light such a candle, by God's grace, in England, as I trust shall never be put out." There was something about their sacrifice that filled me with hope. Despite the daily struggle I still faced over my sexuality, I knew that like these men, I was willing to die for my faith. We were connected by the same Spirit.
All around the university, rainbow flags flapped in the wind. Their presence both troubled and pleased me—a reminder of still feeling in-between. Were they a sign of my liberty or of my oppression? I didn't fit in the gay world anymore, and I didn't fully fit in the Christian one either.
I turned my eyes back to the mosaic of the Martyrs' Cross on the asphalt. _We will all die,_ I thought. _But the question is, what we will die for?_ Like the martyrs who died on that ground, I had to be willing to give my whole life to following Christ, even if that meant living a deeply unpopular life and being mocked or disdained.
I continued my walk past Blackwell's bookstore, where Daniel, my mother's colleague, had bought me Richard Dawkins's _The Selfish Gene_ ten years before. As I selected books for that term's classes, I purchased John Lennox's _Gunning for God,_ his response to Dawkins's New Atheism. _What a difference these years made,_ I thought.
I made my way through the backstreets and past the old sights: the Bodleian Library, Sheldonian Theatre, and Radcliffe Camera. After walking through High Street and past Merton College, I entered the old gate of Christ Church Meadow. As I stood looking at the football pitch surrounded by budding daffodils and crocuses, I pictured my fifteen-year-old self standing just yards away and remembered my words of self-doubt: _I'm not good enough. I'll never study here._
Yet here I was.
God had lifted up, loved, and saved that self-doubting gay boy. He had brought him, through the most unlikely of events, back here. A decade before, I was one of the last people in the world who'd be training as a Christian apologist. But now I stood with a bag full of books and a heart full of love for Jesus.
Under those impossible spires, God the Father was giving me, his son, the desires of my heart.
# [ ** CHAPTER 21
DRAWING THE LINE: ACCEPTANCE VERSUS AFFIRMATION ** ](contents.xhtml#conn_29)
> Without knowledge of self, there is no knowledge of God. Our wisdom, insofar as it ought to be deemed true and solid wisdom, consists almost entirely of two parts: the knowledge of God and of ourselves. But as these are connected by many ties, it is not easy to determine which of the two precedes and gives birth to the other.
**_—John Calvin_**
> The heart has its reasons of which reason knows nothing.
**_—Blaise Pascal_**
**I** was working in Oxford one evening when a ding on my laptop announced I'd received an email. To my shock, I saw it was from the Archbishop of Canterbury's office, inviting me to speak at the Church of England's General Synod about my journey with homosexuality.
Around that same time, a flurry of voices—from within the Church of England and also from the wider evangelical world, including Tony Campolo and Jen Hatmaker—had made pronouncements in support of gay relationships. Just that week, I had been dealing with deep discouragement after hearing that someone prominent in the celibate gay Christian world came out in support of same-sex relationships and marriages in the church. It was a struggle to stand with God, hold to what I knew his Word taught, and not succumb to the immense pressure to affirm such unions.
Others in the church, afraid of repercussions or being judged from the sidelines, kept their mouths shut. It all took a toll on celibate gay Christians like me. It felt as if our personal call to faithfulness and sacrifice to God were insignificant, ignorant, or not based on serious convictions.
Other than in certain corners of the church, and in groups like Spiritual Friendship and Living Out, I had not seen an orthodox perspective that took seriously both the reality of same-sex desire and the biblical witness. People seemed to choose one or the other.
Perhaps pain had blinded us, not only to the Bible but to our own honest hearts. We needed a nuanced approach that acknowledged and accepted our fallen desires but did not affirm their practice, instead using them to invite us into deeper relationship with Christ and the church. We needed a revolution of leadership, beginning with our hearts.
I said yes to the archbishop's invitation, which one ought to do in such situations.
As I prepared to address the synod, I thought about how Alan Manning Chambers had closed Exodus International, which transitioned from an ex-gay therapy ministry in the eighties to a parachurch ministry to provide pastoral support for same-sex-attracted Christians. Most of those involved in Exodus in its last days repudiated the pseudo-Freudian therapies it once promoted. Following an evolution in its understanding of homosexuality, the mainstream ex-gay movement took its last breath.
When Chambers closed the ministry, he said it was the responsibility of the church, not a parachurch ministry, to support same-sex-attracted or gay Christians. Although in many ways I was happy about Exodus's closure, I also saw there was little place in the church for people like me. We desperately needed voices to speak up and offer wisdom and guidance to churches seeking to reach out to same-sex-attracted individuals.
The synod was to meet in York. The date came, and I rode the train north. When I arrived, I felt a heavy responsibility to be prophetically clear as I shared my testimony. I was speaking as a representative of Living Out, a UK-based organization for same-sex-attracted Christians. Three other younger panelists and I who were speaking at Shared Conversations, a closed event at the synod, were each given seven minutes to share our experience of being LGBTQI Christians.
I was the only panel member who believed the traditional biblical position that same-sex acts are sinful. I was the only one who mentioned our society's obsession with marriage and its idolatry of romantic love. The others shared mainly about the depth of their legitimate hurt and pain, but I did not hear any positive moral vision, nor was there any grappling with God's Word or with two thousand years of church tradition.
"What truly matters," I said, after sharing my story of finding Jesus Christ, "is not our view as the church or as a society. What matters is what _Jesus Christ_ is saying to us. The lie we're telling ourselves is that compromising holiness will ensure church growth. That's false. Embracing and raising up those who are sexually faithful and obedient, as witnesses to our culture, _will_ attract the world. Without holiness, Jesus Christ can't be seen in us by the world; and without love, the world will resist the truth of this holiness."
After I spoke, I thought about how in the Victorian era the tendency was to understand the body and its desires as essentially bad, but in today's society all the body's desires are perceived as good and infallible without filter. In response, the church risks falling into one of two extremes. In the first, we push back against that ideology and denigrate the body. The entire physical creation is seen as terribly bad, and hence we must escape the body and its desires in order to find holiness. In the second, we follow the world's lead and render the body supreme. The physical creation and our desires are seen as unquestionably good, meaning there is no fall and no sin.
Both extremes are anti-Christian. We risk either demonizing or elevating complex desires, which cannot fit neatly into straightforward categories of "sinful" or "acceptable." By necessity, the issue of gay marriage requires a complex response.
Having been in many relationships myself, I don't see gay romantic relationships as a separate sphere cut off from the kingdom, as something God is not at all involved with. There may be aspects of gay relationships or unions that Christians should learn to accept and recognize, such as the bond of friendship and the self-sacrificial love I have seen in many of my friends' unions. Christianity has room for affirming so much of the good and beautiful there, while still keeping traditional views of sexual expression and love.
For those in gay relationships or marriages who bravely repent of sexual sin, the solution is anything but simple. It takes time, and many answers are going to be messy. Gay couples often have children and become a family unit. What is their call? Easy answers break down very quickly without the Spirit's leading and discernment.
What a gay person really needs—as does every one of us—is to embrace a new, God-given identity. We have been crucified with Christ, and it is no longer we who live but Christ who lives in us (Gal. 2:20). By definition, this new identity cannot live the old way. We need to repent and put away the old identity. In a gay person's case, the old identity is defined by same-sex desire. While celibacy and identifying as gay are in some sense compatible, staying in a sexually active relationship cannot be compatible with fully embracing a Christian identity. God's Word reveals that we are called to die to our sinful nature and to pursue holiness, by the power of the Spirit.
Every Christian, gay or straight, must offer their body as a living sacrifice to God, like Jesus did on the cross. This is, as Paul says, our spiritual act of worship (Rom. 12:1). That means that for both a gay person and a heterosexual person, living in a sex-obsessed culture, the crucifixion of our old nature and the embrace of our new one is the highest act of worship. This is where in denying ourselves, we receive a new self from God.
The question we must ask is not whether a gay relationship can be made holy. Rather the question is, do sexually active gay relationships reflect God's image, glory, will, and purpose? What matters is God's perspective, not our projection of what we want God to be like and to accept.
This discussion of sexual ethics is one for inside the church, and I do not wish to extend it into the state or political arena. The church is called to live differently than the world. Its primary authority in all matters of faith, practice, and discipleship is Jesus Christ and the Scriptures that testify of him. Love and the purpose for our desires are defined by God, and no longer by us.
## **SAME-SEX DEBATE IN THE CHURCH**
In Christianity, we generally see polarizing approaches to the question of same-sex marriage. Are gay relationships distinct from a marriage between a man and a woman? Some strongly say no; others vehemently say yes. There are others still who prefer not to say what they really think, to avoid consequences.
Activism has not helped, by hindering open discussion in both the church and society. This contributes to leaders who avoid making any comments, for fear of media abuse. The endless polarization makes celibate gay Christians feel like they have to pick a side, instead of focusing their attention on following Christ.
What does this debate look like, and what does each side's view of human nature have to do with it? Progressives claim that Christians who reject same-sex marriage are denying the equality, human rights, and innate dignity of LGBTQI people. They assume our internal desires are right because they are innate to our nature. Many progressives, although not all, label churches that hold to a traditional view of marriage as non-affirming, instantly discouraging onlookers by using a negative term.
Progressives adopt the claim of Western culture, which says, "Whatever I desire is what I ought to have." But this view overlooks the fact that Jesus Christ alone can give meaning to our fallen nature and provide clarity for our desires. We see this with Paul, who in his writings defines marriage and sexual vocation through Christ. God is the one who shows us who we were created to be and who we are to become in him.
Those with the traditional view, on the other hand, maintain that same-sex marriage and sex acts are not permissible. When charitably understood, the traditional or orthodox view has nothing to do with homophobia or denying the equality or rights of LGBTQI people; it is simply a different vision of human sexuality and its purpose in marriage. It comes from a richness of belief, not a poverty of perspective. It's just not as simple as affirming or non-affirming.
I often find there is a progressive bias against celibate gay Christians like me. Some say we can't call ourselves gay unless we affirm same-sex expression. Ironically, this is similar to how some churches have treated and excluded gay couples. There is no real excuse for it, although I believe the progressive view is often driven by a fear of condemnation and an avoidance of real discipleship. Pain can block any of us from understanding obedience by grace and comprehending how a call to celibacy can be joyful, even life-giving. I'm not a traitor to the gay community. I'm just a celibate gay Christian. Is there room for me? Is there a stripe on the flag with my color on it?
What would it mean for both sides to come to a deeper biblical understanding? For those on the traditional end, it might mean being willing to live and love radically for Jesus. This would mean giving up false and empty religion that resists the real Jesus Christ; it would also mean rejecting the idols of wealth and family, being willing to see and respond to the needs of others, and giving up convenience and comfort for the sake of following Jesus.
For progressives, it could mean giving up the idols of sexual liberty, rejecting a victimhood or entitlement mentality, no longer shutting down those who disagree, and repenting of the pride that says, "I don't need the living God; I'll just appeal to my inner self."
Ultimately, both sides of this debate need to look to the resurrection, when one day there will be no same-sex _or_ opposite-sex desire entirely analogous to what we now experience. In Matthew 22:29–30, Jesus said this to the Pharisees and Sadducees who asked him about divorce and marriage: "You are in error because you do not know the Scriptures or the power of God. At the resurrection people will neither marry nor be given in marriage; they will be like the angels in heaven." Like those he was speaking to, we are obsessed with marriage and romance. But these things are only a reflection of greater eternal realities! We are going to be transformed into so much more than sexual beings. Our very nature will be resurrected.
In the end, there will be no "right side" of this issue to be on. There will be only one side, the kingdom of Jesus Christ, and the incredibly rich and diverse people who fill it. It will be free from arguing, division, and the idolatry of self, and filled with resurrected people whose very natures are like Christ's.
I long for that day, pray for that day. I'm working for that day. But I wonder, can I start living it right now? Do I really have to wait?
# [ ** CHAPTER 22
BELOVED FRIENDSHIP ** ](contents.xhtml#conn_30)
> One of them, the disciple whom Jesus loved, was reclining next to him.
**_—John 13:23_**
> But love is lost; the way of friendship is gone, though David had his Jonathan, Christ his John.
**_—George Herbert_**
> Chastity does not mean abstention from sexual wrong; it means something flaming, like Joan of Arc.
**_—G. K. Chesterton_**
**O** n an early summer's day, I took a walk with my friend Mark. We went through a park, the setting where C. S. Lewis, W. H. Auden, and other literary figures had sat to write. It was our favorite spot to relax during the stressful term.
Our friendship had begun months earlier, when many others at Oxford were struggling to understand who I was and what my position on sexuality represented. Mark had admired my faith and decided he was going to make a concerted effort to get to know me.
He was from a small American town and had been a college football player. You couldn't find two people from such different backgrounds, yet we became great friends. Our lives were being radically transformed, and I loved seeing Christ at work in him.
We often attributed our easy closeness to the fact that he had a twin brother, so sharing deeper affection with other men came naturally to him. What had started as his choice to get to know me grew into the deepest Christ-centered male friendship I'd ever known.
We sat on the lawn near River Cherwell, chatting about our futures, then started laughing as we impersonated the idiosyncrasies of our eccentric professors. The whole park was filled with birdcalls, everything at its highest point of life. Dandelion spurs floated on the air, and the underleaves of the trees were the lush, intense green that only the heart of England seems to have perfected. Summer in Oxford was _special_.
As we sat in the grass, Mark reclined his head against me. I didn't have a modern category for this kind of closeness and almost flinched. Thoughts raced through my mind. _Isn't this gay?_ I wasn't used to platonic male affection. One part of me, the optimistic part, loved it and enjoyed the freedom of friendship I had with Mark. Christ's presence seemed evident in the bond we shared. But another part of me, the realist, was worried.
I was unsure that this was even possible, considering my attractions to men. I truly sensed no lust, no possessiveness, either in me or in Mark. But somehow this demonstration didn't fit neatly into the category of brotherly love either. All the labels I'd been taught couldn't help me make sense of it.
I thought of the apostle John, who had reclined against Jesus at the table. There was room in that culture, in that relationship. Had I found a friendship like that, in which such affection could be expressed without being sexualized? Perhaps this was how God had intended friendships all along. If so, was it a taste of the kind of friendship we will have in the heavenly future? If celibacy was indeed an invitation into this kind of relationship, it was surely good news for me.
While I didn't find Mark attractive (yet), he was male, and that spelled fear for me. I was afraid of losing this level of intimacy or having it become something else. If he married, friendships would naturally take a back seat for him. As a straight man, he had the option of finding a spouse. I did not.
Something changed the moment we touched like that. Things grew awkward, and our conversation on the lawn faded away. As we walked home, we didn't speak. Perhaps Mark too was unsure what to make of this level of friendship. Something undefined had arisen between us.
In the following weeks, he pulled back. We stopped walking or studying together. He started spending time with other friends.
## **WRESTLING WITH GOD**
A few days later, as I sat at my favorite café, typing up a theology essay, I realized I was angry with God. I had thought I was free from that old voice of accusation, so different from the voice of his Spirit, that said, _You'll never be loved or accepted; you're nothing but a sexual and relational failure._ But here it was again.
I thought back to all those times I'd been let down, whether in friendships or romantic relationships. I realized that what I was really searching for was a safe, deep, and mutually respectful friendship. I needed a human to help embody God's love for me. It wasn't Mark's lying back against me that was significant; it was the _trust_ that he, as a straight man, had shown me by doing so. He had communicated safety, acceptance.
I had finally experienced a deep bond with another man that wasn't, as far as I could tell, about sex or lust. _God, why would you let me experience such love for a friend and then take it away?_
I took a break from typing and sat thinking about how the love of Christian disciples should break any earthly categories we have for love. This love comes from another source, from above. It is the love that Jesus came to teach and model, a love that gives up its life for a friend.
The problem was that while I was—or at least thought I was—entirely comfortable with God because he is perfect, faithful, and never fails me, even through suffering, the love of other human beings terrified me. People, including me, are fickle, flaky, selfish. I didn't want to love my neighbors because I didn't trust their capacity to love me back. This reality stunned me.
_Your life and ministry are worthless without these kingdom friendships,_ I felt God whisper to me. _I am not going to take away your desire for relationship with others._
Still, I said to God, _I'm so angry that you won't take this desire for deep friendship with Mark away._
From my studies, especially reading _Washed and Waiting,_ it seemed that the Christian tradition had lost vision for this kind of relationship. We'd lost our categories for beloved communion outside of a sexual relationship. Was a love like the love David and Jonathan shared, a bond that was greater than romantic love, even possible? It seemed so removed from the broken masculinity I had seen.
I thought about how Jonathan's father, King Saul, hated his spiritual friendship with David and tried to kill Jonathan because of it (1 Sam. 20:33). In some sense, Jonathan was a type of Jesus, willing to give up his life for his friend. This biblical love seemed to have been entirely forgotten in our sex-obsessed society. Even the church rarely talked about it.
The story of Jesus and John had also always piqued my interest, and I was intrigued that according to tradition, John called himself the Beloved Disciple in his gospel. What a way to describe yourself! And yet it dawned on me that John took that title because he really understood how much Jesus loved him and how unique their friendship was. Calling himself the Beloved Disciple had nothing to do with pride but everything to do with the kind of relationship John experienced with Jesus.
John was at the cross with Jesus. He was the only disciple who remained faithful and stayed with Jesus as he suffered. Their bond pointed to a future reality—a love that every Christian would know with God and, one day, with every other Christian in eternity.
Imagine a world where all people shared this self-sacrificial love with God and each other! God's kingdom was infiltrating this present world, and it wanted to invade through the simple love of friends.
I sensed that God was teaching me one of the secrets of his kingdom: _David, you cannot bring the kingdom of heaven to earth until you've tasted heaven._ I was reminded to truly thank God for my celibacy. I saw that celibacy was not just about enduring a lack of sex but about being a sign of that heavenly future.
Yes, right now my surrendered same-sex desires were painful. But through that pain, God was revealing his glory. Without it, I could never understand my deeper need for intimacy through friendships that pointed to Christ.
## **OVERCOMING FEAR AND REJECTION**
The struggle in my heart over what had happened with Mark still raged. It was so far short of that vision of being a sign of heaven. One day, after reading in my quiet time about Jesus and the Beloved Disciple, I decided to go find Mark. I wanted to tell him about what I had been learning and to try to repair the unspoken breach in our friendship.
"David, sorry, but I'm in the middle of my evening," he said as he came out of his building and met me. "Is everything okay?" I could tell by his tone he was slightly annoyed.
My words came out in a rush. "Mark, I know we haven't been close since that day in the park. I've been thinking about it, and I think God has revealed something really important to me. I really think he's calling us into a beloved friendship. You know, like Jesus and John, or David and Jonathan. All this work at Oxford—everything we're learning about theology and ministry—all of it's worthless without these kinds of friendships."
He studied me. "What do you mean?"
I swallowed. "Well, I've been thinking about the relationship Jesus and John had, and I really want to know that kind of friendship with someone. I think that's what God has been inviting us into."
"David, let me cut this short. I don't really do that kind of intimacy with other men."
His words were like a bullet to my chest.
"Okay. I see. Well, I'd better leave you to your evening, then."
I turned and left in tears. All the old rejection flooded me, only worse because of the hope I had that maybe, _maybe,_ there was real human acceptance for me.
That night, I tossed and turned, sleepless into the morning hours. As I listened to a nightingale sing outside my window, I wondered if Mark may have been afraid I was attracted to him and was trying to pass off a romantic attraction with a false request for friendship. If so, perhaps his fears as a straight male were more profound than his affections for me as a friend. For many weeks we didn't see each other, and it seemed our friendship was all but lost.
Months later I was surprised to discover I had developed feelings for Mark that were no longer platonic, even though I was not particularly attracted to him. Another battle in my war of loves was brewing. _What's going on?_ I wondered. _Was this whole thing really all about lust all along?_
I look back now and wonder if I really know what was going on in my heart. But the more I consider the situation, the more deeply I feel that I was sincere—there was a call to deep friendship here, separate from any romantic involvement.
As I consider it now, I think I was trying to alleviate my sense of rejection by using sexual feelings. Lust was my attempt to define and control intimacy on my own terms and to put it back in familiar territory. It had very little to do with Mark himself.
Like so many in our day, I ran to the counterfeit god of sexuality for meaning, instead of seeking God for love, identity, intimacy, and satisfaction. As C. S. Lewis says, "It would seem that our Lord finds our desires not too strong, but too weak. . . . We are far too easily pleased." I had to learn to find acceptance in God.
Henri Nouwen observed something similar in his own life: "I kept running around it in large or small circles, always looking for someone or something able to convince me of my Belovedness. Self-rejection is the greatest enemy of the spiritual life because it contradicts the sacred voice that calls us the 'Beloved.' Being the Beloved expresses the core truth of our existence."
I resonated with his words, because I too was repeating this cycle, and I longed to break free. But hope glimmered on the horizon. God was going to show me that I had been made for a higher love than physical intimacy, and that in order to try to experience it, I had to give up my control mechanism of selfish sexual desire.
One Sunday, the pastor at our church invited us to the trial run of a course on inner healing. He believed that false images of God were at the root of many of our emotional and psychological problems, and he had paired theology and psychology to address them. He explained to us how our perception of who God is needs to be corrected by Jesus, the image of the invisible God. Only then can we freely experience the Father's true love and intimacy through the Holy Spirit.
To my surprise, Mark was also taking the class. I knew I had to confess my attractions to him to recover our friendship. And yet I so wanted him to know that my original offer of covenant friendship never came from these attractions. Would he trust me?
As we took the seven-week course together, the pastor paired us up. Two broken men from very different backgrounds, one gay and one straight, were learning under Rabbi Jesus to really love each other by laying down their lives and identities for a friend. We both admitted our faults to each other. I told him about the reality of my attractions.
"David, I'm relieved you just owned up to your struggle," Mark told me earnestly. "I needed to hear that you were aware of how our friendship could have been compromised. I was worried you were either unaware of the possibility or trying to hide it. Now that I know what your real intentions are, I'm sorry I pushed you away."
After we shared, we each went off to a prayer counselor who had been assigned to us. In prayer, I felt God say to me, _David, I need you to be like a newborn child in my arms—no defenses and completely exposed before me. Let go of your control and let me_ really _hold you._
I became aware of another wall between myself and God that I had not known existed. Some deep part of me still believed I wasn't loved by God because of my struggle with sexuality. The orphan-hearted part of me both longed for and pulled away from the love of its Father.
Suddenly it felt like the Holy Spirit rushed over me. As Mark and I prayed with our separate prayer counselors at opposite corners of the room, I could feel the Spirit knocking on the door of my heart. _Let me in. Stop resisting._ Anger because of my perceived abandonment and rejection by God came pouring out of me. I realized that only the Father's adoptive love could free me from my sense of rejection.
There, in that eternal moment, I surrendered afresh, and God the Father held me like a baby in his arms. I realized again how tender and loving God the Father was! He was so different from the false perception I had once had of him as an angry old man. He was close. He was kind. He was good and tenderhearted.
My false image of God was broken, and with it went the false image of myself. I knew the Father's love in substance, not just theory. I was my Abba Father's, and he was mine.
Tears soaked my sweater and scarf. As we came out of prayer, I had a wad of used tissues in my hands. The man praying for me hadn't uttered a word but told me he heard the conversation I'd had with God. For a moment, he blinked in surprise; then we laughed together as joy from the deep healing I had just experienced hit me.
Later that night, walking in the low glow of Oxford's streetlamps, Mark and I made our way back to college knowing we had regained our friendship.
Weeks later at a conference in Oxford, I organized a prayer meeting. A professor who was a woman of prayer joined me, Mark, and many others as we interceded for one another. At the end of the meeting, she looked at Mark and said, "I have a word for you from the Lord. He is inviting you into a friendship with David that is like King David and Jonathan, and Jesus and John."
Both Mark and I were amazed that God spoke so directly through her, and I was relieved by his confirmation of what I had heard from him earlier. After this, in the security of God, Mark and I confidently committed to a covenant friendship that continues to bless us immensely today. At last, I was tasting something, in part, of what I had so long desired.
# [ ** CHAPTER 23
LIVING OUT NOW ** ](contents.xhtml#conn_31)
> Carry each other's burdens, and in this way you will fulfill the law of Christ.
**_—Galatians 6:2_**
**L** iving as a celibate gay/SSA Christian has been a huge challenge. I have experienced disgruntlement, prejudice, and social avoidance on both sides of our polarized culture and church. Many have accepted me, of course, but I always feel that, while I have never had a pink triangle pinned to my shirt like Brazda, the reality of my situation—choosing in obedience to Christ to be celibate—is something for which, for better or worse, I have often been judged in and outside the church.
It often seems, from my vantage point, that the gay rights movement isn't always interested in the rights of all gay people but rather is interested in the rights of the majority who believe in same-sex marriage. If there were real diversity and concern for everyone within the gay community, there would be acceptance of those like me and the churches that agree with my choice to embrace celibacy.
When celibate gay Christians choose to share publicly in the church, we are bombarded from all sides. We are asked to justify and explain ourselves. The constant questioning and pressure is exhausting.
Most progressives reject celibacy as a good or default choice for those who are gay or have same-sex desire. They do not see it as a necessary step in discipleship. To them, being gay requires sexual expression or romantic relationships, and our inner nature is a better guide to how we should live than the revelation of Christ in Scripture.
Some conservatives, or traditionalists, often refuse to love and move out toward the gay community, preaching that repentance means requiring gay people to erase their history and identity. Many on the conservative side of the church do not like that I appreciate much of the human rights work done by the gay rights movement. The reality is, I wouldn't have the freedom to write this book without the hard-fought progress achieved by that movement.
Another common criticism I've received is that I've made homosexuality my ultimate identity by calling myself a celibate gay (or SSA) Christian. This is deeply frustrating. It ignores the reality that I have died to my same-sex desires by submitting them to the lordship of Christ and choosing celibacy. My sexual orientation is a profound part of my story, and it is the very weakness that gives God unique glory because I live my life by faith in his Son. Many Christians don't understand that the terms same-sex attraction and homosexuality have questionable backgrounds for most gay people because they are linked to harmful therapies that attempted to cure homosexuals. There is no perfect term.
Both sides make our sexual lives the most important reality rather than focusing on eternal realities and how those impact our walk with Christ. But I cannot wait for progressive and conservative Christians to move on from this sinful divide. I have to live my life in Christ today, regardless of what the cultures around me choose or how we obsess about semantics.
Christians like me need to be held to the same standards as any other disciple and yet listened to and cared for in light of the particular challenges of being same-sex attracted. We need to die to ourselves just like everyone else and have our now-but-not-yet obedience affirmed by our church family. No Christian should carry a cross alone, and if someone is, the church is not fulfilling the law of Christ, as Paul talks about in Galatians 6:2.
Anglican theologian Sarah Coakley says that because the church is like a lightning rod for culture, the broader issues discussed in the culture concentrate in it. The church in the West has been involved in a long and complex conversation about sexuality, which has not been very public, open, or positive for many.
This is nothing new. When the apostle Paul wrote to the various churches under his care, he saw how the Greek and Roman culture in their cities clashed with the culture of God's kingdom. The resulting issues distracted Christians from living under the lordship of Jesus. Paul struggled to establish a unified, Christ-centered, cross-based discipleship for those new Gentile followers.
Paul lovingly rebuked these communities and tried to integrate everything into Jesus Christ, his cross, and his resurrection. The Spirit inspired Paul's writings, and we still cherish them as our applicable, authoratitve guide. We see in these letters Paul's difficult wrestling with the various cultural challenges to the gospel. If it was hard for him, it is bound to be hard for us. Just like in Paul's time, the Christian challenge for us today is to renew our lives and experiences through Jesus Christ and his Word and the Spirit.
The Western church, however, has often failed to resist idolatry. In the last century, it has worshiped family above God and his kingdom, putting pressure especially on sexuality. In the postwar 1950s, the church made the nuclear family the idolatrous center of middle-class life. The 1960s reacted to this idolatry by throwing off the repression of desire and pursuing "free" sexuality. It brought its own set of idolatries.
In his book _The History of Sexuality,_ French philosopher Michel Foucault attempted to uncover Western culture's trend of categorizing "deviant" forms of sexual desire, which were outside the societal normal of heterosexual marriage. Homosexuals were considered to be a separate class of person, akin to the "sodomite" in the medieval world. This reinvention of homosexual people as a perverse or deviant species meant that LGBTQI people lived in abject secrecy and fear for many years. In the 1950s and 1960s, medical speech described homosexuality as a dangerous perversity that threatened the utopic stability of the nuclear family.
Sadly, the church was influenced by these worldly ideas, which disciplined and punished those who reported no change in their sexual desires despite their efforts to eradicate them. The church and science colluded to try to cure gay people through all sorts of therapies (lobotomies and electroshock treatments are just a few). The terms same-sex attraction and homosexuality came out of this crucible. This was not of the Holy Spirit and the kingdom of God but a tragic confusion and abuse of the reality of gay people.
We live in a time in the church when the facade has cracked, and we know these idolatrous ideas no longer work—indeed, never did. But my concern is that the church is capitulating to new pressures from today's culture. We are replacing old idolatries with new ones by developing prideful factions related to homosexuality, instead of repenting and seeking God in the unity of the Spirit and under the clear teaching of God's Word.
I pray each side will be willing to change or repent, to seek God's will alone, to preach the gospel to the world, and to make Jesus the center. Full stop.
## **SPEAKING OF SIDES**
The "sides" terminology was developed by many in the LGBTQI Christian community and by the Gay Christian Network during the 2000s. Its purpose was to help people easily refer to their position on gay marriage and sexual expression. In the sides paradigm, there are four major camps among same-sex-attracted or LGBTQI Christians. (I have included these terms—I realize they are not perfect, but they can help us communicate differences quickly.)
* _Side A:_ Disagrees with Christian tradition; affirms a gay identity and sees sexual expression in a gay marriage as faithful to a Christian ethic
* _Side B:_ Affirms the Christian tradition that sees sexual expression in gay marriage as wrong, but incorporates gay identity under the lordship of Christ through celibacy and other forms of chastity
* _Side X:_ Claims either to no longer experience same-sex attraction or to be ex-gay and to have been freed in the process of sanctification
* _Side Y:_ Agrees with side B but does not identify with LGBTQI; prefers not to identify as gay but is more likely to use the term same-sex attracted or is reluctant to see sexual orientation as a category of identity or personhood
Side A groups affirm same-sex sexual expression in committed partnerships or marriages, while rejecting the sexually unrestrained tendencies of mainstream gay culture.
Those who identify as side B hold my perspective. Same-sex desire is seen as a complex entanglement of our very good humanity that is made for the intimate company of others and our fallen desires resulting from broken worship and the power of sin. These terms have real limitations, and for this reason I often use side B, same-sex attracted, _and_ gay to talk about how I identify.
Side X refers to those who claim to no longer have same-sex attraction. Some claim this was through a form of ex-gay or reparative therapy, while others have arrived at this position through their own self-understanding and experience.
Side Y refers to those who repudiate any association with or identification as gay and describe themselves solely as same-sex attracted, distancing themselves from the LGBTQI movement.
Sadly, people from all of these sides most of the time do very little together. While we have important differences, we choose to fight each other instead of humbly hearing one another. It took me three years before I was willing to submit to God's clear teaching in Scripture. Instead, we have created our own churches and denominations, rejecting each other, our own lives, and our social media spheres. However, the biblical model when there is controversy or even disobedience to the gospel is to meet together, humbly removing both bitterness toward others and our idols, loving our enemies. In so doing, we are able to come to one mind, reaching a clear resolution through submitting to the authority of God's Word by the Holy Spirit. We see this in the Jerusalem Council in Acts 15, when the leaders of the church met to rule on God's adoption of the Gentiles and the place of the law in their newfound Christian identity. The real reformation cannot be a sidestepping of God's revealed word on sexuality but a gracious and passionate embrace of it above and beyond our identites, histories, or politics.
## **SIDE A AND PROGRESSIVE IDOLATRIES**
From my perspective, the side A movement of LGBTQI Christians is founded on revisionist readings of the Bible that often are based on queer theology and queer theory. The starting point is human experience and a different place than the revelation of Jesus Christ and his God-breathed scriptures upon which Christian theology is based. They start from the experiences of LGBTQI people on the margins of theological or social scientific understanding and resist the ignorance that has oppressed them.
So what drives side A Christians? They often have a sincere and profound wish to reconcile God's call to chastity with the real experience of same-sex desire. To them, requiring all gay people to be celibate is absurd. (The difficulty here is that queer theology others gay or same-sex attracted celibacy by its own logic, since those who pursue celibacy are now the ones on the margins of the LGBTQI community!) Side A often (although not always) depicts Christians on the traditional side like me as being able to choose only "bad" celibacy or mixed-orientation marriages (a marriage between two people of the opposite sex, in which one or both spouses are otherwise attracted to the same sex).
According to the progressives, marriage must be extended to gay couples in the church so there can be social and theological affirmation of their partnerships and so they can experience God's sacramental blessing. I truly understand why, at all costs, progressive believers want their partnerships to be celebrated as marriages in the church. I say this because I was a side A Christian for three years, and I deeply empathize with their views.
As I've said already, side A worships the same idol of marriage that many on the traditional end do. They view sex and marriage as the place where true intimacy is found and see a lack of it as a deprivation of our humanity. That is something, they claim, Jesus would not ask of us.
The reality is, Jesus' call of discipleship is a claim on _all_ of our lives. It is a lie that if gay people can't have marriage in the church, we will never be loved and accepted and affirmed as people but will be left as half-life humans, denied the chance to fully flourish that marital sexual expression ultimately provides.
## **SIDE B AND TRADITIONAL IDOLATRIES**
Unfortunately, the side B world has its own (similar) idolatries. When people are wounded or even abusively treated by church leadership or the cultural war, we can be tempted to run to our own idolatries for comfort and identity. We often cling to our personal ideas instead of simply focusing on what it means to be a disciple of Christ.
The risk is that more progressive side B Christians judge more traditional ones, and vice versa. Those in the side B world risk elevating their own individual theologies of sexuality, instead of valuing difference and fidelity to God.
The side B world can sometimes become so focused on its own predicaments that it forgets the wider kingdom mission of Jesus Christ. Chastity can become the point or goal of our lives, a constant gravitational obsession, instead of worshiping and enjoying Christ and living our lives of discipleship in deference to his lordship in the broader community of his church.
There is also a tendency sometimes, although it has been frequently disuaded, to elevate friendship and intimacy to an unhealthy level. While I absolutely affirm the church's vital need for non-nuclear, spiritual families and a strong culture of friendship, and while we are taught by Jesus Christ to have beloved friendship with others, no friendship can entirely provide for our needs. God provides primarily through his Spirit and only secondarily through others. As Augustine teaches, we are to enjoy God through all things and people. That doesn't mean codependency; rather, it means dependency on God.
## **THE SOLUTION: IN CHRIST**
When preaching at a large, multisite church in the United States, I met a young gentleman called David. He told me his story and about his parents, a loving and accepting evangelical couple whom he'd come out to at the age of fifteen.
After the service we sat and talked. He looked at me with a furrowed brow and said, "It's just not fair that as Christians, we have to give up any prospect of a romantic relationship with the person we're attracted to! Everyone else has the option of marriage. I don't. I want to have a family. I want a partner and children. Why can everyone else have that and I can't?"
I deeply identified with David's questions. In him, I saw reflections of my younger self. But I also saw that he, along with countless others in the church, had fallen prey to our culture's idolatry of romantic love. To him, the litmus test of human flourishing was sexual expression in marriage.
"I _completely_ understand the cry of your heart, David," I told him. "I felt the same way for many years and wrestled through this with God."
I went on to explain that I am actually grateful for being gay or SSA, because it means I can no longer worship the gods of our culture. I am barred from their temples.
"I was told for so long that my sexual desires were what defined my humanity. But as a Christian, I learned that giving ourselves to God completely and trusting him with our same-sex desires is precious in his eyes. It helps us see that he is our greatest treasure and what we are really longing for. The goal of our lives isn't to fulfill our culture's expectations and worship our own desires but to follow Jesus and worship God. I have given up a portion of myself. But in return, I found my whole humanity."
"I'd never thought about it like that," David said slowly. "You're saying being same-sex attracted is sort of like an opportunity to really worship God?"
"Yes, that's right," I replied. "In reality, we have only fifty years or so to worship God this way. It's hard but so worth it. There's a reason Jesus said to Thomas, 'Blessed are those who believe and do not see.' But someday, in the new creation, we will see God in front of us. We won't have to trust him with desires like this, because all the effects of sin will have left us. We'll worship God with every fiber of our being because he'll fill every part of us."
The very legitimate fear of giving our everything to Christ is the greatest enemy to discipleship. We fail to recognize that every part of us, not just our sexuality, is baptized into the love of God. Incredibly, he then says, "Have yourself back again, in the way that will truly fulfill you."
Would you be willing to give up brother, mother, sister, or gay partner for the sake of God's kingdom? As Christians, we must be willing to give up anything to follow God. Jesus says to us, as he said to the church in Sardis, "So, because you are lukewarm—neither hot nor cold—I am about to spit you out of my mouth" (Rev. 3:16). Not one thing can be between us and him, or there will always be disunity. It follows, then, that in the church, unity cannot be achieved between those disciples who say, "Jesus, I submit my whole life to you" and those who don't. Ours is the common call, not some exotic one.
The reformation we all need is "in Christ," allowing every part of us—every desire, hope, and longing—to enter into his reality. This is an act of precious worship, like the sinful woman's act of pouring perfume on Christ's feet (Luke 7:36–50). I pray and hope all Christians, especially the "young Davids," would have this revealed to them.
# [ ** PART 5
REFLECTIONS ON HOMOSEXUALITY AND CHRISTIAN FAITHFULNESS ** ](contents.xhtml#conn_32)
# [ ** CHAPTER 24
CELIBATE, GAY, CHRISTIAN: A THIRD WAY ** ](contents.xhtml#conn_33)
> I have been crucified with Christ. It is no longer I who live, but Christ who lives in me. And the life I now live in the flesh I live by faith in the Son of God, who loved me and gave himself for me.
**_—Galatians 2:20 ESV_**
**T** he church needs a new apologetic, a way of thought and life that neither demonizes nor elevates the same-sex desires facing many faithful Christians. For this to happen, our minority living in the tension of grace and truth needs to speak up. Our experiences and stories are valuable and ought to be stewarded for our brothers and sisters to understand us.
This new apologetic must further permit us to form a deeper Christian response to homosexuality, one that honors both Scripture, the wisdom of tradition, _and_ people's real experience. At the same time, such a response needs to recognize that we are waiting, that one day our final redemption will come and a great horizon of heavenly intimacy will be opened to us in Christ and his church, but that day has not yet fully dawned.
Let me sketch seven reasons why I hold to this position.
The first is _scriptural authority_. While Scripture is clear that homosexual acts are sinful, it also maintains that Christians live in tension between the fallen nature, or "flesh," that is at war with God, and the new self, which desires to love and obey God. When we become born again, our old nature is crucified with Christ, but it is also still present, as we feel painfully in moments of temptation or testing. Presently, our victories in Christ are manifested in weakness, not in the strength of resurrected bodies.
The apostle John holds these two realities in tension. "If we claim to be without sin, we deceive ourselves and the truth is not in us," he says (1 John 1:8). Later he speaks of God's sanctifying power: "No one born of God makes a practice of sinning, for God's seed abides in him; and he cannot keep on sinning, because he has been born of God" (1 John 3:9 ESV).
Commenting on 1 Corinthians 6:9–11, J. I. Packer writes with remarkable clarity about Paul's gospel: "With some of the Corinthian Christians, Paul was celebrating the moral empowering of the Holy Spirit in heterosexual terms; with others of the Corinthians, today's homosexuals are called to prove, live out, and celebrate the moral empowering of the Holy Spirit in homosexual terms."
The Holy Spirit's moral empowerment in the midst of our present struggles with sin is what leads many of us to call ourselves celibate gay Christians. To say, "I've been healed from all temptations of the flesh" is to make the same error the Corinthians did when they thought they were already without a fallen nature, and yet behind closed doors were still indulging in sinful behaviors. The scholar Anthony Thiselton coins it "over-realized eschatology," meaning an expectation of heavenly perfection while still in this world. Sorry. It's still hard.
On the flip side, to deny that God will not presently give us victory over sinful desires is to commit the error of "under-realized eschatology," which causes us to live in slavery to sin without hope of any real freedom from it in this life.
But here's the truth: Christians, _all_ Christians, are being made holy. We aren't yet perfect. We still experience the attractions of our old self. Yet because of Christ, we can live in victory. God does not wave a magic wand to remove our desires—at least, that is not the normative experience. It is equally wrong to endorse or to deny the presence of fallen desires, and that is why I call myself a gay or same-sex-attracted _celibate_ Christian.
My second reason is _theological accuracy_. For the gay or same-sex-attracted person, a biblical understanding of what it means to be redeemed is complex. To be attracted to the same sex is not a voluntary behavior, as many have incorrectly argued. Instead it is a result of the creation-wide effects of sin. Wesley Hill, a New Testament professor and celibate gay Christian, states, "Many suggest that a parallel case would be if someone were to label himself an 'adulterous Christian' or a 'stealing Christian.' Those terms are self-evidently problematic in that they make sinful behaviors part of an identity description for believers, and therefore gay Christians should find their chosen label equally problematic. My response to this is that those are not, in fact, parallel cases."
The word gay does not necessarily refer to sexual behavior; it can just as easily refer to one's sexual preference or orientation and say nothing, one way or the other, about how one is choosing to _express_ that orientation. So, whereas "stealing Christian" describes a believer who actively steals as an acted behavior, "gay Christian" may simply refer to one's orientation and nothing more.
This is why I rarely, if ever, use the phrase gay Christian without adding the adjective celibate, meaning committed to a life of chasteness in Christ. To call myself a celibate gay Christian specifies both my sexual orientation _and_ the way I'm choosing to live it out.
We have all been impacted by the fall. The particular challenge for the majority of gay or same-sex-attracted Christians is untangling the sinful aspect of same-sex attraction from their God-given desire for intimacy. Some find that this need for human intimacy is met in celibate friendships; a smaller group report a special God-given attraction to a particular opposite-sex partner in a mixed-orientation marriage. But most side B Christians choose celibacy.
Very few same-sex-attracted or gay people report that when they become Christians, their desires simply disappear. Rather, as in my story, many find that God gives them a special empowering grace to be celibate. That is our experience.
Many of those pressured by Christian culture to say they have been healed live with secret sexual sin and shame as a result of their desires actually not going away, or even intensifying by being locked away out of sight. We must break the culture of silence in many churches and instead encourage a culture of repentant honesty before God and with each other. Anything else will allow spiritual darkness to deepen, grieving the Spirit of truth.
My third reason is to be _prophetic_. Those of us who are orthodox or traditional Christians and who are gay or SSA need to reclaim our space in the conversation over sexuality back from the secular culture. While we have shared experience of same-sex desires with those who are gay and seek to be in gay marriages, including dealing with them in a fallen world that is prejudiced and unloving, we are different, and this needs to be reflected in how we understand what it means to be gay or SSA in broader society. Also, people like me have benefited from the gay rights movement in many ways and would not be able to live the open life we do without many of these wins for human dignity, but we don't want that movement to spell the deprivation of our rights to live in churches that support our choices and obedience to Christ. We can identify with many of its wins for the human dignity of LGBTQI/SSA people, including employment rights, protections from hate crimes, and antidiscrimination laws, even if we may disagree on sexual ethics. We have the unique opportunity to break a culture of victimhood toward traditional Christians, as well as gay/SSA people.
The opposite of homosexuality is not heterosexuality. It is _holiness_. We need to stand for a different way to live in the gay community, and welcome others from that community into the church to receive Jesus' love, without denying so many of the goods won through the gay rights movement.
The fourth reason is related to _identity_. When Christians receive Christ, we repent of what is sinful. But we don't renounce our individual humanity, which is shaped both by God and by our experience in this fallen world and this fallen body. As a gay celibate Christian, I recognize that Christ is my ultimate identity; gay and celibate come second. My identity is first and foremost in Christ, but those other two descriptors tell the redemptive story of God's grace in my life.
When I chose to be celibate, I placed the word gay under the lordship of Christ; it is no longer a competitive identity to "in Christ" but a beautiful reminder of my submission to his lordship over my whole life, including my sexuality.
My fifth reason is _reconciliatory._ Like God, who became human in Christ and reached out across our human experience, we must learn to love others, made in the image of God, by identifying and entering into their experience. Part of that involves learning their language and regarding it with sacred importance so we can love our neighbors and our enemies.
Christians have built a prejudiced stereotype and generalization of the gay community. Promiscuity and sexual orientation must be separated in our thinking. I came to know Jesus when I was heavily involved in the gay rights movement, and I know firsthand that not everything in the gay community is licentious or wrong.
There is a distinction between the gay scene, which can often be commercialized and sexually libertine, and the gay community, which is composed of all people who experience same-sex desires. Christians need a more nuanced and sensitive understanding when they use the word gay.
The gay community is made up of people who are loved by God and need to be told about the love of Christ and the gospel. Are Christians willing to reach out to and enter our world to share and connect? This will always be a two-way discovery. Will Christians be like Jesus, who put the taboo of his day to one side and loved the Samaritan woman, arguably one of the most morally questionable people in his context and time?
Some of us have sinfully failed to reach out to, value, and love the gay community but are very happy to moralize and judge. This is far removed from the radical holiness and truth, on one side, and compassion and mercy, on the other, that Jesus showed to "outsiders." His example leads the way for us.
My sixth reason is _reformative_. Paul was a Jew. That identity he was born with was an integral part of his life and his relationship with Messiah Jesus. However, his view of Judaism and how he related to it changed. It was always part of his identity but was no longer his primary identity. He was now in Jesus, and that changed how he related to Judaism. (Still, his Jewish identity and history gave him the ability to speak about Christ to Jews scattered throughout the Roman world!)
My seventh and final reason is _invitational_. Mainstream secular culture feels alienated by terms like same-sex attracted and gay lifestyle. There is no monolithic gay lifestyle. The term same-sex attracted sounds medical, like a diagnosis—reminiscent of when same-sex desire was seen as a disease. Such terms can place hindrances in the way of those who need to hear the gospel message. When I entered the church and heard these terms, they kept me from feeling included and understood.
On the other hand, the term gay is positive and welcoming for those who are gay or SSA. Christians would do well to focus on removing boundaries—existential, intellectual, and spiritual—in order to know the good news for our own sexual brokenness, and then, further, to share the good news humbly from this place with others.
Identifying with others in the LGBTQI world can open doors to engage people who need to hear about Christ. It can also give us the chance to speak honestly against the horrible ways Christians have often treated the gay community. I pray this third-way apologetic will carry us out of the harmful culture war and into the new frontiers of reaching people for Christ.
# [ ** CHAPTER 25
SPEAKING TRUTH IN LOVE ** ](contents.xhtml#conn_34)
> Any theory divorced from living examples . . . is like an unbreathing statue.
**_—Gregory of Nyssa_**
> Speaking the truth in love, we will grow to become in every respect the mature body of him who is the head, that is, Christ.
**_—Ephesians 4:15_**
> "For this reason a man will leave his father and mother and be united to his wife, and the two will become one flesh." This is a profound mystery—but I am talking about Christ and the church.
**_—Ephesians 5:31–32_**
**I** was coming to the end of my first year of studies at Oxford. Over the last weeks of my ethics classes, I had been asking deeper questions about why God originally created sexual differences, and how sin and death had affected those differences.
I befriended many people at Oxford who were transgender, and one person who was intersex, and was deeply saddened by their stories of being treated horribly by Christians. They didn't fit into the gender-binary view held by most people, including those in the church. Rather than seeing these people and their broken bodies and desires through the lens of Jesus Christ, Christians tended to view them through broken understandings of sexuality and gender.
I had so many questions raised by these relationships. Was a broken heterosexual marriage not centered on Christ superior to a transgender couple seeking Christ for their new lives? Was a Christian view of masculinity that excluded people who didn't fit the stereotype really any better than a view that exalted gay sexual identity above Jesus' call to discipleship?
I did not know all the answers. I still don't. These are hard questions. But I knew that all of us in the church need a deeper desire to know God and hear from him on these issues. Our present realities of gender and fallen sexual desire need to be interpreted through humanity's future redemption in Jesus Christ.
Without knowing Jesus and dying to our old selves, we cannot experience being a new creation. We are slaves, stuck between unrestrained sexual expression and restrictive repression of our desires. Christians also still experience the effects of sin and the fall. But when we become new creations in Christ, God renews our desires and minds through Jesus' resurrection power. This new creation will be completed only when we are raised bodily from the dead. That means our current bodies, which are groaning for renewal, are not our ultimate reality! Our resurrection bodies will far surpass this fallen creation, and their desiring will be righteous.
I had always wavered on my theology of marriage, even as I came to my own personal conclusions. Was what I was personally called to normative? At Oxford, I had paced the stacks of those "beautiful old libraries" Leon had seen, searching for answers.
I pored over Scripture and the writings of Augustine, Karl Barth, Dietrich Bonhoeffer, Sarah Coakley, and many of the church Fathers. I came to understand the profound theological meaning of marriage in the church, and God's revealed purposes for human sexuality became clearer. While I still respected the right of all people to have their monogamous relationship protected by the state, I could no longer support same-sex unions in the church. Appeals to our human experience were not enough to convince me. God's vision for marriage was profound and beautiful. I could not dismiss it.
I knew God was calling me to lovingly _accept_ but not _affirm_ all relationships. My goal was to point toward a fundamental reality: the marriage of Christ and his bride, the church. My doctrine needed to be informed by Jesus' love for his bride, reflected in God's creation of us as male and female.
Some will say marriage is a mere metaphor. It is a metaphor, surely, but it's more than that too. It is, as Paul says, a profound mystery, something we will not understand fully until it is fulfilled in God's kingdom. But one day, it is promised, we will understand it perfectly. We will receive the reality it points us to.
As part of my training at Oxford, I was required to take part in missions at universities around the United Kingdom. When I arrived at one university to support a mission with the Christian Union, I saw posters for an interfaith discussion about gay marriage. Many of my Christian friends there strongly discouraged me from attending, but I decided to go and bring with me a bisexual friend who was also dedicated to giving her desires to Christ.
When we arrived, my heart was pounding. This was the first time in years I had engaged directly with gay activists, but I was excited to share with others my view of marriage. We entered the small brick building and sat in a circle with twenty-five people of different faiths and backgrounds.
A blond man, who described himself as a gay activist, opened the meeting. He reminded me so much of myself from several years before. "We have purposefully held this conversation to hear all of your perspectives on gay marriage, especially as it relates to your faith," he said, smiling. "This is a safe space to share."
Despite his warm welcome, the room was tense. It seemed many in the group were nervous. But as we went around the room, there were no dissenting viewpoints. Every person, whether they were from a Sikh, Muslim, Jewish, or some other background, said they had no problem with gay sexual expression and supported gay marriage.
The time came for me to speak. My heart was still pounding, but an inner peace was there too. I knew I had to be honest about my views, or this dialogue would have lacked the wider perspectives it was supposed to cultivate. It was a safe space, right? And I genuinely loved these people.
"Well, this may not be popular in this room," I said, "but as a gay/same-sex-attracted celibate Christian, I do not believe gay sexual expression is right for me."
The room went silent. Several people recoiled from my words, then looked at me as if I were an alien.
I proceeded to briefly tell my story, then grinned at them. "I even have a personal hashtag. It's #fabulousmadeglorious!"
Everyone in the room laughed. Their posture changed from defensive to open.
"I believe God made our bodies. They matter—matter so much that God became human in Jesus. The fact that God created human beings with two sexes reveals he values both the diversity and unity of human persons, not because he wants to condemn LGBTQI people!" I paused and looked around the circle. "For Christians, marriage between the male and female sexes takes on a deeper meaning only when we understand the relationship of Jesus, who's the Bridegroom, and the church, who's his bride.
"God has called me to trust that he knows best and he knows the eternal story he's writing. In the meantime, he's shown me I can give my same-sex desires to him and find a deeper satisfaction and love in knowing and worshiping him than I ever could through pursuing my desires."
As I said this, people seemed to understand what I was trying to communicate. The gay activist who opened the meeting broke the silence after I shared. "Well, I suppose sex does get a bit old after a while!"
"But worship doesn't!" I replied.
"I suppose not," he said, and the whole room laughed again.
I was grateful to this young activist for respecting my journey. I knew he understood the struggle I had been through. Even if he did not agree with my conclusions, he didn't dismiss me as not truly gay or not part of the community but respected that I wanted to live differently in Christ. His friendly words were one of the greatest kindnesses I had received from the LGBTQI community since my choice to surrender my same-sex desires to Jesus.
Before we finished, I felt compelled to share something more. "If I could leave everyone in this room with one message, it's that human marriage between one man and one woman is just a reflection of a more fundamental marriage. That's the one between Jesus and his church. There is no sexual or gender minority group, no religious group, that's not invited to his wedding."
God worked through it. When I finished, several people were crying. While most of the LGBTQI people there disagreed with my conclusion, they thanked me for sharing so honestly. Some people from other faiths admitted to me that they did not have the courage to share their deeper views, because they didn't want to be perceived as homophobic and unloving. I had managed to be honest without being judgmental. Little did they know the years of work and tears it had taken to get to that place in my own heart. I left that meeting eager for more. I had a real hope now that peaceful, honest exchanges could be possible. Several people who were at this meeting attended our Christian Union events days afterward. Eventually some even came to know Jesus Christ for themselves, each with a remarkable, beautiful story of their journey to faith.
Unless we learn how to accept others without affirming everything, we have lost the art of conversation, because we're suppressing our honest opinions. We can accept and affirm people without agreeing with and affirming _all_ of their desires or beliefs or accepting their actions.
Jesus was teaching me that I could offer both love and truth as I shared my story.
You see, love without truth is not love at all.
And truth without love?
Well, it's not truth.
# [ ** CHAPTER 26
SACRIFICE REGAINED: SALVATION AND HOLINESS ** ](contents.xhtml#conn_35)
> Because your love is better than life, my lips will glorify you.
**_—Psalm 63:3_**
> You are what you worship. And you worship what you love.
**_—James K. A. Smith_**
**T** he Sunday afternoon rain ran down the windowpane to the sill. My phone vibrated.
A text—from a French number.
Hey, David, it's Jerome!
Long time no see! I'm in Oxford.
Can I see you?
My heart skipped a beat. I wondered whether it was wise to text back. The last time I'd seen Jerome was two years ago when I'd broken things off in Strasbourg.
I set out for my friend's room down the hallway and asked her what she thought. I found her sketching a new painting. "Yeah—probably not wise," she said, after I filled her in on the situation.
I left my friend to her art and went back to my room to pray. Strangely, I felt that I should respond, even though I was nervous about what it would bring up in me. _Go, David. You're ready for this,_ I felt God whisper to me. _I will be with you._
Much had changed in two years. I loved my life, this new way of living in Jesus Christ. My existence was far richer than I'd expected. I decided I could meet Jerome without compromising my faith. I just needed to be careful. I remembered those eyes. _Really careful._ I texted him back, friendly but very careful to avoid any hint of flirtation (harder than it sounds when composing a text message). We picked a nearby café to meet.
When the time approached, I pushed open my building's heavy oak door and said a short prayer. "Thank you, Lord. Help me show Jerome who you are."
A spring storm had just passed. The fresh air whirled around me as I walked the streets. I was nervous but excited. I still had profound affections for Jerome and was struggling to push those aside. More than anything, I wanted this man to know Jesus Christ.
When I entered the coffee shop, the French band Air was playing over the speakers. Nostalgia hit me like the smell of a Strasbourg bakery. Jerome was in the corner. His face, with its wide cheekbones, dark ruddy stubble, and wide-framed glasses, hadn't changed a bit. We sat over hot drinks.
Time flew by. There was a lot to catch up on. As we chatted in French, he told me about his time studying political science in Canada. I asked if I could show him around Oxford, and he readily agreed. We walked out into the lovely afternoon.
As we passed the blooming flowers of the university parks, I decided to take him to one of my new favorite spots, Keble College Chapel. We entered the brick building and paused by William Holman Hunt's famous painting _The Light of the World,_ which hangs in a side crypt of the old chapel. The painting is an image of Jesus—his eyes enigmatic, distant almost—holding a lantern in a twilight garden, standing by a door with no handle. It is lush, cryptic, beautiful.
"The door has no handle because Hunt was making a point about how we need to make a decision about who Jesus is," I told Jerome. "He's always waiting on the other side of the door to welcome us into the new creation he started through the cross and in his resurrection. We all have the choice of whether we'll let Jesus come in and eat with us or not. Jesus never forces us to open our hearts. We have to let him in."
He nodded silently and looked around in awe. "I didn't know faith like this existed," he said.
As we wound our way back through the center of Oxford, I had one last stop in mind—Christ Church. I flashed my student card to see if the librarian would also allow us into the college's library. Usually only members of the college were permitted inside, but it was one of my absolute favorite libraries in Oxford. The exterior was bordered with thick Roman columns. The inside was white, with quintessentially Georgian features. Spiral staircases wound up to neat collections of books, split into sections. I took Jerome up one of the staircases to a ledge by the philosophy and theology collection. It was out of view, a place I often frequented.
Jerome looked up at the ceilings and open windows and took in the golden letters of the dusty book titles. "This is beautiful." Then my heart quickened, feeling that familiar energy of mutual attraction. Jerome leaned in slowly for a kiss.
I pulled back, though everything in me screamed not to. "David, are you sure you don't want this?" he said, taking my hand.
The thought of a life together passed through my mind, and my affections were stirred. I shook my head and gently let go of his hand. "No. I'm sure. I'm in love with Jesus Christ. My life is his and not my own," I said quietly.
He didn't try to argue but seemed resigned. "David, ever since I met you, you were different," he whispered in French. "I can't explain what it is about you. You're unique. You're not like the other guys I've met. But I don't understand why you keep denying yourself a relationship."
I shook my head again. "I feel deeply for you, Jerome. But I have to choose Jesus." I smiled at him. "I've given myself to God. _All_ of me. Jesus has made a whole new world, and I'm beginning to be part of it. He's going to recreate everything, our bodies included. All of this"—I paused to look around me—"will be transformed. I want you to be part of _that_ world, so we can enjoy God and each other forever. So no, I'm really not interested. But . . ." I smiled wryly. "I _did_ want to ask you if you'd like to attend church with me tonight."
Jerome nodded. "I know there's something real behind your choice," he said. There was both disappointment and respect in his voice. "Of anyone I've met, you stand out. Your life says that Jesus is real and that he has a love that's—how do I say it—higher. So yes. I will come."
As we walked into my church, Jerome stopped and stared. The whole room reverberated with the sound of diverse Oxford City people singing praise to God at the top of their voices. The sound poured out into the streets. Hundreds of students packed the seats. "If church was like this in France, I'd be there every Sunday!" Jerome whispered to me.
All my friends welcomed Jerome. A few people were perhaps wondering what I was doing with an attractive Frenchman, but I knew God was behind this meeting.
As we made our way to the bus stop to say goodbye, I could see that Jerome was visibly moved. "David, you're set apart _[consacré]_ for God, aren't you?" he said in French. Consecrated! That was it. Exactly.
I was in awe that God was giving me this opportunity to share with Jerome. "Yes, that's right! Every Christian is supposed to be set apart for God. We're called to a higher love. The Bible calls it our first love. I've experienced that love from Jesus, and it's turned my life upside down."
His face lit up with both wonder and bewilderment. "You mean, you're never going to have a gay partner or sex? You'd give that up for God?"
I nodded. "Yes. God's worth that sacrifice any day."
I paused and looked intently at Jerome. "Would you think about following Jesus too? I would give anything to have you in eternity with me! We can share the love of Jesus now and for eternity. I love who you are as a person, Jerome. I wouldn't want a tiny lifetime of sexuality to get in the way of an eternity of friendship."
Jerome's bus pulled up. Our time was coming to a close. He hugged me. We both had tears in our eyes.
"David, if there's anyone I've ever met in my life who has made me seriously think about Christianity, it's you. When we were together in Strasbourg—that time in bed when you were touched by God—I've never been able to shake it. The love of God you have is special. It's worth protecting. I respect you for that. I want you to know that I don't see you as some repressed or self-hating celibate, like some people might say."
"Thank you, Jerome," I told him. "You can have the same love. Open up and you'll find Jesus there. He's knocking! Please don't worry about the sexuality thing. That will work itself out. Just let him in."
We hugged one last time. His face was full of joy as he gave me two final _bisous_ on the cheek. Turning to climb the bus stairs, he said, "Thank you, David."
As the bus pulled away, I realized that Jerome had seen Jesus in me. I did not need to hide myself away from the world or complex situations. Rather I could face them with the help and power of Christ.
I believe that God graciously used holiness as the window through which Jerome could see the reality of a greater intimacy. Without holiness, none of us can see God or his love. There is a horizon so much wider than most of us have ever dreamed. Perhaps only a glimpse of that horizon can help people like Jerome understand that in their search for intimacy, what they really have been looking for is _Jesus_.
They have been knocking on the other side of the door depicted in William Holman Hunt's painting. At the same time, they have been unwilling to open it to Jesus. And the handle is on their side. He will not force himself on anyone.
When we come to Christ, the crucial question is what to do with our identity. The things that make up our identity are fundamental to our nature. They are what we're known for and validated for.
Atheist David Foster Wallace once said, "In the day-to-day trenches of adult life, there is actually no such thing as atheism. There is no such thing as not worshiping. Everybody worships."
Whatever we worship shapes our identity. It could be sexuality, vocation, family, or gender. Whatever it might be, we were made to cleave to God for identity and meaning.
Oliver O'Donovan, former Regius Professor of Moral and Pastoral Theology at Oxford University, states, "If Christianity has a saving message to speak to human beings, it must surely be, 'You may be free from the constraints of your identities.' "
When Jesus Christ is relegated to a hobby for middle-class families and not allowed to be the Lord of our entire lives, we are bound to destroy the witness of his gospel. What the Western church needs is a new identity that recognizes that Jesus isn't just a peripheral interest. He's the center of everything.
It should come as a great relief that we no longer have to be our own gods or be slaves to our old identities, including homosexuality. Compared with eternity, homosexuality is a momentary desire. It will soon pass away with God's new creation in Jesus Christ. The same goes with all other broken desires. The overriding reality is God's kingdom and our new identity in him.
The biblical story of Ruth, more than anything, has taught me this truth. Ruth was a Moabite woman, excluded from the covenant promises of Israel, but incredibly, she became part of the genealogy of Jesus Christ.
After the death of her husband, Ruth chose to remain faithful to her Israelite mother-in-law, Naomi, who was grieving the death of her husband and her sons. Together they journeyed back to Israel, where Ruth threw herself on the faithfulness of God and made him the center of her life. Then Boaz, a kinsmen-redeemer from Naomi's extended family, rescued Ruth from the poverty of being a widow, and Naomi from her childlessness. He covered Ruth with the hem of his garment, as a sign of betrothal.
Boaz is an image of Jesus, who redeems us from our old identities with his covenant love. On the cross, he covered us with the hem of his garment. This beautiful truth is reiterated in Ezekiel 16:8, which uses the same phrase from the book of Ruth: "I spread the corner of my garment over you and covered your naked body. I gave you my solemn oath and entered into a covenant with you, declares the Sovereign LORD, and you became mine."
This covering, or overshadowing, is a theme seen throughout Scripture. When Mary is told she will conceive a child, she is overshadowed by the Holy Spirit. On the Mount of Transfiguration, the Holy Spirit overshadows Jesus like a cloud, and God declares that Jesus is his beloved Son. At Pentecost, the church was born, empowered, and baptized with the Spirit. God poured out his covenant love on a great diversity of his children. From this point until today, those outside of Israel are being adopted into the family of God.
I came to see that God had covered me with the hem of his garment and pledged his covenant love to me as part of his bride, the church. He said to me, _David, you are not ultimately celibate, gay, or any of these titles or labels. While they are part of your reality now, the ultimate reality is that you are betrothed to me. My love is your true identity._
While I still use the words gay and celibate to describe myself, what ultimately defines me is God's overshadowing covenant love. And he invites _all_ people, including those like me, into this same holy, covering relationship.
## **LUKEWARM CHRISTIANS AND ANGRY ACTIVISTS**
I am often asked by Christians, "What can we do to better love our LGBTQI neighbors?" While there are many issues that need serious attention, most of them stem from a Christian failure to really listen and love. Instead of creating a safe place for people like LGBTQI Christians to share, we tend to react from fear, not from the security of the gospel.
God wants _all_ people everywhere to turn from their ways in order to know him. He wants us all to adopt an entirely different view of meaning, transcendence, and worship. Can you imagine how healing it would be for the church to acknowledge that it is just as broken and sinful as the gay community? Can you imagine the power in store if Christians were to humbly repent of hypocrisy before expecting others to repent?
When the church does not demonstrate radical discipleship that is willing and able to meet people where they are, it holds us all back. We become afraid to face head-on the questions that need to be answered if the church is to flourish and mature. Capitulating to secular culture's view of sexuality makes it hard for people like me to accept Jesus' claim on our lives.
A weak culture of friendship and fellowship excludes LGBTQI people and forces them to look for intimacy in the wrong places. We need a community life like the one modeled in Acts, in which believers lived as a new family in the light of Jesus' life and mission to the nations.
We must all humbly name that kind of life as what we want and be willing to pay the price for it to be a reality. We must all call for deeper restoration and renewal of the church. The question of sexuality must always be related to _actual people,_ people who matter to the heart of Christ and the kingdom of God. When we can move beyond seeing homosexuality and same-sex desire as part of a culture war we must (or can) win, we may finally see the people behind the smokescreen of identity politics, truly loving them with the kind of love God has shown us.
What will this look like in action? It means we Christians must open up our private family lives and welcome others into the kind of spiritual families and intimate communities we see demonstrated in the book of Acts and the early church. It means that we must act like what we say we are: a new humanity in Jesus.
There are no easy solutions for LGBTQI people, and instead of acting like there are, we must help them carry their burdens, just as we would embrace or help any brother or sister. The church must be able to admit its weaknesses and moral failures, or else those who are gay, are celibate, have gender dysphoria, or identify as trans will simply not be able to belong. Any pride that shelters homophobia or infers heterosexual superiority is a sinful deterrent to LGBTQI people and has hindered the witness of the church. We need honesty, bravery, and openness to find the way of Jesus through this.
I often hear gay or progressive activists say that celibate gay Christians are the new ex-gay, referring to the harrowing history of conversion therapy. Or these activists call those who support us repressive. I need to name that for what it is: discrimination, and it is as deeply hurtful as any homophobia I experienced as a sexually active gay man.
Being gay is not about having gay sex. That is a moral choice separate from gay identity. Of all communities in the world, gay communities are well poised to accept and understand that distinction. I pray that they will.
## **TO BE AN ABRAHAM**
In saving us, God does not erase us or our history. Rather, as our identities are brought under Christ's lordship, he makes us into who we were meant to be. When we cling to fallen desires more than to God, we miss out on the greater identity God has for us as his children. God's first commandment is to have no other gods before him, and this includes the false worship of our identities. If our love for God is real, every one of us must be willing to give up _anything_ in response to his love so it can be transformed, including our sexuality. Without knowing the love of God, none of us can free ourselves from the identities that cruelly deprive us of true freedom.
In Genesis, we read the story of Abraham and Lot, two men to whom God revealed himself. The Scriptures declare that they were both righteous in God's sight. However, Abraham feared and obeyed God; Lot did not. These two men's lives were marked by different decisions in response to God's grace, love, and faithfulness.
When God called Abraham to leave a secure metropolis for a herding life in the wilderness, I am sure God's command seemed unwise and nonsensical. Likewise, to many, my choice to be celibate as a gay man looks strange and even offensive, as it would have looked to me before I met Christ. Others see it as a harmful form of self-denial.
To our natural minds, God's calling to obedience and holiness often appears foolish. Paul writes in 1 Corinthians that "the foolishness of God is wiser than human wisdom" (1:25) and that "God chose the foolish things of the world to shame the wise; God chose the weak things of the world to shame the strong" (v. 27). The very cross of Jesus, as Paul states, is foolishness to the wise. We who carry it will be seen as foolish, but we have found the wisdom of true worship. We have found the way of God's love.
Like Lot, who chose to dwell in a pagan place at great cost, some trust the voice of today's human wisdom. "Sex is intimacy," that voice says. "You can't live without it. Live out your sexual desires the way you like. This is how God made you, and it's who you are!"
However, like Abraham, a small and brave group of people choose to listen to God's voice and follow it where it takes them. God freely offers the gift of salvation, but it's our choice whether to lay down our sexuality or any other hindrance, pick up our cross, and follow Jesus Christ. True faith is revealed in obedience and good works. We turn from sinfully worshiping our own attempts at working things out instead of loving God.
The question of whether a gay or same-sex-attracted person can be saved reflects a complete misunderstanding of the gospel of Jesus Christ. Of _course_ they can be saved! The real question is, will gay or same-sex-attracted believers live the way the world encourages them to? Or will they give up their plans and desires to follow Jesus in celibacy or another arrangement he provides, even under the ridicule of friends, family, or some members of the church?
Those who choose Abraham's path of faith will be called great in the kingdom of heaven and inherit God's promises, but right now they tread a path of cultural, sexual, and social poverty. Knowing God in Jesus Christ and following him will cost us everything. Yet it is Jesus who leads us, and he promises us relational riches in the kingdom of heaven, both now and in the future. He will give us back infinitely more, today and in the age to come. I have found this to be true. The joy I have now far exceeds anything I knew in my past life.
Those who, like Lot, choose to live their own way face both an uncertain fate and dangerous consequences. The choice is ours. Will we receive this free gift of salvation but insist on controlling our own lives? Or will we follow Jesus wherever he takes us and allow him to define our choices? This is the ultimate war of loves. It is a war for our trust and for our worship.
Our entry into the kingdom of heaven is through faith. But faith without works is dead. One day, God's judgment of each of us will reveal whether our faith was genuine. God calls us to demonstrate our faith now, through his enabling power, by changing our minds, turning from our own way, and giving up everything to follow him.
God promises those who become sexually poor for the sake of his kingdom that, like the eunuchs in Isaiah 56, their name will be an eternal one, which is even better than having sons and daughters. This promise is especially precious for LGBTQI people. Our descendants will be as many as the stars. We will not be a dried-up old tree. We can be like the Ethiopian eunuch in Acts 8, who, according to church tradition, became the spiritual father of the whole continent of Africa. God promises the same glorious progeny in our obedience and in our trust in him. As Christ says in Matthew 6:33, "Seek first his kingdom and his righteousness, and all these things will be given to you as well." Whatever we give up we receive back in a far greater form.
By faith, Abraham trusted that God's reward was more vast than the star-filled sky above him. Abraham was even willing to offer up the future represented by his promised only son, when God told him to take Isaac up to Mount Moriah and sacrifice him, to test that he did not wrongly worship the gift above the giver. But instead, God the Father really did give up his Son for us! We are called, in response, to give up those things most precious to us, including our romantic lives and sexuality.
The love of God is fierce and says, "I will not leave you as orphans" (John 14:18). But it also says, "Pick up your cross and follow me!" (see Matt. 16:24). It's not a cheap love; it is a holy love that changes lives. As Dietrich Bonhoeffer said, "Cheap grace is the preaching of forgiveness without requiring repentance, baptism without church discipline, communion without confession. Cheap grace is grace without discipleship, grace without the cross, grace without Jesus Christ, living and incarnate."
If our lives are not shaped by true grace, we will end up like Lot—broken, shamed, wasted. Every work done or choice made not in faith will be burnt up in God's purifying judgment and cannot be taken with us into eternal life. For the true follower of Jesus, it's never an option to live like Lot. The person transformed by God's grace _wants_ to be and is an Abraham.
God's love, demonstrated on the cross two millennia ago, is not a license to live our own way. Jesus Christ bids us come and die and be resurrected. Whatever our sexual orientation, we all must die to our desires so we may be brought into the new life of God's kingdom. But we cannot do this until we know God's love. As in a human relationship of fidelity and faithfulness, we must lay down anything that gets in the way of our relationship with God. If we turn to him, he promises to make something beautiful from our brokenness.
Jesus said, "Whoever lives by believing in me will never die" (John 11:26). He offers this gift of eternal life to every person, even to an atheistic young activist in a pub in the gay quarter of Sydney. That is my story. I could die to my identity and my desires only when I knew God had given everything for me to know him.
Each of us is given a choice: will we escape our self-imposed death sentence by repenting and believing the incredibly good news that God loves us? Jesus Christ put an end to this war of loves between our idols and the true and living God. He stands ready to welcome us into his embrace, if we are willing to lay down our right to define ourselves.
The love of God is where each of us can find freedom from the prison of our own identity. This is what I have experienced. If my story has any message, it is that the love of God can reach any of us, wherever we are. That includes you. The question I was asked on the night I discovered Jesus is the same one I now pose to you: have you experienced the love of God?
The angry activist that I was, with my bitterness, desire for vengeance, and attempt to force the church to adopt my self-made ethic, was really trying to assert myself as lord over the church. In the same way, the real issue at the heart of our culture war is idolatry. It is a war of worship. Until people bow the knee and confess Jesus Christ as Lord, the culture war cycle will continue. But there is much the church can do to aid in God's work. The gospel of Jesus Christ must become our center. We need a clear position that does not instill shame but offers God's loving grace and revealed will, not just for our sexuality but for our whole lives.
Jesus bought my body on the cross, and my body is not mine to do with it what I will. My ethical stance on gay sex doesn't define me, nor does it disqualify me from being part of the gay _or_ Christian community. Even if you disagree with my conclusions—what I sincerely hold out as hard fought truth to you—the fact remains that God loves you and desires relationship with you. It's only in this love that we know who we are, and have true moral knowledge.
I was simply someone who encountered the love of God in Jesus Christ and had my life turned upside down. I am no longer my own. My identity as a gay man is a temporary reality that will soon be transformed. It could never be greater than Jesus' claim on my life.
Are we willing to give up our identities, and the power associated with them, for the sake of knowing Christ? Are we willing to admit our errors? Are we willing to step, like Jesus, across cultural lines and offer his grace and forgiveness? Are we willing to love and listen to our enemies? I long to see the day we are.
Will you join me? I invite you to come into the Father's loving arms, where our most desperate battles are won and where you, through following Christ, will become forever the person you were created to be.
This is the battle of a lifetime. This is the longing we were made for: always satisfied, never satiated. This is the Christian way—utterly human yet full of God's Spirit.
This is the war of loves.
And day by day, tear by tear, heart by heart, it is being won.
# [ ** APPENDIX 1
WHAT I LEARNED THE SCRIPTURES REALLY SAY ABOUT HOMOSEXUALITY ** ](contents.xhtml#conn_36)
> Biblical commands are not arbitrary decrees but correspond to the way the world is and will be.
**_—Richard Bauckham_**
> Did God really say . . .
**_—Genesis 3:1_**
**S** o what did I discover the Bible really says about homosexuality? What I write here comes from an ever-evolving understanding. It has developed over a decade of existential wrestling with God, as well as through study at Oxford and elsewhere. Ultimately, I found that when I surrendered my sexual desires to the lordship of Jesus, the biblical texts became much clearer and sharper.
What follows is my understanding at this point in my journey and in my scholarly development. (Some of the terminology in this section will require patience.) Whether you agree or disagree with my conclusions, I recommend you keep searching with God, while prioritizing the importance of Jesus Christ through the Scriptures, reason, and Christian tradition. I would encourage you to refer to the list of resources at the end of this book, where I outline a few scholars I recommend for further reading.
## **GENESIS AND JESUS**
As I started to read Jesus' words in the Gospels, I saw that marriage was, in and of itself, between a man and a woman. In Matthew 19:4–5, Jesus quotes directly from the creation narrative in Genesis 1–3: " 'Haven't you read,' he replied, 'that at the beginning the Creator "made them male and female," and said, "For this reason a man will leave his father and mother and be united to his wife, and the two will become one flesh"?' " Jesus says that he is relaunching God's original project of creation, which was interrupted by broken worship and sin.
It was necessary for Jesus to emphasize the word of the Creator in addition to the mere act of creating, or the result of it. He reminds his hearers of the significance of sexual difference, and the significance of marriage between one man and woman, which had ceased to be morally apparent when it came to the contentious problem of divorce. Jesus is clarifying that for a male and a female to become husband and wife—by leaving their families behind and becoming sexually one, forming a new kinship unit—that is not just "how things normally go" but how God has made them and _wishes_ them to be understood: what scholar Bernd Wannenwetsch has called "the norm as ought."
If Jesus, the supreme interpreter of the Old Testament, God in the flesh, reaffirmed this teaching, how could I keep resisting it and call him Lord? Also, Jesus, as the one who fulfilled the law of Moses, says that not one "tittle" will pass from it, including such keenly relevant passages as Leviticus 18 and 20, which clearly condemn same-sex practice. In this sense, when Jesus, as a Jewish rabbi, forbids sexual immorality _(porneai)_ in Mark 7:21, it would refer to, at bare minimum, the Old Testament law and thus same-sex practice. Jesus saw himself as fulfilling a specific way of living, anchored in the requirements of and relationship with Israel's God, his Father, developed over hundreds of years. This was not just a culturally relative definition of immorality.
## **BACK TO THE BIBLE?**
Obviously, there are no quick and easy answers to how we relate to all the Old Testament laws. But does that mean we can pick and choose from them at our leisure? No.
As I reflected further, the old argument comparing shellfish and mixed fibers with same-sex activity in Leviticus 18 and 20 no longer held up when I put the whole story of Scripture together. The legal injunctions of Leviticus and other Old Testament books were written to set Israel apart from the nations that surrounded them, as a sign and outreach to them but also to morally instruct God's people. There is no neat divide between ritual purity and moral purity in the Old Covenant, as they were equated in a way they are no longer in the New Covenant. In the early church, the division between Gentile and Jew was undone by Jesus' life, death and resurrection, making "one new humanity out of the two" (Eph. 2:14–15).
This provided a new means of fulfilling the covenant and putting those outside of Israel's relationship with God in right relationship with him by grace through Christ's faithfulness. It also fulfilled and did away with the temple and its system of sacrifice. Those purity laws relating to shellfish and fibers listed in Leviticus had been fulfilled in the Messiah, but the moral injunctions still provided the basis of moral instruction for the early church and Christians today.
Those who belonged to God were no longer marked by things like not eating shrimp. Rather they were marked by obedience and faith in Israel's Messiah, empowered by the Holy Spirit. Particularly in this case, their personal faith was expressed by abstaining from sexual immorality and living in purity provided by the Holy Spirit.
In Acts 15, the early church met to rule on Paul's view that the Jewish purity laws were no longer applicable to Gentile believers, nor were they the source of God's righteous action in reckoning Gentile Christ followers righteous. Just before outlawing sexual immorality, Peter affirms all whom God adopts: "God, who knows the heart, showed that he accepted [Gentiles] by giving the Holy Spirit to them, just as he did to us. He did not discriminate between us and them, for he purified their hearts by faith (Acts 15:8–9).
God does not discriminate, but he calls believers of all kinds to a standard. While Jesus' death and resurrection is the only source of right standing with God, the early church ruled that all sexual immorality was still forbidden.
## **PAUL'S LETTERS**
As I became more and more comfortable with my decision to be celibate, I could face the Scriptures that I previously found the most confronting. I came to see in my studies at Oxford that the consensus of the vast majority of Pauline scholars, from both the more critical and the more orthodox sides, confirmed that same-sex practice was understood by Paul implicitly as a normal part of fallen humanity. I respected those who admitted that Paul thought same-sex activity was wrong, even if in a loving, committed relationship, but just disagreed with him.
Same-sex desire, like other desires that find their root in the fall, is part of the reality of the broken creation. God is right to save Gentiles through Christ and not through legal obedience to Old Testament law, which had to do with maintenance of an older covenant. We are all broken worshipers, regardless of our orientation or identity. None of us have the right to judge, but this does not change the righteous standard we all fall short of. Jesus alone met that standard for us, and by the power of the Holy Spirit, we can live into it.
N. T. Wright states, "There are no surprises on this in the Bible. For Jews, homosexual behavior wasn't an issue [because it was assumedly out of bounds], except as part of a larger whole to which Jesus refers in traditional biblical terms. For non-Jews, such as those addressed by Paul, it was an obvious issue, since every possible kind of sexual expression was well known in cities like Corinth and Rome (there is a popular belief just now that the ancients didn't know about lifelong same-sex relationships, but this is easily refuted by the evidence both literary and archaeological)."
While there was a general understanding of homosexual acts in the broader Greco-Roman literature of the time as predominantly virile or exploitative expressions of power over another, many counterexamples of loving gay romances and gay love poetry that would echo and resemble a gay marriage also existed, including the Greek tradition of writing on homoerotic love.
There were gay love affairs during the time of emperors such as Caesar Augustus and throughout Greco-Roman history. The emperor Hadrian fell in love with Antinous, who then was made a god in Rome's worship.
While I once believed that Paul never would have heard of an erotic, gay relationship or "marriage" of mutual affectation, I came to realize in my studies that this was historically inaccurate and clutching at straws. In verses 25–26 of the first chapter of Romans, Paul uses the terms _kata physin_ ("according to nature") and _para physin_ ("against nature"). These terms refer to a definition of human nature that isn't determined by innate desires or an internalist view of nature (like philosopher Friedrich Nietzsche describes) or power and identity politics (like Michel Foucault or Judith Butler describe). Rather our behavior either does or doesn't align with our _original_ role to give proper worship to God according to the image in which he made us.
Wesley Hill notes, "Male and female is the creational intention not because we can see that clearly in our present contexts but rather because it is given to us in the pre-fall, pre-sin-and-death narratives of Genesis 1 and 2."
In Judaism, human nature was related to our role as priests and worshipers in God's creation, his "temple" or sacred space. We are like God's mini living statues, which in ancient Near Eastern culture would represent a particular god in its temple. Unlike these false gods, however, Yahweh Elohim's image and likeness was etched on living, breathing human beings. In the Greco-Roman world, "proper use" sums up an approach to human nature. In this context, Paul writes that same-sex acts are counter to the image of God, meaning they do not fit his intentions for worship of him in the sacred space of the world.
In Romans 1, Paul's famous text on homosexuality, same-sex sexual expression is symbolic of all human sin because it represents an inversion of the physical reality of being made male-female in the image of God. Paul is not describing gay people but the effect of sin's entry into the world that has meant we all have desire that runs counter to God's purposes and image.
Human nature was the same then as it is today, and Paul was certainly aware of same-sex-attracted people like me. There are a myriad of other complex and broken desires that are reflected in his vice lists, but he chose same-sex practice in Romans 1 in order to portray sin as a twisting or inversion of God's purposes for our bodies and lives. Remarkably, he doesn't start just with the Levitical reference to two men but includes two women in the picture. This reflects the greater notion in rabbinic thinking of the time that all same-sex practice was wrong. Yet for Paul, as this passage describes, these desires could never disqualify one from receiving the love of God, and in repentance, entering the kingdom of God. They have the power to do so only if one makes them one's ultimate identity, rejecting God's salvation in Christ. Think about that! This was _revolutionary_.
In the first verse of Romans 2, Paul writes, "You, therefore, have no excuse, you who pass judgment on someone else, for at whatever point you judge another, you are condemning yourself, because you who pass judgment do the same things." Paul here comments that sin is a universal issue. Not only do the Jews do the same things as the Gentiles, but the root problem is the same—putting something created into the position of the Creator. Paul then outlines in Romans 3:23 that all of us fall short of the glory of God. Paul is clear that same-sex acts (as with the other vices listed) are a universal reality across cultures and time, reaching into our own.
New Testament scholar Richard B. Hays states, "In sharp contrast to the immediate recollections of the creation story, Paul portrays homosexual behavior as a 'sacrament' of the anti-religion of human beings who refuse to honor God." Augustine's solution is summed up in his axiom "Love God and do as you please," and in this passage, Paul shows that in our self-death to these desires for God, we find a transformative, new, and holy pleasure: true worship of God in the Messiah.
Another passage that made new sense to me was 1 Corinthians 6:9. There Paul transliterates the Hebrew terms _mishav_ ["one who lies with"— _koites,_ in ancient Greek] and _zakur_ [male— _arsen,_ in ancient Greek] from the Greek translation of the Jewish Old Testament (LXX) in Leviticus 18 and 20. He then forms a brand-new term in 1 Corinthians 6 by fusing _arseno_ with _koites_ to describe homosexual practice. This new construction, _arsenokoites,_ is a general term used to translate the Jewish sexual ethic in Leviticus 18 and 20 to the Gentile world, even though other, often more negative and specific Greek terms already existed for homosexual people. Paul insists in 1 Corinthians 6:11 that some of the believers in the Corinthian church, as would have been the case in any population of people, used to be _arsenokoites,_ or people who sleep with members of the same sex: "That is what some of you were. But you were washed, you were sanctified, you were justified in the name of the Lord Jesus Christ and by the Spirit of our God."
E. P. Sanders, one of the most prominent Pauline scholars and himself liberal on the question of homosexuality, agrees that "Paul himself condemned homosexual activity and warned his converts against the pleasures of the flesh, but he did not prohibit passion and desire within marriage." Anytime such a vice list is mentioned, the inference is that there are many in the community who have been redeemed out of behaviors that made these desires ultimate identities.
Why does all this matter? Because far from having my heart crushed, I felt seen by the Bible. Rather than condemning me, these passages indicated my full acceptance, like these earliest Christians, in the church as a gay man with these desires and affirmed my choice to no longer live according to them. The gospel of Jesus Christ, as preached by Paul, is not a law-free gospel but a gospel that reoriented Jewish practices around the Messiah who had come, and that required non-Jewish people to abstain from sexual immorality, including same-sex practice. It was oddly satisfying, oddly _normalizing,_ to see my struggle not as the exotic twistedness of some generation far removed from the early church but as a perennial struggle. Around me, I suddenly felt, was a great company of witnesses—yes, gay believers from every age who had to reckon with these desires, these questions. And some of them, undoubtedly, found the answers. I was _so_ not alone.
N. T. Wright states, "People often suggest that since Paul believed in grace, not law, all the old rules were swept away in a new era of 'tolerance,' but this is a shallow and trivial view. Paul (and most early Christians known to us, right through the centuries) stuck with the bare essentials of Jewish morality: no worship of idols, no sex outside marriage."
Today, God's radical inclusion is offered to all in Christ, but that full acceptance does not deny the moral guidance of the Scriptures. These same laws in Scripture were upheld by the early church, even if they recognized that the law was unable to provide the ultimate salvation found in the Messiah Jesus.
Reading these passages is very hard for anyone who is gay or same-sex attracted, but Wesley Hill reminds us, "One of the most striking things about the New Testament teaching on homosexuality is that, right on the heels of the passages that condemn homosexual activity, there are, without exception, resounding affirmations of God's extravagant mercy and redemption. God condemns homosexual behavior and amazingly, profligately, at great cost to himself, lavishes his love on homosexual persons."
God did this in my life, and these passages—yes, _these very passages that once made me feel the weight of condemnation_ —have now become reminders of God's love and grace. In Romans 8:38–39, Paul reminds us that "neither death nor life, neither angels nor demons, neither the present nor the future, nor any powers, neither height nor depth, nor anything else in all creation, will be able to separate us from the love of God that is in Christ Jesus our Lord."
Certainly, that includes homosexuality. And in that boundless, never-separating love, I was able to find what God wanted to say to me by his Word all along.
# [ ** APPENDIX 2
DESIRING AND IMAGING GOD: THE CHALLENGES ** ](contents.xhtml#conn_37)
## **MARRIAGE NOW AND THEN**
A significant moment in my journey was when I realized that God did not create humans as male and female as a statement to oppress LGBTQI people or because God is a homophobic projection of our culture (although, without our idols removed, God can and has easily become so). Rather, as the author of Genesis writes and then Jesus reiterates, God created us as male and female so we would _reflect his image together_.
The diversity of male and female are vital for God-given relational diversity in the church. This diversity of male and female is God's means to fill the earth with his own image and likeness, as well as to restore the sacred garden of Eden in his new creation.
The Creator wanted to share his own loving nature not with a humanity that was boringly uniform but with a human family that was colorfully diverse, in body and redeemed personhood. Christopher West states, "Each person of the Trinity is unique, unrepeatable, and distinct from the others. Yet each is himself in virtue of his relation to the others, that is, in virtue of the eternal mystery of self-giving and community at the heart of the Trinitarian Life." Each marriage between a man and a woman is a microcosm of God's vision for unity in diversity. This human unity-in-diversity has been broken by the fall, yet Jesus Christ, the heavenly man, restored this image in his life, death, and resurrection.
The author of Genesis iterates, "Then God said, 'Let us make man _in our image, after our likeness_. And let them have dominion over the fish of the sea and over the birds of the heavens and over the livestock and over all the earth and over every creeping thing that creeps on the earth.' So God created man _in his own image, in the image of God_ he created him; male and female he created them" (1:26–27 ESV, emphasis added). Out of this union came procreative life, just as out of the unity of the godhead, God created the whole cosmos. Marriage was envisaged by God as a sacred kinship between male and female—a one-flesh union reflecting the God who is love.
In Genesis 2:18 ("It is not good for the man to be alone. I will make a helper suitable for him") and 2:20 ("For Adam no suitable helper was found"), the word translated as "suitable" is _kenegdo,_ which is used to describe Eve as being "opposite/alike" Adam. These human persons are distinct in bodily sex yet alike. They are equally human.
This distinction inscribed in the bodies of Eve and Adam matters because God's plan of salvation, revealed in the marriage of Christ and his church, is yet to come. The other aspect of biblical marriage that reflects God's intention is the word used of Eve, _ezer,_ which means "helper" or "reinforcement in battle." By himself, Adam is weak and exposed, and the same is true for Eve without him. Eve is a coequal and a person distinct from Adam, made to partner with him in their call to love God and care for his creation.
The implication is that Adam needs Eve, and Eve needs Adam, in order to image God. They cannot socially or biologically work without each other. They are incomplete without God and without each other. They need each other's diversity. Together they both make up the original humanity. Without each other, they are lost, incomplete, and unable to fulfill God's commands.
Sam Allberry says, "If marriage [between a man and woman] shows us the shape of the Gospel, then celibacy shows us the sufficiency of it." Marriage is at the heart of the kingdom that Jesus came to bring into this world.
## **CELIBACY NOW AND THEN**
Of course, marriage between a man and a woman is not the only relational situation that reflects God's image and likeness. It is, however, the only one that involves sexual intercourse, or coming together as "one flesh." This is vital, as often in the conversation, we argue about sexual ethics or falsely equate sex and intimacy, and neglect God's broader invitation to create alternative family structures that fulfill our human need for intimacy.
The church itself became an alternative family structure that didn't fit societal norms, by embracing the minorities the ancient world looked down on, including slaves, women, and sexual minorities like the eunuch from Ethiopia. For its entire history, the church has always created and fostered diverse community structures, whether monasteries, missional communities, or small cells of believers like the Celtic priories. They are an essential of church community, not just add-ons to "family" churches.
In Scripture, we see how God worked through friendships like David and Jonathan, Naomi and Ruth, Jesus and John, Paul and Timothy. God used the love in these various friendships to express truths about his coming kingdom; for example, God's adoption of the Gentiles was foreshadowed in Ruth's story and her covenant faithfulness to Naomi.
In 1 Samuel 18:1, we see the unique spirit-to-spirit love of David and Jonathan. This is not a homoerotic or "one-flesh union" like a marriage but a self-sacrificial friendship: "After David had finished talking with Saul, Jonathan became one in spirit with David, and he loved him as himself." They shared a love that was "wonderful, more wonderful than that of women" (2 Sam. 1:26). Jonathan helped David escape from Saul, then later died alongside his father and brothers. David honored Jonathan after his death by adopting Jonathan's lame relative into his court.
Similarly, John was the only disciple of the Twelve who was at the cross when Jesus was abandoned by his other followers and friends. This is witnessed in John 19:26: "When Jesus saw his mother and the disciple whom he loved standing nearby, he said to his mother, 'Woman, behold, your son!' " (ESV). We see Jesus forming this first kingdom nonnuclear family through the spiritual bond he shared with John and Mary. The church is a family bound not by physical lineage but by the spiritual bond of knowing Jesus.
When we look at the covenant friendship of David and Jonathan, and of Jesus and John, we see that marriage is not ultimate or even the greatest form of intimacy that can be experienced, as is often wrongly communicated by the church and our society at large. Rather the love of friendship is the greatest of the loves. There is a long and rich Christian tradition that has prized this. Of course, marriage is profound and contains friendship itself, but the point here is that a life of celibacy as a gay man does not, as I thought originally, cut me off from the intimacy I was made for.
The lie I had believed was that I must have gay sex to be whole. Like many gay people, my outrage at the church for denying gay marriage came from the belief that sex is a requirement for human flourishing. I came to realize that gay marriage, for a Christian, is an oxymoron, as marriage is framed by God in the Scriptures as solely between a man and a woman. Claiming it can be anything else is to argue from scriptural silence. The practical reality is that friendship not only suffices for me but is the greatest love there is to experience. I don't need marriage.
## **THE PROPHETIC PARADOX OF CELIBACY**
We often hear people say in the Christian church that celibacy was designed only as a gift for a select few. Nothing could be farther from the truth. Celibacy is a theme seen throughout Scripture. The eunuch has a greater progeny (name) than those who can have nuclear families. In Acts 8, the Ethiopian eunuch, we presume, although we're not told this in Scripture, becomes the first spiritual father of the continent of Africa.
Our culture worships erotic love, insisting sex is necessary for human flourishing or, as understood in many polytheistic societies, for "the blessing of the gods." When we in the church elevate marriage or romance above God, we fail to see the prophetic paradox of Jesus' own life. Jesus broke this sexual idol by living as "[a eunuch] for the sake of the kingdom of heaven" (Matt. 19:12).
By adopting this marriageless existence, Jesus embodied a prophetic stance against the rejection of sexual minorities from the temple in Jerusalem, as well as in Greco-Roman society. Not only that, he lived a sexual life that was defined by the restored future, not the broken present. Side B Christians (and other singles) imitate Jesus in this way. We become eunuchs for the sake of the kingdom. We are not sexless, but rather the lack we may feel becomes the place for fullness and glory of God, and the growth of God's family.
Eunuchs or those who were sexually impotent were generally despised and exploited in the ancient royal courts of Greco-Roman culture. Lucian of Samosata records the words of an opponent of a eunuch vying for a chair of philosophy in Athens, which reflect a common attitude toward sexual minorities in the ancient world: "The eunuch is neither man nor woman, but something composite, hybrid and monstrous, alien to human nature." Interestingly, Michel Foucault describes a similar view of homosexuality in medical and religious discourse in the early to late modern era as "an hermaphroditism of the soul." Such a view is plainly unscriptural and not reflective of God's heart. Jesus takes the suffering of LGBTQI people into his own life and suffers alongside them as their Messiah and Savior.
Part of Jesus' cross and his death and suffering was giving up the possibility of having children. This is one of the sufferings that people who are celibate carry with Jesus, identified in his going to the cross, unable to have children or a family. In such a way, celibate followers of Jesus become "eunuchs for the sake of the kingdom of heaven" (Matt. 19:12). It is in this "becoming a eunuch" that God promises a name and progeny superior to even having children or an earthly legacy, as seen in Isaiah 56:4–5 (ESV):
Thus says the LORD:
"To the eunuchs who keep my Sabbaths,
who choose the things that please me
and hold fast my covenant,
I will give in my house and within my walls
a monument and a name
_better than sons and daughters;_
I will give them an everlasting name
that shall not be cut off."
When we are willing to be single, even for a time in our life, God promises to give us a name, a monument, and an everlasting progeny that will not be cut off. This progeny is the children of God in the church. The name is that of Jesus Christ. Becoming a eunuch for the sake of the kingdom of heaven is a sacred form of sacrificial love toward God. If that is the default calling for Christians like me, as it was for Christ, unless otherwise called to the rare option of a mixed-orientation marriage, then we can have nothing but overflowing joy.
## **IMAGING GOD: RESISTING THE COMMODIFICATION OF DESIRE**
The world sees our value reflected in our romantic status. One result of this is that we are seeing unprecedented rates of suicide and loneliness. This focus on our relational and sexual desires is only making us more miserable.
My story has taught me that as Christians, we have the privilege of showing the world what it looks like to no longer live under the constant oppression of desire, especially sexual desire. The Christian has forsaken this worldly commodification in order to be a bright signpost of God's love reflected in Christ, and a foretaste of his coming kingdom.
For me, the war of loves was won only after I died to my sexuality and intimacy was given back to me in the form of spiritual friendships. The church still has a long way to go in making a life like mine not just practicable but one of flourishing and joy, but God has worked despite the church's failures. He is faithful even when we are faithless.
Celibacy (or self-sacrifice in relationships), much like fasting or prayer, draws us more closely to the reality of the union we all experience as part of the church of Christ. Paul describes this union when he says, "Whoever is united [literally, married] with the Lord is one with him in spirit" (1 Cor. 6:17). For this reason, I actually find myself excited about God's invitation to live celibately. Celibacy leaves greater room for commitment to spiritual friendships and for dedicating my life to having spiritual children, like Paul did.
In his essay "The Body's Grace," Rowan Williams, the previous Archbishop of Canterbury, opens up the possibility for the commitment of two members of the same sex to embody God's triune love as a way of resisting this perversion of desire. However, Williams does not face the difficult question of sexual difference in God's creation nor in the sacred analogy of Christ, the Bridegroom, and the church, his bride.
I contend that when God says in Leviticus 18:22, "Do not have sexual relations with a man as one does with a woman; that is detestable," he does so for a reason related to his image, not just for the sake of ritual purity. In the life of Israel, God's image was to be reflected in his people. Any behavior that departed from his law was idolatry and was contrary to their image-bearing nature. The same is true for us. Anything not done in faith in God falls short of true worship. This is the meaning of sin, and it leads to death or spiritual disconnection.
Paul teaches that exchanging the image of God for another image in anything we do (as expressed in male-male and female-female pairing, as Paul outlined in Romans 1) represents a rejection of God himself. As the Center for Faith, Sexuality, and Gender states, "The Fall has corrupted God's original intent for human sexuality in all persons; therefore, all people—straight or non-straight—experience corruption in their sexuality." Any departure from God's intention for sexual expression in marriage misses the mark.
For these reasons and others, I remain unconvinced by arguments affirming same-sex marriage. They rest on the presupposition that same-sex desire wasn't ever understood by biblical authors as involving faithful monogamy in the ancient Near Eastern and Greco-Roman period. If we didn't worship romantic love as a god, I honestly believe, the culture war over sexuality would cease. In Christ, a new creation has dawned, and one day, same-sex and broken heterosexual desire will be no longer, but until then we groan inwardly for our resurrection and the fulfillment of God's coming kingdom.
That said, gay unions and relationships, as many of mine did, can contain deep commitment, friendship, and sacrificial love that, when separated from sexual expression, I am sure, are important to God and are to be honored in these ways as forms of friendship. The church has often, although not always, failed by either celebrating and affirming these relationships and thus changing church doctrine or rejecting them altogether. Neither approach is helpful. There is nuance in each situation.
The God-honoring parts of gay relationships can be enjoyed within God's vision for friendship. Human beings can live without sex, but we cannot live without love. God calls us to repent of sinful sexual relationships. I have many friends who have left gay marriages or relationships to follow Jesus.
The redemption of LGBTQI Christians takes a unique form that the church must learn from, and learn to embrace and empower. The church must also learn how to invite gay couples into it without working against the grace God is pouring out in their lives as he calls them to holiness. This requires relinquishing condescension and embracing humility and patience. As my story demonstrates, it took years to receive what I needed from God before I was willing to live differently and leave gay relationships behind.
My view is that when a gay person becomes a Christian, they must not repress or indulge their erotic longings or base their entire identity on such desires. Rather they need to remember that these longings originate from a more fundamental desire for God himself. The only way same-sex desire can be safely understood is first when it is, as Sarah Coakley says, "both understood in relation to and in its uniqueness from others of its kind, rooted first in a desire for God and therefore, capable of purification or elevation."
Same-sex erotic desires are part of our fallen humanity. They are similar to broken heterosexual desires in that their end can never be righteously expressed in the covenant of marriage. All human desire can be traced back to our desire for God, even if twisted by sin. I listen to my same-sex desires as part of my more fundamental craving for intimacy with God and others, and I also deny them in deference to desiring God's image, will, and person.
Denying same-sex desires simply to obey a law or to belong to the church not only fails but also is a miserable existence leading to sin. However, by understanding that my desires actually point to my desire for God in Christ and in the Holy Spirit, I have come to a place of satisfaction and joy in my celibacy.
Just like bad marriages, there can be bad celibacy. I always recommend that anyone struggling with their desires, but especially all new Christ followers, give God a year to reveal the real root of those desires and to give them answers to the relational challenges they face. Like Christ, who went to the cross, all people must die to themselves in order to live in the new way of resurrection.
Our sinful desires emerge from what Scripture calls the "flesh" or "old man." We give them over to purification where new, holy desires, ecstatic and from the new creation reality, are able to arise. They are part of the new person one becomes in Christ. In doing so, we don't cease to be erotic or sexual without having sex; rather we redirect that energy into service and love for God and our neighbor. Those of us who are celibate start our heavenly vocation now, anticipating the future, in which there will be no marriage.
Because Christ has called me to celibacy, I have great joy. However, my lamentation is that celibate gay Christians like me are often rejected, dismissed, or at times ridiculed by other believers, for several reasons: because of our choice to surrender our sexuality to the lordship of Christ, because of our refusal to apologize for any aspect of gospel living, including sexual purity, and because of our loving acceptance of LGBTQI people. Sometimes we even become a liability in that if people encourage us or associate with us, they pay a social or political price. We live under a pressure few realize, which profoundly tests our trust in the Father.
The way ahead is difficult, as the church continues to deal with pressure, both from within and from outside, to compromise God's revealed truth. Simply changing the doctrine of the church is the most unloving thing that can be done for side B Christians like me. It makes an already tough path even harder. Sometimes it seems as if the idol of self and personal desires reigns everywhere, and there is little respite for Christians, especially celibate gay Christians. And yet God is at work, strengthening and transforming us and freeing us from the sin that attempt to enslave us. Our hope is in him.
I long for a future in which the church offers a clearer, more direct path to God for those who struggle with desire, especially for those in the beloved LGBTQI community. Jesus himself shows the way. His divine love leads us to abundant life and teaches us that any sacrifice for his sake can be transformed into richest ecstasy and joy. As celibate gay Christians, may we follow our beloved Savior, modeling his beautiful, holy vision for our bodies, desires, sexuality—our whole selves.
# **NOTES**
. C. S. Lewis, _Shadowlands_ (London: William Nicholson, 1993).
. Simon LeVay, "A Difference in Hypothalamic Structure between Heterosexual and Homosexual Men," _Science_ 253 (1991): 1034–37. For further reading, see Simon LeVay, _Gay, Straight, and the Reason Why: The Science of Sexual Orientation,_ 2nd ed. (New York: Oxford Univ. Press, 2016).
. P. Lindström, "Brain Response to Putative Pheromones in Homosexual Men," _PNAS_ 20 (2005): 7356–61. See a follow-up study published later on lesbians' pheromonal attraction.
. J. Michael Bailey, Michael P. Dunne, and Nicholas G. Martin, "Genetic and Environmental Influences on Sexual Orientation and Its Correlates in an Australian Twin Sample," _Journal of Personality and Social Psychology_ 78, no. 3 (2000): 524–36.
. I. Savic, H. Berglund, and G. Dörner, "Neuroendocrine Response to Estrogen and Brain Differentiation in Heterosexuals, Homosexuals, and Transsexuals," _Archives of Sexual Behavior_ 17, no. 1 (1988): 57–75.
. Jean-Paul Sartre, _Existentialism and Humanism,_ trans. (from French) Philip Mairet (London: Eyre Meuthuen, 1973), 65.
. Aengus Carroll and Lucas Ramon Mendos, _State-Sponsored Homophobia: A World Survey of Sexual Orientation Laws: Criminalisation, Protection and Recognition,_ 12th ed. (Geneva: ILGA, May 2017).
. Richard Dawkins, _River out of Eden: A Darwinian View of Life_ (New York: Basic Books, 1995), 17.
. C. S. Lewis, _Mere Christianity_ (London: Harper Collins, 2009), 29.
. Michel Foucault, _Power/Knowledge: Selected Interviews and Other Writings, 1972–1977,_ ed. Colin Gordon (New York: Pantheon, 1980), 73–74.
. "You who are trying to be justified by law have been alienated from Christ; you have fallen away from grace" (Gal. 5:4).
. See John Wesley's journey from the nominal Christian faith of his youth and early adulthood to the living faith of his adult years. The faith he received upon reading Paul's letter to the Romans spurred him on to seek—from his experiences of the Moravian Christians, who had absolute peace in suffering—what he called the "new faith." I was renewed in my understanding of how justification by faith applied to all aspects of my life, and particularly homosexuality. Like Wesley, I was liberated from the chains of a law-bound, self-justifying obedience. This is a danger today's evangelical churches must resist through the clear preaching of the gospel. Christian discipleship is an obedience through relational trust of a Person, knowing the free gift of God's self to us in Christ.
. While I now call myself a celibate gay Christian, I mean this primarily in the descriptive sense. _Celibate_ and _gay_ are modifiers to the central noun, which is _Christian_. My ultimate identity is in Christ, related to the coming heavenly reality, where there will be perfect desire, perfect community, perfect love with perfect bodies before a perfect God. Celibacy becomes, then, a sign of this heaven as we wait for a day when Christ will fill and perfect everything, all in all.
. To read my further thoughts on what I found the Bible really teaches on homosexuality and marriage, see appendix 1.
. "A Sermon on the Estate of Marriage (1519)," trans. James Atkinson, in _Luther's Works,_ ed. Helmut T. Lehmann, vol. 44, ed. James Atkinson (Philadelphia, 1966), 10.
. Rudolf Brazda, _L'itineraire d'un triangle rose: La biographie d'un déporté pour motif d'homosexualité,_ trans. Jean-Luc Schwab (2010).
. Phil Davidson, "Rudolf Brazda: Last Known Survivor of the 'Pink Triangle' Gay Inmates of Nazi Concentration Camps," _Independent_ (August 9, 2011), _www.independent.co.uk/news/obituaries/rudolf-brazda-last-known-survivor-of-the-pink-triangle -gay-inmates-of-nazi-concentration-camps-2334053.html_.
. Ibid.
. Ibid.
. Søren Kierkegaard, _Provocations: Spiritual Writings of Kierkegaard,_ ed. Charles Moore (New York: Plough, 2014), 193.
. Wesley Hill, _Washed and Waiting: Reflections on Christian Faithfulness and Homosexuality_ (Grand Rapids: Zondervan, 2010), 111.
. See _The Four Loves_ by C. S. Lewis.
. Andrew Sullivan, _Love Undetectable: Notes on Friendship, Sex, and Survival_ (New York: Random House, 1999), 198.
. Matthew Vines, _God and the Gay Christian_ (New York: Random House, 2014).
. Henri Nouwen, _Lifesigns: Intimacy, Fecundity, and Ecstasy in Christian Perspective_ (New York: Random House, 1989), 44.
. See the exegesis of _'ezer_ and _kenegdo_ in Brian N. Peterson, "Does Genesis 2 Support Same-Sex Marriage? An Evangelical Response," _JETS_ 60, no. 4 (2017): 681–96.
. For example, the Reformation Project, Church Clarity.
. See the different views surrounding the role of the law in John Perry's "Gentiles and Homosexuals: A Brief History of Analogy," especially Ben Witherington's and Richard Bauckham's interpretations.
. Henri Nouwen, _The Life of the Beloved: Spiritual Living in a Secular World_ (New York: Cross Road Publishing, 1992), 33.
. Sarah Coakley, _The New Asceticism: Sexuality, Gender and the Quest for God_ (London: Bloomsbury, 2015), 25.
. There is a wide history of these kinds of gay cure therapies, but see Robert Colvile, "The Man Who Fried Gay People's Brains," _Independent_ (July 6, 2016), _www.independent.co.uk/life-style/health-and-families/health-news/the-man-who-fried-gay-people-s -brains-a7119181.html_.
. Augustine, _On Christian Doctrine (de doctrina Christiana),_ book 1, trans. R. P. H. Green (Oxford: Oxford Univ. Press, 1997), I.1–5.
. J. I. Packer, "Why I Walked: Sometimes Loving a Denomination Requires You to Fight," _Christianity Today_ (January 1, 2003), _www.christianitytoday.com/ct/2003/january/6.46.html_.
. A. Thiselton, "Realized Eschatology at Corinth," _New Testament Studies_ 24, no. 4 (1978): 510–26, doi:10.1017/S0028688 50001451X.
. Welsey Hill, "Once More: On the Label 'Gay Christian,' " _First Things_ (February 1, 2013), _www.firstthings.com/blogs/firstthoughts/2013/02/once-more-on-the-label-gay-christian_.
. David Foster Wallace, _This Is Water: Some Thoughts, Delivered on a Significant Occasion, about Living a Compassionate Life_ (New York: Hachette, 2009), 10.
. See Oliver O'Donovan's reflections in the Pilling Report (2013), compiled by the Church of England.
. Dietrich Bonhoeffer, _Discipleship_ (trans. 1948; London: SCM Press, 2006), 4.
. Bernd Wannenwetsch, "Creation and Ethics: On the Legitimacy and Limitation of Appeals to 'Nature' in Christian Moral Reasoning," in Anthony Clarke and Andrew Moore, eds., _Within the Love of God: Essays on the Doctrine of God in Honour of Paul S. Fiddes_ (Oxford: Oxford Univ. Press, 2014), _www.oxfordscholarship.com_.
. N. T. Wright in Andrew Wilson, "Tom Wright on Homosexuality," _Think_ (July 14, 2014), _http://thinktheology.co.uk/blog/article/tom_wright_on_homosexuality_.
. E. P. Sanders, _Paul: The Apostle's Life, Letters and Thought_ (London: SCM Press, 2016), 727–48.
. Wesley Hill in Preston Sprinkle and Stanley N. Gundry, eds., _Two Views on Homosexuality, the Bible, and the Church_ (Grand Rapids: Zondervan, 2016), 110.
. Richard B. Hays, _The Moral Vision of the New Testament: A Contemporary Introduction to New Testament Ethics_ (London: T&T Clark International, 1997), 386.
. Found in the tract _In epistulam Ioannis ad Parthos_ (Tractatus VII, 8), the passage reads, "Once for all, then, a short precept is given unto you: Love God, and do what you will: whether you hold your peace, through love hold your peace; whether you cry out, through love cry out; whether you correct, through love correct; whether you spare, through love do you spare: In all things, let the root of love be within, for of this root can nothing spring but what is good."
. Richard B. Hays, _The Moral Vision of the New Testament: A Contemporary Introduction to New Testament Ethics_ (London: T&T Clark, 1997), 379–89.
. E. P. Sanders, _Paul: The Apostle's Life, Letters, and Thought_ (London: SCM Press, 2016), 747.
. Wright in Wilson, "Tom Wright on Homosexuality."
. Hill, _Washed and Waiting_ , 62.
. Christopher West, _Theology of the Body Explained: A Commentary on John Paul II's "Gospel of the Body"_ (Leominster, UK: Gracewing, 2003), 119.
. See commentary on _ezer_ (helper) and _kenegdo_ (opposite/alike) in Brian N. Peterson, "Does Genesis 2 Support Same-Sex Marriage? An Evangelical Response," _JETS_ 60, no. 4 (2017): 681–96.
. Ibid.
. Sam Allberry, "How Celibacy Can Fulfill Your Sexuality," _Gospel Coalition_ (August 26, 2016), _www.thegospelcoalition.org/article/how-celibacy-can-fulfill-your-sexuality/_.
. Barry Danylak, _Redeeming Singleness: How the Storyline of Scripture Affirms the Single Life_ (Wheaton, IL: Crossway, 2010), 83–115, 143–73.
. Ibid., 154.
. Ibid., 155.
. Michel Foucault, _The History of Sexuality,_ vol. 1: _An Introduction,_ trans. Robert Hurley (New York: Random House, 1984), 43.
. See the Samaritans' report on suicide and mental health: _www.samaritans.org/about-us/our-research/facts-and-figures-about-suicide_.
. Rowan Williams, "The Body's Grace," _ABC_ (August 24, 2011), _www.abc.net.au/religion/articles/2011/08/24/3301238.htm_.
. See the Center for Faith, Sexuality and Gender's "Statement of Marriage, Sexuality and Gender," _www.centerforfaith.com_.
. Sarah Coakley in Wesley Hill, "Faith's Desire: A Review of _God, Sexuality, and the Self_ " (June 2014), _www.firstthings.com/article/2014/06/faiths-desire_.
# **GLOSSARY**
**LGBTQI:** Lesbian, gay, bisexual, transgender, queer, intersex
**Side A:** Disagrees with Christian tradition, affirming a gay identity and seeing sexual expression in gay marriage as faithful to a Christian ethic
**Side B:** Affirms the Christian tradition; sees sexual expression in gay marriage as wrong but incorporates a gay identity under the lordship of Christ through celibacy and other forms of chastity
**Side Y:** Like side B but does not identify with the term LGBTQI. Prefers not to identify as gay but is more likely to use the term same-sex attracted or is reluctant to see sexual orientation as a category of identity or personhood
**Side X:** Claims either to no longer experience same-sex attraction or to be ex-gay and to have been freed by the process of sanctification
**Intersex:** A set of medical conditions with congenital anomaly of the reproductive and sexual system
**Transgender:** Denoting or relating to a person whose sense of personal identity and gender does not correspond with their birth sex
**Gender dysphoria:** The condition of feeling that one's emotional and psychological identity as male or female are opposite one's biological sex
**Cisgender:** Denoting or relating to a person whose sense of personal identity and gender corresponds with their birth sex
**Queer:** Generally used as an adjective for the LGBTQI community but also can refer to queer theory or queer theology, which are fields of academic discourse. Queer is often used to infer that one does not want to be limited, labelled, or expected to have simply one kind of attraction but has at some point been attracted to the same-sex.
**Heteronormative:** Denoting or relating to a worldview that promotes heterosexuality as the normal and preferred sexual orientation
# **RECOMMENDED RESOURCES**
**Note:** These resources are diverse and may differ at points, but held together, they provide a broad picture I endorse.
Allberry, Samuel. _Is God Anti-Gay?_
Coles, Greg. _Single, Gay, Christian: A Personal Journey of Faith and Sexual Identity_.
Collins, Nate. _All But Invisible: Exploring Identity Questions at the Intersection of Faith, Gender, and Sexuality_.
Danylak, Barry. _Redeeming Singleness: How the Storyline of Scripture Affirms the Single Life_.
Hill, Wesley. _Spiritual Friendship: Finding Love in the Church as a Celibate Gay Christian_.
———. _Washed and Waiting: Reflections on Christian Faithfulness and Homosexuality_.
Hirsch, Debra. _Redeeming Sex: Naked Conversations about Sexuality and Spirituality_.
Nouwen, Henri. _Life of the Beloved: Spiritual Living in a Secular World_.
———. _Lifesigns: Intimacy, Fecundity, and Ecstasy in Christian Perspective_.
———. _The Wounded Healer: Ministry in Contemporary Society_.
Paris, Jenell Williams. _The End of Sexual Identity: Why Sex Is Too Important to Define Who We Are_.
Shaw, Ed. _The Plausibility Problem: The Church and Same-Sex Attraction_.
———. _Same-Sex Attraction and the Church: The Surprising Plausibility of the Celibate Life_.
Sprinkle, Preston. _Living in a Gray World: A Christian Teen's Guide to Understanding Homosexuality_.
———. _People to Be Loved: Why Homosexuality Is Not Just an Issue_.
Tushnet, Eve. _Gay and Catholic: Accepting My Sexuality, Finding Community, Living My Faith_.
West, Christopher. _Fill These Hearts: God, Sex, and the Universal Longing_.
Wilson, Todd. _Mere Sexuality: Rediscovering the Christian Vision of Sexuality_.
Yarhouse, Mark. _Homosexuality and the Christian: A Guide for Parents, Pastors, and Friends_.
**Digging Deeper: Biblical Interpretation and Theological Ethics**
Brock, Brian, and Bernd Wannenwetsch. _The Malady of the Christian Body: A Theological Exposition of Paul's First Letter to the Corinthians_. Eugene, OR: Wipf and Stock, 2016.
Coakley, Sarah. _The New Asceticism: Sexuality, Gender and the Quest for God_ (especially last chapter). London: Bloomsbury, 2015.
Gathercole, Simon. "Sin in God's Economy: Agencies in Romans 1 and 7," in _Divine and Human Agency in Paul and His Cultural Environment_. London: T&T Clark, 2008.
Goddard, Andrew. _God, Gentiles and Gay Christians_. Cambridge: Grove, 2001.
———. _Homosexuality and the Church of England_. Cambridge: Grove, 2004.
Grenz, Stanley J. _Welcoming but Not Affirming: An Evangelical Response to Homosexuality_. Louisville: Westminster/John Knox Press, 1998.
Hays, Richard B. "Homosexuality," in _The Moral Vision of the New Testament: A Contemporary Introduction to New Testament Ethics_. San Francisco: HarperSanFranciso, 1996.
Hooker, Morna D. "Adam in Romans 1," in _From Adam to Christ: Essays on Paul_. Cambridge: Cambridge Univ. Press, 2008.
O'Donovan, Oliver. _A Conversation Waiting to Begin: The Churches and the Gay Controversy_. London: SCM Press, 2009.
Roberts, Christopher C. _Creation and Covenant: The Significance of Sexual Difference in the Moral Theology of Marriage_. London: T&T Clark, 2007.
Saint Andrews Day Statement. _www.ceec.info/st-andrews-day-statement.html_.
Sanders, E. P. _Paul: The Apostle's Life, Letters, and Thought_ (particularly appendix 1 on homosexuality in the Greco-Roman world and the chapter on 1 Corinthians 6). Minneapolis: Fortress Press, 2016.
Sprinkle, Preston and Stanley N. Gundry, eds. _Two Views on Homosexuality, the Bible, and the Church_. Grand Rapids: Zondervan, 2016.
Swartley, Willard. _Homosexuality: Biblical Interpretation and Moral Discernment_. Scottdale, PA: Herald Press, 2003.
Via, Dan O. and Robert A. J. Gagnon. _Homosexuality and the Bible: Two Views_. Minneapolis: Fortress Press, 2004.
West, Christopher. _Theology of the Body Explained: A Commentary on John Paul II's "Gospel of the Body"_ Leominster, UK: Gracewing, 2003.
**Recommended Websites**
The Center for Faith, Sexuality and Gender. _www.centerforfaith.com_.
The Institute for the Study of Sexual Identity. _www.sexualidentityinstitute.org_.
Living Out. _www.livingout.org_.
Revoice. _www.revoice.us_.
Spiritual Friendship. _www.spiritualfriendship.org_.
**Other Important or Differing Views**
Brownson, James V. _Bible, Gender, Sexuality: Reframing the Church's Debate on Same-Sex Relationships_. Grand Rapids: Eerdmans, 2013.
DeFranza, Megan K. _Sex Difference in Christian Theology: Male, Female, and Intersex in the Image of God_. Grand Rapids: Eerdmans, 2015
Lee, Justin. _Torn: Rescuing the Gospel from the Gays-vs-Christians Debate_. New York: Jericho Books, 2012.
Perry, John. "The Author Replies . . . Vocation and Creation: Beyond the Gentile-Homosexual Analogy." _Journal of Religious Ethics_ 40, no. 2 (2012): 385–400.
Perry, John. "Gentiles and Homosexuals: A Brief History of an Analogy." _Journal of Religious Ethics_ 38, no. 2 (2010): 321–47.
Rae, Murray. _More Than a Single Issue: Theological Considerations Concerning the Ordination of Practising Homosexuals_. Hindmarsh: Australian Theological Forum, 2000.
Song, Robert. _Covenant and Calling: Towards a Theology of Same-Sex Relationships_. London: SCM Press, 2014.
Vines, Matthew. _God and the Gay Christian_. New York: Convergent, 2014.
# Table of Contents
1. Cover Page
2. Title Page
3. Copyright Page
4. Dedication
5. Contents
6. Author's Note
7. Foreword
8. Acknowledgments
9. Preface
10. Part 1: The Search
1. 1. Coming Out
2. 2. Quest for Spirituality
3. 3. The French Exchange
4. 4. Boyfriends and Psychics
5. 5. The Gay World
6. 6. University and the Love Triangle
7. 7. Christmas Conflicts
11. Part 2: The Encounter
1. 8. Experiencing the Love of God
2. 9. The Film Festival
3. 10. Providence and Prophecies
4. 11. The Unrelenting Presence of Jesus
5. 12. The Root of Bitterness
6. 13. The Gospel of Grace
12. Part 3: Wrestling With God: Sense and Sexuality
1. 14. Living Under God's Word
2. 15. Marriage and the Church
3. 16. Facing Facts In France
4. 17. God's Greater Romance
5. 18. Romance In France
13. Part 4: The New Identity
1. 19. Understanding Love and Celibacy
2. 20. Bible College and Moving to Oxford
3. 21. Drawing the Line: Acceptance versus Affirmation
4. 22. Beloved Friendship
5. 23. Living Out Now
14. Part 5: Reflections On Homosexuality and Christian Faithfulness
1. 24. Celibate, Gay, Christian: A Third Way
2. 25. Speaking Truth In Love
3. 26. Sacrifice Regained: Salvation and Holiness
15. Appendix 1: What I Learned the Scriptures Really Say About Homosexuality
16. Appendix 2: Desiring and Imaging God: The Challenges
17. Notes
18. Glossary
19. Recommended Resources
## List of Pages
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| {
"redpajama_set_name": "RedPajamaBook"
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<?php
/**
*
* With Db_object The Crud Will Become Very Easy
* For Your All Projects All What You Should To Do
* To Make CRUD For New Database Table
* Create The Class Then Select The Name Of The DATABASE Table
* Then Select The Fields Of The Table And It Will Make The CURD
* Automatically And Also DB OBJECT Making Auto Instantiating
* And Cleaning The Properties ETC.....
*
*
* @category Database OBJECT
* @package DB_OBJECT
* @license http://www.apache.org/licenses/LICENSE-1.0
* @version 1.0.0
*/
class Db_object
{
public $errors = array();
public $upload_errors_array = array(
UPLOAD_ERR_OK => "There is no error",
UPLOAD_ERR_INI_SIZE => "Size exceeds upload_max_filesize in php.ini.",
UPLOAD_ERR_FORM_SIZE => "Size exceeds MAX_FILE_SIZE specified in HTML form.",
UPLOAD_ERR_PARTIAL => "The uploaded file was only partially uploaded.",
UPLOAD_ERR_NO_FILE => "No file was uploaded.",
UPLOAD_ERR_NO_TMP_DIR => "Missing a temporary folder.",
UPLOAD_ERR_CANT_WRITE => "Failed to write file to disk.",
UPLOAD_ERR_EXTENSION => "File upload stopped by extension."
);
public static function find_all()
{
return static::find_by_query("SELECT * FROM " . static::$db_table . " ");
}
public static function find_by_id($id)
{
global $database;
$the_result_array = static::find_by_query("SELECT * FROM " . static::$db_table . " WHERE id = $id LIMIT 1");
return !empty($the_result_array) ? array_shift($the_result_array) : false;
}
public static function find_by_query($sql)
{
global $database;
$result_set = $database->query($sql);
$the_object_array = array();
while ($row = mysqli_fetch_array($result_set)) {
$the_object_array[] = static::instantation($row);
}
return $the_object_array;
}
public static function instantation($the_record)
{
$calling_class = get_called_class();
$the_object = new $calling_class;
foreach ($the_record as $the_attribute => $value) {
if ($the_object->has_the_attribute($the_attribute)) {
$the_object->$the_attribute = $value;
}
}
return $the_object;
}
private function has_the_attribute($the_attribute)
{
$object_properties = get_object_vars($this);
return array_key_exists($the_attribute, $object_properties);
}
protected function properties()
{
$properties = array();
foreach (static::$db_table_fields as $db_field) {
if (property_exists($this, $db_field)) {
$properties[$db_field] = $this->$db_field;
}
}
return $properties;
}
protected function clean_properties()
{
global $database;
$clean_properties = array();
foreach ($this->properties() as $key => $value) {
$clean_properties[$key] = $database->escape_string($value);
}
return $clean_properties;
}
public function save()
{
return isset($thos->id) ? $this->update() : $this->create();
}
public function create()
{
global $database;
$properties = $this->clean_properties();
$sql = "INSERT INTO " . static::$db_table . "(" . implode(",", array_keys($properties)) . ")";
$sql .= "VALUES ('" . implode("','", array_values($properties)) . "')";
if ($database->query($sql)) {
$this->id = $database->the_insert_id();
return true;
} else {
return false;
}
} // Create Method
public function update()
{
global $database;
$properties = $this->clean_properties();
$properties_pairs = array();
foreach ($properties as $key => $value) {
$properties_pairs[] = "{$key}='{$value}' ";
}
$sql = "UPDATE " . static::$db_table . " SET ";
$sql .= implode(", ", $properties_pairs);
$sql .= " WHERE id= " . $database->escape_string($this->id);
$database->query($sql);
return (mysqli_affected_rows($database->connection) == 1) ? true : false;
} // End Of Update Method
public function delete()
{
global $database;
$sql = "DELETE FROM " . static::$db_table . " ";
$sql .= "WHERE id = " . $database->escape_string($this->id);
$sql .= " LIMIT 1";
$database->query($sql);
return (mysqli_affected_rows($database->connection) == 1) ? true : false;
} // End Of Update Method
public static function count_all() {
global $database;
$sql = "SELECT COUNT(*) FROM " . static::$db_table;
$result_set = $database->query($sql);
$row = mysqli_fetch_array($result_set);
return array_shift($row);
}
}
?> | {
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} | 474 |
Francisco Javier "Javi" de Pedro Falque (born 4 August 1973) is a Spanish retired footballer.
He played as a left midfielder, mainly with Real Sociedad, and possessed a thunderous left-foot shot. He also played professionally in four other countries.
De Pedro represented Spain at the 2002 World Cup.
Club career
De Pedro was born in Logroño, La Rioja. A product of Real Sociedad's youth system, he first appeared with the main squad on 7 November 1993, coming on as a substitute in a 1–3 home defeat against UE Lleida. Subsequently, he became an essential element with the La Liga side, creating opportunities and scoring alike: in the 2002–03 season he contributed with 29 games and three goals as the Basques finished in second position, trailing eventual champions Real Madrid by only two points; in the subsequent edition of the UEFA Champions League, he scored a late consolation goal after coming on as a substitute in a 2–4 defeat away to Juventus FC.
De Pedro joined Blackburn Rovers in mid-June 2004, after he had been refused a move to Southampton the previous year, playing out the remaining season of his contract undeterred. He made his debut for his new team on 14 August in a 1–1 Premier League home draw against West Bromwich Albion, before being replaced by Tugay Kerimoğlu for the second half of the match.
On 31 January 2005, in the last day of the campaign's winter transfer window, de Pedro was released by Blackburn on a free transfer and signed for Perugia Calcio, where he played only a few matches before joining Swedish club IFK Göteborg, thanks to the presence of former Real Sociedad teammate Håkan Mild, now their director of football; he left after only a few days for personal reasons, in December.
Afterwards, de Pedro would only play some exhibition matches with Ergotelis F.C. from the Football League (Greece). He subsequently returned to Spain to sign with Burgos CF, but appeared very rarely for the Segunda División B team.
De Pedro started 2007–08, alongside former Real Sociedad and Spain teammate Agustín Aranzábal, with regional club CD Vera in the Canary Islands, but was dismissed by the team's coach due to a lack of commitment. He retired from football after this experience, and subsequently focused on getting a coaching qualification.
International career
Having made his debut with Spain on 23 September 1998 in a friendly match against Russia in Granada, de Pedro appeared at the 2002 FIFA World Cup, where he played in all the matches as a starter. His last cap came in 2003.
De Pedro also played for the Basque Country regional team, scoring against Nigeria and Morocco.
International goals
Personal life
In November 2009, de Pedro was arrested for driving under the influence and with an expired driver's licence. In January 2018, he was arrested for domestic violence.
Honours
Spain U21
UEFA European Under-21 Championship: Runner-up 1996
References
External links
1973 births
Living people
Sportspeople from Logroño
Spanish footballers
Footballers from La Rioja (Spain)
Association football midfielders
La Liga players
Segunda División B players
Antiguoko players
Real Sociedad B footballers
Real Sociedad footballers
Burgos CF footballers
Premier League players
Blackburn Rovers F.C. players
Serie B players
A.C. Perugia Calcio players
IFK Göteborg players
Ergotelis F.C. players
Spain youth international footballers
Spain under-21 international footballers
Spain international footballers
2002 FIFA World Cup players
Basque Country international footballers
Spanish expatriate footballers
Expatriate footballers in Italy
Expatriate footballers in England
Expatriate footballers in Sweden
Expatriate footballers in Greece
Spanish expatriate sportspeople in Italy
Spanish expatriate sportspeople in England
Spanish expatriate sportspeople in Sweden
Spanish expatriate sportspeople in Greece | {
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Les saisons ont un rôle important dans la culture japonaise.
Importance dans la culture japonaise
Poésie
Littérature
Peinture
Les représentations de la nature au fil des saisons .
On peut citer Fleurs et oiseaux des quatre saisons par Kanō Shōei et son fils Kanō Eitoku au et Paysages de printemps et d'automne par Hara Zaishō au .
Cuisine
Nom des saisons en japonais
Le tableau ci-dessous présente les différentes façons d'écrire les saisons () en japonais.
Les quatre saisons se divisent traditionnellement en 24 périodes (sekki) et en 72 « micro-saisons » (kō) inspirées des sources chinoises.
Le terme « est très souvent employé au Japon, pour accentuer le fait qu'il existe quatre saisons distinctes au niveau du climat, des coutumes, des catastrophes naturelles, de la gastronomie ou des évènements sociaux.
Par exemple, le réfère au printemps, les feux d'artifice à l'été, la dégustation de à l'automne et la cérémonie de passage à l'âge adulte se fait en plein hiver.
Références
Voir aussi
Bibliographie
.
Poésie de langue japonaise
Littérature japonaise
Peinture japonaise
Gastronomie japonaise
Vocabulaire japonais | {
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Business and Deals
TV Spending on Auto Ads Expected to Drop in 2015
Online media to post big increases by manufacturers and dealers
Jon Lafayette
TV spending in the key automotive category is expected to be down next year, while digital advertising jumps.
Automakers are expected to increase their spending on cable TV by nearly 10% during 2015, while spending on broadcast will drop by a similar percentage, according to new figures from Borrell Inc.
Auto dealer spending is expected to drop in both broadcast and cable TV.
At $35.5 billion, automotive is the second-largest advertising category, behind general merchandise stores, and a bigger share of spending is going to digital media.
Car sales are up 5% this year and total ad budgets are up 17%, with online media accounting for 95% of this year's increase.
The auto industry illustrates the larger trend that TV advertising growth has slowed and that a chunk of that money appears to be moving to digital.
"It's a landmark year for digital advertising. For the first time, more than half of all automotive ad dollars will be spent on digital media," the Borrell report says. "While it's clearly come at the expense of radio and newspaper budgets, the next phase of erosion will likely affect TV the most."
In total, the amount spent by manufacturers is up 12.2% to $12.3 billion and the amount spent by dealers is up 21.8% to $21.2 billion. Spending by dealer associations is up 1.1% to $1.3 billion and spending by private parties is up $9.5% to $577 million.
For the broadcasters, 2015 would mark the third straight year of lower automaker spending, which is expected to come in at $2.6 billion in 2014 and drop 9.7% to $2.3 billion in 2015.
Automaker spending on cable is expected to rise 9.8% to $1.7 billion in 2015.
Online spending by the automakers is expected to jump 33.7% to $7.4 billion in 2015, dwarfing TV spending for the second straight year.
Dealers' broadcast spending is expected to drop for the third straight year in 2015 to $1.3 billion. Cable spending is expected to be down 0.5% to $$718 million. Online spending is expected to jump 25% to $15.1 billion.
Zenith Forecasts Drop In TV Ad Spending in U.S.
Media agency sees dollars shifting online
TV Ad Spending Drops 6% in April
Big marketers spending more on digital, according to SMI Data
TV Ad Spending Down 4.5% in Second Quarter
Broadcast networks post gain, according to Kantar Media data
TV Ad Spending Drops in October
Soft upfront leads to lower revenue for broadcast, cable
Magna: TV Ad Spending to Drop 0.9% in 2017
After Olympics, demand remains strong, though viewer patterns cause concern
Digital Expected to Push Global Ad Spending Up
TV still accounts for biggest share of media dollars
SMI: TV Ad Spending Rose 0.4% in February
News networks post big gains covering Trump
U.S. TV Ad Spending To Dip 0.2% in 2015
Media agency Zenith sees gains in 2016, 2017 | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 6,309 |
Q: $n$ such that decimal digits of $2^n$ begins with $n$ Are there infinitely many $n$ such that the decimal expansion $2^n$ begins with $n$?
For example, $2^6=64$ and $2^{10} =1024$.
It can easily be shown that this problem is equivalent to the following.
Are there infinitely many $n$ such that
$\{n\log_{10}2-\log_{10}n\}<\log_{10}{(1+\frac{1}{n})}$?
Here, $\{x\}=x-[x]$, where [x] denotes the largest integral number that is smaller than $x$.
More generally, for $\alpha,\beta,\gamma > 0$, are there infinitely many $n$ such that
$\{\alpha n - \beta \log n\}<\frac{\gamma}{n}$?
I think it would help if I know something about the distribution of $\{\log n\}$.
A: Some general information on the problem, which is probably open.
As pointed out by Ivan Neretin at math.stackexchange, this is OEIS A100129. There you can find the first 16 numbers with this property.
According to this paper,
*
*Jan van de Lune, "A note on a problem of Erdős" (1978)
the problem goes back to Erdős:
"Recently my attention was drawn to the following observation made by
P. Erdős: $2^6=64$ and $2^{10}=1024$. Here we have two examples of the
phenomenon that the number $2^n$ starts with the same ordered sequence
of digits as the natural number $n$ itself."
The characterization used in van de Lune's calculations is
$$0\leq \{n\log 2\}-\{\log n\}<\log(n+1)-\log n$$
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 6,888 |
\section{Introduction}
A Banach space $X$ is said to have the Daugavet property if every rank-one operator $T:X\longrightarrow X$ satisfies the equality
\begin{equation}\label{ecuadauga}
\Vert T+I\Vert=1+\Vert T\Vert,
\end{equation}
where $I$ denotes the identity operator. The previous equality is known as \emph{Daugavet equation} because I.~Daugavet proved in \cite{dau} that every compact operator on $\mathcal C([0,1])$ satisfies (\ref{ecuadauga}). Since then, many examples of Banach spaces enjoying the Daugavet property have appeared. E.g. $\mathcal C(K)$ for a perfect compact Hausdorff space $K$; $L_1(\mu)$ and $L_\infty(\mu)$ for a non-atomic measure $\mu$; or preduals of Banach spaces with the Daugavet property (see \cite{kkw,kssw,wer} and references therein for a detailed treatment of the Daugavet property).
In \cite[Section 6]{wer} it is asked whether the space ${\mathrm{Lip}}_0([0,1]^2)$ of Lipschitz functions over the unit square enjoys or not the Daugavet property. A positive answer was given in \cite{ikw}, where it was shown, among other results, that ${\mathrm{Lip}}_0(M)$ has the Daugavet property whenever $M$ is a length metric space.
Here we prove the converse implication, thus obtaining our main theorem (Theorem~\ref{caracolocal}) which completely characterises those complete metric spaces $M$ such that ${\mathrm{Lip}}_0(M)$ has the Daugavet property.
As a consequence of Theorem~\ref{caracolocal} we also get that the space ${\mathrm{Lip}}_0(M)$ has the Daugavet property if, and only if, its canonical predual ${\mathcal F}(M)$ (see the formal definition below) has the Daugavet property, extending the corresponding result in the compact case which was proved in \cite{ikw}.
This paper is organised as follows.
In Section \ref{sec:metric} we introduce necessary definitions and establish several results concerning length and geodesic metric spaces, in particular we show that a complete local space is a length space. We also study sufficient conditions for a metric space to be geodesic.
Section \ref{sec:daugavet} is devoted to the proof of the main theorem, the charaterisation of Lipschitz free spaces and spaces of Lipschitz functions with the Daugavet property.
Section \ref{sec:exposed} includes a characterisation of strongly exposed points in $\closedball{{\mathcal F}(M)}$ (Theorem~\ref{th:charstrexp}).
We use this result to prove in Corollary \ref{caracompa} that, when $M$ is compact, the Daugavet property of ${\mathcal F}(M)$ is equivalent to the absence of strongly exposed points of $\closedball{{\mathcal F}(M)}$.
It is not clear whether the absence of strongly exposed points of $\closedball{{\mathcal F}(M)}$ implies in general that $M$ is a length space.
In the first part of Section~\ref{sec:remarks} we gather some partial evidence to support such a conjecture.
In the second part of Section~\ref{sec:remarks} we study the Daugavet property in the spaces of vector-valued functions ${\mathrm{Lip}}_0(M,X)$.
This is used to give new examples of spaces of linear bounded operators and of projective tensor products enjoying the Daugavet property.
\textbf{Notation:} Throughout the paper we will only consider real Banach spaces. Given a Banach space $X$, we will denote the closed unit ball and the unit sphere of $X$ by $B_X$ and $S_X$ respectively. We will also denote by $X^*$ the topological dual of $X$.
By a \textit{slice} of the unit ball $B_X$ of a Banach space $X$ we will mean a set of the following form
\[ S(B_X,f,\alpha):=\{x\in B_X:f(x)>1-\varepsilon\}\]
where $f\in S_{X^*}$ and $\alpha>0$. Notice that slices are non-empty relatively weakly open and convex subsets of $B_X$ whose complement is also convex.
Given a metric space $M$ and a point $x\in M$, we will denote by $B(x,r)$ the closed unit ball centered at $x$ with radius $r$.
Let $M$ be a metric space with a distinguished point $0 \in M$.
The couple $(M,0)$ is commonly called a \emph{pointed metric space}.
By an abuse of language we will say only ``let $M$ be a pointed metric space'' and similar sentences.
The vector space of Lipschitz functions from $M$ to $\mathbb R$ will be denoted by ${\mathrm{Lip}}(M)$.
Given a Lipschitz function $f\in {\mathrm{Lip}}(M)$, we denote its Lipschitz constant by
\[ \norm{f}_{L} = \sup\set{ \frac{|f(x)-f(y)|}{d(x,y)} : x,y\in M, x\neq y}. \]
This is a seminorm on ${\mathrm{Lip}}(M)$ which is clearly a Banach space norm on the space ${\mathrm{Lip}}_0(M)\subset {\mathrm{Lip}}(M)$ of Lipschitz functions on $M$ vanishing at $0$.
It is well-known that ${\mathrm{Lip}}_0(M)$ is a dual Banach space, whose canonical predual is the \emph{Lipschitz free space}
\[ \mathcal F(M) : = \overline{\operatorname{span}}\{\delta_x : x\in M\}\subset {\mathrm{Lip}}_0(M)^* \]
where $\delta_x(f):= f(x)$ for every $x\in M$ and $f\in {\mathrm{Lip}}(M)$ (see~\cite{GK,wea}, or~\cite{cdw} for the most elementary proof of this fact).
If $N$ is a dense subset of $M$ then $\mathcal F(N)$ and $\mathcal F(M)$ are isometrically isomorphic Banach spaces as every Lipschitz function on $N$ extends uniquely to a Lipschitz function on $M$ with the same Lipschitz constant.
Thus the results about ${\mathcal F}(M)$ or ${\mathrm{Lip}}_0(M)$ can be stated for \emph{complete} $M$ without any loss of generality.
We finally recall two geometric characterisations of the Daugavet property in terms of the slices of the unit ball. We refer the reader to \cite{kssw,wer} for a detailed proof.
\begin{theorem}\label{caragendauga}
Let $X$ be a Banach space. The following assertions are equivalent:
\begin{enumerate}
\item\label{caragendauga1} $X$ has the Daugavet property.
\item\label{caragendauga2} For every $x\in S_X$, every slice $S$ of $B_X$ and every $\varepsilon>0$ there exists another slice $T$ of the unit ball such that $T\subseteq S$ and such that
$$\Vert x+y\Vert>2-\varepsilon$$
holds for every $y\in T$.
\item\label{caragendauga3} For every $x\in S_X$ and every $\varepsilon>0$ the following equality holds:
$$B_X=\mathop{\overline{\mathrm{conv}}}\nolimits(\{y\in (1+\varepsilon) B_X: \Vert y-x\Vert>2-\varepsilon\} ).$$
\end{enumerate}
\end{theorem}
Note that (\ref{caragendauga3}) is particularly useful in those Banach spaces in which there is not a complete description of the dual space.
\section{Length spaces and geodesic spaces}\label{sec:metric}
\begin{definition}
We will say that a metric space $(M,d)$ is a \emph{length space} if, for every pair of points $x,y \in M$, the distance $d(x,y)$ is equal to the infimum of the length of rectifiable curves joining them. Moreover, if that infimum is always attained then we will say that $M$ is a \emph{geodesic space}.
\end{definition}
These definitions are standard, for more details see e.g.~\cite{BH}. Geodesic spaces and length spaces were considered in~\cite{ikw}, where they are called metrically convex spaces and almost metrically convex spaces, respectively.
The following lemma is well-known and easy to prove, see~\cite{BBI}.
\begin{lemma}\label{lemma:charlength}
Let $(M,d)$ be a complete metric space. Then
\begin{enumerate}[(a)]
\item $M$ is a geodesic space if and only if for every $x,y\in M$ there is $z\in M$ such that $d(x,z)=d(y,z)=\frac{1}{2}d(x,y)$.
\item $M$ is a length space if and only if
for every $x,y \in M$ and for every $\delta>0$ the set
\[
\operatorname{Mid}(x,y,\delta):=B\left (x,\frac{1+\delta}{2}d(x,y)\right ) \cap B\left (y,\frac{1+\delta}{2}d(x,y)\right )
\]
is non-empty.
\end{enumerate}
\end{lemma}
The next definition comes from~\cite{ikw}.
\begin{definition}
A metric space $M$ is said to be \emph{local} if, for every $\varepsilon>0$ and every Lipschitz function $f\colon M\to\mathbb R$ there exist $u\neq v\in M$ such that $d(u,v)<\varepsilon$ and $\frac{f(u)-f(v)}{d(u,v)}>\Vert f\Vert_L-\varepsilon$.
Moreover, $M$ is said to be \emph{spreadingly local} if for every $\varepsilon>0$ and every Lipschitz function $f\colon M\to \mathbb R$ the set
\[ \left\{x\in M : \inf_{\delta>0} \norm{f\upharpoonright_{B(x,\delta)}}_{L}>\norm{f}_{L}-\varepsilon\right\}\]
is infinite.
\end{definition}
It has been proved in~\cite{ikw} that length spaces are spreadingly local and that locality implies spreading locality under compactness assumptions.
But in fact we have the equivalence of the three concepts in general.
\begin{proposition}\label{prop:charlengthspace}
Let $M$ be a complete
metric space. The following are equivalent:
\begin{enumerate}[(i)]
\item\label{it:len1} $M$ is a length space.
\item\label{it:len2} $M$ is spreadingly local.
\item\label{it:len3} $M$ is local.
\end{enumerate}
\end{proposition}
\begin{proof}
\ref{it:len2}$\Rightarrow$\ref{it:len3} is trivial and
\ref{it:len1}$\Rightarrow$\ref{it:len2} was proved in~\cite{ikw}, see the remark after Proposition~2.3.
For the reader's convenience we sketch the main idea.
For a given $f \in \closedball{{\mathrm{Lip}}_0(M)}$ and $\varepsilon>0$ let $x,y \in M$ be such that $f(x)-f(y)\geq (1-\frac{\varepsilon^2}{4}) d(x,y)$.
Let $\varphi:[0,d(x,y)(1+\frac{\varepsilon}2)] \to M$ be a 1-Lipschitz map such that $\varphi(0)=x$ and $\varphi(d(x,y)(1+\frac\varepsilon2)=y$.
Then $f(y)=f(x)+\int_0^{d(x,y)(1+\varepsilon/2)} (f\circ \varphi)'(t)\, dt$ and the integrand has to be larger than $1-\frac\varepsilon2$ in a non-negligible subset $A$ of $[0,(1+\varepsilon/2)d(x,y)]$.
It is immediate to check $\varphi(A)$ satisfies the definition of spreading locality for $\varepsilon$.
To show that \ref{it:len3}$\Rightarrow$\ref{it:len1}, assume that $M$ is not a length space.
Then there exist $x,y \in M$ and $\delta>0$ such that $\operatorname{Mid}(x,y,2\delta)=\emptyset$.
Let us denote $r:=\frac{d(x,y)}2$.
Notice by passing that \[\mathop{\mathrm{dist}}\nolimits(B(x,(1+\delta)r),B(y,(1+\delta)r))\geq \delta r.\]
Let $f_i\colon M \to \mathbb R$ be defined by
\[
f_1(t)=\max\set{r-\frac1{1+\delta}d(x,t),0} \mbox{ and }
f_2(t)=\min\set{-r+\frac1{1+\delta}d(y,t),0}.
\]
Clearly $\norm{f_i}_{L}\leq \frac1{1+\delta}$ so $f=f_1+f_2$ is a Lipschitz function.
Since $f(x)-f(y)=d(x,y)$ we have that $\norm{f}_{L}\geq 1$.
Moreover we have that $\set{z:f_1(z)\neq 0} \subset B(x,(1+\delta)r)$ and
$\set{z:f_2(z)\neq 0} \subset B(y,(1+\delta)r)$.
It follows that if $\frac{f(u)-f(v)}{d(u,v)}>\frac{1}{1+\delta}$ then $u \in B(x,(1+\delta)r)$ and $v \in B(y,(1+\delta)r)$. But then $d(u,v) \geq \delta r$ and so $M$ is not local. This shows that~\ref{it:len3}$\Rightarrow$\ref{it:len1}.
\end{proof}
It is clear from Lemma~\ref{lemma:charlength} that every compact length space is geodesic.
But the compactness is not always needed for this implication to hold.
Indeed, in some particular cases, being a length space automatically implies being a geodesic space.
For instance, this is the case for weak*-closed length subsets of dual Banach spaces. In what follows we wish to study geometric properties of a Banach space $X$ that ensure that every complete length subset is geodesic.
Let us recall that the Kuratowski index of non-compactness of a set $D\subset X$ is given by
\[ \alpha(D) = \inf\left \{\varepsilon>0 : \exists x_1,\dotsc, x_n \in X, D\subset \bigcup_{i=1}^n B(x_i, \varepsilon)\right \}. \]
\begin{proposition}\label{prop:lenghtvsgeodesic} Assume that $\lim_{\delta\to 0}\alpha(\operatorname{Mid}(x,-x,\delta))=0$ for every $x\in S_X$. Let $M$ be a complete subset of $X$. Then if $M$ is a length space, it is a geodesic space.
\end{proposition}
\begin{proof}
Let $x,y \in M$ be given, by scaling and shifting we may assume that $x\in S_X$ and $y=-x$. Using Lemma~\ref{lemma:charlength} there is, for every $n\in \mathbb N$, a point $x_n \in \operatorname{Mid}(x,y,\frac1n)$.
It follows by our hypothesis and by $\operatorname{Mid}(x,y,\frac1{n+1})\subset \operatorname{Mid}(x,y,\frac1n)$ that $\lim_{n\to \infty}\alpha(\{x_k:k\geq n\})=0$.
Therefore for every $\varepsilon>0$ there is $N>0$ such that $\{x_n:n\geq N\}$ can be covered by finitely many balls of radius $\varepsilon$.
This suffices for selecting a Cauchy subsequence. Since $M$ is complete, we have that its limit $z$ belongs to $M$.
It is now clear that $d(x,z)\leq 1$ and $d(y,z)\leq 1$ hence $z$ is a metric midpoint between $x$ and $y$. Now Lemma~\ref{lemma:charlength} gives that $M$ is geodesic.
\end{proof}
The hypothesis of Proposition~\ref{prop:lenghtvsgeodesic} admits the following reformulation in terms of an asymptotic property of the Banach space $X$.
\begin{proposition} Let $x\in S_X$. The following are equivalent:
\begin{enumerate}[(i)]
\item\label{caraamuc1} $\lim_{\delta\to 0} \alpha(\operatorname{Mid}(x,-x,\delta))=0$.
\item\label{caraamuc2} For every $0<t<1$ there is $\delta>0$ and a finite codimensional subspace $Y\subset X$ such that
\[ \inf_{y\in S_Y} \max\{||x+ty||,||x-ty||\}> 1+\delta \]
\end{enumerate}
\end{proposition}
\begin{proof}
Follow the same arguments as in~\cite[Theorem 2.1]{DKRRZ16}.
Let us sketch the main idea for reader's convenience.
If \ref{caraamuc2} fails, then for some $t>0$ and every $\delta>0$ it is easy to construct inductively a $t$-separated sequence in $\operatorname{Mid}(x,-x,\delta)$ showing that $\alpha(\operatorname{Mid}(x,-x,\delta))\geq t/2$.
Conversely, let $t>0$ be given and let $Y$ and $\delta>0$ be as in \ref{caraamuc2}.
Since $\operatorname{Mid}(x,-x,\delta)$ is a ball of an equivalent norm on $X$, Lemma~2.13 of \cite{JLPS} shows that there is a finite dimensional $Z \subset X$ so that
\[
\operatorname{Mid}(x,-x,\delta) \subset (Z \cap \operatorname{Mid}(x,-x,\delta)) + 3(Y \cap \operatorname{Mid}(x,-x,\delta)).
\]
Since we have for every $y \in \sphere{Y}$ that $ty \notin \operatorname{Mid}(x,-x,\delta)$, it follows by convexity that
$Y \cap \operatorname{Mid}(x,-x,\delta)\subset t\closedball{X}$.
Therefore $\alpha(\operatorname{Mid}(x,-x,\delta))\leq 6t$.
\end{proof}
In~\cite{DKRRZ16} the \emph{asymptotic midpoint uniformly convex} spaces (AMUC, for short) were introduced as those Banach spaces in which $\lim_{\delta\to 0}\alpha(\operatorname{Mid}(x,-x,\delta))=0$ uniformly in $x\in S_X$, or, in other words, the same $\delta>0$ works for all $x\in S_X$ in the condition \ref{caraamuc2} above. I.e. for every $0<t<1$ there is $\delta>0$ such that
\[ \inf_{x\in S_X}\sup_{\dim X/Y <\infty}\inf_{y\in S_Y} \max\{||x+ty||,||x-ty||\}\geq 1+\delta. \]
In particular, every AUC space is also AMUC.
It is clear that if
\begin{equation}\label{e:MLUR}
\lim_{\delta\to 0}\operatorname{diam}(\operatorname{Mid}(x,-x,\delta))=0 \mbox{ for every } x \in S_X
\end{equation}
then the hypothesis of Proposition~\ref{prop:lenghtvsgeodesic} is satisfied.
The norms which satisfy \eqref{e:MLUR} are called \emph{midpoint locally uniformly rotund} (MLUR).
For example, one can easily see that LUR norms are MLUR (see~\cite[Proposition 5.3.27]{Megginson}).
We are going to resume these comments into the following corollary.
\begin{corollary}
A complete length subset $M$ of a Banach space $X$ is geodesic if any of the following conditions is satisfied:
\begin{itemize}
\item[a)] $X=Y^*$ for some Banach space $Y$ and $M$ is w$^*$-closed (in particular if $M$ is a compact)
\item[b)] $X$ is AMUC (in particular if $X$ is AUC, for example $X=\ell_p$, $1\leq p <\infty$)
\item[c)] $X$ is MLUR (in particular if $X$ is LUR).
\end{itemize}
\end{corollary}
To conclude this section we are going to discuss another metric notion, the property (Z), which is (formally) weaker than being a length space. It was introduced in~\cite{ikw} in order to characterise metrically the local metric spaces in the compact case. We will show in Section~\ref{sec:exposed} that property (Z) characterises the absence of strongly exposed points in $B_{\mathcal F(M)}$.
\begin{definition}\label{d:propertyZ} A metric space $M$ has \emph{property (Z)} if, for every $x,y\in M$ and $\varepsilon>0$, there is $z\in M\setminus\{x,y\}$ satisfying
\[ d(x,z)+d(z,y)\leq d(x,y) + \varepsilon\min\{d(x,z),d(z,y)\} \]
\end{definition}
It is proved in~\cite{ikw} that every local metric space has property (Z), and that the converse statement holds in the compact case. Note that the former also follows immediately from Proposition~\ref{prop:charlengthspace} and Lemma~\ref{lemma:charlength}.
Moreover, it is also shown in~\cite{ikw} that every compact subset of a smooth LUR Banach space with property (Z) is convex. As a consequence of Proposition~\ref{prop:charlengthspace} we have the following:
\begin{corollary} Let $M$ a compact metric space with property (Z). Then $M$ is a geodesic space. If moreover $M$ is a subset of a rotund Banach space then $M$ is convex.
\end{corollary}
\begin{proof} It has been proved in~\cite[Proposition 2.8]{ikw} that a compact metric space with property (Z) is local. Thus the first statement above follows from Proposition~\ref{prop:charlengthspace} and the fact that every compact length space is geodesic. Finally, it is easy to show that every geodesic subset of a rotund Banach space is convex.
\end{proof}
Lemma~\ref{lemma:charlength} says that the complete geodesic spaces are those for which every pair of points has a metric midpoint. However, such characterisation can still be weakened by using the concept of \emph{metric segment}. Given a metric space $M$ and a pair of points $x,y\in M, x\neq y$, we consider the \textit{metric segment joining $x$ and $y$} as the following set:
\[ [x,y]:=\{z\in M: d(x,z)+d(z,y)=d(x,y)\}.\]
\begin{proposition}\label{p:GeneralStandard}
Let $M$ be a complete metric space. Then $M$ is geodesic if, and only if, for each couple $x\neq y \in M$ there is $z\in [x,y]\setminus \set{x,y}$.
\end{proposition}
\begin{proof}
Let $x\neq y \in M$ and assume, with no loss of generality, that $d(x,y)=1$. We show that there is an isometry $\phi:[0,1] \to M$ such that $\phi(0)=x$ and $\phi(1)=y$.
We will do this by Zorn lemma. To this end we consider the set $\mathcal A$ of all $(A,\psi)$ where $\set{0,1} \subset A \subset [0,1]$ is closed and $\psi:A \to X$ is an isometry such that $\psi(0)=x$, $\psi(1)=y$, together with the following partial order ``$\leq$'' on $\mathcal A$: $(A,\psi)\leq (B,\xi)$ if $A\subset B$ and $\xi\upharpoonright_A=\psi$.
Now every chain $(A_i,\psi_i)_{i\in I}$ admits an upper bound. Indeed, take $A=\overline{\bigcup_{i\in I}A_i}$ and $\psi(x):=\psi_i(x)$ if $i \in A_i$. This is an isometry on $\bigcup_{i \in I}A_i$, therefore, since $M$ is complete, it extends uniquely to an isometry on the closure.
Now, let $(A,\phi) \in \max \mathcal A$. If $A\neq [0,1]$ then there are $a<b$ such that $a,b \in A$ and $]a,b[ \cap A=\emptyset$.
By the hypothesis there exists $z \in M$ such that $d(\phi(a),z)+d(\phi(b),z)=d(\phi(a),\phi(b))$. We can define $\phi(a+d(\phi(a),z)):=z$ which is easily seen to be an isometry contradicting the maximality of $(A,\phi)$.
\end{proof}
\section{Metric characterisation of the Daugavet property in Lipschitz-free Banach spaces}\label{sec:daugavet}
We start with an auxiliary result, inspired by~\cite[Theorem 3.1]{pr}.
\begin{proposition}\label{t:circular}
Let $M$ be a pointed metric space. The following assertions are equivalent:
\begin{enumerate}[(i)]
\item\label{hola1} $\mathcal F(M)$ has the Daugavet property.
\item\label{hola2} For each $\varepsilon>0$, each finite subset $N \subset M$ and each norm-one Lipschitz function $g\colon M\longrightarrow \mathbb R$ there are points $u,v \in M$, $u \neq v$, such that $\frac{g(u)-g(v)}{d(u,v)}>1-\varepsilon$ and that
every $1$-Lipschitz function $f\colon N \to \mathbb R$ admits an extension $\tilde{f}:M \to \mathbb R$ which is $(1+\varepsilon)$-Lipschitz and satisfies $\tilde{f}(u)-\tilde{f}(v)\geq d(u,v)$.
\item\label{hola3} For each finite subset $N\subseteq M$ and $\varepsilon>0$, there exist $u,v\in M, u\neq v$, such that
\begin{equation}\label{carametridauga}(1-\varepsilon)(d(x,y)+d(u,v))\leq d(x,u)+d(y,v)
\end{equation}
holds for all $x,y \in N$. Moreover, if we define $A:=\{(u,v)\in M^2\setminus \Delta: \mbox{(\ref{carametridauga}}) \mbox{ holds} \}$, where $\Delta:=\{(x,x)\in M^2: x\in M\}$, then
\[\left\{\frac{\delta_u-\delta_v}{d(u,v)}: (u,v)\in A\right\}\]
is norming for ${\mathrm{Lip}}_0(M)$.
\end{enumerate}
\end{proposition}
For the proof of the Proposition~\ref{t:circular} we will need the following lemma.
\begin{lemma}\label{lemanormante}
Let $X$ be a Banach space with the Daugavet property and let $V\subseteq S_X$ be a norming subset for $X^*$. Then, given $x_1,\ldots, x_n\in S_X$, $\varepsilon>0$ and a slice $S$ of $B_X$, there exists $v\in V\cap S$ such that
\[\Vert x_i+ v\Vert>2-\varepsilon\]
holds for every $i\in\{1,\ldots, n\}$.
\end{lemma}
\begin{proof}
Since $X$ has the Daugavet property then, using $n$-times Theorem~\ref{caragendauga}, we can find a slice $T\subseteq S$ of $B_X$ such that for every $y\in T$ one has
\[\Vert x_i+y\Vert>2-\varepsilon\]
for every $i\in\{1,\ldots, n\}$. Since $V$ is norming for $X^*$ it follows from an easy application of Hahn-Banach theorem that $\overline{\mathop\mathrm{conv}}(V)=B_X$. Thus $\overline{\mathop\mathrm{conv}}(V)\cap T\neq \emptyset$ and so $V\cap T\neq \emptyset$, which concludes the proof.
\end{proof}
\begin{proof}[Proof of Proposition~\ref{t:circular}]
\ref{hola2}$\Rightarrow$\ref{hola1}:
Let $\mu \in S_{{\mathcal F}(M)}$, $g\in \sphere{{\mathrm{Lip}}_0(M)}$ and $\varepsilon>0$. We suppose as we may that $N=supp(\mu) \cup \set{0}$ is finite.
By~\ref{hola2} we can find $u,v\in M, u\neq v$ such that $\frac{g(u)-g(v)}{d(u,v)}>1-\varepsilon$.
Moreover if $f \in \closedball{{\mathrm{Lip}}_0(M)}$ is such that $\duality{f,\mu}=\norm{\mu}$ there exists $\tilde{f}\in {\mathrm{Lip}}_0(M)$ such that $f=\tilde{f}$ on $N$, $\tilde{f}(u)-\tilde{f}(v)\geq d(u,v)$ and $\norm{\tilde{f}}_L\leq 1+\varepsilon$.
Now
\[
\left\Vert\frac{\delta_u-\delta_v}{d(u,v)}+\mu \right\Vert\geq \frac{\frac{\tilde{f}(u)-\tilde{f}(v)}{d(u,v)}+\tilde{f}(\mu)}{1+\varepsilon}\geq\frac{1+\Vert \mu\Vert}{1+\varepsilon}.
\]
It follows that $\norm{Id+g\otimes\mu}\geq\norm{\frac{\delta_u-\delta_v}{d(u,v)}+\duality{g,\frac{\delta_u-\delta_v}{d(u,v)}}\mu}\geq 2-3\varepsilon$
so we conclude that $\mathcal F(M)$ has the Daugavet property, as desired.\\
\iffalse
Pick finitely-supported measures $\mu_1,\ldots, \mu_n\in S_{\mathcal F(M)}$, $\varepsilon>0$ and a slice $S(B_{\mathcal F(M)},g,\alpha)$ for suitable $g\in \mathcal F(M)^*={\mathrm{Lip}}_0(M)$ and $\alpha>0$.
Define $N:=\{0\} \cup \bigcup\limits_{i=1}^n supp(\mu_i)$, which is a finite subset of $M$.
For each $i\in\{1,\ldots, n\}$ we can find $g_i\in S_{{\mathrm{Lip}}_0(N)}$ such that $g_i(\mu_i)=\Vert \mu_i\Vert$.
By~\ref{hola2} we can find $u,v\in M, u\neq v$ such that $\frac{g(u)-g(v)}{d(u,v)}>1-\alpha$ and that, for each $i\in\{1,\ldots, n\}$, there exists $f_i\in {\mathrm{Lip}}_0(M)$ such that $f_i=g_i$ on $N$, $f_i(u)-f_i(v)\geq d(u,v)$ and $\Vert f_i\Vert\leq 1+\varepsilon$.
Pick $i\in\{1,\ldots, n\}$.
Now
\[
\left\Vert\mu_i+\frac{\delta_u-\delta_v}{d(u,v)} \right\Vert\geq \frac{f_i(\mu_i)+\frac{f_i(u)-f_i(v)}{d(u,v)}}{1+\varepsilon}>\frac{g_i(\mu_i)+1}{1+\varepsilon}=\frac{\Vert \mu_i\Vert+1}{1+\varepsilon}.
\]
Moreover, the condition $\frac{g(u)-g(v)}{d(u,v)}>1-\alpha$ implies that $\frac{\delta_u-\delta_v}{d(u,v)}\in S$, so we conclude that $\mathcal F(M)$ has the Daugavet property, as desired.\\
\fi
\ref{hola1}$\Rightarrow$\ref{hola3}: Let $N\subseteq M$ be finite and $\varepsilon>0$. Since $\mathcal F(M)$ has the Daugavet property we can find, using Proposition~\ref{lemanormante}, for every $g\in \sphere{{\mathrm{Lip}}_0(M)}$ and every $\alpha>0$ two elements $u\neq v\in M$ such that $\frac{\delta_u-\delta_v}{d(u,v)}\in S(B_{\mathcal F(M)},g,\alpha)$ and that
\[
\left\Vert \frac{\delta_x-\delta_y}{d(x,y)}+ \frac{\delta_u-\delta_v}{d(u,v)} \right\Vert>2-\varepsilon,
\]
holds for every $x\neq y\in N$.
By an easy convexity argument (see the proof of~\cite[Theorem 3.1]{pr} for details) we conclude that
\[(1-\varepsilon)(d(x,y)+d(u,v))<d(x,v)+d(u,y)\]
holds for every $x\neq y\in N$. In addition, since $g\in S_{{\mathrm{Lip}}_0(M)}$ and $\alpha>0$ were arbitrary we conclude that the set \[\left\{\frac{\delta_u-\delta_v}{d(u,v)}: (u,v)\in A\right\}\]
is norming for ${\mathrm{Lip}}_0(M)$, as desired.\\
\ref{hola3}$\Rightarrow$\ref{hola2}: Let $N \subset M$ finite, $g\in S_{{\mathrm{Lip}}_0(M)}$ and $\varepsilon>0$ be given.
By the assumptions, there are $u,v \in M$, $u\neq v$, such that $\frac{g(u)-g(v)}{d(u,v)}>1-\varepsilon$ and
\[
\frac{1}{1+\varepsilon}(d(x,y)+d(u,v))\leq d(x,u)+d(y,v)
\]
for all $x,y \in N$.
Given a $1$-Lipschitz function $f$ on $N$ we define $\displaystyle\tilde{f}(u)=\inf_{x\in N} f(x)+(1+\varepsilon)d(x,u)$, $\displaystyle\tilde{f}(v)=\sup_{x\in N\cup\{u\}} \displaystyle\tilde{f}(x)-(1+\varepsilon)d(x,v)$.
Clearly $\tilde{f}$ is $(1+\varepsilon)$-Lipschitz on $N \cup \{u,v\}$ so it admits an $(1+\varepsilon)$-Lipschitz extension to the whole of $M$.
It can be easily seen that $\tilde{f}(u)-\tilde{f}(v)\geq d(u,v)$ (see the proof of~\cite[Theorem 3.1]{pr} for details) so the proof is finished.\end{proof}
The main result of the present article is the following theorem. It improves~\cite[Theorem 3.3]{ikw} where the equivalence between points ii) and iii) is proved for $M$ compact.
\begin{theorem}\label{caracolocal} Let $M$ be a complete pointed metric space. The following assertions are equivalent:
\begin{enumerate}[(i)]
\item\label{caracolocal1} $M$ is a length space.
\item\label{caracolocal2} ${\mathrm{Lip}}_0(M)$ has the Daugavet property.
\item\label{caracolocal3} $\mathcal F(M)$ has the Daugavet property.
\end{enumerate}
\end{theorem}
In order to prove Theorem~\ref{caracolocal} we will consider for every $x,y\in M$, $x\neq y$, the function
\[f_{xy}(t):= \frac{d(x,y)}{2}\frac{d(t,y)-d(t,x)}{d(t,y)+d(t,x)}.\]
The properties collected in the next lemma have been proved already in~\cite{ikw2}. They make of $f_{xy}$ a useful tool for studying the geometry of $B_{\mathcal F(M)}$.
\begin{lemma}\label{lemma:IKWfunction} Let $x,y\in M$ with $x\neq y$. We have
\begin{enumerate}[(a)]
\item $\frac{f_{xy}(u)-f_{xy}(v)}{d(u,v)} \leq \frac{d(x,y)}{\max\{d(x,u)+d(u,y),d(x,v)+d(v,y)\}}$ for all $u\neq v \in M$.
\item $f_{xy}$ is Lipschitz and $\norm{f_{xy}}_{L}\leq 1$.
\item Let $u\neq v \in M$ and $\varepsilon>0$ be such that $\frac{f_{xy}(u)-f_{xy}(v)}{d(u,v)}>1-\varepsilon$. Then
\[(1-\varepsilon)\max\{d(x,v)+d(y,v),d(x,u)+d(y,u)\}< d(x,y).\]
\item If $u\neq v \in M$ and $\frac{f_{xy}(u)-f_{xy}(v)}{d(u,v)}=1$, then $u,v\in [x,y]$.
\end{enumerate}
\end{lemma}
\begin{proof}
Statement (a) follows from the next easily proved fact (see~\cite{ikw2}): Given $u_1,v_1,u_2,v_2>0$, we have
\begin{equation*}
\left| \frac{u_1-v_1}{u_1+v_1} - \frac{u_2-v_2}{u_2+v_2}\right| \leq 2\frac{\max\{|u_1-u_2|,|v_1-v_2|\}}{\max\{u_1+v_1,u_2+v_2\}}.
\end{equation*}
Finally, the statements (b),(c) (resp.\ (d)) are a straightforward consequence of~(a) (resp.\ (c)).
\end{proof}
We will need one more lemma, which is an extension of Lemma 3.2 in~\cite{ikw}.
\begin{lemma}\label{lemalocal} Assume that $\mathcal F(M)$ has the Daugavet property. Then for every $x,y\in M$ and every function $f\in S_{{\mathrm{Lip}}_0(M)}$ such that $f(x)-f(y)> (1-\varepsilon)d(x,y)$ there exist $u,v\in M$ such that $f(u)-f(v)> (1-\varepsilon)d(u,v)$ and $d(u,v)<\frac{\varepsilon}{(1-\varepsilon)^2}d(x,y)$.
\end{lemma}
\begin{proof}
Let us consider the following functions:
\[ f_1 = f, f_2(t)=d(y,t), f_3(t)=-d(x,t), f_4(t)=f_{xy}(t) \]
We have $f_1(x)-f_1(y)> (1-\varepsilon)d(x,y)$ and $f_i(x)-f_i(y)=d(x,y)$ for $i=2,3,4$. Moreover, clearly $\norm{f_i}_{L}=1$ for $i=1,2,3$, and $\norm{f_4}_{L}=1$ as a consequence of Lemma~\ref{lemma:IKWfunction}. Consider the function $g=\frac{1}{4}\sum_{i=1}^4 f_i$. First notice that
\[ 1\geq \norm{g}_{L}\geq \frac{1}{4} \sum_{i=1}^4 \frac{f_i(x)-f_i(y)}{d(x,y)} > 1-\frac{\varepsilon}{4}. \]
Now, the characterization given in Proposition~\ref{t:circular} provides $u,v$ in $M$ such that
\begin{equation}\label{eq:e}(1-\varepsilon)(d(x,y)+d(u,v))\leq \min\{d(x,u)+d(y,v),d(x,v)+d(y,u)\}
\end{equation}
and $g(u)-g(v) > (1-\frac{\varepsilon}{4})d(u,v)$, that is,
\[ \frac{1}{4}\sum_{i=1}^4 (f_i(u)-f_i(v)) > \left(1-\frac{\varepsilon}{4}\right )d(u,v) \]
Notice that each of these summands is less or equal than $d(u,v)$. Thus, we get
\begin{equation*}\label{eq:3.4}
\min\{f_i(u)-f_i(v):i\in\{1,2,3,4\}\}>(1-\varepsilon)d(u,v)
\end{equation*}
The case $i=1$ gives us $f(u)-f(v)> (1-\varepsilon)d(u,v)$. Moreover, the cases $i=2,3$ yield
\begin{equation}\label{eq:b}\min\{d(y,u)-d(y,v),d(x,v)-d(x,u)\}>(1-\varepsilon)d(u,v).
\end{equation}
By Lemma~\ref{lemma:IKWfunction} and the case $i=4$ we have
\begin{equation}\label{eq:d}
(1-\varepsilon)\max\{d(x,v)+d(y,v),d(x,u)+d(y,u)\}< d(x,y).
\end{equation}
The above inequalities yield
\begin{align*}
\frac{d(x,y)}{1-\varepsilon}&\mathop{>}\limits^{\mbox{(\ref{eq:d})}} d(x,u)+d(y,u)\\
&\mathop{>}\limits^{\mbox{(\ref{eq:b})}} d(x,u)+d(y,v)+(1-\varepsilon)d(u,v)\\
&\mathop{\geq}\limits^{\mbox{(\ref{eq:e})}} (1-\varepsilon)(d(x,y)+d(u,v))+(1-\varepsilon)d(u,v)
\end{align*}
and so
\[2(1-\varepsilon)d(u,v)< \left(\frac{1}{1-\varepsilon}-(1-\varepsilon)\right)d(x,y) = \frac{\varepsilon(2-\varepsilon)}{1-\varepsilon}d(x,y) < \frac{2\varepsilon}{1-\varepsilon}d(x,y) \]
as desired.
\end{proof}
\begin{proof}[Proof of Theorem~\ref{caracolocal}]
\ref{caracolocal1}$\Rightarrow$\ref{caracolocal2} was proved in~\cite[Theorem 3.1]{ikw}, but let us include a sketch of the proof for completeness. So assume that $M$ is a length space. Then by Proposition~\ref{prop:charlengthspace} $M$ is spreadingly local. In order to prove that ${\mathrm{Lip}}_0(M)$ has the Daugavet property we will apply Theorem~\ref{caragendauga} (\ref{caragendauga3}), so we will prove that, for each $f,g\in S_{{\mathrm{Lip}}_0(M)}$ and every $\varepsilon>0$ we have that
\[g\in \mathop{\overline{\mathrm{conv}}}\nolimits\left\{u\in (1+\varepsilon)B_{{\mathrm{Lip}}_0(M)}: \Vert f+u\Vert>2-\varepsilon\right\}.\]
Fix $n\in\mathbb N$. Since $M$ is spreadingly local we can find $r>0$ and $\delta_0>0$ such that, for every $0<\delta<\delta_0$, there are $x_1,y_1,\ldots, x_n,y_n\in M$ such that $d(x_i,y_i)<\delta$, $\frac{f(x_i)-f(y_i)}{d(x_i,y_i)}>1-\varepsilon$ holds for each $i$ and such that $B(x_i,r)\cap B(x_j,r)=\emptyset$ for all $i\neq j$. Now, for every $i\in\{1,\ldots, n\}$ and for $\delta$ small enough, we can define a $(1+\varepsilon)$-Lipschitz function $f_i:M\longrightarrow \mathbb R$ such that $f_i=f$ in $\{x_i,y_i\}$ and $f_i=g$ in $M\setminus B(x_i,r)$. Since $f_i(x_i)-f_i(y_i)=f(x_i)-f(y_i)$ for every $i$ we deduce that
\[f_i\in \left\{u\in (1+\varepsilon)B_{{\mathrm{Lip}}_0(M)}: \Vert f+u\Vert>2-\varepsilon\right\}\]
holds for every $i\in\{1,\ldots, n\}$. On the other hand notice that, given $x\in M$, the set $\{i\in \{1,\ldots, n\}: f_i(x)\neq g(x)\}$ is, at most, a singleton. From the definition of the Lipschitz norm we deduce that
\[\left\Vert g-\frac{1}{n}\sum_{i=1}^n f_i\right\Vert_L\leq \frac{4+2\varepsilon}{n}.\]
Since $n$ was arbitrary we can conclude that
\[ g\in \mathop{\overline{\mathrm{conv}}}\nolimits\left(\left\{u\in (1+\varepsilon)B_{{\mathrm{Lip}}_0(M)}: \Vert f+u\Vert>2-\varepsilon\right\}\right)\]
as desired.
\ref{caracolocal2}$\Rightarrow$\ref{caracolocal3} follows since the Daugavet property passes to preduals.
\ref{caracolocal3}$\Rightarrow$\ref{caracolocal1}. Assume that $\mathcal F(M)$ has the Daugavet property and let us prove that $M$ is a length space.
By Proposition~\ref{prop:charlengthspace} it is enough to show that $M$ is local.
To this end, let $0<\varepsilon<\frac{1}{4}$ and $f\in S_{{\mathrm{Lip}}_0(M)}$ be given. Pick $x\neq y\in M$ such that $\frac{f(x)-f(y)}{d(x,y)}>1-\varepsilon$. From Lemma~\ref{lemalocal} we can find $x_1\neq y_1\in M$ such that $\frac{f(x_1)-f(y_1)}{d(x_1,y_1)}>1-\varepsilon$ and that $d(x_1,y_1)<\frac{\varepsilon}{(1-\varepsilon)^2}d(x,y)$. A new application of Lemma~\ref{lemanormante} yields the existence of $x_2\neq y_2\in M$ such that $\frac{f(x_2)-f(y_2)}{d(x_2,y_2)}>1-\varepsilon$ and that
\[d(x_2,y_2)\leq \frac{\varepsilon}{(1-\varepsilon)^2} d(x_1,y_1)<\left(\frac{\varepsilon}{(1-\varepsilon)^2}\right)^2 d(x,y).\]
Continuing in this fashion we get a pair of sequences $\{x_n\}, \{y_n\}$ in $M$ such that $\frac{f(x_n)-f(y_n)}{d(x_n,y_n)}>1-\varepsilon$ and that
\[d(x_n,y_n)<\left(\frac{\varepsilon}{(1-\varepsilon)^2}\right)^n d(x,y)\]
holds for each $n\in\mathbb N$. Thus $M$ is local as desired.
\end{proof}
\begin{remark} According to \cite[Definition III.1.1]{hww}, a Banach space $X$ is said to be \emph{$L$-embedded} if $X^{**}=X\oplus_1 Z$ for some Banach space $Z\subseteq X^{**}$. In~\cite[Theorem 3.4]{rueda} it is proved that a separable $L$-embedded space $X$ enjoys the Daugavet property if, and only if, so does its topological dual $X^*$.
\iffalse, given a separable $L$-embedded Banach space $X$, then it enjoys the Daugavet property if, and only if, so does its topological dual $X^*$.
\fi
Theorem~\ref{caracolocal} says that free spaces also behave this way. However, notice that $\mathcal F(M)$ is not in general an $L$-embedded space. Indeed, it follows from~\cite{GK} that for example $\mathcal F(c_0)$ is not even complemented in its bidual.
\end{remark}
\begin{remark}
The proof of~\ref{caracolocal1}$\Rightarrow$\ref{caracolocal2} in Theorem~\ref{caracolocal} actually shows that ${\mathrm{Lip}}_0(M)$ satisfies a stronger version of the Daugavet property whenever $M$ is a complete length space. Let us introduce some notation, coming from~\cite{BKSW05}. Given $A\subset X$, we denote by $\mathop\mathrm{conv}_n(A)$ the set of all convex combinations of $n$ elements of $A$. Given $x\in S_X$ and $\varepsilon>0$, we denote
\[
l^+(x,\varepsilon) = \{y\in (1+\varepsilon)B_X : ||x+y||>2-\varepsilon\}.
\]
The space $X$ is said to have the \emph{uniform Daugavet property} if
\[\lim_{n\to\infty} \sup_{x,y\in S_X} d(y, \mathop\mathrm{conv}_n(l^+(x,\varepsilon)) = 0\]
for every $\varepsilon>0$. In~\cite{BKSW05} is proved that $X$ has the uniform Daugavet property if and only if the ultrapower $X_{\mathcal U}$ has Daugavet property for every free ultrafilter $\mathcal U$ on $\mathbb N$. They also showed that $C(K)$ with $K$ perfect and $L_1[0,1]$ have the uniform Daugavet property. Moreover, Becerra and Martin proved in~\cite{BM06} that the Daugavet and the uniform Daugavet properties are equivalent for Lindenstrauss spaces. That is also the case for spaces of Lipschitz functions. Indeed, the proof of~\ref{caracolocal1}$\Rightarrow$\ref{caracolocal2} in Theorem~\ref{caracolocal} yields that, given $f,g\in S_{{\mathrm{Lip}}_0(M)}$, $n\in \mathbb N$ and $\varepsilon>0$, we have
\[ d(g, \mathop\mathrm{conv}_n(l^+(f,\varepsilon)) \leq \frac{4+2\varepsilon}{n} \]
which goes to $0$ as $n\to \infty$. As a consequence, we get that ${\mathrm{Lip}}_0(M)$ has the Daugavet property if and only if the ultrapower ${\mathrm{Lip}}_0(M)_{\mathcal U}$ has the Daugavet property for every free ultrafilter $\mathcal U$ on $\mathbb N$.
\end{remark}
\section{Extremal structure of the free spaces with Daugavet property}\label{sec:exposed}
Recall that, given a Banach space $X$, a point $x\in S_X$ is said to be a \emph{strongly exposed point} of $B_X$ if there is $f\in S_{X^*}$ such that every sequence $\{x_n\}$ in $B_X$ with $\lim_n f(x_n)=f(x)$ is norm convergent to $x$. Equivalently, the slices of $B_X$ given by $f$ form a neighbourhood basis for $x$ in $B_X$ in the norm topology. In such a case we say that the functional $f$ \emph{strongly exposes} the point $x$. The set of all strongly exposed points of $\closedball{X}$ will be denoted $\strexp{\closedball{X}}$.
In what follows we will first characterise the strongly exposed points of $\closedball{{\mathcal F}(M)}$ which will allow us to characterise the metric spaces $M$ such that the unit ball of the free space ${\mathcal F}(M)$ has a strongly exposed point.
In a general Banach space $X$ the property that $\strexp{\closedball{X}}\neq \emptyset$ is extremely opposite to the Daugavet property.
Our results below yield in particular that for example in the class of free spaces of compact metric spaces these properties are plainly complementary.
For starters, let us reduce the set of possible candidates for a strongly extreme point in $\closedball{{\mathcal F}(M)}$.
\begin{lemma}
Let $M$ be a pointed metric space, then
\[
\strexp{\closedball{{\mathcal F}(M)}} \subset \set{\frac{\delta_x-\delta_y}{d(x,y)}:x\neq y \in M}.
\]
\end{lemma}
\begin{proof}
Assume that $\mu\in \strexp{B_{{\mathcal F}(M)}}$.
The slices of $\closedball{{\mathcal F}(M)}$ determined by the strongly exposing functional form a neighborhood basis of $\mu$ in $\closedball{{\mathcal F}(M)}$ equipped with the norm topology.
By~\cite[Proposition 9.1]{GMZ14}, this condition implies that $\mu$ is a \emph{preserved extreme point}, i.e. $\mu \in \ext{B_{{\mathrm{Lip}}_0(M)^*}}$.
Hence~\cite[Corollary 2.5.4]{wea} yields that $\mu=\frac{\delta_x-\delta_y}{d(x,y)}$ for some $x,y\in M$ with $x\neq y$.
\end{proof}
Let us introduce a bit of notation which will play a central role in the sequel.
\begin{definition}
Let $x\neq y \in M$.
A function $f\in {\mathrm{Lip}}(M)$ is \emph{peaking at $(x,y)$} if $\frac{f(x)-f(y)}{d(x,y)}=1$ and for every open set $U$ of $M^2\setminus\set{(x,x):x\in M}$ containing $(x,y)$ and $(y,x)$, there exists $\delta >0$ such that the condition $(z,t)\notin U$ implies $\frac{|f(z)-f(t)|}{d(z,t)}\leq 1-\delta.$
\end{definition}
This definition is equivalent to: $\frac{f(x)-f(y)}{d(x,y)}=1$ and if $\{u_n\}, \{v_n\}\subset M$, then
\[
\lim\limits_{n\rightarrow +\infty}\frac{f(u_n)-f(v_n)}{d(u_n,v_n)}=1\Rightarrow \lim\limits_{n\rightarrow +\infty} u_n=x \textrm{\ and } \lim\limits_{n\rightarrow +\infty} v_n=y.\]
We will say that $(x,y) \in M^2$ is a \emph{peak couple} if there is a function peaking at $(x,y)$.
Moreover in~\cite[Proposition 2.4.2]{wea} it is proved that if a pair of points $(x,y)$ is a peak couple then $\frac{\delta_x-\delta_y}{d(x,y)}$ is a \emph{preserved extreme point}, that is, an extreme point of $B_{{\mathrm{Lip}}_0(M)^*}$. Below we will give an alternative proof of this fact, showing first that every peak couple corresponds to a strongly exposed point of $B_{\mathcal F(M)}$.
In~\cite[Proposition 2]{dkp} a characterization of peak couples $(x,y)\in M^2$ is given when $M$ is a subset of an $\mathbb R$-tree.
We generalise this characterisation to an arbitrary metric space $M$.
We shall need the following classical notation.
Given $x,y,z \in M$ the \emph{Gromov product of $x$ and $y$ at $z$} is defined as
\[
(x,y)_z:=\frac12(d(x,z)+d(y,z)-d(x,y))\geq 0.
\]
It corresponds to the distance of $z$ to the unique closest point $b$ on the unique geodesic between $x$ and $y$ in any $\mathbb R$-tree into which $\set{x,y,z}$ can be isometrically embedded (such a tree, tripod really, always exists). Notice that $(x,z)_y+(y,z)_x=d(x,y)$ and that $(x,y)_z\leq d(x,z)$ which we will use without further comment.
\begin{definition}
We say that a pair $(x,y)$ of points in $M$, $x\neq y$ satisfies the property (Z) if for every $\varepsilon>0$ there is $z\in M\setminus\{x,y\}$ such that $(x,y)_z\leq \varepsilon\min\{d(x,z),d(y,z)\}$.
\end{definition}
Clearly, $M$ has the property (Z) (see Definition~\ref{d:propertyZ}) if, and only if, each pair of distinct points in $M$ has the property (Z).
We are now ready to give the characterisation of strongly exposed points in $\closedball{\mathcal F(M)}$ involving all the concepts introduced above.
\begin{theorem}\label{th:charstrexp} Let $x,y\in M$, $x\neq y$. The following assertions are equivalent:
\begin{enumerate}[(i)]
\item\label{charstrexp1} $\frac{\delta_x-\delta_y}{d(x,y)}$ is a strongly exposed point of $B_{\mathcal F(M)}$.
\item\label{charstrexp2} There is $f \in {\mathrm{Lip}}_0(M)$ peaking at $(x,y)$, i.e. $(x,y)$ is a peak couple.
\item\label{charstrexp3}
For every $\varepsilon>0$
\begin{equation}\label{e:tang2}
\inf_{u\in M\setminus(\set{x}\cup B(y,\varepsilon))}
\frac{(y,x)_{u}}{(u,y)_x}>0 \mbox{ and } \inf_{u\in M\setminus(\set{y}\cup B(x,\varepsilon))}
\frac{(y,x)_{u}}{(u,x)_y}>0
\end{equation}
(with the convention that $\frac{\alpha}{0}=+\infty$).
\item\label{charstrexp4} The pair $(x,y)$ does not have the property (Z).
\end{enumerate}
\end{theorem}
In the proof we will need the following lemma.
\begin{lemma}\label{lemma:normingsmulyan} Assume that $V\subset S_X$ is a norming subset for $X^*$. Let $v\in V$ and $f\in S_{X^*}$ be so that every sequence $\{v_n\}$ in $V$ with $\lim_n f(v_n)=f(v)$ is norm-convergent to $v$. Then $\norm{\cdot}_{X^*}$ is Fr\'echet-differentiable at $f$. Therefore, $f$ strongly exposes $v$.
\end{lemma}
The classical Smulyan's lemma (see, e.g.~\cite[Theorem 1.4.(ii)]{DGZ93}) states that $f$ strongly exposes a point $x\in S_X$ if and only if $f$ is a point of Fr\'echet differentiability of the norm of $X^*$. The proof of Lemma~\ref{lemma:normingsmulyan} which is a slight modification of the original Smulyan's lemma is left to the reader.
\begin{proof}[Proof of Theorem \ref{th:charstrexp}]
\ref{charstrexp1}$\Rightarrow$\ref{charstrexp2} is clear.
\ref{charstrexp2}$\Rightarrow$\ref{charstrexp1}. Assume that there is $f\in S_{{\mathrm{Lip}}_0(M)}$ peaking at $(x,y)$.
Assume that $\lim_{n\to\infty}\duality{f, \frac{\delta_{u_n}-\delta_{v_n}}{d(u_n,v_n)}} = 1$. Since $f$ peaks at $(x,y)$, we have $\lim_{n\to\infty} d(u_n,x) = \lim_{n\to\infty} d(v_n,y)=0$ and so
$\lim_{n\to\infty}\frac{\delta_{u_n}-\delta_{v_n}}{d(u_n,v_n)}=\frac{\delta_x-\delta_y}{d(x,y)}$.
\iffalse
Therefore
\begin{align*}
\left\lVert\frac{\delta_{u_n}-\delta_{v_n}}{d(u_n,v_n)}-\frac{\delta_x-\delta_y}{d(x,y)}\right\lVert&\leq \left\lVert\frac{\delta_{u_n}-\delta_{v_n}-(\delta_x-\delta_y)}{d(x,y)}\right\lVert\\
& \quad +\left|\frac{1}{d(u_n,v_n)}-\frac{1}{d(x,y)}\right| ||\delta_{u_n}-\delta_{v_n}||\\
&\leq \frac{d(u_n,x)+d(v_n,y)}{d(x,y)}+\left|1-\frac{d(u_n,v_n)}{d(x,y)}\right|
\end{align*}
which tends to $0$ as $n$ goes to $\infty$.
\fi
Thus, recalling that $V=\left\{\frac{\delta_u-\delta_v}{d(u,v)}: u\neq v\in M\right\}$ is norming for ${\mathrm{Lip}}_0(M)$, Lemma~\ref{lemma:normingsmulyan} yields that $\frac{\delta_x-\delta_y}{d(x,y)}$ is strongly exposed by $f$.
\ref{charstrexp2}$\Rightarrow$\ref{charstrexp3}. Assume that there are $\varepsilon>0$ and a sequence $\{u_{n}\}\subset M \setminus (\set{x} \cup B(y,\varepsilon))$ such that
\[
\lim\limits_{n\rightarrow +\infty}\frac{(y,x)_{u_n}}{(u_n,y)_x}=0.
\]
We then clearly have
\[
\lim\limits_{n\rightarrow +\infty}\frac{(y,x)_{u_n}}{d(x,u_n)}=0
\]
since $(u_n,y)_x\leq d(x,u_n)$.
Let $f\in {\mathrm{Lip}}(M)$ be such that $\norm{f}_L=1$ and $\frac{f(x)-f(y)}{d(x,y)}=1$. We may assume that $f(y)=0$ and $f(x)=d(x,y)$.
Consider $b_n$ so that $\{x,y,u_n\}$ embeds isometrically into $\{x,y,u_n,b_n\}$.
Notice that, if we denote $f_n$ the unique $1$-Lipschitz extension of $f\upharpoonright_{\set{x,y,u_n}}$ to $\set{x,y,u_n,b_n}$, then $f_n(b_n)=(u_n,x)_y$ and therefore $\abs{(u_n,x)_y-f(u_n)}\leq (y,x)_{u_n}$.
We have
\begin{align*}
f(x)-f(u_{n})&= (f(x)-(u_n,x)_y)-((u_n,x)_y-f(u_{n}))\\
&=(d(x,y)-(u_n,x)_y)-((u_n,x)_y-f(u_{n}))\\
&\geq (u_n,y)_x-(y,x)_{u_n}\\
&= d(x,u_n)-2(y,x)_{u_n}.
\end{align*}
It follows that
\[
\lim\limits_{n\rightarrow+\infty}\frac{f(x)-f(u_{n})}{d(x,u_{n})}=1.
\]
and so $f$ is not peaking at $(x,y)$ as $(u_n)$ does not converge to $y$.
\ref{charstrexp3}$\Rightarrow$\ref{charstrexp4}. Assume that the pair $(x,y)$ has the property (Z). Then for every $n \in \mathbb N$ there is $z_n \in M\setminus\set{x,y}$ such that $(x,y)_{z_n}\leq \frac1n \min\set{d(x,z_n),d(y,z_n)}$.
Passing to a subsequence and exchanging the roles of $x$ and $y$ we may assume that $d(x,z_n)\leq d(y,z_n)$ for all $n \in \mathbb N$.
We thus have $\displaystyle\frac{(x,y)_{z_n}}{d(x,z_n)} \to 0$ and $d(y,z_n)\geq \frac12d(x,y)$.
Therefore
\[
\inf_{u\in M\setminus(\set{x}\cup B(y,\frac12d(y,x)))}
\frac{(y,x)_{u}}{d(x,u)}=0. \]
Now notice that
\[ \frac{(y,x)_u}{d(x,u)}\geq \frac{(y,x)_u}{2\max\{(u,y)_x, (x,y)_u\}} = \frac{(y,x)_u}{(u,y)_x}\]
whenever the term on the left-hand side is less than $\frac{1}{2}$. It follows that
\[\inf_{u\in M\setminus(\set{x}\cup B(y,\frac12d(y,x)))}
\frac{(y,x)_{u}}{(y,u)_x}=0,
\]
a contradiction.
\ref{charstrexp4}$\Rightarrow$\ref{charstrexp2}. By hypothesis, there is $\varepsilon_0>0$ such that
\[ d(x,z)+d(z,y)>d(x,y)+\varepsilon_0 \min\{d(x,z),d(z,y)\} \]
for every $z\in M\setminus\{x,y\}$.
We will show that $(x,y)$ is a peak couple.
To this end, fix $\varepsilon_1>0$ with $\frac{\varepsilon_1}{1-\varepsilon_1}<\frac{\varepsilon_0}{4}$ and let $f$ be the Lipschitz function defined in~\cite[Proposition 2.8]{ikw}, namely
\[ f(z):=\begin{cases}
\max\left\{\frac{d(x,y)}{2}-(1-\varepsilon_1)d(z,x), 0\right\} & \text{if } d(z,y)\geq d(z,x),\\
& \quad d(z,y)+(1-2\varepsilon_1)d(z,x)\geq d(x,y) \\
-\max\left\{\frac{d(x,y)}{2}-(1-\varepsilon_1)d(z,y), 0\right\} & \text{if } d(z,x)\geq d(z,y),\\
& \quad d(z,x)+(1-2\varepsilon_1)d(z,y)\geq d(x,y)
\end{cases}
\]
which is well defined and satisfies $\norm{f}_{L}=1$, $f(x)-f(y)=d(x,y)$, and
\[ \frac{f(u)-f(v)}{d(u,v)}>1-\varepsilon_1 \text{ implies } \max\{d(x,u),d(y,v)\}<\frac{d(x,y)}{4} \]
for any $u,v\in M$, $u\neq v$ (see the proof of Proposition 2.8 in~\cite{ikw}). Now, take $g=\frac{1}{2}(f+f_{xy})$. We claim that $g$ peaks at $(x,y)$. Indeed, take sequences $\{u_n\}$ and $\{v_n\}$ in $M$ with $\lim_{n\to\infty} \frac{g(u_n)-g(v_n)}{d(u_n,v_n)}=1$. Fix $\varepsilon>0$ and take $0<\gamma<\varepsilon_1$ such that $\frac{\gamma}{1-\gamma}d(x,y)<\varepsilon_0\varepsilon$. Now, take $n_0$ such that
\begin{equation}\label{eq:notzg} \frac{g(u_n)-g(v_n)}{d(u_n,v_n)}>1-\frac{\gamma}{4}
\end{equation}
for every $n\geq n_0$. We will show that $d(x, u_n), d(y, v_n)<\varepsilon$. First, note that~(\ref{eq:notzg}) implies that
\[ \frac{ f(u_n) - f(v_n)}{d(u_n,v_n)} > 1-\frac{\gamma}{2}>1-\varepsilon_1 \]
and so $d(x,u_n), d(y,v_n)<\frac{d(x,y)}{4}$. Therefore $d(x,u_n)<d(y,u_n)$ and $d(y,v_n)<d(x,v_n)$.
Moreover, it also follows from~(\ref{eq:notzg}) that
\[ \frac{f_{xy}(u_n)-f_{xy}(v_n)}{d(u_n,v_n)} > 1-\frac{\gamma}{2}>1-\gamma\]
and so using Lemma~\ref{lemma:IKWfunction} we get $(1-\gamma)\max\{d(x,u_n)+d(y,u_n), d(x,v_n)+d(y,v_n)\}\leq d(x,y)$. This and the hypothesis imposed on the pair $(x,y)$ yield
\[
d(x,y)+\varepsilon_0 d(x, u_n) < d(x,u_n)+d(u_n,y) \leq \frac{1}{1-\gamma} d(x,y).\]
Therefore,
\[ d(x,u_n)\leq \frac{1}{\varepsilon_0}\left(\frac{1}{1-\gamma}-1\right)d(x,y) < \varepsilon \]
for every $n\geq n_0$. Similarly, $d(y, v_n)<\varepsilon$. This shows that $\{u_n\}$ converges to $x$ and $\{v_n\}$ converges to $y$. Thus, $g$ peaks at $(x,y)$ as desired.
\end{proof}
Note that Theorem~\ref{th:charstrexp} generalises~\cite[Proposition 2]{dkp}, where the equivalence between~\ref{charstrexp2} and~\ref{charstrexp3} is proved under the assumption that $M$ is a subset of an $\mathbb R$-tree.
Note that the proof of \ref{charstrexp2}$\Rightarrow$\ref{charstrexp1} in Theorem~\ref{th:charstrexp} actually shows that the following holds:
\begin{corollary} Let $M$ be a pointed metric space, $f\in{\mathrm{Lip}}_0(M)$ and $x,y\in M$, $x\neq y$. Then $f$ peaks at the pair $(x,y)$ if and only if $f$ strongly exposes $\frac{\delta_x-\delta_y}{d(x,y)}$ in $B_{\mathcal F(M)}$.
\end{corollary}
\iffalse
Theorems~\ref{caracolocal} and~\ref{th:charstrexp} allow us to improve~\cite[Theorem 3.3]{ikw}.
\begin{corollary}\label{caracompa}
Let $M$ be a compact metric space. The following assertions are equivalent:
\begin{enumerate}[(i)]
\item\label{caracompa1} ${\mathrm{Lip}}_0(M)$ fails the Daugavet property.
\item\label{caracompa2} The unit ball of $\mathcal F(M)$ has strongly exposed points.
\item\label{caracompa3} There are $x\neq y\in M$ such that $[x,y]=\set{x,y}$
\end{enumerate}
\end{corollary}
\begin{proof}
By Theorem~\ref{caracolocal}, ${\mathrm{Lip}}_0(M)$ fails the Daugavet property if, and only if, $M$ is not a length space, which is in fact equivalent to the fact that $M$ is not local by Proposition~\ref{prop:charlengthspace}. Since $M$ is compact, $M$ is not local if, and only if, $M$ fails the property (Z)~\cite[Proposition 2.8]{ikw}, which is equivalent to the fact that $B_{\mathcal F(M)}$ contains some strongly exposed point by Theorem~\ref{th:charstrexp}. This shows the equivalence between~\ref{caracompa1} and~\ref{caracompa2}.
\ref{caracompa2}$\Rightarrow$\ref{caracompa3}. If $B_{\mathcal F(M)}$ contains some strongly exposed point, say $\mu$, then we know that there is a pair of distinct points $x,y\in M$ such that $\mu=\frac{\delta_x-\delta_y}{d(x,y)}$. Since $\mu$ is a strongly exposed point of the unit ball of $\mathcal F(M)$ then it is in particular an extreme point. It is clear then that $[x,y]=\{x,y\}$.
\ref{caracompa3}$\Rightarrow$\ref{caracompa1}. If ${\mathrm{Lip}}_0(M)$ has the Daugavet property then $M$ is a length space because of Theorem~\ref{caracolocal}, which in turn implies that $M$ is a geodesic space because of compactness of $M$. This condition obviously implies that every segment of $M$ is not trivial, so we are done.
\end{proof}
\fi
In what follows we show that free spaces naturally strengthen their extremal structure. Recall that, given a Banach space $X$, a point $x\in S_X$ is said to be a \emph{weakly exposed point} of $B_X$ if there is an $f\in S_{X^*}$ such that every sequence $\{x_n\}$ in $B_X$ with $\lim_n f(x_n)=f(x)$ is weakly-convergent to $x$. Note that in that case the slices of $B_X$ given by $f$ are neighbourhood basis for $x$ in the weak topology of $B_X$. Thus, every weakly exposed point is also a preserved extreme point.
\begin{proposition}\label{prop:wese} Let $\mu$ be weakly exposed in $B_{{\mathcal F}(M)}$ by $f\in S_{{\mathrm{Lip}}_0(M)}$. Then $\mu$ is strongly exposed by $f$.
\end{proposition}
\begin{proof}
First note that $\mu$ is a preserved extreme point of $B_{\mathcal F(M)}$ and so $\mu = \frac{\delta_x-\delta_y}{d(x,y)}$ for some $x,y\in M$. Now take sequences $\{u_n\}, \{v_n\}$ in $M$ such that $\frac{f(u_n)-f(v_n)}{d(u_n,v_n)}\to 1$. Since $f$ weakly exposes $\mu$ we have that $\frac{\delta_{u_n}-\delta_{v_n}}{d(u_n,v_n)}\stackrel{w}{\to}\mu$. Now, a result by Albiac and Kalton \cite[Lemma 5.1]{AK} ensures that $\{\frac{\delta_{u_n}-\delta_{v_n}}{d(u_n,v_n)}\}$ is norm-convergent to $\mu$. Thus $f$ peaks at $\mu$ and so $\mu$ is strongly exposed by $f$ by Theorem \ref{th:charstrexp}.
\iffalse
Assume that $\mu$ is not a strongly exposed point in order to get a contradiction.
By Theorem~\ref{th:charstrexp} and exchanging the roles of $x$ and $y$ if needed, we get that there is $\varepsilon>0$ and a sequence $\{u_n\}\subset M\setminus (\{x\}\cup B(y,\varepsilon))$ such that $\lim_{n\to\infty} \frac{(y,x)_{u_n}}{(u_n,y)_x}=0$.
Now, the argument given in~\ref{charstrexp2}$\Rightarrow$\ref{charstrexp3} of the proof of Theorem~\ref{th:charstrexp} gives that $\lim_{n\to\infty} \frac{ f(x)-f(u_n)}{d(x,u_n)}=1$ for every function $f\in S_{{\mathrm{Lip}}_0(M)}$ so that $\frac{f(x)-f(y)}{d(x,y)}=1$. In particular, this holds for the function which weakly exposes $\frac{\delta_x-\delta_y}{d(x,y)}$. Therefore, $\frac{\delta_x-\delta_{u_n}}{d(x,u_n)}\stackrel{w}{\to}\frac{\delta_x-\delta_y}{d(x,y)}$. Now take $g$ a Lipschitz function with $g(y)=0$ and $g\upharpoonright_{M\setminus B(y,\varepsilon)}=d(x,y)$. We have that $\frac{g(x)-g(u_n)}{d(x,u_n)} = 0$, whereas $\frac{g(x)-g(y)}{d(x,y)}=1$, a contradiction.
\fi
\end{proof}
As a consequence of Proposition \ref{prop:wese} we get the following:
\begin{corollary} \label{cor:gatfre} Let $M$ be a pointed metric space and $f\in S_{{\mathrm{Lip}}_0(M)}$.
If the norm of ${\mathrm{Lip}}_0(M)$ is G\^ateaux differentiable at $f$, then it is also Fr\'echet differentiable at $f$ (with the derivative $\mu\in {\mathcal F}(M)$ of the form $\mu=\frac{\delta_x-\delta_y}{d(x,y)}$).
\end{corollary}
\begin{proof}
Let us show that if $f \in {\mathrm{Lip}}_0(M)$ does not attain its norm on $B_{{\mathcal F}(M)}$, then $f$ is not a point of G\^ateaux differentiability of the norm $\norm{\cdot}_L$.
Indeed, let $\{x_n\},\{y_n\} \subset M$ be such that $\duality{f,m_{x_ny_n}} \to \norm{f}_L$.
It is enough to show that the functional $g \mapsto \lim \duality{g,m_{x_ny_n}}$ defined on the linear span of $f$ admits two different extensions on ${\mathrm{Lip}}_0(M)$.
First we claim that there is a $g \in {\mathrm{Lip}}_0(M)$ such that $\lim \duality{g,m_{x_ny_n}}$ does not exist.
Indeed, assume that for every $g \in {\mathrm{Lip}}_0(M)$ the limit exists and denote it by $\varphi(g)$.
Then $\varphi \in {\mathrm{Lip}}_0(M)^*$ by the uniform boundedness principle and $\norm{\varphi}\leq 1$.
Now for any two increasing sequences $\{n_k\}$ and $\{m_k\}$ of positive integers we have that $m_{x_{n_k}y_{n_k}}-m_{x_{m_k}y_{m_k}} \to 0$ weakly.
Therefore \cite[Lemma 5.1]{AK} shows that $m_{x_{n_k}y_{n_k}}-m_{x_{m_k}y_{m_k}} \to 0$ in norm.
So $\{m_{x_ny_n}\}$ is norm Cauchy and it follows that $\varphi \in B_{{\mathcal F}(M)}$ which is a contradiction which proves our claim.
Let now $\{n_k\}$ and $\{m_k\}$ be such that $\lim \duality{g,m_{x_{n_k}y_{n_k}}}=\limsup \duality{g,m_{x_ny_n}}$ and $\lim \duality{g,m_{x_{m_k}y_{m_k}}}=\liminf \duality{g,m_{x_ny_n}}$.
It is clear that the Hahn-Banach extensions of these limits are different and they both extend the original limit.
Thus $\norm{\cdot}_L$ is not Gateaux differentiable at the point $f$.
We now assume that the norm is G\^ateaux differentiable at $f$.
By the previous paragraph, the unique norming functional $\mu$ belongs to ${\mathcal F}(M)$.
If $\{\mu_n\}$ is a sequence in $B_{\mathcal F(M)}$ such that $\<f, \mu_n\>\to 1$ then the version of the Smulyan lemma for G\^ateux differentiability (see e.g.\cite[Theorem~1.4.(iv)]{DGZ93}) yields that $\mu_n\stackrel{w}{\to} \mu$ and so $\mu$ is weakly exposed in $B_{{\mathcal F}(M)}$ by $f$. Now apply Proposition \ref{prop:wese} and the version of Smulyan's lemma for Fr\'echet differentiability.
\end{proof}
Finally we show that in free spaces with the Daugavet property there are no preserved extreme points.
\begin{proposition}\label{prop:amcpreserved} Let $M$ be a pointed length space. Then $B_{\mathcal F(M)}$ does not have any preserved extreme point, that is, $\ext{B_{{\mathrm{Lip}}_0(M)^*}}\cap \mathcal F(M) = \emptyset$.\end{proposition}
\begin{proof}
Assume that there is some preserved extreme point of $B_{\mathcal F(M)}$, which must be of the form $\frac{\delta_x-\delta_y}{d(x,y)}$ for some $x,y\in M$, $x\neq y$. Take a sequence $\{u_n\}\subset M$ such that $\max\{d(x,u_n),d(y,u_n)\}\leq \frac{1+1/n}{2} d(x,y)$ for every $n$, which exists since $M$ is a length space. Consider
\[ \mu_n = \frac{2}{1+1/n} \frac{\delta_x-\delta_{u_n}}{d(x,y)}, \quad \nu_n = \frac{2}{1+1/n}\frac{\delta_{u_n}-\delta_y}{d(x,y)}. \]
Then $||\mu_n||,||\nu_n||\leq 1$ and $\frac{\mu_n+\nu_n}{2} \stackrel{\|\hspace*{.35cm}\|}{\to} \frac{\delta_x-\delta_y}{d(x,y)}$. Since $\frac{\delta_x-\delta_y}{d(x,y)}$ is a preserved extreme point, this implies that $\mu_n\stackrel{w}{\to}\frac{\delta_x-\delta_y}{d(x,y)}$~\cite[Proposition 9.1]{GMZ14}. It follows that $\delta_{u_n}\stackrel{w}{\to}\frac{\delta_x+\delta_y}{2}$, which is impossible.
\end{proof}
Note that the previous result proves that, if $M$ is compact, then $\mathcal F(M)$ has the Daugavet property if, and only if, $B_{\mathcal F(M)}$ does not have any preserved extreme point.
\begin{remark}
While preparing the present paper we have learned that Aliaga and Guirao~\cite{AG} have proved that if $M$ is compact and $x,y$ are two distinct points in $M$, then $[x,y]=\{x,y\}$ if and only if the molecule $\frac{\delta_x-\delta_y}{d(x,y)}$ is a preserved extreme point of $B_{\mathcal F(M)}$. This solves in the affirmative the open problem mentioned on page 53 of \cite{wea}. Let us remark that the result does not hold in general when $M$ is not compact. Indeed, in \cite[Example 2.4]{ikw}, a length metric space $M$ is constructed such that $[x,y]=\{x,y\}$ for \emph{all} $x\neq y \in M$.
Despite this, $\closedball{{\mathcal F}(M)}$ has \emph{no} preserved extreme point as is implied by Proposition~\ref{prop:amcpreserved}.
\end{remark}
Let us end the section by giving the following characterisation under compactness assumptions, which improves~\cite[Theorem 3.3]{ikw}.
\begin{corollary}\label{caracompa}
Let $M$ be a pointed compact metric space. The following assertions are equivalent:
\begin{enumerate}[(i)]
\item $M$ is geodesic.
\item For every $x, y\in M$ there is $z\in [x,y]\setminus\{x,y\}$.
\item ${\mathrm{Lip}}_0(M)$ has the Daugavet property.
\item The unit ball of $\mathcal F(M)$ does not have any preserved extreme point.
\item The unit ball of $\mathcal F(M)$ does not have any strongly exposed point.
\item The norm of ${\mathrm{Lip}}_0(M)$ does not have any point of G\^ateux differentiability.
\item The norm of ${\mathrm{Lip}}_0(M)$ does not have any point of Fr\'echet differentiability.
\end{enumerate}
\end{corollary}
\begin{proof}
The equivalence between (i) and (iii) follows from Theorem \ref{caracolocal} and the fact that compact length spaces are geodesic. Moreover, (i)$\Rightarrow$(ii) follows from Lemma \ref{lemma:charlength}. Now, if (ii) holds then every molecule $\frac{\delta_x-\delta_y}{d(x,y)}$ can be written as a non-trivial convex combination as
\[\frac{\delta_x-\delta_y}{d(x,y)} = \frac{d(x,z)}{d(x,y)}\frac{\delta_x-\delta_z}{d(x,z)} + \frac{d(z,y)}{d(x,y)} \frac{\delta_z-\delta_y}{d(z,y)}\]
and so it is not an extreme point of $B_{\mathcal F(M)}$. Since all the preserved extreme points are molecules, (iv) holds.
It is clear that (iv) implies (v). If (v) holds then by Theorem \ref{th:charstrexp} we have that $M$ has property (Z). Since $M$ is compact then Proposition 2.8 in \cite{ikw} says that $M$ is local, and so a length space by Proposition \ref{prop:charlengthspace}. This shows that (v) implies (i). Finally, the equivalence between (v), (vi) and (vii) follows from Corollary \ref{cor:gatfre} and Smulyan's lemma (and holds even in the non-compact case).
\end{proof}
\begin{remark}
Note that the previous corollary means that, whenever $M$ is a pointed compact metric space, then either $\mathcal{F}(M)$ has the Daugavet property or its unit ball is dentable. Such extreme behaviour related to the diameter of the slices of the unit ball does not hold for its dual ${\mathrm{Lip}}_0(M)$. Indeed, in \cite{ivakhno} it is proved that every slice of $B_{{\mathrm{Lip}}_0(M)}$ has diameter two whenever $M$ is unbounded or it is not uniformly discrete.
Consequently $M=[0,1]\cup [2,3]$ is an example of a compact metric space such that every slice of $B_{{\mathrm{Lip}}_0(M)}$ has diameter two but ${\mathrm{Lip}}_0(M)$ fails the Daugavet property.
\end{remark}
\section{Remarks and open questions}\label{sec:remarks}
Corollary \ref{caracompa} motivates the following question.
\begin{question}
Let $M$ be a metric space. If $M$ has the property (Z), is $M$ a length space?
\end{question}
Corollary \ref{caracompa} says that the answer is affirmative when $M$ is compact.
Moreover, the affirmative answer to this problem would imply the following dichotomy for every metric space $M$:
either $\mathcal F(M)$ has the Daugavet property or its unit ball has a strongly exposed point and, in particular, is dentable.
Though we do not know the answer to the previous question in the general case, we can give an affirmative answer in the context of subsets of an $\mathbb R$-tree.
\begin{proposition}\label{(Z)implengthRtree}
Let $T$ be a
real-tree.
Let $M \subset T$ be complete.
If $M$ has (Z), then $M$ is geodesic.
\end{proposition}
In order to prove the previous proposition we need the following result.
\begin{proposition}
Let $M$ be a complete
metric space with property (Z). Then $M$ is connected.
\end{proposition}
\begin{proof}
Let us assume that $U,V \subset M$ are clopen, disjoint and $U \cup V = M$.
Then $U \times V$ is a closed subset of the complete metric space $(M^2,d_1)$ where $d_1((a,b),(c,d))=d(a,c)+d(b,d)$.
Let $\alpha \in (0,1)$.
By the Ekeland's variational principle applied to the function
$d\upharpoonright_{U\times V}$ there is $(x,y) \in U\times V$ such that for every $(u,v) \in U\times V$ we have
\[
d(x,y) \leq d(u,v)+\alpha(d(x,u)+d(y,v)).
\]
Now let $\varepsilon \in (0,1-\alpha)$
and let $z \in M\setminus\set{x,y}$ satisfy (Z) with this $\varepsilon$.
We assume that $z \in V$ and we set $(u,v)=(x,z)$ in the above inequality.
We have
\begin{equation}\label{e:crucial}
\begin{split}
d(x,y)& \leq d(x,z)+\alpha d(y,z)\\
&= d(x,z)+d(y,z)-(1-\alpha)d(y,z)\\
&\leq d(x,y) +\varepsilon \mathop{\mathrm{dist}}\nolimits(z,\set{x,y}) - (1-\alpha) d(y,z)
\end{split}
\end{equation}
This implies that
\[ d(y,z)\leq \frac{\varepsilon}{1-\alpha} d(z,\set{x,y}) < d(z, \set{x,y}) \]
which is a contradiction.
\iffalse
This implies that
$d(y,z) \leq \frac{\varepsilon}{2-\varepsilon}\frac{d(x,y)}{1-\alpha}<\frac{d(x,y)}2$ yielding that $d(y,z)=\mathop{\mathrm{dist}}\nolimits(z,\set{x,y})$.
Substituting this back to \eqref{e:crucial} we get
$(1-\alpha)\leq \varepsilon$ which is a contradiction.
\fi
\end{proof}
This proposition yields immediately that $M$ is perfect (i.e. has no isolated points) whenever $M$ is complete and has (Z).
\begin{proof}[Proof of Proposition \ref{(Z)implengthRtree}]
If $M$ is a connected complete subset of an $\mathbb R$-tree $T$ we get that $M$ is geodesic.
Indeed, for any two points $x,y \in M$ let $\varphi:[0,d(x,y)] \to T$ be the unique 1-Lipschitz map such that $\varphi(0)=x$ and $\varphi(d(x,y))=y$.
We will denote $\pi:T \to \varphi([0,d(x,y)])$ the metric projection onto $\varphi([0,d(x,y)])$.
It is well known to be continuous.
If there is $t \in (0,d(x,y))$ such that $\varphi(t)\notin M$, then by completeness of $M$ there is $\varepsilon>0$ such that $\closedball{T}(\varphi(t),\varepsilon) \cap M =\emptyset$.
Since for every $u \in U=M\cap \pi^{-1}(\varphi([0,t]))$ and every $v \in V=M \cap \pi^{-1}(\varphi((t,d(x,y)]))$
we have $d(u,v)=d(u,\varphi(t))+d(\varphi(t),v)$ it follows that
$\mathop{\mathrm{dist}}\nolimits(U,V)\geq 2\varepsilon$ which is impossible as $M=U\cup V$.
\end{proof}
\iffalse
\begin{lemma}\label{l:Caristi}
Let $M$ be a complete metric space and let us assume that $M$ embeds isometrically into another metric space $N$ (so in fact $M \subset N$).
Then for every $\mu \in N \setminus M$ and every $\alpha \in (0,1)$ there is $x \in M$ such that for every $y \in M \setminus \set{x}$ we have $(x,\mu)_y\geq \alpha (\mu,y)_x$.
\end{lemma}
\begin{proof}
Assume that there are $\mu \in N \setminus M$ and $\alpha \in (0,1)$ such that for every $x \in M$ there exists $T(x) \in M \setminus \set{x}$ with $(x,\mu)_{T(x)} < \alpha (\mu,T(x))_x$.
We then have
\[
\begin{split}
d(x,T(x))&=(\mu,x)_{T(x)}+(\mu,T(x))_x<(1+\alpha)(\mu,T(x))_x\\
&< \frac{1+\alpha}{1-\alpha}\left( (\mu,T(x))_x-(x,\mu)_{T(x)}\right)\\
&=\frac{1+\alpha}{1-\alpha}\left(d(\mu,x)-d(\mu,T(x))\right).
\end{split}
\]
The above inequality means that $d(x,T(x))<f(x)-f(T(x))$ for $f(z):=\frac{1+\alpha}{1-\alpha}d(\mu,z)$, which is clearly l.s.c. (because Lipschitz) on $M$.
By the Caristi's fixed point theorem,
$T$ admits a fixed point which is impossible.
\end{proof}
\begin{proof}[Proof of Proposition (\ref{(Z)implengthRtree})]
Let us assume that $M$ is not geodesic.
Then there are $x,y \in M$ such that $b=\frac{x+y}2 \in T \setminus M$.
We denote $M_{x}=\set{w \in M: \pi(w) \in ]b,x]}$ where $\pi:M \to T$ is the metric projection onto the unique geodesic $[x,y]$ in $T$ which connects $x$ and $y$.
Then $M_{x}$ is closed in $M$.
Indeed, let $(z_n) \subset M_x$ such that $z_n \to z$.
Then $\pi(z_n) \to \pi(z)$ by the continuity of metric projections onto convex sets in real-trees.
Since $d(\pi(z_n),y))>\frac{d(x,y)}{2}$ we have that $d(\pi(z),y)\geq \frac{d(x,y)}{2}$.
If the inequality is strict, $z \in M_x$.
So we may assume that $d(\pi(z),y)=\frac{d(x,y)}2$.
Then $d(z,z_n)=d(z,\pi(z))+d(\pi(z),\pi(z_n))+d(\pi(z_n),z_n)\geq d(z,\pi(z))$.
This implies $d(z,\pi(z))=0$ which shows that $z=b$ which is impossible.
We can thus apply Lemma~\ref{l:Caristi}.
As a result there is $x' \in M_x$ such that we have $(x',b)_z\geq \frac12(b,z)_{x'}$ for every $z \in M_x \setminus \set{x'}$.
Similarly, there is $y' \in M_{y}$ such that $(y',b)_z \geq \frac12(b,z)_{y'}$ for every $z \in M_y \setminus \set{y'}$.
If $M$ has (Z) then for every $\varepsilon>0$ there is $z \in M \setminus \set{x',y'}$ such that
\begin{align*}
(x',y')_z&< \varepsilon\min\set{d(x',z),d(y',z)}\\
&=\varepsilon\min\set{(x',y')_z+(z,y')_{x'},(x',y')_z+(z,x')_{y'}}
\end{align*}
This implies that
\begin{equation}\label{e:both}
(x',y')_z<\frac{\varepsilon}{1-\varepsilon}(z,y')_{x'}\quad \mbox{ and } \quad (x',y')_z<\frac{\varepsilon}{1-\varepsilon}(z,x')_{y'}.
\end{equation}
Now since $M \subset T$, the following is clear:
\[
\begin{split}
z \in M_y &\Longrightarrow (y',x')_z=(y',b)_z \mbox{ and } (b,z)_{y'}=(x',z)_{y'}\\
y \in M_x &\Longrightarrow (y',x')_z=(x',b)_z \mbox{ and } (b,z)_{x'}=(y',z)_{x'}\\
\end{split}
\]
So if one of the above is true we get
\[
\frac{(y',x')_z}{(x',z)_{y'}}\geq \frac12\quad \mbox{ or } \quad \frac{(y',x')_z}{(y',z)_{x'}}\geq \frac12.
\]
which is in contradiction with \eqref{e:both} for small $\varepsilon$.
Thus $\pi(z)=b$ for every $\varepsilon$ small enough.
It follows that $b \in M$ as $M$ is complete.
Contradiction.
\end{proof}
The key lemma from the previous proof has also the following consequence.
\begin{corollary}
If a complete $M$ has property (Z) then $M$ is perfect, i.e. $M$ does not have any isolated point.
\end{corollary}
\begin{proof}
Let us assume that $y \in M$ is isolated. Then $M \setminus \set{y}$ is complete and by Lemma~\ref{l:Caristi} there is $x \in M \setminus \set{y}$ such that for every $u \in M\setminus \set{x,y}$ we have $(x,y)_u\geq \frac12(y,u)_x$.
We readily get that
\[
\inf_{u\notin \set{x}\cup B(y,\varepsilon)} \frac{(x,y)_u}{(u,y)_x}\geq \frac12
\]
for every $\varepsilon>0$.
It remains to check the second infimum in order to apply Theorem \ref{th:charstrexp}.
So let $\varepsilon>0$.
Using the defining property of $x$ we get for every $u\notin \set{y}\cup B(x,\varepsilon)$ that $\varepsilon<d(u,x)=(y,u)_x+(y,x)_u\leq (2+1)(y,x)_u$.
Thus
\[
\frac{(y,x)_u}{(u,x)_y}\geq \frac{(y,x)_u}{d(y,x)}\geq \frac{\varepsilon}{3d(x,y)}.
\]
Hence, by Theorem \ref{th:charstrexp}, $M$ does not have property (Z).
\end{proof}
\fi
Now we will end the section with a problem about the Daugavet property in vector-valued Lipschitz functions spaces, for which we will have to introduce a bit of notation. Given a metric space $M$ and a Banach space $X$, we consider
\[ {\mathrm{Lip}}_0(M,X):=\left\{f\colon M\longrightarrow X: f(0)=0\mbox{ and } \sup\limits_{x\neq y\in M}\frac{\Vert f(x)-f(y)\Vert}{d(x,y)}<\infty\right\}.\]
This space is a Banach space under the norm given by the smallest Lipschitz constant. Note that the space ${\mathrm{Lip}}_0(M,X)$ is isometrically isomorphic to $L(\mathcal F(M),X)$, the space of bounded linear operators from ${\mathcal F}(M)$ to $X$.
\begin{proposition}\label{localvector}
Let $M$ be a length space and let $X$ be a Banach space. Then, for every Lipschitz map $f\colon M\to X$ and every $\varepsilon>0$ there are $x\neq y\in M$ such that $\frac{\Vert f(x)-f(y)\Vert}{d(x,y)}>\Vert f\Vert-\varepsilon$ and that $d(x,y)<\varepsilon$.
\end{proposition}
\begin{proof}
Pick a positive $\varepsilon$, a pair of points $u\neq v\in M$ and $x^*\in S_{X^*}$ such that
\[\frac{x^*(f(u))-x^*(f(v))}{d(u,v)}>\Vert f\Vert-\varepsilon\]
holds. This means that the real Lipschitz function $x^*\circ f$ has Lipschitz norm bigger than $\Vert f\Vert-\varepsilon$. Since $M$ is local we can find $x\neq y\in M$ such that $d(x,y)<\varepsilon$ and that
\[\Vert f\Vert-\varepsilon<\frac{x^*(f(x)-f(y))}{d(x,y)}\leq \frac{\Vert f(x)-f(y)\Vert}{d(x,y)}.\]
Since $\varepsilon>0$ was arbitrary the result follows.
\end{proof}
Let $M$ be a metric space and $X$ be a Banach space. According to~\cite{blr} the pair $(M,X)$ is said to have the \emph{contraction-extension property} if given $N\subseteq M$ and a Lipschitz map $f\colon N\longrightarrow X$, there exists a Lipschitz map $F\colon M\longrightarrow X$ extending $f$ such that
\[\Vert F\Vert_{{\mathrm{Lip}}_0(M,X)}=\Vert f\Vert_{{\mathrm{Lip}}_0(N,X)}.\]
Note that, in the particular case of $M$ being a Banach space, the definition given above agrees with the one given in~\cite{beli}.
Let us give some examples of pairs which have the contraction-extension property. First of all, given a metric space $M$, the pair $(M,\mathbb R)$ has the contraction-extension property (using the infimal convolution formula of McShane-Whitney).
In addition, in~\cite[Chapter 2]{beli} we can find some examples of Banach spaces $X$ such that the pair $(X,X)$ satisfies the contraction-extension property such as Hilbert spaces and $\ell_\infty^n$. Finally, if $Y$ is a strictly convex Banach space such that there exists a Banach space $X$ with $\dim(X)\geq 2$ and verifying that the pair $(X,Y)$ has the contraction-extension property, then $Y$ is a Hilbert space~\cite[Theorem 2.11]{beli}.
Now we can generalise~\ref{caracolocal1}$\Rightarrow$\ref{caracolocal2} in Theorem~\ref{caracolocal} to the vector-valued framework.
\begin{proposition}
Let $M$ be a pointed length space and $X$ be a Banach space such that the pair $(M,X)$ has the contraction-extension property. Then ${\mathrm{Lip}}_0(M,X)$ has the Daugavet property.
\end{proposition}
The proof is identical to the proof of~\ref{caracolocal1}$\Rightarrow$\ref{caracolocal2} in Theorem~\ref{caracolocal} using the contraction-extension property when appropriate.
From the above proposition we get a stability result of the Daugavet property. We will denote by $X\ensuremath{\widehat{\otimes}_\pi} Y$ the projective tensor product of Banach spaces. For a detailed treatment and applications of tensor products, we refer the reader to \cite{rya}.
\begin{corollary}\label{corovector}
Let $M$ be a pointed metric space and $X$ be a Banach space. Then:
\begin{itemize}
\item[(a)] If the pair $(M,X)$ has the contraction-extension property and ${\mathrm{Lip}}_0(M)$ has the Daugavet property then ${\mathrm{Lip}}_0(M,X)=L(\mathcal F(M),X)$ has the Daugavet property.
\item[(b)] If the pair $(M,X^*)$ has the contraction-extension property and $\mathcal F(M)$ has the Daugavet property, then $\mathcal F(M)\ensuremath{\widehat{\otimes}_\pi} X$ has the Daugavet property.
\end{itemize}
\end{corollary}
The question whether the Daugavet property is preserved by projective tensor products from both factors was posed in~\cite{wer}. It remains, to the best of our knowledge, unsolved.
It is known, however, that the Daugavet property can not be preserved by projective tensor products from one factor. Indeed, in~\cite[Corollary~4.3]{kkw} an example of a complex $2$-dimensional Banach space $E$ is given so that $L_\infty^\mathbb C([0,1])\ensuremath{\widehat{\otimes}_\pi} E$ fails to have the Daugavet property (see~\cite[Remark~3.13]{llr} for real counterexamples failing to fulfil much weaker requirements than the Daugavet property). In spite of the previous fact, we get from Corollary~\ref{corovector} that, for a Hilbert space $H$, the space $\mathcal F(H)\ensuremath{\widehat{\otimes}_\pi} H$ has the Daugavet property, a result which we find curious, if nothing else. Moreover, Corollary~\ref{corovector} motivates the following problem.
\begin{question}
Let $M$ be a pointed metric space and $X$ a Banach space. If ${\mathrm{Lip}}_0(M)$ has the Daugavet property, does ${\mathrm{Lip}}_0(M,X)$ or $\mathcal F(M)\ensuremath{\widehat{\otimes}_\pi} X$ have the Daugavet property?
\end{question}
Note that the same problem is open if we replace the Daugavet property with the octahedrality of the norm (see~\cite[Question 2]{blr}).
\section*{Acknowledgements}
The third author is grateful to Departamento de Matem\'aticas de la Universidad de Murcia for the excellent working conditions during his visit in February 2017.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 2,997 |
<html>
<body>
Utility classes for dynamically building LDAP
filters. Filters can be nested and wrapped around each other:
<pre>
AndFilter andFilter = new AndFilter();
andFilter.and(new EqualsFilter("objectclass", "person");
andFilter.and(new EqualsFilter("cn", "Some CN");
OrFilter orFilter = new OrFilter();
orFilter.or(andFilter);
orFilter.or(new EqualsFilter("objectclass", "organizationalUnit));
System.out.println(orFilter.encode());
</pre>
would result in:
<pre>(|(&(objectclass=person)(cn=Some CN))(objectclass=organizationalUnit))</pre>
</body>
</html>
| {
"redpajama_set_name": "RedPajamaGithub"
} | 9,426 |
{"url":"https:\/\/www.numerade.com\/questions\/solve-the-differential-equation-2xy-y-2-sqrt-x\/","text":"\ud83d\udcac \ud83d\udc4b We\u2019re always here. Join our Discord to connect with other students 24\/7, any time, night or day.Join Here!\n\n# Solve the differential equation.$2xy' + y = 2 \\sqrt x$\n\n## $$\\begin{array}{c}{y=\\sqrt{x}+\\frac{C}{\\sqrt{x}}} \\\\ {\\text { Hint: Integrating factor is } \\sqrt{x}}\\end{array}$$\n\n#### Topics\n\nDifferential Equations\n\n### Discussion\n\nYou must be signed in to discuss.\n##### Catherine R.\n\nMissouri State University\n\n##### Kristen K.\n\nUniversity of Michigan - Ann Arbor\n\n##### Michael J.\n\nIdaho State University\n\nLectures\n\nJoin Bootcamp\n\n### Video Transcript\n\nbefore we find the integrating factor, we should divide both sides by two acts in order to get into standard form. Why prime plus y times P of x is Q of axe doing this we have. Why Prime plus y divide by two of acts is one over square root off acts. So now on to the integrating factor, each the integral of one over to axe de acts can be written as each the natural lot of X to the 1\/2 which is the same thing. A squirt of ex each. The natural log is one which means we have squared of acts or extra 1\/2 is our integrating factor. OK, this works out because we now have squared of acts which is our integrating factor. Like I just said, being multiplied by all our terms so you can see I'm doing that right now. I'm multiplying this by all of our terms. Okay, Now that we have this, we know that we have essentially, we're gonna be integrating D of acts on the right hand side. We don't do anything to the left hand side. That remains is why Squared axe now integrating D of X of the same things. Interesting one interpreted. One simply gives us X When we take the integral, we also have to add our seat Constant of integration. Divide both sides by squirt of X to divide all these terms by scores of X, we get why escort of acts plus C divided by square root of X.\n\n#### Topics\n\nDifferential Equations\n\n##### Catherine R.\n\nMissouri State University\n\n##### Kristen K.\n\nUniversity of Michigan - Ann Arbor\n\n##### Michael J.\n\nIdaho State University\n\nLectures\n\nJoin Bootcamp","date":"2021-10-27 10:03:03","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\": 0.8179464340209961, \"perplexity\": 1896.635058458572}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 20, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-43\/segments\/1634323588113.25\/warc\/CC-MAIN-20211027084718-20211027114718-00666.warc.gz\"}"} | null | null |
day: 11
title: Changing IT for the better.
active: true
---
### [Thomas Philipona](https://github.com/phil-pona)
Heute habe ich den [schemaspy](https://github.com/drnoa/schemaspy) um einen TemplateService Test erweitert. Ziel ist es, die Testabdeckung zu erhöhen, damit wir anschliessend refactoren können.
### [Oliver Gugger](https://github.com/guggero)
Habe Version 0.0.3 von [ng-user-auth](https://github.com/puzzle/ng-user-auth) erstellt und das GIT-Repo von meinem eigenen zu dem von Puzzle ITC verschoben. Zudem habe ich mit einer Sample-/Demo-Applikation für das Modul begonnen.
### [Pascal Simon](https://github.com/psunix)
[Cryptopus](https://github.com/puzzle/cryptopus): Es ging weiter mit dem Styling des UIs. Heute war das Login sowie die Navigationsbar an der Reihe.
### [Lorenz Bischof](https://github.com/lbischof)
Dokumentieren wie man Cryptopus in einem Docker Container startet. [pull request](https://github.com/puzzle/cryptopus/pull/33)
### [Martin Gafner](https://github.com/mgafner)
Ich konnte heute selber nichts contributen. Aber dafür hat der Debian Package Manager [micressor](https://github.com/micressor) in den letzten zwei Tagen ein paar Issues von [fadecut](https://github.com/micressor/fadecut) kommentiert und eines konnte er sogar schliessen. Ausserdem hat er das Testing-Framework erweitert. Wir haben uns abgesprochen dass er sich hauptsächlich um die Tests und die Debian Packaging Themen kümmert, während ich weiter an gewünschten Features arbeite.
| {
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} | 765 |
You are always welcome to visit our client service centre, where our Client Services Consultants are on hand to help.
During opening hours, you are also welcome to enjoy the beauty and serenity of our grounds.
Our Customer Care Centre is open Monday to Friday (excluding public holidays). | {
"redpajama_set_name": "RedPajamaC4"
} | 1,691 |
Coroner's Court
Cork residents begin legal action against landlord over 'lockdown parties'
Judge recuses himself from case after locals claim owner failing to control noise at two properties
Fri, Jul 3, 2020, 18:15
Barry Roche
Actions are being brought against landlord Fachtna O'Reilly. Photograph: Cork Courts
A group of residents living near University College Cork have begun legal action against a landlord over what they allege is his failure to control noise at two of his properties where they allege students are holding Covid-19 lockdown parties into the early hours of the morning.
Members of the Magazine Road and Surrounding Areas Residents Association have been campaigning for the past two months to get students to stop holding parties where they allege up to 50 people have attended in contravention of Government guidelines on Covid-19.
On Friday two residents took a case to Cork District Court where they were seeking to bring private prosecutions under the Environmental Protection Agency Act 1992 against a landlord with two properties in the area whom they allege is allowing breaches of noise levels.
Sadie O'Mahony of Gurtharda, Highfield Avenue, College Road, Cork and Mairead O'Callaghan of Lucerne, Connaught Avenue, Cork both brought private prosecutions against landlord, Fachtna O'Reilly of Birchley, Model Farm Road, Carrigrohane in respect of separate properties.
Ms O'Mahony alleges Mr O'Reilly is "the person making, causing, or responsible for the following noise, namely loud music, persistent shouting and rowdy and aggressive behaviour during the day, late into the night and into the early hours of the morning" at 11 Highfield Avenue, College Road.
Ms O'Callaghan alleges Mr O'Reilly is "the person making, causing, or responsible for the following noise, namely loud music, persistent shouting and rowdy and aggressive behaviour during the day, late into the night and into the early hours of the morning" at 4 Dunedin, Connaught Avenue.
They both allege that "the noise is so loud/so continuous/so repeated or of such duration or pitch/ occurring at such times as to give reasonable cause for annoyance to the complainant, any person in any premises in the neighbourhood or any person lawfully using a public place."
On Friday, before solicitor David McCoy could open the case for Ms O'Mahony and Ms O'Callaghan, Judge Con O'Leary said he wanted to explain to the two residents bringing the case that he once owned an apartment in the same area as a property owned by Mr O'Reilly.
"I don't want someone to say afterwards that we (the judge and the landlord) were friends," said Judge O'Leary, adding that he no longer owned the property but he believed that it was best that he adjourned the matter for another judge to hear it, lest it be perceived he was not objective.
Solicitor for Mr O'Reilly, Eamonn Murray, suggested the case would be best dealt with by referring it to the Private Residential Tenancies Board (PRTB) rather than dealing with it under environmental legislation and he asked Judge O'Leary to make an order to that effect, referring to the PRTB.
But Judge O'Leary said that it would not be appropriate for him to make such an order, given he was recusing himself from the case and it was an application Mr Murray could make before Judge Olann Kelleher who would hear the case at 2pm on Tuesday at the Anglesea Street Courthouse.
Mr Murray applied for a longer adjournment but Judge O'Leary said that he did not "live in a bubble" and was aware from prolonged press coverage about residents' concerns about the issue and he was anxious the matter be dealt with as quickly as possible and he adjourned it until Tuesday.
"There is another weekend to be gone through. In the meantime I cannot do anything about that," said Judge O'Leary to the residents as they left the court and he assured them that Judge Kelleher would hear the matter on Tuesday as he knew none of the parties involved.
EU hacking operation 'like having an inside person in every top organised crime group'
Lawyers on criminal legal aid scheme so far paid more in 2020 despite lockdown
Heavyweight champion Tyson Fury reportedly drops Daniel Kinahan as negotiator
Gardaí investigate after tree is felled at site of fatal road incident
Garda who investigated child abuse sues Garda Commissioner and State
Man arrested in Covid-19 payment fraud inquiry
Man who propelled partner down stairs gets 16 years for murder
Gardaí appeal for witnesses to alleged assault of teenage cyclist
Crime rates rose sharply after lockdown restrictions eased, figures show
Minister urged to set up committee to examine social media regulation
Direct provision centre contracts should not be renewed, says Refugee Council
4 Nearly half of passengers arriving into Ireland were on holiday - Taoiseach | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 5,860 |
{"url":"https:\/\/xyz5261941.wordpress.com\/2014\/10\/05\/quadratic-forms-part-2\/","text":"The second post of this series posts will focus on quadratic forms over some particular fields, like the rational numbers, the real numbers, and the $p$-adic numbers.\n\nFirst of all, perhaps we give some introductory materials on $p$-adic fields, here $p$ is a prime integer in $\\mathbb{N}$. We define $\\mathbb{Q}_p=\\{\\sum_{n>N}a_np^n|a_n=0,1,...,p-1, N\\in\\mathbb{Z}\\}$. For its any two elements $a=\\sum a_np^n, b=\\sum b_np^n$, we define a similarity function $s(a,b)=\\sup\\{n\\in\\mathbb{Z}|a_m=b_m,\\forall m\\leq n\\}$(for convention, for the zero element $0=\\sum 0p^n$, we set $s(0,0)=+\\infty$). It is a symmetric function $s:\\mathbb{Q}_p\\times \\mathbb{Q}_p\\rightarrow \\mathbb{N}\\bigcup\\{+\\infty\\}$. What is more, it is easy to verify that for any $a,b,c\\in\\mathbb{Q}_p$, we have that $s(a,b)\\geq min\\{s(a,c),s(c,b)\\}$, which means that $-s$ is a distance function from $\\mathbb{Q}_p$ to the tropical geometry $-\\mathbb{N}\\bigcup\\{-\\infty\\}$. So, we can define a distance into the real world, that is $d(a,b)=e^{-s(a,b)}$, which thus satisfies that $d(a,b)\\leq \\max{d(a,c),d(c,b)}\\leq d(a,c)+d(c,b)$, showing that this distance defines an ultra-metric on $\\mathbb{Q}_p$. Now we say something about the topology defined by this metric. First we consider a subspace of $\\mathbb{Q}_p$, that is the integer ring of it, $\\mathbb{Z}_p=\\{a\\in\\mathbb{Q}_p|s(a,0)\\geq0\\}$. It is easy to see that $\\mathbb{Z}_p=\\{0,1,2,...,p-1\\}^{\\mathbb{N}}=F_p^{\\mathbb{N}}$. What is more, for every inclusion $i_k:F_p\\rightarrow\\mathbb{Z}_p, x\\mapsto xp^k$, the image $i_k(F_p)$ is a finite set, thus is compact, so $\\mathbb{Z}_p$ is compact(using the theorem of Tychonoff). What is more, for any non negative rational number $0\\leq x\\in\\mathbb{Z}[\\frac{1}{p}]$, there is a unique $p$-expansion, $x=\\sum x_np^n$, thus we have an injection, $i:\\mathbb{Z}[\\frac{1}{p}]_{\\geq0}\\rightarrow \\mathbb{Q}_p$. So if we write $0\\neq x=p^us\\in\\mathbb{Z}[\\frac{1}{p}]_{\\geq0}(u\\in\\mathbb{Z},s\\in\\mathbb{Z}_{>0},gcd(s,p)=1)$, then we have that $d(x,0)=e^{-u}$. Viewed as a subspace of $\\mathbb{Q}_p$, we find that $\\mathbb{Z}[\\frac{1}{p}]_{\\geq0}$ is dense in $\\mathbb{Q}_p$. It is not hard to see. In deed, for any $a=\\sum_{n\\geq N}a_np^n\\in\\mathbb{Q}_p$, we define $A_M=\\sum_{N\\leq n\\leq M}a^np^n\\in \\mathbb{Q}_{\\geq0}$. And we find that $s(a,A_M)\\geq M$, thus $d(a,A_M)\\leq e^{-M}\\rightarrow 0(M\\rightarrow +\\infty)$. What is more, suppose that $a(n)\\in\\mathbb{Q}_p$ is a Cauchy sequence, then for any $e^{-M}$, there exists an integer $N$, such that for any $n,m\\geq N$, there is $d(a(n),a(m))\\leq e^{-M}$, which is the same as $s(a(n),a(m))\\geq M$, that is to say, for the terms $a(n)_k,a(m)_k(k\\leq M)$, they are all equal when $n,m\\geq N$. This means that for any fixed $k$, the sequence $a(n)_k$ is stationary. Hence we can define $a_k=\\lim_n a(n)_k\\in F_p$(for those $k$ too negative, $a_k=0$ because the sequence $a(n)$ is Cauchy, thus bounded). And the element $a=\\sum_{n}a_np^n$ lies in $\\mathbb{Q}_p$, which shows that $\\mathbb{Q}_p$ is complete with respect to this metric. Thus we can view $\\mathbb{Q}_p$ as a completion of $\\mathbb{Z}[\\frac{1}{p}]_{\\geq0}$ under this metric. Now we want to define some operations on $\\mathbb{Q}_p$. For example, the addition, the negation, the multiplication. We define $Add:\\mathbb{Z}[\\frac{1}{p}]_{\\geq0}\\times \\mathbb{Z}[\\frac{1}{p}]_{\\geq0}\\rightarrow\\mathbb{Z}[\\frac{1}{p}]_{\\geq0}, (x,y)\\mapsto x+y$. Equipping $\\mathbb{Z}[\\frac{1}{p}]_{\\geq0}^2$ with the product metric $D=d\\times d$, we have that $d(x+y,x'+y')\\leq\\max{d(x+y,y+x'),d(y+x',x'+y')}$ $=\\max{d(x,x'),d(y,y')}\\leq D((x,y),(x',y'))=d(x,x')+d(y,y')$. So this application $Add$ is a continuous function on a dense subset of $\\mathbb{Q}_p^2$. Thus, we can extend $Add$ to all of $\\mathbb{Q}_p^2$, and we call this $Add$ the addition operation on $\\mathbb{Q}_p^2$. Now for positive rational numbers $x=p^us,x'=p^{u'}s',y=p^vt(s,s',t \\text{positive integers prime to} p)$, we have that $d(xy,x'y)=d(p^{u+v}st,p^{u'+v}s't)=e^{-\\min{u+v,u'+v}}=d(y,0)d(x,x')$. So if we define $Mul:\\mathbb{Z}[\\frac{1}{p}]_{\\geq0}\\times\\mathbb{Z}[\\frac{1}{p}]_{\\geq0}\\rightarrow\\mathbb{Z}[\\frac{1}{p}]_{\\geq0},(x,y)\\mapsto xy$, then we see that $d(xy,x'y')\\leq \\max{d(xy,x'y),d(x'y,x'y')}=\\max{d(y,0)d(x,x'),d(x',0)d(y,y')}$ $\\leq (d(y,0)+d(x',0))D((x,y),(x',y'))$, thus showing that $Mul$ is continuous on a dense subset of $\\mathbb{Q}_p^2$, hence we can extend $Mul$ to all of $\\mathbb{Q}_p^2$, which is again continuous, and we call this operation the multiplication on $\\mathbb{Q}_p$. For the present, we see that $(\\mathbb{Q}_p,Add)$ is a semi-group. One way to find the negative of an element $a\\in\\mathbb{Q}_p$ is to go back to $\\mathbb{Z}[{\\frac{1}{p}}]_{\\geq0}$. But this is also a semi-group with respect to the addition operation. But let\u2019s have a try. We know that the number $1\\in\\mathbb{Q}$ in $\\mathbb{Q}_p$ is still $1$. Then which element in $\\mathbb{Q}_p$ corresponds to the negation of $1$? Suppose this element writes as $a=\\sum_{n\\geq N}a_np^n$ with a sequence of rational numbers approximating it $A_M=\\sum_{N\\leq n\\leq M}a_np^n$. We have to guarantee that $d(A_M+1,0)\\rightarrow d(0,0)=0(M\\rightarrow +\\infty)$. A simple calculation shows that $s(a,0)=0$, and $A_M=\\sum_{0\\leq n\\leq M}(p-1)p^n$. So we obtain that $a=\\sum_{n\\geq 0}(p-1)p^n$, which is the negation of $1$, and we can write $-1=\\sum_{n\\geq0}(p-1)p^n$.The semi-group structure of $(\\mathbb{Q}_p-\\{0\\},Mul)$ inherits from \u00a0that of $(\\mathbb{Z}[\\frac{1}{p}]_{\\geq0},Mul)$. And we want to find an inverse for each element in it. \u00a0For example, an non-zero element writes $a=p^ux$ where $x_0\\in F_p-\\{0\\}$. So if we can find an inverse for $x$, say $y$ such that $xy=1$, then it is wasy to see that $p^{-u}y$ is the inverse of $a=p^ux$. So we can just suppose that $a\\in\\mathbb{Z}_p(a_0\\neq0)$.The method is to go back to the $\\mathbb{Z}_{\\geq0}$ world, and then take limits. Specifically, suppose that $a\\in\\mathbb{Z}_p$ with $s(a,0)=0$, then using again the approximation sequence $A_M=\\sum_{0\\leq n\\leq M}a_np^n$. If we can find the inverse $B_M$of $A_M$ for each $M$, then since $A_M$ is a Cauchy sequence, so is $B_M$(because $d(A_M,0)d(B_M,0)=d(A_MB_M,0)=d(1,0)=1$, and $d(A_M,0)$ converge to a non-zero number). So things are reduced to find these $B_M$, or more generally, find the inverse of any positive integer $A$ prime to $p$. Suppose the inverse of $A$ is $b=\\sum_{n\\geq0}b_np^n$(if it exists). Then consider the approximating sequence $B_N$ to $b$. In order that $d(AB_N,0)\\rightarrow d(Ab,0)=1$.For $N=0$, since $gcd(A,p)=1$, there is an integer $b_0\\in F_p$ such that $Ab_0=1(\\text{mod}p)$. So, we have that $d(Ab_0-1,0)\\leq e^{-1}$. For $N=2$, since again $gcd(A,p^2)=1$, there is $b_1\\in F_p$ such that $A(b_0+b_1p)=1(\\text{mod}p^2)$. Similarly, we have that $d(A(b_0+b_1p)-1,0)\\leq e^{-2}$. In fact, $(b_0,b_1)$ is the only element in $F_p^2$ such that $Ab_0=1(\\text{mod}p),A(b_0+b_1p)=1(\\text{mod}p^2)$.\u00a0We can continue this process to any $N$ and until infinity. So, in this way, we find an element $b=\\sum b_np^n\\in\\mathbb{Z}_p$ such that $d(Ab-1,0)=0$, which means that $Ab=1$. Thus we find an inverse for each non-zero element in $\\mathbb{Q}_p$.\u00a0Now combining the above results, for any positive rational number, we can write it as $a=p^u\\frac{A}{B}$ where $A,B$ are coprime positive integers prime to $p$. Since $B$ is invertible in $\\mathbb{Q}_p$, thus we can define $i(a)=p^uAi(B)^{-1}$,\u00a0for a negative number $-a\\in\\mathbb{Q}$, $i(-a)=(-1)i(a)=\\sum_{n\\geq0}(p-1)p^n\\times i(a)$. So\u00a0we get a larger inclusion, $i: \\mathbb{Q}\\rightarrow\\mathbb{Q}_p$.\u00a0From now on, we will mix these two notations $-1$ and $\\sum_{n\\geq0}(p-1)p^n$. And for any element $a\\in\\mathbb{Q}_p$, we set $-a=(-1)\\times a$. It is easy to verify that the addition and multiplication thus defined are compatible, that is multiplication is distributive to addition. Hence we give $\\mathbb{Q}_p$ a field structure. Now some words on $\\mathbb{Z}_p$. Using the fact that $d(xy,0)=d(x,0)d(y,0)$, we see that $\\mathbb{Z}_p$ is closed under multiplication. What is more, $-1$ clearly belongs to $\\mathbb{Z}_p$. In addition, it is not hard to see that $\\mathbb{Z}_p$ is closed under addition and subtraction, thus this space has a ring structure. Then perhaps we would wonder what are the units in this ring? Clearly,if $a\\in\\mathbb{Z}_p$ has that $s(a,0)>0$, then $s(ab,0)>0(b\\in\\mathbb{Z}_p)$, thus $ab\\neq 1$,so $a\\not\\in \\mathbb{Z}_p^*$. So we have to consider those $a$ with $s(a,0)=0$. In fact, these are exactly the units. That is to say,\n\nThe set of invertible elements of $\\mathbb{Z}_p$ is $\\{a\\in\\mathbb{Z}_p|s(a,0)=0\\}$\n\nThe proof utilizes the same method as above, and we omit it. We can say some more about this result. Note that an element in $\\mathbb{Z}_p^*$ is always of the form, $a=a_0+pa'(a'\\in\\mathbb{Z}_p)$ with $a_0\\in F_p-\\{0\\}$. So we have that $\\mathbb{Z}_p^*=(F_p-0)\\times \\mathbb{Z}_p$. Inversely, for any $a\\in\\mathbb{Q}_p$, we have seen that we can write $a=p^{s(a,0)}s$, then we surely would have that $s_{s(s,0)}\\in F_p-0$. So there is $\\mathbb{Q}_p=\\mathbb{Z}\\times \\mathbb{Z}_p^*$, this is a group homomorphism.\n\nThe above serves as a simple explanation of the $p$-adic fields.\n\nQuadratic forms arise naturally from the Euclidean spaces. In Euclidean spaces, we have inner products, we is commonly known also as quadratic forms. In this post, we will consider these forms over some $p$-adic fields. For that, we need the Hilbert symbol.\n\nSuppose that $k$ is a field(here $k$ will be $\\mathbb{R},\\mathbb{Q}_p$, or $\\mathbb{Q}$), and two non-zero elements $a,b\\in k^*$. The Hilbert symbol considers if the equation $ax^2+by^2=z^2$ has non-trivial solutions(different from the solution $(x,y,z)=(0,0,0)$) in $k^3$. If this homogeneous equation has non-trivial solutions, then we define $[a,b]=1$, otherwise we set $[a,b]=-1$. Why do we consider just those non-zero $a,b$? For example, when $a=0$, then the existence of non-trivial solutions can be completely characterized by whether $b$ is a square or not. It is clear that the Hilbert symbol $[,]:k^*\\times k^*\\rightarrow \\{1,-1\\}=\\mathbb{F}_2=\\mathbb{Z}\/2\\mathbb{Z}$ is symmetric. We will show that it is in fact multiplicative in the first variable(hence also in the second variable), that is to say $[aa',b]=[a,b][a',b]$, and it is not degenerate, that is to say, for any $a\\in (k^*)^2$ not a square, we can find a $b\\in (k^*)^2$ such that $[a,b]=-1$.\n\nTo prove these properties, we need some preliminaries. First we want to characterize the Hilbert symbol $[a,b]$ using the field $k(\\sqrt{b})$. In fact, observing the equation $ax^2=z^2-by^2$. If $b'=\\sqrt{b}\\in \\overline{k}$, then if $x\\neq 0$, we have that $a=(z\/x-b'y\/x)(z\/x+b'y\/x)$. So, if $b$ is not a square in $k$, then $[a,b]=1$ implies that $a$ is a norm in $k(\\sqrt{b})$. If $[a,b]=-1$, this implies that $a$ is not a norm in $k(\\sqrt{b})$. For the case where $b$ is a square, we always have $[a,b]=1$, and $k(\\sqrt{b})=k$, thus $a$ is always a norm in $k(\\sqrt{b})$. So we have that $[a,b]=1$ if and only if $a$ is a norm in $k(\\sqrt{b})$. Moreover, it is not hard to see, that for $a,b\\in k^*$, we have $[a,b^2]=1,[a,-a]=1,[a,1-a]=1, [a,c^2b]=[a,b]$. If $[c,b]=1$, then $c$ is a norm in $k(\\sqrt{b})$, using the multiplicative property of the norm function, we have that $ac$ is a norm of $k(\\sqrt{b})$ if and only if $a$ is a norm of this field. So we have that $[ac,b]=[a,b]$.\n\nNow we are ready to prove the following result:\n\nIf $k=\\mathbb{R}$, then $[a,b]=1$ if and only if at least one of them is positive. If $k=\\mathbb{Q}_p$, then we can write $a=p^ux,b=p^vy(x,y\\in\\mathbb{Z}_p^*)$, for $p>2$, there is $[a,b]=(-1)^{uv\\frac{p-1}{2}}(\\frac{x}{p})^v(\\frac{y}{p})^u$; for $p=2$, there is $[a,b]=(-1)^{\\frac{x-1}{2}\\frac{y-1}{2}+v\\frac{x^2-1}{8}+u\\frac{y^2-1}{8}}$.(the symbol $(\\frac{x}{p})$ is the Legendre symbol extended to $\\mathbb{Z}_p$ by $(\\frac{x}{p})=(\\frac{x_0}{p})$. For $\\frac{y-1}{2}$, it is just $y_1(\\text{mod}2)$, and for $\\frac{y^2-1}{8}$, it is just $y_1(y_1+1)\/2+y_2$).\n\nThe case that $k=\\mathbb{R}$ is trivial, and we omit the proof. As for the case $k=\\mathbb{Q}_p(p>2)$. We proceed as follows. Note that the identity depends only on the mod $2$ values of $u,v$ and the values of $x,y$. We will consider these cases separately. Note that the extended Legendre symbol is still multiplicative, what is more, $(\\frac{-1}{p})=(-1)^{(p-1)\/2}$ even when $-1$ is an element in $\\mathbb{Z}_p$.\n\n(1)The case $u=0,v=0$. Then the right hand side is just $1$. What is more, note that since $u,v$ are even numbers, we have $[a,b]=[x,y]$. So we have to show that $[x,y]=1$, that is to show there exists always a non-trivial solution to the equation $xr^2+ys^2=t^2$ with variables $r,s,t$. We use again the method of going back to the world $\\mathbb{Z}$, or rather $\\mathbb{Z}\/p^n\\mathbb{Z}$. We define the result of $a\\in\\mathbb{Z}_p$ modulo $p^n$ to be the number $P_n(a)=\\sum_{0\\leq m\\leq n}s_mp^m$. Clearly the sequence $P_n(a)$ approximates $a$. For $n=0$, we consider $P_0(x)r^2+P_0(y)s^2=t^2(\\text{mod}p)$(For simplicity, we will write this as $xr^2+ys^2=t^2(p)$ when there is no confusion). Using the Legendre symbol, we can show easily that this equation always has non-trivial solutions as long as $P_0(x),P_0(y)\\neq 0(p)$ which is the case. So, we have a first-order approximation non-trivial solution $(r_0,s_0,t_0)\\in F_p^3$. Now suppose that we have found an $(n-1)$-th order approximation non-trivial solution $(r_{n-1},s_{n-1},t_{n-1})\\in F_{p^n}^3$($P_n(x)r_{n-1}^2+P_n(y)s_{n-1}^2-t_{n-1}^2=zp^n$). We set $x(r_{n-1}+rp^n)^2+y(s_{n-1}+sp^n)^2=(t_{n-1}+tp^n)^2(p^{n+1})$. After expansion, we get that $zp^n+2p^n(xr_{n-1}r+ys_{n-1}s-t_{n-1}t)=0(p^{n+1})$. It is the same as $z+2(xr_{n-1}r+ys_{n-1}s-t_{n-1}t)=0(p)$. Note that $(r_{n-1},s_{n-1},t_{n-1})\\neq(0,0,0)(p)$, so is $(2xr_{n-1},2ys_{n-1},-t_{n-1})$, which means that this equation always has a non-trivial solution $(r,s,t)\\in F_p^3$. So the triple $(r_{n-1}+rp^n,s_{n-1}+sp^n,t_{n-1}+tp^n)$ is an $n$-th order approximation non-trivial solution to the original equation. We can continue in this way to infinity, and moreover each sequence $r_n$($s_n,t_n$ respectively) converges to some element $r$($s,t$ respectively) in $\\mathbb{Z}_p$. Thus this non-zero triple $(r,s,t)$ solves the equation $xs^2+ys^2=t^2$.\n\n(2)The case $u=1,v=0$. For the same reason, we have to show that $[px,y]=(\\frac{y}{p})$. Suppose that $(\\frac{y}{p})=1$, then $y_0$ is a non-zero square in $F_p$(that is $y_0=z_0^2(\\text{mod}p)$). Like what we have done in the above, the equation $y=z^2$(in $\\mathbb{Z}_p$) can be obtained by lifting the first-order approximation $z_0$. And thus we get a $0\\neq z\\in\\mathbb{Z}_p$ such that $y=z^2$(we used somewhere the fact that $p\\neq 2$). So one non-trivial solution to the equation $pxr^2+ys^2=t^2$, that is $(0,1,z)$. Conversely, if $(r,s,t)$ is one such non-trivial solution, we can subtract all their common $p$-factors to suppose that at least one of them is a unit. Now modulo $p$, we get that $px_0r_0^2+y_0s_0^2=t_0^2(p)$. That is to say, $y_0s_0^2=t_0^2(p)$. If $s_0=0$, then there is $t_0=0$ too.Now modulo $p^2$, we get that $pxr^2=0(p^2)$. Since $x$ is a unit, thus $r_0=0$. But this contradicts the assumption that at least one of $r,s,t$ is unit. Hence we must have that $y_0=(t_0\/s_0)^2(p)$. So $y$ is a square in $F_p$, $(\\frac{y}{p})=1$.\n\n(3)The case $u=1,v=1$. Again the same reasoning as above leads to the identity $[px,py]=(-1)^{\\frac{p-1}{2}}(\\frac{x}{p})(\\frac{y}{p})$. But note that $[px,-px]=1$, thus $[px,py]=[px,-pxpy]=[px,-xy]$. And according to the preceding paragraph, we have $[px,-xy]=(\\frac{-xy}{p})$, which is exactly the same as $(-1)^{(p-1)\/2}(\\frac{x}{p})(\\frac{y}{p})$.\n\nFor the case $p=2$, the proof is not exactly the same but very similar and not very hard, and we will not prove it here. The only difficulty is that the above lifting strategy has to be carefully dealt with. The fact is that $x\\in\\mathbb{Z}_p^*$ is a square if and only if $x$ is a square modulo $8$, not $2$ or $4$. This is due to the factor $2$ in the square. One simple example is that $5$ is not a square modulo $8$ even though it is a square modulo $2$ or $4$.\n\nThe above result clearly shows that the Hilbert symbol is multiplicative in one variable since the term on the right hand side is always multiplicative in one variable. What s more, the Hilbert symbol is not degenerate. That is\n\nFor any $a\\in k^*$ non square, there is a $b\\in k^*$ such that $[a,b]=-1$.\n\nIn $k=\\mathbb{R}$, $a$ is not a square means that $a<0$. So take $b<0$ and this gives $[a,b]=-1$.\n\nIn the case $k=\\mathbb{Q}_p(p>2)$. When is $a=p^ux(x\\in\\mathbb{Z}_p^*)$ not a square? So when is $a$ a square? Suppose $a=(p^vy)^2(y\\in\\mathbb{Z}_p^*)$, then we must have that $u=2v, x=y^2$. Conversely, if these two conditions were satisfied, then $a$ is a square. So there are three cases where $a$ is not a square, that is $a=p^{2u+1}x$,or $p^{2u}x$(with $(\\frac{x}{p})=-1$) or at last $p^{2u+1}x$ with $(\\frac{x}{p})=-1$. For the first case, we can set $b=y$ with $(\\frac{y}{p})=-1$. For the second case, we set $b=p$, and for the last case we set $b=y$ which is not a square.\n\nIn the case $k=\\mathbb{Q}_2$. The situation is similar, just a little more complex. Write again $a=2^ux$. $a$ is a square if and only if $u$ is an even number and $x$ is a square modulo $8$(which is the same as $x=1(8)$). So if $a=2^{2u}x$(with $x=3(8)$), we can set $b=7$, with $x=5$, we define $b=2$, with $x=7$, we define $b=7$. If $a=2^{2u+1}x$, we can set $b=5$. These can be verified very easily, and we omit it.\n\nThe next paragraph concerns with the product formula of the Hilbert symbol. As we have seen above, there is an inclusion $\\mathbb{Q}\\subset\\mathbb{Q}_p$ for all primes $p$. If we define $P=\\{p \\text{is a prime number or is }\\infty\\}$. And we set $\\mathbb{Q}_{\\infty}=\\mathbb{R}$. These fields $\\mathbb{Q}_p$($p\\in P$) are called local fields, the topological completion of the global field $\\mathbb{Q}$. So for any two non-zero $a,b\\in\\mathbb{Q}$, we define $[a,b]_p$ to be the Hilbert symbol of $a,b$ in the field $\\mathbb{Q}_p$($p\\in P$). An interesting result is that\n\nIf $a,b\\in\\mathbb{Q}^*$, then for almost all $p\\in P$, $[a,b]_p=1$. What is more, we have the product formula of Hilbert symbol: $\\prod_{p\\in P}[a,b]_p=1$.\n\nThe product makes sense since there are only finite many terms not equal to $1$ according to the first part of the result. A simple observation goes first: since each $[a,b]_p$ is multiplicative in one variable, so we can prove the result only for the case $a,b=-1,q$($q$ is a prime integer).\n\nIf $a=-1,b=-1$, then $[-1,-1]_{\\infty}=-1$, and if $p>2$, there is $[-1,-1]_p=1$. And $[a,b]_2=(-1)^{\\frac{-1-1}{2}\\frac{-1-1}{2}}=-1$. So $\\prod_p [-1,-1]_p=1$.\n\nIf $a=-1,b=q$ with $0 a prime number. Then $[-1,q]_{\\infty}=1$. If $q=2$, then for $p>2$, $[-1,2]_p=1$, while $[-1,2]_2=(-1)^{\\frac{-1-1}{2}\\frac{1-1}{2}+0+\\frac{1^2-1}{8}}=1$, so $\\prod_p[-1,2]=1$. If $q>2$, then $[-1,q]_2=(-1)^{\\frac{-1-1}{2}\\frac{q-1}{2}}=(-1)^{\\frac{q-1}{2}}$. For $p\\neq q$, $[-1,q]_p=1$, while $[-1,q]_q=(\\frac{-1}{q})=(-1)^{\\frac{q-1}{2}}$. So we have that $\\prod_p [-1,q]_p=1$.\n\nIf $a=q,b=q'$ two primes such that $q\\neq q'$. Then we have that $[q,q']_{\\infty}=1$. And suppose neither of them is $2$,then $[q,q']_2=(-1)^{\\frac{q-1}{2}\\frac{q'-1}{2}}$. $[q,q']_q=(\\frac{q'}{q})$, $[q,q']_{q'}=(\\frac{q}{q'})$, for other $p$, $[q,q']_p=1$. So we have that $\\prod_p[q,q']=1$ due to quadratic reciprocity law. If $q'=2$, then $[q,2]_2=(-1)^{0+\\frac{q^2-1}{8}}$, $[q,2]_q=(\\frac{2}{p})=(-1)^{\\frac{q^2-1}{8}}$. For other $p$, $[q,2]_p=1$ So, we have that $\\prod_p[q,2]_p=1$.\n\nIf $a=q,b=q$. It is clear that $[q,q]_{\\infty}=1$. If $q=2$, then $[2,2]_2=1$, $[2,2]_p=1$, so $\\prod_p[2,2]_p=1$. If $q>2$, then $[q,q]_2=(-1)^{\\frac{q-1}{2}\\frac{q-1}{2}}$, $[q,q]_q=(-1)^{\\frac{q-1}{2}}$, for other $p$, there is $[q,q]_p=1$, thus we have that $\\prod_p[q,q]_p=1$.\n\nThus we proved the product formula of Hilbert symbols. Note that in the proof we have used the quadratic reciprocity law in an essential way. In fact, this proof means that the quadratic reciprocity law implies the product formula. Whereas inversely, take any two distinct primes, the product formula gives an immediate proof of the quadratic reciprocity law. And thus the product formula is also sometimes called Hilbert\u2019s reciprocity law.\n\nThe importance of Hilbert reciprocity law is that it can be generalized naturally to other algebraic number fields. 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\section{Introduction}\label{sec:introduction}
There is no doubt that inflation is an important part of modern cosmology\cite{Guth:1980zm, Linde:1981mu, Lyth:1998xn, Martin:2016ckm}. In its simplest realizations, an accelerated expansion is driven by a single real scalar field $\phi$, called an inflaton. The dynamical system of equations that describe this period of time includes the Klein-Gordon equation and Friedmann equation. It is generally not possible to solve this system; so standard assumptions like slow roll, in which $\ddot{\phi}\ll H\dot{\phi}$, are made to simplify the dynamics. This assumption yields a simple realization with viable observational predictions; nevertheless, the increase in accuracy of cosmological data over the recent years has been a motivator to go beyond this assumption and generalize the inflation driven by slow rolling field. The cosmological generalizations have been studied either from GR or particle physics point of view \cite{Hazra:2014jka,Kinney:2005vj,Nojiri:2017qvx,Motohashi:2017vdc,Oliveros:2019zkl,delCampo:2012qb,Kehagias:2018uem,Das:2020xmh,Liu:2021diz,Yuennan:2022zml,Palti:2019pca, Andriot:2018mav, Talebian-Ashkezari:2016llx, Firouzjahi:2020jrj, Firouzjahi:2018vet}. An inventive generalization from the latter viewpoint, was developed by Motohashi et. al. \cite{Motohashi:2014ppa}. This is a two-parametric class of models in which the inflaton is assumed to roll with constant rate. The novelty is that by introducing this assumption to the dynamical system, it is $\it{possible}$ to solve the dynamical system exactly and construct the new type of inflation dubbed constant roll (CR) inflation. A considerable number of variants for this model can be found in the literature, some of them are \cite{Awad:2017ign, Odintsov:2019ahz,Micu:2019fju,Gao:2019sbz,Guerrero:2020lng,Shokri:2021rhy,MohseniSadjadi:2019vvs, Oikonomou:2021yks,Shokri:2021jxh,Shokri:2021aum,Shokri:2021iqp,Shokri:2021zqw,Anari:2022tsl,Herrera:2022tad}.
In constant roll construction, inflaton was assumed to be a real scalar field. A complex scalar field has higher degree of freedom that makes its predictions more flexible to match with data. Such fields have been invoked in many different areas of physics. A minimally coupled complex field yields the same field equations as those obtained by two scalar fields. Cosmological scenarios with such fields are extensively studied~\cite{Yurov:2001ud,Yurov:2002nu,Buchmuller:2014epa,Carrion:2021yeh, Scialom:1996yd,Gu:2001tr,Liu:2020bmp,Amendola:1994xf,Scialom:1994uq,Khalatnikov:1992sj,Kamenshchik:1997dmk,Kamenshchik:1995ib} and in the present work we revisit the idea focusing on the constant roll assumption.
The inflaton potential in real field models does not require the parameter defining the constant roll be small. It is important to see the degree of generality of this possibility.
As an assumption, not every interpretation of constant-roll assumptions would be consistent with the dynamical system.
As a dynamical system a relevant question is: Under what constraints (imposed on the value or velocity of fields) a complex field constant roll inflation can be realized? For a real field the constant roll potential is completely fixed; so another relevant question is whether the complex field potentials are also fixed.
The paper is arranged as follows. In sec.~\ref{sec:Background Dynamics} we begin by a short review of a complex field dynamics and then examine couple of traditionally used CR constraints and discuss the possibility of finding inflationary potential. We also derive a sufficient condition on the potential to ensure the compatibility in the constrained dynamical system. In Sec.~\ref{CR Potential}, we find explicit solutions for the field, Hubble parameter and the field potential. This introduces a three-parametric class of solutions that satisfies the constrained system exactly. The subject of (non-)uniqueness of the solutions is also discussed. The dynamical behavior of the fields' solution is the subject of Sec.~\ref{Dynamical Analysis}, where the stability of the parameter space solution are also analyzed. We summarize our results and conclude in Sec.~\ref{Conclusion}. The paper ends with one appendix where the constrained system is formulated in new coordinates and exact solutions are derived.
\section{Constant Roll Dynamical System}\label{sec:Background Dynamics}
In this section, we present a detailed analysis of an expanding Universe with a complex field as the field responsible for the accelerating expansion. We review the Einstein Klein-Gordon equations as a dynamical system and then discuss about the compatibility of a constraint which may be imposed on this system.
\subsection{Einstein Klein-Gordon equations}\label{Einstein Klein-Gordon equations}
We consider a spatially flat FLRW background described by
\begin{equation}
ds^2=-dt^2+a^2(t)d\vec{x}^2.
\end{equation}
The action for the Universe with a minimally coupled complex field is
\begin{equation}
S=\int{\sqrt{-g}d^4 x\left(\frac{R}{2}+\frac{1}{2}g^{\mu\nu}\left(\partial_\mu \Phi^\ast\right)(\partial_\nu \Phi)-V\left(\Phi\right)\right)}.
\end{equation}
One can represent the field degrees of freedom (DoFs) by the amplitude $X\left(t\right)$ and the phase $\theta \left(t\right)$ or $\Phi=\varphi_1(t)+i \varphi_2(t)$. The Lagrangian density can be written in canonical or non-canonical form
\begin{eqnarray}
\mathcal{L}_\Phi&=&-\frac{1}{2}a^3 \left(\dot{\varphi_1}^2+\dot{\varphi_2}^2\right)+a^3 V\left(\varphi_1,\varphi_2\right)\label{Lagrangian phi1-phi2}\\
&=&-\frac{1}{2}a^3 X^2\left[\left(\frac{\dot{X}}{X}\right)^2+\dot{\theta}^2\right]+a^3 V\left(X,\theta\right).
\end{eqnarray}
The variation of the action in the non-canonical form yields the Einstein and the complex field equations of motion as
\begin{gather}
3H^2=\frac{1}{2}\left(\dot{X}^2+X^2\dot{\theta}^2\right)+V(X,\theta),\label{Friedmann1}\\
-2\dot{H}=\dot{X}^2+X^2\dot{\theta}^2,\label{Friedmann2}\\
{\ddot{X}}-\dot{\theta}^2 X+3H \dot{X}+\frac{\partial V}{\partial X}=0,\label{KG-X}\\
X^2\ddot{\theta}+3HX^2\dot{\theta}+2X\dot{X}\dot{\theta}+\frac{\partial V}{\partial \theta}=0.\label{KG-theta}
\end{gather}
For $\dot{\theta}=0$ and $V=V(X)$, the standard equations for a real scalar field is recovered. In real field case, the only field equation is the differential consequence of Friedmann equations. The above set of equations for complex field are not independent as well. In this case, The Bianchi identity guarantees that equations ~\eqref{Friedmann1},~\eqref{Friedmann2} and~\eqref{KG-X} automatically imply ~\eqref{KG-theta} and the above system of equations is also fully determined by the independent equations ~\eqref{Friedmann1} -~\eqref{KG-X}. By taking the time derivative of ~\eqref{Friedmann1} and using ~\eqref{Friedmann2}, we find
\begin{equation}\label{Friedmann time derivative}
\dot{X}\left[{\ddot{X}}-\dot{\theta}^2 X+3H \dot{X}+\frac{\partial V}{\partial X}\right]+\dot{\theta}\left[X^2\ddot{\theta}+3HX^2\dot{\theta}+2X\dot{X}\dot{\theta}+\frac{\partial V}{\partial \theta}\right]=0.
\end{equation}
Therefore any solution of Friedmann equation will imply one of fields equations (~\eqref{KG-X} or~\eqref{KG-theta}), if the other one is already satisfied. In other words, If in the set of comprising Einstein plus two Klein-Gordon equations, one of Klein-Gordon equations be a linear combinations of the other, the system will be under-determined. In such case, both Klein-Gordon equations can be neglected and the the dynamical system shall be fully described by Einstein equations.
If $\partial V/\partial\theta=0$, the phase variable $\theta$ would be cyclic and there would be one independent DoF; so~\eqref{KG-theta} can be solved to give $\dot{\theta}={M}/({a^3 X^2})$, where $M$ is a constant. Clearly, this system would be different from a real field, because if the centrifugal terms in kinetic energy and the field equation is expressed in terms of the conserved quantity $M$, and scale factor $a$, one gets the following set of equation
\begin{equation}
3H^2=\frac{1}{2}\left(\dot{X}^2+\frac{M^2}{a^6 X^2}\right)+V(X), \qquad {\ddot{X}}-\frac{M^2}{a^6 X^3} +3H\dot{X}+\frac{d V}{d X}=0.
\end{equation}
Note, however, that in real field case, there is no explicit dependency on the scale factor in the Klein-Gordon equation.
In the rest of this section, we will study the dynamical system described in this section by imposing the constant roll constraint. Before embarking on that study, we review the constant roll definitions for multi-field inflationary models.
\subsection{Constant Roll Definitions}\label{sec:CR definitions}
The inflationary models with an approximately flat potential yield a sufficiently long period of quasi-de Sitter expansion and a nearly scale invariant spectrum of density perturbations. However, there has been considerable interest to find non-standard inflationary exact solutions to the equations of motion. We now come to the constraints which may be imposed on the dynamical equations (\ref{Friedmann1}-\ref{KG-theta}) to $\it{define}$ a class of non-slow roll inflationary scenarios with constant rates of roll. Starting with a single real field $\phi$, the assumption of a constant rate of roll is formulated by
\begin{equation}\label{CR constraint1}
\ddot{\phi}=-\eta H\dot{\phi}.
\end{equation}
Here $\eta$ is a constant parameter that is equivalent to the second slow-roll parameter for values that describe a dynamically stable system. The standard slow-roll regime occurs at $\eta\simeq0$, while the ultra-slow-roll case corresponds to $\eta=-3$. Although data seem to favor the small values of $\eta$, but the novelty of CR class of models is that the exact inflationary potential can be found without need to consider $\eta$ as a small parameter.\footnote{In Sec.~\ref{Dynamical Analysis} we will talk about a duality relation which suggests that the ultra slow-roll inflationary models may also be consistent with the observations.} One may think of generalizations of this constraint when more degrees of freedom play role in an inflationary scenario. When a complex field is responsible for the CR inflation, three trivial generalizations may be used for
\begin{itemize}
\item Both DoFs constant roll independently, i.e,
\begin{equation}\label{CR constraint 2}
\ddot{X}=-\eta H\dot{X}, \qquad \ddot{\theta}=-\eta H\dot{\theta}.
\end{equation}
\item The constant rate of roll is conjectured only for absolute value of the field velocity,
\begin{equation}\label{CR constraint 21}
\frac{d|\dot{\Phi}|}{dt}=-\eta H|\dot{\Phi}|.
\end{equation}
\item The definition ~\eqref{CR constraint1} has an equivalent form, written in terms of the Hubble parameter,
\begin{equation}\label{CR constraint3}
\ddot{ H}=-2\eta H\dot{H}.
\end{equation}
\end{itemize}
Equation~\eqref{CR constraint3} \emph{seems} to be independent of the matter dynamics and therefore believed to be more fundamental than~\eqref{CR constraint1}. We shall see in next section that the second definition~\eqref{CR constraint 21} can be derived from this form. So, the latter form practically affects on the matter dynamics. It has been used for realizing a constant roll inflation in string theory \cite{Micu:2019fju}. We will see that the definition~\eqref{CR constraint3} fixes the time profile of potential, but there remains some flexibility when expressed in terms of DoFs. In the next subsection we elaborate on these definitions and show that it is actually impossible to construct an exact solution, if the definition~\eqref{CR constraint 2} is added to the system of equations. We also discuss about the consistency condition between the CR definition~\eqref{CR constraint3} and other equations in dynamical system discussed in subsection~\ref{Einstein Klein-Gordon equations}.
\subsection{Consistency Condition}\label{sec: consistency condition}
As we discussed in Subsection \ref{Einstein Klein-Gordon equations}, unlike a real field model, the inflationary potential cannot be determined from Einstein equations plus CR constraint. For a complex field, we show that such a set of equations is considered overdetermined and almost always inconsistent.
Starting with first CR definition, it can be written in the form of $\ddot{X}/\dot{X}=\ddot{\theta}/\dot{\theta}=-\eta H$. This can be integrated to give
\begin{equation}\label{X and theta relation}
X=M\theta+M_0.
\end{equation}
Here $M$ and $M_0$ are integration constants with mass dimension. An expression for the potential is found by applying~\eqref{X and theta relation} to the first Friedmann equation~\eqref{Friedmann1},
\begin{equation}\label{V1}
V\left(X,\theta(X)\right)=3H^2-\frac{1}{2}(1+\frac{X^2}{M^2})\dot{X}^2.
\end{equation}
Now let us apply~\eqref{X and theta relation} to dynamical equations in~\eqref{Friedmann time derivative}. We will have
\begin{equation}\label{Friedmann time derivative2}
\dot{X}\left[{\ddot{X}}+3H \dot{X}-\frac{1}{M^2}\dot{X}^2 X+\frac{\partial V}{\partial X}\right]+\frac{X^2\dot{X}}{M^2}\left[\ddot{X}+3H\dot{X}+2\frac{\dot{X}^2}{X}+\frac{M^2}{X^2}\frac{\partial V}{\partial X}\right]=0.
\end{equation}
It is easy to see that the two squared brackets do not hold simultaneously. In other words, the potential given in~\eqref{V1} does not necessarily satisfies both field equations. One therefore conclude that the above definition of CR complex field model is not mathematically consistent.
A system like above, in which the equations outnumber the unknowns, is overdetermined and almost always inconsistent. It will, however, have solutions in some cases. For imposing CR constraint to the dynamical system one can consider the conditions which render the system under-determined, i.e, some equations are linear combinations of the others. We carry on this section to find a condition to render the field equations dependent. Let us concentrate on kinetic energy and
the relative contribution of different DoFs at each time. We define a smooth function related to the kinetic energy function,
\begin{equation}\label{Z definition}
Z\equiv\dot{X}^2+X^2\dot{\theta}^2,
\end{equation}
in terms of which dynamical equations (\ref{Friedmann1}-\ref{KG-theta}) are given by
\begin{equation}\label{Friedmann3}
3H^2=\frac{1}{2}Z+V, \qquad -2\dot{H}=Z.
\end{equation}
If the contribution of different DoFs in $Z$ be proportional to each other at all times, i.e, $X\dot{\theta}=\lambda\dot{X}$, with $\lambda$=constant, we will get $Z=(1+\lambda^2)\dot{X}^2$ and different DoFs are related by
\begin{equation}\label{theta(X)}
\theta-\theta_0=\lambda \ln(X).
\end{equation}
The special case of real field is recovered by $\lambda=0$ and $\theta(\lambda=0)=\theta_0$, which is a constant. Now let us apply the relation between DoFs~\eqref{theta(X)}, to~\eqref{KG-theta}, we obtain
\begin{equation}\label{KG-theta2}
\lambda X\left(\ddot{X}+3H\dot{X}\right)+\lambda \dot{X}^2+\frac{\partial V}{\partial \theta}=0.
\end{equation}
One strategy is to find a relation between partial derivatives of potential to guarantee that both equations~\eqref{KG-X} and~\eqref{KG-theta} be satisfied simultaneously. We, therefore, replace the expression $\ddot{X}+3H\dot{X}$ in~\eqref{KG-theta2} by its value obtained from~\eqref{KG-X} and get
\begin{equation}\label{consistency condition}
\lambda X\frac{\partial V}{\partial X}-\frac{\partial V}{\partial \theta}=\lambda (1+\lambda^2)\dot{X}^2.
\end{equation}
The $\lambda=0$ case trivially holds and the extension of above discussion to $\lambda=\lambda(t)$, adds an extra term $X\dot{X}\dot{\lambda}$ to the right hand side of~\eqref{consistency condition}. In the following, we consider~\eqref{consistency condition} as the consistency condition that $V(X,\theta)$ must satisfy.
\section{A Consistent CR Potential}\label{CR Potential}
Following the discussion in subsection \ref{sec: consistency condition}, a universal definition for CR multi-field models that can be applied to complex fields is~\eqref{CR constraint3}. Based on this definition, the time profile of Hubble parameter and scale factor are given by
\begin{equation}\label{H(t)}
H(t)=C_1\frac{C_2 e^{C_1\eta t}+e^{-C_1\eta t}}{C_2 e^{C_1\eta t}-e^{-C_1\eta t}}, \qquad a(t)=C_3\left(C_2 e^{C_1\eta t}-e^{-C_1\eta t}\right)^{1/\eta}.
\end{equation}
Here $C_i$s, $(i=1,2,3)$ are integration constants and $C_1$ represents a mass scale. Mathematically,~\eqref{H(t)} gives a solution of~\eqref{CR constraint3} for any complex values of $C_i$s. We, however, focus on the cases with real values. For potential $V(t)$, we get
\begin{equation}\label{V(t)}
V(t)=3 H^2+\dot{H}= C_1^2 \left(3+\frac{4 (3-\eta) C_2}{\left(C_2 e^{C_1 \eta t}-e^{- C_1 \eta t} \right)^2} \right) .
\end{equation}
Substituting the time derivative of the first relation in~\eqref{H(t)} into~\eqref{CR constraint3}, the CR definition can be written in this new equivalent form
\begin{equation}\label{CR constraint4}
\dot{Z}=-2\eta HZ.
\end{equation}
Recalling that $Z=|\dot{\Phi}|^2$, the equivalence of CR definitions~\eqref{CR constraint 21},~\eqref{CR constraint3} and~\eqref{CR constraint4} is evident. Furthermore, from $Z=-2\dot{H}$ and the Hubble parameter expression in~\eqref{H(t)}, it is easy to see that
\begin{equation}\label{Z(t)}
Z(t)=\frac{8\eta C_1^2 C_2}{\left(C_2 e^{C_1\eta t} - e^{-C_1 \eta t}\right)^2}.
\end{equation}
Obviously, to have a positive kinetic energy, we need $Z>0$. This immediately implies that the parameter $\eta$ and the integration constant $C_2$ have the same sign.
By $Z(t)$ in hand, we use the following ansatz $\dot{X}=-\sqrt{Z}\cos(\gamma)$ and $X\dot{\theta}=\sqrt{Z}\sin(\gamma)$ to determine the contribution of different DoFs in kinetic energy, at time $t$.\footnote{Note that for $\cos(\gamma)>0$, the minus sign for $\dot{X}$ is consistent with the real field inflation model.}
Here $\gamma\in\left(-\frac{\pi}{2},\frac{\pi}{2}\right)$ is an arbitrary function of time and by choosing any specific function for $\gamma(t)$, a relation between DoFs shall be established. The main source of this arbitrariness is the fact that in a system with different DoFs, the map between $t$ and DoFs is not generally one-to-one; so the procedure of replacing the time parameter in~\eqref{V(t)} by a function of $X$ and $\theta$ is quite arbitrary. This arbitrariness can be seen in another way in an equivalent form of equation~\eqref{CR constraint4} given by
\begin{equation}\label{CR constraint5}
X^2\dot{\theta}\ddot{\theta}+\dot{X}\ddot{X}+X\dot{X}\dot{\theta}^2=-\eta H(\dot{X}^2+X^2\dot{\theta}^2).
\end{equation}
To pinpoint the CR evolution of DoFs, the above form can be decomposed in different ways. Some simple decompositions are
\begin{subequations}\begin{empheq}[]{align}
&\ddot{X}=-\eta H\dot{X} \qquad X\ddot{\theta}=-\eta H X\dot{\theta}-\dot{X}\dot{\theta}, \label{decomposition 1}\\
&\dot{X}\ddot{X}+X\dot{X}\dot{\theta}^2=-\eta H\dot{X}^2 \qquad \ddot{\theta}=-\eta H\dot{\theta} \label{decomposition 2}.
\end{empheq}\end{subequations}
Either decomposition corresponds to a particular relation between DoFs, for example $X=X(\theta(t),t)$. One can talk about a single-valued map $X(t)$ or $\theta(t)$ iff the decomposition gives $X(t)=X(\theta(t))$. These expressions may be inverted to give $t(X)$ and $t(\theta)$ as well as other dynamical quantities like Hubble parameter, $\dot{\theta}$ or $\dot{X}$ in terms of $X$ or $\theta$.
In the following, we work with~\eqref{decomposition 1} that constraints the absolute value of the complex field by $\ddot{X}=-\eta H\dot{X}$. By imposing the above ansatz into~\eqref{Friedmann3}, we find that $\dot{X}\propto X\dot{\theta}\propto\exp\left(-\eta\int{H dt}\right)$. This yields a relation between DoFs similar to~\eqref{theta(X)}, with $\lambda=\tan(\gamma)=$constant. We recall that by choosing $\gamma=$constant the contribution of each DoF in kinetic energy will be fixed, for all times. In this simple case, the exact expression for $X(t)$ and $\theta(t)$ are given by
\begin{subequations}\begin{empheq}[]{align}
&X(t)=-\cos(\gamma)\int{\sqrt{Z(t)}dt}\propto
\cos(\gamma)\arctanh\left(\sqrt{C_2} e^{C_1 \eta t}\right),\label{X(t)}\\
&\theta(t)=\sin(\gamma)\int{\frac{\sqrt{Z(t)}}{X(t)}dt}=\tan(\gamma)\int{\frac{\sqrt{Z(t)}}{\int^t{\sqrt{Z(\acute{t})}d\acute{t}}}dt}=\tan(\gamma)\ln\left(\frac{X(t)}{\cos(\gamma)}\right).\label{theta(t)}
\end{empheq}\end{subequations}
Although the potential time profile~\eqref{V(t)} is fixed by this CR definition, we discuss how $V(X,\theta)$ can be found, if we work with~\eqref{decomposition 1}. Let us consider the potential in a sum separable form $V=V_1\left(X\right)+V_2(\theta)$, and then find $dV_1/dX$ and $dV_2/d\theta$ from the field equations~\eqref{KG-X} and~\eqref{KG-theta}. After employing the decomposition given in~\eqref{decomposition 1}, we will have
\begin{subequations}\begin{empheq}[]{align}
&V_1=\int{\frac{dV_1}{dX}}dX=\int{(\eta-3)}H\dot{X}dX+\int{X\dot{\theta}^2 dX },\label{V_1} \\
&V_2=\int{\frac{dV_2}{d\theta}d\theta}= \int{X\dot{\theta}\left[(\eta-3)H X-\dot{X}\right] d\theta}.\label{V_2}
\end{empheq}\end{subequations}
The real field potential is obtained from the first integral in~\eqref{V_1}. Furthermore, it is easy to check that the the sum $V_1+V_2$ obtained from equations in~\eqref{V_1} and~\eqref{V_2}, satisfies the consistency condition~\eqref{consistency condition}. Although a more general form of a sum separable potential, i.e, $V=a V_1\left(X\right)+ b V_2(\theta)$, with constant positive definite values for $a$ and $b$, could have been considered, we take the simpler form $a=b=1$, for the consistency condition to be satisfied. Now, to have the exact expression for potential, we apply this procedure to two interesting model groups: 1) $\eta > 0$ and $C_2>0$ and 2) $\eta < 0$ and $C_2<0$. Note that the condition $\eta C_2>0$ is necessary when CR definition~\eqref{CR constraint3} is used.
\subsection{$\eta > 0$ and $C_2>0$}\label{eta positive}
For $C_2>0$ case, one can define $\alpha=\frac{1}{2}\ln{C_2}$ and rewrite solutions~\eqref{H(t)} as
\begin{equation}\label{H(t) eta positive}
H(t)=C_1 \coth\left(C_1 \eta t+\alpha\right), \qquad a(t)=\tilde{C}_3 \sinh^{\frac{1}{\eta}}\left(C_1 \eta t+\alpha\right).
\end{equation}
To avoid singular behavior when $t\rightarrow 0$, we keep $C_2\neq 0$. Moreover, to ensure the positivity of Hubble parameter, $H>0$, we have to take $\left(C_1 \eta t+\alpha\right)\geq 0$ and $C_2>1$. Using~\eqref{X(t)} and following the discussion given in \cite{Anguelova:2017djf} about $\arctanh$ with an argument larger than one, we find that
\begin{equation}\label{X(t), eta positive}
X=\frac{1}{\kappa}\ln\left(\coth{\frac{1}{2}(C_1\eta t+\alpha)}\right),
\end{equation}
where a dimensionless parameter $\kappa:=\frac{\sqrt{2\eta}}{2\cos(\gamma)}$ is defined. As far as $t$ as a function of DoFs is concerned, one can invert~\eqref{X(t), eta positive} and get
\begin{equation}
\coth(C_1\eta t+\alpha)=\cosh\left(\kappa X\right)=\cosh\left(\sqrt{\frac{\eta}{2}}e^{\frac{\theta}{\tan(\gamma)}}\right).
\end{equation}
In the second equality, equation~\eqref{theta(t)} is used. The Hubble parameter, $H$, and the kinetic energy related function, $Z$, expressed in terms of DoFs are given by
\begin{eqnarray}\label{}
H=C_1 \cosh\left(\kappa X\right)=C_1 \cosh\left(\sqrt{\frac{\eta}{2}} e^{\frac{\theta}{\tan(\gamma)}}\right),\\
Z=2\eta C_1^2\sinh^2\left(\kappa X\right)=2\eta C_1^2\sinh^2\left(\sqrt{\frac{\eta}{2}} e^{\frac{\theta}{\tan(\gamma)}}\right).
\end{eqnarray}
This, together with the ansatz $\dot{X}=-\sqrt{Z}\cos(\gamma)$ and $X\dot{\theta}=\sqrt{Z}\sin(\gamma)$ immediately gives $\dot{X}$ and $\dot{\theta}$. Now, we have whatever needed to do the integrations in~\eqref{V_1} and~\eqref{V_2}. We will finally get
\begin{eqnarray}\label{V(X,theta) eta positive}
V(X,\theta)&=&V_1(X)+V_2(\theta)\nonumber\\
&=& \text{constant}+\frac{{C_1^2}}{2}\left\{(3-\eta)\cos^2(\gamma)\cosh\left(2\kappa X\right)-2\eta \sin^2\left(\gamma\right)\left[\Chie\left(2\kappa X\right)-\ln(\kappa X)\right]\right.\nonumber\\
&+ & \left.\sin^2(\gamma)\left[{(3-\eta)}\cosh\left(\sqrt{2\eta}e^{\frac{\theta}{\tan(\gamma)}}\right)+{2\eta} \Chie\left(\sqrt{2\eta}e^{\frac{\theta}{\tan(\gamma)}}\right)-{2\eta} \ln\left(\sqrt{\frac{\eta}{2}}e^{\frac{\theta}{\tan(\gamma)}}\right)\right]\right\}.\nonumber\\
\end{eqnarray}
Here $\Chie(x)$ is the hyperbolic cosine integral defined by
\begin{equation}\label{Chie}
\Chie(x)=\gamma+\ln(x)+\int^x_0{\frac{\cosh(t)-1}{t} dt}.
\end{equation}
A comparison between~\eqref{V(t)} and~\eqref{V(X,theta) eta positive} gives the constant term equal to $\frac{C_1^2}{2}\left(3+\eta\right)$. It can also be found from the $\gamma\rightarrow 0$ limit of~\eqref{V(X,theta) eta positive}.
\subsection{$\eta< 0$ and $C_2<0$}\label{eta negative}
Let us now consider negative values of constant roll parameter. For these models, we substitute $C_2=-|C_2|$ and $\eta=-|\eta|$ in~\eqref{H(t)} and find
\begin{equation}\label{H1(t)}
H(t)=-C_1 \tanh(C_1|\eta| t+\beta), \qquad a(t)=\bar{C}_3\cosh^{\frac{1}{\eta}}(C_1|\eta| t+\beta).
\end{equation}
Here $\beta=-\frac{1}{2}\ln|C_2|$. In these models $t$ is limited to the range $(-\infty,-\frac{\beta}{C_1 |\eta|}]$. Recalling that $\arctanh(i x) =i\arctan(x)$ $\forall x$, we get
\begin{equation}\label{X(t), eta negative}
X=\sqrt{\frac{8}{|\eta|}}\cos(\gamma)\arctan\left(e^{C_1 |\eta| t+\beta}\right)=\frac{2}{\mu}\arctan\left(e^{C_1 |\eta| t+\beta}\right).
\end{equation}
Here $\mu=\frac{\sqrt{2|\eta|}}{2\cos(\gamma)}$ and we assumed $X(-\infty)=0$. Besides, we have
\begin{equation}
\exp(C_1 |\eta| t+\beta)=\tan\left(\frac{\mu}{2}X\right)=\tan\left(\sqrt{\frac{|\eta|}{8}} e^{\frac{\theta}{\tan(\gamma)}}\right).
\end{equation}
Like the previous case, Hubble parameter $H$ and $Z$ are easily found
\begin{eqnarray}
H&=&C_1\cos\left(\mu X\right)=C_1\cos\left(\sqrt{\frac{|\eta|}{2}} e^{\frac{\theta}{\tan(\gamma)}}\right),\\
Z&=&2|\eta|C_1^2\sin^2\left(\mu X\right)=2|\eta|C_1^2\sin^2\left(\sqrt{\frac{|\eta|}{2}} e^{\frac{\theta}{\tan(\gamma)}}\right),
\end{eqnarray}
and potential is given by
\begin{eqnarray}\label{V(X,theta) negative eta}
V(X,\theta)&=&V_1(X)+V_2(\theta)\nonumber\\
&=& \text{constant}+\frac{{C_1^2}}{2}\left\{(|\eta|+3)\cos^2(\gamma)\cos\left(2\mu X\right)+2|\eta|\sin^2(\gamma)\left[\ln(\mu X)-\Ci(2\mu X)\right]\right.\nonumber\\
&+&\left.\sin^2(\gamma)\left[(|\eta|+3)\cos\left(\sqrt{2|\eta|}e^{\frac{\theta}{\tan(\gamma)}}\right)+2|\eta|\left(\Ci\left(\sqrt{2|\eta|}e^{\frac{\theta}{\tan(\gamma)}}\right)-\ln\left(\sqrt{\frac{|\eta|}{2}}e^{\frac{\theta}{\tan(\gamma)}}\right)\right)\right]\right\}.\nonumber\\
\end{eqnarray}
Here, $Ci(x)$ stands for the cosine integrals, defined by\footnote{In the definitions~\eqref{Chie} and~\eqref{Ci} $\gamma$ is Euler–Mascheroni constant and should not mixed up with $\gamma$ used throughout this paper to determine the contributions of DoFs in kinetic energy.}
\begin{equation}\label{Ci}
\Ci(x)=\gamma+\ln(x)+\int^x_0{\frac{\cos(t)-1}{t} dt}.
\end{equation}
In a similar way, the constant term can be found to be $\frac{C_1^2}{2}(3-|\eta|)$.
\section{Dynamical Analysis}\label{Dynamical Analysis}
By combining equation~\eqref{KG-X} and~\eqref{KG-theta}, we get the dynamics of field in terms of the field absolute value\footnote{In the rest of paper we use different notations $X$, $|\Phi|$ or even $x$ equivalent to each other.} $|\Phi|$,
\begin{equation}\label{KG4}
|\dot{\Phi}|\frac{d|\dot{\Phi}|}{dt}+3H|\dot{\Phi}|^2+\frac{d V(|\Phi|)}{dt}=0.
\end{equation}
One can easily find more familiar form of equation~\eqref{KG4}, after applying the ansatz $\frac{d|\Phi|}{dt}=-\cos(\gamma)|\dot{\Phi}|$, as
\begin{equation}
\label{KG41}\frac{d^2|\Phi|}{dt^2}+(3H+\dot{\gamma} \tan(\gamma))\frac{d|\Phi|}{dt}+\cos^2(\gamma)\frac{dV(|\Phi|)}{d|\Phi|}=0.
\end{equation}
The form of potential solution found in previous subsection would be best described by $V(X,\theta)=V(X,\theta(X))$. An equivalent form of this potentials, in terms of canonical coordinates $V(\varphi_1,\varphi_2)=V(\varphi_1,\varphi_2(\varphi_1))$, are given in appendix~\ref{sec:canonical}. If the relation between DoFs is applied to either expression, one can find $V(|\Phi|)$, as follows
\begin{subequations}\label{eqn:V(Phi)}\begin{empheq}[left={V(|\Phi|)= \empheqlbrace}]{align}
&\frac{C_1^2}{2}\left[(3+\eta)+(3-\eta)\cosh\left(2\kappa |\Phi|\right)\right] \quad &\eta > 0, \label{positive} \\
&\frac{C_1^2}{2}\left[(3-|\eta|)+(3+|\eta|)\cos\left(2\mu |\Phi|\right)\right] \quad &\eta < 0. \label{negative}
\end{empheq} \end{subequations}
\label{eq:system}
These potentials have three fixed parameters $(C_1,\eta,\gamma)$. The first parameter determines the inflation scale. The qualitative form of potential depends on the values of $(\eta,\gamma)$ which is invariant under $\gamma\leftrightarrow -\gamma$. A plot of this can be seen in figure \ref{fig:potential plots}.
\begin{figure}\begin{center}
\includegraphics[scale=.25]{potential2.5}
\includegraphics[scale=.25]{potential3.5} \end{center}
\caption{The form of potentials~\eqref{positive} for $\eta=2.5$ and $\eta=3.5$ and different values of $\gamma$ are compared with that of $\gamma=0$. The domain of validity of these potentials is limited to the right half of this plots and the other half is given for the comparison with $\gamma=0$.}%
\label{fig:potential plots}
\end{figure}
Generally, these forms are very much like the potentials found in the literature for real field CR models. For $0<\eta<3$, the potential is a convex function like a hybrid-type inflation, where a kind of transition is needed to end the inflation. For $\eta>3$, the potential is a concave function like a hilltop-type inflation. For $\eta<0$, the potential is again a concave function and is a particular type of hilltop inflation models. Here, the additional DoF has increased the slope of the potential and rescaled the field absolute value. The slope change, which is controlled by either $\kappa$ or $\mu$, is a natural consequence of partitioned kinetic energy. Figure \ref{fig:potential plots} shows that by increasing $\gamma$ the region around the extrema which can be approximated by a quadratic expression is reduced. The size of this region is important in the evolution of the system under the duality relation discussed in the literature \cite{Tzirakis:2007bf, Morse:2018kda,Gao:2019sbz}. $\eta=3$ is the critical value, in which the potential is constant and invariant under $|\Phi|\rightarrow |\Phi|+$constant.
In these particular solutions, in which $\eta$ is assumed to be constant, the inflation seems to take place near the maximum for concave potentials and ends as the field rolls down and in the case of convex potentials, the field asymptote to rest at the bottom of the potential as $|\dot{\Phi}|\rightarrow 0$. To check whether this solution is an attractor or not we will concentrate on the phase space diagrams directed by these potentials, in the following subsection. On the other hand, the parameter $\gamma$ quantifies the contribution of additional DoF in kinetic energy and study of its evolution determines whether there are regimes that the phase of complex field affects the field dynamics. We therefore study the variations of $\gamma$, when the field has reached the attractor path in subsection~\ref{Stability Analysis}.
\subsection{Attractor Behavior-Phase Space Analysis}\label{Attractor Behavior}
Although the potentials given in~\eqref{V(X,theta) eta positive},~\eqref{V(X,theta) negative eta} and~\eqref{V(phi1,phi2)} look different, all three satisfy the following phase space equations
\begin{equation}\label{non-autonomous equations}
\frac{d x}{dt}=-\cos(\gamma(t))y, \qquad \frac{d y}{dt}=-3 H y-\frac{1}{y}\frac{d V}{d t}.
\end{equation}
Here we worked with dimensionless variables: $x\equiv|\Phi|$, $y\equiv|\dot{\Phi}|/C_1$, $t\equiv C_1 t$, $H\equiv H/C_1$, $V\equiv V/C_1^2$ and functions $H(t)$ and $V(t)$ are given by~\eqref{H(t)} and~\eqref{V(t)}, respectively. No matter what the arbitrary function $\gamma(t)$ is given, these non-autonomous nonlinear equations are common between all CR inflationary models which satisfy~\eqref{CR constraint4}. This universality is the result of choosing a CR definition which is independent of individual dynamics of DoFs.
The analysis of the inflationary dynamics for $\gamma=\gamma(t)$ is difficult, if not impossible to do. We, therefore, concentrate on the potentials given in~\eqref{eqn:V(Phi)}, in which $\gamma$ was assumed to be a constant and come back to $\gamma$ variations in next subsection. Using~\eqref{positive}, we will have a set of autonomous equations given by
\begin{equation}\label{autonomous equations}
\frac{d x}{dt}=-\cos(\gamma)y, \qquad \frac{d y}{dt}=-3 \cosh(\kappa x) y+(\eta-3)\sqrt{2\eta}\sinh(2\kappa x).
\end{equation}
We assume $C_2=1$, without any loss of generality. We have plotted the phase space trajectories for different values of $\gamma$ and $\eta=2.5,3.5$ in figure \ref{fig:(gamma,eta)}. In the first row there is an attractor trajectory toward the minimum for the convex potential, whereas for the concave potential plots (second row) there is not. In second row plots we see trajectories that field velocity vanishes before passing the maximum of the potential where the field rolls back. For the trajectories that reach the maximum the field velocity $|\dot{\Phi}|$ may well be nonzero. This is the characteristic feature of a non-slow-roll system since in slow-roll limit $|\dot{\Phi}|\propto V'(|\Phi|)$ which vanishes at extrema.
\begin{figure}
\includegraphics[scale=.1]{gamma,eta=0,2.5}
\includegraphics[scale=.09]{gamma,eta=pi-8,2.5}
\includegraphics[scale=.09]{gamma,eta=pi-4,2.5}
\includegraphics[scale=.09]{gamma,eta=pi-2.5,2.5}
\newline
\includegraphics[scale=.1]{gamma,eta=0,3.5}
\includegraphics[scale=.09]{gamma,eta=pi-8,3.5}
\includegraphics[scale=.09]{gamma,eta=pi-4,3.5}
\includegraphics[scale=.09]{gamma,eta=pi-2.5,3.5}
\caption{Trajectories of Phase space determined by the analytical potential given in~\eqref{positive}. Plots in top and bottom rows are for $\eta=2.5,3.5$ respectively. Plots in the left to right columns are for $\gamma=0,\frac{\pi}{8},\frac{\pi}{4},\frac{\pi}{2.5}$ respectively. The domain of validity of our discussion is limited to the right upper half in these plots and the other parts are given for the comparison with $\gamma=0$.}
\label{fig:(gamma,eta)}
\end{figure}
The attractor solutions in phase space parametrized by $(y,x;\eta)$ should not give an indication of the stability of CR parameter $\eta$. Equation~\eqref{CR constraint 21} shows that this parameter is a measure of field acceleration and may well be time dependent in some phase space regions. Motivated by the duality relation $\eta\longleftrightarrow 3-\eta$ and the argument that slow roll is the unique attractor solution in all cases, the authors in~\cite{Lin:2019fcz} showed that for large $\eta$s, the constant roll solutions cannot be stable and the background perturbations will result in evolving $\eta$ to the smaller value of $\left\{\eta, 3-\eta\right\}$. In the following, we will look at the differently parametrized phase space of CR complex fields to realize how the parameter $\gamma$ affects the asymptotic values of $\eta$. The stability of $\gamma$ under this stability analysis is assumed.
The phase space parametrized by $(y,x;\eta)$ breaks down at $V'\equiv{dV}/{dx}=0$ because the map $\eta(x,y)=3-\frac{V'(x)\cos(\gamma)}{H y}$ is not one-to-one at this point; so regardless of field velocity when the trajectories cross this point are forced to the critical value $\eta=3$. In other words, $\eta=3$ is the fixed point in $(x,\eta)$ plane. To check whether it is the late time attractor or not, the authors in~\cite{Pattison:2018bct} work on the variations of field acceleration around the fixed point. Following this methodology, we recast equation~\eqref{KG4} with $x$ and get the following first-order differential equation
\begin{equation}\label{dy/dx}
\frac{dy}{dx}-\frac{3H}{\cos(\gamma)}+\frac{V'}{y}=0,
\end{equation}
or
\begin{equation}\label{dy/dx equivalent}
\frac{dy^2}{dx}=-2V'\left(1-\frac{1}{\cos(\gamma)}\frac{3Hy}{V'}\right).
\end{equation}
Following the authors in \cite{Pattison:2018bct}, we also introduce the parameter $f=\frac{\eta}{3}$ and express equations~\eqref{dy/dx equivalent} and $y^2$ (or $|\dot{\Phi}|^2$) in terms of $x$ and $f$,
\begin{equation}\label{equations}
\frac{dy^2}{dx}=2V'\frac{f}{1-f},\qquad y^2=V\left[\sqrt{1+\frac{2}{3}\left(\frac{\cos(\gamma)}{1-f}\right)^2\left(\frac{V'}{V}\right)^2}-1\right].
\end{equation}
The combination of equations in~\eqref{equations}, leads us to an equation for the evolution of $f$,
\begin{equation}\label{df/dx}
\frac{df}{dx}=\frac{3}{2}\frac{V}{V'}\frac{(1-f)^2(1+f)}{\cos^2(\gamma)}\left[\sqrt{1+\frac{2}{3}\left(\frac{\cos(\gamma)}{1-f}\right)^2\left(\frac{V'}{V}\right)^2}-\frac{1-f}{1+f}\right]-(1-f)\frac{V''}{V'}.
\end{equation}
In order to study small deviations of complex fields from the $\eta=$ constant in phase plane, we linearise equation~\eqref{df/dx} around $f=\bar{\eta}/3$ by parametrizing
\begin{equation}
f=\frac{\bar{\eta}}{3}-\delta, \qquad |\delta|\ll1,
\end{equation}
and plot trajectories perturbed about a CR analytic solution started from $\bar{\eta}=2.5$ in figure~\ref{phase space1}.
\begin{figure}
\includegraphics[width=\columnwidth]{eta-phi}
\caption{Phase portrait of CR complex field parametrized by $\eta$, $|\Phi|$, for CR (convex) potential $\bar{\eta}=2.5$.}%
\label{phase space1}
\end{figure}
\begin{figure}
\includegraphics[width=\columnwidth]{dot_phi-phi}
\caption{Phase portrait of CR complex field parametrized by $|\dot{\Phi}|$, $|\Phi|$, for CR (convex) potential $\bar{\eta}=2.5$.}%
\label{phase space2}
\end{figure}
In this plot we see one trajectory associated to the analytic solution that reaches the minimum point, at $|\Phi|=0$, with $|\dot{\Phi}|=0$\footnote{We will see that this trajectory with finely tuned initial condition is the only possible trajectory with constant roll as such.} and two other perturbed trajectories with deviations $\delta$ of order $10^{-5}$. For trajectories with $3f<2.5$ (or $\delta>0$), the field relaxes to slow-roll attractor with $\eta=0.5$, before reaching the minimum point. However, for $\delta<0$ enough field speed lets the field to pass the minimum point where $\eta=3$. The authors in~\cite{Gao:2019sbz} showed that if $\epsilon_1<\eta$, the real field rolls past this point and then turns back to it in slow roll. In complex field trajectories also $\eta$ evolves away from $2.5$ toward $0.5$, which is the stable solution as perceived by the duality.
The duality is valid at cosmological perturbation level as well.
The evolution of the mode function $v_k=\sqrt{2}z\zeta_k$, with $z=a y/H$, is governed by the Mukhanov-Sasaki equation
\begin{equation}\label{Mukhanov-Sasaki}
v''_k+\left(k^2-\frac{z''}{z}\right)v_k=0,
\end{equation}
\begin{equation}
\frac{z''}{z}=a^2 H^2\left(2-\epsilon_1+\frac{3}{2}\epsilon_2+\frac{1}{4}\epsilon_2^2-\frac{1}{2}\epsilon_1\epsilon_2+\frac{1}{2}\epsilon_2\epsilon_3\right),
\end{equation}
and can be evaluated for constant roll solutions using
\begin{subequations}\begin{empheq}[left= \empheqlbrace]{align}
&\epsilon_1=2\kappa\tanh^2(\kappa x), \quad & \epsilon_2=2\eta > 0, \qquad & \epsilon_3=2\kappa\tanh(\kappa x),\label{positive1} \\
&\epsilon_1=-2\mu\tan^2(\mu x), \quad & \epsilon_2=2\eta < 0, \qquad & \epsilon_3=-2\mu \tan(\mu x)\label{negative1}
.\end{empheq}\end{subequations}
In either case we then have
\begin{equation}
\frac{z''}{z}=a^2 H^2\left[(\eta-2)(\eta-1)+\left(\eta^2-\frac{3}{2}\eta^3\right)\left(\frac{x}{\cos(\gamma)}\right)^2+O\left(\frac{x}{\cos(\gamma)}\right)^3\right].
\end{equation}
One can see the self-duality of Mukhanov-Sasaki equation under $\eta\rightarrow3-\eta$ in the limit of $\frac{|\Phi|}{\cos(\gamma)}\ll 1$. Outside this region the evolution of background and scalar perturbations are different and the duality between large and small $\eta$ breaks down. The authors in \cite{Gao:2019sbz} showed that the duality in scalar spectral tilt and tensor to scalar ratio expressions is true if $\epsilon_1<\eta<3$. Since the Hubble flow slow-roll parameters in CR complex and real field models are similar, it is easy to see that equations (12-15) in their work are valid for our model; so their result is valid for complex fields as well.
The additional DoF has just restricted the field value range of validity of the duality to a smaller region in the vicinity of potential minimum. This should come as no surprise, since the potential slope is increased and its linear approximation is restricted to the smaller region. It is interesting to see that there is nothing special about $\gamma=0$ in respecting the duality relation except that in this case complex fields leave the analytic (unperturbed) trajectory at smaller field values.
For $\eta>3$, the analysis can be repeated as above. As $|\Phi|\rightarrow 0$, $|\delta|$ will grow causing $\eta$ to evolve away from the initial value either into slow roll (for $\delta>0$) or to $\eta=3$ (for $\delta<0$). In the former case the field rolls back the direction from which it came, down the hill and for the latter, the field rolls over the top of the potential. In both cases the generic attractor path is the dual slow roll regime with parameter $\bar{\eta}$ given by $3-\bar{\eta}$.
\subsection{Relative Kinetic Energy- Stability Analysis}\label{Stability Analysis}
The duality based discussion in above subsection showed that slow roll is the unique attractor solution even in the presence of an additional DoF. In this subsection we study the stability of the solutions by evolving $\gamma$. We would like to know whether there are regimes that the phase of complex field has observational effects. Equation~\eqref{KG41} gives us the form of evolution of $\gamma$ as
\begin{equation}\label{gamma-dot}
\dot{\gamma}=-\frac{1}{\tan(\gamma(t))\frac{d|\Phi|}{dt}}\left[\frac{d^2|\Phi|}{dt^2}+\cos^2(\gamma(t))\frac{{dV}/{dt}}{{d|\Phi|}/{dt}}+3H(t)\frac{d|\Phi|}{dt}\right].
\end{equation}
The three terms in the square bracket that compete together in this evolution are: the acceleration of field, the force from the potential gradient and Hubble friction.
Equation~\eqref{gamma-dot} is valid in the regime that the field has joined the attractor path on which $\eta$ = constant. We begin the stability analysis by substituting Hubble parameter ~\eqref{H(t)} for $\eta>0$ (or~\eqref{H1(t)} for $\eta<0$) and the corresponding potential given in ~\eqref{V(t)} into~\eqref{KG41}, but let the parameter $\gamma$ to be a function of time. We linearise equation~\eqref{gamma-dot} around a fixed value $\bar{\gamma}$ by
\begin{equation}
\gamma=\bar{\gamma}-\delta, \qquad |\delta|\ll 1
\end{equation}
and then plot trajectories in $\gamma-t$ space for different values of $\eta$. The results for different values of $\bar{\gamma}$ and $\eta=3.5$ are shown in figures \ref{fig:gamma instability}.
In this case, the trajectories with $\gamma$ = constant are unstable. The paths with $\delta<0$ asymptote to $\gamma=\pi/2$ (or $\gamma=-\pi/2$) and for $\delta>0$, the paths ends up to $\gamma=0$. The contribution of different terms of square bracket in~\eqref{gamma-dot} is also shown in figure \ref{fig:gamma instability}. For $\eta>3$, the force driven by the concave potential and the frictional force in~\eqref{gamma-dot} have equal signs; so any small change in $\gamma$ (or energy proportions) will be amplified to reach the asymptotic value.
The situation is completely different when the convex potentials play role. As it is shown in figure \ref{fig:gamma stability}, for $\eta<3$, the trajectories with $\gamma$ = constant are stable. On these trajectories the three above mentioned terms cancel each other and any small changes in energy proportion will soon freeze. Figures \ref{fig:gamma instability} and \ref{fig:gamma stability} show that the (in)stability is controlled by the sign and magnitude of potential gradient which is invariant under $\bar{\gamma}\leftrightarrow -\bar{\gamma}$. The symmetry is seen in the (in)stability behavior of system solutions.
Naively, then we must conclude from this surprising result that the concave potential given in~\eqref{positive} should be rectified for $\eta>3$. However, this result is only valid on the attractor path set by the duality relation $\eta\longrightarrow\left\{\eta,3-\eta\right\}$. From the analysis about the cosmological perturbations given in \cite{Gao:2019sbz}, it is easy to see that the time profile of mode functions $v_k$, the spectral tilt and the tensor to scalar ratio depend on the Hubble flow slow-roll parameters, which is similar to that of a real CR field and is stable under $\gamma$ variations.
We, therefore conclude that for the field values far from the range of validity of the duality, $\gamma$ = constant are stable and the potential given in~\eqref{eqn:V(Phi)} very well describe the CR complex field inflationary models.
\begin{figure}
\includegraphics[scale=.59]{1}
\hspace{0.2cm}
\includegraphics[scale=.59]{2}
\caption{A relative comparison between different terms in~\eqref{gamma-dot} for $\eta=3.5$ is given in the left panel. The right panel shows the variation of $\gamma$ parameter and in particular the instability of $\eta$ = constant trajectories controlled by concave potentials. The first value in the legend corresponds to $\bar{\gamma}$ in each case.}\label{fig:gamma instability}
\end{figure}
\begin{figure}
\includegraphics[scale=.59]{3}
\hspace{0.2cm}
\includegraphics[scale=.59]{4}
\newline
\includegraphics[scale=.59]{5}
\hspace{0.2cm}
\includegraphics[scale=.59]{6}
\caption{A relative comparison between different terms in~\eqref{gamma-dot} for values of $\eta=2.5$ and $-1.5$ is given in the left column. The right column shows the stability of $\eta$ = constant trajectories directed by convex potentials for these values of $\eta$. The first value in legends corresponds to $\bar{\gamma}$ in each case.}\label{fig:gamma stability}
\end{figure}
\section{Summary and Conclusion}\label{Conclusion
In a $N$-field cosmological scenario, the dynamical system includes $N+1$ equations governing $N$ matter fields and background scale factor. In this work we discussed that, for $N>1$, solving the coupled non-linear equations for the scalar and gravitational fields needs more caution.
Imposing a relation between value and velocity of fields may result in an over-determined system with generally no solution. In other words, not every constraint, that seems to be physically relevant, is compatible with the $N+1$ dynamical equations and renders the system integrable. In a subset of non-slow roll inflationary models known as constant roll inflation, we worked on complex field dynamical $\Phi$ equations and found a class of models for an appropriate constant roll definition. In these models there exists a degree of flexibility in the form of a function of time, $\gamma(t)$, which makes it possible to define an isomorphism between the field DoFs at each instant of time.
Apart from the mathematical difficulties associated with solving dynamical equations with a general $\gamma(t)$, choosing such a function should be based on physical grounds. In an attempt to surmount the mathematical difficulties, we first focused on a subclass of solutions with an arbitrary but constant value of parameter $\gamma$, where $\gamma=0$ corresponds to the real field model. In this subclass, the $V(\Phi;\gamma)$ potential functions have larger curvature, if compared to the real field CR models at a fixed $\Phi$ value. By performing the stability analysis on the large $\eta$ phase space solutions, we showed that, similar to a real field, this subclass solutions are at most early time transients. Small perturbations to these solutions deviate the phase space trajectory with CR parameter $\eta$ from the larger unstable value of $\left\{\eta, 3-\eta\right\}$, to the smaller value, which is the stable solution. In this transition however, complex fields enter the stable regime at smaller field values. The additional DoF plays two roles in this transition: first by reducing the kinetic term and second by changing in the potential slope. This, however,
does not affect the extent of growth of the conventionally decaying perturbation modes, or the number of $e$-folds from the end of inflation since the time profile of Hubble parameter and the scale factor are unchanged.
We chose to work with constant $\gamma$ initially, but performed the stability analysis on $\gamma$ function space solutions, at the end. We concluded that $\gamma$=constant paths considered in the above discussions are transient for $\eta>3$. These paths are stable whenever the field is rolling down a convex potential or relaxes on an attractor. In other words, only dynamically stable trajectories in phase space are stable under $\gamma$ variations; so the potentials given in~\eqref{eqn:V(Phi)} describe the dynamically stable part of the CR complex field inflationary models, very well. We would like to stress that complex field CR models include this phenomenologically interesting subclass but are not restricted to it.
\section*{Acknowledgements}
We acknowledge the financial support of the research council of the University of Tehran.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 2,522 |
Q: Is it possible to search by daily time range between dates? I can use aggregate to make some stats between two timestamps as following:
{
"size": 0,
"query": {
"bool": {
"filter": [
{
"term": {
"status": "ok"
}
},
{
"term": {
"deviceId": "123456789"
}
},
{
"range": {
"time": {
"gte": 1669852800,
"lt": 1671062400
}
}
}
]
}
},
"aggs": {
"results": {
"date_histogram": {
"field": "time",
"fixed_interval": "60",
}
}
}
}
Is it possible to query the results contain specific time range daily only? For example, 7am - 9am daily between Dec.1 to Dec.15. How to achieve it?
A: I found the solution on elasticsearch v7.15.2 as following:
{
"size": 0,
"query": {
"bool": {
"filter": [
{
"term": {
"status": "ok"
}
},
{
"term": {
"deviceId": "123456789"
}
},
{
"range": {
"time": {
"gte": 1669852800,
"lt": 1671062400
}
}
},
{
"script": {
"script": {
"source": "doc.time.value.getHourOfDay() >= params.min && doc.time.value.getHourOfDay() < params.max",
"params": {
"min": 8,
"max": 10
}
}
}
}
]
}
},
"aggs": {
"results": {
"date_histogram": {
"field": "time",
"fixed_interval": "60"
}
}
}
}
The syntax is slightly different from the comment above, but it works.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 3,777 |
\section{Introduction}
In the near future new galaxy surveys will provide a large number of
spectra, which will enable important measurements of galaxy
properties. For example, the 2 degree field (hereafter 2dF) Galaxy
Survey aims to collect 250,000 spectra. The integrated spectrum of a
galaxy is a measure of its stellar composition and gas content, as
well as its dynamical properties. Moreover, spectral properties often
correlate fairly closely with galaxy morphology. Indeed, as the
spectra are more directly related to the underlying astrophysics, they
could prove a more robust classifier for evolutionary and
environmental studies. Spectra can be obtained to larger redshifts
than ground-based morphologies and, as 1-D data sets, are easier to
analyse. Although the concept of spectral classification goes back to
Humason (1936) and Morgan \& Mayall (1957), few uniform data sets are
available and a number of different approaches to the problem are
possible.
Spectral classification is important for several practical and
fundamental reasons. In order to derive luminosities corrected for
the effects of redshift, the $k$-correction must be estimated for each
galaxy. The rest-frame spectral energy distribution is needed, which
can be obtained by matching the observed spectrum against templates of
local galaxies. The proportion of sources in each class as a function
of luminosity and redshift is of major interest. Apart from its
relevance for environmental and evolutionary studies, new classes of
objects may be discovered as outliers in spectral parameter space.
Furthermore, by incorporating spectral features with other parameters
(e.g. colour and velocity dispersion) an `H-R diagram for galaxies'
can be examined with possible important implications for theories of
galaxy formation.
In this paper we explore the PCA and Artificial Neural Network
(hereafter ANN) combination when applied to noisy galaxy spectra. PCA
has been demonstrated to be a useful tool for spectral classification,
with applications to stellar spectra (e.g. Murtagh \& Heck 1987; von
Hippel et al. 1994), QSO spectra (Francis et al. 1992) and galaxy
spectra (Sodr\'e \& Cuevas 1994; Sodr\'e \& Cuevas 1996; Connolly et
al. 1995). ANNs have been used for classification of images
(Storrie-Lombardi et al. 1992; Naim et al. 1995; Lahav et al. 1995)
and stellar spectra (Storrie-Lombardi et al. 1994) along with a
variety of other astronomical applications. Other approaches have also
been taken, such as analysing the weight of specific components in
each galaxy spectrum (Zaritsky et al. 1995). This approach is similar
to the PCA technique, but the templates do not form an orthogonal set,
although they can be chosen specifically to highlight certain
characteristics in the spectra, such as young stars or emission
lines. However, this approach does not allow for spectral variations
extending outside the scope of the predetermined template set.
In this paper we use PCA on the complete spectra of the data set as
opposed to some other spectral analyses which use specific measured
quantities from the spectra (e.g. line strengths). We prefer to use
the complete data so that we are not restricted to a set of
predetermined measures. By using all the available data, the S/N
inherent in the method is increased.
ANNs, originally suggested as simplified models of the human brain,
are computer algorithms which provide a convenient general-purpose
framework for classification (e.g. Hertz et al. 1991). ANNs are
related to other statistical methods common in Astronomy and other
fields. In particular ANNs generalize Bayesian methods,
multi-parameter fitting, PCA, Wiener filtering and regularisation
methods (e.g. Lahav et al. 1996).
We take the approach of using a fairly small set of high S/N spectra,
and degrade them using the parameters of the 2dF system on the AAT.
This produces simulated spectra for a range of possible noise levels
which allows us to quantify the affect of the increasing noise and put
limits on the success rates we hope to achieve for the spectral
classification. In section 2 we describe the data set and show
examples of the simulations. In section 3 we utilize the technique of
Principal Component Analysis to compress the data set and to extract
the `real' information from the noisy spectra, leading to section 4,
where we look at the spectral reconstructions based on the PCA,
highlighting the ideal methods to use. In section 5 we use an
Artificial Neural Network to operate on the results from the PCA, and
demonstrate the level of classification success attained by this
method. We end with a discussion of the results and the conclusions of
the investigation.
\section[]{Data}
The spectra used in this investigation are taken from the
spectrophotometric atlas of galaxies (Kennicutt 1992) and represent
the integrated spectra of local galaxies. They have been selected to
demonstrate a wide range of spectral signatures. Most of the spectra
have 5-8\AA \ resolution but a few have been observed giving a lower
resolution of 10-25\AA . The spectra cover the wavelength range from
3650-7100\AA , although for the purposes of this paper, we are left
with a slightly shorter range when the simulation process has been
applied (see Appendix A). More details of the observations are given
in Kennicutt (1992). For the purposes of this paper the spectra have
been split into two groups. The `Normal26' spectra have been
selected as being representative spectra for galaxies of normal
morphological type, i.e. galaxies which conform simply to the Hubble
classification scheme (Hubble 1936). The `Unusual29' spectra
comprise the remainder of the galaxies observed by Kennicutt. These
spectra include peculiar and starburst galaxies and also galaxies with
Seyfert nuclei.
\begin{table}
\caption{Morphological groups. Each group is given a name, a number
G (for use in section 5), the T-Types covered by the group and the
percentage of the galaxies in the ESO catalogue which fall into that
group.}
\begin{tabular}{llcl}
\hline
{\em Group} & {\em G} & {\em T-Types} & {\em ESO \%}\\ \hline
\hline
{\bf E,S0} & {1} & $T\leq 0.5$ & 21.0\\
{\bf Sa} & {2} & $0.5<T\leq 2.5$ & 16.9\\
{\bf Sb} & {3} & $2.5<T\leq 4.5$ & 20.9\\
{\bf Scd} & {4} & $4.5<T\leq 8.5$ & 30.1\\
{\bf Irr} & {5} & $8.5<T$ & 11.1\\
\end{tabular}
\end{table}
The Normal26 spectra have been split into five broad groups, based on
their visual morphology. These groups can be seen in Table 1 which
also gives the percentage of galaxies falling into each group for the
ESO catalogue (Lauberts \& Valentijn 1989). We decided to bin the
data in this way so that there are a number of spectra in each group
and the ANN is not over-trained to recognize a specific spectrum for a
particular class. With the small data set that we have, this is still
a risk, but the combination of this binning and using many noisy
deviates of each spectrum helps to alleviate the problem.
Unfortunately the `Irr' group is not well represented in the Normal26
sample, since all but two of these galaxies fall into the Unusual29
set.
\begin{figure}
\label{fig1}
\psfig{figure=fig1.ps,width=3.4in,height=3.4in}
\caption{Simulated spectra based on NGC 3379 (E0).}
\end{figure}
The Unusual29 spectra have also been tentatively placed in these
5 groups, based on their visual morphology where it is
defined. Spectra without a defined morphology, or purely labeled as
peculiar, have been placed in the final bin. Table 2 summarizes the
data set. A notes section is also given for the Unusual29 spectra,
which specifies why they have been categorized as unusual. Two of the
spectra were found to adversely bias the PCA, and so have been removed
from the normal set of spectra. In the case of NGC 1569 this is due to
serious galactic reddening being evident in the continuum. In the case
of MK 487 the reason is less obvious, but visual inspection of the
spectrum (Kennicutt 1992) indicates an erratic continuum.
\begin{table*}
\caption{The selection of galaxy spectra from Kennicutt (1992).}
\begin{tabular}{lllp{1cm}llll}
\hline
\multicolumn{3}{c}{\bf Normal26} && \multicolumn{4}{c}{\bf Unusual29} \\ \hline
\hline
{\em Galaxy} & {\em Morphology} & {\em Group} && {\em Galaxy} & {\em Morphology} & {\em Group} & {\em Notes}\\ \hline
\hline
NGC3379 & E0 & E,S0 && MK487 & Im & Irr & Odd (see text) \\
NGC4472 & E1/S0 & E,S0 && NGC1569 & Sm/Im & Irr & Reddened \\
NGC4648 & E3 & E,S0 && NGC4670 & SB pec & Irr & Peculiar \\
NGC4889 & E4 & E,S0 && NGC3034 & I0 & Irr & Peculiar\\
NGC3245 & S0 & E,S0 && NGC3077 & I0 & Irr & Peculiar\\
NGC3941 & SB0/a & E,S0 && NGC5195 & I0 pec & Irr & Peculiar\\
NGC4262 & SB0 & E,S0 && NGC6240 & I0 pec & Irr & Peculiar\\
NGC5866 & S0 & E,S0 && NGC3310 & Sbc pec & Sb & Global Starburst\\
NGC1357 & Sa & Sa && NGC3690 & Sc pec & Scd & Global Starburst\\
NGC2775 & Sa & Sa && NGC6052 & Sm pec & Irr & Global Starburst\\
NGC3368 & Sab & Sa && UGC6697 & S pec & Irr & Global Starburst\\
NGC3623 & Sa & Sa && NGC2798 & Sa pec & Sa & Starburst Nucleus\\
NGC1832 & SBb & Sb && NGC3471 & Sa & Sa & Starburst Nucleus\\
NGC3147 & Sb & Sb && NGC5996 & SBd & Irr & Starburst Nucleus\\
NGC3627 & Sb & Sb && NGC7714 & S pec & Irr & Starburst Nucleus\\
NGC4750 & Sbpec & Sb && MK35 & pec & Irr & Peculiar\\
NGC2276 & Sc & Scd && MK59 & SBm/Im & Irr & HII Region\\
NGC4775 & Sc & Scd && MK71 & SBm & Irr & HII Region\\
NGC5248 & Sbc & Sb && NGC3516 & S0 & E,S0 & Seyfert I\\
NGC6217 & SBbc & Sb && NGC5548 & Sa & Sa & Seyfert I\\
NGC2903 & Sc & Scd && NGC7469 & Sa & Sa & Seyfert I\\
NGC4631 & Sc & Scd && NGC3227 & Sb & Sb & Seyfert II\\
NGC6181 & Sc & Scd && NGC6764 & SBb & Sb & Seyfert II\\
NGC6643 & Sc & Scd && MK3 & S0 & E,S0 & Seyfert II\\
NGC4449 & Sm/Im & Irr && MK270 & S0 & E,S0 & Seyfert II\\
NGC4485 & Sm/Im & Irr && NGC1275 & E pec & E,S0 & Peculiar\\
& & && NGC3303 & pec & Irr & Peculiar\\
& & && NGC3921 & S0 pec & E,S0 & Peculiar\\
& & && NGC4194 & Sm pec & Irr & Peculiar\\
\end{tabular}
\end{table*}
\begin{figure}
\label{fig2}
\psfig{figure=fig2.ps,width=3.4in,height=3.4in}
\caption{Simulated spectra based on NGC 3627 (Sb).}
\end{figure}
In order to accurately test the methods for spectral reconstruction
and classification it is first necessary to produce a set of galaxy
spectra which resembles the spectra received from large redshift
surveys. Details for the 2dF system (Taylor 1994) on the
Anglo-Australian Telescope are used to degrade the Normal26 spectra,
to simulate spectra from objects with a range of $b_{\rm J}$
magnitudes. Appendix A gives details about the spectral simulation
procedure, detailing how the system response function, sky spectrum,
fibre size and galaxy magnitude are incorporated into the
simulations. It should be noted that it is difficult to predict the
exact performance of the 2dF system and observations will obviously
differ due to conditions, hence the simulations remain approximate,
but demonstrate the level and variation of noise across the
spectrum. We do not deal with the effect of aperture bias (the fact
that a fibre can only sample a small area of a bright galaxy) in this
paper, but acknowledge that it may cause discrepancies between the
morphological and spectral type determined for a galaxy. Zaritsky et
al. (1995) find that in general aperture bias would not constitute a
large effect for the majority of galaxies, but they stress that it may
still pose a problem in some cases. Figures 1-3 show examples of the
simulated spectra for an elliptical galaxy, a spiral galaxy and an
irregular emission line galaxy. In each case the original spectrum and
simulations at a $b_{\rm J}$ magnitude of 19, 20 and 21 are shown. We
refer to the original spectra (from Kennicutt 1992) in the following
sections as the `clean' spectra, and we consider them not to contain
noise. This is a reasonable assumption, since figures 1-3 show that
the low S/N in the noisy simulations makes any noise in the original
spectra negligible. Figures 1-3 indicate the importance of the
emission lines for spectral classification at low S/N, and also reveal
how the additional noise due to sky lines can produce false features
such as those seen in figure 2, at $b_{\rm J}=20$ and $b_{\rm J}=21$.
For this method, the spectra must be compared in their rest frame, so
we have used the redshifts (from Kennicutt 1992) for the galaxies to
de-redshift the spectra (see Appendix A for the full procedure). The
accuracy of the redshifts and resolution of the spectra determine the
number of wavelength points which are used for the PCA.
\begin{figure}
\label{fig3}
\psfig{figure=fig3.ps,width=3.4in,height=3.4in}
\caption{Simulated spectra based on NGC 4485 (Im).}
\end{figure}
\begin{figure}
\label{fig4}
\psfig{figure=fig4.ps,width=3.4in,height=3.4in}
\caption{The variation in signal to noise per 8\AA \ resolution
element measured for simulated spectra as a function of $b_{\rm J}$.}
\end{figure}
A set of 900 spectra are produced in this way for each $b_{\rm J}$
magnitude. These 900 are based upon the Normal26 spectra, but each
spectrum is simulated $N_{\rm s}$ times, where $N_{\rm s}$ is selected
so that the final 900 spectra have the same morphological distribution
as the ESO catalogue, as given in Table 1.
Since our initial data set is limited, this set of 900 spectra does
not contain all the variation in a true observed set of spectra, such
that we acknowledge that this analysis may lead to an optimistic rate
of classification, but it demonstrates the methods we wish to use on
more extensive sets of observed spectra.
The S/N per 8\AA \ resolution element averaged over all wavelengths
for all 900 spectra is calculated when a set of spectra is produced
for a given $b_{\rm J}$. Figure 4 shows a plot of this $\langle S/N
\rangle$ against $b_{\rm J}$ computed in this way which can be used to
associate the $b_{\rm J}$ magnitudes used in this paper with a general
S/N spectrum from any source.
\section[]{Principal Component Analysis}
Principal Component Analysis (hereafter PCA) is a technique for both
data compression and analysis (Murtagh \& Heck 1987) which can be
employed to assess variations in galaxy spectra. By identifying the
linear combination of input parameters with maximum variance, a set of
new axes (principal components) is derived. A mathematical description
is given in Appendix B. Computationally, we use the technique of
Singular Value Decomposition to find the eigenvectors (or principal
components) of the covariance matrix.
The question which arises is how to create the ideal set of principal
components (or PCs) for galaxy spectra. The Normal26 spectra provide a
useful data set, but they are not a representative sample of galaxy
spectra in general. Ideally it would be best to define the PCs from
the observed galaxy spectra of a large survey, but this data would be
noisy and it is not clear at first how the noise would affect the
PCA. Possibly filtering the spectra to reduce the noise level could
improve the analysis, but this will lead to a loss of information.
As explained in section 2, a set of 900 clean spectra are created,
based upon the Normal26 galaxies , which are sampled in 4\AA \ bins
resulting in 768 wavelength bins for each spectrum. PCA is now
conducted on the (768x768) covariance matrix using the techniques
outlined in Appendix B. It should be noted that the speed of the PCA
algorithm is dependent only on the number of wavelength bins used and
not on the number of spectra (we chose 900 purely to produce a large
morphologically weighted data set with many random variations).
\subsection[]{Variance Scaling and normalization}
In the analysis which follows, the spectra are all normalized to have
the same total flux over the wavelength range considered, then the
mean spectrum is subtracted from each of the input spectra. No further
scaling is used.
We did examine the possibility of scaling each input flux to
unit-variance across the sample of spectra. This method is sometimes
recommended for PCA analyses since it places each input on an equal
footing. This would be advantageous when considering object attributes
which are fundamentally different, for example if we were basing a
classification system on galaxy colour, image ellipticity and OII
equivalent width. For spectra, the problem is slightly different since
all the inputs are fluxes for different wavelengths, hence the
relative strengths of the inputs is important and should be retained
in the analysis. Francis et al. (1992) investigate this problem for
PCA on QSO spectra and choose not to scale by the variance.
Scaling by the variance means that the PCs for galaxy spectra at
different noise levels are radically different, since at high S/N the
PCA is sensitive to well correlated small features, but at low S/N
these features are lost. Having chosen not to use this scaling we find
the PCs only vary slightly with noise level, hence the PCs are
intrinsic to the galaxy spectra themselves and not to particular
observing conditions. In this case the PCs relate to both the
magnitude and correlation of the features being chiefly concerned with
regions of the spectra where the signal is strongest, such that they
are not swamped by noise in the continuum. We also did the analysis
with variance scaling, but found it gave a less reliable final
classification, so we do not discuss this further.
Other possibilities are a normalization of each spectrum such that the
integrated flux is the same, or alternatively such that the sums of
the squares of the fluxes across the spectrum is unity (unit scalar
product). This second case has certain mathematical benefits since it
means that each spectrum can be represented by a unit vector in the
parameter space. Connolly et al. (1995) consider these possibilities,
but they find their results are not greatly affected by the choice of
normalization. Hence for simplicity, we opt purely for a normalization
to equal integrated flux.
The other operation we perform is to subtract the mean spectrum from
each of the spectra in the set. This centres the points in the PC
space about the origin, and makes the PCs easier to interpret.
\subsection[]{The meaning of the principal components}
\begin{figure}
\label{fig5}
\psfig{figure=fig5.ps,width=3.4in,height=3.4in}
\caption{Principal components for the Normal26 spectra and for the
entire set, without additional noise.}
\end{figure}
Figure 5 shows the mean and the first 3 PCs for the data set based
upon the Normal26 spectra and Figure 6 shows an enlargement of the
first PC indicating the important features. These are computed without
noise being added to the spectra, but when noise is added, the PC axes
change very little. We quantify this affect in more detail in section
4. We find that the first PC accounts for 87\% of the variance in the
set of 900 clean spectra based on the Normal26 spectra. When the set
is simulated at $b_{\rm J}=22$ $(S/N\sim2.5)$ the plot of the first PC
is qualitatively the same, but only accounts for 11\% of the variance,
since the noise is producing large amounts of uncorrelated
variance. Let us consider the meaning of the correlations which have
been found in the Normal26 spectra. It can be seen that the first PC
represents the correlation in the strength of the emission lines with
the young stellar component. It shows that the OII (3727), OIII (4959
and 5007), $H\alpha$ (6563) and $H\beta$ (4861) lines are all linked
with a blue continuum, demonstrating the effect of the ionizing
photons from young stars exciting the interstellar medium resulting in
strong emission lines. The second PC allows for a range of ionization
levels of the galaxies, since the oxygen and hydrogen lines are
anti-correlated. The third PC indicates numerous other correlations
between absorption and emission features. A parallel study involving
PCA with the Kennicutt sample of galaxies (Sodr\'e \& Cuevas 1996)
finds similar principal components.
\begin{figure}
\label{fig6}
\psfig{figure=fig6.ps,width=3.4in,height=3.4in}
\caption{The first principal component for the Normal26 spectra,
indicating some of the important features.}
\end{figure}
\begin{figure}
\label{fig7}
\psfig{figure=fig7.ps,width=3.4in,height=3.4in}
\caption{The projection onto the first principal component plotted against
T-Type for the Normal26 spectra.}
\end{figure}
\begin{figure}
\label{fig8}
\psfig{figure=fig8.ps,width=3.4in,height=3.4in}
\caption{Projections onto the first 3PCs plotted against one another
for the Normal26 spectra.}
\end{figure}
It is hoped that the amplitude of a small number of these eigenspectra
in any particular spectrum will be sufficient to spectrally classify
the galaxies. Since the projections onto the eigenspectra use
information from the entire spectrum this provides a much less noisy
measure than comparing the strength of particular features. A
simple indication that this may be true can be seen in Figure 7, which
indicates a correlation between the projection (see Appendix B) of
each of the Normal26 spectra onto the first PC and the morphological
type of the galaxy on the T-Type system (de Vaucouleurs 1959; de
Vaucouleurs 1963). A simple fit to this relation (as shown by the
dotted line) allows the projection onto the first PC to be used to
classify the galaxies into a specific T-Type. This has been used later
to provide a comparison to the classifications using the ANN. Further
evidence of an underlying spectral sequence can be seen in Figure 8
where the projections onto the first three PCs are plotted against
each other, with the symbols representing different morphological
types. Segregation in this plot indicates that the PCs are capable of
differentiating between galaxy morphologies and that the Hubble
sequence is clearly evident in the Normal26 spectra and not just their
visual appearance on the sky. The Hubble sequence appears as a
combination of PC1 and PC2, indicating that although one spectral
parameter is sufficient to explain the sequence up to Sc galaxies, a
second parameter (allowing for variation in ionization) becomes very
important for late type and irregular galaxies, where strong star
formation leads to high ionization levels. In their study, Sodr\'e
\& Cuevas (1996) found that stellar synthesis models (Bruzual \&
Charlot 1995) with different ages and star formation rates form a
similar sequence when projected onto PCs derived from the Kennicutt
(1992) sample of galaxies.
Figure 5 also shows the mean and first three PCs for the entire data
set, including the Normal26 and the Unusual29 spectra. These are
derived by the same method as described above. The morphological mix
from Table 1 is again used, but note that this does not necessarily
represent a true spectral mix. This means that the galaxies with
unusual features are over represented, but this allows their affect on
the PCA to be seen. In this case, the first PC is entirely due to the
emission line strength, since the PCA is dominated by the emission
line objects. The young stellar continuum is evident in the second PC
along with anti-correlations between the major emission lines. In this
respect the first PC from the Normal26 spectra is evident as a
combination of the first and second PCs of the entire data set. The
third PC is now quite different, and displays the broad hydrogen lines
characteristic of the galaxies with Seyfert nuclei.
\section[]{Reconstructions from noisy spectra}
We now proceed to investigate the effect of noise on the PCA
technique. It would be useful to perform PCA on a large set of
observed spectra, such as the 2dF spectra, since this set would
contain all the possible variation in galaxy spectra and is
representative of the local universe. However these observed spectra
would be noisy and this may affect the location of the
principal components. Using the spectral simulations we can assess the
nature of this effect, by measuring the ability of the PCs to
reconstruct the original spectrum. Appendix B explains how a
reconstruction of the original data can be found using only a small
number of PCs. Taking a set of noisy simulated spectra we can
reconstruct them and define the total Residue R for the set as
$$
R={1 \over NM}\sum_{ij}(S^{r}_{ij}-S_{ij})^2 , \eqno (1)
$$
where the sum is over all $N$ spectra and $M$ wavelengths, $S^{r}_{ij}$ is
the flux of the ith reconstructed spectrum at wavelength j, and
$S_{ij}$ is the flux of the original clean ith spectrum at wavelength
j. This reconstruction technique suggests the useful ability of PCA to
disregard the noise, which is assumed to be uncorrelated. The major
correlations in the signal are selected by the PCA, and the noise only
interferes with the later PCs, such that a reconstruction using the
most significant PCs can eliminate much of this uncorrelated noise. To
demonstrate this effect, figure 9 shows a plot of R against the number
of PCs used in the reconstruction. Seven different cases are
considered and these are listed in Table 3. In each case two sets of
spectra are used. One set is used to define the principal components
and is labeled `Spectra$_{\rm PCA}$'. The other set is reconstructed
to find the Residue R and is labeled `Spectra$_{\rm REC}$'. This
reflects the possibility of defining the principal components prior to
the observations using a smaller set of high quality spectra. However
this would probably entail using a limited data set, so Table 3 also
contains a case where only half of the Normal26 spectra have been used
to define the PCs. Each set contains 900 spectra mimicking the
morphological mix given in Table 1. There is one other possibility
considered in Table 3, that of filtering the spectra prior to the
reconstruction and we have used the technique of Wiener filtering to
demonstrate this effect (see section 4.2).
\subsection[]{Reconstruction results}
Referring to Figure 9, we can see that the smallest R value is
obtained using the noise free spectra for the Spectra$_{\rm PCA}$ and
the Spectra$_{\rm REC}$ sets (line a). This is to be expected and
represents the ideal condition, but one which is not available for a
real observation since the underlying signal is not known. A set of
clean spectra, such as the spectra we are using, could be used to form
the PCs for use with observed noisy spectra, as lines b and e
demonstrate. However the line d indicates that when only half of the
spectra are used in the PCA the result is considerably worse, which
suggests that a small set of spectra should not be considered
representative of a larger ensemble. Therefore it would be better to
derive the PCs from the noisy spectra themselves. This condition is
shown by lines c and g for two different noise levels. It can be seen
that for $b_{\rm J}$=19 (line c) about 8 PCs still contain meaningful
information, but the later PCs are merely reconstructing the noise (as
indicated by a rise in R). This means that the optimal reconstruction
is found by limiting the PCs used to the point at which R is found to
be a minimum and this then represents the entire meaningful
information that can be extracted from the spectrum. Line g indicates
that for very noisy data only the first PC is still meaningful.
\begin{table}
\caption{The seven PCA combinations used for analysis of reconstruction errors, with the notation for Figure 9.}
\begin{tabular}{llc}
\hline
Spectra$_{\rm PCA}$ & Spectra$_{\rm REC}$ & Notation in Figure 9\\
\hline
\hline
Clean & Clean & a\\
Clean & $b_{\rm J}=19$ & b\\
$b_{\rm J}=19$ & $b_{\rm J}=19$ & c\\
Clean, half data set & Clean & d\\
Clean & $b_{\rm J}=22$ & e\\
$b_{\rm J}=22$ & $b_{\rm J}=22$ filtered & f\\
$b_{\rm J}=22$ & $b_{\rm J}=22$ & g\\
\end{tabular}
\end{table}
\begin{figure}
\label{fig9}
\psfig{figure=fig9.ps,width=3.4in,height=3.4in}
\caption{Reconstruction errors for different sets of spectra. See
Table 3 for explanation of line labels.}
\end{figure}
\begin{figure}
\label{fig10}
\psfig{figure=fig10.ps,width=3.4in,height=3.4in}
\caption{The optimal number of PCs for spectral reconstruction as a
function of $b_{\rm J}$.}
\end{figure}
So given a set of noisy spectra, it is reasonable to perform PCA on
the spectra themselves, but to acknowledge the fact that only a
certain number of the PCs are useful, with this number depending on
the S/N of the spectra. If a set of high S/N spectra are available,
using the PCs from these may extract more of the information (see
lines e and g), but in this case the assumption that the noisy spectra
can be well described by the PCs from the clean spectra must be made,
and (as line d shows) this is not always true. Figure 10 indicates how
the optimal number of PCs (i.e. the number which gives a minimum in R)
varies with $b_{\rm J}$ when Spectra$_{\rm PCA}$ and Spectra$_{\rm
REC}$ are both simulated at $b_{\rm J}$. The exact normalization of
this graph depends on the specific data set being considered,
including factors such as the number of spectra, and the wavelength
sampling. For a very large set of data from a big redshift survey it
may be expected that more PCs would be significant.
\subsection[]{Wiener Filtering}
An alternative method for extracting the meaningful information from
the spectra is Wiener filtering in Fourier space (see Press et
al. 1992 for a full description). This involves a smooth truncation of
modes in a data independent basis, as opposed to the PCA which
involves a sharp truncation in a basis which is adapted to the
data. In Fourier space, let S(k) be the true spectrum of a galaxy,
then the observed spectrum O(k) is given by
$$O(k)=S(k)+N(k) , \eqno (2) $$
where $N(k)$ is the Fourier transform of $n(\lambda)$ (the noise
at each wavelength). Let us define a linear filter in Fourier space, W(k) by
$$S_{\rm r}(k)=O(k)W(k) , \eqno (3) $$
where $S_{r}(k)$ is the best reconstruction of S(k). By a least squares
minimization with respect to $W(k)$ we find
$$W(k)=\frac{|S(k)|^2}{|S(k)|^2+|N(k)|^2} , \eqno (4) $$
where we have ignored terms involving $S(k)N(k)$ since the noise and
signal are considered to be uncorrelated. From equation (4), we define
$W(k)$ as the Wiener filter.
For this method we must first assume an underlying signal $S(k)$ in
the spectrum. To do this we have formed 5 templates, one for each of
the groups given in Table 1 by taking the mean of the Normal26 spectra
in that class. We then take each noisy spectrum and compare it to the
5 templates and look for the best template in the least squares
sense. This template is then used as the prior for the Wiener
filtering. In addition this template matching method is a simple
method of classification where a galaxy spectrum can be allocated to
the group whose template it matches best. We use this later as a
comparison to the classifications from the ANN.
Wiener filtering can be seen as an alternative technique to produce a
reconstruction from a noisy spectrum and it is interesting to compare
the PCA reconstructions and the Wiener reconstructions. This
comparison can be seen in Figure 11 for different levels of noise. It
can be seen that the Wiener filtering reduces the noise, but also
smoothes the signal, such that at low S/N the features are lost and
only the rough continuum shape remains. In comparison the PCA
reconstructions retain much more of the information in the spectrum,
producing a reasonable reconstruction of the spectrum to a $b_{\rm J}$
of 22. At low S/N the noise causes some spurious effects, but many of
the distinguishing spectral features, in this case $H\alpha$ and the
4000\AA \ break are retained. In order to make this reconstruction,
the noisy spectrum is assumed to be characteristic of the set of
spectra used to produce the principal components. This means that the
reconstruction conforms to the correlations laid by the PCA. For some
data sets it is possible that PCA would not provide a good description
of the data and Wiener filtering in Fourier space would be the
prefered method. Ideally a very large set of spectra is required for
the PCA, such that the complete range of spectral possibilities is
encompassed, and we hope to apply the techniques given here to such
data sets in the future.
\begin{figure*}
\label{fig11}
\psfig{figure=fig11.ps,width=7.0in,height=4.5in,angle=270}
\caption{Comparison of spectral reconstructions for NGC3627 (Sb). a)
The simulations for $b_{\rm J}$=20 and $b_{\rm J}$=22. b) Wiener
filtering of the noisy spectra using a group template (see text). c)
PCA reconstructions of the noisy spectra based upon 8PCs derived from
the Normal26 spectra.}
\end{figure*}
Referring back to figure 9, line f is the result of first Wiener
filtering the spectra before projecting onto the PCs. This removes
much of the noise so that the line does not rise so rapidly, but the
action of the filtering also removes much of the meaningful signal in
the spectrum so that the reconstruction is never as good as the single
PC reconstruction based on the noisy data (line g).
\subsection[]{Combining Wiener filtering and PCA}
As an aside, we can see in the previous section that the PCA, which
takes into account correlations between the features, produces a far
superior reconstruction than the Wiener filter used in Fourier space,
but we have also noted that PCA reconstructions of noisy data should
be restricted to only the first few PCs, since the noise interferes
with the later PCs. The PCA works better than the Fourier
representation because the PCA axes are chosen specifically to
represent the data, whereas the Fourier axes are a generalized
orthogonal set and not specific to the data being considered. The
Wiener filter is used to produce a smooth cutoff of the Fourier modes
so that the noisy modes are reduced in weight. Such a procedure could
also be used with the PCA where, instead of truncating after a
determined number of PCs, a filter is used which merely reduces the
weight of the later PCs. In this paper, we actually need a direct
truncation of the PCs, since we want to minimize the number of inputs
to the ANN (hence reducing the number of free parameters of the
network), but for a general spectral reconstruction the filtered PCA
is a promising idea.
\section[]{Spectral classification with an artificial neural network}
Figures 7 and 8 show that the visual morphology and the spectrum of a
galaxy are related and that this relation is embodied in the
projection onto the PCs. This suggests that a useful method for the
classification of galaxy spectra is to associate each spectrum with a
morphological type. This would allow the morphology of galaxies to be
examined at far greater distances and with less subjectivity than
conventional examination of galaxy images. We have trained an ANN to
assign morphological classifications to galaxies, based on their
spectra as represented by the projections onto a small number of PCs.
For each spectrum, the ANN produces an output classification which is
a non linear function of the inputs. The form of the function is
parameterized by a set of weights which are adjusted so that the
output matches the known classifications for a training set. To be
precise, the effect of training the ANN is to perform a minimization
across the ANN weights vector ({\bf w}) given a set of inputs ${\bf
x}_i$ for the ith galaxy (e.g. the spectrum as represented by the PCs)
and known outputs $T_{\rm i}$ (e.g. the morphological group). This is
done by minimizing the cost function
$$
E = {1 \over 2} \sum_i [T_i - F({\bf w}, {\bf x}_i) ] ^2, \eqno (5)
$$
where the non-linear function $F({\bf w}, {\bf x})$ represents the
network and the summation is over the training set of spectra.
\begin{figure}
\label{fig12}
\psfig{figure=fig12.ps,width=3.4in,height=4.0in}
\caption{The percentage of ANN classifications which agree with the
known morphological types for 5 and 3 classes, based upon the Normal26
spectra. Also shown is the success of $\chi^{2}$ template matching and
classification based solely on PC1. The lower graph indicates the
variation in $\delta(group)$ against $b_{\rm J}$ for classifications from
the ANN, and PC1 alone.}
\end{figure}
Once the weights are set, the training is complete and the ANN can be
used to classify the complete galaxy sample. A full description of the
ANN as a tool for data analysis is given in Appendix C (for further
detail see Lahav et al. 1996). We used a quasi-newton ANN code with
the network architecture designed to allow the projections onto the
first 8 PCs (derived from a set of spectra simulated at $b_{\rm
J}=19.0$) to be used as input to the net and a single output being the
morphological group. Between the input and output layers we chose a
single hidden layer with 5 nodes, which provides a level of
non-linearity in the classification. We experimented with
different numbers of nodes and hidden layers and decided upon the
8:5:1 setup as the simplest architecture which gave consistently
successful results. Simpler architectures were not reliable and more
complex nets failed to improve the results. The output from the
ANN could then be scaled and binned to give the five classes as
defined in Table 1. The training process involved weight decay, which
acts as a regularisation during the training, preventing erratic
variations in the weights. The quasi-newton minimization and the use
of weight decay are discussed in more detail in Appendix C.
We chose to use 8 PCs based upon the results in section 4, which
indicate this to be a reasonable compression of the data for the S/N
levels we considered. We produced a set of 900 simulated spectra at
each of 9 values of $b_{\rm J}$ between 18 and 22, resulting in a total
set of 8100 spectra. One third of this set was then repeatedly
submitted to the ANN as a training set until the error between the ANN
classification and the known morphological types of the galaxies began
to converge. The `trained' net was then used to classify the
complete set of 8100 spectra onto a continuous scale defined by the
group G number as given in Table 1. In this way the scaled output from
the ANN was a single number in the range 0.5 to 5.5 and an output
group was found by allocating the galaxy to the nearest group
bin. These classifications could be compared with the known types of
the galaxies to give a level of success at each magnitude. The ANN is
trained, and spectra classified, ten times using this method to give a
mean and standard deviation for the percentage of galaxies allocated
to the correct group, and these results can be seen in Figure 12. In
addition, if only a 3 group classification is required, the Sa, Sb and
Scd groups can be combined to give one large group of spirals. The
success rate for this 3 group binning is also shown in figure 12.
A further measure of success is the $\delta(group)$ statistic given by
$$\delta(group)=\sqrt{{1 \over N}{\sum_{i}(G_{\rm i}-A_{\rm i})^2}} , \eqno
(6) $$ where the sum is over the N spectra (in this case a set of
900), $G_{\rm i}$ is the actual group to which the galaxy belongs, as
defined in table 1 and $A_{\rm i}$ is the neural net classification on
a continuous scale from 0.5 to 5.5.
These results are encouraging, showing that the morphological
variation in the Normal26 galaxies is well represented in their
spectra and that the PCA/ANN technique is capable of extracting this
information even with very noisy spectra.
Figure 12 indicates several other lines for comparison. Two of the
lines refer to the classification success when a classification based
solely upon PC1 is used. A simple relation between T-Type and PC1 is
assumed (as indicated by the line on Figure 7) and the results shown
using 5 and 3 groups. $\delta(group)$ was also calculated for this
method so that it can be compared with the ANN. The classification
based solely on PC1 is found not to be ideal, although it is stable to
high noise levels (since PC1 is the most meaningful correlation in the
data and should not be greatly affected by noise). It is clear that
the ANN is capable of better classifications using more of the
principal components than the single PC result. The later components
are affected by noise to a greater extent, so the ANN classification
does fall as the noise level increases.
The other two lines on Figure 12 refer to a classification based
on $\chi^2$ template matching, from the procedure in section 4.2. This
indicates a reasonable level of success, but is unable to capitalize
on the extra information at high S/N which allows the ANN to refine
the classifications. Since the template matching gives a discrete
group output, $\delta(group)$ is not calculated for this method.
\section[]{Agreement of morphological and spectral types}
We now have an ANN which has been trained to relate the spectral type
and morphological type of normal galaxies, using the projections onto
the first eight PCs (derived from the Normal26 morphologically
weighted sample). We use this to classify the Normal26 and the
Unusual29 spectra without noise, to gain an indication of the
agreement between spectral and morphological type. The results can be
seen in figure 13. The Normal26 spectra form a reasonable sequence,
with a degree of scatter in each group. This scatter is related to the
$\delta(group)$ statistic plotted in Figure 12 (but note that
$\delta(group)$ is summed over a complete morphological sample of 900
spectra at a particular noise level). Some overlap between the groups
can be seen, verifying the fact that we are dealing with a sequence in
galaxy type and not discrete classes. The agreement between
morphological and spectral type indicated in Figure 13 substantiates
the conclusions of the PCA analysis (Figures 7 and 8) which suggested
strong links between spectra and morphology. It is reassuring to see
that the traditional Hubble classification system is telling us about
stellar and gas content in addition to the morphology of the
galaxy.
As expected, the Unusual29 spectra do not conform to this
morphology-spectrum relation. In general, the unusual spectra which
have been morphological classified into groups 1 to 4, produce a
higher spectral class from the ANN. This is due to the presence of
starbursts, Seyfert nuclei and emission features which increase the
`activity' in these spectra, above that of a normal galaxy for that
class. The unusual spectra in morphological group 5 contain galaxies
with T-Types greater than 8.5, which include irregular and peculiar
types along with extreme emission galaxies. The irregular emission
line objects are classified correctly as being extreme in spectral
class (group 5), but the peculiar galaxies reveal a range of spectral
features, such that they are classified into a variety of spectral
classes. We can investigate some particular cases which have been
highlighted in Figure 13, and look at the spectra and comments given
in Kennicutt (1992). The morphologically peculiar galaxy NGC 3077 has
been spectrally classified by the ANN as a late Sb galaxy (ANN output
group 3.15) which broadly agrees with the comments given in Kennicutt
(1992) that this spectrum is similar to that of a normal Sc. In
contrast, the spectrum of NGC 5195 has been spectrally classified as
an elliptical by the ANN (ANN output group 1.25), whereas Kennicutt
(1992) comments that it resembles an old stellar population with weak
emission lines, or an `E+A' galaxy. From a sample of this size, we
cannot say that the ANN is telling us anything very new, but it can be
seen that the ANN is producing a consistent spectral classification
which broadly agrees with a visual analysis of the spectra.
\begin{figure}
\label{fig13}
\psfig{figure=fig13.ps,width=3.4in,height=3.4in}
\caption{The Agreement of spectral and morphological classifications
for the Normal26 spectra and the Unusual29 spectra.}
\end{figure}
It can clearly be seen in Figure 13 that the Unusual29 galaxies show
very little agreement between morphological and spectral type, so in
an observed sample, it would be useful to separate the normal from the
unusual spectra. As Figure 7 shows, the Hubble sequence is clearly
evident in relations between the PCs, so it is reasonable to assume
that the unusual spectra do not have this uniformity, for example they
may show discrepant emission and absorption features, or indicate
strong ionization from a Seyfert nuclei without the presence of a
young stellar population. To test this hypothesis, we have taken the
Normal26 and Unusual29 spectra, simulated them at different noise
levels, but without any morphological weighting, and run the PCA
routine on the entire set. We then train the neural net (using 8PCs)
to output 0 if a galaxy is one of the Normal26, or a 1 if the spectrum
is a member of the Unusual29. When the ANN is trained, we ask it to
reclassify the galaxies itself into these two bins. We find that at
$b_{\rm J}=19.7$ about 95\% of the spectra have been classified correctly
in this way.
\section{Discussion}
We demonstrate in this paper that the combination of the PCA technique
and the ANN analysis produces a useful classification tool. The PCA is
useful in three ways in our technique: (i) It allows a transformation
of the data to a more useful set of axes, to reveal segregation in the
sample. (ii) It allows a reconstruction of a low S/N spectrum. (iii) It
provides an economic set of input parameters for the ANN.
We have shown that a limited number of PCs convey the underlying
information in the spectra, and beyond a certain number of PCs
(defined by the noise level) the PCs are not producing useful
information. When the data is restricted to the Normal26 galaxies, the
projections onto the first few PCs reveal segregation in the data
which is chiefly due to the morphological variation in the spectra. If
the Unusual29 spectra are included, the variance in the data is due to
parameters other than purely the morphological type. We show that the
PCA is best executed on the observed spectra themselves, even if they
are noisy, since the PCs are then highly relevant to that data
set. The alternative approach of projecting the noisy data onto PCs
derived from a small set of high quality spectra can be used, but in
this case, the PCs do not necessarily describe the entire range in the
larger set of observed spectra.
The results from the ANN suggest that a good agreement between
spectral and morphological type can be attained for the Normal26
spectra and that a better classification can be made using this
approach than a simple $\chi^2$ fit to a set of templates. We have
also shown that classification information is not restricted to the
first principal component, such that a classification based purely on
this is not very successful. As expected, little agreement is seen
between the morphology and spectra of the Unusual29 galaxies. One way
to proceed would be to separate these spectra from the main sample,
and then to analyse only the normal galaxies with reference to the
Hubble sequence. We show that it is also possible to use an ANN to
make such a distinction. This would leave a set of unusual spectra
which could be classified separately, or analysed using an alternative
method, such as cluster analysis in the PC space, or one of a variety
of unsupervised data analysis methods which look for trends or
groupings in the data. The ability to highlight unusual spectra would
also prove useful in detecting spectra with bad sky subtraction,
inaccurate fluxing, or incorrect redshift determinations, so that
these could be dealt with separately. The small data set used in this
analysis means we are unable to draw rigorous conclusions as to the
full variation of galaxy spectra. We hope to remedy this situation in
the near future with similar analyses of larger observed data sets
from existing redshift surveys and spectroscopic environmental
studies.
We intend to use the the results of this paper as the basis for
classifying the spectra from the 2dF Galaxy Redshift Survey. We have
shown that a five class classification is obtainable to the proposed
magnitude limit of the survey ($b_{\rm J}=19.7$), but this paper also
demonstrates that it is not necessarily advantageous to restrict the
classification to discovering the morphological types of the
galaxies. It may be better to extend the classification into classes
based entirely on the spectral type. The PCA alone can reveal such
subsets in the data and will provide a powerful tool when used on a
large data set. For the ANN to operate well, a number of the spectra
need to be used as a training set. Several options are available, such
as using morphological classifications from those images bright enough
to be classified by eye, a manual analysis of the high quality spectra
or the use of population synthesis models. A recent investigation
(Sodr\'e \& Cuevas 1996) has successfully related the positions of
observed spectra and model spectra on the PC1/PC2 plane and this
suggests that an ANN trained with model spectra may be able to provide
interesting insights into the physical factors determining galaxy
spectra.
\section{Conclusion}
We have demonstrated a method for the classification of low S/N
spectra using simulations based upon the set of galaxy spectra
presented in Kennicutt (1992). We have developed the simulations to
resemble spectra from the 2dF Galaxy Redshift Survey and show that
reliable classifications, with more than 90\% of the normal galaxies
correctly classified, can be expected to the magnitude limit of the
survey ($b_{\rm J}=19.7$). This may be optimistic, since our small
data set does not encompass the full variation in galaxy spectra, but
our results strongly suggest that the methods in this paper will
provide an interesting analysis technique when the 2dF Galaxy Survey
spectra are available. We have explored the effect of noise on the
Principal Component Analysis of spectra and demonstrate that an ANN is
a useful tool for the classification of noisy spectral data. We show
that the ANN classification is more successful than either a
$\chi^{2}$ template matching approach or a classification based solely
on the projection onto the first principal component. We have also
investigated the agreement of spectral and morphological type and
discussed a method to separate normal from unusual galaxy spectra.
\section*{Acknowledgments}
The authors would like to thank C. Bailer-Jones, R.S. Ellis,
P.J. Francis, J.S. Heyl, M.J. Irwin, A. Naim, L. Sodr\'e, Jr.,
M.C. Storrie-Lombardi, T. von Hippel, and the 2dF Galaxy Survey
collaborators for useful discussions concerning spectral
classification. We would also like to thank B. Ripley for making the
ANN code available.
| {
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svdynamo
Volleybalvereniging SV Dynamo Apeldoorn 28e Errea-Buurman Internationaal Jeugdtoernooi
27 t/m 29 december 2021
Schema en uitslagen
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Schrijf je nu in voor het 24e ENGIE Internationaal Jeugdtoernooi
Wij wensen iedereen een gezellige jaarwisseling en een gelukkig, sportief maar bovenal gezond 2016!
Direct naar wedstrijden op toernooi.nl
28e Internationaal Jeugdtoernooi
27, 28, 29 december 2021
History of the SV Dynamo Youthtournament
In the nineties, when the National Netherlands Tournament ended, people were thinking very hard about organising a following event. This international tournament, with at its top participating National teams from all over the world, had to be followed by another event, one way or the other.
Start in 1992
No longer the tall men and women who already reached the top of their careers, but the tall bays and girls, who are still working hard to reach the top, had to be in the spotlights. Therefor, in the persons of Arie Verbeek and Arjan de Groot, sv Dynamo started preparing the first Youthtournament of sv Dynamo. This resulted in the first edition of our tournament in 1992. The tournament started as a one-day-event. At this day, the best youth teams played for the title.
Multiday tournament
A few years later the organisation decided to make it a tournament that took more days. Because of the overwhelming growth of the amount of participating teams, the tournament became as it is now. Two days for playing in the preliminaries and getting the best place as possible. On the third day playing to get the best final ranking. The overnight stays were still organized in the gym.
A few years later, due to international safety rules, we had to find another way to let the teams stay overnight. Therefor we tried to find a groupaccommodation near Apeldoorn. This accommodation was found in Epe in a youth hostel. In 2008 the club made a very good deal with an other accomodation. This new accommodation is Hostel Stayokay Apeldoorn. These men and women let us use their accommodation for two whole days! Players are able to stay overnight for a good prize in comfortable rooms. SV Dynamo arranges transportation from and to Hostel Stayokay and the Welgelegenhal.
The Gyms
What started as a small tournament for a few teams that came to our Dynamohal 19 years ago, soon became a lot bigger. Therefore the Dynamohal (currently Welgelegenhal) soon became too small to play all the matches in three days. So we started looking for different gyms in the neighbourhood to play in.
In the current history of our tournament we have already played in the Mheenhal, the Sprengeloohal and the Wsv-hal. Since 2008 we are playing in two gyms next to eachother. The 7 courts in Omnisportscentre and Wsv-hal will be ours to play on for three days. Hopefully we will be able to use these courts for many years to come!
From Holland we have had the best clubteams for several years now. These clubs are the best in our national youthchampionships: Sliedrecht Sport, WW/ DOK (now TFM DOK) and of course our friends from Apeldoorn: Dros Alterno (now Kindercentrum Alterno).
From foreign countries we've had teams from good clubs, amongst others: Bayer Leverkusen and Siegen from Germany, Wuustwezel, Leuven and Zoersel from Belgium, Sete and Levallois Paris from France.
Laatst bijgewerkt op zaterdag 19 december 2015
Start toernooi | {
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Q: AngularJS Download Settings from Servers We have an endpoint on our API that includes a set of settings (like default text, other endpoints, etc.). Our frontend is written in AngularJS and we're trying to figure out the best way to get them back to the client, and make them available throughout all directives in the application. Right now our best solution is to include settings as a directive:
angular.module('ourapp')
.factory('settings', function ($http) {
var url = 'http://localhost:8080/settings';
return function (callback){
$http.get(url).success(callback);
};
});
But then all the other calls are wrapped asynchronously.
Is there a better way to do this?
A: Since the settings come asynchronously from the server, their availability will inherently be asynchronous. If your logic depends on the settings being available, then there is probably no better solution than using promises.
angular.module('ourapp').factory('settings', function($http) {
var url = 'http://localhost:8080/settings';
return $http.get(url); // returns a promise
});
You could use $route to resolve the promise before instantiating controllers. The settings would then be synchronously available in the controllers.
You can also simulate promise unwrapping, i.e. immediately (synchronously) returning an object, which later will be filled with real data. This is great for scopes and templates, and was previously a feature of Angular itself. Be aware that the simulated promise unwrapping may cause bugs if not used cautiously, because the settings data may or may not be there.
Example:
angular.module('ourapp').factory('settings', function($http) {
var url = 'http://localhost:8080/settings';
var settings = {};
$http.get(url).success(function(data) {
angular.extend(settings, data); // fills in data from server
});
return settings; // immediately (synchronously) returned
});
| {
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Roblox Game Development/Game design
< Roblox Game Development(Redirected from ROBLOX Game Development/Game design)
Designing your game should be the first step in making your game. Now, oftentimes you will end up designing your game as you go. You'll be constantly reinventing, reevaluating, and remaking your game. If you start using the studio with a game design, make it, and never change a single plan, there is probably something fundamentally wrong with your game. In this chapter, we will go over designing your game, and more specifically, utilizing ROBLOX's cloud-hosted game platform to quickly receive feedback to revise your game. We'll go over what to do, and not to do, in terms of graphics and looks, as well as functionality.
1 Finding an idea
2 Recording your idea
3 Leveraging support
4 Time management
5 Game constituents
Finding an idea[edit]
Finding a game idea can be hard. With many of the ideas you may get, there will be many things wrong with the design. The concept may be unachievable, or just have technical difficulties or restrictions that prevent its accomplishment. In this case, you'll want to refine the design. Remembering finding a game idea isn't the hard part, the hard part is making it, and having the willpower to do so. Here are some suggestions that should help you find a game idea:
What's your favorite game? What irks you about it? What can you improve? Do it!
Pick a genre. Think of what sort of game you would want to play in it. Do it!
Ask on ROBLOX's Game Design forum, or use another such resource—there's always someone there who has a good idea.
Piggyback on someone else's project (there are many groups on ROBLOX that exist for this purpose).
Research it, on the web, for example! Get inspired by what you can find elsewhere, what you've experienced, and what you enjoy.
Ask yourself "Do you really want to make this game?" and "Would I play this game?"
Once you have an idea in mind, you want to analyze it for several things. You want to make sure it's feasible. Think of each component of the game and ask yourself how you can do it and whether you have seen it before: if you haven't seen it before, in particular on ROBLOX, and you can't think of how to do it, ask a more experienced game developer and designer who may have a clear idea on how to do it. People who are more experienced than you will usually have a more clear view of the situation than you, and can share that view with you, which can help you greatly. With all of this in mind, you'll want to start the most important part.
Recording your idea[edit]
Yes, you need to record your idea. You need to write it down. Especially if it's a group project, or a project others will be helping you on. You must do this because recording your idea provides several things for you:
Recording your idea will help prevent loss of motivation. Most people tend to lose motivation in their projects due to not knowing what to do next. By having a specific guide there, in front of you, scheduled out and planned, when you ask yourself "What do I need to do to make this game working?" you will easily have a solution right there in front of you. Oftentimes uploading this document to the cloud can prove most beneficial when working with groups, as you can constantly mark off, and debate over topics in the project. Planning and coordination in a group project are one of the keys to success, more so in the virtual world of ROBLOX where motivation is purely from want—chances are that no one is paying you to make your own game.
Recording your idea will give you something to show off. When recruiting people to a group project, or even when fans gather and ask you about your game, you want something to show off. You need to inspire, make them stop, and differentiate between your project and the dozens of other opportunities that exist on ROBLOX. The best developers are picking the best games, and in order to make your game the best, it must be professional and well planned.
Recording your idea will allow you to plan. As mentioned in the previous paragraph, planning is required. When you plan out your game, you discover potential problems, and can receive feedback before it's made. As a single person you will not be able to catch all the mistakes in your own mind.
Leveraging support[edit]
It is important to remember that, as in the real world, making a successful game that is played not only requires a good idea, a finished and polished core, but also marketing. This is also the case for ROBLOX games, but marketing is much less difficult, because the game is hosted by ROBLOX and is mentioned in various places on the website. Regardless, if you want to get a big community of players to play your game, you will need to spend some time marketing it.
Time management[edit]
Managing your time is essential when developing a game. It is sometimes a good idea when developing a game for ROBLOX to first complete the plan and then to skip the first fourth of the plan to directly get something working, even if it is something that is not as good as what the plan requires. Having a working demonstration makes it possible to get feedback and to have an area where it is possible to try things: with a working demonstration, it is possible to try things in the game directly before the basic infrastructure of the project is completed.
Game constituents[edit]
Games on ROBLOX consist of three elements: the game engine, which is part of ROBLOX and handles the physical world, the rendering (displaying of your game), the networking (the communication between the server and clients) and other things, the game content, which is composed of maps, buildings, images, assets and other items that are created by the developer, and the game code, which is what makes the game interactive and what forms the player experience. The game content was already covered in part in the previous chapter. The game engine will be the subject of the next chapter, and the game code will be the subject of the other chapters, along with the game content.
IntroductionGame engine
Retrieved from "https://en.wikibooks.org/w/index.php?title=Roblox_Game_Development/Game_design&oldid=3538952"
Book:Roblox Game Development | {
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Софи До(у)з, баронесса Фешер (, ; , — , ) — английская авантюристка, любовница, наследница и возможная убийца последнего принца Конде.
Биография
Родилась в семье рыбака-контрабандиста, работала горничной в Портсмуте, а затем служанкой в лондонском борделе на Пикадилли. В 1811 году там она познакомилась с клиентом борделя, жившим в эмиграции французским принцем крови, Луи-Анри, герцогом де Бурбоном, последним в роду принцев Конде. Бурбон снял для любовницы и её матери дом в Лондоне, а после Реставрации привёз её в Париж и занялся её образованием. Даровитая девушка быстро выучила французский, греческий и латынь и приобрела светские манеры. В 1818 году Людовик Генрих (ставший в том же году после смерти отца принцем Конде) выдал её замуж за барона Адриена Виктора де Фешера, майора королевской гвардии. Фешер полагал, что она внебрачная дочь принца крови, и воспринял такой брак как честь для себя. Так Софи стала французской титулованной дворянкой и благодаря красоте и уму стала известна в свете. Когда в 1822 году обман раскрылся, барон Фешер немедленно отослал жену от себя и пожаловался Людовику XVIII. Король приказал не допускать её ко двору, публично ославив баронессу проституткой. В 1827 году Фешеры получили формальный развод.
Однако в царствование Карла X Софи вновь стали принимать в свете, а её племянница и племянник вступили в выгодные браки. Это улучшение статуса стало результатом сделки, которую ей предложили герцог Орлеанский Луи Филипп и его жена: воспользовавшись влиянием баронессы Фешер на престарелого принца Конде, они попросили её добиться, чтобы тот завещал большую часть фамильного состояния их четвёртому сыну, малолетнему герцогу Омальскому, которого Конде крестил. (Единственный сын Конде, родившийся от его распавшегося ещё в 1780 г. брака с тёткой Луи Филиппа Батильдой Орлеанской, герцог Энгиенский, был расстрелян Наполеоном I в 1804 году, после чего богатый род был обречён на вымирание). Завещание было подписано в июле 1829 года, а уже в январе 1830 года Софи вернулась ко двору Карла X, и её племянник получил титул барона. «В конце концов, каких только мерзавцев мы у себя не принимаем…» — сказала невестка короля Мария Тереза. Другим покровителем баронессы был Талейран: в обмен на удачные браки её родственников и приём в свете она делала всё возможное, чтобы Конде был благожелателен к министру, который некогда принимал участие в расстреле его сына.
Вскоре после Июльской революции 1830 года, которая возвела Луи Филиппа на престол, 27 августа, 74-летний принц Конде был найден мёртвым, висящим в петле из двух платков на оконной ручке в одном из своих замков Сен-Лё. Официальное следствие пришло к выводу о самоубийстве; большу́ю часть недвижимости получила баронесса Фешер, а огромный капитал (60 миллионов золотых франков) с процентами — маленький сын нового короля. Однако из-за показаний слуг возникли подозрения, что принц не повесился, а был убит собственной любовницей. Недоумение вызвал и основной наследник — легитимистские убеждения рода Конде были хорошо известны, и завещание в пользу семьи либерала, сына «цареубийцы» Филиппа Эгалите, к тому же только что возглавившего новую революцию, казалось подозрительным. Полагали, что принца убила Софи, по сговору с Луи Филиппом и королевой, из-за попытки Конде вырваться из-под её опеки и изменить завещание (или даже бежать из страны без неё). Распространился и более пикантный слух — о случайной гибели старика в результате аутоэротической асфиксии. Родственники последнего Конде по женской линии, князья де Роганы, оспорили завещание в суде, но проиграли дело во всех инстанциях; во время процесса произносились речи с острой критикой короля. Принятие наследства сильно повредило репутации Луи Филиппа.
Ненависть к баронессе была столь велика, что она была должна покинуть Францию и вернуться в Лондон, где умерла в 1840 году и похоронена на кладбище Кенсал-Грин.
Литературные отзвуки
История Софи, по некоторым данным, была использована Теккереем в образе Бекки Шарп, которую подозревают в убийстве (роман «Ярмарка тщеславия»).
Примечания
Литература
Louis André, La Mystérieuse Baronne de Feuchères (Perrin, coll. «Enigmes et drames judiciaires d'autrefois», 1925).
Guy Antonetti, Louis-Philippe (Arthème Fayard, 1994, pp. 532—535).
Manjonie Bowen, The scandal of Sophie Dawes (1935—1937).
Pierre Cornut-Gentille, La Baronne de Feuchères (Perrin, 2000).
Christian Liger, Les Marches du Palais (Laffont, 1996).
John Lane, Sophie Dawes, Queen of Chantilly, (1912).
Rev. David Low et Sheila White, Over twelve-hundred years in St. Helens, a parish history (St.-Helens, Ryde, 1977).
Victor Macclure, She stands accused; Chapitre V : Almost a Lady, texte en anglais sur The World Wide School, 1997).
Violette Montagu, Sophie Dawes, queen of Chantilly (1911).
Авантюристки
Реставрация Бурбонов
Похороненные на кладбище Кенсал-Грин | {
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Pouting in pink for PH
Written by Mary Ferguson on Friday the 16th of September 2016.
A 'selfie challenge' designed to raise awareness of PH was organised by Kate Jones in memory of her best friend Maddy Hardman.
Kate, who lives in St. Alban's, Hertfordshire, set up a Facebook photo campaign to raise money for PHA UK and generate awareness of the condition. She asked friends to upload photos of themselves wearing pink and pouting, with a caption describing PH and its symptoms. People posting selfies were also encouraged to include details of how to donate £3 to PHA UK by texting 'MADZ95 £3' to 70070.
The hashtags #PinkForMaddy and #PoutForPH were used alongside the selfies, and the campaign caught the attention of Kate's local newspaper, who published a story about it. Text donations totalled almost £400.
Maddy, who lived in Shenley, Hertfordshire, died in December last year aged 20, a year after being diagnosed with PH.
Kate said: "I was sitting on Facebook one day looking through old photos, and one popped up that showed Maddy and I on a school visit to Iceland back in 2011. I realised that she had been displaying signs of illness on that trip, but it took another three years for her to be diagnosed, and it hit home how important it is to raise awareness of PH and its symptoms. That's when I had the idea of the selfies."
Kate set up a JustGiving page when Maddy died and along with launching her Facebook campaign, she took part in the Rock Solid 10k mud run in Exeter earlier this year. Altogether, including general donations and with help from Maddy's family, the page has raised over £5,000 with gift aid for PHA UK. Kate is pictured with Maddy, who is on the right of the photo.
Last medically reviewed: September, 2016 • September, 2019 | {
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2017 shatered giving records. Strong markets and the prospect of tax reform drove total charitable giving past $400 billion for the first time ever1. Meanwhile, at Schwab Charitable, our donors recommended $1.9 billion in grants to philantropic groups last fiscal year—the most in our history—which increased total grants since inception to more than $10 billion.
Lessons on high-impact philanthropy from the Stanford Philanthropy Innovation Summit.
Lessons from the 2017 Stanford PACS Philanthropy Innovation Summit.
More impact. Less cash. A conversation about donating non-cash assets.
Non-cash assets provide a powerful way to increase the impact of charitable giving and maximize tax benefits at the same time.
A solid economy and robust stock market have created appreciated assets that can be donated to charity to offset higher tax bills.
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Charitable giving has averaged 2% of disposable income for decades. Donor-advised funds can help change this.
In this IMPACT conference video, Schwab Charitable's Kim Laughton explains what's ahead for year-end tax planning.
Here are five tips for creating a strategic plan for your charitable giving.
For the second consecutive year, Schwab Charitable President Kim Laughton has been named one of the most influential women in business by the San Francisco Business Times.
Schwab Charitable President Kim Laughton explains why donor-advised funds introduce an entirely different dimension to the advisor-client relationship.
Donor-advised funds have significantly outpaced traditional nonprofit and foundations to become philanthropy's fastest-growing vehicle for giving.
Here are four ways to incorporate charitable giving into your estate plan.
Schwab Charitable President Kim Laughton explains why clients are increasing their charitable giving in 2013 for reasons that go beyond philanthropy.
Schwab Charitable President Kim Laughton discusses how donor-advised funds can facilitate giving for investors at various levels of wealth, and how advisors can bring up the charitable conversation.
Philanthropy plays an important role in developing deep, multigenerational relationships and offers ways for uninitiated advisors to begin incorporating charitable themes into their client communication.
One increasingly popular vehicle for charitable giving is a donor-advised fund, which allows you to donate cash or assets when it makes sense for you and decide later which organizations will benefit.
In this IMPACT conference video, Kim Laughton, president of Schwab Charitable, comments on why investors and advisers have sought out donor-advised funds at a steady clip.
Schwab Charitable has moved quickly to encourage and assist donors in making gifts to benefit relief organizations working on recovery efforts after the recent superstorm.
Charitable giving is one of the highest priorities for Americans, with research showing that people would sooner cut back on travel and eating out than significantly trim the support they provide to their cherished causes.
1. For the resources above that are located outside of schwabcharitable.org, please take note of the following: Schwab Charitable has not reviewed the external sites above and is not responsible for their content or the content of any other sites to which they link. No judgment or warranty is made with respect to the accuracy, timeliness, completeness, or suitability of the content or the services of the sites to which these screens link. A link to a service or site outside of Schwab Charitable is not an endorsement of the service or site, its content, or its sponsoring organization. Schwab Charitable provides links to other Internet sites solely as a convenience to its users. You are linking to these sites at your own risk. | {
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Q: caption placement above and below: subcaption vs. floatrow I have a pretty long document with lots of figures. So far, I have had all captions on top, for both tables and figures, and that's how they are placed in the code.
Now, I want to change the figure captions to be below the corresponding figures without having to change each individual figure in the code, while leaving tables the way they are. I have read that the floatrow package can do this, and so I started looking into it. For regular figures, this works fine, but I'm also using subfigures generated with the subcaption command, and there, floatrow doesn't seem to have an effect.
Is it possible to have floatrow also affect the placement of captions (above or below) generated with the subcaption package - or is there some other, more lightweight package that can take care of this? Floatrow is a really extensive package, and I'm really only interested in changing the top vs. bottom issue of the caption placement.
| {
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\section{Introduction}
The formation of echo-chambers in social media \cite{jamieson2008echo,currin2021depolarization} is thought to strongly affect how opinions spread across a social network and contribute to increased social polarity. This occurs as like-minded people cluster in disjoint networks wherein information produced by any individual is reflected back at her \cite{cinelli2021echo} to increase her confidence artificially. This effect is countered, to a degree, by the diversity of opinions in a network which, naturally, exceeds that of any single individual \cite{dubois2018echo,bruns2017australian,del2018echo}.
Indeed, the formation of echo-chambers appears to depend on the specific interaction rules adopted by different platforms \cite{cinelli2021echo,Huszare2025334119}.
In this paper, we explore the existence of echo-chambers in statistical mechanics models that are often used to study opinion and influence dynamics but are common in many additional contexts -- from magnetic systems to neural networks. We focus most of our attention on the famous Ising model, which describes a ferromagnet as a network of coupled spins \cite{pathria2011statistical}. This model was originally developed to describe equilibrium magnetic systems in statistical mechanics, but is often used to explore how interactions between the individual entities reflect on large-scale system properties, for example, in the context of influence dynamics \cite{mobilia2007role,hartnett2016heterogeneous,liu2010influence,kempe2003maximizing,galam2000universality}. A natural question is therefore whether echo chambers exist in this model. We would say that a spin experiences an \emph{ echo chamber} effect if, when exposed to an external local field, its mean magnetization depends on whether it is isolated or linked to a neutral network. Here, a \emph{neutral network} with respect to the specific spin means a network that does not bias the mean magnetization of this spin when no external field is applied on it. In other words, the spin echo-chamber effect occurs when the connection with the network does not bias an unbiased spin but amplifies the influence of any external field applied on the spin.
Intuitively, one might expect the Ising model to display spin echo-chambers: Consider a spin connected to a network with no external fields on any of its spins and is, therefore, a neutral network. An external field on the specific spin connected to the network biases it in a certain direction and produces mean magnetization. Once this spin is connected to the network, this magnetization breaks the $\pm$ symmetry and biases the neighboring spins in the same direction. The network then has non-zero magnetization. One might expect it would feedback on the local spin to change its bias and mean magnetization, generating an echo-chamber in the system. Surprisingly, we find that although it might exist in other models, this effect is absent from the Ising model. We then identify three cases that can occur in different models: (i) Strong echo-chamber symmetry -- models in which echo-chambers never appear in a neutral network. The Ising model belongs to this class; (ii) Weak echo-chamber symmetry -- where there are no echo chambers in networks that do not have external fields other than on the specific spin, but there might be echo-chambers in networks that have additional biasing fields that balance each other on the specific spin, generating a neutral network. The XY, the vector Potts, and the Heisenberg models belong to this class; (iii) Models without any echo-chamber symmetry, which generically include the echo-chamber effect. For example, the spin $1$ Blume-Capel model belongs to this class.
To prove the absence of spin echo chambers in the Ising model, we use a simple but powerful tool -- the \emph{effective field method}. The mean magnetization of a spin is affected by the external field applied to it and its interactions with the other spins. We show that the two effects decouple and that the interactions with the rest of the network can be fully described by an \emph{effective field}. While an effective field could always be defined for any model, in the Ising model, it is independent of the external field applied on the spin itself. This property turns out to prevent the spin echo chamber effect. Loosely speaking, an effective field implies the lack of echo chambers even in non-neutral networks.
The implications of the effective field method go beyond the proof that some models do not exhibit a spin echo chamber effect. To demonstrate this, we applied it to construct an efficient computational algorithm for an exact calculation of the mean magnetization of each spin in tree networks with general interaction strengths, local external fields, and temperature. Although Monte-Carlo and similar methods are usually efficient in approximating the mean magnetization in such systems to high accuracy, exact calculations as in our algorithm are typically limited by the fact that the partition function grows exponentially with system size. As a proof of concept, we demonstrate this algorithm by calculating the quenched average of the random field Ising model on the Bethe lattice \cite{bruinsma1984random,nowotny2001phase,bleher1998phase}. This system is known to have a phase transition as a function of the temperature and the magnitude of the quenched disordered field. Our method enabled us to exactly calculate the mean magnetization in each realization of the random field and average these to directly demonstrate quenched averaged magnetization on a relatively large system.
Finally, we connect our findings back to the field of social influence networks \cite{friedkin1997social}. Specifically, we consider the optimal ways to exert influence on a network given limited resources \cite{yang2006mining,liu2010influence}. Using the analogy between social networks and the Ising model \cite{liu2010influence,stauffer2008social} it was recently shown that, to maximize influence, either hubs or leaf nodes should be targeted \cite{lynn2017statistical,romero2020continuous}. We validate and expand on these results on a large Barabasi-Albert network \cite{barabasi2014network}, and without the mean-field approximation, \cite{lynn2016maximizing} commonly used to analyze such systems.
\section{The basic model}
We start by considering the Ising spin model on a general undirected graph $G$ in which at each node $i$ there is a spin, denoted by $\sigma_i$. We assume an arbitrary symmetric interaction term $J_{ij}=J_{ji}$ between spins $\sigma_i$ and $\sigma_j$, if the nodes $i$ and $j$ are connected in the the graph $G$. Furthermore, we allow the external field $h_i$ to differ between nodes. The Hamiltonian of this model is given by:
\begin{equation}\label{Eq:Hamiltonian_Def}
\mathcal{H}(\vec\sigma)=-\sum_{\{i,j\}\in G}J_{ij}\sigma_i\sigma_j-\sum_i h_i \sigma_i,
\end{equation}
where $\vec\sigma = (\sigma_1,...,\sigma_N)$ is a specific configuration of the spins, $J_{ij}$ is the coupling strength between the spin $i$ and spin $j$, $h_i$ is the external field on the spin $i$, the first summation is over all the edges of the graph and the last summation is over all spins.
For a system described by the above Hamiltonian, the average magnetization of the $k^{th}$ spin in thermal equilibrium is given by:
\begin{equation}\label{Eq:MeanSigma_k}
\braket{\sigma_k}=\frac{\sum_{\{\sigma\}}\sigma_k e^{\mathcal{-\beta H}(\vec\sigma)}}{\sum_{\{\sigma\}}e^{\mathcal{-\beta H}(\vec\sigma)}} = \frac{\partial_{h_k}Z}{\beta Z},
\end{equation}
where $\sum_{\{\sigma\}}$ is a summation over all spin configurations, $\beta=T^{-1}$ is the inverse temperature in units where the Boltzmann constant is set to 1, and
\begin{eqnarray}
Z = \sum_{\{\sigma\}}e^{\mathcal{-\beta H}(\vec\sigma)}
\end{eqnarray}
is the partition function associated with the model. For the specific case of a single spin, which is used in the definition of the spin echo-chamber effect, the partition function is
\begin{eqnarray}
Z_1 = 2\cosh(\beta h),
\end{eqnarray}
and the mean magnetization is given by
\begin{eqnarray}\label{Eq:SingleSpinMean}
\braket{\sigma} = \tanh(\beta h).
\end{eqnarray}
Even though we focus much of our work on this basic model to demonstrate our findings, some of our results hold for a more general class of models, which we call ``echo-chamber symmetric'' models, as discussed in Sec.(\ref{Sec:OtherModel}).
\section{Illustrative examples in two spin systems}
To demonstrate the echo chamber effect, we start by looking at the simplest network graph, which includes two connected nodes. We show that the Ising model does not exhibit an echo chamber in this example, while a spin $1$ model does. In addition, we provide some heuristic intuition to these results. A more comprehensive analysis expands these simple examples in the following sections.
\subsection{The Ising model lacks an echo chamber}
Let us start by considering a single Ising spin, $\sigma_1$, in an external field of $h_1=1$ and inverse temperature $\beta=1$. As stated above, the mean magnetization of this spin is simply :
\begin{eqnarray}
\braket{\sigma_1} = \tanh(\beta h_1) = \tanh(1)\sim 0.76.
\end{eqnarray}
Next, we connect $\sigma_1$ to the simplest possible network by adding just one more spin, $\sigma_2$, coupled with $J_{12}=1$. There is no external field on $\sigma_2$, namely $h_2=0$. The Hamiltonian in this case, is simply
\begin{equation}\label{Eq:Hamiltonian_Def}
\mathcal{H}(\vec\sigma)=-\sigma_1\sigma_2- \sigma_1.
\end{equation}
Let us calculate the mean magnetization of this second spin. Direct calculation shows that in this case:
\begin{eqnarray}
\braket{\sigma_2} =\frac{e^{2} + e^{-2} - 2}{e^{2} + e^{-2} + 2}\sim 0.58.
\end{eqnarray}
Although no field is directly applied to $\sigma_2$, its coupling with $\sigma_1$ leads to a mean magnetization which agrees with the sign of the external field $h_1$. Since $\braket{\sigma_2}>0$, one might expect that this magnetization may feedback onto $\sigma_1$ and increase its alignment with the field $h_1$. Indeed, if one replaces $\sigma_2$ with a fixed magnet of constant magnetization equal to $\braket{\sigma_2}$ then this would increase the mean magnetization of $\sigma_1$.
Directly calculating the mean magnetization of $\sigma_1$ in the coupled system we obtain:
\begin{eqnarray}
\braket{\sigma_1} =\frac{e^{2} - e^{-2}}{e^{2} + e^{-2} + 2}\sim 0.76,
\end{eqnarray}
which is exactly equal to its mean magnetization in the uncoupled system. Therefore, the expectation for positive feedback does not hold and this system does not exhibit an echo chamber.
The effect of $\sigma_2$ on $\sigma_1$ deviates from that of a constant magnet with the same mean magnetization. Therefore, it must be the fluctuations of $\sigma_2$ responsible for the absence of echo-chamber. Using the ergodicity of the system, which implies that the ensemble average is identical to the time average, we can interpret $\braket{\sigma_2}>0$ as if, on average, $\sigma_2$ spends time $t_+$ in the $\sigma_2=+1$ state and time $t_-$ in the $\sigma_2=-1$ state, such that
\begin{eqnarray}
\frac{t_+-t_-}{t_++t_-}=\braket{\sigma_2}.
\end{eqnarray}
\begin{figure}[h]
\centering
\includegraphics[width=0.7 \textwidth]{Figures/htanPlot.png}
\caption{The blue line is the function $\tanh(\beta h)$, which relates between average magnetization and external field in the Ising model. The red point is $\braket{\sigma_1}$ for an isolated spin with $\beta=h=1$. Coupling this spin to a second spin, $\sigma_2$, with coupling constant $J=1$, changes the external influence on $\sigma_1$ to $\beta(h+J)$ when $\sigma_2=+1$ and to $\beta(h-J)$ when $\sigma_2=-1$ (dark blue and black points, respectively). The concave nature of the hyperbolic tangent implies that for $h>0$ the $\sigma_2=-1$ cause a larger change in the mean magnetization compared to $\sigma_2=+1$ (compare the magnitudes of the red arrows). The time difference $\sigma_2$ spends on each of these states exactly cancels this bias so that the two spin Ising model,lacks an echo-chamber.}
\label{fig:HypTan}
\end{figure}
A key point in this intuitive explanation is then to note that because of the external field $h_1$, $\sigma_2$ affects the mean magnetization of $\sigma_1$ stronger when $\sigma_2=-1$ in comparison to the case $\sigma_2=+1$. This is a result of the concave nature of Eq.(\ref{Eq:SingleSpinMean}) for $h>0$ (see Fig. \ref{fig:HypTan}): Since $h_1>0$, a bias towards $h_1+J$ when $\sigma_2=+1$ has a smaller effect on $\braket{\sigma_1}$ in comparison to the bias towards $h_1-J$ that happens for $\sigma_2=-1$. The surprising fact is that the temporal bias towards $t_+$ is exactly canceled by the smaller effect of $\sigma_2=+1$ on the magnetization of $\sigma_1$. This exact cancellation is special for models that have the echo-chamber symmetry, as we discuss below.
\subsection{The Blume-Capel model displays an echo chamber}\label{Sec:BlumeCapel}
We have seen a simple example of the lack of echo chambers in the Ising model and provided a heuristic argument to explain it. However, the exact cancellation between the fluctuations and bias in the Ising model is somewhat special and does not exist in other models. We, therefore, demonstrate the existence of an echo chamber with a second simple example. To this end, we consider a similar two spin system, but with spin-1 objects, instead of the spin-$\frac{1}{2}$ used in the Ising model. The spin-1 objects $\sigma$ can take the values $1$, $0$ or $-1$. We start with a single particle system. Its Hamiltonian is given by
\begin{eqnarray}
\mathcal{H}(\sigma_1) = -h\sigma_1.
\end{eqnarray}
The partition function of this system is given by
\begin{eqnarray}
Z = e^{-\beta h} + e^{\beta h} + 1 = 2\cosh(\beta h) + 1.
\end{eqnarray}
The mean magnetization is given by
\begin{eqnarray}\label{Eq:BlumeCapelMag}
\braket{\sigma_1} = \frac{\partial_h Z}{\beta Z} = \frac{\sinh(\beta h)}{\cosh(\beta h) + \frac{1}{2}},
\end{eqnarray}
which for $h>0$ is convex in $h$. Next, consider a system of two coupled spins of this type, namely a Hamiltonia
\begin{eqnarray}
\mathcal{H}(\{\sigma\}) = -J\sigma_1\sigma_2 - h_1\sigma_1 - h_2\sigma_2.
\end{eqnarray}
The partition function is now
\begin{eqnarray}
Z
&=&2\left(\cosh(\beta h_1) + \cosh(\beta h_2) + e^{\beta J}\cosh\left(\beta(h_1+h_2) \right) + e^{-\beta J}\cosh\left(\beta(h_1-h_2)\right) \right) + 1,
\end{eqnarray}
and the mean magnetization of say $\sigma_1$ is given by
\begin{eqnarray}\label{Eq:Mean_Sigma_1_coupled}
\braket{\sigma_1} = \frac{2\left(\sinh(\beta h_1) + e^{\beta J}\sinh\left(\beta(h_1+h_2) \right) + e^{-\beta J}\sinh\left(\beta(h_1-h_2)\right) \right)}{2\left(\cosh(\beta h_1) + \cosh(\beta h_2) + e^{\beta J}\cosh\left(\beta(h_1+h_2) \right) + e^{-\beta J}\cosh\left(\beta(h_1-h_2)\right) \right) + 1}.
\end{eqnarray}
Using these we can easily check if there is a spin echo-chamber effect in the system. Namely, we can compare the mean magnetization of $\sigma_1$ at some field $h_1$ when the spin is coupled or uncoupled to the second spin with $h_2=0$. Plugging $h_2=0$ in Eq.(\ref{Eq:Mean_Sigma_1_coupled}) gives:
\begin{eqnarray}
\braket{\sigma_1}
= \frac{\sinh(\beta h_1) }{\cosh\left(\beta h_1\right) + \frac{3}{2\left(1+ 2\cosh({\beta J})\right)}}
\end{eqnarray}
Since this is different from the single spin mean magnetization (Eq. \ref{Eq:BlumeCapelMag}), we see that this model indeed has an echo-chamber effect -- the mean magnetization is larger when the spin is connected to additional spin, and is only equal to it in the case $J=0$ where there is no interaction between the spins. It implies that while the different time fraction that $\sigma_2$ spends at each possible spin value decreases the echo chamber effect, it does not exactly compensate for the convexity of $\braket{\sigma(h)}$. Therefore, there is some degree of the echo chamber effect in the system.
\section{The Effective field}
The examples considered above give some insight into the echo-chamber effect. To further explore this effect in the different models, it is useful to introduce first the notion of an effective field which we present next.
Generally speaking, the mean magnetization of any specific spin at a fixed temperature $\beta$, $\langle\sigma_k\rangle$, is a function of both the magnetic field on this spin, $h_k$, and the magnetic fields on all other spins, namely on $h_j$ for all $j\neq k$. Given the mean magnetization of spin $k$, we can invert Eq.(\ref{Eq:SingleSpinMean}) (or the corresponding relation between mean magnetization and external field for other models) and define the total effective field on this spin as:
\begin{eqnarray}
h_{k}^{tot} = \beta^{-1}\tanh^{-1} \left(\braket{\sigma_k} \right).
\end{eqnarray}
$h_{k}^{tot}$ has the following physical interpretation: when $\sigma_k$ is decoupled from the network, $h_k^{tot}$ would make its mean magnetization identical to $\braket{\sigma_k}$. The mean magnetization $\braket{\sigma_k}$ is affected by both the actual field on the spin, $h_k$, and the interactions with the rest of the network. Thus, it is useful do define the ``network field'' which captures the latter, as
\begin{eqnarray}\label{Eq:EffField_1}
h_{k}^{network} = h_k^{tot}-h_k = \beta^{-1}\tanh^{-1} \left(\braket{\sigma_k} \right) - h_k,
\end{eqnarray}
which can also be written as
\begin{eqnarray}\label{Eq:EffField_3}
\langle\sigma_k\rangle = \tanh\left(\beta(h_k + h_k^{network})\right).
\end{eqnarray}
An analogous network field can be defined for any spin model. However, it is not a useful quantity in most cases (unless some echo-chamber symmetry discussed below exists in the system). This is because $h_k^{network}$ is, in general, a non-trivial function of $h_k$ itself. It implies that, for a general model, the external field on a spin influences the feedback that this spin receives from the network. Hence, the spin is subject to an ``echo-chamber''.
In models where $h_k^{network}$ is independent of $h_k$, we call it the \emph{effective field} and denote it by $h^{eff}$. In these cases it can also be defined as
\begin{equation}\label{Eq:EffField_2}
h_{k}^{eff}=\beta^{-1}\tanh^{-1}(\braket{\sigma_k[h_k=0]}),
\end{equation}
namely as the total effective field when the external field on the specific spin is zero, and $[h_k=0]$ is short-hand notation for the external field configuration $(h_1,h_2,...,h_k=0,...h_N)$.
As we next show, the Ising model displays this special property and, as a result, lacks a spin echo-chamber effect.
\subsection{Effective field in the Ising model}
In this subsection, we prove that one can define an effective field in the Ising model on an arbitrary network. In other words, we show that $h_k^{eff}$, as defined in Eq.(\ref{Eq:EffField_1}), is not a function of $h_k$. We do this by showing that Eq.(\ref{Eq:EffField_2}) holds, regardless of the value of $h_k$. To this end, we first define the following quantities:
\begin{equation}
\mathcal{H}'_k(\vec\sigma) = \mathcal{H}(\vec\sigma)+\sigma_kh_k = -\sum_{\{i,j\}\in G}J_{ij}\sigma_i\sigma_j-\sum_{i\neq k} h_i \sigma_i,
\end{equation}
and
\begin{eqnarray}
A_+&=&\sum_{\{\sigma\neq \sigma_k\}}e^{\mathcal{-\beta H}'(\vec\sigma,\sigma_k=1)};\\
A_-&=&\sum_{\{\sigma\neq \sigma_k\}}e^{\mathcal{-\beta H}'(\vec\sigma,\sigma_k=-1)},
\end{eqnarray}
where the summation in the definitions of $A_{\pm}$ is over all configurations of all the spins except $\sigma_k$, and $\mathcal{H}'(\vec\sigma,\sigma_k=\pm1)$ is calculated at the corresponding configuration but forcing $\sigma_k=\pm 1$, respectively. With this notation, we can write
\begin{eqnarray} \label{Eq:Z_expressed_with_A}
Z &=& e^{\beta h_k}A_+ + e^{-\beta h_k}A_-,\nonumber\\
\partial_{h_k}Z &=& \beta\left(e^{\beta h_k}A_+ - e^{-\beta h_k}A_-\right) ,
\end{eqnarray}
and the mean magnetization can be written as
\begin{equation}\label{origin_mag}
\braket{\sigma_k}=\frac{e^{\beta h_k} A_+-e^{-\beta h_k} A_-}{e^{\beta h_k} A_++e^{-\beta h_k} A_-}.
\end{equation}
Manipulating the above equation:
\begin{equation}
\braket{\sigma_k}=\frac{e^{\beta h_k} A_+-e^{-\beta h_k}A_-}{e^{\beta h_k} A_++e^{-\beta h_k}A_-}=\frac{(e^{\beta h_k} -e^{-\beta h_k})(A_++A_-)+(e^{\beta h_k} +e^{-\beta h_k})(A_+-A_-)}{(e^{\beta h_k} +e^{-\beta h_k})(A_++A_-)+(e^{\beta h_k} -e^{-\beta h_k})(A_+-A_-)},
\end{equation}
where in the right hand side $e^{-\beta h_k}A_+$ and $e^{\beta h_k}A_-$ were added and subtracted from both the numerator and denominator. Next, we multiply the numerator and the denominator by $\beta/2$, and use the identity $A_++A_-=Z(h_k=0)$ as well as $\beta\left(A_+-A_-\right)=\partial_{h_k} Z(h_k=0)$, where $Z(h_k=0)$ is the partition function of the same system with $h_k$ set to be zero (See Eq. \ref{Eq:Z_expressed_with_A}). With these we get:
\begin{equation}\label{effmag}
\braket{\sigma_k}=\frac{\beta \sinh(\beta h_k)Z(h_k=0)+\cosh(\beta h_k)\partial_{h_k}Z(h_k=0)}{\beta \cosh(\beta h_k)Z(h_k=0)+\sinh(\beta h_k)\partial_{h_k}Z(h_k=0)}.
\end{equation}
Dividing numerator and denominator by $\cosh(h_k)\beta Z(h_k=0)$ and using Eq.(\ref{Eq:MeanSigma_k}), we get:
\begin{equation}
\braket{\sigma_k}=\frac{\tanh(\beta h_k)+\braket{\sigma_k[h_k=0]}}{1+\tanh(\beta h_k)\braket{\sigma_k[h_k=0]}}.
\end{equation}
To continue, we use the following identity for hyperbolic tangent:
\begin{eqnarray}
\tanh(a+b)=\frac{\tanh(a)+\tanh(b)}{1+\tanh(a)\tanh(b)},
\end{eqnarray}
to get:
\begin{equation}\label{Eq:UsingH_eff}
\braket{\sigma_k}=\frac{\tanh(\beta h_k)+\braket{\sigma_k[h_k=0]}}{1+\tanh(\beta h_k)\braket{\sigma_k[h_k=0]}} = \tanh\left(\beta h_k + \tanh^{-1}\braket{\sigma_k[h_k=0]}\right).
\end{equation}
Lastly, we note that by definition (see Eq.\ref{Eq:EffField_3}), the above equation implies that
\begin{eqnarray}
h_k^{network} =\tanh^{-1}\braket{\sigma_k[h_k=0]}.
\end{eqnarray}
However, in this case, $h_k^{network}$ is calculated using the mean magnetization of the system when replacing the actual value of $h_k$ with $h_k=0$. This completes the proof that $h_k^{network}$ is $h_k$ independent. Therefore, in the Ising model $h_k^{network}$ can indeed be termed $h^{eff}_k$ as defined above.
We note that this result (and thus everything that follows), fails in the thermodynamic limit if the system has two distinct phases, where ergodicity breaking dictates averaging over a subspace of all micro-states, and one cannot evaluate the mean magnetization using Eq.(\ref{Eq:MeanSigma_k}). As we discuss in what follows, the property we just proved stems from a symmetry of the spin interactions. However, before showing this, we first explain why the existence of an effective field implies that the Ising model has no spin echo-chambers.
\subsection{The Ising model does not display spin echo-chambers}
As discussed above, a spin echo-chamber effect occurs when the coupling of a spin to a neutral network affects its response to an external magnetic field. To explain the effect, consider first the general case of a spin, $\sigma_1$ that can be coupled to a general network of spins $G$. When no external field is applied on any of the spins in the system, the average magnetization of $\sigma_1$ is zero (as is the case for any other spin in the system), namely $\braket{\sigma_1} = \braket{\sigma_k}=0$. We define a network to be \emph{neutral with respect to $\sigma_1$}, or \emph{$\sigma_1$-neutral}, in the following case: if no external field is applied on $\sigma_1$, its mean magnetization is zero regardless of it being connected or disconnected from the network. In other words, the connection to the network does not bias the mean value of $\sigma_1$. We note that by definition, a network is $\sigma_k$-neutral exactly when $h_k^{network}=0$ for $h_k=0$. If there is an effective field in this model, as is the case for the Ising model, then a network is $\sigma_k$-neutral when $h_k^{eff}=0$.
Employing this definition and the effective field described above, it is now straightforward to show that there is no spin echo-chamber effect in the Ising model.
Assume that a spin, which without loss of generality we denote by $\sigma_1$, is coupled to a $\sigma_1$-neutral network, and is subject to some external field $h_1$. By the effective field result, the mean magnetization of the spin is given by
\begin{eqnarray}
\langle\sigma_1\rangle = \tanh\left(\beta(h_1 + h_1^{eff})\right),
\end{eqnarray}
but based on Eq.(\ref{Eq:EffField_2}) and the fact that the network is $\sigma_1$-neutral, it must be that $h_k^{eff}=0$ . Therefore,
\begin{eqnarray}
\langle\sigma_1\rangle = \tanh\left(\beta(h_1 + h_1^{eff})\right) = \tanh(\beta h_1) = \braket{\sigma_1}_{uncoupled},
\end{eqnarray}
where $\braket{\sigma_1}_{uncoupled} = \tanh(\beta h_1)$ is the single spin equilibrium average of $\sigma_1$, namely its mean when it is not connected to any network. In other words, the above argument shows that the mean magnetization of the spin $\sigma_1$ is not affected by a connection to any $\sigma_1$-neutral network, and there is no spin echo-chamber effect in this model.
\subsection{Echo chambers in other models}
\label{Sec:OtherModel}
The argument used above to show that there are no echo-chambers in the Ising model, can be applied to any model with the property that the network influence on a spin is independent of the local field. Namely, there is an effective field in the model. In models for which an effective field can be defined, the mean magnetization of $\sigma_1$ can be written as
\begin{eqnarray}
\langle\sigma_1\rangle = f\left(\beta(h_1 + h_1^{eff})\right),
\end{eqnarray}
where, as in the Ising model -- $h_1$ is the field on the spin $\sigma_1$, $h^{eff}_1$ is the influence of the network on the mean magnetization of $\sigma_1$ and it is independent on $h_1$, and $f$ is the function that relates the external field and the mean magnetization in an uncoupled spin for the specific model -- for example, in the Ising model $f(x) = \tanh(x)$. Since by its definition, the effective field is independent of $h_1$, then without loss of generality it can be calculated for the case $h_1=0$. But for $\sigma_1$-neutral network $h_1^{eff}=0$ in this case. Thus, we have in the above equation
\begin{eqnarray}
\langle\sigma_1\rangle = f\left(\beta h_1 \right) = \braket{\sigma_1}_{uncoupled},
\end{eqnarray}
which implies that there is no spin echo-chamber effect in models for which an effective field can be consistently defined. This also implies that models with an echo-chamber effect would, in general, have no effective field as defined above. However, it is not always easy to understand if an effective field exists in the model or not -- in fact, we are not familiar with other models that have this property. Therefore, we next discuss a different approach towards investigating the existence of the echo-chamber effect.
To directly test the existence of an echo-chamber in a model, we compare two systems. In the first one there is a single, uncoupled spin. Its Hamiltonian is therefore given by
\begin{eqnarray}
\mathcal{H}_1(\sigma_1) = -\bar h_1\cdot\bar \sigma_1.
\end{eqnarray}
In the general case $\bar\sigma_1$ is a vector or a tensor, and $\bar {h}_1\cdot\bar{\sigma}_1$ is a scalar constructed from $\bar\sigma_1$ and the vector or tensor $\bar h_1$. The partition function, in this case is:
\begin{eqnarray}
Z_1 = \sum_{\sigma_1} e^{\beta \bar\sigma_1\cdot \bar h},
\end{eqnarray}
where the sum signifies either discrete summation over all possible spin states (e.g.$\{-1,0,1\}$ for the case of spin $1$) or integration in the case of a continuous variable (e.g. angles for the $XY$ model).
We compare this scenario to a second scenario in which the spin $\bar\sigma_1$ is embedded in a network $G$ of spins with general coupling $J_{i,j}$ and fields $\bar h_i$. We denote the
full Hamiltonian as
\begin{eqnarray}
\mathcal{H}_{N}(\vec\sigma) = -\sum_i \bar h\cdot\bar\sigma_i - \sum_{i,j} J_{i,j}\bar\sigma_i\cdot\bar\sigma_j,
\end{eqnarray}
where again $\vec\sigma = (\bar\sigma_1,...\bar\sigma_N)$, and the partition function is
\begin{eqnarray}
Z_N &=& \sum_{\bar\sigma_i} e^{\beta \bar\sigma_1\cdot\bar h_1 + \beta \sum_{i,j} J_{i,j}\bar\sigma_i\cdot\bar\sigma_j +\beta\sum_{i\neq 1} \bar h_i\cdot\bar\sigma_i} \nonumber\\
&=& \sum_{\bar\sigma_1} e^{\beta \bar\sigma_1\cdot \bar h} \sum_{\sigma \neq \sigma_1} e^{\beta \sum_{i,j} J_{i,j} \bar\sigma_i\cdot \bar\sigma_j +\beta\sum_{i\neq 1}\bar h_i\cdot\bar\sigma_i } \left(e^{\beta \bar\sigma_1 \cdot\sum_{\sigma_k \in G_1} J_{1,k} \bar\sigma_k} \right).
\end{eqnarray}
We define \emph{strong echo-chamber symmetric models} as models in which the term
\begin{eqnarray}\label{Eq:Z_eff_def}
Z_{N-1}^{eff}(\bar\sigma_1) = \sum_{\{\bar\sigma_{k \neq 1}\}} e^{\beta \sum_{i,j} J_{i,j} \bar\sigma_i\cdot\bar\sigma_j +\beta\sum_{i\neq 1} \bar h_i\cdot\bar\sigma_i} \left(e^{\beta \bar\sigma_1\cdot \sum_{\bar\sigma_k \in G_1} J_{1,k} \bar\sigma_k} \right)
\end{eqnarray}
is independent of the specific value of $\sigma_1$ for every neutral network. In such models, $Z_{N-1}^{eff}(\sigma_1)$ is not a function of $\sigma_1$ and it is therefore possible to factorise the partition function:
\begin{eqnarray}\label{Eq:Z_factorization}
Z_N = \left(\sum_{\bar\sigma_1} e^{\beta \bar\sigma_1\cdot\bar h_1}\right)\left( \sum_{\sigma \neq \sigma_1} e^{\beta \sum_{i,j} J_{i,j} \bar\sigma_i\cdot\bar\sigma_j +\beta\sum_{i\neq 1} \bar h_i\cdot\bar\sigma_i} \left(e^{\beta \bar\sigma_1 \cdot \sum_{\sigma_k \in G_1} J_{1,k} \bar\sigma_k} \right)\right) = Z_1\cdot Z_{N-1}^{eff}.
\end{eqnarray}
This factorization of $Z_N$ implies that the magnetization of $\bar\sigma_1$ is independent of the existence of the rest of the network, and hence there is no echo-chamber effect in the model. To show this, we use, again, the relation between the mean magnetization and partition function in Eq.(\ref{Eq:MeanSigma_k}):
\begin{eqnarray}
\braket{\sigma_1} = \frac{\partial_{\bar h_1} Z}{\beta Z} = \frac{\partial_{\bar h_1} Z_1\cdot Z_{N-1}^{eff}}{\beta Z_1\cdot Z_{N-1}^{eff}} = \frac{\partial_{\bar h_1} Z_1 }{\beta Z_1 },
\end{eqnarray}
which is identical to the single spin magnetization, and therefore implies that there is no echo-chamber effect in the model.
As we have already seen by using the effective field method, the Ising model is a rare example of a model with a strong echo-chamber symmetry. However, there are several models with a \emph{weak echo-chamber symmetry}: in such models $Z_{N-1}^{eff}$ is $\bar\sigma_1$ independent for networks where $h_i=0$ for all $i\neq 1$. In such models, There are no echo-chambers for spins connected to networks that do not have additional local fields. Nevertheless, they may still display an echo-chamber effect in $\sigma_k$-neutral networks where the magnetic fields on different spins balance each other out.
We next discuss each of these different cases.
\subsubsection{Models with strong Echo-chamber symmetry}
We first show that the Ising model has strong echo-chamber symmetry. We do this without employing effective field considerations, which turns out to be instructive when considering other models. To this end, we use the fact that the network is $\bar\sigma_1$-neutral. Therefore
\begin{eqnarray}
\braket{\bar\sigma_1}=\left.\frac{\partial_{\bar h_1}Z_N}{\beta Z_N}\right|_{h_1=0,h_2,h_3...h_N}=0,
\end{eqnarray}
which implies that
\begin{eqnarray}
\left.\beta^{-1}\frac{\partial Z_N}{\partial{\bar h_1}}\right|_{h_1=0,h_2,h_3...h_N}=0.
\end{eqnarray}
Substituting the expression for the partition function, we get that:
\begin{eqnarray}\label{Eq:StrongSymmetry}
\sum_{\sigma_1} \bar\sigma_1 \sum_{\sigma \neq \sigma_1} e^{\beta \sum_{i,j} J_{i,j} \bar\sigma_i\cdot\bar\sigma_j +\beta\sum_{i\neq 1} \bar h_i\cdot\bar\sigma_i } \left(e^{\beta \bar\sigma_1 \cdot \sum_{\sigma_k \in G_1} J_{1,k} \bar\sigma_k} \right)=\sum_{\sigma_1} \sigma_1 Z_{N-1}^{eff}(\sigma_1) =0.
\end{eqnarray}
Carrying out the sum over the two possibilities $\sigma_1=\pm 1$, we obtain:
\begin{eqnarray}
Z_{N-1}^{eff}(\sigma_1=+1)=Z_{N-1}^{eff}(\sigma_1=-1),
\end{eqnarray}
and therefore a neutral network implies that $Z_{N-1}^{eff}$ is not a function of $\sigma_1$, hence there is a strong echo-chamber symmetry in this model.
We note, however, that we do not expect many other models to be in the class of the strong echo-chamber symmetry, as in general, Eq.(\ref{Eq:StrongSymmetry}) does not imply Eq.(\ref{Eq:Z_factorization}) holds. Therefore, neutral networks in other models do not generally imply the separability of the partition function.
\subsubsection{Models with weak Echo-chamber symmetry}
Whereas a $\sigma_k$-neutral network is not enough to eliminate the echo-chamber effect in most models, a special case of interest is when the network is $\sigma_k$-neutral because there are no magnetic fields in the system on any spin except $\sigma_k$. The class of models that have the echo-chamber symmetry in this special case but not for general $\sigma_k$-neutral networks, which is the class of weak echo-chamber symmetric models, includes models with the following spin-symmetry: for any change $\sigma_1\to\hat\sigma_1$, there exist a one-to-one transformation $\hat\sigma_k = F_{\sigma_1\to\hat\sigma_1}[\sigma_k]$ such that $\sigma_i\sigma_j = \hat\sigma_i\hat\sigma_j$ for any $i$ and $j$. Mathematically, this implies a symmetry group $F$ of invertible transformations on the possible values of $\sigma$, such that the spin multiplication in the Hamiltonian is invariant under the action of elements of $F$. In this case, $Z_{N-1}^{eff}(\sigma_1)$ is $\sigma_1$ independent regardless of the specific values of $J_{ij}$.
To show that models with a symmetry transformation $F$ have the weak echo-chamber symmetry, we note that a transformation $\sigma_1\to\hat\sigma_1$ generally changes all the elements in the sum over $\{\sigma_{k\neq 1}\}$ in the definition of $Z_{N-1}^{eff}$ (Eq. \ref{Eq:Z_eff_def}), but each of them is equal to another element in the sum, given by the realization corresponding to the transformation in which $\sigma_k \to F_{\sigma_1\to\hat\sigma_1}[\sigma_k]$. Therefore, the contribution of each configuration $\{\sigma_{k\neq 1}\}$ with $\sigma_1$ is equal to the contribution of the configuration $\{\hat\sigma_{k\neq 1}\}$ with $\hat\sigma_1$. This is a result of the multiplication between spins being invariant under any group action, so replacing $\sigma_i\sigma_j$ with $F_{\alpha}\sigma_iF_{\alpha}\sigma_j$ in $Z_{N-1}^{eff}$ does not change its value for any $F_{\alpha}$ in the group. Therefore, the total sum is independent of the value of $\sigma_1$. In other words, changing the value of $\sigma_1$ reshuffles the order of the elements in the sum, but does not change the summation value.
We note, however, that even models that have no such a transformation might nevertheless have the echo-chamber symmetry for some specific realizations of $J_{ij}$.
An example for a model with a weak echo-chamber symmetry is the $XY$ model, where $\sigma_i = (\cos\theta_i,\sin \theta_i)$. In this case, any change of $\sigma_1\to\hat\sigma_1$ corresponds to some change in the angle $\theta_1\to\hat \theta_1 = \theta_1+\Delta\theta$. We can define the transformation $$\hat \theta_k = F_{\theta_1\to\theta_1+\Delta\theta}[\theta_k] = F_{\Delta\theta}\theta_k= \theta_k+\Delta\theta,$$ where $F_{\Delta\theta}$ is a rigid rotation of a spin by the corresponding angle $\Delta\theta$. In this case the symmetry group is $SO(2)$, and it preserves the multiplication in the Hamiltonian.
In the absence of external fields, a realization $\{\theta_{k\neq 1}\}$ contributes with $\theta_1$ exactly as the realization $\{\hat\theta_{k\neq 1}\}$ with $\hat\theta_1$, and therefore the contribution of $Z_{N-1}^{eff}$ is independent of the specific angle of $\sigma_1$. In this case, a change in $\sigma_1$ can be viewed as a change in the reference frame, which does not change $Z_{N-1}^{eff}$. However, this is not the case in the presence of external fields $\vec h$, and therefore the model has only the weak but not the strong echo-chamber symmetry. We note that any model with a similar symmetry group that respects the two spins interaction (e.g., the Heisenberg model and the vector Potts model \cite{wu1982potts}) has a weak echo-chamber symmetry that protects the model from echo-chambers in the absence of external fields. However, we also note that models with weak echo chamber symmetry generally do not have an effective field, as this would imply that they have the strong rather than the weak echo-chamber symmetry.
\subsubsection{Models without Echo-chamber symmetry}
Last, we note that many models of interest have neither the strong nor the weak echo-chamber symmetry. Correspondingly, these models have an echo-chamber effect for most realizations of neutral networks. An example for such a model is the spin-1 Blume-Capel model \cite{blume1966theory,capel1966possibility}, where an echo chamber effect was explicitly demonstrated in Sec. \ref{Sec:BlumeCapel} .
\section{Precise calculation of effective field and magnetization on tree networks}
In the previous section, we have shown that, for models with a strong echo-chamber symmetry, the mean magnetization of each spin can be calculated using an effective field approach, where the effective field is not a function of the field on the spin itself. In this section, we show that in the case of the Ising model on tree networks, the effective field can be calculated using a relatively simple, closed formula. We then introduce an efficient algorithm that uses this formula to calculate the mean magnetization on each spin and the entire system.
\subsection{Effective Field Formula}
\subsubsection{Leaf Spins:}
To explain how the effective field developed above can be used to construct an efficient algorithm to calculate the mean magnetization on a tree, consider first a ``leaf'' edge on a tree, namely a spin connected to only one other spin. Without loss of generality, let us denote the leaf spin as $\sigma_1$, and the spin connected to is as $\sigma_2$. Using the effective field approach, we know that
\begin{eqnarray}
\braket{\sigma_1}=\tanh\left(\beta(h_1+h^{eff}_1)\right),
\end{eqnarray}
and therefore our aim is to calculate $h^{eff}_1$, which can be done by calculating $\braket{\sigma_1}$ with $h_1=0$. The latter is given by:
\begin{equation}
\braket{\sigma_1}[h_1=0]=\frac{\sum_{\{\sigma\}}\sigma_1 e^{\beta(\sum_i h_i\sigma_i+\sum_{\{i,j\}\in G}J_{ij}\sigma_i\sigma_j )}}{\sum_{\{\sigma\}}e^{\beta(\sum_i h_i\sigma_i+\sum_{\{i,j\}\in G}J_{ij}\sigma_i\sigma_j )}}.
\end{equation}
Next, we perform the summation over $\sigma_1 = \pm 1$, and get:
\begin{equation}
\braket{\sigma_1}[h_1=0]=\frac{\sum_{\{\sigma_k\neq \sigma_1\}} e^{\beta(\sum_{i\neq 1} h_i\sigma_i+\sum_{\{i\neq 1,j\neq 1\}\in G}J_{ij}\sigma_i\sigma_j )}\left(e^{\beta J_{1,2}\sigma_2} - e^{-\beta J_{1,2}\sigma_2}\right)}{\sum_{\{\sigma_k\neq \sigma_1\}} e^{\beta(\sum_{i\neq 1} h_i\sigma_i+\sum_{\{i\neq 1,j\neq 1\}\in G}J_{ij}\sigma_i\sigma_j )}\left(e^{\beta J_{1,2}\sigma_2} + e^{-\beta J_{1,2}\sigma_2}\right)}.
\end{equation}
We note that the term $\left(e^{\beta J_{1,2}\sigma_2} + e^{-\beta J_{1,2}\sigma_2}\right)$ in the denominator is independent on the specific value of $\sigma_2$, and is equal to $2\cosh(\beta J_{1,2})$. Similarly, the term $\left(e^{\beta J_{1,2}\sigma_2} - e^{-\beta J_{1,2}\sigma_2}\right)$ is equal to $2\sigma_2\sinh(\beta J_{1,2})$ as $\sigma_2$ can only be $\pm 1$. We can therefore write:
\begin{equation}
\braket{\sigma_1}[h_1=0]=\tanh(\beta J_{1,2})\frac{\sum_{\{\sigma_k\neq \sigma_1\}} \sigma_2 e^{\beta(\sum_{i\neq 1} h_i\sigma_i+\sum_{\{i\neq 1,j\neq 1\}\in G}J_{ij}\sigma_i\sigma_j )}}{\sum_{\{\sigma_k\neq \sigma_1\}} e^{\beta(\sum_{i\neq 1} h_i\sigma_i+\sum_{\{i\neq 1,j\neq 1\}\in G}J_{ij}\sigma_i\sigma_j )}} = \tanh(\beta J_{1,2})\braket{\tilde \sigma_2}
\end{equation}
where $\braket{\tilde \sigma_2}$ is, by the expression in the middle, the mean magnetization of $\sigma_2$ in a system where the spin $\sigma_1$ is deleted, namely the leaf is trimmed from the graph. In terms of the effective field, we can write:
\begin{eqnarray}\label{Eq:h_1_eff_formula}
h_1^{eff} = \beta^{-1}\tanh^{-1}\Big(\tanh(\beta J_{1,2})\braket{\tilde \sigma_2}\Big)
\end{eqnarray}
This structure, in which $h_1^{eff}$ is calculated from a trimmed version of the same tree, naturally calls for a recursion process. However, caution must be made when using the above procedure, since (say in the above example) $\sigma_2$ may be connected to more than two spins, so trimming $\sigma_1$ does not make $\sigma_2$ a leaf spin. As we next show, this result can be generalized to non-leaf spins.
\subsubsection{Non-Leaf Spins:}
Consider a non-leaf spin; namely, it is connected to several spins. Let us denote the specific spin by $\sigma_k$, and its neighboring spins by $\sigma_m$...$\sigma_n$. Since the spin interaction network is a tree graph, deleting the node associated with $\sigma_k$ would make each of the spins connected with it $\sigma_m$...$\sigma_n$, part of a disconnected tree. We denote these trees by the $G_m$...$G_n$ correspondingly, and with this notation, we can write the Hamiltonian as:
\begin{eqnarray}
\mathcal{H}(\{\sigma\}) = \left(\sum_{i\in\{m...n\}}\mathcal{H}_i\left(\{\sigma\}\right) - J_{ki}\sigma_k\sigma_i\right) - h_k\sigma_k,
\end{eqnarray}
where
\begin{eqnarray}
\mathcal{H}_i(\{\sigma\}) = -\sum_{\{l,j\}\in G_i}J_{lj}\sigma_l\sigma_j - \sum_{j\in G_i}h_j\sigma_j.
\end{eqnarray}
In other words, $\mathcal{H}_i(\{\sigma\})$ is the contribution to the Hamiltonian from the sub-tree $G_i$.
Using the notation above, the mean magnetization of the non-leaf spin can be written as:
\begin{equation}
\braket{\sigma_{k}}[h_{k}=0]=\tanh\left(\sum_{h\in \{m...n\}} \tanh^{-1}(\tanh(\beta J_{hk})\braket{\tilde\sigma_h})\right),
\end{equation}
which in terms of the effective field can be written as:
\begin{eqnarray}\label{Eq:h_eff_complete}
h_k^{eff} = \beta^{-1}\sum_{h\in\{m...n\}}\tanh^{-1}\Big(\tanh(\beta J_{hk})\braket{\tilde \sigma_h}\Big).
\end{eqnarray}
In the above equation, $\braket{\tilde \sigma_h}$ is the mean of $\sigma_h$ calculated using $\mathcal{H}_h$, namely as if we cut the connection between the spins $k$ and $h$. The proof of this result involves cumbersome, though straightforward algebra, and is therefore left to the appendix (See appendix \ref{Appendix_NonLeafProof}).
As in the case of the leaf spin, here too the mean magnetization and effective field on the spin $k$ can be calculated from the mean magnetization of the sub-trees connected to the spin $k$. This enables a recursive and efficient calculation of the mean magnetization of each spin, as described in the next section.
\subsection{Algorithm for precise magnetization calculation}\label{Sec:Algo}
The recursion formula for the effective field, as formulated above, allows fast and precise calculation of the mean magnetization of any spin and over the tree network as a whole. For clarity of presentation, the algorithm described below is sub-optimal in terms of running time and memory allocation but is simpler to implement. In this algorithm, we first reshape the tree using the Breadth-first search (BFS) algorithm \cite{silvela2001breadth}, such that the calculations only involve leaf nodes, and never the more complicated case, whereby trimming the node the tree becomes a set of disconnected trees.
To calculate the mean magnetization of a given spin, the algorithm first reshapes the tree such that this spin is the tree root, using the BSF algorithm, which for completeness is provided as a pseudo-code in Appendix \ref{Sec:AppAlgo} (Algorithm 3). The effective field is then calculated recursively (Algorithm 2 in Appendix \ref{Sec:AppAlgo}), starting from the leaves of the resulting tree, removing them after taking into account their effective field and its influence on their neighbors using Eq.(\ref{Eq:h_eff_complete}), and then repeating the same process with the remaining tree until the root is the only node in the graph. By scanning the mean magnetization of all the spins (Algorithm 1 in Appendix \ref{Sec:AppAlgo}), the mean magnetization over the network can be calculated.
The time complexity of this procedure can be compared to the complexity of the direct calculation of the total magnetization by averaging over all microstates, namely all configurations of the system. The time it takes to calculate the mean magnetization in the latter case scales as the number of microstates of the networks, therefore it grows at least exponentially with the number of spins $N$, namely it is $\mathcal{O}(e^N)$. On the other hand, the algorithm presented above includes, for each node, a BFS step required to calculate the depth and parents structure given a specific root and then backtracking over the resulting structure to calculate the effective field. Both of these scale with the number of nodes in the system as $\mathcal{O}(N)$ \cite{silvela2001breadth}. Since this process is repeated for each node the resulting time complexity is $O(N^2)$ (shown in figure \ref{fig:comp_t}), which is significantly faster than direct averaging over the microstates. The algorithm may be made more efficient if one exploits the fact that the trees with nearby roots are very similar in structure. We leave such improvements to later work.
To summarize, the lack of echo-chamber effect in the Ising model translates into a significant decrease in the complexity for calculating the mean magnetization.
\begin{figure}[h]
\centering
\includegraphics[width=0.8 \textwidth]{Figures/runtime.png}
\caption{Run time of the algorithm as a function of the number of spins in the tree (in thousands). As expected, an $\mathcal{O}(N^2)$ dependence is observed.}
\label{fig:comp_t}
\end{figure}
\section{Employing the effective field algorithm }
In this section, we demonstrate the strength of the method presented above on two examples that incorporate large tree networks with hundreds of nodes.
\subsection{Random Field Ising Model on the Bethe Lattice}
Let us demonstrate the algorithm developed above on the famous problem of the Random Field Ising Model (RFIM) on the Bethe lattice \cite{bruinsma1984random,nowotny2001phase,bleher1998phase}. The RFIM is described by the following Hamiltonian,
\begin{eqnarray}
\mathcal{H} = -J\sum_{\{i,j\}\in G}\sigma_i \sigma_j - \sum_i h_i \sigma_i .
\end{eqnarray}
Specifically, we are interested in the case where $G$ is the Bethe lattice, a tree-graph where each spin is connected to the same number of other spins. The number of neighbors each spin has in the tree is called \emph{the coordination number} of the graph. The left panel of Fig.(\ref{fig:3dPT}) depicts the Bethe lattice with coordination number 4. In the thermodynamic limit, this model exhibits a phase transition from a ferromagnetic phase for small random fields to a paramagnetic phase for large fields \cite{bruinsma1984random,nowotny2001phase}. It is, therefore, a good example where averaging the magnetization over different realizations of the quenched disorder can be useful. To this end, we performed the following calculation on a Bethe lattice with 485 spins, coordination number 4 (each spin in the bulk has four neighbors), and five shells, namely from the center of the graph there are five steps until the boundary is reached (see Fig.\ref{fig:3dPT}). For each value of the temperature $T$ and standard deviation $h_0$ of the random fields $h_i$, we chose 100 different realizations of $\vec h$, and for each of these realizations the mean magnetization in the lattice was calculated. The right panel in Fig.(\ref{fig:3dPT}) shows the quenched mean magnetization. We note that in order not to average positive and negative magnetization in the ordered phase, we average over $m=|N^{-1}\sum_i\sigma_i|$, but in a finite system, the absolute value implies that $m$ is not zero, but rather scales as $N^{-0.5}$ even in the disordered phase.
In this example, we used the algorithm developed above to exactly calculate the magnetization in each realization, as a ``tour de force'' application on a system where much is known on its phase diagram \cite{nowotny2001phase}. However, the algorithm is quite general and can be used on many other applications, as we show below.
\begin{figure}[h]
\centering
\includegraphics[width=0.49 \textwidth]{Figures/bethe_lattice.pdf}
\includegraphics[width=0.49 \textwidth]{Figures/contourForPT.png}
\caption{RFIM on the Bethe lattice. Left panel: the Bethe lattice with coordination number 4 and 5 shells on which the mean magnetization was calculated. Right panel: the mean magnetization on this lattice, with random fields sampled from a Gaussian distribution with variance $h_0$ and temperature $T$.}
\label{fig:3dPT}
\end{figure}
\subsection{Influence maximization}
In this section, we use the algorithm introduced earlier to solve a problem with a similar flavor to the echo-chamber effect, which is the main motivation in this manuscript: influence maximization for large social network \cite{liu2010influence,lynn2016maximizing,lynn2017statistical}. In this problem, the goal is to find a small seed in a social network that could maximize the spread of influence. We assume a network of agents with two competing opinion states, such that ``+1'' represents the preferred opinion, and ``-1'' the opposite opinion. The agents have social interaction that tends to ``align" their opinions; namely, an agent tends to change its opinion towards the mean opinion of the agents it is socially connected with. Two additional influences on each agent are: (i) some internal tendency to switch opinion, which we assume to be uniform among all agents. This mechanism is commonly modeled as random fluctuations induced by the physical temperature of the system; (ii) External influence on each agent that can come from advertisements or any other source. This influence is commonly modeled as an external magnetic field on each network node.
Such problems are commonly analyzed using the ferromagnetic Ising model described above, where the mean opinion in the network is given by the mean magnetization at thermal equilibrium \cite{brede2019transmission,lynn2016maximizing,lynn2017statistical,lynn2018maximizing,moreno2019shielding,romero2020continuous}. The main question is then as follows: given a limited budget of external influence (say a limit budget for advertisement), modeled as a limited amount of external field denoted by $$H=\sum_i h_i,$$ where $h_i$ is the local external influence on the site $i$ and $H$ is the total external influence, how should one partition the external influence between the different spins as to maximize mean network magnetization. In other words, find the set $\{h_i\}$ that maximizes $\braket{m}=\braket{\sum_i\sigma_i}$ under the constraints $\sum_ih_i=H$ and $h_i>0$. Mathematically, this can be phrased as:
\begin{equation}\label{mag_der}
h_i = \arg \underset{h_i>0}{\text{max }} \text{ } \langle m[h_i,J,H,\beta]\rangle
\end{equation}
\begin{equation*}
\text{ s.t. } \sum_{i=0}^{N}h_i=H
\end{equation*}
This problem was already addressed in the literature, using mean-field approximation or numerical simulations \cite{brede2019transmission,lynn2016maximizing,lynn2017statistical,lynn2018maximizing}. In the limit of weak field (small $H$), it was shown that the optimal field is strongest at the hubs. Conversely, the optimal field is stronger on the leaves in the strong field limit (large $H$). Using the above method, we calculated the exact magnetization on a large network for different values of the magnetic field on each node.
Using the recursive algorithm introduced in Sec.\ref{Sec:Algo}, we can efficiently calculate the exact value of the total magnetization for each set of local fields $h_i$. Therefore, we could use the Sequential Linear/Quadratic Programming (SLQP) method for optimization \cite{leyffer2010nonlinear}, with which we found the set $\{h_i^{opt}\}$ that maximizes magnetization for a given total field H. Here we choose to work with a Barabasi-Albert random graph, where the degree (the number of neighbors each spin has) is distributed as a power-law \cite{barabasi2014network}, to decrease the probability for loops. The specific graphs we chose (see example in figure \ref{fig:BAopt}) do not contain any loops, so the solution provided by the recursive method is the exact solution.
In general, one may still use this method to approximate non-tree graphs. In such cases, when the algorithm encounters a node that closes a loop, it considers it as connected separately to the first neighbor and then separately to the second one. The second-order connection between the neighbors are ignored, which provide a small correction that can be negligible in the case of very few loops.
Earlier work \cite{brede2019transmission,lynn2016maximizing,lynn2017statistical,lynn2018maximizing,moreno2019shielding,romero2020continuous} has shown that the optimal field should be stronger for the high-connectivity nodes where the total field H is small and stronger on the lower-degree nodes where H is large. In figure \ref{fig:BAopt} we plot the normalized optimal field for each node vs. the node's degree for three different values of the total field H. The presented results depict averages over $R=12$ realizations of Barabasi-Albert graphs with $N=100$ spins and overall nodes with similar degrees (error bars represent the standard error of the mean). As expected, when the total field is weak (H=1) the optimal field is concentrated mostly on the hubs, and when the total field is stronger (H=30), it is concentrated mostly on the leaves. For an intermediate fields strength (H=3), we find that the optimal influence is obtained by concentrating the external field on nodes of intermediate degree (rather than dividing it it between hubs and leaves). Note that these results are general, and are not limited to the BA network \cite{brede2019transmission,lynn2016maximizing,lynn2017statistical,lynn2018maximizing,moreno2019shielding,romero2020continuous}. The assumption in previous work was that the qualitative behavior of the optimal field depends mostly on a node's degree and less so on the structure of the network. Our results show that, even though the average behavior matches with the above assumption, there is significant variation between the optimized local fields on different nodes with the same degree. Our method does not require symmetry assumption and allows for more accurate influence maximization schemes rather than general behaviors.
We note in passing that the dual problem, namely influence minimization, has a somewhat simpler solution: the convexity of the mean magnetization of a spin as a function of the field on it implies that focusing all the field on the spin that has the least effect on the network minimizes the influence of the field on the network.
\begin{figure}[h]
\centering
\begin{minipage}[b]{0.45\textwidth}
\includegraphics[width=\textwidth]{Figures/social_graph.png}
\end{minipage}
\hfill
\begin{minipage}[b]{0.5\textwidth}
\includegraphics[width=\textwidth]{Figures/optimal_local_fields.png}
\end{minipage}
\caption{ Influence maximization on a social network. Left panel: A sample of a scale-free network with $N=100$ nodes. The graph was generated using the Barabashi-Albert model. Right panel: Optimal local field for each node in the network, averaged over 12 different graphs (with $N =100$ nodes each, altogether 1200 nodes). The different colors stand for different value of the total field H (see legend). The results are binned by node degree (the x-axis), allowing us to compare data from networks with different degree distributions. The horizontal error bars are the standard deviation of the degrees of the nodes around each specific bin. We find that the optimal field shift from focusing on the hubs at the weak total field to the leaves at the strong total field. The vertical error bars represent the standard error of the mean across all nodes in a bin and show a significant deviation in the local field between nodes with similar (as well as equal) degrees. Since we consider a power-law graph, the number of nodes with a high degree is much smaller than the number of nodes with a low degree, which means that for H=1 (magenta) the field on the hubs is macroscopic, while for H=30 (black) where the field focus on the leaves, it is divided between many nodes, thus for each leaf, it is quite small.}\label{fig:BAopt}
\end{figure}
\section{Conclusions}
In this manuscript, we have shown that there is no echo-chamber effect in the Ising model. For other spin models, we identified symmetry that forbids the existence of echo-chambers. This symmetry can be strong -- as in the Ising model, and then it prevents any echo-chambers, or it can be weak -- in this case echo-chambers may exist, but only when there are additional fields in the system. A consequence of the lack of echo-chambers in the Ising model is that the mean magnetization of such networks can be efficiently solved in tree graphs, based on effective field calculations. We used this technique to construct an algorithm for finding the mean magnetization in tree graphs. We demonstrated it in two applications: the RFIM on the Bethe lattice and influence maximization.
When an external field is applied on a spin, it biases the spin itself and all the spins connected to it towards the states that minimize the energy at this field. Nevertheless, this bias does not generate echo-chambers in the Ising model. The lack of echo-chamber effect and the existence of an effective field, in this case, are a consequence of the exact cancellation of two different effects: (i) Even in the presence of the external bias, the states of neighboring spins fluctuate, such that they spend more time in the low energy state; (ii) The low energy states of the neighboring spins generate a smaller bias on the spin, in comparison to the high energy states. The fact that these two factors exactly cancel each other is not guaranteed in all models. In fact, the Ising model is a unique case, such that this cancellation occurs even in the presence of additional fields. Other models, such as the XY, Heisenberg, and the vector Potts models, display a weak echo-chamber symmetry, where such cancellations occur only in the absence of external fields in the network.
The existence of an effective field in the Ising model can be interpreted as a stronger version of a ``no echo-chambers'' result, since it implies that an effective field can describe the impact of the network on the spin, $h^{eff}_1$, which is independent of the field on the specific spin, $h_1$. This is true even if the network is not $\sigma_1$-neutral, and therefore can be viewed as a generalization of the no echo-chambers result: the mean magnetization of the spin does not feedback through the network to change its magnetization, even if the network is not neutral for that spin.
The expression for the effective field turned out to have a simple recursion structure in tree networks. Although we have shown that the effective field exists even in non-tree graphs (namely graphs that have loops), the general expression of the effective field for such graphs is not yet known. Extending our result to general graphs is expected to be quite difficult, as the problem of finding the mean magnetization of every spin in a general network is equivalent, in the low-temperature limit, to finding the ground state of the network -- a problem which is known to be NP-complete \cite{barahona1982computational}. Similarly, the separability of the partition function in Eq.(\ref{Eq:Z_factorization}) only holds for $\sigma_1$-neutral networks; therefore, generally, it cannot be applied iteratively since $Z^{eff}_{N-1}$ does not correspond to a neutral network.
Applications of our results for physical systems, especially magnets, are of interest: do physical magnets display an echo-chamber effect? This question is interesting in both macroscopic systems, where ergodicity breaking implies that our results do not hold, as well as in microscopic systems (e.g., trapped ions \cite{kotler2014measurement}) where applying a magnetic field on each spin separately is often used, and the existence or non-existence of echo-chamber effect is therefore of interest.
A natural question that we did not address concerns the cases where a spin echo-chamber effect exists, as in the spin-1 Blum-Capel model: does the existence of the effect imply that the mean magnetization of a spin coupled to a $\sigma_k$-natural network is always larger than the mean magnetization of a single spin (as in the example in section \ref{Sec:BlumeCapel}), or is it possible that coupling with a $\sigma_k$-natural network reduces the mean magnetization of $\sigma_k$? Additional questions of similar interest are the existence of the effect in non-equilibrium systems (e.g., a network with different temperatures for different spins) which is natural for influence maximization problem, or in the thermodynamic limit where phase transitions and the corresponding ergodicity breaking might change our results even in models that do have the echo-chamber symmetry defined above. It would also be of interest to understand the role of echo-chamber effect on opinion dynamic models, for example, by comparing models with and without the echo-chamber symmetry.
We note that the algorithm we constructed is not optimal in terms of run-time, memory allocation, or any other standard performance measure. For example, it might be improved by optimizing its traverse over the tree when calculating the effective field.
Lastly, we note that the Ising model is quite special in that it lacks echo-chambers regardless of the network: most other models do contain echo-chambers, even in neutral networks. This special feature must be considered when using Ising spins in modeling opinion dynamics, especially when echo-chamber effects can play an essential role in the results.
\section*{Acknowledgements}
We would like to thank David Mukamel for useful discussions. We thank Anton Charkin-Gorbulin for help with the BFS algorithm. O.R. is the incumbent of the Shlomo and Michla Tomarin career development chair, and is supported by the Abramson Family Center for Young Scientists, the Minerva and by the Israel Science Foundation, Grant No. 950/19. O.F. is the incumbent of the of the Henry J
Leir Professorial chair and is supported by the Israel Science Foundation, Grant No. 1727/20, the Minerva Foundation, and the European Research Council (ERC) under the European Unions Horizon 2020 research and innovation program (Grant agreement No. 770964).
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 1,339 |
\section{Introduction}
The class of Church-Rosser congruential languages has been introduced by Narendran, McNaughton and Otto in 1988, see \cite{Narendran84phd,McNaughtonNO88}. A language is Church-Rosser congruential if it is a finite union of equivalence classes of a finite length-reducing Church-Rosser rewriting system.
It is natural to ask whether every regular language is Church-Rosser congruential. After some initial progress \cite{Niemann00CRCL, NiemannW02, reinhardtT03, DiekertKW12tcs}, this question has been solved affirmatively, see \cite{DiekertKRW15jacm}.
The main idea of the solution in \cite{DiekertKRW15jacm} is to prove a stronger statement. Instead of proving that for every regular language there exists a length-reducing Church-Rosser system which saturates the language it is proved that for every regular language and every weight function there exists such a weight-reducing Church-Rosser system. In particular, the initial problem is included by choosing length as the weight function.
This result on regular languages became possible by utilizing the concept of local divisors. In this paper we use the same technique of local divisors to study a stronger property. Instead of requiring weight-reducing systems for a given weight we ask the question whether for every regular language there exists a Church-Rosser system which saturates the language and is weight-reducing for every weight function. We call such a rewriting system a Parikh-reducing Church-Rosser system.
Some of the initial progress already satisfied the Parikh-reducing condition, namely the construction for aperiodic languages \cite{DiekertKW12tcs}, for languages of polynomial density \cite{Niemann00CRCL} and for cyclic groups of order two \cite{NiemannW02}. Our result comprises these results. Namely, the following is the main result:
for every language such that its syntactic monoid contains only abelian groups there exists a Parikh-reducing Church-Rosser system which saturates the language.
Moreover, all groups appearing in the corresponding Church-Rosser representation are abelian.
Furthermore, we show the existence of such Parikh-reducing systems for all group languages over a two-letter alphabet.
Having established the existence of Parikh-reducing systems we study the size of the resulting Church-Rosser representations. Naively, analyzing the construction yields a non-primitive function for this size.
We introduce an alphabet reduction technique which reduce the size of the resulting Church-Rosser representations to a quadruple exponential function. On the other side of the spectrum we prove an exponential lower bound for cyclic groups.
\section{Preliminaries}
\paragraph*{Words and Languages
An \kursivdef{alphabet}{alphabet} is a non-empty finite set $A$.
An element of $a\in A$ is called a \kursivdef{letter}{letter}.
A (finite) \kursivdef{word}{word} $w = a_1\cdots a_n$ is a finite concatenation of letters $a_1,\ldots, a_n \in A$.
The set of finite words with letters in $A$ is denoted by $A^*$. The \kursivdef{empty word}{word!empty} is denoted by $1$.
The set of finite words $A^*$ forms a monoid with the concatenation operation, the \kursivdef{free monoid}{free monoid}.
Let $\Abs{\cdot} : A \to \mathbb N$ be a function with $\Abs{a} > 0$ for all $a\in A$. The unique homomorphism, which extends $\Abs{\cdot}$, is also denoted by $\Abs{\cdot}$ and called a \kursivdef{weight}{weight}.
A special weight is \kursivdef{length}{length} $\abs{\cdot} : A^* \to \mathbb N$ which is induced by $\abs{a} = 1$ for all $a\in A$.
For a letter $c\in A$ we also define $\abs{\cdot}_c : A^* \to \mathbb N$ to be the homomorphism which is induced by \[
\abs{a}_c = \begin{cases}
1 & \text{ if } a=c\\ 0 & \text{ else.}
\end{cases}
\]
We set $A^{\leq n} = \set{w\in A^*}{\abs{w} \leq n}$ to be the set of words of length at most~$n$.
A \kursivdef{language}{language} $L$ is a subset of $A^*$.
Let $\varphi : A^* \to M$ be a homomorphism in a finite monoid $M$.
A language $L \subseteq A^*$ is \emph{recognized by $\varphi$} if $L = \varphi^{-1}(\varphi(L))$.
A language $L$ is regular if it can be recognized by some homomorphism in a finite monoid.
\paragraph*{Algebra}
We want to study subclasses of regular languages which are characterized by special classes of monoids.
A \kursivdef{variety}{variety} $\varietyfont{V}$ is a class of finite monoids which is closed under taking submonoids, homomorphic images and finite direct products.
In particular, taking the empty direct product, every variety contains the trivial monoid.
A variety which contains only groups is called a \kursivdef{variety of groups}{variety!groups}.
We assign every variety $\varietyfont{V}$ a corresponding language class $\svarietyfont{V}(A^*)$ such that $L \in \svarietyfont{V}(A^*)$ if and only if there exists a monoid $M \in \varietyfont{V}$ and a homomorphism $\varphi : A^* \to M$ that recognizes $L$.
Examples of such varieties include
the variety $\varietyfont{G}$ of all groups and the variety $\ensuremath{\varietyfont{Ab}}$ of all abelian groups.
Let $\varietyfont{H}$ be a variety of finite groups. We define \[
\overline{\varietyfont{H}} = \set{M}{\text{every group in } M \text{ is in } \varietyfont{H}}
\]
to be the maximal class of monoids whose subsemigroups, which are groups, are in $\varietyfont{H}$. It turns out that $\overline{\varietyfont{H}}$ is the maximal variety such that $\overline{\varietyfont{H}} \cap \varietyfont{G} =
\varietyfont{H}$, see \cite[Proposition V.10.4]{eil76}. Our main result is concerned with the language class $\overline \ensuremath{\varietyfont{Ab}} (A^*)$.
An important concept used in this paper are local divisors.
Let $M$ be a monoid and $c\in M$. We set $M_c = cM \cap Mc$ and introduce a multiplication $\circ$ on $M_c$ given by
$uc \circ cv = ucv$.
Since $uc \in cM$ and $cv \in Mc$, the result of $uc\circ cv$ is in $M_c$. The structure $(M_c,\circ,c)$ forms a monoid, the \kursivdef{local divisor}{local divisor} of $M$ at $c$.
Indeed, $M_c$ is a divisor of $M$, that is, a homomorphic image of a submonoid of $M$, see \cite{DiekertK2015tcs}.
If $c \in M$ is not a unit, then $\abs{M_c} < \abs{M}$ since $1 \not\in cM \cap Mc$.
\paragraph*{Combinatorics on Words}
Let $x = uvw \in A^*$ be a word.
Then we call $u$ a \kursivdef{prefix}{prefix}, $v$ a \kursivdef{factor}{factor} and $w$ a \kursivdef{suffix}{suffix} of $x$.
The factor $v$ is \kursivdef{proper}{factor!proper} if $u$ and $w$ are not empty.
The set of factors is given by $\mathrm{Factors}(w) = \set{u}{u \text{ is a factor of } w}$.
The word $a_1\cdots a_n$, with $a_i \in A$, is a \kursivdef{subword}{subword} of a word~$u$ if $u \in A^* a_1 A^* \cdots A^* a_n A^*$.
The word $u$ is a power of the word $v$ if $u=v^i$ for some $i\in \mathbb N$.
Let $w = a_1\cdots a_n \in A^*$ be a word with $a_i\in A$ letters. We say that $p\in \mathbb N$ is a \kursivdef{period}{period} of $w$ if $a_i = a_{i+p}$ for all $1\leq i \leq n-p$.
The theorem of Fine and Wilf\blinddef{theorem!Fine and Wilf} describes an important property of periods.
\begin{theorem}[Fine and Wilf, \cite{FineWilf65}]\label{thm:finewilf}
Let $p,q$ be periods of some word $w$. If $\abs{w} \geq p+q-\gcd(p,q)$, then $\gcd(p,q)$ is a period of $w$.
\end{theorem}
A word $u$ is called \kursivdef{primitive}{primitive}\blinddef{word!primitive} if it is only a power of itself, that is, if $u=v^i$ with $i\geq 1$ implies $i=1$. The following well-known characterization of primitive words will be useful.
\begin{lemma}\label{lem:charprimitive}
A word $u\in A^*$ is primitive if and only if $u$ is not a proper factor of $u^2$.
\end{lemma}
\paragraph*{Rewriting systems}
A \kursivdef{semi-Thue system}{semi-Thue system} $S$ over the alphabet $A$ is a finite subset of $A^*\times A^*$.
An element $(\ell,r) \in S$ is called a \kursivdef{rule}{rule}, where $\ell$ is the left side and $r$ is the right side of the rule.
The idea of a semi-Thue system is, that left sides of rules can be replaced by right sides of the rule.
Thus, one often also calls a semi-Thue system a \kursivdef{rewriting system}{rewriting system}.
For a semi-Thue system $S$ we define the rewriting relation $\RA{S}$ given by
$u_1\ell u_2 \RA{S} u_1ru_2 \text{ for } u_1,u_2\in A^* \text{ and } (\ell,r)\in S$,
that is, $u \RA{S} v$ if $v$ results from $u$ by replacing the left side of a rule with the right side.
The reflexive transitive closure of $\RA{S}$ is denoted by $\RAS{*}{S}$ and the symmetric closure of $\RAS{*}{S}$ is denoted by $\DAS{*}{S}$.
We write $v\LA{S} u$ for $u\RA{S} v$.
A semi-Thue system $S$ is
\kursivdef{confluent}{semi-Thue system!confluent} or \emph{Church-Rosser}, if $u \RAS{*}{S} v_1$ and $u \RAS{*}{S} v_2$ imply that there exists a word $w\in A^*$ such that $v_1 \RAS{*}{S} w$ and $v_2 \RAS{*}{S} w$.
It is \kursivdef{locally confluent}{semi-Thue system!locally confluent}, if $u \RA{S} v_1$ and $u \RA{S} v_2$ imply that there exists a word $w\in A^*$ such that $v_1 \RAS{*}{S} w$ and $v_2 \RAS{*}{S} w$.
It is \kursivdef{weight-reducing}{semi-Thue system!weight-reducing} for a weighted alphabet $(A,\Abs{\cdot})$, if $\Abs{\ell} > \Abs{r}$ for all rules $(\ell, r) \in S$ and it is
\kursivdef{Parikh-reducing}{semi-Thue system!Parikh-reducing}, if for all $a\in A$ and all rules $(\ell, r) \in S$ it holds $\abs{\ell}_a \geq \abs{r}_a$ and for all rules $(\ell, r) \in S$ there exists a letter $a\in A$ such that $\abs{\ell}_a > \abs{r}_a$.
Furthermore, $S$ is \kursivdef{subword-reducing}{semi-Thue system!subword-reducing}, if $r \neq \ell$ and $r$ is a subword of $\ell$ for each rule $(\ell,r)\in S$.
The notion Parikh-reducing comes from the connection to \kursivdef{Parikh images}{Parikh image}.
A Parikh image of a word $w\in A^*$ is the vector $(\abs{w}_a)_{a\in A}$.
A semi-Thue system $S$ is Parikh-reducing if and only if
the Parikh image $(\abs{r}_a)_{a\in A}$ is smaller than $(\abs{\ell}_{a})_{a\in A}$ for every rule $(\ell,r)\in S$.
By definition every subword-reducing system is Parikh-reducing.
Further, it is rather easy to see that a semi-Thue system $S\subseteq A^*\times A^*$ is Parikh-reducing if and only if it is weight-reducing for every weight $\Abs{\cdot} : A^* \to \mathbb N$.
A classical lemma states that $S$ is confluent if it is Parikh-reducing and locally confluent, see \cite{bo93springer}.
In the following we study different cases which may occur when checking for local confluence.
Let $(\ell,r), (\ell',r') \in S$ be two rules and consider the word $u \ell v \ell' w$. Then
\begin{center}
\begin{tikzpicture}[implies/.style={double,double equal sign distance,-implies}]
\draw (-2.5,0) node (A) {$u \ell v \ell' w$};
\draw (-2.5,-1.5) node (B) {$u r v \ell' w$};
\draw (0,0) node (C) {$u \ell v r' w$};
\draw (0,-1.5) node (D) {$u r v r' w$};
\draw (A) edge[implies] node[right] {$S$} (B);
\draw (A) edge[implies] node[below] {$S$} (C);
\draw (C) edge[implies] node[right] {$S$} (D);
\draw (B) edge[implies] node[below] {$S$} (D);
\end{tikzpicture}
\end{center}
Thus, checking for local confluence in this case is trivial. The only non-trivial cases appear when two rules overlap. There are two different kinds of overlaps:
\begin{enumerate}
\item $w = x\ell = \ell'y$,
\item $w = \ell = x\ell'y$
\end{enumerate}
for rules $(\ell,r),(\ell',r')\in S$.
The resulting pairs $(xr,r'y)$ and $(r,xr'y)$ are called \kursivdef{critical pairs}{critical pair}.
The first kind is called \kursivdef{overlap critical}{critical pair!overlap critical} and the second kind is called \kursivdef{factor critical}{critical pair!factor critical}, see also \prref{fig:cp}.
\begin{figure}
\begin{minipage}[h!]{6.5cm}
\centering
\begin{tikzpicture}[implies/.style={double,double equal sign distance,-implies}]
\def3.5{3.5}
\node [rectangle, thin, draw=black, inner sep = 0pt,minimum height=0.42cm,minimum width = 1.5cm] at (3.5-0.25,1.42) {$x\vphantom{\delta^t}$};
\node [rectangle, thin, draw=black, inner sep = 0pt,minimum height=0.42cm,minimum width = 2cm] at (3.5+1.5,1.42) {$\ell\vphantom{\delta^t}$};
\node [rectangle, thin, draw=black, minimum width = 2cm, inner sep = 0pt,minimum height=0.42cm] at (3.5,1)
{$\ell'\vphantom{\delta^t}$};
\node [rectangle, thin, draw=black, minimum width = 1.5cm, inner sep = 0pt,minimum height=0.42cm] at (3.5+1.75,1)
{$y \vphantom{\delta^t}$};
\end{tikzpicture}
\caption*{overlap critically}
\end{minipage}
\quad\quad
\begin{minipage}[h!]{5cm}
\centering
\begin{tikzpicture}[implies/.style={double,double equal sign distance,-implies}]
\def3.5{3.5}
\def9{9}
\node [rectangle, thin, draw=black, inner sep = 0pt,minimum height=0.42cm,minimum width = 1.5cm] at (3.5-0.25,1) {$x\vphantom{\delta^t}$};
\node [rectangle, thin, draw=black, inner sep = 0pt,minimum height=0.42cm,minimum width = 1.5cm] at (3.5+1.25,1) {$\ell'\vphantom{\delta^t}$};
\node [rectangle, thin, draw=black, inner sep = 0pt,minimum height=0.42cm,minimum width = 1.5cm] at (3.5+2.75,1) {$y\vphantom{\delta^t}$};
\node [rectangle, thin, draw=black, minimum width = 4.5cm,inner sep = 0pt,minimum height=0.42cm] at (3.5+1.25,1.42)
{$\ell\vphantom{\delta^t}$};
\end{tikzpicture}
\caption*{factor critically}
\end{minipage}
\caption{Sources of critical pairs \cite{DiekertKRW15jacm}}\label{fig:cp}
\end{figure}
We say that a critical pair $(u,v)$ resolves if there exists a word $w\in A^*$ such that $u \RAS{*}{S} w \LAS{*}{S} v$ holds.
Summarized, we obtain the following:
\begin{lemma}[\cite{KnuthBendix70}]\label{lem:knuthbendix}
A semi-Thue system is locally confluent if and only if all its critical pairs resolve.
\end{lemma}
\prref{lem:knuthbendix} will be used without explicitly referring to it.
A word $w$ is \kursivdef{irreducible}{irreducible} in $S$ if no left-side of a rule in $S$ appears in $w$.
We denote the set of irreducible elements of $S$ by $\mathrm{IRR}_S(A^*)$.
The relation $\DAS{*}{S}$ is a congruence on~$A^*$. Thus, one can consider the monoid $A^*\! /S = A^*\! /\!\!\DAS{*}{S}$.
The elements of $A^*\! /S$ are equivalence classes $[u]_S = \set{v\in A^*}{u \DAS{*}{S}v}$ of the congruence $\DAS{*}{S}$.
The number of elements in $A^*\! /S$ is called \emph{index} of $S$.
If $S$ is Parikh-reducing and (locally) confluent, then
there is a bijection between $A^*\! /S$ and $\mathrm{IRR}_S(A^*)$.
In this case, we denote elements of the monoid $A^*\! /S$ with the corresponding irreducible words.
In fact, we call a locally confluent Parikh-reducing system a \emph{Parikh-reducing Church-Rosser system}.
Let $\varphi : A^* \to M$ be a homomorphism and $S\subseteq A^*\times A^*$ be a semi-Thue system.
We say that $\varphi$ \kursivdef{factorizes through}{factorize through} $S$ if for all $u\RA{S} v$ it holds $\varphi(u) = \varphi(v)$, that is,
equivalence classes of $S$ map to the same element in $M$.
We also say that $S$ is \emph{$\varphi$-invariant} if $\varphi$ factorizes through $S$.
This notion is algebraically motivated.
Let $S$ be a semi-Thue system such that $\varphi$ factorizes through $S$,
then $\psi : A^*\! /S \to \varphi(A^*)$ given by $\psi([u]_S) = \varphi(u)$ is a well-defined homomorphism.
Let $\pi_S : A^* \to A^*\! /S$ be the natural projection and $L$ be some language which is recognized by $\varphi$ and $\pi_L$ be the syntactic homomorphism of $L$.
Then we obtain the situation in \prref{fig:facthr}. In particular, $\pi_S$ recognizes $L$.
\begin{figure}
\begin{center}
\begin{tikzpicture}[scale=0.7]
\draw (0,0) node (A) {$A^*$};
\draw (3,0) node (M) {$\varphi(A^*)$};
\draw (6,0) node (MM) {$M$};
\draw (3,2) node (S) {$A^* / S$};
\draw (3,-2) node (L) {$\text{Synt}(L)$};
\draw[->] (A) -- node[pos=0.65,above] {$\varphi$} (M);
\draw[->] (A) -- node[above left,outer sep=-2pt] {$\pi_S$} (S);
\draw[->] (S) -- node[right] {$\psi$} (M);
\draw[right hook->] (M) -- node[left] {} (MM);
\draw[->] (A) -- node[pos=0.65,above] {$\pi_L$} (L);
\draw[->] (M) -- (L);
\end{tikzpicture}
\end{center}
\caption{Algebraic situation of $\varphi$ factorizes through $S$ \cite{DiekertKRW15jacm}}\label{fig:facthr}
\end{figure}
Since $\varphi$ factorizes through $S$ if and only if $\varphi : A^* \to \varphi(A^*)$ factorizes through $S$, we may assume that $\varphi$ is surjective.
If further $S$ is a Church-Rosser system, we call $A^*\! /S$ a \kursivdef{Church-Rosser representation}{Church-Rosser!representation} of $\varphi$ (or $M$).
\section{Parikh-reducing Church-Rosser systems}
\subsection{Outline}
In this subsection we give an outline on the proof strategy which will be used in \prref{thm:parikhcomgroup}.
The macro structure of the proof is as follows: Given a homomorphism $\varphi : A^* \to G$, we construct a system $S$ which is $\varphi$-invariant by induction on $A$.
The construction is based on the following lemma:
\begin{lemma}[\cite{DiekertKW12tcs,DiekertKRW15jacm}]\label{lem:bastel}
Let $A$ be an alphabet of size at least two, $\varphi : A^* \to M$ be a homomorphism and
$B = A\setminus\oneset{c}$ for some $c\in A$.
Assume that $R\subseteq B^*\times B^*$ is a Parikh-reducing Church-Rosser system of
finite index which is $\varphi$-invariant. Let $K = \mathrm{IRR}_R(B^*)c$ be a new alphabet and
$T \subseteq K^*\times K^*$ be a Parikh-reducing Church-Rosser system of finite index such that
\[T' := \set{c\ell \to cr}{\ell\to r \in T}\subseteq A^*\times A^*\]
is $\varphi$-invariant.
Then
\begin{enumerate}[a)]
\item\label{enum:bastel:a} $S = R\cup T'\subseteq A^*\times A^*$ is a $\varphi$-invariant
Parikh-reducing Church-Rosser system of finite index.
\item\label{enum:bastel:b} All groups in $A^*\! /S$ are contained in $B^*\! /R$ or in $K^*\! /T$.
\item\label{enum:bastel:c} The index of $A^*/S$ is $\abs{B^*\! /R}+\abs{B^*\! /R}^2\abs{K^*\! /T}$.
\end{enumerate}
\end{lemma}
\begin{proof}
\ref{enum:bastel:a}) is proved in \cite{DiekertKRW15jacm}. By \cite{DiekertKW12tcs}, $A^*\! /S$ is a so-called Rees extension monoid and the statement of \ref{enum:bastel:b}) follows from general properties of Rees extension monoids, see \cite{AlmeidaK16}.
It remains to calculate the size of the index of $S$. Every irreducible word in $S$ which contains no $c$ is contained in $B^*\! /R$. Conversely, every element of $B^*\! /R$ is irreducible in the rewriting system given by $S$. Every irreducible word in $S$ which contains at least one $c$ is of the form $ucvw$ for $u,w\in B^*\! /R$ and $v \in K^*\! /T$. By the definition of the rule set $S$ every such word $ucvw$ is also irreducible. This shows that there are exactly $\abs{B^*\! /R}^2\abs{K^*\! /T}$ irreducible words in $S$ which contains at least one $c$.
\end{proof}
For a fixed letter $c\in A$ we remove $c$ and obtain the alphabet $B = A \setminus \oneset{c}$.
Inductively, one obtains a system $R \subseteq B^*\times B^*$ which factorizes through $\varphi$. Now, consider a new alphabet $K = \mathrm{IRR}_R(B^*)c$. By \prref{lem:bastel}, it remains to construct a system $T \subseteq K^* \times K^*$. The system $T$ contains two kinds of rules: $\Delta$-rules and $\Omega$-rules. The idea of these rules is to deal with different kind of words. The set $T_\Delta$ of $\Delta$-rules deals with long repetitions of short words. Whenever there is no long repetition of short words, this is witnessed by a marker word $\omega$. The set $T_\Omega$ of $\Omega$-rules contains rules of the form $\omega u \omega \to \omega \gamma(u) \omega$ for some normal forms $\gamma(u)$. \prref{lem:tOmegaexist} shows that such rules appear for sufficiently large words and \prref{lem:parikhisconfl} shows the confluence of the constructed system.
\subsection{Commutative Groups}\label{subsec:commgrpcr}
In this section we study Parikh-reducing Church-Rosser systems for abelian groups. Let $\varphi : A^* \to G$ be a homomorphism in an abelian group $G$.
We construct a system for $G$ by sorting the letters $a$ and then reducing them modulo their order.
Thus, we actually construct a Church-Rosser representation for the group $\prod_{a\in A} \mathbb Z/\mathop{\mathrm{ord}}(\varphi(a))\mathbb Z$.
The situation obtained in \prref{thm:parikhcomgroup} is shown in the commutative diagram \prref{fig:parikhcomgroup}.
\begin{figure}
\begin{center}
\begin{tikzpicture}[scale=0.65]
\draw (-3,2) node (A) {$A^*$};
\draw (3,0) node (M) {$\varphi(A^*)$};
\draw (6,0) node (MM) {$G$};
\draw (3,2) node (S) {$\prod_{a\in A} \mathbb Z/\mathop{\mathrm{ord}}(\varphi(a))\mathbb Z$};
\draw (3,4) node (SS) {$A^*\! / S$};
\draw[->] (A) -- node[pos=0.65,below] {$\varphi$} (M);
\draw[->] (A) -- node[above left,outer sep=-2pt] {$\pi_S$} (SS);
\draw[->] (A) -- (S);
\draw[->] (S) -- (M);
\draw[->] (SS) -- (S);
\draw[right hook->] (M) -- node[left] {} (MM);
\end{tikzpicture}
\end{center}
\caption{Commutative diagram in the situation of \prref{thm:parikhcomgroup}.}\label{fig:parikhcomgroup}
\end{figure}
\begin{theorem}\label{thm:parikhcomgroup}
Let $\varphi : A^* \to G$ be a homomorphism to a finite commutative group $G$. Then there exists a Parikh-reducing Church-Rosser system $S$ of finite index which factorizes through $\varphi$. Further, all groups contained in $A^*\! /S$ are isomorphic to some subgroup of $\prod_{a\in A} \mathbb Z/\mathop{\mathrm{ord}}(\varphi(a))\mathbb Z$.
\end{theorem}
\begin{proof}
Let $n$ be the least common multiple of $\mathop{\mathrm{ord}}(\varphi(a))$ for $a\in A$.
We do an inductive proof on the number of letters $\abs A$. If $A = \os{c}$, then we may set $S = \os{c^n \to 1}$.
This system is Parikh-reducing, locally confluent and it holds $A^*\! /S \simeq \mathbb Z/n\mathbb Z$. Thus, we may assume that $\abs A > 1$. Let $A = \os{a_1, \ldots, a_s, c}$ be the alphabet and $c \in A$ be an arbitrary letter of $A$. We consider the alphabet $B = A \setminus \os{c}$. Inductively, $B$ is smaller than $A$, we get a Parikh-reducing Church-Rosser system $R \subseteq B^* \times B^*$ of finite index which factorizes through $\varphi_{|B^*} : B^* \to G$.
The idea is to first reduce the words over~$B^*$ and then work over a new alphabet $K$. Let $K = \mathrm{IRR}_R(B^*)c$ be the new alphabet of irreducible words over $B^*$ appended by the letter $c$ which poses as a separator.
We will first construct a Parikh-reducing (over $A^*$) Church-Rosser system $T \subseteq K^* \times K^*$ of finite index. Note that this system $T$ is not Parikh-reducing over $K^*$.
We will use two different sets of rules. One for long repetitions of short words and one for longer words which are not repetitions of such short words.
%
Let us first define the set of short words as $\Delta = K^{\leq n}\setminus\os{1}$, that is, as the set of nonempty words of length at most $n$.
Let further be $$T_\Delta = \set{\delta^{t+n} \to \delta^t}{\delta \in \Delta}$$ the system of $\Delta$-rules whereas $t = 3n(s+4)+n$.
The choice of the parameter $t$ will be explained later.
For now, the fact that $t > 2n$ is sufficient to obtain that
$T_\Delta$ is a Parikh-reducing (over $K^*$, and thus also over $A^*$) Church-Rosser system by \prref{lem:deltacrsystem}.
\begin{lemma}[\cite{DiekertKRW15jacm}]\label{lem:deltacrsystem}
Let $\Delta \subseteq K^{\leq n}$ be a set of nonempty words of length at most $n$ which is closed under nontrivial factors, $t > 2n$ and $n\geq 1$.
Then \[
T_\Delta = \set{\delta^{t+n} \to \delta^t}{\delta\in \Delta}
\] is a subword-reducing Church-Rosser system. In particular, $T_\Delta$ is Parikh-reducing and weight-reducing for every weight.
\end{lemma}
%
Next, we will introduce marker words. They basically mark the absence of a long repetition of words in $\Delta$, i.e., a long enough word in $K^*$ will either contain a marker word or a rule in $T_\Delta$. The next lemma shows that the length of such markers can be bounded by $2n$.
\begin{lemma}[\cite{DiekertKRW15jacm}]\label{lem:minimalefactorgegenbsp}
Let $\Delta \subseteq K^{\leq n}$ be a set and let $F = \bigcup_{\delta \in \Delta, i \in \mathbb N} \mathrm{Factors}(\delta^i)$.
Then $K^* \setminus F$ is an ideal which is generated by a set $J \subseteq K^{\leq 2n}$ of words of length at most $2n$, that is, $K^* \setminus F = K^* J K^*$.
\end{lemma}
Thus, letting $F = \bigcup_{\delta \in \Delta, i \in \mathbb N} \mathrm{Factors}(\delta^i)$, we obtain $K^* \setminus F = K^* J K^*$ for some $J \subseteq K^{\leq 2n}$.
In order to ensure that we find such a marker which does not start with a $c \in K$, we increase the length of a marker to $3n$. Formally, let $\Omega = K^{3n} \setminus (cK^* \cup F)$ be the set of markers.
%
Let $\preceq$ be a total preorder on $\Omega$ with the following properties:
\begin{itemize}
\item $\omega, \eta \in\Omega$ with
$\omega \in K^*(K\setminus\os{c}) c^i, \eta \in K^*(K\setminus\os{c}) c^j$ and $i>j$
implies $\omega \preceq \eta$.
\item $\preceq$ is a total order on $\Omega \setminus Kc^{3n-1}$.
\item $\omega, \eta \in \Omega\cap Kc^{3n-1}$ implies $\omega \preceq \eta$.
\end{itemize}
Thus, the larger the block of $c$'s at the suffix of an $\omega$, the smaller it is with respect to~$\preceq$.
Additionally, all elements in $\Omega$ with a maximal block of $c$'s at the suffix are equivalent with respect to $\preceq$.
In particular, $\omega \preceq \eta$ and $\eta \preceq \omega$ implies either $\eta = \omega$ or there exists $b_1,b_2 \in K$ with $\omega = b_1 c^{3n-1}$ and $\eta = b_2c^{3n-1}$.
Let $u \in K^* \omega K^*$ for some $\omega \in \Omega$.
We say that $\omega$ is a \kursivdef{maximal $\Omega$-factor}{maximal!$\Omega$-factor} of $u$,
if $u \in K^* \eta K^*$ with $\eta \in \Omega$ implies $\eta \preceq \omega$.
We want to show that every long word contains sufficiently large factors which are surrounded by ``locally'' maximal $\Omega$-factors. The first step is to show the existence of $\Omega$-factors.
\begin{lemma}\label{lem:t0parikhexist}
There exists a number $t_0$ such that for every word $v \in K^*$ with length at least
$t_0$ has a factor $\delta^{t+n}$ for some $\delta \in \Delta$ or a factor $\omega \in \Omega$.
\end{lemma}
\begin{proof}
Let $t_0 = (t+n+3)(n+1)$.
If $v \notin \mathrm{IRR}_{T_\Delta}(K^*)$ the statement is true. Thus, we assume that for all $\delta \in \Delta$ there is no factor $\delta^{t+n}$ of $v$.
There is a factorization $v = c^\ell v_1 v_2$ such that $v_1 \in F$ is maximal and $v_1$ has no $c$ as a prefix.
\begin{figure}
\begin{center}\begin{tikzpicture}[implies/.style={double,double equal sign distance,-implies}]
\def3.5{0}
\def9{9}
\node [rectangle, thin, draw=black, minimum width = 0.6cm, inner sep = 1pt] at (3.5+1.65,1.53) {$c^\ell\vphantom{c^\ell_1}$};
\node [rectangle, thin, draw=black, minimum width = 1.6cm, inner sep = 1pt] at (3.5+2.75,1.53)
{$v_1\vphantom{c^\ell_1}$};
\node [rectangle, thin, draw=black, minimum width = 2.5cm, inner sep = 1pt] at (3.5+4.8,1.53)
{$v_2\vphantom{c^\ell_1}$};
\node [rectangle, thin, draw=black, inner sep = 1pt,minimum width = 0.5cm] at (3.5+2.2,1) {$\delta\vphantom{c^\ell_1}$};
\node [rectangle, thin, draw=black, inner sep = 1pt,minimum width = 0.5cm] at (3.5+2.7,1) {$\delta\vphantom{c^\ell_1}$};
\node [rectangle, thin, draw=black, inner sep = 1pt,minimum width = 0.5cm] at (3.5+3.2,1) {$\delta\vphantom{c^\ell_1}$};
\node [rectangle, thin, draw=black, inner sep = 1pt,minimum width = 1cm] at (3.5+3.85,0.47) {$u\vphantom{c^\ell_1}$};
\node [rectangle, thin, draw=black, inner sep = 1pt,minimum width = 1.4cm] at (3.5+3.65,-0.05) {$u'\vphantom{c^\ell_1}$};
\node [rectangle, thin, draw=black, inner sep = 1pt,minimum width = 1.6cm] at (3.5+3.75,-0.58) {$u''\vphantom{c^\ell_1}$};
\end{tikzpicture}
\end{center}
\caption{Construction of a factor in $\Omega$ as used in \prref{lem:t0parikhexist}.}
\end{figure}
Hence we obtain $\ell < t+n$ and $\abs{v_1} < (t+n)n$ which implies $\abs{v_2} \geq 3n+3 > 3n-1$ by definition of $t_0$.
As $v_1 \in F$, there is some $\delta \in \Delta$ which does not have $c$ as prefix and $v$ is a prefix of $\delta^+$.
Consider the first factor $u$ of length $2n$ of $v_1v_2$ which is not in $F$.
Since $v_1$ is a prefix of $\delta^+$, one must take at most $n-1$ additional letters left from $u$ in order to obtain a factor $u'$ of $v_1v_2$ which is not in $F$, has length at most $3n$ and does not start with a $c$.
Filling up $u'$ with letters from the right, we obtain a factor $u''$ of $v_1v_2$ which is not in $F$, has length $3n$ and does not start with a $c$, that is, $u'' \in \Omega$.
\end{proof}
\begin{lemma}\label{lem:tOmegaexist}
There exists a number $t_\Omega$ such that every word $v\in K^*$ of length at least $t_\Omega$ contains
either
\begin{itemize}
\item a factor $\delta^{t+n}$ for $\delta\in \Delta$ or
\item a factor $\omega u \omega$ with $\omega \in \Omega$, $t < \abs{\omega u \omega} \leq t_\Omega$ and for every $\eta \in \Omega$
with $\omega u \omega\in A^* \eta A^*$ we have $\eta \preceq \omega$.
\end{itemize}
\end{lemma}
\begin{proof}
Let $\Omega_v = \set{\omega \in \Omega}{v \in A^* \omega A^*}$ be the set of $\Omega$-factors of $v$ and
let $t_k$ be defined by the recursion $t_k = 2t_{k-1} + t$.
A quick calculation verifies the explicit formula $t_k = 2^k(t_0+t)-t$.
We prove the following statement by induction on $k$:
For every word $v$ of length at least $t_k$ which has at least $k$ different $\Omega$-factors, i.e., $k \geq \abs{\Omega_v}$ and which does not contain a factor $\delta^{t+n}$ for $\delta \in \Delta$, there exists a factor $\omega u \omega$ of $v$ such that
\begin{itemize}
\item $\omega \in \Omega$,
\item $t < \abs{\omega u \omega} \leq t_k$ and
\item $\omega$ is a maximal $\Omega$-factor of $\omega u \omega$.
\end{itemize}
The case $k=0$ is trivial since by hypothesis every word $v$ with length at least $t_0$ and $\abs{\Omega_v} = 0$ must contain a factor $\delta^{t+n}$ for $\delta \in \Delta$.
Consider the case $k>0$. Since we require that the length of the factor $\omega u \omega$ is smaller or equal to $t_k$,
we consider the prefix of $v$ of length $t_k$.
In particular,
we can assume that every proper factor of $v$ has length smaller than $t_k$.
Consider the factorization $v = pfq$ with $f \in (\omega A^* \cap A^* \omega)$ such that $\omega$ is a maximal $\Omega$-factor of $v$ and $f$ is maximal with regard to length.
If $\abs f \leq t$, we obtain
$$t_k = 2t_{k-1} + t \leq \abs{pfq} = \abs{pq} + \abs f \leq \abs{pq} + t$$
which implies $\abs{pq} \geq 2t_{k-1}$.
Since $p$ and $q$ contain no factor $\omega$, we can apply induction to either $p$ or $q$.
If $\abs f > t$, then $f$ has the form $f = \omega u \omega$ for a word $u$ because of $t> 2\max_{\omega \in \Omega}\abs{\omega}$ and $f \in (\omega A^* \cap A^* \omega)$. The factor $f$ has the required properties since $\abs f \leq \abs v \leq t_k$. This concludes the induction.
We infer the statement of the lemma by setting $t_\Omega = t_{\abs \Omega}$.
\end{proof}
In particular, \prref{lem:tOmegaexist} shows the existence of a number $t_\Omega$ such that every $v \in \mathrm{IRR}_{T_\Delta}(K^*)$
with $\abs v \geq t_\Omega$ contains a factor $\omega u \omega'$
with $\omega, \omega'$ being $\Omega$-maximal for this factor and $t< \abs{\omega u \omega'} \leq t_\Omega$.
The idea is to reduce $u$ to a normal form $\gamma(u)$. This is the part where commutativity of $G$ is needed.
Let $a\in A$ be a letter and $\abs{u}_a$ be the number of occurrences of $a$ in $u$.
Define $\gamma_a(u) = a^{\abs{u}_a \mod \mathop{\mathrm{ord}}(\varphi(a))} c^{3n}$ and $$\gamma(u) = c^{3n} \gamma_{a_1}(v)\ldots \gamma_{a_s}(v)\gamma_c(v).$$
The mapping $\gamma$ is a normal form in the group $\prod_{a \in A} \mathbb Z/\mathop{\mathrm{ord}}(a)\mathbb Z$, i.e., let $\psi : A^* \to \prod_{a \in A} \mathbb Z/\mathop{\mathrm{ord}}(a)\mathbb Z$ be the homomorphism counting the different letters $a$ modulo $\mathop{\mathrm{ord}}(a)$, then $\psi(u) = \psi(v)$ if and only if $\gamma(u) = \gamma(v)$.
By choice of $\gamma_a(u)$ we have $\gamma(u) \in K^*$. Since $\abs{\gamma_a(u)} = 3n$ for $a\in B$ and $3n \leq \abs{\gamma_c(u)} < 4n$, we obtain \[t-7n = 3n(s+2) \leq \abs{\gamma(u)} < 3n(s+2)+n = t - 6n.\]
In particular, $\varphi(u) = \varphi(\gamma(u))$ and $\gamma(u\gamma(u')) = \gamma(uu') = \gamma(u'u) = \gamma(\gamma(u')u)$.
Additionally, if $u\in K^*$ with $\abs{u} \geq 3n(s+2)+n = t -6n$, then $u \mapsto \gamma(u)$ is Parikh-reducing over $A^*$ since at least the number of $c$ decreases.
Note that the inequality $t-n \leq \abs{\omega \gamma(u) \omega'} < t$ is actually the reason for the definition of $t$.
Let $$T_\Omega = \set{\omega u \omega' \to \omega \gamma(u) \omega'}{t\leq \abs{\omega u \omega'} \leq t_\Omega \text{ and } \omega, \omega' \text{ are }\Omega\text{-maximal for } \omega u \omega'}$$
be the set of $\Omega$-rules. By definition of $\gamma$ the set of $\Omega$-rules is Parikh-reducing over~$A^*$.
Note that for a $\Omega$-rule, either $\omega$ and $\omega'$ are minimal elements in $\Omega$ or $\omega = \omega'$.
By \prref{lem:tOmegaexist} the system $T = T_\Delta \cup T_\Omega$ has only finitely many irreducible elements.
It remains to prove that $T$ is Church-Rosser. By \prref{lem:deltacrsystem} the set $T_\Delta$ of $\Delta$-rules is (locally) confluent.
Next, we will study properties of $\Omega$-rules which are crucial for showing that $T$ is Church-Rosser.
First, we show that $T$-rules preserve $\Omega$-maximal elements.
\begin{lemma}\label{lem:omegamax}
Let $u \RA{T} v$ and let $\omega$ be a maximal $\Omega$-factor of $u$.
Then $\eta \preceq \omega$ for every $\Omega$-factor $\eta$ of $v$.
\end{lemma}
\begin{proof}
As $T = T_\Delta \cup T_\Omega$ there are two cases for the rule set of $u \RA{T} v$.
In the case that $u \RA{T_\Delta} v$ there must exists a $\delta \in \Delta$ and a factorization $u = u_1 \delta^{t+n} u_2$ such that $v = u_1 \delta^t u_2$.
By construction, we have $t > 3n = \abs{\omega}$. Thus, every element of $\Omega$ is a factor of $u$ if and only if it is also a factor of $v$.
Since $\omega$ is $\Omega$-maximal for $u$, it is also $\Omega$-maximal for $v$.
If $u \RA{T_\Omega} v$, there is a factorization
$u = u_1 \omega_1 \hat u \omega_2 u_2$ such that $v = u_1 \omega_1 \gamma(\hat u) \omega_2 u_2$ and $\omega_1, \omega_2$ are maximal $\Omega$-factors of $\omega_1 \hat u \omega_2$.
Since every marker in $\Omega$ has fixed length $3n$, it remains to show that $\omega_1 \gamma(\hat u) \omega_2$ has no $\Omega$-factors larger than $\omega_1$ (and by $\omega_1 \preceq \omega$, also no $\Omega$-factors larger than $\omega$).
Note that $\gamma(\hat u)$ has $c^{3n}$ as prefix and suffix.
Every $\Omega$-factor of $\omega_1 \gamma(\hat u)$ which is not an $\Omega$-factor of $\gamma(\hat u)$ has the form $\zeta c^i$ for some $i\geq 0$ and $\zeta$ is a suffix of $\omega_1$. Since the block of $c$'s at the suffix of $\zeta c^i$ may only increase, we obtain $\zeta c^i \preceq \omega_1$ by definition of $\preceq$.
Since every element of $\Omega$ has length $3n$ and does not have $c$ as a prefix,
there is no $\Omega$-factor in $\gamma(\hat u) \omega_2$ which is neither in $\gamma(\hat u)$ nor equals $\omega_2$.
By construction, every $\Omega$-factor of $\gamma(\hat u)$ is of the form $\gamma_a(\hat u)$ for some $a\in B$.
However, $\gamma_a(\hat u)$ is a minimal element of $\Omega$ by construction.
In particular, $\eta \preceq \omega_1 \preceq \omega$ for every $\Omega$-factor $\eta$ of $\omega_1 \gamma(\hat u) \omega_2$.
\end{proof}
Next, as an intermediate step, we show local confluence in the case of a left side $\omega u \omega'$ of a rule in $T_\Omega$. In particular, we show that every word of this form can be reduced to a fixed normal form.
\begin{lemma}\label{lem:parikhnf}
Let $\omega u \omega'$ be a word such that $\omega$ and $\omega'$ are maximal $\Omega$-factors of $\omega u \omega'$ and $\abs{\omega u \omega' }\geq t$. Then $\omega u \omega' \RA{T} v$ implies $v \RAS{*}{T} \omega \gamma(u) \omega'$.
\end{lemma}
\begin{proof}
The statement is clear if $v = \omega \gamma(u) \omega'$ which is why we may assume $v \neq \omega \gamma(u) \omega'$.
We show the lemma inductively on the length of $\omega u \omega'$. In order to apply the induction step we show that $v = \omega v' \omega'$ and $\abs v \geq t$. The precondition that $\omega$ and $\omega'$ are maximal $\Omega$-factors of $v$ is satisfied by \prref{lem:omegamax}.
In the case of $\omega u \omega' \RA{T_\Omega} v$, some rule $\mu u' \mu' \to \mu \gamma(u') \mu' \in T_\Omega$ was applied.
As such rules preserve the prefixes and suffixes of length $3n$, the word $v$ must have the correct form.
In the case of $\omega u \omega' \RA{T_\Delta} v$, some rule $\delta^{t+n} \to \delta^t$ was applied.
Since $t>6n$ and elements of $\Omega$ all have length $3n$, the $\Omega$-factors $\omega$ and $\omega'$ are preserved by the application of the $\Delta$-rule $\delta^{t+n} \to \delta^t$.
In both cases we conclude that $v = \omega v' \omega'$ for some word $v'$.
It remains to show, that $\abs v \geq t$. Since $\abs{\delta^t} \geq t$, the case of an application of a rule in $T_\Delta$ is trivial.
Let $v$ stem from the application of a rule $\mu u' \mu' \to \mu \gamma(u') \mu' \in T_\Omega$.
If either $\mu u'$ or $u' \mu'$ is a factor of $u$, we have that either $\mu \gamma(u')$ or $\gamma(u') \mu'$ is a factor of $v'$.
Thus, using $\abs{\gamma(u')} > t - 7n$ and $\abs{\omega} = 3n$ for every element $\omega\in \Omega$, we obtain \[\abs{v} = \abs{\omega v' \omega'} \geq \abs{\omega} + \abs{\mu \gamma(u')} + \abs{\omega'} > t + 2n > t.\]
It remains to prove $\abs v \geq t$ for the situation which is depicted below.
\begin{center}\begin{tikzpicture}[implies/.style={double,double equal sign distance,-implies}]
\def3.5{3.5}
\def9{9}
\node [rectangle, thin, draw=black, minimum width = 1cm, inner sep = 1pt, minimum height=0.4cm] at (3.5-0.25,1.48)
{$\omega\vphantom{\mu\delta^t}$};
\node [rectangle, thin, draw=black, minimum width = 2.5cm, inner sep = 1pt, minimum height=0.4cm] at (3.5+1.5,1.48)
{$u\vphantom{\mu\delta^t}$};
\node [rectangle, thin, draw=black, minimum width = 1cm, inner sep = 1pt, minimum height=0.4cm] at (3.5+3.25,1.48)
{$\omega'\vphantom{\mu\delta^t}$};
\node [rectangle, thin, draw=black, inner sep = 1pt,minimum width = 1cm, minimum height=0.4cm] at (3.5+0.25,1) {$\mu\vphantom{\mu\delta^t}$};
\node [rectangle, thin, draw=black, inner sep = 1pt,minimum width = 1.5cm, minimum height=0.4cm] at (3.5+1.5,1) {$u'\vphantom{\mu\delta^t}$};
\node [rectangle, thin, draw=black, inner sep = 1pt,minimum width = 1cm, minimum height=0.4cm] at (3.5+2.75,1) {$\mu'\vphantom{\mu\delta^t}$};
\end{tikzpicture}
\end{center}
If $\omega \neq \omega'$, then there exists $b_1,b_2 \in K\setminus\oneset{c}$ such that $\omega = b_1 c^{3n-1}$ and $\omega' = b_2c^{3n-1}$.
However, as no element of $\Omega$ starts with the letter $c$, we can conclude $\omega = \mu$ and thus by $\mu' \preceq \mu$ we obtain $\omega' = \mu'$ by the same argument.
In this case we have $\omega u \omega' = \mu u' \mu'$ and henceforth $v = \omega \gamma(u) \omega'$.
The case that $\mu \neq \mu'$ is similar: $\omega'$ has no $c$ as prefix and thus $\mu' = \omega'$. Again, $\omega = \mu$ and $v = \omega \gamma(u) \omega'$ holds.
Hence, we may assume $\omega = \omega'$ and $\mu = \mu'$.
Combining both overlaps, we obtain the following picture.
\begin{center}\begin{tikzpicture}[implies/.style={double,double equal sign distance,-implies}]
\def3.5{3.5}
\def9{9}
\node [rectangle, thin, draw=black, minimum width = 0.75cm, inner sep = 1pt] at (3.5-0.375,1.48)
{$x\vphantom{\mu\delta^t}$};
\node [rectangle, thin, draw=black, minimum width = 2cm, inner sep = 1pt] at (3.5+1,1.48)
{$\omega\vphantom{\mu\delta^t}$};
\node [rectangle, thin, draw=black, minimum width = 0.75cm, inner sep = 1pt] at (3.5+2.375,1.48)
{$y\vphantom{\mu\delta^t}$};
\node [rectangle, thin, draw=black, inner sep = 1pt,minimum width = 2cm] at (3.5+0.25,1) {$\mu\vphantom{\mu\delta^t}$};
\node [rectangle, thin, draw=black, inner sep = 1pt,minimum width = 1.5cm] at (3.5+2,1) {$y'\vphantom{\mu\delta^t}$};
\node [rectangle, thin, draw=black, inner sep = 1pt,minimum width = 1.5cm] at (3.5,0.52) {$x'\vphantom{\mu\delta^t}$};
\node [rectangle, thin, draw=black, inner sep = 1pt,minimum width = 2cm] at (3.5+1.75,0.52) {$\mu\vphantom{\mu\delta^t}$};
\end{tikzpicture}
\end{center}
In the notation of the picture above we have $u = y u' x$. Thus, $v = \omega y \gamma(u') x \omega$ and by $\gamma(u') > t - 7n$ and $\abs{\omega} = 3n$ it suffices to show $\abs{x'} = \abs{yx} \geq n$.
By $\mu y' = x' \mu$ we have that $\mu$ is a factor of $x'^+$.
We conclude $x'\not\in \Delta$ which implies $\abs{x'} > n$.
In summary, $v = \omega v' \omega'$ and $\abs v \geq t$ holds. If $\abs v \leq t_\Omega$, then we can directly apply the $T_\Omega$-rule with left side $v$. Else, $v$ must be reducible by \prref{lem:tOmegaexist} and we can apply induction.
\end{proof}
Combining the previous lemmas we show that $T$ is locally confluent.
\begin{lemma}\label{lem:parikhisconfl}
$T$ is locally confluent.
\end{lemma}
\begin{proof}
Let $\ell \to r, \ell' \to r' \in T$ be two rules. We have to show that every overlap of the left sides of those rules resolves.
The system $T_\Delta$ is locally confluent by \prref{lem:deltacrsystem}.
Hence, we may assume that $\ell \to r\in T_\Omega$. Let $\omega u \omega' = \ell$ and consequently $r = \omega \gamma(u) \omega'$.
Consider first the case that $\delta^{t+n} = \ell' \to r' \in T_\Delta$.
If $\ell'$ is a factor of $\ell$, that is, if $\ell = x\ell' y$, then $\ell \RAS{}{T} x r' y \RAS{*}{T} r$ by \prref{lem:parikhnf}.
By definition of $\Omega$, the left side $\ell$ which contains an element of $\Omega$ cannot be a factor of $\delta^{t+n}$.
Hence, the system resolves in the case of factor critical pairs.
Consider thus the case of an overlap critical pair $x \ell = \ell' y$ (the case $x \ell' = \ell y$ is symmetric).
Since $\omega$ is no factor of $\delta^+$ and $t \geq 3n$ by definition, we have the following situation:
\begin{center}\begin{tikzpicture}[implies/.style={double,double equal sign distance,-implies}]
\def3.5{3.5}
\def9{9}
\node [rectangle, thin, draw=black, inner sep = 1pt,minimum width = 1cm] at (3.5-1,1) {$\delta^{n}\vphantom{\mu\delta^t}$};
\node [rectangle, thin, draw=black, inner sep = 1pt,minimum width = 2cm] at (3.5+0.5,1) {$\delta^{t}\vphantom{\mu\delta^t}$};
\node [rectangle, thin, draw=black, minimum width = 1cm, inner sep = 1pt] at (3.5+1.5,1.48)
{$\omega\vphantom{\mu\delta^t}$};
\node [rectangle, thin, draw=black, minimum width = 1.5cm, inner sep = 1pt] at (3.5+2.75,1.48)
{$u\omega'\vphantom{\mu\delta^t}$};
\end{tikzpicture}
\end{center}
Let $\delta^t = z_1z_2$ and $\omega = z_2z_3$ be the overlap, then
\begin{align*}
x\ell \RAS{}{T} xr = x \omega \gamma(u) \omega' = \delta^{t+n} z_3\gamma(u) \omega' \RAS{}{T} \delta^t z_3 \gamma(u) \omega' = z_1z_2z_3 \gamma(u) \omega'\\
\ell'y \RAS{}{T} r'y = \delta^ty = z_1 \omega u \omega' \RAS{}{T} z_1 \omega \gamma(u) \omega' = z_1z_2z_3 \gamma(u) \omega'
\end{align*}
Consider the case that $\ell' \to r' \in T_\Omega$ and let $\ell' = \mu v \mu'$. Again, if $\ell' = x\ell y$, then $\ell' \RAS{}{T} x r y \RAS{*}{T} r'$ by \prref{lem:parikhnf}. Hence, by symmetry, it suffices to consider the case $x \ell = \ell' y$. If $\ell$ and $\ell'$ overlap at most $3n$ positions,
\begin{center}\begin{tikzpicture}[implies/.style={double,double equal sign distance,-implies}]
\def3.5{3.5}
\def9{9}
\node [rectangle, thin, draw=black, inner sep = 1pt,minimum width = 1.5cm] at (3.5-0.25,1) {$\mu u'$};
\node [rectangle, thin, draw=black, inner sep = 1pt,minimum width = 1cm] at (3.5+1,1) {$\mu'$};
\node [rectangle, thin, draw=black, minimum width = 1cm, inner sep = 1pt] at (3.5+1.5,1.47)
{$\omega\vphantom{\mu\delta^t}$};
\node [rectangle, thin, draw=black, minimum width = 1.5cm, inner sep = 1pt] at (3.5+2.75,1.47)
{$u\omega'\vphantom{\mu\delta^t}$};
\end{tikzpicture}
\end{center}
then the rules can be applied independently;
let again be $\mu' = z_1z_2$ and $\omega = z_2z_3$ be the overlap, then
\begin{align*}
x\ell \RAS{}{T} xr = x \omega \gamma(u) \omega' = \mu u' \mu' z_3\gamma(u) \omega' \RAS{}{T} \mu \gamma(u') \mu' z_3 \gamma(u) \omega' = \mu \gamma(u')z_1z_2z_3 \gamma(u) \omega'\\
\ell'y \RAS{}{T} r'y = \mu \gamma(u') \mu' y = \mu \gamma(u') z_1 \omega u \omega' \RAS{}{T} \mu \gamma(u') z_1 \omega \gamma(u) \omega' = \mu \gamma(u')z_1z_2z_3 \gamma(u) \omega'
\end{align*}
and the system resolves in this case.
Hence, we assume that $\ell$ and $\ell'$ overlap more than $3n$ positions. In this case $\mu'$ is a factor of $\ell$ and $\omega$ is a factor of $\ell'$.
This implies that $\mu$ and $\omega'$ are maximal $\Omega$-factors of $x\ell = \ell' y = \mu u'' \omega'$. We conclude $x\ell \RAS{}{T} xr \RAS{*}{T} \mu \gamma(u'') \omega'$ and $\ell' y \RAS{}{T} r' y \RAS{*}{T} \mu \gamma(u'')\omega'$
by \prref{lem:parikhnf}.
\end{proof}
By construction, the system $T$ is $\varphi$-invariant and thus the system $$T' = \set{c\ell \to cr \in A^*\times A^*}{\ell \to r \in T}$$ is $\varphi$-invariant. By \prref{lem:tOmegaexist} the system $T$ is of finite index over $K^*$. We can apply \prref{lem:bastel} and obtain a $\varphi$-invariant Parikh-reducing Church-Rosser system $S$ of finite index over $A^*$.
This concludes the proof of the first part of \prref{thm:parikhcomgroup}.
It remains to study the groups in $A^*\! /S$.
As an intermediate step, we study the groups in $K^*\! /T$.
\begin{lemma}\label{lem:groupinT}
Let $H \subseteq K^*\! /T$ be a subsemigroup which is a group and identify $H$ with the corresponding elements in $\mathrm{IRR}_T(K^*)$.
Then either there exists some $\delta \in \Delta$ such that $H \subseteq \os{\delta^{t},\ldots, \delta^{t+n-1}}$ is a cyclic group whose order is divisible by $n$ or there is an injective homomorphism $\eta : H \to \prod_{a\in A} \mathbb Z/\mathop{\mathrm{ord}}(\varphi(a))\mathbb Z$.
\end{lemma}
\begin{proof}
Without loss of generality, we may assume that $H$ is non-trivial.
Let $e^2=e \in H$ be the identity element of $H$.
Note that by definition of the rules $T$ and the set $\Omega$, the irreducible word of every word $w\in K^*\Omega K^*$ also contains an $\Omega$-factor.
Thus, by $ex = x$ and $x^{\abs H} = e$ for all $x\in H$ either all elements in $H\subseteq K^*\! /T$ contain some factor in $\Omega$ or none of the elements contains an $\Omega$-factor. All words $x\in H$ must have length at least $t-n > 2n$ by definition of the rules $T$.
Let us first consider the case that none of the elements contain an $\Omega$-factor.
We show that there exists some $\delta \in \Delta$ such that for all $x\in H$ there exists $i\in \mathbb N$ such that $x=\delta^i$.
Let $u\delta^{t+n} v \RA{T_\Delta} u \delta^t v$ be an application of a rule in $T_\Delta$ and let $w\in J$ be a minimal factor of $u\delta^{t+n}v$ which is not in $F$.
By \prref{lem:minimalefactorgegenbsp} $\abs w \leq 2n$ and since $t > 2n$,
the factor $w$ is also a factor of $u \delta^t v$.
Thus, the number of factors in $J$ does not decrease by an application of a rule in $T_\Delta$.
Consider any $x \in H$. Since the number of factors in $J$ does not decrease by some application of a rule in $T_\Delta$, $x^{\abs{H}+1} = x$ and no rule in $T_\Omega$ is applicable, we deduce that the number of factors in $J$ of $x^{\abs{H}+1}$ and $x$ is the same. In particular, this number is zero and we obtain $x\in F$ for all $x\in H$.
Next, we show that $x = \delta^i$ for some $\delta \in \Delta$.
Since $x\in F$ and $\Delta$ is closed under conjugation, there exists a primitive word $\delta \in \Delta$ and $i\in \mathbb N$ such that $x = \delta^i \delta'$ for some prefix $\delta'$ of $\delta$. In particular, $\abs{\delta}$ is a period of $x$.
Note that $i \geq 2$ since $\abs{x} > 2n$.
Consider the word $x^2$.
By the above, we obtain $x^2 \in F$, that is, again there exists a primitive word $\hat \delta \in \Delta$, a prefix $\hat \delta'$ of $\hat \delta$ and a number $j\geq 2$ such that $x^2 = \hat \delta^j \hat \delta'$.
Therefore, $\abs{\hat \delta}$ is a period of $x^2$ and, hence, also of~$x$.
Since $\abs x > 2n$, we may use \prref{thm:finewilf} and conclude that $\gcd(\abs{\delta}, |\hat\delta|)$ is a period of $x$.
Since $\delta$ is primitive, this implies $\gcd(\abs{\delta}, |\hat\delta|) = \abs{\delta}$. Since $\hat{\delta}$ is a prefix of $x$, this yields that $\hat{\delta}$ is a power of $\delta$ which implies $\delta = \hat \delta$ by primitivity of $\hat{\delta}$.
In particular, $\abs{\delta}$ is a period of $x^2$ and $\delta'\delta$ is a prefix of $\delta^2$.
Since $\delta$ is primitive this implies that $\delta'$ is not a proper prefix of $\delta$ by \prref{lem:charprimitive} and
we conclude that for every $x\in H$ there exists $\delta \in \Delta$ and $i\in \mathbb N$ such that $x = \delta^i$.
Thus, consider $\delta_1^i, \delta_2^j \in H$ with $\delta_1\neq \delta_2$ primitive words in $\Delta$.
Again, $\abs{\delta_1}$ is a period of $\delta_1^i$ and there must exist a period $p\leq n$ of $\delta_1^i\delta_2^j \in F$.
By \prref{thm:finewilf} $\gcd(\abs{\delta_1},p)$ is a period of $\delta_1^2$.
By primitivity of $\delta_1$, this yields that $\abs{\delta_1}$ is a divisor of $p$. In particular, since $p$ is a period of $\delta_1^i \delta_2^j$, this yields $\delta_1^i\delta_2^j = \delta_1^i\delta_1^k \delta_1'$ for some $k\geq 2$ and $\delta_1'$ a prefix of $\delta_1$.
Using \prref{thm:finewilf} again, we see that $\gcd(\abs{\delta_1},\abs{\delta_2})$ is a period of $\delta_2^j$, that is, $\abs{\delta_2}$ is a divisor of $\abs{\delta_1}$ by primitivity of $\delta_2$. By symmetry, this yields $\abs{\delta_1} = \abs{\delta_2}$ and thus $\delta_1 = \delta_2$.
Fix some primitive word $\delta \in \Delta$ such that $H \subseteq \delta^+$. Since $ex = x$ for all $x\in H$ and the right side of rules in $T_\Delta$ have length at least $t$ and since $\delta^{t+n}$ is reducible, we conclude $H \subseteq \os{\delta^t,\ldots, \delta^{t+n-1}}$ and thus $H$ is a subgroup of the cyclic group $\os{\delta^t,\ldots, \delta^{t+n-1}}$ of order $n$ which finishes this case.
The second case is that all words in $H$ contain an $\Omega$-factor.
Consider the maximal $\Omega$-factors of $e$ and factorize
$e = e_1 \omega e_2 \omega' e_3$ with $\omega, \omega' \in \Omega$ maximal for $e$
such that $e_1\omega$ and $\omega' e_3$ contains no other maximal $\Omega$-factors of $e$.
Since $e^2 = e$, we conclude that $e_2$ is some normal form.
By $ex = x = xe$ for all $x\in H$ and \prref{lem:parikhnf},
there must exist a factorization $x = e_1 \omega \hat x \omega' e_3$ such that $\hat x = \gamma(\hat x)$ is a normal form.
In particular, $\widehat{xy} = \gamma(\hat x \omega' e_3 e_1 \omega \hat y)$ by \prref{lem:parikhnf}.
Consider the homomorphism $\psi : A^* \to \prod_{a\in A} \mathbb Z/\mathop{\mathrm{ord}}(\varphi(a))\mathbb Z$
which counts the number of $a\in A$ modulo $\mathop{\mathrm{ord}}(a)$ and the function $\eta : H \to \prod_{a\in A} \mathbb Z/\mathop{\mathrm{ord}}(a)\mathbb Z$
given by $\eta(x) = \psi(\hat x) \cdot \psi(\omega'e_3e_1\omega)$.
Note that $\psi(\widehat{xy}) = \psi(\hat x)\psi(\hat y) \psi(\omega'e_3e_1\omega)$ implies that
$\eta$ is a homomorphism.
It holds $\eta(x) = \eta(y)$ if and only if $\psi(\hat x) = \psi(\hat y)$.
By definition of the normal forms $\gamma(\cdot)$, it holds $\psi(\hat x) = \psi(\hat y)$ if and only if $\hat x = \hat y$
and therefore $\eta$ is injective.
\end{proof}
By \prref{lem:bastel}, we obtain that the subgroups in $A^*\! /S$ are isomorphic to subgroups of $B^*\! /R$ and $K^*\! /T$.
By induction, all groups in $B^*\! /R$ are isomorphic to some subgroup of $\prod_{a\in A} \mathbb Z/\mathop{\mathrm{ord}}(\varphi(a))\mathbb Z$.
All groups in $K^*\! /T$ are either cyclic of order divisible by $n$ or isomorphic to some subgroup of $\prod_{a\in A} \mathbb Z/\mathop{\mathrm{ord}}(\varphi(a))\mathbb Z$ by \prref{lem:groupinT}.
However, since $n$ is defined as the least common multiple of $\mathop{\mathrm{ord}}(\varphi(a))$,
the cyclic group of order $n$ is a subgroup of $\prod_{a\in A} \mathbb Z/\mathop{\mathrm{ord}}(\varphi(a))\mathbb Z$.
This proves the statement.
\end{proof}
\subsection{Group languages over an alphabet of size two}\label{subsec:group2generator}
The same technique as in \prref{subsec:commgrpcr} can be used to obtain Parikh-reducing Church-Rosser systems which factorize through homomorphisms $\varphi : \oneset{a,b}^* \to G$ for an arbitrary group $G$. We will only sketch the proof, as it is essentially the proof of \prref{thm:parikhcomgroup}.
\begin{theorem}
Let $A = \oneset{a,b}$ be an alphabet of size two and let $\varphi : A^* \to G$ be a homomorphism into a finite group $G$. Then there exists a Parikh-reducing Church-Rosser system $S$ of finite index which factorizes through $\varphi$. All groups in $A^*/S$ are subgroups of $G$ or of $\mathbb Z/n\mathbb Z$ where $n$ is the exponent of $G$.
\end{theorem}
\begin{proof}[Sketch of proof]
Let $n$ be the exponent of $G$ and let $R = \oneset{a^n \to 1} \subseteq \oneset{a}^* \times \oneset{a}^*$ be the set of rules over the alphabet $\oneset{a}$. Set $K = \mathrm{IRR}_R(a^*)b = \set{a^ib}{0 \leq i < n}$.
In the remainder of the sketch, we have to construct a system over $K^*$.
As the set of short words we choose $\Delta = K^{\leq n^2} \setminus \oneset{1}$. The corresponding set of rules is $T_\Delta = \set{\delta^{t+n} \to \delta^t}{\delta \in \Delta}$ for $t = n^2(3n+7)$. Note that since $t > 2n^2$ the system $T_\Delta$ is confluent by \prref{lem:deltacrsystem}.
Let $F = \bigcup_{\delta \in \Delta, i \in \mathbb N} \mathrm{Factors}(\delta^i)$ and set $\Omega = K^{3n^2} \setminus (bK^*\cup F)$. Choose a preorder $\preceq$ on $\Omega$ such that
\begin{itemize}
\item $\omega, \eta \in\Omega$ with
$\omega \in K^*(K\setminus\os{b}) b^i, \eta \in K^*(K\setminus\os{b}) b^j$ and $i>j$
implies $\omega \preceq \eta$.
\item $\preceq$ is a total order on $\Omega \setminus Kb^{3n^2-1}$.
\item $\omega, \eta \in \Omega\cap Kb^{3n^2-1}$ implies $\omega \preceq \eta$.
\end{itemize}
In order to complete the construction, it remains to choose the normal forms $v_g$. Note that every representation of $g\in G$ needs less than $n$ a's by the pigeonhole principle. Thus, for every $g\in G$ there exists a word $v_g = b^{3n^2} v_{1} b^{3n^2} \cdots b^{3n^2} v_{n-1} b^{3n^2} \in K^*$ with $\varphi(v_g) = g$ and $v_i \in \set{ab^k, b^k}{1\leq k \leq n}$. For every $g \in G$ we choose such a word $v_g$ such that the number of $a$'s is minimal. Note that by construction $\abs{\abs{v_g}-\abs{v_h}} < n^2$ as a word over $K$. This is the reason for the choice of $\Delta$. Furthermore, $t-7n^2 < \abs{v_g} < t-6n^2$, which explains the choice of the parameter $t$.
The choice of $v_g$ also yields that there are no $\Omega$-factors in $v_g$ apart from $ab^{3n^2}$, which is $\Omega$-minimal.
Adapting the proof of \prref{lem:t0parikhexist}, we prove the existence of a number $t_0$ such that every word $v \in K^*$ of length at least $t_0$ has a factor $\delta^{t+n}$ for a $\delta \in \Delta$ or a factor $\omega \in \Omega$. \prref{lem:tOmegaexist} yields the existence of a number $t_\Omega$ such that every $v \in \mathrm{IRR}_{T_\Delta}(K^*)$ contains a factor $\omega \, u \, \omega'$
with $\omega, \omega'$ being $\Omega$-maximal for this factor and $t< \abs{\omega u \omega'} \leq t_\Omega$.
Again, let \[T_\Omega = \set{\omega u \omega' \to \omega v_{\varphi(u)} \omega'}{t\leq \abs{\omega u \omega'} \leq t_\Omega \text{ and } \omega, \omega' \text{ are }\Omega\text{-maximal for } \omega u \omega'}\] and $T = T_\Delta \cup T_\Omega$.
We want to apply \prref{lem:bastel} to obtain a system $S \subseteq \oneset{a,b}^* \times \oneset{a,b}^*$.
Confluence of $T$ follows along the lines of \prref{lem:omegamax}, \prref{lem:parikhnf} and \prref{lem:parikhisconfl}, whereas the statement about the groups in $A^*/S$ is analogously to \prref{lem:groupinT}.
\end{proof}
\section{Beyond Groups}\label{sec:beyondgroups}
In this section we apply local divisors in order to lift the construction of Church-Rosser systems for groups to the general case of monoids. Instead of directly constructing a system over $K = \mathrm{IRR}_R(B^*)c$, we obtain a system inductively by going over to the local divisor. This decreases the size of the monoid, but increases the size of alphabet. The first part of this theorem has been published in \cite{DiekertKRW15jacm}, whereas the second part is based on the use of Rees extensions, see \cite{DiekertKW12tcs, DiekertWalter16}.
\begin{theorem}\label{thm:group2variety}
Let $\varietyfont{H}$ be a group variety such that for every homomorphism $\varphi : A^* \to G$ for $G\in \varietyfont{H}$ there exists a Parikh-reducing Church-Rosser system $S$ of finite index which factorizes through $\varphi$.
Let $\varphi : A^* \to M$ be a homomorphism with $M \in \overline{\varietyfont{H}}$.
\begin{enumerate}
\item\label{enum:group2variety:a} There exists a $\varphi$-invariant Parikh-reducing Church-Rosser system $S$ of finite index.
\item\label{enum:group2variety:b} If every homomorphism $\varphi : A^* \to G$ in a group $G \in \varietyfont{H}$ has a Church-Rosser representation in $\overline{\varietyfont{H}}$, then $A^*\! /S \in \overline{\varietyfont{H}}$.
\end{enumerate}
\end{theorem}
\begin{proof}
\ref{enum:group2variety:a}. We use induction on $(\abs{M}, \abs{A})$, ordered lexicographically. Since $\overline{\varietyfont{H}}$ is closed
under taking submonoids, we can restrict ourselves on surjective homomorphisms $\varphi$.
If $M$ is a group, then $M\in \varietyfont{H}$ and there exists such a system $S$ by the preconditions.
Thus, we can assume that there is
a letter $c\in A$ such that $\varphi(c)$ is not a unit. Let $B = A\setminus \oneset{c}$.
By induction the restriction
\[
\varphi|_{B^*} : B^*\to M
\]
admits a Parikh-reducing Church-Rosser system $R\subseteq B^*\times B^*$.
Consider the set
\[
K = \mathrm{IRR}_R(B^*)c.
\]
This is a prefix code and will be considered as a new alphabet.
Let $\psi : K^* \to M_{\varphi(c)}$ be the homomorphism to the local divisor at $\varphi(c)$ induced via
$\psi(uc) = \varphi(cuc)$. We have $\abs{M_{\varphi(c)}} < \abs{M}$ and $M_{\varphi(c)} \in \overline{\varietyfont{H}}$ and thus, by induction, there exists a
Parikh-reducing Church-Rosser system $T'\subseteq K^* \times K^*$ of finite index,
such that $T'$ factorizes through $\psi$.
In particular, we have $\psi(\ell) = \psi(r)$ for a rule $(\ell, r) \in T'$.
We show that $\varphi(c\ell) = \varphi(cr)$. For this let $\ell = u_1c \ldots u_nc$ and $r = v_1c \ldots v_mc$. It holds
\begin{align*}
\varphi(c\ell) &= \varphi(cu_1c) \circ \ldots \circ \varphi(cu_nc)\\
&= \psi(u_1c)\circ \ldots \circ \psi(u_nc) \\
&= \psi(\ell) = \psi(r) \\
&= \psi(v_1c)\circ \ldots \circ \psi(v_mc) \\
&= \varphi(cv_1c) \circ \ldots \circ \varphi(cv_mc) = \varphi(cr).
\end{align*}
Hence, the rule $c\ell \to cr$ is $\varphi$-invariant. We set
\[
T = \set{c\ell \to cr}{\ell \to r \in T'}.
\]
The system $S = R\cup T$ has the required properties by \prref{lem:bastel}.
\ref{enum:group2variety:b}.
The statement is clear if $M$ is a group. Consequently, the construction above is applied.
By induction we may assume that $B^*\! /R, K^*\! /T \in \overline{\varietyfont{H}}$ and \prref{lem:bastel} implies that $A^*\! /S \in \overline{\varietyfont{H}}$.
\end{proof}
A direct combination of \prref{thm:parikhcomgroup} and \prref{thm:group2variety} yields the following corollary.
\begin{corollary}
Let $M \in \overline{\ensuremath{\varietyfont{Ab}}}$ be a monoid and $\varphi : A^* \to M$ be a homomorphism, then there exists a Parikh-reducing Church-Rosser system $S\subseteq A^*\times A^*$ such that $S$ factorizes through $\varphi$ and $A^*\! /S \in \overline{\ensuremath{\varietyfont{Ab}}}$.
In particular, every language $L\subseteq A^*$ recognized by $\varphi$ is given as a finite union $L = \bigcup_{u\in L} [u]_S$.
\end{corollary}
In particular, \prref{thm:group2variety} shows that one can control the groups in the Church-Rosser representation. However, in general one may not preserve other properties, for instance, commutativity.
\begin{proposition}
Let $\varphi : A^* \to \mathbb Z/2\mathbb Z$ be the homomorphism mapping each letter to the generator of $\mathbb Z/2\mathbb Z$. If $\abs{A}>1$, there is no abelian Church-Rosser representation of~$\varphi$.
\end{proposition}
\begin{proof}
Assume that there exists a Church-Rosser system $S$ of finite index such that $A^*/S$ is abelian and there exists a homomorphism $\psi : A^*/S \to \mathbb Z/2\mathbb Z$ with $\varphi = \psi \circ \pi_S$. Let $a,b \in A$ be letters such that $a \neq b$. Since $S$ factorizes through $\varphi$, we have $\abs{r} \equiv \abs{\ell} \bmod 2$ for every rule $(\ell,r) \in S$ and it holds $a\neq b$ in $A^*/S$. Since $A^*/S$ is abelian, we obtain $ab = ba$ in $A^*/S$. In particular, $ab \to_S 1 \leftarrow_S ba$ and $A^*/S$ must be a group. Let $2n$ be the order of $a$ and $b$. Then $a^n = a^nb^nb^{n} = b^n$ holds in $A^*/S$ and thus there must be a irreducible word $w$ with $a^n \RAS{*}{S} w \LAS{*}{S} b^n$. By the argumentation above, there exists a number $k<n$ such that $w \in \oneset{a^k,b^k}$. Thus, either $a^{n-k} = 1$ or $b^{n-k} = 1$ which is a contradiction to the definition of $n$.
\end{proof}
\section{Complexity of Church-Rosser systems}\label{sec:crcomplexity}
In this section we analyze the size of a Church-Rosser representation as constructed by \prref{thm:group2variety} and \prref{thm:parikhcomgroup}. We will restrict our analysis on the construction of the Parikh-reducing Church-Rosser representation. Similiar calculations can be made for the analysis of the size of the Church-Rosser system.
Before we prove upper bounds for the size of the constructed Church-Rosser systems, we reconsider the construction.
Our constructions used \prref{lem:bastel} as the basic building block of the construction.
Let $\varphi : A^* \to M$ be a homomorphism.
For $B = A\setminus\os{c}$ and a system $R\subseteq B^*\times B^*$ one needs a system $T\subseteq K^* \times K^*$ for the alphabet $K=\mathrm{IRR}_R(B^*)c$.
Now, unlike in the general case, we are able to reduce the alphabet itself by exploiting the structure of the alphabet.
Let $b_1\cdots b_k c \in K$ with $b_i \in B$ and $k>\abs{M}$. By the pigeonhole principle there exist $i<j$ such that $\varphi(b_1\cdots b_i) = \varphi(b_1\cdots b_j)$ and ${i+(k-j)\leq n}$.
Thus, we may introduce the subword-reducing\footnote{subword-reducing seen as a rule over $A^*$, not over $K^*$.} rule $b_1\cdots b_k c \to b_1\cdots b_i b_{j+1}\cdots b_k c$.
If $b_1\cdots b_i b_{j+1}\cdots b_k$ is reducible in $R$, reduce it further in $R$. Repeating this process yields a new alphabet for $K$ which is a subset of $B^{\leq n}c$ and therefore, if $\abs{B}>1$, has at most $(\abs{B}^{n+1}-1)/(\abs{B}-1)$ elements. One can check, that the proofs of
\prref{thm:group2variety} and \prref{thm:parikhcomgroup} also work adding this reduction technique of the alphabet $K$.
We refrained from directly adding it to the theorems, as they are already quite technical.
\begin{proposition}\label{prop:complexitygroup}
Let $\varphi : A^* \to G$ be a homomorphism in $G\in \ensuremath{\varietyfont{Ab}}$, $n=\abs{G}$ and $m = \abs{A}>1$, then there exists a Parikh-reducing Church-Rosser system $S$ such that $S$ factorizes through $\varphi$ and
$$\abs{A^*\! /S} \in 2^{2^{m^{\mathcal O(n^2)}}}.$$
\end{proposition}
\begin{proof}
Let $S$ be the Parikh-reducing Church-Rosser system constructed using \prref{thm:parikhcomgroup} and the reduction technique described above.
\prref{lem:bastel} shows that for $m>1$ it holds $$\abs{A^*\! /S} = \abs{B^*\! /R} + \abs{B^*\! /R}^2\cdot \abs{K^*\! /T} \leq 2\abs{B^*\! /R}^2\cdot \abs{K^*\! /T}$$ where $B=A\setminus \os{c}$.
In the case of \prref{thm:parikhcomgroup}, $R$ is constructed inductively whereas $T$ is constructed directly.
By \prref{lem:tOmegaexist}, every irreducible word in $\mathrm{IRR}_T(K^*)$ has length at most $t_\Omega$ and therefore $\abs{K^*\! /T} \leq \abs{K}^{t_\Omega}$. The construction of $t_\Omega$ in the proof of \prref{lem:tOmegaexist} shows that $t_\Omega \leq 2^{\abs{\Omega}}(t_0+t)$ whereas $t_0 + t \in \mathcal O(n^2m)$. Since $\Omega \subseteq K^{3n}$ we obtain $$\abs{K^*\! /T} \leq \abs{K}^{\mathcal O(n^2m) \cdot 2^{\abs{K}^{3n}}}.$$
Using the alphabet reduction technique, we can assume $\abs{K} \leq m^{n+1}$.
Note that $\abs{K}^{3n} \leq (m^{n+1})^{3n} = m^{(n+1)3n}$ does not yield another exponential jump.
A straightforward calculation yields the existence of a constant $c\in \mathbb N$ such that $$2\abs{K^*\! /T} \leq 2^{2^{m^{cn^2}}}.$$
Now let $\ensuremath{\mathrm{ms}}(\varphi)$ denote the smallest size of a Parikh-reducing Church-Rosser representation of $\varphi$ and set
\begin{align*}
\ensuremath{\mathrm{ms}}(n,m) = \max\set{\ensuremath{\mathrm{ms}}(\varphi)}{\varphi : A^* \to G, \abs{A}\leq m, G\in \ensuremath{\varietyfont{Ab}}, \abs{G}\leq n}
\end{align*}
to be the complexity over all possible homomorphisms with $\abs{A}\leq m$ and $\abs{G}\leq n$.
We have seen that the recursion
\begin{align*}
\ensuremath{\mathrm{ms}}(n,m) \leq \ensuremath{\mathrm{ms}}(n,m-1)^2 \cdot 2^{2^{m^{cn^2}}}
\end{align*}
holds and show $\ensuremath{\mathrm{ms}}(n,m) \leq 2^{2^{m^{cn^2+2}}}$ inductively using this recursion.
Note that $\ensuremath{\mathrm{ms}}(n,1) = n$ and thus the inequality is true in the base case $m=2$.
Also $\ensuremath{\mathrm{ms}}(1,m) = 1$ and therefore we assume $n>1$.
For $m>2$ and $n>1$ it holds
\begin{align*}
\ensuremath{\mathrm{ms}}(n,m) &\leq \ensuremath{\mathrm{ms}}(n,m-1)^2 \cdot 2^{2^{m^{cn^2}}}\\
&\leq 2^{2^{(m-1)^{cn^2+2}+1}} \cdot 2^{2^{m^{cn^2}}}\\
&= 2^{2^{(m-1)^{cn^2+2}+1} + 2^{m^{cn^2}}} \\
&\leq 2^{2^{(m-1)^{cn^2+2}+1 + m^{cn^2}}}\\
&\leq 2^{2^{m^{cn^2+2}}}.
\end{align*}
The last inequality holds since
\begin{align*}
(m-1)^{cn^2+2}+1 + m^{cn^2} &\leq (m-1)m^{cn^2+1} + 1 + m^{cn^2}\\
&= m^{cn^2+2} + m^{cn^2}\underbrace{(1-m)}_{<0} + 1 \\
&\leq m^{cn^2+2}. \qedhere
\end{align*}
\end{proof}
The triple exponential upper bound given by \prref{prop:complexitygroup} seems huge, however there is already a single exponential lower bound which is fairly easy to see. The lower bound comes from the fact that Church-Rosser systems cannot directly represent group identities which preserve length, such as commutation.
\begin{proposition}\label{prop:lowerbound}
For every $n\in \mathbb N$ there exists a homomorphism $\varphi : A^* \to G$ into an abelian group $G$ of size $n$ such that for every length-reducing Church-Rosser system $S$ which factorizes through $\varphi$ all words of length smaller than $n$ are irreducible, that is, $A^{<n} \subseteq \mathrm{IRR}_S(A^*)$. In particular, if $\abs A > 1$:
$$\abs{A^*\! /S} \geq (\abs{A}^n-1)/(\abs{A}-1).$$
\end{proposition}
\begin{proof}
Consider the cyclic group $G$ of order $n$ and the homomorphism $\varphi : A^* \to G$ which maps all letters $a\in A$ to the same generator $g$ of $G$. Let $S \subseteq A^*\times A^*$ be a length-reducing Church-Rosser system which factorizes through $\varphi$. We show that every word of length less than $n$ is irreducible in $S$. Let $w \in A^*$ be a word with $\abs{w} < n$.
Assume that $w \RAS{}{S} v$ for some word $v$. Since $S$ is length-reducing, $\abs{v} < \abs{w}$.
However, $\varphi(w) = \varphi(v)$ implies $g^{\abs{w}-\abs{v}} = 1$. Since the order of $g$ is $n$, this is a contradiction to $0 < \abs{w}-\abs{v} < n$ and $w$ must be irreducible.
\end{proof}
Note that this proof does not use the Church-Rosser property and thus one could expect a larger size of the Church-Rosser representation.
\begin{example}
Niemann and Waldmann constructed an explicit Parikh-reducing system $S$ for the case $\varphi : A^* \to \mathbb Z/2\mathbb Z$ with $\varphi(a) = 1$ for all $a\in A$ \cite{NiemannW02,NiemannPhD02}. Their system is given by $S = \set{xyz \to \max(x,z)}{x,y,z\in A, y = \min(x,y,z)}$ for some arbitrary order on~$A$.
The irreducible elements in $A^*\! /S$ are exactly the sequences which are first strictly increasing and then strictly decreasing, that is $$\mathrm{IRR}_S(A^*) = \set{a_1 \cdots a_i \cdots a_n}{a_1 < \cdots < a_i \geq a_{i+1} > \cdots > a_n}.$$ This yields $\abs{A^*\! /S} = \abs{\mathrm{IRR}_S(A^*)} = 1+ \sum_{i=1}^{\abs{A}} 2^{2i-1} = (2^{2\abs{A}+1}+1)/3$ which is significantly larger than the lower bound $\abs{A} + 1$ given in \prref{prop:lowerbound}.
\end{example}
In the monoid case, the minimal size of a Church-Rosser representation is bounded by a quadruple exponential function. This increase in complexity, compared to the group case, comes from the fact that, unlike in the group case, the system $T \subseteq K^* \times K^*$ is constructed by induction. However, this is also the reason that the alphabet reduction technique is even more powerful in this case.
Consider the function $f : \mathbb N^2 \to \mathbb N$ given by $f(1,m) = 1$, $f(n,1) = n$ and $f(n,m) = 2f(n,m-1)^2 \cdot f(n-1, f(n,m-1))$ for $n,m>1$. This function gives an upper bound for the maximal size of a Church-Rosser representation of a monoid of size $n$ and an alphabet of size $m$ without any optimization. Consider further the hyperoperation function $A_1(n) = 2n$, $A_k(1) = 2$ and $A_k(n) = A_{k-1}(A_k(n-1))$.\footnote{The notation $A$ comes from Ackermann, since the function $A$ is a modified Ackermann function.}
For fixed $k$, the function $A_k$ is primitive recursive, however the two-variable function $A$ grows faster than any primitive recursive function, see e.g. \cite{DavisWeyuker83}. An induction shows that $f(n,m) \geq A_{n-1}(m)$ for $n>1, m\geq 1$.
Hence, without the alphabet reduction the recursive formula would yield a non-primitive recursive function.
\begin{proposition}
Let $\varphi : A^* \to M$ be a homomorphism in $M\in \overline{\ensuremath{\varietyfont{Ab}}}$, $n=\abs{M}$ and $m = \abs{A}$. Then there exists a Parikh-reducing Church-Rosser system $S$ such that $S$ factorizes through $\varphi$ and
$$\abs{A^*\! /S} \in 2^{2^{m^{\mathcal O\left((n+1)!\right)} + n}}.$$
\end{proposition}
\begin{proof}
If $M \in \ensuremath{\varietyfont{Ab}}$, we know that there exists such a system $S$ with $\abs{A^*\! /S} \in 2^{2^{m^{\mathcal O(n^2)}}}$ by \prref{prop:complexitygroup}.
If $m=1$, then there exists a system $S$ such that $\abs{A^*\! /S} \leq n$.
In the other case we will use the local divisor construction of \prref{thm:group2variety}.
Note that by the alphabet reduction technique we may assume that $\abs{K} < m^{n+1}$.
Let $\ensuremath{\mathrm{ms}}(\varphi)$ denote the smallest size of a Parikh-reducing Church-Rosser representation of $\varphi$ and set
\begin{align*}
\ensuremath{\mathrm{ms}}(n,m) = \max\set{\ensuremath{\mathrm{ms}}(\varphi)}{\varphi : A^* \to M, \abs{A}\leq m, M\in \overline{\ensuremath{\varietyfont{Ab}}}, \abs{M}\leq n}
\end{align*}
to be the complexity over all possible homomorphisms with $\abs{A}\leq m$ and $\abs{M}\leq n$.
The base cases are $m=1$ or $M$ is a group. For $m=1$ there exists a system of size~$n$.
In all other cases we have the following recursion formula for $\ensuremath{\mathrm{ms}}(n,m)$:
\begin{align*}
\ensuremath{\mathrm{ms}}(n,m) \leq 2\ensuremath{\mathrm{ms}}(n,m-1)^2 \cdot \ensuremath{\mathrm{ms}}(n-1,m^{n+1}).
\end{align*}
Note that $n>1$ since $M$ is not a group.
Choose $c \in \mathbb N$ such that $\ensuremath{\mathrm{ms}}(n,m) \leq 2^{2^{m^{c(n+1)!}+n}}$ for all base cases. This is possible since the group case is in $2^{2^{m^{\mathcal O(n^2)}}}$. We show that $$\ensuremath{\mathrm{ms}}(n,m) \leq 2^{2^{m^{c(n+1)!}+n}}$$ in general.
Inductively, it holds
\begin{align*}
\ensuremath{\mathrm{ms}}(n,m) &\leq 2\ensuremath{\mathrm{ms}}(n,m-1)^2 \cdot \ensuremath{\mathrm{ms}}(n-1,m^{n+1})\\
&\leq 2\cdot 2^{2^{(m-1)^{c(n+1)!}+n+1}} \cdot 2^{2^{(m^{n+1})^{cn!}+n-1}}\\
&= 2^{1 + 2^{(m-1)^{c(n+1)!}+n+1} + 2^{m^{c(n+1)!}+n-1}} \\
&\leq 2^{2^{m^{c(n+1)!}+n}}.
\end{align*}
The last inequality holds because for $n,m>1$
\begin{align*}
(m-1)^{c(n+1)!} &\leq (m-1)^2\cdot m^{c(n+1)!-2} \\
&= m^{c(n+1)!} - (2m-1)m^{c(n+1)!-2} \\
&\leq m^{c(n+1)!}-3
\end{align*}
and thus $(m-1)^{c(n+1)!}+n+1 < m^{c(n+1)!}+n-1$.
\end{proof}
\section{Conclusion}
In this paper we introduced the notion of Parikh-reducing Church-Rosser representations. We were able to construct such representations in the case of languages in $\overline{\mathbf{Ab}}$ and for group languages over a two-element alphabet. Furthermore, we studied algebraic properties of such representations and the complexity of the corresponding systems. Several questions remain open as future work. Most importantly,
does there exist a finite Parikh-reducing Church-Rosser representation for every homomorphism into a finite group? Note that this already implies the case for every finite monoid by \prref{thm:group2variety}.
Another interesting open question is which algebraic properties can be preserved by Church-Rosser representations. For example, it seems unlikely that every homomorphism into a finite group has a Church-Rosser representation which is a group again, although it may happen in some special cases.
Additionally, there is a huge gap between our lower and upper bounds for the complexity.
Therefore it is interesting whether there are constructions for Church-Rosser representations which yield a better upper bound and what a good lower bound for the size of a Church-Rosser representation is.
\newcommand{Ju}\newcommand{\Ph}{Ph}\newcommand{\Th}{Th}\newcommand{\Ch}{Ch}\newcommand{\Yu}{Yu}\newcommand{\Zh}{Zh}\newcommand{\St}{St}\newcommand{\curlybraces}[1]{\{#1\}}{Ju}\newcommand{\Ph}{Ph}\newcommand{\Th}{Th}\newcommand{\Ch}{Ch}\newcommand{\Yu}{Yu}\newcommand{\Zh}{Zh}\newcommand{\St}{St}\newcommand{\curlybraces}[1]{\{#1\}}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 1,684 |
As iOS12 drops, we are again reminded that phone-based AR is on hundreds of millions of phones but we still haven't seen any big successes built on the new technologies.
Illumix is hoping that its approach to building games that understand where the user is while serving up content that responds to that space can help accelerate AR's popularity.
The Menlo Park-based company is emerging out of stealth today and sharing that they've raised an $8.6 million seed round co-led by Maveron and Lightspeed Venture Partners. Radar Partners, Unusual Ventures and Michael Bay's 451 Media also participated in the round.
The gaming studio is working on tech that allows gaming content to dynamically scale based on the environment. So, theoretically if you're playing an Illumix title in a big open area like a warehouse, it's going to look a lot different than if you fire up the app in your living room crammed with furniture. The startup is working on a couple of titles but is keeping them under tight wraps for now so I can't speak to how this technology works in practice though the concepts seems pretty technically challenging.
What's key is that this apparently won't require users to pre-scan their space and that the content will effortlessly adapt thanks to "real-time understanding of the environment taken from the way a user would normally hold their phone," Illumix co-founder Kirin Sinha tells TechCrunch.
While the tech is an important part, Sinha claims the company is very much a game studio first and foremost and that the startup's tech serves the creative ambition of their upcoming titles rather than just being developed to prove what is possible.
Next year, the studio plans to release a completely original title as well as a licensed game and will be using this latest bout of funding to grow the team of 11 and invest more in their upcoming work. | {
"redpajama_set_name": "RedPajamaC4"
} | 6,713 |
package io.spikex.filter.input;
import io.spikex.core.AbstractFilter;
import io.spikex.core.helper.Events;
import static io.spikex.core.helper.Events.EVENT_FIELD_TAGS;
import io.spikex.core.util.HostOs;
import io.spikex.filter.internal.CollectdJsonHandler;
import io.spikex.filter.internal.HttpResponse;
import io.spikex.filter.internal.NagiosNrdpHandler;
import io.spikex.filter.internal.ThingseeHandler;
import org.vertx.java.core.AsyncResult;
import org.vertx.java.core.AsyncResultHandler;
import org.vertx.java.core.Handler;
import org.vertx.java.core.VoidHandler;
import org.vertx.java.core.buffer.Buffer;
import org.vertx.java.core.eventbus.EventBus;
import static org.vertx.java.core.http.HttpHeaders.CONTENT_LENGTH;
import static org.vertx.java.core.http.HttpHeaders.CONTENT_TYPE;
import org.vertx.java.core.http.HttpServerRequest;
import org.vertx.java.core.json.JsonArray;
import org.vertx.java.core.json.JsonObject;
/**
*
* @author cli
*/
public final class HttpServer extends AbstractFilter {
private Handler<HttpResponse> m_handler;
private org.vertx.java.core.http.HttpServer m_server;
private static final String CONF_KEY_HOST = "host";
private static final String CONF_KEY_PORT = "port";
private static final String CONF_KEY_INPUT_FORMAT = "input-format";
private static final String CONF_KEY_SSL_ENABLED = "ssl-enabled";
private static final String CONF_KEY_KEYSTORE_PATH = "keystore-path";
private static final String CONF_KEY_KEYSTORE_PASSWORD = "keystore-password";
private static final String CONF_KEY_KEYSTORE_TYPE = "keystore-type";
private static final String CONF_KEY_TRUSTSTORE_PATH = "truststore-path";
private static final String CONF_KEY_TRUSTSTORE_PASSWORD = "truststore-password";
private static final String CONF_KEY_TRUSTSTORE_TYPE = "truststore-type";
private static final String CONF_KEY_CLIENT_AUTH_REQUIRED = "client-auth-required";
private static final String CONF_KEY_ADD_TAGS = "add-tags";
// Input formats
private static final String INPUT_FORMAT_JSON = "json";
private static final String INPUT_FORMAT_COLLECTD_JSON = "collectd-json";
private static final String INPUT_FORMAT_NAGIOS_NRDP = "nagios-nrdp";
private static final String INPUT_FORMAT_THINGSEE = "thingsee";
// Configuration defaults
private static final int DEF_PORT = 44120;
private static final String DEF_HOST = "localhost";
private static final String DEF_INPUT_FORMAT = INPUT_FORMAT_JSON;
@Override
protected void startFilter() {
final int port = config().getInteger(CONF_KEY_PORT, DEF_PORT);
final String host = config().getString(CONF_KEY_HOST, DEF_HOST);
String format = config().getString(CONF_KEY_INPUT_FORMAT, DEF_INPUT_FORMAT);
// Tags to add
JsonArray tags = config().getArray(CONF_KEY_ADD_TAGS, new JsonArray());
switch (format) {
case INPUT_FORMAT_JSON: {
m_handler = new JsonHandler(this, eventBus(), tags);
}
break;
case INPUT_FORMAT_COLLECTD_JSON: {
CollectdJsonHandler handler = new CollectdJsonHandler(this, config(), eventBus(), tags);
handler.init();
m_handler = handler;
}
break;
case INPUT_FORMAT_NAGIOS_NRDP: {
NagiosNrdpHandler handler = new NagiosNrdpHandler(this, config(), eventBus(), tags);
handler.init();
m_handler = handler;
}
break;
case INPUT_FORMAT_THINGSEE: {
ThingseeHandler handler = new ThingseeHandler(this, config(), eventBus(), tags);
m_handler = handler;
}
break;
default: {
m_handler = new JsonHandler(this, eventBus(), tags);
}
break;
}
m_server = vertx.createHttpServer();
m_server.requestHandler(new Handler<HttpServerRequest>() {
@Override
public void handle(final HttpServerRequest request) {
final Buffer body = new Buffer(0);
request.dataHandler(new Handler<Buffer>() {
@Override
public void handle(final Buffer buffer) {
body.appendBuffer(buffer);
}
});
request.endHandler(new VoidHandler() {
@Override
public void handle() {
// The entire body has now been received (keep it small)
String text = body.toString();
HttpResponse response = new HttpResponse(
request,
text);
try {
logger().trace("Received: {}", text);
m_handler.handle(response);
if (response.hasContent()) {
Buffer content = response.getContent();
request.response().putHeader(CONTENT_TYPE, response.getContentType());
request.response().putHeader(CONTENT_LENGTH, String.valueOf(content.length()));
request.response().end(content);
} else {
request.response().end();
}
} catch (Exception e) {
logger().error("Failed to parse: {}", text, e);
request.response().setStatusCode(500).end();
}
}
});
}
});
m_server.listen(port, host,
new AsyncResultHandler<org.vertx.java.core.http.HttpServer>() {
@Override
public void handle(AsyncResult<org.vertx.java.core.http.HttpServer> ar) {
if (ar.succeeded()) {
logger().info("Listening on {}:{}", host, port);
} else {
logger().error("Failed to bind to {}:{}", host, port);
}
}
});
}
@Override
protected void stopFilter() {
m_server.close();
}
private static class JsonHandler implements Handler<HttpResponse> {
private final AbstractFilter m_filter;
private final EventBus m_eventBus;
private final JsonArray m_tags;
private JsonHandler(
final AbstractFilter filter,
final EventBus eventBus,
final JsonArray tags) {
m_filter = filter;
m_eventBus = eventBus;
m_tags = tags;
}
@Override
public void handle(final HttpResponse response) {
// Try to parse json and emit new event
JsonObject data = new JsonObject(response.getBody());
JsonObject event = Events.createMetricEvent(
m_filter,
HostOs.hostName(),
"-",
"-",
"-",
"-",
0,
0);
event.mergeIn(data);
// Add tags
event.putArray(EVENT_FIELD_TAGS, m_tags);
String destAddr = m_filter.getDestinationAddress();
if (destAddr != null && destAddr.length() > 0) {
m_eventBus.publish(destAddr, event);
}
}
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 3,021 |
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What is the Process for Registering a Company in India?
Akshara Bala, created on 02 Nov 2018
If you want to register your company in Delhi, Bengaluru, Mumbai, Chennai or any other Indian city, here is a detailed guide on how you can start a company. Company registration process includes steps from choosing the type of company structure to applying for a certificate of incorporation.
Mandatory provisions to register a company in India have been given under the Companies Act, 2013. Before we move on to the company registration process in India, let's first understand certain basics.
This article is a comprehensive guide to registering a company in India. It covers the following aspects:
What is a Company?
What are the types of Companies that you can Register in India?
What are the minimum requirements for registering a company?
What is the Cost for Company Registration?
Steps for Company Registration in India
What are the Advantages of Registering a Company?
Our procedure for Company Registration
What are the documents required to register a company?
The meaning of a Company in India is any business, established as an artificial person under the law. A group of individuals form a company with the mutual goal of engaging in business for profits or any other such common purposes.
The Indian Companies Act, 2013, defines a company as:
A registered association which is an artificial legal person, having an independent legal entity with perpetual succession, a common seal for its signatures, a common capital comprised of transferable shares and carrying limited liability.
Registration of a Company in India
Company Registration is a process of incorporating a company and give it a legal status under the Indian law. The legal document called the Certification of Incorporation received at the end of the registration process is the legal proof of the existence of the company.
Both pre and post-incorporation formalities are governed by the provisions of the Indian Companies Act, 2013. The same is regulated by the Ministry of Corporate Affairs (MCA), Government of India.
Illegal Association
Any association or company of more than 50 members must be compulsorily registered under the Companies Act or any other India Law.
Failure to do so will go against Section 464 of the Act, and the company will be seen as an 'Illegal Association'.
What are the Types of Companies that You Can Register?
The Companies Act allows different types of companies to be registered in India. Based on the need and requirement, you can choose any business structure for the registration of a company in India.
Here is a brief note on the different structures available for company registration.
This is a type of company that is held by 'private individuals', such as the friends, relatives and associates of the founder. They are called members of the company of shareholder.
This types of company enjoy a separate legal existence, has limited liability and the Board of Directors manages the company.
This probably the most common business structure in India because it allows funding from investors and venture capitalists.
Several known companies like Facebook India and Google India are registered as Private Limited entities.
Read More: Advantages of Private Limited Company
A public company is almost the same as a private company, except regarding the ownership of the company.
Here the shares are freely traded by the public through the National Stock Exchanges and can be held by anyone.
Since the shares can be freely traded, a public company would have to meet more guidelines both under the MCA and SEBI in order to protect investor protection.
This type of company structure is chosen by large business, which has various subsidiaries and also has a lot of capital holding.
Popular examples include Tata Group of Companies and Infosys Technologies Limited.
One Person Company (OPC)
This is a fairly new form of business that was introduced in 2013. This structure gives the advantage of running a sole-proprietorship but with the benefits of a corporate framework.
Here, there is only one owner and promoter of a company.
A promoter can choose to appoint a director, or can himself act as the director of the company
Just like a private and public company, this business structure also enjoys a separate legal existence, and the owner's liability is limited.
More on: Advantages of One Person Company
Limited Liability Partnership (LLP)
LLP also enjoy limited liability but are registered under the Limited Liability Partnership Act, 2008. The partners are the owners and the management of the company.
Section 8 Companies
There are Non-profit companies set up under the Companies Act.
Such companies usually have charitable objectives such as the promotion of art, science, religion, sports, education, research, etc.
As opposed to other company forms, the profits are used for the benefits of people and the surplus, if any, is reinvested into the business.
Apart from this basic difference, Section 8 Companies enjoy all the corporate benefits of any other private or public company.
Other forms of business structures in India include Sole proprietorship, Partnership firms Hindu Undivided Family business. However, it is important to note that, these structures do not fall under the purview of the Companies Act.
Read More: Types of Non-Profit Organization in India
Importance of Choosing the Right Business Structure for Company Registration
Choosing the right business structure will define the way your business functions and would also affect the yearly compliances that the business is to follow.
Here is a look at why you should choose the appropriate business structure before you register your company:
Income tax calculation and filings differ based on the business structure
Different structures have different compliance formalities. This also involves the cost of compliances that also varies for each aspect of compliance. For instance, public companies have more compliance formalities than any other business structure.
Some structures are investor friendly (private companies), while others promote capital growth and business expansion (public companies).
The company registration is process is governed by the provision and guidelines of the Companies Act 2013. The Act specifies certain minimum requirements for incorporating a company in India.
While you have a choice of incorporating any type of company, the least requirements for company registration is for a Private Limited or One-Person Company.
Here are the minimum requirements for registering a private limited company or one person company:
1. Unique Name
To incorporate a company, you need to choose a Unique Name. The MCA would not approve any name which already exists or is similar to an existing company or a registered trademark.
What are the Guidelines for Choosing a Company Name?
The primary requirement for choosing a company name for registration is that is it unique.
The application for name approval is made using the MCA authorised RUN (Reserve Unique Name) online web service. After the application has been submitted, the Central Registration Centre (CRC) examines the application and decides of the approval and rejection of the name.
The MCA has given certain guidelines for choosing a company name. They are as follows:
While it isn't mandatory that the proposed name of the company should include the object of the company such as 'Marketing', 'informatics', 'technologies', etc., it is recommended to ensure uniqueness of the name. In such a situation, the Act prescribes that when the proposed name indicates the primary objective of the company, it should be reflective of the objects clause of the MOA.
The MCA advises applicants to conduct a name search to ensure that the proposed does not contain any prohibited words, is similar to the name of existing companies or is similar to any registered trademark.
If a foreign company is being registered in India, then the same name can be used after including the word 'India' along with the name of the company. Example: Google India, Microsoft India, etc.
The name should be suffixed by the type of business that it follows. Such as Private Company, Public Company, Limited Liability Partnership, etc. The suffix in the name should match the type of business organisation that the company functions as.
Abbreviated names cannot be registered as the name of a new company, such as SLU Private Limited. However, the exception to use abbreviations is allowed for well-known existing companies who can change their names to acronyms. For instance, Hindustan Unilever Limited can be altered to HU Limited.
The proposed name of the company cannot be similar to the name of a liquidated company unless two years have eclipsed from the date of such liquidation or dissolution.
When the name of the company has been struck off from the books of the registrar as a result of action under Section 560 of the Act, then the same name cannot be the proposed name of the new company unless 20 years have passed from the date of such strick-off action.
The proposed name of the company cannot only be limited to the name of a city, state, country or continent, such as Chennai Pvt. Ltd or Asia Limited.
The word 'State' can only be added to the name of the company when such a company is a government body.
If the name of the company includes the words like 'Bank', 'Stock Exchange', 'Asset Management', 'Nidhi', etc., then, the applicant would have to take the prior approval of the regulators such as RBI, SEBI, IRDA, etc.
2. First Shareholders
The shareholder of the company refers to the owners or the members of the company.
To incorporate a private limited company, a minimum of 2 shareholders are required. However, a one-person company will only require one member.
The Companies Act has not specified the minimum percentage of holdings that each member should have. Therefore, any ratio can be chosen.
For instance, one shareholder can hold 99% of the shares, and the other can hold the remaining 1%.
The first shareholders, also known as the promoters or founders of the company play an important aspect of company incorporation. They would float the MOA and AOA, and would also appoint the directors of the company.
3. Directors of the Company
The directors of any company are responsible for the management of the company. While they are separate for the shareholders of the company, the common practice is that the promoters of the company elect to be the first directors as well.
The Act specifies that the minimum amount of directors of a Private Limited Company should be 2, and cannot exceed a total of 15 director
The minimum directors required for a one person company is 1 and cannot exceed 15 directors
The proposed director of a company must have a DIN (Directors Identification Number). The Act specifies that only two people cannot have a DIN to incorporate a company.
Therefore, if three people what to start a company, a minimum of 2 people should have a DIN to be listed as the proposed director of the company. The other one can be the shareholder of the company. They can apply for a DIN later and be appointed as the director after the company can be incorporated.
A company can also be incorporated with foreign directors. However, at least one director should be a Resident of India. Even foreign directors should have a DSC and DIN.
Read More: How to Register for a DIN Number?
4. Capital Requirement
Capital is the amount of money that is required for the existence and functioning of the company.
Under the provisions of the Companies Act, there is no minimum capital requirement for registering a company.
There is no fixed cost for company registration, and it might vary based on several factors.
Here is a look at the factors that affect the total cost of registration
RUN Name Approval form
Government Fees based on the capital contribution
Stamp Duty which would vary from state to state
Notarization Cost
Additional charges for applying for DSCs, DIN, TAN and PAN.
Professional fees and GST if assistance is taken for a professional for company registration.
The Ministry of Corporate Affairs is taking steps to simplify the registration process for a new company. This is being done in an endeavour to promote the ease of doing business in India and encourage an entrepreneurial culture.
The Ministry promotes a very fast-track registration process, which is easily done through an online process. The process involves an online registration form, supported by scanned copies of the relevant documents and validated by the digital signature (DSC) of the applicant.
More on: Checklist documents required for Company Registration
Obtaining DSC (Digital Signature Certificate)
The members of the company who will be involved in the incorporation of the company would need to have a DSC. The DSC of the first shareholders would be required to sign the e-MOA and e-AOA of the company to upload the same with the Registrar of Companies (Roc). This makes DSCs for the first subscribers or promoters mandatory. Additionally, the proposed director would have to obtain a DIN, for which the DSC is compulsory.
Documents for DSC:
Passport photograph
Address proof (Self-attested)
Copy of PAN card (Self-attested)
Obtaining DIN (Director Identification Number)
The DIN numbers of the proposed directors are required to be intimated to the Ministry in the incorporation forms. Therefore, DIN is mandatory for the proposed directors of the company.
Documents for DIN registration:
DSC of the director
Company name via RUN Webservice
Before incorporating a company, the name of the company is to be reserved. To reserve the name of a new company or change the name of an existing company, a simple online service called RUN (Reserve Unique Name) is used.
The application for the company name is processed by the Central Registration Centre(CRC) under Non- Straight-through Processing mode. The CRC will conduct a comprehensive check and give its approval or rejection of the name. Each name submission is to be accompanied by fees of INR 1000.
Once the name is approved, it is valid for:
20 days: For a new company
60 days: For an existing company
Drafting of the e-MOA and e-AOA
The Memorandum of Association and Article of Association are essential documents for the incorporation of any company. Both of these documents define the internal and external relations of the company with its stakeholders.
MOA defines the objectives, capital, registered office, etc.
AOA defines the rules and regulation for running and managing the company.
Both these documents are drafted by professionals and must be submitted along with subscribers' sheet, which contains the DSCs of all the founding members.
Application for Incorporation
Once the necessary documents have been prepared, the following form will have to be filed to incorporate the company.
SPICe-32: Application for company incorporation
The following supporting documents would also have to be attached to these forms
e-MOA and e-AOA along with the signed subscribers' sheet
INC - 9 Affidavit and declaration by the first subscribers and directors of the company
Proof of office address: Lease deed / Conveyance / Rent agreement along with rent receipts
Utility bills of the registered office (not older than two months)
Form DIR – 2 (Consent of directors)
Note that, Form INC-22: Details of registered office address (might be required later if proof of address is not filed with the SPICe form)
Once all the procedures for company registration are complete, the Certificate of Incorporation will be issued to the company.
What is the time taken for company registration?
The Ministry has ensured that not only the incorporation process is simple, but has also expedited the time of company registration in India.
Usually, a company is registered within a period of 15-20 working days - Subject to the fact that all the documents are in order.
There are multiple reasons to register your company as opposed to running your business as a sole proprietorship or partnership entity.
Registration gives the company a positive public image. It creates a professional persona and builds credibility. Banks, financial institutions and investors also prefer a corporate set up for giving loans and investment, rather than a single-person run business structure.
Limited Liability of the Members
In a sole-proprietorship and partnership models, the liability of the proprietor or partners is unlimited. In a company, however, the liability of the members is limited to their investment. This protects their personal assets in the event of loss or debit of the company.
Separate Legal Entity
An incorporated company is a separate legal person in the eyes of the law. This means that the company would be responsible for its own actions and the owners cannot be held liable unless a criminal action is found.
Perpetual Succession
Since the company is established as a separate legal entity, it also means that it doesn't rely on its stakeholders for its survival. For instance, the company started by Dhirubhai Ambani is continuing as Reliance Industries today, year after his death.
Separation of Management
In a sole-proprietorship and partnership models, the owner and the management of the company are one and the same. However, a unique feature of a company is that the ownership is held by the shareholders and the management is done by the Board of Directors. This distinction allows the owners to hire competent people to run the affairs of the company.
Since the liability and gain of the business are not directly tied to the owners, it makes investors keener on investing in the company. Also, since the capital of the company of the company is entitled in shares, the ease of accumulating and distributing capital holdings to the members also becomes easier.
Dissolution of Company
As easy as it is to incorporate the company, it is also easy to dissolve the company and liquidate it. Unless and otherwise there are debts or judicial proceedings, a company can be would-up by making a request to the Registrar of Companies. In such a situation, the assets and the surplus capital will be distributed amongst the shareholder in accordance with their ratio of holdings.
In this article, we have covered all the aspects to register a company. If you need help registering a company in India our team of experts are just a call away.
At QuickComapny.in, we have extensive experience with company registration and related compliance. When you choose to register a company with us, we take care of almost all the compliance formalities, guiding you through each step.
Let's take a quick look at the company registration process that we follow and also a look at the basic documents that we need from you.
1. Understanding your Requirement
Once you book a company registration package with us, our representative will get in touch with you to understand your requirement, such as the type of company you wish to register, the number or first members and directors, the amount of paid-up capital, etc.
2. Obtain DSC, PAN and other documents
We would also help you apply for your various documents such as DSC and DIN for the proposed directors, PAN and TAN of the company. However, note that depending on the package cost, the cost of applying for these additional documents would vary.
3. Name approval
To ensure that you are able to register your company with the name of your liking, our representative will conduct a search to ascertain name availability. Six names would be submitted to the MCA for the process of name approval.
4. Preparing and Submission Application Form
Once the name has been approved, we will proceed to arrange the necessary documents such as e-MoA, e-AoA, SPICe form, etc. Upon your approval, the application is submitted by our representative on your behalf.
5. Incorporation
Once the company is incorporated, we will send all the documents. We will also help you with any other post incorporation compliance if required.
What are the Documents required for Company Incorporation?
We will require the following documents for registering your private limited, one-person company or limited liability partnership.
It is to be noted that, additional documents might be required, in case you would want to incorporate a Nidhi company, or register your business using Udyog Aadhar or as an MSME.
For incorporating a company in India, one scanned copies of the documents are required. This includes but is not limited to:
PAN Card of all directors
Identity proof of the directors such as Aadhar card, Voter ID, Passport (mandatory in the case of a foreign director) or Driving License.
Address Proof of all the directors such as Bank Statements, Electricity bills (or any other utility bill such as a mobile bill). These bills should not be older than two years and must be in the name of the director
Address proof of the registered office of the company:
Electricity bills (or any other utility bill such as a mobile bill). These bills should not be older than two years and must be in the name of the owner of the property.
The parent documents of the property registered office of the company (registration deed or property tax document), along with the No Objection Certificate (NOC) from the owner should be submitted. In such a case it would be assumed that any one of the first shareholders owns the property.
If the property is rented from a third-party, then, along with the NOC from the owner, the rent agreement would also be submitted. While the Ministry doesn't always insist on this, it's always best to submit it to avoid resubmission or the incorporation form.
The digital signatures (DSC) of all the parties involved in the registration process are also required. The DSC of the promoters, the first shareholders and directors, are also required. Based on the company incorporation package you have selected, the application for DSC of two directors would be undertaken; the rest would have to be applied for separately before commencing the incorporation process.
Although the company registration process set by the MCA is simple, it's always best to seek professional help while registering your company. There are various decisions to be made while incorporating a company, and in certain areas, experience goes a long way in simplifying the nitty-gritty of the process.
Click Here: Company Registration Online
FAQs - Company registration in India
Private Limited Company – Definition, Advantages and Incorporation Process
Limited Liability Partnership in India
LLP Registration Process
Foreigners as Shareholders in Private Limited Company
Private Limited Company to Limited Liability Partnership
Conversion of a Private Limited Company
Nidhi Company in India: Process, Eligibility and Benefits | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 1,660 |
{"url":"http:\/\/brane-space.blogspot.com\/2011\/12\/linear-algebra-solutions_30.html","text":"## Friday, December 30, 2011\n\n### Linear Algebra: Solutions\n\nThe last set of problems and their solutions:\n\n1) Recall t^A, found in Ex. 1 and let B =\n(-1...1)\n(1....0)\n\na) Find AB and thence: t^(AB)\n\nSolution:\n\nAB =\n\n(2...1) (-1....1)\n(3...1) (1.....0)\n\n=\n\n(-1.....2)\n(-2.....3)\n\nThen: t^(AB) =\n\n(-1.....-2)\n(2.......3)\n\nb) Verify that: t^AB = t^B t^A\n\nSolution:\n\nFrom Ex. (1) in previous linear algebra blog we found t^A=\n\n(2.....3)\n(1.....1)\n\nGiven the matrix for B in part (a) then, t^B =\n\n(-1...1)\n(1.....0)\n\nthen: t^B t^A =\n\n(-1....1)(2....3)\n(1.....0) (1....1)\n\n=\n\n(-1.......-2)\n(2.........3)\n\n2) Find the trace of: R3(\u0398) =\n\n(cos(\u0398)..........sin(\u0398)..........0)\n(-sin (\u0398)......cos(\u0398)...........0)\n(0 ..................0..................1)\n\nSolution:\n\nIrrespective of dimension the trace Tr is the sum of the diagonal elements. Then, Tr(R3(\u0398)) =\n\ncos(\u0398) + cos(\u0398) + 1 = 2cos(\u0398) + 1\n\n3) Let A =\n\n(cos \u0398 .....cos \u03c6)\n(cos \u03c6 .....sin \u0398)\n\nAnd let B = t^A\n\nFind: AB\n\nFrom this, t^A =\n\n(cos \u0398....cos \u03c6)\n(cos \u03c6......sin \u0398)\n\nThen AB=\n\n(cos \u0398 .....cos \u03c6)(cos \u0398....cos \u03c6)\n(cos \u03c6 .....sin \u0398)(cos \u03c6......sin \u0398)\n\n=\n(cos^2 \u0398 + cos^2 \u03c6...............cos \u0398cos \u03c6 + cos \u03c6 sin \u0398)\n(cos \u03c6 cos \u0398 + sin \u0398cos \u03c6 .............cos^2 \u03c6 + sin ^2\u0398)\n\n4) Find the traces of the following 3 x 3 matrices:\n\na) M1 =\n\n(-i.....0.......0)\n(0.......-7.....0)\n(0.......0.......4)\n\nSolution:\n\ntr(M1) = -i - 7 + 4 = -3 - i\n\nb) M2 =\n\n(3.....-2.......4)\n(1.......-4.....1)\n(-7.......-3......-3i )\n\nSolution:\n\ntr (M2) = 3 + (-4) + (-3i) = -1 - 3i\n\nc) A =\n(1.....-1......1)\n(2.......4.....1)\n(3.......0.......1)\n\nSolution:\n\ntr(A) = 1 + 4 + 1 = 6\n\nd) B =\n\n(3.....1.......2)\n(1.......1.....0)\n(-1.......2.......1)\n\ntr(B) = 3 + 1 + 1 = 5\n\n5) For the last two parts (c and d) of (4), show: tr(AB) = tr(BA)\n\nThis requires multiplying two 3 x 3 matrices:\n\nThen AB =\n\n(1.....-1......1) (3.....1.......2)\n(2.......4.....1)(1.......1.....0)\n(3.......0.......1)((-1....2....1)\n\n=\n\n(1....2.......3)\n(9.......8.....5)\n(8.......5.......7)\n\ntr(AB) = 1 + 8 + 7 = 16\n\nBA =\n\n(3.....1.......2)(1....-1...1)\n(1.......1.....0)(2.....4....1)\n(-1.......2.....1)(3....0...1)\n\n=\n\n(11....1......6)\n(3.......3.....2)\n(6.......9.......2)\n\ntr(BA) = 11 + 3 + 2 = 16\n\nThen: tr(AB) = tr(BA)","date":"2013-12-05 16:07:44","metadata":"{\"extraction_info\": {\"found_math\": false, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8372714519500732, \"perplexity\": 12024.766890572328}, \"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-2013-48\/segments\/1386163046801\/warc\/CC-MAIN-20131204131726-00009-ip-10-33-133-15.ec2.internal.warc.gz\"}"} | null | null |
Yes; after a careful thought and rumination over the issue, I decided to debut on this column on this topic that bothers on patriotism and altruism, two important aspects of true leadership. Yes, the town of Arochukwu, sincerely speaking, needs more of the leaders who will, first of all, think of the town of Arochukwu and what the town needs, and try to give it to her before thinking of what individuals therein will get first before remembering Arochukwu. Yes; first think of what you can do for Arochukwu ….
In the beginning, that was the case of Aro leaders: 'You First; I second.' This is the motto of the oldest college in the former Eastern Region of Nigeria located in the ancient city of Uzuakoli (that was founded in 1923) – Methodist College, Uzuakoli – the alma mater of the columnist. Until just recently, those who attended that citadel of learning were introduced, early in life, to the virtue of thinking about others first before thinking of themselves, including yours faithfully! Yes; students of Methodist College, Uzuakoli, are first introduced to thinking about the welfare, well-being, and the good of others before thinking of their own welfare, prosperity and well-being (as some other leaders had done in the past), and today, more than ninety percent of those who benefited from the training given at that college, have always exhibited acts of patriotism, altruism and selflessness – wherever they find themselves: the Michael Okparas, the Onyema Ugochukwus, the Clement Isongs, et cetera! Yes, the act of patriotism and selflessness has been the characteristic future of good leaders – even as exhibited by Jesus the Christ in the Bible, and all other of his followers and friends! They talked less of themselves and talked more of others, which is why mankind still exists today.
Patriotic and selfless services will always ensure the existence of any society. Self-centeredness and ego-centric actions portray selfishness and retrogression, and do not improve societies. That Nigerians are suffering today is because, unlike the pre-Independence politicians and those of First and Second Republics, today's politicians have 'Nigerianised' politics of self-centeredness and selfishness. While early politicians did all to provide all they could provide for all the people (that ensured societal growth), today's politicians (beginning from 1999) are just after what enters into their pockets as individuals!
This is the case with Arochukwu. While Aro leaders and politicians (of yester-years) had the interest of Aro in mind in all they did, today's Aro leaders (including our political representatives) have become very selfish, self-centered and ego-centric that they do not care for Arochukwu again!
They are after amassing wealth and doing those things that must benefit them first, unlike the thinking of Alvan Ikoku and the other Ikokus, the TK Utchays, the Nwakamma Okoros, the Kanu Ojis, the Udenyis, et cetera. Those did not think for their pockets alone; they wanted the progress of their town too in their pursuits in life.
If Alvan Ikoku had been selfish; if Eze Kanu Oji had been selfish; if Nwakawma Okoro had not been patriotic, they all would have acquired all the pieces of land in Arochukwu that many of us coming behind them would not have been able to see where to build our houses today in Arochukwu!
It is because of selfish leadership in Arochukwu hitherto that all inter- and intra Aro roads have been deplorable but have been built and tarred on television, radio channels and news bulletins on the imagination of these 'leaders'! It is because of selfish life that the construction of the Ozuabam-Ndiokereke-Arochukwu road has lingered since 1985. It is because of selfishness that government appointments have been eluding Arochukwu indigenes. It is because of selfish leadership style of today's Aro leaders that the Aro Civic Hall project (at Oror) has not been completed for about forty years now!
Sincerely speaking, Arochukwu needs more patriotic and selfless leaders now than ever before. Yes, we need more 'You First; I Second' generation of Aro leaders for the town to survive.
Yes, we really need them urgently. | {
"redpajama_set_name": "RedPajamaC4"
} | 2,189 |
\section*{ Reconstruction of $SU(5)$ Grand Unified Model In Noncommutative
Geometry Approach }
Jianming Li\footnote{
Email address: lijm@itp.ac.cn} and Xingchang Song
\\
Department of Physics, Peking University, Beijing 100871, China
\end{center}
\begin{abstract}
Based on the generalized gauge theory on $M^4\times Z_2\times
Z_3$, we reconstructed the realistic $SU(5)$ Grand Unified model by a suitable
assignment of fermion fields.
The action of group elements $Z_2$ on fermion fields is the charge
conjugation while the action of $Z_3$ elements represent generation translation.
We find
that to fit the spontaneous
symmetry breaking and gauge hierarchy of $SU(5)$
model a linear term of curvature has to be introduced. A new mass relation is
obtained in our reconstructed model.
\end{abstract}
\vskip 1cm
{PACS number(s): 02.40. -k, 11.15. -q, 12.10. Dm}
\newpage
\section[toc_entry]{Introduction}
In recent years,
it is believed that Non-commutative geometry extends the basic
geometry framework of physics\cite{connes,madore}. The most remarkable results
are
that in Standard Model the
Higgs fields may be considered as a kind of gauge field by
the same
footing as Yang-Mills fields and the Yukawa couplings can be
introduced as a kind of gauge coupling. These topics have been
studied by many works\cite{conlot}---\cite{morita}.
It is also interesting to quest whether the same description stands when we go
from Standard Model to Grand Unification theories (e.g. $SU(5)$
GUT\cite{georgi}), in which Higgs fields are introduced as input data in model
building.
By enlarging the discrete points model first proposed by A.Connes\cite{connes,
conlot}, A. Chamsedine et al \cite{ali} provided a generalized formula, which
gave a clue to study more extensive model beyond the
Standard Model, such as $SU(5)$ and $SO(10)$ Grand unified
models. But there are lots of details need to be further studied .
In our previous works\cite{mine1,mine2}, we constructed generalized gauge theory
on
discrete group $Z_2$. In this approach, we enlarged space-time to five
dimensions with the 5-th ``coordinate" containing only two points of $Z_2$,
assigned
left and right handed Fermion fields according to the
discrete group
``coordinate'' and wrote down a Lagrangian of fermion
fields,
which is not only the function of the space--time coordinates but also of the
discrete
group "coordinate". The most
important point of this approach was that the derivatives on discrete group were
included in
the Lagrangian. Similar to the case of the ordinary Yang--Mills gauge theory,
when we require
the
Lagrangian be
invariant under the gauge group which is a function of space time
and of discrete
group, then Higgs appear in the covariant derivative and
Yukawa coupling is
naturally introduced by the gauge coupling. Furthermore,we constructed the
Weinberg-Salam model and the Eleactroweak-strong interaction model and
tried to
endow discrete group with some physical meaning .
In this paper, we first develop our previous approach to the case of $M^4\times
Z_2\times Z_3$
and reconstruct the realistic $SU(5)$
Grand Unified model of three
generation fermions with generalized gauge theory on
$M^4\times Z_2\times Z_3$. A similar generalized gauge theory on $M^4\times
Z_2\times Z_3$ has also been discussed in a $CP$ violation toy
model\cite{ding}.
We distinguish the left and right hand parts of fermions by
two
elements of the discrete group $Z_2$, differentiate three families by three
elements of the discrete group $Z_3$ and connect fermions by charge
conjugation
transformation on discrete points of $Z_2$ and by generation translation on
discrete points of $Z_3$. Since there are two mass scales in the $SU(5)$
model
characterizing the spontaneous symmetry breaking of $SU(5)$ to $SU(3)\times
SU(2)\times U(1)$ and then to $SU(3)\times U(1)$, if we want to get this gauge
hierarchy, we need to add the linear term of curvature $F$, which is first
proposed by Sitarz\cite{sitarz}.
The plan of this paper is as follows. In section 2, we give the basic notion
of
gauge theory on
$M^4\times Z_2\times Z_3$. In section 3, we build $SU(5)$ model using the
generalized gauge theory on $M^4\times Z_2\times Z_3$. In section 4, we discuss
the
symmetry broken phenomenon.
\bigskip
\section[toc_entry]{Notation of gauge theory on $M^4\times Z_2\times Z_3$}
In this section we shall give the basic notion of construction
gauge theory on
$M^4\times Z_2\times Z_3$. More detailed account of
construction can be found in
\cite{sitarz, mine1}.
Let $x^\mu$ denote the coordinate on $M^4$ and $g$ label the
points of discrete
group $Z_2\times Z_3$. The differentiation of an arbitrary function on
product space
$M^4\times
Z_2\times Z_3$ has the following form,
\begin{eqnarray}
df=\partial_\mu f dx^\mu+\partial_g f \chi^g, g\in
Z_2\times Z_3,\end{eqnarray}
where
$dx^\mu$ and $\chi^g$ are basis of one forms on $M^4$ and
$Z_2\times Z_3$ respectively.
The partial derivative $\partial_g$ is defined as follows:
\begin{eqnarray}
\partial_g f(x,h)=(f(x,h)-R_g f(x,h))=(f(x,h)-
f(x,h\cdot g)).\end{eqnarray}
From the defination we can obtain a lot of ralations: ones for the product of
one-forms
\begin{eqnarray}\begin{array}{cl}
&dx^\mu \hat\otimes dx^\nu=-dx^\nu \hat\otimes dx^\mu\\
&dx^\mu \hat\otimes \chi^g=-\chi^g\hat\otimes dx^\mu,\end{array}\end{eqnarray}
ones for the multiplication of one-form by functions
\begin{eqnarray}
f(x,h)dx^\mu =dx^\mu f(x,h),~~~\chi^g f(x,h)=R_g f(x,h)
\chi^g,\end{eqnarray}
and ones by acting derivative operator on one forms
$$ddx^\mu=0,~~d\chi^g=-C^g_{p,h} \chi^p\hat\otimes \chi^h,$$
where structure constants
$C^g_{p,h}=\delta^g_p+\delta^g_h-\delta^g_{ph}(\delta^e_{ph}-1)$.
The general gauge potential $A$ on $M^4\times Z_2\times Z_3$
can be written as:
\begin{eqnarray}
A=A_\mu dx^\mu+
\displaystyle\sum_{\tiny \begin{array}{c}g\in Z_2\times Z_3\\ {g\neq
e}\end{array}} \phi_g\chi^g\end{eqnarray}
The unitarity of gauge group enforces that $A^*=-A$. Thus,
since
$(dx^\mu)^*=dx^\mu$ and $({\chi}^{g})^{*}=-{\chi}^{g^{-1}}$,
we obtain
$$(A_\mu)^{\dag}=-A_\mu,~~\phi_g^{\dag}=R_g \phi_{g^{-1}}.$$
The curvature two form
$
F=dA+A\hat\otimes A$ splits into terms,
\begin{eqnarray}
F=\frac 1 2 F_{\mu\nu} dx^\mu\hat\otimes dx^\nu+F_{\mu
g}dx^\mu\hat\otimes \chi^g+
F_{gh} \chi^g\hat\otimes \chi^h,\end{eqnarray}
where
$$F_{\mu\nu}={\partial}_{\mu}A_{\nu}-{\partial}_{\nu}A_{\mu}+
[A_{\mu},A_{\nu}], $$
\begin{eqnarray}
F_{ \mu g}={\partial}_{\mu}\Phi_g+ A_{\mu}\Phi_g-\Phi_g
R_{g}( A_{\mu}),
\end{eqnarray}
$$
F_{gh}={\partial}_{g}{\phi}_{h}+{\phi}_{g}{R}_{g}{\phi}_{h}-
{{C}^k_{gh}}{\phi}_{k}\label{C} $$
with $\Phi_g=1-\phi_g$.
To construct the Yang-Mills action, we need to define the metric
\begin{eqnarray}\begin{array}{cl}
&<{dx}^{\mu},{dx}^{\nu}>=g^{\mu\nu},~~~~<{\chi}^{g},{\chi}^{h}
>=
{\eta}^{gh},\\[4mm]
&<{dx}^{\mu}\wedge {dx}^{\nu},{dx}^{\sigma}\wedge{dx}^{\rho}>=
\frac{1}{2}(g^{\mu\sigma}g^{\nu\rho}-g^{\mu\rho}g^{\nu\sigma})
,\\[4mm]
&<{dx}^{\mu}\otimes{\chi}^{g},{dx}^{\nu}\otimes{\chi}^{h}>=
g^{\mu\nu}{\eta}^{gh},\\[4mm]
&<{\chi}^{g}\otimes {\chi}^{h},{\chi}^{g'}\otimes
{\chi}^{h'}>=
{\eta}^{gg'}{\eta}^{hh'}.\end{array} \end{eqnarray}
where $\eta^{gh}=\eta_g \delta^{gh^{-1}}$. After taking such a form
of the metric, the Yang-Mills Lagrangian becomes
\begin{eqnarray}\begin{array}{cl} {\cal
L}_N=&-{1\over N}\displaystyle\int_G <F,\overline{F}>\\ &={1\over
N}\displaystyle\int_G (-\frac 1 4 F_{\mu\nu}F^{\dag\mu\nu}+ \eta_g F_{\mu
g}F^{\dag\mu}_{ g}-\eta_g
\eta_h F_{gh} F^{\dag}_{gh}) \end{array}\end{eqnarray}
It was found\cite{sitarz} that there exist a
possibility of adding an extra gauge invariant term to the Yang-Mills action,
which is linear in the curvature $<F>$,
\begin{eqnarray} \begin{array}{cl} {\cal L}_{L}=&-{1\over N}\displaystyle\int_G<F>\\ &=-{1\over
N}\displaystyle\int_G F_{gh}\eta^{gh}= -{1\over N}\displaystyle\int_G \eta_g
F_{gg^{-1}}.\end{array} \end{eqnarray}
Let us add this term to Yang-Mills action with an arbitrary
scaling parameter $\alpha$. We obtain the bosonic sector Lagrangian
\begin{eqnarray} {\cal
L}={\cal L}_N+\alpha {\cal L}_L.\end{eqnarray}
In the next section, we will find that this
Lagrangian
is needed in the construction of the $SU(5)$ model.
\setcounter{sec}{3}
\setcounter{equation}{0}
\section[toc_entry]{Generalized $SU(5)$ gauge theory on $M^4\times Z_2\times
Z_3$}
In this section, we build the $SU(5)$ gauge theory on $M^4\times Z_2\times
Z_3$ by using generalized gauge theory on discrete group\cite{mine1, mine2}.
According to the basic
knowledge of $SU(5)$ model, we first set fermion fields on discrete group, then
write down gauge fields in terms of gauge potential, at last give Lagrangian of
gauge
fields by noncommutative differential geometry approach.
\subsection[toc_entry]{Fields on $M^4\times Z_2\times Z_3$}
From the basic knowledge of $SU(5)$ model \cite{licheng}, we know that
one family of left(or right) handed fermions can be accommodated
in an $SU(5)$
reducible representation of $5^*+10$(or $5+10^*$).
According to representation of $SU(5)$, we write down the
first family fermions
as following:
\begin{eqnarray}\begin{array}{cl}
5^*:&\psi_L=\left[\begin{array}{cl}&d_1^C\\&d_2^C\\&d_3^C\\&e^-\\
&-\nu_e\end{array}\right]_L,
~~~~~5:\psi^C_R=\left[\begin{array}{cl}&d_1\\&d_2\\&d_3\\
&e^+\\&-\nu^C_e\end{array} \right]_R\\[15mm]
10:&\chi_L={1\over \sqrt{2}}\left
[\begin{array}{ccccc}0&u^C_3&-u^C_2&u_1&d_1\\
-u^C_3&0&u^C_1&u_2&d_2\\
u^C_2&-u^C_1&0&u_3&d_3\\
-u_1&-u_2&-u_3&0&e^+\\
-d_1&-d_2&-d_3&-e^+&0\end{array}\right]_L,\\[15mm]
10^*:&\chi^c_R={1\over \sqrt{2}}\left
[\begin{array}{ccccc}0&u_3&-u_2&u^C_1&d^C_1\\
-u_3&0&u_1&u^C_2&d^C_2\\
u_2&-u_1&0&u^C_3&d^C_3\\
-u^C_1&-u^C_2&-u^C_3&0&e^-\\
-d^C_1&-d^C_2&-d^C_3&-e^-&0\end{array}\right]_R.\end{array}\end{eqnarray}
The other two families can be written similarly by replacing $u,d,e,\nu_e$
by $c,s,\mu,\nu_\mu$ and $t,b,\tau,\nu_\tau$. From observation of
three
family fermions and
their left-right hand parts, $5^*+10$ and $5+10^*$, we find it
is possible to
assign them with respect
to elements of discrete group $Z_2\times Z_3$, which is
product of discrete
groups $Z_2$ and $Z_3$.
Discrete group $Z_2$ has two elements $Z_2=\{e,Z|Z^2=e\}$,
discrete group $Z_3$
has three elements
$Z_3=\{e,r,r^2|r^3=e\}$. So the direct product group $Z_2\times Z_3$
has six elements
$$Z_2\times Z_3=\{e,r,r^2Z,Z r,Z r^2|Z^2=e,r^3=e,Zr=rZ\}.$$
In this paper, we use two elements of $Z_2$ to distinguish
left-right hand
fermions and use three
elements of $Z_3$ to distinguish three families. So our
working manifold should be
$M^4\times Z_2\times
Z_3$.
According to discrete group $Z_2\times Z_3$,
we arrange Fermions as following:
\begin{eqnarray}\begin{array}{cl}
&\psi(x,e)=\left[\begin{array}{cl}\psi^C\\\chi^C\end{array}\right]^1_R,~~
\psi(x,r)=\left[\begin{array}{cl}\psi^C\\\chi^C\end{array}\right]^2_R,~~
\psi(x,r^2)=\left[\begin{array}{cl}\psi^C\\\chi^C\end{array}\right]^3_R,\\[5mm]
&\psi(x,Z)=\left[\begin{array}{cl}\psi\\\chi\end{array}\right]^1_L,~~
\psi(x,rZ)=\left[\begin{array}{cl}\psi\\\chi\end{array}\right]^2_L,~~
\psi(x,r^2 Z)=\left[\begin{array}{cl}\psi\\\chi\end{array}\right]^3_L\end{array},\end{eqnarray}
where $\left[\right]^i$ represents the $i$-th generation of
Fermions.
It is important to note that the actions $R_g,g\in Z_2\times
Z_3$ on
fermions have definite physical meaning. We find that the
action $R_Z$ is
nothing but the charge
conjugation transformation, which inter-changes left-right hand
fermions in
$5^*+10$ and $5+10^*$
and the action $R_{r^i},i=1,2,3$ is the
translation between
different generations,
$$R_{r^i} \psi^j=\psi^{\left[(i+j)|Mod~ 3\right]},~~~~i=1,2; ~~j=1,2,3$$
As we did in \cite{mine1,mine2}, to build gauge theory on space $M^4\times
Z_2\times Z_3$, we
should introduce free fermion Lagrangian first,
\begin{eqnarray}\begin{array}{cl}
{\cal L}(x,g)=&\overline{\psi}(g)\left [i\gamma^\mu
(\overrightarrow{\partial}_\mu-
{\overleftarrow\partial}_\mu)-U(\partial_Z+\partial_{Zr}+
\partial_{Zr^2})-U_1(\partial_{r}+\partial_{r^2})\right ]\psi(g),\\
&g\in
Z_2\times Z_3\end{array}
\label {ffl}\end{eqnarray}
where $U$, $U_1$ are parameters with mass dimension. Here we just choose two
free parameters in front of partial derivatives of discrete group, a special
case that
depend on the model to be building, since these parameters are
directly related to
the mass
of
Higgs particles and there are only two mass scales of Higgs fields in minimum
$SU(5)$
model. In fact, $U$ and $U_1$ are parameters relate to the distance among
discrete points in non-commutative geometry approach.
Similar to the reason that leads to the introduction of
Yang-Mills fields, it is
reasonable to require that the Lagrangian (\ref {ffl}) be
invariant under gauge
transformations $H(x,g),g \in Z_2\times Z_3$, where $H$ are functions depending
not
only
on $M^4$ but also on discrete group. So one should
introduce covariant
derivative in Lagrangian (\ref {ffl}).
Gauge invariant Lagrangian under $SU(5)$ group should be
written as follows:
\begin{eqnarray}\begin{array}{cl}
&{\cal L}_F(x,g)=\overline{\psi}(g)\left[i\gamma^\mu
(\overrightarrow{D}_\mu-
{\overleftarrow D}_\mu)-U(D_Z+D_{Zr}+
D_{Zr^2})-U_1(D_{r}+D_{r^2})\right]\psi(g),\\[5mm]
&D_\mu=\partial_\mu+ig A_\mu, ~~~~D_g=\partial_g+\phi_g R_g,~~g\in
Z_2\times Z_3,
\label{fflc}
\end{array}
\end{eqnarray}
where
\begin{eqnarray}
A(e)=\left[\begin{array}{cc}\left(
A_{k,l}\right)&\\&\left(A^*_{mn,pq}\right)\end{array}
\right],~~
A(Z)=\left[\begin{array}{cc}\left( A^*_{k,l}\right)&\\&\left(
A_{mn,pq}\right)\end{array}\right],
\end{eqnarray}
$\left(A_{k,l}\right)$ is a $5\times 5$ matrix valued on $24$ generators of
$SU(5)$ group and the
corresponding
matrix elements are $A_{k,l}$; $\left(A_{mn,pq}\right)$ is a
$25\times 25 $
matrix
with $mn,pq$ denoting the row and column indices of the matrix and the
matrix element are
$$A_{mn,pq}=A_{m,p}\delta_{n,q}+A_{n,q} \delta_{m,p}.$$
Because the gauge transformations are independent of
generations, we should set
Yang-Mills potentials to be the same in different generations.This means
$A(e)=A(r)=A(r^2)$ and $A(Z)=A(rZ)=A(r^2 Z)$.
In minimum $SU(5)$ model, there are two Higgs multiplets which belong to the
adjoint and the
vector representations respectively. Only the vector Higgs field
appears in
Yukawa coupling. In Yukawa terms of Lagrangian (\ref {fflc}), it is easy to find
that $\phi_Z$, $\phi_{rZ}$, $\phi_{r^2 Z}$ connect left-right hand fermions and
$\phi_r$,$\phi_{r^2}$ connect fermions with the same chirality. So only
$\phi_Z$,
$\phi_{rZ}$, $\phi_{r^2 Z}$ fields appear in Yukawa terms while
$\phi_r$,$\phi_{r^2}$ fields do not. To get the minimum $SU(5)$ model, we
arrange
vector representation in $\phi_Z$, $\phi_{rZ}$, $\phi_{r^2 Z}$ and adjoint
representation in $\phi_r$, $\phi_{r^2}$. Thus we write down the Higgs fields
as
following,
$$\begin{array}{ccc}
g=e&g=r&g=r^2\\[5mm]
\phi_Z(g)
=\tiny{\left[\begin{array}{cc}0&f_{11}\left(H^*_{i,mn}\right)\\f_{11}
\left(H^*_{pq,j}\right)&e_{11}\left(H_{pq,mn}\right)\end{array}\right]};
&
\tiny{\left[\begin{array}{cc}0&f_{22}\left(H^*_{i,mn}\right)\\f_{22}
\left(H^*_{pq,j}\right)&e_{22}\left(H_{pq,mn}\right)\end{array}\right]};
&
\tiny{\left[\begin{array}{cc}0&f_{33}\left(H^*_{i,mn}\right)\\f_{33}
\left(H^*_{pq,j}\right)&e_{33}\left(H_{pq,mn}\right)\end{array}\right]}
\\[7mm]
\phi_{rZ}(g)
=\tiny{\left[\begin{array}{cc}0&f_{21}\left(H^*_{i,mn}\right)\\f_{12}
\left(H^*_{pq,j}\right)&e_{12}\left(H_{pq,mn}\right)\end{array}\right]};
&
\tiny{\left [\begin{array}{cc}0&f_{32}\left(H^*_{i,mn}\right)\\f_{23}
\left(H^*_{pq,j}\right)&e_{23}\left(H_{pq,mn}\right)\end{array}\right]};
&
\tiny{\left [\begin{array}{cc}0&f_{13}\left(H^*_{i,mn}\right)\\f_{31}
\left(H^*_{pq,j}\right)&e_{31}\left(H_{pq,mn}\right)\end{array}\right]}
\\[7mm]
\phi_{r^2 Z}(g)
=\tiny{\left [\begin{array}{cc}0&f_{31}\left(H^*_{i,mn}\right)\\f_{13}
\left(H^*_{pq,j}\right)&e_{13}\left(H_{pq,mn}\right)\end{array}\right]};
&
\tiny{\left [\begin{array}{cc}0&f_{12}\left(H^*_{i,mn}\right)\\f_{21}
\left(H^*_{pq,j}\right)&e_{21}\left(H_{pq,mn}\right)\end{array}\right]};
&\tiny{
\left [\begin{array}{cc}0&f_{23}\left(H^*_{i,mn}\right)\\f_{32}
\left(H^*_{pq,j}\right)&e_{32}\left(H_{pq,mn}\right)\end{array}\right]}
\end{array}$$
where $\left(H_{i,mn}\right)$ is a $5\times 25 $ matrix,
$\left(H^*_{pq,j}\right)$
is a $25 \times 5$ matrix, $H_{pq,mn}$ is a $25 \times 25$ matrix
and the elements
are
$$H_{i,mn}=H_m\delta_{i,n}-H_n\delta_{i,m},$$
$$H_{pq,j}=H_p\delta_{q,j}-H_q\delta_{p,j},$$
$$H_{pq,mn}=\epsilon_{pqmnk} H_k$$
Higgs fields on discrete points $Z,rZ,r^2 Z$ may be defined by
Hermitian
condition
$\phi^{\dag}_g=R_g \phi_{g^{-1}}$, which are
$\phi^{\dag}_Z=R_Z \phi_Z, \phi^{\dag}_{rZ}=R_{rZ} \phi^{\dag}_{r^2
Z},
\phi^{\dag}_{r^2 Z}=R_{r^2 Z}\phi_{rZ}$.
The other two components of Higgs fields $\phi_r, \phi_{r^2}$
are set as,
{ $$\begin{array}{cccc}
&g=e&g=r&g=r^2\\[5mm]
\phi_r(g)=&I \tiny{\left[\begin{array}{cc}t_1\left(\sum_{i,j}\right)&\\
&s_1\left(\sum^*_{pq,mn}\right)\end{array}\right]};
&I\tiny{\left[\begin{array}{cc}t_2\left(\sum_{i,j}\right)&\\
&s_2\left(\sum^*_{pq,mn}\right)\end{array}\right]};
&I\tiny{\left[\begin{array}{cc}t_3\left(\sum_{i,j}\right)&\\
&s_3\left(\sum^*_{pq,mn}\right)\end{array}\right]}
\end{array}$$
$$\begin{array}{cccc}
&g=Z&g=rZ&g=r^2 Z\\[5mm]
\phi_r(g)=&I\tiny{\left[\begin{array}{cc}t_1\left(\sum^*_{i,j}\right)&\\
&s_1\left(\sum_{pq,mn}\right)\end{array}\right]};
&I\tiny{\left[\begin{array}{cc}t_2\left(\sum^*_{i,j}\right)&\\
&s_2\left(\sum_{pq,mn}\right)\end{array}\right]};
&I\tiny{\left[\begin{array}{cc}t_3\left(\sum^*_{i,j}\right)&\\
&s_3\left(\sum_{pq,mn}\right)\end{array}\right]},
\end{array}$$
where $I=\sqrt {-1}$ and $t_i$ $s_i$ are real parameters,
$$\Sigma_{pq,mn}=\Sigma_{p,q}\delta_{q,n}+\Sigma_{q,n}
\delta_{p,m}$$
$\left(\Sigma_{i,j}\right)$ is a $5\times 5$ traceless Hermitian matrix,i.e
$\left(\Sigma_{i,j}\right)=
\left(\Sigma_{i,j}\right)^{\dag}$ and $Tr \sum$=0.
The Hermitian condition $\phi^{\dag}_{r^2}=R_{r^2} \phi_r$
gives the
values of $\phi_{r^2}$ on discrete points as,
$$\begin{array}{cccc}
&g=e&g=r&g=r^2\\[5mm]
\phi_r(g)=&\tiny{-I\left[\begin{array}{cc}t_3\left(\sum_{i,j}\right)&\\
&s_3\left(\sum^*_{pq,mn}\right)\end{array}\right]};
&\tiny{-I\left[\begin{array}{cc}t_1\left(\sum_{i,j}\right)&\\
&s_1\left(\sum^*_{pq,mn}\right)\end{array}\right]};
&\tiny{-I\left[\begin{array}{cc}t_2\left(\sum_{i,j}\right)&\\
&s_2\left(\sum^*_{pq,mn}\right)\end{array}\right]}
\end{array}$$
$$\begin{array}{cccc}
&g=Z&g=rZ&g=r^2 Z\\[5mm]
\phi_r(g)=&-I\tiny{\left[\begin{array}{cc}t_3\left(\sum^*_{i,j}\right)&\\
&s_3\left(\sum_{pq,mn}\right)\end{array}\right]};
&-I\tiny{\left[\begin{array}{cc}t_1\left(\sum^*_{i,j}\right)&\\
&s_1\left(\sum_{pq,mn}\right)\end{array}\right]};
&-I\tiny{\left[\begin{array}{cc}t_2\left(\sum^*_{i,j}\right)&\\
&s_2\left(\sum_{pq,mn}\right)\end{array}\right]}.
\end{array}$$
Actually, we impose a symmetry
$$R_Z \phi=-\phi^{*}$$
in the assignments of the fields $\phi_r,\phi_{r^2}$. It is
interesting to find
that
this constraint corresponds to the discrete symmetry which was introduced in
standard $SU(5)$
grand unification
model.
In $SU(5)$ model, we require the Higgs potential terms is
invariant under
transformation $H\rightarrow-H$, $\sum\rightarrow -\sum$, which
can remove
unwanted
terms in the potential.
\subsection[toc-entry]{Lagrangian of Model}
After taking the assignments of Yang-Mills fields and Higgs fields ,
now we are ready to write down the Lagrangian of fermionic
sector form (\ref {fflc}) ,
which include couplings
of gauge fields.
\begin{eqnarray}\begin{array}{cl}
{\cal L}_F=&\displaystyle\sum_{A,k}\overline{\psi}_{k,A}i
\gamma^\mu{D}_\mu\psi_{k,A}+
\sum_{A,k,l}\overline{\chi}_{kl,A}i\gamma^\mu{D}_\mu\chi_{kl,A
}\\[5mm]
&\displaystyle+2\sum_{A,B}\sum_{pqklm}M_{1A,B}\overline{\chi^C}_
{pq,A}\chi_{kl,B
}
\epsilon_{pqklm}H_m+h.c.\\[5mm]
&\displaystyle+\sum_{A,B,k,l}M_{2A,B}\overline{\chi^C}_{kl,A}\psi
_{k,B}
H^{\dag}_l+h.c.\end{array}
\end{eqnarray}
where $A,B$ are generation indices, the other indices are that of $SU(5)$ group
and $M_{1A,B}$ $M_{2A,B}$ are elements of matrix $$M_1=\left
[\begin{array}{ccc}f_{11}&f_{12}&f_{13}\\
f_{21}&f_{22}&f_{23}\\f_{31}&f_{32}&f_{33}\end{array}\right]$$
$$M_2=\left
[\begin{array}{ccc}e_{11}&e_{12}&e_{13}\\e_{21}&e_{22}&e_{23}
\\e_{31}&e_{32}&e_{33}\end{array}\right].$$
It is easy to show that
\begin{eqnarray}
\overline{\chi^C}_{ij,A}\chi_{kl,B}\epsilon_{ijklm}H_m=
\overline{\chi^C}_{kl,B}\chi_{ij,A}\epsilon_{ijklm}H_m,\end{eqnarray}
so we set $M_2$ to be symmetric matrix, i.e $e_{AB}=e_{BA}$, or
$$M_2=\left
[\begin{array}{ccc}e_{11}&e_{12}&e_{13}\\e_{12}&e_{22}&e_{23}
\\e_{13}&e_{23}&e_{33}\end{array}\right].$$
The Lagrangian of bosonic sector may be derived from the
generalized differential
calculation on $M^4\times Z_2\times Z_3$. Using those assignments of fields on
discrete groups and the basic knowledge of non-commutative geometry, we can
obtain the Lagrangian of gauge fields. In the calculation, for simplicity, we
set $\eta_Z=\eta_{rZ}=G$ and note $\eta_{r}=G_1$. Because the calculation is
fairly
cumbersome, we only write the result here.
\begin{eqnarray}\begin{array}{clll}
{\cal L}_G &=&-{1\over N}<F,\overline{F}>\\[4mm]
&=& -{g^2\over 4N} 66 F_{\mu\nu} F^{\mu\nu}+
{16\beta\over N} {G\over U^2}D_\mu H^{\dag} D^\mu H\\[4mm]
&&+{4 \alpha\over N}{G_1\over U^2_1} Tr(D_\mu \Sigma^{\dag} D^\mu
\Sigma)-
[V(H,\Sigma)+V(\Sigma)+V(H)]\end{array}\end{eqnarray}
where
$$\alpha=t^2_1+t^2_2+t^2_3+10(s^2_1+s^2_2+s^2_3),$$
$$\beta=Tr(2M_1M^{\dag}_1+3M_2M^{\dag}_2),$$
and
$$\begin{array}{cl}
D_\mu H&=(\partial_\mu+ igA_\mu )H\\
D_\mu \sum&=\partial_\mu \sum +ig(A_\mu
\sum -\sum A_\mu),\end{array}$$
which show that Higgs fields $H$ and $\sum$ are vector and adjoint
representations of $SU(5)$ group.
Here we wrote gauge bosons, Higgs fields $\sum$ and $H$ in their
matrix forms\cite{licheng} as
\begin{eqnarray}
A={1\over \sqrt{2}}\left [\begin{array}{ccccc}
&&&X_{1}&Y_{1}\\
{[G}&-2B/&{{\sqrt{30}]^\alpha}_\beta}&X_{2}&Y_{2}\\
&&&X_{3}&Y_{3}\\
X^{\dag}_{1}&X^{\dag}_{2}&X^{\dag}_{3}&W^3/\sqrt{2}+3B/\sqrt{30}&W^{\dag}\\
Y^{\dag}_{1}&Y^{\dag}_{2}&Y^{\dag}_{3}&W^{-}&W^3/\sqrt{2}+3B/\sqrt{30}\end{array}\right]
\end{eqnarray}
\begin{eqnarray}
\sum=\left [\begin{array}{ccccc}
&&&\Sigma_{X1}&\Sigma_{Y1}\\
{[\Sigma_8 ]^\alpha}_\beta&-&2\Sigma_0/\sqrt
{30}&\Sigma_{X2}&\Sigma_{Y2}\\
&&&\Sigma_{X1}&\Sigma_{Y1}\\
\begin{picture}(0,0)(1,0)
\put(-10,0){\line(1,0){215}}\put(111,-50){\line(0,1){115}}
\end{picture}\\
\Sigma^{\dag}_{X1}&\Sigma^{\dag}_{X2}&\Sigma^{\dag}_{X3}&&\\[-1.5mm]
&&&[\Sigma_3 ]^r_s&+3\Sigma_0/\sqrt 30\\[-1.5mm]
\Sigma^{\dag}_{X1}&\Sigma^{\dag}_{X2}&\Sigma^{\dag}_{X3}&&\end{array}\right],\end{eqnarray}
\begin{eqnarray}
H=\left [\begin{array}{cl}
H_{t_1}\\H_{t_2}\\H_{t_3}\\H_{d_1}\\H_{d_2}\end{array}\right].\end{eqnarray}
Before giving the expression of potential, we normalize the coefficient of
dynamics terms in above Lagrangian, so we can take values of normalization
constant $N$ and metrics $G,G_1$ as follows:
$$N=66 g^2=16 \beta{G\over U^2}=4\alpha{G_1\over U^2_1}$$
$$G={33\over 8} {1\over \beta} g^2U^2$$
$$G_1={33\over 2} {1\over \alpha} g^2 U^2_1.$$ Then the Lagrangian of gauge
fields
becomes:
\begin{eqnarray}\begin{array}{cl}
{\cal L}_G=&-{1\over 4} F_{\mu\nu} F^{\mu\nu}+
D_\mu H^{\dag} D_\mu H
+ Tr(D_\mu \Sigma^{\dag} D^\mu
\Sigma)\\[5mm]
&- [V(H,\Sigma)+V(\Sigma)+V(H)],\end{array}\end{eqnarray}
and the potential is given as following,
$$V(\Sigma)=-m^2_1
Tr\Sigma^2+\lambda_1(Tr\Sigma^2)^2+\lambda_2
Tr\Sigma^4$$
$$V(H)=-m^2_2 H^{\dag}H+\lambda_3(H^{\dag}H)^2$$
$$ V(H,\Sigma)=\lambda_4 (Tr\Sigma^2)
H^{\dag}H+\lambda_5 H^{\dag}
\Sigma^2 H$$
where
\begin{eqnarray}\begin{array}{cl}
&m^2_1=g^2U^2_1({33\over 2\alpha}-{99\over 32}
{\alpha\over\beta^2}
{U^4\over U^4_1})\\
&m^2_2=g^2U^2({33\over 4\beta}-66{1\over \alpha}{U^2_1\over
U^2})\end{array}\end{eqnarray}
$$\begin{array}{cl}
&\lambda_1={99\over 2}{g^2}Tr(SS^{\dag})\\
&\lambda_2={33\over 4}{g^2}Tr(TT^{\dag}+10TrSS^{\dag})\\
&\lambda_3={33\over 4}{g^2\over \beta^2}Tr\{[Diag(M_1
M^{\dag}_1)]^2+
[Diag(M^{\dag}_1 M_1)]^2+2[Diag(M_2 M^{\dag}_2)]^2+
2[Diag(M^{\dag}_2 M_2)]^2\}\\
&\lambda_4={33\over 8}{g^2\over \beta}Tr[Diag(M^{\dag}_1 M)
T+
Diag(M_1 M^{\dag}_1) S+4 Diag(M_2 M^{\dag}_2) S]\\
&\lambda_5={33\over 8}{g^2\over \beta}Tr[Diag(M_1
M^{\dag}_1 )S-2
Diag(M_2 M^{\dag}_2) S-Diag(M^{\dag}_1 M) T].\end{array}$$
In the above expressions, we used the following notations,
$$T={1\over
\alpha}\left [\begin{array}{ccc}t^2_1
+t^2_3&&\\&t^2_1+t^2_2\\&&t^2_2+t^2_3\end{array}\right]
$$
$$S={1\over
\alpha}\left
[\begin{array}{ccc}s^2_1+s^2_3&&\\&s^2_1+s^2_2\\&&s^2_2+s^2_3\end{array}\right].
$$
It is easy to show that $$Tr(T+10 S)=2;$$
For a $3\times 3$ matrix $M$, we define $Diag(M)$ as the diagonal
part of $M$
$$Diag(M)=\left
[\begin{array}{ccc}M_{11}&&\\&M_{22}&\\&&M_{33}\end{array}\right].$$
To express above formulas in a simple form, we redefine parameters by absorbing
some constants in free parameter $U$ and $U_1$,
$$\mu={33 g^2 U\over \beta},~~~~~\mu_1={33 g^2 U_1\over \alpha},$$
and
$$\begin{array}{cl}
&\hat{s}_1={s^2_1+s^2_3\over \alpha},~~~~\hat{t}_1={t^2_1+
t^2_3\over \alpha},\\
&\hat{s}_2={s^2_1+s^2_2\over \alpha},~~~~\hat{t}_2={t^2_1+
t^2_2\over \alpha}\\
&\hat{s}_3={s^2_2+s^2_3\over \alpha},~~~~\hat{t}_3={t^2_2+
t^2_3\over \alpha}\end{array},$$ where $\hat{s}_i,\hat{t}_i$ ($i=1,2,3$),
is positive real
numbers.
So we can write $T$ , $S$ and $m^2_1$ and $m^2_2$ in a simple form as,
$$T=\left
[\begin{array}{ccc}\hat{t}_1&&\\&\hat{t}_2\\&&\hat{t}_3\end{array}\right],~~~~S=\left
[\begin{array}{ccc}\hat{s}_1&&\\&\hat{s}_2\\&&\hat{s}_3\end{array}\right]$$
$$m^2_1=\mu^2_1({1\over 2}-{3\over 32} {\mu^4\over
\mu^4_1}),~~~~m^2_2=\mu^2({1\over 4}-2{\mu^2_1\over \mu^2}).$$
In the previous calculation, we only take into account the term
$<F,\overline F>$. It can be shown that in this case the Higgs potential can't
give correct symmetry breaking
mechanism of
$SU(5)$ group. Fortunately,
if the term $<F>$ is
introduced in the Lagrangian, we can get correct results.
It is easy to show that,
$$<F>= {16\over U^2} G\beta H^{\dag} H+4\alpha{G_1\over
U^2_1}Tr(\Sigma^2)$$
We should introduce Lagrangian as follows
$${\cal L}=-{1\over N}(<F,\overline{F}>+q^{\prime}<F>).$$
One finds that
$$-{q^\prime\over N}<F>=-q^{\prime} H^{\dag} H-q^{\prime}
Tr(\Sigma^2).$$
We set $q^{\prime}= q^2 \mu^2_1$ and recalculate the
Lagrangian
of gauge fields and find that only coefficients $m^2_1,m^2_2$ are modified as,
\begin{eqnarray}\begin{array}{cl}
m^2_1&=\mu^2_1({1\over 2}+q-{3\over 32} {\mu^4\over
\mu^4_1})\\[5mm]
m^2_2&=\mu^2[{1\over 4}+(q-2){\mu^2_1\over \mu^2}].\end{array}\end{eqnarray}
\setcounter{sec}{4}\setcounter{equation}{0}
\section[toc-entry]{The Realistic $SU(5)$ Model and Higgs Mechanism}
In the last section, we have completed the model building of generalized gauge
theory on $M^4\times Z_2
\times Z_3$, where the potential of Higgs fields is derived directly from the
calculation of non-commutative geometry. But some of crucial points need to be
studied further, such as, does the potential provide the desired mechanism of
gauge
symmetries breaking, (i.e $SU(5)\longrightarrow SU(3)\times SU(2)\times
U(1)\longrightarrow SU(3)\times U(1)$) and if the results suit to describe the
physical phenomenon?
\subsection[toc-entry]{Realistic $SU(5)$ Model}
It is known that there are two mass scales in $SU(5)$ model: masses of the
$X$,$Y$ and
of $W$ gauge boson
masses. There exits a vast hierarchy of gauge symmetries, $M_X$ larger than
$M_W$ by something like $12$ order of magnitude. In this section, we will show
that the model we built in last section may give rise the desired symmetries
broken and gauge hierarchy, if we impose the following conditions among
parameters,
\begin{eqnarray}\begin{array}{cl}
&\mu_1\ll\mu\\[5mm]
&F={30 \lambda_4+9\lambda_5\over 60\lambda_1+14\lambda_2} < 1\\[5mm]
&q={4+F\over 2(1-F)}.\end{array} \label{condition}\end{eqnarray}
Now if the
conditions (\ref {condition})
is under consideration, we may write down the Bosonic part
Lagrangian of the
model as
\begin{eqnarray}\begin{array}{cl}
{\cal L}_G=
&-{1\over 4}F_{\mu\nu} F^{\mu\nu}+
D_\mu H^{\dag} D_\mu H
+ Tr(D_\mu \Sigma^{\dag} D^\mu\Sigma)\\[4mm]
&+m^2_1
Tr\Sigma^2-\lambda_1(Tr\Sigma^2)^2-\lambda_2
Tr\Sigma^4\\[4mm]
&+m^2_2 H^{\dag}H-\lambda_3(H^{\dag}H)^2-
\lambda_4 Tr\Sigma^2
H^{\dag}H-\lambda_5 H^{\dag}
\Sigma^2,
\end{array}\end{eqnarray}
where
$$m^2_1={5\over 2(1-F)}\mu^2_1,~~~m^2_2={1\over 4}\mu^2+F m^2_1,$$
\begin{eqnarray}\begin{array}{cl}
\lambda_1=&{99\over 2}{g^2}Tr(SS^{\dag})\\
\lambda_2=&{33\over 4}{g^2}Tr(TT^{\dag}+10TrSS^{\dag})\\
\lambda_3=&{33\over 4}{g^2\over \beta^2}Tr\{[Diag(M_1
M^{\dag}_1)]^2+
[Diag(M^{\dag}_1 M_1)]^2+2[Diag(M_2 M^{\dag}_2)]^2\\
&+
2[Diag(M^{\dag}_2 M_2)]^2\}\\
\lambda_4=&{33\over 8}{g^2\over \beta}Tr[Diag(M^{\dag}_1 M_1)
T+
Diag(M_1 M^{\dag}_1) S+4 Diag(M_2 M^{\dag}_2)S]\\
\lambda_5=&{33\over 8}{g^2\over \beta}Tr[Diag(M_1
M^{\dag}_1) S-2
Diag(M_2 M^{\dag}_2) S-Diag(M^{\dag}_1 M) T]
,
\end{array}\label{lambda}
\end{eqnarray}
In those expressions, matrices $M_1$, $M_2$, $T$ and $S$ are defined as:
$$M_1=\left [\begin{array}{ccc}f_{11}&f_{12}&f_{13}\\
f_{21}&f_{22}&f_{23}\\f_{31}&f_{32}&f_{33}\end{array}\right],~~~M_2=\left
[\begin{array}{ccc}e_{11}&e_{12}&e_{13}\\e_{21}&e_{22}&e_{23}
\\e_{31}&e_{32}&e_{33}\end{array}\right]$$
$$T=\left
[\begin{array}{ccc}\hat{t}_1&&\\&\hat{t}_2\\&&\hat{t}_3\end{array}\right],~~~S=\left
[\begin{array}{ccc}\hat{s}_1&&\\&\hat{s}_2\\&&\hat{s}_3\end{array}\right],$$
where $\hat{s}_i, \hat{t}_i$ are positive real numbers and
satisfy the condition $\frac 1 2 Tr(T+10S)=1$ .
So far we have constructed a realistic $SU(5)$ model. Our
next task is to research whether it gives us the desired physical results.
\subsection[toc-entry]{Symmetry Breaking}
Since for parameters $\lambda_1$ and $\lambda_2$ in (\ref
{lambda}), the
following conditions are true,
$\lambda_2>0$ and $\lambda_1>-{7\over 30} \lambda_2$,
potential $V(\Sigma)$
reachs its minimum at
$$
\Sigma_0=V_1\left [\begin{array}{ccccc}
2&&&&\\&2&&&\\&&2&&\\&&&-3&\\&&&&-3\end{array}\right]$$
where
$V^2_1={m^2_1\over 60 \lambda_1+14 \lambda_2}$, which was derived by
Li\cite{li}.
For the first stage, $SU(5)$ gauge symmetry is spontaneous broken down to
$SU(3)\times SU(2)\times U(1)$ as the scalar $\Sigma$ develops VEV,
$<\Sigma>=\Sigma_0$. Because $\Sigma$ is a scalar in the adjoint representation
of
$SU(5)$, mass terms for the $G^\alpha_\beta$, $W_r$, B fields remain to be
zero,
while
the $X$ and $Y$ bosons acquire their masses
$$M_X=M_Y=\sqrt{{25\over 2}}g V_1$$.
For the second stage, gauge symmetries $SU(3)\times SU(2)\times U(1)$
are broken
to $SU(3)\times U(1)$ as scalar field $H$ takes its VEV as
$$
<H>={1\over 2}\left [\begin{array}{cl}0\\0\\0\\0\\V_2\end{array}\right],$$
where
$V^2_2={m^2_d\over \lambda_3}$,
$$m^2_d=m^2_2-(30 \lambda_4+9 \lambda_5) V^2_1={1\over 4} \mu^2.$$
Then bosons $W$ and $B$ obtain masses,
$$M_W={1\over 2} g V_2, ~~~M_B= \sqrt{2\over 5}g V_2.$$
Meanwhile Higgs fields also obtain their masses in this model, their values are
listed in
the
following table,
\begin{eqnarray}\begin{array}{cc}
\begin{picture}(0,0)(1,0)
\put(-40,0){\line(1,0){160}} \end{picture}\\
Scalar~~ fields&[mass]^2\\
\begin{picture}(0,0)(1,0)
\put(-40,0){\line(1,0){160}} \end{picture}\\
{[\Sigma_8]^\alpha}_\beta&20\lambda_2V^2_1\\
{[\Sigma_3]^\alpha}_\beta&80\lambda_2V^2_1\\
\Sigma_0&4m^2_1\\
H_{t_\alpha}&\lambda_3 V^2_2+5 \lambda_5 V^2_1\\
H_{d_r}&\lambda_3 V^2_2\\
\begin{picture}(0,0)(1,0)
\put(-40,0){\line(1,0){160}} \end{picture}\end{array}\end{eqnarray}
It is interesting to note that
$${m^2_d\over m^2_W}={33\over \beta^2} Tr \{ [Diag(M_1
M^{\dag}_1)]^2+
[Diag(M^{\dag}_1 M_1)]^2+2[Diag(M_2 M^{\dag}_2)]^2+
2[Diag(M^{\dag}_2 M_2)]^2\}$$
is a quantity which depends on fermionic mass matrix. This relation does not
exist in the original $SU(5)$ Grand Unified Model.
Because parameters $\mu$ and $\mu_1$ were chosen to be $\mu\ll\mu_1$ in
conditions (\ref {condition}), it is easy to find $V_2\ll V_1$ in VEV,
which means that we may realize the masses of gauge bosons $X$ and $Y$ to be
as heavy as 12 order of that of gauge bosons $W$ and $B$. Therefore the gauge
hierarchy problem is fitting here.
In fact, to realize $\mu\ll\mu_1$, we should take $U\ll U_1$ in the fermion
lagrangian (\ref {fflc}). From the point view of non-commutative geometry
approach, $U$
is a paramter labeling the distant between two discrete points of $Z_2$ and
$U_1$ is that labeling the distant among three discrete points of $Z_3$,
These two geometry quantities control the mass scales of symmetries broken in
our model.
\section[toc-entry]{Concluding remarks}
We have first constructed a $SU(5)$ model with generalized gauge theory on
$M^4\times Z_2\times Z_3$. We have shown that
the Higgs
mechanism is automatically included in the generalized gauge theory by
introducing the Higgs fields as a kind of gauge fields with respect to the
discrete groups and the Yukawa
couplings automatically given by the generalized
gauge
coupling principle.
Then we arrange the parameters appropriately and obtain the minimum $SU(5)$
grand unified model.
In the model, the Higgs potential can lead to the spontaneous symmetry broken
mechanism of
$SU(5)\longrightarrow SU(3)\times SU(2)\times U(1)\longrightarrow SU(3)\times
U(1)$, and they took place in two different gauge hierarchy scalars. There are
also two scalars $H$ and $\sum$, the vector and adjoint representations of
$SU(5)$ group to break down gauge symmetry and enable the particles massive. In
construction of the model, we arrange $H$ and $\sum$ in the connection matrices
$\phi_Z$, $\phi_{Zr}$, $\phi_{Zr^2}$, $\phi_r$ and $\phi_{r^2}$. I want to
emphasize that this assigements is unique in general, if they are set in a
``wrong'' place, their transformation properties under $SU(5)$ group will not be
satisfied. It is
worthy while to point out that the hierarchy scalars depends on two geometry
quantities, i.e.the distant of two discrete points in $Z_2$ and that of three
discrete points in $Z_3$. One of the interesting starting point of this approach
is to understand the discrete groups $Z_2$ and $Z_3$ as charge conjugation
transformation and generation translation in the free fermion lagrangian,
although they are broken after the arrangements of gauge fields. This is
completely different from preious work.
There exist some differences between the parameters of the reconstructed
model and the standard $SU(5)$ grand unified model. In Standard $SU(5)$ Model,
there are following free parameters:
\begin{itemize}
\item $g$--- SU(5) coupling constant,
\item $M_1,M_2$--- mass matrices,
\item $m^2_1,m^2_2,\lambda_1,\lambda_2,\lambda_3,\lambda_4,\lambda_5$---
parameters in potential.
\end{itemize}
In our reconstructed model, coupling constant $g$, mass matrices $M_1, M_2$ ,
and
$m_1,m_2$ are also free parameters, instead of parameters
$\lambda_1,\lambda_2,\lambda_3,\lambda_4,\lambda_5$, we introduced two matrices
$S$ and $T$ and they
satisfy condition $\frac 1 2 Tr(T+10S)=1$. On apparent observation,
the number of parameters is the same in these two models, but now parameters
$\lambda_1,\lambda_2,\lambda_3,\lambda_4,\lambda_5$ are functions of
$M_1,M_2,S,T$ in the reconstructed model, so they are not as free as in the
standard
$SU(5)$ model. One result
of this property is that the ratio of $M_{H_d}/M_W$ is a function of mass
matrices
which means there exists a complex relation among the masses of
particles at tree level.
Therefore, it
needs
to be studied further whether there are more relations. This approach is also
available to study more extensive models such as the left-right symmetry
model, the
$SO(10)$ grand unified model and the supersymmetry model etc.
We will study these issues elsewhere.
\bigskip
\bigskip
\centerline{\Large \bf Acknowledgement}
\bigskip
\bigskip
This work is supported in part by the National Science Foundation and Chinese
Post Doctoral Foundation.
The authors would like to thank Prof. H-Y Guo, K. Wu and Z.Y. Zhao for helpful
discussions
and Dr. C. Liu for useful comments.
| {
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} | 592 |
Q: First-order properties of Euclidean fields (instead of real closed fields) Let $\mathbb{F}$ be an ordered field.
*
*$\mathbb{F}$ is called Euclidean if $\forall x>0 \in \mathbb{F}\ \exists y \in \mathbb{F} : y^2=x$, i.e. a square root exists.
*$\mathbb{F}$ is called real closed if it is Euclidean and every polynomial of odd degree has at least one zero in $\mathbb{F}$.
Real closed fields have the same first-order properties as the field of real numbers, i.e. statements that involve symbols like $+, \cdot, =,\leq,\dots$ are true for a real closed field $\mathbb{F}$ if and only if they are true over the real numbers $\mathbb{R}$.
If real closed fields are generalisations of the real numbers, then the Euclidean fields are generalisations of the field of constructible numbers. It is wrong to say that Euclidean fields have the same first-order properties as the constructible numbers, since all real closed fields are Euclidean, so the property of having a $n$th root may be different. But is the following true?
A first-order-logic statement holds over the constructible numbers,
but not over the real numbers, if and only if it holds for any
Euclidean field $\mathbb{F}$, but not its real closure $\overline{\mathbb{F}}$.
Is there a counter example? Does one direction hold? Are there references to this? More generally, is there any way in which real closed fields are better behaved under "logical generalisations" than the Euclidean fields?
I am interested in this question because in my research the Euclidean property seems to suffice most of the time, but people just use real closed fields since they have a well established theory.
| {
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} | 1,453 |
class Role < ActiveRecord::Base
include AverageRoles::RoleConcern
end
| {
"redpajama_set_name": "RedPajamaGithub"
} | 2,210 |
Q: Open Twitter app from my iOS 5 app I am trying to open the Twitter app from within my app in iOS 5, but it won't open. Any help would be appreciated, I have included the code I am using below.
[[UIApplication sharedApplication] openURL:[NSURL URLWithString:@"prefs:root=TWITTER"]];
Please help me, and thanks in advance!
A: If you are just trying to open the actual Twitter app then the code is
[[UIApplication sharedApplication] openURL:[NSURL URLWithString:@"twitter://"]];
A: Do you want to launch the Twitter app, Or just send tweets from within your app? I believe that the code you are showing above is to Launch Twitters preferences in your settings app... Which I also believe has been disallowed in 5.1
If you are looking to add Twitter integration to your app Apple provides great sample code to show you how to use Twitter with the built in Twitter frameworks in iOS 5.
Now I recommend you download this sample code and see what else is required to send a tweet (like checking CanTweetStatus) but I'm attaching a basic idea of how to send a tweet in this post.
https://developer.apple.com/library/ios/#samplecode/Tweeting/Introduction/Intro.html#//apple_ref/doc/uid/DTS40011191
- (IBAction)sendCustomTweet:(id)sender {
// Create an account store object.
ACAccountStore *accountStore = [[ACAccountStore alloc] init];
// Create an account type that ensures Twitter accounts are retrieved.
ACAccountType *accountType = [accountStore accountTypeWithAccountTypeIdentifier:ACAccountTypeIdentifierTwitter];
// Request access from the user to use their Twitter accounts.
[accountStore requestAccessToAccountsWithType:accountType withCompletionHandler:^(BOOL granted, NSError *error) {
if(granted) {
// Get the list of Twitter accounts.
NSArray *accountsArray = [accountStore accountsWithAccountType:accountType];
// For the sake of brevity, we'll assume there is only one Twitter account present.
// You would ideally ask the user which account they want to tweet from, if there is more than one Twitter account present.
if ([accountsArray count] > 0) {
// Grab the initial Twitter account to tweet from.
ACAccount *twitterAccount = [accountsArray objectAtIndex:0];
// Create a request, which in this example, posts a tweet to the user's timeline.
// This example uses version 1 of the Twitter API.
// This may need to be changed to whichever version is currently appropriate.
TWRequest *postRequest = [[TWRequest alloc] initWithURL:[NSURL URLWithString:@"http://api.twitter.com/1/statuses/update.json"] parameters:[NSDictionary dictionaryWithObject:@"Hello. This is a tweet." forKey:@"status"] requestMethod:TWRequestMethodPOST];
// Set the account used to post the tweet.
[postRequest setAccount:twitterAccount];
// Perform the request created above and create a handler block to handle the response.
[postRequest performRequestWithHandler:^(NSData *responseData, NSHTTPURLResponse *urlResponse, NSError *error) {
NSString *output = [NSString stringWithFormat:@"HTTP response status: %i", [urlResponse statusCode]];
[self performSelectorOnMainThread:@selector(displayText:) withObject:output waitUntilDone:NO];
}];
}
}
}];
}
Good Luck!
| {
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} | 33 |
{"url":"http:\/\/mathoverflow.net\/feeds\/question\/58420","text":"What is known on finite dimensional nilpotent Lie algebras with maximal index ? - MathOverflow most recent 30 from http:\/\/mathoverflow.net 2013-05-22T18:09:34Z http:\/\/mathoverflow.net\/feeds\/question\/58420 http:\/\/www.creativecommons.org\/licenses\/by-nc\/2.5\/rdf http:\/\/mathoverflow.net\/questions\/58420\/what-is-known-on-finite-dimensional-nilpotent-lie-algebras-with-maximal-index What is known on finite dimensional nilpotent Lie algebras with maximal index ? CLomp 2011-03-14T12:40:12Z 2013-03-30T17:14:41Z <p>The index of a Lie algebra is $\\mathrm{ind}(\\mathfrak{g})=\\mathrm{min}_{\\lambda \\in \\mathfrak{g}^{*}} \\mathrm{dim} \\mathfrak{g}^{\\lambda}$, where $\\mathfrak{g}^{\\lambda} = \\lbrace x\\in \\mathfrak{g} \\mid \\lambda\\circ \\mathrm{ad}_{x} = 0 \\rbrace$.<\/p> <p>Is there any way to classify all complex n-dimensional nilpotent Lie algebra $\\mathfrak{g}$ whose index is $\\mathrm{ind}\\ \\mathfrak{g} = n-2$ ?<\/p> <p>Examples would be the filiform Lie algebras, if I am not mistaken, e.g. $\\mathfrak{g}$ generated by ${x_1, \\ldots, x_n}$ subject to $[x_1,x_i]=x_{i+1}$ for $2\\leq i < n$.<\/p> http:\/\/mathoverflow.net\/questions\/58420\/what-is-known-on-finite-dimensional-nilpotent-lie-algebras-with-maximal-index\/126034#126034 Answer by Dietrich Burde for What is known on finite dimensional nilpotent Lie algebras with maximal index ? Dietrich Burde 2013-03-30T17:14:41Z 2013-03-30T17:14:41Z <p>It is known, that the index of a Lie algebra is a semi-invariant for degenerations (by Ooms and Elashvili), i.e., if $L_1$ degenerates to $L_2$, then $ind(L_1)\\le ind(L_2)$. This is very useful. For example, it follows that any filiform Lie algebra of dimension $n$ has index less or equal than $n-2$, where only the standard graded filiform $L(n)$, which you have defined above, has exactly index $n-2$. In general, there are many other Lie algebras of dimension $n$ and index $n-2$, e.g., also the quasi-filiform Lie algebras $L(n-1)\\oplus \\mathbb{C}$. See here also the work Adini and Makhlouf. The Hasse-diagram of complex nilpotent Lie algebras in dimension 6 gives explicit examples, e.g., we have degenerations from the top algebra $L_{6,20}$ as follows (notation of Magnin for the Lie algebras) $L_{6,20}\\rightarrow L_{6,18}\\rightarrow L_{6,17} \\rightarrow L_{6,16} \\rightarrow L_{5,5} \\oplus \\mathbb{C}\\rightarrow \\mathbb{C}^6$, with index numbers $2 \\rightarrow 2 \\rightarrow 2 \\rightarrow 4 \\rightarrow 4 \\rightarrow 6$. See my paper arXiv:0911.2995 for this, and a discussion on the maximal dimension of an abelian subalgebra $\\alpha (L)$, which is related to the index by $\\alpha (L)\\le (\\dim (L)+ind (L))\/2$.<\/p>","date":"2013-05-22 18:09:40","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\": 0.8420901894569397, \"perplexity\": 438.3083000094928}, \"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-2013-20\/segments\/1368702185502\/warc\/CC-MAIN-20130516110305-00093-ip-10-60-113-184.ec2.internal.warc.gz\"}"} | null | null |
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Designed from the ground up, the recently launched Google Maps for iPhone gives the Native Maps app for iPhone…and Google Maps for Android a run for it's money.
I've you've been living under a rock, then you don't know that Apple has been having some "issues" with its first try at a native map app for iPhone. Since being kicked off the list of "pre-installed" apps list, Google Maps has been hard at work creating a separate app that rivals and even beats the native iOS app.
The Google Maps app should be available now in the App Store. The app has all the features of the native Maps app and pulled additional features from Google Maps on Android like, turn-by-turn navigation and transit information. The navigation functions still run in the background when you are using other apps. I noticed that Google Maps for iOS looks cleaner and is not as cluttered as the Maps for iOS. Browsing around the map, searching for locations, and getting directions seems smoother and more intuitive as well.
Some additions to the Google Maps app are gesture controls that lets users swipe up from the bottom to get more information on a searched location. Users can also drag from the right to left (using the little "three dots" button on the lower-right portion of the screen) to uncover map information like traffic, Public transit, Satellite and Google Earth views.
Overall, the Google Maps experience on the iPhone is very "fly" and in my opinion, trumps the native Maps app. Of course, the advantage the native Maps app has is default settings - The app is baked into other features and functions of iOS so users don't have to copy/paste address information from other searches into Google Maps, for example. I'd venture to say that people won't mind jumping in and out of Google Maps if they can get the nicer experience and better data with Google Maps.
Speaking of venturing to say things, Google Maps for iOS edges Google Maps for Android as far as looks and interaction are concerned. Similar to Apple, Google Maps trumps the iOS app when it comes to deep, deep integration into the Android platform. That still in my books gives Google Maps for Adnroid the edge over Google Maps for iOS.
Overall, the bar has been set for both Maps for iOS and Google Maps for Android. The Google Maps app for iOS is what iPhone users have been looking for in a maps app - Pleasant user experience with solid data. Time will tell if Apple can improve their data miscues and offer up a better experience - Competition is always a good thing. | {
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Paratrichocladius pierfrancescoi är en tvåvingeart som beskrevs av Rossaro 1990. Paratrichocladius pierfrancescoi ingår i släktet Paratrichocladius och familjen fjädermyggor.
Artens utbredningsområde är Italien. Inga underarter finns listade i Catalogue of Life.
Källor
Fjädermyggor
pierfrancescoi | {
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All statements of fact, opinion, or analysis expressed are those of the author and do not reflect the official positions or views of the CIA or any other U.S. government agency. Nothing in the contents should be construed as asserting or implying U.S. government authentication of information or agency endorsement of the author's views. This material has been reviewed by the CIA to prevent the disclosure of classified information.
CONTENTS
Disclaimer
Title Page
Copyright
A Note from the Author
Part One
INTRODUCTION TO THE CLANDESTINE WORLD
Chapter One
Clandestine Concepts Go Corporate: Basic Principles of Intelligence Collection
Chapter Two
Secret Agent Boot Camp: Developing Your Operational Instincts
Chapter Three
Business Counterintelligence
Part Two
INTERNAL APPLICATIONS
Chapter Four
Creating Your Team: Recruitment and Organizational Strategies from the CIA
Chapter Five
Staying Clean in a Dirty World: The Ethics of Espionage
Chapter Six
Crisis Management Strategies (from an Organization That Truly Knows the Meaning of Crisis)
Part Three
EXTERNAL APPLICATIONS
Chapter Seven
Making a Sale the CIA Way
Chapter Eight
Controlling Your Sources: Supply-Chain Management Clandestine Style
Chapter Nine
Spy Versus Spy: Dealing with Competition
Conclusion: Operating in a Competitive World
Acknowledgments
Index
A Note from the Author
Working as an undercover CIA officer more or less ruins your chances of ever being satisfied again in a more traditional job. So when I started thinking about leaving the agency after spending nearly a decade as a clandestine service officer, I found it hard to imagine going back to a job that required normal business attire, had a predictable schedule, and didn't ever involve the use of an alias. Given the choice, I'd pick a war zone assignment over a cubicle any day.
And yet it was clear to me that I had reached a plateau in my career and it was time to make a change. Still, quitting my job as a case officer for the Central Intelligence Agency was a difficult choice. Sure, a clandestine career has plenty of drawbacks: mind-numbing bureaucracy, too much time living out of a suitcase, constant lies to friends and family. But working for the CIA presents opportunities and challenges that no other employer in the world can match. It can be fabulously rewarding, and although Hollywood's depiction of a CIA career is 98 percent inaccurate, it does have its share of glamorous moments, as well as its pulse-quickening, adrenaline-rushing ones. But I had come to a point where further career advancement would have required personal sacrifices that I wasn't willing to make. I had a family I wanted to see more. I wanted to engage in normal conversations at cocktail parties and backyard barbecues without having to excuse myself whenever the inevitable "and what do _you_ do?" question arose. The globe-trotting that had previously seemed a wonderful adventure on the government's dime now had me shudder at the thought of yet _another_ international flight and yet _another_ night in _another_ hotel room. I have absolutely no regrets about my time in the CIA, but I wanted my life and my identity back.
I had a choice: I could make a new career for myself within the clandestine service in a headquarters management role, or I could quit and rejoin the "civilian" world. There was some comfort in the thought of sticking with the CIA, albeit in a different capacity, but the truth is that I share the field officer's aversion to becoming a cog in the headquarters machine.
I had plenty of other skills besides espionage, I told myself. Before joining the CIA, I had hopped from one corporate job to the next. An Ivy League degree and the heady days before the dot-com bubble burst had made it possible for me to dabble in various industries in various capacities, always changing jobs quickly before boredom set in. Granted, I never found a position or a company that I enjoyed for more than about a year's time, but I gained plenty of experience in the normal world outside of the clandestine service.
Upon dusting off my decade-old pre-CIA résumé in search of updatable skills, then, I was surprised to discover that my career in the CIA had taught me more valuable, business-applicable skills than all of my previous corporate positions combined. Granted, not all of my clandestine skills were directly transferable—at least not without the risk of a prison sentence—but they were not nearly as esoteric as I had originally assumed.
This thought process and personal career exploration ultimately led to my decision to write this book. Moreover, I realized that although the CIA employs a constant stream of contractors from the outside world, the outside world rarely gets to benefit from the experience of clandestine service officers. That is, in part, simply because there aren't many of us floating around the private sector. It also stems from the fact that even after leaving the agency, many people find it hard (or inadvisable) to give up their cover stories. Widely broadcasting a previous career as a CIA officer can invite very strong reactions, ranging from curious to confrontational.
Even as this book started to take shape in my mind, though, I hesitated. I had no desire to write a "tell-all"; I don't have any intention of leaking classified information or revealing data that could compromise any person or operation associated with the CIA. Former insiders who leak information are much reviled inside the agency, and I hated the idea that anyone would lump me in with that group. In addition to getting my manuscript approved by the CIA's internal review board prior to publication, as required of all former employees, then, I also set about writing this book very carefully. On the one hand, I truly believe that the corporate world can learn a great deal from some of the practices within the clandestine world, and I wanted readers to have the benefit of examples and anecdotes that illustrate the points discussed in the book. On the other hand, I know how to keep a secret—and there is a great deal of information classified as top secret for very good reason.
My goal in this book is to walk the fine line of sharing enough information for the material to be usable and useful, without giving away any sources or methods that could jeopardize past or present operations. Particularly in the early chapters, therefore, I sometimes rely on hypothetical examples to introduce broad concepts. This does not mean that the examples are untrue or fabricated—just that I used composite characters and situations, and changed the details enough to obscure the underlying people and places. All of the examples that describe my personal experiences are very much true, and very much my own. Again, however, I endeavored to eliminate any detail that could lead to the identification of the other people or places involved.
Purists and former colleagues may object to my interchangeable use of various phrases. So to put the sticklers at ease, let's set the record straight: CIA officers are _not_ "spies." A spy is someone who commits espionage against his or her nation. CIA officers _recruit_ spies. Yet in the pages of this book I make use of a whole slew of phrases to describe CIA officers from the National Clandestine Service: case officer, clandestine service officer, undercover officer, and—yes—once or twice, even spy and spook. All but the last two are accurate, and those are only used flippantly for effect.
The bottom line is that I very much enjoyed my undercover career, and I have immense respect for my former colleagues. This book is intended to share just a small fraction of the wonderful tricks of the clandestine trade with an outside world that stands to benefit.
CHAPTER ONE
Clandestine Concepts Go Corporate: Basic Principles of Intelligence Collection
In the summer of 2003 I had the dubious distinction of being part of the CIA's weapons of mass destruction search team in Iraq. I arrived in Baghdad during an awkward time of investigative limbo—the administration's official position was still that there were weapons of mass destruction hidden in or near Iraq. The evidence, however, was increasingly pointing to the opposite conclusion. The CIA team's orders were a half-vague, half-desperate command to "leave no stone unturned" in our search.
Shortly after my arrival I was asked to look into a suspect biological weapons facility. It was a promising target; we had incriminating satellite imagery and in-depth analysis of the facility's communications with numerous organizations all thought to be part of Iraq's WMD program. The facility, which was run by a PhD biochemist, was under heavy armed guard.
I worked with my military counterparts to develop a plan to raid the site, and several days later I was en route in my first military convoy. I was in an armored car at the center of the convoy, accompanied by my interpreter—a sweet-tempered, slightly nervous woman—and a heavy protective detail manned by Blackwater personnel. Another armored car carried technical specialists who had the ability to run field analyses on any biological weapons (BW) samples that we might collect.
I waited in the car while the compound was secured, then two heavily armed Blackwater guards escorted me into the site's outer courtyard once the facility's guards had been disarmed. The raid was unexpected, and as I entered the compound there must have been a hundred curious—and frightened—eyes on me from the men who had been ordered out of the building, searched for weapons, and made to wait in a secured corner of the courtyard.
A distinguished-looking woman emerged from the building. She appeared shaken, but she remained composed as she introduced herself as the director of the facility and asked more politely than the situation probably warranted how she could be of assistance. I introduced myself in vague terms, using an alias.
I accepted her invitation for tea and started to follow her into her office. The lead Blackwater guard pulled me roughly back, hissing that it had not yet been secured. I peered in, saw nothing but a typical office, and entered anyway.
The director served tea and cookies, and answered all of my questions without hesitation.
The facility was a salt factory. Salt. (Insert your expletive of choice here.) Salt! She pulled out a product sample and offered to taste it in my presence.
She explained everything. The middle-of-the-night deliveries to Iraqi military and prison hospitals? Saline solution. Night deliveries because of the summer heat—a common practice.
The clean-room technology in the facility? To produce the sterile saline solution.
The pits dug into the earth behind the building? For harmless runoff. The residue? You guessed it—salt.
Her PhD in biochemistry? Yes, she was overqualified, she admitted, but it was difficult for a woman to find a management position in Iraq.
The armed guards protecting the building? A necessity in postinvasion Iraq to protect against looting.
We had just conducted an armed raid on a salt factory.
The CIA technicians ran tests that confirmed the director's claims. It really was just a salt factory.
I felt like an incredible jerk.
I looked at the crowd of terrified workers who had been corralled into the courtyard by heavily armed Americans, and felt even worse. The director gracefully accepted my apologies, and our convoy departed in shame.
I learned a valuable lesson that day. For all of the sophisticated imagery, technical intercepts, and expert analysis that had been aimed at the supposed biological weapons facility, the true story was only revealed once I marched in and simply asked someone on the inside. What looked incriminating and suspicious on paper suddenly seemed silly and harmless once I sat down for a cup of tea with the facility's director.
For me, the experience was much like looking through a kaleidoscope: one minute you're looking at a blue star pattern, and then with a small _click,_ suddenly you're seeing a rainbow-hued diamond pattern instead. Human intelligence—the bread and butter of the Central Intelligence Agency— _is_ that click that suddenly transforms the view into something altogether different. There are circumstances in which the right explanation, the inside scoop, the firsthand account can trump even the most sophisticated data analysis. Sometimes you just have to be there to really understand—and if you can't be there, then you need someone who can be there _for_ you.
The click factor exists in the corporate world too. You may diligently read all of the business journals, faithfully study your industry's breaking news, be able to recite from memory your competition's last SEC filing, and _still_ be missing the whole picture. You need the click that can only be gained from the inside—that can only be gained from well-placed human sources. You need the click to tell you whether you're looking at a WMD facility or a salt factory.
It just so happens that I can teach you how.
Let's be clear, though—this book is not a manual of dirty tricks. I won't tell you how to bug your competitor's boardroom or how to interrogate disloyal employees. There are plenty of firms around that, for a hefty sum per billable hour, will Dumpster dive for revealing documents, obtain phone records, or dig up compromising information about your fellow executives. Often staffed by a combination of former feds and ex-CIA spooks, these firms can take care of your less than savory business needs.
This book is different. It will teach you to use techniques from the clandestine world to help you legitimately succeed in the business world—as an individual and as an organization. Specifically, this book will show you the value of using classic spy methods to better understand and to better manipulate (more on _that_ loaded term later) your customers, your competition, and your suppliers. You won't need a trench coat, a false mustache, or any fancy listening devices. You'll just need a lot of common sense, good intuition, a strong strategy, and firm ethical parameters to successfully use the techniques described.
Yet while this book may not be a manual of dirty tricks, neither is it a Pollyannaish recitation of basic business fundamentals wrapped in a layer of patriotic service. Espionage relies on a lot of loaded terms that I will use frequently: manipulation, exploitation, trapping, and elicitation, among others. And yet CIA officers are, for the most part, some of the most ethical, patriotic, principled people you will ever meet. They are simply adept at using controversial methods when the stakes are high in order to obtain a positive outcome.
So on that note, remember the SWOT model that we all learned in Business 101? (That's an analysis of strengths, weaknesses, opportunities, and threats, for those of you who slept through class that day.) For the purposes of this book, forget about the S part of the model. Building the strengths of your company is not the theme here; you can figure out how to build a better widget on your own time. This book will focus more on weakness—human weakness, that is. And by taking a walk on the clandestine side, you will come to live and breathe opportunities and threats. I will not be encouraging anyone to whiteboard their thoughts, conduct brainstorming sessions, or create columns or graphs of their data. To be successful in the clandestine world you need to _intuitively_ recognize both an opportunity and a threat, and then be able to respond reflexively.
To get you started thinking like a spy, I have broken this book into three parts. The first is an introduction to the basic skill sets required in the clandestine world. The chapters in this part identify and distill various techniques used by CIA officers that can also be used by anyone—at any level—in the workplace. Various exercises are included to help readers fine-tune their spy skills.
The second part takes a step back to look at the bigger picture of how lessons from the CIA can benefit entire organizations. The chapters in this section discuss clandestine skills and techniques that can be applied _within_ an organization in order to improve performance and outcomes.
The third part of the book returns the focus to the individual level, and is designed to teach readers to apply their newfound skills to specific business situations. The chapters in this section discuss the use of clandestine techniques as they relate to customers, suppliers, and competitors.
Once again, the purpose of this book is not to teach, encourage, or otherwise promote corporate espionage or any type of unethical practice. Instead, it is intended to share some of the techniques used by loyal and dedicated intelligence officers that can also benefit the corporate world.
THE BASICS
I mentioned earlier that the bread and butter of the clandestine world is the collection of human intelligence. In this context, the term "intelligence" refers to secret information; human intelligence means that the information is obtained directly from a person, as opposed to getting it via technical means—hacking into a computer or tapping a phone, for example. CIA officers get paid to obtain secret information from the people who have access to it. To put it more bluntly, CIA officers get paid to steal secrets from other people.
At this point, you might be wondering what this has to do with business—legitimate, _legal_ business, in particular. After all, a company's proprietary information, while important, is not exactly on par with information about a hostile nation's secret biological weapons arsenal. And most of you (I hope) don't want to _steal_ another company's proprietary information anyway. So why bother reading a business book written by a former spy?
Because, quite simply, the techniques used in the clandestine world are broadly applicable, universal methods for getting what you want from other people.
In the business setting, you may be seeking a new job, a promotion, a big sale, or a regulatory ruling in your company's favor. Whatever it is that you seek, _someone_ has the power to give. This book will teach you how to more effectively get what you need to succeed.
JAMES BOND MEETS THE BOND MARKET
The synergy between clandestine techniques, or _tradecraft,_ as it is often called, and the corporate world may be best demonstrated by comparing examples. We'll start with a classic espionage scenario:
After years of unsuccessfully trying to penetrate the nuclear program of a hostile rogue nation, John, a midcareer CIA officer, finally struck gold—one of the chief architects of the nuclear program had been arrested for drunk driving while on vacation with his family in a cooperative country. By taking advantage of the nuclear official's detention and embarrassment, plus offering a hefty reward for his cooperation, John was able to persuade the official to defect to the United States and to provide invaluable top-secret information about the rogue nation's weapons program. It didn't take long for this coup to have a ripple effect. Knowing that it was only a matter of time until the program was dismantled or worse, a number of other key officials and scientists abandoned the now-compromised program in the hope of both avoiding prosecution and obtaining substantial rewards like their former colleague. Ultimately, the loss of the key officials and scientists decimated the country's capabilities, and the fledgling nuclear program ground to a halt.
Now imagine a parallel (albeit less dramatic) scenario in the business world:
In spite of its high-caliber research and development department, high-tech Company X was continually upstaged by competing Company Y's ability to beat its new products to market. In a cutthroat niche in which being the first to market was critical to a product's success, Company X just couldn't seem to get ahead, in spite of an arguably better product. Finally, Company X's vice president of human resources struck gold. After learning that Company Y's most senior program manager had argued bitterly with the company's president, Company X quickly made him a job offer that he couldn't refuse. The program manager's defection soon produced a ripple effect: it turned out that he was much revered by his staff, so he also brought with him a talented team of loyal subordinates. The group desertion decimated Company Y's program management team and brought both talented employees and a competitive advantage to Company X.
Both examples involve a time-sensitive opportunity to lure a key player from the competition. In each scenario, the time-sensitive opportunity was only known because the principal actor (CIA officer John and Company X's vice president of HR, respectively) had established intelligence networks that alerted them to the opportunities. Then, in both cases, not only did the principal player draft one individual over to his side, but he also managed to recruit that one _key_ individual who could cause a domino effect of defections. In both scenarios, the collection and subsequent use of human intelligence led to a key recruitment that strengthened one side to the detriment of the other.
The parallel examples and synergies between the clandestine and the corporate worlds are endless. Some of the other business needs that can be addressed by the techniques of espionage include:
* Understanding what your customer really wants
* Positioning yourself next in line for promotion
* Identifying supply-chain problems before they become your problems
* Preventing corporate espionage against your company
* Motivating employees during tough times for your company
* Determining who you can really trust
* Identifying team members who will help you to succeed
* Dealing with a crisis
This list could go on and on. Ultimately, the purpose of this book is to teach you to think and act like a spy, and to use human intelligence collection techniques in order to succeed.
PROFILE OF A SPY
If you don't happen to resemble James Bond, you may be skeptical of this book's ability to teach you clandestine tradecraft. Rest assured, there are very few people who look like Sean Connery walking through the halls of the CIA's Langley headquarters. In fact, the most common reaction of new CIA officers reporting to duty on their first day of work is . . . disappointment.
Almost all new hires to the clandestine service exhibit the same behaviors. We show up excited and nervous; many of us didn't sleep well the night before. This isn't like any other first day of work; this is the first day of work at _the CIA_! We make our way uncertainly through the complex security process required just to get in the door. We don't make eye contact with anyone else, because we aren't sure whether it's appropriate to meet and mingle as one might at any other new-employee orientation. Few people shake hands; almost no one introduces themselves—we don't know whether we're allowed to share our names. So we lurk quietly, sipping our coffee, observing everyone else in the new-employee orientation room. And we see . . . ordinary people. We usually start to feel a little silly at this point for even having thought that our fellow employees might look like Hollywood's version of a spy, but we're still surprised by just how average the people around us appear. But appearing ordinary is precisely the point. After all, would someone who looks like Brad Pitt or Angelina Jolie be able to cross borders without drawing attention? Could someone truly remarkable in appearance ever be able to operate in stealth mode?
Yet although CIA officers are for the most part surprisingly ordinary in appearance, their remarkable qualities become more apparent once you get a chance to talk with them for a while. Successful spies rely on their personalities, not their looks. A good CIA officer is charismatic without being flashy, inquisitive without being nosy, friendly without being boisterous, smart without being pedantic, and confident without seeming arrogant. Above all, a good spy is a _great_ listener.
A good CIA officer starts conversations easily, and has a talent for guiding a seemingly idle chat toward a topic of interest. Somewhere along the way you'll find that _you_ are doing most of the talking, allowing the spy to draw information from you effortlessly. And if you bump into that CIA officer later, don't be surprised if he or she has an uncanny ability to remember the details you shared.
Good CIA officers have great personalities. They're charming, witty, and extremely persuasive. But they're not necessarily the "life of the party." They're not usually the ones cracking jokes or buying rounds of drinks. They _are_ the ones who draw you into a very pleasant, long conversation, though, and you will often find yourself uncharacteristically sharing deeply personal information with them.
THE GOAL
Of course, applicants to the CIA are screened for these personality variables. Job candidates are selected, in part, for their ability to converse, charm, think on their feet, and persuade. Applicants go through numerous batteries of personality tests, and are carefully screened by trained psychologists. But not all of a good CIA officer's skills are innate. Our training introduces us to techniques designed to elicit information gently and gracefully from a reluctant source. We are taught to use our natural abilities to pursue a specific goal.
This training, which will be addressed in the next chapter, can benefit you and your organization as well. Anyone can learn to be a better listener, a more influential speaker, and a generally more persuasive person. Whether you are an engineer, a lawyer, a sales rep, or an accountant, you can benefit from training in clandestine methods. Even if your interpersonal skills have long been buried under mountains of paperwork, the drudgery of an eighty-hour workweek, or the infighting of a brutally competitive workplace, I can teach you how to better listen, elicit, and manipulate yourself into success.
CHAPTER TWO
Secret Agent Boot Camp: Developing Your Operational Instincts
CIA clandestine service officers are the world's best salespeople—truly. Consider the fact that it is an officer's job to persuade people to commit espionage—to violate oaths, allegiances, and the law, often betraying friends, colleagues, and even family along the way. By definition, the stakes are always extremely high, since in many cases the penalty for committing espionage is life imprisonment or death. The spy game is serious business indeed, for all participants.
Wouldn't it be nice, then, if there was one tried-and-true method for persuading people to secretly provide sensitive information to the U.S. government? Obviously there isn't, or else we would not be suffering from ongoing, critical intelligence gaps. And yet every day CIA officers are out there, working undercover to slowly but surely eke out the bits and pieces of information that might thwart the next planned terrorist attack, uncover a hidden nuclear arsenal, or unmask the next Aldrich Ames.
Generally speaking, the recruitment cycle used by CIA officers to find new sources is as follows: spot, assess, develop, recruit, then handle (the somewhat pessimistic inside term for "manage") spies. Completing this cycle can take days or it can take years; sometimes the process is smooth and natural, and sometimes you don't know whether you are going to end up with a recruited spy or a stint in a third world prison cell when you finally pop the big question.
CIA officers often begin to truly care about the person they have recruited. In these cases the officer respects the individual's motives and takes very personally the obligation to ensure the recruit's safety. Other times we may despise the "asset," as he or she is coldly referred to in CIA parlance: we steel ourselves before every encounter in order to maintain the charade of caring about the person, and we have to remind ourselves constantly that though the asset may be reprehensible, he has access to critically important information.
The process of recruiting someone to commit espionage is inevitably complicated by language and cultural differences, plus never-ending logistical and security challenges. Yet while each recruitment has its own distinct story, there are several universal elements that serve as the building blocks for each step of the recruitment cycle:
* Targeting
* Strategic elicitation
* Corroboration
* Development of trust and rapport
CIA clandestine service officers go through months and months of training to hone their skills in these areas. Elaborate live scenarios based on actual events are staged with increasing levels of difficulty and consequences so that fledgling officers can perfect the recruitment cycle, with all of its stumbling points and inevitable psychological drama. Because the building blocks are equally valuable in the corporate world, this chapter provides readers with a series of exercises based on the principles underlying all CIA operations. Each lesson provides skills that can be employed in the private sector, both within your own organization and in the greater competitive marketplace. The techniques, as you will soon see, are not just relevant to the spy world. These are universal skills and strategies that can be used in any context.
TARGETING
Targeting is the two-pronged process of obtaining information that will enable you to get close to your person or organization of interest. First, you seek to identify _who_ can get you what you need. Second, you formulate a "hook" that you can use to facilitate contact with that person.
In the world of espionage, targeting is focused on identifying specific individuals who have access to information of interest to the U.S. government. Here's a hypothetical example:
United States authorities suspected the existence of a terrorist sleeper cell in a European capital; according to an anonymous tip, the group planned to attack the U.S. embassy within the next year. Several possible members were identified, but because the terrorists used strict operational security—avoiding phone calls and electronic communication—intelligence officials remained unable to confirm the plans or intentions of the suspect cell. Without concrete evidence of a pending attack, European law enforcement officials were unable to act. The only chance of penetrating the cell was to recruit someone in, or close to, the terrorist organization's inner circle. CIA targeting experts quickly worked to identify possible recruitment candidates. The list of possible informants included family members, neighbors, and a wide assortment of individuals who had ongoing contact with the suspected terrorists. Ultimately, a CIA officer recruited the landlord of the apartment building where the suspect terrorists lived. The landlord, who was happy to help once he learned that the cell members were possibly storing explosive materials in his property, was able to provide information about the comings and goings of the cell members, and physical access to their residence. This access yielded sufficient incriminating evidence to justify the arrest of the cell members. Once in jail, a junior cell member confessed that the group had planned to carry out its attack within a month.
In this case, the "who" was an individual who had physical proximity to the terrorist cell members, but no ideological affiliation with the group. Now let's see how targeting can be used in a corporate setting:
Margaret, the president of a five-person software company, knew that there was a large potential market for her company's product in Asia. The problem was that the company had no in-house expertise in international sales development. Unfortunately, without a significant increase in sales, Margaret couldn't justify hiring anyone qualified to take her company overseas. She was discouraged by the high commissions demanded by so-called international facilitators, and she had already been burned once by an unsuccessful attempt to partner with another company that had made false promises about its ability to tap into the Asian market. In desperation, Margaret convened a staff meeting and instructed all of her employees to network as widely as they possibly could; she noted that the future of the company depended on their ability to find the right expertise. By the end of the day, Margaret had a list of potential candidates. The individuals on the list ranged from the receptionist's cousin, who was an international trade lawyer in Bangkok, to a number of impressively credentialed individuals from various employees' college alumni associations. Ultimately, one of the alumni contacts agreed to work as a consultant for Margaret for very favorable terms in exchange for the promise of a significant bonus upon meeting an ambitious overseas sales goal.
In the corporate example, the "who" yielded by the targeting efforts was someone with significant international sales development experience who also had a personal connection to the company that made him more willing to accept a consultancy with an uncertain payout.
Targeting can also go far beyond the type of strategic networking described in the corporate example, though. In many business scenarios, the "who" may be obvious, while the "hook" is not. In all likelihood, you know exactly _who_ you need to impress in order to get the job, the promotion, or the big sale. If that's the case, then targeting can also be used to determine how to get the critical first meeting with that key decision maker, and also what to use to influence the meeting's outcome.
Targeting How-to: Find Your Hook
Karyn, a second-tour officer posted in a South American country, needed to move quickly. She had been assigned a target months ago, but hadn't managed to make any progress. The target simply wasn't approachable. He didn't travel, he rarely socialized, he didn't accept meetings with unknown entities, and his home was patrolled by private security guards who kept uninvited visitors away. Karyn thought that she had exhausted all of her options for establishing initial contact when she happened upon a critical piece of information: the target's youngest son was applying to universities in the United States.
Armed with this hook, Karyn easily arranged a meeting with the target under the guise of a private foundation offering scholarships to international students. This time, the target eagerly accepted a personal meeting with Karyn. While she initially used a deceptive pretense for the meeting, she gradually revealed her true affiliation after several meetings, and ultimately recruited the elusive target.
CIA officers spend a great deal of time formulating personalized hooks for their targets. A proper hook contains three elements:
* A reason to meet once
* A reason to connect
* A reason to continue to meet
A good hook allows a case officer to establish a mutually beneficial relationship quickly—even if this relationship is based on deception.
In the corporate world, you obviously don't want to start new business relationships with a lie. Therefore, targeting in the private sector is, fundamentally, just focused research designed to uncover your target's hook. In the age of the Internet it's easy to find information that arms you with a reason to approach a person. For example, prior to a sales call at a potential new customer's office, a meeting with executives of your company, or a series of job interviews, research the participants. If you don't know who will be attending the meetings, find out. This is less awkward than it may sound; you can always inquire with the excuse that you plan to bring specifically addressed materials. (Don't be sloppy here—if you give a reason for inquiring, follow through. Have the preaddressed materials ready to hand to the participants, or else run the risk of appearing flighty.)
Online social networking—both a blessing and a curse for intelligence officers—means that more personal information, and more potential hooks, are publicly available than ever before. Although these sites tend to be skewed toward the younger crowd, as opposed to the gray-haired executive set, don't dismiss their value. Even if your company's CEO doesn't have a Facebook page, he or she may be actively involved in charities, alumni organizations, clubs, or professional organizations. All of these affiliations tend to leave an easily researched public footprint that can readily give you insight into the where and the how to meet and "recruit" the person who can get you what you want.
Using this information successfully sometimes requires a subtle hand; you don't want to appear to be stalking your target, since nothing will get you turned down for a job or a sale faster than being a creepy and constant presence. But mentioning in your cover letter that you recently heard your target speak at a charity event, for example, provides an excellent opportunity to establish common ground, and to be complimentary in a professionally appropriate manner.
Since this chapter is titled "Secret Agent Boot Camp," I feel compelled to provide exercises to help you hone your clandestine skills. Even if you don't want to actually complete the challenges, I encourage you to at least go through them mentally. The exercises are as much about providing you with a new strategy and mind-set as they are about learning skills that are used every day by CIA officers.
Targeting Exercise
Let's begin with an easy exercise. In order for you to become more thorough and intuitive at targeting, we'll start out by working backward. Pick three people you know well, but who don't know one another. Ideally, each person will be from a different socioeconomic background and a different geographic area. Try to choose three people who are very different in their interests, occupations, and habits.
Next, make a separate list for each target, detailing how and where you might go about making contact with them if you were not already acquainted. Start with the basics. List items might include:
* Church or place of worship
* Club memberships
* Place of employment
* Hobbies
* Neighborhood
* Professional organizations
* Alumni affiliations, including fraternities or sororities
* Online group memberships
Don't be afraid to get creative. Do you have any mutual acquaintances who could introduce you? List all of them (extra credit if you can go beyond one degree of separation). Do your targets have children? If so, they may be frequent visitors to sporting events, school activities, playgrounds, and other children's activities. Of course, you'd likely be met with little more than resentment and irritation for trying to make a sale at your target's daughter's soccer match, but targeting can be used not just to locate and approach but also to establish commonalities once a more benign or appropriate contact is made.
Now compare your three lists. Are you surprised by the number of possible targeting venues for each person? Which of your three targets appears to be the easiest to approach? Which has the largest public footprint? Because, as part of this exercise, you actually know each of your targets well, consider how they would respond to being approached at or via your list items. Which means of establishing connection would most likely yield a positive response? Which would likely yield a negative response? What is the most subtle, natural means of making contact with each of your targets?
The latter part of this exercise—considering the potential reaction to a given approach—is just as important as being able to generate a lengthy list of targeting venues. Without this consideration, you could engineer the perfect introduction, yet risk burning bridges forever if you are perceived as overly aggressive, unprofessional, or intrusive.
Now that you have gotten the hang of targeting using individuals you already know well, you can apply the same technique to your professional life. Use targeting principles to identify as many people as possible who can get you closer to your goals, whether that means a new job, a new client, a new sale, or a new product.
STRATEGIC ELICITATION
Hollywood often depicts CIA officers engaged in harsh interrogation sessions to get the information that they need from their sources. The reality is that CIA officers spend a great deal of time perfecting a far more subtle and nonviolent technique—they use _elicitation_ rather than _interrogation_. The distinction is important. Strategic elicitation involves getting the answers that you need without ever directly asking the question. You wouldn't march up to a competitor and bluntly ask him or her to reveal trade secrets, would you? To do so would bring ridicule at best, and possibly even professional censure or blacklisting.
Strategic elicitation involves asking benign, nonalerting questions that eventually reveal information that likely would not have been given had you asked directly. This does not mean "tricking" anyone into answering a question; rather, it involves obtaining partial bits of information that you can, unbeknownst to your conversation partner, piece together to provide a complete answer.
In the intelligence world, strategic elicitation is used in network fashion. First, critical intelligence gaps are identified. Second, intelligence analysts formulate the questions that, if answered, could provide answers to fill those gaps. Third, targeting principles are used to identify who might be able to answer the critical questions. Sometimes the information is known to but a single person; other times, there may be a wide variety of people who could shed light on a subject. Generally speaking, the fewer the people who have access to a particular piece of information, the harder it is to get. Finally, intelligence operatives are dispatched to collect the information, in whole or in part, from wherever and whomever they can. The pieces of information are then analyzed in the aggregate, ultimately providing a complete picture.
Consider the following scenario, which demonstrates how the principle of strategic elicitation could be used in the clandestine world:
The intelligence service of a hostile nation was tasked with obtaining information about advances in a strategic missile defense system being developed by the U.S. government. Several clumsy attempts to recruit top U.S. military officials to provide this information resulted in failure and diplomatic sanctions. Stung by the international rebukes, the foreign intelligence service decided to take a more patient and conservative approach. Operatives were dispatched to provide blanket coverage of all of the various parties involved in the development of the defense system. Contact was made with dozens of potential sources of information, including the following individuals: a university professor whose latest research was instrumental to the system's capabilities, a subcontractor who had received technical specifications during the bidding process, a low-level government official who processed paperwork related to the fiscal oversight of the project, a travel agent who made all of the travel arrangements for the various parties attending an important planning meeting, a journalist who had toured a restricted area used for testing the new system for an unrelated story, and a midlevel engineer who had worked on the project but was now seeking other employment. By asking a large number of individuals each a few key questions that in and of themselves did not seem suspicious, the hostile nation was able to obtain a staggering amount of key information that jeopardized national security.
Think that this strategy isn't used in the corporate world? Think again. Trade shows, professional networking events, professional organizations, industry-specific conferences or seminars, and even the good old-fashioned golf course can be used to glean information from unsuspecting sources. The information that seemed so harmless in the bar or in the club locker room can end up being much more revealing than intended when analyzed in the aggregate. This threat will be addressed in more detail in the business counterintelligence chapter later in this book.
Strategic elicitation does not, however, need to be a vast undertaking utilizing a small army of intelligence officers. On an individual level, it can be as simple as identifying exactly what information you need, and then preplanning a variety of questions and/or conversational directions that can get you the data. Note that _how_ and _what_ you ask are both of critical importance. If you are too vague or circumspect, you may never get the information you need. However, being overly blunt or aggressive will also lead to failure.
Strategic elicitation is a particularly ideal technique in two common corporate situations: initial sales meetings and job interviews.
Elicitation in the Real World
Have you ever sat through a job interview where you, the candidate, did almost none of the talking? In my experience (and I am a veteran of an embarrassing number of interviews, since I job-hopped quite a bit before joining the CIA), those were usually the most successful interviews. Quite simply, people like talking about themselves, and they like talking to people who appear interested. It's basic human nature.
Using strategic elicitation in this context, then, involves getting your interviewers to tell _you_ what they want to hear. For starters, it is usually easy to glean information about exactly what an interviewer needs to hear from a successful applicant. Imagine the following exchange, in which the applicant uses strategic elicitation at the most basic level:
**INTERVIEWER:** Before we get started, do you have any questions?
**CANDIDATE:** Well, you mentioned that you've been with the company for over a decade. Could you tell me a little bit about your career progression here, and what has made you successful?
**INTERVIEWER:** Interesting question. When I first started, the company didn't even have an in-house marketing capability. I arrived with very little experience, but I was given an overwhelming amount of responsibility. I built the marketing team from scratch, and along the way proved my resourcefulness. I've been very lucky, because senior management allowed me to be creative, and once I had proved myself, they gave me free rein. I'm happy to say that the company has rewarded me for my hard work along the way with regular promotions, which got me to where I am today.
From this very short conversational exchange, the applicant has learned several key elements that the interviewer values: resourcefulness, creativity, initiative, and a willingness to prove one's worth early in the game. Based on the interviewer's own response, the job candidate is now armed with a set of important details that he or she can work into later interview questions. Imagine the next segment of the job interview:
**INTERVIEWER:** Okay, tell me a little bit about yourself. What makes you a good candidate for this job?
**CANDIDATE:** Well, I've been with my current employer for several years now, and I've learned a great deal from some truly outstanding mentors. Now I feel ready to stretch my wings a bit and take on a bit more responsibility. I think that you'll find that I'm an out-of-the-box thinker, so I'm looking for a position in a company where I can really make a mark. I'm definitely a self-starter, so I feel as if I'm ready to move into a position that will allow me to prove exactly what I'm capable of.
So what exactly did the candidate reveal about himself here? Absolutely nothing (other than a talent for using corporate clichés). And a skilled interviewer will be waiting for more detail to substantiate all of the candidate's generalized claims and buzzwords. But the candidate has set himself up with a response framework that includes all of the elements the interviewer has already told him are important in order to succeed within the company.
Note that the candidate did not parrot the interviewer's responses verbatim. This is a critical part of strategic elicitation. Had the candidate used the exact verbiage provided by the interviewer ("I'm creative and resourceful, and looking to be rewarded for my hard work"), the answer would have been far too obvious and ham-handed. Instead, the candidate elicited details about what the interviewer thinks are critical for success, processed them, and then used those details to craft his own substantively similar but not identical response.
In order to practice your strategic elicitation skills, try the following exercise, which can be quite challenging for all but the most outgoing individuals.
Strategic Elicitation Exercise
The last exercise let you off easily by allowing you to practice targeting using information about people you already know well. To practice your strategic elicitation skills, however, it's time to exit your comfort zone and practice on a complete stranger. If you're really up for a challenge, pick a practice target who comes from a different culture than you, and who maybe isn't even fully fluent in your native language. These are challenges faced by CIA officers every day! Not sure where to find your target? Try dining at an ethnic restaurant or shopping at an ethnic grocery store staffed by employees from a culture you don't know well, and then strike up a conversation. As a customer, you have a built-in reason to initiate an exchange.
Before starting out, identify one or two questions that you would like answered during the course of your conversation. Here's the hard part: you can't ask for the information directly, and it needs to be totally unrelated to the nature of your business transaction. No fair asking the waitress at the Thai restaurant if the pad kee mao is spicy! Your quest does not have to be difficult or complex; it simply needs to be totally divergent from your task at hand. For example, find a way to get the bartender at the Russian restaurant to tell you his favorite color. Or try to learn what kind of car the butcher at the halal grocery store drives.
This can be a very difficult task, and can even be excruciating for those of you who tend to be shy. Bluntly asking your intended question would be awkward and out of context, so you need to work out a reason in advance to elicit your information in the context of your natural encounter.
The strategic elicitation exercise above may seem awkward and forced, because you are attempting to segue from the natural flow of a normal interaction (simply entering and making a purchase, for example, without extraneous conversation) to eliciting seemingly random information. Don't fret, however. The more consistent your strategic elicitation with your overt interaction, the easier it is to gradually draw out the information you need. So you will likely be pleased to discover that strategic elicitation in the corporate world is actually far easier than the exercise. Getting your customer to tell _you_ exactly what she needs to hear in your sales pitch will seem like a cinch if you've already mastered the art of drawing out far more esoteric information from people you don't even know.
Elicitation How-to: Helpful Hints
Some people are harder to chat up than others. So what can you do when you need to elicit information from someone particularly tight-lipped? Here are a few helpful techniques from the clandestine world:
**Give to get.** Having trouble homing in on your goal? Try a strategy that some of us in the clandestine world refer to as "give to get." Talk about your _own_ career plans, financial problems, or other personal details. If this is done correctly—in a conversational manner that invites mutual exchange—it naturally draws out reciprocal information from your target. Be careful here, though. If you end up divulging more information about _yourself_ than you obtain from your target, then the whole purpose of the strategy is lost.
**Strategic segues.** A sly segue can be a manipulator's best friend. If you are eliciting information that is touchy or sensitive in nature, tread toward your topic lightly by first creating a "segue road map" before you ever talk to your contact. Preplan several relevant, reasonable, and, most important, nonthreatening conversational topics from which you can then appear to effortlessly transition closer and closer to the more sensitive—and more important—real topic of interest. Some topics are so benign and universal—sports and weather, for example—that they can be used as gentle springboards to artfully get your target warmed up for the stickier subjects. Advance planning and a subtle touch are critical here.
**The referral.** A referral from a trusted—or even a neutral, for that matter—third party can do wonders for making your target more comfortable talking to you about sensitive matters. Use this by casually dropping a referral source and a specific insight. For example, something as simple as, "Sheila tells me that you are a veritable patent law guru," conveys to your target that you are more trustworthy by virtue of your connection to a mutual acquaintance, and that you already have some insight into the nature of your target's work, so therefore there must be no harm in further discussing the topic with you.
CORROBORATION
There is usually more to getting the information that you want, however, than just asking the right questions. Sometimes, improving your listening and observational skills yields just as much success as cultivating your elicitation skills. After all, the information you seek may be readily available if you simply pay attention to the right clues. Think about how many meetings you have sat through where participants interrupted one another, talked over other speakers, text messaged, or otherwise mentally checked out? Granted, useless meetings can be a plague to productivity, but a fast-paced corporate culture and constant multitasking has trained many of us to tune out the world (and, along with it, important information) in our constant quest for efficiency. For this reason, CIA officers are trained to use not just verbal elicitation, but also active listening and skillful observation in order to obtain the information they need. Information from different sources can then either corroborate or contradict what you obtain through conversation. When the stakes are high, you can't rely on just one person's version of the facts.
Moreover, some information can't be obtained simply through strategic questioning. For example, motivations. CIA officers are constantly seeking to understand what might motivate a potential spy to agree to hand over top-secret information. Some spies do it for the money, some for ideological reasons, some for revenge, and some just for the thrill of it. There are as many complex sets of motivations as there are spies. It is a CIA officer's job to discern and exploit a potential recruit's vulnerabilities in order to turn them into a motivation to spy.
The ability to identify and understand vulnerabilities and motivations is equally important in the corporate world—whether we're talking about your boss, your client, your peers, or your rivals. Perhaps your boss shows favoritism toward fellow graduates from his college, your client likes to win on the golf course, your colleague plans to retire soon, or your closest rival is a sucker for an attractive blonde. Such knowledge helps you predict behavior, can help you avoid traps, and can enable you to exploit vulnerabilities and motivations to your advantage. This type of information is usually highly personal, though, and can be obtained only through careful observation over time. All the more reason, then, to practice your powers of observation.
Corroboration Exercise 1
CIA officers often repeat the mantra "Trust, but verify." Information obtained through one means is good, but the same information corroborated by multiple sources is better. This exercise is a fairly easy one on the surface; the challenge is to absorb the technique and use it on a constant basis.
First, select your target. For this exercise, pick someone whom you interact with on at least a fairly routine basis, but whom you do not know particularly well. A co-worker you do not know on a personal level is an ideal target here.
Your challenge is to obtain a personal detail, and then confirm it two more times, using two different methods of information collection. In other words, you will be collecting the same piece of information three different ways.
A simple place to start is to find out where your target went to college. This is an easy piece of information to obtain during a casual conversation; a colleague isn't likely to be suspicious when you ask where he or she went to school. Next, check out your co-worker's desk; many people have coffee mugs or other school paraphernalia lying around. What about a bumper sticker on his or her car? A class ring, or a T-shirt with a university logo worn on a casual attire day? There's also the Internet; some universities have searchable databases of alumni, and many people now have their résumés and bios posted online for either personal or professional reasons. Finally, you could ask another colleague. Careful—make sure that it's not someone who is likely to report back to your target. You look suspicious if your target learns that you have been asking about him or her.
Once you have collected the same information three different ways, consider it a verified fact. Also, notice how your observational skills increased during the exercise. Be honest—would you normally have noticed the bumper sticker on a distant co-worker's car? And yet you never know when background information that is as easily collectible via an attentive glance can be very useful when the time comes to interact with that colleague.
In addition to learning which school your co-worker attended, try practicing with a few other easy-to-obtain bits of information on other targets. Investigating whether your target has an interest in a specific sport is another easy way to practice—a bike rack on the car, a quote from Lance Armstrong as an e-mail signature, and shaved legs (on a man) all point to an interest in cycling, for example.
To avoid going about this task too bluntly or aggressively, consider yourself to have failed if at any point anyone asks you why you want to know something. If this happens, take a step back, choose a new target and a new piece of information to collect, and proceed more cautiously and patiently.
The point here is not to snoop or collect dirt on your co-workers. The point is to gain an appreciation for the myriad ways that you can obtain information, and to train yourself to absorb the personal details that you otherwise have likely been ignoring every day.
So what about the details and information that can't be gleaned from a T-shirt or a bumper sticker? For example, how can you corroborate a person's character, values, or motivations? How do you determine and then corroborate that a person is trustworthy, or loyal, or talented? You can gather this information over a lengthy period, of course, by observing behavior in different situations and conditions. But if you need to make decisions about people without adequate "time on target," as CIA officers say, then you need to at least train yourself not to make common mistakes.
Business leaders and CIA officers are forced to make snap judgments all the time. For example, CIA officers sometimes have to make an on-the-spot assessment of whether a target is ready to hear a recruitment pitch. An erroneous decision to ask someone to risk their life to spy for the U.S. government can have drastic consequences for the officer (being arrested is _not_ considered a career-enhancing move for a clandestine service officer). Similarly, business executives often have to fill important, highly paid positions using only a one-page résumé and a rushed interview to assess candidates. And _all_ of us have, at one time or another, scrambled to figure out, off the cuff, exactly what our irate boss/client/spouse needs to hear in order to defuse a bad situation.
To minimize the chance of making the wrong decision in an urgent situation, we use the information that we have at hand. And when there is no data to corroborate the little information that we have, we make assumptions, rely on educated guesses, or sometimes just roll the dice. Unfortunately, taking these chances can often do more harm than good.
Using assumptions in place of corroborating data is toxic to good decision making, especially when you are making a consequential judgment about a person. This is because assumptions about people's characters, values, and motivations are often based on stereotypes. Stereotypes are like mental junk food—filling, but lacking much in the way of nutrients. By using them over time, we become lazy, and we fill in the blanks with the "information" that we pull from our heads, rather than expending the time and effort to obtain facts and corroborating data.
There's not much you can do when decision time rolls around and you need to make a choice without all of the facts. However, at a minimum, you need to understand and account for the mental shortcuts that you tend to take, and the stereotypes and biases you tend to rely on. The following exercise is intended to bring out, and then analyze, the assumptions that _you_ tend to make about people.
As an aside, I encourage you to pay _particularly_ careful attention to the results of the following exercise if you have ever referred to yourself as a "good judge of character," if you believe that you have a better than average ability to detect lies, or if you consider yourself to be more intuitive than most people. Why? Because, frankly, you are probably wrong. More often than not, these beliefs indicate little more than an overconfidence in one's own assumptions and biases. Fortunately, this tendency can be corrected with a combination of mental discipline and greater self-awareness of internal biases.
Corroboration Exercise 2
As a child, I used to play a game to pass time while waiting for a flight. I would try to guess where the other people in the airport were going based on their attire and characteristics. The people dressed unseasonably were the easiest—passengers wearing shorts in the middle of winter were usually going to a tropical vacation destination (unless, of course, they were already sunburned, in which case they were heading home), and the people wearing heavy parkas were en route to ski destinations. I would try to spot which gate my targets went to, and I won a point for each correct guess.
This exercise is a spin-off of this childhood game. Far from childish, however, these techniques and observations are used by law enforcement and intelligence agencies to develop usable profiles of potential suspects or recruitment targets. Profiling is controversial for good reason, though: depending on how it is used, it can be either a useful tool or a counterproductive assumption. All the more reason to better understand its use!
To start, you will need a situation in which you can observe people prior to making their acquaintance. Parties or weddings are ideal; you can also practice on new co-workers, whom you will eventually get to know better.
First, observe your target from a distance. Pay attention to attire, mannerisms, appearance, facial expressions, body language, and whom he gravitates toward when he interacts with other people. Try to learn as much as you possibly can without actually speaking to your target, but do it reasonably quickly, and try not to get caught staring.
On the basis of your observations, try to establish a "story" for your target. Who is he? Where is he from? Next, make your best guess as to the following:
* Ethnic origins
* Education
* Profession
* Religion
* Income bracket
* Marital status
* Hobbies or activities
Also try to create a quick personality profile of your target. Is he outgoing? Intelligent? Funny? Abrasive? Condescending? Kind? Observe both your target's behavior and the behavior of the people he interacts with to formulate your personality profile from a distance.
For each response that you come up with about your target, try to pinpoint exactly which behavior or other variable led you to your conclusion. For example, did you decide that your target was Scandinavian because of his complexion? Did you decide that his hobby was basketball because of his height? Did you decide that he was a well-off lawyer because of his expensive, conservative suit?
In many cases, identifying the variable that triggered your guess is difficult. Often we base our assumptions on vague impressions or fleeting clues. Identifying which clues _you_ tend to use to formulate opinions, however, is a critical part of this exercise. It is important to be able to identify, articulate, and, most of all, _improve_ upon our natural tendency to make assumptions.
Next comes the hard part. To the best of your ability, you need to determine the accuracy of your profile. Depending on the context, you can do this directly, by talking to your target and eliciting information, or indirectly, by asking a mutual acquaintance. Be tactful, no matter what you do. Waltzing up and asking a stranger how much money he makes doesn't usually go over well. You can, however, use your strategic elicitation skills to obtain information that will either corroborate or repudiate your profile.
Repeating this exercise with multiple targets will give you a good collection of data to analyze. This analysis of your accuracy is the most important part of the exercise. What did you guess correctly, and what did you miss by a mile? Which clues yield the most accurate guesses? Are you more accurate when you base a guess on a behavior, or on a physical characteristic? Are you more accurate when it comes to profiling men, or women? Young targets, or old? By gaining an appreciation for which variables tend to steer you _wrong,_ you can improve your assessment abilities over time.
Generally speaking, the accuracy of our assessments of people tends to increase when we share similarities with our targets. Think about it—you're more likely to identify a class ring if you went to the same university or know someone who did. You're more likely to identify the expensive Italian loafers if you own a pair yourself. Former marines always seem to be able to pick one another out of a crowd, simply based on that special military bearing.
Having said this, however, you should also know that, generally speaking, people tend to be highly inaccurate at profiling. Don't be surprised if you did poorly on the exercise; the accuracy of your performance is not the point. The point of the exercise is to identify your own biases and assumptions, and then to understand how and when they steer you wrong. That way, when you have to make a snap decision, you can at least control for your personal preconceptions so that you don't mistakenly use them for corroboration. The ability to make correct decisions with limited data is important in both the clandestine _and_ the corporate worlds.
BUILDING RAPPORT
The fourth and final skill set utilized by CIA officers as they work their way through the recruitment cycle is a constant effort to build rapport and trust with their target. This is just as straightforward as it sounds. You want your target to take a risk on your behalf? It doesn't matter whether you are recruiting a spy to sell you government secrets or asking your boss to promote you ahead of your peers. In either case you need your target to trust and respect you.
Notice that I did not say that he or she has to _like_ you. Building rapport does not mean that you need to become your target's new best friend. In fact, I would caution against it. No one chooses a brain surgeon based on likability, right? You aren't trying to establish a friendship—you are trying to establish a mutually beneficial professional relationship.
Along these lines, now may be the appropriate moment in this book to take a step back and add a note of caution.
A LESSON IN HUMILITY
In the last chapter I mentioned that the typical first-day-of-work reaction for new CIA officers is disappointment. Fast-forward a year, after the same officers have undergone extensive and rigorous training at "the Farm," the CIA's notoriously tough training ground, and the most common trait you will find among the newly minted officers is now . . . arrogance. Don't worry—it's only temporary. It does, however, lead to a passing tendency to use the training too literally and too forcefully.
See, clandestine service trainees are kept in a bizarre bubble during their training, isolated from the real secret missions while they learn the skills that will make them successful and keep them safe when they embark upon their careers overseas. The training is intense, and both the failure and dropout rates are high. But for all of its intensity, the training consists of elaborate but ultimately fictional scenarios. Upon its completion, the trainees _all_ end up with a brag sheet of successfully accomplished "missions." They have all successfully survived mock interrogations, learned how to detect staged surveillance, and carried large sums of fake money across fake borders. This make-believe success, plus a year of being told that they are the "elite," the "cream of the crop," and the "best of the best," tends to inflate the trainees' egos a bit.
At one point I held a position in which I supervised a number of newly trained officers. The officers were bright, eager, and most had already achieved career success in a variety of fields prior to joining the agency. After the grueling year of training, they were ready to conquer the world; they quite literally swaggered. Their cockiness reminded me of two things: first, of my own class of CIA novices when we finished our training; and second, of my fellow graduates from my Ivy League university, all of whom had been heavily courted by future employers and lavished with generous starting salaries and signing bonuses. So rather than being put off by their arrogance, I was amused. I knew that these new officers, just like the new college grads, would soon enough come face-to-face with the real world, and that humility would reign once again.
The new officers' cockiness was mostly demonstrated by their overemphasis on being "Charming"—with a capital C. They were all extended handshake, wide smile, and slightly overbearing eye contact; they laughed too loudly and spent too much time on warm-up small talk, rather than just getting down to business. They made a point to use my name frequently during our initial conversations, and several emphasized their points by reaching out and gently touching my arm, as if the physical contact would add gravity to what they were saying. Annoying, right? And we've all seen it—it is the stereotypical used-car salesman technique, with an added dash of self-help guru and a splash of pop psychology. It puts most of us on edge when someone with whom we are trying to do business becomes overly friendly in a forced and artificial manner.
In fact, this excessive dose of personality is so common within the CIA that there exists a frequently used comeback among peers in the clandestine service—"Don't try to 'case officer' me." In this context, the term "case officer" as a verb means to schmooze, to bullshit, or to aggressively manipulate. Don't do it! In the corporate world, this type of behavior will be interpreted by your clients as insincerity, by your management as overconfidence, by your peers as braggadocio, and by your subordinates as patronizing.
For this reason, rather than including an exercise to develop your ability to establish rapport, which is a highly personalized task anyway, I instead include a note of caution. Establish trust and rapport through natural and _gradually_ progressive contact and actions. Seek out small opportunities to demonstrate your skills and your trustworthiness in a professional capacity. Bringing your client a latte at every meeting may endear you on a caffeine level, but it won't get you a contract extension. It is far better to slowly and surely build a track record of integrity, directness, and skill.
By skillfully targeting the person who can most effectively help you get ahead, using strategic elicitation to get the information that you need in order to be successful, and then methodically and patiently developing trust and rapport with your target, you will find yourself becoming indispensable in no time.
CHAPTER THREE
Business Counterintelligence
The hotel bar had been crowded with trade show attendees all evening, but it was getting late and only a few stragglers remained. A man in a disheveled suit was nearing the bottom of his glass when a woman sat down on the barstool next to his. She wearily hoisted a heavy canvas bag emblazoned with the trade show logo onto the empty seat on her other side. She glanced at the lone man's name tag briefly and then pointed to her own, indicating that they were both attending the same event. "So," she asked, "are you celebrating or drowning your sorrows? It seems like a pretty tough sell out there this year."
In fact, the man had been having terrible luck lately with sales, and with several strong drinks already in his system, he didn't mind telling the stranger in the business suit that he was getting fed up with his current line of work. When she told him that she knew of a possible job opening for someone with his background, the man perked up and shifted immediately into interview mode. Eager to impress the woman who might be able to help him get a more lucrative position, he bragged at great length about both his current position and his previous experience working as a technician in a government laboratory in his home country. He might have embellished his track record slightly, but the woman seemed impressed, and she insisted on buying the next few rounds of drinks.
The woman in the business suit was me. The man was a target I had been studying and watching from afar for quite some time. When I finally found him sitting in the bar without any of his colleagues or fellow countrymen, and with his tongue already loosened by a few drinks, I knew that I had a golden opportunity. In his heavy accent, the man told me everything I needed to know about his background, including some compromising details about the research being conducted in the highly classified laboratory where he used to work. For the price of a few drinks and the hint of a job opportunity, the conference attendee provided me with information of great value to the U.S. government.
Most of us would like to believe that we wouldn't be such easy prey. Before you scorn the man for being an easy target, though, put yourself in his situation. Imagine yourself constantly on the road, traveling from trade show to client site to corporate retreat and back again. You spend your days in airports and your nights in hotels that have all started to look the same. You live out of a suitcase and rarely see your friends or family. When a well-dressed stranger with whom you clearly have business in common strikes up a friendly, benign conversation, wouldn't you welcome the opportunity to chat? The man wasn't necessarily an easy target—he was just a typical lonely business traveler. I'm quite sure that he had no idea whatsoever that the information he was providing was compromising or valuable.
If you had been in his place, would you have recognized the situation for what it was? It's doubtful. And if not, how do you enhance your sense of personal and business counterintelligence? Read on! The purpose of this chapter is to teach you what you need to know in order to protect yourself and your organization in a competitive business climate in which private citizens are increasingly facing some of the same threats that CIA officers have been dealing with for years.
NEW REALITIES = NEW RULES
The key to business counterintelligence is to avoid ever falling victim to information thieves who may target you without your even knowing it. If you think that you can safely skip this section of the book because your job doesn't give you access to "secrets," think again, since the very definition—and value—of secret information is constantly changing.
When the Cold War ended, the prevailing currency of the spy game changed. State secrets were devalued by the new openness of glasnost and the improvement of diplomatic relations between former enemies. Within the private sector, on the other hand, the value of trade secrets skyrocketed as the concept of a worldwide economy grew, and technology made the world suddenly seem to become a much smaller place. The post–Cold War changes in the global political economy turned the spy world on its head. Suddenly there was less need for clandestine officers within the traditional political arenas, and more need for them in the business world. Spies, being an entrepreneurial bunch by nature, embraced the shift.
With these changes, however, the predictability of espionage decreased. Whereas it was once fairly obvious what the KGB was after, for example, and just how far they would go to get it, suddenly a whole new target set emerged. Traveling business executives began to suspect that someone had been in their hotel rooms while they were out. Sales reps at highly specialized trade shows suddenly became very popular, and found themselves on the receiving end of numerous invitations to socialize. Business travelers in certain parts of the world were surprised by late-night knocks on their hotel room doors from attractive, scantily clad women claiming an overwhelming desire to "practice English." Those who gave in to temptation often discovered their pockets a little lighter the next morning. Briefcases and laptops were stolen with alarming frequency. American engineers of Chinese heritage were approached by Chinese officials who made aggressive pitches for sensitive information focused on ethnic and cultural loyalty. Spy tactics had trickled into the business world, and many executives were caught unawares.
It didn't take long for the rules and parameters of espionage to change forever.
State secrets are no longer the goal of choice for entrepreneurial spies; the spy game has now shifted toward private industry. The reason is simple: money. In fact, the FBI now estimates that losses stemming from industrial espionage are in the billions of dollars annually. Billions! It's no surprise, considering just how many ways—both legal _and_ illegal—there are to obtain sensitive data from a company. To name just a few:
* Public record searches
* Dumpster diving
* Electronic surveillance*
* Interviews with former employees
* Reverse engineering
* Computer network intrusions
* Soliciting information from unwitting employees at industry events
* Planting of "mole" employees within a company
* Press articles
* Analysis of a company's Web traffic
* Computer theft
* Regulatory rulings obtained via Freedom of Information Act (FOIA) requests
* Patent reviews
* Creating mirror Web sites or phishing portals from a company's Web site
* Identity theft
* Fake job applicants
* Analysis of employee travel patterns
* Information obtained from consultants or contractors eager to share "success stories"
* Theft by disgruntled employees
* Internet worms
* Data confiscated by foreign officials during overseas travel
* Hiring away of key employees
From the mundane (data mining) to the sensational (blackmail), there are countless ways for your competitors to obtain information that you would rather not share, and then use it to their advantage. Business counterintelligence refers to efforts to identify and thwart such damaging corporate espionage.
Don't skip this chapter just because your job doesn't give you access to information that is considered sensitive in the traditional sense. Certainly, companies that work on top-secret government contracts have extensive safeguards in place, and typically employ in-house security experts (many of whom are former CIA or FBI officers) who provide rigorous counterintelligence training to employees with access to classified information. But just because the information that you deal with on a daily basis isn't classified by the U.S. government doesn't mean that it isn't of significant value to _someone_.
For example, employees in human resource functions have access to personal information about other employees, as well as advance knowledge of key personnel changes. Lawyers, accountants, and finance professionals possess sensitive client information; many government employees have access to regulatory information that would be of great value to the regulated parties; hospital workers are in control of highly personal medical information; software engineers have access to source codes; research and development scientists know what their company is coming out with next; administrative professionals know their boss's home address, travel, and meeting schedules (and in many cases, his or her vices); network administrators have access to all of a company's electronic data; the janitor has physical access to the building and the computers when no one else is around . . . the list is endless. _The possible leaks are endless._
Before you start protesting any of the above examples by citing the various laws, statutes, rules of professional conduct, or ethical standards that _should_ prevent any of these groups of people from divulging information, take a moment to consider the reality. Yes, it may be illegal, unfair, counterproductive, and just plain wrong, _but it happens_. Insider trading happens. Source code is leaked to overseas manufacturers who produce pirated versions. Tabloid magazines obtain and publish highly personal medical data about celebrities—including Britney Spears and Whitney Houston in two highly publicized cases. Films and music albums appear for sale overseas well in advance of their official release dates. Employees sell data, leak data, or even just accidentally leave laptops containing data in the back of a cab. It happens.
Like it or not, there is an enormous and powerful market for stolen information. People who make their living by dealing in black market data are shrewd, manipulative, and proficient at obtaining information from both complicit and unwitting sources.
Feeling paranoid yet? Pristine information security practices and judicious use of nondisclosure agreements can be very helpful in protecting your sensitive data, but legal and technical precautions can go only so far. Ultimately, there is no foolproof method to protect against the collection of human intelligence. Your best defense is an acute sense of awareness, and a practiced ability to sense a scam. And what better way to hone your senses than to know what it feels like to be on the _other_ side.
COUNTERINTELLIGENCE EXERCISE
In order to know what it feels like to be unwittingly solicited for information, you need more experience in the fine art of strategic elicitation. This exercise brings more of a business focus to the new skill set that you practiced in the last chapter. If this exercise seems slightly repetitive, it is because the more times you go through the mental gymnastics associated with unobtrusive, successful elicitation, the better you will be at detecting someone else's efforts to pump you for information.
This exercise has two parts—one involving a stranger, and one involving a colleague. You'll see why later.
First, you'll need to find a target with whom you are _not_ already acquainted. This exercise is best conducted using a captive audience; a fellow business traveler seated next to you on an airplane or train is ideal. Using the elicitation skills that you learned in chapter 2, your goal is to learn something specific about your target's future professional plans. Depending on his or her occupation, this could be a plan to switch employers, a hoped-for promotion, a pending retirement, or a specific professional accomplishment.
This goal is not overly intrusive or even outside of the bounds of a normal conversation with a fellow business professional, so it may seem fairly easy. However, there is an important lesson to be learned. The precept to focus on here is the concept of a multipronged line of elicitation. In order to achieve your goal, you will need to: first initiate contact and establish rapport, subsequently determine your target's profession, then direct your conversation toward your target's industry, then focus your conversation on your target's career, and finally elicit future professional plans.
So although it would not be uncommon for a casual chat between airplane-seat neighbors naturally to reveal the very information you are seeking in this exercise, the key learning point is to chain your questions in such a way that your elicitation appears to be nothing more than a logically flowing conversation.
Don't be surprised to find that when you have a specific goal and a finite amount of time to achieve it, you may be frustrated by veering, tangential topics or a conversation-dominating target. This happens to CIA officers all the time! Sometimes you may just want the answer to a simple technical question, but your target insists upon talking endlessly about problems with his mother-in-law. Try to strike a balance between maintaining control of the conversation and letting the discussion flow naturally.
Next, repeat the exercise with either a colleague or a business professional with whom you _are_ already acquainted. Pick a target whom you know on a professional, but not a personal level. This time, seek information about either your target's future career plans or specific information about the future of one of his or her ongoing projects.
You will quickly discover that you can be far more direct in your elicitations with someone who is in your field, and with whom you already have a professional connection. You will undoubtedly achieve your goal far more rapidly than you did with your stranger target. This is only natural—in the second part of this exercise, you are dealing with someone who already knows you and your professional background. You have a built-in reason to elicit business-related information. Unlike in the first part of the exercise, you therefore don't have to spend time developing rapport and circuitously getting to your ultimate goal.
" _So what?"_ you may be wondering about this exercise. Well, the effect of the trust and rapport afforded by a preexisting connection is well known to those people who make it their business to steal secrets. That's why in the scenario described in the opening of this chapter, I made it a point to carry my conference tote, to draw attention to my conference name tag, and to wear a business suit. These physical cues established an instant commonality between me and my target. We were at the same conference, which implied that we worked in the same industry, which meant that we could speak more openly with one another than with a perfect stranger. Had I approached my target at a random venue wearing a tourist's casual clothing and simply struck up a chance conversation, I would have had to work much harder to turn the conversation toward professional matters, and my target would likely have considered my approach to be suspicious and unnatural.
COUNTERINTELLIGENCE SECURITY TIPS
Now that you have experience being the elicit _or_ in various contexts, you are better prepared to recognize the warning signs that someone is trying to manipulate _you_ into divulging information. Here are some steps that you can take to further protect yourself:
**Travel with only as much data as you need for the trip.** Consider having a laptop computer dedicated to travel; this laptop should be kept free of personal data, saved passwords, or any other sensitive information. Take advantage of readily available technology to help protect your data, including biometric access devices, removable hard drives, encryption software, and data-wiping programs. You are far more likely to fall victim to theft while traveling, so plan ahead.
**Be wary of public electronic venues.** If possible, avoid Internet cafés, hotel business center computers, and public Wi-Fi access points. If you don't control the security of the network that you are using, assume that it is compromised, and use it accordingly.
**Shred!** This is basic, but important. Dumpster divers can't do anything with shredded documents.
**Be aware of your public footprint.** Conduct due diligence on your own identity by searching the Internet and knowing what is available through public records. I recently helped a friend investigate his public footprint. Within just a few minutes of searching, I discovered where he worked as a teacher, his photo, that he was a coach for a sports team, and the schedule for the entire season's games, including locations. I also discovered postings on a gourmet food site in which he inquired about recommended restaurants for an upcoming international trip, including dates. Publicly available property records revealed his address, and the rather steep price that he had paid for his house. Had I been interested in robbing his expensive home, I would have a long list of dates and times when he was certain to be away.
**Be wary of social networking sites, blogs, and Twitter.** They may be wonderful for keeping in touch with friends and family, but they should be used with the _assumption_ that someone, somewhere is watching what you post with less than noble motives. No matter how much attention you pay to security settings when you set up your account profiles, understand that social networking tools were created to _share_ data, not protect it.
**Don't be lulled into a false sense of security by familiarity or professional qualifications.** Your cubicle neighbor may suddenly be much chattier than usual because he is competing with you for a promotion, just as the friendly person on the barstool next to yours at the convention may have an ulterior motive for asking so many questions.
**Trust your instincts.** If your "spidey sense" tells you that something is awry, take action. Change the subject, divert and distract, or leave the room, as necessary. If your conversation partner doggedly pursues an uncomfortable line of questioning, he or she is either rude, oblivious, or eliciting. In each of those cases, you're well justified in ending the conversation.
**Maintain firm boundaries.** It may seem tempting to share information in order to prove your knowledge during a job interview with a competing company, but a reputable interviewer should be more interested in learning about _you_ than about your previous employer.
**Save the party for later.** It can be tempting to use alcohol or sleep aids to help you grab a little rest during those dreadful red-eye flights, or when your internal clock refuses to catch up with multiple time zone changes. Be mindful, though, that alcohol can be a spy's best friend. I quite often plied my targets with drinks in order to impair their judgment and encourage booze-induced chattiness. You may think that you are in control as long as you aren't drunk and disorderly, but trust me—you are a far easier target even when you are just slightly under the influence.
In a world where information has a price, it pays to be vigilant. However, at the risk of contradicting myself, I would also caution you against paranoia. I know many CIA officers who are so protective of their clandestine status that they are reluctant to reveal even harmless personal details. Not only does this make it extremely difficult to have a normal conversation with them, but they also manage to stand out suspiciously because of their overly secretive demeanor.
Moreover, the reality is that business counterintelligence is generally of more concern at the organizational than the personal level. Other than the most senior executives, it is the rare private-sector individual who is targeted for reasons other than proximity and vulnerability (in other words, for being in the wrong place at the wrong time). Unless you have a particularly sensitive position or unique access to highly compartmentalized data, information thieves typically view you as interchangeable with any of your colleagues (just when you were feeling special!). _You_ are only one of many different ways to get at data. As a result, even basic precautions and vigilant situational awareness can drastically reduce your chance of falling prey to scams. Just as a burglar will choose to skip the house with the barking dog in order to rob the less protected house next door, so will data thieves opt for the easiest target.
Nevertheless, a healthy sense of caution and fine-tuned observational skills can benefit anyone, in any position—whether the threat comes from organized industrial espionage or simply a co-worker who is trying to sabotage your chances of promotion. Business counterintelligence fundamentals are valuable tools whether you are flying first class to Shanghai or just riding the metro in from the suburbs.
ORGANIZATIONAL COUNTERINTELLIGENCE
Counterintelligence is a more difficult subject to tackle at the organizational than the personal level, for a variety of reasons.
First, at the organizational level an overemphasis on security and compartmentalization is counterproductive, and even detrimental. While an overly secretive individual will simply appear to be strangely reserved or standoffish, an organization with an overabundance of secrecy will fail to flourish. Can you imagine a company in which the senior management team is not allowed to share data, even with one another? Their information would be secure, but their ability to make informed decisions would be severely diminished.
Organizational security, by definition, restricts communication and collaboration. There are pros and cons to enforcing security, then. No matter how sensitive the industry, a certain level of transparency and communication within an organization is necessary in order to leverage intellectual capital, minimize redundancy, and to simply ensure that everyone has the information they need to get their jobs done. Balancing communication and security can be a difficult task. The CIA has struggled endlessly with the dueling requirements to both share and protect information; there exists a perennial internal battle in the intelligence community between analysts who need access to data in order to produce finished intelligence and the clandestine collectors who have to personally deal with the sometimes horrible repercussions of leaked information. There is no easy answer, and CIA officials have become accustomed to navigating the difficult and perpetually changing gray area between too much and not enough secrecy.
Organizational counterintelligence is also a difficult subject to tackle because good counterintelligence practices can be highly variable depending on the industry, the product, the nature of your competitive advantage, the critical skill sets, the relative strength of the competition, the geographic location, and even the economy. Nevertheless, the need to use good business counterintelligence practices applies whether you are a one-person business in which you, the sole employee, work at home in your pajamas, or a multinational corporation with a global presence. If you have even a single competitor—whether that competitor is a co-worker or a rival company—you have a valid reason to safeguard your competitive advantage.
Most companies fall into the trap of believing that adequate physical and IT security will suffice to protect their business from industrial espionage or sabotage. But if you rely on door locks and firewalls, you are still leaving yourself open to each and every person who has a key and a password, and your business will only be as secure as your most unethical/disgruntled/sloppy/debt-ridden (pick your vulnerability) employee. Take it from someone who spent years stealing secrets from people—security and counterintelligence plans that ignore human frailties are incomplete at best. Consider the following hard lesson in counterintelligence:
For several long decades, the CIA believed that it had a thriving Cuban intelligence collection program. Most of the program's assets were disgruntled Cuban officials who in many cases had simply walked into a U.S. embassy to volunteer their services and their data. Claiming to be motivated by frustration with or mistreatment from Fidel Castro's regime, the sources provided detailed information that could be corroborated by the reporting of separate, unrelated assets. This corroboration, plus the fact that most of the Cuban assets passed polygraphs, was taken as proof that these spies were the real deal. Because the information provided by the Cuban sources was used to make critical foreign policy and military decisions, intelligence consumers and policy makers pushed for more and more detail. Over time, the assets were tasked with increasingly sensitive collection requirements, and were trained in clandestine communications and operations.
Then the worst-case scenario happened. In the late 1980s, the CIA's clandestine Cuba program was blown apart by stunning revelations from several high-level Cuban intelligence officials who defected to the United States. These "real" defectors revealed that most, if not all, of the CIA's Cuban assets were in fact double agents. Not only had they been providing false information, but they had been reporting back to the Cuban government all of the sensitive taskings and training provided by their CIA handlers. As a result, Cuban intelligence officials gained a clear picture of exactly what the United States did and did not know, and perhaps even more damaging, Cuba learned the methods and technology used by the CIA, along with the identities of many of our undercover officers. In the wake of the defectors' revelations, Castro gloated publicly about the long-term deception, and Cuban television aired humiliating footage of CIA officers who had been secretly videotaped while engaged in what they believed to be clandestine activities.
The Cuban double-agent fiasco is an embarrassing chapter in CIA history, and a great deal of effort has gone into trying to understand what went wrong. Myriad after-action reports and investigations placed blame on everyone from the polygraphers who failed to catch signs of deception to the case officers who failed to spot the surveillance tracking their every move to the policy makers who put pressure on the CIA to aggressively collect information, even in the face of mounting discrepancies and warning signs. The bottom line is that the Cuban double agents were able to circumvent both technical security measures (they had received extensive training that enabled them to pass polygraph exams) and physical ones (surveillance detection proved useless against the Cuban intelligence service's scrutiny).
So how difficult would it be to pose a similar threat to private industry? Not very difficult at all, unfortunately. Consider the following, parallel example:
Nathan, the founder of a medium-sized construction firm, considered himself to be security-conscious and technology-savvy. After falling victim to equipment theft on several work sites early in his career, he made it a point to meticulously secure both his office and his job sites, and his employees were required to complete a security checklist at the end of each business day to make sure nothing fell through the cracks. In addition, he contracted with an IT consultant who meticulously kept his company's computers up to date with security software. His employees did not know that he periodically monitored their Internet use or read their e-mails; he considered it to be management's prerogative to know what his employees were doing during working hours. Nathan considered himself to be an excellent judge of character, and even though his company's head count had increased greatly over the years, he still insisted on personally interviewing each and every job candidate. On more than one occasion, he had rejected an applicant simply because of a gut feeling that the person was dishonest.
Nathan had done well in a difficult market, but in 2008 he started losing bids with disturbing frequency, and by midyear he was forced to lay off several project managers and his office manager. Out of a sense of fairness, he implemented a "last in, first out" policy, laying off the most junior employees first. Shortly after the layoffs his luck seemed to turn around, and he won the bids for several large jobs in a row. Happily, he felt confident enough about the future of the company to reach out to the recently laid-off employees to offer them their jobs back. Because he seemed to have misplaced his Rolodex in the chaos of the down period, he did a quick Internet search to find the contact information for his former office manager, who had been with the company for less than a year before he had to let her go.
Nathan's Internet search revealed much more than the office manager's contact information, however. He was horrified to discover that his office manager, whom he had believed to be a diligent and efficient addition to his company, was in fact the daughter-in-law of one of his biggest competitors, a man who had a reputation for playing dirty. Staring at the recent wedding announcement, which was accompanied by a smiling picture of his former office manager and her new in-laws, Nathan realized that his company's dry spell had been due to much more than bad luck. The office manager had helped him compile and finalize all of his sealed bids—for the same jobs that he had lost to the very man who was smiling proudly in the wedding photo. It was painfully clear that his trusted assistant had been leaking information that allowed her father-in-law's company to undercut Nathan's bids. To add insult to injury, it suddenly occurred to Nathan that his Rolodex, which had contained years of accumulated industry contacts, had gone missing on the office manager's last day.
After a discouraging consultation with his lawyer, Nathan decided not to pursue the matter. Both his bottom line and his pride had been wounded, and he was haunted by the feeling that his competitors were laughing at him for being such a fool. Deeply shaken by the experience, he knew that although he would recover financially, he would never again be able to trust his ability to judge a person's character.
In both examples, the "double agents" were able to inflict great damage to their targets in large part because the respective organizations relied too heavily on flawed and incomplete screening systems. Once the double agents made it past the initial screening, they were considered trustworthy, and were able to easily wreak havoc from within.
Worth noting, too, is that in both cases the damage was inflicted by relatively unsophisticated means against organizations that otherwise paid close attention to technical and physical security. In the first example, many of the Cuban double agents literally walked into U.S. embassies and volunteered their services. In the second example, the perpetrator easily obtained an entry-level job and simply reported basic data back to the competition. Why bother hacking into computers, tapping phones, or taking the risk of a physical intrusion if you can just send an agent right through your target's front door? And yet many companies that spend huge amounts of money on computer and physical security continue to ignore the more basic risks from within.
In both examples, the screening processes failed to protect. Cuban double agents were able to deceive polygraphers and to corroborate one another's information, and the office manager appeared to be trustworthy and competent. Yet while effective screening processes, which will be addressed in detail in the next chapter, are extremely important, they are only a small part of good counterintelligence practices. In fact, to most thoroughly protect your organization against corporate espionage or sabotage, you need to _assume_ that there is already a threat lurking within.
Assuming the existence of an internal threat may sound paranoid and extreme, particularly for those of you who trust and value your employees and co-workers. And if you start to treat your fellow professionals as potential spies, you likely won't have a loyal team around you for long. Therefore, it is important that you don't adopt the assumption of an internal threat as a _mind-set,_ but rather that you use it as a factual hypothesis with which to drive your security and counterintelligence practices.
Here is how to use the assumption of an internal threat in a positive, proactive manner:
**1. Make sure that your network has deep roots.** Too many business executives rise through the corporate ranks without ever looking back. After all, who doesn't want to leave the lean years behind? But in surrounding yourself with a network made exclusively of your ever more senior peers, you lose out on a critical information source. Who do you think is more difficult for a CIA officer to recruit: a senior diplomat who comes from a wealthy family, or the man who works in the embassy's mailroom, hasn't received a promotion in over a decade, and is struggling to support his ailing parents and three young children? The mail clerk has far more obvious vulnerabilities, and with his access to the very same sensitive documents as the diplomat, he would be a prime target for recruitment.
This does _not_ mean that you should treat lower-level employees as more likely to be potential spies. Rather, it means that you should stay connected with people at all levels in your organization. Maintaining a reputation for being open and responsive to communication from all sources will ensure that whoever notices something amiss will bring that information to you right away. Besides, most corporate espionage attempts begin with low-level probes. You could be tipped off to early warning signs by the customer service representative who notices a string of strange inquiries, by the night janitor who sees men going through the Dumpsters outside your building, or by the HR assistant who notices that quite a few of your employees are quitting to go work for a particular competitor. If your subordinates don't have confidence that you will be receptive to their observations, they won't bring them to you, and you will miss out on valuable opportunities to catch threats early.
**2. Respect data _and_ intuition.** CIA officers funnel their collected intelligence to analysts who are experts in using the aggregate data to observe trends, detect subtle shifts, and track changes. Unless your organization has its own dedicated competitive intelligence function, _you_ will need to be your own trend analyst.
Most companies are scrupulous about analyzing financial data and trends, but ignore other information that can have just as much impact on the bottom line. Your best allies in trend spotting are those individuals in your organization who have the most pervasive contact with your employees and your customers: typically HR, sales, and customer service.
Important trends to watch will vary from industry to industry. However, from a basic counterintelligence standpoint, any company, large or small, should be mindful of changes to the following:
* Where are your former employees going to work?
* Which employees (e.g., from which department, division, branch, or skill set) are leaving?
* Where are your new hires coming from?
* What is the public saying about your company?
* Who is getting your lost clients/customers?
* How quickly are your competitors matching your changes and improvements?
Shifts in the aggregate responses to these questions can tell you whether someone is siphoning off your talent, planting employees, poisoning your reputation, or stealing company secrets. Many companies seek to answer the questions above by using employee exit questionnaires and formal customer satisfaction surveys. While these forms of data collection do have value, I would argue that they are insufficient. For one thing, there will always be a response bias. In the case of employee exit questionnaires, let's be honest. Few of us fill them out truthfully. Mindful of the need to leave on a good note (if nothing else because of the possible need for future job references), many employees who have legitimate gripes refrain from documenting the real reasons for their departure. Saying that you are "leaving for a shorter commute" is far less controversial than admitting "my new employer offered me a bonus for every client I bring with me," even if the latter is true.
Customer satisfaction surveys also have a response bias, since only your most and least satisfied customers will be inclined to take the time to answer the questions. Moreover—let's be honest again here—they can be just plain annoying. We're all inundated by calls, e-mails, and letters asking us to "answer a few questions" about our recent experiences with everything from small online purchases to medical appointments. I certainly appreciate the importance of this data collection, but as a busy consumer, I for one simply ignore most of these requests.
There are many consulting and research firms that, for a steep price, will administer and analyze your data; some of them claim to be able to eliminate the response bias with sophisticated statistical analysis. Even so, by the time a trend becomes quantifiable and the data is then collected, compiled, analyzed, and reported . . . you've lost valuable time.
Instead, as I mentioned in chapter 1, you need to develop an _instinctive_ ability to spot threatening trends. The ability to sniff out a threat by trend spotting comes from an in-depth knowledge of your industry, information from your organization's front lines, and constant attention to subtle changes. With these factors, _you_ can be a far better trend spotter, and therefore a far better barometer of looming counterintelligence threats, than any questionnaire.
**3. Listen to your detractors.** For CIA officers, nothing is as important as obtaining secret information from the groups and nations most likely to cause harm to our country. Information about a terrorist network's plans and capabilities, or a hostile nation's military preparedness, is of far more value than, say, inside information about a friendly nation's political maneuverings. In fact, officers posted to some of the cushier assignments in Western Europe are often derided as being "on the cocktail circuit," instead of spending their time in the hardship posts. Generally speaking, the more critical and potentially damaging the information, the closer attention the intelligence community will pay, and the more accolades the CIA officer will receive for obtaining it. In a strange way, then, the more negative the information reported by a spy, the better it is for his or her career.
It is just the opposite in the business world, where no one wants to be the bearer of bad news, and no one likes to hear from detractors. One reason for this is the compensation goal bias. Most compensation systems reward the achievement of goals, and most goals are structured as positive accomplishments (e.g., a bonus will be paid out for achieving X goal, or for meeting Y timeline). Obviously, people are much more inclined to draw attention to data that gets them closer to their goals, and therefore closer to their bonus payouts. As a result, achievements are reported and celebrated, but problems remain unspoken. This compensation goal bias increases exponentially the higher you go in an organization, particularly as base pay becomes a smaller and smaller component of an overall compensation package. Unlike CIA officers, then, CEOs get paid to achieve positive results, not to seek out bad news—as well they should. However, when you ignore detractors you are also ignoring potential threats.
Listening to detractors goes hand in hand with trend spotting. One unhappy client can be chalked up as the price of doing business. A series of clients with similar complaints is a threatening trend that needs to be addressed. The same holds true within organizations: mass resignations, diminishing morale, rapid turnover within senior positions, or any other negative trend warrants careful attention, even when there is no immediately apparent effect on the bottom line. Since I've already expressed my concerns about relying exclusively on surveys, here are a few tips for other ways to effectively monitor dissenting opinions, both internally and externally:
**Know who is leaving unhappy.** A relatively senior member of the management team should conduct exit interviews for all departing employees. The CIA is very wary of employees leaving on an unhappy note—a disgruntled individual leaving with information from years' worth of access to top-secret data can be a dangerous thing indeed. Disgruntled private-sector employees should also be a thing to avoid. Exit interviews, if conducted in a consistent, supportive, confidential manner, can yield far more accurate information than a written survey. The data may yield one of two things: legitimate complaints about the employer that should be addressed, or invalid gripes from individuals who simply didn't fit in the organization. Even in the case of an employee who never should have been hired, though, it is better to know where you stand before the former employee walks out the door for the last time, for several reasons. First, recognizing hiring errors can help improve your organization's recruitment process. In addition, knowing who is leaving unhappy can also identify possible threats to the organization. Disgruntled former employees can provide information to your competitors, damage your reputation, or even sabotage ongoing projects. Most departing employees will do no such thing, of course, but it is in everyone's best interest for your employees to walk out the door without bitterness or anger. The CIA has an extensive exit process, consisting of multiple interviews for departing officers to ensure that they have a full understanding of both the reasons and, perhaps more important, the risks associated with each and every employee departure.
**Assess the "mood."** In addition to collecting quantifiable data about customer complaints, develop a sense for the customer service atmosphere. Does this sound a bit like hocus-pocus? It's not. Just picture the difference between two long queues of people: one consists of the people who lined up many hours in advance just to be one of the first to buy the latest-generation iPhone; the other consists of travelers waiting at the airline customer service counter after learning that their flight has been canceled. You don't have to be a terribly perceptive person to observe that the people in the first line are eager and excited, while the people in the second line are weary and irate. _That's_ the mood of your customer base.
Consumer mood can, of course, be influenced by many factors that are not within your company's sphere of control. But just as a CIA officer's recruitment strategy is influenced by a target's preexisting perception of the United States and its representatives, so should business strategy be influenced by its customers' perceptions—whether those perceptions are shaped by internal or external variables.
**Understand your company's public footprint.** There are online consumer reviews for just about every product and service. Know what reviewers are saying about your organization—both on the major review sites for your industry and on individual blogs and comments. Know what comes up when people plug your organization's name into the various popular search engines. Set up Google Alerts so that you know when your organization is being written about online. You may or may not agree with what you find, but you should always be aware. The CIA requires all employees—current and former—to submit drafts of books, articles, or speeches for approval prior to public release. Obviously, private organizations cannot enforce this type of requirement, but just because you can't censor critics doesn't mean that you should ignore what they are saying about you in the public domain.
**4. Acknowledge your weaknesses and vulnerabilities—even those you've worked hard to cultivate.** To their credit, most business leaders are focused on building strengths and eliminating or minimizing weaknesses. But let's get a little bit Zen here: it is possible for your organization's greatest strength to also be one of its greatest vulnerabilities. This is true on several levels.
For starters, the tougher the market and the greater the disparity between competitors, the more vulnerable the top player is to espionage. In the intelligence world, this plays out in the form of dramatically increased efforts to spy on the United States during times of economic crisis or military conflict. In the private sector, it plays out in the form of the hungriest underdog competitors being willing to be more aggressive, and sometimes more unscrupulous, during market downturns. If your organization is thriving in a tough field, be proud, but watch your back.
Strength as vulnerability is also true on a more specific level: your competitive advantage is what your foes most want to steal.
In the clandestine world, this can be seen most clearly in the counterproliferation arena of the spy game. Because the acquisition of nuclear capabilities would give certain hostile nations an unacceptable military advantage, CIA officers labor endlessly to identify, thwart, and destroy burgeoning nuclear programs among rogue nations. The stronger the developing program, the more resources that are thrown against it. Therefore, a strong nuclear development program can be more of a vulnerability than an asset for hostile nations—it tends to invite much more unwanted attention from the CIA than any nation wants to deal with.
In the private sector, the concept of strength as vulnerability means that your organization's competitive advantage also serves as a big flashing target for your competitors. Is your competitive advantage a stellar reputation for customer care? Then you are all the more vulnerable to negative publicity orchestrated by your rivals. Is your competitive advantage your ability to attract the top talent in your industry? Then the headhunters employed by your competitors will seek out your employees first. Is innovation your competitive advantage? Then your foes will try to learn and copy your plans. Is your low price point your greatest strength? Then your competitors can try to steal, corrupt, or duplicate your supplier and distribution networks.
In the same vein, you also need to understand your _competitors'_ weaknesses in order to understand your own vulnerabilities. Your competitors will naturally seek what they lack, and if your organization has it in abundance, you are vulnerable. For example, if your competition lacks an effective marketing strategy, treat your marketing team well, since they are coveted experts vulnerable to recruitment efforts.
Use your assessment of your organization's vulnerabilities to strategically protect your competitive advantage against all potential threats.
RED CELLS
Within the walls of the CIA is a special room—a safe haven for paranoia, delusional thinking, conspiracy theories, outlandish statements, and extremism of all sorts. Here meets the so-called Red Cell team, whose purpose is to concoct elaborate and often implausible disaster and attack scenarios and then determine how our country's security defenses would react. If an idea is ever criticized as too preposterous, participants are reminded that an attack involving flying airplanes into skyscrapers also once sounded ridiculous.
The purpose of a Red Cell is to imagine the unlikely, predict the unpredictable, and then hypothetically test possible responses and outcomes. Lest you think that this might be an ineffective endeavor in the private sector, consider the "unforeseeable" toll that the subprime mortgage crisis has taken on the financial industry, and the commensurate effects on nearly every sector out there. As I write this, the very future of a number of industry titans in sectors ranging from aerospace to retail is uncertain. Not long ago, the executives of these companies likely thought the possibility of imminent collapse was absurd.
But what if they had at least considered the possibility? What if they had identified the early indicators of looming failure and acted sooner? No one can predict the future, but adopting the CIA's Red Cell techniques can at least help organizations (or individuals, for that matter) articulate and plan for scenarios that would otherwise catch them unawares and unprepared.
Red Cell Exercise
For this exercise, I want you to serve as your own Red Cell. You can answer as either an individual or as an organization. Let's begin:
* First, come up with two competitors. They can either be real-life competitors or they can be theoretical. One competitor should be legitimate and conventional; assume that this party will operate within the constraints of the law. The second competitor should be as devious and unethical as they come; assume that this party will use any means necessary to get what it wants.
* Now list your strengths or competitive advantages. What makes you or your organization a rival, and therefore a target?
* Next, list your weaknesses and vulnerabilities.
* Finally, come up with a list of all of the different ways that each competitor could (a) exploit your vulnerabilities, and (b) steal or destroy your competitive advantage.
In order to make the most out of this task, you need to strike a balance somewhere between letting your imagination run completely amok and conventional, "in the box" thinking. This should be an exercise in structured paranoia, if you will. No fair, then, listing "zombie apocalypse" as one of the threats against your organization. Do, however, get creative and try to imagine the unimaginable.
Once you have completed your lists, focus on the differences between the possible threats from the ethical versus the dirty competitor. Are there substantial differences? Or can your vulnerabilities be just as readily exploited by conventional, legal methods?
Can you realistically protect yourself or your organization from the possible threats posed by the two competitors? How? Or will you just have to accept the risks as the price of doing business?
Using Red Cell techniques to identify and analyze even the wildest of possible threats is useful both for planning purposes and to further develop your ability to intuitively sense threats and opportunities. Besides, as William S. Burroughs once wrote, "Sometimes paranoia's just having all the facts."
FINDING SECURITY IN AN INSECURE WORLD
Now that you know your vulnerabilities and how to identify attempts to exploit them, you are well on your way to being secure. Surprised that it is this simple? The world of industrial counterintelligence is full of misconceptions, one of which is that economic espionage can only be countered by expensive and elaborate means worthy of Hollywood. In reality, business counterintelligence practices are usually not complicated or cloak-and-dagger; they don't involve secret passwords or late-night meetings in dark alleyways. Instead, business counterintelligence is primarily about vigilance, good security practices, and checks and balances.
It is another common fallacy that counterintelligence is important only to businesses whose intellectual property worth exceeds their brick-and-mortar worth. Business counterintelligence does not just address information theft. It also deals with employee or skill set theft, customer theft, and product piracy.
Similarly, many believe that only the top executives in major companies are at risk for becoming victims of corporate espionage, or that only companies dealing in secretive or classified industries are vulnerable. To the contrary, even the smallest companies in any industry can be victims.
Nevertheless, there _are_ factors that heighten your organization's CI risk:
* Frequent foreign travel by employees
* Foreign subsidies or partnerships
* Extensive use of subcontractors
* Highly competitive industries with limited, high-stakes opportunities
* IT vulnerabilities
* Interaction with foreign governments for regulatory or compliance purposes
* Disgruntled employees (either current or former)
* Manufacture of frequently pirated goods
* Highly specialized skill set required of employees, combined with an overall shortage of qualified people
* Executives with exploitable vulnerabilities such as alcoholism or drug use, or behaviors that make them susceptible to blackmail
As you can see, some of these risks are controllable, and some are not—this is the very nature of business counterintelligence. No matter what your position, your industry, or your competition, there is always the possibility of industrial espionage or sabotage. The risks can be minimized, however, with scrupulous attention to proper counterintelligence practices. To be aware and secure is to be protected.
CHAPTER FOUR
Creating Your Team: Recruitment and Organizational Strategies from the CIA
Now that I've filled your head with visions of sabotage and planted moles, and probably made you generally suspicious of human contact, would it seem strange for me to begin this chapter by parroting the oft-repeated mantra that "your employees are your greatest asset"? We've already established, after all, that they are your company's greatest vulnerability.
And yet I can't help but agree that organizations rise and fall with the talent found within.
Your employees are your greatest strength _and_ your greatest weakness. This duality is simply human nature.
The recruitment strategy used by the CIA not only acknowledges this duality—it actually embraces it. After all, the CIA has to narrow down its many thousands of applicants to the small group of people who are (a) squeaky clean enough to pass a brutally thorough background check, (b) mentally sound enough to pass batteries of psychological tests, (c) personable and intelligent enough to make it through numerous interviews with former case officers who can be very tough judges of character, and (d) healthy enough to pass comprehensive physical screenings. From this group of virtuous, smart, sane, healthy, and likable individuals, CIA recruiters then need to cull out those applicants who are _also_ willing to lie, cheat, and steal for their country. In other words, the recruiters have to find those people who are willing and able to skillfully engage in dodgy behavior, but who have a strong enough moral code that they have not yet done so. (I have heard the ideal candidate described as a "Boy Scout with a latent dark side.") With these paradoxical requirements, I don't envy CIA recruiters their jobs.
The successful candidates represent a very, very small subset of the overall applicants, let alone the American population. Low government starting salaries then discourage some of those who make it through the screening process and receive job offers; it is quite common for new hires to take significant pay cuts in order to become CIA officers. Other offer recipients decide that they don't like the idea of lying to friends and family—a necessary evil for undercover work. The group of those who are chosen and who then accept the job offer is subsequently diminished even further by a grueling yearlong training program. Many opt out once they see the realities of the undercover life, and many are asked to leave as it becomes clear that they aren't cut out for the rigors of the top-secret world.
The CIA's actual recruitment and training budget is classified, but it is no secret that it is very, _very_ expensive. No other organization in the world could possibly justify the cost per hire accrued by the agency.
So, given the fact that no one in their right mind wants to emulate the CIA's recruitment costs, nor to employ the teams of psychologists and polygraphers, accept the staggering attrition rate, or take up to several years to complete a single hire—what can you possibly borrow from the CIA's recruitment process?
Plenty.
ORGANIZATIONAL PROFILING
It's no surprise that the CIA, with its staff psychologists, expert profilers, and large cadre of experienced officers, has a very specific idea about what type of person has the potential to become a good case officer. They have determined, through years of trial and error, as well as empirical research, which skills, personality traits, previous experiences, and even beliefs serve as measurable indicators that an applicant not only has the ability to perform the basic work of a case officer, but also the fortitude to withstand the emotional pressures of the undercover lifestyle. For a job as demanding, important, and sometimes dangerous as that of an undercover CIA officer, it is critical that the hiring decisions be as informed and accurate as humanly possible. The average hiring decisions within _your_ organization may not have quite as much at stake, but that doesn't mean that you can't develop equally rigorous standards in order to build a better team.
Whether you are hiring a new employee, choosing who to promote from within, or simply selecting someone for a temporary assignment, you need to have a firm grasp of the critical skill set required for the position as well as a profile of the ideal person for the job. This may sound obvious, but I have observed organizations making the following three mistakes, over and over again:
**1. Hiring by gut.** I warned you in chapter 2 that people who consider themselves to be superior judges of character are often simply the most overconfident in their assumptions and biases. And yet it is disturbingly common for otherwise intelligent, detail-oriented, experienced professionals to base their hiring decisions on their "gut feelings" about a candidate.
Proponents of intuition-based hiring argue that they know whom they like, whom they can get along with, and who they can work alongside. One hiring manager at a prestigious consulting firm told me that by the time candidates walked through his door for an interview, their educational credentials and past work experience had already been prescreened by the HR recruiting team. He therefore felt free to assume that all of the candidates were thoroughly qualified in terms of skills, and thus that he should be making the final decision based primarily on personality.
This is _almost_ a convincing argument. After all, if you know that two people are qualified to do the job, why not hire the candidate who seems more likable?
There are several flaws in this logic, however. First, even if you are scrupulously applying your strategic elicitation and observational skills from chapter 2, a job interview is a highly artificial environment and is not conducive to making accurate personality assessments. Job candidates are wearing their best suits, using their firmest handshakes, and spitting out their best (i.e., most rehearsed) answers to your questions. The problem drinkers are abstaining during the interview lunch, the sexual harassers are keeping their eyes front and center, and the liars are spinning their most convincing tales. Prescreening may mean that everyone who walks into your office for an interview is _smart_ , but there are plenty of smart liars, thieves, and jerks in the world.
Another problem with hiring by your gut is the problem of "like attracts like." This is a concept that has been borrowed and distorted a bit by some recent popular pop psychology books. Don't worry—I'm not getting mystical on you here. For my purposes, it refers to the tendency to be drawn to those people with whom you share the most in common. It's only natural to feel more comfortable conversing with someone with whom you share an alma mater, a mutual friend, or a favorite pastime. The problem with this is that the tendency to favor those who are the most like you can result in a one-dimensional, homogeneous workforce (not to mention a major Equal Employment Opportunity problem).
When interviewing, keep in mind that you don't need to _like_ your employees. You should respect and trust them, and be able to work side by side without conflict or animosity. Friendship in the workplace, however, should be a happy coincidence— _not_ an employment requirement. Let your gut guide you if you think that there is something amiss during a job interview, but base your hiring decisions on facts instead of intuition.
**2. Vague parameters.** The second mistake that I see companies making repeatedly is the creation of vague, flowery hiring parameters. A number of years ago it became de rigueur to craft mission and value statements, and many companies created subsets of these statements for their hiring practices. These value statements appear prominently on corporate Web sites and in glossy recruiting brochures, and are often quoted in vacancy announcements.
I did a quick random Internet search of the recruitment Web sites of various large employers, and found that they were soliciting job seekers who demonstrated attributes such as the following: "best-in-class capabilities," "energy and enthusiasm," "active collaboration," "boundless determination," and "inclusive style." And appearing most frequently on the list of desired attributes? Passion. Employer after employer emphasized passion for various things, big and small. In my quick search, I found employers seeking "passion for" each of the following: innovation, people, technology, customer service, helping, excellence, continuous improvement, travel, fitness, design, banking, fashion, food, botany, excellence, learning, discovery, putting clients first, payroll, detail, drivetrains, online ad targeting, and "encouraging the use of primary materials" (this one was for a library job). Winning the prize for most generic passion statement was the stated desire for "passion for the job"—a phrase that I found over and over again.
From a marketing standpoint, listing these fuzzy qualities may be appropriate, but from a functional, internal standpoint, these value statements are utterly useless—particularly when they are used in lieu of more specific but less flashy lists of critical requirements against which to measure candidates.
Now consider the verbiage found on the CIA's public Web site. Clandestine service job seekers are advised the following:
[Officers] deal with fast-moving, ambiguous, and unstructured situations by combining their "people and street smarts" with subject matter expertise and a knowledge of foreign languages, areas, and cultures. . . . Operations Officers are given great amounts of responsibility and trust early in their careers. While they work in teams, they often need to "think on their feet," using common sense and flexibility to make quick decisions on their own. [They] have demanding responsibilities, often requiring them to work long, irregular hours so it is essential that they be physically and psychologically fit, energetic, and able to cope with stress. They must know themselves very well and a sense of humor is also a plus.
It's an ambitious job description, but it's a little more specific than "passion for the job," isn't it? And internally, you'd better believe that the applicant requirements are _far_ more specific.
The tendency to use vague verbiage, however, is just a symptom of a bigger issue. The actual problem is that many employers utilize lofty and unrealistic parameters (Passion for payroll? Really?) instead of identifying the truly critical skill sets and articulating exactly what type of candidate is most likely to succeed in a given position, within a given organizational context.
Take the time to create a specific, actionable profile of your ideal new hire. Doing so will save you time in the long run, as it helps narrow down a large pool of candidates, and it will help ensure that your vision for the future of your organization is realized a step further with the entrance of each new employee.
**3. Reinventing the wheel.** On the opposite side of the spectrum from those organizations with poetic but ultimately useless hiring values statements are the employers who are so literal in their individual hiring practices that they never end up with any kind of a cohesive plan for growing their organizations into something better than the sum of the parts. Critical skill requirements are thought of in terms of specific degrees, exact minimum numbers of years of experience, and certifications necessary to complete the immediate task at hand. As such, the hiring goals are written on a very specific, case-by-case basis, and the organization's talent growth strategy is reinvented with each and every job opening. Each new hire is "ideal" only for the specific position and the specific hiring manager—not necessarily for the organization.
Somewhere between the fluff and the literal exists a recruitment strategy that can attract and select candidates who not only feel right on an interpersonal level, but who can also _measurably_ demonstrate the skills critical for the immediate job, the next job in the succession model, and the organization as a whole. It may be a challenging task, but if the CIA can identify and hire "Boy Scouts with a latent dark side," your organization can surely identify the indicators of a talented, pleasant professional with the skill set and temperament for the job _and_ for the organization.
EFFECTIVE SCREENING
The CIA's screening process is without doubt one of the most rigorous selection procedures in existence. The psychological tests, live scenario exercises, physical exams, confrontational interviews, and intrusive background investigations are topped off with the controversial and nerve-racking polygraph exam. And yet this screening is not used just to keep inappropriate applicants _out;_ it is also used to help keep people _in_.
CIA recruiters make no secret of the rigors of the job. Even the online description for a case officer, quoted earlier in this chapter, makes full disclosure that the job is physically and psychologically demanding and requires long, irregular hours. These negative aspects are not disclosed for compassionate reasons; instead, CIA recruiters want to avoid going through the expense of hiring and training new officers, only to have them quit at the end of their training once they realize what the job actually entails.
Utilizing this type of disclosure does not mean that your job ads need to literally spell out all of the negatives. ("Seeking applicants for tedious clerical work for verbally abusive boss in a windowless office. Must be passionate about the job.") It does, however, mean that you need to understand and acknowledge that no job is perfect. The "best" (on paper) applicant you interview may also be the most likely to quit after two weeks if the job and the organization don't live up to the expectations that you as the employer have inaccurately conveyed. You would do better to assess candidates not only for how well they can meet the requirements, but also for how they might fare in the toughest circumstances that they are likely to face.
In general, of course, screening is used more often for the purpose of keeping unqualified applicants _out_. The CIA's screening methods may be a bit extreme, but any organization can borrow from its methods in order to narrow down the candidate pool to the best and the brightest. To do so, you'll need to draw on some of the skills that you practiced in chapter 2. Corroboration, in particular, is critical to effective screening.
**1. Corroborate the facts.** I am continually surprised by how many employers fail to verify résumé entries. At a minimum, you need to confirm previous employment and education; _any_ false claim should instantly rule out a candidate.
Unfortunately, checking the references given by the applicant can be of minimal use, because the references have been preselected as those most likely to say positive things about the job candidate. No one uses as a reference the boss who fired them two weeks ago for incompetence! To combat this problem, CIA background investigators not only contact the references given by applicants, but they also ask _those_ references for the names of additional contacts. They continue to branch out to additional references other than those originally supplied until they are satisfied. You can replicate this by maintaining a deep network within your industry and tapping into your contacts when you need to hear the _real_ story. Within the clandestine service, this is often referred to as getting the "hall file"—as in the employee details discussed only in hushed tones in the hallway, rather than those found inside the formal personnel file. A candidate's "hall file" can be excellent or it can be grim; either way, the details are a very useful supplement to what you are likely to learn if you only take a cursory glance at a candidate's résumé.
**2. Corroborate the skills.** Don't take an applicant's word for skills and strengths; ask him or her for specific, concrete examples. Your top candidate claims to be a good writer? Ask for samples. She claims to be an effective manager? Ask for an example of how she dealt with a problem employee. He claims to be proficient in real estate law? Ask him a challenging legal question that he _should_ be able to answer. She claims to have excellent customer service skills? Role-play a scenario with her in which you portray a difficult customer, and see how she responds.
Developing an interview that can elicit and corroborate critical skills has the added advantage of allowing you to tap into a wider array of potential applicants. If you are relying exclusively on reading the right words on a résumé and hearing the right prememorized buzzwords during an interview, you may be missing out on better candidates who have a less traditional job history. By structuring your interview to elicit specific examples of critical skills, you free yourself from the tyranny of previous job titles. The lazy hiring manager only extends offers for an account executive position to those candidates with the requisite number of years in identically titled jobs. Managers with more confidence in their ability to elicit and corroborate the ideal skills for that position can seek potentially better candidates from outside of the traditional but often stale talent pool.
As an example, the CIA has recently started relaxing its strict language requirements in order to cast its hiring net a little wider. In this case, however, recruiters have loosened their standards for one reason and one reason only: sheer desperation. The CIA has struggled for years now with a dire shortage of officers with Arabic-language capabilities. When targeted job advertisements and linguistic recruitment goals failed to produce enough Arabic speakers, recruiters took a step back and began seeking applicants with a general aptitude for learning foreign languages and an interest in Arab culture. The CIA would, of course, prefer to hire applicants already fluent in Arabic; it is an extremely difficult language to master. However, given an increasingly severe skill shortage, recruiters had no choice but to seek _aptitude_ rather than preexisting ability.
It is the best of all possible worlds when you have an ample supply of enthusiastic and well-qualified applicants for all of your job openings. As anyone who has ever had to fill an important assignment knows, however, this is rarely the case. Implementing a meaningful strategy and relaxing rigid and archaic requirements can open up a much deeper talent pool from which to draw.
A LESSON FROM THE DARK SIDE: OFFENSIVE RECRUITING
In the interest of national security, CIA officers engage in an awful lot of "recruiting" behaviors that would be illegal and downright immoral in any other context. When the circumstances warrant, they will lie, cheat, mislead, surveil, trap, threaten, and even detain. Clearly, these are not behaviors that I want readers to adopt. As a result, this chapter has focused primarily on the recruitment techniques that can be learned from the CIA's _internal_ hiring practices. However, there are also lessons to be learned from the darker side—from the recruiting practices of spies and from covert operations.
Corporate hiring practices are typically reactive in nature. A position becomes vacant, advertisements go out in various media, résumés are compared, applicants are interviewed, and the best candidate gets an offer. The proliferation and success of online résumé databases has changed the paradigm somewhat, in that organizations can now search for qualified individuals at any time, and therefore no longer have to passively wait for job seekers to apply for their specific positions. So-called headhunters also tend to be less reactive; the most successful among them typically have a large stable of well-qualified individuals waiting in the wings, to be placed as appropriate jobs arise. However, in each of these cases, hiring is still done on a case-by-case basis.
What if, instead, you could cherry-pick from your competitors' best employees, thereby not only bolstering the talent set within your own organization but also dealing a harsh blow to your competitors? What if your recruiting practices focused on the most critical skill sets within your industry, and in doing so caused a crippling brain drain to impede your competition's ability to function at peak capacity?
Many readers may balk at this; "stealing" a team of employees certainly sounds unsavory. But in practice, I am not advocating anything sleazy or underhanded. Instead, you can achieve this by systematically creating a better environment for the superstars in your industry. This is akin to "stealing" customers by delivering a superior product—no better and no worse.
Begin by identifying which of your competitors has the deepest bench of talent for the function or skill set that is most critical to your organization's success. Depending on your industry and your organization's position within it, the critical function could be sales, research and development, production, or any number of skill-oriented categories. Rarely will an individual senior-level executive actually bring a true competitive advantage to an organization (although you would certainly think so from today's executive compensation packages). Instead, focus on identifying those people who _do, create,_ or _change_ something tangible or quantifiable. I don't intend to disparage the value of strong executive leadership, but the idea that I would like to replicate from covert operations is that of diminishing your competitor's capabilities while at the same time enhancing your own.
Next, identify the "target" who, if hired, would be most capable of helping your company build its dream team by propagating a brain drain among your competitors. You are looking for someone to create and lead a new team within your organization, so your target needs to be someone with sufficient talent, experience, and charisma to make other people _want_ to work for him or her. Note that seniority alone does not mean anything; your ideal target may be someone relatively junior, but fully capable of rapid success.
Finding your "hook" with this coveted employee and the talented new hires you hope to attract is also part of the targeting process. What if your industry superstars are perfectly content with their present jobs? How will you even lure your targets to an interview, much less persuade them to accept a job? You should have a good idea of what will pique your targets' interest before you even initiate contact.
Obviously, compensation is king—at first glance. It is difficult to lure anyone without a competitive salary package. But not every organization has the luxury of doling out bigger and bigger salary packages; limited budgets and head-count capacities are a simple fact of corporate life. All the more reason, then, to study how the CIA manages to attract and retain incredibly talented individuals to perform dangerous, difficult work for far lower salaries than they are capable of making in the private sector. If you want to engage in offensive recruiting—the act of hiring talent for the purpose of adding to your organization's capabilities at the same time as you enervate your competition—you need to create an environment in which the best and the brightest _want_ to work.
ORGANIZATIONAL STRATEGIES FROM THE CLANDESTINE WORLD
One of the best parts of working for the CIA is the opportunity to work with an incredibly varied, talented, and adventurous group of people. Consider the backgrounds of just a few of my former colleagues who come to mind: A former professional athlete turned investment banker who was already a millionaire when he started over near the bottom of the government pay scale. A corporate attorney fluent in Mandarin Chinese and French. An architect with a high-degree black belt and an impressive number of difficult mountain summits to her name. An Ivy League doctorate-holder who speaks five languages. A former Special Forces officer with an MBA from one of the nation's top universities. A former prosecutor whose sense of humor and gregarious personality enabled him to talk people into doing just about anything.
The CIA manages to recruit some pretty incredible individuals. The pay, though? Eh.
Of course, the CIA _is_ able to offer its clandestine service employees perks that you won't find anywhere else. I, for one, was thrilled to no end by the chance to spend a week jumping out of airplanes during the agency's condensed airborne school, receive disguise training, and go through a high-speed "crash and bang" driving course that included a lesson in smashing through blockades. Never mind that these newfound skills played little to no role in my subsequent day-to-day duties—it was incredible fun! I would happily forgo a corporate bonus or two for these opportunities.
Obviously, though, the CIA is not a perfect place, and the job isn't for everyone. As with any job, there are pros and cons to the undercover profession. The bureaucracy can be maddening, advancement can be slow, and there are plenty of incompetent jerks, just like in any large organization.
Yet the clandestine service manages to retain many officers whose skills, education, and experiences would allow them to pursue their choice of opportunities in the outside world. In fact, the retention rate in the clandestine service compares very favorably to the private sector. So why do the employees stay?
A big part of the reason for the impressive retention is because of the CIA's mission. Case officers believe in what they do, and they like making a difference in the world. The travel opportunities, the glamour of the job, and the excitement also keep people around. But while these factors are not fully replicable in the corporate world, the CIA also utilizes a number of organizational strategies that can certainly be duplicated by private employers to keep talented and in-demand employees happy and productive.
The following organizational structures and strategies used by the CIA are listed not only because they appeal to high-performing _individuals_ , but because they also contribute to high performance for _organizations:_
**1. Encourage frequent rotation.** CIA officers change assignments frequently. My own assignments have lasted everywhere from sixty-day stints in war zones with minimal infrastructure to almost three years in a more stable position. Perhaps more important, each of my assignments was drastically different from the last. For a self-confessed job-hopper such as me, this was very appealing. There was little opportunity to get bored, and ample opportunity to learn.
High performers hate stagnant environments. Small companies in particular, though, frequently face headroom limitations that make upward mobility difficult. A company with only six employees simply can't justify promoting to the management ranks everyone who shows potential; to do so would result in a top-heavy, unproductive organization. However, allowing talented employees to move between departments, functions, and locations breeds a multidimensional workforce, and also helps to circulate knowledge and talent throughout your organization. It also keeps things interesting for your employees, who might otherwise begin to feel stuck. The next item is related:
**2. Be a résumé builder.** Ironically, the best employers are often those who make it the easiest to find work elsewhere. That's because the top employers provide the best training opportunities, the most challenging assignments, the most capable mentors, and the most diverse experiences. The better and the more challenging the job, the better it makes as an entry on a résumé.
It's hard to beat "Clandestine Service Officer, Central Intelligence Agency" for an eyebrow-raising résumé entry. By becoming an employer recognizable in your own right for the quality and talent of your workforce, though, you become more attractive not only to the top candidates, but also to your customers and clients.
**3. Match the person, not the title, to the task.** After I finished my year of training to become a clandestine service officer, I reported for my first day of work expecting not much more than instructions on where to find my desk and introductions to my new colleagues. I was stunned, then, when the first words out of my new boss's mouth were, "Did you pass your firearms training?" I had—in fact I had done surprisingly well for someone who doesn't like guns—but I couldn't imagine why she was asking. It turns out that she wanted me to head to Afghanistan. As soon as possible. It was not the first day on the job that I had anticipated, but this was shortly after 9/11, so I quickly agreed to go.
Fast-forward a few blurry weeks later and I found myself—still in my twenties and barely a year out of my former corporate life—wearing a bulletproof vest and a gun, sitting in the back of a jeep driven by a heavily armed Afghan man, with my feet literally resting on a Stinger missile. This was the first of many moments when all I could do was shake my head and wonder how on earth I had come to be in that situation. I enjoyed many things about my career at the CIA, but the single best part of it was the existence of incredible opportunities and huge responsibilities from the first day I reported to duty.
If you are serious about attracting the top talent in your industry, you can't afford to let your employees languish in unchallenging positions. Too often, employers recruit bright and talented individuals, but then hesitate to give them any real responsibility until they are more "seasoned" or more senior in the organization. In the meantime, the talented recruits are bored out their minds, and likely to spend their ample free time surfing the Internet for a better job.
I'm not advocating that employers put untested new hires in situations where a beginner's mistake could be costly for the organization. I do, however, believe that employees' skills and abilities— _not_ their seniority or job title—should determine who is best qualified for the most high-stakes assignments.
When the CIA identifies a high-profile target, careful attention is given to selecting the right officer for the job. Consideration is given to language, nationality, personality, gender, age, and area of expertise. It does not always make sense for a fifty-five-year-old English-speaking white male electrical engineer from Wisconsin to try to recruit a twentysomething female hijab-wearing Middle Eastern student who speaks only Arabic, for example—even if the fifty-five-year-old is a highly skilled senior officer.
Similar employee-customer "matches" are also important in the private sector, although using different criteria. I know one senior partner in a well-known law firm who still does not know how to use a computer—his secretary prints out his e-mails for him, and he dictates the responses. He is a brilliant lawyer, but he was obviously not the most appropriate legal counsel for one of the firm's most important clients—a high-tech Internet-based company. Although the law firm has a history of making hierarchy-based assignments—pairing the junior associates with the less lucrative and lower-profile clients—the managing partners finally decided that they would need to tap into some of their more tech-savvy but newer lawyers or risk losing a client that didn't want to have to explain technology basics to its high-priced legal counsel.
While it is not advisable to match customers and employees based on demographic variables like nationality, gender, or age (in fact, doing so would likely put you in violation of EEO laws) when making assignments, _do_ consider an employee's personality, skill set, language capabilities, and whatever else may impress your customer. Just as CIA officers find it easier to establish rapport and trust with targets when they share something in common, so will your employees thrive when their assignments are matched to their skills. Eliminating hierarchy-based assignment practices ultimately benefits both employees _and_ your relationship with your customers.
**4. Spice things up.** Clearly, not every work assignment is glamorous, not every client is high profile, and not every account is career enhancing. On the other hand, _every_ organization has mundane work that simply needs to be done, and someone has to do it. Given this reality, it is all the more important to make sure that employee enthusiasm is not extinguished by endless dreary tasks, and that initiative is not crushed by distance from organizational power.
CIA officers lead exciting lives, but even spies need to do their accounting. Furthermore, the clandestine service is kept operational by an enormous cast of support officers. Their jobs—logistics, health, administration, and travel, among others—are not the jobs depicted in Hollywood's version of the CIA. But the functions are critical, and these folks often find themselves performing their support roles in dangerous, high-pressure environments—just like their more high-profile clandestine service colleagues.
So, how to keep support staff involved and motivated? The CIA does it by keeping support staff involved and motivated.
That is not a facetious statement. Instead, it is the best way to describe the CIA's use of cross-functional teams that include members from a wide variety of backgrounds and pay grades. (Now, hear me out and don't skip this section quite yet. I am fully aware that using cross-functional teams was in vogue in management literature a decade or two ago, and that the use of these teams was of mixed value, depending on the industry and application.) The CIA does not use cross-functional teams for the purpose of employee satisfaction, or simply as an academic exercise in trendy organizational design. Instead, it organizes groups of officers from different functions across the agency—not just the clandestine service—in order to get in, get things done, and get out as safely and efficiently as possible.
When was the last time your organization included anyone but the usual cast of executives in an important planning session? Yet the CIA would never be able to move quickly on a fast-breaking operation if it didn't involve people from across the organization. Getting one case officer in front of a high-profile target on an urgent basis requires analytical support, logistical planning, medical clearance, finance, and appropriate documents (whether forged or authentic), along with numerous other supporting elements. Your organization certainly has its own activities and events that require substantial involvement from multiple departments. So shouldn't the members of the various departments work together on a regular basis?
The CIA utilizes many different kinds of cross-functional teams. Quick-response teams drill together to be able to deploy on a moment's notice. Red Cell teams, discussed in chapter 3, combine the unlikeliest people to brainstorm the unlikeliest threats. Surveillance teams intentionally include the most diverse possible memberships so that at least one team member can blend in just about anywhere. Task forces bring in members from different government organizations, military branches, and law enforcement agencies. Career evaluation panels consisting of individuals from various ranks are used to assess officer performance. Case assessment teams bring together experts from both the analytical and the operational sides of the house. Strategic planning teams consist of members with years of field experience who have been asked to complete a headquarters-based management tour. Recruitment teams incorporate members from each of the CIA's directorates to do joint presentations for recruiting events all over the country. In each of these cases, the teams are composed of people from widely varying backgrounds who come together to accomplish a single objective.
In the highly compartmentalized atmosphere of the CIA, the formation of these teams is critical to communications, efficiency, and the achievement of results. The teams were created to function, not to educate, but members always walk away with a broader understanding of the organization (for better or for worse). And this only makes the organization stronger. Participation can be enjoyable, or it can be frustrating. Just as a group of physicists will usually walk, talk, and dress differently from a group of graphic designers, the different functions within the CIA also have distinct personalities and practices. Sometimes the clash of cultures can be distracting, and sometimes even amusing. But most important? The teams get the job done, and the members are always rewarded for their involvement. In fact, participation in multidisciplinary teams is considered crucial for promotion.
Every industry has its own specialists and its own critical skills, and cross-functional teams naturally work better in some environments than in others. Every type of organization, however, can benefit from the use of quick-response teams to deal with predictable but urgent matters. Red Cell teams to play devil's advocate and deal with unpredictable matters, and task forces to deal with the most difficult challenges with the minimum number of bureaucratic obstacles. These teams, which are designed to predict, react, and facilitate as effectively as possible in extreme circumstances, can be just as valuable in the private sector as in the CIA. Participation is rewarding for both the organization and the employees, and it keeps _everyone_ —not just your superstars or senior executives—motivated and involved.
**5. Make room for lone wolves.** At the risk of contradicting myself after the last section extolling the virtue of teams, I hasten to advise readers not to _force_ collaboration onto talented individuals who are superstars in their own right but don't necessarily work well with others. Some people thrive on team participation, out-of-specialty rotational assignments, and constant developmental opportunities. Other people do their jobs well and just want to be left alone to do what they were hired for.
I had one colleague who was a grizzled, gruff, unsmiling sort. How he ever became a case officer was beyond me, because not only did he lack the winning personality possessed by most CIA officers, but he also seemed to quite literally dislike most other people in the world. And yet he was brilliant at his job. He possessed an encyclopedic knowledge of weapons systems and defense strategies, and he was uniquely able to spot, assess, and develop other people just like himself—targets with highly specialized knowledge who shunned most of the traditional approaches used by case officers. He excelled in getting taciturn, tough, and grizzled officials from target nations to spill their secrets, because he was just like them. I suspect that, on average, his conversations with his recruited assets consisted of a small fraction of the number of words used in parallel conversations between other officers and assets. Yet in his gruff, taciturn way he got the job done when no one else could.
This superb officer would have been a disastrous manager, though, and a thoroughly unpleasant team member. So he was promoted over the course of the years on the basis of his solo work and left alone to achieve his results.
Not all superstars are cut out for management, and not all will benefit from or contribute to teams. The best employers understand this and do not try to force these talented solo operators into roles that would detract from their individual successes. The CIA has plenty of ambitious sorts who yearn to be in senior management as soon as possible; it also has its share of clandestine officers who thrive in the independence afforded to spies in the field. (Incidentally, these field-preferring officers refer to CIA headquarters as the "Death Star," and will go to great lengths to avoid management positions there.) Fortunately, the organizational structure quite effectively accommodates both tracks.
Human resource practices within the CIA are substantially different from those within a private organization. Because of the nature of the work and the requirement for top-secret security clearances, clandestine careers can be far more intrusive and emotionally involved than a typical nine-to-five job. Moreover, CIA officers are in demand from private-sector employers, and—yes—sometimes even from foreign governments that are just as eager as we are to establish penetrations of rival intelligence services. All the more reason, then, for the CIA to employ an organizational and personnel structure that facilitates critical work while simultaneously motivating and monitoring employee performance.
Whether or not national security depends upon _your_ organization's success, your workforce can benefit from some of the CIA's recruiting and organizational strategies. Whether you are hiring a CEO or a fry cook, you should have confidence that your selection process is fair, accurate, and effective. And once you have built an organization, you should put in place a structure that maximizes performance and attracts and retains top talent.
Paradoxically, however, the highest achievers can also be the most difficult to manage. For better or worse, they have the confidence to stand up to authority, the intelligence to debate, and the bravery to defy—all of which can amount to a serious management challenge. Although I said earlier in this chapter that your employees do not need to be your friends, it _is_ imperative that you be able to trust their ability to make the right choices when you give them the autonomy they deserve. The next chapter, on ethics, addresses this issue in depth.
CHAPTER FIVE
Staying Clean in a Dirty World: The Ethics of Espionage
The asset chain-smoked through the turnover meeting, but did not otherwise seem fazed to learn that he would no longer be meeting with the officer who had been his handler for the past several years. Tom introduced me as the officer who would be replacing him, and then handed the asset a large envelope of cash—a substantial payment for the last several months of clandestine work.
The asset shook hands cheerfully with Tom, wished him luck in the future, and then pulled from the envelope a stack of large bills. Smiling broadly, he handed the money to Tom and said that the money was "for charity." "Perhaps you have a fund for the children of fallen CIA officers?" he asked with a wink. He was from a part of the world where bribery and kickbacks were a normal part of doing business, and it was crystal clear to me that the money was intended as a farewell gift for Tom in the form of a sizable kickback.
I didn't say a word about this exchange, during or after the meeting. I was still a junior officer, and I thought that it would be better to simply watch and see what happened to the money.
Almost immediately upon our return from the trip, then, I was pleasantly surprised to be copied on an internal e-mail from Tom earnestly describing the "generous donation" and documenting the transfer of the money to the agency's scholarship fund.
To this day, I do not know whether Tom even realized that the asset intended for him to pocket the money. I am, however, quite certain that keeping it never crossed Tom's mind for a second.
Why on earth would anyone ever trust a CIA officer? Not only are we selected in part because of our willingness and ability to tell a convincing lie, but we also receive specialized training in deception. We can expertly evade, fabricate, obscure, equivocate, distract, and just flat-out lie to your face. We understand the roles that body language, eye contact, timing, and detail play in persuasion. Add to that years of practice in our professional capacities, plus lying even to friends and family in order to maintain our cover, and it seems hard to believe that any of us even remember what the truth is.
And yet, as I stated earlier in this book, CIA officers are some of the most principled people you will ever meet.
How can this level of integrity and this skill at deception possibly coexist?
CIA clandestine service officers can simultaneously possess these two ostensibly contradictory traits because they live by a strict ethical code that keeps them clean in what can sometimes be a filthy, dirty world. In fact, the concept of integrity is pervasive throughout the agency, running like lifeblood through the veins of an organization that operates primarily in the shadows.
If undercover CIA case officers were known more for their ability to tell a lie than for their integrity, they would never be effective. Because of this, officers may manipulate or lie in order to get face-to-face with a target, but once the mask comes off, the lying stops. In order to persuade potential spies to risk their lives to reveal secrets, CIA officers have to demonstrate that they can be trusted with the information. A spy's welfare rests in his case officer's hands: sloppy tradecraft or poor security practices can get a source arrested or killed. In order to earn the trust necessary to work in the high-stakes clandestine world, then, CIA officers need to constantly demonstrate that they are trustworthy and dependable. As a result, the unwritten ethical code of the clandestine world is as strong as steel, and there are certain lines that a CIA case officer will _never_ cross.
The business world, on the other hand, tends to view ethics and commerce as two distinct concepts that _can_ overlap if the stars align. Companies that manage to be both profitable _and_ ethical are lauded as if they had won two separate races at the same time. This chapter, however, will show how business professionals—like CIA officers—can use ethical practices to give them a distinct advantage in achieving the bottom line.
In fact, take it from someone whose career involved lying, cheating, and stealing on a daily basis: the dirtier, messier, and rougher the business, the more important it is to have strong principles and absolute standards.
HARDBALL ETHICS
Case officers don't adhere to strict ethical guidelines because to do so is "nice." In fact, case officer ethics are not rooted in humanitarian principles at all. Establishing trust is simply part of a CIA officer's job. Trust is as important to the clandestine world as capital is to the private sector—it is necessary to stay in business.
This trust is built through ongoing demonstrations of integrity and strict adherence to a code of conduct. I firmly believe that the ethical principles that guide CIA officers are 100 percent transferable to the corporate world. Unfortunately, the topic of business ethics sometimes gets a bad rap in tough markets. No one, of course, wants to act _un_ ethically. However, as I was once told by a senior executive, "You won't find ethics manuals on the bookshelves of CEOs who play hardball."
The idea that adherence to strict ethical standards is somehow "soft" is further perpetuated by business ethics books that discuss the topic solely in academic, moralistic, or philosophical terms. (I still shudder when I remember grad school assignments that required analysis of tedious chapters of academic ethical theories derived from Kantian philosophy.) CIA officers, however, learn early on in their careers that earning a reputation for integrity and dependability can pay very real dividends when times are tough. Read on for a list of hardball principles and lessons that are neither soft nor theoretical:
**1. Treat and protect your reputation and integrity as you would cold, hard cash.** I like nice people; I really do. I am not, however, advocating that you act with integrity just because doing so is _nice_. Your reputation is an asset, because trust is a currency. You can earn it, you can grow it, you can spend it, you can gamble with it, and you can lose it. The more trust capital you have banked with a person or organization, the more you can ask of them. Remember those old bumper stickers that used to tell us to "practice random acts of kindness"? The clandestine world's version would read "practice strategic acts of trustworthiness." It may not be as warm and fuzzy, but it does serve a purpose.
**2. Understand that sharks are cannibals.** (Google it if you don't believe me—you'll learn more about "intrauterine cannibalism" than you ever wanted to know.) In certain industries and professions, it is considered positive to be a "shark." Lawyers who advocate aggressively for their clients are often referred to in this way, as are aggressive salespeople. There is nothing wrong with strong, bold, fearless, and decisive behavior in the workplace. Most people I know who could be considered sharks, though, tend to pursue their career goals with a single-mindedness that renders them incapable of seeing anything but the goal.
Managers often seek out sharks for their teams because, whether you like them or not, they get the job done. But these managers sometimes learn about sharks' cannibalistic tendencies the hard way—when their hard-charging employee turns on his team.
The ethical principle here is that your team members are a reflection on _you_. If you tolerate unprincipled behavior among your peers or subordinates in the interest of achieving results, you shouldn't be surprised when the sharks start circling back on you. Guess what? An employee who is willing to do anything to make a sale is also willing to do whatever it takes to get _your_ job.
The CIA takes the behavior of its employees very seriously. Not only is the initial screening for all new hires rigorous, but officers are subject to frequent background and financial reinvestigations as well as regular polygraphs throughout their careers. Unprincipled conduct is referred to as a "suitability issue" in CIA parlance, because ethical lapses are understood to mean that an individual is no longer suitable for employment or security clearance. No officer wants to work with a teammate whose ethical lapses could result in disastrous consequences. "Aggressive" case officers are welcome. Sharks, on the other hand, are not.
**3. Compartmentalize.** The CIA is often criticized for failing to adequately share information with policy makers, the rest of the intelligence community, and the public. In some cases, this criticism is deserved. In others, information is withheld because it _must_ be, for any number of reasons ranging from national security to doubts about the accuracy of the data. The general rule is that information is disseminated on a "need to know" basis.
In the corporate world, compartmentalization can serve a similar function. We all know that knowledge is power. Secrets, of course, can be incredibly powerful indeed. Just as in the clandestine world, though, you need to use your knowledge of secrets judiciously. Don't boast about your knowledge, don't spread information for malicious purposes, and don't share other people's secrets gratuitously. You lose trust capital with every loose secret, so make sure that your revelations are worth the price. (And sometimes they are _well_ worth the price.)
**4. Know when to lie.** This is a slightly facetious way of saying just the converse—know when _not_ to lie. This includes the most common type of lie within organizations—lies of omission. You should be known as someone who can take a secret to your grave (see compartmentalization, above), but also as someone who will never withhold information unnecessarily. Too many midlevel managers, in particular, treat information as a competitive advantage; they withhold it from peers and subordinates in order to have a greater share of the power. There are many reasons to withhold information, but putting your teammates at a disadvantage is not one of them.
Within the CIA, even a small lie to colleagues is considered a serious offense. Clandestine officers rely on every member of their team to keep operations running smoothly and safely. Even an inconsequential lie would cast doubts on a colleague's suitability and trustworthiness. Therefore, although officers may practice their cover stories (the elaborate lies that allow them to pursue their real agendas) with one another, they will never lie to a colleague.
You may also be surprised to hear that CIA officers try to lie as little as possible, even when dealing with targets. Generally speaking, the closer one's cover story is to the truth, the easier it is to remember, and the easier it is to defend. Because of this, a CIA officer's undercover identity will typically consist of blatant lies woven with half-truths, glued together with real facts. The closer your story is to the truth, the easier it is to convince a hostile immigration officer, a cynical target, or just a nosy stranger that you are who you say you are.
I don't mean for this to sound as if I'm encouraging readers to lie at all, whether big lies or small ones. Quite the opposite, in fact—I'm simply attempting to explain that even those people who _must_ lie, like CIA officers, try to keep the mistruths to a minimum. Why risk getting caught up in a tangled web of lies when the truth will suffice?
**5. Own the solution, not the mistake.** Schoolyard ethics extol the virtues of admitting one's mistakes. That's all good and fine, but when the stakes are high, creating the solution is a lot more important than owning the mistake.
A CIA officer would _never_ show up to a meeting with an asset to announce, "By the way, you've been compromised; we're working on it, and I'll get back to you later this week." Instead, news of a possible compromise would be accompanied by a detailed exfiltration plan, a new identity, and travel documents in hand. And yet somewhere along the line the corporate world seemed to come to a belief that simply identifying and taking credit for a mistake was laudable. Stating that you "take full responsibility" for a mistake is not a magnanimous act. Finding and implementing the fix _is_.
**6. Acknowledge that personal life does reflect on business life.** CIA officers aren't allowed much privacy. They have to disclose intimate relationships, submit to medical and psychological screening, and regularly take the dreaded "lifestyle" polygraph. Unlike other polygraph exams that test strictly for veracity on a very specific topic, the lifestyle polygraph requires officers to discuss excruciatingly personal topics while hooked up to the lie detection machine. It can be an unpleasant, nerve-racking experience for even the cleanest-living individuals. This mandatory confessional of sorts is such a ubiquitous part of the work culture that CIA officers often joke that "that's between you and your polygrapher" when a colleague reveals overly personal information.
Personally, I don't believe that the polygraph exams used by the CIA are particularly effective, both because there are countermeasures and because the interpretation of results is more art than science, and therefore highly subjective. That's a topic for another book, however. Yet although I am not a fan of the polygraph, I _do_ believe in one of the reasons for its use—the premise that your personal life can and does reflect on your business life.
I certainly do not advocate corporate witch hunts to determine employees' foibles and faults. However, employers who become aware of issues either criminal or simply unethical should not be so quick to dismiss the impact on the organization just because the crime occurred on personal time. Spousal abusers _are_ violent people, and are more likely to commit additional acts of aggression at home or at the office. Philanderers _are_ more likely to conduct their liaisons on company time, or to use company funds to pay for their activities. Drug or alcohol abuse _does_ impair judgment, even if an employee is sober during work hours. Racist comments posted on an employee's personal blog _do_ give you fair notice that your employee is also likely to espouse the same viewpoint with co-workers.
It's simple: past behavior predicts future behavior. Disreputable behavior on personal time is an indicator of a greater likelihood of disreputable behavior on _your_ clock. Character and integrity are constants, and any display of a lack thereof should be taken seriously. To combat this problem, seek out individuals who can be aggressive in a business setting but compassionate on an interpersonal level. Furthermore, don't draw an arbitrary distinction between behavior that occurs on versus off the clock. Regardless of whether you learn about unethical conduct from an employees' activities at work, a police report, or photos on a Facebook page, the take-home lesson should be the same: zero tolerance on your payroll.
**7. Accept that allegiances shift.** Look at Afghanistan for a classic example of shifting allegiances. Once the enemy of our Cold War enemy, this nation was treated by the United States as an ally against the USSR. Fast-forward to 2001, however, and the Stinger missiles that we provided for use against Soviet troops were now being aimed at our own soldiers, and the Russians were advising us on strategies against the Taliban.
Corporate buyouts, mergers, joint ventures, and even personnel changes can similarly result in yesterday's enemy being today's ally. Just look at the long history of JPMorgan Chase: it's a veritable soap opera of mergers and acquisitions, involving a staggering number of overlapping competitors. All the more reason, then, to demonstrate integrity even when dealing with your toughest competitors, and to maintain civility with even your most despised rivals. The world changes quickly, and it can be impossible to predict when your interests might align with some surprising players.
**8. Sleep with the enemy . . . with one eye open**. In a world of shifting allegiances, there are always enemies. Don't be afraid to proceed—cautiously—should a mutually beneficial opportunity to work with your enemy arise.
There are places where CIA officers simply can't go. Remember how the profile of an ideal clandestine officer is sometimes referred to as a Boy Scout with a secret dark side? Well, Boy Scouts stick out like sore thumbs in many parts of the world. Terrorists rely on this when they select their base of operations, such as when Osama bin Laden chose to make his headquarters in places like Sudan and Afghanistan—both extremely difficult environments for CIA officers to operate in. But there are a number of nations that are hostile toward both the United States _and_ terrorist training camps within their borders. The CIA relies on limited partnerships with these "enemy" states to capture, detain, and sometimes extradite suspected terrorists. These joint operations often go on in spite of public animosity between the two countries.
On a (hopefully) less dramatic front, organizations should similarly be willing to partner with their "enemy"—whether that be a competitor, an unpleasant former colleague, or an investigating regulatory agency—when the benefits outweigh the risks. Protect your assets as you proceed, but be open to opportunities that may arise with the unlikeliest partners.
**9. Act urgently when things are urgent.** Sound like a no-brainer? Yet there are personality types and work styles that treat _everything_ as a crisis. In certain organizations, a "sense of urgency" is extolled as an important virtue, even when the reality of the situation is anything _but_ urgent. In many situations, rushing things can actually do more harm than good.
One of the more difficult aspects of a clandestine officer's job is knowing when a target is ready to hear a recruitment pitch. Just imagine yourself in a potential spy's shoes. Say a person with whom you have developed an increasingly close and trusting relationship suddenly tells you that she has a secret. She reveals that much of what she has told you about herself is a lie—she is actually an undercover CIA officer, and she wants _you_ to risk your life and livelihood to pass her top-secret information on a regular basis. Obviously, this is not an easy request to process. An officer who rushes the developmental process and fails to establish sufficient rapport and trust runs the risk of having her target balk, refuse, or even report her to the authorities. Even when the target possesses information of an urgent nature, officers need to be careful not to unnecessarily rush the situation. To do so would be counterproductive.
Yet I have known managers in the corporate world who believe that anything _but_ a sense of urgency is unacceptable. They like their employees to jump when they call, and to have all tasks completed _yesterday_. Not only does this style of management promote sloppy, rushed work, but it also abuses employees who are perfectly aware that the report that they worked on all weekend could have waited, but for their manager's impatience. It also doesn't leave room for shifting priorities. If your team members have a true grasp of what is urgent and what is not, they can instantly adapt and prioritize when something _truly_ critical arises.
**10. Revere the law of unintended consequences.** CIA officers are always on the lookout for political, economic, and even industrial changes that may have indirect consequences for targets of interest. A military coup somewhere, for example, means that there are suddenly quite a few former senior officials who have been displaced from power, and are likely both to carry a grudge against the new regime and be in need of a new paycheck. In other words, they are ripe for recruitment. Nepotism also yields benefits for case officers on the prowl for new spies. When a country's leader appoints his son-in-law to a prominent position rather than the career official who has been toiling for years in hope of a promotion, there is suddenly a disgruntled official just waiting for a visit from his friendly U.S. government representative.
The corporate world can also take advantage of unintended consequences. Your competitor is considering possible layoffs? Now is the time to siphon off their top talent—even those who will likely be immune from layoffs will be eager to find more stable employment. Lawsuits and unfavorable regulatory rulings against your suppliers may mean that they are more eager than ever to lock in long-term contracts at discounted rates. A senior partner at the competing law or consulting firm gets bad publicity in the local press? Once-loyal clients are suddenly willing to consider switching.
Make it a point to keep current on local and industrial news, with the intention of extrapolating unintended consequences with potential benefit for you or for your organization. This is also yet another example of where you can benefit from having an extended network of contacts within your industry: the earlier you learn of impending changes, the faster you can act. Senior personnel moves, legal rulings, changing market conditions, and many other changing variables throughout your competition's supply chain and customer pool can all have positive consequences for you.
Is this predatory? A bit, perhaps. Would your competition happily return the favor if the circumstances were reversed? Of course.
**11. Take responsibility for the integrity of your supply chain.** The CIA gets a lot of information from an extremely wide variety of sources. Some of that information is accurate, urgent, and of major consequence. Some is decidedly not. All clandestine officers have to learn to sort out the accurate information from the erroneous. Information can be bad for myriad reasons: sometimes sources struggle with language barriers, sometimes they fabricate or lie in the hope of receiving payment for false information, and—surprisingly often—information comes from delusional individuals who harbor conspiracy theories involving the CIA. (The agency's public Web site, in particular, receives some unbelievably off-the-wall e-mails.) One of my colleagues had to maintain a straight face during a meeting with a potential "source" who reported that Osama bin Laden was living in Florida and had managed to escape detection because he went everywhere dressed as a clown, with full face makeup including a red rubber nose. The source claimed to know this because of his psychic abilities.
Fortunately, the overwhelming majority of incoming information is not quite so bizarre. Nevertheless, not all sources are created equal, and determining whether a report is legitimate can be difficult. When reporting collected information to the intelligence community, then, CIA officers have a responsibility to notify recipients about factors that cast doubt on the credibility of a source's report. Clearly, a report from a semicoherent drunk with an obvious goal of seeking political asylum should not be given as much weight as a report from someone whose demeanor and supporting details indicate a high likelihood that the source is telling the truth.
The corporate world also bears a responsibility to its consumers to continually evaluate its sources. Companies like Nike and Reebok learned the hard way that consumers _will_ blame them for having subcontractors who use child labor; plausible deniability did not appease company critics for a second. Mattel, among other major toy companies, has had to recall millions of toys because Chinese suppliers used lead paint. Clearly, this was _not_ a high point for the company's brand reputation. The topic of evaluating suppliers will be covered in more detail later in the book, but suffice it to say that it behooves both the CIA _and_ the private sector to constantly and carefully evaluate sources.
**12. Count your nickels and dimes.** The clandestine world is a cash economy. After all, a spy can't exactly accept a personal check, right? Because of this, CIA officers have access to large sums of cash, and a great deal of discretion in how it is spent. They also have quite a few expenses that would be, well, _unusual_ in the corporate world. For example, I had a colleague who received approval to use government funds for eyebrow waxing, because the CIA disguise team decided that her dark, distinctive eyebrows made it too difficult to alter her appearance when necessary.
Perhaps _because_ it would be so easy for an officer to filch a little money here and a little money there, even the tiniest of financial irregularities are grounds for immediate dismissal. Case officers are very aware that they are spending taxpayer dollars, and they don't mess around with their cash or their accounting. Moreover, this goes back to the principle that even small ethical lapses are indicative of character flaws and integrity issues that can render an individual unsuitable for employment in a job that requires as much trust as the CIA.
The corporate world, on the other hand, regularly suffers from very well-publicized integrity lapses in the form of inappropriate spending. Former Tyco International CEO Dennis Kozlowski, for example, who was convicted in 2005 for misappropriation of corporate funds. His spending habits, which included using Tyco funds to pay for a million-dollar-plus birthday party for his wife, and for his now-infamous $6,000 shower curtains, received incredulous media attention. In 2008, the CEOs of the big three U.S. automakers, GM, Chrysler, and Ford, were publicly shamed for using luxury private jets to fly to Washington, D.C., in order to plead for public funds to avoid bankruptcy. (And no, of course they did not carpool—each CEO traveled in his own jet.) That same year the public was furious to learn that millions of dollars of government-funded bailout money for the financial sector was used to pay hefty bonuses to some of the very same Wall Street investment bankers whose trading and investment activities had led to the collapse that prompted the bailout. Taxpayers scratched their heads with a feeling of outraged déjà vu when in 2011 reports came out detailing the multimillion-dollar bonuses paid to top executives of Fannie Mae and Freddie Mac for decidedly less than stellar performance during a period when both organizations were still very much dependent upon ongoing federal bailouts.
In each case, the expenditures quite understandably elicited ridicule and anger from taxpayers and shareholders toward the respective companies. It was clear to people on the outside that these events demonstrated more than just frivolous spending—they suggested serious and systemic ethical problems that eroded public trust in the organizations in question.
Clearly, a company does not go from scrupulous fiscal responsibility to writing off millions of dollars of luxury overnight. Instead, inappropriate expenditures of this magnitude come from a pervasive lack of respect for the source and purpose of funds. Nickels and dimes misspent can all too quickly become millions of dollars misspent, so principled accounting and financial practices should be adopted at all levels of an organization in order to avoid this slippery slope.
DEALING WITH ETHICAL CHALLENGES
It's easy to preach ethics in a book. It can be far more challenging to practice principled behavior in a competitive field where it seems like everyone else is playing dirty. The best strategy is to have firm, resolute principles and an unwavering boundary that you never cross.
The real world is never black and white, though, and even the strongest ethical beliefs can start to blur when the situation gets messy and gray. Prior to 9/11, for example, most CIA officers had never even heard of waterboarding. One day and four airplanes later, however, traditional agency tactics were turned on their head overnight. This is not the book to discuss or debate CIA interrogation techniques, but suffice it to say that for many of those directly involved in managing the aftermath of 9/11, what had once seemed unfathomable suddenly became a grim reality. Suddenly officials had to make decisions about how far to go during interrogations of terrorist detainees, or whether or not to render a captured terrorist to a country known to commit human rights violations. I can assure you that _no one_ took these subjects lightly, and that there has never been a firm internal consensus on tough subjects such as these.
The corporate world may not have to debate the definition of torture, but many decisions made in the private sector _do_ have life-and-death implications. Pharmaceutical trials, environmental impact studies, medical insurance policy decisions, safety standards . . . there are plenty of difficult topics in the business world that have profound consequences for people's lives and livelihoods.
To make matters more complicated, the law does not always give clear instructions to guide corporate behavior. The law has loopholes, ambiguities, conflicting precedents, and unexplored territories. For some multinational transactions, it isn't even always clear which country's laws apply. Furthermore, depending on your organization's risk tolerance, the urgency of the situation, the importance of the matter, the impact on others, and the norms of the industry, you might have a very different threshold than another reader in a different business climate.
Given these complexities, it isn't always easy to identify, much less pursue, the "right" path. As CIA officers know all too well, in the midst of a dirty world, it can be difficult to stay clean. All the more reason, then, to identify and honor your ethical absolutes. You never know when your business may depend upon it.
CHAPTER SIX
Crisis Management Strategies (from an Organization That Truly Knows the Meaning of Crisis)
On September 11, 2001, I was sitting in a conference room along with the rest of my fellow clandestine service trainees. We were listening to a panel of guest speakers; the visiting presenters were various Pentagon officials talking to us about CIA cooperation with the military. Suddenly the course director walked in and announced that an airplane had just flown into one of the Twin Towers in New York City. He commandeered the remote control for the room's audiovisual system, turned on the television, and grimly left the room.
We all, of course, assumed that the announcement was part of yet another mock training exercise—just like the dozens that we had already completed. The speakers chuckled, thinking that they had been included in a surprise instructional scenario. The trainees didn't even blink; we were mere weeks away from the end of our year of training, and we were weary. We waited patiently for the drill to be further explained.
Then the beeping started. Cell phones aren't allowed in CIA buildings, but pagers are. In rapid succession, our guest speakers checked their pagers and then rushed from the room, all looking stunned.
It took several more minutes of horrible live footage playing out on the screen at the front of the room for the rest of us to realize that this time it wasn't a drill. This time, the crisis was real.
Several years before 2001 I was a trainee in a very different program. I was in a management development program within a large high-tech company—a position that I started straight out of grad school. The job was supposed to be prestigious—it was billed as a "fast track" to more senior management positions. Unfortunately, my timing was lousy. Unbeknownst to me, the dot-com bubble that had made the high-tech world so alluring to my fellow recent graduates and me had sprung a leak. Although numerically speaking the bubble wouldn't actually burst for a while, certain parts of the technology sector were already feeling the pain. Within weeks of my first day of work, my employer began to stumble. Layoffs were rumored, and then announced. An entire division was spun off, and then another division was just plain sold off.
My first rotation in the management development program was in the executive compensation department. One of my first tasks during this rotation was to decipher the complex golden parachute that was waiting for the chief executive officer. There wasn't much actual work being done elsewhere in the company as people waited to see whether or not they still had jobs, but I kept busy poring over a thick legal contract and turning it into a one-page "if-then" PowerPoint version of what would happen, financially speaking, should the CEO quit, retire, or be fired under various conditions.
The circumstances that caused my employer's plummet were not, of course, as devastating as a terrorist attack, but the company was definitely in crisis.
My respective experiences as a junior employee within two organizations in crisis could not have been more different. The crisis triggers might have been drastically dissimilar, and the stakes might have been worlds apart, but organizational psychology is filled with constants, and there are many universal reactions when a person's livelihood is threatened.
In my subsequent work as a federal investigator for the National Labor Relations Board (I told you that I job-hopped a lot!), I observed many more companies in crisis. I investigated all shapes and sizes of labor strikes, accusations of union vote fraud, allegations of picket line violence, threats from supervisors, unlawful terminations, and illegal management surveillance of union meetings. I saw organizations that responded productively and purposefully to perceived threats, and I also witnessed counterproductive, foolish, and sometimes outright criminal reactions. During the course of my investigations, I observed some of the ugliest and also some of the most collaborative reactions to organizational threats.
I am spelling out my firsthand experience with organizational crises because, based on my personal observations of numerous entities in the midst of major changes and predicaments, the CIA responded significantly more effectively, more quickly, more flexibly, and more positively than any of the other organizations I observed. Yes, the CIA made mistakes in the aftermath of 9/11—some of them tragic. But on an organizational level, its crisis management cannot be beat, and I am convinced that the private sector could learn a valuable lesson from the clandestine world's response to a crisis.
Listed here are some of the ways that the CIA responded more effectively to a crisis than what I have witnessed in the corporate world.
In its immediate reaction to 9/11, the CIA:
* Focused attention and action outward instead of inward
* Continued to acknowledge and reward performance
* Made senior management more accessible than ever
* Articulated crystal-clear directives
* Handed out extraordinary empowerment
* Redirected and refocused resources
* Went to great lengths to protect employees on the ground
* Created loyalty by inspiring it and trust by earning it
These crisis management strategies may be listed here as separate items, but they are all very much interrelated. In fact, as I wrote this book I originally attempted to create a fancy flow chart or graphic display of the CIA's response to the 9/11 crisis in order to depict how each factor strengthened the others. My relationship chart, however, very quickly became a convoluted spiderweb that would most certainly make readers' eyes glaze over. I won't torture your eyesight with the insult of an overly complicated graphic, but I _will_ endeavor to articulate how every response to a crisis can and will impact subsequent actions.
CRISIS MANAGEMENT STRATEGY 1: FOCUS ATTENTION OUTWARD
Finger-pointing began within hours after the events of 9/11. The entire world wanted to know who could have possibly committed such atrocities. One of the logical follow-on questions, then, was who could have _prevented_ the attacks. As details began to emerge and the perpetrators were identified, the CIA fell into the crosshairs of an angry, wounded public. As we all know now in retrospect, more could have been done to prevent the events of 9/11. Information should have been shared more effectively, emerging terrorist groups should have been neutralized when we had the chance, and dots should have been connected.
At the time, however, those of us in the CIA didn't have time for blame or recriminations. Every last employee was too busy responding. From the special operations officers who deployed to Afghanistan even before the military, to the support employees who worked around the clock at headquarters for months on end without a break, everyone was focused on finding, capturing, and bringing to justice the individuals who had planned and conducted the attacks. All attention was focused outward, toward achieving the final objective.
This experience was worlds apart from what I have observed in the private sector. In the corporate world, the focus during times of crisis tends to be overwhelmingly internal. Once it becomes clear to everyone that their company is going downhill fast, productivity grinds to a screeching halt. After all, no one knows if they are going to have a job the next day, much less whether or not their projects will continue. Everyone continues to show up to work, but chances are high that if you see someone busily working at a computer, he or she is drafting a résumé or searching the Web for a new job. In my experience, this was not just true at the junior employee level; the executives were also focused on their own careers rather than the salvation of the company. (The executive compensation department at my first employer was kept humming with a dramatic uptick in requests for information about the disposition of deeply underwater stock options.) Unfortunately, an internal focus during a crisis can be a destructive morale crusher.
I am aware that, to a large extent, I am comparing apples and oranges. Whereas a crisis brought on by a terrorist attack represents a threat to one's life and one's nation, a company crisis due to changing market conditions typically impacts little more than one's employment status. But when a company in turmoil fails to rally its employees to maintain an outward focus, its negative trajectory becomes steeper and steeper.
In order to accomplish an outward focus during times of crisis, it is absolutely necessary for organizations to uphold the following three standards:
**1. Brutal honesty.** In most cases, the rumors that circulate during an organizational crisis are at least as bad, if not worse, than the reality. If you keep your employees apprised of the good, the bad, and the ugly, you allow them to spend more time on their work and less time speculating about what _might_ be happening around them.
**2. A sense of purpose.** Employees with an uncertain future in an organization with an uncertain future need a unifying, motivating sense of purpose. If an organization is already being brutally honest, then management can also set brutally realistic goals: to stay in business for one more week, to slow the losses, to prevent additional negative publicity, and so on. These goals may sound depressing, but at least they give employees something to strive toward in the midst of chaos, and a sense of pride for continuing achievement.
**3. Realistic commitments.** It is exceedingly difficult for employees to keep an outward focus if they are worried about their ability to provide food and shelter for their families. Retention bonuses are helpful during an organizational crisis, but they are not, of course, always realistic for small employers or organizations whose financial state does not allow for the expense. Organizations in crisis therefore need to make realistic minimum commitments that will allow nervous employees to focus on the job, instead of the job search. Whether that involves a commitment to avoid layoffs for a week at a time, a commitment to pay generous bonuses once (if) the crisis abates, or a commitment to severance packages, employers need to make whatever commitments possible to ensure that employees' personal needs don't surmount organizational needs.
Keeping an outward focus during an organizational crisis ensures continuing productivity, maintenance of customer service standards, and a more positive corporate image to people inside and outside of your organization. It can also foster purpose, urgency . . . and hope. In addition, an outward focus enhances other crisis management responses:
* An outward focus **protects your frontline employees** from infighting, stress from uncertainty, and misplaced blame.
* An outward focus allows for successes to be measured and for **performance to be rewarded** even during a crisis.
* An outward focus serves as a platform for **clear directives** and **communication** as everyone rallies toward a common goal.
CRISIS MANAGEMENT STRATEGY 2: CONTINUE TO ACKNOWLEDGE AND REWARD PERFORMANCE
Organizations in crisis tend to take on a sort of collective depression. A sense of malaise and indifference sets in, and performance begins a downward spiral. Compounding this tendency, rewards and accolades for a job well done often fall to the bottom of the priority list as organizations struggle to stay afloat.
In the aftermath of 9/11, it would have been understandable for CIA performance rewards to have gone by the wayside; to some degree the act of thwarting another attack should have been motivation and reward enough on its own, right? Yet CIA management continued to acknowledge and extol successes. Details of accomplishments in the field were shared on a regular basis, and high honors were handed out regularly to much-deserving heroes. Not only did this boost the morale of the CIA officers who were facing danger and personal hardships on the front line in Afghanistan, but it also instilled a sense of organizational pride and inclusiveness among the many headquarters-based employees who were far removed from the front line but were putting in long, stressful hours themselves.
I was in Kabul, Afghanistan, in early 2002. The pace of work was grueling, the living conditions stark, and the risks were constant. Amid the chaos of a war zone, though, came small perks that made a world of difference to people working on the front line. Small luxuries were sent at great expense by the CIA to employees in the field: Starbucks coffee beans. Pringles. Ingredients for a holiday dinner on Easter. Magazines. It doesn't sound like much, but these little gifts were always accompanied by notes of appreciation, and the value of the gesture was far greater than the sum of the parts.
In most companies in crisis, on the other hand, the little perks are the first to go. Free sodas in the office refrigerator are eliminated during budget cuts. Once-lavish office holiday parties turn into potluck celebrations, or, worse yet, employees are required to buy tickets to defray the costs of the annual gala. (Note to managers: Please. Don't. Ever. Do. This. If your organization can't afford a party, then neither can your employees. They are saving their money in case you decide to lay them off.) I once worked with a company that required employees to bring their own pens from home; the office manager claimed that employee carelessness with office-issued pens was costing the organization too much money.
During organizational crises, stinginess does not only appear in the form of these morale-deteriorating but minimally effective cost cuts. Compliments and accolades also tend to vanish when a management team is under stress. Senior management may bear the brunt of organizational crises, but ceasing to motivate and acknowledge your subordinates means that you have stopped performing one of your most important roles at a time when your company can least afford it.
Take it from someone who nearly wept with gratitude when those gourmet coffee beans showed up after far too long drinking only weak tea or wretched instant coffee: rewards and incentives are more effective than ever during a crisis.
By continuing to acknowledge and reward performance, you can enhance your other crisis management techniques in several ways:
* Acknowledgment of accomplishments provides an opportunity to accompany bad news with good news during critical communication from senior management.
* Continued rewards, even small ones, provides an opportunity to **create loyalty by inspiring it**. During one of my interactions with a company in crisis, I worked with a group of employees who positively revered their boss. Why? Because he made a point to order in pizza, at personal expense, every time the group had to work late. Their company was in the middle of a devastating product recall, so late nights were common. This small gesture made a big difference to the employees on the front line of the recall.
* Rewards and acknowledgments make it easier to **redirect and refocus resources.** You are less likely to hear your employees protest that "that's not _my_ job" if you are rewarding them for working outside of their normal job descriptions during times of crisis.
CRISIS MANAGEMENT STRATEGY 3: MAKE SENIOR MANAGEMENT MORE ACCESSIBLE THAN EVER
After 9/11, senior CIA officials had a lot of explaining to do, even before they had much information to explain. They had to explain to the media. They had to explain to Congress. They had to explain to closed committees, military officials, law enforcement, and foreign governments. They had to explain to the president.
With this kind of pressure, it might have been understandable if they had left employees to manage on their own for a while.
But they didn't.
In fact, George Tenet, the CIA director at the time, became famous for tromping through the cubicles of the CIA counterterrorism center with the now-infamous unlit cigar in his mouth, asking even junior officers to report extemporaneously on the latest developments. Other senior officials issued regular, formal updates that went to a wider audience than ever before—they recognized that this was not the time to compartmentalize. _All_ of the CIA's employees were now involved in the hunt for terrorists. Senior management was more visible than ever before, communicating both successes and setbacks.
This visibility and accessibility of senior management contrasts sharply with my first experience with organizational crisis in the private sector. During that experience, I worked in a cubicle just around the corner from Executive Row. Just before layoffs started (although well after _rumors_ of impending layoffs had started), my neighboring colleagues and I used to play a game called "spot the CEO." This would sound laughable if it wasn't true: members of the company's senior management team seemed literally to go into hiding. They arrived late and left late. They avoided eye contact and walked briskly. They entered silently and grimly, and they kept their office doors closed. I can commiserate, somewhat—it must be terrible to know before anyone else that the fate of thousands of employees' careers is in the lurch.
I witnessed this same phenomenon in other organizations over the years. During times of stress and uncertainty, senior executives often go to ground. Sometimes it is because there are legal implications and they can't divulge information prematurely. Other times it's because the future of the company is uncertain and they don't want to communicate anything until they know for sure. In one case, it was because one of the executives was facing serious criminal charges. Unfortunately, avoiding difficult questions does nothing to assuage a crisis—rather, it just fuels the rumor mills.
If senior CIA officials could manage to maintain visibility and to communicate frequently and honestly during the post-9/11 maelstrom, then surely so could management in the corporate world. If nothing else, it is a point of honor during a crisis: bad news should be communicated directly, honestly, and in a timely manner, by whoever is in command. A crisis— _any_ type of crisis—is not the time for leaders to hunker down.
Maintaining senior management accessibility facilitates several of the other crisis management strategies:
* When information comes from the top, employees have the opportunity to hear **clear directives** straight from the source, rather than filtered through layers of intermediate management.
* Accessibility **instills trust** when the workforce sees that senior officials are personally invested in getting through times of organizational crisis.
* Within organizations suffering from the shackles of bureaucracy (i.e., most organizations with more than one employee), unmistakable directives that come straight from the top official help clear the way to **redirect and refocus resources**.
CRISIS MANAGEMENT STRATEGY 4: ARTICULATE CRYSTAL-CLEAR DIRECTIVES
In late 2001 and early 2002, CIA officers heading to Afghanistan in the aftermath of 9/11 were given a very clear directive: to capture or kill Al Qaeda terrorists. For the seasoned special operations officers who hit the ground first, this was a logical order. We were at war, after all, against the people who had committed a horrible act of terrorism on U.S. soil. Still, when I arrived in Kabul mere weeks after finishing my training, this directive—given to me within an hour of arriving in Afghanistan—was startling, to put it mildly. I didn't have any military experience, and the gun that I had just been issued felt unfamiliar and uncomfortable. I am far more corporate than I am commando, and my very presence in a war zone felt surreal.
Yet there it was. A directive that couldn't be any clearer. _My_ job was not to literally do any of the capturing or killing; I was only responsible for collecting the intelligence that would support this effort. Still, up until now, my "first day on the job" experiences had been limited largely to learning my way around the building and trying to locate office supplies. To be given such a brutally blunt objective from the grizzly, bearded deputy chief of station shocked me deeply. It's not that I was naïve (well, perhaps a bit)—I knew what I was getting into when I agreed to deploy to Kabul. It's just that this directive was _so_ blunt that it really brought home the gravity of the situation. It was a sobering moment.
The corporate world has seen plenty of its own crises recently. But in many of the industries hardest hit (that would be _you_ , automotive, financial services, and real estate sectors), senior leadership came out of the gate seemingly in denial about the gravity of the situation. Instead of acknowledging the crisis and issuing blunt directives in hopes of reversing course, the organizations delivered mixed messages to employees, shareholders, and Congress. They predicted near-term improvements while asking for bailouts; they spent lavishly on some things (corporate jets and year-end bonuses) while simultaneously cutting costs and downsizing; they promised innovation while putting projects on hold. I have an acquaintance (who shall remain nameless, because he has thus far managed to hold on to his management position in a well-known, and fast-sinking, financial services company) who describes his department as being "like the Wild Wild West":
No one knows what to do, because we aren't getting any specific information from above. So half the office sits around and does nothing, and the other half is running around trying out all sorts of half-baked ideas in the hopes that they'll be seen as stars once the crisis blows over. It's chaos.
A chaotic organization is not, of course, well equipped to respond to a crisis.
As I stated earlier in this chapter, midcrisis is not the time for senior management to go AWOL. Not only should company officials be more accessible than ever, but they also need to be blunter and clearer than ever when issuing directives. After all, organizations in crisis are filled with employees who have a vested interest in trying to help turn things around.
Let them help.
To do this, you don't need to become a military commander overnight. You don't need to write flowery speeches, fake your way through insincere corporate pep rallies, or start spouting motivational platitudes. Instead, effective crisis leadership simply requires honest, clear, prompt, realistic, and, yes, blunt communication. It's actually quite straightforward, and should involve as many members of your organization as possible:
1. Honestly communicate the gravity of the situation.
2. Honestly communicate the options—even when there are few.
3. Narrowly define the short-term crisis management strategy, down to the departmental or even individual level, if possible.
4. Define more broadly the midrange goals.
5. Update often.
The third item is the most important in a crisis, as this is the step that enables your employees to act, to help, to produce. Make your instructions clear, empowering, and unmistakable, and then step back to let the members of your organization do their jobs.
I sincerely doubt that senior CIA officials thought of their communications as formally as this section may imply. Instead, their successful communication strategy emerged organically from a sincere desire and a frank need for every member of the organization to immediately hear, know, and act on breaking information as it developed.
Crystal-clear directives enhance other crisis management strategies as well:
* The clearer the objectives are, the more you can **empower** your employees to act above and beyond their normal capacities.
* Identifying and articulating clear directives during a crisis **inspires loyalty** by demonstrating effective management during a crisis.
* Clear, actionable directives help keep **an outward focus** and maintain productivity.
CRISIS MANAGEMENT STRATEGY 5: HAND OUT EXTRAORDINARY EMPOWERMENT
Unlike for most private organizations in crisis, money was not an issue for the CIA after 9/11. War is a cash economy, and fortunately for us, cash was abundant. In Afghanistan we paid cash for tactical intelligence. We paid cash for informants. We paid cash for protection, and cash for real estate. We paid cash to buy back the Stinger missiles that we had given out back when we thought that the Soviets were the bigger threat. Officers were given funds in chests, boxes, and bags. We were responsible for providing receipts and accounting for the money that we handed out, of course, but it was still sometimes a bit dizzying to see so many bills all at once. I remember once hesitating to sign a receipt for a large brown bag full of cash that I was to deliver to a local Afghan warlord for his cooperation; I was signing my responsibility for a value that exceeded my yearly salary. I wanted to read the fine print first, but in a war zone there are no lawyers and there is no fine print.
Even among the more experienced CIA officers deployed to Afghanistan, the level of empowerment was unprecedented. Most of the officers on the ground were given far more funding and far more responsibility than they had ever had in their careers. They were given the authority and the means to accomplish a herculean task, and they did it well.
The empowerment given to officers on the front line also changed a long-standing, somewhat destructive organizational dynamic. The CIA's clandestine service has long been marked by a barely disguised antipathy between headquarters and the field. Headquarters, or the "Death Star," is reviled by field-based officers for its risk aversion, glacial pace, and mind-numbing meetings. Headquarters "weenies" are criticized for being naïve, unsupportive, and bureaucratic. Case officers in the field, on the other hand, are criticized for being overly aggressive, impetuous, and prone to action without understanding the big picture.
Keep in mind that CIA clandestine officers rotate jobs frequently, so most headquarters officers have spent plenty of time in the field, and vice versa. It doesn't matter. The moment officers begin their latest job—whether at headquarters or overseas—they become one of "them."
This us-versus-them mentality all but vanished during the period after 9/11. Field-based officers were permitted to make significant commitments and decisions without having to cable back to headquarters for permission. Headquarters invited the field to make wish lists of supplies, funding, authorizations, people, and gear—and then provided everything that the field requested. Immediately. It was this extraordinary empowerment that enabled those officers who deployed to Afghanistan first to make extraordinary progress in a very difficult situation.
Now, let's compare this to what tends to happen to a corporation in crisis. Because abundant funding is typically _not_ an option for troubled organizations, expenditures are often the first decisions to be bumped up to a more senior level. Suddenly, junior managers are required to get authorization before booking a plane ticket. Customer service representatives have to seek management approval before granting customer refunds. Conference attendance fees are reconsidered at a higher level. Performance bonuses have to be signed off on personally by the CEO.
When a crisis is financial in nature, this is understandable, of course. But disempowerment can be a slippery slope. A company on thin ice, financially speaking, tends to become increasingly conservative in _all_ matters. Marketing plans are deemed too risky, given the circumstances. Building expansion is curtailed. A hiring freeze goes into effect. These decisions to cut back, hold off, delay, and reduce come from higher and higher. The employees on the front line lose nearly all ability to commit or act. Ultimately, extraordinary _dis_ empowerment leads to an extraordinary inability to perform.
Empowerment in a time of crisis is risky. When the future of your organization is on the line, every decision and every commitment takes on a monumental importance. But if you can't trust those employees on the front line—meaning those employees who deal most closely with your customers—to continue to make the right decisions in a time of crisis, then your hiring, training, and management practices are so flawed that your organization may very well be doomed to fail, regardless of senior-level intervention. The CEO can't flip every burger.
I hope that by now I have established that I have a seething hatred for buzzwords. In grad school I used to play "buzzword bingo" with my classmates—we created bingo cards with the business jargon du jour, and we'd cross out the words as the lecturer uttered them. Any card with the word "strategic" was a ringer for sure, since business professors use that word more often than a teenager says "like." "Empowerment" was another ubiquitous term, and therefore one that I hesitated to use here. To clarify, then, I need to emphasize that I do not use the word "empowerment" in a namby-pamby, feel-good-about-yourself kind of way. I am referring to something specific and concrete. Extraordinary empowerment means granting more decision-making authority, and more _control_ , than ever to employees on lower rungs of the corporate ladder. A time of crisis is the time to let the experts—those who have been doing the job day-to-day since well before the crisis—do what they do best.
Extraordinary empowerment enhances several other crisis management strategies:
* It allows your employees to _do something_ to help allay the crisis, and thereby maintain an **external focus**.
* Empowering all ranks of your organizations allows senior leadership to be **more accessible than ever** , because they are free to lead rather than micromanage.
* Extraordinary empowerment allows you to **redirect and refocus** resources, because it allows your employees the authority to do more than ever before.
CRISIS MANAGEMENT STRATEGY 6: REDIRECT AND REFOCUS
Immediately after 9/11, CIA officers started to come out of the woodwork. There literally were not enough desks or computer monitors to accommodate all of the officers who came in to do work well outside of their job descriptions. They donated their time after completing their day-to-day duties, giving up their evenings and weekends. Retired officers and officers who had resigned from the agency years before came back to offer their services. Officers gave up plum overseas assignments to return to relatively less glamorous but now-critical headquarters positions in the agency's Counterterrorism Center. Trainees wrapped up long, strenuous days of surveillance detection classes and then headed into headquarters at night to help out in any way possible. In the chaotic aftermath of the terrorist attacks, job descriptions meant very little. If you were there, you were capable, and you were willing, then you were put to work.
Once the dust started to settle somewhat, it became clear that life at the CIA would never be the same again. The agency's mission, methodology, and mind-set were drastically and irrevocably altered. For decades the stars of the clandestine world had been the Cold War warriors—those officers who spoke Russian, had spent their careers chasing and being chased by the KGB, and had developed a taste and a tolerance for vodka. But after 9/11, the skill sets that served officers well for Iron Curtain operations suddenly seemed quaint, overly cerebral, and excessively regimented.
The new superstars? The new hotshots in the clandestine world were the officers who spoke Arabic, Farsi, and Dari. They were more familiar with the social intricacies associated with sharing a cup of tea than a bottle of vodka. And whereas it used to be the rare clandestine officer who ever handled a firearm, suddenly weapons training became mandatory. (Imagine my bemusement when I discovered that my own, hastily organized M4 assault rifle qualification course was also attended by a sweet, diminutive grandmother of three!) Officers traded custom-tailored suits for Kevlar, and it became common to overhear casual hallway conversations about the pros and cons of the different types of antimalarial medications.
The CIA's clandestine service had to reinvent itself after 9/11, and this was no small undertaking. The change in the agency's focus required changes to nearly every aspect of business—training, hiring, logistics, technology. Without a hint of nostalgia, the clandestine service stepped up and began a metamorphosis that isn't yet complete more than a decade later.
The corporate world is certainly no stranger to reinvention either. Some drastic changes in focus are strategic—an effort to capture a new market segment, for example—while at other times they come from necessity and/or crisis. As the innumerable consulting firms that claim to be experts in change management can attest, reinvention is risky. (Anyone remember Starbucks' brief foray into home decor and furniture? I thought not.) But whatever the impetus for change, the simple fact is that once you go, there's no going back.
The CIA's reinvention was not seamless, of course, but the agency did manage to redirect and refocus its resources quickly, effectively, and intelligently. Here are some of the strategies used by the CIA that could apply equally well in any organization:
**1. Make assignments based on skill set, not job title.** After 9/11, the CIA urgently needed specific language skills, paramilitary capabilities, and target-specific technology. Because the critical skill sets were not abundant within the agency, officers with these capabilities were put immediately into positions of leadership. In a crisis, let skills and abilities supersede seniority. When your company's computers crash, the executives stand back and let the IT experts do their jobs, don't they? The same deference should apply to anyone who has the skills to get your organization out of a jam—whether the critical skill set resides in the HR department, such as during a strike, in accounting during an audit, or in the marketing department when bad publicity hits. The most successful leaders know when to lead, and when to stand back and let their experts run the show.
**2. Deploy agile teams to work autonomously in the field, unencumbered by the bureaucratic quicksand back home.** This is where the quick-response teams mentioned in chapter 4 come in handy. Get employees with critical skill sets away from the organizational obstacles and slowdowns that always accompany large changes. Give them the resources and the authority to do their jobs, and then fill them in on the changes back home later.
**3. Let go of the past without sentimentality.** In the wake of 9/11, the CIA needed its officers— _all_ of its officers—to focus on the terrorist threat. The agency may have had plenty of funding, but it did not possess an abundance of officers with the appropriate skill sets. Senior officials operated with brutal efficiency to declare that certain regions of the world, certain targets, certain languages, and certain programs were no longer needed. Funding was diverted, assignments were curtailed, and programs were canceled. The impacted people and resources were still needed; they were just needed _elsewhere_. These changes affected junior and senior officers alike, and those who didn't like the new reality were invited to look for a new career. Corporate changes—particularly those induced by crisis—can and should be just as thorough, definitive, and comprehensive as the CIA's.
Redirecting and refocusing corporate resources in order to respond effectively to a crisis overlaps significantly with a couple of the CIA's other crisis management strategies:
* By redirecting and refocusing resources, you are—by definition—articulating a **crystal-clear directive** to change.
* By refocusing and redirecting, you are **empowering** your workforce by giving them the resources they need to operate in the new reality.
CRISIS MANAGEMENT STRATEGY 7: PROTECT THE EMPLOYEES ON THE GROUND
To say that CIA officers in post-9/11 Afghanistan were busy would be like saying that Enron executives had a small habit of fibbing—both are dramatic understatements. CIA officers back at Langley's headquarters were also busy— _very_ busy. Not only were they providing twenty-four-hour support to critical and sensitive field operations, but they were also feverishly responding to congressional and Executive Office requests for briefings, after-action reports, and analysis. The requests were perfectly valid (mostly), but they were also often redundant, time-consuming, and never-ending. The requests came in with priorities ranging from immediate to yesterday. _Everything_ was urgent.
For the most part, CIA headquarters did an admirable job of protecting its frontline employees—those officers deployed to Afghanistan—from the furor back home. The finger-pointing, retroactive quests for accountability, and endless requests for data stayed back home so that the employees on the ground could accomplish their primary mission and stay safe doing so. The only symptoms of bureaucracy that slipped through were the fairly regular CODELS—congressional delegations that often involved a sizable entourage and typically required a lot of hand-holding, time-consuming briefings, and resource-intensive security measures. Other than duties associated with the CODELS, which were viewed about as favorably as a migraine, officers were left alone to do their jobs.
Even if your organization's crisis doesn't involve a war zone, you still have frontline employees. Your "troops" are those employees who have to face the public and deal with your customers as if nothing out of the ordinary was happening internally. These employees are the ones you need to protect the most from the turbulence associated with an organizational crisis. Give them the information, the resources, and the shelter from the internal power struggles that they need to convince your customers that your organization is just as capable as ever to provide them with the service they expect. Give them the authority and the protection to continue to carry on your organization's core business.
Protecting your frontline employees is related to a couple of other crisis management strategies:
* Employees who are protected from internal strife can more effectively **focus attention and action outward instead of inward.**
* Protecting your employees on the ground allows you to **redirect and refocus resources** in a way that is transparent to your customers, who expect service as usual.
CRISIS MANAGEMENT STRATEGY 8: CREATE LOYALTY BY INSPIRING IT AND TRUST BY EARNING IT
I saved this strategy until the end, because it doesn't truly fit here. For starters, this final strategy isn't really an independent line item. Rather, it is the culmination and the aggregate effect of using the first seven strategies described in this chapter. Managers who faithfully demonstrate the first seven strategies will, by definition, inspire loyalty and earn trust.
Moreover, inspiring loyalty and earning trust is not a concept unique to the clandestine world. In any industry, loyalty is created when employees see that senior management continues to work for the cause, rather than pulling the ripcord on the golden parachute at the first hint of crisis. Trust is earned when employees observe management communicating honestly and following through consistently.
Although these concepts are not unique to the clandestine world, I think that the CIA's response to 9/11 epitomizes both the application of the strategies and the resulting benefits.
I've already described the organizational turmoil within the CIA after the terrorist attacks, as well as the personal sacrifices and the long hours undertaken by officers. It truly made a difference that the grueling pace, the difficult working conditions, and the health and safety issues were borne equally by the most junior and the most senior members of the agency. I may have picked up a nasty intestinal parasite during my war zone travels (true, alas), but even in the throes of the worst abdominal cramps I knew full well that I had it easy compared to George Tenet's public grillings before Congress. The—ahem—unpleasantness did _not_ sink to the bottom at the CIA.
Furthermore, the organizational trust that was built extended far beyond the clandestine service. The CIA _needed_ to be a trusted organization post-9/11, since it was calling for unprecedented favors and support from nations all over the globe. Individual officers on the ground also relied on a trustworthy reputation when they made commitments to tribal leaders and warlords in Afghanistan for support, information, and protection. The atmosphere of loyalty and trust trickled outside the walls of the CIA, and influenced individual transactions, conversations, and commitments. In chapter 5, I described trust as a currency that can be saved and spent. The surplus of trust built up by the CIA during its response to 9/11 turned out to be just as valuable as the free-flowing cash.
Following the first seven crisis management strategies listed here can similarly build up a trust reserve to be doled out as necessary to get through difficult periods. The CIA—an organization that _truly_ knows the meaning of crisis—is a testament to this fact.
CHAPTER SEVEN
Making a Sale the CIA Way
Persuading a target to conduct espionage is much like making a sale. Some targets are uncomplicated buyers. They're the easy ones, of course. Their motivations are clear, they know what they want, and it doesn't take much persuading to get them to sign on the dotted line. A case officer's lucky day is when a volunteer with bona fide access to sensitive data comes marching right into the U.S. embassy, stating that he has important information to provide to the U.S. government. The case officer gets credit for "recruiting" a spy who volunteers, even if the officer did nothing but take notes.
A step up in difficulty are the potential spies who can best be described as coy. Ultimately, they're pretty sure that they're going to make a deal, but they want a little convincing—a little wining and dining. As a CIA officer gets closer and closer to a final recruitment pitch, the officer's cover intentionally starts to slip. Bit by bit, the questions become more direct and the meetings more discreet, until finally the officer and the spy just seem to fall into a clandestine relationship.
Some of the toughest potential recruits are those who seem to willfully refuse to acknowledge what is happening during the final acts of the recruitment cycle. These targets are the ones who might have already disclosed sensitive information, but they don't want to think of themselves as a "spy." It's one thing for people who fall into this category to hand over classified data now and then, but it is a far greater hurdle to persuade them to consciously commit espionage. They don't mind leaking information, but they don't want to think of themselves as traitors.
For this last category in particular, by the time a CIA officer makes a recruitment pitch, the officer's claim to be anything _but_ a CIA officer is typically a very thin veneer. The officer has for some time been asking for detailed, sensitive information, making obvious efforts to keep meetings secret and avoiding communications via telephone or e-mail. Anyone paying attention would at least suspect that they were being wooed by an intelligence officer. In spite of this, stubborn targets tend to ignore the obvious, and they don't respond to subtle test pitches. These types of recruits wait until the officer has no choice but to make a blunt, explicit recruitment pitch. Of course, the more blunt the pitch ("I want you to steal secret information from your government in order to provide it to the U.S. government"), the easier it is to refuse. It takes a talented officer to maneuver an obdurate potential spy into accepting a daunting, direct proposal. An overly aggressive pitch will scare off the target, while a more subtle approach can drag on endlessly with no deal in sight.
Crafting the right approach depends entirely on the individual, the circumstances, and the chemistry between the officer and the target.
Sound familiar? It should. It's akin to any high-stakes sale—just with a twist of danger and a side of extra anxiety.
COLD PITCHES VERSUS DEVELOPMENTALS
CIA officers base most of their recruitments on the creation of a well-developed relationship. It takes time to establish the trust necessary to persuade someone to become a spy; potential recruits need to be thoroughly convinced that their handling officer will watch out for their safety and will honor commitments. The ideal recruitment pitch comes after months—or even years—of relationship building.
Sometimes, however, reality gets in the way of the process. In some circumstances a proper developmental effort just isn't possible. Your typical North Korean nuclear official, for example, doesn't get out much. He's not likely to spend his time vacationing in Mallorca or attending conferences in Los Angeles. Obviously, it's hard to develop a relationship with a person you can't even arrange to meet. In this type of situation, a CIA officer may resort to a "cold pitch." Cold pitches are less than ideal; they require a case officer to make a blunt appeal to the target with no opportunity to develop trust or rapport. They usually involve large sums of money, in the hope that a target will be sufficiently motivated by a generous financial offer. Not surprising, most cold pitches are declined. Would _you_ agree to put your life at risk simply because a stranger approached you out of the blue and offered you a bundle of cash? Furthermore, an unsuccessful cold pitch can have consequences far worse than a simple refusal. If sufficiently offended or frightened by the pitch, a declining target may even report the CIA officer to local authorities. This can result in anything from diplomatic censure, to arrest, to being "PNGed" (a term referring to the act of expelling an officer from a foreign country and declaring him or her persona non grata, meaning that the officer can never reenter the country).
Like it or not, the corporate world also has to rely on cold pitches sometimes—for example, for consumer decisions that are made spontaneously, with little to no research or thought process. Or in the case of potential clients who are difficult to access or contact, a cold pitch may be the one and only opportunity to make a sale. A telephone interview for a coveted new job also requires a sort of cold pitch, since it is difficult to establish rapport during a brief phone call.
When possible, the developmental route is always the best—and not only because of the opportunity that it affords to develop trust and rapport. Just as important, developmental "time on target" is the only way to properly assess your target's vulnerabilities in order to help you craft the ultimate pitch with the greatest chance of success.
Depending on your industry and your product, you may be able to establish a unique one-on-one relationship with a potential customer. In other business situations, for example when products are sold through third-party vendors, developmental opportunities may be limited to the creation of a trusted brand image. No matter how little time you have, _some_ development is always better than a cold pitch. The next section reveals techniques used by CIA officers to maximize developmental opportunities.
INCREASING THE ODDS
Because reality sometimes dictates that a sales pitch needs to be delivered before you have had the chance to thoroughly establish a trusting relationship, CIA officers use a number of techniques to maximize the chances that a pitch will be accepted. After all, in the clandestine world, an unsuccessful pitch can mean more than just time and resources wasted. Some failed pitches become full-blown international incidents, with charges, sanctions, and a one-way, do-not-pass-go ticket home for the embarrassed case officer. The following section provides eight techniques used by CIA officers to increase the odds that their target will accept a pitch. Each of these techniques is equally applicable in the corporate world and can help business professionals avoid being "PNGed" from a potential customer site.
Technique #1: Be a Chameleon
Whether you are selling _yourself_ as the "product" during an interview or trying to broker a major deal, you can benefit from a thorough assessment of your potential customer. Do your homework up front, of course, and try to learn as much as possible about your target before you ever meet face-to-face. The most important assessment work, however, needs to happen during your initial contact.
Use the elicitation and corroboration skills that you developed while reading chapter 2 to complete a quick and dirty assessment. First, identify common interests or background elements that can help establish an early rapport with your target. ("You went to the University of Washington? Me too!") A _genuine_ personal connection is invaluable for reducing some of the pressure and formality of a business interaction.
Next, figure out what type of customer your target is and what his or her vulnerabilities might be. Is he the type that will respond to a backslapping, expensive-dinner-buying approach? Or is she the type who will respond negatively to this tactic, mentally adding the cost of the dinner to the company's sale invoice? It goes without saying, of course, that you'd better have a whole arsenal of approaches at your disposal, ready to deploy quickly once you get a sense of your target's personality and vulnerabilities. This assess-and-adapt technique isn't sleazy or underhanded; it is simply a means of determining whether or not there is enough compatibility to justify a second meeting. As I will explain in the next point, for CIA officers a second meeting alone is well worth the mental quickstepping required to establish an early and enduring rapport.
Technique #2: Get a Second Date
CIA officers know that a patient, methodical approach is usually the best way to achieve a valuable recruitment. Often, then, an officer's one and only goal during an initial approach is to get a second meeting with the target. Even if the officer fails to obtain a shred of reportable data, a second meeting on the books is considered a success.
Why such a humble goal? Because getting a difficult target to agree to a second meeting means that you have met several important objectives. You have established a reason for continued contact. You have established enough rapport that the target is willing to spend more time talking to you. You have established an opportunity to meet again in a more controlled environment in which you can more purposefully advance your agenda.
This means that if you happen to meet your dream client on the golf course, don't try to finalize a deal by the eighteenth hole. Instead, use the chance meeting to broker a second, _focused_ meeting. If you meet your dream boss in an elevator, forget the conventional advice to blurt out a rushed and all-encompassing "elevator pitch"; instead, use the ride to persuade her to schedule a proper interview. A major deal is too much to consider during a brief elevator ride together; a second meeting is not. When your ultimate objective is a high-stakes, long-term business relationship, don't be afraid to take time with the development process. Ultimately, it is worth the effort invested.
Technique #3: Lose the Canned Pitch
Ah, the canned pitch—remedy to a thousand different ailments. Nervous about public speaking? Many of us try to counteract those nerves by rehearsing a presentation over and over _and over_ again until we could give it in our sleep. Been on the interview circuit long? Soon enough, the questions become predictable—and so do your answers. Pitched your product a thousand times already? You may find that not only have your words become robotic, but so have your jokes, gestures, and verbal tics. Delivering a difficult message to a difficult audience? Extensive practice can blunt some of the emotional cost to the speaker, but also some of the emotional appeal to the audience.
The canned pitch is a crutch that can do more harm than good. For starters, it is often painfully obvious. People who shift from casual conversation to an overly rehearsed soliloquy tend to give away the transition with a number of behavioral clues: they stand or sit up a little straighter, their language becomes either more formal or more unnaturally animated, they sometimes insert verbal artifices such as rhetorical questions ("have you ever wondered why . . ."), and the tone and pitch of their voice tends to change slightly. None of these things are bad per se, but all too often sincerity takes a backseat when your rehearsed pitch is given verbatim at the expense of responsiveness to your audience.
Worse yet, a canned pitch tends to put speakers on autopilot. Speakers in autopilot mode have a bad habit of ignoring audience cues that could prompt them to go in a different direction, or of not listening carefully to questions. A memorized interview response to an anticipated question can lead the speaker to miss the subtleties and nuances of the specific question. Do yourself a favor and ditch the canned speech in favor of knowing your product inside and out and giving yourself the ability to speak extemporaneously.
Technique #4: Maintain Input _and_ Output
My first recruitment as a CIA officer was nerve-racking. I had gone through the recruitment cycle dozens of times in training, but this was the real deal. I was asking someone to quite literally put his life in danger in order to provide me with sensitive information. I was painfully aware that should he accept my offer, every piece of data that he collected for me, and every time he met with me, was at great personal risk to him. It's a lot to ask of someone, and I was nervous.
In an effort to calm my nerves I prepared an elaborate and flowery recruitment speech. I wanted him to know that I took his safety very seriously. I wanted to convey to him just how important his role would be and just how positive the impact of his cooperation could be. I wanted to address his concerns up front; I wanted to convince, reassure, and express gratitude all at once. I silently rehearsed this pitch continually during the long flight to our meeting destination.
Less than a minute into my little speech, my target glanced at his watch. A few seconds later he fidgeted. Then he glanced out the window. Then fidgeted some more.
The fact was, he didn't need the speech. He had long since divined where we were going with our relationship. He knew what I was asking, and he had already made up his mind to say yes. My flowery speech was unnecessary, and quite clearly annoying to him. I cut it short, cut to the chase, and we were toasting our new arrangement minutes later.
Would he have turned down my pitch if I had continued to blather along as I originally planned? Probably not, but I'm still glad that I managed to gauge his reaction before I rambled any longer.
Too often people choose either input _or_ output. They're either listening _or_ they're talking. But if you are trying to make a sale, you need to maintain constant vigilance, even midspeech. The best speakers and the best salespeople can detect the moment when they begin to lose their audience. Watch for the signs as part of your ongoing assessment, and correct course instantly.
This does not mean that you need to obsequiously play up to your listener or kowtow meekly to your audience. In fact, depending on your strategy, you may be very well served by eliciting anger, skepticism, or some other seemingly negative reaction. The key is to know how you want your audience to react, and then to manipulate accordingly.
Technique #5: Analyze Your Own Weaknesses
Not even the best actors are infinitely versatile when it comes to playing a role. You can be as observant, responsive, and flexible as humanly possible, but there are always going to be situations in which you are, by nature of your appearance, your personality, or any other immutable characteristic, at a disadvantage. Perhaps you made a lousy first impression that your audience is not willing to forgive. Perhaps you remind the person who is interviewing you of her ex-husband. Perhaps you just can't manage to achieve personal rapport with your client, no matter how hard you try.
In the clandestine world, much thought is given to pairing the right officer with the right target. In most cases, the more similarities, the better. Matching language, ethnicity, gender, and professional background provides an automatic platform for the creation of a relationship. This is not, of course, always realistic, or even necessarily desirable. In fact, the overwhelming majority of targets I worked against in my career were significantly older men with whom I shared neither religious nor ethnic background. And yet I made it work. I was able to work successfully with people from vastly different sociopolitical backgrounds with little to no difficulty largely because I acknowledged and took into account the targets' biases and probable reactions to a much younger, Caucasian, Western female.
On the other hand, there were also target populations that I was fairly certain I would never be effective against. My background, personality, appearance, and language capabilities were simply not target compatible. I therefore opted not to even pursue certain target sets because I knew that the odds were stacked against me before I even made initial contact.
I am definitely _not_ advocating that readers pursue only opportunities that are a cultural/religious/ethnic/gender/favorite sports team match. Far from it, since I believe that some of the most advantageous business relationships exist between vastly dissimilar partners. I am, however, advocating that you know in advance how your audience is likely to respond to you, and that you have a plan for negating biases that are likely to work against you.
The key to self-awareness in this regard is to know how people tend to perceive you, for better or for worse. Think back to the times when you rubbed people the wrong way. Are there any commonalities? Do certain types of people tend to find you too brash, too arrogant, too passive, too quiet . . . too _anything_? Are there any similarities between circumstances in which you have felt misjudged? Are there any situations in which you tend to freeze up, get defensive, overcompensate for nerves, or otherwise react poorly?
If you lack self-awareness, you can do all the homework in the world to research your targets' backgrounds and vulnerabilities and still fail.
One of the best ways to gain awareness of how you come across to others is to conduct your own play-by-play analysis. When possible, have someone video record you during your sales pitch, presentation, or interview. If necessary, role-play the event if a live recording is not an option. Put the recording away for a few days without watching. After some time has passed, review your performance as critically as possible. While watching your video, try to understand which elements of your performance could be judged negatively. Don't just pick apart the technicalities; also try to understand how other people might respond to you on an emotional or interpersonal level. Are you likable? Professional? Interesting? Charismatic? Articulate? Authoritative? Or are you domineering, rambling, overly casual, or perhaps just visibly nervous? Do you mumble? Do you make eye contact? Do you frown? Dissect your performance down to the micro-expression.
If you can bear it, it also helps to have your most brutally honest acquaintance critique your video performance. Invite the worst—you need to know it. The whole purpose is to understand what tendencies, habits, and personality characteristics you need to compensate for with particular audiences. Understanding your worst helps you perform your best.
Technique #6: Sense Weakness in Others
CIA officers try to assess and learn targets' vulnerabilities as quickly as possible, in order to exploit them as systematically as possible. Here are just a few of the vulnerabilities I have taken advantage of in targets: a love of booze but a home in a dry nation; hatred of the regime in power; a strong desire to move to the United States; a polka-dot fetish (you'd better believe that I stocked up on clothing in that hideous print as soon as I learned this); the need for someone to listen to his political poetry; money; ego; money; ego . . . Let me repeat that a few more times: money; ego; money; ego . . . ego; ego; ego. Sense a trend?
It isn't terribly complicated. People like money—no big revelation there. People also like to be liked, they like to be heard, and they like to feel important. Generally speaking, focusing your development on these vulnerabilities is likely to at least get you moving in the right direction.
Business development, though, is not all about getting the customers to like their sales rep. It helps, but it is usually just one of many other factors. You can read all the books you want on how to get people to like you, but if your product isn't priced competitively or doesn't meet quality standards, you won't make many sales for all the charm in the world.
In the corporate world, then, detecting vulnerabilities is twofold. You need to identify both the business _and_ the personal vulnerabilities of each of your targets. If you're lucky, the two will overlap. Usually you won't have such good fortune. You may in fact find yourself trapped between the personal and the corporate—woe to the sales rep with a client who is authorized to purchase only the cheapest of services, but whose personal weakness involves the costliest wining and dining.
Detecting business vulnerabilities is mostly about casting a wide net. You need to identify as many sources of information as possible in order to help you figure out how to direct your developmental efforts as early as possible. Background research goes without saying; the rest will depend on your industry. Various sources of information about your targets include former employees (or even current ones, for that matter), suppliers, resellers, online product reviews, and competition. Know what's going wrong with your target's business and be prepared to address this vulnerability. Be careful, though—it's hard to boost someone's ego if you are too busy pointing out his company's flaws!
Assessing vulnerabilities, whether business or personal, is simply one part research to one part intuitive assessment. Be prepared to act on whatever weaknesses you uncover—even if it means wearing an ugly polka-dot shirt to every meeting.
Technique #7: Regularly Rerecruit
A bit of a tongue twister, this one. It happens all the time—a CIA officer conducts a careful and thorough development of a target, pops the question, and gets a positive response. But then the newly minted spy goes home and starts to reflect on what he just agreed to do. He thinks of questions that he should have asked, but the case officer has instructed him not to call on an unsecure phone line. He wants to do some research, but he knows better than to use his home computer to search espionage-related topics on the Internet. He tells his wife, who begins to cry and accuses him of jeopardizing his family. He starts to have doubts—very serious doubts. Depending on just how cold his feet get, he may or may not even show up to the next meeting with his case officer.
Because of this phenomenon, which basically boils down to a highly emotional version of buyer's remorse, CIA officers are taught to always use the next meeting after the recruitment to "rerecruit." Valuable time is spent answering lingering questions, quelling fears, and erasing doubts.
The rerecruitment is repeated at regular intervals, and following any extraordinary events. A change in case officers, a close call while crossing the border, suspicious questions from a nosy colleague . . . all of these events merit time spent rerecruiting.
In the corporate world, rerecruiting need not be so emotionally laden. Instead, the rerecruitment process should consist of a regular examination of the business relationship and the reestablishment of interpersonal rapport. Don't take your clients or customers for granted, and don't wait until they threaten to move to your competitor before you rerecruit. Rerecruitment should be a regular, ongoing habit, even _within_ your organization. We've all had bosses who seemed to sour on us over time or peers who grew distant; this can be fixed by regular efforts to rerecruit even co-workers.
Technique #8: Don't Negotiate
I originally considered writing an entire chapter on the clandestine approach to negotiations, but it quickly became apparent that it would be a very short one. You see, CIA officers don't negotiate. Or at least they avoid formal negotiations like the plague.
CIA officers tend to watch their American diplomatic counterparts, with whom they work closely, with bemused puzzlement. Quite unlike the clandestine world, the diplomatic world is full of complex protocols, formalities, resolutions, lengthy titles, and painfully regimented negotiations. Diplomats pride themselves on their debating skills and their knowledge of the United Nations' rules of procedure; they thrive in tightly controlled environments.
A clandestine service officer, on the other hand, starts to get antsy at the first sign of formality. When it comes to venues for important meetings, case officers prefer bars to boardrooms, and a restaurant table to a negotiating table. You'll never, ever get a case officer into a courtroom.
CIA officers do "negotiate" in the sense that they engage in discussions intended to produce agreements. But the clandestine version of negotiations looks quite unlike anything you will see in either the diplomatic or the corporate worlds. Here's a rundown of negotiation strategies, such as they exist, clandestine style:
**Minimize the number of participants.** CIA officers prefer as few people to be involved in a decision as possible. More people mean more leaks, more risks, more biases, more arguments, more time, more possible naysayers, and more minds to change.
**Aim high.** Why bother negotiating with an entire team when you can go straight to the top? Clandestine officers generally go directly to the committing official of any organization. Fortunately, CIA credentials give enough clout to permit officers to get on the calendars of even very busy, very prominent leaders.
**Identify the decision maker.** The committing official is not always the decision maker. Make it your business to learn whether the top official in the organization with whom you are negotiating has a confidant or adviser. Whether because of lack of expertise, lack of confidence, lack of time, or lack of interest, senior leaders sometimes turn decisions over to a trusted subordinate. The person who actually makes the decision is the one you want to persuade.
**Meet on neutral ground.** Agreeing to meet at your negotiating opponent's office makes it too easy for them to bring in other participants, such as legal advisers or assistants. Establish control by choosing a venue that is more conducive to small meetings. In fact, use the idea of a meeting on a sailboat as your gold standard. Participation is limited, privacy is maximized, the surroundings are conducive to pleasure and relaxation, and you maintain total control over the timing. Even if you can't _literally_ procure a sailboat for your meeting site (not many of us can), always make an effort to woo your negotiating opponent before getting down to business.
**Make an offer that can't be refused.** If you have a deep understanding of your opponent's vulnerabilities, you have the ability to make an offer that can't be refused. This tactic may involve putting together an offer that is so attractive that demurral would be foolish. Or it may be a polite version of arm-twisting. (No, legal folks, I am not advocating blackmail here, just an explicit awareness of consequences that would be unacceptable to your opponent, such as losing your business to a chief competitor.) Avoid the back-and-forth antics and posturing associated with formal negotiations by beginning and ending with the only offer you plan to make.
**Follow through.** Whether you have made promises or threats, follow through. You may be back at the negotiating table sooner than you think; a reputation for bluffing will not serve you well.
**Keep it positive.** In spite of the previous bullets that advocate the use of vulnerabilities, CIA officers use carrots far more often than sticks. An eager, willing partner is always preferable to a begrudging, reluctant one. Establish mutual benefits and shared gains whenever possible; the most productive negotiations always hinge on positive benefits rather than negative consequences.
Are you getting the sense that CIA "negotiations" sound quite unlike business negotiations? If so, you're right. You'd be amazed at the number of very important international matters that have been resolved over a cordial meal and a bottle of wine. As is the case in most clandestine affairs, clandestine negotiations are based on reputation, rapport, and strategic exploitation of vulnerabilities.
TRADECRAFT IN THE REAL WORLD
If you are reading this chapter and muttering to yourself that the book is emphasizing interpersonal matters over product or service differentiation, you are correct. CIA officers don't sell products. We don't claim to be better, faster, or more reliable than our competitors. We don't do product demonstrations or launch parties. We have impractical notions of finance, and we freely disregard laws that get in our way.
Clandestine service officers focus more on the sale than the product because the CIA obtains its product—secret information— _from_ its targets. This circular business model simply would not hold up in the private sector.
If you take the information for what it's worth, though, you'll see the merits of this otherwise unorthodox approach to sales. The clandestine approach doesn't emphasize the product. It emphasizes interpersonal relationships, background information, vulnerabilities, reputations, and rapport. CIA officers go after unbelievably difficult targets, and using little more than an alias, some background research, a lot of chutzpah, a dose of charm, and ton of idealism, they manage to persuade people to do incredibly risky things.
CHAPTER EIGHT
Controlling Your Sources: Supply-Chain Management Clandestine Style
In August 2009, Interpol conducted a massive raid on a cocoa plantation in Côte d'Ivoire, resulting in the rescue of fifty-four children who had been purchased for use as slave laborers. The children, who were as young as eleven years old and had been taken from seven different countries, had been forced to live and work in brutal conditions; they received no salary or education.
Ivorian cocoa is used by most of the world's major chocolate companies.
Because of a history of exploitation in the cocoa industry, a well-publicized labor rights initiative called the Cocoa Campaign has stepped up the pressure on candy companies to do more to prevent similar abuses. They have a compelling cause: the image of children enslaved for the purpose of cheaper cocoa is horrifying; the children's plight seems to come straight from the darkest of Grimm's fairy tales.
Clearly, this is the type of nightmare scenario that no company wants to be a part of.
Unfortunately, the children's horrendous experience is not uncommon; UN statistics put the number of child laborers at more than 200 million worldwide. Don't be lulled into believing that this is only a third world problem either; certain industries in the United States, including the dangerous meatpacking business, are regularly cited for underage employees. Other human rights and safety violations in the name of commerce show up disturbingly often in the news headlines. Scores of major Western companies in a wide variety of industries have been publicly lambasted for their suppliers' practices: Nike, Reebok, Gap, Starbucks, Firestone, Coca-Cola, Mattel, and Monsanto are just a few.
It's midnight—do you know what your suppliers are doing?
Unless you are an Amish furniture craftsman, your business likely relies on numerous suppliers and third-party service providers. Those sources have their own supply chains, and the subsources have their own suppliers . . . and so on. Within this extended supply chain, every degree of separation means a loss of control and oversight. With a loss of control and oversight, of course, comes all sorts of problems that you never in a million years thought you would have to deal with.
Supplier problems are not limited to child labor, nor are they exclusive to factories outside of North America. The U.S. Consumer Product Safety Commission directs dozens of nationwide product recalls every month, for reasons ranging from lead paint in children's toys to toxic ingredients in dog food to car engines that spontaneously burst into flames. There are an infinite number of ways that supplier problems can negatively impact your business.
And guess what? Customers don't give a damn that the issue was caused by your supplier's supplier's supplier. If _your_ brand name is emblazoned on the finished product, then the problem is all yours.
THE . . . SOLUTION?
When I decided to leave my job as an investigator for the National Labor Relations Board, I interviewed for a position in a well-known consumer goods company that had been the target of copious negative publicity stemming from the labor practices of several of the company's overseas suppliers. Part of the job was oversight of the company's newly implemented supplier compliance program.
The job sounded interesting, and I eagerly asked questions about the compliance inspection program. I had my own ideas about how the labor practices of far-flung suppliers could be scrutinized, and I was curious about what steps the company had already taken.
I was stunned to learn that the inspection process relied heavily on the suppliers' local management. To begin the process, the corporate manager would contact the supplier's manager to initiate a "short notice" inspection. The company defined short notice as two weeks. As part of the inspection, the supplier was required to make employee representatives available for "confidential" interviews.
* **Problem #1:** Just imagine how much whitewashing can be done in two weeks.
* **Problem #2:** The supplier selected which employees would be interviewed.
* **Problem #3:** Interviews took place at the supplier's facilities.
* **Problem #4:** The supplier was responsible for providing the interpreter for the interviews.
Clearly, there wasn't much confidentiality involved. A handpicked employee representative being questioned on company property in the presence of an interpreter who is also in the employ of the supplier is not, of course, going to provide derogatory information about your supplier's practices. Not surprising, then, the company's first "inspections" had resulted in glowing reviews of supplier labor practices. Also not surprising, more than a decade later this company continues to struggle publicly with supplier problems.
I wish that I could say that this company's efforts were uniquely ineffective. Unfortunately, that is not the case.
CIA officers are proficient at identifying factors that impede their ability to obtain controversial data. All case officers know that, at a minimum, sources need to feel _safe_ disclosing information, and _motivated_ to tell the truth. The business world needs accurate, reliable information just as much as the clandestine world does. All the more reason, then, to borrow CIA techniques for getting the true story, even in difficult circumstances.
CORPORATE COMPLIANCE REALITY CHECKS
So, going back to the case of the Ivorian cocoa plantation, let's say that you are a candy maker with a good heart. You genuinely want to ensure that all of your raw ingredients come from suppliers who adhere to your corporate code of conduct. What's a kindhearted chocolate maker to do to ensure that nothing untoward is happening at the plantations that produce his cocoa? Well, most companies rely on the following techniques to ensure compliance:
* Require suppliers to sign an agreement promising compliance with your corporate code of conduct, which pledges adherence to legal standards and ethical principles.
* Reality check: Any employer willing to use child slave labor will not hesitate for a moment to sign your code of conduct, and then go right back to business as usual. The reality is that corporate codes of conduct are voluntary, and strict adherence is low. Sorry, folks—the bad guys think that your corporate code is a joke.
* Require suppliers to complete regular self-assessments and self-report any instances of noncompliance with corporate code of conduct.
* See above reality check. I wouldn't even include this item, which I find ludicrous, except for the fact that it is actually used by a number of very large, successful corporations. Really, readers—let's not be naïve. Self-reporting is _not_ an effective solution.
* Require suppliers to provide documentation for all employees to prove compliance with labor and employment laws.
* Reality check: Documentation, particularly from foreign countries, can easily be falsified. In the case of the Ivorian cocoa factory, the children were obviously not "on the books"—they weren't even getting paid!
* Conduct routine inspections of supplier facilities during site visits.
* Reality check: All evidence of wrongdoing will be gone long before you arrive for your quarterly site visit, and violations will resume within a matter of hours after your departure.
* Hire one of the external auditing firms that offer compliance inspection and certification services, including "surprise" inspections.
* Reality check: Although some of these firms brag of consultants with law enforcement backgrounds, unscrupulous suppliers can easily evade most of their checks. Imagine the sight of a carload of American business consultants barreling down the dirt roads toward a remote African cocoa plantation. They don't exactly blend. You may pay a lot of money for their reports, but I promise you that they were spotted long before they could obtain evidence of wrongdoing. (By the way, that they likely made reservations at one of few nearby business-class hotels, hired local drivers, and hired local interpreters also means that their presence was announced long before they even arrived in country.) The Interpol raid on the Ivorian plantations was successful because it involved _eight_ teams of _local_ law enforcement officers who simultaneously raided the facilities in question; additional officers blocked the roads surrounding the plantations and searched cars for additional victims. Your expensive auditing firm is not likely to do this.
* Offer whistleblower awards for verifiable reports of noncompliance with corporate standards.
* Reality check: Although well intentioned, this method can result in an avalanche of claims from disgruntled former employees, competitors, and outside rumormongers. There may very well be genuine reports mixed in there too, but the time and resources required to separate the false claims from the legitimate ones will be overwhelming.
You're getting the point. In many industries and in many parts of the world, conventional methods of monitoring supplier compliance are useless. So let's go back to our example of the kindhearted chocolate maker. If he truly wants to know whether something is amiss at his supplier's facilities, he has only one surefire way to find out: human intelligence.
Like the CIA, businesses can be well served by intelligence networks. Recruiting a single well-placed informer can provide far more information than a stack of monthly reports of questionable accuracy. The following section provides tips and techniques used by CIA officers to establish reliable intelligence networks than can be worth their weight in gold.
SOURCES WITHIN SOURCES: BUILDING YOURSELF A SUPPLIER INTELLIGENCE NETWORK
If your business relies heavily on suppliers or subcontractors, you have already relinquished control. After all, part of the reason companies choose to outsource is because they don't _want_ responsibility for every detail and task. Because relinquishing control does not, however, always relinquish liability, it is imperative that you address problems quickly and directly. Whether you are trying to get to the bottom of chronic quality problems, head off costly delays, or ensure that your supplier is adhering to proper labor standards, you need real-time insight into your supply chain.
You _could_ rely on self-reporting from your vendors. You _could_ choose to conduct formal, scheduled inspections. You _could_ chat with employees in break rooms and hope that the plant manager breathing over your shoulder won't discourage them from telling you the truth. You _could_ rely on the monthly reports.
If, however, conventional means of monitoring your suppliers are failing you and you _really_ want to understand the ground-truth realities at your supplier facilities, you need to create an intelligence network that extends throughout your supply chain.
For the purposes of this chapter, let's assume the most difficult scenario: multiple suppliers, each of whom uses a variety of subcontractors, located in remote areas of the world, and a workforce with whom you do not share a common language. It only gets easier from here! If your supplier happens to be located just down the street, then just take what you need from this section. The techniques work even if your "supplier" is simply a different department down the hall.
To start, an intelligence network needs—of course—spies. The ideal person to report on the realities of your supply chain is someone who:
1. Has access
2. Has motivation
3. Has the ability to communicate with you
4. Has proof
Not coincidentally, these are the same characteristics that CIA officers look for in potential spies.
**1. Access.** If you are trying to understand production control issues, it doesn't make sense for you to recruit a spy who works in the payroll department. If you are trying to confirm that your supplier isn't using child labor, it doesn't make sense to recruit the night watchman as a spy. The ideal source of information is a person who has access to the people, the records, and the plans that you need to know about. Depending on the complexity of your supply network, you may need multiple sources, each with unique access.
**2. Motivation.** Your sources will understand just as well as you do that if they produce enough derogatory information about your supplier, you are likely to terminate your business relationship and choose a new vendor. That, of course, would mean that your sources may very well be out of a job if their employer is forced to cut back in the face of your lost business. It is often in the best interest of employees, then, to toe the party line and report that nothing is amiss.
Because of this self-protection bias, you need a source who is motivated to provide you with the truth. Motivation may come in negative guise; your best source could be a disgruntled former employee with an ax to grind. Conversely, your best source may be a member of junior management who is willing to take the risk of becoming a whistleblower for a shot at a job within _your_ company. It is important to be acutely aware of your sources' motivations, however, since their versions of "the truth" may be skewed by their reasons for cooperation.
**3. Communication.** If your source discovers information that you need to know on an immediate basis, will he or she be able to get you the data quickly and safely? CIA officers receive extensive training in clandestine communications, and they have access to all sorts of Hollywoodesque technology to help. Corporate spies don't usually require much in the way of bells and whistles, but you may need to go to some effort to enable your source to report back to you. This may involve managing language barriers, lack of Internet access, limited ability to make international phone calls, and time zone differences. Even face-to-face meetings may be impossible; if your supplier is located in a remote area, there may be no hotels nearby in which to hold a meeting. Your appearance at a source's home in an impoverished barrio would certainly draw attention, and your source may not have transportation to meet you out of the area.
Unfortunately, I don't have a one-size-fits-all communication plan to offer to you; no such plan exists. Every spy requires a unique and personalized communications strategy to get you the information when you need it. Work with your source to establish a context-specific communication plan that allows you to obtain critical information immediately.
**4. Proof.** You wouldn't terminate a contract over a rumor, so the members of your intelligence network need to be able to substantiate their reports. Unfortunately, your sources may need to go to considerable risk to back up their claims. When possible, you want your spies to clandestinely obtain photos, copies of lab reports, copies of personnel records, or any other incriminating data. If you are running the intelligence network, however, then _you_ are responsible for giving your sources the technology and the training necessary to obtain proof in a way that does not jeopardize their safety or livelihood.
If this is all starting to sound a little too cloak-and-dagger to you, recall the above example of the enslaved child laborers discovered working at the Ivorian cocoa plantation. It is unlikely that the major candy companies had any inkling that one of many sources of raw ingredient was involved in such abusive practices. However, the fact that cocoa produced by slave labor made its way into the candy companies' products means they now share some of the responsibility to prevent such atrocities in the future. You'd better believe that it would have been in the candy companies' best interest, both from a moral and a publicity standpoint, to have known about the problem before they learned about it from an Interpol press release.
THE RISKS
I would be remiss if I didn't at least acknowledge the risks associated with using human intelligence collection techniques in international business. Although you may not break any laws by establishing sources to give you the inside scoop about supplier practices and problems, the application of clandestine methodology in the corporate world should always be done carefully, and with advice from legal counsel. But even if your activity is strictly legal, there are still risks:
**Embarrassment.** Whoops, you just tried to recruit an internal source to report on your supplier, and it turns out that he's the plant manager's cousin. Not only does he turn down your "consultancy" offer, but he also reports your pitch to his cousin and the rest of the supplier management team. Needless to say, this is not going to have a favorable impact on your future business dealings.
* Avoid this by scrupulously researching all possible candidates and thoroughly evaluating their access, motivations, and relationships to key players. Never try to recruit a source without doing your homework! Also, try "soft pitching" first, when possible—this involves recruiting in baby steps. Give noncontroversial assignments first, then build up to the real tasks gradually, all the while assessing your source's willingness.
**Risk to your source.** What happens if your source gets caught while trying to take photos of unsanitary conditions at your supplier's facilities? He loses his job, of course—at a minimum.
* Avoid this by anticipating risks, and give your sources adequate training and resources to avoid detection. See chapter 3 for more information about business counterintelligence techniques that can protect you and your sources.
**Double agents.** Being a double agent is even more lucrative in the private sector than it is in the clandestine world. After all, if your newly recruited spy reports back to his employer, he may very well get a nice bonus for providing you with regular, falsely positive reports about your supplier's compliance practices.
* Avoid this by having multiple sources in different positions within your supply chain; this will allow you to corroborate reports.
**The truth hurts.** Be prepared for the possibility that your new spy may report back on some truly egregious practices occurring at your longtime supplier's facility. After all, which is worse from both a moral and a legal standpoint: turning a blind eye to the _possibility_ of misconduct, or doing business with someone you _know_ to be involved in misconduct?
* Be ready and willing to act on reports of unacceptable supplier practices—whether that means terminating your business relationship or reporting your supplier to the authorities.
**Jail.** I have advised readers repeatedly throughout this book always to obey the letter of the law. However, don't forget that some countries have blurred lines between state-run facilities and private enterprise. If this is the case, activities that may not violate business or trade laws may actually be considered espionage.
* Avoid this by _never_ trying to build an intelligent network within any organization or entity with ties to the government. Espionage is something you never want to be charged with, no matter how skilled your legal team.
CREATING AN INTELLIGENCE NETWORK SAFELY AND LEGALLY
In the case of Ivorian cocoa plantations, I would advise cocoa end users to stop at nothing in the future to ensure that their suppliers are not engaged in abusive or unsafe practices. There are certain industries and certain parts of the world that have developed a reputation for repeatedly engaging in harmful practices. The garment industry, rug manufacturers, the diamond industry, and meatpacking companies, for example, have more than their fair share of labor problems. Other industries are chronically plagued with quality problems—as a parent, I am continually infuriated by the number of toys and baby products sourced from China that are determined to contain lead. When there is a history and a pattern of problems, not only should the buyer beware—the buyer should assume the worst until proven otherwise.
But what about the readers who aren't in one of the high-risk industries, and don't do business in parts of the world known to have problems? What if you just want to get an advance warning that your widget delivery is going to be delayed again? In truth, the creation of an intelligence network within your supply chain doesn't have to be a sneaky, risky affair. Particularly in the case of domestic suppliers, who are held to the same legal standards as you are, it doesn't really have to amount to much more than strategic networking, fueled by a healthy dose of skepticism. Running sources can be as simple as maintaining a positive relationship and regular contact with individuals who are willing and able to give you a heads-up when problems arise that may impact your business.
So for those of you who don't feel a need to issue clandestine communication plans or hold secret meetings with your sources, here are a few tips for being a more effective networker in order to be the first to know—spy lite, if you will:
**1. Look for the people with dirty hands.** I don't mean this in a derogatory sense. You want to know what's really happening in your supplier facilities? You need to have contacts outside of the executive offices. The people in the suits are not even necessarily aware of problems any sooner than you are. Know someone who actually _does_ the work. Too often people obtain positions in management and never look back to the laboring ranks. That leads to an enormous blind spot—but one that is easily remedied.
When I went to Iraq in 2003 as part of the WMD search team, we still believed that there were weapons of mass destruction to be found. We interviewed senior scientists and politicians, all of whom denied the existence of a WMD program . . . and all of whom had been coached in propaganda. Because we could not rely on their rehearsed version of events, we started to look for sources who may not have been as well versed in the party line. We interviewed technicians, nurses, security guards, truck drivers, and people who just claimed to know someone who knew something. We interviewed exhaustively. Ultimately, it became clear that, lo and behold, there really was no secret WMD stockpile to be found. It wasn't until we had thoroughly explored all of the ranks, however, that we could be certain that we were hearing the truth and not just the cover story. The entire experience was enlightening for me in many regards; one of the lessons that I learned was just how differently people from different walks of life can interpret the same events and facts.
**2. Learn a new language.** It's amazing how much information is lost in translation—and I'm not just talking about foreign languages. If you're in marketing, you need to understand the engineers. If you're in HR, you need to understand production. Every industry and every career path has its own jargon; mastering the "language" used by the people who can provide you with critical information makes you much more approachable when the need arises. If you are unlikely to understand the explanation, then people don't want to bother bringing you into the loop.
This, of course, holds true for foreign languages as well. If your company outsources extensively to South America, _trust me_ —you will benefit tremendously from learning Spanish. Being able to communicate directly, instead of through the prism of a translator, is always beneficial.
CIA officers who speak Arabic are a hot commodity. Arabic is a difficult language for Americans to master, and true fluency takes years to acquire. I don't speak Arabic, but I have had the opportunity on many occasions to use interpreters to communicate with Arabic speakers. I have also had the opportunity to witness Arabic-speaking colleagues in action. There is a world of difference between the two experiences. Working through an interpreter results in stilted conversation, and the tendency is for both sides to speak to the interpreter rather than to each other. Not even the best interpreters (and skill level varies widely) can fully convey subtleties such as underlying humor or threats; you will always be limited to literal translations that leave much unheard. I watched in awe as my Arabic-speaking colleagues not only managed to exchange information, but also to develop rapport and cultural understanding in a way that I never could by working through an interpreter.
By establishing yourself as someone who speaks their language—whether technical jargon or actual idiom—you let potential sources know that you have the capacity to hear and to understand.
**3. Be generous with favors.** The clandestine world is not altruistic. It is, however, generous. CIA officers in the field are often in a position to broker introductions, to help out with visa or passport problems, and to intervene in minor legal problems. They do so generously—not out of the kindness of their hearts, but because such small favors, which require little effort, often come back in spades.
By becoming someone who is generous with favors, you actually build yourself a powerful platform. It's human nature to dislike the feeling of debt or obligation, so the majority of people who receive a favor from you will be eager to repay the act whenever possible. Today's kind gesture just may turn into tomorrow's inside tip.
**4. Establish your authority.** CIA case officers are not known for their low self-esteem—they are not a timid lot. After all, if you're the type to stammer and sweat when an armed customs officer aggressively demands to know why you're carrying such a large amount of cash into the country, you won't last long in the industry. The ability to coolly, confidently defuse a stressful situation is a critical skill.
As I've mentioned, my very first assignment after completing my clandestine service training was to get on an airplane to Kabul. I found myself, still in my twenties, regularly meeting with roomfuls of armed Afghan men, most of whom hadn't seen a nonrelative female without the cover of a burqua in many years. Yet even though many of these men literally had not looked directly into an unrelated woman's eyes for decades, not a single one ever treated me with so much as an ounce of disrespect. Why? I'm fairly certain that it was because I walked confidently into every meeting, offered my hand for a firm handshake, never demurred, and always led the conversation. Oh yeah—and I also made it clear that I controlled the money. These men, who were totally unaccustomed to conducting business with women, had no choice but to shrug off whatever cultural discomfort they might have felt and sit down to get to work.
In the context of establishing a network within your supply chain, the same behaviors apply. Make yourself known as the one who is paying the bills, the one who can terminate the contract at any time, and the one who won't tolerate any deception. This doesn't have to be done aggressively or insultingly; rather, let it be known via your demeanor, your position, and your actions. Even if your act is nine-tenths bluff, establishing yourself as an alpha figure makes it much harder for people to lie to your face.
SUPPLY-CHAIN INTELLIGENCE
Are you surprised by how much I am emphasizing behavioral techniques above anything 007-ish? The reality of the clandestine world is that undercover work is far more psychological than technological. You don't need gadgets nearly as much as you need the ability to manipulate perceptions.
When the circumstances call for an aggressive approach toward addressing supply-chain problems, like in the case of the Ivorian cocoa plantations, then clandestine techniques such as infiltration and recruitment of internal spies may be justified. When, however, such aggressive tactics are uncalled for, a somewhat more passive approach may be perfectly effective. In that case, using the techniques adopted by CIA officers to establish themselves in positions that entice, invite, and encourage full disclosure can go a long way toward getting you the information you need from _all_ of your sources.
CHAPTER NINE
Spy Versus Spy: Dealing with Competition
During a clandestine meeting that had taken several months to arrange, one of my high-priority assets happened to mention that he was traveling to Paris the following week. "Oh?" I asked, instantly on alert. "For work or for pleasure?" This was an individual whose job did not allow him much opportunity to travel, so a trip to Paris was definitely unusual.
It turned out that the journey was a little of both. A mysterious French businessman had invited him on an all-expenses-paid trip for the ostensible purpose of a very brief business meeting. My asset wasn't entirely clear about the purpose of the meeting, nor did he really care; he had accepted the invitation solely because he had always wanted to visit the Louvre. The asset was an intelligent, educated man, but he was also stunningly naïve. I was not, however, quite so naïve, and a few more questions gave me all the information I needed. It was painfully clear to me that the French contact was an intelligence officer using an aggressive but well-known recruitment strategy. As I carefully picked apart all of my asset's conversations with the man, it also became clear that he had already revealed way too much.
I was concerned about my asset's safety, because even unwitting involvement with _any_ intelligence officer added to the risk that his clandestine relationship with the CIA would be revealed. I was also furious on a more personal level. Someone had dared encroach on _my_ turf! He was my asset, damn it, and everyone else had better just keep their grubby hands off. I instructed the spy to immediately cease all contact with his French suitor and to cancel his "business meeting." He sulked briefly, but agreed to do as I requested.
I sighed heavily after the meeting, thinking to myself, "Headquarters is _not_ going to like this."
So you see—CIA officers have to deal with pesky competitors horning in on their business too. The clandestine world is a small community, and there are only so many high-priority targets to chase. In fact, it is not unheard of for top-tier targets to "shop around" in search of the best deal. Perhaps Mossad is offering more money. Or maybe MI6 is willing to consider offering expedited British citizenship. Can the CIA top their offers? As you can probably guess, this sort of bidding war can get very messy, and it is in everyone's best interest to sort things out quickly before the entrepreneurial target gets himself arrested, or worse. Rivalry and turf battles in the intelligence community, however, are a constant fact of life.
This is the chapter of the book where I have to tread most carefully. CIA officers are well versed in dealing with competition; after all, it is part of the clandestine service's mission to penetrate and sabotage other nations' intelligence functions. However, the vast majority of the techniques used by the CIA to deal with "the competition" are not at all conducive to the business world; in fact, they'd probably land you in jail fairly quickly. So I had to think long and hard about what a former CIA officer could offer you in the way of advice on this topic without crossing any legal or ethical lines. Ultimately, I decided that while I won't tell you how to clandestinely enter your competitor's facilities, sabotage a rival's new product release, or capture your foes' electronic communications, I _can_ teach you the strategy and planning process used in the clandestine world to deal with competition.
IN-HOUSE COMPETITION
In an ideal work environment, you value your colleagues and respect your management. You may have developed friendships and camaraderie within your peer group, and you may seek guidance and mentorship from those co-workers with more seniority than you. If you enjoy such an idyllic work environment, or even if you just tolerate your mostly satisfactory job, it may not have occurred to you to create a dossier of sorts on your colleagues. Doing so may even feel mercenary and devious.
Get over it.
Your most talented, hardest-working, most gregarious, best-liked co-workers are your biggest threats.
That might sound a bit nasty, but the fact of the matter is, you are constantly being compared to your colleagues when it comes to decisions about promotions, bonuses, or career-enhancing opportunities. There's no need for you to do anything dastardly with the information you collect about your peers. Opportunities for advancement are finite, though, so it behooves all of us to identify and analyze our individual competition _within_ our organizations. Use the following analytical framework to better understand where you fall in the organizational pecking order and how you can improve your chances for advancement:
**1. Start at the top.** To improve your professional trajectory, you need to understand your organization's leadership. The CIA has an entire analytical department dedicated exclusively to leadership analysis. Does this sound interesting? If so, the agency is hiring! The job description for leadership analysts is posted on the agency's public Web site. It states that leadership analysts
produce assessments of foreign leaders and other key decision-makers in the political, economic, military, science and technology, social and cultural fields. These assessments are prepared at the request of senior U.S. policymakers in the executive and legislative branches to help them understand and deal with their foreign counterparts.
The assessments produced by the leadership analysts are used by policy makers to more effectively craft negotiating strategies, to understand vulnerabilities, and to predict behavior. You'd better believe that the president of the United States never goes into a meeting with a foreign leader without knowing what type of reception and response he is likely to receive. Even small personal details, such as knowing in advance about a foreign leader's dietary restrictions or rocky marital status, can help U.S. leaders avoid embarrassing errors of diplomacy.
Some of the leadership assessments compiled by the analysts are dry and dull—they can be based on anything from a detailed examination of decades of legislative decisions to minutiae gleaned from legal or financial records. Other assessments read like tabloid magazines—they can include tawdry details ranging from sexual proclivities to mental health assessments. The assumption behind the analysis is that foreign leaders' decisions and actions are influenced by their previous experiences, their personal vulnerabilities and foibles, and their psychological tendencies.
You may not have access to the same amount or type of data as the leadership analysts, but you'd be surprised at how easy it is to compile a meaningful assessment of the leaders of your own organization. After all, you interact with them, you read their internal communications, and you listen to their speeches. You see how they dress, what they drive, and what hours they keep. You see who they choose to fill positions of trust and responsibility, and you see who they hire and fire. It's as easy as watching and learning—all of the data that you need to complete your analysis can be collected in plain sight.
To truly understand your in-house competition, you need to be able to identify who your organization's leadership considers to be your competition. You may think that the guy in the cubicle to your left is the smartest, most diligent employee in the company (well, second to you, of course), but we all know that, unfortunately, intelligence and hard work don't necessarily have anything to do with professional success (long live the Peter Principle!).
To complete your leadership assessment, observe and analyze your organization's decision makers with the intention of answering the following questions:
* What are the characteristics of the people in the leader's inner circle?
* Who does the leader reward for successes?
* Who does the leader blame for failures?
* What are the differences between the people the leader has promoted from within and the people the leader has hired externally?
By studying your organization's senior leadership, as well as the leaders' prime influencers, you can assess what types of attributes and accomplishments tend to be rewarded. We all hope that our management will consider talent, intelligence, and dedication above all else, but the reality is often decidedly more complicated. Some senior executives demonstrate near-exclusive loyalty to former co-workers from previous organizations—they are the ones who bring entire staffs with them from their prior company. Others tend to surround themselves with people just like themselves (the so-called yes-men). Some value personal relationships over technical skills; others hire by "pedigree"—they insist that their subordinates come from prestigious universities and have previous experience working at prestigious firms.
Building a profile of your organization's leadership allows you to identify the characteristics of those who are fast-tracked into the positions that _you_ want, and allows you to emulate the behaviors that may enhance your own career path—or at least to avoid the behaviors that are viewed unfavorably by your organization's leadership.
**2. Study your rivals.** At the risk of sounding a tad Sun-tzu here, a clear understanding of your rivals is critical to success. First you need to identify your competition, using the success criteria gleaned from your leadership assessment. After all, corporations are keenly aware of their competitors—shouldn't you be just as aware on an individual basis? Identifying your competition allows you to address the shortcomings that your organization's leadership sees in you in comparison to your rivals.
Identifying and analyzing your rivals does _not_ mean that you should engage in overt competition. Far from it, in fact. Among your rival group will always be individuals who, by virtue of skill, luck, or personal connection, will ascend faster than you. These peers of today, then, may turn out to be your management of tomorrow. Rather than striking them as a hypercompetitive, backstabbing shark, it behooves you to gain their respect while you are still operating as peers.
The CIA similarly seeks to identify individuals likely to be promoted quickly when it engages in what are called "seeding" operations. In a seeding operation, a clandestine relationship is developed with a person who may not be in a position of power or access _today,_ but is deemed likely to rise into an important position in the future. Because it is often easiest to establish contact, and then ultimately to recruit individuals who are not yet ensconced in positions of power, CIA officers invest a great deal of time and resources into recruiting these future leaders in the hope that their predictions of future success will come true.
You can engage in your own seeding operation by working as hard to earn the trust and respect of your fast-tracking peers as you do with your management. Whether a person is invited onto the fast track because of skill, personal connections, or pedigree, establishing a relationship with a high-potential colleague while you are still peers gives you an added edge when your target gets promoted into a position in which he or she has the ability to reach back and bring you along for the ride.
**3. Build an empire.** I don't care if you work in the mailroom—everyone needs an empire of their own. By empire, I mean an entire system of individuals who are watching out for you. Too many competitive individuals look only skyward as they make their way up the organizational ladder; worse yet are those people who use the "kiss up, kick down" style of management that makes them hated by everyone whose shoulders they've ever trampled on.
Conversely, the best CIA officers as well as the most effective executives know that valuable information can come from highly unexpected sources. In fact, most intelligence services in the world maintain large networks of "support assets" whose value comes _not_ from access to sensitive data but from their ability to do some of the behind-the-scenes work critical to a successful espionage mission. Support assets are the ones who maintain safe houses for clandestine meetings, purchase disposable cell phones for untraceable communications, or check secret message drop sites. A small subgroup of CIA support assets is used solely for the purpose of alerting a handling officer in the event that some kind of trigger occurs; this type of asset may be on the books, for example, to alert the CIA when a particular ship comes into port, or when a particular individual is seen engaging in suspicious behavior.
Support or alert assets are not usually prominent individuals; they are more likely to be sympathetic, low-profile, often low-ranking individuals whose value lies more in unobtrusive proximity to information than in inside access to secret data.
In the corporate world, having a network of access agents may mean that you get the computer upgrade first, that your messages are placed at the top of the in-box, that you are able to cut through bureaucracy more effectively than your colleagues, or that you get the office closest to (or farthest away from, depending on your preference) the boss. Having a network of alert assets means that you are discreetly notified _before_ someone gets fired, that you know in advance about upcoming opportunities, or that you get a heads-up that today is _not_ a good day to approach the boss with a request. These little favors and tips can be tremendously valuable, and can give you a strong competitive edge against your in-house competition.
So don't forget where you came from as you rise in the corporate ranks, and don't be reluctant to befriend the receptionists, valets, assistants, and janitors of the world. You never know what you might learn from your empire.
Anyone in the corporate world can emulate the CIA's strategy of 360-degree intelligence collection by studying their company's leadership, analyzing their peers, and building a network throughout their organization. This strategy sets you up for success and career ascension by helping you to become the go-to person when the organizational climate shifts, assisting you to establish a reputation as someone who always seems to be a step ahead, and giving you the ability to benefit from the successes and avoid the mistakes of those who came before you.
It goes without saying that none of this will make a difference (or at least it will make a much smaller difference) if you can't perform the basic functions of your job with a minimum level of competence. Assuming an acceptable level of expertise and effort, though, this method will allow you to work your way through the briar patch of your organization's culture in a way that mere technical proficiency does not.
EXTERNAL COMPETITION
So, how badly do you want to know what your competitor's next move will be? Given that this book is not a corporate espionage how-to manual, I am once again going to avoid all topics that could land either one of us in jail. The clandestine world's analytical models and strategies, though, apply just as well to the study of external competition as they do to internal competition.
**1. Study the competition's MO.** Although there are plenty of universal techniques and strategies in the clandestine world, every intelligence agency around the globe also has its own distinct modus operandi. There are the "gentleman spies" of the world who conduct mild, almost polite operations. There are also the thugs, who employ as much brute force as they do clandestine tradecraft. Certain countries have state-of-the-art technology; their advances in biometrics and crowd analysis make undercover officers and fugitives alike break out in a cold sweat. Other countries rely on cheap labor; they seem to have a surveillance officer posted at every street corner and in every hotel.
In order to operate safely, undercover CIA officers need to be familiar with the MO of the intelligence service in every country they visit. A case officer should always utilize good tradecraft, of course. In certain parts of the world, however, extra precautions are necessary in order to avoid detection. Based on a careful study of a country's intelligence practices, a case officer can make educated guesses about where surveillance units are likely to lurk, which hotel rooms are likely to be bugged, and which airports should be avoided at all costs. The information used to make these critical predictions comes from penetrations, analysis of past practices, and a thorough understanding of the current state of technology in use by the various intel services.
Private-sector organizations also have predictable patterns of behavior. A company's MO might vary in the case of a drastic change in management, breakout technology, or an intentional reversal of strategy. Barring these rare events, however, it is possible for you to reasonably predict how the competition is likely to respond in a particular situation.
Identifying your competitor's MO requires a thorough understanding of your rival company's history, a comprehensive leadership analysis, and awareness of important personnel changes. Generally speaking, you will find that the past predicts the future. Organizations are run by people, and people are complicated creatures. Because of this, human behavioral prediction models are imprecise at best. However, organizations are, by nature, resistant to change. This means that knowledge of your competition's history plus an awareness of potential triggers of change can help you predict your rival's next move . . . which should, of course, influence _your_ next move.
**2. Exploit your rivals' changes.** CIA officers overseas put in a lot of overtime whenever there is a regime change in the country to which they are posted. Even if the new leadership is ostensibly friendly to U.S. interests, drastic changes in control are carefully scrutinized, and case officers scramble to collect intelligence on the new players in the game. This is because even when a new leader is a known entity, a change in power often results in dramatic organizational changes. New leaders are under pressure to be "different" and "better"; they are eager to put their mark on their position by making bold changes, whether or not such changes are necessary.
New leaders making drastic changes for change's sake can create weaknesses in an otherwise strong organization. Feathers get ruffled within the organization, while outside, customers get nervous, wondering whether they can expect uninterrupted service and quality. CIA officers _love_ to exploit these cracks during regime shifts; it is far easier to recruit penetrations of a foreign government when people feel slighted or resentful of a headstrong new leader. Private organizations, similarly, have opportunities to pounce when the competition's leadership changes.
It's easy to think of organizations as faceless blobs, or as behemoth entities devoid of personality. And in truth, individual personnel changes rarely cause more than a ripple of difference, particularly in the long term. However, in the case of senior management changes in a competing company, be on high alert and ready to exploit organizational vulnerabilities that may appear as a result of an individual's actions.
**3. Use denial and deception.** The CIA uses denial and deception techniques to mislead rival intelligence services; the goal is to keep the other service spinning with false leads and incorrect information so that the _real_ work can go on undetected. I don't encourage readers to do anything unethical or unsafe, _but_ if you become aware of a competitor's efforts to commit corporate espionage against your company, you have a golden opportunity. Rather than immediately firing the mole, investigating the leak, changing your hacked e-mail account's passwords, or otherwise shutting off your rival's source within your company, consider using the source _against_ your scheming competitor. When you control the information being leaked, you gain control over your rival's responses.
**4. Build an alliance.** Everyone knows that building relationships is a critical part of doing business, but most organizations view relationship building as a function belonging only to sales and marketing. Instead of using relationships only to drive sales, consider the possible intelligence value of strong relationships with suppliers, consultants, legal and financial representatives, and any other organization that your company regularly comes into contact with.
The Central Intelligence Agency relies heavily on alliances with foreign governments—even those whom we are actively spying against. In the case of a crisis, or even an isolated, mutually beneficial opportunity, our rival intelligence services temporarily share resources and information that are critical to success. It may be a self-serving gesture in many cases, but who cares? Similarly, the CIA follows a duty-to-warn doctrine that requires agency officials to notify foreign governments when credible information is received about an impending threat of attack; the agency abides by this doctrine even in the case of enemy nations.
Building business relationships that may have nothing to do with sales can be beneficial in highly unexpected ways. If nothing else, the creation of alliances with external organizations gives you additional sources of information that can impact your business. At a certain level within every industry, it becomes a very small world. Your vendor may have once worked with your rival's new CEO, or the head of the consulting firm that you use regularly may be considering hiring someone from your competitor. The type of information that can be passed through industry alliances, wittingly or unwittingly, can provide a genuine business advantage.
CONCLUSION
Operating in a Competitive World
It's a competitive world out there, and it can be tempting to play dirty—particularly if "fair" seems to be a foreign concept to your rivals. Playing hardball, though, tends to result in _all_ of the players getting battered. In the corporate world as in the clandestine, it simply isn't worth the hit to your reputation (or your legal defense fund), no matter how tempting it is to bend the rules to get to the top.
I mentioned earlier in the book that integrity is a valuable commodity. Rather than emphasizing the negative aspects of dealing with competition in the clandestine world, then, I'd prefer that readers walk away with the notion that a solid reputation for integrity is far more valuable than any kind of dirty trick that an ex-spook can teach you.
Don't get me wrong—I'm not playing Girl Scout here. I highly recommend strong defensive counterintelligence practices, pristine security procedures, and the use of good tradecraft to protect your organization's interests. But today's rival can be tomorrow's ally. Responding to competition intelligently, perceptively, even aggressively can hardly be faulted. Using dirty tricks to gain a small advantage, on the other hand, can—and often does—come back to haunt you.
CIA officers may not face the same legal, logistical, or financial constraints that business executives do. They do, however, have goals, objectives, and aspirations, just like their counterparts in the corporate world. As someone who has spent time in both the spy business and in more traditional business settings, I have come to realize that many of the unique skills taught to CIA officers to help them achieve their mission are equally applicable in the private sector.
I have endeavored throughout this book to make it clear that I am _not_ advocating corporate espionage or any type of practice that could be considered legally or morally questionable. I _am_ , however, offering readers the rare opportunity to learn from the successful practices used by hardworking and talented CIA officers every day.
Overall, if I had to sum up the most important business lesson from the clandestine world, it would be this: there is information for the taking that can change the entire playing field for you and your organization. Getting this information is a matter of asking the right people the right questions in the right way. This may require manipulation of individuals and exploitation of both organizational and personal vulnerabilities. However, by adhering to firm ethical parameters, it is possible to use clandestine techniques to get ahead in the corporate world while still maintaining your integrity.
Acknowledgments
It's difficult to write acknowledgments when I can't name so many of the people I'd like to thank. But I do want to express my gratitude for those CIA officers who have been my mentors, my friends, my travel companions, my war zone roommates, and my colleagues. Your job presents more challenges and asks more sacrifices than most; it was an honor to serve with you.
I also want to recognize the team at Portfolio / Penguin for its patience and hard work—this book was a work in process for much longer than any of us expected.
Finally, I'd like to thank my mother for tolerating my globetrotting and thrill-seeking ways from such a young age. It's only now that I'm a parent that I realize what I must have put you through. May my children never give me as many gray hairs as I'm sure I have given you!
Index
The page numbers in this index refer to the printed version of this book. To find the corresponding locations in the text of this digital version, please use the "search" function on your e-reader. Note that not all terms may be searchable.
Alliance-building
for competitive advantage, 188–89
shifting allegiances, 107
Background checks, 85–86
Business counterintelligence
CIA examples, 43–55
detecting, exercise for, 49–52
information leaks, sources for, 47–49
losses from, 46
necessity of, 45–46, 48–49
protecting against, tips for, 52–55, 72
Canned sales pitch, 147–48
Career evaluation teams, 95
Case assessment teams, 95
Character traits
ethical lapses, meaning of, 106, 111–12
intrusion in business life, 105–7
CIA and CIA strategies
Arabic speakers, need for, 86, 133, 173
clandestine service officers, recruitment, 16–41
competitive advantage methods, 177–189
crisis management, 115–138
deception, skill for, 100–101
ethical standards, 99–114
exit interviews for, 66–67
interrogation tactics, 113
job seekers, Web site information on, 82, 84
leadership analysis, 180–82
lifestyle polygraph, 105–6
negotiation strategies, 154–56
ongoing screening, 103, 105–6
person-to-job matching, 93
PNGed, 143–44
private-sector demand for, 98
profile/characteristics of, 11–13
recruitment process, 77–79
Red Cell team, 69–71
retention of agents, 90–98
sales techniques, 143–157
screening process, 84–86
and September 11 terrorism. _See_ September 11 attacks
supply-chain management, 159–175
team approach, 95–96, 134
Clandestine service officers, 16–41
corroboration, 31–38
double agents, 57–61, 169–170
personality traits, 40–41, 173–74
pitching to. _See_ Sales techniques
rapport building, 38–41
strategic elicitation, 24–31, 108–9
supply-chain monitoring, 165–68
targeting, 17–23
training, 13, 16, 39–40
Cold pitch, 143–44
Compartmentalization, 103–4
Compensation goal bias, 65
Competitive advantage, 177–189
alliance building, 188–89
CIA examples, 177–79
denial and deception, use of, 187–88
empire building, 183–85
and external competition, 185–89
and in-house competition, 179–85
knowledge treated as, 104
leadership analysis, 180–82
leadership change, exploiting, 187
MO of competition, study of, 185–87
rivals, study of, 182–83
as vulnerability, 68–69
Compliance of supplier. _See_ Supply-chain management
Confidence, 40–41, 173–74
Corroboration, 31–38
versus assumption, 35
background/skill checks, 85–86
in business setting, 32, 34–35
CIA use, 31–32, 34
perfecting, exercises for, 32–38
Counterintelligence. _See_ Business counterintelligence; Organizational counterintelligence
Cover stories, 104–5
Crisis management, 115–38
directives, clarity of, 126–29
empowerment during, 129–32
frontline employees, protecting, 135–37
future uncertainty, addressing, 120–21
loyalty and trust during, 137–38
outward focus in, 118–21
performance, rewarding, 121–23
reinvention following, 132–35
senior management visibility, 124–26
Crisis situations
business examples, 116–17
terrorist attacks. _See_ September 11 attacks
Cross-functional teams, 94–96
Customer mood assessment, 67
Decision making, immediate, 34–35
Detractors, learning about, 65–66
Developmental sales pitch, 144
Directives during crisis, 126–29
Double agents
in business setting, 58–61, 169–70
Cuban, 57–58, 61
Empire building, 183–85
Employees, hiring and keeping. _See_ Recruitment strategies; Retention of employees
Empowerment and crisis, 129–32
Espionage personnel. _See_ Clandestine service officers
Ethical standards, 99–114
and allegiance shifts, 107
challenges, dealing with, 113–14
CIA officers, 99–102
compartmentalization, benefits of, 103–4
and employee characteristics, 102–3
enemy, working with, 107–8
fiscal responsibility, 111–13
and life/death implications, 113–14
lying, situations for, 104–5
personal life, impact on professional life, 105–7
solutions versus mistakes as focus, 105
and supply-chain, 110–11
trust building, 101–2, 104
unintended consequences, awareness of, 109–10
urgent action, recognizing, 108–9
Exit interviews, 66–67
Fiscal responsibility, 111–13
Give to get method, 30
Google Alerts, 67
Hook, 20–21
Human intelligence, 8
Inspection of suppliers. _See_ Supply-chain management
Instincts
hiring by gut, 79–81
internal threats, detecting, 53, 64
Intelligence collection, 8–11. _See also_ Clandestine service officers; _entries under_ CIA and CIA strategies
relationship to business, 8, 11
Internal threats. _See_ Vulnerabilities
Internet
Google Alerts, use of, 67
personal data on, 21, 53, 60
public footprint on, 52–53, 67–68
social networks and information, 21, 53
Interrogation
human rights violations, 113
versus strategic elicitation, 24–31
Job interview candidates. _See also_ Recruitment strategies
information leaks, preventing, 54
strategic elicitation by, 26–28
Job rotation, 91
Leadership
analysis of competition, 180–82
change in, exploiting, 187
visibility during crisis, 124–26
Like attracts like, 80–81
Listening skills, 31–38
Lying and deception. _See also_ Ethical standards
CIA training in, 100
Mistakes
outward focus as response, 118–21
versus solutions, 105
Negotiation strategies, 154–56
Observation exercise, 36–38
Organizational counterintelligence, 55–69
in business setting, 58–61
CIA examples, 57–58, 65
and double agents, 58–61
heightened, factors in, 72–73
Red Cell exercise, 69–71
tip-offs indicating, 62–69
Organizational security
communication/security balance, 56, 61–62
negative impact of, 55–56
Organizational strategies of CIA. _See_ CIA and CIA strategies
Outward focus and crisis, 118–21
Paranoia versus caution, 54–55
Passion, job requirement error, 81–82
Personality traits
CIA officers, 12–13
clandestine service officers, 40–41, 173–74
Personal life, impact on professional life, 105–7
Polygraph screening, CIA agents, 103, 105–6
Profiling exercise, 36–38
Quick-response teams, 95–96, 134
Rapport building, 38–41
Recruitment strategies
background/skill checks, 85–86
for CIA officers, 77–79
competition, seeking talent from, 87–89
disclosure about job, 84–85
for espionage personnel. _See_ Clandestine service officers
hiring by gut, avoiding, 79–83
literal requirements, avoiding, 83–84
sales method of, 153–54
screening process, 84–87
sharks, avoiding, 102–3
vague requirements, avoiding, 81–82
Recruitment teams, 95
Red Cell team, 69–71
functions of, 69–70, 96
perfecting, exercises for, 70–71
Referrals, naming in strategic elicitation, 31
Reinvention after crisis, 132–35
Response bias, 64
Retention strategies, 90–98
challenges, presenting to employees, 91–92
CIA success, reasons for, 90–98
and job rotation, 91
lone wolves, accommodating, 96–98
person-to-job matching, 92–94
support staff, motivating, 94–96
Rewards
during crisis, 121–23
doing favors, 173
Sales techniques, 143–57
canned pitch, avoiding, 147–48
cold pitch, 143–44
developmental method, 144
input with output, 148–49
negotiation strategies, 154–56
personal connection, making, 145–46
recruitment as, 153–54
second focused meeting, 146–47
self-awareness in, 149–51
target, full understanding of, 145–46
weakness of others, assessing, 151–53
Screening process, 84–87. _See also_ Recruitment strategies
CIA process, 84–86
ongoing screening, 103
Seeding operations, 183
Self-awareness, and selling, 149–51
September 11 attacks, 115–16
CIA, post–9/11 reorganization, 132–35
CIA crisis response to, 118–38
and interrogation practices, 113
prevention, aspects of, 118–19
Shredding paper, 52
Social networks. _See_ Internet
Spies versus CIA officers, x
Strategic elicitation, 24–31
in business setting, 26–28, 108–9
CIA examples, 25, 108
counterintelligence detection, exercise for, 49–52
give to get method, 30
intelligence process of, 24
versus interrogation, 24
perfecting, exercise for, 28–30
tips for use, 30–31
Strategic planning teams, 95
Supply-chain management, 159–75
child labor example, 111, 159–60, 168
compliance weaknesses, 162–64
industry jargon, understanding, 172–73
and inspection flaws, 161–62
intelligence network monitoring, 165–68
nonclandestine methods, 170–74
problems, business examples, 160
spying, risks related to, 168–70
supplier, assuming responsibility for, 110–11
Surveillance teams, 95
Targeting
in business setting, 18–19, 21–22
CIA examples, 17–18, 17–23, 20
hook, elements of, 20–21
perfecting, exercise for, 22–23
Task forces, 95
Teams
cross-functional, 94–96
versus lone wolves, 96–97
quick-response, 95–96, 134
for unpredictable scenarios. _See_ Red Cell team
Travel, data protection during, 52, 54
Trend spotting, for internal threats, 63–64
Trust building
and CIA officers, 101–2, 104
and crisis situation, 120, 137–38
Verifying information. _See_ Corroboration
Vulnerabilities
acknowledging, 68
and crisis. _See_ Crisis management
data/information gathering. _See_ Counterintelligence
of others, in sales situation, 151–53
Red Cell team, 69–71
strength as, 68–69
unintended consequences, awareness of, 109–10
unpredictable scenarios, 69–71
* Think that this is an extreme example that doesn't happen outside of Tom Clancy novels? So did members of Hewlett-Packard's board of directors before their phone records were obtained and scrutinized back in 2005. Even vice presidential candidate Sarah Palin's personal e-mail account was hacked in 2008. And new allegations of phone tapping perpetrated by British tabloid newspapers owned by Rupert Murdoch seemed to be coming out daily as I wrote this book. It happens!
| {
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Eberhard Schockenhoff (* 29. März 1953 in Stuttgart; † 18. Juli 2020 in Freiburg im Breisgau) war ein deutscher Moraltheologe und römisch-katholischer Priester.
Leben
Nach dem Abitur am Friedrich-Schiller-Gymnasium Ludwigsburg studierte Eberhard Schockenhoff von 1972 bis 1979 katholische Theologie an der Eberhard Karls Universität Tübingen und Päpstlichen Universität Gregoriana in Rom, wo er 1978 die Priesterweihe als Priester des Bistums Rottenburg-Stuttgart empfing. 1979 beendete er ein Lizenziatsstudium der Moraltheologie bei Klaus Demmer. Von 1979 bis 1982 war er Vikar in Ellwangen (Jagst) und Stuttgart, anschließend Repetent im Wilhelmsstift in Tübingen. 1986 wurde er zum Dr. theol. bei Alfons Auer promoviert.
Von 1986 bis 1988 war Eberhard Schockenhoff Assistent an der Katholisch-Theologischen Fakultät Tübingen der Universität Tübingen bei Walter Kasper, wo er sich 1989 habilitierte. Von 1990 bis 1994 war er Professor für Moraltheologie an der Universität Regensburg und ab 1994 Professor für Moraltheologie an der Albert-Ludwigs-Universität Freiburg. Von 1992 bis 2004 war er außerdem Geistlicher Assistent der Katholischen Ärztearbeit Deutschland (KÄAD), von 1995 bis 2005 Mitglied der ökumenischen Dialogkommission Church and Justification zwischen dem Lutherischen Weltbund und der katholischen Kirche.
Ab 1996 war Eberhard Schockenhoff Mitglied im Kuratorium des Johann-Adam-Möhler-Institut für Ökumenik in Paderborn und ab 2001 Geschäftsführender Herausgeber der Zeitschrift für medizinische Ethik. Im Jahr 2001 wurde er durch Beschluss des Bundeskabinetts in den Nationalen Ethikrat berufen, 2008 ebenso in das Nachfolgegremium Deutscher Ethikrat, dessen stellvertretender Vorsitzender Schockenhoff von 2008 bis 2012 war. Im Jahr 2012 wurde er erneut berufen.
1998 lehnte er einen Ruf an die Ludwig-Maximilians-Universität München als Nachfolger von Johannes Gründel ab und 2006 lehnte er einen Ruf an die Universität Tübingen als Nachfolger von Gerfried W. Hunold ab.
Ab 2009 war er ordentliches Mitglied der Heidelberger Akademie der Wissenschaften. 2011 war er Unterzeichner des Memorandums "Kirche 2011: Ein notwendiger Aufbruch". Im Rahmen der Herbstvollversammlung der Deutschen Bischofskonferenz 2016 wurde Schockenhoff zum Präsidenten des Katholischen Akademischen Ausländerdienstes ernannt. Für 2017 wurde ihm der Theologische Preis der Salzburger Hochschulwochen zugesprochen.
Von seiner Schulzeit an war er im Bund Neudeutschland. Er war Mitglied der katholischen Studentenverbindungen AV Albertus Magnus Tübingen (Theologengesellschaft, ursprünglich nur Studenten des Wilhelmsstifts), der KStV Alamannia Tübingen im Kartellverband katholischer deutscher Studentenvereine und der KDStV Hercynia Freiburg im Breisgau im Cartellverband der katholischen deutschen Studentenverbindungen.
Sein Bruder war der Politiker Andreas Schockenhoff.
Am 18. Juli 2020 starb er im Alter von 67 Jahren in Freiburg im Breisgau nach einem Sturz in seiner Wohnung an den Folgen des Unfalls.
Wirken
Schockenhoff forschte vor allem zu speziellen moraltheologischen Fragestellungen wie der theologischen Sichtweise der Stammzellenforschung oder Abtreibung. Darüber hinaus bezog er Stellung zum Naturrecht, zum Verhältnis von menschlicher Freiheit und göttlicher Vorsehung und näherte sich in seinem Buch Wie gewiss ist das Gewissen? dem Thema Gewissen.
Schockenhoff bezeichnete im April 2010 während einer Sendung aus der Reihe Report Mainz die Piusbruderschaft als "rechtsradikalen Sumpf" und Fall für den Verfassungsschutz. Daraufhin wurde er von der Piusbruderschaft wegen Verleumdung angezeigt. Zudem forderte die Vereinigung den Entzug seiner Lehrberechtigung, nachdem er in einem Interview das Verhältnis der katholischen Kirche zu Homosexuellen kritisiert hatte.
In dem Artikel Guter Hoffnung? in der Frankfurter Allgemeinen Zeitung (FAZ) nahm er im September 2010 zur Zulassung der Präimplantationsdiagnostik (PID) in Deutschland Stellung.
2011 unterzeichnete Schockenhoff das Memorandum Kirche 2011: Ein notwendiger Aufbruch.
In der Diskussion im Juli 2012 um den Umgang mit Katholiken, die nach einer Scheidung wieder heiraten, sah er die Lösung darin, dass "die Kirche die zivile Zweitehe im Vertrauen auf das Gewissensurteil der Betroffenen toleriert und diese nicht länger vom Kommunionempfang ausschließt". Einen nationalen Alleingang hielt er "nicht für ausreichend, denn es geht um ein Problem der Weltkirche. Aber eine nationale Bischofskonferenz könne den Vorreiter spielen und eventuell die Dinge beschleunigen".
Im März 2019 forderte Schockenhoff in einem Referat bei der Frühjahrsvollversammlung der Deutschen Bischofskonferenz in Lingen eine Reform der römisch-katholischen Sexualmorallehre.
Schockenhoff war mit Josef Wehrle und Sven van Meegen Herausgeber der Buchreihe Bibel und Ethik.
Werke (Auswahl)
Bonum hominis. Die anthropologischen und theologischen Grundlagen der Tugendethik des Thomas von Aquin (= Tübinger theologische Studien. Bd. 28). Matthias-Grünewald-Verlag, Mainz 1987, ISBN 3-7867-1307-3 (Zugleich: Tübingen, Universität, Dissertation, 1986).
Im Laboratorium der Schöpfung. Gentechnologie, Reproduktionsbiologie und Menschenwürde. Schwabenverlag, Ostfildern 1991, ISBN 3-7966-0687-3.
Sterbehilfe und Menschenwürde. Die Begleitung zu einem "eigenen Tod". Pustet, Regensburg 1991, ISBN 3-7917-1297-7.
Genug Platz für alle? Bevölkerungswachstum, Welternährung und Familienplanung. Schwabenverlag, Ostfildern 1992, ISBN 3-7966-0701-2.
Ethik des Lebens. Ein theologischer Grundriss. Matthias-Grünewald-Verlag, Mainz 1993, ISBN 3-7867-1720-6.
Bevölkerungspolitik und Familienplanung in der Dritten Welt. Eine ethische Perspektive (= Berichte aus den Sitzungen der Joachim-Jungius-Gesellschaft der Wissenschaften e. V. Jg. 14, H. 3). Vandenhoeck & Ruprecht, Göttingen 1996, ISBN 3-525-86290-3.
Naturrecht und Menschenwürde. Universale Ethik in einer geschichtlichen Welt. Matthias-Grünewald-Verlag, Mainz 1996, ISBN 3-7867-1899-7.
Zur Lüge verdammt? Politik, Medien, Justiz, Wissenschaft und die Ethik der Wahrheit. Herder, Freiburg (Breisgau) u. a. 2000, ISBN 3-451-27369-1.
Krankheit, Gesundheit, Heilung. Wege zum Heil aus biblischer Sicht (= Topos-plus-Taschenbücher. Bd. 406). Pustet, Regensburg 2001, ISBN 3-7867-8406-X.
Wie gewiss ist das Gewissen? Eine ethische Orientierung. Herder, Freiburg (Breisgau) u. a. 2003, ISBN 3-451-27696-8.
Grundlegung der Ethik. Ein theologischer Entwurf. Herder, Freiburg (Breisgau) u. a. 2007, ISBN 978-3-451-28938-5.
Theologie der Freiheit. Herder, Freiburg (Breisgau) u. a. 2007, ISBN 978-3-451-29701-4.
mit Christiane Florin: Gewissen. Eine Gebrauchsanleitung. Herder, Freiburg (Breisgau) u. a. 2009, ISBN 978-3-451-30118-6.
Chancen zur Versöhnung? Die Kirche und die wiederverheirateten Geschiedenen. Herder, Freiburg (Breisgau) u. a. 2011, ISBN 978-3-451-34117-5.
Ethik des Lebens. Grundlagen und neue Herausforderungen. Herder, Freiburg (Breisgau) u. a. 2. Auflage, 2013, ISBN 978-3-451-30758-4.
Entschiedenheit und Widerstand. Das Lebenszeugnis der Märtyrer. Herder, Freiburg (Breisgau) u. a. 2015, ISBN 978-3-451-33650-8.
Kein Ende der Gewalt? Friedensethik für eine globalisierte Welt. Herder, Freiburg (Breisgau) u. a. 2018, ISBN 978-3-451-37812-6.
Frieden auf Erden? Weihnachten als Provokation. Herder, Freiburg (Breisgau) u. a. 2019, ISBN 978-3-451-38546-9.
Die Kunst zu lieben: Unterwegs zu einer neuen Sexualethik. Herder, Freiburg (Breisgau) u. a. 2021, ISBN 978-3-451-83975-7 (484 S., posthum).
Literatur
Markus Enders: Eberhard Schockenhoff (29. 3. 1953–18. 7. 2020). In: Jahrbuch der Heidelberger Akademie der Wissenschaften für 2020. Heidelberg 2021, S. 146–151 (online).
Weblinks
Website bei der Universität Freiburg
Einzelnachweise
Moraltheologe
Christlicher Sozialethiker
Medizinethiker
Mitglied des Deutschen Ethikrates
Römisch-katholischer Theologe (20. Jahrhundert)
Römisch-katholischer Theologe (21. Jahrhundert)
Römisch-katholischer Geistlicher (20. Jahrhundert)
Hochschullehrer (Universität Regensburg)
Hochschullehrer (Albert-Ludwigs-Universität Freiburg)
Sachbuchautor
Literatur (Deutsch)
Christliche Literatur
Essay
Mitglied der Heidelberger Akademie der Wissenschaften
Absolvent der Eberhard Karls Universität Tübingen
Korporierter im KV
Korporierter im CV
Deutscher
Geboren 1953
Gestorben 2020
Mann | {
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{"url":"http:\/\/www.knowswhy.com\/why-is-kcl-neutral\/","text":"# Why is KCL Neutral?\n\nWhy is KCL Neutral?\n\nExperts had long agreed that KCL or potassium chloride is considered as a neutral solution. It has a strong base, as well as strong acids that harmonize together to form a neutral solution.\nA good example of a neutral solution is pure water. Neutral solutions are also classified based on their PH Level (Power of Hydrogen). There are other elements that also have a neutral state, neither acidic nor alkaline in nature.\n\nPH is used to measure the acidity or basicity of a solution. It ranges from 0-14, and 7 is the middleman among the calculations of acidity or basicity. If the solution is below 7 then it is called an acidic solution. If the PH scale is higher than 7 it is called a basic solution. The difference between these two factors allows people to know whether the solution is acidic or not. Since water is a neutral solution, other solutions mixed with water can either become acidic or basic.\n\nWhen potassium chloride is dissolved in water, the result will be a neutral solution. Since the ions of potassium chloride don\u2019t generally affect the properties of water (it dissolves and harmonizes completely with water), it stays as a neutral solution.\n\nPotassium chloride is a solution that affects the functions of the human body. It is a drug that greatly affects our body particularly the heart, muscles and our blood. You can say that its neutrality can also be described on how a person uses it. When it is used within its right limits, it can be very beneficial to our body. When it is used in excess, it will cause complications that might even lead to fatalities.","date":"2016-09-27 01:50:20","metadata":"{\"extraction_info\": {\"found_math\": false, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8066835999488831, \"perplexity\": 864.4208284281394}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": false}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2016-40\/segments\/1474738660931.25\/warc\/CC-MAIN-20160924173740-00210-ip-10-143-35-109.ec2.internal.warc.gz\"}"} | null | null |
{"url":"https:\/\/nigerianscholars.com\/past-questions\/physics\/question\/290720\/","text":"Nigerian Scholars \u00bb \u00bb A converging lens of focal length 15cm forms a virtual image at a point 10cm fro...\n\n# A converging lens of focal length 15cm forms a virtual image at a point 10cm fro...\n\n### Question\n\nA converging lens of focal length 15cm forms a virtual image at a point 10cm from the lens. Calculate the distance of the object from the lens\n\nA) 10.00cm\n\nB) 6.00cm\n\nC) 5.00cm\n\nD) 1.50cm\n\n### Explanation:\n\n$$\\frac{1}{u} + \\frac{1}{v} = \\frac{1}{f} = \\frac{1}{15} + \\frac{1}{10}$$\n\nu = 6.00\n\n## Dicussion (1)\n\n\u2022 $$\\frac{1}{u} + \\frac{1}{v} = \\frac{1}{f} = \\frac{1}{15} + \\frac{1}{10}$$\n\nu = 6.00","date":"2019-11-22 14:39:16","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.7152218222618103, \"perplexity\": 1824.5082577722376}, \"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-2019-47\/segments\/1573496671363.79\/warc\/CC-MAIN-20191122143547-20191122172547-00333.warc.gz\"}"} | null | null |
IN A timely boost to the Rockhampton Leagues Club Capras' fortunes, Brisbane Broncos fullback Ben Barba says he could be suiting up in the Intrust Super Cup club's colours in the near future.
The Capras lost 38-8 to ISC leaders Norths Devils at Browne Park on Saturday night and are yet to register a win from their first six matches of the season.
A mixed bag for the Broncos in Friday night's 12-8 loss to the Gold Coast saw Barba produce two polar opposite plays within 10 minutes.
Barba produced a stunning try-saving tackle on Titans forward Mark Minichiello midway through the second half.
Nine minutes after, the former Dally M Player of the Year allowed a high kick to bounce before leaping in his own in-goal to defuse it, only to have Titans five-eighth Aidan Sezer strip the ball and score the match-winner.
If he can't become more consistent, Barba says he may end up with his feeder club the Capras.
"It was terrible," Barba told The Sunday Mail.
"I was happy with that (Minichiello tackle) but in saying that, I have one job in particular ... and that's to be safe under the high ball.
"I have to find something soon or I could find myself playing Queensland Cup in the next few weeks."
Fellow Bronco Corey Oates is a slim chance of playing for the Capras in Thursday's round eight clash with Wynnum Manly Seagulls at Gladstone's Marley Brown after leaving the field midway through the second half.
Oates suffered what's thought to be a high hamstring strain and with just three days until the Capras play again, it's unlikely he'll be fit.
The Devils opened their account on Saturday night just four minutes into the match when lock Dean Sheppard crossed to give the competition leaders a 6-0 lead.
The Capras hit back shortly after through Oates after consecutive sets on the Devils' tryline.
The rangy backrower dived under a couple of defenders on the 15th minute mark to score his second try of the season in Capras' colours and close the gap to two points.
Both sides traded sets for the next 10 minutes but a string of penalties to the Devils saw them perched down on the Capras' tryline.
Devils five-eighth Todd Murphy made the most of his opportunities to score the first of his two tries on the night.
Ever-consistent centre Smith Samau helped the Capras back into the game with a short-side play two minutes before half-time to have the home side trailing 12-8.
Devils' second rower Chris Faust scored five minutes into the second half to extend their lead to 12 points before the home side was denied an opportunity to close the gap when a short pass from half Duncan Paia'aua to Oates was called forward.
Oates left the field shortly after and it wasn't long before centre Dylan Galloway took the Devils' lead to 26-8 midway through the second half.
NORTHS DEVILS 38 (Todd Murphy 2, Dylan Galloway, Chris Faust, Lachlan Maranta, Dean Sheppard tries; Todd Murphy 7 goals) def CQ CAPRAS 8 (Smith Samau, Corey Oates tries) at Browne Park.
RESULTS: PNG Hunters 36 def Tweed Heads Seagulls 26, Wynnum Manly Seagulls 36 def Sunshine Coast Falcons 0, Redcliffe Dolphins 34 def Souths Logan 6, Burleigh Bears 22 def Mackay Cutters 14. Northern Pride v Easts Tigers match postponed to July 6 due to weather. | {
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This is the second exercise in the **React Track** of this Apollo Client Tutorial!
<iframe width="560" height="315" src="https://www.youtube.com/embed/Mds3w8ebudM?list=PLn2e1F9Rfr6neWxkWtlTAwshh07-m1p5I" frameborder="0" allowfullscreen></iframe>
## Goal
The **goal** of this exercise is to query information on your very own trainer node. We will use it to add a personal touch to the greeting to our pokedex:
We will learn how to query information from a GraphQL server with Apollo Client.
## Introduction
Move to the second exercise, install the dependencies and start the pokedex React app from your console
```sh
cd pokedex-react/exercise-02
yarn install # or npm install
yarn start # or npm start
```
The schema exposed by our GraphQL server includes the following models
```graphql
type Trainer {
id: String!
name: String!
ownedPokemons: [Pokemon]
}
type Pokemon {
id: String!
url: String!
name: String!
trainer: Trainer
}
```
We can manage pokemon trainers that are related to multiple pokemons and are identified by both an id and a name. A pokemon has a url and a name and is related to its trainer.
Let's now build a GraphQL query together to get the information of your trainer node stored on the server and change the message displayed in `src/components/Pokedex.js`.
## Displaying information of your trainer
Queries offer a flexible way to state data requirements. With Apollo Client, we first define queries and then inject their response to the inner component. As far as the inner component is concerned, the data could be coming from *anywhere*, which means we have a good decoupling between data source and data consumer.
### Building Queries
The GraphQL server for the Pokedex App is configured so that we can identify trainers by their name. To query the information of a trainer given his name, you can use the following query:
```graphql
query TrainerQuery {
Trainer(name: "__NAME__") {
id
name
}
}
```
With Apollo, we need to denote queries like this by using the `gql` tag contained in the `graphql-tag` package.
```js
const TrainerQuery = gql`
query TrainerQuery {
Trainer(name: "__NAME__") {
name
}
}
`
```
If you signed up with GitHub, we already inserted your name in this query.
But how do we access the query result in our Pokedex component? We can use `graphql` exposed from the `react-apollo` package to inject query results to React components via the `data` prop.
```js
const PokedexWithData = graphql(TrainerQuery)(Pokedex)
```
### Using query results in React components
Wrapping components like this with `graphql` injects a new `data` object to the props of the inner component. We can stress this by updating the `propTypes` of the `Pokedex` component:
```js
static propTypes = {
data: React.PropTypes.shape({
loading: React.PropTypes.bool,
error: React.PropTypes.object,
Trainer: React.PropTypes.object,
}).isRequired,
}
```
The `data` object provides several things, in particular
* `data.loading` signifies whether a query is currently being sent to the server and we are waiting for the query response
* If something went wrong with the query and errors are returned, `data.error` will contain detailed information
* once `loading` is `false`, we know that the query response arrived and all the fields from the query are available via `data`. In our case, this is a `Trainer` object with the `id` and `name` properties, available at `data.Trainer`
So let's now change the message to display the name of the trainer once `loading` is `false` and no error occurred:
```js@src/component/Pokedex.js
render () {
if (this.props.data.loading) {
return (<div>Loading</div>)
}
if (this.props.data.error) {
console.log(this.props.data.error)
return (<div>An unexpected error occurred</div>)
}
return (
<div className='w-100 bg-light-gray min-vh-100'>
<Title className='tc pa5'>
Hey {this.props.data.Trainer.name}, there are 0 Pokemons in your pokedex
</Title>
</div>
)
}
```
### Putting it all together
Now let's put the previous steps together and modify our Pokedex component in `src/components/Pokedex.js`. First, we need to include the new dependencies:
```js@src/component/Pokedex.js
import { graphql } from 'react-apollo'
import gql from 'graphql-tag'
```
We also include the `data` prop to the `propTypes` and use `data.loading` and `data.Trainer` as discussed above:
```js
class Pokedex extends React.Component {
static propTypes = {
data: React.PropTypes.shape({
loading: React.PropTypes.bool,
error: React.PropTypes.object,
Trainer: React.PropTypes.object,
}).isRequired,
}
render () {
if (this.props.data.loading) {
return (<div>Loading</div>)
}
if (this.props.data.error) {
console.log(this.props.data.error)
return (<div>An unexpected error occurred</div>)
}
return (
<div className='w-100 bg-light-gray min-vh-100'>
<Title className='tc pa5'>
Hey {this.props.data.Trainer.name}, there are 0 Pokemons in your pokedex
</Title>
</div>
)
}
}
```
Finally, we are defining the `TrainerQuery` (insert your name!), connect it to our `Pokedex` component and finally export the new component:
```js@src/component/Pokedex.js
const TrainerQuery = gql`
query TrainerQuery {
Trainer(name: "__NAME__") {
name
}
}
`
const PokedexWithData = graphql(TrainerQuery)(Pokedex)
export default PokedexWithData
```
## Hello, Trainer!
If you finished all the changes to `src/components/Pokedex.js` successfully, open [http://localhost:3000](http://localhost:3000) in your browser and you should see the updated greeting.
## Excursion: Redux DevTools
[Coming soon](/excursions/excursion-01).
## Recap
Nice, you executed your first GraphQL query with Apollo Client and used it to display your trainer name. In this exercise we learned a lot! Let's recap that:
* The shape of valid queries depend on the **schema from the GraphQL server** (explore them in the data browser on this page!)
* Before executing them, we have to **define queries using the `gql` tag** from the `graphql-tag` package
* **Wrapping a component with `graphql`** from `react-apollo` using a query injects the `data` prop to the inner component
* Once **`data.loading` becomes `false`**, the **`data` prop will contain the fields of the query**. We can render a loading state as long as `data.loading` is `true`.
| {
"redpajama_set_name": "RedPajamaGithub"
} | 8,773 |
Q: how to handle 1 to 3 fingers swipe gesture in iOS I use the following code to handle 1 finger swipe in my code:
UISwipeGestureRecognizer *swipe = [[UISwipeGestureRecognizer alloc] initWithTarget:self action:@selector(handleViewsSwipe:)];
[swipe setDirection:UISwipeGestureRecognizerDirectionLeft];
[swipe setDelaysTouchesBegan:YES];
[[self view] addGestureRecognizer:swipe];
I know i can add the following line to make it handle 2 fingers swipe:
[swipe setNumberOfTouchesRequired:2];
However when I add the above code 1 finger swipe is no longer detected since the number of touches required is now 2. What can I do to make my code work for 1, 2 or 3 fingers swipe?
I tried using the following code but this doesn't do what I want to do.
UIPanGestureRecognizer *panRecognizer = [[UIPanGestureRecognizer alloc] initWithTarget:self action:@selector(handleViewsSwipe:)];
[panRecognizer setMinimumNumberOfTouches:1];
[panRecognizer setMaximumNumberOfTouches:3];
[panRecognizer setDelaysTouchesBegan:YES];
[[self view] addGestureRecognizer:panRecognizer];
[panRecognizer release];
Thank you.
A: In your handleViewsSwipe you can get the numberOfTouches property from the gesture recognizer.
- (void)handleViewsSwipe:(UISwipeGestureRecognizer *)recognizer {
NSUInteger touches = recognizer.numberOfTouches;
switch (touches) {
case 1:
break;
case 2:
break;
case 3:
break;
default:
break;
}
}
Just switch the same method for what to do depending on how many touches you get.
A: Add three swipe gesture recognizers to your view:
for (int i = 1; i <= 3; ++i) {
UISwipeGestureRecognizer *swipe = [[UISwipeGestureRecognizer alloc] initWithTarget:self action:@selector(handleViewsSwipe:)];
swipe.numberOfTouchesRequired = i;
swipe.direction = UISwipeGestureRecognizerDirectionLeft;
swipe.delaysTouchesBegan = YES;
[self.view addGestureRecognizer:swipe];
}
Worked for me.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 1,068 |
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There're available for save, if you'd rather and want to own it, just click save symbol on the web page, and it will be instantly down loaded to your laptop computer. Lastly if you'd like to have new and latest graphic related to Awesome 33 Design Excel Chart Save as Template, please follow us on google plus or bookmark this blog, we try our best to provide daily up-date with fresh and new graphics. We do hope you love keeping here. | {
"redpajama_set_name": "RedPajamaC4"
} | 3,723 |
// Copyright 2014 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 "content/browser/android/in_process/synchronous_compositor_factory_impl.h"
#include "base/command_line.h"
#include "base/observer_list.h"
#include "base/sys_info.h"
#include "base/thread_task_runner_handle.h"
#include "content/browser/android/in_process/context_provider_in_process.h"
#include "content/browser/android/in_process/synchronous_compositor_external_begin_frame_source.h"
#include "content/browser/android/in_process/synchronous_compositor_impl.h"
#include "content/browser/android/in_process/synchronous_compositor_output_surface.h"
#include "content/browser/gpu/browser_gpu_memory_buffer_manager.h"
#include "content/common/gpu/client/context_provider_command_buffer.h"
#include "content/common/gpu/client/gpu_channel_host.h"
#include "content/common/gpu/client/webgraphicscontext3d_command_buffer_impl.h"
#include "content/gpu/in_process_gpu_thread.h"
#include "content/public/browser/browser_thread.h"
#include "content/public/browser/gpu_data_manager.h"
#include "content/renderer/gpu/frame_swap_message_queue.h"
#include "content/renderer/render_thread_impl.h"
#include "gpu/blink/webgraphicscontext3d_in_process_command_buffer_impl.h"
#include "gpu/command_buffer/client/gl_in_process_context.h"
#include "gpu/command_buffer/common/gles2_cmd_utils.h"
#include "gpu/command_buffer/service/gpu_switches.h"
#include "ui/gl/android/surface_texture.h"
#include "ui/gl/gl_surface.h"
#include "ui/gl/gl_surface_stub.h"
using cc_blink::ContextProviderWebContext;
using gpu_blink::WebGraphicsContext3DImpl;
using gpu_blink::WebGraphicsContext3DInProcessCommandBufferImpl;
namespace content {
namespace {
struct ContextHolder {
scoped_ptr<WebGraphicsContext3DInProcessCommandBufferImpl> command_buffer;
gpu::GLInProcessContext* gl_in_process_context;
};
blink::WebGraphicsContext3D::Attributes GetDefaultAttribs() {
blink::WebGraphicsContext3D::Attributes attributes;
attributes.antialias = false;
attributes.depth = false;
attributes.stencil = false;
attributes.shareResources = true;
attributes.noAutomaticFlushes = true;
return attributes;
}
ContextHolder CreateContextHolder(
const blink::WebGraphicsContext3D::Attributes& attributes,
scoped_refptr<gpu::InProcessCommandBuffer::Service> service,
const gpu::GLInProcessContextSharedMemoryLimits& mem_limits,
bool is_offscreen) {
gpu::gles2::ContextCreationAttribHelper in_process_attribs;
WebGraphicsContext3DImpl::ConvertAttributes(attributes, &in_process_attribs);
in_process_attribs.lose_context_when_out_of_memory = true;
scoped_ptr<gpu::GLInProcessContext> context(gpu::GLInProcessContext::Create(
service, NULL /* surface */, is_offscreen, gfx::kNullAcceleratedWidget,
gfx::Size(1, 1), NULL /* share_context */, attributes.shareResources,
in_process_attribs, gfx::PreferDiscreteGpu, mem_limits,
BrowserGpuMemoryBufferManager::current(), nullptr));
gpu::GLInProcessContext* context_ptr = context.get();
ContextHolder holder;
holder.command_buffer =
scoped_ptr<WebGraphicsContext3DInProcessCommandBufferImpl>(
WebGraphicsContext3DInProcessCommandBufferImpl::WrapContext(
context.Pass(), attributes));
holder.gl_in_process_context = context_ptr;
return holder;
}
scoped_ptr<WebGraphicsContext3DCommandBufferImpl> CreateContext3D(
const blink::WebGraphicsContext3D::Attributes& attributes,
const content::WebGraphicsContext3DCommandBufferImpl::SharedMemoryLimits&
mem_limits) {
DCHECK(RenderThreadImpl::current());
CauseForGpuLaunch cause =
CAUSE_FOR_GPU_LAUNCH_WEBGRAPHICSCONTEXT3DCOMMANDBUFFERIMPL_INITIALIZE;
scoped_refptr<GpuChannelHost> gpu_channel_host(
RenderThreadImpl::current()->EstablishGpuChannelSync(cause));
CHECK(gpu_channel_host.get());
int surface_id = 0;
bool lose_context_when_out_of_memory = true;
return make_scoped_ptr(new WebGraphicsContext3DCommandBufferImpl(
surface_id, GURL(), gpu_channel_host.get(), attributes,
lose_context_when_out_of_memory, mem_limits, NULL));
}
} // namespace
class SynchronousCompositorFactoryImpl::VideoContextProvider
: public StreamTextureFactorySynchronousImpl::ContextProvider {
public:
VideoContextProvider(
scoped_refptr<cc::ContextProvider> context_provider,
gpu::GLInProcessContext* gl_in_process_context)
: context_provider_(context_provider),
gl_in_process_context_(gl_in_process_context) {
context_provider_->BindToCurrentThread();
}
scoped_refptr<gfx::SurfaceTexture> GetSurfaceTexture(
uint32 stream_id) override {
return gl_in_process_context_->GetSurfaceTexture(stream_id);
}
gpu::gles2::GLES2Interface* ContextGL() override {
return context_provider_->ContextGL();
}
void AddObserver(StreamTextureFactoryContextObserver* obs) override {
observer_list_.AddObserver(obs);
}
void RemoveObserver(StreamTextureFactoryContextObserver* obs) override {
observer_list_.RemoveObserver(obs);
}
void RestoreContext() {
FOR_EACH_OBSERVER(StreamTextureFactoryContextObserver,
observer_list_,
ResetStreamTextureProxy());
}
private:
friend class base::RefCountedThreadSafe<VideoContextProvider>;
~VideoContextProvider() override {}
scoped_refptr<cc::ContextProvider> context_provider_;
gpu::GLInProcessContext* gl_in_process_context_;
base::ObserverList<StreamTextureFactoryContextObserver> observer_list_;
DISALLOW_COPY_AND_ASSIGN(VideoContextProvider);
};
SynchronousCompositorFactoryImpl::SynchronousCompositorFactoryImpl()
: record_full_layer_(true),
use_ipc_command_buffer_(false),
num_hardware_compositors_(0) {
SynchronousCompositorFactory::SetInstance(this);
}
SynchronousCompositorFactoryImpl::~SynchronousCompositorFactoryImpl() {}
scoped_refptr<base::SingleThreadTaskRunner>
SynchronousCompositorFactoryImpl::GetCompositorTaskRunner() {
return BrowserThread::GetMessageLoopProxyForThread(BrowserThread::UI);
}
bool
SynchronousCompositorFactoryImpl::RecordFullLayer() {
return record_full_layer_;
}
scoped_ptr<cc::OutputSurface>
SynchronousCompositorFactoryImpl::CreateOutputSurface(
int routing_id,
scoped_refptr<content::FrameSwapMessageQueue> frame_swap_message_queue) {
scoped_refptr<cc::ContextProvider> onscreen_context =
CreateContextProviderForCompositor(RENDER_COMPOSITOR_CONTEXT);
scoped_refptr<cc::ContextProvider> worker_context =
CreateContextProviderForCompositor(RENDER_WORKER_CONTEXT);
return make_scoped_ptr(new SynchronousCompositorOutputSurface(
onscreen_context, worker_context, routing_id, frame_swap_message_queue));
}
InputHandlerManagerClient*
SynchronousCompositorFactoryImpl::GetInputHandlerManagerClient() {
return synchronous_input_event_filter();
}
scoped_ptr<cc::BeginFrameSource>
SynchronousCompositorFactoryImpl::CreateExternalBeginFrameSource(
int routing_id) {
return make_scoped_ptr(
new SynchronousCompositorExternalBeginFrameSource(routing_id));
}
bool SynchronousCompositorFactoryImpl::OverrideWithFactory() {
return !use_ipc_command_buffer_;
}
scoped_refptr<ContextProviderWebContext>
SynchronousCompositorFactoryImpl::CreateOffscreenContextProvider(
const blink::WebGraphicsContext3D::Attributes& attributes,
const std::string& debug_name) {
DCHECK(!use_ipc_command_buffer_);
ContextHolder holder =
CreateContextHolder(attributes, GpuThreadService(),
gpu::GLInProcessContextSharedMemoryLimits(), true);
return ContextProviderInProcess::Create(holder.command_buffer.Pass(),
debug_name);
}
scoped_refptr<cc::ContextProvider>
SynchronousCompositorFactoryImpl::CreateContextProviderForCompositor(
CommandBufferContextType type) {
// This is half of what RenderWidget uses because synchronous compositor
// pipeline is only one frame deep. But twice of half for low end here
// because 16bit texture is not supported.
unsigned int mapped_memory_reclaim_limit =
(base::SysInfo::IsLowEndDevice() ? 2 : 6) * 1024 * 1024;
blink::WebGraphicsContext3D::Attributes attributes = GetDefaultAttribs();
if (use_ipc_command_buffer_) {
WebGraphicsContext3DCommandBufferImpl::SharedMemoryLimits mem_limits;
mem_limits.mapped_memory_reclaim_limit = mapped_memory_reclaim_limit;
scoped_ptr<WebGraphicsContext3DCommandBufferImpl> context =
CreateContext3D(GetDefaultAttribs(), mem_limits);
return ContextProviderCommandBuffer::Create(context.Pass(), type);
}
gpu::GLInProcessContextSharedMemoryLimits mem_limits;
mem_limits.mapped_memory_reclaim_limit = mapped_memory_reclaim_limit;
ContextHolder holder =
CreateContextHolder(attributes, GpuThreadService(), mem_limits, true);
return ContextProviderInProcess::Create(holder.command_buffer.Pass(),
"Child-Compositor");
}
scoped_refptr<StreamTextureFactory>
SynchronousCompositorFactoryImpl::CreateStreamTextureFactory(int frame_id) {
scoped_refptr<StreamTextureFactorySynchronousImpl> factory(
StreamTextureFactorySynchronousImpl::Create(
base::Bind(
&SynchronousCompositorFactoryImpl::TryCreateStreamTextureFactory,
base::Unretained(this)),
frame_id));
return factory;
}
WebGraphicsContext3DInProcessCommandBufferImpl*
SynchronousCompositorFactoryImpl::CreateOffscreenGraphicsContext3D(
const blink::WebGraphicsContext3D::Attributes& attributes) {
DCHECK(!use_ipc_command_buffer_);
ContextHolder holder =
CreateContextHolder(attributes, GpuThreadService(),
gpu::GLInProcessContextSharedMemoryLimits(), true);
return holder.command_buffer.release();
}
gpu::GPUInfo SynchronousCompositorFactoryImpl::GetGPUInfo() const {
DCHECK(!use_ipc_command_buffer_);
return content::GpuDataManager::GetInstance()->GetGPUInfo();
}
void SynchronousCompositorFactoryImpl::CompositorInitializedHardwareDraw() {
base::AutoLock lock(num_hardware_compositor_lock_);
num_hardware_compositors_++;
if (num_hardware_compositors_ == 1 && main_thread_task_runner_.get()) {
main_thread_task_runner_->PostTask(
FROM_HERE,
base::Bind(
&SynchronousCompositorFactoryImpl::RestoreContextOnMainThread,
base::Unretained(this)));
}
}
void SynchronousCompositorFactoryImpl::CompositorReleasedHardwareDraw() {
base::AutoLock lock(num_hardware_compositor_lock_);
DCHECK_GT(num_hardware_compositors_, 0u);
num_hardware_compositors_--;
}
void SynchronousCompositorFactoryImpl::RestoreContextOnMainThread() {
if (CanCreateMainThreadContext() && video_context_provider_.get())
video_context_provider_->RestoreContext();
}
bool SynchronousCompositorFactoryImpl::CanCreateMainThreadContext() {
base::AutoLock lock(num_hardware_compositor_lock_);
return num_hardware_compositors_ > 0;
}
scoped_refptr<StreamTextureFactorySynchronousImpl::ContextProvider>
SynchronousCompositorFactoryImpl::TryCreateStreamTextureFactory() {
{
base::AutoLock lock(num_hardware_compositor_lock_);
main_thread_task_runner_ = base::ThreadTaskRunnerHandle::Get();
}
// Always fail creation even if |video_context_provider_| is not NULL.
// This is to avoid synchronous calls that may deadlock. Setting
// |video_context_provider_| to null is also not safe since it makes
// synchronous destruction uncontrolled and possibly deadlock.
if (!CanCreateMainThreadContext()) {
return
scoped_refptr<StreamTextureFactorySynchronousImpl::ContextProvider>();
}
if (!video_context_provider_.get()) {
DCHECK(android_view_service_.get());
blink::WebGraphicsContext3D::Attributes attributes = GetDefaultAttribs();
attributes.shareResources = false;
// This needs to run in on-screen |android_view_service_| context due to
// SurfaceTexture limitations.
ContextHolder holder =
CreateContextHolder(attributes, android_view_service_,
gpu::GLInProcessContextSharedMemoryLimits(), false);
video_context_provider_ = new VideoContextProvider(
ContextProviderInProcess::Create(holder.command_buffer.Pass(),
"Video-Offscreen-main-thread"),
holder.gl_in_process_context);
}
return video_context_provider_;
}
void SynchronousCompositorFactoryImpl::SetDeferredGpuService(
scoped_refptr<gpu::InProcessCommandBuffer::Service> service) {
DCHECK(!android_view_service_.get());
android_view_service_ = service;
}
base::Thread* SynchronousCompositorFactoryImpl::CreateInProcessGpuThread(
const InProcessChildThreadParams& params) {
DCHECK(android_view_service_.get());
return new InProcessGpuThread(params,
android_view_service_->sync_point_manager());
}
scoped_refptr<gpu::InProcessCommandBuffer::Service>
SynchronousCompositorFactoryImpl::GpuThreadService() {
DCHECK(android_view_service_.get());
// Create thread lazily on first use.
if (!gpu_thread_service_.get()) {
gpu_thread_service_ = new gpu::GpuInProcessThread(
android_view_service_->sync_point_manager());
}
return gpu_thread_service_;
}
void SynchronousCompositorFactoryImpl::SetRecordFullDocument(
bool record_full_document) {
record_full_layer_ = record_full_document;
}
void SynchronousCompositorFactoryImpl::SetUseIpcCommandBuffer() {
use_ipc_command_buffer_ = true;
}
} // namespace content
| {
"redpajama_set_name": "RedPajamaGithub"
} | 7,415 |
\section{Introduction}
The recent (completed and on-going) galaxy redshift surveys
(e.g. LCRS, 2dFGRS, 6dF, SDSS) of our local universe have
enormously increased our knowledge of galaxies and of their large
scale distribution. These large-scale structure data sets provide
also a powerful tool for breaking many of the parameter degeneracies
associated with the CMB data (Spergel et al. \cite{sper}). Clusters
of galaxies, the largest virialised systems known, have a vital role
in understanding cosmological structure formation. In particular,
following the evolution of clustering with redshift, we can put direct
constraints on models for the evolution of density perturbations
(Munshi et al. \cite{mun}).
However, it is impossible to study cosmological evolution, using only
such local surveys. Thanks to recent developments in instrument
technology there are several new surveys designed to probe at
increasingly higher redshifts, in order to study the early evolution
of galaxies and their systems. We shall list a few of them.
The DEEP2 redshift survey is planned to study the evolution of
properties of galaxies and the evolution of the clustering of galaxies
from $z \sim 1.5$ to $z=0$, using the DEIMOS spectrograph on the 10 m
Keck II telescope. The results will be compared with those of the
local surveys, e.g., as the LCRS (Coil et al. \cite{Coil}).
The ALHAMBRA photometric survey (Moles et al. \cite{moles05}) has similar
goals.
It will cover 4 square degrees of sky, and will find galaxies up to
redshifts $z\approx5$.
The VIRMOS galaxy redshift survey, using VIMOS on the VLT telescope,
is also designed to study the formation of galaxies and large-scale
structure over the redshift range ($0<z<5$), covering sixteen square
degrees of the sky in four separate fields (Virmos Consortium,
http://www.oamp.fr/virmos/).
GOODS (the Great Observatories Origins Deep Survey) aims to unite
extremely deep multi-wavelength observations (up to $z\approx 6$) both
from ground-based (VLT, Keck, Gemini, NOAO, Subaru) and space
telescopes: Hubble (HST Treasure program), SIRTF (Legacy Program), and
Chandra. Observations cover two fields ($10'\times16'$), centered on
the Hubble Deep Field North and the Chandra Deep Field South. The
primary goal of the GOODS program is to provide observational data for
tracing the mass assembly of galaxies throughout most of cosmic
history (Dickinson \& Giavalisco \cite{dic}).
The Galaxy Evolution Explorer (GALEX) satellite was launched in 2003
(Martin et al. \cite{m05a}). In combination with ground based optical
observations this satellite allows to study the star formation rate,
the galaxy luminosity function and other parameters of galaxy
evolution over the redshift range $0<z<5$, and even beyond this
limit (see http://www.galex.caltech.edu).
Several recent studies have revealed clustering of Ly alpha objects,
quasars and radio galaxies at very high redshifts (Ouchi et
al. \cite{ouch}, Venemans et al. \cite{ven}, Malhotra et
al. \cite{mal05}, Wang et al. \cite{wang05}, and
Stiavelli et al. \cite{stia05}).
For example, Ouchi et al. (\cite{ouch}) reported about the discovery
of primeval dense structures at redshift 6 containing Lyman alpha
emitters (LAEs). Ouchi et al. estimated that masses of these
structures - progenitors of present-day large scale structures are of
order of $10^{12} M_{\sun}$ - $10^{13} M_{\sun}$ and dimensions are
less than 10 $h^{-1}$\thinspace Mpc.
By these surveys, observations are reaching the scales where the
evolution of galaxies along the light-cone plays an essential role.
Comparison of deep surveys with our theoretical understanding of
structure formation and evolution has become even more topical and
thus simulations, or mock catalogs, have become an important tool for
the design of observational projects and for later data analysis. A
properly constructed simulation can allow us to compare the
observations directly with modern models of structure formation, can
serve to test the data processing algorithms for biases, and to
quantify the impact of numerous observational selection effects (Yan
et al. \cite{yan}).
We believe that light-cone simulations mimic better the
observational datasets than conventional simulations at $z=0$, and
at different ``snapshots'' at fixed redshifts. The light-cone
algorithm stores 'light-cone particles' on-the-fly, allowing us to
follow continuously the evolution of structure. Although not
difficult in principle, light-cone simulations tax heavily computer
resources -- the volumes are too large to model them with necessary
mass resolution. The best-known light-cone, ``the Hubble
simulation'' (Colberg et al. \cite{colberg}), was run on specialised
parallel shared-memory computers, and remains the only one with
publicly available data.
The goal of this paper is to present a new method to perform
light-cone simulations of deep pencil beams, typical for deep
surveys. Our method is rather efficient and allows to perform and
analyse the simulation on single workstations. We shall build a
light-cone from $z=0$ to $z=6$ in a ``concordance'' cosmological
model, and shall follow the evolution of dark matter (DM) haloes with
the cosmic epoch. Visualizations of DM-haloes in the light-cone model
can be seen at Tartu Observatory web pages ({\tt
http://www.aai.ee/$\sim$maret/lc.html}).
When our project was almost finished we learned that a similar
light-cone project MoMaF has been realized by Blaizot et al.
(\cite{blaizot05}). Below we shall compare their approach with ours.
\section{The light-cone simulation}
\subsection{Method}
We use the Multi Level Adaptive Particle Mesh code (MLAPM, Knebe et
al. \cite{knebe}) with light-cone output.
The MLAPM code is adaptive, with sub-grids being adaptively formed in
regions where the density exceeds a specified threshold. There are
similar codes, as the ART code, Kravtsov et al. (\cite{kratso}); it is
essential that simulations are done with different codes, to
cross-check the results of the complex dynamics of the cosmic
structure formation.
We base the light-cone on periodic replicas of our simulation
cube. This could, of course, introduce extra periodicities in the
results, but we shall demonstrate that a clever choice of the
light-cone parameters will avoid those, at least for pencil-beams. If
we choose the pencil-beam along one of the coordinate axes, we will
sample the same regions of the cube many times; but if the direction
of the beam is oblique, and the beam narrow, we will use different
regions of the cube along the beam.
In order to collect the light-cone, we find first the co-moving
light-cone radius and determine all the copies of the original
simulation cube, which intersect with the spherical surface of that
radius (cover it). For the simplest geometries (almost full-sky) that
is enough, but for a pencil-beam patch geometry we have to use three
additional checks:
\begin{enumerate}
\item find if the cube copy vertices lie inside the patch;
\item find if the patch edges intersect the copy's faces;
\item find if the patch planes intersect the copy's edges.
\end{enumerate}
If nothing this happens, the copy-cube does not include the
light-cone. This cube list may seem to be an unnecessary complication,
but it will speed up light-cone processing for the most interesting
deep and narrow light-cones.
When the cube list is completed, we check for all particles their
positions in all the candidate cubes, and if the (copy) particle
has crossed the light-cone between the preceding $z$ and the present $z$,
we find the crossing redshift and coordinates by linear interpolation.
Then we check for the patch geometry, if necessary, and write the
(copy)-particle data.
Detailed instructions on generation of the light-cone simulations can
be found in the MLAPM user guide
(http://www.aip.de/People/AKnebe/MLAPM).
The MoMaF project (Blaizot et al. \cite{blaizot05}) takes a slightly
different approach, saving first a large number of snapshots and
using these later to build the light-cone. When assembling the
light-cone, they randomly rotate the snapshots, in order to
eliminate the influence of periodicities. As this destroys the
continuity of the structure, we prefer not to scramble our cubes. In
fact, MoMaF allows such an approach too, for pencil-beam surveys,
although Blaizot et al. (\cite{blaizot05}) devote most of their
attention to the scrambled case.
\subsection{Application}
We simulate a pencil-beam mock survey, similar to the contemporary
observational surveys. We use a simulation with $256^3$ dark matter
particles in a $256^3$ grid. We follow the evolution from $z=6$ to
present time. Our simulation covers $2^{\circ} \times 0.5^{\circ}$ in
the sky.
We use a flat cosmological model with the parameters derived by the
WMAP microwave background anisotropy experiment (Bennett et
al. \cite{bennet}): the dark matter density $\Omega_m=0.226$, the
baryonic density $\Omega_b=0.044$, the vacuum energy density
(cosmological constant) $\Omega_{\Lambda}=0.73$, the Hubble constant
$h=0.71$ (here and throughout this paper $h$ is the present-day Hubble
constant in units of 100 km s$^{-1}$ Mpc$^{-1}$) and the rms mass
density fluctuation parameter $\sigma_8=0.84$.
The initial data for our simulation was generated in a cube of
200~$h^{-1}$\thinspace Mpc\ co-moving size, for $z=30$. Thus, each particle has a mass
of $3.57\cdot 10^{10} h^{-1}\mbox{M}_{\sun}$. The transfer function for our
model was computed using the COSMIC code by E.~Bertschinger ({\tt
http://arcturus.mit.edu/cosmics/}).
\begin{figure*}[ht]
\centering
\resizebox{1.57\columnwidth}{!}{\includegraphics*{pekka_fig1a.eps}}
\resizebox{1.57\columnwidth}{!}{\includegraphics*{pekka_fig1b.eps}}
\caption{The density field of the 6 Gpc deep dark matter
light-cone simulation smoothed with a
$r = 1.0$~$h^{-1}$\thinspace Mpc\ kernel (upper panels), and
with a $r = 16.0$~$h^{-1}$\thinspace Mpc\ kernel (lower panels).}
\label{fig:1}
\end{figure*}
Figure \ref{fig:1} shows the projected (dark-matter) density fields
of our light-cone simulation from $z=0$ to $z=6$ (for the
cosmological model chosen $z=6$ corresponds to 5981.42 $h^{-1}$\thinspace Mpc. The
density was calculated, using an Epanechnikov kernel
($h(x)\sim(1-x^2/r^2)$ of radii $r$ 1.0~$h^{-1}$\thinspace Mpc, 16.0~$h^{-1}$\thinspace Mpc\ - i.e., for
the characteristic scales of clusters and superclusters of galaxies.
The full amount of light-cone data (positions and velocities of dark matter
particles) can have enormous. The evident way to compress
the data is to extract catalogues of dark matter haloes; this are the
objects that can be associated with observed galaxies and clusters of
galaxies.
As the amount of data is large, we used the simplest algorithm
(friends-of-friends, FOF) to identify dark matter haloes. The
simulations reported in this paper were run in early 2004; now we
would have used a new feature of MLAPM, its halo finder (see Gill
et al. \cite{gill04}) that uses the basic adaptive density
tree of the simulation, and outputs haloes at all required
snapshots. It should not be difficult to adapt that to output
light-cone halo catalogs on the fly; this remains to be done. Deep
light-cones generate huge amounts of data, and the only practical way
to handle this is to keep only the haloes.
FOF uses a linking length $b$ to collect particles in groups with
spacing closer than $b$ times the mean inter-particle spacing. The
linking length is frequently determined from the virialisation density
$\rho_v$ (see Bryan and Norman \cite{bry}), obtained from the solution
for the collapse of a spherical top-hat perturbation. The density
$\Delta_c$ dependence on background cosmology via the matter density
parameter
\[
\Omega_M(z)=\Omega_0(1+z)^3/E(z)^2,
\]
where
\[
E^2=\Omega_0(1+z)^3 +\Omega_R(1+z)^3+\Omega_{\Lambda}.
\]
Bryan and Norman \cite{bry} give an approximate formula
for that:
\[
\Delta_c=\rho_v/\rho_{\mbox{crit}}=18 \pi^2+82x-39x^2,
\]
where $x=\Omega_M(z)-1$ and $\rho_{\mbox{crit}}$ is the density in the
Einstein-deSitter model ($\Omega_{\Lambda}=0, \Omega_M=1$). The
actual mean density is $\Omega(z)\rho_{\mbox{crit}}$. Thus the
linking length that would select virialised haloes at a given redshift
$z$ can be written as $b=(\Omega_M(z)\Delta_c)^{\frac{1}{3}}$.
The assumption that objects populate only virialised haloes could be a
bit extreme. We normalised the linking length by its present value,
comparing the amplitude of the simulated halo mass function (at it's
massive end) with an observational mass function of galaxy groups of
the Las Campanas Loose Groups of Galaxies, hereafter LCLG,
Hein\"am\"aki et al. (\cite{hei03}). In order to obtain this mass
function, we ran the MLAPM code in the snapshot mode, with the same
initial data we used for the light-cone simulation.
Using this normalisation, we chose the present epoch ($z=0$) linking
length as $b=0.23$ (in units of the mean particle separation), which
corresponds to the matter density contrast $\delta n/n = 80$. This is
somewhat lower than the virial density, but not much, and delineates
well galaxy groups, as seen in the LCLG Catalog (Tucker et al.
\cite{tucker}).
Figure ~\ref{fig:4} shows how the linking length we used changes with
redshift. Due to the accelerated expansion at later epochs the haloes
need higher density contrasts (and smaller linking lengths) for
virialisation.
\begin{figure}[h]
\centering
\resizebox{1.0\columnwidth}{!}{\includegraphics[angle=-90]{pekka_fig2.eps}}\\
\caption {The FOF linking length as a function of redshift,
for the light-cone simulation.}
\label{fig:4}
\end{figure}
We extracted several populations of dark matter haloes from our
light-cone: haloes with 2 or more particles
($M_h \ge 7.1\cdot 10^{10}h^{-1}\mbox{M}_{\sun}$), haloes with more than 20
particles ($M_h \ge 7.1\cdot10^{11}h^{-1}\mbox{M}_{\sun}$), and a conservative
sample of haloes with more than 100 dark matter particles
($M_h\ge3.6\cdot10^{12}h^{-1}\mbox{M}_{\sun}$), We cleaned all the group
catalogues, using the virial equilibrium condition
$E_r=E_{kin}/|E_{pot}|<0.5$ ($E_{pot}$ is the potential energy and
$E_{kin}$ -- the kinetic energy of a group) for groups to be included
in our final group catalogue.
The number of small haloes is considerably reduced by the virial
condition, which is natural -- many of such haloes are random
encounters. From the $n_{\mbox{min}}=20$ halo sample, 6.5\% of haloes
are rejected, and only a few haloes from the rich halo sample do not
satisfy the virial condition. This indicates that the linking length
we have chosen does not pick up too many non-virialised objects. The
final full halo sample includes about 600,000 haloes, the intermediate
sample has 14016 haloes and the sample of rich haloes includes 4088
haloes.
\section{Checking for periodicities}
Assembling a light-cone from periodic replicas of a simulation cube
will lead to several statistical biases. These are thoroughly
discussed in Blaizot et al. (\cite{blaizot05}). The main bias comes
from scrambling the snapshots; as we do not use scrambling, we
bypass this bias.
Another bias is caused by the finite volume of the simulation cube
and can be corrected for; Blaizot et al. (\cite{blaizot05}) show how
to do that. We can also, in principle, to modify the light-cone by
linear large-scale modes; this would allow us to model better
correlation functions and number counts.
There is one more effect to worry about -- as our light-cone is
composed of periodic replicas of a much smaller simulation cube, it
could have periodicities at scales of about the cube size. The
easiest way to check for that is to look at the two-point
correlation function of the light-cone. The total number of
light-cone mass points is very large; in order to calculate the
correlation function we chose the full halo sample, and diluted it
randomly, by a factor of six, to keep the $O(N^2)$ calculation time
within reasonable limits. The number of haloes used was about
10,000. We are worried about large-scale correlation, thus we chose
the Landy-Szalay estimator, which is one of the best estimator for
large scales (see, e.g., Mart{\'\i}nez \& Saar \cite{martsaar}).
The rms error of the estimator was taken to be twice the Poisson
error. We show this correlation function in Fig.~\ref{fig:corr}.
\begin{figure}
\centering
\resizebox{\columnwidth}{!}{\includegraphics*{pekka_fig3.eps}}
\caption{The large-scale
correlation function of DM haloes in the light-cone.
The solid line with error-bars shows the correlation function
for the whole sample, dotted bars show the correlation
function and its 1-$\sigma$ deviation for the redshift
interval $z\in[0,1]$.
\label{fig:corr}}
\end{figure}
As we see, no periodicity at scales around 200~$h^{-1}$\thinspace Mpc\ can be
seen. The dip in the correlation function at $\sim$50 $h^{-1}$\thinspace Mpc\ and the
maximum around $\sim$120 $h^{-1}$\thinspace Mpc\ are real, and are seen both in
simulations and in the observed large-scale correlations (e.g., for
Abell clusters, Einasto et al. \cite{ein97}, see also Einasto et
al. \cite{ein94} and Tago et al. \cite{tago02}). A slight indication
of periodicity could be seen in the closest redshift interval
($z=0\dots1$, shown with dotted error-bars). However, even there
$\xi(r)=0$ for distances $r>30$$h^{-1}$\thinspace Mpc, within $2\sigma$ limits
(the volume and the number of haloes are small, and the estimate is
rather uncertain). For other redshift intervals the correlation
functions practically coincide with the mean for the whole sample.
This can be explained by the good choice of the light-cone
geometry. An oblique direction of the light-cone with respect the
symmetry axes of the cube will cause the light-cone to sample
different regions of the simulation cube in its different replicas. We
can quantify this by counting the number of times each cube volume
element is included in the light-cone. In order to estimate that, we
choose a simple algorithm -- we populate the light-cone with a Poisson
point process, fold it back onto the original simulation cube, and
find the resulting one-point density distribution in this cube. When
properly normalised, this distribution approximates the volume
multiplicity distribution.
The volume multiplicity distribution for our light-cone is shown in
Fig.~\ref{fig:volmult}. The two different histograms show the results
for two different oversampling factors (the ratio of the density of
the Poisson process to the mean light-cone density) -- the higher this
factor, the better the estimate, and the larger the computer time.
\begin{figure}
\centering
\resizebox{\columnwidth}{!}{\includegraphics*{pekka_fig4.eps}}
\caption{The volume multiplicity histograms of the light-cone.
\label{fig:volmult}}
\end{figure}
We see that most of the volume of the simulation cube is used only
twice in our light-cone. The worst choice of the light-cone
direction, along an axis of the cube, would give a factor close to
30 (the depth of the light-cone divided by the cube size). We can
use the mean of the histogram or its rms error as the
figure-of-merit $M$ for the volume use; maybe the best choice would
be to use a a combination of these:
\[
M^2=\sigma^2_m+\bar{m}^2,
\]
where $m$ is the volume multiplicity, and $\bar{m}$ its mean value.
Thus, the figure-of-merit for an ideal case (e.g., the Hubble volume
$\pi/8$ sterradian light-cone, Colberg et al. \cite{colberg}) would
be 1; for our light-cone it is 2.9 (but could be over 30). Another
relevant characteristic could be the distribution of distances
between point replicas. A rough estimate of the mean replica
distance for our light-cone is 6000/3=2000 $h^{-1}$\thinspace Mpc; this is why we do
not see periodicities in the correlation function.
The light-cone figure-of-merit can be found before simulations, and
can be used to select the best orientation parameters for a given
light-cone geometry (its size and the size of the simulation cube).
Its value will also characterise the possible periodicities in the
light-cone. We plan to include the figure-of-merit code in the tools
section of the MLAPM code package.
\section{Evolution: redshift dependence of the dark matter haloes}
\subsection{Spatial density of haloes}
Light-cones as ours can be used for many purposes. As this paper is
mainly meant to present the light-cone construction method, we shall
give only a few examples below.
First, as our light-cone is pretty deep, we can follow the formation
of first massive haloes. Smaller haloes form earlier yet, and their
study would require a deeper light-cone.
Figure ~\ref{fig:5} illustrates the appearance of the first dark
matter haloes. In panel (a), DM haloes with masses $M\ge 3.6 \cdot
10^{12}\mbox{M}_{\sun}$ are shown. Halos, placed on the density field map
(smoothed with 1 $h^{-1}$\thinspace Mpc\ kernel), are marked with black circles. As we
see, the very first massive haloes appear at about D=5600 $h^{-1}$\thinspace Mpc\
(z=4.97). Panel (b) shows shows haloes of mass $M\ge 7.1 \cdot
10^{11}\mbox{M}_{\sun}$. In this case the very first haloes appear already at
$D=5900$ $h^{-1}$\thinspace Mpc\ ($z= 5.62$). Smaller haloes exist in our light-cone from
its start, $z=6$ already.
\begin{figure}
\resizebox{\columnwidth}{!}{\includegraphics*{pekka_fig5.eps}}\\
\caption{The density field of the simulation. Halos are marked with
black circles. The figure shows the most distant part of the
light-cone, from 4 to 6 Gpc. The upper panel shows rich haloes ($M\ge
3.6\cdot 10^{12}h^{-1}\mbox{M}_{\sun}$), and the lower panel shows also the
intermediate-mass haloes ($M\ge 7.1\cdot 10^{11}h^{-1}\mbox{M}_{\sun}$).
\label{fig:5}}
\end{figure}
The spatial densities $\rho_{halo}$ of all our DM haloes as a function
of redshift (the number of haloes per co-moving volume at redshift bins
of width 0.2) for different halo mass limits are shown in Figure
~\ref{fig:6}. Each line indicates different halo mass limits, from
$10^{10} \mbox{M}_{\sun}$ (at the top) to $10^{14}\mbox{M}_{\sun}$ (at the bottom of the
figure). As can be expected, rich haloes appear later than poor ones.
Haloes with masses smaller than $10^{12}\mbox{M}_{\sun}$ exist in our light-cone
from the beginning. Overall density evolution of haloes of the two
smaller mass ranges is the same; in the redshift range $z=5.7\dots 4$
the spatial density of haloes increases about an order of magnitude.
More rapid increase occurs in the redshift interval $z=3.7\dots
3$. These transitions are also seen in the density behaviour of haloes
of masses $M\ge 10^{13}\mbox{M}_{\sun}$.
The halo density reaches its maximum at $\sim z=0.9$, after that it
decreases. It could be caused by merging of smaller haloes, but could
also be a statistical fluctuation, due to the small volume of our
pencil beam at redshifts less than one.
The first haloes of mass $M \ge 10^{14}\mbox{M}_{\sun}$ appear at $z \sim 3$.
The large variation in their density evolution is due to rareness of
such objects and to a small volume of the sample. There is also two
overall slopes seen in mass scales less then $10^{14}\mbox{M}_{\sun}$. We also
notice that density evolution on almost all mass scales (excepting the
the largest mass interval) between z=5.5 and z=3 is more rapid than
the later density evolution, between z=3 to z=1. The reason for that
could be gradual merging of smaller haloes to form bigger systems.
\begin{figure}
\centering
\resizebox{\columnwidth}{!}{\includegraphics*{pekka_fig6.eps}}
\caption{Spatial density of the haloes as a function of redshift for
five different mass limits.
\label{fig:6}}
\end{figure}
\subsection{Halo mass history}
Figure ~\ref{fig:8} shows the cumulative mass function (MF) for dark
matter haloes, defined as the number density of haloes above a given
mass $M$, \mbox{$n(>M)$}. The solid line shows the mass function for
the intermediate mass light-cone haloes ($n\ge20$). The dotted line
shows the MF for a similar halo sample, obtained in our MLAPM
simulation, for the final snapshot (a 200 $h^{-1}$\thinspace Mpc\ box at $z=0$). The
mass functions differ by an order of magnitude at $10^{11}\mbox{M}_{\sun}$, due
to the smaller overall halo density in the deep light-cone. Another
difference can be seen at the high mass end of the MF-s -- the $z=0$
MF extends to larger masses. This is due to the narrowness of the
pencil beam, that occupies only about $10^{-4}$ of the simulation box
at $z=0$. Statistics of such surveys should be taken with caution, at
least for redshifts less than $z\approx 1$. Without this cosmic
variance effect, the light-cone MF should follow the snapshot MF
throughout the whole mass range. The dotted line shows the light-cone
mass function for all halo masses; this grows steeply, showing that
small haloes dominate in number, especially at early epochs, when
massive haloes did not exist yet.
\begin{figure}
\resizebox{\columnwidth}{!}{\includegraphics*{pekka_fig7.eps}}\\
\caption{The halo mass function for the light-cone
(intermediate sample, $n\ge 20$) (solid line) and for a conventional
simulation for the present time (dashed). The dotted line
shows the light-cone halo mass function for all haloes.}
\label{fig:8}
\end{figure}
The light-cone can be also used to study the evolution of the halo mass
function. We plot this function for different redshift intervals in
Fig.~\ref{fig:9}. The overall shape of the mass functions between
$z=0$ to $z=1$ and $z=1$ to$z=2$ is quite similar to the mass function
of the whole sample, for the mass interval $M\ge 10^{12}\mbox{M}_{\sun}$ (see
Fig.~\ref{fig:8}). The mass functions steepen with redshift, showing
the dominance of small haloes at large redshifts. The characteristic
halo masses decrease with redshift, with the maximum halo mass at the
largest redshift interval $z=5\dots6$ being $1.5\cdot 10^{12}\mbox{M}_{\sun}$.
\begin{figure}
\resizebox{\columnwidth}{!}{\includegraphics*{pekka_fig8.eps}}\\
\caption{Halo mass functions for different redshift intervals.}
\label{fig:9}
\end{figure}
The most easier objects to observe at any epoch are the most luminous
(most massive) ones. In Fig.~\ref{fig:7} we plotted the maximum halo
mass for a given redshift. This figure shows that the maximum masses
increase exponentially with decreasing redshift, down to the redshift
$\sim 0.9$, where the cosmic variance limit appears. This interesting
trend, shown in the figure, can be approximated by an intriguingly
simple formula
\begin{equation}
\label{eq:maxmass}
M_{\mbox{max}}(z)\approx 10^{15}\mbox{M}_{\sun} 10^{-0.5z}\approx 10^{15}\mbox{M}_{\sun} e^{-z}.
\end{equation}
This relation is shown by a dashed line in the figure.
\section{Early haloes and black holes}
As an example of an application of light-cone models, we discuss an
interesting possibility that masses of supermassive black holes (BH)
may correlate with masses of dark matter (DM) haloes.
Using a sample of 37 local galaxies Ferrarese (\cite{fer}) obtained a
relation between the masses of BH and circular velocities of galaxy
disks, similar to the well-known relation between the` BH mass and the
bulge velocity dispersion (e.g. Magorrian et al. \cite{mag},
$M_{BH}/M_{bulge}=3\cdot 10^{-3}$). Using Bullock et al.'s
(\cite{bul}) simulations (their result $M_{DM}=2.7\cdot
10^{12}(v_{vir}/200~km ~s^{-1})^3\mbox{M}_{\sun}$ agrees well with our results)
together with Ferrarese's observational results, the best fit for the
ratio between $M_{BH}$ and $M_{DM}$ can be written as
\begin{equation}
\label{eq:massratio}
M_{BH}/10^8\mbox{M}_{\sun}\sim 0.10(M_{DM}/10^{12}\mbox{M}_{\sun})^{1.65}
\end{equation}
(see figure 5 in Ferrarese's paper). Ferrarese pointed out (see the
references therein) that the critical DM mass for the BH formation
could be about $5\cdot 10^{11}\mbox{M}_{\sun}$, while less massive haloes might
not offer favorable conditions for BH formation. According to the
previous equation, this limits the BH masses by $\sim 10^6\mbox{M}_{\sun}$ in
such DM haloes. Ferrarese concluded also, that according to the
results by Haehnelt et al. (\cite{hahn}) only haloes with masses $M\ge
10^{12}\mbox{M}_{\sun}$ may host a black hole with $M_{BH}\ge 10^6\mbox{M}_{\sun}$. In
our light-cone the spatial density of such host haloes is less than $2
\cdot 10^{-7}\mbox{Mpc}^{-3}h^3$ at redshifts larger than $z=5.5$.
\begin{figure}
\resizebox{\columnwidth}{!}{\includegraphics*{pekka_fig9.eps}}\\
\caption{Masses of the most massive haloes for different redshifts}
\label{fig:7}
\end{figure}
If we assume that Ferrarese's $M_{BH}/M_{DMhalo}$ relation also holds
at high redshifts, and combine it with our maximum halo mass relation
(\ref{eq:maxmass}), we obtain a simple relation for the BH masses
likely to reside in the most massive dark matter haloes as a function
of redshift:
\begin{equation}
\label{eq:bhmass}
\frac{M_{BH}}{10^{12}\mbox{M}_{\sun}}(z)=10^{-0.83z}.
\end{equation}
McLure \& Dunlop (\cite{mc}) concluded, based on virial BH mass
estimates from the SDSS first release and for 12698 quasars, that
quasars' SBH (super massive black hole) masses lie between $\simeq
10^7\mbox{M}_{\sun}$ and $\simeq 10^9\mbox{M}_{\sun}$. If we substitute these limits in
equation (\ref{eq:bhmass}), we find that the most prominent quasars
exist between the redshifts $\sim 6$ to $\sim 2$. Haloes massive
enough to form SBH and hence quasars, either did not exist before the
redshift $z\approx 6$, or they were very rare, with the number density
$n_{h}<10^{-7}Mpc^{-3}h^3$.
\section{Conclusions and perspectives}
We have presented a new method for simulating pencil-beam type
light-cones, using periodic replicas of a base $N$-body cube. Such
light-cones are typical for extremely deep optical surveys, either
underway or in the planning stage. We have shown that by a careful
choice of the light-cone parameters, it is possible to avoid extra
periodicities in the light-cone.
We have simulated a deep (up to $z=6$) light-cone, generated the dark
matter halo catalogue, and studied its properties. We find that early
light-cone is dominated by small haloes, and the maximum halo mass can
be clearly traced throughout all the epochs.
We find a simple approximation for the dependence of maximum dark
matter halo mass on redshift, and use it to explain the redshift
limits of the quasar distribution.
In summary, the algorithm we use to simulate light-cones is
lightweight and fast. The code is in the public domain, included in
the MLAPM package. Nevertheless, the main bottleneck of any
light-cone model is the vast amount of data, proportional to $D^3$
($D$ is the depth of the light-cone). The only way to overcome this
is to discard most of the hard-obtained simulation data, the
positions and velocities of dark matter particles along the
light-cone, and to store only the data on dark matter haloes,
creating and analysing them on-the-fly. This could happen soon, as
our base MLAPM code already includes the MHF halo finder, which
outputs halo catalogues for fixed-time snapshots.
Such halo catalogs can be directly used to
predict the SZ effect from early galaxy clusters
for the Planck mission. Moreover, as gravitational
lensing directly traces the total matter density in the universe,
our light-cone catalogs are good tools to study the weak lensing
of the light emitted by distant quasars, and of the CMB.
These are the lines of our present work.
Another important problem in simulating light-cones to compare with
observational data is populating dark matter haloes with galaxies,
and assigning the galaxies the features an observer sees. In fact,
the MoMaF project (Blaizot et al. \cite{blaizot05}) already gives
galaxy populations in light-cones, using semi-analytic recipes. We
plan to include such recipes in our code, also.
\begin{acknowledgements}
We thank Alexander Knebe for for his support and interest in the
work; Mirt Gramann for stimulating discussions, and Vicent
Mart{\'\i}nez for valuable suggestions. The present study was
supported by the Estonian Science Foundation grants 4695 and 6104,
by the Estonian Ministry for Education and Science grant TO
0060058S98, by the University of Valencia through a visiting
professorship for Enn Saar and by the Spanish MCyT project
AYA2003-08739-C02-01 (including FEDER). Pekka Hein\"am\"aki was
supported by the Jenny and Antti Wihuri foundation.
\end{acknowledgements}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 6,418 |
U.S. Rep. Bill Shuster, a Republican representing the 9th Congressional District, said the Marcellus shale gas drilling industry offers a tremendous opportunity to revitalize the economy and create jobs in Fayette County and throughout Pennsylvania.
But as the gas drilling industry continues to grow, Shuster stressed the importance of making sure companies comply with state and federal guidelines so the environment continues to be protected.
"I want to make sure there are good-paying jobs in this area," he told a crowd of about 100 people who gathered at the AMVETS Post 103 in Hopwood on Thursday.
"But as the industry grows, I want to make sure the gas companies don't stray away from responsible drilling practices," he said to applause.
Although states like Oklahoma and Texas have embraced the oil and gas industry and its pipelines for many years, Shuster said, the industry is new to Pennsylvania and people are concerned.
In the past, Shuster said, Pennsylvania was a very powerful state with a strong economy because of its coal, steel, timber and other booming industries.
Shuster represents only the eastern portion of Fayette County, including the Hopwood area and the South Connellsville area.
He explained the 9th Congressional District in Pennsylvania could expand to include Fayette County and parts of Washington and Greene counties if redistricting is approved.
If redistricting takes place, U.S. Rep. Mark Critz, a Democrat, will no longer represent Fayette County.
Shuster said he remembers the first time he came to Fayette County 10 years ago.
"When I was driving through the mountains on my way here today, I saw the National Pike Water Authority, which was one of the first projects I worked on in Fayette County," he said. "I drove past the Hopwood streetscape project, and I had fond memories of working on that project. | {
"redpajama_set_name": "RedPajamaC4"
} | 291 |
Q: pod is not recognized as an internal or external command in react native I've installed image picker in my react native project and i am going to link the package in ios
I run these commands:
cd ios && pod install
But i'm getting this error:
pod is not recognized as an internal or external command
I am coding in windows 7 and my react native version is: "0.61.5"
How can i fix this?
A: pod is command for Cocoapods, dependency manager for xcode project, so it means that cocoapods is expected to be running on macOS. However if you want to try, you can see this article about running pod commands on windows.
A: In windows you add path of npm module (C:\Users\your user name\AppData\Roaming\npm) to system variables instead of user variables
In Mac or Linux:
Try installing react-native-cli globally by
npm install -g react-native-cli
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 6,929 |
Q: iOS: is it possible to change the hyperlink text to a different name yet still redirects you to the same site? For example, the code below creates a hyperlink to google.com. However, I need the text to say "click here" and still go to google.com. I must have this in text form (no buttons or any other object).
Edit : myView is a textView. Sorry, forgot to add that in.
myView.text = @"http://google.com";
myView.editable = NO;
A: Yes it's possible. You need to use an attributed string
NSMutableAttributedString * str = [[NSMutableAttributedString alloc] initWithString:@"click here"];
[str addAttribute: NSLinkAttributeName value: @"http://www.google.com" range: NSMakeRange(0, str.length)];
myView.attributedText = str;
Also be sure that you conform to the UITextViewDelegate and implement this method
- (BOOL)textView:(UITextView *)textView shouldInteractWithURL:(NSURL *)url inRange:(NSRange)characterRange
{
return YES;
}
One caveat - it looks like NSLinkAttributeName prefers an NSURL but the docs say it should also work with a string.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 2,020 |
{"url":"https:\/\/www.thenakedscientists.com\/forum\/index.php?topic=57661.0","text":"# How do gravity and buoyancy relate?\n\n\u2022 37 Replies\n\u2022 5128 Views\n\n0 Members and 1 Guest are viewing this topic.\n\n#### gazza711\n\n\u2022 Sr. Member\n\u2022 144\n##### How do gravity and buoyancy relate?\n\u00ab on: 08\/11\/2014 19:29:05 \u00bb\nwow.Thats so kool what replies I got.Its all in the SUBJECT words.I too believe that we are pushed to the earth,not pulled.what are your thoughts anyone?\n\n#### chiralSPO\n\n\u2022 Global Moderator\n\u2022 Neilep Level Member\n\u2022 1932\n##### Re: How do gravity and buoyancy relate?\n\u00ab Reply #1 on: 08\/11\/2014 19:47:14 \u00bb\nwow.Thats so kool what replies I got.Its all in the SUBJECT words.I too believe that we are pushed to the earth,not pulled.what are your thoughts anyone?\n\nIf gravity is a push-type force, why does it depend so much on the masses of the bodies involved? The force of gravity exerted by the Earth on my body is much more than the force that would be exerted by Mars, if I were on the surface of Mars. If it were something from outside pushing down, presumably the forces would be essentially the same since the \"outside\" of Earth is essentially the same as the \"outside\" of Mars.\n\u00ab Last Edit: 13\/06\/2015 16:15:56 by chiralSPO \u00bb\n\n#### gazza711\n\n\u2022 Sr. Member\n\u2022 144\n##### Re: How do gravity and buoyancy relate?\n\u00ab Reply #2 on: 08\/11\/2014 20:06:42 \u00bb\nUhuh.I like people like you.Im eager to discuss this.\n\nWhy does the moon keep us on its surface?Same reason as mars situation.But were still attracted somehow.The force exerted is earths atmosphere,not earth itself.So on mars,there is a small atmosphere-just like on the moon-yes,the moon has a sodium atmosphere.Why is there more pressure the deeper we go in water.Its buoyancy that's keeps all that we see pushed to the ground like a helium balloon is pushed to ur ceiling in ur living room.\n\nHave I lost you yet?\n\nIf a feather and bowling ball were dropped at the same time in a near perfect vacuum,99.99999% vacuum,the objects fall extremely slowly towards the ground.why.The other .001111111% gases are doing the pushing on the objects maybe.Gallileo experiment.\n\nThanks for ur response dude.\n\n#### gazza711\n\n\u2022 Sr. Member\n\u2022 144\n##### Re: How do gravity and buoyancy relate?\n\u00ab Reply #3 on: 08\/11\/2014 21:41:43 \u00bb\nwhy would it depend so much on the masses of the bodies involved?\n\n#### chiralSPO\n\n\u2022 Global Moderator\n\u2022 Neilep Level Member\n\u2022 1932\n##### Re: How do gravity and buoyancy relate?\n\u00ab Reply #4 on: 13\/06\/2015 16:31:09 \u00bb\n\nthe moon has a sodium atmosphere.\n\nNo it doesn't. Where did you get this (mis)information? The moon does have an atmosphere, but the pressure is about 3x10\u201315 times the pressure on Earth 99.999999999997% vacuum compared to Earth's atmosphere. Mostly it is made of helium, neon and hydrogen.\n\nWhy is there more pressure the deeper we go in water.Its buoyancy that's keeps all that we see pushed to the ground like a helium balloon is pushed to ur ceiling in ur living room.\n\nThere is more pressure under deep water because there is more water above you, and all of it is being pulled down by gravity.\n\nBuoyancy has to do with relative densities in a gravitational field. If the helium balloon has less mass than an equal volume of the air around it, the air around it will fall as it rises. This process will continue until the balloon reaches a point where the air around it has the same density, or until the balloon bursts.\n\nIf a feather and bowling ball were dropped at the same time in a near perfect vacuum,99.99999% vacuum,the objects fall extremely slowly towards the ground.why.The other .001111111% gases are doing the pushing on the objects maybe.Gallileo experiment.\n\nNo. The Gallileo experiment has been performed in near perfect vacuum, and the objects fall faster in vacuum than in air.\n\nhttps:\/\/www.youtube.com\/watch?v=E43-CfukEgs (note the vacuum drop starts at about 2:50, and is shown in slow motion, this is not how fast they actually fell; also shown at 4:15)\n\n#### evan_au\n\n\u2022 Neilep Level Member\n\u2022 4309\n##### Re: How do gravity and buoyancy relate?\n\u00ab Reply #5 on: 15\/06\/2015 22:25:52 \u00bb\nI think the hypothesis here is backwards:\n\u2022 It is proposed that atmospheric pressure causes gravity\n\u2022 When in fact gravity causes atmospheric pressure\n\nAtmospheric pressure is caused by gravity, but it is a very non-linear relationship, since\n\u2022 a very light body (like the Moon) will lose virtually all its atmosphere\n\u2022 while a heavier body (like the rocky core of Jupiter) will retain almost all its atmosphere, including hydrogen & helium\n\u2022 So this hypothesis badly underestimates the gravity on the Moon, and overestimates the gravity on Jupiter\n\nAtmospheric pressure is also affected by multiple other factors, like:\n\u2022 Strength of the Solar Wind: This is very strong near Mercury, and much weaker out past Jupiter. The solar wind can tear away at the upper atmosphere.\n\u2022 Strength of the planetary magnetic field: A strong magnetic field (like Earth or Jupiter) tends to deflect the more energetic outbursts of the solar wind around the planet.\n\u2022 Temperature: A hot planet like Venus will drive all liquids and gases into the atmosphere, producing an enormous atmospheric pressure. On the other hand, on Mars, liquid water is frozen out under the surface, producing a very low atmospheric pressure. However, the surface gravity of both bodies is similar.\n\u2022 History: The position in the solar system where the planet formed, which determines how it reached its current mass. The orbits of planets in the Solar System does change over astronomical time periods.\n\nSo any relationship between atmospheric pressure and gravity is very indirect, with lots of confounding factors.\n\nHowever, as Newton showed, mass causes gravity, and there is quite a simple relationship between the mass of the bodies, the distance between them, and the gravitational force of attraction between them.\n\n#### gazza711\n\n\u2022 Sr. Member\n\u2022 144\n##### Re: How do gravity and buoyancy relate?\n\u00ab Reply #6 on: 20\/06\/2015 07:22:53 \u00bb\nI think the hypothesis here is backwards:\n\u2022 It is proposed that atmospheric pressure causes gravity\n\u2022 When in fact gravity causes atmospheric pressure\n\nAtmospheric pressure is caused by gravity, but it is a very non-linear relationship, since\n\u2022 a very light body (like the Moon) will lose virtually all its atmosphere\n\u2022 while a heavier body (like the rocky core of Jupiter) will retain almost all its atmosphere, including hydrogen & helium\n\u2022 So this hypothesis badly underestimates the gravity on the Moon, and overestimates the gravity on Jupiter\n\nAtmospheric pressure is also affected by multiple other factors, like:\n\u2022 Strength of the Solar Wind: This is very strong near Mercury, and much weaker out past Jupiter. The solar wind can tear away at the upper atmosphere.\n\u2022 Strength of the planetary magnetic field: A strong magnetic field (like Earth or Jupiter) tends to deflect the more energetic outbursts of the solar wind around the planet.\n\u2022 Temperature: A hot planet like Venus will drive all liquids and gases into the atmosphere, producing an enormous atmospheric pressure. On the other hand, on Mars, liquid water is frozen out under the surface, producing a very low atmospheric pressure. However, the surface gravity of both bodies is similar.\n\u2022 History: The position in the solar system where the planet formed, which determines how it reached its current mass. The orbits of planets in the Solar System does change over astronomical time periods.\n\nSo any relationship between atmospheric pressure and gravity is very indirect, with lots of confounding factors.\n\nHowever, as Newton showed, mass causes gravity, and there is quite a simple relationship between the mass of the bodies, the distance between them, and the gravitational force of attraction between them.\nHi.What are the chances anyones going to answer to a post from 18\/11\/15.I am very honoured as I thought I was mearly a blip on your radio.\nMars and venus have way different gravity's.\nA lot of 'facts' in planetology might involve a lot of assumptions.Cavendish experiment predicted a lot of things.\nSo if air we breath has a weight(mass),it must have a downward force of some sort?\nSo a trillion cazillion atoms in the atmosphere with mass can(entrophic idea maybe)exert a force.water is in most things.without the water,most things would break up and disappear.So when we talk about gravities on other planets and moons for example,you might find that temps on most planets cause the gas,liquid and solid formations.when a gas in the atmosphere is cooled-what happens-gravity or density displacement?\nA bit like a bucket of sand.The sand is the atmosphere pressurised by the outside vacuum.you are a spec of something at the bottom of that bucket.\nWith regards to gravities on other planets and moons-I think the atmosphere is cleverer than we think.\nThe problem I have in all of this as you know is-what modern proof do we have that objects attract?using lead or metal objects to do experiments is biased-I believe.\nI believe that you might have an interest in my findings?or just bored to scroll through peoples old posts-HMMMM.Thanks for the reply.Really enjoying ur comments.Thank you\n\n#### gazza711\n\n\u2022 Sr. Member\n\u2022 144\n##### Re: How do gravity and buoyancy relate?\n\u00ab Reply #7 on: 20\/06\/2015 07:27:10 \u00bb\nwow.Thats so kool what replies I got.Its all in the SUBJECT words.I too believe that we are pushed to the earth,not pulled.what are your thoughts anyone?\n\nIf gravity is a push-type force, why does it depend so much on the masses of the bodies involved? The force of gravity exerted by the Earth on my body is much more than the force that would be exerted by Mars, if I were on the surface of Mars. If it were something from outside pushing down, presumably the forces would be essentially the same since the \"outside\" of Earth is essentially the same as the \"outside\" of Mars.\n1.well unless you could weigh planets-which we cant-then you cannot assume their mass.\n2.thus we cannot say gravity depends on the bodies involved.\n3.how can the outside of earth be the same as the outside of mars?\n4.if it was,we wouldn't be going on holiday on earth-mars is the same isn't it.cant see that one happening.\n\n#### PmbPhy\n\n\u2022 Neilep Level Member\n\u2022 2804\n##### Re: How do gravity and buoyancy relate?\n\u00ab Reply #8 on: 20\/06\/2015 12:05:59 \u00bb\nQuote from: gazza711\nwow.Thats so kool what replies I got.Its all in the SUBJECT words.I too believe that we are pushed to the earth,not pulled.what are your thoughts anyone?\nI don't think you understand the different between something being pushed or pulled. It really only has meaning for macroscopic objects with a finite length, width and height.\n\nPush - To push something means that a force is exerted on the surface of the body directed into the body. Such a force acting in this way acts to compress the body. So you know something is being pushed if the body is being compressed along its length parallel to the direction of the force.\n\nPull - A body is being pulled if a force is exerted on the surface of a body directed outward from the inside of the body. Such a force acts to extend the body. There will be a tension in the object under such a force.\n\nYou could also drill a hole through the body and insert a rod and then exert a force on the rod. Then some parts of the body will be pushed while other parts will be pulled depending on where the rod is inserted. You could also grasp a rod with your hand and exert a force parallel to the rod's length. The part of the rod above the hand in the direction of the force is being pushed while the other part is being pulled.\n\nGravity does neither of those since it exerts a force not simply on the surface of the object but on each point of the body at the same time.\n\n#### gazza711\n\n\u2022 Sr. Member\n\u2022 144\n##### Re: How do gravity and buoyancy relate?\n\u00ab Reply #9 on: 20\/06\/2015 12:52:53 \u00bb\nQuote from: gazza711\nwow.Thats so kool what replies I got.Its all in the SUBJECT words.I too believe that we are pushed to the earth,not pulled.what are your thoughts anyone?\nI don't think you understand the different between something being pushed or pulled. It really only has meaning for macroscopic objects with a finite length, width and height.\n\nPush - To push something means that a force is exerted on the surface of the body directed into the body. Such a force acting in this way acts to compress the body. So you know something is being pushed if the body is being compressed along its length parallel to the direction of the force.\n\nPull - A body is being pulled if a force is exerted on the surface of a body directed outward from the inside of the body. Such a force acts to extend the body. There will be a tension in the object under such a force.\n\nYou could also drill a hole through the body and insert a rod and then exert a force on the rod. Then some parts of the body will be pushed while other parts will be pulled depending on where the rod is inserted. You could also grasp a rod with your hand and exert a force parallel to the rod's length. The part of the rod above the hand in the direction of the force is being pushed while the other part is being pulled.\n\nGravity does neither of those since it exerts a force not simply on the surface of the object but on each point of the body at the same time.\nSo a balloon submerged deep in water.is it being pulled or pushed to the surface?surely the inside of the balloon is too being affected-as a stone drops in water due to......gravity?\nSure,so if water has the same characteristics as the air we breath,then we are dealing with the same thing at different temperatures.\n\n#### alancalverd\n\n\u2022 Global Moderator\n\u2022 Neilep Level Member\n\u2022 4893\n\u2022 life is too short to drink instant coffee\n##### Re: How do gravity and buoyancy relate?\n\u00ab Reply #10 on: 20\/06\/2015 13:21:57 \u00bb\nSure,so if water has the same characteristics as the air we breath,then we are dealing with the same thing at different temperatures.\n\nSpeak for yourself, but I think most of our correspondents are mammals, not fish.\nhelping to stem the tide of ignorance\n\n#### PmbPhy\n\n\u2022 Neilep Level Member\n\u2022 2804\n##### Re: How do gravity and buoyancy relate?\n\u00ab Reply #11 on: 20\/06\/2015 13:22:56 \u00bb\nQuote from: gazza711\nSo a balloon submerged deep in water.is it being pulled or pushed to the surface?\nSince neither definition applies it's neither pushed nor pulled, just like gravity.\n\n#### jeffreyH\n\n\u2022 Global Moderator\n\u2022 Neilep Level Member\n\u2022 4175\n\u2022 The graviton sucks\n##### Re: How do gravity and buoyancy relate?\n\u00ab Reply #12 on: 20\/06\/2015 14:39:34 \u00bb\nGazza, PmbPhy told you what the distinction was between gravity and other types of forces. This is a very important point and you should take it on board. Unless you grasp the concept that gravity acts on every part of a body all at once you will be stuck in your incorrect way of viewing things. Forum members such as Alan, PmbPhy, Evan and Chiral, that are bothering to reply to you, know what they are talking about. By all means ask questions but make no assumptions that anything you believe is right simply because it has popped into your head.\nFixation on the Einstein papers is a good definition of OCD.\n\n#### gazza711\n\n\u2022 Sr. Member\n\u2022 144\n##### Re: How do gravity and buoyancy relate?\n\u00ab Reply #13 on: 20\/06\/2015 20:22:19 \u00bb\nGazza, PmbPhy told you what the distinction was between gravity and other types of forces. This is a very important point and you should take it on board. Unless you grasp the concept that gravity acts on every part of a body all at once you will be stuck in your incorrect way of viewing things. Forum members such as Alan, PmbPhy, Evan and Chiral, that are bothering to reply to you, know what they are talking about. By all means ask questions but make no assumptions that anything you believe is right simply because it has popped into your head.\nReally-are you a scientist?\n\n#### gazza711\n\n\u2022 Sr. Member\n\u2022 144\n##### Re: How do gravity and buoyancy relate?\n\u00ab Reply #14 on: 20\/06\/2015 20:23:29 \u00bb\nSure,so if water has the same characteristics as the air we breath,then we are dealing with the same thing at different temperatures.\n\nSpeak for yourself, but I think most of our correspondents are mammals, not fish.\nand the others?Arent whales mammals?\n\n#### gazza711\n\n\u2022 Sr. Member\n\u2022 144\n##### Re: How do gravity and buoyancy relate?\n\u00ab Reply #15 on: 20\/06\/2015 20:28:30 \u00bb\n\nthe moon has a sodium atmosphere.\n\nNo it doesn't. Where did you get this (mis)information? The moon does have an atmosphere, but the pressure is about 3x10\u201315 times the pressure on Earth 99.999999999997% vacuum compared to Earth's atmosphere. Mostly it is made of helium, neon and hydrogen.\n\nWhy is there more pressure the deeper we go in water.Its buoyancy that's keeps all that we see pushed to the ground like a helium balloon is pushed to ur ceiling in ur living room.\n\nThere is more pressure under deep water because there is more water above you, and all of it is being pulled down by gravity.\n\nBuoyancy has to do with relative densities in a gravitational field. If the helium balloon has less mass than an equal volume of the air around it, the air around it will fall as it rises. This process will continue until the balloon reaches a point where the air around it has the same density, or until the balloon bursts.\n\nIf a feather and bowling ball were dropped at the same time in a near perfect vacuum,99.99999% vacuum,the objects fall extremely slowly towards the ground.why.The other .001111111% gases are doing the pushing on the objects maybe.Gallileo experiment.\n\nNo. The Gallileo experiment has been performed in near perfect vacuum, and the objects fall faster in vacuum than in air.\n\nhttps:\/\/www.youtube.com\/watch?v=E43-CfukEgs (note the vacuum drop starts at about 2:50, and is shown in slow motion, this is not how fast they actually fell; also shown at 4:15)\nYes.I felt a bit of an idiot when I wrote that.I thought I was onto something whilst watching Brian Cox do the Gallileo experiment. Didn't think it through.Was obvious once I pressed the POST button.OOPS\n\n#### PmbPhy\n\n\u2022 Neilep Level Member\n\u2022 2804\n##### Re: How do gravity and buoyancy relate?\n\u00ab Reply #16 on: 20\/06\/2015 21:18:14 \u00bb\nGazza, PmbPhy told you what the distinction was between gravity and other types of forces. This is a very important point and you should take it on board. Unless you grasp the concept that gravity acts on every part of a body all at once you will be stuck in your incorrect way of viewing things. Forum members such as Alan, PmbPhy, Evan and Chiral, that are bothering to reply to you, know what they are talking about. By all means ask questions but make no assumptions that anything you believe is right simply because it has popped into your head.\nReally-are you a scientist?\nYes. Among other things, I consider Jeff to be a scientist. Do you actually know what a scientist is? Please look it up.\n\n#### gazza711\n\n\u2022 Sr. Member\n\u2022 144\n##### Re: How do gravity and buoyancy relate?\n\u00ab Reply #17 on: 20\/06\/2015 22:11:12 \u00bb\nGazza, PmbPhy told you what the distinction was between gravity and other types of forces. This is a very important point and you should take it on board. Unless you grasp the concept that gravity acts on every part of a body all at once you will be stuck in your incorrect way of viewing things. Forum members such as Alan, PmbPhy, Evan and Chiral, that are bothering to reply to you, know what they are talking about. By all means ask questions but make no assumptions that anything you believe is right simply because it has popped into your head.\nReally-are you a scientist?\nYes. Among other things, I consider Jeff to be a scientist. Do you actually know what a scientist is? Please look it up.\nJust asked. I have never made an assumption. I just don't ask in a scientific way. I simply ask-why do you believe all tings attract. Theres more posts on the internet disproving newton and saying GR is far fetched as well. Actually newton disproved many times. they said the world was flat not long before that....So if your a scientist-prove attraction not repulsion(my argument)using more than silly examples like Cavendish and schiehallion.how do we find the mass of planets without formulas,equations etc. astronomy is based on assumptions everyday. The fact is that im stating repulsion and the \"CASIMIR EFFECT\" looks plausible maybe.\n\n#### alancalverd\n\n\u2022 Global Moderator\n\u2022 Neilep Level Member\n\u2022 4893\n\u2022 life is too short to drink instant coffee\n##### Re: How do gravity and buoyancy relate?\n\u00ab Reply #18 on: 22\/06\/2015 23:25:31 \u00bb\n\nand the others?Arent whales mammals?\n\nTo the best of my knowledge, all whales and all correpondents to this forum, know that water and air do not \"have the same characteristics\".\nhelping to stem the tide of ignorance\n\n#### PmbPhy\n\n\u2022 Neilep Level Member\n\u2022 2804\n##### Re: How do gravity and buoyancy relate?\n\u00ab Reply #19 on: 23\/06\/2015 04:51:50 \u00bb\nQuote from: gazza711\nTheres more posts on the internet disproving newton and saying GR is far fetched as well. Actually newton disproved many times.\nAnd not one of them by anybody who knows what they're talking about. Only crackpots make those claims. Newton's laws and Einstein's theories have withstood the test of time and their validity have been borne out by experiment countless times. So what you read was absolute total garbage. What else is new?\n\n#### rmolnav\n\n\u2022 Sr. Member\n\u2022 114\n##### Re: How do gravity and buoyancy relate?\n\u00ab Reply #20 on: 24\/06\/2015 10:42:45 \u00bb\nGazza711, #9\n\"So a balloon submerged deep in water.is it being pulled or pushed to the surface?\"\nAny submerged object experiences water pressure all around its surface. That pressure is due and equal to the weight of a column of water with a surface unit section, and going from water surface to the considered point of the object surface (water pressure PUSHES object surface ...)\nIntegration of all forces due to that pressure (pressures multiplied by surfaces) gives an upward push. Arquimedes discovered that: net total push is equal to the weight of the liquid previously filling the space where the object is situated.\nIf that upward push is bigger than object own weight, the push not compensated by object weight will make it move up.\nIf object weight is bigger (it would mean its average density is higher than water\u00b4s), then the object would further sink (not compensated weight would PULL it down: gravity is attraction between massive objects, kind of \"tele-pull\").\n\n#### PmbPhy\n\n\u2022 Neilep Level Member\n\u2022 2804\n##### Re: How do gravity and buoyancy relate?\n\u00ab Reply #21 on: 24\/06\/2015 11:27:09 \u00bb\nQuote from: gazza711\nis it being pulled or pushed to the surface?\nI can't believe that you asked me this question in reply #9 since I just answered it in reply #8, i.e. the part that you quoted. So why on Earth id you ignore it?\n\nDo you even know what those terms, i.e. push and pull mean?\n\u00ab Last Edit: 24\/06\/2015 11:28:40 by PmbPhy \u00bb\n\n#### gazza711\n\n\u2022 Sr. Member\n\u2022 144\n##### Re: How do gravity and buoyancy relate?\n\u00ab Reply #22 on: 25\/06\/2015 14:10:44 \u00bb\nQuote from: gazza711\nis it being pulled or pushed to the surface?\nI can't believe that you asked me this question in reply #9 since I just answered it in reply #8, i.e. the part that you quoted. So why on Earth id you ignore it?\n\nDo you even know what those terms, i.e. push and pull mean?\nOk.are attracted or repelled then as the other words are incorrect.dont answer without self evidence.\n\n#### gazza711\n\n\u2022 Sr. Member\n\u2022 144\n##### Re: How do gravity and buoyancy relate?\n\u00ab Reply #23 on: 25\/06\/2015 14:19:58 \u00bb\n\nand the others?Arent whales mammals?\n\nTo the best of my knowledge, all whales and all correpondents to this forum, know that water and air do not \"have the same characteristics\".\nOk.so air and water have similar characteristics.theyre breathable,use convection to help create movement,you could swim in air(drag),water is part oxygen.any suggestions on more similarities?\n\n#### chiralSPO\n\n\u2022 Global Moderator\n\u2022 Neilep Level Member\n\u2022 1932\n##### Re: How do gravity and buoyancy relate?\n\u00ab Reply #24 on: 25\/06\/2015 14:33:24 \u00bb\n\nOk.so air and water have similar characteristics.theyre breathable,use convection to help create movement,you could swim in air(drag),water is part oxygen.any suggestions on more similarities?\n\nEvery fluid has drag and can convect. Oxygen is the most common element on Earth (by mass).\nYou're really grasping at straws here. This is not at all scientific.\n\nWater and air are also both transparent in the visible region (but so is glass, diamond, polycarbonate plastic, hydrofluoric acid, etc. etc. etc.), but that has nothing to do with gravity... Water and air both have mass (so does pretty much all matter), and that does have to do with gravity, but isn't very helpful. Water and air are both fairly nontoxic (you can drink enough water to kill you, enough nitrogen will result in narcosis, coma or death, too much oxygen is neurotoxic and carcinogenic...)\n\n#### gazza711\n\n\u2022 Sr. Member\n\u2022 144\n##### Re: How do gravity and buoyancy relate?\n\u00ab Reply #25 on: 25\/06\/2015 14:55:48 \u00bb\n\nOk.so air and water have similar characteristics.theyre breathable,use convection to help create movement,you could swim in air(drag),water is part oxygen.any suggestions on more similarities?\n\nEvery fluid has drag and can convect. Oxygen is the most common element on Earth (by mass).\nYou're really grasping at straws here. This is not at all scientific.\n\nWater and air are also both transparent in the visible region (but so is glass, diamond, polycarbonate plastic, hydrofluoric acid, etc. etc. etc.), but that has nothing to do with gravity... Water and air both have mass (so does pretty much all matter), and that does have to do with gravity, but isn't very helpful. Water and air are both fairly nontoxic (you can drink enough water to kill you, enough nitrogen will result in narcosis, coma or death, too much oxygen is neurotoxic and carcinogenic...)\nWell said.just that it was said they don't have same characteristics.nuthin to do with gravity at all.i know.but surely 7lbs\/sq inch of downforce with an atmisphere that is 100k feet high that has mass must contribute to something.and all that in a perfect vacuum of ether or something like that.\n\n#### chiralSPO\n\n\u2022 Global Moderator\n\u2022 Neilep Level Member\n\u2022 1932\n##### Re: How do gravity and buoyancy relate?\n\u00ab Reply #26 on: 25\/06\/2015 15:25:54 \u00bb\nsurely 7lbs\/sq inch of downforce with an atmisphere that is 100k feet high that has mass must contribute to something.\n\nBut it can also be a 7 lbs per square inch of an up force (or a sideways force). Suction cups (https:\/\/en.wikipedia.org\/wiki\/Suction_cup) can stick to an appropriate surface in any direction as long as there is pressure on them from the outside.\n\n#### PmbPhy\n\n\u2022 Neilep Level Member\n\u2022 2804\n##### Re: How do gravity and buoyancy relate?\n\u00ab Reply #27 on: 25\/06\/2015 17:34:14 \u00bb\nQuote from: gazza711\nOk.are attracted or repelled then as the other words are incorrect.dont answer without self evidence.\nSo, you think that the difference between push and pull is the direction of the force. Suppose that we use the electric force as an example so as to illustrate your point about being pushed and pulled.\n\nLet there be two large sheets of charge parallel to the xz-plane. One has a positive charge density +$$\\sigma$$ that passes through the y-axis at y = +d, the other having a negative charge density -$$\\sigma$$ that passes through the y-axis at y = -d. There is an electric field in the region -d < y < -d. Place a positively charged particle in the region -d < y < +d. In between the plates there is a uniform electric field directed in the +y direction. Outside the region -d < y < +d the electric field is zero.\n\nNow place a positively charged particle at y = 0. In this instance is the particle pushed or pulled?\n\nNow take away the sheet of positive charge. There is still a uniform electric field in the region -d < y < +d. The only difference being the magnitude of the particle. Is the positive particle at y = 0 being pushed or pulled?\n\nNow put the sheet of positive charge back at y = +d and take away the sheet of negative charge. There is still a uniform electric field in the region -d < y < +d. Again, the only difference being the magnitude of the particle. Is the positive particle at y = 0 being pushed or pulled?\n\u00ab Last Edit: 26\/06\/2015 01:48:57 by PmbPhy \u00bb\n\n#### gazza711\n\n\u2022 Sr. Member\n\u2022 144\n##### Re: How do gravity and buoyancy relate?\n\u00ab Reply #28 on: 25\/06\/2015 20:07:14 \u00bb\nQuote from: gazza711\nOk.are attracted or repelled then as the other words are incorrect.dont answer without self evidence.\nSo, you think that the difference between push and pull is the direction of the force. Suppose that we use the electric force as an example so as to illustrate your point about being pushed and pulled.\n\nLet there be two large sheets of charge parallel to the xz-plane. One has a positive charge density $$+\\sigma$$ that passes through the y-axis at y = +d, the other having a negative charge density $$-\\sigma$$ that passes through the y-axis at y = -d. There is an electric field in the region -d < y < -d. Place a positively charged particle in the region -d < y < +d. In between the plates there is a uniform electric field directed in the +y direction. Outside the region -d < y < +d the electric field is zero.\n\nNow place a positively charged particle at y = 0. In this instance is the particle pushed or pulled?\n\nNow take away the sheet of positive charge. There is still a uniform electric field in the region -d < y < +d. The only difference being the magnitude of the particle. Is the positive particle at y = 0 being pushed or pulled?\n\nNow put the sheet of positive charge back at y = +d and take away the sheet of negative charge. There is still a uniform electric field in the region -d < y < +d. Again, the only difference being the magnitude of the particle. Is the positive particle at y = 0 being pushed or pulled?\nI'm done with the push\/pull convo.\n\n#### gazza711\n\n\u2022 Sr. Member\n\u2022 144\n##### Re: How do gravity and buoyancy relate?\n\u00ab Reply #29 on: 25\/06\/2015 20:19:22 \u00bb\nsurely 7lbs\/sq inch of downforce with an atmisphere that is 100k feet high that has mass must contribute to something.\n\nBut it can also be a 7 lbs per square inch of an up force (or a sideways force). Suction cups (https:\/\/en.wikipedia.org\/wiki\/Suction_cup) can stick to an appropriate surface in any direction as long as there is pressure on them from the outside.\nWell a massive suction cup would have more force upon it.air moves at about 500 miles\/hour.when u pour a drink,air is displacing it.suction is using air pressure.there is a force on everything.when you spin a 1kg metal disc for example at sat 2k revs a minute,you could throw it in the air and it might not come down providing it's still spinning at that speed.this would mean that no force is influencing it except the spinning.now,if I was correct,gravity would cease to exist as an attractive force?i could be wrong but it's a standard science experiment of making something lighter.no experiment has been done the way I say.if a force isn't moving,we can only measure what is moving so 7lbs could be more like a force equal to the density of the object.its clear water is lighter than air if not bonded.\n\n#### chiralSPO\n\n\u2022 Global Moderator\n\u2022 Neilep Level Member\n\u2022 1932\n##### Re: How do gravity and buoyancy relate?\n\u00ab Reply #30 on: 25\/06\/2015 21:11:19 \u00bb\nspinning a disk does not make it lighter (actually, if you can spin it really, really fast, it would get slightly heavier--but that's beside the point).\n\nspinning a disk can make it easier to lift, but that has to do with torque, not gravity. (https:\/\/www.youtube.com\/watch?v=GeyDf4ooPdo)\n\n#### PmbPhy\n\n\u2022 Neilep Level Member\n\u2022 2804\n##### Re: How do gravity and buoyancy relate?\n\u00ab Reply #31 on: 26\/06\/2015 01:51:10 \u00bb\nQuote from: chiralSPO\n(actually, if you can spin it really, really fast, it would get slightly heavier--but that's beside the point).\nBy this he's referring to a relativistic effect that I derive here: http:\/\/home.comcast.net\/~peter.m.brown\/sr\/rotating_cylinder.htm\n\n#### rmolnav\n\n\u2022 Sr. Member\n\u2022 114\n##### Re: How do gravity and buoyancy relate?\n\u00ab Reply #32 on: 26\/06\/2015 06:21:51 \u00bb\nEnglish is not my mother tongue, so I could be wrong in relation to most precise definition of PULL. But the way I put it in #20 regarding gravity attraction is very widely used in scientific literature:\n\nPD: Sorry I said Archimedes in Spanish, with \"qu\" instead of \"ch\" ...\n\n#### PmbPhy\n\n\u2022 Neilep Level Member\n\u2022 2804\n##### Re: How do gravity and buoyancy relate?\n\u00ab Reply #33 on: 26\/06\/2015 06:55:38 \u00bb\nEnglish is not my mother tongue, so I could be wrong in relation to most precise definition of PULL. But the way I put it in #20 regarding gravity attraction is very widely used in scientific literature:\n\nPD: Sorry I said Archimedes in Spanish, with \"qu\" instead of \"ch\" ...\nIt's best to forget all this nonsense about \"push\" and \"pull\" because those terms are rarely, if ever, used in physics. In fact in all the physics texts that I've read in the last 35 years I've never once seen it used. The only related term with any meaning is force.\n\n#### gazza711\n\n\u2022 Sr. Member\n\u2022 144\n##### Re: How do gravity and buoyancy relate?\n\u00ab Reply #34 on: 26\/06\/2015 11:01:43 \u00bb\nspinning a disk does not make it lighter (actually, if you can spin it really, really fast, it would get slightly heavier--but that's beside the point).\n\nspinning a disk can make it easier to lift, but that has to do with torque, not gravity. (https:\/\/www.youtube.com\/watch?v=GeyDf4ooPdo)\nWell the effect is wherever you influence the direction.the point is weightlessness in a sense.the weight changes.why?if air moves incredibly fast,preventing its molecules from applying a force on an object because the object is moving faster and thus breaking its grip on the object.i bet the brown experiment could cause anti gravity or indeed does!\nLexus reckons it's got ah overboard on concrete apparantly.lol.wont use push and pull words again,that's for sure!\n\n#### chiralSPO\n\n\u2022 Global Moderator\n\u2022 Neilep Level Member\n\u2022 1932\n##### Re: How do gravity and buoyancy relate?\n\u00ab Reply #35 on: 26\/06\/2015 14:51:54 \u00bb\nWell the effect is wherever you influence the direction.the point is weightlessness in a sense.the weight changes.\n\nNo, this experiment has nothing to do with weightlessness. It is not so difficult to lift the 19 kg flywheel if you are holding on to the wheel itself. Putting the wheel at the end of a stick and trying to lift from the other end introduces a lot of torque, and that is why it is difficult to lift. Again, lifting from the end of the stick close to the flywheel is not so hard, but lifting from the far end is hard. This torque is eased when the flywheel is spinning, but the mass and weight remain (effectively) constant.\n\n#### gazza711\n\n\u2022 Sr. Member\n\u2022 144\n##### Re: How do gravity and buoyancy relate?\n\u00ab Reply #36 on: 26\/06\/2015 15:01:59 \u00bb\nWell the effect is wherever you influence the direction.the point is weightlessness in a sense.the weight changes.\n\nNo, this experiment has nothing to do with weightlessness. It is not so difficult to lift the 19 kg flywheel if you are holding on to the wheel itself. Putting the wheel at the end of a stick and trying to lift from the other end introduces a lot of torque, and that is why it is difficult to lift. Again, lifting from the end of the stick close to the flywheel is not so hard, but lifting from the far end is hard. This torque is eased when the flywheel is spinning, but the mass and weight remain (effectively) constant.\nIt could have been 50kg.i think u missed the point.\n\n#### chiralSPO\n\n\u2022 Global Moderator\n\u2022 Neilep Level Member\n\u2022 1932\n##### Re: How do gravity and buoyancy relate?\n\u00ab Reply #37 on: 29\/06\/2015 13:33:56 \u00bb\nNo, you have missed the point. watch the video I posted again, it gives an excellent explanation of the phenomenon.","date":"2017-02-20 13:20:48","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.6490404605865479, \"perplexity\": 1819.8523772943856}, \"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-2017-09\/segments\/1487501170562.59\/warc\/CC-MAIN-20170219104610-00578-ip-10-171-10-108.ec2.internal.warc.gz\"}"} | null | null |
O Canal do Itajuru é um canal com seis quilômetros de extensão navegáveis localizado no estado do Rio de Janeiro. Liga a laguna Araruama ao oceano Atlântico. Está localizado nos municípios de São Pedro da Aldeia e, na sua maior parte, em Cabo Frio.
Há diversas opções de passeios de barco com roteiros diferenciados. Há também o calçadão, a feira de artesanato e lindas mansões ao longo dos condomínios Moringa e Moringuinha. Tem seu ponto mais conhecido no centro da cidade, em frente ao bairro da Gamboa, em Cabo Frio. Também é lá que as escunas ficam ancoradas para passeios por todo o Canal do Itajuru, incluindo roteiros em diversas praias. Caminhando na Av. dos Pescadores, ao final de onde se pode admirar o canal a pé, fica a praia de São Bento.
Em 1907 foi erguida nas águas do Canal do Itajuru a estátua de um anjo de asas abertas, chamada Deusa da Vitória, com nove metros de altura. A força das correntezas inclinou a estátua, levando a população à batizá-la de Anjo Caído. A estátua foi construída para comemorar a abertura dos canais da laguna, que facilitaram a entrada das embarcações de sal na cidade.
Nos últimos anos o canal foi alargado para oxigenar a laguna Araruama, em detrimento da mortandade de animais marinhos provocados pelo baixo fluxo aquífero e principalmente, pelo esgoto não tratado lançado in natura tanto na lagoa quanto na orla do canal.
O canal possui marinas e praias de grande beleza localizadas na Ilha do Japonês.
Geografia de São Pedro da Aldeia
Geografia de Cabo Frio
Canais do Brasil | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 8,564 |
{"url":"https:\/\/ngreifer.github.io\/WeightIt\/reference\/trim.html","text":"Trims (i.e., truncates) large weights by setting all weights higher than that at a given quantile to the weight at the quantile. This can be useful in controlling extreme weights, which can reduce effective sample size by enlarging the variability of the weights.\n\n# S3 method for weightit\ntrim(w, at = 0, lower = FALSE, ...)\n\n# S3 method for numeric\ntrim(w, at = 0, lower = FALSE, treat = NULL, ...)\n\n## Arguments\n\nw\n\nA weightit object or a vector of weights.\n\nat\n\nnumeric; either the quantile of the weights above which weights are to be trimmed. A single number between .5 and 1, or the number of weights to be trimmed (e.g., at = 3 for the top 3 weights to be set to the 4th largest weight).\n\nlower\n\nlogical; whether also to trim at the lower quantile (e.g., for at = .9, trimming at both .1 and .9, or for at = 3, trimming the top and bottom 3 weights).\n\ntreat\n\nA vector of treatment status for each unit. This should always be included when w is numeric, but you can get away with leaving it out if the treatment is continuous or the estimand is the ATE for binary or multinomial treatments.\n\n...\n\nNot used.\n\n## Details\n\ntrim() takes in a weightit object (the output of a call to weightit() or weightitMSM()) or a numeric vector of weights and trims them to the specified quantile. All weights above that quantile are set to the weight at that quantile. If lower = TRUE, all weights below 1 minus the quantile are to set the weight at 1 minus the quantile. In general, trimming weights decreases balance but also decreases the variability of the weights, improving precision at the potential expense of unbiasedness (Cole & Hern\u00e1n, 2008). See Lee, Lessler, and Stuart (2011) and Thoemmes and Ong (2015) for discussions and simulation results of trimming weights at various quantiles. Note that trimming weights can also change the target population and therefore the estimand.\n\nWhen using trim() on a numeric vector of weights, it is helpful to include the treatment vector as well. The helps determine the type of treatment and estimand, which are used to specify how trimming is performed. In particular, if the estimand is determined to be the ATT or ATC, the weights of the target (i.e., focal) group are ignored, since they should all be equal to 1. Otherwise, if the estimand is the ATE or the treatment is continuous, all weights are considered for trimming. In general, weights for any group for which all the weights are the same will not be considered in the trimming.\n\n## Value\n\nIf the input is a weightit object, the output will be a weightit object with the weights replaced by the trimmed weights, while will have an additional attribute, \"trim\", equal to the quantile of trimming.\n\nIf the input is a numeric vector of weights, the output will be a numeric vector of the trimmed weights, again with the aforementioned attribute.\n\n## References\n\nCole, S. R., & Hern\u00e1n, M. \u00c1. (2008). Constructing Inverse Probability Weights for Marginal Structural Models. American Journal of Epidemiology, 168(6), 656\u2013664.\n\nLee, B. K., Lessler, J., & Stuart, E. A. (2011). Weight Trimming and Propensity Score Weighting. PLoS ONE, 6(3), e18174.\n\nThoemmes, F., & Ong, A. D. (2016). A Primer on Inverse Probability of Treatment Weighting and Marginal Structural Models. Emerging Adulthood, 4(1), 40\u201359.\n\n## Author\n\nNoah Greifer\n\nweightit(), weightitMSM()\n\n## Examples\n\nlibrary(\"cobalt\")\ndata(\"lalonde\", package = \"cobalt\")\n\n(W <- weightit(treat ~ age + educ + married +\nnodegree + re74, data = lalonde,\nmethod = \"ps\", estimand = \"ATT\"))\n#> A weightit object\n#> - method: \"ps\" (propensity score weighting)\n#> - number of obs.: 614\n#> - sampling weights: none\n#> - treatment: 2-category\n#> - estimand: ATT (focal: 1)\n#> - covariates: age, educ, married, nodegree, re74\nsummary(W)\n#> Summary of weights\n#>\n#> - Weight ranges:\n#>\n#> Min Max\n#> treated 1.0000 || 1.0000\n#> control 0.0222 |---------------------------| 2.0438\n#>\n#> - Units with 5 most extreme weights by group:\n#>\n#> 10 8 4 3 1\n#> treated 1 1 1 1 1\n#> 411 595 269 409 296\n#> control 1.3303 1.4365 1.5005 1.6369 2.0438\n#>\n#> - Weight statistics:\n#>\n#> Coef of Var MAD Entropy # Zeros\n#> treated 0.000 0.000 -0.00 0\n#> control 0.823 0.701 0.33 0\n#>\n#> - Effective Sample Sizes:\n#>\n#> Control Treated\n#> Unweighted 429. 185\n#> Weighted 255.99 185\n\n#Trimming the top and bottom 5 weights\ntrim(W, at = 5, lower = TRUE)\n#> Trimming the top and bottom 5 weights where treat is not 1.\n#> A weightit object\n#> - method: \"ps\" (propensity score weighting)\n#> - number of obs.: 614\n#> - sampling weights: none\n#> - treatment: 2-category\n#> - estimand: ATT (focal: 1)\n#> - covariates: age, educ, married, nodegree, re74\n#> - weights trimmed at the top and bottom 5\n\n#Trimming at 90th percentile\n(W.trim <- trim(W, at = .9))\n#> Trimming weights where treat is not 1 to 90%.\n#> A weightit object\n#> - method: \"ps\" (propensity score weighting)\n#> - number of obs.: 614\n#> - sampling weights: none\n#> - treatment: 2-category\n#> - estimand: ATT (focal: 1)\n#> - covariates: age, educ, married, nodegree, re74\n#> - weights trimmed at 90%\n\nsummary(W.trim)\n#> Summary of weights\n#>\n#> - Weight ranges:\n#>\n#> Min Max\n#> treated 1.0000 || 1.0000\n#> control 0.0222 |-------------------------| 0.9407\n#>\n#> - Units with 5 most extreme weights by group:\n#>\n#> 10 8 4 3 1\n#> treated 1 1 1 1 1\n#> 303 296 285 269 264\n#> control 0.9407 0.9407 0.9407 0.9407 0.9407\n#>\n#> - Weight statistics:\n#>\n#> Coef of Var MAD Entropy # Zeros\n#> treated 0.000 0.000 -0.000 0\n#> control 0.766 0.682 0.303 0\n#>\n#> - Effective Sample Sizes:\n#>\n#> Control Treated\n#> Unweighted 429. 185\n#> Weighted 270.58 185\n#Note that only the control weights were trimmed\n\n#Trimming a numeric vector of weights\nall.equal(trim(W$weights, at = .9, treat = lalonde$treat),\nW.trim\\$weights)\n#> Trimming weights where treat is not 1 to 90%.\n#> [1] TRUE\n\n#Using made up data and as.weightit()\ntreat <- rbinom(500, 1, .3)\nweights <- rchisq(500, df = 2)\nW <- as.weightit(weights = weights, treat = treat,\nestimand = \"ATE\")\nsummary(W)\n#> Summary of weights\n#>\n#> - Weight ranges:\n#>\n#> Min Max\n#> treated 0.0782 |-----------------| 7.3680\n#> control 0.0030 |---------------------------| 11.3178\n#>\n#> - Units with 5 most extreme weights by group:\n#>\n#> 203 333 436 335 103\n#> treated 5.5532 6.1825 6.2122 7.1462 7.368\n#> 408 337 201 196 45\n#> control 8.8746 8.9234 9.7306 9.8349 11.3178\n#>\n#> - Weight statistics:\n#>\n#> Coef of Var MAD Entropy # Zeros\n#> treated 0.808 0.640 0.309 0\n#> control 0.929 0.714 0.391 0\n#>\n#> - Effective Sample Sizes:\n#>\n#> Control Treated\n#> Unweighted 370. 130.\n#> Weighted 198.76 78.93\nsummary(trim(W, at = .95))\n#> Trimming weights to 95%.\n#> Summary of weights\n#>\n#> - Weight ranges:\n#>\n#> Min Max\n#> treated 0.0782 |---------------------------| 6.1935\n#> control 0.0030 |---------------------------| 6.1935\n#>\n#> - Units with 5 most extreme weights by group:\n#>\n#> 203 333 436 335 103\n#> treated 5.5532 6.1825 6.1935 6.1935 6.1935\n#> 152 131 115 114 45\n#> control 6.1935 6.1935 6.1935 6.1935 6.1935\n#>\n#> - Weight statistics:\n#>\n#> Coef of Var MAD Entropy # Zeros\n#> treated 0.790 0.635 0.301 0\n#> control 0.848 0.692 0.354 0\n#>\n#> - Effective Sample Sizes:\n#>\n#> Control Treated\n#> Unweighted 370. 130.\n#> Weighted 215.45 80.28","date":"2022-08-15 02:57:23","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\": 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\": 0.4704108238220215, \"perplexity\": 9372.642851130666}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2022-33\/segments\/1659882572127.33\/warc\/CC-MAIN-20220815024523-20220815054523-00237.warc.gz\"}"} | null | null |
Q: Pandas dataframe print string + changing variable I am building a program that prompts the user to load a csv file. The csv file always contains the columns StudentID, Name, Assignment1,2,3... The number of assignments varies.
I am trying to display a list of names, with one grade for each assignment and the final grade which I calculate from my imported function computeFinalGrade.
How can I change the last line my code to print the grades and the final grades for the right number of assignments?
Desired output:
if the csv only has "Assignment1", the output should be:
"Michael Andersen has obtained the grades 10. The final grade is 10"
if the csv contains 5 assignments, the output should be:
"Michael Andersen has obtained the grades 10,7,12,7,10. The final grade is 10"
My code:
grades = np.genfromtxt(filename, delimiter=";", skip_header=1)
e = grades[:,2:]
f = computeFinalGrades(e)
df = pd.read_csv(filename,sep=';')
df['FinalGrade'] = f
for index, row in df.iterrows():
print('{} has obtained the grades {}, {}, {}. The final grade is {}'.format(row['Name'],row['Assignment1'],row['Assignment2'],row['Assignment3'],row['FinalGrade']))
A: Use:
df = pd.read_csv(filename,sep=';')
#filter DataFrame by positions
df1 = df.iloc[:,2:]
#count computeFinalGrades
f = computeFinalGrades(df1.values)
#all Assignments convert to joined string
df['Assignment'] = df1.astype(str).apply(', '.join, axis=1)
df['FinalGrade'] = f
#zip columns together and loop
for name, assign, final in zip(df['Name'],df['Assignment'],df['FinalGrade']):
#python 3.6+ f-strings
print(f'{name} has obtained the grades {assign}. The final grade is {final}')
#python bellow with format
print('{} has obtained the grades {}. The final grade is {}'.format(name, assign, final))
Sample:
df = pd.DataFrame({
'Name':list('abcd'),
'StudentID':[7,8,9,4],
'Assignment1':[1,3,5,7],
'Assignment2':[5,3,6,9],
})
print (df)
Name StudentID Assignment1 Assignment2
0 a 7 1 5
1 b 8 3 3
2 c 9 5 6
3 d 4 7 9
#sample function
def computeFinalGrades(x):
return x.sum()
#filter DataFrame by positions
df1 = df.iloc[:,2:]
#count computeFinalGrades
f = computeFinalGrades(df1.values)
#all Assignments convert to joined string
df['Assignment'] = df1.astype(str).apply(', '.join, axis=1)
df['FinalGrade'] = f
print (df)
Name StudentID Assignment1 Assignment2 Assignment FinalGrade
0 a 7 1 5 1, 5 39
1 b 8 3 3 3, 3 39
2 c 9 5 6 5, 6 39
3 d 4 7 9 7, 9 39
for name, assign, final in zip(df['Name'],df['Assignment'],df['FinalGrade']):
print(f'{name} has obtained the grades {assign}. The final grade is {final}')
a has obtained the grades 1, 5. The final grade is 39
b has obtained the grades 3, 3. The final grade is 39
c has obtained the grades 5, 6. The final grade is 39
d has obtained the grades 7, 9. The final grade is 39
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 6,436 |
Our termly report pack is designed to save you time in school. We compile all your Y1 to Y6 Teacher Assessment Summative data and send it to you in one easy-to-read PDF pack.
Please note: this is an extra service to your OTrack licence and so it comes with an extra charge. Please see the 'How much does it cost?' info below. All the data in this pack is available in OTrack, so the additional charge is for the time it takes us to compile the data for you.
The prices below are an introductory price and may change in future terms.
You can order these packs for all terms or one, or two, or three etc – it's completely up to you. Let us know by ordering, using the button above.
When you complete the order form, tell us the date you want the pack sending. We will send the PDF pack to you on that date. | {
"redpajama_set_name": "RedPajamaC4"
} | 1,732 |
This Thai Massaman Beef Curry recipe is sumptuous and very flavorful. It's a homemade recipe with no need for any store-bought curry paste or powder. The ingredient list may seem long, but the sauce is quite easy to make. Just toss all sauce ingredients into the curry pot as you prepare them, and simmer together with the meat.
Note that lamb and chicken are often traditionally substituted for beef and that all types of meat make for a delicious Massaman curry. Bay leaves are normally used in Massaman curry rather than the harder-to-find kaffir lime leaves seen in many Thai curry dishes. Other vegetables that are good in this curry include eggplant, green beans, and tomato.
Tip: In this recipe, the meat has been pre-boiled for more tenderness—it takes longer, but the resulting taste is worth it. If you're in a hurry, you can easily cut back on this step. If simmering meat 30 minutes or less, leave off the lid or reduce stock to 2 cups.
Place stock in a large pot over high heat. Add the meat, onion and bay leaves. If using fresh lemongrass, add the upper leftover stalk pieces.
Bring to a boil, reduce heat to low to a simmer. Cover or partially cover with a lid and simmer 40 minutes to 1 hour and 20 minutes, stirring occasionally, until meat is tender or near-tender.
Add all curry sauce ingredients, stirring with each addition. If desired, hold back a few tablespoons of the coconut milk for serving.
Add the potatoes. Return to a boil, then continue simmering 30 more minutes or until potatoes are tender, stirring occasionally.
Taste-test the curry, adding more fish sauce for increased flavor/saltiness, or more chili if you want it spicier. If too sour, add a little more sugar. If too salty or sweet for your taste, add a touch more tamarind or lime juice. If too spicy, add more coconut milk (regular dairy cream or milk will work too).
Transfer to a serving bowl, or spoon onto individual plates or bowls. Top with fresh coriander or basil plus some additional nuts if desired. Drizzle over reserved coconut milk (if desired), and serve with Thai jasmine rice. | {
"redpajama_set_name": "RedPajamaC4"
} | 8,562 |
Moto E4 Plus Goes On Sale In The US Tomorrow
2:19 pm August 2, 2017 By Roland Hutchinson
The Motorola E4 and E4 Plus were made official back in June. The Moto E4 has been available in the US for a while and now the Moto E4 Plus is also launching.
From tomorrow the Moto E4 Plus will be available in the US. The smartphone will cost $179.99 and it will be available from Best Buy, Amazon and other retailers.
The Motorola Moto E4 Plus comes with a 5.5 inch display that features a HD resolution of 1280 x 720 pixels.
The Moto E4 Plus is powered by a MediaTek MT6737 mobile processor and it comes with 3GB of RAM and 16GB of include storage. The handset features a 5 megapixel front camera for Selfies and a 13 megapixel rear camera for photos and videos.
Source Android Guys
Filed Under: Android News | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 7,864 |
using System;
using System.Collections.Generic;
using System.ComponentModel.Composition;
using System.Diagnostics;
using System.IO.Abstractions;
using System.Reflection;
using FluentAssertions;
using Microsoft.VisualStudio.TestTools.UnitTesting;
using Moq;
using SonarLint.VisualStudio.Integration;
using SonarLint.VisualStudio.Integration.UnitTests;
using SonarLint.VisualStudio.TypeScript.NodeJSLocator;
namespace SonarLint.VisualStudio.TypeScript.UnitTests.NodeJSLocator
{
[TestClass]
public class NodeLocatorTests
{
[TestMethod]
public void MefCtor_CheckIsExported()
{
MefTestHelpers.CheckTypeCanBeImported<NodeLocator, INodeLocator>(null, new[]
{
MefTestHelpers.CreateExport<INodeLocationsProvider>(Mock.Of<INodeLocationsProvider>()),
MefTestHelpers.CreateExport<ILogger>(Mock.Of<ILogger>())
});
}
[TestMethod]
public void Locate_NoCandidateLocations_Null()
{
var testSubject = CreateTestSubject();
var result = testSubject.Locate();
result.Should().BeNull();
}
[TestMethod]
public void Locate_ReturnsFirstCompatiblePath()
{
var candidateLocations = new List<string>
{
"does not exist",
"bad version",
null,
"compatible1",
"compatible2"
};
var fileSystem = new Mock<IFileSystem>();
SetupFileExists(fileSystem, "does not exist", false);
SetupFileExists(fileSystem, "bad version", true);
SetupFileExists(fileSystem, "compatible1", true);
SetupFileExists(fileSystem, "compatible2", true);
var versions = new Dictionary<string, Version>
{
{"bad version", new Version(11, 0)},
{"compatible1", new Version(12, 0)},
{"compatible2", new Version(12, 0)}
};
Version GetNodeExeVersion(string path) => versions[path];
var testSubject = CreateTestSubject(
fileSystem.Object,
GetNodeExeVersion,
candidateLocations);
var result = testSubject.Locate();
result.Should().Be("compatible1");
}
[TestMethod]
[DataRow(9, false)]
[DataRow(10, true)]
[DataRow(11, false)]
[DataRow(12, true)]
[DataRow(13, true)]
public void IsCompatibleVersion_ReturnsTrueFalse(int majorVersion, bool expectedResult)
{
var version = new Version(majorVersion, 0);
var result = NodeLocator.IsCompatibleVersion(version);
result.Should().Be(expectedResult);
}
[TestMethod]
public void GetNodeVersion_ReturnsFileProductVersion()
{
var assemblyPath = Assembly.GetAssembly(typeof(ExportAttribute)).Location;
var assemblyVersion = FileVersionInfo.GetVersionInfo(assemblyPath);
var expectedVersion = new Version(assemblyVersion.ProductMajorPart,
assemblyVersion.ProductMinorPart,
assemblyVersion.ProductBuildPart);
// The implementation relies on checking a file in the file system, so we pass a file that we know already exists and has a product version
var result = NodeLocator.GetNodeVersion(assemblyPath);
result.Should().BeEquivalentTo(expectedVersion);
}
private void SetupFileExists(Mock<IFileSystem> fileSystem, string path, bool exists)
{
fileSystem.Setup(x => x.File.Exists(path)).Returns(exists);
}
private NodeLocator CreateTestSubject(IFileSystem fileSystem = null, Func<string, Version> getNodeExeVersion = null, IReadOnlyCollection<string> candidateLocations = null)
{
candidateLocations ??= Array.Empty<string>();
var locationsPovider = new Mock<INodeLocationsProvider>();
locationsPovider.Setup(x => x.Get()).Returns(candidateLocations);
var logger = Mock.Of<ILogger>();
return new NodeLocator(locationsPovider.Object, logger, fileSystem, getNodeExeVersion);
}
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 7,204 |
Moschato (in greco: Σταθμός Μοσχάτου) è una stazione della linea 1 della metropolitana di Atene.
Altri progetti
Stazioni della metropolitana di Atene | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 2,213 |
Q: Stay $\|f\| \in W^{1,1}(0,T;\mathbb{R})$ provided $f \in W^{1,1}(0,T;H)$ Supose that $f \in W^{1,1}(0,T; H)$ where $H$ is a Hilbert space. Can we conclude that $\|f\| \in W^{1,1}(0,T;\mathbb{R})$?
Since $f \in L^1(0,T;H)$ its clear that $\|f\|:(0,T) \to \mathbb{R} \in L^1(0,T;\mathbb{R})$ but if $f' \in L^1(0,T;H)$ i can't justify that $\|f\|' \in L^1(0,T;\mathbb{R})$. First, i think that is important understant $\|f\|'$ and $f'$, looking the Evans book I see that the weak derivative $f'=v \in L^1(0,T;H)$ is the function that satisfy
$$\int_0^T\phi'(t) f(t) dt=-\int_0^T \phi(t) f'(t) dt$$
for all scalar test function $\phi \in C_c^{\infty}(0,T)$. So the work is now prove that
$$\int_0^T\phi'(t) \|f\|(t) dt=-\int_0^T \phi(t) \|f\|'(t) dt$$
for all $\phi \in C_c^{\infty}(0,T)$. One important remark is that $\|f'\|$ is not necessary equal to $\|f\|'$. Can somebody give me anyone hint?
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 1,432 |
Today's Cool Album of the Day (#590 in the Series) is Heart, Dreamboat Annie.
So I bet your first thought when you saw Heart as "Cool of the Day" was something along the line of, "What? Seriously?" Well, yeah absolutely this is a cool album.
When was the last time you listen to it? And I don't mean just hearing "Magic Man" or "Crazy on You" on the radio. I bet it's been awhile.
One of the things I'd forgotten about while reading listening to "Dreamboat Annie" is that the radio friendly versions were quite shorter than the album versions, this is especially true with "Crazy On You." I'd forgotten about the long acoustic guitar solo that opens that track. I'm pretty sure it was on my 8-track version as well!
The other thing that people sometimes forget about "Dreamboat Annie" was the great contribution by guitarist Roger Fisher. Everyone remembers Ann Wilson and Nancy Wilson, and rightly so, but Roger Fisher had a lot to do with this album.
As a matter of fact, Heart was originally Roger's band. He helped form the band in Seattle in the late 60s, the Wilson sisters joined later. Roger was would stay with the band for three more albums he left in 1980.
"Crazy on You" and "Magic Man" are probably the two most well-known songs here, but when I go back and listen to it again the title cut "Dreamboat Annie" and "Sing Child Sing" are two standouts as well.
"Dreamboat Annie" reach #7 on the Billboard Top 200 album chart. As far as the singles, "Crazy on You" peaked at #35 on the Billboard Hot 100 chart, "Dreamboat Annie" at # 42, while "Magic Man" reached the top 10 at #9.
Here's some cool live "Dreamnboat Annie" tunes.
Or maybe The Decemberists covering Heart? | {
"redpajama_set_name": "RedPajamaC4"
} | 483 |
Die Point Reyes National Seashore ist ein Schutzgebiet an der Pazifikküste im Marin County, etwa 55 Kilometer nördlich von San Francisco im US-Bundesstaat Kalifornien. Sie umfasst nahezu die volle Fläche einer geologisch bemerkenswerten Halbinsel sowie einen kleinen Streifen des Ozeans. Das knapp 290 km² große Schutzgebiet wurde am 13. September 1962 unter US-Präsident John F. Kennedy eingerichtet, wird vom National Park Service verwaltet und von über zwei Millionen Besuchern im Jahr zum Wandern, Zelten und zur Naturbeobachtung besucht.
Geologie
Das Gebiet verdankt seine Besonderheit der Plattentektonik. Die Point Reyes Halbinsel liegt auf der Pazifischen Platte, die sich im Verhältnis zur Nordamerikanischen Platte nach Norden bewegt. Zwischen ihnen verläuft die San-Andreas-Verwerfung. Das Granit-Gestein der Halbinsel entspricht geologisch dem der Tehachapi Mountains, rund 500 Kilometer weiter südlich, zwischen Bakersfield und Los Angeles. Heute ist der Verlauf der San-Andreas-Verwerfung durch die Küstenlinie im Süden des Gebietes und die 20 Kilometer lange, aber nur einen Kilometer breite Tomales Bay östlich der Halbinsel markiert. Ein Earthquake-Trail genannter Lehrpfad informiert über die Geologie, die Geschichte und die Erdbeben in der Region.
Landschaftsbild
Die Halbinsel hat grob die Form eines Dreiecks, dessen Spitze in westsüdwestlicher Richtung in den Pazifik zeigt. Der südliche Teil des Gebietes ist eine überwiegend bewaldete Hügelkette, deren höchster Punkt der Mount Wittenberg mit 428 Meter ist. Der Norden besteht aus einer langgezogenen Landzunge, die die Tomales Bucht vom Meer trennt. Die Spitze des Dreiecks ist auf ihrer Südseite durch eine Drakes Estero genannte Bucht mit mehreren tiefen Fingern gegliedert. Am äußersten Punkt liegt der Point Reyes Leuchtturm.
Das Kap ist der windigste Punkt der nordamerikanischen Pazifikküste, die höchste gemessene Windgeschwindigkeit betrug 212 km/h, und zugleich der Ort mit dem zweithäufigsten Auftreten von Nebel auf dem nordamerikanischen Kontinent.
Flora und Fauna
Die harschen klimatischen Bedingungen auf dem baumfreien Felsplateau haben eine an diese Bedingungen angepasste Pflanzenwelt geschaffen. Die als California coastal prairie bezeichnete Lebensgemeinschaft ist geprägt durch kurzhalmige Gräser, die mit vielfältigen, überwiegend einjährigen Blütenpflanzen durchsetzt sind. Darunter sind mehrere Arten, die nur an wenigen Standorten überlebt haben. Die Sonoma spineflower (Chorizanthe valida) aus der Familie der Knöterichgewächse wuchs bis im Jahr 2000 in nur einem kleinflächigen Bestand im Schutzgebiet und wurde seither von den Rangern an einem zweiten Standort etabliert.
Für das Gebiet typisch sind die Douglas-Iris (Iris douglasiana), mehrere Arten der Gattung Waldlilien (Trillium), Haselwurzarten und mehrere Nachtkerzengewächse. Das Areal enthält auch das südlichste Vorkommen der seltenen und ausschließlich an der kalifornischen Küste vorkommenden Lilium maritimum.
Die Hügelkette im Süden der Halbinsel ist großteils bewaldet, auf der Nordflanke auf Granitboden ist die Bischofs-Kiefer die Leitart der Wälder. Die Südseite mit Böden aus Schiefer und Sandstein wird überwiegend von Douglasien bestanden. Hier kommt der bedrohte Fleckenkauz vor.
Die Strände von Point Reyes sind das wichtigste Brutgebiet des Seeregenpfeifers in Kalifornien, sein Schutz war der wesentliche Grund für die Unterschutzstellung 1962. Im Gebiet kommen aber auch andere bedeutende Arten vor, wie die Schopfwachtel, der symbolische Staatsvogel Kaliforniens, der Coho-Lachs, die Stahlkopfforelle und das Stummelschwanzhörnchen. Kalifornische Seelöwen leben in einer besonders exponierten Bucht.
In den 1970er-Jahren wurden zehn Tule-Wapiti im Gebiet angesiedelt. Aus ihnen entstanden bis heute (Stand: 2014) zwei Herden mit zusammen etwa 500 Tieren. Davon lebt knapp die Hälfte in einem eingezäunten Gebiet der ehemaligen Pierce Point Ranch am Tomales Point, die anderen verteilen sich frei im Rest des Gebiets. Der Wanderfalke wird seit kurz nach der Jahrtausendwende in einem Wiedereinbürgerungsprojekt gefördert. Er brütete früher in einer größeren Population in der Steilküste.
Point Reyes ist in besonderem Maße für die Vogelwelt bedeutend. Im Gebiet wurden rund 490 Arten nachgewiesen, das ist annähernd die Hälfte aller Vogelarten Nordamerikas. Diese herausragende Biodiversität verdankt die Halbinsel der Kombination der Lage im milden, feuchten Klima am Vogelzug-Weg entlang der Küste, den vielfältigen Landschaften mit Küste, Hügeln verschiedener Höhenlage, Felsstrukturen, offenen Landschaften, sowie dem großflächigen Schutzgebiet.
In den Monaten Mai und November können von der Küste Grauwale auf ihrem Zug entlang der Küste beobachtet werden.
Geschichte
Die ursprünglichen Bewohner der Point-Reyes-Halbinsel waren Coast Miwoks. Sie lebten in Dörfern aus Rundhütten mit zwischen 75 und mehreren hundert Bewohnern an Fluss- und Bachläufen. Als Jäger und Sammler lebten sie ganzjährig von Meeresfrüchten aller Art, jagten Weißwedelhirsche, Kaninchen, Hühnervögel wie die Schopfwachtel und ausweislich von Funden auch den Eichelspecht.
Im Jahr 1579 kam Francis Drake auf seiner Weltumseglung an die Küste Kaliforniens. Die Bucht Drake Estero auf der Südseite des Halbinsel ist nach ihm benannt, es ist jedoch nicht sicher, dass sich seine Flotte wirklich hier aufhielt. Ende des 16. Jahrhunderts entwickelte sich eine Route der spanischen Flotte von den Philippinen nach Mexiko, die die Strömungen des Pazifischen Ozeans ausnützte und an der Küste vorbeiführte. Der Portugiese Sebastián Rodríguez Cermeño stand in spanischen Diensten, als er 1595 in der Bucht Schiffbruch erlitt. Am 6. Januar 1603 benannte Sebastián Vizcaíno das Kap nach den Heiligen Drei Königen als Punta de los Reyes.
Ein Klostergut der Franziskaner (OFM) hatte 1817 die erste Rinderfarm auf die Nordseite der Bucht von San Francisco gebracht. In der Folge siedelten sich in der Region und auch auf der Point-Reyes-Halbinsel Milchviehbetriebe an. Mit dem kalifornischen Goldrausch kam Kapital an die Westküste und 1857 kauften Rechtsanwälte aus San Francisco namens Shafter, Shafter, Park, and Heydenfeldt über 20.000 ha auf der Halbinsel. Sie banden die bestehenden Farmen zusammen mit durch europäische Einwanderer bewirtschafteten neuen Betrieben in ein gemeinsames Marketingkonzept ein und produzierten Butter unter der Marke Point Reyes. Die Milchwirtschaft litt unter Überweidung einerseits und Verbuschung andererseits und kurz nach dem San-Francisco-Erdbeben von 1906 schlossen einige Betriebe. Die Weltwirtschaftskrise von 1929 führte zur Schließung weiterer Farmen in den 1930er Jahren und dem Zusammenbruch der Familienunternehmen Shafter, Park und Hydenfeldt.
Der Leuchtturm von Point Reyes liegt an einer der exponiertesten Stellen der kalifornischen Küste. Extreme Winde und der häufige Nebel gefährden die Schifffahrt entlang der Küste und zur Bucht von San Francisco. Deshalb wurde bereits 1870 ein Leuchtturm errichtet. Die Fresnellinse war modernste Technik und musste aus Frankreich importiert werden.
Auf der Südseite des Kaps liegt eine ehemalige Seenotrettungsstation. Ihr Vorgänger wurde 1888 am westlichen Sandstrand errichtet und zog 1927 an die heutige Stelle um. Sie wurde zunächst vom United States Life-Saving Service, nach deren Gründung von der United States Coast Guard betrieben und 1968 eingestellt. Das Bootshaus mit der Helling ist erhalten, sowie einige Nebengebäude der Wohnhäuser für die Besatzung der Station. Im Bootshaus befindet sich das originale Motorrettungsboot, Baujahr 1953, vom Typ TRS mit 36 Fuß Länge, das ein Standardtyp der Coast Guard war, von dem aber nur wenige erhalten sind. Die Station ist als National Historic Landmark registriert.
Nach dem Zweiten Weltkrieg siedelten sich Veteranen in der Bay Area an und auch auf der Point-Reyes-Halbinsel gab es Pläne zur Erschließung mit Siedlungen. Dem gegenüber standen Bestrebungen von Naturschutzorganisationen unter der Führung des Sierra Club, die schon seit 1936 um Point Reyes ein großflächiges Naturschutzgebiet für die Küstenökosysteme forderten. 1962 wurde der größte Teil der Halbinsel als National Seashore ausgewiesen.
Situation und Naturschutz
Teile des Gebietes sind durch menschliche Nutzung über knapp etwa ein Jahrhundert vor der Unterschutzstellung stark beeinträchtigt. Landwirtschaft, insbesondere in Form der Milchviehhaltung prägte das Zentrum der Halbinsel. Dadurch veränderte sich auch die Zusammensetzung der Tier- und Pflanzenwelt. Heute werden eingewanderte Pflanzenarten, wie Ginster und Efeu in mühevoller Handarbeit aus dem Gebiet entfernt, um die ursprüngliche Artenzusammensetzung wiederherzustellen. Bis heute arbeiten etwa 30 Milchviehbetriebe auf der Halbinsel unter Lizenz des National Park Service und nutzen rund ein Viertel der Gesamtfläche des Gebietes.
In den 1950er Jahren war die Errichtung mehrerer Siedlungen im heutigen Schutzgebiet geplant, was schließlich zur Unterschutzstellung beitrug. Etwa 45 Prozent des Schutzgebietes unterliegen seit 1976 als Phillip Burton Wilderness dem weitergehenden Schutz eines Wilderness Areas. 2002 wurde beschlossen, dass die Drakes Bay ab 2012 ebenfalls als Wilderness ausgewiesen werden soll, wenn die Betriebserlaubnis für die bis zu diesem Jahr noch genehmigte Austern-Farm ausliefe.
Die Austernfarm wurde 2005 an einen neuen Betreiber verkauft, der trotz der auslaufenden Betriebsgenehmigung und der anstehenden Ausweisung als Wildnis auf einen längeren Betrieb hoffte. Ende 2012 erhob er Klage gegen die Nicht-Verlängerung seiner Betriebserlaubnis und suchte Verbündete in der regionalen und nationalen Politik. Seine Klagen wurden von allen Instanzen abgewiesen, während der Verfahren ging der Betrieb weiter. In der Zwischenzeit wurde am 4. Dezember 2012 die gesamte Bucht als Wilderness Area ausgewiesen. Im Oktober 2014 schlossen die Austern-Farm und der National Park Service einen außergerichtlichen Vergleich, nachdem der Betrieb der Farm zum Jahresende 2014 eingestellt wurde.
Eine Bedrohung des Schutzgebietes stellt der illegale Anbau von Cannabis dar. In den abgelegenen, bewaldeten Teilen werden Hanf-Plantagen errichtet, die teilweise mit Mitteln der industriellen Landwirtschaft ausgebaut werden. Sie zeichnen sich durch den Einsatz von Düngemitteln und Bewässerungsanlagen aus und gehen offenkundig von der organisierten Kriminalität aus. Daneben stehen kleine Pflanzungen privater Anbauer. Jedes Jahr werden Pflanzen, aus denen Marihuana im Straßenpreis von mehreren Millionen Dollar gewonnen werden kann, im Gebiet entdeckt und entfernt. Die Anlage von Bewässerungsanlagen und der Einsatz von Düngemitteln schädigen das Schutzgebiet nachhaltig.
Erholung
Die über zwei Millionen Besucher im Jahr sind weit überwiegend Tagesbesucher aus dem Großraum San Francisco, für den Point Reyes ein wichtiges Naherholungsgebiet darstellt. Knapp 250 Kilometer Wanderwege und 130 Kilometer unberührte Küstenlinie ziehen vor allem Wanderer an. Das Kap mit dem Leuchtturm ist der meistbesuchte Ort im Gebiet. Schwimmen ist im Pazifik nicht möglich, das Wasser ist ganzjährig zu kalt und die harte Brandung ist lebensgefährlich. Ein kleiner Badestrand liegt knapp außerhalb des Schutzgebietes an der flachen und geschützten Tomales Bucht.
An der Spitze des Point Reyes liegt der Endpunkt des American Discovery Trail, einem Fernwanderweg von 10.800 Kilometer Länge quer durch die USA.
Zur Hauptsaison der Walbeobachtung zwischen Ende Dezember und Ende April werden an Wochenenden mit gutem Wetter die Straßen im Schutzgebiet für den privaten Verkehr gesperrt und stattdessen ein Shuttlebus-System angeboten.
Es gibt keine Restaurants oder ausgebauten Übernachtungsmöglichkeiten im Gebiet. Für Mehrtages-Wanderer und nur zu Fuß erreichbar sind im Hinterland vier Campingplätze ausgewiesen.
Benachbarte Schutz- und Erholungsgebiete sind:
Golden Gate National Recreation Area
Muir Woods National Monument
Samuel Taylor State Park
Tomales Bay State Park (mit Badestrand)
Wissenswertes
In Point Reyes wurde ein Großteil des Horrorfilms The Fog – Nebel des Grauens von John Carpenter gedreht. Vor allem der Leuchtturm spielt in diesem Film eine zentrale Rolle.
Weblinks
National Parks Conservation Association: Point Reyes National Seashore – A Resource Assessment, 2002 und Reassessement 2009
Einzelnachweise
Geographie (Kalifornien)
National Seashore (Vereinigte Staaten)
Marin County
Küste in den Vereinigten Staaten
Schutzgebiet (Umwelt- und Naturschutz) in Nordamerika
Küste in Nordamerika | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 248 |
Parapagurus sibogae är en kräftdjursart som beskrevs av de Saint Laurent 1972. Parapagurus sibogae ingår i släktet Parapagurus och familjen Parapaguridae. Inga underarter finns listade i Catalogue of Life.
Källor
Tiofotade kräftdjur
sibogae | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 4,420 |
Contents
Cover
TITLE PAGE
DEDICATION
ACKNOWLEDGMENTS
PREFACE
_BRAMARE_ : (ARCHAIC) TO YEARN FOR
A HOUSE AND THE LAND IT TAKES TWO OXEN TWO DAYS TO PLOW
SISTER WATER, BROTHER FIRE
THE WILD ORCHARD
WHIR OF THE SUN
_FESTINA TARDE_ (MAKE HASTE SLOWLY)
A LONG TABLE UNDER THE TREES
SUMMER KITCHEN NOTES
CORTONA, NOBLE CITY
_RIVA, MAREMMA_ : INTO WILDEST TUSCANY
TURNING ITALIAN
GREEN OIL
FLOATING WORLD: A WINTER SEASON
WINTER KITCHEN NOTES
ROSE WALK
_SEMPRE PIETRA_ (ALWAYS STONE)
RELICS OF SUMMER
_SOLLEONE_
_BEN TORNATI_ (WELCOME BACK)
CONVERSION CHARTS
_SWAN_ EXCERPT
CRITICAL ACCLAIM FOR _Under the Tuscan Sun_
An Excerpt from _Under Magnolia_
EXPERIENCE FRANCES MAYES'S TUSCANY...
COPYRIGHT
_For Ann Cornelisen_
ACKNOWLEDGMENTS
Many thanks to my agent, Peter Ginsberg, of Curtis Brown Ltd., to Charlie Conrad, my editor at Broadway Books, and to the spectacular staff at Broadway Books. Jane Piorko of _The New York Times_ , Elaine Greene of _House Beautiful_ , and Rosellen Brown, guest editor of _Ploughshares_ , published early versions of parts of this book: _mille grazie_. Friends and family members deserve at least a bottle of Chianti and a handful of Tuscan poppies: Todd Alden, Paul Bertolli, Anselmo Bettarelli, Josephine Carson, Ben Hernandez, Charlotte Painter, Donatella di Palme, Rupert Palmer, Lyndall Passerini, Tom Sterling, Alain Vidal, Marcia and Dick Wertime, and all the Wilcoxons. Homage to the memory of Clare Sterling for the gift of her verve and knowledge. To Ed Kleinschmidt and Ashley King, incalculable thanks.
Preface
"WHAT ARE YOU GROWING HERE?" the upholsterer lugs an armchair up the walkway to the house but his quick eyes are on the land.
"Olives and grapes," I answer.
"Of course, olives and grapes, but what else?"
"Herbs, flowers—we're not here in the spring to plant much else."
He puts the chair down on the damp grass and scans the carefully pruned olive trees on the terraces where we now are uncovering and restoring the former vineyard. "Grow potatoes," he advises. "They'll take care of themselves." He points to the third terrace. "There, full sun, the right place for potatoes, red potatoes, yellow, potatoes for _gnocchi di patate._ "
And so, at the beginning of our fifth summer here, we now dig the potatoes for our dinner. They come up so easily; it's like finding Easter eggs. I'm surprised how clean they are. Just a rinse and they shine.
The way we have potatoes is the way most everything has come about, as we've transformed this abandoned Tuscan house and land over the past four years. We watch Francesco Falco, who has spent most of his seventy-five years attending to grapes, bury the tendril of an old vine so that it shoots out new growth. We do the same. The grapes thrive. As foreigners who have landed here by grace, we'll try anything. Much of the restoration we did ourselves; an accomplishment, as my grandfather would say, out of the fullness of our ignorance.
In 1990, our first summer here, I bought an oversized blank book with Florentine paper covers and blue leather binding. On the first page I wrote ITALY. The book looked as though it should have immortal poetry in it, but I began with lists of wildflowers, lists of projects, new words, sketches of tile in Pompeii. I described rooms, trees, bird calls. I added planting advice: "Plant sunflowers when the moon crosses Libra," although I had no clue myself as to when that might be. I wrote about the people we met and the food we cooked. The book became a chronicle of our first four years here. Today it is stuffed with menus, postcards of paintings, a drawing of a floor plan of an abbey, Italian poems, and diagrams of the garden. Because it is thick, I still have room in it for a few more summers. Now the blue book has become _Under the Tuscan Sun,_ a natural outgrowth of my first pleasures here. Restoring, then improving, the house; transforming an overgrown jungle into its proper function as a farm for olives and grapes; exploring the layers and layers of Tuscany and Umbria; cooking in a foreign kitchen and discovering the many links between the food and the culture—these intense joys frame the deeper pleasure of learning to live another kind of life. To bury the grape tendril in such a way that it shoots out new growth I recognize easily as a metaphor for the way life must change from time to time if we are to go forward in our thinking.
During these early June days, we must clear the terraces of the wild grasses so that when the heat of July strikes and the land dries, we'll be protected from fire. Outside my window, three men with weed machines sound like giant bees. Domenico will be arriving tomorrow to disc the terraces, returning the chopped grasses to the soil. His tractor follows the looping turns established by oxen long ago. Cycles. Though the weed machines and the discer make shorter work, I still feel that I fall into this ancient ritual of summer. Italy is thousands of years deep and on the top layer I am standing on a small plot of land, delighted today with the wild orange lilies spotting the hillside. While I'm admiring them, an old man stops in the road and asks if I live here. He tells me he knows the land well. He pauses and looks along the stone wall, then in a quiet voice tells me his brother was shot here. Age seventeen, suspected of being a Partisan. He keeps nodding his head and I know the scene he looks at is not my rose garden, my hedge of sage and lavender. He has moved beyond me. He blows me a kiss. _"Bella casa, signora."_ Yesterday I found a patch of blue cornflowers around an olive tree where his brother must have fallen. Where did they come from? A seed dropped by a thrush? Will they spread next year over the crest of the terrace? Old places exist on sine waves of time and space that bend in some logarithmic motion I'm beginning to ride.
I open the blue book. Writing about this place, our discoveries, wanderings, and daily life, also has been a pleasure. A Chinese poet many centuries ago noticed that to re-create something in words is like being alive twice. At the taproot, to seek change probably always is related to the desire to enlarge the psychic place one lives in. _Under the Tuscan Sun_ maps such a place. My reader, I hope, is like a friend who comes to visit, learns to mound flour on the thick marble counter and work in the egg, a friend who wakes to the four calls of the cuckoo in the linden and walks down the terrace paths singing to the grapes; who picks jars of plums, drives with me to hill towns of round towers and spilling geraniums, who wants to see the olives the first day they are olives. A guest on holiday is intent on pleasure. Feel the breeze rushing around those hot marble statues? Like old peasants, we could sit by the fireplace, grilling slabs of bread and oil, pour a young Chianti. After rooms of Renaissance virgins and dusty back roads from Umbertide, I cook a pan of small eels fried with garlic and sage. Under the fig where two cats curl, we're cool. I've counted: the dove coos sixty times per minute. The Etruscan wall above the house dates from the eighth century B.C. We can talk. We have time.
_Cortona, 1995_
Bramare:
(Archaic) To Yearn For
I AM ABOUT TO BUY A HOUSE IN A FOREIGN country. A house with the beautiful name of Bramasole. It is tall, square, and apricot-colored with faded green shutters, ancient tile roof, and an iron balcony on the second level, where ladies might have sat with their fans to watch some spectacle below. But below, overgrown briars, tangles of roses, and knee-high weeds run rampant. The balcony faces southeast, looking into a deep valley, then into the Tuscan Apennines. When it rains or when the light changes, the facade of the house turns gold, sienna, ocher; a previous scarlet paint job seeps through in rosy spots like a box of crayons left to melt in the sun. In places where the stucco has fallen away, rugged stone shows what the exterior once was. The house rises above a _strada bianca,_ a road white with pebbles, on a terraced slab of hillside covered with fruit and olive trees. Bramasole: from _bramare,_ to yearn for, and _sole,_ sun: something that yearns for the sun, and yes, I do.
The family wisdom runs strongly against this decision. My mother has said "Ridiculous," with her certain and forceful stress on the second syllable, "RiDICulous," and my sisters, although excited, fear I am eighteen, about to run off with a sailor in the family car. I quietly have my own doubts. The upright seats in the _notaio's_ outer office don't help. Through my thin white linen dress, spiky horsehairs pierce me every time I shift, which is often in the hundred-degree waiting room. I look over to see what Ed is writing on the back of a receipt: Parmesan, salami, coffee, bread. How can he? Finally, the signora opens her door and her torrential Italian flows over us.
The _notaio_ is nothing like a notary; she's the legal person who conducts real-estate transactions in Italy. Ours, Signora Mantucci, is a small, fierce Sicilian woman with thick tinted glasses that enlarge her green eyes. She talks faster than any human I have ever heard. She reads long laws aloud. I thought all Italian was mellifluous; she makes it sound like rocks crashing down a chute. Ed looks at her raptly; I know he's in thrall to the sound of her voice. The owner, Dr. Carta, suddenly thinks he has asked too little; he _must_ have, since we have agreed to buy it. We think his price is exorbitant. We _know_ his price is exorbitant. The Sicilian doesn't pause; she will not be interrupted by anyone except by Giuseppe from the bar downstairs, who suddenly swings open the dark doors, tray aloft, and seems surprised to see his _Americani_ customers sitting there almost cross-eyed in confusion. He brings the signora her midmorning thimble of espresso, which she downs in a gulp, hardly pausing. The owner expects to claim that the house cost one amount while it really cost much more. "That is just the way it's done," he insists. "No one is fool enough to declare the real value." He proposes we bring one check to the _notaio's_ office, then pass him ten smaller checks literally under the table.
Anselmo Martini, our agent, shrugs.
Ian, the English estate agent we hired to help with translation, shrugs also.
Dr. Carta concludes, "You Americans! You take things so seriously. And, _per favore,_ date the checks at one-week intervals so the bank isn't alerted to large sums."
Was that the same bank I know, whose sloe-eyed teller languidly conducts a transaction every fifteen minutes, between smokes and telephone calls? The signora comes to an abrupt halt, scrambles the papers into a folder and stands up. We are to come back when the money and papers are ready.
A WINDOW IN OUR HOTEL ROOM OPENS ONTO AN EXPANSIVE view over the ancient roofs of Cortona, down to the dark expanse of the Val di Chiana. A hot and wild wind—the _scirocco—_ is driving normal people a little crazy. For me, it seems to reflect my state of mind. I can't sleep. In the United States, I've bought and sold a few houses before—loaded up the car with my mother's Spode, the cat, and the ficus for the five- or five-thousand-mile drive to the next doorway where a new key would fit. You _have_ to churn somewhat when the roof covering your head is at stake, since to sell is to walk away from a cluster of memories and to buy is to choose where the future will take place. And the place, never neutral of course, will cast its influence. Beyond that, legal complications and contingencies must be worked out. But here, absolutely everything conspires to keep me staring into the dark.
Italy always has had a magnetic north pull on my psyche. Houses have been on my mind for four summers of renting farmhouses all over Tuscany. In the first place Ed and I rented with friends, we started calculating on the first night, trying to figure out if our four pooled savings would buy the tumbled stone farm we could see from the terrace. Ed immediately fell for farm life and roamed over our neighbors' land looking at the work in progress. The Antolinis grew tobacco, a beautiful if hated crop. We could hear workers shout _"Vipera!"_ to warn the others of a poisonous snake. At evening, a violet blue haze rose from the dark leaves. The well-ordered farm looked peaceful from the vantage point of our terrace. Our friends never came back, but for the next three vacations, the circuitous search for a summer home became a quest for us—whether we ever found a place or not, we were happening on places that made pure green olive oil, discovering sweet country Romanesque churches in villages, meandering the back roads of vineyards, and stopping to taste the softest Brunello and the blackest Vino Nobile. Looking for a house gives an intense focus. We visited weekly markets not just with the purchase of picnic peaches in mind; we looked carefully at all the produce's quality and variety, mentally forecasting birthday dinners, new holidays, and breakfasts for weekend guests. We spent hours sitting in piazzas or sipping lemonade in local bars, secretly getting a sense of the place's ambiance. I soaked many a heel blister in a hotel bidet, rubbed bottles of lotion on my feet, which had covered miles of stony streets. We hauled histories and guides and wildflower books and novels in and out of rented houses and hotels. Always we asked local people where they liked to eat and headed to restaurants our many guidebooks never mentioned. We both have an insatiable curiosity about each jagged castle ruin on the hillsides. My idea of heaven still is to drive the gravel farm roads of Umbria and Tuscany, very pleasantly lost.
Cortona was the first town we ever stayed in and we always came back to it during the summers we rented near Volterra, Florence, Montisi, Rignano, Vicchio, Quercegrossa, all those fascinating, quirky houses. One had a kitchen two people could not pass in, but there was a slice of a view of the Arno. Another kitchen had no hot water and no knives, but the house was built into medieval ramparts overlooking vineyards. One had several sets of china for forty, countless glasses and silverware, but the refrigerator iced over every day and by four the door swung open, revealing a new igloo. When the weather was damp, I got a tingling shock if I touched anything in the kitchen. On the property, Cimabue, legend says, discovered the young Giotto drawing a sheep in the dirt. One house had beds with back-crunching dips in the middles. Bats flew down the chimney and buzzed us, while worms in the beams sent down a steady sifting of sawdust onto the pillows. The fireplace was so big we could sit in it while grilling our veal chops and peppers.
We drove hundreds of dusty miles looking at houses that turned out to be in the flood plain of the Tiber or overlooking strip mines. The Siena agent blithely promised that the view would be wonderful again in twenty years; replanting stripped areas was a law. A glorious medieval village house was wildly expensive. The saw-toothed peasant we met in a bar tried to sell us his childhood home, a windowless stone chicken house joined to another house, with snarling dogs lunging at us from their ropes. We fell hard for a farm outside Montisi; the _contessa_ who owned it led us on for days, then decided she needed a sign from God before she could sell it. We had to leave before the sign arrived.
As I think back over those places, they suddenly seem preposterously alien and Cortona does, too. Ed doesn't think so. He's in the piazza every afternoon, gazing at the young couple trying to wheel their new baby down the street. They're halted every few steps. Everyone circles the carriage. They're leaning into the baby's face, making noises, praising the baby. "In my next life," Ed tells me, "I want to come back as an Italian baby." He steeps in the piazza life: the sultry and buffed man pushing up his sleeve so his muscles show when he languidly props his chin in his hand; the pure flute notes of Vivaldi drifting from an upstairs window; the flower seller's fan of bright flowers against the stone shop; a man with no neck at all unloading lambs from his truck. He slings them like flour sacks over his shoulder and the lambs' eyeballs bulge out. Every few minutes, Ed looks up at the big clock that has kept time for so long over this piazza. Finally, he takes a stroll, memorizing the stones in the street.
Across the hotel courtyard a visiting Arab chants his prayers toward dawn, just when I finally can fall asleep. He sounds as though he is gargling with salt water. For hours, he rings the voice's changes over a small register, over and over. I want to lean out and shout, "Shut up!" Now and then I have to laugh. I look out, see him nodding in the window, a sweet smile on his face. He reminds me so much of tobacco auctioneers I heard in hot warehouses in the South as a child. I am seven thousand miles from home, plunking down my life savings on a whim. Is it a whim? It feels very close to falling in love and that's never really whimsical but comes from some deep source. Or does it?
EACH TIME WE STEP OUT OF THE COOL, HIGH ROOMS OF THE hotel and into the sharp-edged sun, we walk around town and like it more and more. The outdoor tables at Bar Sport face the Piazza Signorelli. A few farmers sell produce on the steps of the nineteenth-century _teatro_ every morning. As we drink espresso, we watch them holding up rusty hand scales to weigh the tomatoes. The rest of the piazza is lined with perfectly intact medieval or Renaissance _palazzi._ Easily, someone might step out any second and break into _La Traviata._ Every day we visit each keystoned medieval gate in the Etruscan walls, explore the Fiat-wide stone streets lined with Renaissance and older houses and the even narrower _vicoli,_ mysterious pedestrian passageways, often steeply stepped. The bricked-up fourteenth-century "doors of the dead" are still visible. These ghosts of doors beside the main entrance were designed, some say, to take out the plague victims—bad luck for them to exit by the main entrance. I notice in the regular doors, people often leave their keys in the lock.
Guidebooks describe Cortona as "somber" and "austere." They misjudge. The hilltop position, the walls and upright, massive stone buildings give a distinctly vertical feel to the architecture. Walking across the piazza, I feel the abrupt, angular shadows fall with Euclidean purity. I want to stand up straight—the upright posture of the buildings seems to carry over to the inhabitants. They walk slowly, with very fine, I want to say, _carriage._ I keep saying, "Isn't she beautiful?" "Isn't he gorgeous?" "Look at _that_ face—pure Raphael." By late afternoon, we're sitting again with our espressi, this time facing the other piazza. A woman of about sixty with her daughter and the teenage granddaughter pass by us, strolling, their arms linked, sun on their vibrant faces. We don't know why light has such a luminous quality. Perhaps the sunflower crops radiate gold from the surrounding fields. The three women look peaceful, proud, impressively pleased. There should be a gold coin with their faces on it.
Meanwhile, as we sip, the dollar is falling fast. We rouse ourselves from the piazza every morning to run around to all the banks, checking their posted exchange rates. When you're cashing traveler's checks for a last-minute spree at the leather market, the rate doesn't matter that much, but this is a house with five acres and every lira counts. A slight drop at those multiples makes the stomach drop also. Every hundred lire it falls, we calculate how much more expensive the house becomes. Irrationally, I also calculate how many pairs of shoes that could buy. Shoes, before, have been my major purchase in Italy, a secret sin. Sometimes I'd go home with nine new pairs: red snakeskin flats, sandals, navy suede boots, and several pairs of black pumps of varying heels.
Typically, the banks vary in how much commission they bite when they receive a large transfer from overseas. We want a break. It looks like a significant chunk of interest they'll collect, since clearing a check in Italy can take weeks.
Finally, we have a lesson in the way things work. Dr. Carta, anxious to close, calls his bank—the bank his father and his father-in-law use—in Arezzo, a half hour away. Then he calls us. "Go there," he says. "They won't take a commission for receiving the money at all, and they'll give you whatever the posted rate is when it arrives."
His savvy doesn't surprise me, though he has seemed spectacularly uninterested in money the entire time we have negotiated—just named his high price and stuck to it. He bought the property from the five old sisters of a landowning family in Perugia the year before, thinking, he said, to make it a summer place for his family. However, he and his wife inherited property on the coast and decided to use that instead. Was that the case, or had he scooped up a bargain from ladies in their nineties and now is making a bundle, possibly buying coast property with our money? Not that I begrudge him. He's smart.
Dr. Carta, perhaps fearing we might back out, calls and asks to meet us at the house. He roars up in his Alfa 164, Armani from stem to stern. "There is something more," he says, as though continuing a conversation. "If you follow me, I will show you something." A few hundred feet down the road, he leads us up a stone path through fragrant yellow broom. Odd, the stone path continues up the hill, curving along a ridge. Soon we come to a two-hundred-degree view of the valley, with the cypress-lined road below us and a mellow landscape dotted with tended vineyards and olive groves. In the distance lies a blue daub, which is Lake Trasimeno; off to the right, we see the red-roofed silhouette of Cortona cleanly outlined against the sky. Dr. Carta turns to us triumphantly. The flat paving stones widen here. "The Romans—this road was built by the Romans—it goes straight into Cortona." The sun is broiling. He goes on and on about the large church at the top of the hill. He points out where the rest of the road might have run, right through Bramasole's property.
Back at the house he turns on an outside faucet and splashes his face. "You'll enjoy the finest water, truly your own abundant _acqua minerale,_ excellent for the liver. _Eccellente!_ " He manages to be at once enthusiastic and a little bored, friendly and slightly condescending. I am afraid we have spoken too bluntly about money. Or maybe he has interpreted our law-abiding American expectations about the transaction as incredibly naive. He lets the faucet run, cupping his hand under the water, somehow leaning over for a drink without dislodging the well-cut linen coat tossed over his shoulders. "Enough water for a swimming pool," he insists, "which would be perfect out on the point where you can see the lake, overlooking right where Hannibal defeated the Romans."
We're dazzled by the remains of a Roman road over the hill covered with wildflowers. We will follow the stone road into town for a coffee late in the afternoons. He shows us the old cistern. Water is precious in Tuscany and was collected drop by drop. By shining a flashlight into the opening, we've already noticed that the underground cistern has a stone archway, obviously some kind of passageway. Up the hill in the Medici fortress, we saw the same arch in the cistern there and the caretaker told us that a secret underground escape route goes downhill to the valley, then to Lake Trasimeno. Italians take such remains casually. That one is allowed to own such ancient things seems impossible to me.
WHEN I FIRST SAW BRAMASOLE, I IMMEDIATELY WANTED TO hang my summer clothes in an _armadio_ and arrange my books under one of those windows looking out over the valley. We'd spent four days with Signor Martini, who had a dark little office on Via Sacco e Vanzetti down in the lower town. Above his desk hung a photo of him as a soldier, I assumed for Mussolini. He listened to us as though we spoke perfect Italian. When we finished describing what we thought we wanted, he rose, put on his Borsolino, and said one word, _"Andiamo,"_ let's go. Although he'd recently had a foot operation, he drove us over nonexistent roads and pushed through jungles of thorns to show us places only he knew about. Some were farmhouses with roofs collapsed onto the floor, miles from town and costing the earth. One had a tower built by the Crusaders, but the _contessa_ who owned it cried and doubled the price on the spot when she saw that we really were interested. Another was attached to other farmhouses where chickens were truly free range—they ran in and out of the houses. The yard was full of rusted farm equipment and hogs. Several felt airless or sat hard by the road. One would have required putting in a road—it was hidden in blackberry brambles and we could only peer in one window because a coiled black snake refused to budge from the threshold.
We took Signor Martini flowers, thanked him and said good-bye. He seemed genuinely sorry to see us go.
The next morning we ran into him in the piazza after coffee. He said, "I just saw a doctor from Arezzo. He might be interested in selling a house. _Una bella villa,_ " he added emphatically. The house was within walking distance of Cortona.
"How much?" we asked, although we knew by then he cringes at being asked that direct question.
"Let's just go take a look," was all he said. Out of Cortona, he took the road that climbs and winds to the other side of the hill. He turned onto the _strada bianca_ and, after a couple of kilometers, pulled into a long, sloping driveway. I caught a glimpse of a shrine, then looked up at the three-story house with a curly iron fanlight above the front door and two tall, exotic palm trees on either side. On that fresh morning, the facade seemed radiant, glazed with layers of lemon, rouge, and terra-cotta. We both became silent as we got out of the car. After all the turns into unknown roads, the house seemed just to have been waiting all along.
"Perfect, we'll take it," I joked as we stepped through the weeds. Just as he had at other houses, Signor Martini made no sales pitch; he simply looked with us. We walked up to the house under a rusted pergola leaning under the weight of climbing roses. The double front door squawked like something alive when we pushed it open. The house's walls, thick as my arm is long, radiated coolness. The glass in the windows wavered. I scuffed through silty dust and saw below it smooth brick floors in perfect condition. In each room, Ed opened the inside window and pushed open the shutters to one glorious view after another of cypresses, rippling green hills, distant villas, a valley. There were even two bathrooms that functioned. They were not beautiful, but _bathrooms,_ after all the houses we'd seen with no floors, much less plumbing. No one had lived there in thirty years and the grounds seemed like an enchanted garden, overgrown and tumbling with blackberries and vines. I could see Signor Martini regarding the grounds with a countryman's practiced eye. Ivy twisted into the trees and ran over fallen terrace walls. _"Molto lavoro,"_ much work, was all he said.
During several years of looking, sometimes casually, sometimes to the point of exhaustion, I never heard a house say _yes_ so completely. However, we were leaving the next day, and when we learned the price, we sadly said no and went home.
During the next months, I mentioned Bramasole now and then. I stuck a photo on my mirror and often wandered the grounds or rooms in my mind. The house is a metaphor for the self, of course, but it also is totally real. And a _foreign_ house exaggerates all the associations houses carry. Because I had ended a long marriage that was not supposed to end and was establishing a new relationship, this house quest felt tied to whatever new identity I would manage to forge. When the flying fur from the divorce settled, I had found myself with a grown daughter, a full-time university job (after years of part-time teaching), a modest securities portfolio, and an entire future to invent. Although divorce was harder than a death, still I felt oddly returned to myself after many years in a close family. I had the urge to examine my life in another culture and move beyond what I knew. I wanted something of a _physical_ dimension that would occupy the mental volume the years of my former life had. Ed shares my passion for Italy completely and also shares the boon of three-month summer breaks from university teaching. There we would have long days for exploring and for our writing and research projects. When he is at the wheel, he'll _always_ take the turn down the intriguing little road. The language, history, art, places in Italy are endless—two lifetimes wouldn't be enough. And, ah, the foreign self. The new life might shape itself to the contours of the house, which already is at home in the landscape, and to the rhythms around it.
In the spring, I called a California woman who was starting a real-estate development business in Tuscany. I asked her to check on Bramasole; perhaps if it had not sold, the price had come down. A week later, she called from a bar after meeting with the owner. "Yes, it's still for sale, but with that particular brand of Italian logic, the price has been raised. The dollar," she reminded me, "has fallen. And that house needs a lot of work."
Now we've returned. By this time, with equally peculiar logic, I've become fixed on buying Bramasole. After all, the only thing wrong is the expense. We both love the setting, the town, the house and land. If only one little thing is wrong, I tell myself, go ahead.
Still, this costs a _sacco di soldi._ It will be an enormous hassle to recover the house and land from neglect. Leaks, mold, tumbling stone terraces, crumbling plaster, one funky bathroom, another with an adorable metal hip bathtub and a cracked toilet.
Why does the prospect seem fun, when I found remodeling my kitchen in San Francisco a deep shock to my equilibrium? At home, we can't even hang a picture without knocking out a fistful of plaster. When we plunge the stopped-up sink, forgetting once again that the disposal doesn't like artichoke petals, sludge seems to rise from San Francisco Bay.
On the other hand, a dignified house near a Roman road, an Etruscan (Etruscan!) wall looming at the top of the hillside, a Medici fortress in sight, a view toward Monte Amiata, a passageway underground, one hundred and seventeen olive trees, twenty plums, and still uncounted apricot, almond, apple, and pear trees. Several figs seem to thrive near the well. Beside the front steps there's a large hazelnut. Then, proximity to one of the most superb towns I've ever seen. Wouldn't we be crazy not to buy this lovely house called Bramasole?
What if one of us is hit by a potato chip truck and can't work? I run through a litany of diseases we could get. An aunt died of a heart attack at forty-two, my grandmother went blind, all the ugly illnesses... What if an earthquake shakes down the universities where we teach? The Humanities Building is on a list of state structures most likely to fall in a moderately severe quake. What if the stock market spirals down?
I leap out of bed at three A.M. and step in the shower, letting my whole face take the cold water. Coming back to bed in the dark, feeling my way, I jam my toe on the iron bed frame. Pain jags all the way up my backbone. "Ed, wake up. I think I've broken my toe. How can you sleep?"
He sits up. "I was just dreaming of cutting herbs in the garden. Sage and lemon balm. Sage is _salvia_ in Italian." He has never wavered from his belief that this is a brilliant idea, that this is heaven on earth. He clicks on the bedside lamp. He's smiling.
My half-on toenail is hanging half off, ugly purple spreading underneath. I can't bear to leave it or to pull it off. "I want to go home," I say.
He puts a Band-Aid around my toe. "You mean Bramasole, don't you?" he asks.
THIS SACK OF MONEY IN QUESTION HAS BEEN WIRED FROM CALIFORNIA but has not arrived. How can that be, I ask at the bank, money is wired, it arrives instantaneously. More shrugs. Perhaps the main bank in Florence is holding it. Days pass. I call Steve, my broker in California, from a bar. I'm shouting over the noise of a soccer match on the TV. "You'll have to check from that end;" he shouts back, "it's long gone from here and did you know the government there has changed forty-seven times since World War II? This money was well invested in tax-free bonds and the best growth funds. Those Australian bonds of yours earned seventeen percent. Oh well, _la dolce vita._ "
The mosquitoes ( _zanzare_ they're called, just like they sound) invade the hotel with the desert wind. I spin in the sheets until my skin burns. I get up in the middle of the night and lean out the shuttered window, imagining all the sleeping guests, blisters on their feet from the stony streets, their guidebooks still in their hands. We could still back out. Just throw our bags in the rented Fiat and say _arrivederci._ Go hang out on the Amalfi coast for a month and head home, tanned and relaxed. Buy lots of sandals. I can hear my grandfather when I was twenty: "Be realistic. Come down out of the clouds." He was furious that I was studying poetry and Latin etymology, something utterly useless. Now, what am I thinking of? Buying an abandoned house in a place where I hardly can speak the language. He probably has worn out his shroud turning over in his grave. We don't have a mountain of reserves to bail us out in case that mysterious something goes wrong.
WHAT IS THIS THRALL FOR HOUSES? I come from a long line of women who open their handbags and take out swatches of upholstery material, colored squares of bathroom tile, seven shades of yellow paint samples, and strips of flowered wallpaper. We love the concept of four walls. "What is her house like?" my sister asks, and we both know she means what is _she_ like. I pick up the free real-estate guide outside the grocery store when I go somewhere for the weekend, even if it's close to home. One June, two friends and I rented a house on Majorca; another summer I stayed in a little _casa_ in San Miguel de Allende in which I developed a serious love for fountained courtyards and bedrooms with bougainvillea cascading down the balcony, the austere Sierra Madre. One summer in Santa Fe, I started looking at adobes there, imagining I would become a Southwesterner, cook with chilies, wear squash blossom turquoise jewelry—a different life, the chance to be extant in another version. At the end of a month I left and never have wanted to return.
I love the islands off the Georgia coast, where I spent summers when I was growing up. Why not a weathered gray house there, made of wood that looks as though it washed up on the beach? Cotton rugs, peach iced tea, a watermelon cooling in the creek, sleeping with waves churning and rolling outside the window. A place where my sisters, friends, and their families could visit easily. But I keep remembering that anytime I've stepped in my own footprints again, I haven't felt renewed. Though I'm susceptible to the pull to the known, I'm just slightly more susceptible to surprise. Italy seems endlessly alluring to me—why not, at this point, consider the opening of _The Divine Comedy:_ What must one do in order to grow? Better to remember my father, the son of my very literal-minded, penny-pinching grandfather. "The family motto," he'd say, "is "Packing and Unpacking.' " And also, "If you can't go first class, don't go at all."
Lying awake, I feel the familiar sense of The Answer arriving. Like answers on the bottom of the black fortune-telling eight ball that I loved when I was ten, often I can feel an idea or the solution to a dilemma floating up through murky liquid, then it is as if I see the suddenly clear white writing. I like the charged zone of waiting, a mental and physical sensation of the bends as something mysterious zigzags to the surface of consciousness.
What if you did _not_ feel uncertainty, the white writing says. Are you exempt from doubt? Why not rename it excitement? I lean over the wide sill just as the first gilded mauve light of sunrise begins. The Arab is still sleeping. The undulant landscape looks serene in every direction. Honey-colored farmhouses, gently placed in hollows, rise like thick loaves of bread set out to cool. I know some Jurassic upheaval violently tossed up the hills, but they appear rounded as though by a big hand. As the sun brightens, the land spreads out a soft spectrum: the green of a dollar bill gone through the wash, old cream, blue sky like a blind person's eye. The Renaissance painters had it just right. I never thought of Perugino, Giotto, Signorelli, et al., as realists, but their background views are still here, as most tourists discover, with dark cypress trees brushed in to emphasize each composition the eye falls on. Now I see why the red boot on a gold and blond angel in the Cortona museum has such a glow, why the Madonna's cobalt dress looks intense and deep. Against this landscape and light, everything takes on a primary outline. Even a red towel drying on a line below becomes totally saturated with its own redness.
Think: What if the sky doesn't fall? What if it's glorious? What if the house is transformed in three years? There will be by then hand-printed labels for the house's olive oil, thin linen curtains pulled across the shutters for siesta, jars of plum jam on the shelves, a long table for feasts under the linden trees, baskets piled by the door for picking tomatoes, arugula, wild fennel, roses, and rosemary. And who are we in that strange new life?
FINALLY THE MONEY ARRIVES, THE ACCOUNT IS OPEN. HOWEVER , they have no checks. This enormous bank, the seat of dozens of branches in the gold center of Italy, has no checks to give us. "Maybe next week," Signora Raguzzi explains. "Right now, nothing." We sputter. Two days later, she calls. "I have ten checks for you." What is the big deal with checks? I get boxes of them at home. Signora Raguzzi parcels them out to us. Signora Raguzzi in tight skirt, tight T-shirt, has lips that are perpetually wet and pouting. Her skin glistens. She is astonishingly gorgeous. She wears a magnificent square gold necklace and bracelets on both wrists that jangle as she stamps our account number on each check.
"What great jewelry. I love those bracelets," I say.
"All we have here is gold," she replies glumly. She is bored with Arezzo's tombs and piazzas. California sounds good to her. She brightens every time she sees us. "Ah, California," she says as a greeting. The bank begins to seem surreal. We're in the back room. A man wheels in a cart stacked with gold ingots—actual small bricks of gold. No one seems to be on guard. Another man loads two into dingy manila folders. He's plainly dressed, like a workman. He walks out into the street, taking the ingots somewhere. So much for Brinks delivery—but what a clever plainclothes disguise. We turn back to the checks. There will be no insignia of boats or palm trees or pony express riders, there will be no name, address, driver's license, Social Security number. Only these pale green checks that look as though they were printed in the twenties. We're enormously pleased. That's close to citizenship—a bank account.
Finally we are gathered in the _notaio's_ office for the final reckoning. It's quick. Everyone talks at once and no one listens. The baroque legal terms leave us way behind. A jackhammer outside drills into my brain cells. There's something about two oxen and two days. Ian, who's translating, stops to explain this archaic spiral of language as an eighteenth-century legal description of the amount of land, measured by how long it would take two oxen to plow it. We have, it seems, two plowing days worth of property.
I write checks, my fingers cramping over all the times I write _milione._ I think of all the nice dependable bonds and utility stocks and blue chips from the years of my marriage magically turning into a terraced hillside and a big empty house. The glass house in California where I lived for a decade, surrounded by kumquat, lemon, mock orange, and guava, its bright pool and covered patio with wicker and flowered cushions—all seem to recede, as though seen through the long focus in binoculars. _Million_ is such a big word in English it's hard to treat it casually. Ed carefully monitors the zeros, not wanting me to unwittingly write _miliardo,_ billion, instead. He pays Signor Martini in cash. He never has mentioned a fee; we have found out the normal percentage from the owner. Signor Martini seems pleased, as though we've given him a gift. For me this is a confusing but delightful way to conduct business. Handshakes all around. Is that a little cat smile on the mouth of the owner's wife? We're expecting a parchment deed, lettered in ancient script, but no, the _notaio_ is going on vacation and she'll try to get to the paperwork before she leaves. _"Normale,"_ Signor Martini says. I've noticed all along that someone's word is still taken for that. Endless contracts and stipulations and contingencies simply have not come up. We walk out into the brutally hot afternoon with nothing but two heavy iron keys longer than my hand, one to a rusted iron gate, the other to the front door. They look nothing like the keys to anything I've ever owned. There is no hope for spare copies.
Giuseppe waves from the door of the bar and we tell him we have bought a house. "Where is it?" he wants to know.
"Bramasole," Ed begins, about to say where it is.
"Ah, Bramasole, _una bella villa!_ " He has picked cherries there as a boy. Although it is only afternoon, he pulls us in and pours a _grappa_ for us. "Mama!" he shouts. His mother and her sister come in from the back and everyone toasts us. They're all talking at once, speaking of us as the _stranieri,_ foreigners. The _grappa_ is blindingly strong. We drink ours as fast as Signora Mantucci nips her espresso and wander out in the sun. The car is as hot as a pizza oven. We sit there with the doors open, suddenly laughing and laughing.
WE'D ARRANGED FOR TWO WOMEN TO CLEAN AND FOR A BED to be delivered while we signed the final papers. In town we picked up a bottle of cold _prosecco,_ then stopped at the _rosticceria_ for marinated zucchini, olives, roast chicken, and potatoes.
We arrive at the house dazed by the events and the _grappa._ Anna and Lucia have washed the windows and exorcised layers of dust, as well as many spiders' webs. The second-floor bedroom that opens onto a brick terrace gleams. They've made the bed with the new blue sheets and left the terrace door open to the sound of cuckoos and wild canaries in the linden trees. We pick the last of the pink roses on the front terrace and fill two old Chianti bottles with them. The shuttered room with its whitewashed walls, just-waxed floors, pristine bed with new sheets, and sweet roses on the windowsill, all lit with a dangling forty-watt bulb, seems as pure as a Franciscan cell. As soon as I walk in, I think it is the most perfect room in the world.
We shower and dress in fresh clothes. In the quiet twilight, we sit on the stone wall of the terrace and toast each other and the house with tumblers of the spicy _prosecco,_ which seems like a liquid form of the air. We toast the cypress trees along the road and the white horse in the neighbor's field, the villa in the distance that was built for the visit of a pope. The olive pits we toss over the wall, hoping they will spring from the ground next year. Dinner is delicious. As the darkness comes, a barn owl flies over so close that we hear the whir of wings and, when it settles in the black locust, a strange cry that we take for a greeting. The Big Dipper hangs over the house, about to pour on the roof. The constellations pop out, clear as a star chart. When it finally is dark, we see that the Milky Way sweeps right over the house. I forget the stars, living in the ambient light of a city. Here they are, all along, spangling and dense, falling and pulsating. We stare up until our necks ache. The Milky Way looks like a flung bolt of lace unfurling. Ed, because he likes to whisper, leans to my ear. "Still want to go home," he asks, "or can this be home?"
A House and the
Land It Takes Two
Oxen Two Days to Plow
I ADMIRE THE BEAUTY OF SCORPIONS. THEY look like black-ink hieroglyphs of themselves. I'm fascinated, too, that they can navigate by the stars, though how they ever glimpse constellations from their usual homes in dusty corners of vacant houses, I don't know. One scurries around in the bidet every morning. Several get sucked into the new vacuum cleaner by mistake, though usually they are luckier: I trap them in a jar and take them outside. I suspect every cup and shoe. When I fluff a bed pillow, an albino one lands on my bare shoulder. We upset armies of spiders as we empty the closet under the stairs of its bottle collection. Impressive, the long threads for legs and the fly-sized bodies; I can even see their eyes. Other than these inhabitants, the inheritance from the former occupants consists of dusty wine bottles—thousands and thousands in the shed and in the stalls. We fill local recycling bins over and over, waterfalls of glass raining from boxes we've loaded and reloaded. The stalls and _limonaia_ (a garage-sized room on the side of the house once used for storing pots of lemons over the winter) are piled with rusted pans, newspapers from 1958, wire, paint cans, debris. Whole ecosystems of spiders and scorpions are destroyed, though hours later they seem to have regenerated. I look for old photos or antique spoons but see nothing of interest except some handmade iron tools and a "priest," a swan-shaped wooden form with a hook for a hanging pan of hot coals, which was pushed under bedcovers in winter to warm the clammy sheets. One cunningly made tool, an elegant little sculpture, is a hand-sized crescent with a worn chestnut handle. Any Tuscan would recognize it in a second: a tool for trimming grapes.
When we first saw the house, it was filled with fanciful iron beds with painted medallions of Mary and shepherds holding lambs, wormy chests of drawers with marble tops, cribs, foxed mirrors, cradles, boxes, and lugubrious bleeding-heart religious pictures of the Crucifixion. The owner removed everything—down to the switchplate covers and lightbulbs—except a thirties kitchen cupboard and an ugly red bed that we cannot figure out how to get down the narrow back stairs from the third floor. Finally we take the bed apart and throw it piece by piece from the window. Then we stuff the mattress through the window and my stomach flips as I watch it seem to fall in slow motion to the ground.
The Cortonese, out for afternoon strolls, pause in the road and look up at all the mad activity, the car trunk full of bottles, mattress flying, me screaming as a scorpion falls down my shirt when I sweep the stone walls of the stall, Ed wielding a grim-reaper scythe through the weeds. Sometimes they stop and call up, "How much did you pay for the house?"
I'm taken aback and charmed by the bluntness. "Probably too much," I answer. One person remembered that long ago an artist from Naples lived there; for most, it has stood empty as far back as they can remember.
Every day we haul and scrub. We are becoming as parched as the hills around us. We have bought cleaning supplies, a new stove and fridge. With sawhorses and two planks we set up a kitchen counter. Although we must bring hot water from the bathroom in a plastic laundry pan, we have a surprisingly manageable kitchen. As one who has used Williams-Sonoma as a toy store for years, I begin to get back to an elementary sense of the kitchen. Three wooden spoons, two for the salad, one for stirring. A sauté pan, bread knife, cutting knife, cheese grater, pasta pot, baking dish, and stove-top espresso pot. We brought over some old picnic silverware and bought a few glasses and plates. Those first pastas are divine. After long work, we eat everything in sight then tumble like field hands into bed. Our favorite is spaghetti with an easy sauce made from diced _pancetta,_ unsmoked bacon, quickly browned, then stirred into cream and chopped wild arugula (called _ruchetta_ locally), easily available in our driveway and along the stone walls. We grate _parmigiano_ on top and eat huge mounds. Besides the best salad of all, those amazing tomatoes sliced thickly and served with chopped basil and mozzarella, we learn to make Tuscan white beans with sage and olive oil. I shell and simmer the beans in the morning, then let them come to room temperature before dousing them with the oil. We consume an astonishing number of black olives.
Three ingredients is about all we manage most nights, but that seems to be enough for something splendid. The idea of cooking here inspires me—with such superb ingredients, everything seems easy. An abandoned slab of marble from a dresser top serves as a pastry table when I decide to make my own crust for a plum tart. As I roll it out with one of the handblown Chianti bottles I rescued from the debris, I think with amazement of my kitchen in San Francisco: the black and white tile floor, mirrored wall between cabinets and counter, long counters in gleaming white, the restaurant stove big enough to take off from the San Francisco airport, sunlight pouring in the skylight, and, always, Vivaldi or Robert Johnson or Villa Lobos to cook to. Here, the determined spider in the fireplace keeps me company as she knits her new web. The stove and fridge look starkly new against the flaking whitewash and under the bulb hanging from what looks like a live wire.
Late in the afternoons I take long soaks in the hip bath filled with bubbles, washing spiderwebs out of my hair, grit from my nails, necklaces of dirt from around my neck. I have not had a necklace of dirt since I used to play Kick the Can on long summer evenings as a child. Ed emerges reborn from the shower, tan in his white cotton shirt and khaki shorts.
The empty house, now scrubbed, feels spacious and pure. Most of the scorpions migrate elsewhere. Because of the thick stone walls, we feel cool even on the hottest days. A primitive farm table, left in the _limonaia,_ becomes our dining table on the front terrace. We sit outside talking late about the restoration, savoring the Gorgonzola with a pear pulled off the tree, and the wine from Lake Trasimeno, just a valley away. Renovation seems simple, really. A central water heater, with a new bath and existing baths routed to it, new kitchen—but simple, soul of simplicity. How long will the permits take? Do we really need central heat? Should the kitchen stay where it is, or wouldn't it really be better where the ox stall currently is? That way, the present kitchen could be the living room, with a big fireplace in it. In the dark we can see the shadowy vestiges of a formal garden: a long, overgrown boxwood hedge with five huge, ragged topiary balls rising out of it. Should we rebuild the garden with these strange remnants? Cut them out of the hedge? Take out the ancient hedge altogether and plant something informal, such as lavender? I close my eyes and try to have a vision of the garden in three years, but the overgrown jungle is too indelibly imprinted in my brain. By the end of dinner, I could sleep standing up, like a horse.
The house must be in some good alignment, according to the Chinese theories of Feng Shui. Something is giving us an extraordinary feeling of well-being. Ed has the energy of three people. A lifelong insomniac, I sleep like one newly dead every night and dream deeply harmonious dreams of swimming along with the current in a clear green river, playing and at home in the water. On the first night, I dreamed that the real name of the house was not Bramasole but Cento Angeli, One Hundred Angels, and that I would discover them one by one. Is it bad luck to change the name of a house, as it is to rename a boat? As a trepid foreigner, I wouldn't. But for me, the house now has a secret name as well as its own name.
THE BOTTLES ARE GONE. THE HOUSE IS CLEAN. THE TILE FLOORS shine with a waxy patina. We hang a few hooks on the backs of doors, just to get our clothes out of suitcases. With milk crates and a few squares of marble left in the stall, we fashion a couple of bedside tables to go with our two chairs from the garden center.
We feel prepared to face the reality of restoration. We walk into town for coffee and telephone Piero Rizzatti, the _geometra._ The translations "draftsman" or "surveyor" don't quite explain what a _geometra_ is, a professional without an equivalent in the United States—a liaison among owner, builders, and town planning officials. Ian has assured us that he is the best in the area, meaning also that he has the best connections and can get the permits quickly.
The next day Ian drives out with Signor Rizzatti and his tape measurer and notepad. We begin our cold-eyed tour through the empty house.
The bottom floor is basically five rooms in a row—farmer's kitchen, main kitchen, living room, horse stall, another stall—with a hall and stairs after the first two rooms. The house is bisected by its great stairwell with stone steps and handwrought iron railing. A strange floor plan: The house is designed like a dollhouse, one room deep with all the rooms about the same size. That seems to me like giving all your children the same name. On the upper two floors, there are two bedrooms on either side of the stairs; you must go through the first room to get to the other. Privacy, until recently, wasn't much of an issue for Italian families. Even Michelangelo, I recall, slept four abed with his masons when he worked on a project. In the great Florentine _palazzi,_ you must go through one immense room to get to the next; corridors must have seemed a waste of space.
The west end of the house—one room on each floor—is walled off for the _contadini,_ the farm family who worked the olive and grape terraces. A narrow stone stairway runs up the back of that apartment and there's no entrance from the main house, except through that kitchen's front door. With their door, the two doors going into the stalls, and the big front door, there are four French doors across the front of the house. I envision them with new shutters, all flung open to the terrace, lavender, roses, and pots of lemons between them, with lovely scents wafting into the house and a natural movement of inside/outside living. Signor Rizzatti turns the handle of the farm kitchen door and it comes off in his hand.
At the back of the apartment, a crude room with a toilet cemented to the floor—one step above a privy—is tacked onto the third floor of the house. The farmers, with no running water upstairs, must have used a bucket-flush method. The two real bathrooms also are built off the back of the house, each one at a stair landing. This ugly solution is still common for stone houses constructed before indoor plumbing. Often I see these loos jutting out, sometimes supported by flimsy wooden poles angling into the walls. The small bath, which I take to be the house's first, has a low ceiling, stone checkerboard floor, and the charming hip bath. The large bathroom must have been added in the fifties, not long before the house was abandoned. Someone had a dizzy fling with tile—floor-to-ceiling pink, blue, and white in a butterfly design. The floor is blue but not the same blue. The shower simply drains into the floor, that is to say, water spreads all over the bathroom. Someone attached the showerhead so high on the wall that the spray creates a breeze and the angled shower curtain we hung wraps around our legs.
We walk out onto the L-shaped terrace off the second-floor bedroom, leaning on the railing for the stupendous view of the valley from one direction and of fruit and olive trees from the others. We're imagining, of course, future breakfasts here with the overhanging apricot tree in bloom and the hillside covered with wild irises we see the scraggly remains of everywhere. I can see my daughter and her boyfriend, slathered in tanning oil, reading novels on chaise longues, a pitcher of iced tea between them. The terrace floor is just like the floors in the house, only the tile is beautifully weathered and mossy. Signor Rizzatti, however, regards the tiles with a frown. When we go downstairs, he points to the ceiling of the _limonaia,_ just underneath the terrace, which also is caked with moss and is even crumbling in some spots. Leaks. This looks expensive. The scrawls on his notepad cover two pages.
We think the weird layout suits us. We don't need eight bedrooms anyway. Each of the four can have an adjoining study/sitting room/dressing room, although we decide to turn the room next to ours into a bathroom. Two bathrooms seem enough but we'd love the luxury of a private bath next to the bedroom. If we can chop out the farmer's crude toilet attached to that room, we'll have a closet off the bath, the only one in the house. With his metal tape, the _geometra_ indicates the ghost of a door leading into the farmer's former bedroom from the bedroom we'll have. Reopening it, we think, will be a quick job.
On the bottom floor, the line of rooms is not that convenient. When we first saw the house, I'd said airily, "We can knock these walls out and have two big rooms down here." Now our _geometra_ tells us we may open the walls only about six feet because of earthquake precautions. Staying here has given me an inner sense of the construction. I see how the first floor walls bow near the floor, accommodating the large stones in the foundation. The house was built in a way not unlike the stone terraces, without mortar, stones stacked and wedged. From the depths of the doorways and windowsills, I see that the walls thin as they go up. The yard-thick walls on the first floor are maybe half that on the third. What holds the house together as it goes up? Can inserting a few modern I beams of steel in those openings do the job of stones I couldn't even reach around?
When the great dome of the _duomo_ was conceived in Florence, no one knew the technique for constructing so large a half sphere. Someone proposed building it over an immense mound of dirt piled in the cathedral. Money would be hidden throughout the pile and, on completion of the dome, the peasants would be invited to dig for coins and cart away the dirt. Fortunately, Brunelleschi figured out how to engineer his dome. I hope someone built this house on solid principles also but still I begin to have misgivings about taking out the fortress-thick walls on the first floor.
The _geometra_ is full of opinions. He thinks the apartment's back staircase should come out. We love it, a secret escape. He thinks we should replaster the cracked and crumbling stucco facade, paint it ocher. No way. I like the colors that change as the light does and the intense glow of golds when it rains, as though the sun seeps into the walls. He thinks our first priority should be the roof. "But the roof doesn't leak—why bother it, when there are so many other pressing things?" We explain to him that we won't be able to do everything at once. The house cost the earth. The project will have to be spread out. We will do much of the work ourselves. Americans, I try to explain, sometimes are "do it yourself" people. As I say this I see a flash of panic cross Ed's face. "Do it yourself" doesn't translate. The _geometra_ shakes his head as though all is hopeless if he has to explain things as basic as these.
He speaks to us kindly, as if through precise enunciation we will understand him. "Listen, the roof must be consolidated. They will preserve the tiles, number them, place them again in the same order, but you will have insulation; the roof will be strengthened."
At this point, it's either the roof or central heating, not both. We debate the importance of each. After all, we'll be here mostly in the summer. But we don't want to freeze at Christmas when we come over to pick the olives. If we're ever going to put heat in, it needs to go in at the same time as the water system and plumbing. The roof can be done anytime—or never. Right now, water is held in a cistern in the farmer's bedroom. When you shower or flush, a pump comes on and well water gurgles into the cistern. Individual hotwater heaters (miraculously, they work) hang above each shower. We'll need a central water heater, a large cistern connected to it so that the noisy pump isn't continuously working.
We decide on the heating. The _geometra,_ feeling sure that we will come to our senses, says he will apply for a roof permit as well.
At some low point in the house's life, someone madly painted the chestnut beams in every room with a hideous vinegar varnish. This unimaginable technique once was popular in the South of Italy. You paint over real beams with a sticky goo, then comb through it to simulate wood! Sandblasting, therefore, is a top priority. An ugly job but fast, and we'll do the sealing and waxing ourselves. I once refinished a sailor's sea chest and found it fun. We'll need door and window repairs. All the window casements and interior shutters are covered with the same faux wood concoction. This genius of the beams and windows is probably responsible for the fireplace, which is covered with ceramic tiles that resemble bricks. What a strange mind, to cover the real thing with an imitation of something real. All this must go, along with the blue tiles covering the wide windowsill, the butterflies in the bathroom. Both the main kitchen and the farmers' kitchen sport ugly cement sinks. His list is now three pages long. The farmers' kitchen has floors made of crushed marble tiles, super ugly. There are a lot of ancient-looking wires coiled near the ceilings on white porcelain knobs. Sometimes sparks come flying out when I switch on a light.
The _geometra_ sits on the terrace wall, mopping his face with an enormous monogrammed linen handkerchief. He looks at us with pity.
RULE ONE IN A RESTORATION PROJECT: BE THERE. WE WILL BE seven thousand miles away when some of the big work is done. We brace ourselves for bids for the work.
Nando Lucignoli, sent to us by Signor Martini, drives up in his Lancia and stands at the bottom of the driveway, looking not at the house but at the view of the valley. I think he must be a deep admirer of landscape but see that he is talking on a cellular phone, waving his cigarette and gesturing to the air. He tosses the phone onto the front seat.
_"Bella posizione."_ He waves his Gauloises again as he shakes hands, almost bowing to me. His father is a stonemason and he has become a contractor, an extraordinarily good-looking one. Like many Italian men, his cologne or aftershave surrounds him with a lemony, sunny aura only slightly dispelled by the cigarette smoke. Before he says anything more, I'm sure he's the contractor for us. We take him on a tour of the house. _"Niente, niente,"_ he repeats, nothing. "We'll run the heating pipes in channels on the back of the house, a week; the bathroom—three days, signora. One month, everything. You'll have a perfect house; just lock the door, leave me the key and when you come back, everything will be taken care of." He assures us he can find old bricks to match the rest of the house for the new kitchen in the stall. The wiring? He has a friend. The terrace bricks? He shrugs, oh, some mortar. Opening the walls? His father is expert in that. His slicked-back black hair, wanting to revert to curls, falls over his forehead. He looks like Caravaggio's Bacchus—only he has moss-green eyes and a slight slouch, probably from leaning into the speed of his Lancia. He thinks my ideas are wonderful, I should have been an architect, I have excellent taste. We sit out on the stone wall and have a glass of wine. Ed goes inside to make coffee for himself. Nando draws diagrams of the water lines on the back of an envelope. My Italian is charming, he says. He understands everything I try to say. He says he will drop off his estimate tomorrow. I am sure it will be reasonable, that through the winter Nando and his father and a few trusted workers will transform Bramasole. "Enjoy yourself—leave it to me," he says as his tires spin on the driveway. As I wave good-bye, I notice that Ed has stayed on the terrace. He's noncommittal about Nando, saying only that he smelled like a _profumeria,_ it's affected to smoke Gauloises, and that he didn't think the central heating could be installed that way at all.
Ian brings up Benito Cantoni, a yellow-eyed, solidly built short man who bears a strange resemblance to Mussolini. He's around sixty so he must have been a namesake. I remember that Mussolini actually was named for the Mexican Benito Juárez, who fought French oppression. Odd to think of that revolutionary name travelling through the dictator and into this quiet man whose wide, blank face and bald head shine like a polished nut. When he speaks, which is little, he uses the local Val di Chiana dialect. He cannot understand a word either of us says and we certainly can't understand him. Even Ian has trouble. Benito worked on the restoration of the chapel at Le Celle, a nearby monastery, a solid recommendation. We're even more impressed when Ian drives us out to look at a house he's restoring near Castiglione del Lago, a farmhouse with a tower supposedly built by the Knights Templar. The work looks careful. His two masons, unlike Benito, have big smiles.
Back at Bramasole, Benito walks through, not even taking a note. He radiates a calm confidence. When we ask Ian to request an estimate, Benito balks. It is impossible to know the problems he might run into. How much do we want to spend? (What a question!) He is not sure about the floor tiles, of what he will uncover when he takes the bricks off the upstairs terrace. A small beam, he notices, needs replacing on the third floor.
Estimates are foreign to builders around here. They're used to working by the day, with someone always at home to know how long they were there. This projecting is just not the way they do business, although they will sometimes say "Under three days" or _"Quindici giorni." Quindici giorni—_ fifteen days—we learned is simply a convenient term meaning the speaker has no idea but imagines that the time is not entirely open ended. _"Quindici minuti,"_ we'd learned by missing a train, means a few minutes, not the fifteen it indicates, even when spoken by the train conductor about a departure. I think most Italians have a longer sense of time than we do. What's the hurry? Once up, a building will stand a long, long time, perhaps a thousand years. Two weeks, two months, big deal.
Removing the walls? He doesn't advise it. He makes gestures, indicating the house collapsing around us. Somehow, Benito will come up with a number and will give it to Ian this week. As he leaves he flashes a smile at last. His square yellow teeth look strong enough to bite through brick. Ian endorses him and discounts Nando as "the playboy of the western world." Ed looks pleased.
Our _geometra_ recommends the third contractor, Primo Bianchi, who arrives in an Ape, one of those miniature three-wheel trucks. He, too, is miniature, scarcely five feet tall, stout and dressed in overalls with a red kerchief around his neck. He rolls out and salutes us formally with an old word, _"Salve, signori."_ He looks like one of Santa's workers, with gold-rimmed glasses, flyaway white hair, tall boots. _"Permesso?"_ he asks before we go through the door. At each door he pauses and repeats, _"Permesso?"_ as though he might surprise someone undressing. He holds his cap in his hand in a way I recognize from my father's mill workers in the South; he's used to being the "peasant" speaking to the _"padrone."_ He has, however, a confident sense of himself, a pride I often notice in waiters, mechanics, delivery people here. He tries the window latches and swings the doors. Pokes the tip of his knife in beams to check for rot, wiggles loose bricks.
He comes to a spot in the floor, kneels and rubs two bricks that are a slightly lighter color. _"Io,"_ he says, beaming, pointing to his chest, _"molti anni fa."_ He replaced them many years ago. He then tells us he was the one who installed the main bath and that he used to come every December and help haul the big lemon pots that lined the terrace into the _limonaia_ for the winter. The house's owner was his father's age, a widower then, whose five daughters had grown and moved away. When he died, the daughters left the house vacant. They refused to part with it but no one cared for the place for thirty years. Ah, the five sisters of Perugia I imagine in their narrow iron beds in five bedrooms, all waking at once and throwing open the shutters. I don't believe in ghosts, but from the beginning I sensed their heavy black braids twisted with ribbons, their white nightgowns embroidered with their initials, their mother with silver brushes lining them up before the mirror each night for one hundred strokes.
On the upstairs terrace, he shook his head. The bricks must come up, then an underlayer of tarpaper and insulation installed. We had a feeling he knew what he was talking about. The central heating? "Keep the fire going, dress warmly, signora, the cost is formidable." The two walls? Yes, it could be done. Decisions are irrational. We both knew Primo Bianchi was the right man for the restoration.
IF THE GUN IS ON THE MANTEL IN CHAPTER ONE, THERE MUST be a bang by the end of the story.
The former owner had not just affirmed the bounty of water, he had waxed lyrical. It was a subject of great pride. When he showed us around the property's borders, he'd opened a garden faucet full blast, turning his hands in the cold well water. "This was a watering spot for the Etruscans! This water is known to be the purest—the whole Medici water system," he said, gesturing to the walls of the fifteenth-century fortress at the top of the hill, "runs through this land." His English was perfect. Without doubt, he knew about water. He described the watercourses of the mountains around us, the rich supply that flowed through our side of Monte Sant'Egidio.
Of course, we had the property inspected before we bought it. An impartial _geometra_ from Umbertide, miles away over the hills, gave us detailed evaluations. The water, he agreed, was plentiful.
While I am taking a shower after six weeks of ownership, the water slows, then trickles, then drips, then stops. Soap in hand, I stand there without comprehension for several moments, then decide the pump must have been turned off accidentally, or, more likely, the power has gone off. But the overhead light is on. I step out and rub off the soap with a towel.
Signor Martini drives out from his office bringing a long string marked with meters and a weight on the end. We lift the stone off the well and he lowers the weight. _"Poca acqua,"_ he announces loudly as the weight hits bottom. Little water. He hauls it up, black roots hanging off, and only a few inches of string are wet. The well is a measly twenty meters deep, with a pump that must have ushered in the Industrial Revolution. So much for the expertise of the impartial _geometra_ from Umbertide. That Tuscany is in the third year of a serious drought doesn't help either.
_"Un nuovo pozzo,"_ he announces, still louder. Meanwhile, he says, we will buy water from a friend of his who will bring it in a truck. Fortunately, he has a "friend" for every situation.
"Lake water?" I ask, imagining little toads and slimy green weed from Trasimeno. He assures us it's pure water, even has fluoride in it. His friend simply will pump umpteen liters into the well and it will be adequate for the rest of the summer. In fall, a new _pozzo,_ deep, with fine water—enough for a swimming pool.
The swimming pool had become a leitmotif while we were looking for houses. Since we are from California, everyone who showed us a house assumed that naturally we would want a pool first thing. I remembered that years ago, while visiting in the East, I was asked by the pale-faced son of a friend if I taught my classes in my bathing suit. I liked his vision. After owning a pool, I think the best way to enjoy the water is to have a friend who has a pool. Dealing with overnight neon green transformations of water is not in my vacation plans. There is trouble enough here.
And so we buy a truckload of water, feeling half foolish and half relieved. We only have two weeks left at Bramasole and paying Martini's friend certainly is cheaper than going to a hotel—and not nearly as humiliating. Why the water doesn't just seep into the dried-out water table, I don't know. We shower fast, drink nothing but bottled water, eat out frequently, and enrich the dry cleaners. All day we hear the rhythmic pounding of well-drilling equipment rising from the valley below us. Others, it seems, don't have deep wells either. I wonder if anyone else in Italy ever has had a load of water dumped into the ground. I keep confusing _pozzo,_ well, with _pazzo,_ crazy, which is what we must be.
By the time we start to get a grasp on what the place needs—besides water—and who we are here, it's time to go. In California, students are buying their texts, consulting their class schedules. We arrange for permit applications. The estimates are all astronomical—we'll have to do more of the work ourselves than I imagined. I remember getting a shock when I changed the switchplate on an electrical outlet in my study at home. Ed once put his foot through the ceiling when he climbed into the attic to check for a roof leak. We call Primo Bianchi and tell him we'd like for him to do the main work and will be in touch when the permits come through. Bramasole, fortunately, is in a "green zone" and a " _belle arti_ zone," where nothing new can be built and houses are protected from alterations that would change their architectural integrity. Because permits require both local and national approval, the process takes months—even a year. We hope Rizzatti is as well-connected as we have heard he is. Bramasole must stand empty for another winter. Leaving a dry well leaves a dry taste as well.
When we see the former owner in the piazza just before we leave, he is congenial, his new Armani tossed over his shoulders. "How is everything at Bramasole?" he asks.
"Couldn't be better," I reply. "We love everything about it."
AS I CLOSED THE HOUSE, I COUNTED. SEVENTEEN WINDOWS, each with heavy outside shutters and elaborate inside windows with swinging wooden panels, and seven doors to lock. When I pulled in the shutters, each room was suddenly dark, except for combs of sunlight cast on the floor. The doors have iron bars to hook in place, all except the _portone,_ the big front door, which closes with the iron key and, I suppose, makes the elaborate locking of the other doors and windows moot, since a determined thief easily could batter his way in, despite the solid _thumft, thumft_ of the lock turning twice. But the house has stood here empty through thirty winters; what's one more? Any thief who pushed into the dark house would find a lone bed, some linens, stove, fridge, and pots and pans.
Odd, to pack a bag and drive away, just leave the house standing there in the early morning light, one of my favorite times, as though we'd never been there at all.
We head toward Nice, across Tuscany toward the Ligurian coast. The toasted hills, fields of drooping sunflowers, and the exit signs with the magical names flash by: Montevarchi, Firenze, Montecatini, Pisa, Lucca, Pietrasanta, Carrara with its river milky with marble dust. Houses are totally anthropomorphic for me. They're so _themselves._ Bramasole looked returned to itself as we left, upright and contained, facing the sun.
I keep hearing myself singing, "The cheese stands alone" as we whiz in and out of tunnels. "What _is_ that you're singing?" Ed is passing cars at 140 kilometers an hour; I'm afraid he has taken rather naturally to the blood sport of Italian driving.
"Didn't you play The Farmer in the Dell in first grade?"
"I was into Capture the Flag. Girls played those singing games."
"I always liked it at the end when we boomed out, "The cheese stands alone,' emphasizing every syllable. It's sad to leave, knowing the house will just stand there all winter and we'll be busy and won't even think about it."
"Are you crazy—we'll be thinking every day about where we want things, what we'll plant—and how much we're going to be robbed."
At Menton, we check into a hotel and spend the late afternoon swimming in the Mediterranean. Italy is now that far off arm of land in the hazy twilight. Somewhere, light years away, Bramasole is now in shadow; the afternoon sun has dipped below the crest of the hill above us. Further light years away, it's morning in California; light is spilling into the dining room where Sister the cat is warming her fur on the table under the windows. We walk the long promenade into town and have bowls of _soupe au pistou_ and grilled fish. Early the next day we drive to Nice and fly away. As we speed down the runway, I glimpse a fringe of waving palms against the bright sky; then we lift off and are gone for nine months.
Sister Water,
Brother Fire
JUNE. WE'RE TOLD THAT WINTER WAS fierce and spring was unusually profligate with bloom. Poppies have lingered and the fragrance of spiky yellow broom still fills the air. The house looks as if more sun soaked in during these months I've been gone. The finish that faux painters all over creation are trying to perfect, the seasons have managed admirably. Otherwise, all is the same, giving me the illusion that the months away were only a few days. A moment ago I was hacking weeds and now I'm at it again, though frequently I stop. I am watching for the man with the flowers.
A sprig of oleander, a handful of Queen Anne's and fennel bound with a stem, a full bouquet of dog roses, dandelion puffs, buttercups, and lavender bells—every day I look to see what he has propped up in the shrine at the bottom of my driveway. When I first saw the flowers, I thought the donor was a woman. I would see her soon in her neat navy print dress with a market bag hung over the handlebars of a battered bicycle.
A bent woman in a red shawl does come early some mornings. She kisses her fingertips, then touches them to the ceramic Mary. I have seen a young man stop his car, jump out for a moment, then roar off. Neither of these brings flowers. Then one day I saw a man walking down the road from Cortona. He was slow and dignified. I heard the crunch of his steps on the road stop for a moment. Later, I found a fresh clump of purple sweet peas in the shrine, and yesterday's wild asters thrown down into the pile of other wilting and dead bundles.
Now I wait for him. He examines what wildflowers the roadside and fields offer, leans to pick what he fancies. He varies his selection, bringing new blooms as they spring up. I'm up on a high terrace, hacking ivy off stone walls and chopping off dry limbs of neglected trees. The profusion of flowers stops me every few minutes. I don't know enough of the English names, much less the Italian. One plant, shaped like a little tabletop Christmas tree, is spiked all over with white flowers. I think we have wild red gladioluses. Lusty red poppies literally carpet the hillsides, their vibrancy cooled by clusters of blue irises, now withering to an ashy gray. The grass brushes my knees. When I stop just to look, the pilgrim is approaching. He pauses in the road and stares up at me. I wave but he does not wave back, just blanky stares as though I, a foreigner, am a creature unaware of being looked at, a zoo animal.
The shrine is the first thing you see when you come to the house. Cut into a curved stone wall, it's an ordinary one in these parts, a porcelain Mary on a blue background, in the Della Robbia style, centered in an arched niche. I see other shrines around the countryside, dusty and forgotten. This one is, for some reason, active.
He's an old man, this wayfarer with his coat draped over his shoulders and his slow contemplative walk down the road. Once I passed him in the town park and he gravely said, _"Buon giorno,"_ but only after I spoke first. He had taken off his cap for a moment and I saw a fringe of white hair around his bald crown, which is bright as a lightbulb. His eyes are cloudy and remote, a stony blue. I also have seen him in town. He is not gregarious, does not join friends for coffee at bars, does not stop his stroll through the main street to greet anyone. I begin to get the idea that he is possibly an angel, since his coat always hangs around his shoulders, and since he seems to be invisible to everyone but me. I remember the dream I had the first night I spent here: I would discover one hundred angels one by one. This angel, though, has a body. He wipes his forehead with his handkerchief. Perhaps he was born in this house, or he loved someone here. Or the pointed cypresses that line this road, each one commemorating a local boy who died in World War I (so many from such a small town), remind him of friends. His mother was a great beauty and stepped into carriages on this spot, or his father was tight as a whip and forbade him to enter the house ever again. He thanks Jesus daily for saving his daughter from the perils of surgeons in Parma. Or perhaps this is just the far point of his daily walk, a pleasant habit, a tribute to the Walk God. Whatever, I hesitate to wipe the road dust from Mary's face, or shine the blue to gloss with a cloth, even to disturb the mound of stiff bouquets piled on the ground, still intact. There's a life in old places and we're always passing through. He makes me feel wide circles surrounding this house. I will be learning for years what I can touch and what I can't, and how I can touch. I imagine the five sisters of Perugia who held this family property, letting the closed stone rooms grow coats of fluffy white mold, letting vines strangle the trees, letting plums and pears thud to the ground summer after summer. They would not let go. As girls here, did they wake at the same moment in the mornings, push open the shutters of five bedrooms, and draw the same breath of new green air? Some such memory held the house to them.
Finally they let go and I, who simply happened by, now hold eighteenth-century maps showing where the property ends. At a triangular point below that, I discover cantilevered steps jutting out of a stone wall that was put together as neatly as a crossword puzzle. The sculptural integrity of limestone stairs extending into the air was only some farmer's ingenious method of stepping up to the next terrace. Lacy blue and gray lichen over the years erased the evidence of a foot, but when I run my hand over the step, I feel a slight dip in the center.
From this high terrace I look down on the house. In places where the plaster is broken, the stone called _pietra serena,_ square and solid, shows. In front, the two palm trees rising on either side of the front door make the house look as though it should be in Costa Rica or Tangier. I like palms, their dry rattle in the wind and their touch of the exotic. Over the double front door, with its fanlight, I see the stone and wrought-iron balcony, just large enough to step out on and admire the spilling geraniums and jasmine I will plant.
From this terrace, I can't see or hear the workers' chaos going on below. I see our olive trees, some stunted or dead from the famous freeze of 1985, others flourishing, flashing silver and green. I count three figs with their large improbable leaves, visualizing yellow lilies beneath them. I can rest here marveling over the hummocky hills, cypress-lined road, cerulean skies with big baroque clouds that look as if cherubs could peer from behind them, distant stone houses barely brushed in, neat (will ours ever look like that?) terraces of olive and grape.
That I have acquired a shrine amazed me. What amazes me more is that I have taken on the ritual of the man with the flowers. I lay the clippers down in the grass. He approaches slowly, the bouquet almost behind him. When he is at the shrine I never watch. Later, I will walk down the terrace, down the driveway to see what he left. The brilliant yellow broom called _ginestra_ and red poppies? Lavender and wheat? I always touch his blade of weed tying that ties them together.
ED IS TWO LEVELS UP, CHOPPING RAMPAGING IVY OUT OF A black locust tree. At every ominous crack or snap I expect to see him careening down the terraces. I pull at tough runners in a stone wall. Ivy kills. We have miles of the stuff. It causes stone walls to fall. Some of the trunks are as big as my ankle. I think of the ivy I have in pretty jardinières on my mantle in San Francisco, imagine that in my absence they will bolt, strangle the furniture, cover the windows. As I move along this wall, my footing becomes more canted because the terrace starts to angle down. The cool scents of crushed lemon balm and _nepitella,_ tiny wild mint, rise from around my feet. I lean into the wall, cut a runner of ivy, then rip it out. Dirt flies in my face and little stones crumble out, hitting my shoes. I disturb not at all a long snake taking a siesta. Its head is (how far?) in the wall, tail dangling out about two feet. Which way would he exit—back out or go farther in and U-turn? I skip ten feet on either side and begin to snip again. And then the wall disappears and I almost disappear into a hole.
I call Ed to come down. "Look—is this a well? But how could there be a well _in_ the wall?" He scrambles down to the terrace just above me and leans over to look. Where he is, both ivy and blackberries are unnaturally dense.
"It looks like an opening up here." He turns on the weed machine then, but when blackberries keep choking the filaments, he resorts to the grim-reaper scythe. Slowly, he uncovers a chute lined with stones. The immense back stone curves down like a playground slide and disappears underground, opening in the wall I'm trimming. We look at the terrace above him—nothing. But two terraces up, in a line from here, we see another unnaturally large blackberry clump.
Perhaps we just have water and wells on the brain. A few days before, when we arrived for the summer, we were greeted by trucks and cars along the road and a pile of dirt in the driveway. The new well, drilled by a friend of Signor Martini, was almost finished. Giuseppe, the plumber who was installing the pump, somehow had driven his venerable _cinque cento_ over a low stone edge of the driveway. He introduced himself to us politely, then turned to kick and curse the car. _"Madonna serpente! Porca Madonna!"_ The Madonna is a snake? A pig? He raced the engine but the three wheels remaining on the ground couldn't get enough traction to spin his axle off the stone. Ed tried to rock the car and dislodge it. Giuseppe kicked his car again. The three well drillers laughed at him, then helped Ed literally lift the toy-sized car off and over to level ground. Giuseppe hoisted the new pump out of the car and headed for the well, still muttering about the Madonna. We watched them lower it the three hundred feet down. This must be the deepest well in Christendom. They had hit water quickly but Signor Martini told them to keep going, that we never wanted to run out of water again. We found Signor Martini in the house, overseeing Giuseppe's assistant. Without our even thinking of it, they have moved the water heater from the older bathroom to the kitchen so we'll have hot water in our improvised kitchen this summer. I'm touched that he has had the house cleaned and has planted marigolds and petunias around the palm trees—a touch of civilization in the overgrown yard.
He looks tanned already and his foot is healed. "How is your business?" I ask. "Sell many houses to unsuspecting foreigners?"
_"Non c'è male,"_ not bad. He beckons for us to follow. At the old well, he pulls a weight out of his pocket and plunks it down the opening. Immediately we hear it hit water. He laughs. _"Pieno, tutto pieno."_ Over the winter the old well has completely filled.
I read in a local history book that Torreone, the area of Cortona where Bramasole sits, is a watershed; on one side of us, water runs to the Val di Chiana. On the other, water runs down to the valley of the Tiber. We already are intrigued by the underground cistern near the driveway. Shining a light down the round opening, we've contemplated the stone arch tall enough to stand under and a deep pool our longest stick can't measure. I remember a Nancy Drew I liked at nine, _The Mystery in the Old Well,_ though I don't recall the story. Medici escape routes seem more dramatic. Looking down into the cistern taps my first memory of historical Italy—Mrs. Bailey, my sixth-grade teacher, drawing the soaring arches of a Roman aqueduct on the board, explaining how ingenious the ancient Romans were with water. The Acqua Marcia was sixty-two miles long—that's two thirds of the way from Fitzgerald, Georgia, to Macon, she pointed out—and some of the arches still exist from the year 140. I remember trying to grasp the year 140, meanwhile overlapping the arches onto the Ben Hill County highway north.
The cistern opening seems to disappear into a tunnel. Though there is footing on either side of the pool, neither of us is brave enough to lower ourselves the fifteen dank feet underground to investigate. We stare into the dark, wondering how large the scorpions and vipers are, just out of sight. Above the cistern a _bocca,_ a mouth, opens in the stone wall, as though water should pour into the cistern.
As we strip the ivy's thick roots and webs off the stone walls, we realize that the chute we're uncovering must be connected to the opening above the cistern. Over the next few days we discover four stone chutes running downhill from terrace to terrace and ending at a large square mouth that goes underground for about twenty-five feet, then reappears on the lowest terrace above the cistern, just as we suspected. The backs of all the chutes have the big single stone curved for the water to flow down. When the channels are cleaned out, water will cascade into the cistern after rains. I start to wonder if, with a small recirculating pump connected to the cistern, perhaps some of the water can fall all the time. After the experience of the dry well, the trickle and splash of falling water would be music indeed. Fortunately, we didn't stumble into these chutes last year as we blithely meandered the terraces admiring wildflowers and identifying fruit trees.
On the third-level terrace wall, a rusted pipe crumbles off as we hack at thorny blackberries. At the base, we discover a flat stone. As we shovel off dirt and pour on water, it grows. Something gigantic is buried here. Slowly, we uncover the roughly carved stone sink that once was used in the kitchen, before the "improved" concrete sink was installed. I'm afraid it's broken but we scrub mud away, wedge it out of its hole with a pick, and find intact the single stone, four feet long, about eighteen inches wide and eight inches thick, with a shallow indented basin for washing and with drainage ridges chipped out on either side. The corner drain is clogged with roots. We've been sorry our house didn't have this original and very characteristic object. Many old houses have similar sinks in place, draining directly out the kitchen wall and off a scallop-shaped stone shelf into the yard. I would like to wash my glasses in this prototype sink. We'll put it against the house outside under the trees, a place to keep ice and wine for parties and to wash up after gardening. It has been used to scrub enough crusty pots in its day; from now on: an honored place to fill a glass, a place for a pitcher of roses on the stone. It will be returning to good use after many years buried in dirt.
After a few more minutes of chopping, I'm about twelve feet down from the stone sink when two rusted hooks appear under the leaves. Beneath them, again we see a glimpse of flat stone. Ed shovels off a mound of dirt. In the middle, he hits a latch, around which is twisted a rusty coil of wire. We make out a circular opening. He has to angle the shovel in the crack to pry up the long-covered stone lid.
It is late afternoon, just after a thunderstorm, when the light turns that luminous gold I wish I could bottle and keep. Off comes the lid and the light that falls down strikes clear water in a wide natural cleft of white stone. We can see another undulation of the stone, too, where the water becomes aqua. We lie on our stomachs on the ground, taking turns sticking our heads and the flashlight down the hole. Fig roots seeking moisture slither down the rock wall. On the bottom, we see a big can on its side and easily read the magnified green words _Olio d'Oliva._ Not exactly like finding a Roman torso or amphora with dancing satyrs. A rusty pipe leans against the back of the white stone and we notice that it emerges just below the two hooks—someone stopped it up with a wine cork. It now seems obvious that the hooks once secured a hand pump and that this is a lost natural spring, hidden for years. How long? But wait. Just beneath the stone covering lies a remnant of another opening. What appears to be a corner of two layers of carved travertine lintel angles for a couple of feet, then disappears into rock. If the top were dug away, would this be an open pool? I read about a man nearby who went in his backyard on Christmas Eve to pick lettuce for dinner and caved into an Etruscan tomb with elaborate sarcophagi. Is this simply a fortuitous opening in rock that supplied water for farming? Why the carving? Why was the carving recovered with a plainer stone? This must have been covered when the second well nearby was dug. Now we have a third well; we're the latest layer of water seekers, our technology—the high-whining drills able to pierce any rock—long removed from that of the discoverer of this secret opening in the earth.
We call Signor Martini to come see this miraculous finding. Hands in pockets, he doesn't even lean over. _"Boh,"_ he says ( _boh_ is an all purpose word, sort of "Well," "Oh," "Who knows?" or dismissal), then he waves a hand over it. _"Acqua."_ He regards our fascination with abandoned houses and such things as ancient wells as further evidence that we are like children and must be humored in our whimsies. We show him the stone sink and explain that we will dig it out, clean it, and have it put up again. He simply shakes his head.
Giuseppe, who has come along, gets more excited. He should have been a Shakespearean actor. He punctuates every sentence with three or four gestures—his body totally participates in every word he speaks. He practically stands on his head looking down the hole. _"Molta acqua."_ He points in both directions. We thought the well opened only in one, but because he is dangling upside down, he sees that the natural declivity of the rock extends in the opposite direction also. "O.K., yes!" These are his only English words, always uttered with arms wide apart, embracing an idea. He wants to install a new hand pump for garden use. We already have seen bright green pumps in the hardware store out in the Val di Chiana farm country. We buy one the next day, uncork the pipe, and place the pump right on the old hooks. Giuseppe teaches us to prime the pump by pouring water into it while pumping the handle rhythmically. Here's a motion long lost to my gene pool, but the creaky-smooth movement feels natural. After a few dry gulps, icy fresh water spills out into the bucket. We do have the presence of mind not to drink untested water. Instead, we open a bottle of wine on the terrace. Giuseppe wants to know about Miami and Las Vegas. We're looking out over the jungle growth on the hills. Giuseppe thinks the palm trees are what we really need to tend to. How will we ever trim them? They're taller than any ladder. After two glasses, Giuseppe shimmies up to the top of the taller one. He has the biggest grin I've ever seen. The tree leans and he slides down fast, too fast, lands in a heap on the ground. Ed quickly opens another bottle.
AS IT TURNS OUT, THE FORMER OWNER WAS RIGHT ABOUT THE water. If the water setup doesn't exactly rival the gardens of the Villa d'Este, it is ingenious enough to keep us digging and exploring for many days. The elaborate underground system makes us understand precisely how precious water is in the country. When it flows, you figure out ways to save it; when it is plentiful, as now, you must respect it. St. Francis of Assisi must have known this. In his poem "The Canticle of the Creatures," he wrote, "Be praised, O Lord, for Sister Water, the which is so useful, humble, precious and chaste." We convert instantly to short showers, to turning off the water quickly when washing dishes and brushing our teeth.
Interesting that this oldest well has channels on either side of it to divert runoff so that any extra water flows into the cistern. As we clean around the cistern, we find two stone tubs for washing clothes and more hooks in the stone wall above it, where another pump must have hung. Do not waste a drop. And there, not five feet away from the natural well, the old one that went dry last summer—now replenished fully by the winter rains. The hand pump for potted plants, Ed decides, the old well for the grass, and for the house, our fine new _pozzo,_ a hundred meters deep, drilled through solid rock.
"Wonderful water," the _pozzaiolo,_ the well driller, assures us as we pay him a fortune, "down to inferno but cold as ice." We count out the cash. He does not want a check; why would anyone use a check unless they didn't actually have the money? _"Acqua, acqua,"_ he says, gesturing over the entire property. "Enough water for a swimming pool."
WE NOTICED, VAGUELY, WHEN WE BOUGHT THE HOUSE THAT A stone wall perpendicular to the front had tumbled down in a few places. Weeds, sumac, and fig sprouted along the fallen rocks. The first time we saw the house the section of the yard above that wall was topped with forty feet of rose-covered pergola lined with lilacs. When we returned to negotiate for the purchase, the pergola was gone, torn down in a zeal to clean up the place. The roses and lilacs were leveled. When I lifted my eyes from that debacle to the house, I saw that the faded green shutters were repainted a glossy dark brown. Stunned, we hardly noticed the heaps of stones. Later, we realized that a 120-foot-long wall of immense stone would have to be rebuilt. We forgot about the romantic pergola with its climbing roses.
During those few weeks here last summer after buying the house, Ed started to take down parts of the wall adjacent to the tumbled sections. He thought stone building sounded gratifying—finding just the right stone to slide into place, tapping it in with a mallet, scoring stone surfaces, hitting them precisely to direct the split. The ancient craft is appealing; so is the good hard labor. An alarming pile of stones grew daily, as did his muscles. He became a little obsessed. He bought thick leather gloves. Big rocks went in one line, small ones in another, and flat ones in another. Like all the terrace walls on the property, this was drywall, with a depth of more than a yard: nicely fitted and stacked stones in front, neat as a jigsaw, with smaller ones behind. The structure leaned backward, to counteract the natural downward heave of the hillside. Unlike the lovely stone fences of New England, which cleared the fields of stone, these actually are structural; only with braced terraces is a hillside like ours an olive farm or vineyard. On one terrace where the stones fell, a large almond tree also toppled.
When we had to leave, about thirty feet of the wall lay in orderly piles. Ed was enthusiastic about stonework, though slightly daunted by the excavation and the surprising depth of stonework behind the facade of the wall. But instead of the miles to go, we noticed the huge heaps of stones he'd stacked.
Over the winter we read _Building with Stone_ by Charles McRaven. Ideas such as sealing out moisture and foundations and frost lines started to crop up. The height of the remaining wall was not the actual height the rebuilt wall would have to be to support the broad terrace leading up to the house. Besides being 120 feet long, the wall must be fifteen feet high, buttressed from behind. As we read about packed fill, thrust, balance, and all the ways the earth shifts when it freezes, we began to think we had the Great Wall of China on our hands.
We were absolutely right. We've just had several experienced _muratori,_ masons, out to view the remains. This job is a monster. Restoration work inside seems dwarfed beside this project. Still, Ed envisions himself apprenticed to a rugged man in a cap, a stone artist. _Santa Madonna, molto lavoro,_ much work, each _muratore_ exclaims in turn. _Molto. Troppo,_ too much. We learn that Cortona recently adopted codes for walls such as this one because we're in an earthquake zone. Reinforced concrete will be required. We are not prepared to mix concrete. We have five acres of blackberry and sumac jungle to deal with, trees that need pruning. Not to mention the house. The wall estimates are astronomical. Few even want to tackle the job.
This is how in Tuscany we build the Great Wall of Poland.
Signor Martini sends a couple of his friends by. I forewarn him that we are interested in getting the work done immediately and that we want a price for _fratelli,_ brothers, not for _stranieri,_ foreigners. We are recovering from the new well and still awaiting permits so the major house work can begin. His first friend says sixty days of labor. For his price we could buy a small steamer and motor around Greece. The second friend, Alfiero, gives a surprisingly reasonable estimate, plus has the terrific idea that another wall should run along the row of linden trees on an adjacent terrace. When you don't speak a language well, many of your cues for judging people are missing. We both think he is fey—an odd quality for a mason—but Martini says he is _bravo._ We want the work done while we are in residence, so we sign a contract. Our _geometra_ doesn't know him and cautions us that if he's available he probably is not good. This kind of reasoning doesn't sink in with us.
The schedule calls for work to begin the following Monday. Monday, Tuesday, and Wednesday pass. Then a load of sand arrives. Finally, at the end of the week, Alfiero appears with a boy of fourteen and, to our surprise, three big Polish men. They set to work and by sundown, amazingly, the long wall is down. We watch all day. The Poles lift one-hundred-pound stones as though they were watermelons. Alfiero speaks not a word of Polish and they speak about five words of Italian. Fortunately, the language of manual labor is easy to act out. _"Via, via,"_ Alfiero waves at the stones and they have at them. The next day they excavate dirt. Alfiero exits, to go to other jobs, I suppose. The boy, Alessandro, purely pouts. Alfiero is his stepfather and evidently is trying to teach the boy about work. He looks like a little Medici prince, petulant and bored as he stands around listlessly kicking stones with the toe of his tennis shoe. The Poles ignore him. From seven until twelve they don't stop. At noon they drive off in their Polski Fiat, returning at three for five more solid hours of labor.
The Italians, who have been "guest workers" at many times and in many countries, are thrown by the phenomenon happening in their own country. During this second summer at Bramasole, the newspapers are tolerant to indignant about Albanians literally washing up on the shores of southern Italy. Living in San Francisco, a city where immigrants arrive daily, we cannot get excited about their problem. Americans in cities have realized that migrations are on the increase; that the whole demographic tapestry is being rewoven on a vast scale in the late twentieth century. Europe is having a harder time coming to grips with this fact. We have our own poor, they tell us incredulously. Yes, we say, we do, too. Italy is amazingly homogeneous; it is rare to see a black or Asian face in Tuscany. Recently, Eastern Europeans, finding the German work force at last full of people like themselves, began arriving in this prosperous part of northern Italy. Now we understood Alfiero's estimate for the work. Instead of paying the normal Italian twenty-five thousand to thirty thousand lire per hour, he is able to pay nine thousand. He assures us they are legal workers and are covered by his insurance. The Poles are pleased with the hourly wage; at home, before the factory went kaput, they barely earned that much in a day.
Ed grew up in a Polish-American Catholic community in Minnesota. His parents were born of Polish immigrants and grew up speaking Polish on farms on the Wisconsin-Minnesota border. Of course, Ed knows no Polish. His parents wanted the children to be All American. The three words he tried out with the Poles they couldn't understand. But these men he can't understand seem very familiar. He's used to names like Orzechowski, Cichosz, and Borzyskowski. Passing in the yard, we nod and smile. The way we finally make contact with them comes through poetry. One afternoon I come across a poem by Czeslaw Milosz, long exiled in America but quintessentially a Polish poet. I knew he'd made a triumphant journey back to Poland a few years ago. When Stanislao crossed the front terrace with the wheelbarrow, I asked, "Czeslaw Milosz?" He lit up and shouted to the two others. After that, for a couple of days, when I passed one or the other of them, he would say, "Czeslaw Milosz," as though it were a greeting, and I would answer, _"Sì,_ Czeslaw Milosz." I even knew I was pronouncing the name correctly because I'd once practiced his name when I had to introduce the poet at a reading. For several days before that, I'd referred to him to myself as "Coleslaw" and had anxiety that I would stand up before the audience and introduce him that way.
Alfiero becomes a problem. He lights like a butterfly on one project after another, starting something, doing a sloppy job, then taking off. Some days he just doesn't show up at all. When reasonable questioning doesn't work, I revert to the old Southern habit of throwing a fit, which I find I still can do impressively. For a while, Alfiero straightens up and pays attention, then like the whimsical child that he is, he loses his focus. He has a charm. He throws himself into playful descriptions of frog races, fast Moto Guzzis, and quantities of wine. Patting his belly, he speaks in the local dialect and neither of us understands much of what he says. When it's time to throw a fit, I call Martini, who does understand. He nods, secretly amused, Alfiero looks abashed, the Poles let no expression cross their faces, and Ed is mortified. I say that I am _malcontenta._ I use waving gestures and shake my head and stamp my foot and point. He has used rows of tiny stones under rows of big stones, there are vertical lines in the construction, he has neglected to put a foundation in this entire section, the cement is mostly sand. Martini begins to shout, and Alfiero shouts back at him, since he dares not shout at me. I hear the curse _"Porca Madonna"_ again, a serious thing to say, and _"Porca miseria,"_ pig misery, one of my favorite curses of all times. After a scene, I expect sulking but, no, he turns up sunny and forgetful the next day.
_"Buttare! Via!"_ Take it down, take it away. Signor Martini starts to kick at Alfiero's work. "Where did your mother send you to school? Where did you learn to make cement like sand castles?" Then they both turn and shout at the Poles. Now and then Martini rushes in the house and calls Alfiero's mother, his old friend, and we hear him shouting at her, then subsiding into soothing sounds.
They must think, privately, that we are brilliant to know so much about wall building. What neither Signor Martini nor Alfiero realizes is that the Poles let us know when something is not right. _"Signora,"_ Krzysztof (we call him Cristoforo, as he wishes) says, motioning to me, _"Italia cemento."_ He crumbles too-dry cement between his fingers. _"Polonia cemento."_ He kicks a rock-hard section of the retaining wall. This has become a nationalistic issue. "Alfiero. _Poco cemento._ " He puts his fingers to his lips. I thank him. Alfiero is using too little cement in his mixture. Don't tell. They begin to roll their eyes as a signal, or, after Alfiero departs, which usually is early in the day, to show us problems. Everything Alfiero touches seems bad, but we have a contract, they work for him, and we are stuck with him. However, without him, we would not have met the Poles.
Near the top of the wall, they uncover a ground-level stump. Alfiero maintains it is _non importa._ We see Riccardo shake his head quickly, so Ed says authoritatively that it will have to be dug out. Alfiero relents but wants to pour on _gasolio_ to kill it. We point to the pristine new well not twenty feet away. The Poles began to dig and two hours later are still digging. Beneath the exposed stump, a mammoth three-legged root has wrapped itself around a stone as big as an automobile tire. Hundreds of inveigling roots shoot out in all directions. Here is the reason much of the wall had fallen in the first place. When they finally wrench it out, they insist on evening the legs and top, the stone still entwined. They load it in a wheelbarrow and take it up to the lime tree bower, where it will remain, the ugliest table in Tuscany.
They sing while they heave stone and their voices begin to sound like the way the work of the world should sound. Sometimes Cristoforo sings in a falsetto, a strangely moving song, especially coming from his big brown body. They never skimp on a minute's work, even though their boss is gone all the time. On days when their supplies are gone because Alfiero forgets to reorder, he capriciously tells them not to work. We hire them to help clear the terraces of weeds. Finally we have them sanding all the inside shutters. They seem to know how to do everything and work about twice as fast as anyone I've ever seen. At the end of the day, they strip and rinse off with the hose, dress in clean clothes, then we have a beer.
Don Fabio, a local priest, lets them live in a back room of the church. For about five dollars apiece, he feeds all three of them three meals a day. They work six days a week—the priest does not allow them to work on Sunday—exchanging all the lire they make into dollars and stashing it away to take home for their wives and children. Riccardo is twenty-seven, Cristoforo thirty, and Stanislao forty. During the weeks they work, our Italian deteriorates. Stanislao has worked in Spain, so our communication begins to be an unholy mixture of four languages. We pick up Polish words: _jutro,_ tomorrow; _stopa,_ foot; _brudny,_ dirty; _jezioro,_ lake. Also something that sounds like _grubbia,_ which was their name for Signor Martini's sloping stomach. They learned "beautiful" and "idiot" and quite a few Italian words, mostly infinitives.
Despite Alfiero, the wall is strong and beautiful. A curving flight of stairs, with flat tops on either side for pots of flowers, connects the first two terraces. The well and cistern have stone walls around them. From below, the wall looks immense. It's hard to get used to, since we liked the tumbled look, too. Like the other walls, soon it will have tiny plants growing in the cracks. Because the stone is old, it already looks natural in the landscape, if a bit tall. Now comes the pleasure of planning the walkway from the driveway around the well to the stone steps, the flowers and herbs for the border, and the flowerings and shadows of small trees along the wall. First we plant a white hibiscus, which pleases us by blooming immediately.
On a Sunday morning the Poles arrive after church, dressed in pressed shirts and trousers. We've seen them only in shorts. They've bought identical sandals at the local supermarket. Ed and I are clipping weeds when they arrive. We're dirty, wearing shorts, sweaty—reversed roles. Stanislao has a Soviet Union camera that looks to be from the thirties. We have Coca-Cola and they take several pictures. Anytime we serve them Coke, they always say, "Ah, America!" Before changing for work, they take us down to the wall and dig the dirt away from a few feet of the foundation. In large letters, they've written POLONIA in the concrete.
BRAMASOLE'S STAIRCASE ASCENDS THREE FLOORS WITH A HANDMADE wrought-iron railing, whose symmetrical curves add a little rhythm to climbing. The fanlight, the bedroom terrace railing, only slightly rusted, and the railing around the balcony above the front door all employed some blacksmith for a long winter. The gate at the bottom of the driveway once was a stately entrance but like most things here, has been left to time far too long. The bottom bulges where lost tourists banged into it while turning around, after realizing they were on the wrong road to the Medici fortress. The lock has long since rusted and the hinges on one side have given way at the top, letting the gate drag.
Giuseppe has brought a friend, a maestro of iron, to see if our front gate can be salvaged. Giuseppe thinks not. We need something more suitable for the _bella villa._ The man who unfolds from Giuseppe's _cinque cento_ could have stepped from behind a time shield of the Middle Ages. He is as tall and gaunt as Abraham Lincoln; he wears black overalls and his unusually black hair has no gleam. Hard to account for his strangeness; somehow he looks as though he's made out of something else. He uses few words but smiles shyly. I like him at once. Silently, he fingers the gate all over. Everything he has to say runs through his hands. It's easy to sense that he has given his life to this craft out of love. Yes, he nods, the gate can be repaired. The question is time. Giuseppe is disappointed. He envisions something grander. He draws shapes in the air with his arms, an arching top with arrows. A new one, more elaborate, with lights and an electronic device so we can be buzzed in the house and merely press a button for the gate to swing open. He has brought us this artist and we want him to _repair_?
We go to the shop to see the possibilities. En route, Giuseppe careens to the roadside and we leap out to see other gates this maestro has made. Some with swordlike designs, some with complex interlinking circles and wheat sheaves. One is topped with the initials of the owner, one, oddly, with a crown. We like the curved tops, the hoops and rings more than the more formidable arrow-topped ones, which seem like remnants of the time when the Guelfs and Ghibellines were looting and burning each other. All are obviously made to last forever. He rubs each one, saying nothing, letting the quality of his work speak for itself. I begin to imagine a small stylized sun at the center of ours, with twisted rays.
_Ferro battuto,_ wrought iron, is an ancient craft in Tuscany. Every town has intricate locks on medieval doors, curly lanterns, holders for standards, garden gates, even fanciful iron animals and serpents shaped into rings for tying horses to the wall. Like other artisan traditions, this one is fast disappearing and it's easy to see why. The key word in blacksmith is black. His shop is charred, soot covers him, the antiquated equipment, and the forges that seem to have changed very little since Hephaestus lit the fire in Aphrodite's stove. Even the air seems hung with a fine veil of soot. All his neighbors have gates made by him. It must be satisfying to see one's work all around like that. His own house has a square patterned balcony, a flirtation, no doubt, with _moderne,_ redeemed by attached baskets for flowers. The shop faces the house and between them are hens, ten or so cages of rabbits, a vegetable garden, and a plum tree with a handmade wooden ladder leaning up into the laden branches. After supper, he must climb up a few rungs and pick his dessert. My impression that he stepped out of time strengthens. Where _is_ Aphrodite, surely somewhere near this forge?
"Time. Time is the only thing," he says. "I am _solo._ I have a son but . . ."
I can't imagine, at the end of the twentieth century, someone choosing this dark forge with traffic whizzing by, this collection of bands for wine barrels, andirons, fences, and gates. But I hope his son does step into it, or someone does. He brings over a rod that ends with a squared head of a wolf. He just holds it out to me, without a word. It reminds me of torch holders in Siena and Gubbio. We ask for an estimate to repair the _cancello,_ also for an estimate for a new gate, rather simple but with a running form similar to the iron stair railing in the house, maybe a sun shape at the top closing, to go with the house's name. For once, we don't start asking for the date of completion, the one thing we've learned to insist on to counter the enviable Latin sense of endless time.
Do we really need a handmade gate? We keep saying, Let's keep it simple, this is not our real home. But somehow I know we'll want one he makes, even if it takes months. Before we leave, he forgets us. He's picking up pieces of iron, holding them in both hands for the heft or balance. He wanders among the anvils and hot grates. The gate will be in good hands. Already I can imagine its clank as I close it behind me.
THE WELL AND THE WALL FEEL LIKE SIGNIFICANT accomplishments. The house, however, still is untouched. Until the main jobs are finished, there is little to do. No point in painting, when the walls will have to be opened for the heating pipes. The Poles have stripped the windows and have begun scrubbing down the whitewash in preparation for painting. Ed and I work on the terraces or travel around selecting bathroom tile, fixtures, hardware, paint; we look, too, for the old thin bricks for the new kitchen's floor. One day we buy two armchairs at a local furniture store. By the time they're delivered, we realize they're awkward and the dark paisley fabric rather weird, but we find them sumptuously comfortable, after sitting upright in the garden chairs for weeks. On rainy nights we pull them face-to-face with a cloth-covered crate between them, our dining table with a candle, jam jar with wildflowers, and a feast of pasta with eggplant, tomatoes, and basil. On cool nights we build a twig fire for a few minutes, just to take the damp chill off the room.
Unlike last summer, this July is rainy. Impressive storms hit frequently. In the daytime, I'm thrilled because of my childhood in the South, where they really know how to put on the sound and light. San Francisco rarely has thunderstorms and I miss them. "This heat has to break," my mother would say, and it would, with immense cracks and bolts followed by sheet lightning when the whole sky flashes on a million kilowatts. Often the storms seem to arrive at night. I'm sitting up in bed, drawing kitchen and bathroom plans on graph paper; Ed is reading something I never expected to see him reading. Instead of the Roman poets, tonight it's _Plastering Skills._ Beside him is _The Home Water Supply._ Rain starts to clatter in the palm trees. I go to the window and lean out, then quickly step back. Bolts spear into the ground—jagged like cartoon drawings of lightning—four, five, six at once, surrounding the house. Thunderheads swarm over the hills and the quiet rolling suddenly changes its tune and starts to explode so close it feels like my own backbone snapping. The house shakes; this is serious. The lights go out. We fasten the windows inside and still the wind whips rain through cracks we didn't know were there. Spooky wind sucks in and out of the chimney. Wild night. Rain lashes the house and the two silly palms give and give in the wind. I smell ozone. I am certain the house has been struck. This storm has selected our house. It won't move on; we're the center and may be washed downhill to Lake Trasimeno. "Which would you prefer," I ask, "landslide or direct hit by lightning?" We get under the covers like ten-year-olds, shouting "Stop!" and "No!" each time the sky lights up. Thunder enters the walls and rearranges the stones.
When the big storm starts passing to the north, the black sky is left washed clean for stars. Ed opens the window and the breeze sends in pine scent from blown-down limbs and scattered needles. The electricity still is out. As we sit propped up on pillows, waiting for our hearts to slow down, we hear something at the window. A small owl has landed on the sill. Its head swivels back and forth. Perhaps its perch was blown down or it is disoriented by the storm. When the moon breaks through the clouds, we can see the owl staring inside at us. We don't move. I'm praying, Please don't come in the room. I am deathly afraid of birds, a holdover phobia from childhood, and yet I am entranced by the small owl. Owls seem always to be more than themselves, totemic in America, symbolic at least, and here, mythological as well. I think of Minerva's owl. But really it's just a small creature that belongs to this hill. We have seen its larger forebears several times at evening. Neither of us speaks. Since it stays, we finally fall asleep and wake in the morning to see that it has flown. At the window, only the quarter of six light—raked gold angling across the valley, suffusing the air briefly before the sun clears the hills and lifts into the absolved, clear day.
The
Wild Orchard
THE WATERMELON HOUR—A FAVORITE pause in the afternoon. Watermelon is arguably the best taste in the world, and I must admit that the Tuscan melons rival in flavor those Sugar Babies we picked hot out of the fields in South Georgia when I was a child. I never mastered the art of the thump. Whether the melon is ripe or not, the thump sounds the same to me. Each one I cut, however, seems to be at its pinnacle—toothy crispness, audacious sweetness. When we're sharing melon with the workers, I notice that they eat the white of the melon. When they finish, their rind is a limp green strip. Sitting on the stone wall, sun on my face, big slice of watermelon—I'm seven again, totally engrossed in shooting seeds between my fingers and spooning out circles from the dripping quarter moon of fruit.
Suddenly, I notice the five pine trees edging the driveway are full of activity. It sounds as though squirrels are pulling Velcro apart, or biting into _panini,_ those hard Italian rolls. A man leaps from his car, quickly picks up three cones, and speeds off. Then Signor Martini arrives. I expect he's bringing news of someone who can plow the terraces. He picks up a cone and shakes it against the wall. Out come black nubs. He cracks one with a rock and holds up a husk-covered oval. _"Pinolo,"_ he announces. Then he points to the dusky beads scattered all over the driveway. _"Torta della nonna,"_ he states, in case I missed the significance. Better still, I think, pesto to make with all the proliferating basil that resulted from sticking six plants in the ground. I love pine nuts on salads. Pine nuts! And I've been stepping on them.
Of course I knew that _pinoli_ come from pine trees. I've even inspected trees in my yard at home to see if, somewhere hidden in the cone, I would find pine nuts. I never thought of the trees lining the driveway as the bearers; thus far they simply have been trees that need no immediate attention. They're those painterly-looking pines, sometimes stunted by coastal winds, that line many Mediterranean beach towns, the kind Dante wandered among at Ravenna when he was in exile there. These along the driveway are feathery and tall. Imagine that plain _pino domestico_ (I see in my tree book) will yield those buttery nuts, so delicious when toasted. One of the _nonnas_ who make all those heavy _pinolo_ studded tarts must have lived here. She must have made delectable ravioli with ground _nocciole,_ hazelnut, stuffing, and macaroons and other _torte,_ too, because there also are twenty almonds and a shady hazelnut tree that droops with its crop of nuts. The _nocciola_ grows with a chartreuse ruff around the nut, as though each one is ready to be worn in a lapel. The almonds are encased in tender green velvet. Even the tree that collapsed over the terrace and must be dying has sent out a plentiful crop.
Perhaps Signor Martini should be back at the office, prepared to show more foreign clients houses without roofs or water, but he joins me picking up the _pinoli._ Like most Italians I've met, he seems to have time to give. I love his quality of becoming involved in the moment. The sooty covering quickly blackens our hands. "How do you know so many things—were you born in the country?" I ask. "Is this the one day the cones fall?" He has told me previously that the hazelnuts are ripe on August 22, feast day of the foreign St. Filbert.
He tells me he grew up in Teverina, on down the road from Bramasole's _località,_ and lived there until the war. I would love to know if he turned partisan or if he stuck to Mussolini until the end, but I merely ask if the war came near Cortona. He points up to the Medici fortress above the house. "The Germans occupied the fort as a radio communication center. Some of the officers quartered in the farmhouses came back after the war and bought those places." He laughs. "Never understood why the peasants weren't helpful." We've piled twenty or so cones on the wall.
I don't ask if this house was occupied by Nazis. "What about the partisans?"
"Everywhere," he says, gesturing. "Even thirteen-year-old boys—killed while picking strawberries or tending sheep. Shot. Mines everywhere." He does not continue. Abruptly, he says his mother died at ninety-three a few years ago. "No more _torta della nonna._ " He is in a wry mood today. After I squash several _pinoli_ flat with a stone, he shows me how to hit so that the shell releases the nut whole. I tell him my father is dead, my mother confined since a major stroke. He says he is now alone. I don't dare ask about wife, children. I have known him two summers and this is the first personal information we have exchanged. We gather the cones into a paper bag and when he leaves he says, _"Ciao."_ Regardless what I've learned in language classes, among adults in rural Tuscany _ciao_ is not tossed about. _Arrivederla_ or, more familiarly, _arrivederci_ are the usual good-byes. A little shift has occurred.
After half an hour of banging pine nuts, I have about four tablespoons. My hands are sticky and black. No wonder the two-ounce cellophane bags at home are so expensive. I have in mind that I will make one of those ubiquitous _torta della nonnas,_ which seem sometimes to be the beginning and end of Italian desserts. The French and American variety of desserts is simply not of interest in the local cuisine. I'm convinced you have to have been raised on most Italian sweets to appreciate them; generally, their cakes and pastries are too dry for my palate. _Torta della nonna,_ fruit tarts, perhaps a _tiramisu_ (a dessert I loathe)—that's it, except in expensive restaurants. Most pastry shops and many bars serve this grandmother's torte. Though they can be pleasing, sometimes they taste as though _intonaco,_ plaster, is one of the ingredients. No wonder Italians order fruit for dessert. Even gelato, which used to be divine all over Italy, is not dependably good anymore. Though many advertise that the gelato is their own, they neglect to say it's sometimes made with envelopes of powdered mix. When you find the real peach or strawberry gelato, it's unforgettable. Fortunately, fruit submerged in bowls of cool water seems perfect at the end of a summer dinner, especially with the local _pecorino,_ Gorgonzola, or a wedge of _parmigiano._
Translating grams into cups as best I can, I copy a recipe from a cookbook. Hundreds of versions of _torta della nonna_ exist. I like the kind with polenta in the cake and a thin layer of filling in the middle. I don't mind the extra hour to pound open the pine nuts that at home I would have pulled from the freezer. First, I make a thick custard with two egg yolks, 1/3 cup flour, 2 cups milk, and ½ cup sugar. This makes too much, for my purposes, so I pour two servings into bowls to eat later. While the custard cools, I make the dough: 1–½ cups polenta, 1–½ cups flour, 1/3 cup sugar, 1–½ teaspoons baking powder, 4 oz. butter cut into the dry ingredients, one whole egg plus one yolk stirred in. I halve the dough and spread one part in a pie pan, cover with custard, then roll out the other half of the dough and cover the custard, crimping the edges of the dough together. I sprinkle a handful of toasted pine nuts on top and bake at 350° for twenty-five minutes. Soon the kitchen fills with a promising aroma. When it smells done, I place the golden _torta_ on the kitchen windowsill and dial Signor Martini's number. "My _torta della nonna_ is ready," I tell him.
When he arrives I brew a pot of espresso, then cut him a large piece. With the first forkful, he gets a dreamy look in his eyes.
_"Perfetto"_ is his verdict.
BESIDES THE NUTS, THE ORIGINAL _NONNA_ PLANNED MORE OF an Eden here. What's left: three kinds of plums (the plump Santa Rosa type are called locally _coscia di monaca,_ nun's thigh), figs, apples, apricots, one cherry (half dead), apples, and several kinds of pears. Those ripening now are small green-going-to-russet, with a crisp sweetness. Her gnarly apples—I'd love to know what varieties they are—may not be salvageable, but they're now putting forth dwarfish fruit that looks like the before pictures in ads for insect sprays. Many of the trees must be volunteers; they're too young to have been alive when someone lived here, and often they're in odd places. Since four plums are directly below a line of ten on a terrace, they obviously sprang from fallen fruit.
I'm sure she gathered wild fennel, dried the yellow flowers, and tossed the still-green bunches onto the fire when she grilled meat. We uncover grapes buried in the brush along the edges of the terraces. Some aggressive ones still send out long tangles of stems. Tiny bunches are forming. Along the terraces like a strange graveyard, the ancient grape stones are still in place—knee-high stones shaped like headstones, with a hole for an iron rod. The rod extends beyond the edge of the terrace, thereby giving the grower more space. Ed strings wire from rod to rod and lifts the grapes up to train them along the wire. We're amazed to realize that the whole place used to be a vineyard.
At the huge _enoteca_ in Siena, a government-sponsored tasting room where wines from all over Italy are displayed and poured, the waiter told us that most Italian vineyards are less than five acres, about our size. Many small growers join local cooperatives in producing various kinds of wine, including _vino da tavola,_ table wine. As we hoe weeds around the vines, naturally, we begin to think of a year 2000 Bramasole Gamay or Chianti. The uncovered grapes explain the heaps of bottles we inherited. They may yield the rough-and-ready red served in pitchers in all the local restaurants. Or perhaps the flinty Grechetto, a lemon white wine of this area. Ah, yes, this land was waiting for us. Or we for it.
_Nonna's_ most essential, elemental ingredient surely was olive oil. Her woodstove was fired with the prunings; she dipped her bread in a plate of oil for toast, she doused her soups and pasta sauces with her lovely green oil. Cloth sacks of olives hung in the chimney to smoke over the winter. Even her soap was made from oil and the ashes from her fireplace. Her husband or his employee spent weeks tending the olive terraces. The old lore was to prune so that a bird could fly through the main branches without brushing its wings against the leaves. He had to know exactly when to pick. The trees can't be wet or the olives will mildew before you can get them to the mill. To prepare olives to eat, all the bitter glucoside must be leached out by curing them in salt or soaking them in lye or brine. Besides the practical, a host of enduring superstitions determine the best moment to pick or plant; the moon has bad days and good. Vergil, a long time ago, observed farmers' beliefs: Choose the seventeenth day after the full moon to plant, avoid the fifth. He also advises scything at night, when dew softens the stubble. I'm afraid Ed might veer off a terrace if he tried that.
Of our olives, some are paradigms—ancient, twisted, gnarled. Many are clusters of young shoots that sprang up in a circle around damaged trunks. In this benign crescent of hillside, it's hard to imagine the temperature dropping to minus six degrees, as it did in 1985, but gaps between trees reveal huge dead stumps. The olives will have to be revived from their long neglect. Each tree needs to be cleared of encroaching sumac, broom, and weeds, then pruned and fertilized. The terraces must be plowed and cleaned. This is major work but it will have to wait. Since olives are almost immortal, another year won't hurt.
"An olive leaf he brings, pacific sign," Milton wrote in _Paradise Lost._ The dove that flew back to the ark with the branch in its beak made a good choice. The olive tree does impart a sense of peace. It must be, simply, the way they participate in time. These trees are here and will be. They were here. Whether we are or someone else is or no one, each morning they'll be twirling their leaves and inching up toward the sun.
A few summers ago, a friend and I hiked in Majorca above Soller. We climbed across and through miles of dramatic, enormous olives on broad terraces. Up high, we came upon stone huts where the grove tenders sheltered themselves. Although we got lost and encountered a pacing bull in a meadow, we felt this immense peace all day, walking among those trees that looked and may have been a thousand years old. Walking these few curving acres here give me the same feeling. Unnatural as it is, terracing has a natural feel to it. Some of the earliest methods of writing, called boustrophedon, run from right to left, then from left to right. If we were trained that way, it probably is a more efficient way to read. The etymology of the word reveals Greek roots meaning "to turn like an ox plowing." And that writing is like the rising terraces: The U-turn space required by an ox with plow suddenly loops up a level and you're going in the other direction.
THE FIVE _TIGLIO_ TREES, OLD WORLD LINDENS OR LIMES, bear no fruit. They provide shade along the broad terrace beside the house when the sun will not allow us on the front terrace. We have lunch under the _tigli_ almost every day. Their blossoms are like pearly earrings dangling from the leaves, and when they open—all it seems on the same day—fragrance envelopes the whole hillside. At the height of bloom, we sit on the upstairs patio, just adjacent to the trees, trying to identify the fragrance. I think it smells like the perfume counter in the dime store; Ed thinks it smells like the oil his uncle Syl used to slick back his hair. Either way, it attracts every bee in town. Even at night, when we take our coffee up to the patio, they are working the flowers over. Their collective buzz sounds like a major swarm approaching. It's both lulling and alarming. Ed stays in the doorway at first because he's allergic to bee sting, but they aren't interested in us. They have their honey sacs to fill, their legs to dust with pollen.
Allergic or not, Ed longs for beehives. He tries to get me interested in being the beekeeper. He takes the fact that I never have been stung by a bee to mean that they won't sting me. I point out that I once was stung by a whole nest of wasps but somehow that doesn't count. He imagines a row of hives at the end of the lime trees. "You'll be fascinated when you look in the hive," he says. "When it's hot, dozens of workers stationed at the door whir their wings to cool the queen." I've noticed that he has collected lots of local honeys. Frequently there's a pot of hot water on the stove with a jar of waxy, stiff honey softening in it. The acacia is pale and lemony; the dark chestnut is so thick a spoon will stand up straight in it. He has a jar of _timo,_ thyme honey, and, of course, the _tiglio._ The wildest is _macchia,_ from the salty coastal shrubs of Tuscany. "The queen bee's life is totally overrated. All she does is lay eggs, lay eggs. She takes _one_ nuptial flight. That one stuns her with enough fertile power to be trapped in the hive forever. The workers—the sexually undeveloped females—have the best life. They have fields of flowers to roll in. Imagine turning over and over inside a rose." I can tell he's carried away with the idea. I'm getting interested myself.
"What do they eat inside the hive all winter?"
"Beebread."
"Beebread? Are you serious?"
"It's a mixture of pollen and honey. And the worker excretes gold wax from her stomach for the comb. Those neat hexagons!"
I try to imagine the size of a worker bee's intestinal system, how many times she must fly from the hive to the _tiglio_ to make even a tablespoon of honey. A thousand times? A jar must represent a million flights of bees carrying a heavy cargo of honeydew, their legs sticky with pollen. In _The Georgics,_ which is sort of an ancient farmer's almanac, Vergil writes that bees lift small stones to ballast themselves as they fly through boisterous east winds. He is wise on the subject of bees but not entirely to be trusted; he thought they would generate spontaneously from the decayed carcass of a cow. I like the image of a bee clutching a small stone, like a football player holding the ball to his chest as he barrels down the field. "Yes, I can see four hives painted green. I like the beekeeper's gear, that medieval-looking veil, lifting the dark combs—we could roll our own candles from the wax." Now I'm drawn into this idea.
But he stands up and leans out into the dizzying fragrance. Practicality has left him. "The wasps are anarchistic, whereas the bees . . ."
I gather up the coffee cups. "Maybe we should wait until the house is done."
FIGS REVEAL WATER. ON THE TERRACES THEY GROW NEAR THE stone chutes we discovered. The natural well has webby roots crawling down into it from the fig above. I'm mixed on figs. The fleshy quality feels spooky. In Italian, _il fico,_ fig, has a slangy turn into _la fica,_ meaning vulva. Possibly because of the famous fig leaf exodus from Eden, it seems like the most ancient of fruits. Oddest, too—the fig flower is inside the fruit. To pull one open is to look into a complex, primitive, infinitely sophisticated life cycle tableau. Fig pollination takes place through an interaction with a particular kind of wasp about one eighth of an inch long. The female bores into the developing flower inside the fig. Once in, she delves with her oviposter, a curved needle nose, into the female flower's ovary, depositing her own eggs. If her oviposter can't reach the ovary (some of the flowers have long styles), she still fertilizes the fig flower with the pollen she collected from her travels. Either way, one half of this symbiotic system is served—the wasp larvae develop if she has left her eggs or the pollinated fig flower produces seed. If reincarnation is true, let me not come back as a fig wasp. If the female can't find a suitable nest for her eggs, she usually dies of exhaustion inside the fig. If she can, the wasps hatch inside the fig and all the males are born without wings. Their sole, brief function is sex. They get up and fertilize the females, then help them tunnel out of the fruit. Then they die. The females fly out, carrying enough sperm from the tryst to fertilize all their eggs. Is this appetizing, to know that however luscious figs taste, each one is actually a little graveyard of wingless male wasps? Or maybe the sensuality of the fruit comes from some flavor they dissolve into after short, sweet lives.
THE WOMEN IN MY FAMILY ALWAYS HAVE MADE BREAD AND butter pickles and muscadine jellies and watermelon rind pickles and peach preserves and plum butters. I feel drawn to the scalding kettle, with a flat of rapidly softening raspberries leaking juice on the counter, to the syrupy clove-scented bowls of sweet peaches about to be poured into an astringent vinegar bath, to ring-finger-sized cucumbers. In California, I've cried over rubber sealing rings that turned to gum, over jams that wouldn't jam, over a cauldron of guavas that made two dozen jars of gray jelly instead of the clear exotic topaz I expected. I don't have the gene my mother had for laying-by rows of crimson and emerald jars of fruit preserves and the little pickled things called _sottaceto_ (under vinegar) here. When I look at the product of a sweating afternoon, all I can think is "Botulism?"
This long-lost owner who placed the fruit trees on a terrace so they sweetly dangle over a grassy walk, she, I'm sure, had a shelf under the stairs for her confitures, and no qualms about breaking open her spicy plums on a January morning. Here, I think, I'll master the art my mother should have passed to me as easily as she passed her taste for hand-painted china and expensive shoes.
From the Saturday market I lug a box of prime peaches downhill to the car. They are so beautiful all I really want to do is pile them in a basket and look at the delicious colors. In the one cookbook I have here so far, I find Elizabeth David's recipe for peach marmalade. Nothing could be simpler: The halved peaches simply are cooked with a little sugar and water, cooled, then cooked again the next day, until the preserves set when ladled onto a saucer. Elizabeth David notes, "This method makes a rather extravagant but very delicious preserve. Unfortunately it tends to form a skin of mold within a very short time, but this does not affect the rest of the jam, some of which I have kept for well over a year, even in a damp house." I'm a little bothered by this mold note, and she's vague about sterilizing jars and never mentions listening for the _whoosh_ of the seal I heard as Mother's green tomato pickles cooled. I remember my mother tapping the tops to make sure the lid had sucked down. It sounds as though Elizabeth David just dishes it up into the jars then forgets it, scraping off mold with impunity before spreading some on her toast. Still, she says "rather extravagant but very delicious," and if Elizabeth David says that, I believe her. Since I have all these peaches, I decide to make seven pounds and just eat the rest. We'll use the preserves this summer before an unappetizing mold can form in this damp house. I'll give some to new friends, who will wonder why I'm not painting shutters instead of stirring fruit.
I drop the peaches into boiling water for a moment, watching the rosy colors intensify, then spoon them out and slide the skins off as easily as taking off a silk slip. This recipe is simple, not even a few drops of lemon juice or a grating of nutmeg or a clove or two. I remember my mother putting in a kernel from inside the peach pit, an almond-scented secret nut. Soon the kitchen fills with a fly-attracting sweetness. The next day, I boil the jars for good measure, while the fruit cooks down again, then spoon it in. I have five lovely jars of jam, peachy but not too sweet.
The _forno_ in Cortona bakes a crusty bread in their wood oven, a perfect toast. Breakfast is one of my favorite times because the mornings are so fresh, with no hint of the heat to come. I get up early and take my toast and coffee out on the terrace for an hour with a book and the green-black rows of cypresses against the soft sky, the hills pleated with olive terraces that haven't changed since the seasons were depicted in medieval psalters. Sometimes the valley below is like a bowl filled up with fog. I can see hard green figs on two trees and pears on a tree just below me. A fine crop coming in. I forget my book. Pear cobbler, pear chutney, pear ice, green figs (would the wasps already be in green figs?) with pork, fig fritters, fig and _nocciola_ tart. May summer last a hundred years.
Whir of the Sun
THE HOUSE, ONLY TWO KILOMETERS FROM town, feels like a deep country place. We can't see any neighbors, although we hear the man way above us calling _vieni qua,_ come here, to his dog. The summer sun hits like a religious conviction. I can tell time by where the sun strikes the house, as though it were a gigantic sundial. At five-thirty, the first rays smack the patio door, routing us out of bed and giving us the pleasure of dawn. At nine, a slab of sunlight falls into my study from the side window, my favorite window in the house for its framed view over the cypresses, the groves in the valley, and out into the Apennines. I want to paint a watercolor of it but my watercolors are awful, fit only to be stored on a closet shelf. By ten, the sun swings high over the front of the house and stays there until four, when a cut of shadow across the lawn signals that the sun is heading toward the other side of the mountain. If we walk to town that way in late afternoon, we see a prolonged, grandiose sunset over the Val di Chiana, lingering until it finally just dissolves, leaving enough streaked gold and saffron behind to light a way home until nine-thirty, when indigo dark sets in.
On moonless nights it is as black as inside an egg. Ed has gone back to Minnesota for his parents' fiftieth wedding anniversary. A shutter bangs; otherwise, the silence reverberates so strongly that I think I can hear my own blood circulating. I expect to lie awake, to imagine a drug-crazed intruder with an Uzi creeping up the stairs in the dark. Instead, in the wide bed with flowered sheets, I spread my books, cards, and notepaper around me and indulge in the rare act of writing letters to friends. A second indulgence goes straight back to high-school days—consuming a plate of brownies and a Coke while copying paragraphs and verses I like into my notebook. If only Sister, my black long-haired cat, were here. She is truly a good companion for solitude. It's far too hot for her to sleep against my feet, as she likes to do; she would have to stay on a pillow at the foot of the bed. I sleep like one newly born and in the morning have coffee on the patio, walk to town for groceries, work on the land, come in for water, and it is only ten o'clock. Hours go by without the need to speak.
After a few days, my life takes on its own rhythm. I wake up and read for an hour at three A.M.; I eat small snacks—a ripe tomato eaten like an apple—at eleven and three rather than lunch at one. At six I'm up, but by siesta time, the heat of the day, I'm ready for two hours in bed. Slumber sounds heavier than sleep, and with the hum of a small fan, it's slumber I fall into. At last, I have time to take a coverlet outside at night and lie on my back with the flashlight and the star chart. With the Big Dipper easily fixed right over the house, I finally locate Pollux in Gemini and Procyon in Canis Minor. I forget the stars and here they are, so alive all along, pulsing and falling.
A French woman and her English husband walk up the driveway and introduce themselves as neighbors. They've heard Americans bought the place and are curious to meet those mad enough to take on this ordeal of restoration. They invite me to lunch the next day. Since both are writers and are restoring their small farmhouse, we fall into instant camaraderie. Should they have the staircase here or there, what to do with this tiny room, would a bedroom in the animal stall downstairs be too dark? The _comune_ won't allow you to cut windows, even in almost airless farmhouses; exteriors must remain intact on historical property. They invite me to dinner the next night and introduce me to two other foreign writers, French and Asian-American. By the time Ed returns in a week, we're invited to the house of these writers.
The table is set under a shady grape arbor. Cold salads, cold wine, fruit, a grand cheese soufflé somehow steamed on top of the stove. Heat shimmers around the olive trees in the distance. On the stone patio, we're cool. We're introduced to the other guests: novelists, journalists, translators, a nonfiction writer—all older expatriates who've settled in these hills and restored properties. To live wholly in another country fascinates me. I'm curious how the trip or assignment to Italy turned into a lifetime for each of them and I ask Fenella, the international journalist, on my right, about this. "You can't imagine what Rome was in the fifties. Magic. I simply fell in love—like you fall in love with a person—and schemed to find a way to stay there. It wasn't easy. I got on as a stringer for Reuters. Look at the old movies and you'll see there were almost no cars. This was not long after the war and Italy was devastated, but the _life_! It was unbelievably cheap, too. Of course we didn't have much money but we lived in enormous apartments in grand _palazzi_ for nothing. Every time I went back to America, I just couldn't wait to get back. It wasn't a rejection—or maybe it was. Anyway, I've never wanted to be anywhere else."
"We feel the same way," I say, and then realize that's not really the truth. I succumb totally to the "magic" of this place, but I know the appeal to me is partly the balance it restores to my life in America. I'm not about to leave there, even if I could. I try to amend what I've said. "My job at home is hard but I really love it—I'm pushed by it. And San Francisco is not home at the blood root, but it's a lucky, very beautiful place to live, earthquakes and all. Spending time here lets me escape the craziness and violence and downright surreal aspects of America, and my own overscheduled life. Three weeks after arrival, I realize I've let down some guard that is so instinctive to me, living in an American city, that I don't realize I have it." She looks at me with sympathy. At this point, the violence in America is hard for anyone to comprehend. "Literally, my pulse slows," I continue. "Even so, I sense that I can best develop my thinking there—it's my culture, my rough edge, my past." I'm not sure I've explained myself well. She raises her glass to me.
" _Esatto,_ my daughter feels the same. You didn't come along in time to know Rome back then. It's terrible now. But then it was irresistible." I suddenly realize they're in double exile, from the United States and from Rome.
Max joins in. He had to go to Rome last week and the traffic was horrendous, then the gypsies accosted him, as if he were a tourist, pressing their cardboard against him in an effort to distract him while they tried to pick his pocket. "Long ago, I learned to put the evil eye on them," he tells Ed and me. "They scatter then." They all agree, Italy is not what it used to be. What is? All my adult life I've heard how Silicon Valley used to be all orchards, how Atlanta used to be genteel, how publishing used to be run by gentlemen, how houses used to cost what a car costs now. All true, but what can you do but live now? Our friends who've recently bought a place in Rome are wild about the city. We love it. Maybe living with Bay Bridge traffic and San Francisco prices prepares us for anything.
One guest is a writer I have long admired. She moved here about twenty years ago, after living for years in the postwar wild south of Italy and then in Rome. I knew she lived here and even had been given her telephone number by a mutual acquaintance in Georgia, where she now spends a part of every year. Cold calls always have been hard for me to make and I am a little awed by the woman who wrote, in luminous, austere prose, about the dark, raucous, convoluted lives of women down in ravaged Basilicata.
Elizabeth is across the table and down from me. I see her cover her glass with her hand as Max starts to pour wine. "You know I never drink wine at lunch." Ah, the austerity. She wears a blue cotton shirt with some vaguely religious-looking medallion around her neck. She has a dead-level blue gaze, fair skin, and a voice I think has a touch of my own accent.
I lean forward and venture, "Is that a trace of a Southern accent?"
"I certainly hope not," she snaps—do I see a hint of a smile?—and quickly turns back to the famous translator beside her. I look down into my salad.
By the time Richard serves his lemon gelato made with mascarpone, the gathering is mellowing. Several empty wine bottles stand on a side table. The intense sun is now caught in the limbs of a chestnut. Ed and I join in where we can but this is a lively group of old friends with years of shared experiences. Fenella talks about her research trips to Bulgaria and Russia; her husband, Peter, tells a story about bringing a gray parrot in his coat pocket when he came back from an assignment in Africa. Cynthia talks about a family dispute over her famous mother's notebooks. Max makes us laugh over his unbelievable luck in sitting next to a film producer on a flight to New York, launching into a description of his script to this captive, who finally said to send him the script. Now the producer is coming to visit and has bought the option. Elizabeth looks bemused.
As the party breaks up she says, "You were supposed to call me. I've tried to get your number but there's no listing. Irby [a friend of my sister's] told me you've bought a house here. In fact, I met your sister at a dinner in Rome—Georgia, that is." I make excuses about the confusions of the house, then impulsively ask her to dinner on Sunday. Impulsively, because we don't have furniture, dishes, linen—only the rudimentary kitchen with a few pots and plates.
I PICK UP A LINEN CLOTH AT THE MARKET TO COVER THE ramshackle table left behind in the house, arrange wildflowers in a jar and place it in a flowerpot, plan dinner carefully but keep it simple: ravioli with sage and butter, sautéed chicken and _prosciutto_ rolls, fresh vegetables and fruit. As Elizabeth arrives, Ed is moving the table out to the terrace. The entire top and one leg fall off—either an icebreaker or a disaster. She helps us piece the table together and Ed pounds in a few nails. Covered and set, it looks quite nice. We tour the big empty house and begin to talk drainpipes, wells, chimneys, whitewash. She completely restored a noble _casa colonica_ when she moved here. As a wall came down the first day, she found an angry sow left behind by the peasants. Quickly, it becomes clear that she knows _everything_ about Italy. Ed and I begin what is to become the ten thousand questions. Where do you get your water tested? How long was a Roman mile? Who's the best butcher? Can you buy old roof tiles? Is it better to apply for residency? She has been an intense observer of Italy since 1954 and knows an astonishing amount about the history, language, politics, as well as the telephone numbers of good plumbers, the name of a woman who prepares _gnocchi_ with the lightest touch north of Rome. Long dinner under the moon, hoping the table won't keel over. Suddenly we have a friend.
Every morning, Elizabeth goes into town, buys a paper, and takes her espresso at the same café. I'm up early, too, and love to see the town come alive. I walk in with my Italian verb book, memorizing conjugations as I walk. Sometimes I take a book of poetry because walking suits poetry. I can read a few lines, savor or analyze them, read a few more, sometimes just repeat a few words of the poem; this meditative strolling seems to free the words. The rhythm of my walking matches the poet's cadence. Ed finds this eccentric, thinks I will be known as the weird American, so when I get to the town gate, I put away my book and concentrate on seeing Maria Rita arranging vegetables, the shopkeeper sweeping the street with one of those witch brooms made of twigs, the barber lighting his first smoke, leaning back in his chair with a tabby sleeping on his lap. Often I run into Elizabeth. Without plan, we begin to meet a morning or two a week.
IN TOWN, TOO, ED AND I ARE BEGINNING TO FEEL MORE AT home. We try to buy everything right in the local shops: hardware, electrical transformers, contact lens cleaner, mosquito candles, film. We do not patronize the cheaper supermarket in Camucia; we go from the bread store to the fruit and vegetable shop, to the butcher, loading everything into our blue canvas shopping bags. Maria Rita starts to go in back of her shop and bring out the just-picked lettuces, the choice fruit. "Oh, pay me tomorrow," she says if we only have large bills. In the post office, our letters are affixed with several stamps by the postmistress then individually hand-canceled with vengeance, _whack, whack, "Buon giorno, signori."_ At the crowded little grocery store, I count thirty-seven kinds of dried pasta and, on the counter, fresh _gnocchi, pici,_ thick pasta in long strands, fettuccine and two kinds of ravioli. By now they know what kind of bread we want, that we want the _bufala,_ buffalo milk mozzarella, not the _normale,_ regular cow's milk kind.
We buy another bed for my daughter's upcoming visit. Box springs don't exist here. The metal bed frame holds a base of woven wood on which the mattress rests. I thought of the slats in my spool bed when I was growing up, how the mattress, springs and all, collapsed when I jumped up and down on the bed. But this is securely made, the bed firm and comfortable. A very young woman with tousled black curls and black eyes sells old linens at the Saturday market. For Ashley's bed I find a heavy linen sheet with crocheted edges and big square pillowcases of lace and embroidery. Surely these accompanied a bride to her marriage. The condition is so good I wonder if she ever took them from her trunk. They have dusty lines where they've been folded, so I soak them in warm suds in the hip bath, then hang them out to dry in the midday sun, a natural strong bleach that turns them back to white.
Elizabeth has decided to sell her house and rent the former priest's wing attached to a thirteenth-century church called Santa Maria del Bagno, Saint Mary of the Baths. Although she won't move until winter, she begins to sort her belongings. Perhaps out of memory of that first dinner, she gives us an iron outdoor table and four curly chairs. Years ago, when she worked on a TV show about Moravia, he demanded a place to rest between shoots. She bought the set then. I give the "Moravia table" a fresh coat of that blackish green paint you see on park furniture in Paris. We also are the recipients of several bookcases and a couple of shopping bags full of books. The fourteenth-century hermits who lived on this mountain still might approve of our white rooms so far: beds, books, bookcases, a few chairs, a primitive table. Big willow baskets hold our clothes.
On the third Saturday of each month, a small antiques market takes place in a piazza in the nearby castle town of Castiglione del Lago. We find a great sepia photograph of a group of bakers and a couple of chestnut coatracks. Mostly we browse around, astonished at the crazy prices on bad garage sale furniture. On the way home, we come upon an accident—someone in a tiny Fiat tried to pass on a curve—the Italian birthright—and rammed into a new Alfa Romeo. The upside-down Fiat still has one spinning wheel and two passengers are being extracted from the crumpled car. An ambulance siren blares. The smashed Alfa is standing, doors open, no passengers in the front seat. As we inch by, I see a dead boy, about eighteen, in the backseat. He is still upright in his seat belt but clearly is dead. Traffic stops us and we are two feet from his remote blue stare, the trickle of blood from the corner of his mouth. Very carefully, Ed drives us home. The next day, when we are back in Castiglione del Lago for a swim in the lake, we ask the waiter at the bar if the boy killed in the accident was local. "No, no, he was from Terontola." Terontola is all of five miles away.
WE'RE EXPECTING THE PERMITS SOON. MEANWHILE, THE MAIN project we hope to finish before we go home at the end of August is the sandblasting of the beams. Each room has two or three large beams and twenty-five or thirty small ones. A big job.
_Ferragosto,_ August 15, is not just a holiday for the Virgin, it is a signal for work to cease and desist all over Italy both before and after that day. We underestimated the total effect of this holiday. When we began calling for a sandblaster, after the wall was finished, we found only one who would think of taking the job in August. He was to arrive on the first, the job to last three days. On the second we began to call and have been calling ever since. A woman who sounds very old shouts back that he is on _vacanza al mare,_ he's over on the coast walking those sandy beaches instead of sandblasting our sticky beams. We wait, hoping he will appear.
Although we can't paint until after the central heating is installed, we begin to scrub down the walls in preparation. On Saturdays and odd days when they're not working elsewhere, the Poles come over to help us. The flaky whitewash brushes off on our clothes if we rub against it. As they clean the walls with wet cloths and sponges, they uncover the earlier paints, most prevalent a stark blue that must have been inspired by Mary's blue robes. Renaissance painters could get that rare color only from ground lapis lazuli brought from quarries in what is now Afghanistan. Faintly, we see a far-gone acanthus border around the top of the walls. The _contadina_ bedroom used to be painted in foot-wide blue and white stripes. Two upstairs bedrooms were clear yellow, like the _giallorino_ Renaissance painters favored, made from baked yellow glass, red lead, and sand from the banks of the Arno.
From the third floor, I hear Cristoforo calling Ed, then he calls me. He sound urgent, excited. He and Riccardo talk at once in Polish and point to the middle of the dining room wall. We see an arch, then he rubs his wet cloth around it and scumbles of blue appear, then a farmhouse, almond green feathery strokes of what may be a tree. They have uncovered a fresco! We grab buckets and sponges and start gently cleaning the walls. Every swipe reveals more: two people by a shore, water, distant hills. The same blue that's on the walls was used for the lake, a paler blue for sky and soft coral for clouds. The biscuit-colored houses are the same colors we see all around us. Vibrant when wet, the colors pale as they dry. An electrical line, buried at some point in the wall, mars a faux-framed classical scene of ruins in a panel over the door. We rub all afternoon. Water runs down our arms, sloshes on the floor. My arms feel like slack rubber bands. The lake scene continues on the adjoining wall and it is vaguely familiar, like the villages and landscape around Lake Trasimeno. The naive style reveals no newly discovered Giotto but it's charming. Someone didn't think so and whitewashed it. Luckily, they didn't use tougher paint. We will be able to live with this soft painting surrounding our dinners indoors.
A HUNDRED YEARS MAY NOT BE LONG ENOUGH TO RESTORE this house and land. Upstairs I rub the windows with vinegar, shining the green scallop of the hills along the sky. I spot Ed on the third terrace, waving a long spinning blade. He's wearing red shorts as bright as a banner, black boots against the locust thorns, and a clear visor to shield his eyes from flying rocks. He could be a powerful angel, coming to announce a late annunciation, but he is only the newest in an endless line of mortals who've worked to keep this farm from sliding back into the steep slope it once was, perhaps long before the Etruscans, when Tuscany was a solid forest.
The ugly whine of the weed machine drowns out the whinnies of the two white horses across the road and the multicultural birds that wake us up every morning. But the dry weeds must be cut in case of fire, so he works in the fiery sun without his shirt. Each day his skin darkens. We've learned the gravity of the hillside, the quick springs pulling down dirt and the thrust of the stone walls which must be sluices and must push back harder than the downward pull of the soil. He bends and slings olive prunings to a stack he's building for fires on cool nights. What a body of work this place is. Olive burns hot. The ashes then are returned to the trees for fertilizer. Like the pig, the olive is useful in every part.
The old glass sags in places—strange that glass which looks so solid retains a slow liquidity—distorting the sharp clarity of the view into watery Impressionism. Usually, if I am polishing silver, ironing, vacuuming at home, I am highly conscious that I am "wasting time," I should be doing something more important—memos, class preparation, papers, writing. My job at the university is all-consuming. Housework becomes a nuisance. My houseplants know it's feast or famine. Why am I humming as I wash windows—one of the top ten dreaded chores? Now I am planning a vast garden. My list includes sewing! At least a fine handkerchief linen curtain to go over the glass bathroom door. This house, every brick and lock, will be as known to me as my own or the loved one's body.
Restoration. I like the word. The house, the land, perhaps ourselves. But restored to what? Our lives are full. It's our zeal for all this work that amazes me. Is it only that once into the project, what it all means doesn't come up? Or that excitement and belief reject questions? The vast wheel has a place for our shoulders and we simply push into the turning? But I know there's a taproot as forceful as that giant root wrapped around the stone.
I remember dreaming over Bachelard's _The Poetics of Space,_ which I don't have with me, only a few sentences copied into a notebook. He wrote about the house as a "tool for analysis" of the human soul. By remembering rooms in houses we've lived in, we learn to abide (nice word) within ourselves. I felt close to his sense of the house. He wrote about the strange whir of the sun as it comes into a room in which one is alone. Mainly, I remember recognizing his idea that the house protects the dreamer; the houses that are important to us are the ones that allow us to dream in peace. Guests we've had stop in for a night or two all come down the first morning, ready to tell their dreams. Often the dreams are way-back father or mother dreams. "I was in this car and my father was driving, only I was the age I am now and my father died when I was twelve. He was driving fast . . . ." Our guests fall into long sleeps, just as we do when we arrive each time. This is the only place in the world I've ever taken a nap at nine in the morning. Could this be what Bachelard meant by the "repose derived from all deep oneiric experience"? After a week or so, I have the energy of a twelve-year-old. For me, _house,_ set in its landscape, always has been crypto-primo image land. Bachelard pushed me to realize that the houses we experience deeply take us back to the _first_ house. In my mind, however, it's not just to the first house, but to the first concept of self. Southerners have a gene, as yet undetected in the DNA spirals, that causes them to believe that place is fate. Where you are is who you are. The further inside you the place moves, the more your identity is intertwined with it. Never casual, the choice of place is the choice of something you crave.
An early memory: Mine is a small room with six windows, all open on a summer night. I'm three or four, awake after everyone has gone to bed. I'm leaning on the windowsill looking out at the blue hydrangeas, big as beach balls. The attic fan pulls in the scent of tea olive and lifts the thin white curtains. I'm playing with the screen latch, which suddenly comes undone. I remember the feel of the metal hook and the eye I almost can stick my little finger into. Next, I'm climbing up on the sill and jumping out the window. I find myself in the dark backyard. I start running, feeling a quick rush of what I now know as freedom. Wet grass, glow of white camellias on the black bush, the new pine just my height. I go out to my swing in the pecan tree. I've just learned to pump. How high? I run around the house, all the rooms of my sleeping family, then I stand in the middle of the street I am not allowed to cross. I let myself in the back door, which never was locked, and into my room.
That pure surge of pleasure, flash flood of joy—to find the electric jolt of the outside place that corresponds to the inside—that's it.
In San Francisco, I go out on the flower-filled tiny back deck of my flat and look three stories down at the ground—a city-sized terrace surrounded with attractive low-maintenance flower beds on a drip system, cared for by a gardener. It does not lure me. That the jasmine on the high fences has climbed to my third floor and blooms profusely around the stair railing, I am thankful for. At night after work, I can step out to water my pots and watch for stars and find the tumbling vines sending out their dense perfume. Such flowers—jasmine, honeysuckle, gardenia—spell South, metabolic home, to my psyche. A fragmental connection though—my feet are three stories off the earth. When I leave my house, concrete separates my feet from the ground. The people who have bought the flats on the first and second floors are friends. We have meetings to discuss when to repair the steps or when to paint. I look into or onto the tops of trees, wonderful trees. My house backs onto the very private gardens unhinted at by the joined fronts of Victorian houses in my neighborhood. The center of the block is green. If all of us took down our fences, we could wander in a blooming green sward. Because I like my flat so much, I didn't know what I missed.
Was there really a _nonna,_ a presiding spirit who centered this house? This three-story house rooted to the ground restores some levels in my waking and sleeping hours. Or is it the house? A glimmer: _Choice_ is restorative when it reaches toward an instinctive recognition of the earliest self. As Dante recognized at the beginning of _The Inferno:_ What must we do in order to grow?
At home I dream of former houses I've lived in, of finding rooms I didn't know were there. Many friends have told me that they, too, have this dream. I climb the stairs to the attic of the eighteenth-century house I loved living in for three years in Somers, New York, and there are three new rooms. In one, I find a dormant geranium, which I take downstairs and water. Immediately, Disney-style, it leafs and breaks into wild bloom. In house after house (my best friend's in high school, my childhood home, my father's childhood home), I open a door and there is more than I knew. All the lights are on in the New York house. I am walking by, seeing the life in every window. I never dream of the boxy apartment I lived in at Princeton. Nor do I dream of my flat I am so fond of in San Francisco—but perhaps that is because I can hear from my bed before I fall asleep foghorns out on the bay. Those deep voices displace dreams, calling from spirit to spirit, to some underlying voice we all have but don't know how to use.
In Vicchio, a house I rented a few summers ago brought the recurrent dream to reality. It was a huge house with a caretaker in a side wing. One day I opened what I'd assumed was a closet in an unused bedroom and found a long stone corridor with empty rooms on either side. White doves flew in and out. It was the second floor of the housekeeper's wing and I hadn't realized it was uninhabited. In many waking moments since, I've opened the door to the stony light of that hallway, oblong panels of sunlight on the floor, caught a glimpse and flutter of white wings.
Here, I am restored to the basic pleasure of connection to the outdoors. The windows are open to butterflies, horseflies, bees, or anything that wants to come in one window and out another. We eat outside almost every meal. I'm restored to my mother's sense of preserving the seasons and to _time,_ even time to take pleasure in polishing a pane of glass to a shine. To the house safe for dreaming. One end of the house is built right against the hillside. An omen of reconnection? Here, I don't dream of houses. Here, I am free to dream of rivers.
THOUGH THE DAYS ARE LONG, THE SUMMER IS SOMEHOW short. My daughter, Ashley, arrives and we have mad, hot days driving around to sights. When she first walked up to the house, she stopped and looked up for a while, then said, "How strange—this will become a part of all our memories." I recognized that knowledge we sometimes get in advance when travelling or moving to a new city—here's a place that will have its way with me.
Naturally, I want her to love it but I don't have to convince her. She begins talking about Christmas here. She chooses her room. "Do you have a pasta machine?" "Can we have melon every meal?" "A swimming pool could go up on that second terrace." "Where's the train schedule to Florence? I need shoes."
The minute she graduated from college, she lit out for New York. The artist's life, the odd-job life, the long hot summer, health problems—she's ready for the icy mountain-fed pool run by a priest back in the hills, for trips to the Tyrrhenian coast, where we rent beach chairs and bake all day, for strolls in stony hill towns at night after dinner in a strictly local _trattoria._
The days stream by and soon it is time for both of us to leave. I must be at work but Ed will stay another ten days. Maybe the sandblaster will come.
Festina Tarde
(Make Haste Slowly)
WALKING OUT OF THE SAN FRANCISCO airport, I'm shocked by cool foggy air, smelling of salt and jet fumes. A taxi driver crosses the street to help with luggage. After a few pleasantries, we lapse into silence and I'm grateful. I have been travelling for twenty-four hours. The last leg, from JFK, where Ashley and I said good-bye, to SF seems cruel and unusual, especially the extra hour it takes because of the prevailing wind. The houses on the hills are necklaces of light, then along the right, the bay almost laps the freeway. I watch for a certain curve coming up. After rounding it, suddenly the whole city rises, the stark white skyline. As we drive in, I anticipate the breath-stopping plunges over hills and glimpses between buildings where I know there's a wedge or slice or expanse of rough blue water.
Still, imprinted on my eyes are the stone towns, mown fields, and sweeping hills covered with vineyards, olives, sunflowers; this landscape looks exotic. I start to look for my house key, which I thought was in the zippered inside pocket of my bag. If I've lost it—what? Two friends and a neighbor have keys to my place. I imagine getting their answering machines, "I'm out of town until Friday . . ." We pass Victorian houses discreetly shuttered and curtained, porch lights shining on wooden banisters and pots of topiary. No one, not even a dog walker or someone running to the store for milk, is out. I feel a pang for the towns full of people who leave their keys dangling in their locks, for the evening _passeggiata_ when everyone is out and about, visiting, shopping, taking a quick espresso. I've left Ed there because his university starts later than mine and the sandblasting still is a dream of accomplishment for the summer. The taxi lets me out and speeds off. My house looks the same; the climbing rose has grown and tried to wind around the columns. Finally I find the key mixed in with my Italian change. Sister comes to greet me with a plaintive meow and a quick brush of her sides against my ankles. I pick her up to smell her earthy, damp leaf smell. In Italy, I often wake up thinking she has leapt on the bed. She jumps on top of my bag and curls down for a nap. So much for having suffered in my absence.
Lamps, rugs, chests, quilts, paintings, tables—how amazingly comfortable and cluttered this looks after the empty house seven thousand miles away. Bookshelves, crammed, the glass kitchen cabinets lined with colorful dishes, pitchers, platters—so much of everything. The long hall carpet—so soft! Could I walk out of here and never look back? Virginia Woolf, I remember, lived in the country during the war. She rushed back to her neighborhood in London after a bombing and found her house in ruins. She expected to be devastated but instead felt a strange elation. Doubtless, I would not. When the earth quaked, I was shaken for days over my whiplashed chimney, broken vases, and wineglasses. It's just that my feet are used to the cool _cotto_ floors, my eyes to bare white walls. I'm still _there,_ partly here.
There are eleven messages on the answering machine. "Are you back?" I need to get your signature on my graduation form . . ." "Calling to confirm your appointment . . ." The housesitter has left a list of other calls on a pad and stacked the mail in my study. Three kneehigh stacks, mostly junk, which I compulsively begin to go through.
Because I have stayed away as long as possible, I must return to the university immediately. Classes begin in four days, and regardless of faxes from Italy and the good offices of an excellent secretary, I am chair of the department and need to be bodily present. By nine, I'm there, dressed in gabardine pants, a silk print blouse. "How was your summer?" we all say to one another. The start-up of a school year always feels exhilarating. Everyone feels the zest in the air. If the bookstore were not crowded with students buying texts, I probably would go over and buy a supply of fine-point pens, a notebook with five-subject index, and a few pads. Instead, I sign forms, memos, call a dozen people. I go into racing gear, ignoring jet lag.
Stopping for groceries after work, I see that the organic store has added a masseuse to the staff. I could pause in a little booth and get a seven-minute massage to relax me before I begin selecting potatoes. I'm temporarily overwhelmed by the checkout rows, the aisles and aisles of bright produce and the tempting cakes at the new bakery just installed in the front of the store. Mustard, mayonnaise, plastic wrap, baking chocolate—I buy things I haven't seen all summer. The deli has crab cakes and stuffed baked potatoes with chives, and corn salad and tabouli. So much! I buy enough "gourmet takeout" for two days. I'm going to be too busy to cook.
It's eight A.M. at Bramasole. Ed probably is chopping weeds around an olive tree or pacing around waiting for the sandblaster. As I turn in my garage I see Evit, the one-toothed homeless man, rifling through our recycle bin for bottles and cans. My neighbor has posted a VISUALIZE BEING TOWED sign on his garage door.
The last message on the machine starts with static, then I hear Ed's voice; he sounds raspy. "I was hoping to catch you, sweetheart; are you _still_ at work? The sandblaster was here when I got home from the airport." Long pause. "It's hard to describe. The noise is deafening. He's got this huge generator and the sand really does _blast_ out and fall into every crack. It's like a storm in the Sahara. He did three rooms yesterday. You can't believe how much sand is on the floors. I took all the furniture out on the patio and I'm just camped in one room, but the sand is _all_ over the house. The beams look _very good;_ they're chestnut, except for one elm. I don't know _how_ I'm going to get rid of this sand. It's in my _ears_ and I'm not even in the room with him. Sweeping is out of the question. I _wish_ you were here." He usually doesn't speak with so many italics.
When he calls next, he's on the _autostrada_ near Florence, en route to Nice and home. He sounds exhausted and elated. The permits have come through! The blasting is over. Primo Bianchi, however, won't be able to do our work because he must have a stomach operation. Ed met again with Benito, the yellow-eyed Mussolini look-alike, and has worked out a contract with him. Work is to start immediately and to finish in early November, easily in time for Christmas. The clean-up goes slowly; the sandblaster says to expect sand to trickle down for five years!
Ian, who helped us with the purchase, will oversee the work. We left diagrams of where electrical outlets, switches, and radiators should go, how the bathroom should be laid out, how the kitchen should be installed—even the height of the sink and the distance between the sink and the faucet—where to pick up the fixtures and tile we selected for the bathroom, everything we can think of. We are anxious for word that work is under way.
The first fax arrives September 15; Benito has broken his leg on the first day of the job and start-up will be delayed until he is able to walk.
_FESTINA TARDE_ WAS A RENAISSANCE CONCEPT: MAKE HASTE slowly. Often it was represented by a snake with its tail in its mouth, by a dolphin entwined with an anchor, or by the figure of a seated woman holding wings in one hand and a tortoise in the other: The great wall of Bramasole in one, the central heating, kitchen, patio, and bathroom in the other. The second fax, October 12, warns that "delays have occurred" and that "some changes in installation can be expected" but he has full confidence and not to worry.
We fax back our encouragement and ask that everything be covered well with plastic and taped.
Another fax, just after, says the opening of the three-foot-thick wall between the kitchen and dining room has begun. Two days later, Ian faxes us the news that when a very large boulder was pulled out, the whole house creaked and all the workers ran out because they feared a collapse.
We called. Didn't they brace the rooms? Had Benito used steel? Why hadn't they known what to do? How could this happen? Ian said stone houses were unpredictable and couldn't be expected to react the way American houses react and the door is now in and looks fine, although they didn't make it as wide as we wanted because they were afraid to. I vacillated between thinking that the workers were incompetent and fearing that they might have been crushed by an unstable house.
By mid-November, Benito has finished the upstairs patio and the opening of the infamous door, plus they've opened the two upstairs doors that connect to the _contadina_ apartment. We decide to cancel the opening of the other large door that would join the living room to the _contadina_ kitchen. The image of all Benito's men fleeing the premises does not inspire confidence. The next delays Ian mentions concern the new bath and the central heating. "Almost certainly," he advises, "there will be no heat when you come for Christmas. In fact, the house will not be habitable due to the fact that the central heating pipes must be inside the house, not on the back as we were originally told." Benito asks him to relay that his charges are higher than anticipated. Items listed on the contract have been farmed out to electricians and plumbers and their overlapping bills have become incomprehensible. We have no way of knowing who did what; Ian seems as confused as we are. Money we wire over takes too long to get there and Benito is angry. What is clear is that we are not there and our house's work is done between other jobs.
HOPING FOR MIRACLES, WE GO TO ITALY FOR CHRISTMAS. Elizabeth has offered us her house in Cortona, which is partly packed for her move. She also wants to give us a great deal of her furniture, since her new house is smaller. As we drive out of the Rome airport, rain hits the windshield like a hose turned on full blast. All the way north we face foggier and foggier weather. When we arrive in Camucia, we head straight to the bar for hot chocolate before we go to Elizabeth's. We decide to unpack, have lunch, and face Bramasole later.
The house is a wreck. Canals for the heating pipes have been cut into the inside walls of every room in the house. The workers have left rock and rubble in piles all over the unprotected floors. The plastic we'd requested was simply tossed over the furniture so every book, chair, dish, bed, towel, and receipt in the house is covered in dirt. The jagged, deep, floor-to-ceiling cuts in the wall look like open wounds. They are just beginning on the new bathroom, laying cement on the floor. The plaster in the new kitchen already is cracking. The great long sink has been installed and looks wonderful. A workman has scrawled in black felt-tip pen a telephone number on the dining room fresco. Ed immediately wets a rag and tries to rub it clean but we're stuck with the plumber's number. He slings the rag onto the rubble. They've left windows open all over and puddles have collected on the floor from this morning's rain. The carelessness apparent everywhere, such as the telephone being completely buried, makes me so angry I have to walk outside and take gulps of cold air. Benito is at another job. One of his men sees that we are extremely upset and tries to say that all will be done soon, and done well. He is working on the opening between the new kitchen and the cantina. He's shy but seems concerned. A beautiful house, beautiful position. All will be well. His bleary old blue eyes look at us sadly. Benito arrives full of bluster. No time to clean up before we arrived, and anyway it's the plumber's responsibility, he has been held up himself because the plumber didn't come when he said he would. But everything is _perfetto, signori._ He'll take care of the cracked plaster; it didn't dry properly because of the rains. We hardly answer. As he gestures, I catch the worker looking at me. Behind Benito's back he makes a strange gesture; he nods toward Benito, then pulls down his eyelid.
The upstairs patio seems perfect. They've laid rose-colored brick and reattached the rusty iron railings so that the patio is secure but still looks old. Something was done well.
By four, twilight begins; by five, it's night. Still, the stores are opening after siesta. A morning of work, siesta, reopening at dark for several hours: the winter rhythm unchanged from the massively hot summer days. We stop by and greet Signor Martini. We're cheered to see him, knowing he'll say, _"Boh,"_ and _"Anche troppo,"_ one of his all-purpose responses that means yes, it's too bloody much. In our bad Italian we explain what's going on. As we start to go, I remember the strange gesture. "What does this mean?" I ask, pulling down my eyelid.
_"Furbo,"_ cunning, watch out, he answers. "Who's _furbo?_ "
"Apparently our contractor."
WARM HOUSE. THANK YOU, ELIZABETH. WE BUY RED CANDLES, cut pine boughs and bring them in for some semblance of Christmas. Our hearts are not into cooking, although all the winter ingredients in the shops almost lure us to the kitchen. We love the furniture Elizabeth has given us. Besides twin beds, coffee table, two desks, and lamps, we'll have an antique _madia,_ whose top part was used to knead bread and let it rise. Beneath the coffin-shaped bread holder are drawers and cabinet. The chestnut's warm patina makes me rub my hand over the wood. On the list she's left for us, we find her immense _armadio,_ large enough to hold all the house linens, a dining room table, antique chests, a _cassone_ (tall storage chest), two peasant chairs, and wonderful plates and serving pieces. Suddenly we will live in a furnished house. With all our rooms, there will be plenty of space, still, for acquiring our own treasures. Amid all the restoration horrors, this great act of generosity warms us tremendously. Right now, the pieces seem to belong to her orderly house, but before we leave we must move everything over to the house full of debris.
As Christmas nears, work slows then stops. We had not anticipated that they would take off so many holidays. New Year's has several holidays attached to it. We'd never heard of Santo Stefano, who merits one day off. Francesco Falco, who has worked for Elizabeth for twenty years, brings his son Giorgio and his son-in-law with a truck. They take apart the _armadio,_ load everything into the truck except the desk, which is too wide to exit the study. Elizabeth has written all her books at that desk and it seems that it was not meant to leave the house. I'm taking boxes of dishes to our car when I look up and see them lowering a desk by rope out the second-floor window. Everyone applauds as it gently lands on the ground.
At the house, we cram all the furniture into two rooms we've shoveled out and swept. We cover everything with plastic and shut the doors.
There is absolutely nothing we can do. Benito does not answer our calls. I have a sore throat. We've bought no presents. Ed has grown silent. My daughter, sick with flu in New York, is spending her first Christmas alone because the construction debacle threw off her plans to come to Italy. I stare for a long time at an ad for the Bahamas in a magazine, the totally expected photo of a crescent of sugar-sand beach along clear, azure water. Someone, somewhere, drifts on a yellow striped float, trailing her fingers in a warm current and dreaming under the sun.
On Christmas Eve we have pasta with wild mushrooms, veal, an excellent Chianti. Only one other person is in the restaurant, for _Natale_ is above all a family time. He wears a brown suit and sits very straight. I see him slowly drink wine along with his food, pouring out half glasses for himself, sniffing the wine as though it were a great vintage instead of the house carafe. He proceeds through his courses with care. We're through; it's only nine-thirty. We'll go back to Elizabeth's, build a fire, and share the _moscato_ dessert wine and cake I bought this afternoon. While Ed waits for coffee, our dinner partner is served a plate of cheese and a bowl of walnuts. The restaurant is silent. He cracks a shell. He cuts a bit of cheese, savors it, eats a walnut, then cracks another. I want to put my head down on the white cloth and weep.
ACCORDING TO IAN, THE WORK FINISHED SATISFACTORILY AT the end of February. We paid for the amount contracted but not for the exorbitant extra amount Benito tacked on. He listed such charges as a thousand dollars for hanging a door. We will have to be there to determine exactly what extra work he did. How we'll settle the final amount is a mystery.
In late April, Ed returns to Italy. He has the spring quarter off. His plan is to clear the land and treat, stain, and wax all the beams in the house before I arrive on June first. Then we will clean, paint all rooms and windows, and restore the floors to the condition they were in before Benito's restoration. The new kitchen has in it only the sink, dishwasher, stove, and fridge. Instead of cabinets, we plan to make plastered brick columns with wide plank shelves and have marble cut for countertops. We have a major incentive: At the end of June, my friend Susan has planned to be married in Cortona. When I asked why she wanted her wedding in Italy, she replied cryptically, "I want to get married in a language I don't understand." The guests will stay with us and the wedding will take place at the twelfth-century town hall.
Ed tells me he's confined to the room on the second floor that opens onto the patio, his little haven amid the rubbish. He cleans one bathroom, unpacks a few pots and dishes, and sets up rudimentary housekeeping. Benito hauled several loads out of the house but only made it as far as the driveway, now a dump. On the front terrace he left a small mountain of stone that was taken out of the wall. The patio and bedroom brick form another small mountain. Even so, Ed is elated. They're gone! The new bathroom, with its foot square tiles, _belle époque_ pedestal sink, and built-in tub, feels large and luxurious, a stark contrast to the former bucket-flush bathroom. Spring is astonishingly green and thousands of naturalized irises and daffodils bloom in long grass all over our land. He finds a seasonal creek pouring over mossy rocks where two box turtles sun themselves. The almond and fruit trees are so outrageously beautiful that he has to tear himself away from working outside.
We try not to call; we tend to get into long conversations, then decide that we could have done x at the house for the money the call has cost. But there is a great need to recount what you've done when you're working on a house. Someone needs to hear that the beams look really great after their final waxing, that your neck is killing you from working above your head all day, that you're on the fourth room. He relates that each room takes forty hours: beams, ceiling, walls. Floors will come last. Seven to seven, seven days a week.
Finally, finally, June—I can go. With all the work Ed has described, I expect the house to glow when I arrive. But, naturally enough, Ed has concentrated on telling me his progress.
When I first arrive, it's hard to focus on how far he has come. The beams look beautiful, yes. But the grounds are full of rubbish, plaster, the old cistern. The electrician has not shown up. Six rooms haven't been touched. All the furniture is piled into three rooms. It's strictly a war zone. I try not to show how horrified I am.
I'm ready for r & r. Unfortunate, because there's nothing to do but launch into this work. We have about three weeks to get ready for our first major onslaught of guests. The wedding! It seems ludicrous that anyone could stay here.
Ed is 6′2″. I am 5′4″. He takes the ceiling I take the floor. Biology is destiny—but which is better? He actually loves finishing the beams. Painting the brick ceiling is less fun but is rewarding. Suddenly the gunky beams and flaking ceiling are transformed into dark substantial beams, pristine white-brick ceiling. The room is defined. Painting goes quickly with the big brushes made of wild boar hair. Pure white walls—white on plaster is whiter than any other white. As each room is finished, my job is to paint the _battiscopa,_ a six-inch-high gray strip along the bases of the walls, a kind of pseudo-moulding that is traditional in old houses of this area. Usually it's a brick color but we prefer the lighter touch. The word means broom-hit. The darker paint doesn't show the marks of the mops and brooms that must constantly pass over these floors. Almost upside down, I measure six inches in several places, tape the floor and wall, then quickly paint and pull off the tape. Naturally, the tape pulls off some white paint, which then has to be retouched. Twelve rooms, four walls each, plus the stairwell, landings, and entrance. We're leaving the stone cantina as is. Next, I decalcify the floor. The first step is to sweep up all the large chunks and dirt, then vacuum. With a special solution I spread, the residue from dirt, plaster, and paint drippings is dissolved. After that, I rinse the floor with a wet mop three times, the middle time with a mild soap solution. I'm on my knees. Next: mop again with water and a little muriatic acid. Rinse, then paint the floor with linseed oil, letting it soak in and dry. After it dries for two days, I wax. On the floor again, char style. My knees, totally unused to this, rebel and I suppress groans when I stand up. Last step: buff with soft cloth. The floors come back, rich and dark and shiny. Each room pops into place, looking very much as they did when we bought the house, only now the beams are right and the radiators are in place. _"Brutto,"_ ugly, I said to the plumber when I saw them. "Yes," he replied, "but beautiful in winter."
As Ed told me, seven to seven: seven days a week. We spread the rubble down the driveway, which is chewed up anyway from all the trucks. We dig in the larger stones and bricks, spread grass cuttings on top. Gradually, it will settle in. We hire someone to take away a truckload that Benito failed to haul. On a walk a few days later, we see a pile of awful rubble dumped along a road about a mile from our house, and to our horror, spot our plaster with the madonna blue coat of paint underneath.
From high school through graduate school, Ed worked as a house mover, busboy, cabinetmaker, refrigerator hauler. A friend calls him "the muscular poet." He's thriving on this work, though he, too, is sapped at night. I never have done manual labor, except spurts of refinishing furniture, pruning, painting, and wallpapering. This is an order of bodily exertion to shock my system. Everything aches. What _is_ water on the knee? I think I may get it. I die at night. In the mornings, we both have surges of new energy that come from somewhere. We plug right back in. We're consumed. I'm amazed: the relentlessness we've developed. I never will feel the same toward workers again; they should be paid fortunes.
When I seal the patio bricks with linseed oil, the sun feels especially deadly. I'm determined to finish and keep working until I start to reel with the fumes and the heat. Now and then I stand up and breathe in great draughts of the honeysuckle we've planted in an enormous pot, stare off into the great view, then dip the brush into the pot again. Who would think to ask, when paying a lot for a new patio, whether the job included finishing the brick's surface? It never occurred to either of us that we would have to treat the kitchen and patio bricks to several coats of this gloppy stuff.
After we clean up late in the day, we walk around assessing what's left, how we've done. We will not have any children together but decide that this is the equivalent of having triplets. As each room is finished, we get to bring in the furniture for it. Gradually, rooms are set up, still spare but basically furnished. I've brought over white bedspreads for the twin beds. We take a morning in Arezzo and buy a few lamps from a place that still makes the traditional majolica vases of the area into lamps. A fabulous feeling—things are shaping up, they're done, it's clean, we'll be warm in winter—we've done it! This feels giddy and fuels us to keep going.
A week before the wedding, our friends Shera and Kevin arrive from California. We see them get off the train way down the track. Kevin is maneuvering something enormous that looks like a coffin for two. His bicycle! We keep working while they go to Florence, Assisi, and on the Piero della Francesca trail. At night we make great meals together and they tell us all the wonders they've seen and we tell them about the new faucet we want to install for the hip bath. They fall instantly in love with the whole area and seem to want to hear our daily saga of cleaning the new bricks on the kitchen floor. When they're not travelling, Kevin is off on long bicycle trips. Shera, an artist, is captive here. She is painting milky blue half circles over the windows in a bedroom. We've picked a star from one of Giotto's paintings and she makes a stencil of it and fills the half domes with gold leaf stars. A few stars "fall" out of the dome and onto the white walls. We're preparing the bridal chamber. At an antique shop near Perugia, I buy two colored prints of the constellations with mythological beasts and figures. At the Cortona market, I find pretty linen and cotton sheets in pale blue with cutwork in white. We're preparing, too, for our first houseparty. We buy twenty wineglasses, linen tablecloths, pans for baking the wedding cake, a case of wine.
There is no way everything can be finished in time for the wedding (or ever?), but we manage an extraordinary amount. The day before everyone arrives, Kevin comes downstairs and asks, "Why does the toilet steam? Is there something peculiar about Italian toilets?" Ed brings in the ladder, climbs up to the wall-mounted tank, and dips in his hand. Hot water. We check the other bathrooms. The new one is O.K. but the other old one also has hot water. We hardly have used those bathrooms and had not let water run long enough for the hot water to arrive, so we had not noticed that neither bathroom had cold water at all. As soon as guests started using the baths, it became noticeable. Shera says she thought the shower was awfully hot, once it finally warmed up, but hadn't wanted to complain. The plumber cannot come for a few days, so we will go through the wedding with quick showers and smoking toilets!
The front terrace is still rough but we have potted geraniums along the wall to distract from the torn-up ground. At least we removed the rubble. Four rooms have beds. Susan's two cousins from England and Cole's brother and sister-in-law are arriving. Shera and Kevin will move to a hotel in town for a couple of days. Other friends are coming from Vermont.
By day, we are twelve in the house. Many hands to help with drinks and lunch. The cake must be improvised because the oven is small. I envisioned three tiers of sponge cake with a hazelnut butter-cream frosting, to be served with whipped cream and cherries steeped in sugared wine. We couldn't find a large pan for the bottom and finally bought a tin dog dish to bake it in. The cake is lovely, if a bit lopsided. We decorate it with flowers all around. Everyone is running off in different directions sightseeing and shopping.
We're having the prenuptial dinner here on a clear warm night, everyone in pale linens and cottons. Many photos are taken of us arm in arm on the steps and leaning over the balcony. Susan's cousin brings out champagne he has brought from France. After drinks with _bruschette_ and dry olives, we start with cool fennel soup. I've made a rustic casserole of chicken, white beans, sausage, tomatoes, and onions. There are tiny green beans, baskets of bread, and a salad of arugula, radicchio, and chicory. Everyone tells wedding stories. Mark was to have married a Colorado girl who ran away on the wedding day and married someone else in a week. Karen was a bridesmaid on a boat wedding and the bride's mother, in teal chiffon, tipped into the drink. When I married at twenty-two, I wanted a midnight wedding with everyone wearing robes and carrying candles. The minister said absolutely not, that midnight was a "furtive hour." Nine was as late as he'd go. And instead of a robe, I wore my sister's wedding dress and carried a leatherbound Keats down the aisle. My mother pulled my skirt and I leaned over for her words of wisdom. She whispered, "It won't last six months." But she was wrong.
We should have an accordion player, à la Fellini, and maybe a white horse for the bride to ride, but we do well with the fabulous night, and the CD player inspires a little dancing in the dining room. The white peach tart with pine nuts should end this dinner but Ed's description of the _crema_ and the hazelnut _gelati_ in town sends everyone to the cars. They're amazed that such a small town is still hopping at eleven, everyone outdoors with coffee, ice cream, or perhaps an _amaro,_ an after-dinner bitter. Babies in strollers still as wide-eyed as their parents, teenagers sitting on the town hall steps. The only thing sleeping is a cat on top of the police car.
The morning of the wedding Susan, Shera, and I pick a bouquet of lavender, pink, and yellow wildflowers for Susan to carry. When we're all dressed in silks and suits, we walk into town over the Roman road. Ed carries our good shoes in a shopping bag. Susan has brought Chinese painted paper parasols for everyone because of the midday sun. We walk through town and up the steps of the twelfth-century town hall. It's a dark, high-ceilinged room with tapestries and frescoes and high judicial-looking chairs, an impressive room to sign a treaty in. The city of Cortona has sent red roses and Ed has arranged for Bar Sport to come over right after the ceremony with cold _prosecco._ Susan's cousin Brian runs all around with his video camera, getting shots from every angle. After the brief ceremony, we cross the piazza to La Logetta for a Tuscan feast beginning with a selection of typical _antipasti: crostini,_ little rounds of bread topped with olives, peppers, mushroom, or chicken liver; _prosciutto e melone,_ fried olives stuffed with _pancetta_ and spicy bread crumbs; and the local _finocchiona,_ a salami studded with fennel seeds. Next they bring out a selection of _primi,_ first courses to try, including ravioli with butter and sage, and _gnocchi di patate,_ little "knuckles" of potato served here with pesto. Course after course arrives, culminating in platters of roast lamb and veal and the famous grilled Val di Chiana steak. Karen notices the grand piano in the corner under a massive vase of flowers and prevails upon Cole, who is a pianist, to play. Ed is at the other end of the table but he catches my eye as Cole begins Scarlatti. Three weeks ago this was a dream, a long shot, a frightening prospect. "Cheers!" the English cousins call out.
Back at home, we're all stunned by the food and heat and decide to postpone the wedding cake until late afternoon. I hear someone snoring. In fact, I hear two people snoring.
Though the cake lacks that professional touch, it may be the best cake I ever tasted. I'll credit our tree for the nuts. Shera and Kevin are dancing in the dining room again. Others stroll out to the point where our land ends for the view of the lake and valley. We can't decide whether to eat again or forget it. Finally we run down to Camucia for pizza. Our favorite places are closed, so we end up in a definitely downscale, unatmospheric place. The pizza is excellent, however, and no one seems to notice the dust gray curtains or the cat who has leapt on the adjoining table and is polishing off the remains of someone's dinner. At the end of the table our bride and groom, holding hands, are in a charmed circle of two.
Susan and Cole have headed to Lucca then back to France; their family guests are gone.
Shera and Kevin are here for a few more days. Ed and I visit the _marmista_ and choose thick white marble for the countertops. The next day he cuts and bevels them and Ed and Kevin load them into the back of the car. Suddenly the kitchen looks the way I thought it would: brick floor, white appliances, long sink, plank shelves, marble counters. I sew a blue plaid curtain to go under the sink and hang a braid of garlic and some dried herbs from the wall shelves. In town we find an old peasant dish and cup rack. The dark chestnut looks great against the white walls. At last, a place for all the cups and bowls we're buying in the local ceramic patterns.
Everyone has gone. We eat the last of the wedding cake. Ed begins one of his many lists—we should paper a room with them—of projects he hopes to accomplish now. The kitchen is looking irresistible and we're moving into high season for vegetables and fruit. July fourth: Much of summer is left. My daughter is coming. Travelling friends will stop in for lunch or for a night. We're ready.
A Long Table
Under the Trees
MARKET DAY FALLS ON THURSDAYS IN Camucia, the lively town at the bottom of Cortona's hill, and I'm there early before the heat sets in. Tourists pass right through Camucia; it's just the modern spillover from the venerable and dominant hill town above it. But modern is relative. Among the _frutta e verdura_ shops, the hardware and seed stores, you happen on a couple of Etruscan tombs. Near the butcher's shop are remnants of a villa, an immense curly iron gate and swag of garden wall. Camucia, bombed in World War II, has its share of chestnut trees, photographable doors, and shuttered houses.
On market day, a couple of streets are blocked to traffic. The vendors arrive early, unfolding what seems like whole stores or supermarket aisles from specially made trucks and wagons. One wagon sells local _pecorino,_ the sheep's milk cheese that can be soft and almost creamy, or aged and strong as a barnyard, along with several wheels of _parmigiano._ The aged cheese is crumbly and rich, wonderful to nibble as I walk around the market.
I'm hunting and gathering food for a dinner for new friends. My favorite wagons belong to the two _porchetta_ maestros. The whole pig, parsley entwined with the tail, apple—or a big mushroom—in its mouth, stretches across the cutting board. Sometimes the decapitated head sits aside at an angle, eyeing the rest of its body, which has been stuffed with herbs and bits of its own ears, etc. (best not to inquire too closely), then roasted in a wood oven. You can buy a _panino_ (a crusty roll) with nothing on it but slabs of _porchetta_ to take home, lean or with crispy, fatty skin. One of the lords of the _porchetta_ wagons looks very much like his subject: little eyes, glistening skin, and bulbous forearms. His fingers are short and porky, with bitten-down nails. He's smiling, extolling his pig's virtues, but when he turns to his wife, he snarls. Her lips are set in a permanent tight half smile. I've bought from him before and his _porchetta_ is delicious. This time I buy from the milder man in the next stand. For Ed, I ask for extra _sale,_ salt, which is what the indefinable stuffing is called. I like it but find myself picking through to see if there's something peculiar in it. Though the pig is useful and tasty in all its parts and preparations, the slow-roasted _porchetta_ must be its apogee. Before I move on to the vegetables, I spot a pair of bright yellow espadrilles with ribbons to wind around the ankles; I balance my shopping bags while I try on one. Perfect, and less than ten dollars. I drop them in with the _porchetta_ and _parmigiano._
Scarves (bright Chanel and Hermès copies) and linen tablecloths float from awnings; toilet cleaners, tapes, and T-shirts are stacked in bins and on folding tables. Besides buying food, you can dress, plant a garden, and stock a household from this market. There are a few local crafts for sale but you have to look for them. The Tuscan markets aren't like those in Mexico, with wonderful toys, weaving, and pottery. It's a wonder these markets continue at all, given the sophistication of Italian life and the standard of living in this area. I find the iron-working traditions still somewhat in evidence. Occasionally, I see good andirons and handy fireplace grills. My favorite is a holder for whole _prosciutto,_ an iron grip with handle mounted on a board for ease in slicing; maybe someday I'll find I need that much _prosciutto_ and buy one. One week I bought handwoven baskets made from dark supple willow twigs, the large ones perfect for kitchen supplies and the small round ones for the ripe-right-now peaches and cherries. One woman sells old table and bed linens with thick monograms, all of which must have been gathered from farms and villas. She has three mounds of yellowed lace. Perhaps some of it was made on the nearby island, Isola Maggiore in Lake Trasimeno. Women still sit in the doorways there, hooking lace in the afternoon light. I find two enormous square linen pillowcases with miles of inset lace and ribbons—ten thousand lire, same as the sandals, seems to be the magic number today. Of course, I will have to have the pillows especially made. When I buy some striped linen dishtowels, I notice several goat skins hanging from a hook. I have in mind that they would look terrific on the _cotto_ floors at my house. The four the man has are too small but he says to come back next week. He tries to convince me that his sheepskins would be better anyway, but they don't appeal to me.
I'm wending my way toward the produce, but walk up to the bar for a coffee. Actually, I stop with an excuse to stare. People from surrounding areas come not only to shop but to greet friends, to make business arrangements. The din around the Camucia market is a lovely swarm of voices, many speaking in the local Val di Chiana dialect; I don't understand most of what they're saying but I do hear one recurring habit. They do not use the _ch_ sound for _c,_ but slide it into an _s_ sound. "Shento," they say for _cento_ (one hundred), instead of the usual pronunciation "chento." I heard someone say "cappushino," for cappuccino, though the usual affectionate shortening of that is "cappuch." Their town is pronounced not "Camuchia," but "Camushea." Odd that the _c_ is often the affected letter. Around Siena, people substitute an _h_ sound for _c—_ "hasa" and "Hoca-Hola." Whatever the local habit with _c,_ they're all talking. Outside the bar, groups of farmers, maybe a hundred men, mill about. Some play cards. Their wives are off in the crowd, loading their bags with tiny strawberries, basil plants with dangling roots, dried mushrooms, perhaps a fish from the one stand that sells seafood from the Adriatic. Unlike the Italians who take their thimbleful of espresso in one quick swallow, I sip the black, black coffee.
A friend says Italy is getting to be just like everywhere else—homogenized and Americanized, she says disparagingly. I want to drag her here and stand her in this doorway. The men have the look of their lives—perhaps we all do. Hard work, their faces and bodies affirm. All are lean, not a pound of extra fat anywhere. They look cured by the sun, so deeply tan they probably never go pale in winter. Their country clothes are serviceable, rough—they don't "dress," they just get dressed. They wear, as well, a natural dignity. Surely some are canny, crusty, cruel, but they look totally present, unhidden, and alive. Some are missing teeth but they smile widely without embarrassment. I look in one man's eyes: The left one is white with milky blue veins like those in an exploded marble. The other is black as the center of a sunflower. A retarded boy wanders among them, neither catered to nor ignored. He's just there, living his life like the rest of us.
At home I plan a menu ahead, though I frequently improvise as I shop. Here, I only begin to think when I see what's ripe this week. My impulse is to overload; I forget there are not ten hungry people at home. At first I was miffed when tomatoes or peas had spoiled when I got around to cooking them a few days later. Finally I caught on that what you buy today is ready—picked or dug this morning at its peak. This also explained another puzzle; I never understood why Italian refrigerators are so minute until I realized that they don't store food the way we do. The Sub-Zero giant I have at home begins to seem almost institutional compared to the toy fridge I now have here.
Two weeks ago, small purple artichokes with long stems were in. We love those, quickly steamed, stuffed with tomatoes, garlic, yesterday's bread, and parsley, then doused with oil and vinegar. Today, not a one. The _fagiolini,_ slender green beans, are irresistible. Should I have two salads, because the beans also would be good with a shallot vinaigrette? Why not? I buy white peaches for breakfast but for tonight's dessert, the cherries are perfect. I take a kilo, then set off to find a pitter back in the other part of the market. Since I don't know the word, I'm reduced to sign language. I do know _ciliegia,_ cherry, which helps. I've noticed in French and Italian country desserts that the cooks don't bother to pit the cherries, but I like to use the pitter when they're served in a dish. These I'll steep in Chianti with a little sugar and lemon. I decide on some tiny yellow potatoes still half covered with dirt. Just a scrubbing, a dribble of oil and some rosemary and they'll roast in the oven.
I could complete my shopping for this meal right here. I pass cages of guinea hens, ducks, and chickens, as well as rabbits. Since my daughter had a black angora rabbit as a pet once, I can't look with cold eyes on the two spotted bunnies nibbling carrots in the dusty Alitalia flight bag, can't imagine them trembling in the trunk of my car. I intend to stop at the butcher's for a veal roast. The butcher's is bad enough. I admit it's not logical. If you eat meat, you might as well recognize where it comes from. But the drooped heads and closed eyelids of the quail and pigeon make me stop and stare. Rooster heads, chicken feet (with yellow nails like Mrs. Ricker's, my grandmother's Rook partner), the clump of fur to show the skinned rabbit is not a cat, whole cows hanging by their feet with a square of paper towel on the floor to catch the last drops of blood—all these things make my stomach flip. Surely they're not going to eat those fluffy chicks. When I was a child, I sat on the back steps and watched our cook twist a chicken's neck then snap off the head with a jerk. The chicken ran a few circles, spurting blood, before it keeled over, twitching. I love roast chicken. Could I ever wring a neck?
I have as much as I can carry. The other stop I'll make is at the cooperative cantina for some local wine. Near the end of the sinuous line of market stalls, a woman sells flowers from her garden. She wraps an armful of pink zinnias in newspaper and I lay them under the straps of my bag. The sun is ferocious and people are beginning to close down for siesta. A woman who has not sold many of her striped lime and yellow towels looks weary. She dumps the dog sleeping in her folding chair and settles down for a rest before she begins to pack up.
On my way out, I see a man in a sweater, despite the heat. The trunk of his minuscule Fiat is piled with black grapes that have warmed all morning in the sun. I'm stopped by the winy, musty, violet scents. He offers me one. The hot sweetness breaks open in my mouth. I have never tasted anything so essential in my life as this grape on this morning. They even smell purple. The flavor, older than the Etruscans and deeply fresh and pleasing, just leaves me stunned. Such richness, the big globes, the heap of dusty grapes cascading out of two baskets. I ask for _un grappolo,_ a bunch, wanting the taste to stay with me all morning.
AS I UNLOAD MY CLOTH SACKS, THE KITCHEN FILLS WITH THE scents of sunny fruits and vegetables warmed in the car. Everyone coming home from market must feel compelled to arrange the tomatoes, eggplants ( _melanzane_ sounds like the real name and even aubergine is better than dreary-sounding eggplant), zucchini, and enormous peppers into a still life in the nearest basket. I resist arranging the fruit in a bowl, except for what we'll eat today, because it's ripe this minute and all we're not about to eat now must go in the fridge.
I'm still amazed that the kitchen is finished. Though there still is the ghost of a circle above the outside door, where a saint or cross hung in a niche when this was the chapel for the house, there is no sign at all of the room's later inhabitants, oxen and chickens. When the mangers were ripped out, we found the remains of elaborate scroll designs on the crumbling plaster. As the nasty pen came down, we saw green faux marble designs. Now and then in the restoration we stopped and said, "Did you ever expect to be scraping decades of mold from animals' uric acid off a wall?" and "You realize we'll be cooking in a _chapel?_ "
Now, oddly, it looks as though the kitchen always could have been this way. Like those in the rest of the house, the floors are waxed brick, the walls white plaster, and the ceiling has (oh, Ed's neck and back!) dark beams. We avoided cabinets. It was easy to construct the plaster-covered brick supports built for thick plank shelves we envisioned when we spent our evenings drawing on tablets of grid paper. Ed and I cut and painted them white. The baskets from the market hold utensils and staples. The two-inch-thick white Carrara marble tops are smooth to my eye and always cool to the touch or to the pizza dough and pastry I roll on it. We hung the same rough shelves on another wall for glasses and pasta bowls. To secure the brackets, Ed drilled toggle bolts into solid rock, spewing stones and straining the drill to its highest whine.
THE _SIGNORA_ WHO LIVED HERE A HUNDRED YEARS AGO COULD walk in now and start to cook. She'd like the porcelain sink, big enough to bathe a baby in, its drain board and the curved chrome faucet. I imagine her with a pointed chin and shiny black eyes, her hair swept up and twisted in a comb. She's in sturdy shoes that tie and a black dress with the sleeves pushed up, ready to roll out the ravioli. She'd be ecstatic, no doubt, to see appliances—the dishwasher, stove, and frost-free fridge (still a novelty in Tuscany), but otherwise, she'd feel quite at home. In my next life, when I am an architect, I always will design houses with kitchens that open to the outdoors. I love stepping out to head and tail my beans while sitting on the stone wall. I set dirty pots out to soak, dry my dishcloths on the wall, empty excess clean water on the arugula, thyme, and rosemary right outside the door. Since the double door is open day and night in summer, the kitchen fills with light and air. A wasp—is it the same one?—flies in every day and drinks from the faucet, then flies right out.
The one absolutely American feature is the lighting. Terrifically high utility costs explain the prevalence of forty-watt bulbs hanging in so many houses. I cannot bear a dim kitchen. We chose two bright fixtures and a rheostat, causing Lino, the electrician, extreme consternation. He'd never installed a rheostat, which intrigued him. But the lights! "One is enough. You are not performing surgery in here," he insisted. He needed to warn us that our electrical bill—he had no words, only the gesture of loosely shaking both hands in front of him and shaking his head at the same time. Clearly, we are headed for ruin.
On the brick ledge behind the sink, I've begun to accumulate local hand-painted majolica platters and bowls. I've thought of luring Shera back to paint a stencil of grapes, leaves, and vines around the top of the walls. But for the moment, the kitchen is _finita._
WE POURED SO MUCH ENERGY INTO THE KITCHEN BECAUSE A dominant gene in my family is the cooking gene. No matter what occasion, what crisis, the women I grew up among could flat out hold forth in the kitchen, from delicate timbales and pressed chicken to steaming cauldrons of Brunswick stew. In summer, my mother and our cook, Willie Bell, went into marathons of putting up tomatoes, pickling cucumbers, stirring vats of scuppernongs for jelly. By early December they had made brandied cakes and shelled mountains of pecans for roasting. Never was our kitchen without tins of brownies and icebox cookies. Or without a plate of cold biscuits left over from dinner. I still miss toasted biscuits for breakfast. At one meal we already were talking about the next.
My daughter showed every sign of breaking the legacy of my mother and Willie, whose talents destined my sisters and me to shelves of cookbooks, constant plans for the next party, and—ultimate test—even the fate to cook when eating alone. Throughout her childhood, except for an occasional batch of obsidian-like fudge, Ashley disdained the kitchen. Shortly after she graduated from college, she began to cook and immediately started calling home for recipes for chicken with forty cloves of garlic, profiteroles, risotto, chocolate soufflé, potatoes Anna. Without meaning to, she seemed to have absorbed certain knowledge. Now, when we're together, we, too, go into paroxysms of planning and cooking. She has taught me a great marinated pork tenderloin recipe and a buttermilk lemon cake. These familial connections give me a helpless feeling: Cooking is destiny.
This inexorable inheritance notwithstanding, in recent years, I've worked more and more. In our normal life in San Francisco, everyday cooking becomes, at times, a chore. I confess to an occasional supper of ice cream from the carton, eaten with a fork while leaning against the kitchen counter. Sometimes we both get home late and find in the fridge celery, grapes, withered apples, and milk. No problem, since San Francisco has great restaurants. On weekends we try to roast two chickens or make minestrone or a big pasta sauce to get us to Tuesday. On Wednesday: a stop at Gordo's for super carnitas burritos with sour cream, guacamole, extra hot sauce, and a thousand grams of fat. In rushes of super organization, I freeze plastic tubs of soup and chili and stew and stock.
The leisure of a summer place, the ease of prime ingredients, and the perfectly casual way of entertaining convince me that this is the kitchen as it's meant to be. I think of my mother's summer tables often. She _launched_ meals, seemingly with ease. Finally it dawns on me—maybe I'm not simply inadequate. It was easier then. She had people around her, as we do here. I sat on the ice cream churn while my sister turned the handle. My other sister shelled peas. Willie was totally capable. My mother directed kitchen traffic, arranged the table. I use her recipes often, and have a measure of her ease with guests but, please, no fried chicken. Here, I have that prime ingredient, time. Guests really do want to pit the cherries or run into town for another wedge of _parmigiano._ Also, cooking seems to take less time because the quality of food is so fine that only the simplest preparations are called for. Zucchini has a real taste. Chard, sautéed with a little garlic, is amazing. Fruit does not come with stickers; vegetables are not waxed or irradiated, and the taste is truly different.
Nights turn cool at fifteen hundred feet. That suits us because we can prepare some of the hearty foods that are not at all suitable in the sun. While _prosciutto_ with figs, chilled tomato soup, Roman artichokes, and pasta with lemon peel and asparagus are perfect at one, the fresh evenings fuel the appetite. We serve spaghetti with _ragù_ (I finally learned that the secret ingredient of a _ragù_ is chicken liver), minestrone with globes of pesto, _osso buco,_ grilled polenta, baked red peppers stuffed with ricotta and herb custard, warm cherries in Chianti with hazelnut pound cake.
When tomatoes are ripe, nothing is better than cold tomato soup with a handful of basil and a garnish of polenta croutons. _Panzanella,_ little swamp, is another tomato favorite, a salad of oil, vinegar, tomatoes, basil, cucumber, minced onion, and stale bread soaked in water and squeezed dry—a true invention from necessity. Since bread must be bought every day, Tuscan cooking makes good use of leftovers. The rough loaves work perfectly for bread puddings and for the best French toast I've ever had. We go for days without meat and don't even miss it, then a roasted _faraona_ (guinea hen) with rosemary, or sage-stuffed pork loin, remind us of how fabulous the plainest meats can be. I cut a small basketful of thyme, rosemary, and sage, wishing I could beam one of each plant to San Francisco, where I keep a window box of faltering herbs going. Here, the sun doubles their size every few weeks. The oregano near the well quickly spreads to a circle about three feet wide. Even the wild mint and lemon balm I dug up on the hill and moved have taken off. Mint thrives. Vergil says deer wounded by hunters seek it for wounds. In Tuscany, where hunters long since have driven out most wildlife, the mint is more plentiful than deer. Maria Rita, at the _frutta e verdura,_ tells me to use lemon balm in salads and vegetables, as well as in my bathwater. I think I would like cutting herbs even if I weren't cooking. The pungency of just-snipped herbs adds as much to the cook's enjoyment as to taste. After weeding the thyme, I don't wash my hands until the fragrance fades from my hands. I planted a hedge of sage, more than I ever could use, and let most flower for the butterflies. Sage flowers, along with lavender, look pretty in wildflower bouquets. The rest I dry or use fresh, usually for white beans with chopped sage and olive oil, a favorite of Tuscans, who are known as "bean eaters."
Anytime we grill, Ed tosses long wands of rosemary on the coals and on the meat. The crispy leaves not only add flavor, they're good to nibble, too. When he grills shrimp, he threads them on rosemary sticks.
I have pots of basil by the kitchen door because it is supposed to keep out flies. During the wall-building and well-drilling weeks, I saw a worker crush leaves in his hand and smear his wasp sting. He said it took away all the pain. A larger patch grows a few feet away. The more I cut off, the more seems to grow. I use whole leaves in salad, bunches for pesto, copious amounts in sautéed summer squashes and tomato dishes. Of all herbs, basil holds the essence of Tuscan summer.
THE LONG STRETCH OF SUMMER LUNCHES CALLS FOR A LONG _tavola._ Now that the kitchen is finished, we need a table outdoors, the longer the better, because inevitably the abundance at the weekly market incites me to buy too much and because inevitably guests gather—friends from home, a relative's friends from somewhere who thought they'd say hello since they were in the area, and new friends, sometimes with friends of _theirs._ Add another handful of pasta to the boiling pot, add a plate, a tumbler, find another chair. The table and the kitchen can oblige.
I have considered my table, its ideals as well as its dimensions. If I were a child, I would want to lift up the tablecloth and crawl under the unending table, into the flaxen light where I could crouch and listen to the loud laughs, clinks, and grown-up talk, hear over and over _"Salute"_ and _"Cin-cin"_ travelling around the chairs, stare at kneecaps and walking shoes and flowered skirts hiked up to catch a breeze, the table steady under its weight of food. Such a table should accommodate the wanderings of a large dog. At the end, you need room for an enormous vase of all the flowers in bloom at the moment. The width should allow platters to meander from hand to hand down the center, stopping where they will, and numerous water and wine bottles to accumulate over the hours. You need room for a bowl of cool water to dip the grapes and pears into, a little covered dish to keep the bugs off the Gorgonzola ( _dolce_ as opposed to the _piccante_ type, which is for cooking) and _caciotta,_ a local soft cheese. No one cares if olive pits are flung into the distance. The best wardrobe for such a table runs to pale linens, blue checks, pink and green plaid, not dead white, which takes in too much glare. If the table is long enough, everything can be brought out at once, and no one has to run back and forth to the kitchen. Then the table is set for primary pleasure: lingering meals, under the trees at noon. The open air confers an ease, a relaxation and freedom. You're your own guest, which is the way summer ought to be.
In the delicious stupor that sets in after the last pear is halved, the last crust scoops up the last crumbles of Gorgonzola, and the last drop empties into the glass, you can ruminate, if you are inclined that way, on your participation in the great collective unconscious. You are doing what everyone else in Italy is doing, millions of backsides being shined by chairs at millions of tables. Over each table, a miniature swarm of gnats is gathering. There are exceptions, of course. Parking attendants, waiters, cooks—and thousands of tourists, many of whom made the mistake of eating two wedges of great sausage pizza at eleven and now have no inclination to eat anything. Instead, they wander under the unbearable sun, peeking through metal grates covering shop windows, pushing at the massive doors of locked churches, sitting on the sides of fountains while squinting into minuscule guidebooks. Give it up! I've done the same thing. Then, later, it's hard to deny yourself the luscious _melone_ ice cream cone at seven, when the air is still hot and your sandals have rubbed your heels raw. Those weak ones ( _mea culpa_ ) who succumb possibly will have another wedge, artichoke this time, on the way to the hotel; then, when Italy begins eating at nine, the foreign stomach doesn't even mumble. That happens much later, when all the good restaurants are full.
The rhythm of Tuscan dining may throw us off but after a long lunch outside, one concept is clear—siesta. The logic of a three-hour fall through the crack of the day makes perfect sense. Best to pick up that Piero della Francesca book, wander upstairs and give in to it.
I know I want a wooden table. When I was growing up, my father had dinners for his men friends and a few employees on Fridays. Our cook, Willie Bell, and my mother spread a long white table under a pecan tree in our yard with fried chicken cooked right there on our brick barbecue, potato salad, biscuits, iced tea, pound cake, and bottles of gin and Southern Comfort. The noon meal often lasted most of the day, sometimes ending with the swaying men, arm in arm singing "Darktown Strutter's Ball" and "I'm a Ramblin' Wreck from Georgia Tech" slowly as if on a tape that warped in the sun.
From the very first weeks we lived in the house, we used the abandoned worktable, a crude prototype of the table I imagined us eventually setting under the line of five _tigli_ trees. At a market stall, I bought tablecloths, long to keep splinters from digging into our knees. With napkins to match, a jar of poppies, Queen Anne's lace, and blue bachelor's buttons on the table, our yellow plates from the COOP, we served forth, mainly to each other.
My idea of heaven is a two-hour lunch with Ed. I believe he must have been Italian in another life. He has begun to gesture and wave his hands, which I've never seen him do. He likes to cook at home but simply throws himself into it here. For a lunch he prepares, he gathers _parmigiano,_ fresh mozzarella, some _pecorino_ from the mountains, red peppers, just-picked lettuces, the local salami with fennel, loaves of _pane con sale_ (the bread that isn't strictly traditional here since it has salt), _prosciutto,_ a glorious bag of tomatoes. For dessert, peaches, plums, and, my favorite, a local watermelon called _minne di monaca,_ nun's tits. He piles the bread board with our cheeses, salami, peppers, and on our plates arranges our first course, the classic _caprese:_ sliced tomatoes, basil, mozzarella, and a drizzle of oil.
In the _tigli_ shade, we're protected from the midday heat. The cicadas yammer in the trees, that deeply heart-of-summer sound. The tomatoes are so intense we go silent as we taste them. Ed opens a celebratory bottle of _prosecco_ and we settle down to recap the saga of buying and restoring the house. Oddly, we now omit the complications and panic; we've begun the selection process, the same one that insures the continuance of the human race: forgetting the labor. Ed starts drawing up plans for a bread oven. We dream on about other projects. The sun through the flowering trees bathes us in gold sifted light. "This isn't real; we've wandered into a Fellini film," I say.
Ed shakes his head. "Fellini is a documentary filmmaker—I've lost my belief in his genius. There are Fellini scenes everywhere. Remember the brilliant motorcycle that comes around and around in _Amarcord_? It happens _all_ the time. You're nowhere in a remote village, no one in sight, and suddenly a huge Moto Guzzi streaks by." He peels a peach in one long spiral and just because this was all too pleasant we open a second bottle of _prosecco_ and wile away another hour before we drift in to rest and revive our energy for a walk into town to case out the restaurants, stroll along the parterre overlooking the valley, and, hard to contemplate, begin the next meal.
WE HAVE CALLED THE SHY AND SILENT CARPENTERS, MARCO and Rudolfo. They seem amused no matter what work they do here. The idea of a painted table seating ten seems to stun them. They're used to chestnut stain. Are we certain? I see them swap a glance with each other. But it will have to be repainted in two years. Too impractical. We've sketched what we want and have the paint sample, too—primary yellow.
They return four days later with the table, sealed and painted—a miracle turnaround time anywhere but especially for two as busy as they are. They laugh and say the table will glow in the dark. It does pulsate with color. They haul it to the spot with the broadest view into the valley. In the deep shade, the yellow shines, luring us to come forth from the house with jugs and steaming bowls, baskets of fruit and fresh cheeses wrapped in grape leaves.
DINNER TONIGHT IS FOR AN ITALIAN COUPLE, THEIR BABY, AND our compatriot writers. This Italian baby girl, at seven months, chews on piquant olives and looks longingly at the food. Our friends have been amused by our adventures in restoration, safely amused since their houses were restored before workmen disappeared and before the dollar dove. Each knows an astonishing amount about wells, septic systems, gutters, pruning—minute technical knowledge acquired by years under the roofs of quirky old farmhouses. We're awed by their fluency with Italian, their endless knowledge of the intricacies of telephone bills. Though I imagine conversations about the currents in Italian literature, opera, and controversial restorations, we seem to discuss most passionately olive pruning, grease traps, well testing, and shutter repair.
The menu: with drinks, _bruschette_ with chopped tomatoes and basil, _crostini_ with a red pepper confit. The first course, _gnocchi,_ not the usual potato but light semolina _gnocchi_ (small servings—it's rich), followed by veal roasted with garlic and potatoes, then garnished with fried sage. The little green beans, still crisp, warm, with fennel and olives. Just before they arrive, I pick a huge basket of lettuces. At the start of summer, I scattered two envelopes of mixed lettuces as an edging along a flower bed. They were up in a week and in three, bolted the border. Now they're everywhere; it feels odd to be weeding the flower bed and accumulating dinner at the same time. Some look unfamiliar; I hope we're not eating just-sprouting calendula or hollyhocks. The cherries, simmered and cooled, have attracted bees to them all afternoon. One of the tiny hummingbirds made a quick foray into the kitchen, drawn possibly by the scent of the deep red wine syrup.
When they arrive it will be the soft, slow Tuscan twilight, fading after drinks from transparent to golden to evening blue, then, by the end of the first course, into night. Night happens quickly, as though the sun were pulled in one motion under the hill. We light candles in hurricane shades all along the stone wall and on the table. For background music, a hilarious chorus of frogs tunes up. _Molti anni fa,_ many years ago, our friends begin. Their stories weave an Italy around us that we know only through books and films. _In the sixties . . . In the seventies . . . A true paradise._ That's why they came—and stayed. They love it but it's downhill now in comparison to the four armoires from that nutty contessa. _How alive the streets of Rome were with people, and remember the theater with the roof that rolled back, how sometimes it would rain?_ Then the talk shifts to politics. They know everyone. We're all horrified at the car bombing in Sicily. Is there a Mafia here? Our questions are naive. The fascist leaning in recent elections disturbs everyone. Could Italy go back? I tell them about the antique dealer in Monte San Savino. I saw a photo of Mussolini over his shop door and he saw me looking at it. With a big smile he asks if I know who that is. Not knowing if the photo is a campy object or one of veneration, I give him the fascist salute. He goes crazy, thinking I approve. He's all over me, talking about what a bold and _bravo_ man Il Duce was. I want to get out with my strange purchases—a big gilt cross and the door to a reliquary—but now the prices come down. He invites me back, wants me to meet his family. Everyone advises me to take full advantage.
I feel immersed here; my "real life" seems remote. Odd that we're all here. We were given one country and we've set ourselves up in another—they much more radically than we; they defined their lives and work by _this_ place, not _that._ We feel so much at home, pale and American as we are. We could just stay here, go native. Let my hair grow long, tutor local kids in English, ride a Vespa into town for bread. I imagine Ed on one of those tiny tractors made for terraced land. Imagine him starting a little vineyard. Or we could make tisanes of lemon balm. I look at him but he is pouring wine. I almost feel our strange voices—English, French, Italian—spreading out around the house, over the valley. Sound carries on the hills. _(Stranieri,_ foreigners, we're called, but it sounds more dire, more like strangers, an oddly chilling word.) Often we hear parties of invisible neighbors above us. We've shifted an ancient order of things on this hillside, where the tax collector, the police captain, and the newsstand owner (our nearest neighbors although we can't see any of them) heard only Italian until we encamped here.
The Big Dipper, clear as a dot-to-dot drawing, seems about to pour something right on top of the house, and the Milky Way, so pretty in Latin as the _via lactia,_ sweeps its bridal train of scattered stars over our heads. The frogs go silent all at once, as if someone shushed them. Ed brings out the _vin santo_ and a plate of _biscotti_ he made this morning. Now the night is big and quiet. No moon. We talk, talk, talk. Nothing to interrupt us except the shooting stars.
Summer Kitchen
Notes
ONE SPRING WHEN I STUDIED COOKING with Simone Beck at her house in Provence, she said some things I never forgot. Another student, a caterer and cooking teacher, kept asking Simca for the technique for everything. She had a notebook and furiously wrote down every word Simca said. The other four of us were mainly interested in eating what we'd prepared. When she asked one time too many, Simca said crisply, "There _is_ no technique, there is just the way to do it. Now, are we going to measure or are we going to cook?"
I've learned here that simplicity is liberating. Simca's philosophy applies totally to this kitchen, where we no longer measure, but just cook. As all cooks know, ingredients of the moment are the best guides. Much of what we do is too simple to be called a recipe—it's just the way to do it. I vary the ubiquitous _prosciutto e melone_ with halved figs. The cold tomato soup I make is simply chopped herbs—mainly basil—and ripe tomatoes stirred into clear chicken stock and popped in the freezer until chilled. I roast whole heads of garlic in a terra-cotta dish with a little olive oil—great to squeeze the cloves onto bread. One of the best pastas is spaghetti tossed with chopped arugula, cream, and minced _pancetta,_ then sprinkled with _parmigiano._ Green beans served with black olives, sliced raw fennel, spring onions, and a light vinaigrette or lemon juice must be one of the nicest things ever to happen to a bean. Ed's invention couldn't be easier: He splits figs, pours on a little honey, runs them under the broiler, then drizzles them with cream. Sliced peaches with sweetened mascarpone and a crumbling of _amaretti_ cookies have become a standby. Some favorites are a bit more involved, though nothing to make me wonder what madness led me to get involved.
Growing such a plethora of herbs induces me to squander them. All platters are garnished with what's left in the basket: a bunch of flowering thyme scattered over vegetables, the roast presented on a bed of sage, sprigs of oregano around the pasta. Lavender, grape and fig leaves, and airy fennel greens are fun to use as garnishes, too. With a few wildflowers, cut herbs in a terra-cotta pot look right at home on the table.
Here are a few quick, personal recipes that guests have raved over or that have sent us secretly to the fridge the next morning to taste the leftovers. Italians wouldn't consider risotto or pasta a main course, but for us, often it is. The oil of choice is, of course, olive oil, unless otherwise specified. All herbs in these recipes are fresh.
~ANTIPASTI~
Red Peppers (or Onions) Melted with Balsamic Vinegar
The immense, convoluted, lustrous peppers in primary red, green, and yellow are my favorite vegetable of summer because they wake up so many dishes. A quick sauté of a mixture of the three adds zip to any plate. And there's red pepper soup, mousse of yellow peppers, old-fashioned stuffed green ones . . .
_~Seed and slice 4 peppers thinly and cook slowly in a little olive oil and ¼ cup of balsamic vinegar until very soft, about an hour. Stir occasionally; peppers should almost "melt." Season with salt and pepper. Add oil and balsamic vinegar once or twice if they look dry. Run under the broiler (or grill) about 25 rounds of bread sprinkled with olive oil. Rub a cut clove of garlic over each piece. Spoon peppers onto bread and serve warm. Try the same method with thinly sliced onions, adding a teaspoon of brown sugar to the balsamic and letting the onions slowly carmelize. Both versions of this are rich accompaniments for roast chicken. Leftovers are good on pasta or polenta. With cheese and/or grilled eggplant, very savory sandwiches can be made quickly._
Pea and Shallot Bruschetta
New peas pop right out of the crisp pods. I thought shelling them was a meditative act until I saw a woman in town sitting outside her doorway with her cat sleeping at her ankles. She was shelling an immense pile of peas and already had filled a large dishpan. She looked up and said something rapidly in Italian and I smiled, only to realize as I walked on that she'd said, "It shouldn't happen to a dog."
_~Mince 4 shallots. Shell enough peas to fill 1 cup. Mix and sauté in butter until the peas are done and the shallots are wilted. Add a little chopped mint, salt, and pepper. Chop coarsely in a food processor or by hand and spoon onto 25 rounds of bread as prepared in the recipe above._
Basil and Mint Sorbet
I tasted this unlikely but tantalizing sorbet at the ancient _fattoria-_ turned-restaurant Locanda dell'Amorosa in nearby Sinalunga. The next day I tried to duplicate it at home. At the restaurant, it was served after the pasta and fish courses and before the main course. More informally, it starts out a dinner on a warm summer night.
_~Make a sugar syrup by boiling together 1 cup of water and 1 cup of sugar, then simmering it for about 5 minutes, stirring constantly. Cool in the fridge. Purée ½ cup of mint leaves and ½ cup of basil leaves in 1 cup of water. Add another cup of water, 1 tablespoon of lemon juice, and chill. Mix the sugar syrup and the herbal water well and process in an ice cream maker according to manufacturer's instructions. Scoop into martini glasses or any clear glass dishes and garnish with mint leaves. Serves 8._
~PRIMI PIATTI~
Cold Garlic Soup
As in chicken with 40 cloves of garlic, the amount of garlic in this recipe is no cause for alarm. The cooking process attenuates the strength but leaves the flavor.
_~Peel 2 whole heads of garlic. Chop 1 small onion and peel and dice 2 medium potatoes. Sauté the onion in 1 tablespoon of olive oil and, when it begins to turn translucent, add the garlic. The garlic should soften but not brown; cook gently. Steam the diced potatoes and add to the onion and garlic, along with 1 cup of chicken stock. Bring just to a boil, then quickly lower heat and simmer for 20 minutes. Purée in a food processor, then pour back into the pot and add 4 more cups of stock and 1 tablespoon of chopped thyme. (If you don't have a food processor, mince the garlic and onion before you cook them; after steaming, put the potatoes through a ricer.) Whisk in ½ cup of heavy cream. Season with salt and pepper, then chill. Stir before serving with chopped thyme or chives on top. Serves 6._
Fennel Soup
_~Thinly slice 2 fennel bulbs and 2 bunches of spring onions. Sauté briefly in a little olive oil. Add 2 cups of chicken stock to the pan and simmer until the fennel is cooked. Stir frequently. Purée until smooth. Whisk in 2-½ more cups of stock. Season with salt and pepper and cover. Bring to a boiling point, then lower the heat and simmer for 10 minutes. Whisk in ½ cup of mascarpone or heavy cream. Remove from heat immediately. Serve cold or warm, garnished with toasted fennel seeds. Serves 6._
Pizza with Onion Confit and Sausage
Pizza is endless in variety. Ed's favorite is Napoli: capers, anchovies, mozzarella. I like fontina, olives, and _prosciutto._ Another favorite is arugula and curls of _parmigiano._ We're also enamored of potato pizza, as well as all the standard ones. When we cook outside, we always grill lots of extra vegetables and sausages for salads and pizza the next day. A great vegetarian combination is grilled eggplant with sundried tomatoes, olives, oregano, basil, and mozzarella.
_~Thinly slice 3 onions and "melt" in a frying pan on low heat, using a small amount of olive oil and 3 tablespoons of balsamic vinegar. Onions should be caramel colored and limp. Season with marjoram, salt and pepper. Grill or sauté 2 large sausages. Here we use the local pork sausage seasoned with fennel seeds. Slice. Grate 1 cup of mozzarella or_ parmigiano.
_Dough: Dissolve 1 package of yeast in ¼ cup of warm water for 10minutes. Mix the following: ½ teaspoon of salt, 1 teaspoon of sugar, 3 tablespoons of olive oil, 1 cup of cool water, and pour into a mound of 3-¼ cups of flour. Knead on a flat surface until elastic and smooth. If you're using a food processor, pulse until the dough forms a ball, then remove and knead by hand. Place dough in a buttered and floured bowl and let rest for 30 minutes. Roll into 1 large or 2 smaller circles and brush with oil. Scatter cheese, onions, and sausage over the surface and bake at 400° for 15 minutes. Cut into 8 pieces._
Semolina Gnocchi
_Gnocchi_ 's usual knuckle shape changes in this grand and rich dish. Unlike the potato _gnocchi_ or the light spinach and ricotta _gnocchi,_ the _gnocchi_ made with semolina are biscuit-sized. I used to buy these from a woman down in the valley until I found out how easy they are to make.
_~Bring 6 cups of milk almost to a boil in a large saucepan. Pour in 3 cups of semolina in a steady stream, stirring constantly. Cook on low, as you would cook polenta, continuing to stir for 15 minutes. Remove from heat, beat in 3 egg yolks, 3 tablespoons of butter and ½ cup of grated_ parmigiano. _Season with salt, pepper, and a little nutmeg. Beat briefly, lifting the mixture to incorporate air. Spread mixture in a circle 1 inch thick on the lightly floured counter or cutting board and let it cool. Cut into biscuit-sized circles with the rim of a glass or a cookie cutter. Place in a well-buttered baking dish. Pour 3 tablespoons of melted butter over the top, then sprinkle with ¼ cup of_ parmigiano. _Bake, uncovered, at 400° for 15 minutes. Serves 6._
Everything Pasta Salad with Baked Tomatoes
When making soups, ratatouille, or this salad, I steam everything separately. This keeps the flavors distinct and allows me to cook each vegetable to its first point of doneness. I've never seen pasta salad on an Italian menu, but it's a marvelous American import. This goes easily to a picnic in a big plastic container.
_~Prepare vinaigrette: ¾ cup of olive oil, red wine vinegar to taste (about 3 tablespoons), 3 cloves of crushed garlic, 1 tablespoon of chopped thyme, salt, and pepper. Shake in a jar._
_Fresh vegetables: 8 medium carrots, 5 slender zucchini, 2 big red peppers, 2 hot peppers, about one-half pound of green beans, and one bunch of spring onions. Cut in small pieces, except for hot peppers—mince these. Steam one by one until just done. Cool._
_Chicken: Rub 2 whole breasts with olive oil and place in an oiled pan. Season with thyme, salt, and pepper. Roast at 350°for about 30 minutes. Cool and slice into julienne strips._
_Pasta:_ Fusilli, _the short, spiraled pasta, is best for salad. Cook two 1-pound packages and drain; immediately toss with 2 tablespoons of olive oil. Season and cool._
_Mix everything well in a large container, such as a turkey roasting pan, and chill until an hour before serving. Toss again and divide between two large bowls._
_For the tomatoes: Select one for each person (plus a few more for leftovers). Cut a cone-shaped hollow from the stem end and spoon out seeds. Trim off the bottom. Sprinkle with salt and pepper, then stuff tomato with a mixture of bread crumbs, chopped basil, and toasted pine nuts. Drizzle with olive oil. Bake at 350° for about 15 minutes._
_To serve, place tomato in the center of the plate, surround with pasta salad, garnish with black olives and thyme sprigs and/or basil leaves. Makes 16–20 very pretty servings._
~SECONDI~
Risotto with Red Chard
Risotto has become soul food to me. Like pasta, pizza, and polenta, it's another dish of infinite variety. In spring, barely cooked asparagus, tiny carrots, and a little lemon make a light risotto. I especially like it with fava beans that have been sautéed with minced shallots in a covered pan, then stirred into the risotto. Other good choices: chopped fennel, barely cooked, with rock shrimp; sautéed fresh mushrooms or dried _porcini_ soaked in tepid water until plumped; grilled radicchio and pancetta. In Italy, you can buy _funghi porcini_ bouillon cubes in grocery stores. They're excellent for risotto when no stock is at hand. Many recipes call for too much butter; if you have a good stock, butter is unnecessary and only a little olive oil is needed to start things off. If any risotto is left the next day, heat a tablespoon of olive oil in a nonstick pan, spread and pat down the risotto, and cook over a medium flame until crisp on the bottom. Flip over with a large spatula and crisp the other side. A fine lunch.
_~Chop, then sauté, 1 medium onion in 1 tablespoon of oil for about 2 minutes. Add 2 cups of Arborio rice and cook for a couple of minutes. Meanwhile, in another pot, heat 5-½ cups of seasoned stock (chicken, veal, or vegetable) and ½ cup of white wine to a boil and reduce heat to a simmer. Ladle the stock and wine gradually into the rice, stirring each ladle into the rice until it is absorbed before adding more. Keep both the stock mixture and the rice at a simmer. Stir and stir until rice is done. It should be_ al dente _and rather soupy. Add ½ cup of grated_ parmigiano. _Thoroughly wash a bunch of chard, preferably red. Chop in shreds and quickly sauté in a little olive oil and minced garlic. Stir into risotto. Serve and pass a bowl of grated_ parmigiano. _Serves 6._
Rich Polenta Parmigiana
This is more of a California polenta than a traditional Italian one. So much butter and cheese! Classic polenta is cooked by the same method—don't stop stirring—with two or even three more cups of water. You then pour the polenta out on a cutting board and let it rest until firm. Often it's served with a _ragù_ or with _funghi porcini._ I've served this version to Italians and they've loved it. Leftover polenta, either plain or this richer one, is sublime when sautéed until crisp.
_~Soak 2 cups of polenta in 3 cups of cold water for 10 minutes. In a stock pot, bring 3 cups of water to a boil and stir in the polenta. Let it come to a boil again, then turn down the heat immediately and stir for 15 minutes on a gentle flame that is strong enough to keep slow, big bubbles rising. Add salt and pepper, 8 tablespoons of butter, and 1 cup of grated_ parmigiano. _Add more water if the polenta is too thick. Stir well and pour into a large buttered baking dish. Run in the oven at 300° for about 15 minutes. Serves 6._
A Sauce of Porcini
When available, fresh _porcini_ are a treat. They're at their finest simply brushed with olive oil and grilled, a dish that is as substantial as steak, which they're often paired with on the grill. Out of season, the dried ones have many talents. Though they seem expensive, a little bit adds a lot of flavor. Spoon this sauce over polenta or serve as a risotto or pasta sauce.
_~Soften about 2 ounces of dried_ porcini _in 1-½ cups of warm water. This takes about one half hour. Peel and dice five cloves of garlic and gently sauté in 2 tablespoons of olive oil. Add 1 tablespoon each finely chopped thyme and rosemary, 1 cup of tomato sauce, and salt and pepper. Strain the mushroom water through cheesecloth and add it to the tomato mixture. Chop and add the mushrooms and simmer the sauce until thick and savory, about 20 minutes. 6 servings for polenta, 4 for pasta._
Chicken with Chickpeas, Garlic, Tomatoes, and Thyme
One of those recipes that can expand to accommodate any number.
_~Simmer 2 cups of dried chickpeas in water with 2 cloves of garlic, salt, and pepper until tender but with plenty of bite, about 2 hours. In hot olive oil, quickly brown 6 breasts that have been shaken in a bag of flour. Arrange pieces in a baking dish. Drain chickpeas and scatter over chicken. Add a little olive oil to the same pan and sauté 1 coarsely chopped onion and 3 cloves of minced garlic; add 4 ripe tomatoes, also chopped coarsely, 1 teaspoon of cinnamon, and 2 tablespoons of thyme. Simmer 10minutes. Spread over the chicken. Season with salt, pepper, sprigs of fresh thyme, and ½ cup of black olives. Bake, uncovered, at 350° for about 30 minutes, depending on the size of the chicken breasts. This is attractive in a terra-cotta dish. Serves 6._
Basil and Lemon Chicken
A last-minute favorite, this chicken, served with a platter of summer squash and sliced tomatoes, tempers the hottest July night.
_~In a large bowl, mix ½ cup each of chopped spring onions and basil leaves. Add the juice of 1 lemon, salt and pepper. Mix and rub onto 6 chicken pieces and place in a well-oiled baking pan. Dribble with a little olive oil. Roast, uncovered, at 350° for about 30 minutes, depending on the size of the chicken. Garnish with more basil leaves and lemon slices. Serves 6._
Turkey Breast with Green and Black Olives
Turkey is popular here, though the whole bird is rare except at Christmas. In this recipe, the breast is sliced into cutlets, like _scaloppine._ You can use flattened chicken breasts instead of turkey. If you don't pit the olives, warn your guests. I use the rest of the breast for distinctly un-Tuscan stir-fry with peppers.
_~In a large pan, sauté 6 turkey cutlets in olive oil until almost done and remove to a platter. Add a little more oil to the pan and sauté 1 finely chopped onion and 2 cloves of crushed garlic. Add 1 cup of vermouth and bring to a boil, then quickly reduce heat to a simmer. Cover for 2 or 3minutes, then add the turkey again, as well as the juice of 1 lemon and 1 cup of mixed green and black olives. Cook for 5 minutes or until the turkey is done. Season with salt and pepper and stir in a handful of chopped parsley. Serves 6._
~CONTORNI~
Fried Zucchini Flowers
When this is good it's very, very good and when it's limp it's a disaster. I've made it both ways. The mistake was in the oil, which must be hot. Peanut or sunflower are the best oils for these delicate summer flowers.
_~Choose a fresh bunch of flowers, about a dozen. If they're slightly droopy, don't bother. Don't wash the blossoms; if moist, pat dry. Place a thin strip of mozzarella inside each one, dip in batter. To prepare the batter, beat 2 eggs with ¼ teaspoon of salt and pour in 1 cup of water and 1-¼ cups of flour. Mix well, breaking any lumps with a fork. Make sure the oil is hot (350°) but not smoking. Fry until golden and crispy. Drain quickly on paper towels and serve immediately._
Baked Peppers with Ricotta and Basil
Stuffed peppers were my favorite dorm food in college. This ricotta filling is the polar opposite of the "mystery meat" we faced at Randolph-Macon. Fresh ricotta, made from ewe's milk, is a treat. The special baskets for making it imprint the sides of the cheese with a woven pattern. We often buy it at farms around Pienza, which is sheep country and also the source of _pecorino._
_~Singe 3 large yellow peppers quickly over a gas flame or a grill. The peppers should char all over, but don't cook them so long that they turn limp. Cool in a plastic bag, then slide off the burned skin. Cut in half and clean out ribs and seeds. Drizzle with olive oil. In a bowl, mix 2 cups of ricotta, ½ cup of chopped basil, ½ cup of finely sliced green onions, ½ cup minced Italian parsley, salt and pepper. Beat in 2 eggs. Fill peppers and bake at 350° for 30 minutes. Garnish with basil leaves. Serves 6._
Fried Sage
Too often sage is associated with that green dust that comes in little jars and makes you sneeze. Fresh sage has an assertive punch that complements meat.
_~Wash 20 or 30 sprigs of sage, pat with paper towels, and allow to dry completely. Heat 2 inches of sunflower or peanut oil until it is very hot but not smoking. Dip sprigs in batter (see recipe for Fried Zucchini Flowers) and drop them in hot oil (350°) for about 2 minutes or until the leaves are crisp. Drain on paper towels. A splendid garnish for lamb, pork, or any meat._
Sage Pesto
I found a pestle of olive wood at the monthly antique market in Arezzo and put it to use with an old stone mortar rescued from a friend who used it as a copious ashtray. These big mortars, she explained, originally were used for grinding coarse salt. Until recently, salt, a heavily taxed and government-controlled monopoly, was sold only in tobacco shops. The cheaper coarse salt was widely used. The large old mortars are handy for pesto; the pestle and rough stone release oils from the herbs and bind the essences of all the ingredients. Extrapolating on the basic basil pesto, I've made a lemon-parsley pesto for fish, an arugula pesto for pasta and _crostini,_ and a mint pesto for shrimp. I've come to prefer the texture of these pestos to the smoother ones I'm used to. Traditional Tuscan white beans with sage and olive oil taste even better with a daub of this sage pesto. I like it on _bruschetta._ Passed separately in a bowl, it's a good accompaniment for grilled sausages.
_~Chop a big bunch of sage leaves, 2 cloves of garlic, and 4 tablespoons of pine nuts. Grind together in the mortar (or food processor), slowly adding olive oil to form a thick paste. Transfer to a bowl, mix again, add salt and pepper and a handful of grated_ parmigiano. _Makes about 1-½ cups._
~DOLCI~
Hazelnut Gelato
Super rich, this gelato makes me want to give up my citizenship and decamp permanently. Even people who claim not to like ice cream slip into a swoon over this one.
_~Toast 1-½ cups of hazelnuts in a moderate oven for five minutes. Watch the nuts carefully; they burn easily. Remove, wrap in a dish towel, and rub off the fine brown skin. Chop coarsely. Beat 6 egg yolks and gradually stir in 1-½ cups of sugar, beating until nicely incorporated. Heat 1 quart of half-and-half until almost boiling, then remove from the heat and quickly whisk in the egg and sugar mixture. In a double boiler, cook the mixture gently until it thickens and coats a wooden spoon. Cool in the fridge. Whisk in 2 tablespoons Fra Angelico (hazelnut liqueur) or vanilla, and 2 cups of heavy cream. Add hazelnuts and the juice and zest of one lemon. Pour the mixture into an ice cream maker and process according to manufacturer's instructions. Makes about 2quarts._
Cherries Steeped in Red Wine
All through June we buy cherries by the kilo and start eating them in the car on the way home. Almost nothing you can invent improves the taste of the plain cherry. We've planted three cherry trees and have uncovered three more from the ivy and brambles. Two neighboring trees are necessary for fruit production.
_~Stem and pit 1 pound of cherries. Pour 1 cup of red wine and the zest of a lemon over them and simmer for 15 minutes, stirring occasionally. Cover and let stand for 2 or 3 hours. Serve in bowls with plenty of juice and a big dollop of sweetened whipped cream or mascarpone. Little slices of hazelnut pound cake or cookies also might be served. You can use plums or pears instead of cherries. Serves 4._
Folded Peach Tart with Mascarpone
I first learned to make folded pie crusts from a Paula Wolfert cookbook. On a cookie sheet, you spread the crust, pile the filling in the middle, then loosely fold the edges toward the center, forming a rustic tart with a spontaneous look. The peaches here—both the yellow and the white varieties—are so luscious that eating one should be a private act.
_~Roll out your favorite crust a little larger than you normally do for a pie pan. Slide to a nonstick cookie sheet or baking dish. Slice 4 or 5 peaches. Mix 1 cup of mascarpone, ¼ cup of sugar, and ¼ cup of toasted almond slices. Combine this gently with peaches. Spoon into the center of the crust, and flop the pastry edges over, pressing them down a bit into the fruit mixture. Don't seal over the top—leave a four- or five-inch hole. Bake at 375° for about 20 minutes. Serves 6._
Pears in Mascarpone Custard
This is an Italian version of the fruit cobblers I must have first tasted at the age of six months in the South, where they almost always were made of peaches or blackberries.
_~Peel and slice 6 medium pears (or peaches or apples) and arrange in a buttered baking dish. Sprinkle with 1 teaspoon of sugar. Cream 4 tablespoons of butter and ½ cup of sugar until light. Beat in 1 egg, then 2/3 cup of mascarpone. Stir in 2tablespoons of flour last and mix well. Spoon over the fruit. Bake at 350° until just set, about 20 minutes. Serves 6 generously._
Cortona,
Noble City
ITALIANS ALWAYS HAVE LIVED OVER THE store. The _palazzi_ of some of the grandest families have bricked-in arches at ground level, with remains of waist-high stone counters where someone used to ladle out preserved briny fish from a vat to customers, or carve the stuffed pig, a job now performed in sleek open-sided trucks that ply the weekly markets or sell from roadsides. I run my hand over these worn stone counters when I pass them. From odd windows at ground level, the _palazzo's_ house wine was sold. First floors of some grand houses were warehouses. Today, my bank in Cortona is the bottom of the great Laparelli house, which rests on Etruscan stones. On the top floors, windows open to the night show antique chandeliers, big armfuls of light. Often the residents are leaning out, two, sometimes three to a window, watching one more day pass in the history of this piazza. The main shopping streets, lined with great houses, are everywhere converted on the ground floor to the businesses of hardware, dishes, food, and clothing. For many buildings, probably it always has been so.
On the facades, I notice how many times previous occupants have changed their minds. The door should be here—no, here—and the arch should be a window, and shouldn't we join this building to the next one or add a continuous new facade across all three medieval houses now that the Renaissance is here? The medieval fish market is a restaurant, the Renaissance private theater is an exhibition space, the stone clothes-washing sinks still just await the flow of water, the women with their baskets.
But the clock repairer in his four-by-six-foot shop under the eleventh-century stairway of the city offices has been there for all this time, though he may now be changing the battery on the Swatch watch of an exchange student. He used to blow the glass and sift the white sand from the Tyrrhenian at Populonia for his hourglasses. He studied the water clocks drip by drip. I never have seen him stand; his back must be a hoop from slouching over the tiny parts for so many centuries. His face is lost behind the lenses he wears, so thick that his eyes seem to lunge forward. As I stop in front of his shop, he is working by the light that always angles in just so on the infinitesimal wheels and gold triangles, the numbers of the hours that sometimes fall off the white face, four and five and nine sprinkled on his table.
Perhaps my own teaching activities are immortal and I just don't see it because the place doesn't have this backdrop of time; in fact, my building at the university is a prime earthquake hazard, slated to be demolished. We're to move to a new building next fall, one with a flexible structure suited to a foundation that is partly sand dune. A postwar structure, the current Humanities Building already is obsolete: fifty-year turnaround.
The cobbler, however, seems permanent in his cave-shaped shop, which expands around him only enough for his bench, his shelf of tools, the shoes to be picked up, and one customer to squeeze into. A red boot like one on an angel in the Museo Diocesano, Gucci loafers, a yard of navy pumps, and a worn work shoe that must weigh more than a newborn baby. A small radio from the thirties still brings in the weather from the rest of the peninsula as he polishes my repaired sandal and says it should last for years.
At the _frutta e verdura,_ it is the same, the same white peaches at the end of July. The figs that are perfect now and overripe by the time I get them to the kitchen. Apricots, a little basket of rising suns, and bunches of field lettuce still wet with dew. The Laparelli girl, who became a saint and now lies uncorrupted in her venerated tomb, stopped here for her grapes before she gave up eating, in order to feel His suffering more clearly. "From my garden this morning," she heard, as I do when Maria Rita holds up the melon for me to smell the fruit's perfume and her clean hand so often in the earth. When she takes me in the back of her shop to show me how much cooler it is, I step back into the medieval rabbit warren many buildings still are, behind their facades and windows filled with camcorders, silk skirts, and Alessi gadgets. We're under stone stairs, where she has a sink to wash the produce, then, another step down, we're in a narrow stone room with a twist into darkness at the end. _"Fresca,"_ she says, fanning herself, and she shows me her chair among the wooden crates, where she can rest between customers. She doesn't get much rest. People shop here for her cascades of laughter, as well as for the uncompromising quality of her produce. She's open six and a half days a week, plus she cares for a garden. Her husband has been ill this year, so she's shifting crates every day as well. By eight, she's smiling, washing down her stoop, wiping a speck off a pyramid of gargantuan red peppers.
We shop here every day. Every day she says, _"Guardi, signora,"_ and holds up a misshapen carrot that looks obscene to her, a luscious basket of tomatoes, or a cunning little bunch of radishes. Every garlic head, lemon, and watermelon in her shop has been lavished with attention. She has washed and arranged. She makes sure her best customers get the most select produce. If I pick out plums (touching is a no-no in produce shops and I sometimes forget), she inspects each, points out any deficiency she detects, mumbles, takes another. Each purchase comes with cooking tips. You can't make minestrone without _bietola;_ chard is what makes minestrone. And toss in a heel of _parmigiano_ for flavor. Just melt these onions for a long time in olive oil, a dash of balsamic vinegar, serve them on _bruschetta._
Many of her customers are tourists, stopping in for some grapes or a few peaches. A man buys fruit and makes motions of washing his hands. He points to the fruit. She figures out that he's asking her where he can wash it. She explains that it is washed, no one has touched it, but, of course, he can't understand, so she leads him by the elbow down the street and points to the public water fountain. She finds this amusing. "Where is he from that he thinks the fruit isn't clean?"
All along the streets, artisans open their shop doors to the front light. As I glimpse the work inside, I think medieval guilds might still be practicing their crafts. A young man works on elaborate fruit and flower marquetry of a seventeenth-century desk. As he trims a sliver of pear wood, he's as intent as a surgeon reattaching a severed thumb. In another shop near the Porto Sant'Agostino, Antonio of the dark intent gaze is framing botanical prints. I step in to look and spot a lovely old mirror on his shelf. _"Posso?"_ May I, I ask before I touch it. When I lift it, the top of the frame comes loose in my hand and the fragile, silver-backed antique mirror crashes to the floor. I want to dissolve. But his main concern is my seven years of bad luck. I insist on paying for the mirror, over his protests. He will make a couple of small mirrors with the old foxed shards and he will repair my frame and put in a new mirror. As I leave, I see him carefully picking up the pieces.
Most fascinating to look into is the place where paintings are restored. Strong fumes emanate from this workshop where two women in white deftly clean layers of time off canvases and rework spots that have been punctured or damaged. Renaissance painters used marble dust, chalk, and eggshells as paint bases. Sometimes they applied gold leaf onto a mordant made of garlic. Their black paint came from lampblack, burned olive sticks, and nutshells; some reds from insect secretions, often imported from Asia. Ground stones, berries, peach pits, and glass yielded other colors, which were applied with brushes made from boar, ermine, feathers, and quills: spiritual art coming directly out of nature. To duplicate the colors of those mulberry dresses, mauve cloaks, azurite robes, modern alchemical processes must go on in this little shop.
In holes in the wall all over town, the refinishing of furniture goes on. Many men make tables and chests from old wood. There's no subterfuge involved, no attempt to pass them off as antiques; they know the aged wood won't crack, will take the stain and wax, in short, will look _right,_ that is, old. We take our tools to be sharpened in a blackened room where the _fabbro_ apologizes because he can't get them back before tomorrow. When we pick up the ten hoes, scythes, sickles, etc., their knife edges gleam. Tempting, but I do not run my finger across the edge.
The tailor does not wear glasses and his stitches could be done by mice. In his dark shop with the sewing machine by the window and the spools lined up on the sill, I see a new white bicycle, a water bottle attached for long trips, nifty leather saddlebags over the back wheel. When I see him later, though, he is only in the town park, feeding three stray cats food from his saddlebags. He unwraps the scraps they are so clearly expecting. He and I are the only ones out on Sunday morning, when most people who live here are doing something else. When I gave him my pants to hem last week, he showed me a circle of photos tacked up on the back wall. His young wife with parted lips and wavy, parted hair. _Morta._ His mother like an apple doll, also dead. His sister. There was one of him, too, as a young soldier for the Pope, restored to youth, with black hair, his legs apart and shoulders back. He was twenty-five in Rome, the war just ended. Now fifty more years have passed, everyone gone. He pats the white bicycle. _I never thought I'd be the one left._
CORTONA MERITS ALMOST SEVEN PAGES IN THE EXCELLENT _Blue Guide: Northern Italy._ The writer meticulously directs the walker up each street, pointing out what's of interest. From the gates to the city, further excursions into the surrounding countryside are recommended. Each side altar in the _duomo_ is described according to its cardinal orientation, so that, if you happen to know which way east is, after travelling the winding roads, you can locate yourself and self-guide through the nooks and crannies. The writer has even identified all the murky paintings in the choir area. Reading the guide, I'm overwhelmed once again by all the art, architecture, history in one little hill town. This is only one of hundreds of such former marauder lookouts, perched picturesquely for views now.
Now that I know this one place a little, I read with doubled perception. The guide directs me to the acacia-shaded lane along the inside wall of the town, and I immediately remember the modest stone houses on one side, the view over the Val di Chiana on the other. I see, too, the three-legged dog I know lives in the house that always has the enormous underpants drying on a line. I see the cane-bottomed chairs all the people who live along that glorious stretch of wall pull out at evening when they view the sunset and check in with the stars. Yesterday, walking there, I almost stepped on a still soft dead rat. Inside one of the doorways that opens right out onto the narrow street, I glimpsed a woman holding her head in her hands at the kitchen table. Whether she was weeping or catching a catnap, I don't know.
Whatever a guidebook says, whether or not you leave somewhere with a sense of the place is entirely a matter of smell and instinct. There are places I've been which are lost to me. When I was there, I followed the guide faithfully from site to site, putting check marks in the margins at night when I plotted my route for the next day. On my first trip to Italy, I was so excited that I made a whirlwind, whistlestop trip to five cities in two weeks. I still remember everything, the revelation of my first espresso under the arcades in Bologna, remarking that it stung my throat. Climbing _every_ tower and soaking my blistered feet in the bidet at night. The candlelit restaurant in Florence where I first met ravioli with butter and sage. The pastries I bought to take to the room, all wrapped and tied like a present. The dark leather smell of the shoe store where I bought (inception of a lifelong predilection) my first pair of Italian shoes. Discovering Allori in a corner of the Uffizi. The room at the foot of the Spanish Steps where Keats died, and dipping my hand in the boat-shaped fountain just outside, thinking Keats had dipped his hand there. I kept no record of that trip. On later trips, I began to carry a travel journal because I realized how much I forgot over time. Memory is, of course, a trickster. I remember little of three days in Innsbruck—the first bite of autumn air, a beautiful woman with red hair at the next table in a restaurant—but I can still touch every stone of Cuzco; little is left of Puerto Vallarta but the Yucatan is bright in memory. I loved the Mayan ruins seen through waves of hallucinatory heat, a large iguana who slept on the porch of my thatched room, the dogged solitude of the people, crazy storms that blew out the lights, mosquito netting waving around the bed, and candles melting astonishingly fast.
Although a getaway weekend may be just that, most trips have an underlying quest. We're looking for something. What? Fun, escape, adventure—but then what? "This trip is life-changing," my nephew said. Did he know that at the outset, come to Italy looking for affirmation of a change he felt rising in him? I suspect not; he discovered this in travelling. Another guest compared the water, the architecture, the landscape, the wine—all she saw to her hometown's more excellent version. It irritated me to the point of surliness. I wanted to tape her mouth, point her to an eleventh century monastery and say "Look." I felt she went home having seen nothing. Shortly after, she wrote that she was getting a divorce (no word of this while she was here) after a fourteen-year marriage to a man who has decided he is gay. When I thought back on her attitudes here, I understood that she desperately had looked for the comfort of a home which was no longer there. A guest earlier in the summer was on one of those marathon seven countries in three weeks trips. It's tempting to mock that impulse but to me it's extremely interesting when one chooses to power through that many miles. First of all, it's very American. Just _drive,_ please. And far and quickly. There's a strong "get me out of here" impetus behind such trips, even when they're disguised as "seeing the lay of the land so I'll know the places I want to come back to." It's not the destinations; it's the ability to be on the road, happy trails, out where no one knows or understands or cares about all the deviling things that have been weighing you down, keeping you frantic as a lizard with a rock on its tail. People travel for as many reasons as they don't travel. "I'm so glad I went to London," a friend told me in college, "Now I don't ever have to go again." The opposite end of that spectrum is my friend Charlotte who crossed China in the back of a truck, an alternate route into Tibet. In his poem "Words from a Totem Animal," W.S. Merwin cuts to the core:
_Send me out into another life_
_lord because this one is growing faint_
_I do not think it goes all the way._
Once _in_ a place, that journey to the far interior of the psyche begins or it doesn't. Something must make it yours, that ineffable _something_ no book can capture. It can be so simple, like the light I saw on the faces of the three women walking with their arms linked when the late afternoon sun slanted into the Rugapiana. That _light_ seemed to fall like a benison on everyone beneath it. I, too, wanted to soak my skin under such a sun.
THE IDEAL APPROACH TO MY NEW HOMETOWN IS FIRST TO SEE the Etruscan tombs down in the flatland below the town. There are tombs from 800 to 200 B.C. near the train station in Camucia and on the road to Foiano, where the custodian never likes the tip. Maybe he's in a bad mood because he spends eerie nights. His small farmhouse, with a bean patch and yard-roaming chickens, coexists with this _tomba_ that would appear strangely primordial in the moonlight. A little uphill, a rusted yellow sign is all that points to the so-called tomb of Pythagoras. I pull over and walk along a stream until I reach a short lane, cypress lined, leading to the tomb. There's a gate but it doesn't look as if anyone ever bothers to close it. So there it is, just sitting on a round stone platform. Niches for the upright sarcophagi look like the shrine at the bottom of my driveway. The ceiling is partially gone but enough of the curve is left that I can see the dome shape. I'm standing inside a structure someone put together at least two thousand years ago. One massive stone over the door is a perfect half moon.
The mysterious Etruscans! My knowledge of them, until I started to come to Italy, was limited to the fact that they preceded the Romans and that their language was indecipherable. Since they built with wood, little remained. I was almost all wrong. Not much of their written language has been found, but much has been translated by now, thanks to the crucial find of some strips of linen shroud from an Egyptian mummy that travelled to Zagreb as a curio and were preserved later in the museum there. How the Etruscan linen, inscribed with text in ink made from soot or coal, became the wrapping for a young girl is still unknown. Possibly Etruscans migrated to Egypt after they were conquered by Rome around the first century B.C. and the girl was actually Etruscan. Or perhaps the linen was simply a convenient remnant, torn into strips by embalmers who used whatever was at hand. The mummy carried enough Etruscan text to provide several key roots, although the language still isn't totally translated. It's too bad what they left written on stone is gravestone information and government fact. A friend told me that last year a local _geometra_ discovered a bronze tablet covered with Etruscan writing. He kicked it up in the dirt of a farmhouse where he was overseeing a renovation and took it home. The police heard about this and called on him that night; presumably, it is in the hands of archaeologists.
Of the local Etruscan culture, an astonishing amount continues to be unearthed. Beside one of the local tombs, a seven-step stairway of stone flanked with reclining lions intertwined with human parts—probably a nightmare vision of the underworld—was discovered in 1990. Nearby Chiusi, like Cortona one of the original twelve cities of Etruria, only recently found its town walls. Both Cortona and Chiusi have extensive collections of Etruscan artifacts found both by archeological digs and by farmers turning up bronze figures in their furrows. In Chiusi, the museum custodian will take you out to see some of the dozens of tombs found in that area. The Romans considered Etruscans warlike (the Romans weren't?), so they come down to us with that rap on them, but the tombs, enormous clay horses, bronze figures, and household objects reveal them to be a majestic, inventive, humorous people. Certainly, they must have been strong. Everywhere they've left remains of walls and tombs constructed of stupendous stone.
In the land around Cortona, tombs that have been found are called _meloni_ locally, for the curved shape of the ceilings. To stand under one of these for a few moments is all you need to absorb the sense of time that prepares you for Cortona.
Leaving the tombs, I start uphill, gently at first, then in a series of switchbacks, I begin to climb, glimpsing through the windshield terraced olives, the crenelated tower of Il Palazzone, where Luca Signorelli fell off scaffolding and died a few months later, a broken watchtower and tawny farmhouses. A soft palate: the mellow stone, olive trees flickering moss green to platinum; even the sky may be veiled by thin mist from the lake nearby. In July, small mown wheat fields bordering the olives turn the color of lion's fur. I glimpse Cortona, noble in profile as Nefertiti. At first I'm below the great Renaissance church of Santa Maria del Calcinaio, then, for a 280-degree loop of the road, level with its solid volumes, then above, looking down on the silvery dome and the Latin cross shape of the whole. The shoe tanners built this church, after the common occurrence of the appearance of the Virgin's face on their tannery wall. She is Saint Mary of the Lime Pits because they used lime in tanning leather and the church is erected on their quarry grounds. Odd how often sacred ground remains sacred: The church rests on Etruscan remains, possibly of a temple or burial ground.
A quick look back—I see how far I have climbed. The wide-open Val di Chiana spreads a fan of green below me. On clear days I can spot Monte San Savino, Sinalunga, and Montepulciano in the distance. They could have sent smoke signals: big _festa_ tonight, come on over. Soon I've reached the high town walls, and to get one more brush with the Etruscans, drive all the way to the last gate, Porta Colonia, where the big boggling Etruscan stones support the base, with medieval and later additions built on top.
Whizzing past, I love the fast glimpses into the gates. In town, they sell old postcards of these views and they look exactly the same as now: the gate, the narrow street sloping up, the _palazzi_ on either side. When I enter the town, the immediate sense is that I am _inside_ the gates—a secure feeling if hoards of Ghibellines, Guelfs, or whoever is the current enemy, are spotted in the distance waving their lances, or even if I've only managed to survive the _autostrada_ without getting my car mirror "kissed" by a demon passing in a car half the size of mine.
If I come by car, I walk in on Via Dardano, a name from deep in time. Dardano, believed to have been born here, was the legendary founder of Troy. Right away on the left, I pass a four-table trattoria, open only at midday. No menu, the usual choices. I love their thinly pounded grilled steak served on a bed of arugula. And love to watch the two women at the wood-fired stove in the kitchen. Somehow they never appear to be sweltering.
I'm fascinated by the perfect doors of the dead on this street. Traditionally, they're considered to be exits for the plague dead—bad juju for them to go out the door the living use. If this is so, the custom must have come from some superstition much older than Christianity, which was firmly the religious preference of that time. Some suggest that the raised, narrow doors were used in times of strife when the _portone,_ the main door, was barricaded. I've wondered if they were not simply doors used when stepping out of a carriage or off a horse and right into the house in bad weather—rather than stepping down into the wet, probably filthy, street—or even in good weather to protect a long silk skirt. George Dennis, nineteenth-century archaeologist, described Cortona as "squalid in the extreme." That the doors are rather coffin shaped, however, lends a certain visual reinforcement to the door of the dead theory.
The _centro_ consists of two irregular piazzas, joined by a short street. No town planner would design it this way but it is charming. A fourteenth-century town hall with twenty-four broad stone steps dominates the Piazza della Repubblica. The steps serve as ringside seats at night when everyone is out having _gelato—_ a fine place to take in the evening spectacle below. From here, you can see a loggia on the level above across the piazza, where the fish market used to be. Now it's terrace seating for a restaurant and another perch for viewing. All around are harmonious buildings, punctuated by streets coming up from three gates. The life in the street buzzes, thrives. The miracle of no cars—how amazingly that restores human importance. I first feel the scale of the architecture, then see that the low buildings are completely geared to the body. The main street, officially named Via Nazionale but known locally as Rugapiana, the flat street, is only for walking (except for a delivery period in the morning) and the rest of the town is inhospitable to drivers, too narrow, too hilly. A street connects to a higher or lower one by a walkway, a _vicolo._ Even the names of the _vicoli_ make me want to turn into each one and explore: Vicolo della Notte, night, Vicolo dell'Aurora, dawn, and Vicolo della Scala, a long rise of shallow steps.
In these stony old Tuscan towns, I get no sense of stepping back in time that I've had in Yugoslavia, Mexico, or Peru. Tuscans are of this time; they simply have had the good instinct to bring the past along with them. If our culture says burn your bridges behind you—and it does—theirs says cross and recross. A fourteenth-century plague victim, perhaps once hauled out of one of the doors of the dead, could find her house and might even find it intact. Present and past just coexist, like it or not. The old Medici ball insignia in the piazza until last year had a ceramic hammer and sickle of the Communist party right beside it.
I walk through the short connecting leg of street to Piazza Signorelli, named for one of Cortona's hometown boys. Slightly larger, this piazza swarms on Saturday, market day, year round. It hosts an antique fair on the third Sunday in summer months. Two bars' outdoor tables extend into the piazza. I always notice the rather forlorn-looking Florentine lion slowly eroding on a column. No matter how late I go into town, people are gathered there; one last coffee before the strike of midnight.
Here, too, the _comune_ sometimes sponsors concerts at night. Everyone is out anyway, but on these nights the piazza fills up with people from the nearby _frazioni_ and farms and country villas. In this town of dozens of Catholic churches, a black gospel choir from America is singing tonight. Of course, this is no spontaneous Baptist group from a Southern church but a highly produced, professional choir from Chicago, complete with red and blue floodlights and cassettes for sale for twenty-thousand lire. They belt out "Amazing Grace" and "Mary Don't You Weep." The acoustics are weird and the sound warps around the eleventh-and twelfth-century buildings surrounding this piazza, where jousts and flag throwers have performed regularly, and where on certain feast days, the bishops hold aloft the relics of saints, priests swing braziers of burning myrrh, and we walk through town on flower petals scattered by children. The sound engineer gets the microphones adjusted and the lead singer begins to pull the crowd to him. "Repeat after me," he says in English, and the crowd responds. "Praise the Lord. Thank you, Jesus." The English and American forces liberated Cortona in 1944. Until tonight, this many foreigners may never have gathered here since, certainly not this many black ones. The choir is big. The University of Georgia's students from the art program in Cortona are all out for a little down-home nostalgia. They, a smattering of tourists, and almost all the Cortonese are crushed into Piazza Signorelli. "Oh, Happy Day," the black singers belt out, pulling an Italian girl onstage to sing with them. She has a mighty voice that easily matches any of theirs, and her small body seems all song. What are they thinking, this ancient race of Cortonese? Are they remembering the tanks rolling in, oh happy, happy day, the soldiers throwing oranges to the children? Are they thinking, Mass in the duomo was never like this? Or are they simply swaying with the crude American Jesus, letting themselves be carried on his shoulders by the music?
The piazza's focus is the tall Palazzo Casali, now the Etruscan Academy Museum. The most famous piece inside is a fourth-century B.C. bronze candelabrum of intricate design. It's remarkably wild. A center bowl fed oil to sixteen lamps around the rim. Between them, in bold relief, are animals, horned Dionysus, dolphins, naked crouching men _in erectus,_ winged sirens. One Etruscan word, _tinscvil,_ appears between two of the lamps. According to _The Search for the Etruscans_ by James Wellard, _Tin_ was the Etruscan Zeus and the inscription translates "Hail to Tin." The candelabrum was found in a ditch near Cortona in 1840. In the museum, it is hung with a mirror above so you can get a good look. I once heard an English woman say, "Well, it is interesting, I suppose, but I wouldn't buy it at a jumble sale." In glass cases, you see chalices, vases, bottles, a wonderful bronze pig, a two-headed man, many lead soldier-sized bronze figures from the sixth and seventh centuries B.C., including some in _tipo schematico,_ an elongated style that reminds the contemporary viewer of Giacometti. Besides the Etruscan collection, this small museum has a surprising display of Egyptian mummies and artifacts. So many museums have excellent Egyptian exhibits; I wonder sometimes if anything from ancient Egypt ever was lost. I always visit several paintings I like. One, a portrait of the thoughtful Polimnia wearing a blue dress and a laurel crown, was long thought to be Roman, from the first century A.D. She's the muse of sacred poetry and looks quite pensive with the responsibility. Now she's believed to be an excellent seventeenth-century copy. The museum has not changed the more impressive date.
Appealing family crests emblazoned with carved swans, pears, and fanciful animals cover the side of the Palazzo Casali. The short street below leads to the Duomo and the Museo Diocesano, formerly the Chiesa del Gesù, which I sometimes pop into. Upstairs, the treasure is the Fra Angelico _Annunciation,_ with a fabulous neon orange-haired angel. The Latin that comes out of the angel's mouth heads toward the Virgin; her reply comes back to him upside down. This is one of Fra Angelico's great paintings. He worked in Cortona for ten years and this triptych and a faded, painted lunette over the door of San Domenico are all that remain from his years here.
Just to the right of Palazzo Casali is Teatro Signorelli, the new building in town, 1854, but built in a quasi-Renaissance style with arched portico, perfect to shade the vegetable sellers from sun or rain. Inside is an opera house straight out of a Márquez novel: oval, tiered, little boxes and seats upholstered in red, with a small stage on which I once witnessed a ballet troupe from Russia thump around for two hours. It serves now as the movie theater in winter. Midway through the movie, the reel winds down. Intermission. Everyone gets up for coffee and fifteen minutes of talk. It's hard, when you really love to talk, to shut up for an entire two hours. In summer, the movies are shown _sotto le stelle,_ under the stars, in the town park. Orange plastic chairs are set up in a stone amphitheater, kind of like the drive-in with no cars.
Off both of these piazzas, streets radiate. This way to the medieval houses, that to the thirteenth-century fountain, there to the tiny piazzas, up to the venerable convents and small churches. I walk along all of these streets. I never have not seen something new. Today, a _vicolo_ named Polveroso, dusty, though why it should be more or less dusty than others was impossible to see.
If you're in great shape, you'll still huff a little on a walk to the upper part of town. Even in the mad-dog sun right after lunch, it's worth it. I pass the medieval hospital, with its long portico, saying a little prayer that I never have to have my appendix out in there. At mealtimes, women dash in carrying covered dishes and trays. If you're hospitalized, it's simply expected that your family will bring meals. Next is the interminably closed church of San Francesco, austerely designed by Brother Elias, pal of Saint Francis. At the side the ghost of a former cloister arcs along the wall. Up, up, streets utterly clean, lined with well-kept houses. If there are four feet of ground, someone has planted tomatoes on a bamboo tepee, a patch of lettuces. In pots, the neighborhood hands-down favorite, besides geraniums, is hydrangeas, which grow to bush size and always seem to be pink. Often, women are sitting outside, along the street on chairs, shelling beans, mending, talking with the woman next door. Once, as I approached, I saw a crone of a woman, long black dress, black scarf, hunched in a little cane chair. It could have been 1700. When I got closer, I saw she was talking on a cellular phone. At Via Berrettini, 33, a plaque proclaims it to be the birthplace of Pietro Berrettini; I finally figured out that's Pietro da Cortona. A couple of shady piazzas are surrounded by townhouse-style old houses, with pretty little gardens in front. If I lived here, I'd like _that_ one, with the marble table under the arbor of Virginia creeper, the starched white curtain at the window. A woman with an elaborate swirl of hair shakes out a cloth. She is laying plates for lunch. Her rich _ragù_ smells like an open invitation, and I look longingly at her green checked tablecloth and the capped bottle of farm wine she plunks down in the center of the table.
The church of San Cristoforo, almost at the top, is my favorite in town. It's ancient, ancient, begun around 1192 on Etruscan foundations. Outside, I peer into a small chapel with a fresco of the Annunciation. The angel, just landed, has chalky aqua sleeves and skirts still billowing from flight. The door to the church is always open. Actually, it's always half open, just ajar, so that I pause and consider before I go in. Basically a Romanesque plan, inside the organ balcony of curlicued painted wood is a touching country interpretation of Baroque. A faded fresco, singularly flat in perspective, shows Christ crucified. Under each wound, a suspended angel holds out a cup to catch his falling blood. They're homey, these neighborhood churches. I like the jars (six today) of droopy garden flowers on the altar, the stacks of Catholic magazines under another fresco of the Annunciation. This Mary has thrown up her hands at the angel's news. She has a you've-got-to-be-kidding look on her face. The back of the church is dark. I hear a soft honking snore. In the privacy of the last pew, a man is having a nap.
Behind San Cristoforo is one of the staggering valley views, cut into diagonally by a slice of fortress wall, amazingly high. What has held them up all these centuries? The Medici castle perches at the top of the hill, and this part of its extensive walls angles sharply down. I walk up the road to the Montanina gate, the high entrance to town. Etruscan, too; isn't this place ancient? I often walk this way into town. My house is on the other side of the hill and from there the road into this top layer of Cortona remains level. I like to go through the upper town without having to climb. One pleasure of my walk is Santa Maria Nuova. Like Santa Maria del Calcinaio, this church is situated on a broad terrace below the town. From the Montanina road, I'm looking down at its fine-boned shape, rhythmic curves, and graceful dome, a deeply glazed aquamarine and bronze in the sun. Though Calcinaio is more famous, having been designed by Francesco di Giorgio Martini, Santa Maria Nuova pleases my eye more. Its lines counter a sense of weight. The church looks as though it alighted there and easily could fly, given the proper miracle, to another position.
Turning back from the gate toward town, I walk to the other treasure of a church, San Niccolò. It's newer, mid-fifteenth century. Like San Cristoforo's, the decorations are amateurish and charming. The serious piece of art is a Signorelli double-sided painting, a deposition on one side and the Madonna and baby on the other. Meant to be borne on a standard in a procession, it now can be reversed by the custodian. On a hot day, this is a good rest. The eye is entertained; the feet can cool on the stone floor. On the way out, almost hidden, I spot a small Christ by Gino Severini, another Cortona boy. As a signer of the Futurist manifesto and an adherent to the slogan "Kill the moonlight," Severini doesn't readily associate in my mind with religious art. The Futurists were down on the past, embraced velocity, machines, industry. Around town, in restaurants and bars, I've seen posters of Severini's paintings, all color, swirl, energy. Then, over a table in Bar Sport, I noticed that the modern Madonna nursing a baby is his. The woman, unlike any Madonna I've seen, has breasts the size of cantaloupes. Usually a Madonna's breasts look disassociated from the body; often they're as round as a tennis ball. The Severini original in the Etruscan museum just escapes being lugubrious by being tedious. A separate room devoted to Severini is filled with an interesting hodge-podge of his work. Nothing major, unfortunately, but a taste of the styles he ran through: Braque-like collages with the gears, pipes, speedometers the Futurists loved, a portrait of a woman rather in the style of Sargent, art school-quality drawings, and the more well-known Cubist abstractions. A couple of glass cases hold his publications and a few letters from Braque and Apollinaire. None of this work shows the verve and ambition he was capable of. Of course, all the Futurists have suffered from their early enthusiasm for Fascism; baby went out with the bathwater. They've suffered more from the tendency we have had, until recently, to look to France for the news about art. Many astounding paintings from the Futurists are unknown. For whatever reasons, Severini, in his later years, returned to his roots for subjects. I think there's a microbe in Italian painters' bloodstreams that infects them with the compulsion to paint Jesus and Mary.
As I leave San Niccolò, walking down, I pass several almost windowless convents (they must have large courtyards), one of which is still cloistered. If I had lace needing of repair, I could place it on a Catherine wheel, where it is spun in to a nun to mend. Two of the convents have chapels, strangely modernized. On down the hill, I encounter Severini again in a mosaic at San Marco; if I climb this street, I'm on a Crucifixion trail he designed. A series of stone-enshrined mosaics traces Christ's progress toward the Crucifixion and then the Deposition. At the end of that walk (on a hot day I feel I've carried a cross), I'm at Santa Margherita, a large church and convent. Inside, Margherita herself is encased in glass. She has shrunk. Her feet are creepy. Most likely, a praying woman will be kneeling in front of her. Margherita was one of the fasting saints who had to be coaxed to take at least a spoon of oil every day. She shouted of her early sins in the streets. She would be neurotic, anorectic today; back then they understood her desire to suffer like Christ. Even Dante, it is believed, came to her in 1289 and discussed his "pusillanimity." Margherita is so venerated locally that when mothers call their children in the park, hers is the name most often heard. A plaque beside the Bernada gate (now closed) proclaims that through it she first entered the city in 1272.
The major street off the Piazza della Repubblica leads to the park. The Rugapiana is lined with cafés and small shops. The proprietors often are sitting in chairs outside or grabbing an espresso nearby. From the _rosticceria,_ tempting smells of roasting chicken, duck, and rabbit drift into the street. They do a fast business in lasagne at lunch and all day in _panzarotti,_ which means rolled bread but loses something in the translation. It's rolled around a variety of stuffings, such as mushrooms or ham and cheese. Sausage and mozzarella is one of the best. Past the circular Piazza Garibaldi—almost every Italian town has one—you come to the proof, if you have not intuited it before, that this is one of the most civilized towns on the globe. A shady park extends for a kilometer along the parterre. Cortonese use it daily. A park has a timeless quality. Clothing, flowers, the sizes of trees change; otherwise it easily could be a hundred years ago. Around the cool splash of the fountain of upside-down nymphs riding dolphins, young parents watch their children play. The benches are full of neighbors talking. Often a father balances a tiny child on a two-wheeler and watches her wobble off with a mixture of fear and exhilaration on his face. It's a peaceful spot to read the paper. A dog can get a long evening walk. Off to the right, there's the valley and the curved end of Lake Trasimeno.
The park ends at the _strada bianca_ lined with cypresses commemorating the World War I dead. After walking along that dusty road toward home for about a kilometer, I look up and see, at the end of the Medici walls, the section of Etruscan wall known as Bramasole. My house takes its name from the wall. Facing south like the temple at Marzabotto near Bologna, the wall may have been part of a sun temple. Some local people have told us the name comes from the short days in winter we have on this side of the hill. Who knows how old the name, indicating a yearning for the sun, might be? All summer the sun strikes the Etruscan wall directly at dawn. It wakes me up, too. Behind the pleasure and fresh beauty of sunrise, I detect an old and primitive response: The day has come again, no dark god swallowed it during the night. A sun temple seems the most logical kind anyone ever would build. Perhaps the name does go back twenty-six or so centuries to the ancient purpose of this site. I can see the Etruscans chanting orisons to the first rays over the Apennines, then slathering themselves with olive oil and lying out all morning under the big old Mediterranean sun.
Henry James records walking this road in his _The Art of Travel._ He "strolled forth under the scorching sun and made the outer circuit of the wall. There I found tremendous uncemented blocks; they glared and twinkled in the powerful light, and I had to put on a blue eye-glass in order to throw into its proper perspective the vague Etruscan past . . ." A blue eye-glass? The nineteenth-century equivalent of sunglasses? I can see Henry peering up from the white road, nodding wisely to himself, dusting off his uppers, then, no doubt, heading back to his hotel to write his requisite number of pages for the day. I take the same stroll and attempt the same mysterious act, to throw the powerful light of the long, long past into the light of the morning.
Riva, Maremma:
Into Wildest Tuscany
FINALLY, WE'RE READY TO LEAVE BRAMASOLE , if only for a few days. The floors are waxed and gleaming. All the furniture Elizabeth gave us shines with beeswax polish and the drawers are lined with Florentine paper. The market supplied us with antique white coverlets for the beds. Everything works. We even oiled the shutters one Saturday, took each one down, washed it, then rubbed in a coat of the ubiquitous linseed oil that seems to get poured onto everything. The can of mixed garden flowers I flung along the Polish wall bloom with abandon, ready to bolt at any moment. We live here. Now we can begin the forays into the concentric circles around us, Tuscany and Umbria this year, perhaps the south of Italy next year. Our travels are still somewhat housebased: We are ready to stock a wine cellar, to begin to build up a collection of wines associated with places where we have enjoyed them with local food. Many Italian wines are meant to be drunk immediately; our "cellar" under the stairs will be for special bottles. In the cantina off the kitchen, we'll keep our demijohn and the cases of house wine.
Along the way we plan to taste as much of the Maremma cuisine as possible, bake in the sun, track down other Etruscan sites. Ever since reading D.H. Lawrence's _Etruscan Places_ years ago, I have wanted to see the ancient diving boy, the flute player in his sandals, the crouching panthers, to experience the mysterious verve and palpable _joie de vivre_ hidden underground all those centuries. For several days we've plotted our route. This seems like a journey into the far interior, though, in reality, it's only about a hundred miles from our house to Tarquinia, where acres and acres of Etruscan tombs are still being explored. Time keeps bending on me here. The _density_ of things to see in Tuscany makes me lose sight of our California sense of distance and freeway training, where Ed drives fifty miles to work. A week will be short. The area called the Maremma, moorland, is no longer swampy. The last of the marshy waters were long since drained off. Its history of killing malaria, however, kept this southwestern stretch of Tuscany relatively unpopulated. It's the land of the _butteri,_ cowboys, of the only unsettled piece of coast along the Tyrrhenian, and of wide-open spaces interrupted only by small stone huts where shepherds used to shelter.
Soon we arrive in Montalcino, a town built for broad views along a bony ridge of hills. The eye seems to stop before the waving green landscape does. Small wine shops line the street. A table with white cloth and a few wineglasses waits right inside each door, as though inviting you in for an intimate drink with the proprietor and a toast to the great vintages.
The hotel in town is modest, indeed, and I'm alarmed that the electrical switches for the bathroom are located in the shower. I aim the showerhead as far into the opposite corner as possible and splash as little as possible. I do not want to fry before tasting the local wines! Compensation is our panorama of the tile rooftops and into the countryside. The _belle époque_ café in the center of town doesn't appear to have changed an iota since 1870—marble tables, red velvet banquettes, gold mirrors. The waitress polishing the bar has cupid-bow lips and a starchy white blouse with ribbons on the sleeves. What could be more sensuous than a lunch of _prosciutto_ and truffles on _schiacciata,_ a flat bread like _focaccia,_ with salt and olive oil, along with a glass of Brunello? The utter simplicity and dignity of Tuscan food!
After siesta, we walk to the fourteenth-century _fortezza,_ now a fantastic _enoteca._ In the old lower part, which used to store crossbows and arrows, cannons and gunpowder, all the wines of the area are available for tasting. It's brilliantly sunny outside. In the _fortezza,_ the light is dim, the stone walls musky and cool. Vivaldi is playing while we try a couple of good whites from Banfi and Castelgiocondo vineyards. Appropriately, the music changes to Brahms as we taste the dark Brunellos from several vineyards: Il Poggiolo, Case Basse, and the granddaddy of all Brunello, Biondi. Brilliant, totally evolved wines that make me want to rush to a kitchen and prepare the kind of hearty food they deserve. I can't wait to cook for these wines—rabbit roasted with balsamic vinegar and rosemary, chicken with forty cloves of garlic, pears simmered in wine and served with mascarpone. The man serving us insists that we try some dessert wines. We fall for one called simply "B" and another Moscadello from Tenuta Il Poggione. The enologist must have been a former perfume maker. No dessert would be needed with these, except perhaps a white peach, just ripe. On second thought, a lemon soufflé might be just the touch of heaven. Or my old Southern favorite, crème brÛlée. We buy a few bottles of the luxurious Brunellos. Just the memory of the price at home makes us indulgent. At Bramasole, we have good wine storage in two spaces under the stone stairs. We can shove cases in, lock the door, and start taking them out in a few years. Since long-term planning is not a strong suit of either of us, we buy a couple of cases of less costly Rosso di Montalcino, drinkable now, in fact, smooth and full bodied. I doubt if the dessert wines will be around by the end of summer.
In late afternoon we drive the few miles to Sant'Antimo, one of those places that feels as if it must be built on sacred ground. From a distance, you see it over in a field of manicured olives, a pale travertine Romanesque abbey, starkly simple and pure in style. It does not look Italian. When Charlemagne passed this way, his soldiers were struck by an epidemic and Charlemagne prayed for it to stop. He promised to found an abbey if his prayer was granted and in 781 he built a church. Perhaps it is the heritage that gives the present church, built in 1118, its slender French lines. We arrive as vespers begin. Only a dozen people are here and three of these are women fanning themselves and chatting just behind us. Usually, the habit of regarding the church as an extension of the living room or piazza charms me, but today I turn and stare at them because the five Augustinian monks who strode in and took up their books have begun the Gregorian chant of this hour. The lofty, unadorned church amplifies their voices and the late lambent sun turns the travertine translucent. The music is piercing to my ear, as some birds' songs that almost can hurt. Their voices seem to roll and break, then part and converge on downward humming tones. The chanting disengages my mind, releases it from logic. The mind goes swimming and swims through large silence. The chant is buoyant, basic, a river to ride. I think of Gary Snyder's lines:
_stay together_
_learn the flowers_
_go light_
I glance at Ed and he is staring up into the pillars of light. But the women are unmoved; perhaps they come every day. In the middle, they saunter noisily out, all three talking at once. If I lived here, I'd come every day, too, on the theory that if you don't feel holy here, you never will. I'm fascinated by the diligence of the monks performing this plainsong for the six liturgical hours of every day, beginning with _lodi,_ prayers of praise, at seven A.M., and ending with _compieta,_ compline, at nine. I would like to come back for a whole day and listen. I see in the brochure that those on spiritual retreat can stay in guest quarters and eat at a nearby convent. We walk around the outside, admiring the stylized hooved creatures supporting the roof.
A cool evening to ride over dirt roads admiring the land, sniffing like a dog out the window the fresh country smells of dry hay. We arrive at Sant'Angelo in Colle, a restaurant operated by Poggio Antico vineyards. A wedding party is in uproarious progress and all the waitresses are enjoying the action. We're put in a back room alone, with the rousing party echoing around us. We don't mind. A stone sink is piled with ripe peaches, scenting the room. We order thick onion soup, roast pigeon, potatoes with rosemary, and what else, the house's Brunello.
WILDEST TUSCANY IS SOMEWHAT OF AN OXYMORON. The region, as a whole, has been tamed for centuries. Every time I dig in the garden, I'm reminded of how many have gone before me on the land. I have a big collection of fragments of dishes, dozens of patterns, so many that I wonder if other women fling their dishes into the garden. Crockery colanders, edges of lids, delicate cup handles, and assorted pieces of plates gradually have collected on an outdoor tabletop, along with jawbones of a boar and a hedgehog. The land has been trod and retrod. A glance at terraced farming shows how the hills have been reshaped for the convenience and survival of humans. Still, the Maremma area remained, until less than a hundred years ago, a low coastal plain inhabited by cowboys, shepherds, and mosquitoes. Its _mal aria_ was definitely associated with chills and fever. Farmhouses are occasional whereas the rest of Tuscany is dotted with them. The Renaissance touched lightly here; towns, generally, are not permeated with monumental examples of architecture and adorned by the great names in painting. The bad air, now soft and fresh, probably kept the extensive Etruscan tombs safer. Although many were recklessly pillaged, an astonishing number remain. Were Etruscans immune to malaria? All evidence shows that the area was quite populated in their time.
Our next base is a villa, now a small hotel, on the Acquaviva vineyard property outside Montemerano. Ed has cased the _Gambero Rosso_ guide and spotted this tiny village with three excellent restaurants. Since it is central for most of what we want to see, we decide to stay put for a few days rather than checking in and out of hotels. A tree-lined drive leads to a park-sized garden with shady places to sit outside and look over the rolling vineyards. We have a room right on the garden. I push open the shutters and the window fills with blue hydrangea. We quickly unpack and take off again; we can relax later.
Pitigliano must be the strangest town in Tuscany. Like Orvieto, it sits on top of a tufa mass. But Pitigliano looks like a drip castle, a precipitous one looming above a deep gorge. Who could look down, while trying to see the town and the road at the same time? Tufa isn't the strongest rock in the world, and sections of it sometimes weaken, erode, or veer off. Pitigliano's houses rise straight up; they're literally living on the edge. The tufa beneath the houses is full of caves—perhaps for the storage of the area's Bianco di Pitigliano, a wine that must derive its astringent edge from the volcanic soil. In town, the bartender tells us that many of the caves were Etruscan tombs. Besides wine, oil is stored and animals are housed. Medieval towns have a dark and twisted layout; this town's feels darker, more twisted. Many Jews settled here in the fifteenth century; it was outside the realm of the Papal States, who were busy persecuting. The area where they lived is called a ghetto. Whether there was a strict ghetto here, as there was in Venice, where Jews had to keep to a curfew, had their own government and cultural life, I don't know. The synagogue is closed for reconstruction but it does not appear that anything much is happening. Almost everything seems to be for sale. In this life or the next, some of the rim houses are going to find themselves in the gorge. Perhaps this contributes to the gloomy feel the town gives me. On the way out, we buy a few bottles of the local white for our growing collection. I ask how many Jews lived there during World War II. "I don't know, signora, I'm from Naples." Winding downhill, I read in a guidebook that the Jewish community was exterminated in the war. I'd never trust a guidebook on a fact and hope that this is wrong.
Tiny Sovana, nearby, has the feeling of a ghost town in California, except that the few houses along the main street are immensely old. People are outnumbered, it seems, by Etruscan tombs built into the hillsides. We spot a sign and pull over. A path takes us into a murky wooded area with a stagnant stream just made for female anopheles mosquitoes. Soon we're scrambling on slippery paths, up along a steep hillside. We begin to see the tombs—tunnels into the hills, stony passageways leading back, probably to vipers. The entrances in that wildness look undisturbed for the centuries. Nothing is attended—no tickets sold, no guides waiting; it is as though you discover these strange haunted sepulchers yourself. Vines dangle, as in the Mayan jungles around Palenque, and the eroded carvings in the tufa also have that strangely Eastern aspect that many of the Mayan carvings have, as though long ago art was the same everywhere. It's very clear that becoming an Etruscan archaeologist is a good move. Endless areas are awaiting further investigation. We climb for hours, encountering only a large white cow standing up to its knees in the stream. When we emerge, I have bleeding scratches on my legs but not a single mosquito bite. I have the feeling that this is a place I will think about on nights of insomnia. Down the road, we see another sign. This points to the remains of a temple, which looks carved out of the tufa hillside. We walk among eerie arches and columns, partly excavated and looking quite abandoned. Those Etruscans are going to stay mysterious. What did they do here? An Art in the Park summer concert series? Strange rites? The guidebooks refer to this as a temple, and perhaps here in the center a wise person practiced haruspication, the art of divining by reading a sheep's liver. A bronze model of one was found near Piacenza, with the liver divided into sixteen parts. It is thought that the Etruscans similarly divided the sky, and that the way the liver was sectioned also determined the layout of Etruscan towns. Who knows? Perhaps the forerunners of talk shows held forth here or it was the market for seafood. In places such as Machu Picchu, Palenque, Mesa Verde, Stonehenge, and now here, I always have the odd and somber consciousness of how time peels us off, how irretrievable the past really is, especially in these hot spots where you sense some matrix of the culture took place. We can't help but push our own interpretations on them. It's a deep wish of philosophers and poets to search for theories of eternal return and time past being time present. Bertrand Russell was closer when he said the universe was created five minutes ago. We can't recover the slightest gesture of those who chopped out this rock, not the placing of the first stone, the lighting of a fire to make lunch, the stirring of a pot, the sniffing of an underarm, the sigh after lovemaking, _niente._ We can walk here, the latest little dots on the time line. Knowing that, it always amazes me that I am intensely interested in how the map is folded, where the gas gauge is pointed, whether we have withdrawn enough cash, how everything matters intensely even as it is disappearing.
We've seen enough for the day but can't resist a walk through ancient Sorano, also poised on an endangered tufa mass. There seem to be no tourists in this whole area. Even the roads are empty. Sorano looks the same way it did in 1492, when Columbus found America. The last building must have gone up around then. There's a somber feel to the narrow streets, a gray light that comes off the dark stone, but the people seem extraordinarily friendly. A potter sees us looking in and insists that we visit his workshop. When we buy two peaches, the man rinsing off his crates of grapes with a hose gives us a bunch. _"Speciale!"_ he tells us. Two people stop to help us out of a tight parking place, one gesturing come on, the other gesturing stop.
We're dusty and worn out as we pull into our parking spot near Acquaviva's garden. Before dinner, we shower, change, and take glasses of their own white wine, a Bianco di Pitigliano, out to the comfortable chairs and watch the sun drop behind the hill, just as two Etruscans might have in this exact place.
Montemerano is only a few minutes away, a high castle town, beautiful and small.
It has its requisite fifteenth-century church with the requisite Madonna—this one with a difference. It's entitled _Madonna della Gattaiola, Madonna of the Cat Hole._ The bottom part of the painting had a hole to let the cat out of the church. Everyone in town seems to be outside. A few local boys and men are playing some jazz right in the center of town. The woman running the bar slams the door. Apparently she's heard enough. Absolutely everyone stares when a tall and gorgeous man in riding boots and a tight T-shirt strides by. But he's aloof, takes no notice. I see him check out his image in the shop windows he passes.
We're ravenous. As soon as the magic hour of seven-thirty arrives and the restaurant opens the door, we rush in. We're the only ones in Enoteca dell'Antico Frantoio, a former olive mill, now remodeled to the extent that it looks like a reproduction of itself. Although it has lost its authentic feel, the result is rather like an airy Napa Valley restaurant, so we feel quite at home. The menu, however, reveals the Maremma roots: _Acquacotta,_ served all over Tuscany, is a particular local specialty, the "cooked water" soup of vegetables with an egg served on top; _testina di vitella e porcini sott'olio,_ veal head and porcini mushrooms under olive oil; _pappardelle al ragù di lepre,_ broad pasta with _ragù_ made of hare; _cinghiale in umido alle mele,_ smoked boar with apples. In _trattorie_ over most of Tuscany, menus are almost interchangeable: the usual pastas with _ragù,_ butter and sage, pesto, or tomato and basil, the standard selection of grilled and roasted meats, the _contorni_ usually consisting of fried potatoes, spinach, and salad. No one seems interested in varying the classics of the cuisine. In this less settled, less travelled region, the cuisine of Tuscany is closer to its origins, the hunter bringing home the kill, the farmer using every part of the animal, the peasant woman making soup with a handful of vegetables and an egg. Usually you do not find the above items; nor do you see _capretto,_ kid, or _fegatello di cinghiale,_ boar liver sausage, on menus. The Frantoio has its more delicate side, too: _ravioli di radicchio rosso e ricotta,_ ravioli with red radicchio and ricotta, and _sformato di carciofi,_ a mold of baked artichoke. We start with _crostini di polenta con pure di funghi porcini e tartufo,_ polenta squares with a purée of porcini and truffles—rich and savory. Ed orders the rabbit, roasted with tomatoes, onions, and garlic, and I bravely order the kid. It's delicious. The wine of the region is the Morellino di Scansano, black as the wine of Cahors, a discovery for us. This enoteca's own is the Banti Morellino, big and accomplished. Now I'm really happy.
In the morning, I have one of the favorite experiences of my life. We get up at five and go to the hot waterfall near Saturnia. No one is there at that hour, although the hotel manager warned us of crowds later in the day. Pale blue but clear water cascades over tufa, which the falls have hollowed out in many places, forming perfect places to sit down and let the warm water flow over and around you. When I first heard of the falls, I thought we might emerge smelling like old Easter eggs, but the sulphur is mild. The current has enough force so that you feel massaged, not enough to sweep you away. Bliss. Where are the water nymphs? Whatever it is supposed to cure, I'm sure it does. After an hour I feel as though I have no bones in my body. I am utterly relaxed, limp, speechless. We leave just as two cars pull up. Back at Acquaviva, we have breakfast on the terrace: fresh orange juice, nut bread, toast, something like pound cake, and pots of coffee and warm milk. It's hard to leave. Only the lure of the Etruscans stirs us to pick up our map and go.
Tarquinia is out of Tuscany, a few miles into Lazio. It gets ugly along the way, industrial and crowded. I'm less able to visualize the Etruscans here than in the green and dreamy Maremma. Traffic annoys us after so many empty roads. Soon we're in the busy town of Tarquinia, where hoards of items from the tombs are exhibited in a fifteenth-century palazzo. Staggering, amazing, fantastic, and worth the trip alone are two terra-cotta winged horses from the fourth or third century B.C. These were found in 1938 near the steps leading to a temple, now just a two-level base of square limestone blocks. The horses must have been ornaments. I wonder about their connection to Pegasus, who started the flow of the sacred Hippocrene with a dash of his hoof, who always is linked with poetry and the arts. These are fabulously vigorous horses with muscles, genitals, ribs, perky ears, and feathered wings. The chronological arrangement of the museum is useful for sorting out when there were Attic influences, when they began using stone sarcophagi, how design changed. Everything from cinerary urns to perfume burners makes you feel the creative energy and spirit behind these objects. Several tomb paintings have been brought here to prevent deterioration. The tomb of the Triclinium, with its prancing musician and young dancer swathed in what looks like a chiffon throw, would melt the heart of a stone. In almost any museum, I fade after a couple of hours and can wander by with a glance at something that would have stopped me for minutes when I first arrived. We resolve to come back, though, because there is so much to linger over.
The field of tombs could be any field, the necropoli like outhouses attached to sheds. The structures built over tombs open to the public are simply entrances with a flight of steps leading down. The tombs are lit. We're disappointed to find that only four a day are open. Why? No one seemed to know; they're on a rotation system, that's all. Now we know we'll come back because the Hunting and Fishing Tomb is not on view today. We see the Lotus Flower one, with decorations that have almost a Deco style, then the Lionesses one, famous for the reclining man holding up an egg—symbolic of resurrection, as in Christian belief, the shell like the tomb broken open. Dancers cavort here, too. I notice their elaborate sandals with straps crossed and wound around the ankles just like the ones I'm wearing—did the Italians always love shoes? We're lucky to see the Jugglers' tomb, rather Egyptian looking, except for what appears to be a Middle Eastern belly dancer about to go into her act. In the two-chambered tomb of the Orcas remains, amid much faded scenes of a banquet, a startling portrait of a woman in profile with a crown of olive leaves.
After a quick bite, we drive the few kilometers to Norchia, which we've heard is the site of many recent finds. It does not appear that anyone has been about in decades. The broken sign points up to the sky. After we wander about, a farmer points us in the right direction. At the end of a dirt road we park and set out along the edge of a wheat field. A few meters down the path, we encounter a severed goat head covered with flies. Here, indeed, is a sign—a primitive one of sacrifice. "This is getting spooky," I say as we step around it. The terrain becomes precipitous. We're climbing down and all I can think about is the climb back up. A few rusted hand railings indicate we're going in the right direction. The declivity becomes sharper; we're skidding, holding on to vines. Haven't we seen enough of these tombs? When it levels out, we start to see the openings into the hillside, dark mouths, vines, and brush. We venture into two, breaking through impressive spiderwebs with sticks. Inside, it's as black as, well, a tomb. We see slabs and pits where the bodies and urns lay. Vipers must coil here now. We walk about half a mile along this level. The tombs are more numerous than at Sovana and poke into the hillside at various levels. There's an oppressive feeling of danger I can't identify. I just want to leave. I ask Ed if he thinks this is a weird place and he says, "Definitely, let's go." The way out is as awful as I expected. Ed stops to empty dirt out of his loafer and a sliver of bone falls out. We come to the place where we saw the goat head; it is no longer there. When we get back to the car, another one is parked near us. A young couple is kissing and rolling around with such intensity that they don't hear us. This dispels the bad aura and we head back to the hotel, saturated with Etruscan voodoo.
Ah, dinner, the favorite hour. Tonight it's Caino, which we expect to be the gastronomic highlight of our trip. Before driving into Montemerano, we take a little detour to Saturnia, perhaps the oldest town in Italy if Cortona isn't. It would have to be if, as legend has it, Saturn, son of sky and earth, founded it. The warm waterfall, legend also tells us, first poured forth when the horse of Orlando (Roland in English) pawed the ground with his hoof. A town on Via Clodia has to be older than anything I can grasp. I practice saying "I live on Via Clodia," imagining a life on such an ancient street. The town is shady and active, not at all lost in time. A few highly bronzed people from the expensive hotel near the falls seem to be looking for something to buy but the shops are plain. They settle at an outdoor café and order colorful drinks in tall glasses.
Caino, a jewel: two gracious small rooms with flowers on the tables, pretty china and wineglasses. With glasses of _spumante,_ we settle into the menu. Everything looks good and I have a hard time deciding. They, too, have a combination of sophisticated choices and the rustic Maremma specialties, such as _zuppa di fagioli,_ white bean soup, pasta with rabbit sauce, _cinghiale all'aspretto di mora,_ boar with blackberry sauce. For our _antipasti,_ we're attracted to _flan di melanzane in salsa tiepida di pomodoro,_ eggplant flan with tepid tomato sauce, and _mousse di formaggi al cetriolo,_ a mousse of cheeses and cucumber. We both want _tagliolini all'uovo con zucchine e fiori di zucca,_ egg pasta with zucchini and squash blossoms, for first courses. After that, it's roast lamb for Ed and duck breast in a sauce of grape must vinegar for me. We take the waiter's suggestion for tonight's Morellino, the Le Sentinelle Riserva 1990 by Mantellassi. Praise Allah! What a wine. The dinner is superb, every bite, and the service attentive. Everyone in the small restaurant has noticed the young couple at the table in the middle from the moment they were seated. They look like twins. Both have that curly, magnificent black hair and hers has jasmine flowers caught in its ripples. Both have the sultry eyes my mother used to refer to as "bedroom eyes" and lips like those on archaic Greek statues. They're dressed out of Milan or Rome boutiques, he in a somewhat rumpled tan linen suit and she in a yellow puckered silk sundress that was melted onto her. The waiter pours champagne for them, an oddity in an Italian restaurant. We all avert our eyes as they toast each other and seem to disappear into each other's eyes. Our salads look as if someone picked them from a field this afternoon, and perhaps they did. We're falling into a deep relaxation and exhilaration by now, just what a vacation is supposed to be. "Would you like to go to Morocco?" Ed asks out of nowhere.
"What about Greece? I never intended not to go to Greece." Seeing new places always brings up the possibility of other new places. We're riveted again by the beautiful couple. I see the other diners discreetly staring, too. He has moved from his chair across from her to the one next to her and has taken her hand. I see him reach into his pocket and take out a small box. We turn back to our salads. We will have to forego _dolci_ but with our coffee they bring a plate of little pastries anyway, which we manage to eat. This is one of the best dinners I've had in Italy. Ed proposes that we stay a few more days and eat here every night. The lustrous girl now is holding out her hand, admiring a square emerald surrounded by diamonds I can see from here. They both smile at everyone, who they suddenly realize has followed this engagement. Spontaneously we all lift our glasses in a toast and the waiter, sensing the moment, rushes in to refill. The girl shakes back her long hair and little white flowers fall on the floor.
When we leave, the village is dark and silent until we get to the bar at the end of the street, where the whole town must be playing cards and having a last coffee.
In the morning we drive over to Vulci, another ancient-sounding name, with a humpbacked bridge and a castle turned museum. The bridge is Etruscan, with Roman and medieval repairs and additions. Why it's so highly arched is impossible to know because the Fiora, little more than a mighty stream, runs far below in a gorge. But humped it is. Whatever road it once joined has disappeared, so the bridge has a strangely surreal aspect. The castle fortress at one end was built much later. A Cistercian monastery surrounded by a moat, it now serves as a museum, like Tarquinia's, full of astonishing things. Too bad the glass separates us from the objects. They are extremely appealing to the touch. I want to pick up each little votive hand, fawn-shaped perfume bottle, to rub the monumental stone sculptures, such as the boy on the winged horse. Here's the real news about the Etruscans—their art is fortifying, the remains of people who lived in the moment. D.H. Lawrence certainly caught that—but who could not, having seen as much as he did. Rereading him along the way, I'm struck often with what an _ass_ he was. The peasants are dullards because they do not immediately see to the wishes of this obnoxious foreigner. No one is just waiting to take him miles into the country to see ruins. No one is equipped with candles the minute he asks. What an inconvenient country! The train schedules are unlike those at Victoria Station; the food is not to his liking. I forgive him now and then, when he totally disappears from the text and just writes what he sees.
Remains of the Etruscan, then Roman, town lie out in the field—stone foundations and bits of floor, some with black and white mosaic, subterranean passageways and remnants of baths: a floor plan of the town, actually, so that you walk around imagining the walls around you, the activities, the views across to the bridge. Off to the side, we see the stark Roman remains of a brick building, walls, a few windows, and holes for beams to hold up a floor. Vulci, a lavish archeological area. Unfortunately, the area's painted tombs are closed today—another reason to return.
We're amazed by the restaurants, too. Enoteca Passaparola, on the road leading up to Montemerano, serves robust food in a very casual ambience—paper napkins, chalkboard menu, plank floors. If there are cowboys left in the Maremma, I think they would head here. We order big plates of grilled vegetables and wonderful green salads with a bottle of Lunaia, a Bianco di Pitigliano made by La Stellata, another gorgeous local wine. The waiter tells us about the area's Cantina Cooperativa del Morellino di Scansano, then brings over a glass for us to taste. We find our house wine for the rest of the summer. At about $1.70 a bottle, it has a deep mellifluous taste that surprises us. More straightforward than the _reserve_ Morellinos we've tried, this wine definitely stands up to be counted. We still have the backseat where we can pile a couple of cases.
At the next table an artist draws caricatures of us. Mine looks like Picasso's Dora Maar. When we toast him and begin to chat, he opens a satchel and starts showing us catalogues of his shows. Soon we're nodding politely. He pulls out reviews, pours more wine. His wife looks not mortified but resigned; she's been to restaurants with him before. They're at the _terme,_ taking the waters for his liver. I can imagine him cornering people there as they sip their measures of mineral water. He slides his chair over, leaving her at their table. I'm torn between the pleasure of the berry tart listed on the chalkboard and the pleasure of getting the check and leaving. Ed asks for the check and we exit. Up in town we have coffee, then on the way back to the car, we look in the window and see that Signor Picasso is gone. So we have the berry tart after all. The waiter brings us a complimentary _amaro._ "They come here every night," he complains. "We're counting the days until he goes back to Milano with his liver."
Saturated with the Etruscans, well fed, pleased with the hotel, we pack and take off for Talamone, a high-walled town over the sea. The water must be pure here. It's clear as far out as I can wade and quite cold. At our modern hotel, there's no beach, just rocks jutting straight up, with concrete platforms on the water where you can sit in a striped chair and sunbathe. We chose Talamone because it is adjacent to the Maremma's preserved seashore, the only long stretch of Tuscan coast unblemished by development. Most sand beaches are a series of concessions for umbrellas and rows of chairs as deep as the beach is wide, leaving only a strip along the water for walking. Often these concessions have changing rooms, showers, and snack bars. Italians seem to like this way of being at the beach. So many people to talk to! And, usually, families or groups of friends are together. As a Californian, I'm unhappy to be surrounded. Beaches I grew up on in Georgia and my years of loving the raw windy stretches of sand at Point Reyes unequip me for the Old World beaches. Ed and my daughter like the umbrellas. They've dragged me to Viareggio, Marina di Pisa, Pietrasanta, insist it's just different; you have to get into it. I like to lie on the beach and listen to the waves, to walk with no one in sight. The Tuscan beaches are as crowded as streets. The Maremma preserve, however, even has wild horses, foxes, boar, and deer, according to the brochure. I love the smell of the _macchia,_ the wild salty shrubs sailors say they can smell when still out of sight of land. Mostly there's nothing—trails with wild rosemary and sea lavender through sandy hills, the vacant beaches. We walk and sit on the beach all morning. Tyrrhenian, Tyrrhenian the waves say, that ancient sea. We've brought mortadella sandwiches, a hunk of _parmigiano,_ and iced tea. Except for a small group of people down the beach, I have my wish to be in nature alone. What color is the sea? Cobalt is close. No, it's lapis lazuli, exactly the color of Mary's dress in so many paintings, with a tesselated sheen of silver. It's good to walk, after days of chasing sites in the car. I'm trying to read but the sun is blaring—perhaps an umbrella _would_ be nice.
In the morning we move on to Riva degli Etruschi, coast of the Etruscans. We can't get away from them. This beach does have the rented chairs but, since it joins the preserve, it's not as crowded. We're able to take a long, long walk on the beach followed by a siesta in our tiny individual cottage. We're near San Vincenzo, where Italo Calvino summered. The town shops sell rubber beach balls, rafts, and sand pails. At evening, everyone strolls around buying postcards and eating ice cream. Beach towns are beach towns. We find an outdoor restaurant and order _cacciucco,_ a big fish stew. Several kinds of fish, filleted at the cart, are piled in a large white bowl and a hot broth is poured over them. The waiter spreads creamy roasted garlic on slices of toasted bread and we float them in the soup, breathing in the heady aroma. Two fierce little bug-eyed lobsters eye us from our bowls. The waiter keeps coming around, ladling in enough to keep the bread afloat. When he brings the salad, he wheels over a cart of olive oils in crocks, clear bottles, colorful ceramic ones, dozens of choices for our salad. We ask him to select for us and he pours from on high a thin stream of pale green oil onto a bowl of red and green radicchio.
En route to Massa Marittima, we detour to Populonia, simply because it is close and it sounds too ancient to miss. Every little pause makes me want to linger for days. In a café where we stop for coffee, two fishermen bring in buckets of fish, their night's catch. Lunch is not for hours, unfortunately. A woman from the kitchen starts writing up the menu of the day on a blackboard. We drive on into town and park under an immense fortress, the usual castle and wall like those in old books of hours. Ah, another Etruscan museum and I must see every object. Ed is through, for now, with anything that happened before the last millennium, so he goes off to buy honey from bees that have buzzed around in the coastal shrubs. We meet in a shop where I find an Etruscan clay foot for sale. Whether it's genuine or fake, I don't know. I decide to think about it while we take a walk but when we come back to buy it, the shop is closed. As we leave, I see a sign to an Etruscan site but Ed presses on the accelerator; he's tombed out.
Last overnight—the town I have chronically mispronounced. The accent, I find, is on Marit'tima. I've said Maritti'ma. Will I ever, ever learn Italian? Still so many basic errors. Once close to the sea, the town gradually became surrounded by silt, which eventually filled in, leaving Massa Marittima far inland but with a sense of outlook as it rises high over the grassy plain. We could be in Brazil, a remote outpost that appeals to magic realist novelists. It's two towns really, the old town and the older town, both austere, with deep shadows and sudden sunlight. We're a little tired. We check in and for the first time, our room has a TV. A World War II film, faded and in odd Italian, is on and we get hooked. A village, occupied by Germans, depends on an American soldier hiding in the countryside to help them. They must evacuate. They pile everything on a few donkeys and set out, for where we don't know. I doze. Someone is trying to open the shutters at Bramasole. I wake up. Another soldier is in the hayloft. Something is burning. Is Bramasole all right? Suddenly I realize this is our one day in Massa Marittima.
In two hours, we've covered every street. The Maremma keeps reminding me of the American West, its little out of the way towns the freeway missed by fifty miles, the shop owner staring out the window, the wide sky in his gaze. Certainly the piazza and fabulous cathedral are nothing like the West—the similarity is under the skin of the place: a loneliness, an eye on the stranger.
EN ROUTE HOME, WE PAUSE AT SAN GALGANO, LOVELIEST OF ruins, a graceful French Gothic church that lost its floor and roof centuries ago, leaving the open-windowed skeleton to grass and clouds. A romantic wedding could take place here. Where the large rose window was, only the imagination can color the space scarlet and blue; where monks lit candles at side altars, birds nest in the corners. A stone stairway leads nowhere. A stone altar remains, so disassociated from Christian function that human sacrifice could have taken place on it. The place fell into ruin when an abbot sold the lead in the roof for some war. Now it's a home for several cats. One has a litter of multicultural kittens; several fathers must have contributed to the ginger, black, and striped pile curled around the large white mother.
Home! Hauling in the wine, throwing open the shutters, running to water the drooping plants. We settle the wine into crates in the dark wedge of closet under the stairs. The spirit of all the grapes we saw ripening, now bottled and mellowing for those occasions we hope to celebrate. Ed closes the door, leaving them to dust and scorpions for now. Only a week away. We missed the house and come back understanding the next few circles around us. Qualities those of us with northern blood envy—that Italian insouciance and ability to live in the moment with gusto—I now see came down straight from the Etruscans. All the painted images from the tombs seem charged with meaning, if we only had the clues to read it. I close my eyes and look at the crouching leopards, the deft figure of death, the endless banqueting. Sometimes Greek myths come to mind, Persephone, Actaeon and the dogs, Pegasus, but the instinct I have is that the tomb images—and the Greek ones—each came from further back, and those further back came from something even earlier. The archetypes keep appearing and we find in them what we can, for they speak to our oldest neurons and synapses.
When I lived in Somers, New York, I had a large herb garden beside the eighteenth-century house I still dream of. Often I turned up brown and amber medicine bottles. As I was planting a border of santolina, the branches of which used to be spread on church floors in the Middle Ages to keep the human scents down, my trowel unearthed a small iron horse, rusty, stretched into full-out running position. I propped the horse on my desk as my private totem. Earlier this summer, I was digging up stones and my shovel sent flying a small object. When I picked it up, I was stunned to find that it was a horse. Is it Etruscan or is it a toy from a hundred years ago? This horse, too, is running.
A few years ago I read a section in the _Aeneid_ about the decision to found Carthage on the spot where the wanderers dug up an omen:
_the head of a spirited horse, for by this sign_
_it was shown that the race would be distinguished_
_in war and abound with the means of life_
(I, 444)
The war in the line doesn't thrill me but "means of life" does. The hoof of Orlando opened the hot spring. The winged horses at Tarquinia, unearthed from stone rubble and dirt, keep appearing in my vision. I prop a postcard photo of them next to my own two horses. Means of life. The Etruscans had it. In certain times and places, we find it. We can run full out, if not fly.
Turning Italian
THE ITALIAN ED IS A LIST MAKER. ON THE dining room table, the bedside table, the car seat, in shirt and sweater pockets, I find folded pieces of notepaper and crumpled envelopes. He makes lists of things to buy, things to accomplish, long-range plans, garden lists, lists of lists. They're in mixed English and Italian, whichever word is shorter. Sometimes he knows only the Italian word if it's a special tool. I should have saved the lists during the restoration and papered a bathroom with them, as James Joyce did with his rejection slips. We've exchanged habits; at home, he rarely makes even a grocery list—I make lists there, letters to write, chores, and especially of my goals for each week. Here, I usually don't have any goals.
It is hard to chart such changes of one's own in response to a new place but shifts are easy to spot in another person. When we first started coming to Italy, Ed was a tea drinker. As an undergraduate, he took a semester off to study on his own in London. He lived in a cold-water bed-sitter near the British Museum and sustained himself on cups of tea with milk and sugar while reading Eliot and Conrad. Espresso, of course, is pandemic in Italy; the _whoosh_ of steam is heard in every piazza. During our first summer in Tuscany, I remember seeing him eye the Italians as they stepped up to the bar and ordered, in a clipped voice, _"un caffè."_ At that time, espresso was rarely seen in America. When he ordered like the Italians, at first the bartenders asked him, _"Normale?"_ They thought surely a tourist was making a mistake. We require big cups of brown coffee, as the Italians, with a touch of wonder, call it.
_"Sì, sì, normale,"_ he answered, with a slight tone of impatience. Soon he was ordering with authority; no one asked again. He saw the locals down it at once, instead of sipping. He noticed the brands different bars used: Illy, Lavazza, Sandy, River. He began commenting on the _crema_ on top. Always he took it black.
"Your life must be sweet," one _barrista_ told him, "to take your coffee so bitter." Then Ed began to notice the sugar boats all the bars have, to notice how when the bartender put down the saucer and spoon, the sugar bowl would be pushed over and opened with a flourish. The Italians shoveled in an incredible amount—two, three mounded spoons. One day, I was shocked to see Ed, too, pouring in the sugar. "It makes it almost a dessert," he explained.
The second year we visited Italy, he went home at the end of the summer carrying a La Pavoni, purchased in Florence, a gleaming stainless-steel machine with an eagle on top, a hand-operated classic. I was the beneficiary of cappuccino in bed, our guests of after dinner espresso served in tiny cups he bought in Italy.
Here, he also has bought a La Pavoni, this one automatic. Before going to bed, he has his final cup of elixir, either at home or in town. There is something he likes about ordering in bars. Sometimes they have curvy Deco-era La Faema machines, sometimes chic Ranchillios. He examines the _crema,_ swirls the cup once, and gulps it down. It gives him, he says, the strength to sleep.
The second major cultural experience he took to with zest is driving. Most travellers here feel that driving in Rome qualifies as an experience that can be added to one's _vita,_ that everyday _autostrada_ trips are examinations in courage and that the Amalfi coast drive is a definition of hell. "These people really know how to drive," I remember him saying as he swung our no-power rented Fiat into the passing lane, turn signal blinking. A Maserati zooming forward in the rearview mirror blasted us back to the right lane. Soon he was admiring daring maneuvers. "Did you see _that_? He had two wheels dangling in thin air!" he marveled. "Sure, they have their share of duffers riding the center lane but most people keep to the rules."
"What rules?" I asked as someone in a tiny car like ours whizzed by going a hundred. Apparently there _are_ speed limits, according to the size of the engine, but I never have seen anyone stopped for speeding in all my summers in Italy. You're dangerous if you're going sixty. I'm not sure what the accident rate is; I rarely see one but I imagine many are caused by slow drivers (tourists perhaps?) who incite the cars behind them.
"Just watch. If someone starts to pass and it's at all dicey, the person behind him won't pull out until the person has passed—he gives him the chance to drop back. No one ever passes on the right, ever. And they stay out of the left lane entirely except to pass. You know how at home someone figures he's going at the speed limit, he can stay in whatever lane he wants."
"Yes, but—look!—they pass on curves all the time. Here comes a curve, time to pass. They must learn that in driving school. I bet the instructor has an accelerator instead of a brake on his side of the car. You just _know,_ if someone is behind you, he's planning to pass—it's his obligation."
"Yes, but all the oncoming traffic knows that. They adjust because they know cars are coming out."
He's delighted to read what the mayor of Naples says about driving there. Naples is the most chaotic city for drivers on earth. Ed loved it—he got to drive on the sidewalk while the pedestrians filled the street. "A green light is a green light, _avanti, avanti,_ " the mayor explained. "A red light—just a suggestion." And yellow? he was asked. "Yellow is for gaiety."
In Tuscany, people are more law abiding. They may jump the gun but they do stop for signals. Here, the challenge is the medieval streets with inches to spare on either side of the car and the sudden turn a bicycle barely could make. Fortunately, most towns have closed their historic centers to cars, a boon all around because the scale of piazza life is restored. A boon for my nerves, too, as the twisted streets lured Ed and we have backed out of too many when they became impassable, all the locals stopping and staring as we reverse through their town.
He was most impressed that the police drove Alfa Romeos. The first year after we went home he bought a twenty-year-old silver GTV in perfect condition, surely one of the prettiest cars ever made. He got three speeding tickets in six weeks. One he protested. He was harassed, he told the judge. The highway patrol picks on sports cars and this time he was not speeding. In a simple miscarriage of justice, the judge told him to sell the car if he didn't like the system and he doubled the fine on the spot.
For a while, we exchanged cars. We had to. He was in danger of losing his license. I drove the silver arrow to work and never got a ticket; he drove my vintage Mercedes sedan, unaffectionately known as the Delta Queen. "It lumbers," he complained.
"It's very safe, though—and you haven't been stopped."
"How could I in the gutless wonder?"
When we returned to Italy, he was back in his element. Most of our trips are on small roads. We've learned not to hesitate to take the unpaved roads if the route looks appealing. Usually, they're well maintained or at least navigable. We've been known to go off road to get to an abandoned thirteenth-century church and, as in the tiny towns, to back up when necessary. No problem to one who has ice water in his veins. To back uphill on a curvy one-lane road is an experience to delight the manic driver. "Whoa!" he shouts. He's turned around, one hand on the back of my seat, the other on the wheel. I'm looking down—straight down—into a lovely valley far below. There are perhaps five inches between the wheel and the edge. We encounter a car coming down. They jump out to confer, then they, too begin to back up; now we are a convoy of idiots. They're in a red Alfa GTV like Ed's at home. We all get out where the road widens and they discuss the car at length, going over its particular kind of mirror, the problem with the turn signal, value today, ad infinitum. I've spread the ordinance map on the hot hood of the Fiat, trying to figure how we can escape this ravine where, obviously, the collapsed monastery is not located.
One reason Ed likes the _autostrada_ so much is that he gets to combine his pleasures. Autogrills appear every thirty or so miles. Sometimes they're quick stop places with a bar and gas. Others arch over the freeway and have a restaurant and shop, even a motel. He appreciates the clean efficiency of the bars. He nips his espresso, often has a quick _panino_ of thick bread and mortadella. I will have a capuccino, unorthodox in afternoon, and he patiently waits. He never would malinger at the bar. In and out. That's the way it's done. Then back on the road, with the fully leaded espresso zinging through him, the speedometer climbing to cruising speed. _Paradiso!_
At a more fundamental level, he has been changed by the land. At first we thought we wanted twenty or thirty acres. Five seemed small, until we started clearing it of jungle, until we started maintaining it. The _limonaia_ is full of tools. At home we have our tools in a shiny red metal toolbox—the small size. We did not expect to have pole digger, chain saw, hedge clippers, weed machine, a whole line of hoes, rakes, a corner for stakes, innumerable hand tools that look pre-Industrial Revolution—sickles, grape cutters, and scythe. If we thought, I suppose we thought we'd clear the land, prune the trees, and that was it. An occasional mowing, fertilizing, trimming. What we never knew is the tremendous resurgent power in nature. The land is implausibly regenerative. My experience with gardening led me to think plants must be coaxed along. Ivy, fig, sumac, acacia, blackberry can't be stopped. A vine we call "evil weed" twines and chokes. It must be dug out down to its carrot-sized root; so must nettles. It's a wonder nettles have not taken over the world. Digging them out, even with heavy gloves, it's almost impossible not to get "stung" by their juices. Bamboo, too, has its runners constantly sending shoots into the driveway. Limbs fall. New olives must be restaked after storms. The terraces must be plowed, then disced. The olives must be hoed around, fertilized. The grapes still need weeks of attention. In short, we have a little farm here and we must have a farmer. Without constant work, this place would revert in months to its previous state. We could either feel burdened by this or enjoy it.
"How's Johnny Appleseed?" a friend asks. She, too, has seen Ed up on a high terrace examining each plant, fingering the leaves of a new cherry tree, picking up stones. He has come to know every ilex, boulder, stump, and oak. Perhaps it was the clearing that forged the bond.
Now he walks the terraces daily. He has taken to wearing shorts, boots, and a "muscle shirt," one of those cutaway undershirts my father used to wear. His biceps and chest muscles bulge like "after" pictures on the backs of old comic books. His father was a farmer until the age of forty, when he had to give up and work in town. His ancestors must have come out of the Polish fields. They, I'm certain, would recognize him across a field. Although he never remembers to water the houseplants in San Francisco, he hauls buckets up to the new fruit trees in dry spells, babies a special lavender with scented foliage, reads into the night about compost and pruning.
HOW ITALIAN WILL WE EVER BE? NOT VERY, I'M AFRAID. TOO pale. Too unable to gesture as a natural accompaniment to talking. I saw a man step outside the confining telephone booth so he could wave his hands while talking. Many people pull over to the side of the road to talk on their car phones because they simply cannot keep a hand on the wheel, one on the telephone, and talk at the same time. We never will master the art of everyone talking at once. Often from the window, I see groups of three or four strolling down our road. All are talking simultaneously. Who's listening? Talking can be about talking. After a soccer game, we'll never gun through the streets blowing the horn or drive a scooter around and around in circles in the piazza. Politics always will passeth understanding.
_Ferragosto,_ at first, baffled us as a holiday until we began to understand it as a state of mind. We, gradually, have entered this state of mind ourselves. Simply put, _ferragosto,_ August 15, marks the ascension of the corporeal body and soul of the Virgin Mary into heaven. Why August 15? Perhaps it was too hot to remain on earth another day. The domed ceiling of the cathedral in Parma depicts her glorious skyward rise, accompanied by many others. From the perspective below, you're looking up their billowing skirts as they balloon above the cathedral floor. This is a triumph of art—no one's underwear shows. But the day itself is only a marker in the month, for the broader meaning of the word is August holidays and a period of intense _laissez-faire._ We're coming to understand that everyday work life is suspended for _all_ of August. Even though throngs of tourists descend on a town, the best _trattoria_ may have tacked up a _chiuso per ferie_ sign, closed for vacation, and the owners have packed and taken off for Viareggio. American business logic does not bear up; they do not necessarily rake in money during tourist season and take their holiday during April or November when tourists are gone. Why not? Because it is August. The accident rates soar on the highways. The beach towns are mobbed. We have learned to forget all projects more complicated than putting up jam. Or to abandon even that—I fill my hat with plums then sit down under the tree, suck the juice, and toss skin and seed over the wall. All over Italy, the feast of the Assumption calls for a celebration. Cortona throws a grand party: the _Sagra della bistecca,_ a _festa_ for the great beefsteaks of the area.
_Sagra_ is a wonderful word to look for in Tuscany. Foods coming into season often cause a celebration. All over the small towns, signs go up announcing a _sagra_ for cherries, chestnuts, wine, _vin santo,_ apricots, frog legs, wild boar, olive oil, or lake trout. Earlier this summer, we went to the _sagra della lumaca,_ the snail, in the upper part of town. About eight tables were set up along the street and music blared over them, but because of no rain the snails had disappeared and a veal stew was served instead. At the _sagra_ in a mountain _borgo,_ I came within one number of winning a donkey in the raffle. We ate pasta with _ragù,_ grilled lamb, and watched a dignified old couple, him in a starched collar and her in black to her ankles, dance elegantly to the accordion.
Preparations for Cortona's two-day feast start several days in advance. Town employees construct an enormous grill in the park—a knee-high brick foundation about six by twenty feet and a foot high, with iron grills placed over the top, somewhat like the barbecue pits I remember from home. On the same spot, the grill is used later in the year for the town's _festa_ for the autumn _porcini._ (Cortona claims to use the largest frying pan in the world for the mushrooms. I've never been here for that _festa_ but can imagine the savory aroma of _porcini_ filling the whole park.) The men arrange tables for four, six, eight, twelve under the trees and decorate with lanterns. Little booths for serving go up near the grill, then the ticket booth is taken out of a shed, dusted off, and set up at the entrance to the park. Walking through, I glimpse stacks of charcoal in the shed.
The park, normally closed to cars, is opened these two days of the year to accommodate all the people arriving for the _sagra._ Bad news for our road, which links to the park. Traffic pours by starting at around seven, then pours by again from eleven on. We decide to walk in over the Roman road to avoid clouds of white dust. Our neighbor, one of the grill volunteers, waves.
Big steaks sizzle over the huge bed of red coals. We join the long line and pick up our _crostini,_ our plates and salad and vegetables. At the grill, our neighbor spears two enormous steaks for us and we lurch to a table already almost full. Pitchers of wine pass round and round. The whole town comes out for the _sagra_ and, oddly, there seem to be no tourists here, except for a long table of English people. We don't know the people we're with. They're from Acquaviva. Two couples and three children. The baby girl is gnawing on a bone and looks delighted. The two boys, in the well-behaved way of Italian children, focus on sawing their steaks. The adults toast us and we toast back. When we say we're Americans, one man wants to know if we know his aunt and uncle in Chicago.
After dinner, we walk through town, along with throngs of people. The Rugapiana is jammed. The bars are jammed. We manage to obtain hazelnut ice cream cones. A bunch of teenagers is singing on the steps of the town hall. Three small boys toss firecrackers, then try to look innocent of the act without succeeding. They double over with laughter. I wait outside listening to them while Ed goes in a bar for a shot of the black elixir he loves. On the way home, we pass back through the park. It's almost ten-thirty and still the grill is smoking. We see our neighbor dining with his gorgeous wife and daughter and a dozen friends. "How long has the town had this _sagra_?" Ed asks them.
"Always, always," Placido answers. Scholars think the first commemoration of Mary's feast day was celebrated in Antioch back in 370 A.D. That makes this year's the 1,624th event for her. Old as Cortona is, perhaps killing the white cow and serving it forth in honor of some deity goes back even farther than that.
AFTER _FERRAGOSTO,_ CORTONA IS UNUSUALLY QUIET FOR A FEW days. Everyone who was coming to town has been. The shopkeepers sit outside reading the paper or looking absently down the street. If you've ordered something, it won't be coming until September.
OUR NEIGHBOR, THE GRILL MASTER, IS ALSO THE TAX COLLECTOR. We know the time by when he passes our house on his Vespa in the morning, at lunch, after siesta, and as he comes home at night. I have begun to idealize his life. It is easy for foreigners to idealize, romanticize, stereotype, and oversimplify local people. The drunk who staggers down the road after unloading boxes at the market in the mornings easily falls into the Town Drunk character from central casting. The hunched woman with blue-black hair is known as The Abortionist. The red and white terrier who visits three butchers to beg for scraps each morning turns into Town Dog. There's the Mad Artist, the Fascist, the Renaissance Beauty, the Prophet. Once the person is really known, of course, the characterization blessedly fades. Placido, the neighbor, however, owns two white horses. He sings as he rides by on his Vespa. We hear him clearly because he coasts by our house on his way in. Starts the motor down the road where the hill levels out. He keeps peacocks and geese and white doves. In early middle age, he wears his light hair long, sometimes tied with a bandanna. On horseback, he looks totally at home, a born rider. His wife and daughter are unusually pretty. His mother leaves flowers in our shrine and his sister refers to Ed as that handsome American. All this—but what I idealize is that Placido seems utterly happy. Everyone in town likes him. "Ah, Plary," they say, "you have Plary for a neighbor." He walks through town to greetings from every door. I have the feeling that he could have lived in any era; he is independent of time there in his stone house on the olive terraces with his peaceable kingdom. To reinforce my instinct, he has appeared, my Rousseau paradigm neighbor, at our door with a hooded falcon on his wrist.
With my bird phobia, left from some forgotten childhood transference, the last thing I want to see at the door is a predatory bird. Placido has a friend with him and they are beginning to train the falcon. He asks if they can go out on our land to practice. I try not to show the extent of my fear. _"Ho paura,"_ I admit, thinking how accurate the Italian is: I _have_ fear. Mistake. He steps forward with the twitchy bird, inviting me to take it on my arm; surely I won't be afraid if I see the magnificence of this creature. Ed comes downstairs and steps between us. Even he is somewhat alarmed. My phobia gradually has rubbed off on him. But we are happy that our Placido feels neighborly enough toward the _stranieri_ to come over, and we walk out to the far point of land with him. His friend takes the bird and stands about fifty feet away. Placido removes something from his pocket. The falcon extends its wings—a formidable span—and flaps madly, rising up on his talons.
"A live quail. Soon I'll take pigeons from the piazza," he laughs. The friend unfastens the cunning little leather hood and the bird shoots like an arrow to Placido. Feathers start to fly. The falcon devours quickly, making bloody work of the former quail. The friend signals with a whistle and the falcon flies back to his wrist and takes the hood. A chilling performance. Placido says there are five hundred falconers in Italy. He has bought his bird in Germany, the little hood in Canada. He must train it every day. He praises the bird, now immovable on his wrist.
This sport certainly does nothing to subtract from my impression that Placido lives across time. I see him on the white horse, falcon on his wrist, and he is en route to some medieval joust or fair. Walking by his house, I see the bird in its pen. The stern profile reminds me of Mrs. Hattaway, my seventh-grade teacher. The sudden swivel of its head brings back her infallible ability to sense when notes were tossed across the room.
I'M PACKING FOR MY FLIGHT HOME FROM ROME WHEN A stranger calls me from the United States. "What's the downside?" a voice asks on the telephone. She's read an article I wrote in a magazine about buying and restoring the house. "I'm sorry to bother you but I don't have anyone to discuss this with. I want to do _something_ but I don't know exactly what. I'm a lawyer in Baltimore. My mother died and . . ."
I recognize the impulse. I recognize the desire to surprise your own life. "You must change your life," as the poet Rilke said. I stack like ingots all I've learned in my first years as a part-time resident of another country. Just the satisfaction of feeling many Italian words become as familiar as English would be pleasure enough: _pompelmo, susino, fragola—_ the new names of everything. What I feared was that with the end of my marriage, life would narrow. A family history, I suppose, of resigned disappointed ancestors, old belles of the country looking at the pressed roses in their world atlases. And, I think, for those of us who came of age with the women's movement, there's always the fear that it's not real, you're not really allowed to determine your own life. It may be pulled back at any moment. I've had the sensation of surfing on a big comber and soon the spilling wave will curl over, sucking me under. But, slow learner, I'm beginning to trust that the gods are not going to snatch my firstborn if I happen to enjoy my life. The woman on the other end of the line has somehow, through the university, obtained my number in Italy.
"What are you thinking of doing?" I ask this total stranger.
"The islands off the coast of Washington, I've always loved them. There's this place for sale, my friends think I'm crazy because it's all the way across the country. But you go by ferry . . ."
"There's no downside," I say firmly. The waterfall of problems with Benito, the financial worries, the language barriers, the hot water in the toilet, the layers of gunk on the beams, the long flights over from California—this is _nothing_ compared to the absolute joy of being in possession of this remarkable little hillside on the edge of Tuscany.
I have the impulse to invite her over to visit. Her desire makes her familiar to me so that we would immediately be friends and talk long into the night. But I'm leaving soon. As I speak to her in her highrise office, the half moon rises above the Medici fortress. Way up, I see the bench Ed made for me under an oak tree. A plank over two stumps. I like to zigzag up the terraces and sit there in late afternoons when the gilded light starts to sift over the valley and shadows stretch between the long ridges. I was never a hippie but I ask her if she ever heard the old motto "Follow your bliss."
"Yes," she replies, "I was at Woodstock twenty-five years ago. But now I handle labor disputes for this transnational conglomerate . . . I'm not sure this makes sense."
"Well, does it seem that you'd be moving into a larger freedom? I've had an incredible amount of fun here." I don't mention the sun, how when I'm away and picture myself here, it's always in full light; I feel _permeable_ now. The Tuscan sun has warmed me to the marrow. Flannery O'Connor talked about pursuing pleasure "through gritted teeth." I sometimes must do that at home but here pleasure is natural. The days right themselves one after another, as easily as the boy holding up the jingling scale easily balances the fat melon and the rusty iron discs.
I am waiting to hear if she took the clapboard cottage with its own deep-water pier.
I see her blue bicycle leaning against a pine tree, morning glories climbing up the porch railing.
BRAVE GIRL! PLACIDO IS WALKING WITH HIS DAUGHTER OUT to the point. She holds up the falcon on her wrist. Her long curls bounce as she walks. Even something to fear is layering into memory; I'm going to dream about this over the winter. Perhaps the falcon will fly through a nightmare. Or perhaps it only will accompany these neighbors in late afternoon as they walk up the cypress drive and out to where they release the bird, allowing it to fly farther each time. So much more to take home at the end of summer. "The Night," by Cesare Pavese, ends:
_At times it returns,_
_in the motionless calm of the day, that memory_
_of living immersed, absorbed, in the stunned light._
Green Oil
"DON'T PICK TODAY—TOO WET." MARCO observes us taking down the olive baskets. "And the moon's wrong. Wait until Wednesday." He's hanging the doors, two original chestnut ones he oiled and repaired, and new ones, virtually indistinguishable from the old, that he has made during the fall while we were gone. They replace the hollow-core doors our great improver in the fifties preferred.
We're already late for the olive harvest. All of the mills close before Christmas and we've arrived with a week to spare. Outside, a gray drizzle blurs the intense green grasses that thrived on November rains. I put my hand on the window. Cold. He's right, of course. If we pick today, the wet olives might mildew if we don't finish and get them to the mill. We gather our osier baskets that strap around the waist—so handy for stripping a branch—and the blue sacks the olives are loaded into, the aluminum ladder, our rubber boots. Still jet-lagged and dazed, we're up early, thanks to Marco's arrival at seven-thirty when it barely was light. He tells us to go make an appointment at a mill; maybe it will clear up later. If so, the sun will dry the olives quickly.
"What about the moon?" I ask. He just shrugs. He wouldn't pick now, I know.
We feel like tumbling back into bed, having had no time since arriving last night to get beyond the twenty-hour trip, with storms buffeting the plane most of the way across the ocean. I felt like kissing the ground when we stepped out on the tarmac at Fiumicino. We crazily went into Rome to do a little shopping, then were really beyond thinking as we drove to Cortona in a hilarious rented Twingo, purple with mint green interior. We hit the _autostrada_ in a bumper car and in a state of exhaustion. Still, the wet and vibrant landscape filled us with elation—that lit-from-within green and many trees still twirling colored leaves. When we left in August, it was sere and dry; now the freshness has reasserted itself. At dark we finally arrived. In town we picked up bread and a pan of veal _cannelloni._ The air felt charged and invigorating; we no longer wanted to collapse. Laura, the young woman who cleans, had turned up the radiators two days ago and the stone walls had time to lose their chill. She even had brought in wood, so on our first night here, we had a little feast by the fire, then wandered from room to room, checking and touching and greeting each object. And so to bed, until Marco aroused us this morning. "Laura said you arrived. I thought you'd want the doors right away." Always, always when we arrive there is something to haul from A to B. Ed helped him hoist the doors and held them steady while Marco wiggled the hinges onto the metal spurs.
The venerable mill at Sant'Angelo uses the purest methods, Marco tells us, cold-pressing each person's olives individually, rather than requiring small growers to double up with someone else. However, you must have at least a _quintale,_ one hundred kilograms. Our trees, not yet recovered from thirty years of neglect, may not give us that bounty yet. Many trees have nothing at all.
The mill smells thickly oleaginous and the damp floor feels slippery, possibly oily. Rooms where grapes and olives are pressed have the odors of time, as surely as the cool stone smell of churches. The permeating ooze and trickle must move into the workers' pores. The man in charge tells us of several mills that press small batches. We never knew there were so many. All his directions involve turning right at the tallest pine or left beyond the hump or right behind the long pig barn.
Before we leave, he extols the virtues of the traditional methods and to prove his point dips two tablespoons into a vat of new oil and hands them to us to taste. It can't be poured onto the floor; there's nothing to do but swallow the whole thing. I can't but I do. First, a tiny taste and the oil is extraordinary, of a meltingly soft fragrance and essential, full olive taste. The whole spoon at once, however, is like taking medicine. _"Splendido,"_ I gulp and look at Ed, who still hesitates, pretending to appreciate the greeny beauty. "What happens to that?" I ask, gesturing to troughs of pulp. Our host turns and Ed quickly slips his oil back in the vat, then tastes what's left on the spoon.
_"Favoloso,"_ Ed says to him. And it is. After the first cold pressing, the pulp is sent on to another mill and pressed again for regular oils, then pressed last for lubricating oils. The dried-out remains, in a wonderful cycle of return, often are used to fertilize olive trees.
As we start to drive away, we see that the doors of San Michele Arcangelo, a church we've admired, are open today. The threshold is scattered with rice _—arborio,_ I notice, the rice for risotto. A wedding has taken place and someone must be coming to take down the pine and cedar boughs. The church is almost a thousand years old. Just across the road from each other, the church and mill have served two of the basic needs—and the grain and the vine are not far away. The beamed and cross-beamed ceilings of these old churches often remind me of ship hulls. I've never mentioned this before but now I do. "The church structures reminded someone else of boats, too. "Nave' comes from _"navis'_ in Latin—ship," Ed tells me.
"And what does "apse' come from then?" I ask, since the lovely rounded forms remind me of bread ovens standing alone in farmyards.
"I believe that root means a fastening together of things, just practical, no poetry there."
There is poetry in the rhythm of the three naves, the three apses, the classic basilica plan in miniature. The lines rhyme perfectly in their stony movement along such a small space. The only adornment is the scent of evergreens. As much as I love the great frescoed churches, it's these plain ones that touch me most deftly. They seem to be the shape and texture of the human spirit, transformed into stone and light.
Ed swings the car out onto what once was a Roman road. Later it led pilgrims on their way to the Holy Land. San Michele was a place to rest and restore. I wonder if a mill stood here, too. Perhaps the pilgrims rubbed oil into their weary feet. We, however, are just searching for a mill that will transform our sacks of black olives into bottles of oil. Two of the mills already have closed. At the third, a woman in about six layers of sweaters comes down her steps and tells us we're too late, the olives should have been picked and now the moon is wrong. "Yes," we tell her, "we know." Her husband has closed his mill for the season. She points down the road. At a grand stone villa, we turn in. A discreet sign, IL MULINO, directs us to the rear but when we drive around, two workers are hosing off their equipment. Too late. They direct us to the large mill near town.
Whizzing along, I look at the winter gardens. Everyone's growing pale, stalky _cardi,_ cardoons—called _gobbi_ in the local dialect—and green-black _cavolo nero,_ black cabbage, which grows not in a head but in upright plumes. Red and green radicchio star in every garden. Most have a few artichoke plants. Until winter, I never knew there were so many persimmon trees. With the lacquered orange fruit dangling in bare limbs, the trees look composed of quick brush strokes, like Japanese drawings of themselves.
At the mill, everyone is so busy that we're ignored. We walk around watching the process and aren't drawn to having our precious olives pressed here. It's all quite mechanized looking. Where are the big stone wheels? We can't really tell if they use heat, a process that supposedly damages the taste. We watch a customer come in, have his fruit weighed, then see it dumped into a large cart. Maybe the olives are all the same and mixing doesn't matter but somehow, this time, we would love to have the pleasure of oil from the land we've worked on. We exit quickly and drive to our last hope, a small mill near Castiglion Fiorentino. Outside the door, three huge stone wheels lean against the building. Just inside, wooden bins of olives are stacked, each one with a name on it. Yes, they can press ours. We are to come back tomorrow.
The afternoon warms and clears. Marco gives us the O.K. to begin. Moon or no, we start picking. It's fast. We empty our baskets into the laundry basket and, as that fills, pour the olives into the sack. Few have fallen though they yield easily to our fingers. A strong wind could cause a lot of damage unless one had spread nets under the trees. The shiny black olives are plump and firm. Curious about the raw drupe, I bite one and it tastes like an alum stick. How did anyone ever figure out how to cure them? The same people, no doubt, who first had the nerve to taste oysters. Ligurians used to cure them by hanging bags in the sea; inland people smoked them over the winter in their chimneys, something I'd like to try. We peel off jackets, then sweaters as we work, hanging them in the trees. The temperature has climbed to about fifty-five degrees and although our boots are wet, the air feels balmy. Off in the distance, we see the blue swath of Lake Trasimeno under an intense blue sky. By three, we have stripped every single olive off twelve trees. I've put my sweater on again. Days are short here in winter and already the sun is headed for the rim of the hill behind the house. By four, our red fingers are stiff and we quit, hauling the sack and basket down the terraces into the cantina.
Not for the first time in our history here, my body is jarred into awareness. Today: shoulders! Nothing would be nicer than a long soak in a bubble bath and a massage. I have left my body oil to warm on the radiator in anticipation. But with only twenty days here every minute counts. We force ourselves to go into town to stock up on food. My daughter and her boyfriend Jess arrive in three days. We're planning several major feasts. We drive in just as the stores are reopening after siesta. Strange—it's already dark as the town comes back to life. Swags of white lights strung across the narrow streets swing in the wind. The A & O market, where we shop, has a rather ratty artificial tree (the only tree in town) outside and big baskets of gift foods inside.
From our brief Christmas visit last year, we know that the focus of the season is twofold: food and the _presepio,_ the crèche. We're ready to launch into one and are intrigued by the other. The bars display fancy candies and that lighter Italian parallel to our ubiquitous Christmas fruitcake, the _panettone,_ in colorful boxes. A few shops have distinctly homemade wreaths. That's it for decoration, except for the crèches in all the churches and in many windows. _"Auguri, auguri,"_ everyone says, best wishes. No one is rushing about. There seems to be no gift wrap, no hype, no frantic search.
The window of the _frutta e verdura_ is steamed. Outside, where we're used to seeing the fruits of summer, we find baskets of walnuts, chestnuts, and fragrant clementines, those tiny tangerines without seeds. Maria Rita, inside in a big black sweater, is cracking almonds. _"Ah, benissimo!"_ she greets us. _"Ben tornati!"_ Where there were luscious tomatoes, she has piled stacks of _cardi,_ which I've never tasted. "You boil it but first you must take off all the strings." She cracks a stalk and peels back the celerylike filaments. "Throw it in some lemon water quickly or it will turn black. Then boil. Now it's ready for the _parmigiano,_ the butter."
"How much?"
"Enough, enough, signora. Then the oven." Soon she's telling us to make _bruschetta_ on the grill in the fireplace and pile on it chopped black cabbage cooked with garlic and oil in a frying pan. We buy blood oranges and tiny green lentils from a jar, chestnuts, winter pears, winy little apples, and broccoli, which I've never seen in Italy before. "Lentils for the New Year," she tells us. "I always add mint." She piles in our bags all the ingredients for _ribollita,_ the wintery soup.
At the butcher's, new sausages are in, looped along the front of the meat case. A man with a sausage-shaped nose himself elbows Ed and acts out saying the rosary, then points to the long links of fat sausages. It takes us a moment to make the connection, which he thinks is very funny. Quail and several birds that look as though they should be singing in a tree lie still in their feathers in the case. Color photos on the wall show the butcher's name written on the backsides of several enormous white cows, source of the Val di Chiana steak that Tuscany celebrates. There's Bruno with his hand possessively around the neck of a great beast. He motions for us to follow him. He opens the freezer room and we follow him in. A cow the size of an elephant hangs from ceiling hooks. Bruno slaps a flank affectionately. "The finest _bistecca_ in the world. A hot grill, rosemary, and a little lemon at the table." He turns up both hands, a gesture that adds "What else is there in life?" Suddenly, the door slams shut and we are locked inside with this massive body encased in white fat.
"Oh, no!" I flash on the three of us caught as in the child's game of Freeze. I swing around toward the door but Bruno is laughing. He easily opens the door and we rush out. I don't want any steak.
WE INTENDED TO COOK BUT WE HAVE LINGERED. WE DEPOSIT all the food in the car and walk back to Dardano, a favorite _trattoria,_ for dinner. The son who has waited tables since we came here suddenly looks like a teenager. The whole family sits around a table in the kitchen. Only two other customers are here, local men bent over their bowls of _penne,_ each eating as though he were alone. We order pasta with black truffles, a carafe of wine. Afterward we walk around in the quiet, quiet streets. A few boys play soccer in the empty piazza. Their shouts ring in the cold air. The outdoor tables are stored, the bar doors closed tight with everyone inside breathing smoke. No cars. A lone dog on a walk. Totally emptied of foreigners, except us, the town reveals its silences, the long nights when men play cards way past the nine o'clock bells, the deserted streets that look returned to their medieval origins. At the _duomo_ wall, we look out over the lights of the valley. A few other people lean on the wall, too. When we're really freezing we walk back up the street and open the bar door to a burst of noise. The cocoa, steamed on the espresso machine, is thick as pudding. One day back and I'm falling in love with winter.
AT FIRST LIGHT, WE ARE OUT ON THE TERRACES, EVEN THOUGH heavy dew is on the olives. We intend to finish today, not leaving them time to mildew. Below us the valley surges with fog as thick as mascarpone. We are above it in clear, frosty air, utterly fresh and sharp to inhale, as if we're looking down from a plane: a disembodied feeling—this hillside is floating. Even the red roof of our neighbor Placido's house has disappeared. The lake gives this landscape some of its mystery. Large mists rise off the water and spread over the valley. Fog billows and rises. As we pick olives, wisps of clouds pass us. Soon the sun asserts itself and begins to burn off the fog, showing us first the white horse in Placido's pen, then his roof and the olive terraces below him. The lake stays hidden in a pearly swirl of clouds. We come to trees with nothing on them, then a laden tree. I take the lower branches. Ed leans the ladder into the center and reaches up. To our joy, Francesco Falco, our caretaker of the olives, joins us. He's the quintessential olive picker in his rough wool pants and tweed cap, basket strapped to his waist. He sets to work like the pro he is, picking more than we're able to. He's not as careful, just lets twigs and leaves fall in, whereas we've fastidiously removed any stray leaf after reading they add tannin to the taste of oil. Now and then he pulls out his machete from the back of his pants (how does he not get poked in the bottom?) and hacks off a sucker sprouting up. We must get the olives in, he tells us, a big freeze may be coming. We pause for a coffee but he keeps picking. All fall he has cut back the dead wood so that new growth is encouraged. By spring he will have hacked off everything except the most promising limbs and cleared around each tree. We ask about bush olives, more experimental techniques of pruning we've read about but he will hear nothing of those. The way to take care of olives is second nature, unquestionable. At seventy-five, he has the stamina of someone half his age. The same stamina, I suppose, that gave him the strength to walk home to Italy from Russia at the end of World War II. We identify him so totally with the land around Cortona that it's hard to imagine him as the young soldier stranded thousands of miles from home when the ugly war ended. He jokes constantly but today he has left his teeth at home and we have a hard time understanding him. Soon he heads for the lower terraces, an area still overgrown, because he has seen from the road that some of the olives there are bearing fruit.
With the olives from below, we do have a _quintale._ After siesta, which we've worked through, we hear Francesco and Beppe coming up the road on a tractor pulling a cart of olives. They've taken the sacks of their friend Gino and are on their way to the mill. They load Gino's olives into Beppe's Ape and help us load ours on, too. We follow them. It's almost dark and the temperature is dropping. Many California winters have dimmed my memory of real cold. It's a presence of its own. My toes are numb and the Twingo heater is sending out a forlorn stream of tepid air. "It's only about twenty-five degrees," Ed says. He seems to radiate warmth. His Minnesota background reawakens anytime I complain that I'm cold.
"Feels like Bruno's freezer to me."
OUR SACKS ARE WEIGHED, THEN THE OLIVES ARE POURED INTO a bin, washed, then crushed by three stone wheels. Once mashed, they're routed to a machine that spreads them on a round hemp mat, stacks on another mat, spreads more until there is a five-foot stack of hemp circles with the crushed olives sandwiched between each. A weight presses out the oil, which oozes down the sides of the hemp into a tank. The oil then goes through a centrifuge to get all the water out. Our oil, poured into a demijohn, is green and cloudy. The yield, the mill owner tells us, was quite high. Our trees have given us 18.6 kilograms of oil from our _quintale—_ about a liter for each fully bearing tree. No wonder oil is expensive. "What about the acid?" I ask. I've read that oil must have less than one percent of oleic acid to qualify as extra virgin.
"One percent!" He grinds his cigarette under his heel. _"Signori! Più basso, basso,"_ he growls, lower, lower, insulted that his mill would tolerate inferior oil. "These hills are the best in Italy."
At home we pour a little into a bowl and dip in pieces of bread, as people all over Tuscany must be doing. Our oil! I've never tasted better. There's a hint of a watercress taste, faintly peppery but fresh as the stream watercress is pulled from. With this oil, I'll make every _bruschetta_ known and some as yet unknown. Perhaps I'll even learn to eat my oranges with oil and salt as I've seen the priest do.
The sediment will settle in the big container over time but we like the murky, fruity oil, too. We fill several pretty bottles I've saved for this moment, then store the rest in the semidarkness of the cantina. Along the marble counter, we line up five bottles with those caps bartenders use to pour drinks. I've found those perfect for pouring slowly or dribbling oil. The little lid flaps down after you pour so the oil stays clean. We'll cook everything this holiday season in our oil. Our friends will have to visit and take bottles home with them; we have more than we can use and no one to give it to, since everyone here has their own, or at least a cousin who supplies them. When our trees yield more, we may sell the extra oil to the local consortium. I've bought the terrific _comune_ oil in a gallon jug for about twenty dollars. I once lugged one home and it was worth the long flight with the cold jug balanced between my feet.
Our herbs still thrive, despite the cold. I cut a handful of sage and rosemary sprigs, quarter onions and potatoes, and arrange them around a pork roast and pop it in the oven, after a liberal sprinkling of our first season's oil baptizes the pan.
The next afternoon, we find an olive oil tasting in progress, the town's first _festa_ for _olio extravergine del colle Cortonese,_ the extra virgin oil of the Cortona hills. I remember my tablespoon at the _mulino,_ but this time there's bread from the local bakery. Nine growers' oils are lined up along a table in the piazza, with pots of olive trees around for ambiance. "I couldn't have imagined this, could you?" Ed asks me as we try the fourth or fifth oil. I couldn't. The oils, like ours, are profoundly fresh with a vigorous element to the taste that makes me want to smack my lips. The shades of difference among the oils are subtle. I think I taste that hot wind of summer in one, the first rain of autumn in another, then the history of a Roman road, sunlight on leaves. They taste green and full of life.
Floating World:
A Winter Season
THERE IS SOMETHING AS INEVITABLE AS LABOR that takes over around Christmas. I feel impelled to the kitchen. I feel deep hungers for star-shaped cookies and tangerine ices and caramel cakes, things I never think of during the rest of the year. Even when I have vowed to keep it simple, I have found myself making the deadly Martha Washington Jetties my mother made every year on the cold back porch. You have to make them in the cold because the sinful cream, sugar, and pecan fondant balls are dipped by toothpick into chocolate and held up to set before being placed on the chilled wax-papered tray. The chocolate dip, of course, constantly turns hard and must be taken into the kitchen and heated. My mother made Jetties endlessly because her friends expected them. We professed to find them too rich but ate them until our teeth ached. I still have the cut-glass candy jar they spent their brief tenures in.
The other absolute was roasted pecans. Nuts roasted in butter and salt; the arteries tense even to read this—we ate them by the pound. I cannot get through a Christmas without them, although now I usually give most to friends and save only a small tin for the house. For guests, of course.
This year, no Jetties. But our almond crop must be used so roasted almonds seem inevitable. This weather demands the red soup pot. In preparation for Ashley and Jess's arrival, I'm making the big pot of _ribollita,_ a soup for ending a day of fieldwork, or, as I think of it, for arriving from New York. Reboiled is the unappetizing translation and, naturally, it is, like so many peasant dishes, a soup of necessity: beans, vegetables, and hunks of bread.
Winter food makes me understand Tuscan cooking at a deeper level. French cooking, my first love, seems light years away: the evolution of a bourgeois tradition as opposed to the evolution of a peasant tradition. A local cookbook talks about _la cucina povera,_ the poor kitchen, as the source of the now-abundant Tuscan cuisine. _Tortelloni in brodo,_ a Christmas tradition here, seems like a sophisticated concept. Three half moons of stuffed pasta steaming in a bowl of clear broth—but, really, what is more frugal than to combine a few leftover _tortelloni_ with extra broth? More than pasta, bread is the basic ingredient of the repertoire. Bread soups, bread salads, which seem rich and imaginative in California restaurants, were simply someone's good use of leftovers, possibly when there was little in the house except a little stock or oil to work with. The clearest example of the poor kitchen must be _acquacotta,_ cooked water—probably a cousin of stone soup. This varies all over Tuscany but always involves invention around a base of water and bread. Fortunately, wild edibles always abound along the roadsides. A handful of mint, mushrooms, a little sweet burnet, or various greens might flavor cooked water. If an egg was handy, it was broken into the soup at the last moment. That Tuscan cooking has remained so simple is a long tribute to the abilities of those peasant women who cooked so well that no one, even now, wants to veer into new directions.
ASHLEY AND JESS ARRIVE WITHIN AN HOUR OF EACH OTHER, A miracle of scheduling since she is coming to Chiusi from the Rome train and he is coming into Camucia from Pisa and Florence after landing from London. We pick her up, then speed the forty minutes back and arrive just as he steps off the train.
The people one's children bring home are problematic. One came to visit when we were renting a house in the Mugello, north of Florence. He was deeply into Thomas Wolfe and sat in the backseat engrossed in _Look Homeward Angel._ We madly drove all over Tuscany to show them (both artists) the Piero della Francescas but he only turned pages and sighed now and then. Once he looked up and saw the round gold bales of hay in the lovely fields and said, "Cool, those look like Richard Serra sculptures." We never were sure anything else penetrated. A young woman Ashley brought over suffered from dire toothache except when shopping was mentioned. She miraculously recovered long enough to buy everything in sight—she had an excellent eye for design—then relapsed in her room, requiring meals on trays. Nothing was wrong with her appetite. When she returned to New York, she had to have extensive root canal work on three teeth, so her forays into the shops _were_ remarkable mental triumphs over pain. Another never paid me for his round-trip New York-Rome ticket, which was charged to my AmEx because Ashley picked up their tickets. Naturally, we have been wondering about the person who will be spending a couple of weeks.
If I'd had a boy, I'd have wanted him to be like Jess. We both fall right away for Jess's humor, intellectual curiosity, and warmth. He arrives with a wicker hamper of smoked salmon, Stilton, oat biscuits, honeys, and jams. He spent his last two days in London buying beautifully wrapped gifts for everyone. Best of all, we don't seem like capital P parents to him but potential friends. Relieved that this will be effortless, I'm bouyed, too, by that expansion I feel when someone new is admitted into my life. My Iranian friend maintains that attractions among people are based on smell, which seems logical enough to me. Most of those most important to me I've liked instantaneously and have known I wanted a permanent friendship. (The times the connection has not lasted still sting.) Jess knows all the words to every rock song. Ashley is laughing. We're already singing in the car. What luck.
It's midday and too warm for _ribollita._ We stop in town and have sandwiches at a bar and Jess tells us about the wedding he was just in at Westminster Abbey. Ashley has had the longer trip and wants to fade. Ed and I take a walk, then, because the day is warm and the force of habit strong, we start to work in the garden. I pull weeds away from herbs and lift geraniums out of pots, shake off dirt from the roots and wrap them in newspaper to store over the winter. Ed mows the long grass and rakes. Everything is drenched, sweet, lush; even the weeds are beautiful. I decorate the shrine with boughs of spruce and its nuts, olive branches and a gold star over Mary's head. Ed tries to burn a pile of leaves we never were able to burn last summer because of the dryness. They're so wet now that they just smoke. When Ashley and Jess reappear, we drive to the nursery and buy a living tree and a big pot to plant it in. Small as it is, it dominates the living room. Since we have nothing for decoration except a string of white lights, we decide to go to Florence tomorrow and buy a few ornaments. I've brought over some candles shaped like stars and some distinctly non-Tuscan _farolitos,_ a Santa Fe custom I've kept since spending a Christmas there once and loving the candles in paper bags outlining the adobe houses. These are glazed bags with cut-out stars. We line the front stone wall with a dozen of them and they look magical with their glowing stars. We fill the fireplace overhang with pinecones and branches of cypress Ed cut this afternoon. How easy everything seems and what a pleasure to recover the fun of Christmas. The bowls of _ribollita_ and a fire act as knock-out drops. In the big armchairs, we're wrapped in mohair blankets, listening to Elvis singing blue, blue, blue Christmas on the CD.
AT THE OUTDOOR MARKET IN FLORENCE, WE FIND papier-mÂché balls and bells with decoupage angels. A wagon off to the side serves bowls of _trippa,_ tripe, a special love of the Florentines. Business looks brisk. If I thought yesterday that I was falling in love with winter, today it's certain. Florence is redeemed and magnificent on a cold December morning. As in all the towns, the decorations are sweet—lights strung across the narrow streets at short intervals, necklaces of light with dangling pendants. Obviously the women of this city have not heard of cruelty to wildlife; I never have seen so many long, lavish fur coats. We look in vain for fake fur. The men are dressed in fine wool overcoats and elegant scarves. Gilli, one of my favorite bars, is crowded with noisy voices and clinks of cups and constant rushes of steam from the espresso machine. In the middle of the street, Ed pauses and holds up his hands. "Listen!"
"What is it?" We all stop.
"Nothing! How could we not have noticed? No motorcycles. It must be too cold for them."
Ashley wants boots for Christmas. Obviously, this is the place. She finds black boots and brown suede ones. I see a black bag I really admire, don't need, and manage to resist. Just before everything closes, we dash over to San Marco, the serene monastery with Fra Angelico frescoes in the cells. Jess never has seen it and the twelve angel musicians seem good to look at during this season. Siesta catches up with us, so we settle into a long lunch at Antolino's, a righteous _trattoria_ with a potbellied stove in the middle of the room. The menu lists pastas with hare and boar _ragù,_ duck, polentas and risottos. The waiters rush by with platters of big roasts.
There's plenty of time for a long walk before the town reopens. Florence! The tourists are gone, or if they're here, the fine misty rain must keep them inside. We pass the apartment we rented five years ago, when I swore off Florence. In summer, wads of tourists clog the city as if it's a Renaissance theme park. Everyone seems to be eating. That year, a garbage strike persisted for over a week and I began to have thoughts of plague when I passed heaps of rot spilling out of bins. I was amazed that long July when waiters and shopkeepers remained as nice as they did, given what they had to put up with. Everywhere I stepped I was in the way. Humanity seemed ugly—the international young in torn T-shirts and backpacks lounging on steps, bewildered bus tourists dropping ice cream napkins in the street and asking, "How much is that in dollars?" Germans in too-short shorts letting their children terrorize restaurants. The English mother and daughter ordering _lasagne verdi_ and Coke, then complaining because the spinach pasta was _green._ My own reflection in the window, carrying home all my shoe purchases, the sundress not so flattering. Bad wonderland. Henry James in Florence referred to "one's detested fellow-pilgrim." Yes, indeed, and it's definitely time to leave when one's own reflection is included. Sad that our century has added no glory to Florence—only mobs and lead hanging in the air.
In early morning, though, we'd walk to Marino's for warm brioche, take them to the middle of the bridge and watch the silvery celadon light on the Arno. Most afternoons we sat in a café at Piazza Santo Spirito, where a sense of neighborhood still exists even in summer. The sun angling through the trees hit that grand undecorated sculptural facade of Brunelleschi's, with the boys playing ball beneath it. Somehow it must make a difference to grow up bouncing your ball against the wall of Santo Spirito. Perhaps many who come to Florence in summer are able to find moments and places like this, times when the city gives itself over by returning to itself.
Today, the stony streets take a shine from the mist. We walk right in the Brancacci chapel. No line; in fact, only a half dozen young priests in long black gowns, following an older priest as he points and lectures about the Masaccio frescoes. I haven't seen Adam and Eve leaving Eden since the vines over their genitals, painted during some fit of papal modesty, were removed and the frescoes cleaned and restored. Shocking to see them lifted out of the film of centuries of candle smoke: all these distinct faces and the chalky rose and saffron robes. Every face, isolated and examined, reveals character. "I wanted to see what made each one that one," Gertrude Stein said about her desire to write about many lives. Masaccio had a powerful sense of character and narrative and a sharp eye for placing the human in space. A neophyte kneels in a stream to be baptized. Through the transparent water we see his knees and feet. San Pietro flings the basin, showering his head and back with water. All the symbolism of earlier art is abandoned for the cold splash on the boy. Another pleasure is Masaccio's (and Masolino's and Lippi's, whose hands are apparent) attention to architecture, light, and shadow. Here's Florence as he saw, or idealized it, with the sun falling logically—not the sourceless light of his predecessors—on this cast of characters who surely walked the streets of this city.
We hurry to the six-nineteen train and miss it. As we wait, I mention the black bag I didn't buy and Ed decides it would be a terrific Christmas present, although we have said we only are buying things for the house. He and Jess literally _run_ back to the shop, halfway across town from the train station. Ashley and I are uneasy when it's five minutes until departure but here they come, smiling and panting, waving the shopping bag just as the train is announced.
On Christmas Eve eve, we take off on a quest in Umbria. Ed thinks we must have one of his favorite reds for Christmas dinner, the Sagrantino, impossible to find this far from its origins. I am after the ultimate _panettone._ I called Donatella, an Italian friend who's a wonderful cook, and asked if we could make one together, thinking the homemade would be better than the commercial ones stacked in colorful boxes in every grocery and bar. "It takes twenty hours of rising," she says. "It must rise four times." I remember how many times I've killed the yeast when making simple bread. When her mother was small, she tells me, _panettone_ was just ordinary bread with some nuts and dried fruits tucked into the dough. _La cucina povera_ again. "It's really best to buy it." She gave me several brands and I picked out one for Francesco's family. As I was about to take another, a woman buying at the same time told me that the very best are made in Perugia. She wrote the name of a shop, Ceccarani, on a piece of paper. So we are off to Perugia.
Ceccarani's window display is a full crèche intricately executed in glazed bread dough. Dough must be a good medium; the figures have expressive faces, sheep look woolly, fronds on the palm trees are finely detailed. The nativity scene is surrounded by marzipan mushrooms and _panettoni_ hollowed out on the side. Inside each—what else but a miniature crèche? Incredible!
Throngs of women fill the shop. I push to the back and select a _panettone_ as tall as a top hat.
Deeper into Umbria, we come to Spello and walk all over the steeply terraced town. Coming down from Spello, we see the early moon hoisting itself over the hills. We keep losing it as we turn then face it again, the largest, whitest, spookiest moon I've ever seen. All the way to Montefalco, home of the Sagrantino, we dodge the moon. Two or three times we see it rise again, over a different hill. Jess has taken to calling Ed "Montefalco" for his black leather jacket and tendency to speed. He makes up Montefalco adventures as we take several wrong turns. In the piazza, the wine store is open but the proprietor is missing. We look around, look outside, come back—no sign of him. We take a walk around the piazza. The store stands wide open but still the owner is gone. Finally, we ask at the bar and the bartender points to a man playing cards. We buy our four bottles and head home, chasing the moon across Umbria.
On Christmas Eve, Ashley and I launch into cooking. Jess, a novice, is given tasks and entertains us with rock lyrics. Ed dedicates the morning to squeezing silicone around the windows. He runs into town to pick up tonight's first course, _crespelle,_ from the fresh pasta shop. The delicate crÊpes are filled with truffles and cream. Our menu after the _crespelle:_ a warm salad of _porcini,_ roasted red peppers, and field lettuces, grilled veal chops, the local cardoons with béchamel and toasted hazelnuts. For dessert, a family cake I know by heart and _castagnaccio,_ the classic Tuscan chestnut flour cake. My neighbor says not to try it. Her grandmother used to make it when they were very poor. "All it takes is chestnut flour, olive oil, and water," she says, grimacing. "My grandmother said that they always had those. They flavored it with rosemary and some pine nuts, fennel seeds, and raisins if they had some." I've never worked with chestnut flour, an ingredient I'd considered esoteric until I learned that it was a staple of _la cucina povera._ This recipe is decidedly weird. As my neighbor indicates, it must be one of those acquired tastes.
"But where are the sugar and eggs—can this really turn into a cake? And how much water to use? The recipe only says to use enough for the batter to pour easily." My neighbor just shakes her head. I'm intrigued. This cake will send us back to the roots of Tuscan cooking. Ashley and Jess are not so sure they want to be transported that far.
Before siesta, we walk over the Roman road into town for last-minute lettuces and bread. Where is our "angel"? In winter, he does not seem to come to the shrine. I watch for his slow approach, his eyes on the house, then his long pause while he places his flowers. Would he bring a twig of bright rose hips, a shriveled bunch of dried grapes, a spiny chestnut casing split to reveal three brown nuts? Perhaps he walks elsewhere in winter, or stays in his medieval apartment, feeding logs into the woodstove.
Cortona is hopping. Everyone carries at least one _panettone_ and one basket of cellophane-wrapped gift foods. No shop plays that canned, generic Christmas music I find so dispiriting at home. People crowd the bars, stoking themselves with coffee and hot chocolate because the sharp _tramontana_ has started to blow in from the north, bringing frigid air from the Alps and northern Apennines.
Peaceful eve, bountiful feast, dessert by the fire. We all hate the chestnut cake. Flat and gummy, it probably has the exact taste of a Christmas dessert during the last war, when chestnuts could be foraged in the forest. We trade it for a platter of walnuts, winter pears, and Gorgonzola, a dessert for the gods. Long before midnight mass, which we'd hoped to experience in one of the small churches, we fade.
ED CALLS UP FROM DOWNSTAIRS, "LOOK OUT THE WINDOW." Snow fell in the night, just enough to dust the fronds of the palm tree and glaze the terraces with a sheen of white.
"Beautiful! Turn up the heat." My bare feet feel icy. I pull on a sweatshirt, jeans, and shoes and run downstairs. The front doors are wide open, the frosty light pouring in. Ed scrapes a snowball off the outdoor table. I jump aside and it lands in the hall. The sleeping beauties have not yet emerged. We take our coffee to the wall, brush it off, and watch the fog below us moving like an opalescent sea. Snow on Christmas!
Is this much happiness allowed? I secretly ask myself. Will the gods not come down and confiscate this health, abundance of cheer, these bright expectations? Is this the old scar, this rippling of want and fear? My father died on the eve of Christmas Eve when I was fourteen. The funeral day was rainy, so rainy that the coffin floated for a moment before it settled into the earth. My pink tulle Christmas dance dress hung on the back of my closet door. Or is this unrest just part of the great collective holiday blues all the newspapers focus on every year? Many Christmases in my adult life have been exquisite, especially when my daughter was a child. A few have been lonely. One was very rocky. Either way, the season of joy comes with a primitive urge that runs deep into the psyche.
After breakfast, we build up the fire and open presents. We brought over a few and slowly have accumulated the usual pile around the tree. We hadn't intended to have so many but the day in Florence inspired us to pick out soaps, notebooks, sweaters, and a surprisingly huge quantity of chocolate. One of our gifts is a chestnut roasting pan, which we put to immediate use. We're gathering at four at Fenella and Peter's and one of our contributions will be roasted chestnuts in red wine. We cut a thin slit on each, shake them over the coals for less than ten minutes, then prepare to ruin our nails peeling them. Perhaps because they are fresh, the shells come right off, revealing the plump toasted nut. Everyone takes a job and we fly through the preparation of two _faraone,_ guinea hens, and a rustic apple tart made by rolling a large round of pastry on a cookie sheet, piling the buttered and sugared fruit and toasted hazelnuts in the center, then flapping the pastry irregularly around it. Our cook, Willie Bell, would be proud of my variation on her cream gravy. To the _faraone_ pan juices, I add béchamel and chopped roasted chestnuts. I want chestnuts in everything. Fenella is preparing a pork roast and polenta, Elizabeth will bring salad, and Max is in charge of another vegetable and dessert. We could fast before such a feast but we have a light lunch of wild mushroom lasagne. A Christmas walk is a long tradition, for Ashley and me at least. Ed and I haven't told them yet where we are going.
We drive to the end of a road near our house and get out. We discovered this walk purely by chance one day when we walked this road and spotted a path at the end of it. We kept walking and made a fantastic discovery. It was one of the great walks I've ever had and we decided then to come back at Christmas. Water is flowing where I've never seen it in summer. Sudden streams gush out of crevices and wash over the road. We come to a waterfall and several torrents. Soon we're in a chestnut and pine forest of huge ancient trees. We see a few patches of snow in the woods and more snow higher up in the distance. The air, deeply moist, smells of wet pine needles. We come to paving stones laid end to end. "Look, a path," Ashley says. "What is this? It's wider up ahead." Out here in nowhere, we're on a Roman road in incredibly good condition for long stretches. We never have reached the end but Beppe, who knows it from childhood, told us it goes to the top of Monte Sant'Egidio, twenty kilometers away. Instead of winding and skirting, Roman roads tend to go straight to the top. The chariots were light and the shortest distance between two points seemed to have governed their surveyors. I've read that some of their roadbeds go down twelve feet. We're on the lookout for the distance markers but they have disappeared. Cortona lies below us, and below the town the valley and the horizon look polished and gleaming. We see mountains in the distance we've never seen, and the hilltowns of Sinalunga, Montepulciano, and Monte San Savino rise sharply like three ships sailing against the sky. The last knot of my unrest unravels. I start to hum "I saw three ships come sailing in on Christmas Day, on Christmas Day in the morning." A red fox leaps down onto the path ahead of us. He sweeps his plumy tail back and forth, regards us for a moment, then darts into the woods.
THE ROAD TO FENELLA AND PETER'S NOBLE FARMHOUSE IS rough enough in summer. Now we're holding on to pots and trays and trying not to empty them into one another's laps. The poor Twingo's axle! We ford several impromptu streams and almost get stuck in a washout of near-ditch proportions. When we arrive everyone is gathered by the gigantic fireplace, already into the red wine. This is one of the most magnificent houses in the local vernacular. The living room, formerly a granary, soars two stories high with rows of dark beams. The immense room is filled with a lifetime collection of antiques, rugs, and treasures. The space is too large to heat, however, so we settle into big sofas in the former kitchen, with its fireplace large enough for the original cooks to set their chairs inside it and tend their pots. Downstairs the thirty-foot-long table is laid with pine boughs and red candles. Ghosts of Christmases past join us in everyone's stories of other holidays. Fenella pours the hot polenta onto a cutting board. Ed carves the _faraone_ while Peter slices the succulent roast. We pile our plates. Fenella has journeyed to Montepulciano for a stash of her favorite _vino nobile,_ which travels around the table. "To absent friends," Fenella toasts. "To the polenta!" Ed rejoins. Our little expatriate band is merry, merry.
En route home, we stop in town for a coffee. We expect the streets to be deserted on Christmas night at nine o'clock, but _everyone_ is out, every baby and grandmother and everyone in between. Walking and talking, always talking. "Well, Jess, you're objective," I say. "You're new here so you must tell me if I'm under an illusion—or is this the most divine town on the planet."
Without a pause, he says, "I'd say so. Yes. Extra _primo_ good."
The _passeggiata_ activity is to stroll from church to church, viewing the scenes of Christ's birth. The reminder of birth is everywhere, is still the major focus of Christmas here. Pagan, I suppose I am, but I think what a glorious _metaphor_ the birth is at year's end, the dark and dead end of the year. The one cry of the baby in the damp straw and death is denied. The baby in every scene has a nimbus of light around his head. The sun heads toward the celestial equator, bringing back the days I love. One foot over and we're on a swing toward light. That restless urge at this season, maybe it's the desire to find the light of one's own again. I've read that the body contains minerals in the exact proportions that the earth does; the percentages of zinc and potassium in the earth are the same amounts we have in our bodies. Could the body have an innate desire to imitate the earth's push toward rebirth?
All the Cortona churches display their _presepi,_ nativity scenes. Some are elaborate reproductions of paintings in wax and wood models with elaborate architecture and costume; some are terra-cotta. One crib is made of ice cream sticks. At the middle school's exhibit of students' _presepi,_ we're touched to see the children's less ornate versions. Most are traditional, with small dolls, twig trees, and hand-mirror ponds, but one astonishes us. Paolo Alunni, aged perhaps ten, is a true heir of the Futurists and their love for the mechanical and its energy. His crèche—stable, people and animals—is constructed entirely of keys. The animal keys are horizontal and it's clear which are sheep, which are cows. The humans are upright except for the cunning little diary-sized key that is the baby Jesus. He's made the stable roof from a hinge. Eerie and effective—a stunning piece of art among all the earnest projects.
EVERY MORNING I LOOK OUT THE WINDOW AT THE VALLEY filled with fog, pink tinted at dawn on clear days, a roiling gray when high clouds blow across from the north. These are seamless days of walks and books, of taking trips to Anghiari, Siena, Assisi, and nearby Lucignano, whose town walls describe a graceful ellipse. At night, we grill in the fireplace _—bruschetta_ with melted _pecorino_ and walnuts, slices of fresh _pecorino_ with _prosciutto,_ and sausages. _Scamorza,_ more native to the Abruzzo but growing popular in Tuscany, is a hard rind cheese shaped like an 8. It melts to almost a fondue and we spread it on bread. I learn to use the hearth to warm plates and keep food hot, just as my imagined _nonna_ must have done. Our favorite pasta becomes _pici con funghi e salsiccie,_ pencil-thick pasta with wild mushrooms and the grilled sausages. A seven-mile walk along the fire road cancels the effects of one evening of grilling.
On New Year's Eve, I am coming home from town with a carload of groceries. We're cooking the traditional lentils (tiny coin shapes are the symbol of prosperity) and _zampone,_ sausage in the shape of a pig's foot. As I climb the road toward home, I pass the dome of Santa Maria Nuova below me. Fog completely surrounds the church and the dome floats above the clouds. Five intersecting rainbows dive and arch around the dome. I almost run off the road. At the curve, I stop and get out, wishing everyone were with me. This is staggering. If it were the Middle Ages, I'd claim a miracle. Another car stops and a man dressed in fancy hunting clothes jumps out. Probably he is one of the murderers of song birds but he, too, looks stunned. We both just stare. As the clouds shift, the rainbows disappear one by one but the dome still drifts, ready for any sign that might be about to happen. I wave to the hunter. _"Auguri,"_ he calls.
BEFORE ASHLEY AND JESS GO BACK TO NEW YORK, where serious winter waits to kick in, and before we go back to San Francisco, where paper-white narcissi already are blooming in Golden Gate Park, we plant the Christmas tree. I expect the ground to be hard but it is not. Loamy and rich, it yields to the shovel. As Jess shovels dirt, the white skull of a hedgehog turns up with its perfectly articulated jaw and teeth still attached by a string of ligament. _Memento mori,_ a useful thought as the end of one year folds into the new. The sturdy tree looks immediately at home on the lower terrace. As it grows it will tower over the road below. From the upstairs, we'll see its peak growing higher and higher each year. If the rains these first few years are plentiful, in fifty years it may be the giant tree of the hillside. Ashley, old by then, may remember planting it. Because she is flush with beauty, I can't imagine her old. She will come with her friends or family, all of whom will marvel. Or strangers who own the house may take its lower limbs for firewood. Surely Bramasole will still be here, with the olives we've planted thriving on the terraces.
Winter Kitchen
Notes
CIBO, FOOD, A BASIC WORD. I'M GATHERING a bag of _cibo_ to take back to California with me. I'm not sure exactly when my carry-on bag became a grocery bag in disguise. Besides olive oil (each of us carries back two liters), I take tubes of those pastes that are marvelous for quick hors d'oeuvres: white truffle, caper, olive, and garlic. They're very inexpensive here and easy to transport. I take boxes of _funghi porcini_ bouillon cubes, which I can't get at home, and a pound or so of dried _porcini._ The bright boxes and foil bags of Perugina chocolates make handy gifts. I would like to take a wheel of _parmigiano_ but my bag is not that accommodating. This time I'm stuffing in a truffle-flavored vinegar and a good _aceto balsamico._ I notice that Ed has added a bottle of _grappa_ to the bag, as well as a jar of chestnut honey.
To the question "Are you carrying any food items?" on the customs form, I must answer yes. As long as products are sealed, no one seems to care. A friend who had special sausages from his hometown of Ferrara stuffed in his raincoat pockets was sniffed by airport beagles and stripped of his heirlooms.
The only kitchen item I usually bring with me _to_ Italy is plastic wrap; the Italian kind always gets off to a bad start, leaving me untangling a two-inch strip. This time, however, I have brought one bag of Georgia pecans and a can of cane syrup, pecan pie being a necessary ingredient of Christmas. All the other ingredients of Christmas in Tuscany seem new. One pleasure of the cook is that now and then you learn all over again.
Winter food here recalls the hunter stepping in the door with his jacket pockets filled with birds, the farmer bringing in the olive harvest and beginning the cold-weather work of clearing and preparing the trees, trimming back vines for spring. Tuscan food of this season calls for massive appetites. For us, long walks build us up to the hefty dishes that we order in _trattorie:_ pasta with wild boar _ragù, lepre,_ hare, fried mushrooms, and polenta. The rich smells drifting from our kitchen are different in winter. The light summer fragrances of basil, lemon balm, and tomatoes are replaced by aromas of succulent pork roast glazed with honey, guinea hens roasting under a layer of _pancetta,_ and _ribollita,_ that heartiest of soups. Subtle and earthy, the fine shavings of Umbrian truffle over a bowl of pasta prick the senses. At breakfast, the perfumed melons of summer are forgotten and we use leftover bread for slabs of French toast spread with plum jam I made last summer from the delicate _coscia di monaca,_ nun's thigh, variety that grows along the back of the house. The eggs always startle me; they're so _yellow._ The freshness does make a tremendous difference, so that a platter of eggs scrambled with a big dollop of mascarpone becomes a very special treat.
I didn't anticipate the extent of the excitement of cooking in winter: The entire shopping list is changed by the cold season. In winter here, there are no asparagus from Peru, no grapes from Chile. What's available, primarily, is what grows, though citrus comes up from the south and Sicily. A mound of tiny orange clementines, bright as ornaments, shines in a blue bowl on the windowsill. Ed eats two or three at a time, tossing the peels into the fire, where they blacken and shrivel, sending out the pungent scent of their burning oil. Because the days are so short, the evening dinners are long, and long prepared for.
~ANTIPASTI~
Winter Bruschette
_Crostini,_ the _antipasti_ that appear on every menu in Tuscany, and _bruschette_ are both pieces of bread onto which various toppings are piled or spread. The _crostini_ are rounds of bread; the baguette-shaped loaves are sold at the _forno._ A typical platter of _crostini_ includes several choices; _crostini di fegatini,_ chicken liver spread, is the most popular. I often serve _crostini_ with garlic paste and a grilled shrimp on each. _Bruschette_ are made from regular bread, sliced, dipped quickly in olive oil, grilled or broiled, then rubbed with a clove of garlic. In summer, topped with chopped tomatoes and basil, it appears frequently as a first course or snack. Winter's robust _bruschette_ are fun to prepare at the fireplace. When friends stop in, we open a hefty _vino nobile._
Bruschette with Pecorino and Nuts
_~Prepare_ bruschette _as described above. For each_ bruschetta, _slowly melt a slice of_ pecorino _(or_ fontina) _in a pan on hot coals or on the stove. When slightly melted, sprinkle chopped walnuts over the cheese. With a spatula, slide the cheese onto the grilled bread._
Bruschette with Pecorino and Prosciutto
_~Prepare_ bruschette. _In an iron skillet over the coals or in a nonstick pan on the stove, slightly melt slices of_ pecorino, _top with_ prosciutto, _then another slice of_ pecorino. _Flip over so that both sides melt and are crisp around the edges. Slide onto bread._
Bruschette with Greens
_~Chop_ cavolo nero, _black cabbage (or Swiss chard). Season and sauté in olive oil with 2 cloves of minced garlic. Spread 1 or 2 tablespoons on each_ bruschetta.
Bruschette con Pesto di Rucola
This variation on the standard pesto is equally good with pasta. Arugula is satisfying to grow. It sprouts quickly and the young peppery leaves are best. By the time the leaves are large, the taste usually turns bitter.
_~Prepare_ bruschette, _this time cutting the bread into small pieces. In a food processor or mortar, combine a bunch of arugula, salt and pepper, 2 cloves of garlic, and ¼ cup of pine nuts. Blend together, then slowly incorporate enough olive oil to make a thick paste. Add ½ cup of grated_ parmigiano. _Spread on grilled bread. Makes about 1-½ cups._
Bruschette with Grilled Eggplant
I've often burned eggplant on the grill—by the time it's done it's black—so now I bake the whole eggplant in the oven for about 20 minutes, then slice it and, for taste, just finish it off on the grill.
_~Bake an eggplant on a piece of foil in a moderate oven until it is almost done. Slice and salt. Let rest on paper towels for a few minutes. Brush each slice lightly with olive oil, sprinkle with pepper, and grill. Chop ½ cup of fresh parsley, mix with some chopped fresh thyme and marjoram. Lightly brush the eggplant with oil again if it looks dry. Place a slice on a piece of prepared_ bruschetta, _sprinkle with some of the herb mixture and a little grated_ pecorino _or_ parmigiano. _Heat briefly in the broiler to melt cheese slightly._
~PRIMI PIATTI~
Wild Mushroom Lasagna
Dried lasagna in boxes leaves me cold—those wavy edges like tractor tires, the gummy pasta. Thin sheets of fresh pasta create a light, light lasagna. I watched a real pro with pasta in a local shop. Hers is thin as a bedsheet and supple. In summer, this recipe works well with vegetables instead of mushrooms: sliced zucchini, tomatoes, onions, and eggplant, seasoned with fresh herbs. Both recipes can be used as a filling for long, rolled _crespelle,_ crÊpes, as well.
_~Cut sheets of pasta to fit 6 layers in a large baking dish. (Some of the middle layers can be in more than 1 piece.) Prepare abéchamel sauce: Melt 4 tablespoons of butter. Stir in 4 tablespoons of flour, and cook but do not brown. After 3 or 4 minutes, remove from heat and whisk in 2 cups of milk all at once. Return to heat, stir and simmer until the sauce thickens. Mince 3 cloves of garlic and add it to the sauce, along with 1 tablespoon of chopped thyme, salt and pepper. Grate 1-½ cups of_ parmigiano. _In a large pan, heat 2 tablespoons of olive oil or butter and sauté 3 cups of sliced fresh mushrooms—preferably_ porcini _or portobello. If you don't have wild mushrooms, use a mixture of button mushrooms and dried_ porcini _that have been revived by soaking them for 30 minutes in stock, water, wine, or cognac._
_Assembly: Cook 1 sheet of pasta until it is barely done, remove it from the boiling water, and let it briefly drain on a cloth towel spread on the counter. Place the semidry pasta sheet in the lightly oiled baking dish and cover it with a layer of béchamel sauce, a layer of sautéed mushrooms, and a sprinkling of the cheese. Continue cooking the next pasta sheet as you prepare each layer. Add a spoonful or two of the pasta water to the sauce if you've used too much on the first layers. Tuscan cooks usually use some of the pasta water in their sauces. Top the dish with buttered bread crumbs and more_ parmigiano. _Bake, uncovered, at 350° for 30 minutes. Serves 8._
Ribollita
A thick, soul-stirring soup with white beans, the ubiquitous bread, and vegetables. As the translation "reboiled" indicates, this is a soup that is easily made using leftovers, probably from a big Sunday dinner. The classic recipe calls for hunks of bread to be added to the pot at the end. Tuscans pour oil into each bowl at the table. The soup, with a salad, is a complete meal—unless you've been out plowing. Almost any vegetable can be used. If I say "zuppa" to Maria Rita, she piles in everything I'll need, plus handfuls of fresh parsley, basil, and garlic. I take her advice to include the heel of the _parmigiano._ Once cooked, the softened heel is the cook's treat.
_~Prepare a pound of white beans by washing them well. Cover with water in a stock pot and bring them to a boil. Take them off the heat and let them sit in the water for a couple of hours. Add more water to cover, add seasonings, and simmer until barely done. They should be watched because they tend to become mushy soon after they're done. Clean and cut into medium dice: 2 onions, 6 carrots, 4 ribs of celery, a bunch of curly cabbage or chard, 4 or 5 cloves of garlic, and 5 large tomatoes (or a box of chopped tomatoes in winter). Mince a bunch of parsley. Sauté the onions and carrots in olive oil. After a few minutes, add the celery, then the chard and the garlic, adding more oil as needed. Cook 10 minutes, then add the tomatoes, a heel of_ parmigiano, _and the beans. Add enough stock (vegetable, chicken, or meat) to cover. Bring to a boil, then simmer 1 hour to blend flavors. Add the cubes of bread. Allow to rest for several hours. Add the parsley, reheat, and serve with grated_ parmigiano _on top and olive oil to pass around the table. Leftover pasta, green beans, peas,_ pancetta, _and potatoes all can be added to the pot the next day. At least 15 servings, depending on the amount of stock used._
Pici with Quick Tomato-Cream Sauce
Hearty sauces of hare and boar adhere especially well to the long, thick strands of this local pasta, which is almost as thick as a pencil. I use this sauce on _fusilli_ and _pappardelle_ or any broad pasta. This is a favorite.
_~Cook 4 or 5 slices of_ pancetta, _drain on paper towels, then crumble and set aside. Chop 2 medium onions and 2 or 3 cloves of garlic and sauté in olive oil for 5 minutes. Chop and add 1 large red pepper and 4 or 5 tomatoes. Season and cook 5 minutes more. Season with chopped thyme, oregano, and basil. Stir in ½ cup of light cream and ¾ cup of puréed tomatoes. Add a spoonful or so of the pasta water to the sauce. Stir the_ pancetta _into the sauce at the last minute to retain crispness. Cook and drain enough pasta for 4. Mix the pasta with half the sauce; serve the rest of the sauce over the pasta. Pass the_ parmigiano! _Serves 4._
~SECONDI~
Quail, Slowly Braised with Juniper Berries and Pancetta
My father was a hunter and our cook, Willie Bell, often was lost in a cloud of tiny feathers as she plucked a mound of quail. The drooping little heads all fell in the same direction. I wouldn't eat them, even after she smothered them with cream and pepper in the huge covered frying pan on the outdoor fireplace. With more equanimity, I've met them in a new guise. The balsamic vinegar should come from Modena. Those that are labeled _Aceto Balsamico Tradizionale di Modena_ and are marked _API MO_ are the real thing, aged for at least twelve years. Some of the ancient balsamics are so fine that they're sipped like liqueur. I think Willie Bell would approve of these quail.
_~Flour and quickly brown 12 quail (2 per person) in hot olive oil. Arrange the quail in a heavy casserole with a tight-fitting lid and pour in ¼ cup of balsamic vinegar. Cover quail with strips of_ pancetta _and 2 minced shallots. Sprinkle with sprigs of thyme, crushed peppercorns, and juniper berries. Braise in a slow oven (275°) for 3 hours. Turn the quail over after about an hour and a half. Moisten with a little red wine or more balsamic vinegar if they look dry. They are excellent served with polenta. Serves 6._
Roast Chickens Stuffed with Polenta
In Georgia when I was growing up, the Christmas turkey always was stuffed with a cornmeal dressing. This adaptation of my mother's recipe uses Italian ingredients.
_~Soak 2 cups of polenta in 2 cups of cold water for 10 minutes, then add it to 2 cups of boiling water in a stock pot. Bring to a boil, then lower the heat and cook, stirring constantly, for 10minutes. Stir in 1 cup of butter. Remove from the heat and beat in 2 eggs. Add 2 cups of fresh croutons, 2 chopped onions, 3ribs of chopped celery, and season generously with salt, pepper, sage, thyme, and marjoram. Stuff 2 chickens (or 1 turkey) loosely, tie the legs together, and scatter sprigs of thyme over the birds. Roast on oiled racks in a large pan. 25 minutes a pound at 350°is a rough estimate for the perfectly roasted bird—but start testing sooner. Leftover stuffing can be baked separately in a buttered dish. Serves 8._
Faraone (Guinea Hens) with Fennel
Delicate and flavorful, guinea hens are always available at the butcher. For Christmas, we roasted two and presented them on a large platter, surrounded by grilled local sausages and a wreath of herbs. The bones made a rich stock for soup the next day. Oven-roasted potatoes with rosemary and garlic are a natural companion.
_~I'm afraid the_ faraone _must first be approached with tweezers to remove remaining pin feathers. Wash and dry 2 birds well. Simplest preparation is best—the flavor of the bird is emphasized. Lay rosemary branches on an oiled roasting pan and place the birds on top. Rub with a mixture of chopped rosemary, basil, and thyme, then lard with strips of_ pancetta. _Remove the tough outer portions of 2 fennel bulbs. Cut in half-inch crescents, drizzle with olive oil, and scatter them around the birds, along with a couple of quartered onions. Roast at 350° at 20 minutes per pound. These birds are leaner than chickens; be careful not to overcook. For a rich sauce, add béchamel sauce (see recipe) roasted chestnuts to the pan juices. Serves 4._
Rabbit with Tomatoes and Balsamic Vinegar
_Coniglio,_ rabbit, is a staple of the Tuscan diet. At the Saturday market, a farm woman usually has three or four fluffy bunnies looking up at you from an old Alitalia flight bag. In the butcher's case, they're more remote, clean and lean, ruddy pink, sometimes with a bit of fur left on the tail to prove it's not cat. Unappetizing as this note is, the rabbit, simmered in thick tomato sauce with herbs, is delightful. Just call it _coniglio_ for the children's sake.
_~Have the rabbit cut into pieces. Flour them and quickly brown in olive oil. Arrange in a baking dish and cover with the following tomato-balsamic sauce. Sauté 1 large chopped onion and 3 or 4 cloves of minced garlic until translucent. Chop 4 or 5 tomatoes and add them to the pan. Season with ½ teaspoon of turmeric, rosemary, salt, pepper, and toasted fennel seeds. Stir in 4 tablespoons of balsamic vinegar and simmer until sauce is thick and reduced. Roast the rabbit, uncovered, for about 40 minutes in a 350° oven. Midway, baste with 2 to 3 tablespoons of additional balsamic vinegar. Serves 4._
Polenta with Sausage and Fontina
In winter, the local fresh pasta shop sells polenta with chopped walnuts, a simple but interesting accompaniment to roasts or chicken. The polenta and sausages, with a grand salad, is a robust meal in itself.
_~Prepare classic polenta (see recipe). Pour half of the polenta into an oiled baking dish. Thinly slice or grate 1-½ cups of Fontina and spread over the layer of polenta. Season with salt and pepper. Pour on the rest of the polenta. Slice 6 sautéed Italian sausages over the top and pour on the pan juices. Bake for 15 minutes at 300°. Serves 6._
Honey-Glazed Pork Tenderloin with Fennel
The tenderest, leanest pork is the tenderloin. One tenderloin serves two hungry people and the fennel pairs well with the pork. Wild fennel grows all over our land. Whether its local popularity first came from its aphrodisiacal powers or its curative uses for eye problems, I don't know. I like its feathery foliage and its mythic connections. Prometheus is said to have brought the first fire to humans inside the thick, hollow stalk.
_~Brush 2 tenderloins lightly with honey. In a mortar or food processor, crush 1 tablespoon of fennel seeds. Add them to 1 tablespoon of finely chopped rosemary, salt, pepper, and 2 cloves of minced garlic. Spread this mixture on the pork. Place in a shallow, oiled pan. Roast in the oven at 400° until the pork is faintly pink in the middle, about 30 minutes. Meanwhile, cut 2 fennel bulbs in ½-inch slices. Toss out the tough root end. Steam for about 10minutes, until cooked but not soft. Purée until smooth, then add ¼ cup of white wine, ½ cup of grated_ parmigiano, _and ½ cup of_ mascarpone _(or sour cream). Place tenderloins into a buttered dish and pour sauce over; top with buttered bread crumbs. Cook at 350°for about 10minutes. Garnish tenderloins with fennel leaves, if available, or with wands of fresh rosemary. Serves 4._
~CONTORNI~
Chestnuts in Red Wine
Even though I'm living near a chestnut forest, chestnuts still seem luxurious. We roast a few every night to enjoy with a glass of _amaro, grappa,_ or a last coffee. Just a short gash or x in the shell before they're put in the pan and they open easily while still hot. Many cookbooks advise roasting chestnuts for up to an hour! In the fireplace, they're ready quickly—15 minutes at the most, depending on how hot the coals are. Jiggle the pan often and remove them at the first sign of charring. Chestnuts taste good with all the flavorful winter meats, especially with guinea hens.
_~Roast and peel 30 or 40 chestnuts. Simmer the chesnuts in just enough red wine to cover for half an hour, long enough for the two flavors to intertwine. Pour off most of the wine. Serves 6._
Garlic Flan
Excellent with any roast.
_~Separate the cloves from a large head of garlic. Without peeling, place the cloves in boiling water for 5 minutes. Cool, and squeeze out the garlic. Mince and crush the cloves with a fork, then stir into 2 cups of cream. Bring cream and garlic just to a simmer in a saucepan. Add a little ground nutmeg, salt, and pepper. Remove from the flame and beat in 4 egg yolks. Pour into 6 individual molds, well-oiled, or into a shallow baking pan. Bake in a_ bains-marie _at 350° for 20 minutes or until set. Cool for 10 minutes before unmolding._
Cardoons
As long as your arm, prickly, and pale green, cardoons are trouble but worth it. This vegetable was new to me. I learned to strip the tough, stringy exterior from the stalks—the stalks are somewhat like celery—and quickly place the cardoon pieces in water and lemon juice because they otherwise turn dark in a hurry. At first I steamed them but they never seemed to get done. I found that boiling them is best, just to the point of fork tenderness. They have a taste and texture similar to heart of artichoke—not surprising since they come from the same family.
_~After stripping a large bunch of cardoons and bathing them in acidulated water, cut in two-inch pieces and boil until just done. Drain and arrange in a well-buttered baking dish. Season with salt and pepper and lightly cover with a béchamel sauce (see recipe), dots of butter, and a sprinkling of_ parmigiano. _Bake at 350° for 20 minutes._
Warm Porcini (or Portobello) Salad with Roasted Red and Yellow Peppers
Serve this colorful composed salad as a first or main course.
_~Grill 2 large mushrooms or sauté them topside down in olive oil (this prevents them from losing their juices). Slice and drizzle lightly with vinaigrette. Grill 2 peppers, one red and one green, and let them cool in a bag, then slide off the charred skin. Slice and drizzle with the vinaigrette. Separate a Bermuda (red) onion into rings. Toast ¼ cup of pine nuts. Toss greens—radicchio, arugula, and other lettuces of varying textures and colors—with vinaigrette and arrange on each plate. Arrange the warm peppers, rings of onion, and mushroom slices over the greens and top with pine nuts. Serves 6._
~DOLCI~
Winter Pears in Vino Nobile
Steeped pears are pretty to serve. Their taste seems heightened when served along with some Gorgonzola, toasted bread, and walnuts roasted with butter and salt.
_~Peel 6 firm pears and stand them upright in a saucepan. Leave stems on, if they still have them. Squeeze lemon juice over each. Pour 1 cup of red wine over them and sprinkle ¼ cup of sugar over the tops. Add ¼ cup of currants, a vanilla bean, and a few cloves to the wine. Cover and simmer for 20 minutes (or longer, depending on the size and ripeness of the pears); don't allow them to become soft. Midway, turn pears on their sides and baste several times with the wine sauce. Transfer to serving dishes, pour the currants and some of the wine over each, and garnish with thin strips of lemon peel. Serves 6._
Rustic Apple Bread Pudding
I'm surprised that the gnarly apples I find at the Saturday market have intense flavor. Even our long-neglected apple trees bravely put forth their scrawny crop. Too tiny to slice, they at least make a respectable apple butter. For this husky dessert, cut the apples in chunky slices.
_~Peel, core, and cut 4 or 5 crisp baking apples in large slices. Squeeze lemon juice over them, then dust with nutmeg. Toast 1 cup of sliced almonds. Remove any hard crust from a loaf of leftover bread (fresh bread would be too soft for this recipe). Cut the bread into slices and lay some of them on the bottom of a buttered rectangular pan, 9 by 12 inches or so. In a sauté pan, melt 6 tablespoons of butter and 6 tablespoons of sugar. Add ¾ cup of the toasted almonds, 2 tablespoons of lemon juice and ¼ cup of cider or water. Toss the apple chunks in this. Layer the apple mixture and bread in the pan, ending with a layer of bread. Beat together 6 tablespoons of softened butter and 4 tablespoons of sugar. Beat in 4 eggs, then 1-¼ cups of milk and ¾ cup of light cream. Pour evenly over the bread. Sprinkle the top with a little sugar, nutmeg, and the remaining toasted almonds. Bake at 350° for an hour. Allow to rest for 15 or 20 minutes. Serve with sweetened mascarpone or whipped cream. Serves 8._
Tangerine Sorbet
If I'd grown up here, I'm sure the fragrance of citrus would be indelibly associated with Christmas. The holiday decorations in Assisi are big lemon boughs on all the stores. Against the pale stones, the fruit glows like lighted ornaments and the scent of lemons infuses the cold air. Outside the groceries all over Cortona, baskets of clementines brighten the streets. Bars are squeezing that most opulent of juices, the dark blood orange. The first taste, tart as grapefruit, quickly turns to a deep aftertaste of sweetness. This sorbet, which works wonders as a pause in a winter dinner, can be made with other juices. Equally good as a light dessert, the sorbet is delectable served with thin chocolate butter cookies.
_~Make a sugar syrup from 1 cup of water and 1 cup of sugar by bringing them to a boil, then simmering for about 5 minutes. Stir in 1-¼ cups of fresh tangerine juice, 1 cup of water, 1 tablespoon of lemon juice, plus the zest of the tangerines you've used. Chill thoroughly in the fridge—until cold to the touch. Process in an ice cream machine, according to manufacturer's instructions. Serves 6._
Lemon Cake
A family import, this Southern cake is one I've made a hundred times. Thin slices seem at home here with summer strawberries and cherries or winter pears—or simply with a small glass of one of the many fantastic Italian dessert wines, such as Banfi's B.
_~Cream together 1 cup of sweet butter and 2 cups of sugar. Beat in 3 eggs, one at a time. The mixture should be light. Mix together 3 cups of flour, 1 teaspoon of baking powder, ¼ teaspoon of salt, and incorporate this with the butter mixture alternately with 1 cup buttermilk. (In Italy, I use one cup of cream since buttermilk is not available.) Begin and end with the flour mixture. Add 3 tablespoons of lemon juice and the grated zest of the lemon. Bake in a nonstick tube pan at 300° for 50minutes. Test for doneness with a toothpick. The cake can be glazed with ¼ cup of soft butter into which 1-½cups of powdered sugar and 3 tablespoons of lemon juice have been beaten. Decorate with tiny curls of lemon rind._
Rose Walk
IN THE TEN HOURS UPRIGHT IN MY AISLE seat, headed toward Paris, I read with intense concentration a history of experimental French poetry, the flight magazine, even the emergency instruction card. So many crises happened at work before I left San Francisco at the end of May that I wanted to be loaded onto the plane on a stretcher, wrapped in white, put in the front aisle of the plane with curtains around me, the flight attendant looking in now and then with a cup of warm milk—or a sapphire gin martini. I left a week before Ed finished his classes, fled, really, on the first plane smoking on the runway the day after graduation.
After a short wait at Charles de Gaulle, I caught an Alitalia flight. The pilot wasted no time in heading straight up. An Italian driver, I guess, is an Italian driver; suddenly I felt a surge of energy. I wondered if he was trying to pass someone. Soon he aimed down, almost straight down, toward the Pisa airport. No one seemed alarmed, so I practiced breathing evenly and holding up the plane by the armrests.
I'm staying overnight. If we had been late, the prospect of changing trains in Florence at night sounded exhausting. I check into a hotel and find I'm ready to walk. It's _passeggiata_ hour. Hoards of people mingling, visiting, strolling, running errands. The tower still leans, tourists still take photos of themselves leaning to one side or the other in front of it. The pastel and ocher houses still curve along the river like an aquarelle of themselves. Women with shopping bags crowd into the fragrant bread store. Splendid to arrive alone in a foreign country and feel the assault of difference. Here they are all along, busy with living; they don't talk or look like me. The rhythm of their day is entirely different; I am thoroughly foreign. I have dinner at an outdoor restaurant on a piazza. Ravioli, roast chicken, green beans, salad, a half carafe of local red. Then my elation ebbs and a total, delicious tiredness rushes over me. After a soaking bath with all the hotel's bubble bath, I sleep for ten hours.
The first morning train takes me through fields of red poppies in bloom, olive groves, and by now familiar stony villages. Haystacks, nuns in white four abreast, bed linens flung out the window, sheepfold, oleander, Italy! I stare out the window the whole way. As we approach Florence, I worry about banging my new small computer against something while juggling my bag. Most of my summer clothes are at the house so I can travel lightly. Even so, I feel like a pack animal with my handbag, computer, and carry-on bag hanging on me. But it's fun to get off at the Florence station, which always brings me the fresh memory of my first trip to Italy almost twenty-five years ago, the exotic, smoky sound of the loudspeaker announcing the arrival from Rome on _binario undici_ and the departure for Milano on _binario uno,_ the oily train smells and everyone going somewhere.
Fortunately, the train is almost empty and I easily stow my bags. Midway home ( _home,_ I've said to myself), a cart comes through with sandwiches and drinks. The train doesn't stop at Camucia so I get off at Terontola, about ten miles away, and call a taxi.
Fifteen minutes later a taxi pulls up. As soon as I get in, a second taxi pulls alongside us and the driver starts to shout and gesture. I assumed the taxi I got in was the one I called but no, he just happened along. He does not want to give up the fare. I tell him I called a taxi but he starts to take off. The other driver bangs on the door shouting louder, he was having lunch, he drove here especially for the _Americana,_ he has to earn his bread, too. Spit gathers in the corners of his lips and I'm afraid he's about to foam at the mouth. "Stop, please, I should go with him. I'm very sorry!" He growls, slams on brakes, jerks my bag out. I get in the other taxi. They face off to each other, both talking at once, jowls and fists shaking, then abruptly come to terms and start shaking hands, smiling. The deserted driver comes around to me, smiles, and wishes me a good trip.
When I arrive, my sister, nephew, and friends of theirs have been at the house for a couple of weeks. My sister has had all the pots planted with white and coral geraniums. The green smell of freshly cut grass tells me Beppe must have mown the lawn this morning. Despite my severe pruning in December, the roses we planted last summer are as tall as I am. They're profuse with bloom—apricot, white, pink, yellow. Hundreds of butterflies flitter among the lavender. The house has vases of gold lilies and daisies and wildflowers. It's clean and full of life. My sister even has a pot of basil going outside the kitchen door.
They are on a day trip to Florence when I arrive so I have the afternoon to pull the duffel out from under the bed and air out my summer clothes. Since five others are here and settled, I will be sleeping in my study for a few days. I make up the narrow bed with yellow sheets, set up the computer on my travertine desk, open the windows, and I'm here.
Late, I find my boots and walk the terraces. Beppe and Francesco have cut the weeds. Again, I've lost the battle of the wildflowers. In their zeal to clear, they have stopped for nothing, not even the wild (what I know as Cherokee) roses. Poppies, wild carnations, some fluffy white flower, and the host of yellow blooming weeds survive only along the terrace edges. The big news is the olives. In March, they planted thirty in the gaps on the terraces, bringing us up to a hundred and fifty trees. Already they're flowering. We ordered larger trees this year than the ten Ed planted last year; at the rate olives grow, we want to be around to collect a little oil. Beppe and Francesco staked each new tree and stuffed a nest of weeds between the stake and the trunk to prevent chaffing. Ed knew to dig a big hole for each tree but he didn't know to dig an enormous, deep one; Beppe explained that the new trees need a big _polmone,_ a lung. Around each, they've dug to a circumference of about four feet. They also planted two more cherries, to go with the ones Ed planted last spring.
For a week, we cook, run around to Arezzo and Perugia, walk, buy scarves and sheets at the Camucia market, and catch up on family news. Ed arrives in time for a farewell dinner with liberal pourings of several Brunellos my nephew bought in Montalcino, then they pack, pack, pack (so much to buy here) and are gone.
They've had a warm May; now it begins to rain. The run-rampant roses bend and sway in the wind. We run out with shovels and stake them, getting soaked. Ed digs while I clip off the dead blooms, cut back some of the stalky branches, and give them fertilizer, though I'm afraid it will promote even more of the Jack and the Beanstalk mode. I cut an armful of white ones that bloom in ready-made bouquets. Inside, we iron our clothes, rearrange what has been shifted as many people made themselves comfortable to their own tastes. Everything quickly falls into place. Eons ago, it seems, I arrived in June to find ladders, workmen, pipes, wires, rubble, and dust everywhere. Now we just begin living.
A pot of minestrone for the rainy nights. A walk over the Roman road into town for cheese, arugula, coffee. Maria Rita's cherries are the best ever; we eat a kilo every twenty-four hours. All the stump and stone removal and clearing has paid off. Cleaning up the land is easier now. Not as many rocks fly up when the weed machine splits through the weeds. How many stones have we picked up? Enough to build a house? Fireflies flickering on the terraces at night, cuckoos (don't they say _whoocoo_ instead?) in the soft blue dawns. A timid bird that sings "Sweet, sweet." Hoopoes all dressed up in their exotic plumage with nothing more to do than peck in the dirt. Long days with birdsongs instead of the sound of the telephone.
We plant more roses. In this area of Tuscany, they bloom spectacularly. Almost every garden spills and flourishes with them. We select a Paul Neyron, with ruffled hot-pink petals like a tutu and an astonishing lemony-rose scent. I must have two of the soft pink ones the size of tennis balls called Donna Marella Agnelli. Their perfume carries me back to the memory of being hugged to the bosom of Delia, one of my grandmother's friends, who wore immense hats and was a kleptomaniac no one ever accused because it would embarrass her husband to death. When he noticed a new object around the house, he would stop into the store he figured it came from and say, "My wife completely forgot to pay for this—just walked right out with it in her hand and remembered last night. How much do I owe you?" Perhaps her powdery rose perfume was stolen.
"Don't plant any Peace roses," a friend and connoisseur of roses advised. "They're such a cliché." But not only are they dazzling, the vanilla cream, peach, and rosy blush colors repeat the colors of the house. They belong in this garden. I plant several. Last year's gold-orange roses open to flagrant size, the rash colors contributing to their beautiful vulgarity. Now we have a line of roses all along the walk up to the house, with lavender planted between each one. I'm coming to believe in aromatherapy. As I walk to the house through waves of scent, it's impossible not to inhale deeply and feel an infusion of happiness.
At the steps up to the front terrace, the old iron pergola remains at the top and bottom, with jasmine we planted two years ago twining around them and down the iron railings of the steps. Now we decide on another long row of roses on the other side of the walk and a pergola at the opposite end of that walk. This restores the impression of the original rose pergola that existed when we first saw the house, but now we want the open feeling to the wide walk instead of reconstructing the continuous pergola. Two roses we choose—one milky pink, one a velvet red—are Queen Elizabeth and Abe Lincoln (pronounced Eh-bay Lin-cÓnay at the nursery). Nice to think of those two forces side by side. My favorites start as one color and open to another. _Gioia,_ Joy, is pearly as a bud and full blown turns straw yellow, with some petals still veined and edged with pink. We plant more of the apricot-dawn roses, one that's traffic-light yellow, a Pompidou, and one named for Pope John XXIII. So many important people just blooming in our garden. I don't resist a decadent, smoked lilac one that looks as if it belongs in the hand of someone in a coffin.
We visit a _fabbro,_ blacksmith, just over the river in Camucia. His two boys gather near as we talk to their father, their chance to see weird foreigners up close. One boy, about twelve, has icy, eerie green eyes. He's lithe and tan. I can't help but stare back at him. All he needs is a goatskin and a crude flute. The _fabbro_ also has green eyes but of a more direct color. By now, I've visited the workshops of five or six _fabbri._ The craft must attract particularly intense men. This shop is open on one side so it doesn't have the sooty air of most. He shows us his well covers and manhole grids, practical items. I think of the brooding _fabbro_ we first met, now dead from stomach cancer, him wandering in his own world in his blackened shop, fingering the serpentine torch holder and the archaic animal-headed staffs. Our gate still leans open; he died before he repaired it and we've grown used to its rust and bends. The green-eyed _fabbro_ shows us his garden and nice house. Perhaps his faun son will follow him in the craft.
Some things are so easy. We'll simply dig holes, fix the iron poles, then fill the holes with cement. We choose a pink climbing rose ("What's its name?" "No name, signora, it's just a rose. _Bella, no_?") for either side.
I've had several gardens but never have planted roses. When I was a child, my father landscaped around the cotton mill he managed for my grandfather. With a single-mindedness I can only wonder at, he planted a thousand roses, all the same kind. _L'étoile de Holland,_ a vital heart's blood red rose, is the flower of my father. To put it mildly, he was a difficult man and to complicate that, he died at forty-seven. Until he died, our house always was filled with his roses, large vases, crystal bowls, single silver bud vases on every available surface. They never wilted because he had someone cut a fresh armful every day during seasons of bloom. I can see him at noon coming in the back door in his beige linen suit, somehow not rumpled from the heat. He carries, like a baby in his arms, a cone of newspaper around a mass of red, red buds. "Would you look at these?" He hands them to Willie Bell, who already is waiting with scissors and vases. He twirls his Panama hat on the tip of his finger. "Just tell me, who needs to go to heaven?"
In my gardens I have planted herbs, Iceland poppies, fushsias, pansies, sweet William. Now I am in love with roses. We have enough grass now that I can walk out in the dew barefooted every morning and cut a rose and a bunch of lavender for my desk. Memory cuts and comes again: At the mill, my father kept a single rose on his desk. I realize I have planted only one red one. As the morning sun hits, the double fragrance intensifies.
NOW THAT SO MUCH WORK IS FINISHED, WE TASTE THE FUTURE. Time is coming when we will just garden, maintain (astonishingly, some of the windows inside already need touching up), refine. We have a list of pleasurable projects such as stone walkways, a fresco on the kitchen wall, antique hunting trips to the Marche region, an outdoor bread oven. And a list of less glorious projects: figuring out the septic system, which sends out a frightening turnip smell when lots of people are using the house; cleaning and repointing the stone walls of the cantina; rebuilding sections of stone walls that have collapsed on several terraces; retiling the butterfly bathroom. These would have seemed major once and now just seem like things on a list. Still, days are near when we will work with an Italian tutor, take the wildflower book on long walks, travel to the Veneto, Sardinia and Apulia, even take a boat from Brindisi or Venice to Greece. To embark from Venice, where the first touch of the East is felt!
That time is not yet, however; the last big project looms.
Sempre Pietra
(Always Stone)
PRIMO BIANCHI CHUGS UP THE DRIVEWAY in his Ape loaded with bags of cement. He jumps out to direct a large white truck full of sand, steel I-beams, and bricks as it backs up the narrow driveway, scraping its mirror on the pine trees and pulling off one limb of a spruce with a loud crack. Primo was our choice for remodeling three years ago but was unable to work then because of a stomach operation. He looks the same—like an escapee from Santa's workshop. We go over the project. The yard-thick living room wall will be opened to connect with the _contadina_ kitchen, which will get a new floor, new plaster, new wiring. He nods. _"Cinque giorni, signori,"_ five days. This crude room, totally untouched, serves as a storage room for garden furniture over the winter and as the last bastion for scorpions. Because of earthquake standards, the opening will be only about five feet, not as wide as we wanted. But there will be doors opening to the outside, and the rooms, at last, will be joined.
We tell him about Benito's men running out of the house when they opened the wall between the new kitchen and the dining room. I'm reassured when he laughs. Will they start tomorrow? "No, tomorrow is Tuesday, not a good day for starting work. Work started on Tuesday never ends—an old superstition, not that I believe it but my men do." We agree. We definitely want the project to end.
On evil Tuesday, we take all the furniture and books out of the living room, remove everything from the walls and fireplace. We mark the center of the wall and try to visualize the expanded room. It's the imagination that carries us through the stress of these projects. Soon we will be happy! The rooms will look as though they've always been one! We'll have lawn chairs on that end of the front terrace and can listen to Brahms or Bird wafting out of the _contadina_ kitchen door. Soon it will not be called that anymore; it will be the living room.
_Intercapedine_ is a word I know only in Italian. My dictionary translates it as "gap, cavity." It's a big word in the lingo of restoring humid stone houses. The _intercapedine_ is a brick wall constructed part of the way up a humid wall. A gap _due dita,_ two fingers, wide is left between the two so that moisture is stopped by the brick barrier. The _contadina_ kitchen has such a wall on the far end of the house. It looks deeper than is usual. Impatient, Ed and I decide to take down some of it, to see if possibly the _intercapedine_ could be moved farther back toward the wall, thus enlarging the small room. As the bricks fall, we are stunned to find that there _is_ no end wall of the house on the first floor; it was built directly _into, onto_ the solid stone of the hillside. Behind the _intercapedine_ we find Monte Sant'Egidio! Craggy, huge rock! "Well, now we know why this room had a moisture problem." Ed is pulling out fig and sumac roots. Along the edge of the floor, he uncovers the rubble-filled remains of a moisture canal that must have functioned once.
"Great wine cellar," is all I can think of to say. Not knowing what else to do, we take a few photos. This discovery definitely doesn't conform to the transcendent dream of a hundred angels.
Auspicious Wednesday arrives and with it, at seven-thirty, Primo Bianchi with two _muratori,_ masons, and a worker to haul stone. They arrive without any machinery at all. Each man carries a bucket of tools. They unload scaffolding, sawhorses, called _capretti,_ little goats, and T-shaped metal ceiling supports called _cristi_ (named for the cross Jesus was crucified on). When they see the natural stone wall we uncovered, they stand, hands on hips, and utter a collective _"Madonna mia."_ They're incredulous that we took the wall down, especially that I was involved. Immediately, they go to work—first spreading heavy protective plastic on the floor—opening the wall between this room and the living room. Next, they remove a line of stones along what will be the top of the door. We hear the familiar _chink, chink_ sound of chisel on stone, the oldest building song there is. Soon, the I-beam goes in. They pack in cement and bricks to hold it in place. Until the cement dries there's nothing more they can do on the door so they begin to take up the ugly tile floor with long crowbars.
They talk and laugh as fast as they work. Because Primo is a little hard of hearing, they've all learned to converse in a near shout. Even when he's not around, they continue. They're thoroughly neat, cleaning up as they go: no buried telephone this time. Franco, who has glistening black, almost animal eyes, is the strongest. Although he's slight, he has that wiry strength that seems to come more from will than from muscle. I watch him lift a square stone that served as a bottom step for the back stairway. When I marvel, he shows off a bit and hoists it to his shoulder. Even Emilio, whose job it is to haul, actually seems to enjoy what he's doing. He looks perpetually amused. Hot as it is, he wears a wool cap pulled down so far that his hair all around sticks out in a ruff. He looks to be around sixty-five, a little old for a _manovale,_ manual laborer. I wonder if he was a _muratore_ before he lost two fingers. As they lift out the hideous tile and a layer of concrete, they find a stone floor underneath. Then Franco lifts some of these stones and discovers a second layer of stone floor. _"Pietra, sempre pietra,"_ he says, stone, always stone.
True. Stone houses, terrace walls, city walls, streets. Plant any rose and you hit four or five big ones. All the Etruscan sarcophagi with likenesses of the dead carved on top in realistic, living poses must have come out of the most natural transference into death they could imagine. After lifetimes of dealing with stone, why not, in death, turn into it?
The next day, they open the same cavity along the top of the door on the living room side. They call us in. Primo pokes the end of a major beam with his chisel. _"è completamente marcia, questa trava."_ He pokes the exposed part. _"Dura, qua."_ It's completely rotten inside the wall, although the exposed part is sound. _"Pericoloso!"_ The heavy beam could have sheared, bringing down part of the floor above. They support the beam with a _cristo_ while Primo takes a measurement and goes off to buy a new chestnut beam. By noon the I-beam on that side is in. They take no breaks, go off for lunch for one hour, and are back at work until five.
By the third full day of work they've accomplished an amazing amount. This morning the old beam comes down as easily as pulling a loose tooth. With long boards held up by _cristi_ on either side of the beam, they secure the brick ceiling, knock out stones, wiggle the beam a bit, and lower it to the floor. The new one slides right in. What fabulously simple construction. They wedge rocks around it, pack in cement, then pack more cement into the small space between the beam and the ceiling. Meanwhile, two men shovel and dig the floor. Ed, working in the yard just outside the door, hears _"Dio maiale!"_ a strange curse meaning God-pig. He looks in and sees underneath the enormous stone Emilio is propping up with his bar a third layer of stone. The first two layers were of smooth, big stones, burdensome to lug out; this layer is rough—suitcase-sized boulders, some jagged and deep in the ground. From the kitchen, I hear alarming groans as they upend them and roll them up a plank and dump them out the door. I'm afraid they're going to strike water soon. Emilio carts the small stones and dirt to the driveway, where a mountain of rubble is growing. We will keep the giant ones. One has elongated glyphic markings. Etruscan? I look at the alphabet in a book but can't correlate these markings with anything. Perhaps they are a farmer's diagram of planting or prehistoric doodling. Ed hoses off the stone and we look at it sideways. The carving then makes perfect sense. The Christian IHS topped by a cross, with another crude cross off to the side. A gravestone? An early altar? The stone has a flat top and I ask them to drag it aside; we can use it for a small outdoor table. Emilio shows no interest. _"Vecchia,"_ old, he says. But he insists there always will be a use for such stones. All afternoon, they dig. I hear them muttering _"Etruschi, Etruschi,"_ Etruscans, Etruscans. Under the third layer they come to the stone of the mountain. By now they've uncorked a bottle of wine and take gulps now and then.
_"Come Sisyphus,"_ like Sisyphus, I try to joke.
_"Esattamente,"_ Emilio replies. In the third layer, they're uncovering lintels and _una soglia,_ a threshold in _pietra serena,_ the great building stone of the area. Evidently, an earlier house's stones were used in building this house. These they line up along the wall, exclaiming at the fineness of the stone.
OUT ON ONE OF THE TERRACES, WE HAVE A STACK OF _cotto_ for the floor, saved when the new bathroom was built and the upstairs patio was replaced. We hope to salvage enough of them to use in the new room. Ed and I pull the good ones, chip off mortar, wash them in a wheelbarrow, and scrub them with wire brushes. We have a hundred and eighty of them, a few of which are too pitted but may be useful as half bricks. The men are still hauling stones. The floor level is down about two feet now. The white truck maneuvers up the driveway again to deliver long, flat tiles about ten by twenty-five inches, with air channels through them. Regular bricks are laid in ten lines on the dug-out, leveled floor, now mostly bedrock, with some mountain rock locally referred to as _piscia,_ piss, for its characteristic dribble of water in crevices. The bricks form drainage channels. Long tiles are cemented over them. They mix cement as though it were pasta dough—they dump sand into a big mound on the ground, then make a hole and start stirring in cement and water, kneading it with a shovel. On top of the tiles, they spread _membrane,_ something that looks like tar paper, and a grid of thick iron wire reinforcement. On that, a layer of cement. A day's work, I'd say.
We're spared the whining churn of a cement mixer. We laugh to remember Alfiero's mixer in the summer of the great wall. One day he mixed cement, worked awhile, then ran off to another job. When he came back, we saw him beating the mixer with his fists; he forgot the cement, which by afternoon was solid. We laugh now at the other foibles of past workers; these are princes.
Plaster cracks, like the ones in my dining room in San Francisco after the earthquake, have appeared on the second and third floors above where the door is being opened. Some large chunks have fallen. _Could_ the whole house simply collapse into a heap? By day, I'm excited by the project. I dream each night the oldest anxiety dreams—I must take the exam, I have no blue book, I don't know what the course is. I have missed the train in a foreign country and it is night. Ed dreams that a busload of students drives up to the house with manuscripts to be critiqued before tomorrow. In the morning, slightly awake at six, I burn the toast twice.
The wall is almost open. They've inserted a third steel beam over the opening, made the brick supporting column on one side, and have worked on the new double-thick brick wall that will separate us from the mountain. Primo looks over the bricks we've cleaned. As he lifts one, a large scorpion scuttles out and he smacks it with his hammer, laughing when I wince.
Later, reading in my study, I see a tiny scorpion crawling up the pale yellow wall. Usually, I trap them in a glass and escort them outside; this one I just let crawl along the wall. From here, the stone tapping of three masons takes on a strange, almost Eastern rhythm. It's hot, so hot I want to run from the sun, as from a rainstorm. I'm reading about Mussolini. He collected wedding rings from the women of Italy to finance his Ethiopian war, only he never melted them down. Years later, when he was caught trying to escape, he still had a sack of gold rings. In one photo, he has popping eyes, distorted hairless skull, set jaw. He looks demented or like Casper the ghost. The _chink, chink_ sounds like a gamelan. In the last photo, he's hanging upside down. The caption says a woman kicked him in the face. I'm sleepy and imagining the men in an Indonesian dance with Il Duce downstairs.
THE MOUNTAIN OF STONE ON EITHER SIDE OF THE DOOR grows daunting. We must get a start on moving it. Stanislao, our Polish worker, comes at dawn. At six, Francesco Falco's son Giorgio arrives with his new plow, ready to ply the olive terraces, and Francesco follows shortly on foot. As usual, he has his cutting tool, a combination machete and sickle, stuffed into his pants in back. He prepares to help Giorgio by clearing stones from the path of the tractor, holding aside branches, and smoothing out the ground. But our pitchfork is wrong. "Look at this." He holds it out, prongs up, and it quickly turns over, prongs down. He hammers the metal until it separates from the handle, turns the handle, then reattaches it. He then holds out the pitchfork, which does not flip over. We've used the pitchfork a hundred times without noticing but, of course, he's right.
"The old Italians know everything," Stanislao says.
Wheelbarrow after wheelbarrow, we haul stone to a pile out on one of the olive terraces. I lift only the small and medium stones; Ed and Stanislao wrestle with the giants. Low-impact aerobics video, eat your heart out. Drink eight glasses of water a day? No problem, I'm parched. At home, in my burgundy leotard, I lift and lift, and one and two, and lift . . . but this is work versus workout. Bend and stretch—easy when I'm clearing a hillside. Whatever, I'm worn out by this labor and I also like it tremendously. After three hours, we've moved about one fourth of the stones. _Madonna serpente!_ Don't try to calculate how many more hours we're in for—and all the really huge stones are in the other pile. Dirt and sweat run down my arms. The men are bare-chested, smelly. My damp hair is clotted with dust. Ed's leg is bleeding. I hear Francesco above us on a terrace talking to the olive trees. Giorgio's tractor tilts amazingly on one of the narrow terraces but he is too skilled to come tumbling down the mountain. I think of the long, melting bath I will take. Stanislao begins to whistle "Misty." One stone they can't budge is shaped like the enormous head of a Roman horse. I take the chisel and start to work on eyes and mane. The sun wheels in great struts across the valley. Primo hasn't seen us at hard labor. He's shouting at his men about it. He has worked on many restorations. The foreign _padrone,_ he says, only stands and watches. He poses with his hands on his hips, a curled lip. As for a woman working like this, he raises his arms to heaven. Late in the afternoon, I hear Stanislao curse, _"Madonna sassi,"_ Madonna-stones, but then he goes back to whistling his theme song, "It's cherry pink and apple blossom white when you're in love . . ." The men come down and we drink beer on the wall. Look at what we've done. This is really fun!
THE WHITE TRUCK IS BACK, DELIVERING SAND FOR PLASTER—plaster, they are nearing the end—and hauling away a mound of rubble. The three workers shout about the World Cup soccer matches taking place in the United States, about ravioli with butter and sage, about how long it takes to drive to Arezzo. Thirty minutes. You're crazy, twenty.
Claudio, the electrician, arrives to reroute the plait of dangling wires that somehow provides electricity for that section of the house. He has brought his son Roberto, fourteen, who has continuous, glorious eyebrows and almond-shaped Byzantine eyes that follow you. He is interested in languages, his father explains, but since he must have a practical trade, he is trying to train him this summer. The boy leans indolently against the wall, ready to hand tools to his father. When his father goes out to the truck for supplies, he grabs the English newspaper that protects the floor from paint and studies it.
Canals for wire must be dug in the stone walls before the plastering. The plumber must move the radiator we had installed when the central heating went in. I've changed my mind about the location. So much action. If they hadn't had days of excavating those levels of stone floor, the primary work would be finished. The Poles, who were in Italy working the tobacco fields, now have gone home. Only Stanislao stayed. Who will move all those great stones? Before the masons leave, they show us a neatly woven swirl of grass and twig they found in the wall, a _nido di topo,_ so much nicer in Italian than rat's nest.
They're slinging the base for the plaster, literally slinging so it sticks to the wall, then smoothing it out. Primo brought old _cotto_ for the floor from his supply. Between his and ours, we must have enough. Since the floor is last, surely we're nearing the end. I'm ready for the fun part; it's hard to think of the furniture when the room looks like a gray solitary confinement space. Finally, we're treated to the first machine noise of the project. The electrician's son, with some uncertainty, attacks the walls with a drill, making channels for the new wiring. The electrician himself left, after receiving a shock when he touched one of the frayed wires. These _must_ be among the sorriest wires he's ever come across.
The plumber who installed the new bath and the central heating sends out two of his assistants to move the radiator pipes they disconnected last week. They, too, are extremely young. I remember that students not on an academic track finish school at fifteen. Both are plump and silent but with ear-to-ear grins. I hope they know what they're doing. Everyone talks at once, most of them shouting.
Maybe all will come together quickly now. At the end of each day, Ed and I drag in yard chairs and sit in the new room, trying to imagine that soon we will sit there with coffee, perhaps on a blue linen loveseat with an old mirror hanging above it, music playing, discussing our next project. . . .
BECAUSE THE UNDERCOAT FOR THE PLASTER HAS TO DRY, Emilio is working alone, scratching off the old plaster in the back stairwell, carting off fuming loads of it to the rubble mountain.
The electrician can't finish until the plaster is on. I can see the boon of the invention of wallboard. Plastering is an arduous business. Still, it's fun to see the process, which hardly has changed since the Egyptians slathered the tombs. The plumber's boys didn't cut off the water line as far back as they should have and we have to call them to come back. To escape, we drive over to Passignano and have an eggplant pizza by the lake. The five-day estimate! I'm longing for days of _dolce far niente,_ sweet to do nothing, because in seven weeks, I must go back. I hear the first cicada, the shrill yammering that alerts us that deep summer is here. "Sounds like a duck on speed," Ed says.
Saturday, and a scorcher. Stanislao brings Zeno, who recently arrived from Poland. They dispense with shirts right away. They're used to heat; both are laying pipes for methane during the week. In less than three hours, they've hauled away a ton of stone. We've separated the flat ones for paths and for large squares of stone around each of the four doors along the front to prevent tracking in. They set to work after lunch digging, laying a sand base, chipping and fitting stone, filling in the cracks with dirt. They easily pull up the puny semicircles we laid out last year from stones we found on the land. The stones from the floor they're choosing are as big as pillows.
I'm weeding when I brush my arms against a patch of nettles. Those plants are fierce. They "sting" immediately, the hairy leaves letting out an irritating acid on contact. Odd that the tiny ones are good in risotto. I run in the house and scrub down with a skin disinfectant but my arms feel alive, as though hot electric worms are crawling on me. After lunch, I decide to bathe, put on my pink linen dress, and sit on the patio until the shops open. Enough work. I find a breeze there and pleasantly waste the afternoon looking at a cookbook and watching a lizard, who appears to be watching a parade of ants. It's a magnificent little creature in sparkling green and black with deft and intricate feet, palpitating throat, and an inquisitive head that jerks. I would like for it to crawl on my book so I could see more, but my every move sends it scuttling. It keeps coming back to look over the ants. What the ants watch, I don't know.
In town, I buy a white cotton dress, navy linen pants and shirt, some expensive body cream, pink nail polish, a bottle of great wine. When I get back, Ed is showering inside. The Poles have slung the hose over a tree limb and opened the nozzle to spray. I glimpse them stripping down for a rinse-off before changing their clothes. The four doorways are now protected by well-fitted entrances of stone.
FRANCO BEGINS THE SMOOTH FINAL COAT OF PLASTER. THE owner of the plumbing company, Santi Cannoni, arrives in blue shorts to inspect the work his boys have done. We have known him since his company installed our central heating—but only fully dressed. He looks as though he simply forgot his pants. His hairless, moon-white legs so far below his pressed shirt, distinguished tanned face, and gray coifed hair keep drawing my eye. That he has on black silky socks and loafers contributes to his obscene look of undress. Since his boys moved the radiator, the one in the next room has begun to leak.
Francesco and Beppe pull up in the Ape with their weed machines, ready to massacre wild roses and weeds. Beppe speaks clearly and we understand him better, mainly because Francesco still refuses to wear his teeth. Since he loves to talk, he gets mad when Beppe interprets for him. Naturally, when Beppe sees that we don't understand, he explains. Francesco starts calling Beppe _maestro,_ teacher, with heavy sarcasm. They argue about whether Ed's blades need to be sharpened or turned over. They argue about whether the stakes in the grape stones should be iron or wood. Behind Beppe's back, Francesco shakes his head at us, eyes turned to heaven: Can you believe this old coot? Behind Francesco's back, Beppe does the same.
A load of sand arrives for the floor but Primo says his old bricks are not the same size as ours and that he must locate another fifty before the floor can be laid.
_Piano, piano,_ the watchword of restoration, slowly, slowly.
More plastering. The mixture looks like gray gelato. Franco says he has a tiny old house and it's all he wants; these big houses, always something wrong. He patches the walls upstairs that cracked when the living room stones were removed, and I ask him to break the plaster and look at what holds up the doors Benito reopened. He finds the original long stones. No sign of the steel I-beams he was supposed to install. Franco says not to worry, stone is just as good on a regular-sized door.
The walls look dry to me but not to them. Another day off. We're anxious to get in there, scrub down the walls, stain the beams, scrape and paint the brick ceiling. We're ready, past ready, to move in. Four chairs have gone to the upholsterer with yards of blue and white checked linen my sister sent for two, and a blue and yellow striped cotton I found in Anghiari for the others. We have ordered the blue loveseat and two other comfortable chairs. The CD player has been in a pile of boxes and books, the chairs and bookcase stuffed into other rooms. Will this go on forever?
During the Renaissance, it was a custom to open Vergil at random and place a finger on a line that would foretell the future or answer a burning question. In the South, we used to do this with the Bible. People always have had ways to grasp for revelation: The Etruscans' haruspication, reading omens from sacrificed animals' livers, is no stranger than the Greeks' finding significance in the flight patterns of birds and the droppings of animals. I open Vergil and put my finger down on "The years take all, one's wits included." Not very encouraging.
TUSCANY IS A XERIC LAND IN SUMMER BUT THIS YEAR IT IS deeply green. From the patio the terraces seem to ripple down the hill. No use moving today. Under the barbed sun, I'm reading about saints, admiring especially Giuliana Falconieri, who asked, when dying, to have the host placed on her breast. It dissolved into her heart and disappeared. A pheasant is pecking away at my plot of lettuces. I read on about Colomba, who ate only hosts, then vomited them into a basket, which she stored under her bed. I'm enchanted with Veronica, who chewed five orange seeds in memory of Christ's five wounds. Ed brings up enormous sandwiches and iced tea with a little peach juice in it. I'm progressively more fascinated with the women saints, their politics of denial. Perhaps it's a corrective for the voluptuousness of Italian life. There's always a mystery within a sudden attraction to a subject. Why is one suddenly lugging home four books on hurricanes or all the operas of Mozart? Later, much later sometimes, the reason for the quest emerges. What will I come to realize from these quirky women?
Primo arrives with still more old bricks and Fabio starts cleaning them. He's working in spite of toothache and shows us the rotting lower left area of his mouth. I bite my lip to keep from looking startled. He's having four pulled next week, all at once.
Primo's tools for laying out the floor are some string and a long level. His skill is sure and quick; he knows instinctively where to tap, what fits where. After all the stone is hauled out, the floors between the two rooms are almost even; he builds in a slight rise, barely noticeable, in the doorway. They begin tamping down and leveling. Fabio cuts through bricks with a high wheezing machine that sends up a cloud of red dust. His arms are brick-colored up to his elbows. Laying brick looks fun. Soon the floor is down, matched to the interlocking L pattern of the adjoining room.
Houseguests arrive, despite the plastic-covered piles of lamps, baskets, books in the hallways, the living room furniture scattered around the house. Simone, a colleague of Ed's, is celebrating her Ph.D. with a trip to Greece, and Barbara, a former student who is just finishing a two-year stint in Poland with the Peace Corps, is en route to Africa. I suppose Italy always has been a crossroads. Pilgrims to the Holy Land skirted Lake Trasimeno in the Middle Ages. Latter pilgrims of all sorts traverse Italy; our house is a good spot to rest for a few days. Madeline, an Italian friend, and her husband, John, from San Francisco are coming for lunch.
We're running back and forth between guests and decisions that need to be made. The workers are finishing today! The well-timed lunch is a double celebration. We've ordered _crespelle_ from Vittorio, who makes fresh pasta in town. His crÊpes are air. Though we are only six, we've ordered a dozen each of the _tartufo_ (truffle), the pesto, and, our favorite, _piselli e prosciutto_ (peas and cured ham). Before that, _caprese_ (tomato, mozzarella, and basil salad dribbled with oil) and a platter of olives, cheeses, breads, and slices of various local salami. We're able to make the salad from the arugula in our garden. The wine we bought at Trerose, a chardonnay called Salterio, may be the best white I've tried in Italy. Many chardonnays, especially California ones, are too oaky and syrupy for my taste. This one has a peach-tinged, flinty taste with just a faint hint of oak.
The long table under the trees is set with yellow checked linen and a basket of sun-colored broom. We offer wine to the workmen but no, they're pressing into the final hours. They've spread cement over the floor to fill in the narrow cracks between bricks. To clean up, they wash down the floor, then sprinkle sawdust and sweep. They build two columns against the outside of the house for the stone sink we discovered in the dirt. It has rested these two years in the old kitchen. Primo calls to Ed to help move the monstrous stone. Two men "walk" it across the front terrace and up the three steps into the shady area where we are having lunch. Our guest, John, jumps up to help. Five men lift. _"Novanta chili, forse cento,"_ Primo says. The sink weighs around two hundred pounds. After that, they load their _cristi,_ their tools, and that's it—the room is finished. Primo stays to make a few repairs. He takes a bucket of cement and patches minor cracks in the stone wall, then goes upstairs to secure a few loose floor tiles.
Doesn't everything reduce in the end to a poetic image—one that encapsulates an entire experience in one stroke?
Not only this project but the whole major restoration that has stretched over three years is ending today. We're entertaining friends in the sun-dappled bower, just as I envisioned. I go into the kitchen and begin arranging a selection of local cheeses on grape leaves. I'm flushed and excited in my white linen dress with short sleeves that stand out like little wings. Above me, Primo is scraping the floor. I look up. He has removed two tiles and there is a hole in the ceiling. Just as I look back at my cheese platter, Primo accidentally kicks over his bucket and cement pours onto my head! My hair, my dress, the cheese, my arms, the floor! I look up and see his startled face peering down like a cherub in a fresco.
The humor is not entirely lost on me. I walk out to the table, dribbling cement. After dropped jaws and stunned looks, everyone laughs. Primo runs out, hitting the heel of his hand to his forehead.
The guests clear up while I shower. With Primo, they're all sitting along the sun-warmed wall when I come down. Ed is asking about Fabio's dental surgery. He only missed two days of work and will get new teeth in a month. Now Primo _will_ join us in a toast. The guests are toasting an amusing day and the end of the project. Ed and I, having been literally doused in this restoration, raise our glasses, too. Primo just enjoys himself. He launches into a history of his own teeth and shows us big gaps in his mouth. Five years ago he had such a toothache—he holds his head and leans over moaning—that he pulled out his own tooth with the pliers. _"Via, via,"_ he shouts, motioning the tooth out of his jaw. _Via_ somehow sounds more emphatic than "go."
I DON'T WANT HIM TO GO. HE HAS BEEN SUCH A CHARMER and so careful as a _muratore._ The work is impeccable as well as miraculously reasonable. Yes, I do want him to go! This project was estimated to last five working days; this is day number twenty-one. No way, of course, to predict three levels of stone floor and a rotten beam. He'll be back next summer—he will retile the butterfly bathroom and repoint the stones in the cantina. He hoists his wheelbarrow into the Ape. Those are small projects, _cinque giorni, signori,_ five days. . . .
Relics of Summer
THE FONTS IN ALL THE CHURCHES ARE DRY. I run my fingers through the dusty scallops of marble: not a drop for my hot forehead. The Tuscan July heat is invasive to the body but not to the stone churches that hold on to the dampness of winter, releasing a gray coolness slowly throughout the summer. I have a feeling, walking into one, then another, that I walk into palpable silence. A lid seems to descend on our voices, or a large damp hand. In the vast church of San Biagio below Montepulciano, there is an airy quiet as you enter. Right under the dome, you can stand in one spot and speak or clap your hands and far up against the inner cup of the dome an eerie echo sends the sound rapidly back. The quality of the sound is not like the hello across a lake but a sharp, repeated return. Your voice flattened, otherworldly. It is hard to think a mocking angel isn't hovering against the frescoes, though more likely a pigeon rests there.
Since I have been spending summers in Cortona, the major shock and joy is how at home I feel. But not just at home, _returned_ to that primal first awareness of home. I feel at home because dusty trucks park at intersections and sell watermelons. The same thump to test for ripeness. The boy holds up a rusty iron scale with discs of different sizes for counterweight. His arm muscle jumps up like Popeye's and the breeze brings me a whiff of his scent of dry grasses, onions, and dirt. In big storms, lightning drives a jagged stake into the ground and hailstones bounce in the yard, bringing back the smell of ozone to me from Georgia days when I'd gather a bowlful the size of Ping-Pong balls and put them in the freezer.
Sunday is cemetery day here, and though our small-town Southern plots are austere compared to these lavish displays of flowers on almost every grave, we, too, made Sunday pilgrimages to Evergreen with glads or zinnias. I sat in the backseat, balancing the cool teal vase between my knees while my mother complained that Hazel never turned her hand to pick one stem and it was _her_ own mother lying there, not just a mother-in-law. Gathered around Anselmo Arnaldo, 1904–1982, perhaps these families are saying, as mine did, Thank God the old goat's lying here rather than still driving us crazy.
Sweltering nights, the air comes close to body temp, and shifting constellations of fireflies compete with stars. Mosquito nights, grabbing at air, the mosquito caught in my hair. Long days when I can taste the sun. I move through this foreign house I've acquired as though my real ancestors left their presences in these rooms. As though this were the place I always came home to.
Living near a small town again certainly is part of it. And living again with nature. (A student of mine from Los Angeles visited. When I walked him out to the end of the point for the wide-angle view of lake, chestnut forests, Apennines, olive groves, and valleys, he was unprepared. He stood silently, the first time I'd known he could, and finally said, "It's, uh, like nature.") Right, nature: Clouds swarm in from over the lake and thunder cracks along my backbone, booms like waves boom far out at sea. I write in my notebook: "The dishwasher was struck. We heard the sizzle. But isn't it good, the gigantic storm, the flood of terror they felt beside fires in the cave? The thunder shakes me like a kitten the big cat has picked up by the neck. I ricochet home, heat lightning; I'm lying on the ground four thousand miles from here, letting rain soak through me."
Rain flays the grapes. Nature: What's ripe, will the driveway wash away, when to dig potatoes, how much water is in the irrigation well? Early life reconnects. I go out to get wood; a black scorpion scuttles over my hand and suddenly I remember the furry tarantulas in the shower at Lakemont, the shriek when my barefooted mother stepped on one and felt it crunch, then squash up soft as a banana between her toes.
Is it the spill of free days? I dream my mother rinses my tangle of hair with a bowl of rainwater.
Sweet time, exaggerated days, getting up at dawn because when the midsummer sun tops the crests across the valley, the first rays hit me in the face like they strike some rock at Stonehenge on the solstice. To be fully awake when the sky turns rose-streaked coral and scarves of fog drift across the valley and the wild canaries sing. In Georgia, my father and I used to get up to walk the beach at sunrise. At home in San Francisco what wakes me is the alarm at seven, or the car pool horn blowing for the child downstairs, or the recycle truck with its crashing cascade of glass. I love the city and never have felt really at home there.
I was drawn to the surface of Italy for its perched towns, the food, language, and art. I was pulled also to its sense of lived life, the coexistence of times that somehow gives an aura of timelessness—I toast the Etruscan wall above us with my coffee every morning—all the big abstracts that act out in everything from the aggression on the _autostrada_ to the afternoon stroll through the piazza. I cast my lot here for a few short months a year because my curiosity for the layered culture of the country is inexhaustible. But the umbilical that is totally unexpected and elides logic reaches to me through the church.
To my surprise I have bought a ceramic Mary with a small cup for home use of holy water. As a fallen-away Methodist, then a fallen-away Episcopalian, I suppose my holy water is a sham. However, I have taken it from the spring I discovered near the house, the artesian spring where clear water rises in a declivity of white stone. This looks like holy water to me. It must have been the house's original source. Or it's older than the house—medieval, Roman, Etruscan. Though some interior juggling is going on, I do not expect to emerge as a Catholic, or even as a believer. I am essentially pagan by birth. Southern populism was boiled into my blood early; the idea of a pope with the last word gives me hives. "Idolatrous," our minister called the worship of Mary and the saints. "Mackerel snapper," my classmates teased Andy Evans, the lone Catholic in our school. Briefly, in college, I was drawn to the romance of the Mass, especially the three A.M. fishermen's Mass in St. Louis's Cathedral in New Orleans. I lost interest in the whole show when my good friend, a New Orleans Catholic, told me in complete seriousness that mortal sin began if you kissed longer than ten seconds. A ten-second French kiss was O.K., but a dry twenty-second kiss would land you in trouble. Though I still like rituals, even empty ones, what magnetizes me here feels more radical.
Now I love the quick Mass in tiny upper Cortona churches, where the same sounds have provided a still point for the residents for almost eight hundred years. When a black Labrador wandered in, the priest interrupted his holy spiel to shout, "For the love of God, somebody get that dog out of here." If I stop in on a weekday morning, I sit there alone, enjoying the country Baroque. I think: _Here I am._ I love the parade of relics through the streets, with gold-robed priests travelling along in a billow of incense, their way prepared by children in white, scattering the streets with petals of broom, rose, daisy. In the noon heat, I almost hallucinate. What's in the gold box held aloft with banners—a splinter from the cradle? Never mind we thought Jesus was born in a lowly manger; this is the splinter of the true cradle. Or am I confused? It's a splinter of the true cross. It is on its way through the streets, brought out into the air one day a year. And suddenly I think, What did that hymn mean, _cleft for me,_ rising years ago, perpendicular from the white board church in Georgia?
IN MY SOUTH, THERE WERE SIGNS ON TREES THAT SAID "repent." Halfway up a skinny pine, up beyond the tin trough that caught the resin, hung a warning, "Jesus is coming." Here, when I turn on the car radio, a lulling voice implores Mary to intercede for us in purgatory. In a nearby town, one church has as its relic a phial of Holy Milk. As my student would say, that's from, like, Mary.
On the terrace at noon, I'm tanning my legs as I read about early martyrs and medieval saints. I'm drawn to the martyred San Lorenzo, who was put on a grill for his troublesome faith and seared until he reportedly said, "Turn me over, I'm done on this side," and thereby became the favorite saint of chefs. The virginal young women martyrs all were raped, stabbed, tortured or locked away because of their devotion to Christ. Sometimes the hand of God reached down and swept one away, like Ursula, who did not wish to marry the barbarian Conan. With her ten thousand virgins (all avoiding men?) loaded into boats, she was lifted miraculously by God and sailed across the unfriendly skies, then deposited in Rome, where they all bathed in lime-scented water and formed a sacred order. Stunning, the prevalence of the miracle. In the Middle Ages, some of the venerated women found the foreskin of Jesus materialized in their mouths. I don't know if there exists a relic of that. (Would it look like a chewed rubber band? A dried wad of bubble gum?) The foreskin stops me for a good ten minutes and I stare out at the bees swarming the _tigli_ trees, trying to imagine that event happening, and not just once. The moment of recognition, what she said, what the reaction was—a boggling speculation. Somehow, I'd never heard of these kinkier saints in America, although someone once sent me a box of new books, each one about a saint's life. When I called the bookstore, they told me my benefactor wished to remain anonymous. Now I read on and find that some had "holy anorexia" and lived on the wafer alone. If a saint's bones were dug up, a flowery fragrance filled the town. After Saint Francis preached to the birds, they flew up into the shape of a cross then separated into the four directions. The saints would eat the pus and lice of the poor to show their humility; in turn, the faithful liked to drink the bathwater of a holy person. If, after a death, a saint's heart was cut out, perhaps an image of the Holy Family carved in a ruby would be found inside. _Oh,_ I realize, _here's where they put their awe. I understand that._
I understand because this everyday wildness and wonder come back so naturally from the miracle-hungry South. They almost seem like memories somehow, the vertebrae of the Virgin, the toenail of San Marco. My favorite, the breath of San Giuseppe, foster father of Christ. I imagine an opaque green glass bottle with a ground stopper, the swift exhaling of air as it opened. At home when I was small, our seamstress kept her jar of gallstones on the windowsill above her Singer. Marking my hem, her mouth full of pins, she'd say, "Lord, I don't want to go through nothing like that again. Now you turn round. Those things won't even dissolve in gasoline." Her talisman against sickness. Emblems and omens.
Santa Dorotea immured in her cell for two years, against a high-walled pit in the dank cathedral. Communion through a grate and a diet of bread and gruel. I hated visiting Miss Tibby, who treated the corns on my mother's little toes, shaving yellow curls of skin off with a vegetable peeler, then rubbing her feet with thick lotion that smelled like crank case oil and Ovaltine. The bare bulb lit not only my mother's foot on a cushion but also a coffin where Miss Tibby slept at night so there would be no surprises later.
In high school my friends and I parked a block away and secretly peered in the windows of the Holy Rollers, who spoke in tongues, sometimes screaming with a frightening ecstatic look on their faces and falling to the floor writhing and jerking. We were profane, smothering our laughter at the surely sexual fervor and the contorted postures. Later we'd sit in the car, Jeff smoking, and watch them file out of the peeling church, looking as normal as anyone. In Naples, the phial of San Gennaro's congealed blood liquifies once a year. There's also a crucifix that used to grow one long hair of Jesus that would have to be barbered once a year. That one seems particularly close to Southern sensibilities.
In the United States, I think there is no _sanctioned_ place to put such fixated strangeness so it just jumps out when it has to. Driving through the South recently, I stopped near Metter, Georgia, for a barbecue sandwich. After the sweet salty pork and iced tea, I was directed out back to the bathroom by the owner; pork-bellied, sweating over his pit, he merely nodded toward the rear. No sign at all that as I opened the screen door I would encounter two molting ostriches. How they came to be in that remote town in South Georgia and what iconographical necessity led the family to gaze on and house these dusty creatures is a philosophical gift I've been given to ponder in nights of insomnia.
Growing up in the God-fearing, faith-healing, end-of-the-world-is-at-hand South gave me many chances to visit snake collections beside gas stations when my parents stopped to fill up; to drive past roadside religious ceremonies in which snakes were ecstatically "handled"; to see shabby wonders-of-the-world exhibits—reliquaries of sorts—in the towns bordering the swamps. I know a box of black cat's bones makes a powerful conjure. And that a bracelet of dimes can ward it off. I was used to cages of baby alligators crawling on the back of the mother of all, a fourteen-foot beauty who opened her jaws wide enough that I could have stood in them. The sagging chicken-wire fences couldn't save you if those sleeping logs rose up and decided to take off after you—alligators can run seventy miles an hour. Albino deer covered with ticks that leapt on my hand when I petted their mossy noses, a stuffed painter (panther) with green marbles for eyes, a thirty-foot tapeworm in a jar. The owner explains that it was taken from the throat of his seventeen-year-old niece when the doctor lured it out of her stomach with a clove of garlic on a toothpick. They waited until it showed its head, lured it out further, then grabbed, chopped off its head with a straight razor while hauling the thing out of Darleen's stomach like a rope out of the river.
Wonders. Miracles. In cities, we're less and less capable of the imagination for the super real, ground down as we are by reality. In rural areas, close to the stars and groves, we're still willing to give it a whirl. So I recover the cobra, too, so much more impressive with his flattened head than rattlesnakes, whose skins paper the office of the owner of the Eighth Wonder of the World, where we have stopped for gas at the Georgia border. We are close to Jasper, Florida, where my mother and father were married in the middle of the night. I am amazed, despite my mother's warning that the owners are carnival people and it is not worth seeing and I have exactly ten minutes or they will go on to White Springs without me. The slight thrill at the possibility of being left behind on this curve of road lined with moss-draped oaks, the silverbullet trailer set up on concrete blocks, a woman glimpsed inside, washing her hair over a tin bowl and the radio blaring "I'm So Lonesome I Could Cry." I knew then and still know that the man with the phosphorescent glow-in-the-dark torch tattooed on his back and the full-blown roses tattooed on his biceps believed his wonders were real. I follow him to the bamboo hut, where the cobra from darkest Calcutta rises to the song made by blowing on a comb covered with cellophane. The cobra mesmerizes the mangy dog thumping his tail in the doorway. The peacock gives a powerful he-haw, shakes himself into full regalia, the blues in his fan of feathers more intense than my own or my mother's eyes, and, as everyone knows, we have the purest sky-blue eyes. The peacock's eyes look exactly like the snake's. The owner's wife comes out of the trailer with a boa constrictor casually draped around her neck. She checks on another snake, to whom she has fed a large rat without even cutting it up. The rat is simply disappearing, like a fist into a sweater sleeve. I buy a Nehi and an oatmeal cookie sandwich, run out to the Oldsmobile vibrating in the heat. My father scratches off; gravel spumes behind us. "What have you got?" My mother turns around.
"Just a cold drink and this." I hold up the large cookie.
"Those things have lard in the middle. That's not icing—that's pure-T lard with enough powdered sugar to make your teeth crack."
I don't believe her but when I break open the cookie, it is crawling with maggots. I quickly throw it out the window.
"What did you see in that awful gyp joint?"
"Nothing," I answer.
Growing up, I absorbed the Southern obsession with place, and place can seem to me somehow an extension of the self. If I am made of red clay and black river water and white sand and moss, that seems natural to me.
However, living as a grown woman in San Francisco, I never have that belonging sensation. The white city with its clean light on the water, the pure, heart-stopping coast, and the Marin hills with the soft contours of sleeping giants under blankets of green—I am the awed tourist, delighted to have made this brief escape, which is my adult life. My house is just one of thousands; my life could be just another story in the naked city. My eye looks with insouciance at the scissors point of the Transamerica pyramid and jagged skyline I can see from my dining room window. Everyone seems to have cracked the door two inches to see who's there. I see you through my two inches; you see me through yours. We are monumentally self-reliant.
I NEVER TIRE OF GOING INTO ITALIAN CHURCHES. THE vaulted arches and triptychs, yes. But each one also has its characteristic blue dust smell, the smell of time. The codified Annunciations, Nativities, and Crucifixions dominate all churches. At the core, these all struggle with the mystery of the two elementals—birth and death. We are frangible. In the side altars, the high arches, the glass manuscript cases in the crypts, the shadowed curves of the apse, these archetypal concerns and the dreamland of religious fervor lock horns with the painterly subject matter in individualized ways. I'm drawn to a bizarre painting that practically leaps off the wall. In a dark, high panel close to the ceiling in San Gimignano, there's Eve rising boldly out of supine Adam's open side. Not the _whoosh_ of instantaneous creation I've imagined from reading Genesis, when she appeared as easily as "Let there be Light." This is graphic, someone's passion to be _present_ at the miracle. As graphic as the wondrous cobra of Calcutta spiraling up in the humid air of South Georgia before my very eyes. Adam is meat. The vision grabs the viewer like the glow-in-the-dark torch. Now hear this, loud and clear. In Orvieto's Duomo, Signorelli's humans, just restored to their flesh on Judgment Day, stand grandly and luxuriously beside the grinning skeletons they were just moments before. Parts of the body still glow with the aura of the bare bone, a gauzy white light emanating from the firm, new flesh in its glory. A strange turn—we're used to thinking of the decay of the flesh; here's the dream of rejuvenation. Flitting around in the same arena of that cathedral are depictions of hell, green-headed devils with snaky genitals. The damned are twisted, poked, jabbed, while one voluptuous blonde (no doubt what _her_ sins were) flies away on the back of a devil with stunted, unaerodynamic wings. Clearly we are in someone's head, midnight imaginings of the descent, the fall, the upward turn. The paintings can be sublime but there is a comic book aspect to much church painting, a wordless progression of blunt narrative very close to those of fire-and-brimstone fundamentalists who still hold forth in the South. If there was more than one word, Repent, hanging on those Southern pines, it was bound to be Doomsday.
Wandering around in churches, I see over and over San Sebastiano pierced with arrows, martyred Agata holding out her breasts on a plate like two over-easy eggs, Sant'Agnes kneeling piously while a lovely youth stabs her in the neck. Almost every church has its locked relic box like a miniature mausoleum, and what does this mean? Thorn from the crown. Finger digits of San Lorenzo. The talismans that say to the viewers, "Hold on; like these, have faith." Standing in the dim crypt in a country church where a handful of dust has been venerated for several hundred years, I see that even today, toward the end of the century, the case is remembered with fresh carnations. I uncover my second realization: _This is where they put their memories and wants._ Besides functioning as vast cultural repositories, these churches map intimate human needs. How familial they begin to seem (and how far away from the historical church, the bloody history of the Papacy): the coarse robe of St. Francis, another phial of Mary's, this one filled with tears. I see them like the locket I had, with a curl of light brown hair, no one remembered whose, the box of rose petals on the closet shelf behind the blue Milk of Magnesia bottle and the letters tied with frayed ribbon, the translucent white rock from Half Moon Bay. _Never forget._ As I wax the floor tiles and wring out the mop, I can think of Santa Zita of Lucca, saint of housekeeping, as was Willie Bell Smith in my family's house. Basketmaker, beggar, funeral director, dysentery sufferer, notary, speleologist—everyone has a paradigm. _I once was lost but now I'm found._ The medieval notion that the world reflects the mind of God has tilted in my mind. Instead, the church I perceive is a relief map of the _human_ mind. A thoroughly secular interpretation: that _we_ have created the church out of our longing, memory, out of craving, and out of the folds of our private wonders.
If I have a sore throat from drinking orange juice when I know I'm allergic to it, the saint is there in his monumental church at Montepulciano, that town whose syllables sound like plucked strings on the cello. San Biagio is a transubstantiated metaphor and a handful of dust in a wrought box. Its small keyhole reminds us of what we most want to be reminded of, _you are not out there alone._ San Biagio focuses my thoughts and throws me beyond the scratchy rawness of my own throat. _Pray for me, Biagio, you are taking me farther than I go._ When the TV is out of whack and the buttons won't improve the picture, nor will slapping the side soundly, Santa Chiara is out here somewhere in saintland. _Chiara,_ clear. She was clairvoyant and from there is only a skip and jump to _receiver,_ to patron saint of telecommunications. So practical for such a transcendent girl. A statue of her on top of the TV won't hurt a thing. Next year on July 31, the wedding ring of Mary will be displayed in the Duomo in Perugia. The history says it was "piously stolen"—isn't that an oxymoron—from a church in Chiusi. Without a shred of literal belief, I, for one, will be there.
AT THE TOP OF THE STAIRS, I TOUCH THE SPRING WATER IN my ceramic Mary with my fingertip and make a circle on my forehead. When I was baptized, the Methodist minister dipped a rose in a silver bowl of water and sprinkled my hair. I always wished I'd been baptized standing knee deep in the muddy Alapaha, held under until the last moment of breath then raised to the singing congregation. My spring water in Mary's cup is not transformed to wash away my sins or those of the world. She always seems like _Mary,_ the name of my favorite aunt, rather than Santa Maria. Mary simply became a friend, friend of mothers who suffered their children's pain, friend of children who watched their mothers suffer. She's hanging over almost every cash register, bank teller, shot giver, bread baker in this town, and I've grown used to her presence. The English writer Tim Parks says that without her ubiquitous image to remind you that all will go on as before, "you might imagine that what was happening to you here and now was unique and desperately important . . . I find myself wondering if the Madonna doesn't have some quality in common with the moon." Yes. My unblessed water soothes. I pause at the top of the stairs and repeat the lovely word _acqua._ Years ago, the baby learned to say _acqua_ on the lake shore at Princeton, under a canopy of trees blooming madly with pink pompons. _Acqua, acqua,_ she shouted, scooping up water and letting it rain on her head. _Acqua_ sounds closer to the sparkle and fall, closer to wetness and discovery. Her voice still reverberates but now I touch my little finger as I remember. The gold signet ring, a family treasure, slipped off in the grass that day and was not to be found. _Water of life. Intimacy of memory._
_Intimacy._ The feeling of touching the earth as Eve touched it, when nothing separated her.
In paintings, the hilltop town rests in the palm of Mary's hand or under the shelter of her blue cloak. I can walk every street of my Georgia town in my mind. I know the forks in the pecan trees, the glut of water in the culverts, the hog pear in the alley. Often the Tuscan perched villages seem like large castles—extended homes with streets narrow as corridors, and the _piazze,_ like public receptions rooms, teeming with visitors. The village churches have an attitude of privacy; the pressed linen and lace altar cloths and scarlet dahlias in a jar could be in family chapels; the individual houses, just suites in the big house. I expand, as when my grandparents' house, my aunt's, my friends', the walls of home were as familiar to me as the lines in my own palm. I like the twisted streets up to the convent where I may leave a bit of lace to be mended on a Catherine wheel, spin it in to the invisible nun, whose sisters have tatted in this great arm of the castle for four hundred years. I do not glimpse even the half moons of her nails or the shadow of her habit. Outside two women who must have known each other all their lives sit in old wooden chairs between their doorways and knit. The stony street slopes abruptly down to the town wall. Beyond that stretches the broad valley floor. Here comes a miniature Fiat up this ridiculously steep street no car should climb. Crazy. My father would drive through swollen streams that flooded sudden dips in the dirt roads. I was thrilled. While he laughed and blew the horn, water rose around the car windows. Or was the water really that high?
We can return to live in these great houses, unbar the gates, simply turn an immense iron key in the lock and push open the door.
Solleone
SOLLEONE. HOW USEFUL THE -ONE SUFFIX in Italian; the noun expands. _Porta,_ door, becomes _portone,_ and there's no doubt which is the main door. _Torre_ becomes _torreone,_ the name of our part of Cortona, where a great tower must have stood once. _Minestrone,_ then, always is a big soup. Days of the sun in Leone (Leo): _Solleone_ —big sun. Dog days we called them in the South. Our cook told me the name was because it was so hot that dogs went mad and bit people and I would be bitten if I didn't mind her. Eventually, I was disappointed to find the name only meant that Sirius, the dog star, was rising and setting with the sun. The science teacher said Sirius was twice the size of the sun and I thought, secretly, that somehow the heat was augmented by that fact. Here, the expanded sun fills the sky, as in the archetypal child's drawing of house, tree, and sun. The cicadas are in the know—they provide the perfect accompaniment to this heating up. By dawn they're hitting their horizon note of high screech. How a finger-sized insect can make such a racket only by vibrating its thorax, I don't know. As they tune up to their highest pitch, it sounds as though someone is shaking tambourines made from the small bones of the ear. By noon, they've switched to sitars, that most irritating of instruments. Only the wind quiets them; perhaps they must hang on to a limb and can't clutch and vibrate at the same time. But the wind seldom blows, except for the evil appearance now and then of the _scirocco,_ which gusts but doesn't cool, while the sun roars. If I were a cat, I would arch my back. This hot wind brings particles of dust from the African deserts and deposits them in your throat. I hang out the clothes and they're dry in minutes. The papers in my study fly around like released white doves, then settle in the four corners of the room. The _tigli_ are dropping a few dry leaves and the flowers suddenly seem leached of color, although we have had enough rain this summer that we have been able to water faithfully every day. The hose pulls water directly from the old well and they must feel blasted at the end of the hot day by the rush of icy water. Perhaps this has exhausted them. The pear tree on the front terrace has the look of a woman two weeks overdue. We should have thinned the fruit. Branches are breaking under the weight of golden pears just turning ruddy. I can't decide whether to read metaphysics or to cook. The ultimate nature of being or cold garlic soup. They are not so far apart after all. Or if they are, it doesn't matter; it's too hot to think about it.
The hotter the day, the earlier I walk. Eight, seven, six o'clock, and even then I rub my face with number thirty sunblock. The coolest walks start at Torreone. A downhill road leads to Le Celle, a twelfth-century monastery where Saint Francis's minute cell still opens onto a seasonal torrential stream. Many of the first Franciscan monks who lived as hermits on Monte Sant'Egidio started Le Celle in 1211. The architecture, a stacked stone honeycomb up against the hillside, recalls their caves. When I walk there, peace and solitude are palpable. In early summer, the rush of water down the steep canyon makes its own music and sometimes, above that, I hear singing. By now the stream is almost dry. Their vegetable garden looks like a model. One of the Capuchin friars who lives there now trudges uphill barefooted toward town. He's wearing his scratchy brown robe and strange pointed white hat (hence cappuccino), using two sticks to pull himself along. With his white beard and fierce brown eyes, he looks like an apparition from the Middle Ages. When I pass him he smiles and says, _"Buon giorno, signora. Bene qua,"_ nice here, indicating the landscape with a rotation of his beard. He glides by, Father Time on cross-country skis.
But I take the slightly uphill road this morning, passing a few new houses, then a kennel, where dogs go into an uproar until I am about five feet beyond their pen; the road is then just a white track through pine and chestnut forests, no cars, no people. The shoulders look as though someone scattered one of those cans of native wildflowers seeds and they all took root, then flourished. I climb a hill to look at an abandoned house so old that it still has a thick slate roof. Brambles surround the doors and windows. I glimpse dark rooms with stone walls. In front, I look down on a 180-degree view of Cortona in profile and on the entire length of the Val di Chiana, a yellow and green patchwork of sunflower and vegetable fields. The upstairs must have a low ceiling, right for a crude bed made of chestnut limbs, a white goose-down quilt. The terrace should go there—in front of the lilac bushes. A pink rose still blooms its heart out without any care at all. Whose was it? The wife of a silent woodcutter who smoked his pipe and drank _grappa_ in the winter evenings when the _tramontana_ shook the windows on the back of the house? Perhaps she growled at him for sticking her so far in the country. No, she was content with her work embroidering the linens for the _contessa._
The house is small—but who would stay inside when there's a broad terrace overlooking the world? The waiting house: all potential. To see one and start dreaming is to imagine being extant in another version. Someone eventually will buy it and perhaps will run all over Tuscany looking for old slate to restore the roof authentically. Or the new owner might rip off the roof and put on flat new tiles. Whatever the predilections, the owner will respond to the aerie's isolation, that and the magnetic pull of the panorama, a place to linger and soothe the restless beast every day.
At the end of the road, a path through the woods leads to our favorite Roman road. I suppose it was laid by slaves. When I first heard about the Roman road near our house, I assumed it was unique. Not long after that I saw a rather thick book on the many Roman roads of this area. Walking alone, I try to think of chariots tearing down the hill, though the only thing I'm likely to meet is a _cinghiale,_ a wild boar, roaming around. One stream still has a trickle of water. Maybe a Roman messenger verging on heat stroke paused here and cooled his feet, as I do, when running south with news of how Hadrian's wall was coming along. There have been more recent visitors; on the grassy bank, I see a condom and a wad of tissue.
When I walk into town, I see a shriveled, pasty man who, clearly, is dying. He has been propped in the doorway with the sun fully on him, his last chance for revival. He spreads out his fingers on his chest, warming everything he can. He has enormous hands. Yesterday I received a shock so hard my thumb went numb for half an hour. I was trying to pull the cord that turns on the overhead light in my study from the inside of the radiator, where it somehow had fallen. The clicker I had hold of split, leaving me with my thumb on the hot wires, my other hand on the metal radiator. I screamed and jumped back. That mindless, animal feeling of shock—I wonder if the man in the doorway feels that way in the sun. His life force siphoning off, the great solar energy coming at him, filling him up. His wife sits beside him and appears to be waiting. She's not mending or pinching back her flowers. She's his guard for his trip to the underworld. Perhaps she'll dry his dead body, then anoint his bones with olive oil and wine. Or maybe the heat is getting to me, too, and he's just recovering from an appendectomy.
WE MUST GO TO AREZZO, ABOUT HALF AN HOUR AWAY, TO pay our insurance for next year. They seem to expect us to turn up rather than send a check. We park in the broiling train station lot. The station's full-sun digital thermometer-clock says it is 36°(97°F). After our pleasant interview with Signor Donati, an ice cream, a stop for Ed to buy a shirt at his favorite store, Sugar, and one for me to buy hand towels at my favorite shop, Busatti, we come back to the car and find the big 40 (104°) flashing over the car. The door handles appear to be on fire. The heat inside slams into us. We air out the car and finally get in. My eyelids and earrings are hot. Ed touches the steering wheel with his thumbs and index fingers. My hair seems to be steaming. Stores are closing; it's the hottest part of the hottest day of the year. At home, I lower myself into a cool bath, wet washcloth over my face, and just lie there until my body takes on the temperature of the water.
Siesta becomes a ritual. We pull in the shutters, leaving the windows open. All over the house, ladders of light fall across the floor. If I am mad enough to take a walk after one-thirty, no one is out, not even a dog. The word _torpor_ comes to mind. All shops close during the sacred three hours. If you need something for bee sting or allergy, too bad. Siesta is prime time for TV in Italy. It's prime time for sex, too. Maybe this accounts for the Mediterranean temperament versus the northern: children conceived in the light and children conceived in the dark. Ovid has a poem about siesta, written before the first millennium turned. He's lying relaxed in sultry summer, one shutter closed, the other ajar, "the half-light shy girls need," he wrote, "to hide their hesitation." He goes on to grab the dress, which didn't hide much. Well, everything is always new under the sun. Then, as now, a quick wash in the bidet and back to work.
What a marvelous concept. For three hours in the middle of the day, you are invited to your own interests and desires. In the good part of the day, too, not just the evening after an eight- or nine-hour day slogging away.
Inside the high-roomed, shuttered house, it's completely silent. Even the cicadas have quit. Peaceful, dreamy afternoon. Partly for the pleasure of my feet sliding on soothing _cotto_ floors, I walk from room to room. The classic look—I've seen it eleven times before and now I see it again in the new living room: dark beams, white brick ceiling, white walls, waxy brick floors. To my eye, the rugged textures and the strong color contrasts of the typical Tuscan house create the most welcoming rooms of any architectural style I know. Fresh and serene in summer, they look secure and cozy in winter. Tropical houses with bamboo ceilings and shuttered walls that open to catch every breeze, and the adobe houses of the Southwest, with their banquettes and fireplaces that are rounded like the curves of the human body, impart the same connected sense: _I could live here._ The architecture seems natural, as if these houses grew out of the land and were easily shaped by the human hand. In Italian, a coat of paint or wax is a _mano,_ a hand of that substance. Before the plastering started, I noticed Fabio's initials scratched in a patch of wet cement. The Poles, I remembered, wrote POLONIA at the base of the stone wall. I wonder if archaeologists find many reminders of the anonymous hands behind enduring work. On the wall of the prehistoric Pech Merle cave in France, I was stunned to see handprints, like ones children make in kindergarten, above the spotted horses. The actual "signature" of the preliterate artist outlined in blood, soot, ashes! When the great tombs of Egypt were opened, the footprints of the last person out before the entrances were sealed remained in the sand: the last work finished, a day's work over.
A butterfly, trapped inside, bats and bats the shutter but does not find the way out. As I fall asleep, the fan drones, a shimmering head looking left and right.
I LOVE THE HEAT. I LOVE THE EXCESSIVE INSISTENCE. SOMETHING in me says yes. Maybe it's only that I grew up in the South, but it feels like a basic yes, devolving back to those old fossil heads of the first people who came into being under a big sun.
The landscape appears cool although it's cooking. The terraces aren't bleached this year, as they sometimes are. Our view to the Apennines is green and forested. In someone's swimming pool at the bottom of the valley, I see a little stick figure jump in.
Since we're up high, nights cool off to a lovely softness. In late afternoon, heaps and piles of clouds cross over, their shadows roving across the green hills. Tonight the Perseids shower, it's San Lorenzo's night of the shooting stars—cause for a celebratory dinner. We've seen them before and we know the gasps, our quick pointing a second too late, the bright cascade of a meteor, so momentary, so long expired. The garlic soup, chosen over Boethius, is chilling in the fridge. Lemon and Basil Chicken, an accidental discovery, and a terra-cotta dish of Gratin Dauphinois, an old Julia Child potato favorite I've made for years, are ready to cook. I have enough ripe pears to peel and slice and improvise a mascarpone custard for them to bake into. I scrub the bird droppings off the yellow table, spread the cloth I made over the winter from leftover fabric I used for the wicker on my Palo Alto patio fifteen years ago. I spent days on the double welting around the cushion for the chaise longue. I could walk out of that dining room door right now, fluff those cushions, tell the dog "Down," walk into the yard filled with kumquat and loquat, mock orange and olive. Or could I? Everything stays. What chance, when I bought that yellow-flowered bolt at Calico Corners, to think it would end up on a table in Italy, with me in a new life.
Like fanning through a deck of cards, my mind flashes on the thousand chances, trivial to profound, that converged to re-create this place. Any arbitrary turning along the way and I would be elsewhere; I would be different. Where did the expression "a place in the sun" first come from? My rational thought processes cling always to the idea of free will, random event; my blood, however, streams easily along a current of fate. I'm here because I climbed out the window at night when I was four.
ALL THE SUMMER FRUITS OF THE GREAT MEDITERRANEAN SUN have ripened. Beginning with cherries when I arrive, the summer progresses to yellow peaches. Along the Roman road up Sant'Egidio, we pick handfuls of the most divine fruit of all, the minute wild strawberries that dangle like jewels under their jagged leaves. Then come the white peaches with pale and fragrant flesh. Gelato made of these makes you want to dance. Then the plums, all the varieties—the small round gold, the dusky purple-blue, and the pale green ones larger than golf balls. Grapes start to arrive from farther south. A few ruddy apples, then the first pears ripen. The small green ones couldn't be ripe but they are, then the globular speckled yellows. In August, the figs just start to plump up, not reaching their peak until September. But, finally, the blackberries, that heart-of-summer fruit, are ripe.
Days before I go home, at the end of August, I can take out my colander and pick enough for breakfast. Every morning the birds are wild for them but can't manage to eat quite all. Picking blackberries—a back-to-basics pleasure—passing over the ones still touched with a hint of red and those that squish to the touch, pulling off only the perfectly ripe ones until my fingers are rosy. The taste of sun-warmed berries brings me the memory of filling my jar with them in an abandoned cemetery. As a child, I sat down on a heaped mound of dirt, unconsciously eating luscious berries from a plant whose roots intertwined with old bones.
Bees burrow in the pears. Where they've fallen, thrushes feast. Who knows how the wants of our ancestors act out in us? The mellow scents somehow remind me of my mean Grandmother Davis. My father privately called her The Snake. She was blind, with Greek-statue eyes, but I always believed she could see. Her charming husband had lost all the land she inherited from her parents, who owned a big corner of South Georgia. On Sunday rides, she'd always want Mother to drive her by the property she'd lost. She couldn't see when we got there but she could smell peanut and cotton crops in the humid air. "All this," she'd mutter, "all _this."_ I'd look up from my book. The brown earth on either side of the car spread flat to the horizon. From there, who could believe the world is round? I first thought of her when we had the terraces plowed and the upturned earth was ready for planting. Fertile earth, rich as chocolate cake. Big Mama, I thought, biscuit-face, old snake, just look at this dirt, all _this._
The heat breaks with a fast rain, a pelting determined rain that soaks the ground then quits—gone, finished. The green landscape smears across the windows. The sun bounces back out but robbed of its terror now. Here, the edge of autumn. What is it? The smell of leaves drying. A sudden shift in the air, a slightly amber cast to the light, then a blue haze hanging over the valley at evening. I would love to see the leaves turn, pick up the hazelnuts and almonds, feel the first frost and build a little olive wood fire to take the chill off the morning. My summer clothes go in the duffle under the bed. I make a few wreathes of grape vine and twine them with sage, thyme, and oregano, herbs I can use in December. The fennel flowers I've been drying on a screen go in a painted tin I found in the house. Perhaps the _nonna_ I've grown fond of kept hers here, too.
The man with his coat over his shoulders stops in front of the shrine with his handful of dried yarrow. He brushes out the shrine with the side of his hand. All fall, when I am busy with students, he will walk the white road, perhaps wearing an old knitted sweater, later a scarf around his neck. The man is walking away. I see him stop in the road and look back at the house. I wonder, for the thousandth time, what he is thinking. He sees me at the window, adjusts his coat over his shoulders, and turns toward home.
Scattered books go back to their proper shelves: my house in order. One final blackberry cobbler and I'm gone. A lizard darts in, panics, flees out the door. The thought of the future spins through me. What magnet out there is pulling now? I stack pressed sheets on the _armadio_ shelves. Clearing my desk, I find a list: copper polish, string, call Donatella, plant sunflowers, double hollyhocks. The sun hits the Etruscan wall, turning the locust trees to lace. Two white butterflies are mating in midair. I walk from window to window, taking in the view.
Ben Tornati
(Welcome Back)
ON OUR FIRST MORNING BACK IN CORTONA, after several months in California, my husband Ed and I walk into town for groceries. First, I drop off film to be developed at Giorgio and Lina's photo shop. _"Ben tornati,"_ Giorgio shouts, welcome back. Lina comes from behind the counter and all four of us exchange the ritual cheek kisses. Finally, I've learned to go to the right, then left, thereby avoiding head swivels or full-lip encounters. Lina wastes no time. In the confusion of other customers and the small space, I piece together, "We must go for dinner," "In the country, but close," and the ultimate praise, "She cooks like my mother."
Giorgio interrupts. "Saturday or Sunday? I prefer Saturday but would make the supreme sacrifice." He looks like an older, more mischievous version of Caravaggio's Bacchus. He's the town photographer, present at every wedding and festival, and is known to like dancing. Last summer we shared an all-goose feast with him and Lina—and, of course, about twenty others. Every celebration involves an infinitely expandable table. "The pasta with duck . . ." He shakes his head. "That duck squawked in the pen in the morning and came to the table at night."
"What's the sacrifice?" Ed asks.
"Soccer in Rome."
"Then we'll go Saturday." Ed knows soccer is sacred.
We cross the piazza and run into Alessandra. "Let's go for coffee," she says, sweeping us into the bar to catch up on news. She is newly pregnant and wants to discuss names. As we leave her and head toward the grocery store, we see Cecilia with her English husband and two magical little girls, Carlotta and Camilla. "Dinner," they say. "Come when you can. Any night."
When we arrive home with our groceries, Beppe, who helps us with the olive trees and the vegetable garden, has left a dozen eggs on the outdoor table. His fresh eggs cause any soufflé to hit the top of the oven. Our friend Guisi has left _cenci,_ "rags" of fried pastry dusted with powdered sugar.
The next day, Giorgio—another Giorgio, who is Ed's good friend—stops by with a hunk of _cinghiale,_ wild boar. We know well his wife Vittoria's vinegar marinade and slowly roasted loin.
"Did you murder this poor pig?" I tease. He knows I'm horrified that Tuscans shoot and eat songbirds, as well as anything else that moves, including porcupine.
"You like it! So you have the problem." He tells us that his hunting group shot twenty boars this season. Later Beppe comes around again, bringing a rabbit.
And so it goes. One day back, and this is only a part of what happens. The return to Cortona always astounds me. The innate hospitality and generosity of the people visit my life like a miracle.
OVER A DECADE AGO, I BOUGHT BRAMASOLE, A GONE-TO-RUIN house in the Tuscan countryside, and began to spend part of each year there. Slowly, the abandoned olive trees have responded to pruning, plowing, and organic fertilizer. Slowly, the house has awakened from its long slumber and seems itself again, festooned with trailing geraniums and filled with the furniture we have brought in piece by piece from antique markets. Because we loved the restoration process, we have begun another project. Last summer we were picking blackberries with our neighbor Chiara and spotted a stone house where Little Red Ridinghood might have visited Grandmother. We crawled through brambles and found a nine-hundred-year-old structure, so old it had a stone roof. Not long after, we began a historically correct restoration, which drains the coffers but is so exciting. We love the land, especially during the olive harvest every fall, which culminates in a trip to the mill to press our year's supply of pungent green oil. This September, we bought another grove just below us and acquired 250 more of these magical presences, the olive trees. At the corner of the grove, embedded in a stone wall, Ed spotted a slender marble column. We pulled it out of the wall and saw letters engraved. I scrubbed and found incised a memorial to a young soldier who fell in World War I.
We are now accustomed to such finds; the land has a long memory here, constantly giving us something from the past and constantly renewing for the future. Even the ancient grape vines continue to rebound on Bramasole's terraced land. Last October, we made wine, with Beppe's help. Our yield—twelve bottles. When we opened the first one, we thought twelve probably was more than enough, but we like tasting the flinty, sour wine that comes straight from the dirt on our steeply terraced land. When Riccardo heard of our bad wine, he brought us a hundred new vines. Now a friend with a backhoe has dug a deep trench along a terrace. Beppe will tell us when we can plant.
Living here, I've intensely reconnected with nature. The land, we've learned, is always in a state of lively evolution. The lane of cypresses and lavender we planted is beginning to look as though it has always been there. The slender cypresses, just my height when we planted them, now look like those exclamation points we see punctuating the Tuscan landscape. Between them, the lavender's amethystine radiance lights the path. Roses, marguerites, lavender, pale yellow petunias, and lilies on our front terraces have made the ivy and blackberry jungles just a memory. The biggest change is grass. Grass is not Tuscan. We lived with a mown and watered weed lawn for several years. Lovely in spring and early summer, it looked forlorn in August. No amount of precious water kept it alive. One September week, with the help of three neighbors, we unrolled miles of sod trucked from Rome. The irrigation system looks like the Chicago Fire Department's command central. Neither of us understands it completely. Now, a few years later, the clovers and tiny flowers have staged a comeback—grass giving over to weed again.
When we had to disguise a large gas tank for our heating system, we nudged it against a hillside and had a stone wall built in front of it. I asked the masons to incorporate an old window from the house and to build a shrine at one end. They made the top of the wall irregular, and now it looks like a remnant of an old house. The top is planted with lavender, which draws thousands of white butterflies. We were all amused at this little folly. While the workers finished, I slapped cerulean-blue paint inside the shrine, the traditional background for all the shrines in this area. I already had a della Robbia–type ceramic Mary and Jesus ready to hang, but as the paint dried, the workmen began exclaiming, half ironically, half seriously, over the "miracle" in the shrine. "Don't tell the pope," they advised, "or the _pellegrini_ [pilgrims] will arrive by the hundreds." I had no idea what they were talking about. "Look what has happened." I looked.
Faintly, but surely, I saw the white wings, face, and flowing robes of a hovering angel. An accident of the thin paint. I quietly propped my ceramic Mary in the corner and left the "miracle" to preside over the pomegranate and hawthorn.
A few weeks later, at the height of red-poppy season, a dozen white poppies sprang into bloom beneath the shrine. In all the fields rampant with bloom in Tuscany, I'd never seen a white poppy, nor had the workmen, who'd moved on to another project. We joked and stared.
Many local people believe that this area is hot in spiritual spots. "Can't you feel something on the steps of San Francesco's church?" I've been asked. Well, no. Nothing. But I consider the rogue white poppies and the cloudy angel, and I venture a small belief in that direction.
Now we are having a new stone wall built so that I can plant a cutting garden. Above that level, at the end of the vegetable garden, we sow hundreds of girasole seeds every year. The sunflowers, just the height of a friend's nine-year-old girl, fill my house with their sunny presence.
I have many plans for other projects—a third fountain, a raspberry patch, a chestnut fence for wild hot-pink rugosas to sprawl over.
The house and garden's changes over a decade (our first years we only hacked and cleared) parallel the changes in our lives among the Italians. Once we were the _stranieri,_ the foreigners, who'd been crazy enough to take on a house abandoned for thirty years. Now we just live here. It is a commonly accepted idea that when Americans move to a foreign country, the local people never really accept them. Equally mistaken is the assumption that these expats regard all locals as amusing stereotypes. Cortona is home. We did not intend to make such a spiritual shift but it happened. We have a tribe of Italian friends and everyone we know there is vividly singular. Our neighbors are as close as family. What luck—the intense sense of community that we once observed in this small hilltown now includes us. We are comfortable in a wider, deeper sense than I ever dreamed.
My realization of the profound change in my life happened at the ceremony when I was made an honorary citizen of this noble town. No one does ceremonies like the Italians. I followed a group in medieval dress with trumpets blaring across the piazza. The _carabinieri_ in their spiffy uniforms escorted me into the fourteenth-century Town Hall. Thrilling. The horror was that I had to give a ten-minute speech in Italian. I was so scared. But then I looked out at all my friends in the audience, smiling, holding flowers, pleased.
The event symbolized just how wildly unexpected my life had become. We are changed by place. I'm fascinated to the core to learn how fundamentally different Italy is; to learn that the world is not small; that they are not like us. I am so happy for that.
When I first came to Cortona, I used to think, What can I give back? I thought in terms of tutoring or helping to raise money for scholarships. I had no idea that I was about to write three books about a new life in that place, and that the unexpected response to those books would startle not only Ed and me but our adopted town as well. When _Under the Tuscan Sun_ was published, I never imagined that anyone in Cortona would read it. Originally published in a tiny edition, I expected it to go forth in the world as my books of poetry had done—to extended family, colleagues, and friends and perhaps to friends of friends. Still, I changed names out of a respect for privacy. After the books appeared in Italian, people would pull me aside and say, "But why did you change my name?" Now, often, someone will tell me of an experience in World War II, or something about old wheat festivals, or a personal story. "You can write about it, can't you?" each one asks. This quite significant for me.
When travellers who had read my books began to come to Cortona, the merchants and the citizens were thrilled, not only for the economy but because those travellers who seek out a place because they have read a book are interested in the culture, art, and history. Everyone dreads oblivious or obnoxious tourists. Cortona has extremely few of those. At our house, we frequently see people in the road below, sketching or taking a picture or visiting with others they've met on the walk from town. If we're outside, we chat. I've met more people in the last five years than I met in my entire previous life. Local artists sell paintings of our house in the shops in town. It's still a shock to see Bramasole hanging on a restaurant wall but I have not minded any of this. I'm flattered that someone would walk a mile to see something I wrote about. Rather than causing a problem, which many people assume, the books actually wove us more deeply into the rich fabric of everyday life. "Where's the house of that American writer?" I heard someone ask the policeman. "Get in the car—I'll take you there," he answered. We have heard endless stories of travellers who have been invited to dinner, picked up on the road, offered a glass of _vin santo._ The openness and generosity we experience here are offered as well to strangers of three nights.
"Come on, it can't be as idyllic there as you say," I'm often scolded.
"It's even better," I reply. If only I could do justice to the beauty of living among the Cortonesi.
NOW DISNEY HAS COME TO TOWN.
For much of the fall, I have been travelling on a book tour for my novel, _Swan._ Ed has been here since the very first scouts arrived to look for a villa that could be transformed into a replica of our house, Bramasole. He has sent photos of the piazza transformed by snow for a Christmas scene and of the six-foot diameter cake with _Under the Tuscan Sun_ spelled out in berries, which was served for the kick-off party at a gorgeous villa. Everyone in the photos looked dazzling, especially to me, dashing through awful airports in order to stand in long lines, while I headed for a different city every day.
Finally, on arriving in Cortona late in the filming, I find the town charged with cinematic energy. It seems surreal that all this has anything to do with me. Exciting, astonishing, exhilarating, shocking—all those, but mostly surreal. The Villa Laura, which Ed now calls Bramasole Due, was, like our house, abandoned for many years. I have some resistance to it, thinking loyally that the real Bramasole is more poetic and sacred. Diane Lane looks like a fairy princess. On the set, she's reenacting the day when I was scrubbing down the walls and finding a fresco, the storm when an owl perched on my windowsill, even the feasts I cooked. She's playing me. What a strange expression. What a surprising turn in my private writing life. How will this take a place in my history? I wonder.
Audrey Wells, the director and screenwriter, seems as if she could be a daughter of mine. Like my daughter, she's intense and brilliant, shy about her beauty. We spent a few days together before she began the screenplay, and then I waited to see how she would transform my pages into the visual world of film.
When the screenplay arrived, I couldn't touch it for a whole day, then I read it straight through, captivated by her wit and her ability to isolate an incident and pare it down. Though much had been changed, I felt the spirit of the book was intact, and even enhanced by her vision. Reading lines to Ed, I laughed out loud. She added an Italian lover for the Frances character. "Too bad I missed that," I joked to Ed.
Everyone says, "What will this movie do to your book?" But there on my study shelf, the English _Under the Tuscan Sun_ leans on the French, Estonian, Hebrew, Chinese, and other translated editions. The film is another translation, and at the same time, will have a fate of its own.
I'm fascinated by the symbiotic process of a Hollywood movie company interacting with the people of this walled hilltown. But the Tuscans are anciently sophisticated—nothing shocks or throws them or even wows them. They are not star-struck. I begin to think there are books to write or movies to make about this movie being made. The young assistant to the Italian producer soon starts a romance with the gorgeous local travel agent. Diane Lane, the star, is seen shopping for antiques along the main street. Partners of crew members enroll in Italian classes. Restaurants begin to give discounts to actors and staff. The mayor offers the keys to the city and finds spacious offices for the production group. Placido and Fiorella, our neighbors, have feasts at least once a week which include us, producer Tom Sternberg, and his assistant. Johnny, Audrey's husband, spends an afternoon falconing. Laura Fattori, the Italian line producer, falls for Cortona and starts to look at thirteenth-century apartments in town.
Half the town seems to be in the movie as extras and the other half seems to be working on it. We see Piero, a famous stonemason in his late eighties, all dressed up in the piazza. We're afraid someone has died, but no, he says, he is about to be filmed in a street scene. We take many friends to marvel over the Bramasole set, which is now painted the color of the original, with fresco-covered rooms and extensive outside stone walls created out of resin by the set staff from Rome and then fastened to wooden frames. Even the expert Placido is fooled until he taps the stone and hears a hollow sound. I covet the long marble kitchen sink from a convent. A garden of pergola and lemon trees is plugged in overnight. Friends and family from the U.S. come over to witness this miracle event. We all ride over to Montepulciano to see a medieval pageant scene filmed in the piazza. Hannibal over the Alps! What massive movement of equipment, how many moving-van trucks, what huge organization to set up meals for the crew and cast, how many miles of electrical cord! For one scene, a fiberglass fountain is erected in Cortona. While waiting for Ed to come out of the post office, I hear a tour guide tell her group, "This is Cortona's famous baroque fountain now under restoration." The Atlas figure in the center of the fountain has quite a large piece of male equipment. In fact, crowds are gathering. Someone complains about the dignity of the town to the mayor and the next morning the Disney people are out there sawing away.
When books go out into the world, they take on a life. Sometimes that life is a quiet and dusty one, waiting in the nether regions of library stacks. I have books of poetry like that. With others, the book's life is one of surprise because the book keeps on making its way, on its own, into intriguing and larger spaces. I have been pulled along in the wake of _Under the Tuscan Sun_ with great joy.
AT THE LONG TABLE IN THE COUNTRY ON SATURDAY night, I'm sitting between Ed and a woman with the mythic name of Leda. We're facing Giorgio and a man from Rome. As every stupendous platter is put before us, Lina smiles at me from on down the line. Five _antipasti_ , a traditional polenta and cabbage soup from time immemorial, then _gnudi_ , those delectable little balls of spinach and ricotta. And, ah, the duck that was squawking this morning, served with Ed's favorite local pasta, _pici_. The din rises. More bottles of wine and water arrive. Donatella and her daughter, Lucia, who have created this feast in their home, visit around the table. Then the roast pork, the rabbit suffused with fennel, the roasted potatoes. Two desserts. _Vin santo, grappa,_ kisses all around, good night, good night. We whiz back to Cortona and Giorgio drops us at the _duomo_ , where we left our car. The bell sounds its one lone gong, marking the first hour of a new day in this ancient place.
Following is an excerpt from _Swan: A Novel_ by Frances Mayes, a Broadway Books paperback, available now.
J. J. STOOD ON THE END OF THE DOCK, FEELING AS IF THE four pilings might rip loose in the current and send him rafting. But the dock held. He loved the smell of rivers. In July heat, in wavy air, in the throbbing of cicadas, in the first light on the river, he was what he would call happy. A full moon angled down between pines, casting a spiraling silver rope across the curve of the water. He watched the light, flicking through his mind for words to describe it. _Luminous, flashing._ Ordinary. The light seemed liquid, alive, annealed to the water, too changeable for any word. The river rode high after two storms. A cloud of gnats swarmed his foot, then moved as a single body over a swirl in the current. He stepped out of his faded red bathing suit—automatically he pulled on this suit every morning when he got out of bed—and climbed down the ladder into the water. His morning libations, he called this routine. In all the good months, and sometimes in the cold ones just for sheer cussedness, he dipped himself in the river early in the morning. Near the dock he could stand on the bottom, feeling the swiftness or languidness of the current, sometimes jumping as a fish nipped at the hairs on his legs and chest. He floated for a minute, listening to water whirl around his head, letting himself be carried, then turned his body sharply and swam over to the crescent of washed-sand beach his parents had cleared years ago. From there he could walk out of the river and follow a trace covered in pine needles back to the dock. He noticed a fallen sourwood sapling, tangled with muscadine vines, and leaned to pull it out of the water. As he jerked loose the roots, a wedge of earth cleaved from the bank, spilling dirt onto his wet legs. At his feet he saw something white—a bone, a stick bleached by the sun? He waded back into the river and rinsed off.
Maybe what he glimpsed was an arrowhead. J. J. had found hundreds. He turned over the earth with his foot. There—he picked it up, blew off the dirt, and washed it. Never had he found one of these. He held a perfect bone fish spear, three inches long, with exquisitely carved barbs like a cat's claws on each side. He admired the skill—the delicate hooked end of each barb would bite into flesh while the fisherman dragged in the fish. At one end he saw slight ridges where the line was tied over and over by the Creek Indian who once fished these waters. Ginger, he thought, Ginger should see this. But his sister's green eyes were light-years away. He pawed through the dirt and pulled out other roots from the bank, but found only a smashed can. What a beauty, this small spear in the palm of his hand. He took in a breath of pine air as far as he could, the air driving out of his head the familiar surge of what felt similar to hunger and thirst. Ginger was not there, so to whom could he show his treasure? He regarded it intently for himself. He had no talent for needing someone else. He shook his hair and banged the side of his head to knock the water out of his ear. Rainy night in Georgia, he mocked himself. Last train to Clarksville.
He dressed in khaki shorts, not bothering with underwear. Six-thirty and already hot, heavily hot, steamy hot, the best weather. Nothing to eat in the refrigerator but some rice and a piece of left-over venison from a week ago, when he'd brought Julianne, the new schoolteacher from Osceola, out here. She'd said it was so interesting that he lived way in the woods all alone. As down-to-earth as she looked, she turned out to be afraid for her feet to touch the bottom of the river. She'd hung on to his back, her laugh verging toward a squeal, and he felt her soft thighs on his. She was hot to the touch, even under water. But then she couldn't eat venison because she thought of Bambi. She cooked the rice, which, as he remembered, had hard kernels at the center of the grain. Then she looked at his wild salad as though it were a cow pie. J. J. often went for days eating only greens he picked and fish he caught. He chewed slowly, watching her. If she was beautiful, as Liman MacCrea had promised, why did he think her skin looked so stretched tight across her face that it might split like a blown-up pork bladder? And eyes that close together made a person look downright miserly.
Then he'd rubbed his temples and looked again. A pleasant face, kind and expectant. Warm. What is she wanting? he wondered as she smiled. Then he noticed her teeth, which were ground down, like an old deer's.
"Pokeweed and lamb's-quarters? I've heard of dandelion greens before. Can you eat these? That's so interesting." She pushed the fresh, pungent greens around with her fork. With the one bite she took, grit crunched between her teeth. Something she saw in his eyes appealed to her, some waiting quality. Not just a flirt or the good ol' boy he sometimes appeared to be, he was someone to solve, she told herself as she changed into her bathing suit in his room. She looked carefully at his things, comparing her own box bedroom to his, her pink chenille spread and the prints of Degas dancers on the wall, the lace curtains and view out onto an empty street, to his crammed bookcases, twenty or more ink pens, mounted fish and deer heads, his rough Indian blanket on the bed. I have no way to reach him, she thought, and would I want to? She felt suddenly tired but practiced a big smile in the mirror, lifting her thick chestnut hair off her neck. Her teeth gleamed white and even. The new red maillot certainly showed off her Scarlett O'Hara waist. "Cherry Bomb," she whispered. Cherry Bomb had been her nickname at Sparta High, when she was Homecoming queen. But that was twelve years ago. She wished she had washed the lovely greens because she was not about to eat grit.
J. J. thought if she said "so interesting" again, he'd drive the fork through her eyes. He poured glasses of bourbon. "Let's toast your seventh-grade class who gets to spend all that time with you." She lowered her eyes with pleasure, which shamed him. Was he becoming a God damned hermit? He wondered how he would feel with her legs wrapped around him. Lost in outer space? He knew he'd find fault with Christ Almighty. She played the flute, had a degree in music education. So what if she turned freaky in the woods? Still, he had felt a tidal wave of boredom flood through him, a craving to be alone so intense that he shuddered. Although he'd expected to be driving her home at one or two in the morning, top down, a little night music, he was burning up the road at nine-thirty.
He made a pot of coffee and heated Julianne's leftover clump of bad rice with some butter. The kitchen table was littered with chert, flint, a flat stone, and two antlers. Lately, he'd tried to teach himself flintnapping, using only tools the Indians had used. He'd ordered _A Guide to Flintworking_ and driven over to a rock shop in Dannon to buy pieces big enough to work. He wanted to make a stone knife for gutting fish, but so far he'd split a lot of stones and created a pile of waste flakes and chips. One try, by accident, actually resembled a scraper.
He held up the fish spear to the sunlight at the window, admiring the fine symmetry. Balancing coffee, bowl, and notebook, the spear held lightly between his teeth, he pushed open the kitchen door with his elbow. Yellow jackets worked the scuppernongs, and bees burrowed into the rose that sprawled among the vines, his mother's yellow rose, still blooming and her gone an eon, a suicide. He did not want to think about that. She had loved the cabin as much as he did. Her rose had long since climbed from the arbor and bolted into the trees. He placed the fish spear on a piece of white paper and opened his notebook to record his find. July 7, he wrote. The early sun through the grape arbor cast mottled light onto the table. He might love the light at the cabin even more than the water, but no, they were inseparable. The emerald longleaf pines tinted the light at all hours, casting a blue aura early and late, and in full sun softened the hard edges of objects. He moved the paper into a splotch of sun. The bone looked like ivory. First he measured the length, then in light pencil carefully he started to draw. What kind of bone, he wondered, maybe boar, maybe beaver. How long would it have taken the Indian to carve it?
He quickly went over his lines in black with his Rapidograph. Drawing, he thought, never captures the thing itself. At least mine doesn't. Maybe Leonardo da Vinci could get this right. But Leonardo never heard of the Creeks, or of the belly of the beast, south Georgia. Easy to get the _likeness._ The unlikeness is what's hard. Where the object ends and everything around it begins, that's the impossible part to negotiate. He held up the spear and turned it around. He decided to look at it under his father's microscope. He might find a speck of blood from the fish that swam away with the spear in its side. Too bad Ginger's not here, he thought. She ought to see this.
CRITICAL ACCLAIM FOR
_Under the TuscanSun_
"An intense celebration of what [Mayes] calls "the voluptuousness of Italian life . . . appealing and very vivid . . . [The] book seems like the kind of thing you'd tuck into a picnic basket on an August day . . . or better yet, keep handy on the bedside table in the depths of January."
— _New York Times Book Review_
"Armchair travel at its most enticing . . . Mayes's delightful recipes, evocative descriptions of the nearby village of Cortona, and thoughtful musings on the Italian spirit only add to the pleasure. Can we really blame ourselves for wanting to strap Mayes down in some ratty armchair while we go live in her farmhouse?"
— _Booklist_
"Mayes [has] perfect vision . . . I do not doubt that centuries from now, whoever lives in Bramasole will one day uncover bits of pottery used at Mayes's table. She has, by the sweat of her brow and the strength of her vision, become a layer in the history of this place."
— _Los Angeles Times_
"Can we bear yet another book about buying and remodeling a tumble-down house in some sunny foreign country? The answer, in the case of _Under the Tuscan Sun_ , is a simple, unqualified yes . . . Warmth and light nearly glow from these pages, a tribute to the sun, symbol of hope and renewal."
— _Cleveland Plain Dealer_
Carefully written . . . an unusual memoir of one woman's challenge to herself and its successful transformation into a satisfying opportunity to improve the quality of life."
— _Library Journal_
"A model for the open, curious mind and the questioning soul . . . Those who want to find parts of themselves they didn't know existed, take risks, have an adventure . . . and discover another culture altogether, with its different rhythms, tastes, smells, and ways of being human—those readers will find in Mayes a kindly, eager, tough-spirited guide."
— _Houston Chronicle_
"Luscious . . . delightful . . . In the search for writers who thrill you just with their mastery of the language, include Frances Mayes."
— _San Jose Mercury News_
"A report from our dream Italy, still rural, still devoted to beauties that are not artificial . . . Mayes has a profoundly sensual relation to everything she touches, from texture to food . . . Her description of meals that we, alas, didn't get to eat evoke in me satisfaction without jealousy, like paintings."
— _Boston Globe_
Read on for an excerpt from _New York Times_ bestselling author Frances Mayes's latest memoir,
**_Under Magnolia_**
Available wherever books are sold
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A SILVER GLOBE IN THE GARDEN
As I open a book that I once pulled from the ashes of my grandparents' house, the dusty, mildewed scent catapults me to their back hallway.
Through the double door, made of tiny mullioned panes, I see the entrance hall waver, a quivering of claret and sunlight from the front door. Wafting from the kitchen, the smell of chicken smothered in cream and pepper until it's falling off the bone. I'm playing an ancient wind-up record left over from when my father was a boy; "K-K-K-Katy" crackles in my ear. Through my grandmother's open bedroom door, I glimpse chintz dust ruffles, hatboxes, the slender oval mirror over the dressing table, where she leans, and I see her dab the fluffy puff between her legs.
That's it: brief cloud of bath powder, grinding consonant K-K-K-Katy ( _I'll be waiting at the k-k-k-kitchen door_ ), warped light throwing rainbows back through the door. And I wonder, always, why do such fragments remain forever engraved, when, surely, significant ones are lost? The kitchen fragrance, no mystery. For who, ever, could forget Fanny's smothered chicken?
An early memory of my father: He opens his buff hunting coat, and in all the small interior pockets, doves' heads droop. He and his friends Bascom and Royce break out the bourbon. From my room in the back of the house, right off the kitchen, I see through the keyhole (keyholes are a large part of childhood) the doves he's killed piled on the counter, and someone's hand cleaning a shotgun barrel with a dishrag. The terrible plop-ploop sound of feathers being plucked makes me bury my face under the pillow. When his friends go, my father stays at the table with his tumbler of bourbon. I'm reading with a flashlight under the covers. My specialty is orphans on islands where houses have trapdoors into secret passageways that lead to the sea. Rowboats, menace, treasure, and no parents in the story. As the water darkens and danger grows, I hear my father talking to himself. When I quietly crack the door, I see his head in his hands, his bloodstained coat hung on a hook. Very late, he hits the wall with his fist, and says over and over, "Beastly, Christly, beastly, Christly." I put the palm of my hand over the spot where he is pounding with his fist and feel the vibration all the way up my arm. I press my nose to the window screen and look out at the still backyard.
A tea olive tree grows outside my bedroom window, its scent airy, spicy, and I prefer it to the dizzy perfume of the gardenias and magnolias that rule the neighborhood. Tough ovoid leaves scrape the screen; the tiny flower clusters are fit only for dollhouse bouquets. Then the back door slams and the car screeches out the driveway.
My father's parents live two blocks away. I like to gaze into the silver globe under the giant oak in their backyard. My face looks distorted and moony, especially when I cross my eyes and stick out my tongue. In the mirrored sphere, the yard curves back, foregrounded with oak branches like enormous claws. On the latticed back porch, my grandmother Mayes washes a bowl of peaches with her maid, Fanny Brown. Mother Mayes's hair is as silvery as the garden globe, and her crepey skin so white she's almost blue. She looks as though she might dissolve or disappear—her pale eyes always seem fixed on somewhere just beyond me.
Late in the afternoon, she puts up her bare feet on an ottoman. With the lamp haloing her hair, she's ethereal, but then I see crude, tough yellow corns on the last two toes of each foot. They're translucent in the lamp's glow, as she relaxes with _The Upper Room_ , a church book of devotional reading, open on her lap.
Dove heads, tea olive, silver globe, bowl of peaches, church books. Images are the pegs holding down memory's billowing tent. From them, I try to figure out who my people were and where we lived, what they did and what they could have done.
South Georgia, where I was born, may look to a stranger speeding down I-75 like lonesome country where you can drive for miles without seeing more than a canebrake rattlesnake cross the road. At the city limits of our town a sign said IF YOU LIVED HERE YOU'D BE HOME NOW. The logic is irrefutable. Thin roads shimmering in the heat lead into Fitzgerald from Ocilla, Mystic, Lulaville, Osierfield, Pinetta, Waterloo, Land's Crossing, Bowen's Mill, and Irwinville, where Jefferson Davis was captured by the Yankees. Then, no I-75 existed.
To those whose ribs were formed from red clay, the place is complex, exhilarating, charged, various: mighty brown rivers to float along, horizons drawn with an indigo pen, impossibly tall long-leaf pines, virulent racism (then, and not all erased now), the heat that makes your heart beat thickly against your chest, the self-satisfaction of those of us who have always lived there, tornadoes twirling in a purple sky, the word "repent" nailed to trees. A place of continuous contradiction, a box with a false bottom. A black rag doll becomes a white doll when I turn her upside down. I jump onto soft green moss behind the cotton mill and sink into sewage. Daddy in his white suit fishes me out, shouting curses. I'm born knowing that the place itself runs through me like rain soaking into sand.
We are fabric people, as others are the Miwok people, circus people, lost people. In the cotton mill—my father's business—the light is gray because lint catches in the screened windows. Oily black machines, gigantic strung looms as beautiful as harps, their shuttles pulled by lean women. Bins to climb and then dive from into piled raw cotton. In the tin cup of the scale over the bin I ride, the needle jerking between fifty and fifty-five pounds, then fly out, the landing not as gentle as I expect. Rayon is softer, and squeaks as I fall in. But to fly, actually, as in dreams. A natural act, as later I would swing out over the spring on vines at night, dropping into cold black water below, crawl up the slippery bank, grabbing roots, then swing out again and again for that moment of falling. Water moccasins, thick as my leg, thirty-pound rockfish with primitive snouts, even crocodiles lived in these deep streams I dove into, pushing my fist into the icy "boils," that bubbling force at the bottom.
While my father ran the cotton mill and hunted birds, my mother gathered, and created perfect bridge luncheons, with the aid of Willie Bell. The house pulsated with cleanliness. My two sisters were both in college by the time I was eight, but I stayed in my room at the back of the house instead of moving into theirs. Often I rifled through their scrapbooks and high school notebooks in their closet, and tried on their left-behind dresses that had more flounces than mine, and the flowery scent of White Shoulders lingering in the tucks and pleats.
I loved the square brick Carnegie library, the quiet that engulfs you as you gently close the door, the globe to spin and stop, with a finger on Brazil or China, the cold light in the high windows in winter, the way the bookcases jut out to make little rooms, my yellow card with due-date stamps, the brass return slot, the desk where presides the librarian, who looks like a large squirrel. Before kindergarten, my sisters showed me the low bookcase for my age. I moved year by year to a different section of the back room. So much later, I may cross the threshold into the main library where I can check out only two, then four books.
Other literature was mail order. I never had seen a real bookstore. We had Book of the Month. We subscribed to _Harper's Bazaar_ , for copying dresses, _Reader's Digest_ , required for school, and, for some reason, _Arizona Highways_.
Fitzgerald, where I might have lived forever, was as rigidly hierarchical as England. We had our aristocracy, with dukes, bar sinisters, jokers, local duchesses in black Cadillacs, many earls, and, of course, ladies, ladies, ladies, many of them always in waiting. Everything and everyone had a place and everything and everyone was in it. It was a cloying, marvelous, mysterious, and obnoxious world, as I later came to know, but fate placed me there and, although the house was not lilting, I was _happy as the grass was green_.
We were not normal. We lived next door to normal people, so I knew what normal was. The father worked for the state agriculture department, the mother gave a perm called a "Toni" to her sisters and friends, and they laughed and had fun as they breathed in ammonia fumes. Their boy sang in the choir, and the daughter, Jeannie, with wild hair, was my playmate. We found house-paint cans in the barn and brushed black and white enamel over each other. Our irate mothers scoured us with kerosene, and Jeannie seemed to be lifted in the jaws of her mother like a kitten and taken home. Her father built a swing set with a pair of rings that we learned to grip, push off into a somersault, vault up on our feet, and hang upside down. On the swings we could pump so high we'd almost flip over the top. He took us to farms in his truck and we sat in back eating raw peanuts we'd pulled from the ground. They tasted like dirt. Jeannie and I made hideouts in the vacant lot next to her house, elaborate setups of pallets and cardboard boxes, with tin doll dishes and stolen kitchen knives. We sat on a pile of sour grass weed poring over the Sears, Roebuck catalog. _What would you choose if you could choose anything on this page?_ After pelting rains, our walls sagged. On Christmas mornings, she and I ran back and forth between our houses, looking at what Santa left, long before anyone awoke. We strung tin cans with string between our bedrooms, but never could hear a thing. Her mother, Matrel, had lively sisters named Pearl, Ruby, and Jewel. Her uncle always called us "Coosaster Jane," which we thought was German he'd learned in the war. She called her daddy "Pappy." He was strong, redheaded, and sweet. I wonder why I did not envy them. I think small children may have no imagination for a life that is not their own lot.
Other families were happy, too. "The Greeks" were happy even though their daughter Calliope had polio and had to walk with crutches and go to Warm Springs and lie in an iron lung, that awful water heater turned on its side. The Lanes were happy even though the father drove a potato chip truck for endless hours and the delicate mother had a problem so that their bathroom was stacked to the ceiling with sanitary napkin boxes. I was in awe over how they pampered Rose Ann. My best friend, Edna Lula, was the only child in the perfect family. She was doted on and prettily plump; their house had beds with warm dips in the middle like nests, and French doors that opened onto a long porch with a swing. Happy mother and daddy who called her by a nickname left over from baby talk. I could not be at her house enough. There, I fell under their bountiful love. They thought I was funny. They called me by my family nickname, Bud. There was no chink. Ribbon candy always filled the same dish on the sideboard. We licked peach ice cream off the wooden beater, loved pouring the rock salt slush out of the churn. They were admiring, told jokes, hugged; their garden fish pool had a statue of a naked boy, clean water coming out of his thing, landing on the old goldfish in the murk. There was a baby grand piano. My friend plunked out "Song of the Volga Boatman," and "Blest Be the Tie That Binds." Church not only Sunday morning but the evening service, too. (I drew the line at that.)
Copyright © 1996 by Frances Mayes
Excerpt from _Under Magnolia_ copyright © 2014 by Frances Mayes
All rights reserved.
Printed in the United States by Broadway Books, an imprint of the Crown Publishing Group, a division of Random House LLC, a Penguin Random House Company, New York.
www.crownpublishing.com
Broadway Books and its logo, B \ D \ W \ Y, are trademarks of Random House LLC.
A hardcover edition of this book was originally published in 1996 by Chronicle Books. It is here reprinted by arrangement with Chronicle Books. First Broadway Books trade paperback edition published 1997.
This book contains an excerpt from _Under Magnolia_ by Frances Mayes. This excerpt has been set for this edition only and may not reflect the final content of the forthcoming edition from Crown Publishers.
Library of Congress Cataloging-in-Publication Data
Mayes, Frances.
Under the Tuscan sun : at home in Italy / by Frances Mayes.
p. cm.
Excerpts from this book appeared in the New York Times, Ploughshares, and House Beautiful
1. Tuscany (Italy)—Description and travel. 2. Tuscany (Italy)—
Social life and customs. 3. Mayes, Frances. 4. Cookery, Italian.
I. Title.
DG734.23.M38 1997
945′.5—dc21
ISBN 978-0-7679-0038-6
eISBN 978-0-7679-1745-2
v3.0_r6
# _What's next on
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| {
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} | 9,568 |
Charlotte Petriello is a long time Boulder City artist working primarily with oil paints. Like a lot of artists she has painted some watercolors and acrylics but her first love is oil.
Mostly self taught from books and art shows on television, her first Art Award came when she was in junior high school and then again in high school, and she then became a member of the art fraternity at Marshall University. She found Steve Lesnick when she came to Boulder City and has studied several semesters with him.
She paints a lot for kids. She painted gifts for the fair at Andrew Mitchell Elementary School and designed several logos for T-shirts. She had help from a lot of the students in making the final design. At that time the students at Mitchell called themselves "Junior Eagles" obviously reflecting their desire to get into high school and become an "Eagle." Their choice was a logo with an eagle chick just hatching from an egg.
Charlotte has been an active member of the Boulder City Art Guild for nearly 30 years. During this period she has won numerous merit awards including a 3rd place judged by the late Cliff Segerblom, two theme awards, a 1st place and Guild award ribbons. | {
"redpajama_set_name": "RedPajamaC4"
} | 789 |
Berberin är en alkaloid som finns i roten och veden av berberisväxter (bland annat Berberis vulgaris). Ämnet bildar gula, tunna kristallnålar som är luktlösa men med mycket bitter smak.
Berberin används till gulfärgning av läder, trä, ull och silke. I ultraviolett ljus avger berberin ett starkt gult fluorescerande sken. Det sker en omfattande forskning för att klarlägga och förstå de positiva effekter som berberin kan ge inom en rad olika medicinska områden.
Källor
Alkaloider
Bensodioxoler
Farmakologi | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 7,640 |
'use strict';
var affix = require('../shared').common.affix;
var archiver = require('archiver');
var async = require('../shared').common.async;
var fs = require('fs');
var path = require('path');
var request = require('./request');
var tempSuffix = '.mrdownload';
/**
* Represents an agent.
* @constructor
* @implements {IAgent}
* @param {string} chapterPath
* @param {!Array.<!IProcessor>} processors
* @param {boolean} jacket
* @param {Meta=} meta
*/
function Agent(chapterPath, processors, jacket, meta) {
this._chapterPath = chapterPath;
this._disposed = false;
this._initialized = false;
this._jacket = jacket;
this._meta = meta;
this._processors = processors;
this._zip = archiver.create('zip', {store: true});
}
/**
* Adds a page from a HTTP resource.
* @param {string} address
* @param {number=} number
* @param {function(Error, boolean=)} done
*/
Agent.prototype.add = function(address, number, done) {
var that = this;
if (this._disposed) return done(undefined, false);
if (!number && this._jacket) return done(undefined, false);
request(address, 'binary', function(err, data) {
if (err || !data) return done(err || new Error('No image: ' + address));
var buffer = new Buffer(data, 'binary');
var extension = _detect(buffer);
if (!extension) return done(new Error('Invalid image: ' + address));
_processors(that, buffer, function(err, buffer) {
if (err || !buffer) return done(err);
extension = _detect(buffer);
if (!extension) return done(new Error('Unprocessed image: ' + address));
_initialize(that, function() {
var key = affix(String(number || 0), 3) + '.' + extension;
if (that._meta) that._meta.add(key, number);
that._zip.append(buffer, {name: key});
done(undefined, true);
});
});
});
};
/**
* Marks a page as disposed.
* @param {number} number
* @param {function(Error, boolean=)} done
*/
Agent.prototype.dispose = function(number, done) {
this._disposed = true;
done(undefined);
};
/**
* Populates the resource from a HTTP resource.
* @param {!{address: ?string}} resource
* @param {string} encoding
* @param {function(Error)} done
*/
// /var/www/html/test/testme/mangarack.js/lib/shared/provider/index.js:80
// var children = populate($);
// alter(children);
Agent.prototype.populate = function(resource, encoding, done) {
//test
//debugger;
request(resource, encoding, done);
};
/**
* Publishes the mediated result.
* @param {function(Error)} done
*/
Agent.prototype.publish = function(done) {
if (!this._initialized) return done(undefined);
if (this._meta) this._zip.append(this._meta.xml(), {name: 'ComicInfo.xml'});
this._zip.finalize();
if (this._disposed) return fs.unlink(this._chapterPath + tempSuffix, done);
fs.rename(this._chapterPath + tempSuffix, this._chapterPath, done);
};
/**
* Creates directories.
* @private
* @param {string} directoryPath
* @param {function()} done
*/
function _create(directoryPath, done) {
var directoryPaths = [];
var currentPath = directoryPath;
var previousPath = '';
while (previousPath !== currentPath) {
previousPath = currentPath;
directoryPaths.push(currentPath);
currentPath = path.resolve(currentPath, '..');
}
async.eachSeries(directoryPaths.reverse(), function(directoryPath, next) {
fs.mkdir(directoryPath, function() {
// IGNORE: The error is ignored. While the error can be valid (due to
// permissions, for example), it is considered likely to be the result of
// multiple chapters attempting to create the same folder simultaneously.
next();
});
}, done);
}
/**
* Detects the image format.
* @private
* @param {!Buffer} buffer
* @returns {string|undefined}
*/
function _detect(buffer) {
if (buffer.slice(0, 2).toString('hex') === '424d') return 'bmp';
if (buffer.slice(0, 3).toString('hex') === '474946') return 'gif';
if (buffer.slice(0, 2).toString('hex') === 'ffd8') return 'jpg';
if (buffer.slice(0, 4).toString('hex') === '89504e47') return 'png';
return undefined;
}
/**
* Initializes the agent.
* @private
* @param {!Agent} that
* @param {function()} done
*/
function _initialize(that, done) {
if (that._initialized) return done();
_create(path.dirname(that._chapterPath), function() {
that._zip.pipe(fs.createWriteStream(that._chapterPath + tempSuffix));
that._initialized = true;
done();
});
}
/**
* Run the processors.
* @private
* @param {!Agent} that
* @param {!Buffer} buffer
* @param {function(Error, Buffer=)} done
*/
function _processors(that, buffer, done) {
if (!that._processors.length) return done(undefined, buffer);
var resultBuffer = buffer;
async.eachSeries(that._processors, function(processor, next) {
processor(resultBuffer, function(err, nextBuffer) {
if (err || !nextBuffer) return done(err);
resultBuffer = nextBuffer;
next();
});
}, function() {
done(undefined, resultBuffer);
});
}
module.exports = Agent;
| {
"redpajama_set_name": "RedPajamaGithub"
} | 8,426 |
Mojžíš Uherský, též Mojsej Uhrín (asi 983 – 26. července 1043), je jeden z prvních slovenských světců. Je uctíván zejména u řeckokatolické a pravoslavné církve.
Životopis
Mojžíš Uherský pocházel sice z východního Slovenska, ale působil na Kyjevské Rusi na dvoře knížete sv. Borise. Když kníže sv. Boris zahynul v bratrovražedném boji se Svatoplukem, Mojžíš se vrátil do Kyjeva a usiloval o jeho svržení. Nakonec se podařilo knížeti sv. Jaroslavu Moudrému Svatopluka vyhnat do Polska. Když byl však za pomoci polského panovníka Boleslava Chrabrého Svatopluk v roce 1018 dosazen na trůn, nechal Mojžíše uvěznit.
Podle legendy se Mojžíš v Polsku zalíbil významné ženě z bližšího okruhu Boleslava Chrabrého, která se za něj chtěla provdat. On to však odmítl, protože chtěl strávit svůj život v mnišství.
Jeho ostatky se dodnes nacházejí v katakombách svatého Antonína u kláštera Kyjevskopečerská lávra.
Odkazy
Literatura
BUGAN, Bystrík: Mojžiš Uhorský (Mojsej Uhrín) a jeho bratia v kontexte slovenských dejín. In: Bobák, J. a kol.: Historický zborník č. 19, 2/2009. Martin, Vydavateľstvo Matice slovenskej, 2009, s. 137-146
Ctihodný Mojsej Uhrin. Zemplín: MPCO Zemplín, 2008
Mojžiš Uhrín, prepodobný: 26. júl. In: Antonín Čížek: Synaxár: Životy svätých. Prešov: Spolok biskupa Petra Pavla Gojdiča, 1998, s. 295.
Reference
Související články
Seznam světců a mučedníků katolické církve
Externí odkazy
Životopis Mojžíše Uherského
Slovenští svatí
Římskokatoličtí svatí
Pravoslavní svatí
Středověcí světci
Narození v 10. století
Osoby s nejistým datem narození
Úmrtí 26. července
Úmrtí v roce 1043
Muži | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 932 |
Q: find parent array of numpy slice array Is it possible to find the parent array of a slice ie. the array that the slice is taken from? I would like to do this so I can add functionality to matplotlib plots which allows you to change which slice of an array you are viewing interactively in a plot. For instance, if I do this
plt.pcolormesh(myArray[0,:,:])
I would like to be able to run some code to change the plot to
plt.pcolormesh(myArray[1,:,:])
but to do that I need to know that myArray[0,:,:] is a slice of myArray.
Thanks
Niall
A: With simple slices, you can look at the base attribute:
a = np.arange(50)
b = a[10:20]
print (b.base is a)
However, I don't believe that this is guaranteed to work in all circumstances...(depending on contiguousness of a, etc.)
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 1,112 |
Terres de Bord é uma comuna francesa na região administrativa da Normandia, no departamento de Eure. Estende-se por uma área de 22.44 km².
Foi criada em 1 de janeiro de 2017, após a fusão das antigas comunas de Montaure (sede) e Tostes.
Comunas de Eure | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 39 |
Q: Can't get array and sum it up - input is through java dialog I am currently trying to figure out how to grab the dialog inputed number by the user and put it in an array in order to count all the numbers to come out with the sum. I currently only need help with the sum not the product towards the bottom. I am only allowed to change what is inside the sums() method.
This is what I had in my sums() so far but it does not display anything when I input. I am supposed to input an infinite number of data and then stop when the user hits 0. The dialog input works but I cant figure out how to do this using the method using a single parameter. Any help is greatly appreciated!
int sum = 0;
int counter = 1;
while(counter > 1) {
int[] numberArray = new int[counter];
(numberArray[counter]) = number;
sum = sum + number;
System.out.println(sum);
counter = counter + 1;
}
// int counter = 0;
// int[] numm = new int[counter];
// (numm[counter]) = number;
This is the code with comments:
// SumAndProduct.java - This program computes sums and products.
// Input: Interactive.
// Output: Computed sum and product.
import javax.swing.*;
public class SumAndProduct
{
public static void main(String args[])
{
int number;
String numberString;
numberString = JOptionPane.showInputDialog("Enter a positive integer or 0 to quit: ");
number = Integer.parseInt(numberString);
while(number != 0)
{
// call sums() method here
sums(number);
// call products() method here
products(number);
numberString = JOptionPane.showInputDialog("Enter a positive integer or 0 to quit: ");
number = Integer.parseInt(numberString);
}
System.exit(0);
} // End of main() method.
// Write sums() method here.
public static void sums(int number) {
//sums
}
// Write products() method here.
public static void products(int number) {
// products
}
}
// End of SumAndProduct class.
A: Just declare two static member to hold the sum and the product so that you can access them from inside the methods.
public class SumAndProduct
{
private static long sum = 0;
private static long product = 1;
public static void sums(int number) {
sum += number;
}
public static void products(int number) {
product *= number;
}
}
A: You can also try to play with streams and it is close to your idea - to load everything to array and then sum:
import javax.swing.*;
import java.util.*;
import java.lang.*;
class Main
{
public static void main(String args[])
{
int number;
String numberString;
numberString = JOptionPane.showInputDialog("Enter a positive integer or 0 to quit: ");
number = Integer.parseInt(numberString);
ArrayList<Integer> numbers = new ArrayList<>();
while(number != 0)
{
// here is just adding to ArrayList
numbers.add(number);
numberString = JOptionPane.showInputDialog("Enter a positive integer or 0 to quit: ");
number = Integer.parseInt(numberString);
}
sums(numbers);
System.exit(0);
} // End of main() method.
// Write sums() method here.
public static void sums(ArrayList<Integer> numbers) {
int sum = numbers
.stream()
.mapToInt(i -> i.intValue())
.sum();
System.out.println(String.format("Sum: %s", sum));
}
}
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 3,125 |
Getty Images, the world leader in visual communications, today announced it has appointed Gallo Images to be the primary distributor of its award-winning creative and editorial content in the Czech Republic and Slovakia. The agreement will also see iStock by Getty Images, the web's original resource for crowd sourced royalty-free stock images, media and design elements, supported by an in-market sales team. The sales support will give customers unprecedented assistance and access to iStock's millions of premium quality images, vectors, videos and music tracks, all available at an unbeatable price.
"Gallo Images is a long-standing content partner and master delegate for Getty Images, so we are excited to be working with them to bring our innovative and award-winning editorial and creative content to more customers in the Czech Republic and Slovakia," said Lee Martin, Senior Vice President Sales EMEA, Getty Images.
Gallo Images will trade as Getty Images Czech Republic and will serve customers in Czech Republic and Slovakia through a central office in Prague from Monday 5th January, 2015. | {
"redpajama_set_name": "RedPajamaC4"
} | 2,291 |
La hierba de San Cristóbal (Actaea simplex) es una especie perteneciente a la familia Ranunculaceae.
Descripción
Es oriunda de Japón y el extremo oriental de Siberia, tiene la floración más tardía del género, a finales del otoño. Es la más pequeña y alcanza una altura cercana a 1,2 m. Las flores son blancas, nacen en largas varas arqueadas y el follaje está muy dividido.
Taxonomía
Actaea simplex fue descrita por (DC.) Wormsk. ex Prantl y publicado en Botanische Jahrbücher für Systematik, Pflanzengeschichte und Pflanzengeographie 9(3): 246. 1888.
Etimología
Actaea: nombre genérico que proviene del griego: aktaía, latinizado = actea que significa "costera.simplex: epíteto latíno que significa "simple".
Sinonimia
Actaea cimicifuga var. simplex DC.
Cimicifuga cimicifuga var. intermedia (Regel) Graebn. & P. Graebn.
Cimicifuga dahurica var. tschonoskii Huth
Cimicifuga foetida var. intermedia Regel
Cimicifuga foetida f. laciniata Makino
Cimicifuga foetida f. purpurea Makino
Cimicifuga foetida var. simplex (Wormsk.) G.Don
Cimicifuga foetida var. simplex (DC.) Regel
Cimicifuga ramosa (Maxim. ex Franch. & Sav.) Nakai
Cimicifuga simplex Wormsk. ex DC.
Cimicifuga simplex (DC.) Wormsk. ex Turcz.
Cimicifuga simplex var. intermedia (Regel) Nakai
Cimicifuga simplex var. ramosa Maxim. ex Franch. & Sav.
Cimicifuga taquetii H. Lév.
Cimicifuga ussuriensis Oett.
Thalictrodes simplex'' (DC.) Kuntze
Referencias
Enlaces externos
Ranunculaceae
Flora de Japón
Plantas descritas en 1888
Plantas descritas por de Candolle
Plantas descritas por Wormskjöld
Plantas descritas por Prantl | {
"redpajama_set_name": "RedPajamaWikipedia"
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It was one of those rare days in London when the sun shone on clean streets and the air did not smell of rotten vegetables and horse dung. A night of heavy rain had washed the streets clean without, mercifully, overloading the sewer system, and the cobbles and brickwork of the city glistened proudly like a man showing off his freshly cut and oiled hair. Sherlock knew it wouldn't last for long, but for a while it made London into somewhere he thought he could live, one day.
Sherlock and his tutor, Amyus Crowe, had left Farnham earlier that morning. Sherlock's brother Mycroft had invited them for lunch at his club – the Diogenes. His reason, which he explained in a letter that had arrived the day before, was that he wanted to talk about Sherlock's schooling. Having been removed from Deepdene School for Boys and placed in the care of the big American Amyus Crowe, it seemed to Sherlock that Mycroft was now wondering if he had done the right thing. Mr Crowe was a brilliant teacher, but only on certain subjects. Survival in the wilderness, tracking animals, fishing for carp and trout, identifying poisonous fungi, a little bit of recent political history and the logical analysis of evidence – these were all his strong points. Mathematics and Latin – not so much.
Sherlock would much rather study the things that Amyus Crowe was teaching him, because he could see their value, but his brother had a strange regard for those areas of the syllabus for which Sherlock could see no earthly use. Every now and then he threatened to bring in another tutor to complement Crowe's lessons, and Sherlock had either to avoid the subject entirely or try to talk him out of it. 'If you want to make something of yourself,' he would say, 'then you need to learn dead languages, theology and the more obscure facts of history. There is no alternative, I'm afraid.' The fact that Sherlock had no idea what he wanted to make of himself cut no ice with his brother. 'You will go into the Civil Service, of course,' he would rumble. 'Either that or banking.'
The hansom cab that Sherlock and Crowe had taken from Waterloo Station dropped them outside the Diogenes Club, which lurked behind an unremarkable door. Crowe, resplendent in his white suit and hat, flicked a coin up to the driver and strode across the pavement to the door, but as he did so a passing man in a suit and bowler hat jostled against him. Crowe turned to deliver a sharp rebuke, but the man unexpectedly pushed him in the chest. Crowe staggered backwards into two other men who were passing. Within moments, all four men were arguing.
Unsure what to do, Sherlock stepped away from the cab. As he did so he heard movement behind him. Someone had come around the side of the cab and was looming at his shoulder. He turned his head, but liquid sprayed his eyes and nose. Gasping, he raised a hand to wipe his face clear, but his arm suddenly seemed to be moving in slow motion. His attention became fixated on his fingers and thumb. They looked like they weren't even a part of him: pink, fleshy things that moved of their own accord. The lines on his palm took on the appearance of rivers crossing a landscape, like a map seen at a distance.
What was happening to him?
He felt nauseous. His head felt like it had doubled in weight, and as he laboriously swung it around to look for Amyus Crowe he saw that the big American was staring at him in concern, but Crowe's face was swimming in and out of focus, and although his lips were moving Sherlock couldn't hear anything apart from what sounded like the tolling of a distant bell. The cab and the sky and the brickwork of the buildings were all bleeding together into a mishmash of colours that made him feel as if he was looking at the world through a stained-glass window. He needed to rest, to sit down and gather his wits, but when he took a step forward his feet tangled together and he stumbled. He fell, and it seemed to take an awfully long time before he hit the ground. A hand grabbed at his shoulder, but when he looked up, all he could see was a grotesquely distorted face looming over him. He struck out with his fists, again and again, flailing around in a world of jumbled shapes and colours. Someone was screaming, and he thought he recognized the voice. He thought it was his own voice, but it was a long, long way away.
Then there was darkness, and the feeling that his arms were being tightly held. And then there was just the darkness.
The realization that he was lying on a bed of straw in a brick-lined room came slowly. He didn't know at what point he understood where he was: there came a moment, as he was staring at the brickwork, that he realized that he _had_ understood some time ago, but the information just hadn't meant anything to him.
He was in a brick room, and he was lying on straw. That was a starting point.
And his name was Sherlock. Sherlock Holmes.
The rest seeped back gradually, like the sea washing over the beach as the tide comes in. The Diogenes Club. The cab. The fight. The liquid that had been sprayed over his face.
He checked his clothes, running his hands down his body. He was still wearing the same jacket, shirt and trousers that he had been wearing earlier. That, at least, was something to hold on to. They were stained with dust and dirt, but not ripped.
The room was like the inside of a stable, but there was no smell of animals. The straw was clean and dry, and had been laid down on flagstones. The brickwork that formed the walls was whitewashed and dry too: no moss, no trickling water, and the air was chilly but not damp. At first he'd thought he was in some sort of outbuilding, but the evidence suggested otherwise. He was indoors – just not in a particularly well-appointed room.
There was a window in one wall, but it was tall and thin, barely wide enough for him to get his arm through if he tried. Certainly not large enough for him to escape. Even his friend Matty wouldn't be able to get through that. The glass looked dirty, from where he lay.
The wall opposite the window was interrupted by a door. It was heavy, and studded with big metal rivets like the heads of arrows that had been shot through from the other side. A small window in the centre of the door was barred, and it looked as if a wooden shutter had been closed across it from the other side.
As Sherlock's mind began to speed up, he realized that there were no hinges on the door. Or, at least, there were no hinges on the inside of the door. The hinges must have been on the outside, which meant that the door opened outwards, not inwards. Sherlock didn't think that he'd ever been in a room where the door opened outwards.
No, that wasn't right. He _had_ been in a room like that: the room in Bow Street Police Station where he and Amyus Crowe had spoken with his brother Mycroft a few months before. The door to that room had been designed so that people in the room could not pry the hinges apart and thus remove the door, or hide behind the door when it opened and attack whoever came in.
He was in a cell.
He sat up suddenly, shocked into complete wakefulness. He was in a cell! Surely he hadn't been arrested? Now that the blood was flowing more swiftly through his brain he remembered vague images of himself flailing around in the street, punching people who came too close – but Amyus Crowe would have protected him, wouldn't he? Protected him from arrest?
Unless Crowe had been arrested too. The big American had been on the verge of a fight, after all.
He checked his knuckles. They were scraped, and covered with dried blood.
He tried to work out how long he had been unconscious. His throat and mouth were dry, but he wasn't particularly hungry. He couldn't have been out for more than a couple of hours. It was still the same day.
He climbed unsteadily to his feet. His toes tingled with pins-and-needles as the circulation returned to them, and he shuffled from one foot to another to try to get the pain to subside. As soon as he could stand up straight he crossed to the window. It was above his head, but by reaching up and hooking his fingers over the sill and then pulling himself up, scrabbling with the toes of his boots to get purchase against the mortared ridges between the bricks, he could get his head up to a level where he could just about see out.
Beyond the wall lay a manicured garden of lawns and bushes, and beyond them, just the other side of a wall, he could see the tops of hansom carriages going past. Lots of carriages. Pigeons were perched all along the top of the wall. It looked as if he was still in London.
At least that was something.
He dropped back down to the stone-flagged ground, brushing his hands against his trousers, and crossed to the door. There was no handle on the inside. He pushed experimentally at it. The door didn't budge. Presumably it was bolted on the other side.
He threw his weight against it, but it didn't shift.
He glanced back at the window. He may have been imprisoned but at least he wasn't in the countryside, or even in France. That had happened before. He was in London. Amyus Crowe would get him out.
Assuming that Crowe wasn't in the next cell. The thought sent a cold shiver of fear through him. If he and Crowe were _both_ imprisoned here, and if Mycroft didn't know where they were, then there was nobody left to get any of them out. They might rot there forever.
'Mister Crowe!' he called. 'Can you hear me? Are you there?'
Nothing. No response.
No, that wasn't entirely true. He _could_ hear something. Now that he was listening properly he could make out a faint cacophony of moans and cries coming from the other side of the door. It seemed to have got louder when he shouted. And he could hear banging as well: metal against metal in a regular, mindless rhythm. It was like listening to a musical recital in hell.
The window in the door suddenly slid open. He jerked his head back, startled. A face stared in at him, framed in the wood: eyes wary and skin scabbed.
'Back away,' a rough voice said. 'Back across to the other side of the room. This door ain't openin' till you do.'
Sherlock shuffled away until his back was against the wall, feeling the straw piling up behind his feet as they scuffed across the floor.
The window slid closed with a _thud_. Moments later he heard the solid _clunk_ of a large bolt being drawn, and then the door creaked open.
Two men stood in the doorway. They both wore uniforms of blue canvas. Their hands were dirty and their faces unshaven. And they were both holding short wooden clubs.
'Try anythin' an' you'll be measurin' your length on the floor, understand?' The speaker was the man on the left. He was slightly smaller than his companion, and his eyes were blue. 'Tell me you understand. Talk properly now.'
'I understand,' Sherlock said, voice unsteady. 'Where am I?'
The man turned to his companion. 'You 'ear that? He don't know where 'e is!' He turned back and smiled at Sherlock. His mouth was empty of all but three blackened teeth. 'You're in Bedlam, mate! Now come over 'ere, careful like. The Resident wants to take a look at you.'
The two men backed away, leaving a path through the door. Sherlock walked gingerly forward, still trying to process what they had told him. Where was 'Bedlam'? Who was 'the Resident'?
The men stepped back as he walked through the door. He noticed that they were holding their clubs ready, in case he attacked them. He was smaller than them, and unarmed, but they seemed to be scared of him. Or, at least, wary.
Outside, he found himself in a long, wide gallery lined with doors on one side and narrow, barred windows on the other. The floor was wood, apparently polished by years of feet brushing against it. The ceiling of the gallery was curved, with iron rods every few feet making it seem as if Sherlock was standing inside the ribcage of some vast beast: an impression reinforced by the bloody glow emitted by a cave-like fireplace a few yards away. The fireplace was covered by a black metal cage which had been bolted to the wall.
There were people in the gallery. Off to one side, four men were playing cards at a small table. Another man, in a black suit and top hat, was standing by one of the windows and looking out. The expression on his face was desperately sad. Other men – and they were all men, Sherlock noticed – were walking up and down the gallery, some slowly, with their hands reaching out to trail along the brickwork, and others rapidly, as if they had somewhere urgent to be.
One man brushed past Sherlock with a curse. He walked ten feet further on, then stopped for a moment and turned around. He walked back, brushing past Sherlock again as if he had never seen him before, and strode off in the opposite direction. As Sherlock watched, he stopped again, turned around and walked back towards Sherlock once more.
Now that he was out of his cell, he could hear the cacophony of voices more clearly. It sounded like several hundred people all having conversations and arguments with themselves, or singing, or wailing, all at once, and all in ignorance of the others.
The voices came from behind the doors which lined one side of the gallery.
Turning, he spotted a blackboard bolted to the wall beside his door. On it were chalked the words _Unknown boy – Acute mania_ , along with the date.
The words were like spears of ice thrust into his heart.
_Acute mania_.
'This is a lunatic asylum,' he said, and he could hear his voice verging on breaking. 'This is where they send mad people.'
'Like I said,' the attendant said: 'Bedlam. Or Bethlehem Hospital, to the gentry. Or the madhouse, to those of us who work 'ere.'
Sherlock's keen eyes noticed that the bolt on his door was huge – probably a foot or more long. It was a design he'd seen elsewhere: a metal cylinder that slid back and forth inside a couple of metal brackets across into a narrow brass barrel on the doorframe to secure the door. The cylinder could then be rotated by its handle so that it caught behind one of the brackets on the door, stopping it from being slid back unless it was rotated again. Very simple, and quite foolproof. Even if Sherlock could have picked locks, which he couldn't, there was no obvious way out of the room. Accessing the bolt outside the door from inside would be almost impossible.
If he was going to escape.
'Now, 'ead down that way, to the end,' the attendant said, interrupting his chain of thought. 'That's where the Resident's office is. 'E likes to see all the new inmates. Very conscientious, is the Resident.' He pushed Sherlock's shoulder, backing away immediately in case Sherlock suddenly turned and grabbed him.
Sherlock started to walk. A few doors were open, others were locked with the bolts pointing firmly downwards. Whoever ran this place liked an orderly system, the appearance of control. As he passed each locked door the noise of the occupant got suddenly louder, then quieter. He could hear words, sobs, screams, and in a couple of cases what sounded like music-hall songs.
Perhaps the worst were the doors behind which he could hear no noise at all, but sense a malign presence, watching and waiting, like a spider in its web.
A hand pushed Sherlock between his shoulder blades. He nearly went sprawling to the ground.
'Move yourself,' the attendant called. 'We ain't got all day.'
With the two attendants behind him, Sherlock walked the length of the gallery, past innumerable wooden doors and narrow windows and occasional caged fires which blasted heat all around them. At one of the cages an enterprising inmate was holding a long wooden stick in the flames, toasting something. For a few moments Sherlock thought it was a chunk of bread, but as he got closer he realized that it was a mouse, curled up and blackened.
The man with the stick watched Sherlock and the attendants pass. 'I saw her again when they were all sleeping,' he said in a reasonable, calm voice. 'She walks in beauty, like the night.'
'Good,' Sherlock replied. It was the only thing he could think of to say.
One of the attendants snorted with laughter. 'Yeah, look out for ghosts, boy. Make sure you say your prayers and sleep nicely or you ain't going to like what you see.'
The attendants pushed him to the end of the gallery, where a large grille, like a portcullis, separated it from the space beyond. It was a circular hall, with a domed roof. One of the attendants opened a door in the grille with a key selected from a bunch that hung from his belt and pushed it open. He went through, leaving his colleague behind Sherlock, and gestured to Sherlock to follow him. The two of them had obviously done this many times before. They had the whole process down pat.
The domed hall into which they led Sherlock was opulent: painted white with gold-leaf ornamentation, and beautiful paintings hanging up on the walls. This area didn't have flagstones on the floor: it had black and white tiles. On Sherlock's left was a large door that, he guessed from the position of the windows along the gallery, led out into the grounds. On his right was a smaller, internal door. It wasn't locked or secured. Presumably it led into administrative areas: offices, examination rooms, kitchens, that sort of thing. And ahead of him, mirroring the floor-to-ceiling grille through which he had just passed, was another grille leading into another gallery. Vaguely, in the red firelight glow beyond, he thought he could see shapes moving. Women? A gallery for women, just as his was a gallery for men? More than likely.
The toothless attendant pushed him towards the door to his right. 'Through there, then first door on your left. We'll be waiting outside. All the Resident has to do is shout, and we'll be straight in.' He suddenly lashed out with his club, catching Sherlock behind his left knee and sending a spike of sick agony up his thigh. Sherlock dropped to the floor, his leg suddenly unable to support his weight. His elbow hit the tiles, sending another wave of agony through him. He had to clench his jaw shut and swallow hard to stop himself from throwing up. 'And if we have cause to come in, you'll remember it for a very long time. Just bear that in mind.'
He hauled Sherlock to his feet and pushed him towards the door. It swung open beneath the pressure of Sherlock's extended hand. Beyond it was a long corridor lined with doors. Attendants were walking along it, much as the inmates had walked along the gallery, and with the same mixture of purpose and purposelessness.
Sherlock saw a door immediately on his left. A brass sign had been screwed to it. The words engraved on it said: _William Rhys Williams MD MRCS MRCPE – Resident Physician & Superintendent_.
Sherlock glanced backwards, at the attendants. They were watching him carefully. He wondered if this was some kind of test: what would he do – knock politely, just stand there, or open the door and walk in unannounced?
He knocked and waited.
'Come in,' a voice called. He twisted the knob, pushed the door open and entered.
The room inside was carpeted, panelled and curtained. It was, in a strange way, reminiscent of the Diogenes Club in its plushness and its quietness. A large desk was placed to one side, in front of a large window. Bookshelves to either side of the window were filled with leather-bound volumes. A man wearing a black suit, high-collared shirt and striped waistcoat sat behind the desk, writing with a quill pen in a ledger. He was bald, apart from a fringe of black hair running around the back of his head like a small curtain.
The man glanced up at Sherlock. His gaze flickered all over Sherlock's face, hands, clothes, everything. He nodded, as if he had just confirmed a conclusion that he had reached before Sherlock had entered.
'Stand in front of the desk,' he said. His voice was thin, whispery. 'My name is Doctor Williams. I am the Resident Physician at this institution. That means I have the final say when it comes to any decision regarding the inmates – of which you are one. I should warn you that if you make any move to come around the desk, or exhibit any violent or unwarranted behaviour, I will have no hesitation in calling on my attendants for assistance. Do you understand?'
'I understand, sir,' Sherlock said, moving to the front of the desk. 'There has been a terrible mistake. I am—'
'Be quiet. Answer questions when I ask them. Do not volunteer information, or I will have you removed back to your room.' Williams paused, and glanced down at the ledger on his desk. Sherlock noticed a small brass bell beside it. 'Do you know your name?'
'Holmes, sir. Sherlock Scott Holmes.' He was about to say something else, but thought better of it.
'Memory appears intact,' Williams murmured, making a note in the ledger. 'Locomotion and posture are reasonable for a boy of age –' he glanced up at Sherlock. 'How old are you?'
'Fourteen, sir.'
'– of age fourteen,' he continued. He leaned back in his chair, which creaked beneath his weight. 'I make it a habit formally to interview all new inmates. You have been sent here because you exhibited severe manic behaviour in a public place. The police restrained you, and a doctor present at the scene certified you insane. You will stay here until I – and I only – am convinced that you have recovered. Do you understand?'
Sherlock's head was spinning. He was desperate to explain himself. 'I understand,' he said, 'but I am not insane!'
'Nobody who is insane believes themselves to be insane,' Williams said. 'It is, I dare say, one of the defining characteristics of insanity.' He nodded. 'I have, as you might expect, made no small study of insanity. I was previously Assistant Doctor firstly at Derby County Asylum and then at the Bedfordshire, Hertfordshire and Huntingdonshire County Asylum. Eight years ago I was appointed Assistant Physician here under Doctor William Hood, whom I succeeded six years ago as Resident Physician. I tell you this so that you know there is no way you can pull the wool over my eyes. I can tell when someone is mad, and I can tell when they are sane.'
'But, sir—' Sherlock started desperately.
Williams kept talking, as if he hadn't heard the interruption. 'I am of the firm opinion that insanity is a hereditary disease of the brain. I have, for instance, seen several cases of babies delivered of women – I can hardly call them "ladies" – who are inmates here at Bethlehem. These babies were steeped in madness as they lay in the womb, and my attendants have told me that they have acted like devils from the moment they were born.'
It occurred to Sherlock that any baby born in a place like Bedlam, with all its screams and cries and the slamming of doors, would be likely to scream and cry themselves, and that was regardless of whether their mothers were properly able to take care of them, but he kept quiet. He suspected that Dr Williams did not like to be interrupted when he was pontificating.
'Under my predecessor, the esteemed Doctor Hood,' Williams continued, 'insanity was treated – if you can call it that – with drugs and with rest and with seclusion. This is not an approach that I believe works well. I would rather tie a patient down constantly than keep him always under the influence of a powerful drug. I have known cases of chronic insanity benefit materially – although not be cured entirely, of course – by a prolonged period of time in a padded cell. I have also observed several patients who were destructive and aggressive become as meek as lambs after several hours restrained in baths of warm water. This is _my_ approach, and you will experience its benefits yourself. I hope that in time you will recover from the mania which you have so obviously displayed, and that you will be able to be released into society again.' His gaze met Sherlock's. 'Now, do you have any questions?'
Sherlock's brain raced. How could he best convince Dr Williams that he wasn't mad?
'Am I displaying signs of mania now?' he asked quietly.
'You appear to be in a placid phase of your insanity,' Williams said. 'Mania goes in cycles.'
'Then how do you know that I _was_ displaying signs of mania?'
'I have the reports of the policemen and other members of the public at the scene.'
'If I do _not_ display any further signs of mania,' Sherlock went on carefully, 'then how long will it be before you decide that I am either cured or that I was never mad at all?'
'As to the first,' Williams said, 'I cannot observe you at all times. Just because you display no signs of mania now, that does not mean that at three o'clock tomorrow morning you will not be raving in your cell and banging your head against the walls. As to the second – well, of _course_ you are mad to begin with. Why would you have been sent here otherwise?'
Before Sherlock could respond to this obviously stupid remark, Williams rang the bell that sat beside the ledger.
'If madness is hereditary,' Sherlock said desperately, hearing the door opening behind him, 'then how _can_ it be cured? Surely by that definition people are born with it, in the same way that they might be born with red hair.'
Williams stared at Sherlock as if he was disappointed by him. 'Ah, a display of argumentativeness,' he murmured. 'A classic sign of incipient mania.' He made a note in the ledger. 'Take him away,' he said, without looking up.
A hairy hand closed over Sherlock's shoulder. 'Don't make any trouble,' the attendant advised. 'Remember what I said.'
Sherlock allowed himself to be pushed out of the room, across the hall, through the grille gate and along the gallery. Despair filled him. Unless something happened, unless Amyus Crowe could get him out, then he might be incarcerated there forever. How could Sherlock persuade a man like Dr Williams that he was sane when Williams believed that insanity was inherited, and that even arguing was a sign of madness? Nothing that Sherlock could do would change his mind!
Padded cells. Being tied down. Restrained in a warm bath for hours on end. Was this what his future held for him? Was this the shape of the rest of his life?
Not if he could help it.
As he was led along the gallery, past the caged fires and the slitted windows, past the various men who paraded up and down or just stood around motionless, his brain was racing. If he couldn't rely on the medical profession to realize that he was sane, and if he couldn't rely on Amyus Crowe or brother Mycroft to get him out, then it was left to him. He had to escape by himself.
'You're allowed free association wiv the other inmates,' the toothless attendant said. 'Until lights out, that is, then you're locked in your cell. Sorry, I mean your _room_. Your palatial accommodation.' He laughed. Sherlock could smell something rank coming from his mouth: a combination of tooth decay and tobacco. 'Food trays will be bought along later. If there's any trouble – if you start a fight, or start trying to cut yourself – then we'll lock you up early. Understand?'
'I understand,' Sherlock said.
'Good lad. I don't think you're goin' to be any trouble at all, are you? I got a sense about these things. Be good and the years will just fly past.'
He was still laughing as he got to the grille at the end of the gallery.
Sherlock gazed around. There were six other inmates in the gallery. Two of them were walking up and down like mechanical toys, three were playing dice and the sixth was sitting against the wall, arms around his knees, rocking to and fro. The man who had been toasting the mouse earlier had vanished back into his cell, presumably to eat his feast in comfort. There were also two attendants: one at each end of the gallery. They were standing in a position where they could get a clear line of sight all the way down, but they looked bored. As long as a fight didn't break out, Sherlock didn't think they would be interested.
Casually, he wandered back into his room. His _cell_. The moment he was out of sight of the attendants he slipped his jacket off. He ran his hands along the sleeves until he located a tear. It had probably been caused by whatever fracas he had got into just before he had been taken away to Bedlam.
Carefully he pulled at a thread until it came loose. He followed the thread along the sleeve, pulling at it all the time, until he found the other end. A quick tug and it was away: a section of thread about a foot long. The material of the jacket sleeve was wrinkled now, pulled out of shape, but that didn't bother him too much. Working rapidly but carefully, he managed to get another five threads loose. Once he had them all in his hand he put the jacket down and tied the threads together so that he had two long strands. Cautiously he tugged at them. The knots held firm.
It was a start, at least.
If there was one thing Sherlock was sure about, it was that he wasn't going to spend the next few years in the Bethlehem Hospital. One way or the other, he was getting out.
Sherlock ambled out of his straw-matted, brick-lined room, the threads from his jacket held bundled in his hand. He leaned against the door frame, as if watching what was going on in the corridor, but he was waiting for something. He was waiting for a distraction, and given that he was in a lunatic asylum he was fairly sure that a distraction was going to come along soon.
It took nearly half an hour, but, just as he was about to give up, one of the dice players suddenly stood bolt upright. His hand was groping inside his jacket pocket.
'My watch,' he snarled. 'It's gone!' He glowered at the man nearest him. 'It was you, wasn't it? You fell against me a few minutes ago. You must've taken it then! You black dog!'
A fight broke out, both men rolling on the flagstones of the gallery, trying to claw each other's eyes out, while the gallery quickly filled up with shouting observers lured out of their rooms by the noise. The attendants rushed from opposite ends of the gallery, brandishing their clubs, hitting out to the left and to the right to clear a way through the growing crowd.
Sherlock slipped to the other side of his door: the outside. The large metal bolt was at head height. Taking one thread he tied it around the handle of the bolt and then trailed it up the door and over the top, pressing it into a gap between two planks. The loose end now hung down on the inside of the door. When the door was closed and locked, it would be on Sherlock's side.
The second thread he also tied around the handle of the bolt, but this time he trailed it horizontally, towards the hinges. He passed the thread through the gap between the door and the frame, letting it rest on one of the hinges so that it didn't fall. Again, he passed it through to the inside of the door, catching it on one of the rivets that held the door together so that it didn't slip down.
He checked over his shoulder. Nobody was watching. The attendants were laying into the fight now, splitting people up and cracking heads.
Sherlock bent down and rubbed his hands on the flagstones, picking up as much dirt and dust as he could. Quickly he rubbed his hands along the two threads, blackening them and making them less visible. He imagined the attendants sliding the bolt across, flicking the handle down and locking him in for the night. If he was lucky they would do it automatically – _slide, across, down_ – and the threads would be intact and unnoticed. And maybe – maybe – that would be the start of his escape.
Finished for the time being, he moved out into the gallery to watch the fight being broken up. There was blood on heads, on the clubs and on the floor.
'In your cells, all of you!' one of the attendants called. 'Now!'
'What about food!' someone yelled.
'No food tonight. You've lost that privilege. Nothing till breakfast for you animals, and you'll like it or lump it!'
As the attendants began pushing people into their cells and bolting the doors, starting at the far end of the gallery, Sherlock glanced sideways. A man was standing in the doorway of the next cell along. His clothes were threadbare: so dusty that although they had started off different colours they were all now approaching the same shade of grey. His beard and hair were grey. Even his skin was grey.
He glanced over at Sherlock. His eyes weren't grey: they were a faded, watery blue.
'Do I detect a new arrival?'
'That's right. I'm Sherlock. Sherlock Holmes.'
'My name is Richard Dadd. I am exceptionally pleased to meet you.' He extended a hand towards Sherlock. As Sherlock shook it, he noticed that Dadd's hand was coloured in various shades of green and blue.
Dadd noticed the direction of his gaze. 'They allow me to paint,' he explained. 'They provide me with canvas and oils and turpentine. It makes the days pass quicker. The endless days.'
Sherlock gazed at Dadd. 'You seem . . . normal.'
Dadd smiled. 'You mean sane?' He shrugged. 'I believe that I am. Doctor Williams believes that I am not. We have a difference of opinion. Unfortunately, his opinion counts for more than mine does in this establishment.'
The attendants had moved to about halfway between the end of the gallery and Sherlock's cell now. Every few seconds another door would thud closed, and the bolt would be shot across, locking it. Within a few moments he would be locked away as well. Alone. Desperate for human conversation, if only with a lunatic, he asked: 'What . . . what happened . . . to get you locked up here?'
'It's very simple, and very sad. My father was possessed by the very Devil himself. I killed him in Cobham Park. I stabbed him to death.'
Sherlock felt as if someone had doused him in cold water. 'And that's why you are here?' he heard himself saying.
'That,' Dadd admitted, 'and the fact that I was apprehended on my way to murder the Austrian Emperor. It's all a tragic misunderstanding, but Doctor Williams refuses to see it as such.'
The attendants would be with them in a few moments. The gallery was becoming quieter and quieter as the inmates were locked away, one by one.
'Take my advice,' Dadd said urgently.
'What's that?' Sherlock asked.
'Beware the Lady who walks in the night.'
'The Lady?' Sherlock asked, confused.
'She walks the galleries late into the night on noiseless feet,' Dadd confided, leaning towards Sherlock with a serious expression on his face. 'They say she was a serving girl who fell in love with the son of the man in whose house she worked. When this son left home he gave her a guinea coin – pressed it into her hand as a gift. He got into his coach and drove away, but the next thing the family knew she was chasing after the coach, screaming. The family ran after her, but the shock of the son leaving had driven her senses from her. She was committed here, to Bedlam, and spent several years here, and all that time she clutched that guinea in her fist and would not let it go, whatever the proffered compensation. She died with it still in her hand, they say, and her last request was that she be buried with the coin, but the story goes that a heartless attendant prised it from her cold, dead fingers. And so her spirit roams the corridors of this ghastly place every night since, forever searching for that lost coin, that gift from the man she loved and who loved her not. Her fingers clutch our trinkets in place of what she has lost.'
'That's rubbish,' Sherlock said, but he could hear the uncertainty in his own voice. He didn't believe in ghosts, but there was something about Dadd's serious expression, and the conviction in his voice, that gave Sherlock pause.
'Perhaps so,' Dadd said. 'Perhaps so, but be watchful nevertheless. There _are_ strange things that walk these galleries at night. Believe me. The boy who was in that room before you – he disappeared. Vanished suddenly and noiselessly. My suspicion is that the Lady came looking for her coin, and he saw her, so she took him instead.'
The attendants had reached Dadd by now. He nodded his head to them courteously, and backed into his room. 'Gentlemen,' he said as he went. 'Goodnight to you.'
Next it was Sherlock's turn. He backed into his room before they got to him. The thud of the door closing, and the metallic rattle of the bolt sliding shut, were the two most terrible sounds he had ever heard.
He waited until the attendants had moved on, and he had heard the door and bolt on the next room thudding home, before he checked the threads. They were both intact. He tugged experimentally on both of them, taking up the slack. They seemed to be all right. Maybe, just maybe, his plan would work.
But he had to wait until well after midnight to try it out.
Aware that his stomach was empty and that he wasn't going to get anything for at least another twelve hours, he sat on the straw-covered floor and rested his back against the cold, dank bricks. How did people survive here, night after night? How did they manage to keep . . . sane? The moment the word popped into his mind he found himself laughing. Of course. Most of them weren't sane. _Most_ of them. But Sherlock was, and he suspected that at least a handful of other people imprisoned in Bedlam were sane as well. Maybe they were eccentric, maybe they had opinions that were abhorrent to politicians or Church leaders, but that didn't make them mad.
He must have fallen asleep while he was thinking, because the next thing he knew, the only light coming in through the slitted window was the pale, white light of the moon. He watched as the distorted rectangle it cast slid down the wall, like a piece of paper stuck to the bricks with treacle.
The next thing he knew, the rectangle of light was on the floor. He must have slept again for a while. His shoulders ached from the cold of the wall, and the muscles of his legs felt weak and tingly.
And someone was watching him through the wooden hatch in the door.
He could see light silhouetting a head, and he could sense eyes, malicious eyes, staring at him intently. He didn't move, didn't speak. Eventually, with a soft squeak, the hatch closed again.
It wasn't one of the attendants: that much he was sure of. They wouldn't have bothered being quiet. They would have just slammed the hatch open, taken a look and then slammed it closed again. Whoever had been watching Sherlock through the hatch hadn't wanted him to know about it.
The sensible thing would have been to have waited for a while before making his move, but he was burning with curiosity now. He wanted to know who it was that had been interested in him.
Silently he climbed to his feet and crossed to the door. He cautiously felt for the two threads that he'd left there earlier, trailing from the handle of the bolt. They were fragile, thin, and he was worried that they might have been disturbed by the opening of the hatch, but after a few moments of groping around he found first one, and then the other.
He had to do the next bit very carefully. There was no room for error: he would only get one chance.
The way the bolt was designed, it had to be rotated through a quarter-turn before the handle could slide past the brackets. One of the threads – the one that trailed over the door – he could use to rotate the bolt. If he was lucky. The other one he could use to pull the bolt back, out of its catch.
Experimentally, he pulled on the thread that ran up and over the door. It gradually pulled taut. He tugged on it. Nothing. He felt a growing frustration churning in his chest. He wanted to pull hard, but if he did that then the thread might snap, or the knots might give. Maybe it was snagged on a rivet, or a splinter, or something. It might even have become caught up between the door and the frame when the door closed. Forcing himself to focus, Sherlock felt the tight band around his chest ease slightly. He pulled again on the thread. This time he felt something give, and from the other side of the door he heard a grating noise. In his mind he could see the thread pulling on the handle of the bolt, but with the brackets stopping it from moving and with the handle offset, the only freedom of movement it had was for the bolt to rotate around its own longitudinal axis. So, reluctantly, it did.
Sherlock had to judge the amount of rotation very carefully. If it rotated the bolt too much – if he ended up with the handle pointing directly upward – then it would not open. The only clear path the handle had was when it was pointed outward at ninety degrees to the door. If he pulled too far then there was no way to get the bolt down again. This was a one-time-only opportunity for freedom.
Sherlock stopped pulling while there was still some play in the thread. He wanted to pull further, but he knew he shouldn't. Time to try the other thread now, and pray that it worked.
Keeping the tension on the first thread, he pulled on the second one, which ran horizontally around the edge of the door. If he'd worked things out correctly then this one should pull the bolt back along the door, out of the catch. _If_ he had worked things out correctly.
There was some resistance, but the thread moved, and he could feel an increase in tension in the first thread, the vertical one. On the other side of the door he could hear the grating of metal against metal as the bolt slid back. Elation filled him. He stopped breathing, in case the movement of his chest disturbed the delicate balance of the threads.
After a minute or so of gradual movement, the thread went tight. The bolt couldn't move any more. If Sherlock was right, then it had been pulled completely back, and the door was unlocked.
He pushed against the wood.
Nothing. The door didn't move.
He pushed again, harder.
This time, the door shifted slightly. He'd forgotten how heavy it was! He threw his weight against it, and the door opened an inch.
He braced his boots against a gap between the flagstones of his cell and pushed with his shoulder.
The door swung open.
He caught it before it could go too far, and slipped through the gap and into the gallery.
Firelight flickered along its length. The windows were thin rectangles of blackness. Silence, apart from the crackle of burning coals.
A figure moved silently down the corridor, away from him. It was a woman, dressed entirely in black. Her head was covered in a shawl, and as she came level with each door she paused for a moment and gazed towards the cell, then moved on down the gallery. He couldn't see her feet; she seemed to glide noiselessly across the floor.
Sherlock realized that she was gliding in the opposite direction from the grille that closed off the space between the gallery and the entrance hall. He suspected that if he was going to get out then he had to go back, towards the entrance. Part of him desperately wanted to follow the woman in black – the _ghost_ in black, part of his mind said – but the more sensible part wanted to get to freedom. He didn't have a plan for getting past the grille, but at least he'd managed to get out of his cell. That was an accomplishment in its own right.
With a last, regretful glance along the gallery, where the woman in black had stopped outside one of the cells, Sherlock moved in the opposite direction.
He could hear a mixture of sounds coming from the cells as he moved rapidly along. From some of them came heavy snoring, from others muffled sobs and from the remainder either silence or voices praying. He wished he could do something for them, but he wasn't in a position to lead a mass escape attempt, and even if he could he was in no position to distinguish between the sane and the mad. He had to save himself.
He got to the grille at the end of the gallery. The hall beyond was in shadow. He had a vague idea that he might be able to pick the lock, or take the door off its hinges, or even hide behind one of the enormous flowerpots until morning and sneak out behind the backs of the attendants, but he was amazed to see that the grille was unlocked. He glanced around, expecting a trap, but nobody jumped out at him. He pulled the door open and slipped into the hall.
Freedom.
Almost.
He kept to the shadows around the edge of the hall, rather than crossing the tiled expanse of the centre, until he came to the double doors that led outside. Nervously he pushed them open, expecting at any moment that an alarm bell would be sounded, or that somebody would shout after him, but nothing happened.
The air outside was the freshest he could ever remember breathing. It was like drinking clear, cold water from a stream.
It was still night, and the road on the other side of the wall was quiet. He looked around, getting his bearings. If he could make it to the road then he could hail a cab and persuade the driver to take him . . . where? Amyus Crowe hadn't booked them into a hotel, and he didn't know where the big man had gone. He supposed he could head for the Diogenes Club. It was the only place that Crowe might think to use as a rendezvous.
He ran down the steps and on to the path that led away from Bedlam.
'Oy!'
The voice was loud, aggrieved. He wanted to run, pell-mell, down the path to freedom, but something made him turn around.
The toothless attendant was standing on the steps, club in one hand and a whistle in the other. 'You come right back 'ere, son, or I'll call the Peelers, so I will. If you come now I promise I won't break any bones. If I have to get the police to get you back it'll reflect badly on me, and that means I'll take it out on you. I guarantee you'll walk crooked for the rest of your short life.'
Sherlock was about to tell the attendant to go to hell, and run, but someone yelled out from inside the hall. The attendant turned to call back. 'It's all right – I got 'im out 'ere!' he shouted. He turned back, whistle coming up to his mouth, but he looked at Sherlock and the hand holding the whistle slowly dropped down to his side again. His expression was a mask of confusion.
'If there's any breakin' of bones to be done around here,' a deep, deceptively calm voice said, 'then I believe I have priority. And, by the way, considerable experience as well.'
Sherlock didn't have to turn his head to know that Amyus Crowe was standing directly behind him, close enough that if Sherlock stepped back then he knew he'd bump into him.
''E's an escaped madman!' the attendant exclaimed.
'I don't think so,' Crowe observed. 'I have in my pocket a piece of paper signed by three separate doctors, all confirming the sanity of this boy. I think a mistake has been made, a serious mistake, and if you don't want it to reflect on you then you should just let us walk away now.'
'We can't,' Sherlock said quietly.
'Why not?'
He sighed. 'There's something I have to do. Inside. I have to talk to the Resident Physician.'
'Son, there're times when life offers you a free gift.' Crowe's voice was urgent, insistent. 'This is one of those times. If we walk away now, you're safe. If we go inside, I can't guarantee what will happen. They might find a way of keeping you.'
'I know, but there're more important things at stake here. I need to see the Resident Physician.'
This time it was Crowe who sighed. 'I gotta say, life as your tutor is never boring.' He raised his voice. 'You – the man with the club and the badly fittin' uniform. I want to see the Resident Physician. Tell him I'll be waiting in his office for an explanation as to why he saw fit to imprison a perfectly sane boy.' Whispering now, as the attendant gaped blankly at them, he said to Sherlock: 'Lead the way, son. Let's let him find us in his office, with me sittin' behind his desk. It'll keep him off balance.'
Sherlock led Crowe past the attendant, who ran past them, into the hall, and across to the door that led to the offices and administrative areas. He looked for a moment as if he was going to bar their way, but instead he ran off down the corridor.
'The Resident Physician sleeps on the premises,' Crowe rumbled as Sherlock led the way into the oak-lined office. 'That's one thing I found out about this institution.' He looked around. 'Nice place. He obviously gets paid well.'
'Who pays him?' Sherlock asked. 'Who funds this place?'
'As I understand it, families pay for their loved ones to be "looked after", whether they need it or not. There're rumours of women bein' sent here because they wouldn't get married, or wanted to marry someone unsuitable, or had gotten themselves married but didn't love their husbands. Obvious sign of madness, I'm sure you'll agree.'
'But there _is_ such a thing as _real_ madness, isn't there?' Sherlock asked.
'There is,' Crowe agreed, 'but I wouldn't bet on the doctors here recognizing it unless it ran up an' bit them on the nose.' He frowned. 'Which, bein' madness, it probably would.'
'So,' Sherlock said, his thoughts suddenly catching up with what had been said, 'who paid for _me_ to be incarcerated here?'
'That's the six thousand dollar question.' Crowe walked over to the other side of the desk and sat down. 'Answer is, I don't know, but someone did. You probably saw that I got involved in an altercation. You started actin' strangely, but before I could extricate myself from my situation you'd been carted away. Whoever did this had a carriage an' a doctor ready an' waitin'. Come and join me, by the by. Stand by my shoulder.'
'So what happened?' Sherlock asked, moving to stand behind Crowe. 'What did I do?'
'You went wild, throwin' yourself on the ground an' shoutin' about fire an' birds an' suchlike. You were out of control. Never seen anythin' like it in my life – 'cept once when Ginny and I were on the boat comin' over here an' a passenger ran across the deck, screamin' that he couldn't stand the waves and the sky starin' at him any more. Threw himself over the railin's. The Captain turned around to try an' find him, but he'd gone. Drowned.'
Sherlock felt his breath catch in his throat. 'What _made_ me act like that?'
'I suspect that somethin' was added to your drink, or sprayed in your face. Remember that substance in the pocket of the dead man in the Diogenes Club some time ago – the spray we think caused your brother to have a blackout while still standin'? I think you'll find whatever was used on you was a similar thing, but designed to cause temporary hallucinations, rather than blackouts.'
'But why?'
'I don't rightly know, but my money is on the Paradol Chamber. You've stepped in their way twice now and managed to stop their international criminal activities – once with Baron Maupertuis an' once in Russia. I think they want to get you out of the way.'
Sherlock was about to ask how Crowe had found him when the door burst open and Dr William Rhys Williams rushed in. He was wearing an embroidered dressing gown over a nightshirt, and had a tasselled velvet cap on his head. He was furious: red in the face and wide-eyed.
'What in heaven's name do you think you are doing, facilitating the escape of an inmate of this institution? I should have you horsewhipped!'
'Is that an approved medical treatment?' Crowe rumbled. 'Or just somethin' you enjoy as a recreational activity?'
'Get out from behind my desk!' Williams shouted.
'Not your desk for much longer,' Crowe said calmly.
'What do you mean?'
'I know your General Medical Council ain't been around for long, but I doubt they'd look too kindly on one of their members accepting sane people into a lunatic asylum for cash.'
'This child is not sane,' Williams snapped. 'I examined him myself.'
'I have three doctors who say he is,' Crowe replied, holding up an envelope. 'I'd be happy to set them against you in a court of law and see who comes out ahead, but before I do that my friend here has somethin' to say.' He looked up at Sherlock. 'All yours, son.'
'I saw something,' Sherlock said, trying to control his breathing. Looking at Williams's florid face made him feel sick. Just a few short hours ago, this man had said that Sherlock was obviously insane.
'Saw what?' Williams asked. 'This is a lunatic asylum. All kinds of things happen in here that don't happen in the world outside.'
'I saw a ghost,' Sherlock said calmly.
Williams glanced at Crowe and raised an eyebrow, as if to say _I told you so_. 'A ghost?' he said in a reasonable voice. 'Please, tell us more. Did it walk through walls?'
'No,' Sherlock replied, 'and that's what made me realize that it wasn't really a ghost. It was meant to look like one – dressed all in black, and supposedly the spirit of a poor servant girl who died here – but what ghost needs to leave a door open so that it can move about, or use a hatch to look at someone in their cell?'
'You think it was someone dressed up?' Crowe asked from beside him, face alert. 'Why?'
'There are people here who have privileges. I suspect that long-term inmates get to furnish their cells and wear their own clothes. I think that long-term inmates who aren't obviously dangerous can be quite comfortable here. And I think that one of the attendants is stealing from them – getting into their cells while they are asleep and stealing stuff, like watches, or coins.' He paused, remembering the fight between the dice players. 'I've only been here a day and I've noticed that inmates are losing possessions. They're like sitting ducks – vulnerable, easy to take advantage of.'
'Why on earth would any such thief dress as a ghost?' Dr Williams said dismissively.
'If someone who has been diagnosed as being insane says that a ghost has stolen things from them, who will believe them?' Sherlock asked simply.
'And has anything else strange happened?' Crowe asked. He was talking to Sherlock, but his face was stern as he stared at Williams.
'A boy who was in my cell before me died,' Sherlock said. 'They said he'd seen the ghost, but I think he'd worked it out.'
'Had he?' Crowe's gaze was fixed on Williams. 'Or is there something goin' on here worse than theft?' He stood up abruptly. 'We'll be takin' our leave of you, Doctor Williams. I think you can expect a visit from the General Medical Council and the police in the near future. I think you can expect them to look into any unexplained deaths that have occurred here – especially of young people. And I think if you don't cooperate fully with them, then you'll hang along with whoever actually _is_ responsible – assumin', of course, that you're not the person wearin' the ghost costume an' stalkin' these corridors at night.'
'I know nothing about this,' Williams said, but his face was as white as if he had seen a ghost himself. Perhaps, Sherlock thought, he'd glimpsed a vision of his own future, and he didn't like what he'd seen.
'It stops,' Crowe said as he walked out from behind Williams's desk and past the doctor. 'It stops _now_.'
'Do you think things in there will change?' Sherlock asked as they walked out of the building and into the cool, fresh air.
'I'll make sure they do,' Crowe replied. 'Sad to say, son, but things like this go on all over the place. Wherever there're people in a position of power an' other people who are vulnerable, there's theft, an' abuse, an' worse.' He shook his head. 'It ain't within the gift of a man to change the world. All he can do is change the things he sees around him. If enough people do that, then maybe the world will change anyway.' He glanced at Sherlock. 'I'll talk to your brother. He can pull some strings – get the place checked over officially. An' I'll make sure they know what they're lookin' for.'
Sherlock nodded. 'Thank you.'
They walked on in silence for a few moments.
'That was good figurin' out, by the way,' Crowe said.
'What was?'
'The bit about the ghost – workin' out that only livin' people need open doors.'
Sherlock smiled. 'It just seems obvious. A ghost that can't walk through walls, or bars, isn't a ghost at all. And that's why I can't believe in ghosts, by the way.'
Crowe raised an enquiring eyebrow. 'Go ahead – I'm all ears.'
'Well, we assume that ghosts can walk through walls, but they apparently still need to walk on floors. People say they've seen ghosts on stairs, or in first-floor bedrooms, or wherever. It doesn't make any sense. If walls aren't any barrier to ghosts then floors shouldn't be either – they should just fall straight through them. Or, rather, they shouldn't be able to climb up stairs in the first place. Maybe, logically, there's something about the _ground_ that means they can't move through it, the ground being natural, but if they can move through vertical barriers like walls then they can move through horizontal barriers like floors, and if they _can't_ move through horizontal barriers then they can't be ghosts.'
Crowe considered for a moment. 'I like your style of thinkin'. Most people argue for or against the existence of ghosts on a spiritual basis. You're applying rigorous logic. Are you doin' this to everythin' in your life?'
'Bit by bit.'
'Try not to turn your attention to religion _just_ yet. Remember, you still have to live in your uncle's house, an' I suspect that his heart wouldn't stand the strain if you tried to persuade him logically that God don't exist.'
Crowe headed towards a carriage that was waiting patiently for them. Sherlock hung back.
'Can we trust it?' he asked uncertainly.
'As much as we can trust anything,' Crowe rumbled. 'It's the cab I took to get here. To be on the safe side, I waited for three to pass before I hailed it.' He placed a hand on Sherlock's shoulder. 'You're spooked, son, an' that's natural. The Paradol Chamber have taken a shot at you, an' it blew up in their face. I don't think they'll try anythin' else for a while. If nothin' else, this was a warnin'. They want you to know they're watchin' you, an' they don't want you interferin' in their plans again.'
Sherlock felt something harden within his head. 'Then I don't have a choice, do I?' he asked.
Crowe just cocked an enquiring eyebrow.
'If I want to walk safely in the streets,' Sherlock said grimly, 'then I have to bring the Paradol Chamber down. I have to crush them so they never threaten anybody else again.'
Crowe nodded. 'I reckon,' he said, 'that's a logical course of action to take.'
**AUTHOR'S NOTE**
The text that forms the majority of this story was originally written for the third Young Sherlock Holmes adventure – _Black Ice_. It formed a self-contained section just after Sherlock is attacked by a steel-clawed falcon in the Passmore-Edwards Museum and just before he heads off to Russia. It was removed because it slowed the story down, and because it didn't have very much to do with the rest of the plot. I always regretted its loss, so I present it here as a short story in its own right. The action now takes place between the end of _Black Ice_ and the beginning of the fourth Young Sherlock Holmes adventure, _Fire Storm_.
Sherlock's brief imprisonment in the madhouse known as 'Bedlam' (or, more properly, the Bethlehem Hospital) is as accurate as I could make it. Actually, I could have put a lot more detail in there, but I wasn't sure that a full-blown description of a London madhouse of the 1860s was entirely appropriate for a story like this. They weren't nice places. Anyway, the books I used for research were:
_Bedlam: London and Its Mad_ by Catharine Arnold (Simon & Schuster, 2008)
_Bedlam: London's Hospital for the Mad_ by Paul Chambers (Ian Allan Publishing, 2009)
Richard Dadd, the artist who engages Sherlock in conversation in the asylum, was indeed a patient at Bedlam for a number of years. He was, at one stage, moved to the newly opened Broadmoor Criminal Lunatic Asylum, but I'm assuming in this story that he was moved back to Bedlam for a while – possibly for good behaviour.
The building occupied by the Bethlehem Hospital is now the Imperial War Museum in South London. My grandmother used to live just around the corner from it, and I have distinct memories as a child of being taken through the grounds, past the building, and looking up at it nervously, knowing that it had once been inhabited by lunatics. Apparently the staff of the museum still don't like going down into the basement to the storerooms. They say there's a 'feeling' about the place. Sherlock wouldn't believe in 'feelings', but me? I'm not so sure . . .
Andrew Lane
**ABOUT THE AUTHOR**
Andrew Lane is the author of some twenty previous books. Some are original novels set in the same universes as the BBC TV programmes _Doctor Who_ , _Torchwood_ and _Randall and Hopkirk (Deceased)_ , some are contemporary novels written under a pseudonym, and some are non-fiction books about specific film and TV characters (notably James Bond, and Wallace & Gromit). He has also written for the _Radio Times_ and its US equivalent, _TV Guide_. Andrew lives in Dorset with his wife, his son and a vast collection of Sherlock Holmes books, the purchase of which over the past twenty years is now a justifiably tax-deductible expense.
_Also by Andrew Lane_
Young Sherlock Holmes: Death Cloud
Young Sherlock Holmes: Red Leech
Young Sherlock Holmes: Black Ice
Young Sherlock Holmes: Fire Storm
This electronic edition first published 2011 by Macmillan Children's Books
a division of Macmillan Publishers Limited
Pan Macmillan, 20 New Wharf Road, London N1 9RR
Basingstoke and Oxford
Associated companies throughout the world
www.panmacmillan.com
ISBN 978-1-4472-1287-4 EPUB
Copyright © Andrew Lane 2011
The right of Andrew Lane to be identified as the author of this work has been asserted by him in accordance with the Copyright, Designs and Patents Act 1988.
You may not copy, store, distribute, transmit, reproduce or otherwise make available this publication (or any part of it) in any form, or by any means (electronic, digital, optical, mechanical, photocopying, recording or otherwise), without the prior written permission of the publisher. Any person who does any unauthorized act in relation to this publication may be liable to criminal prosecution and civil claims for damages.
A CIP catalogue record for this book is available from the British Library.
Visit **www.panmacmillan.com** to read more about all our books and to buy them. You will also find features, author interviews and news of any author events, and you can sign up for e-newsletters so that you're always first to hear about our new releases.
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Q: Loop doesn't work, nasm I made a program to output counts from 1-9, but after compiling I only get a "0". I have no idea, where I made a mistake. I would like to ask for help. Below I place a code:
section .text
global _start
_start:
xor esi,esi
mov esi,[variable]
_middle:
mov [variable],esi
mov eax,4
mov ebx,1
mov ecx,variable
mov edx,[length]
int 80h
inc esi
cmp esi,57
jbe _middle
_end:
mov eax,1
int 80h
section .data
variable db 48
length dd $-variable
A: You increment esi but you forget to store it into variable, so at the top of the loop the original value is read again. Move the line that stores esi after the label _middle. (And you don't need the line to retrieve variable into esi anymore.)
As it seems you are working with ASCII values, you should not start variable with the value 0 but with 48:
_start:
mov esi, 48
_middle:
mov esi,[variable]
Alternatively, start with variable initialized:
variable db '0'
but that requires some more rewriting.
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Trump's blacklist of Chinese firms with 'military ties' is a blatant attempt to keep Boeing king of the skies
23 Nov, 2020 14:07
FILE PHOTO: U.S. President Donald Trump visits Boeing in St. Louis © Reuters / KEVIN LAMARQUE
Tom Fowdy is a British writer and analyst of politics and international relations with a primary focus on East Asia.
As America drafts a new list of Chinese companies that cannot do business with US suppliers, President Trump's intention is clear – to ensure Boeing remains No1 in the aviation industry, and lock out a new Shanghai-made contender.
Donald Trump may be on the way out, but he's far from finished on China. On Monday, it was announced that an additional 89 Chinese firms are to be added to a US blacklist and considered a 'national security threat' over their purported ties to Beijing's military.
The firms, almost all in the aviation sector, will be prohibited from purchasing US-made parts and technology without approval. It marks yet another escalation in the White House's technology war against China, with the Trump administration seeking to cement a legacy on the issue, which would be political suicide for Joe Biden to reverse.
But what's really at stake here? The exclusive focus on aviation is notable, and, while a link to the military is inevitable for such a sector, this isn't as much about national security as it is about big business. And, in particular, it's about preserving the global primacy of Boeing.
Also on rt.com Asia-Pacific trade deal is a big win for China and a blow for US. America First has in fact put America Last on the world stage
As much as Chinese aviation firms are linked to China's military, so American companies are associated with the US military and, in turn, maintaining the uncontested global pre-eminence of Boeing has long been an objective of many US presidential administrations. Any competing firm, from Europe's Airbus to Canada's Bombardier, has discovered this over the years, and with China's new Comac C919 about to pose a market challenge to Boeing's 737, Washington isn't playing nice.
Boeing is arguably one of the most strategically important companies in the US. For decades, the firm has enjoyed supremacy in global aviation. We've all flown in one of its products at some point. Not only that, but Boeing is also key to America's own defense industry. It is no surprise, then, that Washington policymakers have continually sought to keep the firm top of the aerospace food chain, employing punitive tactics to do so. Any overseas competitor who threatens the firm's hegemony is met with a response from Washington that cannot be described as anything other than aggressive.
For example, it is quite obvious the US is no fan of Airbus. It has long accused the European Union of giving the company subsidies to boost its standing, a dispute which has lasted over a decade. This was at the root of Trump slapping tariffs on EU exports. Likewise, Bombardier has also faced hefty American tariffs. Yet this is restrained compared to what the US has done on occasion; for example, Washington has resorted to outright espionage against 'allied' countries, using this tactic to sabotage at least one Airbus deal. The bottom line is, if you compete against Boeing, the US may very well play dirty.
In addition to this backdrop, it's been a bad couple of years for Boeing. The Covid-19 pandemic has crashed global aviation markets and frozen new orders. Demand for aircraft isn't going to increase any time soon. In addition, the firm's reputation was badly damaged after the 737 MAX's high-profile crashes, which saw the plane grounded. Boeing is now aiming to reintroduce it. The firm desperately needs a win and the Military-Industrial Complex that backs it in Washington isn't in the mood for new competitors that might undermine its market share.
Within this context, the US isn't thrilled that China, of all countries, is launching its own challenge to Boeing, in the shape of the C919, created by Shanghai aerospace firm Comac and due to launch next year. This is bad news for Boeing, especially given that China constitutes the world's largest aircraft market, and one that is growing fast.
Also on rt.com US' new policy roadmap on China shows how it risks isolating itself in the same way the Eastern Bloc did
Now, with more than 300 orders placed for the C919, which will almost certainly undercut Boeing in price, the US firm's market share is instantly threatened. And so, not surprisingly, the solution put forward by the Trump White House is to simply try to undermine China's aviation sector in its entirety, by locking it out from key parts and components that it depends on the US for – a brazen attempt to force Beijing to rely on Boeing purchases. China's aviation complex now essentially faces technology-related sanctions.
This, however, isn't going to buy Boeing much relief. China initiated the global pushback against the 737 MAX to begin with and, given Beijing's influence, the US needs its approval for its market share to be restored. This provides an obvious route of counter-attack. While China is still too reliant on Boeing aircraft to sanction the firm outright, it can respond by continuing to blacklist the 737-MAX as unsafe and thus dent its sales.
Irrespective of this, in the long run, US sanctions will not stop China from developing self-sufficiency in aircraft and eventually displacing Boeing at home, and in many other countries too. This is a last-gasp attempt at market protectionism by Trump, but its chances of success are slim. After all, there's little question that European aviation suppliers will be happy to fill the gap faced by 89 Chinese firms who can't buy from US companies anymore.
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"redpajama_set_name": "RedPajamaCommonCrawl"
} | 1,261 |
\section{Introduction}
\label{s:intro}
The study and characterization of the internal dynamics of galaxy
clusters is an important way to understand their evolutionary history,
which is itself related to the evolutionary history of the
universe. The most classical way to characterize the dynamics of
clusters is through the analysis of the projected phase space
distribution of their member galaxies, e.g. via methods based on the
Jeans equation \citep{BT87}, such as the Dispersion-Kurtosis
\citep{LM03}, distribution-function \citep{Wojtak+09} and MAMPOSSt
\citep{MBB13} methods, or the Caustic method calibrated on numerical
simulations \citep{DG97}. All these methods assume spherical symmetry
and most of them (except the Caustic method) also assume dynamical
relaxation of the cluster. These methods have been applied to several
nearby (and massive) clusters of galaxies
\citep[see][]{KG82,vanderMarel+00,BG03,LM03,BK04,KBM04,Biviano06b,Lokas+06,WL10}.
\begin{figure*}
\begin{center}
\includegraphics[width=13cm]{HST_caustics.ps}
\end{center}
\caption{HST image of the core of LCDCS~0504. The size of the field is 38$\times$34
arcsec$^{2}$, corresponding to $285 \times 255$~kpc$^{2}$ at $z = 0.794$. Multiple
imaged systems used in this work are labeled. From the best fit strong lensing model, we draw in red the tangential critical curve at z=3 and the corresponding caustic lines in orange}
\label{f:multiple}
\end{figure*}
Given that clusters formed relatively recently according to the
hierarchical scenario of structure evolution in the universe
\citep[e.g.][]{BG01}, accretion of matter from the surrounding field,
in the form of galaxy groups, complicate their internal
structure. Detection of secondary structures, or substructures, in
clusters is obtained using other methods, either based on the
projected distributions of cluster galaxies
\citep[e.g.][]{DS88,Escalera+94,Biviano+96,SG96,Barrena+02,GB02,Ramella+07}
or on X-ray data for the intra-cluster gas
\citep{Briel+91,MFG93,Neumann+01,OHara+04,PBF05,Bohringer+10}. Detection
and characterization of these substructures is a direct way to
constrain the cluster building history \citep[e.g.][ and references
therein]{Adami+05}.
These last years, the characterization of the mass distribution and
substructures of galaxy clusters has been made possible by
investigating deep and high quality data that enable the
measurement of weak lensing signal and the detection of strong
gravitationally lensed features
\citep[e.g.][]{Cypriano+04,Markevitch+04,Bardeau+05,Jee+05,Coe+10,LKG11}. It
is still relatively uncommon to see cluster dynamical studies based
simultaneously on the Jeans analysis, and on the X-ray and lensing
data, especially for high redshift clusters. This is due to the
extreme difficulty in obtaining both deep and high resolution X-ray
imaging, deep optical and infrared imaging, and faint galaxy
spectroscopy. As a consequence, our information on the internal
structure and dynamics of distant clusters is still relatively
limited.
In this paper, we perform a detailed study of the internal structure
and dynamics of the rich cluster LCDCS~0504 at redshft $z=0.7943$,
also known as Cl~J1216.8-1201 \citep{Nelson+01}, using simultaneously
spectroscopic optical data for cluster galaxies, as well as X-ray and
strong lensing (SL, hereafter) data. This cluster is part of the
DAFT/FADA survey \citep{Guennou+10} and the analysis presented here is
a proof of concept for similar analysis to be performed on other
clusters of the DAFT/FADA sample.
In Sect.~\ref{s:data} we present our data-set. Our SL determination of
the cluster mass distribution is described in Sect.~\ref{s:sl}. In
Sect.~\ref{s:x} we use the X-ray emission from the hot intra-cluster
medium (ICM) to constrain the cluster mass profile. This is also
determined using galaxies as tracers in Sect.~\ref{s:kin}. We compare
the different mass profile determinations in Sect.~\ref{s:cmp}. In
Sect.~\ref{s:bary} we analyse the cluster hot gas mass fraction. We
discuss our results in Sect.~\ref{s:summ}, where we also draw our
conclusions.
Throughout this paper we adopt $H_0=70$ km~s$^{-1}$~Mpc$^{-1}$,
$\Omega_m=0.3$, $\Omega_{\Lambda}=0.7$. In this cosmology, 1 arcmin
corresponds to 449 kpc at the cluster redshift.
\begin{table}
\begin{center}
\caption{Available data for the LCDCS~0504 cluster.}
\label{t:datasumm}
\begin{tabular}{lcc}
\hline
& Archival data & DAFT/FADA data \\
\hline
& & \\
Optical imaging & $VRIz$ (VLT/FORS2) & B (Blanco/MOSAIC) \\
& $F814W$ (HST/ACS) & \\
& & \\
IR imaging & Spitzer/IRAC1 and 2 & \\
& & \\
Optical & VLT/FORS2 & Gemini/GMOS \\
spectroscopy & & \\
& & \\
X-ray imaging & XMM-Newton & \\
& (PN/MOS1/MOS2) & \\
\hline
\smallskip
\end{tabular}
\end{center}
\end{table}
\section{The data}
\label{s:data}
The DAFT/FADA survey is described at http://cesam.oamp.fr/DAFT/. Here
we focus on the description of the data available for LCDCS~0504,
summarized in Table~\ref{t:datasumm}.
\subsection{Optical and near-infrared imaging}
\label{ss:imaging}
We refer to \citet{Guennou+10} for a complete description of the
optical and infrared imaging data and for the evaluation of photometric
redshifts, $z_{\rm p}$. These photometric redshifts are characterized by typical
uncertainties lower than 0.1 up to $z \sim$1.5 for galaxies
brighter than $F814W=22.5$, or up to $z \sim$1 for galaxies brighter than
$F814W=24$. The photometric redshifts are used here to define
cluster membership in the absence of spectroscopic information (see
Sect.~\ref{ss:nr}).
\subsection{Optical spectroscopy}
\label{ss:spectro}
We collected 116 galaxy redshifts from the NED database, originally
from \citet{Halliday+04}, obtained with VLT/FORS2 observations in a 5
arcmin radius around the cluster center. The average error on these
redshift measurements corresponds to 90 km~s$^{-1}$ in velocity. This
sample of spectroscopic redshifts is limited to $z \leq 1.1$. The
magnitude distribution of the spectroscopic sample peaks at an
$I$-band magnitude of 22, and is limited to $I \leq 24$.
\sethlcolor{yellow}
We were awarded 6 hours of Gemini/GMOS time (program GS2011A-014) to observe
spectroscopically the three brightest giant arcs. The initial
spectral resolution was 150, but was degraded to 10~\AA/px in order to
increase the S/N. This theoretically provides a redshift uncertainty
of the order of 0.0015 (i.e. $\sim 500$~km~s$^{-1}$), corresponding
to an uncertainty of 1~pixel in the line location. Following the
identification labels of the observed objects in
Fig.~\ref{f:multiple}, we measured $z \sim 2.988$ for the object
1.3/1.4, $z \sim 3.005$ for the object 1.2, and $z \sim 3.009$ for the
object 1.1. Assuming that the 3 objects are multiple images of a
single background object, we stacked the 3 spectra together (see
Fig.~\ref{f:arc}) and measured a redshift of 3.005 for the stacked
spectrum. From the best fit strong lensing model, we draw in red the tangential critical curve at z=3 (location where the amplification diverges) and in orange the caustic lines (which are generated by de-lensing the critical lines in the source plane)
\begin{figure}
\begin{center}
\includegraphics[width=6truecm,angle=-90.0]{arc.ps}
\end{center}
\caption{Summed spectrum of arcs 1.1, 1.2, and 1.3. The best redshift is 3.005.}
\label{f:arc}
\end{figure}
\onltab{
\begin{table*}
\begin{center}
\caption{Coordinates, magnitudes, and redshifts of the
LCDCS~0504 spectroscopic galaxy catalogue. Asterisks mark data from
our GMOS run.}
\begin{tabular}{cccc|cccc}
\hline
RA (J2000) & Dec (J2000) & $I$ & redshift & RA (J2000) & Dec (J2000) & $I$ & redshift \\
\hline
12 16 35.84 &--12 03 16.4 & 22.20 & 0.7850 & 12 16 44.70 &--12 01 28.2 & 21.28 & 0.7865 \\
12 16 35.90 &--12 00 29.4 & 21.62 & 0.7930 & 12 16 44.72 &--12 01 23.4 & 22.25 & 0.7945 \\
12 16 36.13 &--12 00 43.8 & 22.04 & 0.6740* & 12 16 44.74 &--11 59 16.2 & 22.10 & 0.7998 \\
12 16 36.14 &--11 59 01.4 & 21.52 & 0.4816 & 12 16 44.84 &--12 01 30.9 & 21.97 & 0.7984 \\
12 16 36.27 &--12 03 29.0 & 21.34 & 0.5894 & 12 16 44.87 &--12 01 20.3 & 21.54 & 0.8035 \\
12 16 36.37 &--11 59 20.0 & 22.74 & 0.6650* & 12 16 44.87 &--12 00 43.5 & 22.93 & 0.7824 \\
12 16 36.41 &--12 00 08.7 & 21.64 & 0.7868 & 12 16 44.91 &--12 02 13.9 & 20.90 & 0.6691 \\
12 16 36.51 &--12 00 31.9 & 22.38 & 0.6740* & 12 16 44.91 &--12 02 03.6 & 21.50 & 0.7938 \\
12 16 36.54 &--12 02 29.8 & 22.90 & 0.4700* & 12 16 45.09 &--11 58 49.3 & 21.18 & 0.7969 \\
12 16 36.62 &--12 02 29.8 & 22.00 & 0.4700* & 12 16 45.12 &--12 00 35.9 & 23.02 & 0.7883 \\
12 16 37.18 &--12 00 41.9 & 21.03 & 0.6606 & 12 16 45.18 &--11 58 20.0 & 21.54 & 0.2327 \\
12 16 37.74 &--12 03 48.6 & 21.72 & 0.7940 & 12 16 45.24 &--12 03 13.4 & 21.60 & 0.7933 \\
12 16 38.01 &--12 02 51.4 & 21.89 & 0.7900* & 12 16 45.26 &--12 01 17.6 & 20.66 & 0.7955 \\
12 16 38.12 &--12 03 26.6 & 21.26 & 0.7939 & 12 16 45.32 &--12 01 20.9 & 21.30 & 0.8054 \\
12 16 38.23 &--12 02 51.7 & 21.08 & 0.7900 & 12 16 45.37 &--12 00 01.7 & 21.70 & 0.7996 \\
12 16 38.40 &--11 59 15.2 & 20.62 & 0.2758 & 12 16 45.60 &--11 58 38.3 & 22.85 & 0.7925 \\
12 16 38.74 &--12 01 50.3 & 21.50 & 0.8008 & 12 16 45.65 &--12 01 08.0 & 21.64 & 0.8058 \\
12 16 38.74 &--12 03 12.0 & 21.19 & 0.7958 & 12 16 45.83 &--12 01 05.6 & 22.94 & 0.7921 \\
12 16 38.83 &--12 02 44.2 & 20.79 & 0.4167 & 12 16 45.91 &--12 03 29.4 & 21.69 & 0.2252 \\
12 16 39.08 &--12 00 15.6 & 22.40 & 0.8890* & 12 16 46.10 &--12 01 14.3 & 20.61 & 0.7997 \\
12 16 39.08 &--12 03 35.7 & 22.55 & 0.6601 & 12 16 46.18 &--12 02 25.3 & 21.55 & 0.7866 \\
12 16 39.11 &--11 58 53.6 & 21.59 & 0.6640* & 12 16 46.20 &--12 00 31.0 & 22.27 & 0.7952 \\
12 16 39.13 &--11 58 39.9 & 21.60 & 0.6650* & 12 16 46.23 &--12 00 07.3 & 22.06 & 0.7847 \\
12 16 39.24 &--11 58 03.4 & 22.41 & 0.8816 & 12 16 46.35 &--12 03 25.7 & 22.34 & 0.7966 \\
12 16 39.41 &--12 03 46.4 & 21.05 & 0.5888 & 12 16 46.39 &--11 59 34.0 & 22.64 & 0.7936 \\
12 16 39.69 &--12 03 07.2 & 22.00 & 0.5437 & 12 16 46.67 &--11 59 37.8 & 21.77 & 0.6669 \\
12 16 39.88 &--11 58 17.0 & 20.55 & 0.2727 & 12 16 46.83 &--12 02 22.6 & 21.39 & 0.7987 \\
12 16 39.91 &--11 59 52.9 & 22.81 & 0.7416 & 12 16 46.90 &--12 01 23.9 & 22.40 & 0.7910* \\
12 16 39.96 &--11 58 48.1 & 20.50 & 0.2329 & 12 16 46.97 &--11 59 26.7 & 21.70 & 0.7971 \\
12 16 40.05 &--12 02 35.2 & 21.12 & 0.8022 & 12 16 47.61 &--12 02 28.0 & 20.41 & 0.5434 \\
12 16 40.19 &--12 01 59.3 & 19.34 & 0.3463 & 12 16 48.00 &--12 00 22.0 & 21.74 & 0.7860 \\
12 16 40.27 &--12 02 02.9 & 22.18 & 0.7976 & 12 16 48.18 &--12 03 18.6 & 22.73 & 0.8039 \\
12 16 40.27 &--11 58 19.8 & 22.90 & 0.6655 & 12 16 48.42 &--11 59 10.3 & 19.58 & 0.2735 \\
12 16 40.32 &--11 58 25.4 & 22.95 & 0.2733 & 12 16 48.84 &--11 58 30.7 & 21.90 & 0.1504 \\
12 16 40.33 &--12 02 01.4 & 21.41 & 0.7972 & 12 16 48.92 &--12 01 23.8 & 22.36 & 0.7940* \\
12 16 40.35 &--11 58 27.7 & 19.91 & 0.2739 & 12 16 48.93 &--11 58 57.9 & 22.10 & 1.0742 \\
12 16 40.70 &--12 03 44.0 & 21.00 & 0.7930 & 12 16 48.96 &--12 00 09.1 & 21.65 & 0.7863 \\
12 16 40.91 &--12 02 48.8 & 22.94 & 0.9480 & 12 16 49.03 &--12 01 42.6 & 22.41 & 0.8000* \\
12 16 41.58 &--11 58 46.4 & 22.93 & 0.8644 & 12 16 49.03 &--12 01 53.1 & 22.01 & 0.7998 \\
12 16 41.62 &--11 59 30.8 & 21.94 & 1.0771 & 12 16 49.43 &--11 59 16.5 & 22.38 & 0.4082 \\
12 16 41.70 &--12 03 05.4 & 21.36 & 0.8012 & 12 16 49.77 &--12 01 35.8 & 21.87 & 0.7882 \\
12 16 41.75 &--12 00 44.9 & 21.66 & 0.7967 & 12 16 49.78 &--11 58 34.4 & 23.02 & 0.7885 \\
12 16 41.91 &--12 02 44.0 & 22.10 & 0.8028 & 12 16 49.80 &--12 01 39.2 & 21.21 & 0.7965 \\
12 16 42.03 &--12 01 50.9 & 20.62 & 0.7941 & 12 16 49.97 &--12 01 10.6 & 21.46 & 0.6980* \\
12 16 42.26 &--12 01 57.2 & 22.95 & 0.7950* & 12 16 50.20 &--12 00 03.8 & 22.17 & 0.6660 \\
12 16 42.44 &--12 02 34.8 & 20.65 & 0.2631 & 12 16 50.29 &--11 59 59.4 & 22.95 & 0.7906 \\
12 16 42.80 &--12 03 39.5 & 21.33 & 0.7955 & 12 16 50.36 &--12 00 12.0 & 22.57 & 0.9312 \\
12 16 42.95 &--11 59 53.6 & 22.01 & 0.7951 & 12 16 50.42 &--12 00 48.0 & 21.92 & 0.7886 \\
12 16 43.05 &--11 59 36.5 & 22.18 & 0.2760 & 12 16 50.81 &--11 57 57.6 & 21.18 & 0.6501 \\
12 16 43.11 &--11 58 11.3 & 22.50 & 1.0579 & 12 16 50.87 &--12 02 05.7 & 20.93 & 0.7960* \\
12 16 43.18 &--12 02 40.7 & 22.46 & 0.3194 & 12 16 51.36 &--12 00 31.3 & 22.90 & 0.7841 \\
12 16 43.18 &--11 59 44.4 & 22.54 & 0.7948 & 12 16 51.57 &--12 01 30.6 & 22.04 & 0.7220 \\
12 16 43.37 &--12 02 12.8 & 22.05 & 0.7839 & 12 16 52.20 &--12 02 26.1 & 20.92 & 0.4062 \\
12 16 43.53 &--12 03 50.2 & 21.31 & 0.6693 & 12 16 52.21 &--12 00 59.5 & 22.28 & 0.7882 \\
12 16 43.76 &--12 02 15.5 & 22.37 & 0.8028 & 12 16 52.33 &--12 00 22.4 & 22.39 & 0.7583 \\
12 16 43.77 &--11 58 15.5 & 22.83 & 0.6558 & 12 16 52.65 &--12 02 55.3 & 21.53 & 0.8263 \\
12 16 43.78 &--12 02 11.1 & 21.57 & 0.7913 & 12 16 53.08 &--12 00 45.3 & 22.05 & 0.6490* \\
12 16 43.80 &--12 00 53.6 & 21.10 & 0.7945 & 12 16 53.24 &--12 01 36.2 & 21.74 & 0.7930* \\
12 16 43.87 &--11 58 42.5 & 22.79 & 0.7956 & 12 16 53.28 &--11 58 54.0 & 21.15 & 0.4763 \\
12 16 43.92 &--12 00 23.3 & 22.20 & 0.7831 & 12 16 53.39 &--12 01 38.0 & 22.20 & 0.7925* \\
12 16 44.00 &--11 57 51.6 & 21.92 & 0.7917 & 12 16 53.70 &--11 59 27.6 & 22.18 & 0.2723 \\
12 16 44.33 &--12 01 38.4 & 21.72 & 0.7861 & 12 16 54.14 &--11 57 55.9 & 22.49 & 0.8748 \\
12 16 44.35 &--12 01 42.9 & 21.05 & 0.7918 & 12 16 54.43 &--12 01 32.9 & 22.48 & 0.7900* \\
12 16 44.47 &--12 01 53.3 & 20.52 & 0.6703 & 12 16 54.76 &--11 57 45.1 & 21.24 & 0.8746 \\
12 16 44.51 &--12 03 35.9 & 18.48 & 0.2344 & 12 16 54.81 &--11 58 03.9 & 22.66 & 0.9827 \\
12 16 44.53 &--12 01 07.5 & 23.55 & 0.7934 & 12 16 54.96 &--11 58 10.2 & 20.58 & 0.1034 \\
12 16 44.59 &--12 01 08.9 & 21.83 & 0.8001 & 12 16 55.26 &--11 59 23.4 & 22.36 & 0.7950* \\
12 16 44.61 &--12 02 35.8 & 21.93 & 0.6698 & 12 16 56.23 &--11 59 39.1 & 22.92 & 0.8740* \\
12 16 44.67 &--12 02 33.7 & 21.61 & 0.6708 & & & & \\
\hline
\end{tabular}
\label{t:spectro}
\end{center}
\end{table*}
}
Remaining slits were put on galaxies along the cluster line-of-sight
(los). For a cross check and for comparison, we included 13 galaxies
in this sample with redshifts already available in the
literature. Combined with publicly available data, our final sample
contains 137 galaxies with redshifts, all with $z \leq$1.15 and $I
\leq 24.5$ (the $I$ magnitude distribution of our sample peaks at
$I=22.5$). Coordinates and redshifts for this sample are given in
Table~\ref{t:spectro} (available electronically only).
Among the 13 galaxies in
common between our GMOS measurements and the literature, only one
(with a low S/N in the GMOS data) showed discrepant redshift
measurements (0.6605 in GMOS vs. 0.7220 in the literature). The
discrepancy probably arises from a different identification of a
spectral feature that we attributed to an H$\delta$ absorption line,
while it was attributed to the Ca H line in the literature. Our
redshift measurements for the other 12 galaxies are in very good
agreement with the previous measurements, with a mean difference of
$-0.0003 \pm 0.0013$. This uncertainty is in agreement with the
expected uncertainty of our GMOS measurements. We adopt
390~km~s$^{-1}$ as the average velocity error for these data.
\subsection{X-ray data}
We have downloaded the publicly available XMM-\textit{Newton} observations of LCDC~0504: ID 0143210801, observed in 07/2003, PI D. Zaritsky, and ID 0651770201, observed in 12/2010, PI B. Maughan. Both observations were reprocessed with SAS~1
\footnote{Science Analysis System from the XMM-Newton team,
http://xmm.esac.esa.int/sas/current/sas\_news.shtml}$\!$, using the
latest available calibration files. High background (flares) time
intervals were removed with a $\sigma$-clip method using the
light-curve of the 2.0--12.0 keV band.
The final exposure times, after flare subtraction, are, for the 2003
observation: 22.71, 22.34, and 18.36~ks for the MOS1, MOS2, and pn,
respectively. For the 2010 observation we have 59.96, 63.83, and
27.89~ks for the MOS1, MOS2, and pn, respectively.
For each observation and detector we have produced exposure-map
corrected images in the 0.3--7.0 keV band. All these images were
merged together using the task imcombine/IRAF, and the result is shown
in Fig.~\ref{fig:LCDCS0504allxmm0.3_7.0}.
\begin{figure}
\begin{center}
\includegraphics[width=8.8cm]{LCDCS0504allxmm0.3_7.0.eps}
\end{center}
\caption[]{XMM-Newton image using all available data. The cluster is shown
inside the yellow central circle of radius equal to
$30^{\prime\prime}$. The other visible X-ray sources are point
source AGNs.}
\label{fig:LCDCS0504allxmm0.3_7.0}
\end{figure}
\section{Mass profile from strong lensing}
\label{s:sl}
Motivated by the spectroscopy of the blue lensed features in the cluster core
(Section~\ref{ss:spectro}) and after inspection of both the high resolution
HST/ACS image and the ground based $B, R, I$ images, we propose that
objects 1 through 3 in Table 3 are the result of a
\emph{single} background galaxy at $z=3.0$ is being strongly lensed
by Cl\,1216. We observe two images of this background source.
Each image is resolved into three sub-images, which correspond to different
sub-structures of the background source.
They are labelled systems 1, 2 and 3 (Fig.~\ref{f:multiple}).
We also conjugate two close images, forming system 4.
Having no redshift information for this system, we let its redshift free during the optimization.
Beginning with this set as constraints, we modeled the cluster mass
distribution using a dual Pseudo Isothermal Elliptical Mass Distribution
\citep[dPIE, hereafter;][]{Limousin+05,Eliasdottir+07}. The dPIE model is based
on the Pseudo Isothermal mass profile, characterized by the 3D mass
profile\footnote{This is the total mass enclosed within a radius $r$,
sometimes written as $M(<r)$ in the literature.}
\begin{equation}
M(r) = 2\,{s\,\sigma_0^2\over G\,(s-a)}\,\left[ s\,\tan^{-1} \left ({r\over s}\right) - a\,\tan^{-1}\left({r\over a}\right) \right] \ ,
\end{equation}
provides a 3D density profile:
\begin{equation}
\rho(r) = {\sigma_0^2 \over 2\pi G}\,{s\,(a+s)\over (r^2+a^2)\,(r^2+s^2)} \ ,
\end{equation}
where $G$ is the gravitational constant, $r$ is the 3D clustercentric
radial distance, $a$ the core radius, $s$ the scale radius, $\sigma_0$
the central velocity dispersion. This profile is not isothermal
(slope $-2$) at all radii but only in the intermediate radial range
$a \leq r \leq s$. This $M(r)$ corresponds to the
projected mass density profile,
\begin{equation}
\Sigma(R)={s \, \sigma_0^2 \over 4 {\rm G} \, (s-a)} \, [(R^2+a^2)^{-1/2}-(R^2+s^2)^{-1/2}] \, ,
\end{equation}
where $R$ is the 2D projected clustercentric radial distance. The
dPIE is obtained by replacing $R$ with
\begin{equation}
\widetilde R^2 = {X^2 \over (1+\epsilon)^2} + {Y^2 \over (1-\epsilon)^2} \, ,
\end{equation}
where the ellipticity is defined as $\epsilon \equiv (A-B)/(A+B)$,
with $A, B$ the semi-major and, respectively, semi-minor axis, and $X,
Y$ are the spatial coordinates along the major, and, respectively,
minor axes. There are 6 free parameters in the dPIE model, the two
coordinates of the cluster center, the ellipticity, the orientation
angle, the velocity dispersion, and the core and scale radii.
We rely on the dPIE model results to identify and search for other gravitational
arcs. We note, though, that we could not distinguish between the
dPIE model and a NFW model \citep{NFW97}
with our SL analysis, given the uncertainties. However,
we prefer using a dPIE profile since the parameters can be constrained by our
SL analysis, whereas the NFW profile (in particular the scale radius) is out
of reach of the SL constraints (but not out of reach of modeling based on
kinematics data, see Sect.~\ref{s:kin}).
We fix the scale radius $s$ to 1 Mpc since it cannot be constrained by
our data. Furthermore, after some tests, we figured out that the core
radius was constrained to be smaller than $\sim 5\arcsec$,
i.e. smaller than the range where multiply imaged systems are
found. We fix it to 2$\arcsec$.
Note that with this choice of parametrization, the cluster is modelled
using a mass profile which is close to isothermal. Given the circular
aspect of this cluster, we impose its position to be within $\pm$ 5$\arcsec$
from the BCG galaxy. Together with the ellipticity and the position angle
of the mass distribution, this gives 5 parameters to be optimized. On top of
this smooth component, we include perturbations from the brighest
cluster members located close (i.e. less that $\sim 5\arcsec$) to the
multiply imaged systems. This gives 11 individual galaxies. Following
earlier works \citep[e.g.][]{Limousin+07b}, we describe these
perturbers using a dPIE profile, whose geometrical parameters
(position, ellipticity, position angle) are set to the one measured
from their light distribution. Their core radius is set to 0, and
their scale radius to 45\,kpc, which describe compact dark matter
haloes, as expected for central cluster galaxies within a tidal
stripping scenario \citep{Limousin+07}. Their velocity dispersion is
scaled with their luminosity (see Limousin et~al. 2007, ApJ for more
details). Therefore, the perturbers are modeled using one extra
parameter. Using the 8 constraints provided by the multiply imaged
systems, we optimize the mass model in the image plane, using the
\textsc{Lenstool}\footnote{http://www.oamp.fr/cosmology/lenstool/}
software \citep{Jullo+07}. We find that this simple unimodal
model is able to reproduce accurately the multiply imaged systems,
with an RMS of 0.15$\arcsec$ (image plane).
The mass model predicts a third central image for the strongly lensed
background galaxy at $z=3.0$, predicted to be more than 5 magnitudes
fainter than the main images. System 4 is predicted to be at
$z=2.4\pm0.4$. Finally, we have not been able to reliably find the
counterimage of the blue feature located at $\alpha=184\fdg18761,
\delta=-12\fdg024721$ (yellow circle on Fig.~\ref{f:multiple}). One
possibility is that it is singly imaged. In that case, its redshift
should be smaller than 1.35.
\begin{table}
\begin{center}
\caption{Multiply imaged systems for the SL analysis.
}
\begin{tabular}{ccccc}
\hline
ID & R.A. & Decl. & $z_{\rm spec}$ & $z_{\rm model}$ \\
& (J2000) & (J2000) & & \\
\hline
1.1 &184.19186 &--12.01878 & 3.0 & --- \\
1.2 &184.18402 &--12.02390 & 3.0 & --- \\
2.1 &184.18985 &--12.01758 & 3.0 & --- \\
2.2 &184.18683 &--12.02611 & 3.0 & --- \\
3.1 &184.18965 &--12.01752 & 3.0 & --- \\
3.2 &184.18752 &--12.02630 & 3.0 & --- \\
4.1 &184.19216 &--12.01974 & assumed & 2.3$\pm 0.5$ \\
4.2 &184.19171 &--12.01922 & assumed & 2.3$\pm 0.5$ \\
\hline
\end{tabular}
\end{center}
\label{t:multi}
\end{table}
\begin{table}
\begin{center}
\caption{dPIE mass model parameters.}
\begin{tabular}{ll}
\hline
R.A. (arcsec) & --1.1$\pm$0.8 \\
Decl. (arcsec) & 0.5$_{-2.1}^{+0.9}$ \\
$\epsilon$ & 0.07$\pm$0.04 \\
orientation angle (degrees) & 91$\pm$8 \\
$\sigma_0$ (km\,s$^{-1}$) & 839$\pm$14 \\
$a$ (kpc) & [14] \\
$s$ (kpc) & [1\,000] \\
\hline
\end{tabular}
\tablefoot {Coordinates are given in arc-seconds with respect to the cD
galaxy located at $\alpha =184\fdg18845$, $\delta = -12\fdg021472$.
Error bars correspond to $1\sigma$ confidence level as inferred from
the Monte Carlo Markov Chain optimization.}
\end{center}
\label{t:sl}
\end{table}
\section{Mass profile from X-ray data}
\label{s:x}
We have produced a surface brightness image of LCDCS~0504 by merging all the individual detectors (MOS1, MOS2, and pn from both 2003 and 2010 exposures) exposure-map corrected images. We then fitted the X-ray surface-brightness profile of
LCDCS~0504 by a 2D, elliptical $\beta$-model\footnote{We use $\beta_X$ for the parameter of the model to distinguish it from the kinematics $\beta$, see eq.~\ref{e:beta}.
\citep{CFF76}, with a flat background added to it:}
\begin{equation}
I(R) = I_0\,\left[1 + \left({R\over r_c}\right)^2\right]^{1/2-3\beta_X} + B ~,
\label{eq:beta2D}
\end{equation}
with best-fit values $\beta_X = 0.52 \pm 0.06$ and $r_c = (113 \pm 19)$ kpc, see Fig.~\ref{fig:2dxrayfit}.
\begin{figure}[htb]
\begin{center}
\includegraphics[width=8cm]{fit2D_sherpa_LCDCS0504.eps}
\end{center}
\caption[]{ 2D surface brightness fit. Left: LCDCS~0504 image in the [0.5-7.0 keV] band with point sources and artefacts (CCD gap) masked out. Middle: best-fit $\beta$-model (see text for details) shown with the same color coding of the original image. Right: residuals, data minus best-fit model. No apparent structure is seen on the residual image.}
\label{fig:2dxrayfit}
\end{figure}
The fit with a $\beta$-model is good, and this suggests the
cluster is not cool-core, as a cuspy density profile is usually
observed in cool-core clusters. In non cool-core clusters the
temperature is usually isothermal inside $r_{500}$. We therefore opt
for using a single mean temperature for the dynamical modeling.
In any case, the data are too sparse to determine such
a significant non-isothermal nature of the gas so as to change our
conclusions. It is not feasible to obtain a meaningful radial
temperature profile with the $\sim 5800$ net counts (i.e.,
background subtracted and masking the bright point source to the
West) resulting from the LCDCS0504 X-ray flux of $(1.0 \pm 0.4) \,
10^{-13}$ erg~s$^{-1}$~cm$^{-2}$, inside 1 arcmin in the [0.5--10.0]
keV band.
A spectral analysis was used to compute the central gas density, as
well as its temperature, that was estimated with XSPEC v12, from
HEASARC\footnote{http://heasarc.gsfc.nasa.gov/}. The X-ray spectrum
was extracted within a region of radius 1~arcmin (point sources were
masked) and modeled as an emission from a single temperature plasma
\citep[mekal model;][]{KM93,LOG95}. We have fitted simultaneously all the spectral data, MOS1, MOS2 and pn from both 2003 and 2010 observations. The photoelectric absorption -- mainly due to Galactic neutral hydrogen -- was computed using the
cross-sections given by \citet{BCM92}, available in XSPEC. Metal
abundances (metallicities) were scaled to the \citet{AG89} solar values.
For the MOS spectra, we restricted our fit to the interval 0.5--7.0~keV,
while for the pn data, we used the 0.7--7.0~keV. We kept the hydrogen
column density fixed for the fit at the Galactic value, $N_{\rm H} =
3.26 \times 10^{22}$~cm$^{-2}$, in the direction of LCDCS~0504
\citep[LAB survey,][]{Kalberla+05}.
Our best fit, shown in Fig.~\ref{fig:Xspectralfit} had a reduced $\chi^2 = 0.867$ for 491 degrees of freedom
with the following free parameters: $kT = 5.1^{+0.66}_{-0.55}$~keV and
$Z = 0.23^{+0.17}_{-0.15} Z_\odot$. Inside a radius of 1~arcmin the
fitted spectral model implies a bolometric X-ray luminosity of $L_X =
(2.90 \pm 0.18) \times 10^{44}$~erg~s$^{-1}$. Our spectral fit agrees
quite well with the thorough analysis done by \citet{Johnson+06}, who
used only the first, shallower XMM observation.
\begin{figure}[htb]
\begin{center}
\includegraphics[width=8.8cm]{mekal_xmmall1.eps}
\end{center}
\caption[]{ Best-fit absorbed MEKAL model. Top: All detectors from both XMM-\textit{Newton} observation are fitted simultaneously, as described in the text. Bottom: Plot of the residual contribution to the $\chi^2$ per energy bin of the best fit spectrum.}
\label{fig:Xspectralfit}
\end{figure}
Assuming an isothermal plasma, the 3D deprojection of Eq.~(\ref{eq:beta2D}) is:
\begin{equation}
n(r) = n_0 \, \left[1 + \left({r\over r_c}\right)^2\right]^{-3\beta_X/2} \ ,
\label{eq:ngasbeta}
\end{equation}
where $n_0$ is the central particle number density in units of
cm$^{-3}$ and the radii $r$ and $r_c$ are given in kpc. The central
density was obtained by normalizing the X-ray flux measured with the
expected bremsstrahlung flux from an isothermal $\beta$-model
distribution. From the spectral analysis we obtain $n_0 = (6.5 \pm
0.7) \times 10^{-3}$~cm$^{-3}$.
The total mass profile, assuming isothermal hydrostatic equilibrium
and a spherical $\beta$-model, is given by:
\begin{equation}
M(r) = 6.68 \times 10^{10}\, \frac{\beta_X kT}{\mu r_c^2}\,
{r^3\over 1 + {r^2}/{r_c^2} }\,
M_\odot \, ,
\label{eq:mdynx}
\end{equation}
where $\mu = 0.6$, $kT$ is in keV, while $r$ and $r_c$ are in kpc.
The values of $\rvir$ and $\rs$ corresponding to this mass profile are
given in Table~\ref{t:dyn}. Note that also in this case, as for the
SL determination, the value of $\rvir$ is based on an extrapolation
of the mass profile beyond the region where it is constrained.
The total density profile corresponding to the mass profile of
equation~(\ref{eq:mdynx}) is
\begin{equation}
\rho(r) \propto {r^2+3 r_c^2\over (r^2+r_c^2)^2} \ .
\label{eq:rhox}
\end{equation}
\section{Mass profile from kinematics}
\label{s:kin}
Here, we use the projected phase space distribution of cluster galaxies
to constrain the mass distribution of the cluster. We adopted three
methods of deriving a mass model based solely on the optical data, two
based on the Jeans equation \citep[e.g.][]{BT87}, and one based on the
Caustic method \citep{DG97,Diaferio99}. The methods based on the Jeans
equation are ``Dispersion-Kurtosis'' \citep[][DK hereafter]{LM03}, and
``MAMPOSSt'' \citep{MBB13}. All three methods assume spherical
symmetry.
The DK method performs a simultaneous best-fit of the parameters of a
model mass profile, $M(r)$, and of a model velocity anisotropy
profile,
\begin{equation}
\beta(r) = 1 - {\sigma_\theta^2(r) + \sigma_\phi^2(r) \over
2\,\sigma_r^2(r)} = 1 - {\sigma_\theta^2(r) \over \sigma_r^2\rm{(r)}}
\label{e:beta}
\end{equation}
where $\sigma_\theta, \sigma_\phi$ are the two tangential components,
and $\sigma_r$ the radial component, of the velocity dispersion, and
the last equivalence is obtained in the case of spherical symmetry.
The fit is done by minimizing the summed $\chi^2$ of the fits to the
binned line-of-sight velocity dispersion profile,
$\slos(R)$, and to the binned line-of-sight kurtosis profile, $K(R)$,
corrected for the known statistical bias using the expression in \citet{decarlo97}.
Using these two profiles rather than just one allows to partially
break the degeneracy between the $M(r)$ and $\beta(r)$
parameters. A limitation of this method is that it assumes that
$\beta(r)$ is constant with radius.
The MAMPOSSt method, like the DK method, determines the best-fit
parameters of model $M(r)$ and $\beta(r)$, but unlike the DK method it
requires no binning of the observables, since it performs a maximum
likelihood fit of the full projected phase space distribution of
cluster members. Unlike\footnote{this is no longer the case with Richardson \& Fairbairn 2013} the DK method, it has no limitation on the
choice of the $\beta(r)$ model. It must however assume a shape for the
3D velocity distribution, and this is taken to be Gaussian in our
analysis.
Both the DK and MAMPOSSt methods assume the cluster to be in dynamical
equilibrium, so their domain of application is limited to the virial
region of the cluster. The Caustic method drops this requirement, and
therefore can be used to determine $M(r)$ also outside the virial
region. However, the Caustic method is less accurate than DK and
MAMPOSSt near the center, and tends to overestimate $M(r)$ at small
radii \citep{Serra+11}. The Caustic method determines the cluster
mass profile non-parametrically, from the velocity amplitude of the
caustics in projected phase space, but it must assume knowledge of
$\beta(r)$.
\subsection{Cluster membership}
\label{ss:members}
Identification of the cluster members is required in the three
methods, there are several methods to identify real cluster members
(e.g. \citealp{Wojtak+07,MBB13}). We applied two of them here to estimate the
uncertainty in the derived results. We used the method of
\citet{dHK96} and the `Clean' method of \citet{MBB13}. We selected
these 2 approaches out of the several discussed as the former was
shown by \citet{Wojtak+07} to perform marginally better than many
other techniques, and the latter is a new method based on the
analysis of the internal dynamics of cluster-sized halos in numerical
simulations \citep{MBM10}.
Both methods identify real cluster members on the basis of their
location in projected phase space\footnote{\label{fn:gal}For each
galaxy in the cluster, $R$ is the projected cluster-centric distance
from the cD galaxy, and ${v_{\rm rf}}$ is the rest-frame velocity
\mbox{${v_{\rm rf}} \equiv ({v-v_{\rm cl}})/(1+{v_{\rm cl}/c})$},
where ${v_{\rm cl}}$ is the mean velocity of the cluster. This is
re-defined at each new iteration of the membership selection, until
convergence. The cluster center is defined to be the position of the
cD galaxy.}, $R, {v}_{\rm rf}$. The two methods identify the
same galaxies as members of LCDCS~0504, 75 in total (see
Fig.~\ref{f:rvcau}). Based on this sample we estimate the cluster
velocity dispersion $\slos=974_{-76}^{+83}$ km~s$^{-1}$ \citep[biweight
estimate, see][]{BFG90}.
\begin{figure}
\begin{center}
\begin{minipage}{0.5\textwidth}
\resizebox{\hsize}{!}{\includegraphics{rvm_cau_new.ps}}
\end{minipage}
\end{center}
\caption{The projected phase space distribution of galaxies with
redshifts in the cluster region. Selected cluster members are shown
as filled dots. The chosen caustic in the Caustic method is shown in
green.}
\label{f:rvcau}
\end{figure}
\subsection{Galaxy number density profile}
\label{ss:nr}
In both the DK and MAMPOSSt methods, the number density profile of the
tracers of the gravitational potential, $n(r)$, needs to be
estimated. This determination of $n(r)$ is the only occurrence in our
dynamical analysis where completeness, or correction for
incompleteness, is necessary. Since our spectroscopic sample is not
complete, we use the 100\% complete sample of galaxies with magnitude
$F814 \leq 24$ and measured photometric redshifts, $z_{\rm p}$, for the
determination of $n(r)$.
\begin{figure}
\begin{center}
\begin{minipage}{0.5\textwidth}
\resizebox{\hsize}{!}{\includegraphics{zp_new.ps}}
\end{minipage}
\end{center}
\caption{The adaptive-kernel smoothed distribution of photometric
redshifts for galaxies in the cluster region. The vertical (blue) line
shows the average cluster redshift. The solid (red) curve shows
the selected $z_{\rm p}$ range for the sample used for the determination
of $n(r)$.}
\label{f:zp}
\end{figure}
Our photometric observations fully cover the cluster only out to $\sim
2$ arcmin from the adopted cluster center, the cD galaxy. Beyond this
radius we estimate the radial geometrical completeness, $C_g(R)$, as
the fractions of circular annuli covered by our observations. $C_g(R)$
drops below 50\% beyond 3.3 arcmin.
We select the $z_{\rm p}$-range for defining cluster membership as
follows. We smooth the $z_{\rm p}$ distribution by an adaptive kernel
technique with a kernel size of 0.045, i.e. half the value of the
typical uncertainty on the photometric redshifts. Larger values of
the kernel size would lead to un-necessary over-smoothing of the
$z_{\rm p}$ distribution, while smaller values are likely to
emphasize noise-related features. We identify the main peak of
the $z_{\rm p}$ distribution closest to the mean cluster
redshift. We define the extremes of this peak in $z_{\rm p}$ in such a
way as to avoid contamination from other peaks in the distribution,
$0.64 \leq z_{\rm p} \leq 0.93$ (see Fig.~\ref{f:zp}).
\begin{figure}
\begin{center}
\begin{minipage}{0.5\textwidth}
\resizebox{\hsize}{!}{\includegraphics{nr_fit_new.ps}}
\end{minipage}
\end{center}
\caption{The projected number density profile of $z_{\rm p}$-selected
cluster members (points with 1$\sigma$ error bars) and the best-fit
model (projected-NFW + constant density background; solid curve).
The reduced $\chi^2$ of the fit is 0.8.}
\label{f:nr}
\end{figure}
We perform a maximum-likelihood fit of the spatial distribution of the 375
galaxies in the selected $z_{\rm p}$-range, weighting each galaxy by
$C_g(R_i)^{-1}$, where $R_i$ is the radial position of galaxy $i$, to
account for geometrical incompleteness. We limit the fit of the number
density profile to the radii where $C_g \geq 0.5$. The fitted model
is NFW in projection \citep{Bartelmann96,LM01} to which we add a
constant density background to account for interlopers in our $z_{\rm p}$
selection. Of the two free parameters of the NFW model, we are only
interested in the scale radius of the galaxy number density, $\rtr$,
because the other parameter, that sets the normalization of $n(r)$,
cancels out in the Jeans equation. We find $\rtr=0.27_{-0.15}^{+0.44}$
Mpc, and a background density corresponding to 38\% background
contamination in our $z_{\rm p}$-selected sample.
Since the uncertainties on $\rtr$ are very large, we also consider an
alternative estimate, based on the spectroscopic sample of cluster
members (see Sect.~\ref{ss:members}). The radial geometrical
completeness, $C_g(R)$, is the same for this sample as for the
$z_{\rm p}$-selected sample. In addition, the spectroscopic sample
suffers from radially-dependent completeness because the fraction of
galaxies with measured redshifts is higher near the cluster center. We
evaluate this spectroscopic completeness, $C_s(R)$, as the ratio
of the number of galaxies with measured redshifts to the total number
of galaxies (134 and 713 in total)
in radial bins, down to $F814 \leq 23$. We find $C_s(R)=0.22$
outside the central bin, i.e. at $R \geq 0.11$ arcmin, and
$C_s(R)=0.50$ inside this bin. We then run a maximum-likelihood
fit of the spatial distribution of spectroscopic members weighting
each galaxy by $[C_g(R_i) \times C_s(R_i)]^{-1} $. We find
$\rtr=0.48_{-0.24}^{+0.46}$ Mpc, and a background density
corresponding to 4\% background contamination. The background
contamination, which is much lower than for the $z_{\rm p}$-selected sample,
as expected. The $\rtr$ value is consistent within the (large) error bars
with that obtained using the $z_{\rm p}$-selected sample.
In the dynamical analysis with the DK and MAMPOSSt methods, we will
use both estimates of $\rtr$, to understand how much our
limited knowledge of $\rtr$ affects our estimate of the cluster mass
profile. The knowledge of $\rtr$ is not required for the dynamical
analysis with the Caustic method.
\subsection{Results}
\label{ss:dynres}
For both the DK and MAMPOSSt methods we use the NFW
model for $M(r)$ \citep{NFW97},
\begin{equation}
M(r)=\mvir {\ln(1+r/\rs)-r/\rs \, (1+r/\rs)^{-1} \over \ln(1+\cvir)-\cvir/(1+\cvir)},
\end{equation}
where $\cvir \equiv \rvir/\rs$ is the mass profile concentration. The
model has two free parameters, the virial mass and concentration, or,
equivalently, the virial and scale radii $\rvir$ and $\rs$. Note that
the total mass density scale-length is different from the scale-radius
of the galaxy number density profile, i.e. $\rs \neq \rtr$ (Sect.
\ref{ss:nr}), since we allow the ditribution of the total mass and
that of the galaxies to be different in our analysis. For the Caustic
technique, for the sake of comparison with the other two methods, we
also fit a NFW model to the mass density profile determined from
differentiation of the non-parametrically determined mass profile.
The MAMPOSSt method is the only one among the three where there is
complete freedom in the choice of $\beta(r)$. We use a
simplified version of the model of \citet{Tiret+07},
$\beta(r)=\beta_{\infty} \, r/(r+\rs)$, where
$\beta_{\infty}$ is the asymptotic value of the anisotropy reached at
large radii, and $\rs$ is the scale radius of the NFW mass
density distribution. This model was shown by \citet{MBM10} to provide
a good fit to cluster-mass halos extracted from cosmological
numerical simulations. In this model, galaxy orbits are isotropic near
the cluster center and become increasingly radially anisotropic outside.
In the Caustic technique, we use Gaussian adaptive kernels for the
density estimation in projected phase space, with an initial kernel
size equal to the optimal kernel size of \citet{Silverman86}. Before
the density estimation, we scale the velocity coordinates such that the
scaled velocity dispersion is the same as the dispersion in the radial
coordinates. In the equation that connects $M(r)$ to the Caustic
amplitude \citep[eq. 13 in][]{Diaferio99},
we adopt either ${\cal F}_{\beta}=0.5$ as recommended by
\citet{Diaferio99} and \citet{GDRS13}, or ${\cal F}_{\beta}=0.7$ as
recommended by \citet{Serra+11}. For the estimation of the $M(r)$ error
we adopt the recipe of \citet{Diaferio99}. \citet{Serra+11} have found
that these error estimates correspond to 50\% confidence levels; we
therefore scale them up by a factor of 1.4 to have $\sim 1\sigma$
level error estimates. The chosen caustic is displayed in
Fig.~\ref{f:rvcau}.
The domain of application of the DK and MAMPOSSt methods is the virial
region. Since almost all our cluster members are in the virial region,
we only exclude the very central region, 25 kpc, where the
gravitational potential is likely to be dominated by the cD and therefore
unlikely to follow a purely NFW profile.
\begin{table}
\begin{center}
\caption{\label{t:dyn}Best-fit $M(r)$ and $\beta$ parameters from kinematics.}
\begin{tabular}{lllc}
\hline
\\
Method & $\rvir$ & $\rs$ & Velocity \\
& [Mpc] & [Mpc] & anisotropy \\
\\
\hline
\\
DK ($p$) & $1.28_{-0.06}^{+0.16}$ & $0.05_{-0.03}^{+0.26}$ & $-3_{-1}^{+3}$ \\
\\
DK ($s$) & $1.28_{-0.10}^{+0.12}$ & $0.05_{-0.05}^{+0.35}$ & $-3_{-2}^{+3}$ \\
\\
MAMPOSSt ($p$) & $1.32_{-0.09}^{+0.14}$ & $0.16_{-0.10}^{+0.34}$ & $0.5_{-0.2}^{+0.4}$ \\
\\
MAMPOSSt ($s$) & $1.28_{-0.12}^{+0.10}$ & $0.19_{-0.12}^{+0.43}$ & $0.5_{-0.2}^{+0.4}$ \\
\\
Caustic, ${\cal F}_{\beta}=0.5$ & $1.27_{-0.20}^{+0.16}$ & $0.14_{-0.04}^{+0.06}$ & -- \\
\\
Caustic, ${\cal F}_{\beta}=0.7$ & $1.42_{-0.22}^{+0.18}$ & $0.16_{-0.04}^{+0.04}$ & -- \\
\\
Weighted average & $1.30 \pm 0.05$ & $0.14 \pm 0.07$ & -- \\
\\
\hline
\end{tabular}
\tablefoot{The DK and MAMPOSSt estimates are obtained using the number
density profile based on the photometric ($p$) or the spectroscopic
($s$) samples of cluster members. The velocity anisotropy is the
constant value of $\beta$ for the DK method, and $\beta_{\infty}$ in
the simplified Tiret model for the MAMPOSSt method.}
\end{center}
\end{table}
\begin{figure}
\begin{center}
\begin{minipage}{0.5\textwidth}
\resizebox{\hsize}{!}{\includegraphics{vdp_new.ps}}
\end{minipage}
\end{center}
\caption{The observed line of sight velocity dispersion profile (points with
1~$\sigma$ error bars) and those predicted by the best-fit NFW
models, obtained with the DK (dashed red line), and MAMPOSSt (solid
blue line) methods. Only those solutions obtained using the $\rtr$
value found with the $z_{\rm p}$ sample of members are shown, for clarity.}
\label{f:vdp}
\end{figure}
\begin{figure}
\begin{center}
\begin{minipage}{0.5\textwidth}
\resizebox{\hsize}{!}{\includegraphics{rvrs_new_mar.ps}}
\end{minipage}
\end{center}
\caption{The best-fit $M(r)$ NFW parameters from the kinematics
analyses, within 1~$\sigma$ confidence level contours, obtained with
the DK (red squares), MAMPOSSt (blue dot and circle), and Caustic
(green filled and open diamond) methods. The filled (resp. open)
symbols are for the solutions obtained using the $\rtr$ value from
the photometric (resp. spectroscopic) sample of members. The dashed
red (resp. dash-dotted blue) contour represents the 1 $\sigma$
confidence region on the best-fit parameters of the DK
(resp. MAMPOSSt) method, obtained using the $\rtr$ value from the
photometric sample of members. The solid (resp. dotted) green
contour represents the 1 $\sigma$ confidence region on the best-fit
parameters for the Caustic method obtained using ${\cal
F}_{\beta}=0.5$ (resp. ${\cal F}_{\beta}=0.7$).
The magenta solid (resp. dash-dotted) inclined line is the
theoretical predictions for relaxed clusters at the mean redshift of
LCDCS~0504 from \citet{BHHV13} \citep[resp.][]{DeBoni+13}.
The black dot with error bars is the weighted average of the DK, MAMPOSSt and
Caustic results.
}
\label{f:rvrs}
\end{figure}
The results of the dynamical analysis are summarized in
Table~\ref{t:dyn} and displayed in Fig.~\ref{f:rvrs}, where we show
the confidence contour in the $[\rvir, \rs]$ plane. We also list
and display a weighted average of the DK, MAMPOSSt, and Caustic
results. We multiply the formal error on this average by $\sqrt{5}$
to take into account that the five averaged results are not
independent. The constraints on the $\beta$ parameters obtained by
the DK and MAMPOSSt methods are very loose, so we do not display them
here.
There is a good agreement between the values of $\rvir$ obtained by
the DK, MAMPOSSt and Caustic methods. The Caustic solution obtained
with ${\cal F}_{\beta}=0.5$ is closer to those from the other two
methods. This would argue in favor of using this value, rather
than ${\cal F}_{\beta}=0.7$, in the Caustic technique, as done
recently by \citet{GDRS13}. However, \citet{Gifford+13} have
recently suggested using the intermediate value ${\cal F}_\beta$=0.65.
Moreover, for $\beta=\rm cst$ NFW models, at the half-mass
radius of $\approx 2\,r_{-2}$, ${\cal F}_\beta=0.5$ corresponds to
$\beta=-1.1$ while ${\cal F}_\beta=0.7$ corresponds to
$\beta=0.3$. The very tangential anisotropy for ${\cal F}_\beta=0.5$
is not what most analysis extract for galaxies in clusters
\citep[e.g.][and references therein]{Biviano+13}, so the agreement
of the ${\cal F}_{\beta}=0.5$ solution with those of the DK and
MAMPOSSt methods may just be fortuitous.
The DK and MAMPOSSt methods pose very weak constraints on $\rs$. \cite{MBB13}
already noted that the determination of the dark matter scale radius is
inefficient, which \cite{SLM04} had previously noted for the concentration
parameter.
The constraints obtained by the Caustic technique are tighter, and
almost independent of the value of ${\cal F}_{\beta}$. The Caustic
technique is able to better constrain the $\rs$ parameter of the mass
distribution than the DK and MAMPOSSt techniques possibly because,
unlike these, it is the only free parameter in the model fit. In fact
$\beta(r)$ is fixed when the value of ${\cal F}_{\beta}$ is assumed,
and $\rvir$ is estimated non-parametrically directly from the Caustic
mass profile.
The agreement between the MAMPOSSt and DK solutions is also
evident from Fig.~\ref{f:vdp} where we show the projection of the
best-fit DK and MAMPOSSt solutions on the observed line-of-sight
velocity dispersion profile\footnote{We remind the reader that the DK
best-fit solution is obtained by a simultaneous fit of both the
observed velocity dispersion profile and the observed kurtosis
profile, while the MAMPOSSt best-fit solution is obtained by a fit
of the full line-of-sight velocity distribution. Fig.~\ref{f:vdp}
is just a way of presenting the best-fit models.}.
In Fig.~\ref{f:rvrs} we also show the theoretical predictions of
\citet{BHHV13} and \citet{DeBoni+13} for the concentration-mass
relation of relaxed clusters at the redshift of LCDCS~0504, converted
in the $\rvir$-$\rs$ plane. Both theoretical predictions predict
too high a concentration for a cluster of the mass and at the redshift
of LCDCS~0504. Since the prediction of \citet{DeBoni+13} is based on
hydrodynamic simulations, while that of \citet{BHHV13} originates from
DM-only simulations, the discrepancy between theoretical
predictions and observation cannot be explained by baryonic
processes affecting the cluster dynamical structure.
\section{Comparing the different mass profile determinations}
\label{s:cmp}
The methods based on SL, X-ray, and kinematics to determine the
cluster mass profile have different sensitivities on different
scales. It would therefore be misleading to either extrapolate the
SL and X-ray mass estimates to $\rvir$ to compare with the result
from kinematics, or to restrict the spectroscopic data-sample to a
smaller region to directly infer $r_{2500}$ or $r_{500}$ from the
kinematics analysis, with loss of statistics. Rather than comparing
the mass profile parameters, a more appropriate comparison is that
between the different mass profiles themselves, in the regions
where they overlap.
The three $M(r)$ from the SL, X-ray, and kinematics analyses are shown
in the top panel of Fig.~\ref{f:mr}, their ratios are shown in the
bottom panel of the same figure\footnote{To compare the mass
distribution obtained with the SL analyses with the others, we take
the spherical approximation also for the SL method. In practice we
force to zero the ellipticity parameter $\epsilon$ of the SL
model.}. The SL and kinematics $M(r)$ are in agreement within the
errors. The significant difference in the $\rvir$ values of these two
profiles is therefore due to the uncertain extrapolation of the SL
$M(r)$, which is considerably flatter than the kinematics $M(r)$.
On the other hand, within inner 100 kpc, the $M(r)$ obtained by the
X-ray analysis
is significantly below both the SL and the kinematics mass profiles.
In this case, the discrepancy is real and cannot be attributed to
extrapolation uncertainties.
\begin{figure}
\begin{center}
\begin{minipage}{0.5\textwidth}
\resizebox{\hsize}{!}{\includegraphics{mprof_new.ps}}
\end{minipage}
\end{center}
\caption{{\em Top panel:} The mass profiles and their 1~$\sigma$
confidence regions obtained from the SL (red dashed line and yellow
region), X-ray (black dashed line and grey region), and kinematics
(blue solid line and cyan region) analyses. {\em Bottom panel:}
the ratios of the three mass profiles and their 1~$\sigma$ confidence
regions. Solid blue line and grey-cyan region: ratio of the kinematics to
X-ray mass profiles. Dashed-dotted blue line and green region: ratio
of the kinematics to SL mass profiles. Dashed black line and orange
region: ratio of the X-ray to SL mass profiles. In both panels the profiles
are shown in the radial range where they are constrained by the data.}
\label{f:mr}
\end{figure}
We will discuss the possible origin of the differences between the mass
profiles in Sect.~\ref{s:summ}.
\section{The gas mass fraction}
\label{s:bary}
We compute the intra-cluster gas mass profile with the integral of
the gas density profile of equation~(\ref{eq:ngasbeta})
over a spherical volume. For the present
cluster we have:
\begin{equation}
M_{\rm gas}(r) = 1.205 \times 10^8\, n_0 \, r^3 \, {}_2F_1\left(\frac{3}{2},\frac{3 \beta_X}{2},\frac{5}{2}, - \frac{r^2}{r_c^2} \right) M_\odot \, ,
\label{eq:mgas}
\end{equation}
where $_2F_1(a,b,c,x)$ is the standard hypergeometric function.\footnote{For
$\beta_X=1/2$, consistent with our fit to the X-ray surface brightness
profile, a useful approximation to the hypergeometric function of
equation~(\ref{eq:mgas}) is
${}_2F_1\left(\frac{3}{2},\frac{3}{4},\frac{5}{2}, - \frac{r^2}{r_c^2}
\right)
\simeq 6 \left [(x^3/3)^{-\gamma}+(2 x^3/3)^{-\gamma}\right]^{-1/\gamma}$,
where $\gamma = 2^{1/8} \simeq 1.0905$,
which is accurate to better than 2.7\% for all radii
(see \citealp{ML05b}).}
Dividing Eq.~(\ref{eq:mgas}) by Eq.~(\ref{eq:mdynx}) yields the gas
mass fraction, $f_{\rm gas}$. Figure~\ref{fig:xraymass} shows the mass
profiles, gas and total, in the upper panel and the gas fraction
radial profile in the bottom panel. The cluster gas mass fraction
increases with $r$, as seen in most clusters \citep[see,
e.g.,][]{BS06,Allen+08,FHHR09}. At $r>300$ kpc, the gas mass
fraction reaches a value that is consistent with the cosmic gas
fraction, which is $\simeq 83$\% of the cosmic baryon fraction
\citep{FHP98,Hinshaw+12,PlanckCollaboration+13}.
A comparison with the results of \citet{Eckert+13} shows that the gas
mass fraction profile of LCDCS~0504 is very similar to that of
lower-$z$ clusters, except near the cluster center, where it is
significantly below. This is shown in the top panel of
Fig.~\ref{f:fgas} where we plot the results of \citet{Eckert+13}
for the average gas mass fraction of cool-core and non-cool-core
clusters, together with our results, based in both cases on the
total mass determined from X-ray analysis. If we instead use
the total mass determined from kinematics, we can compare our
result with that of \citet{BS06}. This comparison is shown in
the bottom panel of Fig.~\ref{f:fgas}. In this case the gas fraction of
LCDCS~0504 appears to lie below that for a sample of nearby clusters
at almost all radii.
Finally, we compare the LCDCS~0504 gas mass fraction computed using
the total mass derived from our lensing analysis (see
Sect.~\ref{s:sl}) with those of \citet{Zhang+10}, also derived using
total mass estimates from lensing, except that in their case it was
the weak, not the strong lensing effect that was used. The comparison
is shown in Fig.~\ref{f:fgaslens}, where we plot the gas mass fractions
as a function of the cluster mass, both determined at $r_{2500}$.
This is the smallest radius at which \citet{Zhang+10} have given
their determinations and still it is beyond the region where
SL is detected in LCDCS~0504, $r_{2500}=0.49$ Mpc for the SL $M(r)$.
From Fig.~\ref{f:fgaslens} we see that the gas mass fraction of
LCDCS~0504 at this radius is not anomalous. This is consistent
with the conclusions we obtained using the X-ray- and
kinematics-determined total masses (Fig.~\ref{f:fgas}), LCDCS~0504
shows an anomalous (low) gas mass fraction only at small radii.
We will discuss in the next Section the possible origin of this
central gas fraction deficiency.
\begin{figure}[htb]
\centering
\includegraphics[width=8.8cm]{Mass_dyn_gas_frac_LCDCS0504_gal.eps}
\caption[]{{\em Top panel}: The intra-cluster gas mass profile
(lower curve) and the hydrodynamical derived total mass radial
profiles. The grey shaded regions represent $1 \sigma$ confidence
levels. Vertical lines indicate $r_{image}$, the limit where the
cluster is detected with the combined XMM data (using both
exposures), and $r_{500}$ and $\rvir$, computed from the X-ray
derived mass profile. {\em Bottom panel}: the gas mass fraction
radial profile. As a reference we also show the universal gas
fraction, as obtained by the cosmic baryon fraction
$\Omega_{b}/\Omega_{m}$ value from WMAP-9yr \citep{Hinshaw+12}
and Planck 1st release \citep{PlanckCollaboration+13} (including
their uncertainties), reduced by 17\%}
\label{fig:xraymass}
\end{figure}
\begin{figure}[!htb]
\begin{center}
\includegraphics[width=8.8cm]{fgas.ps}
\end{center}
\caption{{\em Top panel:} The ratio of gas mass to total mass from the
X-ray analysis. The grey shaded region within solid lines is the 1
$\sigma$ interval on the observed gas mass fraction of LCDCS~0504.
The blue and red shaded regions (the blue one below the red one at
large radii) are the average gas mass fractions for cool-core and
non-cool-core clusters from \citet{Eckert+13}. {\em Bottom panel:}
The ratio of gas mass to total mass, the latter derived from the
kinematics analysis. The grey shaded region within solid lines is
the 1 $\sigma$ interval on the observed gas mass fraction of
LCDCS~0504. The green shaded region is the average gas mass fraction
for nearby clusters from \citet{BS06}.}
\label{f:fgas}
\end{figure}
\begin{figure}[!htb]
\begin{center}
\begin{minipage}{0.5\textwidth}
\resizebox{\hsize}{!}{\includegraphics{fgas_lens.ps}}
\end{minipage}
\end{center}
\caption{The ratio of gas mass to total mass determined from lensing
analyses for the clusters of \citet{Zhang+10} (diamonds) and for
LCDCS~0504 (dot). Error bars are 1 $\sigma$.}
\label{f:fgaslens}
\end{figure}
\section{Discussion and conclusions}
\label{s:summ}
We have analyzed the mass profile $M(r)$ of a $z \approx 0.8$ cluster
with the SL technique, using the X-ray emission from the intra-cluster
hot gas, and using galaxies as tracers of the gravitational
potential. The different determinations of the cluster $M(r)$ disagree,
especially in the inner regions.
The SL $M(r)$ is slightly above but still consistent with the kinematic determination, but both are significantly above the X-ray $M(r)$ determination.
This discrepancy is unlikely to be caused by an unrelaxed
dynamical status of the cluster. This could cause an overestimate of
the cluster velocity dispersion and hence the cluster mass estimate
from kinematics \citep[see, e.g.,][]{Biviano+06} and an incomplete
thermalization of the intra-cluster gas, leading to an underestimate
of the cluster mass estimates from X-ray \citep[e.g.][]{Rasia+06},
but it would not affect the lensing mass estimate. Moreover, an
unrelaxed dynamical status is not supported by the analyses of
substructures by \citet{Guennou+13}.
In that paper, we have
used the \citet[][SG hereafter]{SG96} hierarchical method for the
detection of substructures in the distribution of galaxies and
searched for substructures in the X-ray data (described in
Sect.~\ref{ss:imaging}), by analysing the residuals of the subtraction
of a symmetric elliptical $\beta$-model from the X-ray image (see
Guennou et al. 2013 for details). Seven substructures were detected by
the SG technique, all with masses below 10\% of the total cluster
mass. Of these, only one was also detected in X-rays, with an X-ray
luminosity of $\approx 8 \%$ the total cluster X-ray luminosity. This
analysis indicates that any major perturbation of the LCDCS~0504
dynamical status must thus have occurred sufficiently long ago for the
remnants of the merging groups to have disappeared.
Another interesting possibility is that we see the cluster with
its major axis along the line-of-sight. This is suggested by the
circularly symmetric SL configuration and by the small ellipticity
of the cD galaxy, since the elongation of cD galaxies generally
reflects those of their host clusters \citep[e.g.][]{RK87,KASL02}
(see Fig.~\ref{f:multiple}). It has been shown both on numerical
simulations \citep{KE05} and observationally \citep{Wojtak13}, that
clusters are prolate not only in position space but also in velocity
space, and the major axes of the spatial and velocity distributions
are aligned. The orientation of the cluster with the major axis
along the line-of-sight then results in an overestimate of the
cluster mass estimatd from SL and velocity dispersion. According to
\cite{Wojtak13}, the mean ratio of the velocity dispersions along
the minor and major axes of a cluster is $\simeq 0.78$. This implies
a ratio of the velocity dispersion along the major axis to the mean
cluster velocity dispersion of 1.16, i.e. a 32\% mass overestimate
at a given radius. This is still not sufficient to remove the
systematic difference between the mass profile derived from
kinematics and that derived by the X-ray analysis.
The alignment effect just discussed could also induce an
overestimate of mass profile concentration value. This could
explain the disagreement we find with the theoretical predictions
of \citet{BHHV13} and \citet{DeBoni+13} (see
Fig.~\ref{f:rvrs}).
Whatever the cause for the X-ray vs. kinematics and SL $M(r)$
discrepancy, substantial systematic underestimates of cluster masses
by the X-ray methodology could be interesting for cosmology, as it
could alleviate the tension between the $\sigma_8$ values found by the
Planck collaboration using the Cosmic Microwave Background
power-spectrum on one hand and cluster counts obtained by the
Sunyaev-Zeldovich effect (using X-ray masses as mass calibrators
\citealp{Planck13}): If X-ray masses are underestimated at given SZ
signal, this means the distribution of SZ counts above a given mass
threshold is underestimated, meaning that $\Omega_{\rm m}$
($\sigma_8$) is underestimated (overestimated), which would bring the
best-fit value more in line with the CMB value.
Another intriguing result of our analysis is the discovery that the
gas mass fraction is anomalously low near the center of the LCDCS~0504
cluster. Given the relaxed, symmetric morphology of the X-ray emission
(see Fig.~\ref{fig:LCDCS0504allxmm0.3_7.0}), it is unlikely that this
anomaly could be attributed to the effects of a major merger
displacing the gas from the center, as in the case of the Bullet
cluster \citep{Barrena+02,Markevitch+02}. Alternatively, the gas could
have been ejected by AGN outbursts, while the effects of SNe explosions
should not be significant \citep{CO08,Dubois+13}. \citet{Dubois+13}
predict a 30\% loss in the core due to AGN outflows, which is not to
far from our observed deficiency (with respect to the average of
other clusters) of \mbox{$\simeq 60$}\% (see Fig.~\ref{f:fgas}), given the large
observational uncertainties.
The main issue with the AGN hypothesis is that there is no evidence of
a radio source in the NVSS catalog or in the X-rays as there is no
detectable point source at the location of the cD, although there is a
hint of a cool core. Also, we have no evidence of broad lines in the
optical spectrum of the cD. All this lack of evidence does, however,
tell us, is that the assumed AGN activity have subsided long enough
ago so that all strong electromagnetic signatures of AGN activity have
now subsided.
In the near future, we plan to extend the dynamical and structural
analysis presented here to clusters with sufficient spectroscopic
information in the full DAFT/FADA cluster set. Expanding our
data-sets should allow us to determine if the anomalies identified in
LCDCS~0504 are a characteristic of high-$z$ clusters or
not. Hopefully, with a larger sample we will be able to unveil the
hidden systematics causing discrepant determinations of cluster mass
profiles by different methods, and to relate these systematics to the
currently not well understood physics of the intra-cluster baryons.
\begin{acknowledgements}
We wish to express our sincere condolences and grief to the family of
Alain Mazure who unexpectedly passed away during the preparation of
this paper. We wish to thank the anonymous referee for her/his suggestions.
ML acknowledges the Centre National de la Recherche Scientifique
(CNRS) for its support. The Dark Cosmology Centre is funded by the
Danish National Research Foundation. This work has been conducted
using facilities offered by CeSAM (Centre de donn\'eeS Astrophysique
de Marseille -- http://www.lam.fr/cesam/). FD acknowledges long-term
support from CNES and CAPES/COFECUB program 711/11. AB acknowledges
the hospitality of the Inst. d'Astroph. de Paris and of the Obs. de la
C\^ote d'Azur. This research has made use of the NASA/IPAC
Extragalactic Database (NED) which is operated by the Jet Propulsion
Laboratory, California Institute of Technology, under contract with
the National Aeronautics and Space Administration. GBLN and ESC acknowledge
the support of the Brazilian funding agencies FAPESP and CNPq. Based on
observations obtained at the Gemini Observatory, which is operated by the
Association of Universities for Research in Astronomy, Inc., under a
cooperative agreement with the NSF on behalf of the Gemini partnership:
the National Science Foundation (United States), the National Research
Council (Canada), CONICYT (Chile), the Australian Research Council
(Australia), Minist\'{e}rio da Ci\^{e}ncia, Tecnologia e Inova\c{c}\~{a}o
(Brazil) and Ministerio de Ciencia, Tecnolog\'{i}a e Innovaci\'{o}n Productiva
(Argentina). I.M. acknowledges financial support from the Spanish grant
AYA2010-15169 and from the Junta de Andalucia through TIC-114 and the
Excellence Project P08-TIC-03531.
\end{acknowledgements}
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import React, { Component, PropTypes } from 'react'
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import UpdatePostButton from '../update/UpdatePostButton'
import SharePanel from './../share/SharePanel'
import TagGroup from '../tag/TagGroup'
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\section{Introduction}
Hyperbolic metric spaces are ubiquitous in geometric group theory. They are the key tools for studying small cancellation groups, mapping class groups, right-angled Artin groups, and numerous other groups. In light of this, it is a natural problem to try to give a complete description of all of the (isometric) actions of a given group on hyperbolic metric spaces. We call such actions \emph{hyperbolic actions}.
In general, this goal is too lofty. For instance, using the combinatorial horoball machinery of Groves and Manning \cite{GrovesManning}, one can produce uncountably many distinct hyperbolic actions of any countable group. However, such pathological examples can be ruled out by considering only \emph{cobounded} actions, that is, actions such that the quotient of the space by the action has finite diameter
(see Section \ref{section:background} for the precise definition). For this reason, we restrict our focus in this paper to cobounded hyperbolic actions.
For many groups studied by geometric group theorists, even the goal of describing all cobounded hyperbolic actions is still too lofty. For instance, all acylindrically hyperbolic groups (including most of the groups mentioned in the first paragraph and many others) admit uncountably many cobounded hyperbolic actions that are, in a natural sense, inequivalent \cite{ABO} (see Section \ref{section:background} for the definition of equivalent actions). Nonetheless, significant progress has recently been made in describing the cobounded hyperbolic actions of families of classically studied \emph{solvable} groups. The second author initiated this study by giving a complete description of the cobounded hyperbolic actions of the lamplighter groups $(\mathbb Z/n\mathbb Z)\wr \mathbb Z$ for $n \geq 2$ in \cite{Bal}. The first and third authors then completely described the hyperbolic actions of Anosov mapping torus groups in \cite{Largest} and the hyperbolic actions of solvable Baumslag-Solitar groups in \cite{AR}.
These descriptions also provide additional information about the relationships between the various actions. The first two authors and Osin showed in \cite{ABO} that the set $\mathcal{H}(G)$ of equivalence classes of cobounded hyperbolic actions of a group $G$ admits a partial order, which roughly corresponds to collapsing equivariant families of subspaces to obtain one hyperbolic action from another (see Section \ref{section:background} for the precise definition).
Each of the papers \cite{Bal}, \cite{AR}, and \cite{Largest} gives a complete description of the poset $\mathcal{H}(G)$ for the group $G$ in question.
The starting point for the techniques developed in \cite{Bal, AR, Largest} is a theory developed by Caprace, Cornulier, Monod, and Tessera in \cite{Amen} that describes the cobounded hyperbolic actions of certain groups with rank one abelianizations, that is, groups whose abelianizations are virtually infinite cyclic. This includes groups $G= H\rtimes \mathbb Z$, with $\mathbb Z$ corresponding to a finite index subgroup of the abelianization. The theory they develop shows that the cobounded hyperbolic actions of such groups are in correspondence with a certain class of subsets of $H$ that they define, called \emph{confining subsets}.
Crucially, the solvable groups discussed in the previous two paragraphs all have rank one abelianizations, and so the authors were able to apply the work of \cite{Amen} directly.
However, the techniques developed in \cite{Bal, AR, Largest} do not immediately extend to solvable groups whose abelianizations have higher rank. In this paper we begin the work necessary to extend the theory of Caprace, Cornulier, Monod, and Tessera in \cite{Amen} to finitely generated solvable groups in general. In particular, we develop a theory of confining subsets for semidirect products of the form $H\rtimes \mathbb Z^n$. Such semidirect products arise whenever there is a section of the homomorphism from a group to the free abelian part of its abelianization. This allows us to completely describe the cobounded hyperbolic actions of certain solvable groups that were previously out of reach. In contrast to lamplighter groups and solvable Baumslag-Solitar groups, whose posets of cobounded hyperbolic actions are finite, these groups \emph{always} admit uncountably many inequivalent actions on lines, because $\mathbb Z^n$ does when $n>1$ (see, for example, \cite[Example~4.23]{ABO}). However, we show that for a certain family of groups, the remaining cobounded hyperbolic actions can be understood in a straightforward way.
Our two main theorems give a correspondence between confining proper subsets and quasi-parabolic actions for groups $H\rtimes \mathbb Z^n$ and should be compared to \cite[Theorem~4.1]{Amen} in the case $n=1$. For solvable groups, every non-elementary hyperbolic action is quasi-parabolic, so this correspondence yields a complete description of the hyperbolic actions in most cases. The terms in the statements of the following theorems are defined precisely in Sections \ref{section:background} and \ref{section:main}; we give brief intuitive explanations here. If $\gamma \colon \mathbb Z^n \to \op{Aut}(H)$ is a homomorphism and $G=H\rtimes_\gamma \mathbb Z^n$, then a subset $Q\subseteq H$ is confining under $\gamma$ with respect to a homomorphism $\rho:\mathbb Z^n\to \mathbb R$ roughly when $H$ is \emph{attracted into} $Q$ under elements of $\mathbb Z^n$ with large image under $\rho$ and $Q$ is \emph{nearly closed} under the group operation of $H$. The subset $Z_\rho \subseteq \mathbb Z^n$ consists of the elements of $\mathbb Z^n$ with small image under $\rho$. The notation $\Gamma(G,S)$ stands for the Cayley graph of $G$ with respect to the (possibly infinite) generating set $S$. A \emph{quasi-parabolic action} is a hyperbolic action with a fixed point on the Gromov boundary and infinitely many loxodromic elements. Finally, the \emph{Busemann pseudocharacter} of this action measures the translation of group elements towards or away from the fixed point.
Our first main result allows us to construct cobounded quasi-parabolic actions from confining subsets for a group $G$ as in the previous paragraph.
\begin{thm}\label{thm:main}
Let $G= H\rtimes_\gamma \mathbb Z^n$, where $\gamma: \mathbb Z^n \to \op{Aut}(H)$ is a fixed homomorphism, and fix a homomorphism $\rho\colon \mathbb Z^n\to \mathbb R$. Let $Z_\rho$ be as in \eqref{eqn:Zrho}. If $Q\subseteq H$ is confining under $\gamma$ with respect to $\rho$, then
\begin{enumerate}[(i)]
\item the Cayley graph $\Gamma(G, Q\cup Z_\rho)$ is hyperbolic;
\item if $Q$ is strictly confining, then $G\curvearrowright \Gamma(G,Q\cup Z_\rho)$ is quasi-parabolic, and otherwise this action is lineal; and
\item the Busemann pseudocharacter for the action $G \curvearrowright \Gamma(G, Q\cup Z_\rho)$ is proportional to $\rho$ .
\end{enumerate}
\end{thm}
Our second main result allows us to recover a strictly confining subset from a cobounded quasi-parabolic action of the group $G$ under certain conditions.
\begin{thm}\label{prop:main}
Let $G = H \rtimes_\gamma \mathbb Z^n$, and let $G\curvearrowright X$ be a cobounded quasi-parabolic action on a hyperbolic space $X$. Let $p$ be the Busemann pseudocharacter associated to this action, and assume that $p(H) =0$. Then there exists a subset $Q\subseteq H$ which is strictly confining under the action of $\gamma$ with respect to $p$, such that $X$ is $G$--equivariantly quasi-isometric to $\Gamma(G,Q\cup Z_p)$, where $Z_p$ is as in \eqref{eqn:Zrho}.
\end{thm}
We note that the assumption that $p(H)=0$ is not too restrictive. In particular, one can check that this holds whenever $H$ is abelian.
To illustrate the use of this theory, we give a complete description of the cobounded hyperbolic actions of a class of groups $G_k$ related to solvable Baumslag-Solitar groups. If $k=p_1^{m_1}\cdots p_n^{m_n}$ is the prime factorization of $k$, then $G_k := \mathbb Z\left[\frac1k\right] \rtimes_\gamma \mathbb Z^n$, where, under $\gamma$, the $i$\textsuperscript{th} generator of $\mathbb Z^n$ acts on $\mathbb Z[\frac1k]$ by multiplication by $p_i^{m_i}$. Thus \[G_k = \left\langle a, t_1,\ldots,t_n \ \big\vert \ [t_i,t_j]=1, t_iat_i^{-1}=a^{p_i^{m_i}} \text{ for all } i,j\right\rangle\] (here $a$ corresponds to a normal generator of the subgroup $\mathbb Z[\frac{1}{k}]$). Note that the cobounded hyperbolic actions of $G_k$ when $k$ is a power of a prime have already been classified in \cite{AR}.
\begin{restatable}{thm}{Gk} \label{thm:Z1k}
For any $k\geq 2$ which is not a power of a prime, the poset $\mathcal H(G_k)$ has the following structure: $\mathcal H_{qp}(G_k)$, the subposet of quasi-parabolic actions, consists of $n+1$ incomparable elements. Each quasi-parabolic action dominates a single lineal action; there are uncountably many lineal actions; and all lineal actions dominate a single elliptic action (see Figure \ref{fig:Z[1/k]Structure}). Moreover, every element of $\mc H(G_k)$ contains either an action on a tree, the hyperbolic plane, or a point.
\end{restatable}
\begin{figure}[h]
\centering
\def0.5{0.6}
\input{hyp_str_H_semi_Zn.pdf_tex}
\caption{The poset of hyperbolic structures on the group $G_k=\mathbb Z[\frac1k]\rtimes_\gamma \mathbb Z^n$.}
\label{fig:Z[1/k]Structure}
\end{figure}
\noindent
We also give a precise geometric description of the hyperbolic actions of $G_k$ in Section \ref{section:actiongeometry} using $k$--adic numbers; see in particular Figure \ref{fig:bstrees}.
The proof of Theorem \ref{thm:Z1k} reveals that cobounded hyperbolic actions of solvable groups with higher rank abelianizations may sometimes be reduced to the rank one case. Specifically, to prove Theorem \ref{thm:Z1k} we utilize the classification of cobounded hyperbolic actions of the Baumslag-Solitar group $BS(1,k)$ given in \cite{AR}. In light of this and the classification of cobounded hyperbolic actions of wreath products $(\mathbb Z/n\mathbb Z)\wr \mathbb Z$ given in \cite{Bal}, a natural next step would be to apply Theorems \ref{thm:main} and \ref{prop:main} and the techniques developed in \cite{Bal,AB,Largest} to attempt to classify the hyperbolic actions of wreath products $A\wr B$ and extensions $A\rtimes B$ when $A$ and $B$ are finitely generated abelian groups.
\section{Background} \label{section:background}
\subsection{Comparing generating sets and group actions}
Throughout this paper, all group actions on metric spaces are assumed to be isometric. Given a metric space $X$, we denote by $\d_X$ the distance function on $X$. If $G$ is a group and $S$ is a generating set of $G$, then $\|\cdot\|_S$ denotes the word norm on $G$ and $d_S$ denotes the word metric $d_S(g,h)=\|gh^{-1}\|_S$.
\begin{defn}[{\cite[Definition 1.1]{ABO}}]\label{def-GG}
Let $S$, $T$ be two (possibly infinite) generating sets of a group $G$. We say that $S$ is \emph{dominated} by $T$, written $S\preceq T$, if the identity map on $G$ induces a Lipschitz map between metric spaces $(G, \d_T)\to (G, \d_S)$. This is equivalent to the requirement that $ \sup_{t\in T}\|t\|_S<\infty$. The relation $\preceq$ is a preorder on the set of generating sets of $G$, and therefore it induces an equivalence relation in the standard way:
$$
S\sim T \;\; \Leftrightarrow \;\; S\preceq T \; {\rm and}\; T\preceq S.
$$
This is equivalent to the condition that the Cayley graphs $\Gamma(G,S)$ and $\Gamma(G, T)$ are $G$--equivariantly quasi-isometric. We denote by $[S]$ the equivalence class of a generating set $S$, and by $\mathcal{G}(G)$ the set of all equivalence classes of generating sets of $G$. The preorder $\preceq$ induces a partial order $\preccurlyeq $ on $\mathcal{G}(G)$ by the rule
$$
[S]\preccurlyeq [T] \;\; \Leftrightarrow \;\; S\preceq T.
$$
\end{defn}
For example, all finite generating sets of a finitely generated group are equivalent and the equivalence class containing any finite generating set is the largest element of $\mathcal{G}(G)$. For every group $G$, the smallest element of $\mathcal{G}(G)$ is $[G]$. Note also that this order is ``inclusion reversing": if $S$ and $T$ are generating sets of $G$ such that $S\subseteq T$, then $T\preceq S$.
To define a hyperbolic structure on a group, we first recall the definition of a hyperbolic space. In this paper we employ the definition of hyperbolicity via the Rips condition.
\begin{defn} A metric space $X$ is called \emph{$\delta$--hyperbolic} if it is geodesic and for any geodesic triangle $\Delta $ in $X$, each side of $\Delta $ is contained in the union of the closed $\delta$--neighborhoods of the other two sides.
\end{defn}
\begin{defn}[{\cite[Definition 1.2]{ABO}}]
A \emph{hyperbolic structure} on $G$ is an equivalence class $[S]\in \mathcal{G}(G)$ such that $\Gamma (G,S)$ is hyperbolic. Since hyperbolicity of a space is a quasi-isometry invariant, this definition is independent of the choice of a particular representative in the equivalence class $[S]$. We denote the set of hyperbolic structures by $\mathcal{H}(G)$. It is a sub-poset of $\mathcal{G}(G)$ with the restriction of the partial order on $\mathcal{G}(G)$. \end{defn}
The poset $\mathcal{H}(G)$ classifies the \emph{cobounded} hyperbolic actions of $G$ up to coarsely equivariant quasi-isometry, as we now summarize.
\begin{defn}
The action $G\curvearrowright X$ is \emph{cobounded} if for some (equivalently any) $x\in X$ there exists $R>0$ such that every point of $X$ is distance at most $ R$ from some point of the orbit $Gx$. Given two cobounded hyperbolic actions $G\curvearrowright X$ and $G\curvearrowright Y$, a map $f:X\to Y$ is \emph{coarsely equivariant} if for any $x\in X$ we have \[\sup_{g\in G} d_Y(f(gx),gf(x))<\infty.\] Given $C>0$, the map $f$ is \emph{$C$--coarsely Lipschitz} if \[d_Y(f(x),f(y))\leq Cd_X(x,y)+C\] for all $x,y\in X$. It is a \emph{$C$--quasi-isometry} if it is $C$--coarsely Lipschitz and also satisfies \[\frac{1}{C}d_X(x,y)-C\leq d_Y(f(x),f(y)).\]
\end{defn}
Given a cobounded hyperbolic action $G\curvearrowright X$, there is an associated hyperbolic structure given by the \emph{Schwarz-Milnor Lemma}:
\begin{lem}[{\cite[Lemma 3.11]{ABO}}]\label{lem:MS}
Let $G\curvearrowright X$ be a cobounded hyperbolic action of $G$. Let $B\subseteq X$ be a bounded subset such that $\displaystyle \bigcup_{g\in G} gB=X$. Let $D=\operatorname{diam}(B)$ and let $x\in B$. Then $G$ is generated by the set \[S=\{g\in G: d_X(x,gx)\leq 2D+1\},\] and $X$ is $G$--equivariantly quasi-isometric to $\Gamma(G,S)$.
\end{lem}
Thus, up to equivariant quasi-isometries, hyperbolic actions of $G$ correspond to actions of $G$ on its hyperbolic Cayley graphs. There is an equivalence relation on hyperbolic actions given by $G$--coarsely equivariant quasi-isometry and a preorder on hyperbolic actions given by $G$--coarsely equivariant coarsely Lipschitz maps. With these relations, the set of \emph{equivalence classes of cobounded hyperbolic actions} of $G$ becomes a poset. This poset turns out to be isomorphic to $\mathcal{H}(G)$. We refer the reader to \cite[Section 3]{ABO} for more details.
\subsection{General classification of hyperbolic actions}
We now recall some standard facts about groups acting on hyperbolic spaces. For details the reader is referred to \cite{Gro}. Given a hyperbolic space $X$, we denote by $\partial X$ its Gromov boundary. In general, $X$ is not assumed to be proper, and its boundary is defined as the set of equivalence classes of sequences convergent at infinity. Given a group $G$ acting on a hyperbolic space $X$, we denote by $\Lambda (G)$ the set of limit points of $G$ on $\partial X$. That is, $$\Lambda (G)=\partial X\cap \overline{Gx},$$ where $\overline{Gx}$ denotes the closure of a $G$--orbit in $X\cup \partial X$, for any choice of basepoint $x\in X$. This definition is independent of the choice of $x\in X$. The action of $G$ is called \emph{elementary} if $|\Lambda (G)|\le 2$ and \emph{non-elementary} otherwise. The action of $G$ on $X$ naturally extends to a continuous action of $G$ on $\partial X$.
\begin{defn} Given an action of a group $G$ on a hyperbolic space $X$, an element $g\in G$ is called
\begin{enumerate}
\item[(i)] \emph{elliptic} if $\langle g\rangle $ has bounded orbits;
\item[(ii)] \emph{loxodromic} if the map $n \mapsto g^nx, n \in \mathbb Z$ is a quasi-isometric embedding for some (equivalently any) $x \in X$;
\item[(iii)] \emph{parabolic} otherwise.
\end{enumerate} \end{defn}
Every loxodromic element $g\in G$ has exactly $2$ fixed points $g{^{\pm \infty}}$ on $\partial X$, where $g{^{+\infty}}$ (respectively, $g{^{-\infty}}$) is the limit of the sequence $(g{^{n}}x)_{n\in \mathbb N}$ (respectively, $(g{^{-n}}x)_{n\in \mathbb N}$) for any fixed $x\in X$. Thus $\Lambda (\langle g\rangle) =\{ g{^{\pm \infty}}\}$.
The following theorem summarizes the standard classification of groups acting on hyperbolic spaces due to Gromov \cite[Section 8.2]{Gro} and the results \cite[Propositions 3.1 and 3.2]{Amen}.
\begin{thm}\label{ClassHypAct}
Let $G$ be a group acting on a hyperbolic space $X$. Then exactly one of the following conditions holds.
\begin{enumerate}
\item[1)] $|\Lambda (G)|=0$. Equivalently, $G$ has bounded orbits. In this case the action of $G$ is called \emph{elliptic}.
\item[2)] $|\Lambda (G)|=1$. In this case the action of $G$ is called \emph{parabolic}. A parabolic action cannot be cobounded.
\item[3)] $|\Lambda (G)|=2$. Equivalently, $G$ contains a loxodromic element and any two loxodromic elements have the same limit points on $\partial X$. In this case the action of $G$ is called \emph{lineal}.
\item[4)] $|\Lambda (G)|=\infty$. Then $G$ always contains loxodromic elements. In turn, this case breaks into two subcases.
\begin{enumerate}
\item[(a)] $G$ fixes a point of $\partial X$. Equivalently, any two loxodromic elements of $G$ have a common limit point on the boundary. In this case the action of $G$ is called \emph{quasi-parabolic} or \emph{focal}.
\item[(b)] $G$ does not fix any point of $\partial X$. In this case the action of $G$ is said to be of \emph{general type}.
\end{enumerate}
\end{enumerate}
\end{thm}
The following classification of hyperbolic structures is an immediate consequence of the above theorem.
\begin{thm}[{\cite[Theorem 4.6]{ABO}}]\label{main00}
For every group $G$, $$\mathcal{H}(G)=\mathcal{H}_e(G)\sqcup \mathcal{H}_{\ell} (G)\sqcup \mathcal{H}_{qp} (G)\sqcup \mathcal{H}_{gt}(G)$$
where the sets of elliptic, lineal, quasi-parabolic, and general type hyperbolic structures on $G$ are denoted by $\mathcal{H}_e(G)$, $\mathcal{H}_{\ell} (G)$, $\mathcal{H}_{qp} (G)$, and $\mathcal{H}_{gt}(G)$ respectively.
\end{thm}
\subsection{The Busemann pseudocharacter} A function $q\colon G\to \mathbb R$ is a \emph{quasi-character} (or \emph{quasi-morphism}) if there exists a constant $D$ such that $$|q(gh)-q(g)-q(h)|\le D$$ for all $g,h\in G$. We say that $q$ has \emph{defect at most $D$}. If, in addition, the restriction of $q$ to every cyclic subgroup of $G$ is a homomorphism, $q$ is called a \emph{pseudocharacter} (or \emph{homogeneous quasi-morphism}). Every quasi-character $q$ gives rise to a pseudocharacter $p$ defined by the following limit, which always exists, for any $g\in G$:
$$
p(g)=\lim_{n\to \infty} \frac{q(g{^{n}})}n.
$$
The function $p$ is called the \emph{homogenization of $q$.} It is straightforward to check that
$$
|p(g) -q(g)|\le D
$$
for all $g\in G$ if $q$ has defect at most $D$.
Given any action of a group on a hyperbolic space fixing a point on the boundary, one can associate the \emph{Busemann pseudocharacter}. We briefly recall the construction and necessary properties here, and refer the reader to \cite[Sec. 7.5.D]{Gro} and \cite[Sec. 4.1]{Man} for further details.
\begin{defn}\label{Bpc}
Let $G$ be a group acting on a hyperbolic space $X$ and fixing a point $\xi\in \partial X$.
Fix any $x\in X$ and let ${\bf x}=(x_i)$ be any sequence of points of $X$ converging to $\xi$. Then the function $q_{\bf x}\colon G\to \mathbb R$ defined by
$$
q_{\bf x}(g)=\limsup\limits_{n\to \infty}\left(\d_X (gx, x_n)-\d_X(x, x_n)\right)
$$
is a quasi-character. Its homogenization $p_{\bf x}$ is called the \emph{Busemann pseudocharacter}. It is known that this definition is independent of the choice of $\bf x$ (see \cite[Lemma 4.6]{Man}), and thus we can drop the subscript in $p_{\bf x}$. An element $g\in G$ is loxodromic with respect to the action of $G$ on $X$ if and only if $p(g)\ne 0$. In particular, $p$ is not identically zero whenever $G \curvearrowright X$ is quasi-parabolic. If $p$ is a homomorphism, then the action $G\curvearrowright X$ is called \emph{regular}.
\end{defn}
\subsection{Quasi-parabolic structures on $H \rtimes \mathbb Z$}
Consider a group $G=H\rtimes_\alpha \mathbb Z$ where a generator $t\in \mathbb Z$ acts on $H$ by conjugation via $tht^{-1}=\alpha(h)$ for any $h\in H$. Let $Q$ be a \emph{symmetric} subset of $H$. The following definition from \cite[Section~4]{Amen} forms the basis of the work we do in this paper. Here $Q\cdot Q$ denotes the set of elements $\{gh \in H \mid g,h\in Q\}$.
\begin{defn}\label{genconfine} Let $(H, \cdot)$ be a group and $Q$ be a subset of $H$, and let $\alpha$ be an automorphism of $H$. We say that the action of $\alpha$ is \textit{(strictly) confining $H$ into $Q$} if it satisfies the following conditions$\colon$
\begin{itemize}
\item[(a)] $\alpha(Q)$ is (strictly) contained in $Q$.
\item[(b)] $H = \displaystyle \bigcup_{n \geq 0} \hspace{5pt} \alpha^{-n}(Q)$.
\item[(c)] $\alpha^{n_0}(Q \cdot Q) \subseteq Q$ for some non-negative integer $n_0$.
\end{itemize}
We also call the set $Q$ \emph{confining under $\alpha$}.
\end{defn}
The definition of a confining subset given in \cite{Amen} does not require symmetry of the subset $Q\subseteq H$. However, according to \cite[Theorem~4.1]{Amen}, to classify regular quasi-parabolic structures on a group it suffices to consider only confining subsets which are symmetric. See also \cite[Proposition~2.6]{AR}.
\begin{prop}[{\cite[Proposition 4.6]{Amen}}]\label{niceprop} Let $H$ be a group and $\alpha$ an automorphism of $H$ which confines $H$
into some subset $Q \subseteq H$. Consider the group $G=H\rtimes_\alpha \mathbb Z$, and let $t$ denote a generator of $\mathbb Z$. Define $S=Q\cup \{t^{\pm 1}\}\subseteq G$. Then $\Gamma(G,S)$ is Gromov hyperbolic. If $\alpha(Q) \subsetneq Q$, then the action $G\curvearrowright \Gamma(G,S)$ is (regular) quasi-parabolic.
\end{prop}
If the action is confining but not strictly confining, that is, if $\alpha(Q) =Q$, then the above theorem still holds with the difference that $\Gamma(G,S)$ is quasi-isometric to a line; see the discussion after the statement of \cite[Theorem~4.1]{Amen}. The resulting action is thus lineal.
\section{Proofs of main theorems} \label{section:main}
Let $G= H\rtimes_\gamma \mathbb Z^n$, where $\gamma: \mathbb Z^n \to \op{Aut}(H)$ is a fixed homomorphism. An element $z\in \mathbb Z^n$ acts on $H$ by conjugation via $zhz^{-1}=\gamma(z)(h)$. The following generalizes the definition of a confining subset from \cite{Amen} to all cases when $n \geq 1$.
\begin{defn} \label{def:confining}
Fix a (non-zero) homomorphism $\rho\colon \mathbb Z^n \to \mathbb R$. A symmetric subset $Q$ of $H$ is \emph{confining under $\gamma$ with respect to $\rho$} if the following three conditions hold.
\begin{itemize}
\item[(a)] For all $z\in \mathbb Z^n$ with $\rho(z)\geq 0$, $\gamma(z)(Q)\subseteq Q$.
\item[(b)] For each $h\in H$, there exists $z\in \mathbb Z^n$ such that $\gamma(z)(h)\in Q$.
\item[(c)] There exists $z_0\in\mathbb Z^n$ such that $\gamma(z_0)(Q\cdot Q)\subseteq Q$.
\end{itemize}
If there exists $z\in\mathbb Z^n$ such that $\gamma(z)(Q)\subsetneq Q$, then $Q$ is \emph{strictly} confining under $\gamma$ with respect to $\rho$.
\end{defn}
\begin{rem} \label{rem:equivconditions}Condition (b) is equivalent to the following: For any $h \in H$, there exists $R_h \in \mathbb R$ such that $ \gamma(z)(h) \in Q$ for any $z\in \mathbb Z^n$ with $\rho(z) \geq R_h$. Moreover, condition (c) is equivalent to the following: There exists $R_0\in \mathbb R$ such that $\gamma(z)(Q\cdot Q)\subseteq Q$ for \emph{any} $z$ with $\rho(z)\geq R_0$. Further, although not stated explicitly, the condition for $Q$ to be strictly confining must be satisfied by an element $z \in \mathbb Z^n$ such that $\rho(z) > 0$. All these facts can be checked using condition (a) and the fact that $\rho$ is a homomorphism.
\end{rem}
\begin{rem}
While we choose to work in the context of groups $G=H\rtimes \mathbb Z^n$, we could equally well have considered groups $G=H\rtimes A$ where $A$ is an infinite, finitely generated abelian group. If $A=T\times \mathbb Z^n$ for some $n$ where $T$ is torsion, then any group $H\rtimes A$ can be written as $H'\rtimes \mathbb Z^n$ where $H'=H\rtimes T$. Thus we do not lose any generality in assuming $G=H\rtimes \mathbb Z^n$ .
\end{rem}
\subsection{Actions from confining subsets}
The goal of this section is to prove Theorem \ref{thm:main}.
Fix a generating set $\{t_1,\dots, t_n\}$ of $\mathbb Z^n$. Given a non-zero homomorphism $\rho\colon \mathbb Z^n\to \mathbb R$, we construct a (possibly infinite) generating set of $\mathbb Z^n$ as follows. Fix a constant $C_\rho>0$ such that $\rho(t_i) \in [-C_\rho, C_\rho]$ for all $i \in \{1,2,\dots,n\}$ and there exists $y\in \mathbb Z^n$ such that $\rho(y)=C_\rho$, and let
\begin{equation}\label{eqn:Zrho}
Z _\rho= \{z \in \mathbb Z^n \mid |\rho(z)| \leq C_\rho \}.
\end{equation}
Suppose that $Q\subseteq H$ is confining under $\gamma$ with respect to $\rho$. It is straightforward to check that $Q\cup Z_\rho$ is symmetric, and $Q\cup Z_\rho$ generates $G$ by Definition \ref{def:confining}(b). We denote the word norm on $G$ with respect to $Q\cup Z_\rho$ by $\|\cdot\|_{Q\cup Z_\rho}$.
Since $\rho$ is a non-zero homomorphism, $Z_\rho$ is a proper subset of $\mathbb Z^n$ which generates $\mathbb Z^n$ by definition. By \cite[Lemma 4.15]{ABO}, the Cayley graph $ \Gamma(\mathbb Z^n, Z_\rho)$ is a quasi-line (that is, quasi-isometric to a line) and the action of $\mathbb Z^n $ on $ \Gamma(\mathbb Z^n, Z_\rho)$ is lineal. For the rest of the section, we fix a hyperbolicity constant $\delta'$ for $\Gamma(\mathbb Z^n,Z_\rho)$.
Our first goal is to prove that $\Gamma(G,Q\cup Z_\rho)$ is hyperbolic, which we will do by understanding what happens to a path when we put its label into a normal form. Our strategy follows the structure of the proof of \cite[Proposition~4.6]{Amen}, though our more general situation provides additional complications.
We begin by bounding the length of geodesic edge paths in $\Gamma(G,Q\cup Z_\rho)$ whose labels are in $H$. Recall that in a Cayley graph of a group with respect to a (possibly infinite) generating set, each edge comes with a label that is an element of the generating set. Thus any path $\gamma$ in the Cayley graph has a label $\operatorname{Lab}(\gamma)$ which is the word formed by reading off the labels of the edges in the path, in the order they are traversed.
\begin{lem}[{cf. \cite[Lemma 4.7]{Amen}}] \label{control}There exists a $k_0 \in \mathbb{N}$ such that any geodesic edge path in $\Gamma(G, Q\cup Z_\rho)$ each of whose edge labels lies in $Q$ has length at most $k_0$. \end{lem}
\begin{proof} Let $B(r)$ denote the ball of radius $r$ centered at the identity in $\Gamma(G, Q\cup Z_\rho)$. By $B(r)\cap H$, we mean the intersection of the zero skeleton of the ball $B(r)$ with the subgroup $H$. Thus $B(1) \cap H = Q$. By Definition \ref{def:confining}(c), we have $Q^2 = Q \cdot Q \subseteq \gamma(z_0)^{-1}(Q)=\gamma(z_0^{-1})(Q)$, and, more generally,
$$Q^{2^m} \subseteq \gamma(z^{-m}_0)(Q).$$
For any $q \in Q$,
\[
\|\gamma(z_0^{-m})(q)\|_{Q\cup Z_\rho}=\|z_0^{-m}qz_0^m\|_{Q\cup Z_\rho}\leq 2m\|z_0\|_{Q\cup Z_\rho}+1.
\]
Letting $\ell_0=\|z_0\|_{Q\cup Z_\rho}$, we have
\[
\left( B(1) \cap H \right)^{2^m}=Q^{2^m}\subseteq \gamma(z_0^{-m})(Q)\subseteq B(2m\ell_0 + 2) \cap H.
\]
In particular, it follows that any geodesic edge path such that the label of each edge is in $Q$ that has length at most $ 2^m$ must satisfy $$2^m \leq 2m\ell_0 +2.$$ But then $m$ is bounded by $\kappa= 4 \log_2(\ell_0 +2)$, and so the length is bounded by $k_0 = 2\kappa \ell_0 +2$.
\end{proof}
\begin{rem}\label{rem:Hnoloxos}
Lemma \ref{control} shows that $H$ cannot contain any loxodromic isometries with respect to the action of $G$ on $\Gamma(G,Q\cup Z_\rho)$. To see this, notice that given any $h\in H$, there is some $z\in \mathbb Z^n$ such that $\gamma(z)(h)=zhz^{-1}\in Q$. In other words, every $h\in H$ is conjugate to an element of $Q$. As $Q$ is exponentially distorted, it contains no loxodromic elements with respect to this action. Thus neither does $H$.
\end{rem}
The next lemma provides a preferred form for paths in $\Gamma(G,Q\cup Z_\rho)$ and shows that any geodesic is at uniformly bounded Hausdorff distance from a path in this preferred form. This is related to \cite[Lemma 4.8]{Amen}.
\begin{lem} \label{newpaths}
Let $\alpha$ be an edge path of length $m$ in $\Gamma(G, Q\cup Z_\rho)$ with exactly $k$ edges whose labels are in $Q$ and such that all subpaths with labels in $\mathbb Z^n$ are geodesics. Then there exists a path $\beta$ with the same endpoints as $\alpha$ of the form
\[
\beta=\beta_1\beta_2\beta_3
\]
with $\operatorname{Lab}(\beta_1)=a_1a_2\ldots a_s$, $\operatorname{Lab}(\beta_2)=g_1g_2\ldots g_k$, and $\operatorname{Lab}(\beta_3)=b_1b_2\ldots b_r$ that satisfies the following properties:
\begin{itemize}
\item $\beta\subset \mc N_{2(k+1)\delta' +2k}(\alpha)$, where $\delta'$ is the hyperbolicity constant of $\Gamma(\mathbb Z^n,Z_\rho)$;
\item $\beta_1$ and $\beta_3$ are geodesics;
\item $g_i\in Q$ for all $1\leq i\leq k$;
\item $a_j\in Z_\rho$ satisfies $\rho(a_j)<0$ for each $1\leq j\leq s$;
\item $b_l\in Z_\rho$ satisfies $\rho(b_l) \geq 0$ for each $1\leq l\leq r$; and
\item $s + k + r \leq m$
\end{itemize}
Moreover, if $\alpha$ is a geodesic edge path in $\Gamma(G, Q\cup Z_\rho)$, then $\beta$ is also a geodesic edge path, and $\alpha$ and $\beta$ are at Hausdorff distance at most $2(k_0 +1)\delta' + 2k_0$.
\end{lem}
\begin{proof} For every $q \in Q$ and $z \in Z_\rho$, either $\gamma(z)(q) \in Q$ (if $\rho(z) \geq 0$) or $\gamma(z^{-1})(q) \in Q$ (if $\rho(z) <0$). Thus when $\rho(z) \geq 0$, we have $zq = \gamma(z)(q)z=q'z$, where $q' =\gamma(z)(q)\in Q$. Similarly, when $\rho(z) < 0$, we may replace $qz$ with $zq''$ where $q'' =\gamma(z)^{-1}(q)=\gamma(z^{-1})(q)\in Q$. If we perform one such operation to the label of a path, the result is a new path at distance at most 1 from the original path in $\Gamma(G, Q\cup Z_\rho)$ (see Figure \ref{fig1}). Now suppose we have a word $z_1\ldots z_m\in \mathbb Z^n$ with $z_i\in Z_\rho$ and $\rho(z_i)\geq 0$ for each $1\leq i\leq m$. Let $q\in Q$ and consider a path $\zeta$ with label $z_1\ldots z_m q$. By performing this operation $m$ times, each time moving one letter in $Z_\rho$ past $q$, we obtain a sequence of paths $z_1\ldots z_{m-i}q_iz_{m-i+1}\ldots z_m$. To see that they are mutually at Hausdorff distance one see Figure \ref{fig:Movingzs}.
\begin{figure}
\centering
\def0.5{0.6}
\input{Fig1.pdf_tex}
\caption{Performing a single operation $z_1q_1=q_1'z_1$ results in a path at distance at most one from the original path in $\Gamma(G,Q\cup Z_\rho)$.}
\label{fig1}
\end{figure}
\begin{figure}
\centering
\def0.5{0.7}
\small{\input{Movingzs.pdf_tex}}
\caption{Performing $m$ operations $z_1z_2\ldots z_mq = q_mz_1\ldots z_m$ results in a path at distance at most one from the original path in $\Gamma(G,Q\cup Z_\rho)$.}
\label{fig:Movingzs}
\end{figure}
Let $\operatorname{Lab}(\alpha) = e_1e_2\ldots e_m$ be the label of the given path $\alpha$ in $\Gamma(G, Q\cup Z_\rho)$. The $k$ edges whose labels are in $Q$ partition this path into at most $k+1$ segments containing edges whose labels are in $Z_\rho$, each of which is a geodesic segment by assumption, and at most $k$ segments whose edges have labels in $Q$. We may thus think of the path $\alpha$ as having the form
$$
\alpha=\omega_1\mu_1\omega_2\mu_2\ldots \mu_l\omega_{l+1}
$$
where each $\omega_i$ is a geodesic whose edges all have labels in $Z_\rho$, each $\mu_j$ is a path whose edges all have labels in $Q$, and $l \leq k$. Let $\operatorname{Lab}(\omega_i)=w_i$ and $\operatorname{Lab}(\mu_i)=u_i$.
Since $\mathbb Z^n$ is abelian, we may reorder the letters in the word $w_1$ so that $w_1=v_1^-v_1^+$, where each letter in $v_1^-$ has negative image under $\rho$ and each letter in $v_1^+$ has non-negative image under $\rho$.
We replace the geodesic $\omega_1$ with a path (which is also necessarily geodesic) whose label is $v_1^-v_1^+$. Since $\Gamma(\mathbb Z^n,Z_\rho)$ is $\delta'$--hyperbolic, this results in a path at Hausdorff distance at most $\delta'$ from $\alpha$ with label
\[
v^-_1 v^+_1u_1w_2u_2\ldots u_l w_{l+1}.
\]
Let $u\in Q$ be the first letter in $u_1$. As described in the first paragraph, we have $v_1^+u=u'v_1^+$, where $u'=\gamma(v_1^+)(u)$. We replace the collection of edges in $\alpha_1$ labeled by $v_1^+u$ with a new path labeled by $u'v_1^+$. If $q$ is the second letter of $u_1$, then we again replace the subpath of this new path labeled by $v_1^+q$ with a path labeled by $q'v_1^+$, where $q'=\gamma(v_1^+)q$. Continuing in this manner, we may move the subpath labeled by $v^+_{1}$ past all the edges contained in $\mu_1$. Each step in this process produces a path at Hausdorff distance 1 from the previous path, and thus in the end we have produced a path $\alpha'$ at Hausdorff distance at most $\delta' + \ell(\mu_1)$ from $\alpha$ with label
$$
v^-_1u'_1 v^+_1w_2u_2\ldots u_l w_{l+1},
$$
for some word $u_1'$, each letter of which is in $Q$.
The subpath of $\alpha'$ labeled by $v^+_1w_2$ is a concatenation of two geodesic paths.
Let $\nu_2$ be a geodesic in $\Gamma(\mathbb Z^n,Z_\rho)$ with the same endpoints,
so that $\operatorname{Lab}(\nu_2)\in \mathbb Z^n$. As before, since $\mathbb Z^n$ is abelian, we may rearrange the edges in $\nu_2$ so that $\operatorname{Lab}(\nu_2)=v_2^-v_2^+$, where each letter of $v_2^-$ has negative image under $\rho$ and each letter of $v_2^+$ has non-negative image under $\rho$. Since $\nu_2$ was a geodesic, so is the path with label $v_2^-v_2^+$.
The concatenation of the subpath labeled by $v_1^+w_2$, and the subpath labeled by $v_2^-v_2^+$ forms a geodesic triangle in $\Gamma(\mathbb Z^n, Z_\rho)$. Replacing the subpath of $\alpha'$ labeled by $v^+_1w_2$ with the geodesic labeled by $v_2^-v_2^+$ yields a new path contained in the $\delta'$--neighborhood of $\alpha'$.
This new path has label
\[
v^-_1u'_1v^-_2v^+_2u_2\ldots u_{l}w_{l+1}
\]
and is contained in the $(2\delta'+\ell(\mu_1))$--neighborhood of $\alpha$.
As above, the properties of $Q$ allow us to move all the edges of the subpath labeled by $v^+_2$ past all the edges from $u_{2}$ to obtain a path with label
$$
v^-_1u'_1v^-_2u'_2v^+_2 w_3\ldots u_{l}w_{l+1}
$$
which is contained in the $(2\delta' + \ell(\mu_1)+\ell(\mu_2))$--neighborhood of $\alpha$.
Continuing this process, we eventually obtain a path $\alpha''$ with label
$$
v^-_1 u'_1v^-_2u'_2\ldots u'_l v^-_{l+1}v^+_{l+1}
$$
where every letter in $v^+_{l+1}$ has non-negative image under $\rho$, every letter of $v_i^-$ has negative image under $\rho$ for $1\leq i\leq l+1$, and every letter in each $u'_j$ is in $Q$. This path $\alpha''$ is contained in the $((k+1)\delta' + k)$--neighborhood of $\alpha$ since $l\leq k$ and the total number of edges from $Q$ is $k$. Let $\mu_i'$ be the subpaths of $\alpha''$ with labels $u_i'$.
We now move each edge of the subpath labeled by $v^-_{l+1}$ past all the edges in the subpath labeled by $u'_l$ by using the properties of $Q$ in an analogous way as above. This yields a path with label
$$
v^-_1 u'_1v^-_2u'_2\ldots v^-_lv^-_{l+1} u''_lv^+_{l+1}
$$
which is contained in the $((k+1)\delta' +k + \ell(\mu_l'))$--neighborhood of $\alpha$. Again using the properties of $Q$, we move each edge of the subpath labeled by $v^-_lv^-_{l+1}$ past each edge of $\mu'_{l-1}$. By continuing this process, we eventually obtain a path $\beta'$ with label
$$
v^-_1 v^-_2 \ldots v^-_{l+1}(u''_1u''_2 \ldots u''_l)v^+_{l+1}
$$
that is contained in the neighborhood of $\alpha$ of radius \[(k+1)\delta'+k+\ell(\mu_1')+\cdots+\ell(\mu_l')=(k+1)\delta'+2k.\]
For the final step, we form the path $\beta$ by replacing the subpath $\beta''$ of $\beta'$ labeled by $v_1^-v_2^-\ldots v_{l+1}^-$ with a geodesic $\beta_1$ between its endpoints formed in the following way.
Let $v=v_1^-v_2^-\ldots v_{l+1}^-$, and note that $\rho(v)=\displaystyle \sum_{i=1}^{l+1}\rho(v_i^-)<0$. Let $m=\left \lfloor \dfrac{-\rho(v)}{C_\rho} \right \rfloor$. Since $\rho$ is a homomorphism and no element of $Z_\rho$ has image under $\rho$ whose absolute value is larger than $C_\rho$, we have $m\leq \|v\|_{Z_\rho}\leq m+1$, and $\|v\|_{Z_\rho}=m$ exactly when $\dfrac{-\rho(v)}{C_\rho}\in \mathbb Z$. If $\|v\|_{Z_{\rho}}=m$ we must have $v=v_1'v_2'\ldots v_m'$ where $\rho(v_i')=-C_\rho$ for all $i$. In this situation we let $\beta_1$ be the geodesic between the endpoints of $\beta''$ labeled by $v_1'v_2'\ldots v_m'$. Now suppose $\|v\|_{Z_\rho}=m+1$, and recall that by definition there is an element $z\in Z_\rho$ with $\rho(z)=-C_\rho$. Consider the element $z^{-m}v\in \mathbb Z^n$. Then $-C_\rho< \rho(z^{-m}v)<0$, and so $z^{-m}v\in Z_\rho$. In this case, we let $\beta_1$ the geodesic between the endpoints of $\beta''$ labeled by $z^m(z^{-m}v)\in \mathbb Z^n$. In either case, the geodesic $\beta_1$ has the property that each edge is labeled by an element whose image under $\rho$ is negative. Moreover, since $\beta''$ is the concatenation of $l+1\leq k+1$ geodesics, $\beta_1$ is contained in its $(k+1)\delta'$--neighborhood.
We claim $\beta$ satisfies the first statement of the lemma. Let $\beta_2$ be the subpath of $\beta$ with label $u_1''u_2'' \ldots u_l''$ and $\beta_3$ the subpath with label $v^+_{l+1}$. Then the following hold by construction: $\beta_1$ and $\beta_3$ are geodesics; each letter in $\operatorname{Lab}(\beta_2)$ is in $Q$; every letter in $\operatorname{Lab}(\beta_1)$ has negative image under $\rho$; and each letter of $\operatorname{Lab}(\beta_3)$ has non-negative image under $\rho$. Further, $\beta$ is contained in the $(2(k+1)\delta' +2k)$--neighborhood of $\alpha$ and has the same endpoints as $\alpha$. Finally, notice that this process does not increase the length of the path we started with, and so the final bullet point of the statement of the lemma holds. This completes the proof of the first statement of the lemma.
The final bullet point immediately implies that if $\alpha$ is a geodesic, then so is $\beta$. To prove the second part of the ``moreover" statement, notice that the only times in this procedure when we do not get a bound on the Hausdorff distance between paths at successive stages is when we have a subpath whose label is of the form $vw$, where $v,w\in \mathbb Z^n$, which we replace with a geodesic $\nu$ between its endpoints. (We think of the final step in the above procedure as iterating this $l$ times.) In general, the subpath labeled by $vw$ is only a concatenation of geodesics and may not be a geodesic itself. In particular, there may be backtracking at the concatenation point, and so we do not always get a bound on the Hausdorff distance at this step. However, if there is backtracking, then $\ell(\nu)$ is strictly less than the length of the subpath labeled by $vw$. In particular, we must have $\ell(\beta)<\ell(\alpha)$. Since $\alpha$ and $\beta$ have the same endpoints, this contradicts our assumption that $\alpha$ is a geodesic. Therefore, whenever $\alpha$ is a geodesic, the subpath with label $vw$ must be a geodesic, and thus replacing this subpath with $\nu$ results in a bound on the Hausdorff distance between the paths. (In fact, in this situation we may skip this step altogether.) Therefore, in this case we conclude that the Hausdorff distance between $\alpha$ and $\beta$ is at most $2(k+1)\delta' +2k$. Finally, since $\beta$ is a geodesic, the subpath $\beta_2$ of $\beta$ is also a geodesic and has length $\displaystyle \sum_{i=1}^l\ell(\mu_i'')= \sum_{i=1}^l\ell(\mu_i)=k$. This label is an element of $H$, and so by Lemma \ref{control}, we conclude that $k\leq k_0$. Therefore, the Hausdorff distance between $\alpha$ and $\beta$ is uniformly bounded by $2(k_0+1)\delta' +2k_0$. This concludes the proof of the lemma.
\end{proof}
\begin{lem}\label{moveQ} Suppose $\mu=\mu_1\mu_2$ is a path in $\Gamma(G,Q\cup Z_\rho)$ with $\operatorname{Lab}(\mu_1)= x_1x_2 \ldots x_m$ and $Lab(\mu_2) = q_1q_2 \ldots q_k$, where $ x_j \in Z_\rho$ and $q_i \in Q$. Further assume that $\rho(x_j) \geq 0 $ for all $1 \leq j \leq m$. Let $\nu$ be the path with the same endpoints as $\mu$ provided by Lemma \ref{newpaths}, so that $\nu=\nu_1\nu_2$ satisfies $Lab(\nu_1) = q_1' q_2' \ldots q_k'$ and $Lab(\nu_2) = x_1x_2 \ldots x_m=\operatorname{Lab}(\mu_1)$, where $q_i' \in Q$.
If $v$ is any vertex on $\mu$ (respectively, $\nu$), then there exists a vertex $v'$ on $\nu_2$ (respectively, $\mu_1$) such that $d(v,v')\leq k$. In particular, if $\mu$ is a geodesic, then we have $d(v,v')\leq k_0$, where $k_0$ is the constant from Lemma \ref{control}.
\end{lem}
\begin{proof} We use the procedure described in Lemma \ref{newpaths} in the special case $\mu=\mu_1\mu_2$ to obtain the new path $\nu=\nu_1\nu_2$. In this situation, we need only apply the first step of the procedure, which consists of moving $\operatorname{Lab}(\mu_1)$ past each letter $q_i$ in $\operatorname{Lab}(\mu_2)$. Each time we move $\operatorname{Lab}(\mu_1)$ past some $q_i$, we form a new path at Hausdorff distance one from the previous path; see Figure \ref{squares}. Indeed, moving $x_m$ past $q_1$ yields a new path with the label $x_1x_2 \ldots x_{m-1} q_{1,1}x_mq_2q_3\ldots q_k$ at Hausdorff distance one from $\mu$. After moving each letter $x_j$ of $\operatorname{Lab}(\mu_1)$ past $q_1$ we have a path with label $q_{1,m}x_1\ldots x_m q_2\ldots q_k$, which is still at Hausdorff distance one from $\mu$. Repeating this procedure $k$ times to move $\operatorname{Lab}(\mu_1)$ past each $q_i$ forms a rectangle. Setting $q_i'=q_{i,m}$ in the statement of the lemma results in a path of the desired form.
\begin{figure}
\centering
\def0.5{0.6}
\input{Lemma3_5.pdf_tex}
\caption{Applying Lemma \ref{newpaths} to the path $\mu=\mu_1\mu_2$.}
\label{squares}
\end{figure}
It can be seen from Figure \ref{squares} that any vertex $v$ of $\mu$ (respectively, $\nu$) is at distance at most $k$ from a vertex of the path $\nu_2$ (respectively, $\mu_1$). Indeed, if $v$ is a vertex of $\mu$ (respectively, $\nu$), then there is a vertical path consisting of at most $k$ edges from $v$ to a vertex of $\nu_2$ (respectively, $\mu_1$).
The final statement of the lemma follows from applying Lemma \ref{control}.
\end{proof}
The proof of the following lemma is similar to that of \cite[Proposition 4.6]{Amen}. However, since in our situation $\Gamma(\mathbb Z^n,Z_\rho)$ is only quasi-isometric to a line and not actually a line, some additional subtleties arise.
\begin{lem} \label{hyp}
$\Gamma(G, Q\cup Z_\rho)$ is hyperbolic.
\end{lem}
\begin{proof}
We will consider paths in the Cayley graph $\Gamma(G,Q\cup Z_\rho)$. We consider $\Gamma(\mathbb Z^n,Z_\rho)$ as a subgraph of $\Gamma(G,Q\cup Z_\rho)$ in the natural way. Recall that $\delta'\geq 0$ is a hyperbolicity constant of $\Gamma(\mathbb Z^n,Z_\rho)$. Let $k_0$ be the constant from Lemma \ref{control}, and let $A=2(k_0+1)\delta'+2k_0$ be the constant from Lemma \ref{newpaths}.
Recall that a \emph{geodesic bigon} is a concatenation $\alpha_1\alpha_2$ where $\alpha_1$ and $\alpha_2$ are geodesics such that the initial point of $\alpha_1$ is the endpoint of $\alpha_2$ and the endpoint of $\alpha_1$ is the initial point of $\alpha_2$. We will show that geodesic bigons in $\Gamma(G,Q\cup Z_\rho)$ are $\delta$--slim for $\delta=4\delta'+3k_0+2A$; that is, each side is contained in the $\delta$--neighborhood of the other. Papasoglu shows that this suffices to prove hyperbolicity of $\Gamma(G,Q\cup Z_\rho)$ in \cite[Theorem~1.4]{Papa}. (While Papasoglu stated this result only for Cayley graphs of groups with respect to finite generating sets, it is straightforward to see that the proof only relies on the fact that the space is a connected graph with the simplicial metric. This was explicitly noted, for example, in \cite{NeumannShapiro}.)
Consider a geodesic bigon $\alpha_1'\alpha_2'$ in $\Gamma(G,Q\cup Z_\rho)$. By Lemma \ref{newpaths}, there is a pair of $A$--Hausdorff close geodesics $\alpha_1$ and $\alpha_2$ with the same endpoints such that for $i=1,2$ the label of each $\alpha_i$ has the form $p_iu_iq_i$, where $u_i$ is a word in $Q$ with length $\leq k_0$, and $p_i,q_i\in \mathbb Z^n$ are words $p_i=p_i^1\ldots p_i^{j_i}$ and $q_i=q_i^1\ldots q_i^{m_i}$ satisfying $\rho(p_i^s)\leq 0$ and $\rho(q_i^r) \geq 0$ for all $1\leq s\leq j_i$ and $1\leq r\leq m_i$. Thus we have $$\operatorname{Lab}(\alpha_1\alpha_2)= (p_1u_1q_1)(p_2u_2q_2).$$ We will show that the bigon $\alpha_1\alpha_2$ is $(4\delta'+3k_0)$--slim, which will prove the result.
Let $\alpha_i=\sigma_i\mu_i\xi_i$, where $\operatorname{Lab}(\sigma_i)=p_i$, $\operatorname{Lab}(\mu_i)=u_i$, and $\operatorname{Lab}(\xi_i)=q_i$ for $i=1,2$, so that
\[
\alpha_1\alpha_2=(\sigma_1\mu_1\xi_1)(\sigma_2\mu_2\xi_2).
\]
Suppose that $y_0$ is a point on $\alpha_1$. We will find a point on $\alpha_2$ at distance at most $4\delta'+3k_0$ from $y_0$. (If $y_0$ is a point on $\alpha_2$, an analogous argument will hold.) If $y_0$ lies on $\mu_1$, then since $\|u_1\|_{Q\cup Z_\rho}\leq k_0$, there are points on $\sigma_1$ and $\xi_1$ at distance at most $k_0$ from $y_0$. Moreover, if $\sigma_1$ (respectively, $\xi_1$) has length at most $2\delta'+k_0$ and $y_0$ lies on $\sigma_1\mu_1$ (respectively, on $\mu_1\xi_1$) then $y_0$ is at distance at most $2\delta'+2k_0$ from $\alpha_2$. Thus it suffices to assume that $y_0$ lies on $\sigma_1$ or $\xi_1$, at least $2\delta'+k_0$ from the common endpoint with $\mu_1$, and find a point on $\alpha_2$ at distance at most $2\delta'+k_0$ from $y_0$. We will assume $y_0$ lies on $\sigma_1$. If $y_0$ lies on $\xi_1$, then a symmetric argument will prove the result.
First, we use the fact that $\mathbb Z^n$ is abelian to replace the concatenation of geodesics $\xi_1\sigma_2$ with a geodesic $\nu^-\nu^+$ in $\Gamma(\mathbb Z^n,Z_\rho)$, where the label of each edge in $\nu^+$ has non-negative image under $\rho$ and the label of each edge in $\nu^-$ has negative image under $\rho$. (In the case $y_0$ lies on $\xi_1$, then the first step is to replace $\xi_2\sigma_1$ with the geodesic $\nu^-\nu^+$, instead.) Thus we have a path $(\sigma_1\mu_1\nu^-)(\nu^+\mu_2\xi_2)$ whose label is equal in $G$ to $\operatorname{Lab}(\alpha_1\alpha_2)$; see Figure \ref{fig:bigon}.
By Lemma \ref{moveQ}, there are paths $\omega^-\mu_1'$ and $\mu_2'\omega^+$ at Hausdorff distance at most $k_0$ from $\mu_1\nu^-$ and $\nu^+\mu_2$, respectively, where $\omega^+,\omega^-$ are geodesics in $\mathbb Z^n$ with the same labels as $\nu^+, \nu^-$, respectively, and $\mu_1',\mu_2'$ are geodesic with labels $u_1,u_2\in H$, respectively. Consequently, $\mu_i'$ has length $\leq k_0$ for $i = 1,2$.
\begin{figure}
\centering
\def0.5{0.5}
\input{alt_breakB_real.pdf_tex}
\caption{The decomposition of the bigon $\alpha_1\alpha_2$ in the case $y_0$ lies on $\sigma_1$.}
\label{fig:bigon}
\end{figure}
Since $\alpha_1\alpha_2$ is a loop, its label is the identity element of $G$, and so the image of $\operatorname{Lab}(\alpha_1\alpha_2)$ under the natural projection $G\to \mathbb Z^n$ is the identity element 0 of $\mathbb Z^n$. In particular, we have $$p_1 + q_1 + p_2 + q_2 =\operatorname{Lab}(\sigma_1) + \operatorname{Lab}(\xi_1) + \operatorname{Lab}(\sigma_2) + \operatorname{Lab}(\xi_2) = 0,$$
where $p_i,q_i$ are considered as elements of $\mathbb Z^n$.
Since $q_1 + p_2 $ and $ \operatorname{Lab}(\nu^-)+\operatorname{Lab}(\nu^+)$ represent the same element of $\mathbb Z^n$, we have $$p_1 + \operatorname{Lab}(\nu^-) + \operatorname{Lab}(\nu^+) + q_2 =0.$$ Since $\omega^-, \omega^+$ have the same labels as $\nu^-, \nu^+$ respectively, this gives us that $$p_1 + \operatorname{Lab}(\omega^-) + \operatorname{Lab}(\omega^+) + q_2 =0.$$ Therefore the path $\omega^+\xi_2\sigma_1\omega^-$ is a loop in $\Gamma(\mathbb Z^n,Z_\rho)$ and hence in $\Gamma(G,Q\cup Z_\rho)$. Moreover, since $\nu^-\nu^+$ is a geodesic, so is $\omega^- \omega^+$. Consequently, $\sigma_1 \omega^- \omega^+ \xi_2$ is a geodesic triangle in $\Gamma(\mathbb Z^n,Z_\rho)$, and $\mu'_1 \mu'_2$ is a geodesic bigon, as shown in Figure \ref{fig:bigon}.
By the hyperbolicity of $\Gamma(\mathbb Z^n,Z_\rho)$, there is a point $y_1$ on $\omega^- \omega^+\xi_2$ which is at distance at most $\delta'$ from $y_0$. If $y_1$ lies on $\xi_2$, then we are done, as $\xi_2$ is a subpath of $\alpha_2$.
Suppose $y_1$ lies on $\omega^-$. Then Lemma \ref{moveQ} provides a point $y_2$ on $\nu^-$ at distance at most $k_0$ from $y_1$. The path $\nu^-\nu^+\sigma_2^{-1}\xi_1^{-1}$ is a geodesic triangle in $\Gamma(\mathbb Z^n,Z_\rho)$ (recall that $\nu^-\nu^+$ is a geodesic), and therefore there is a point $y_3$ on $\xi_1\sigma_2$ which is at distance at most $\delta'$ from $y_2$. Suppose that $y_3$ lies on $\xi_1$. Then we have $d(y_0,y_3)\leq \displaystyle \sum_{i=0}^2d(y_i,y_{i+1})\leq 2 \delta' +k_0$. However, $y_0$ and $y_3$ both lie on the geodesic $\alpha_1$. Since $y_0$ is at least $2\delta' +k_0$ from the terminal endpoint of $\sigma_1$ while $y_3$ lies on $\xi_1$, this is a contradiction. We conclude that $y_3$ must lie on $\sigma_2$. As we still have $d(y_0,y_3)\leq 2\delta' + k_0$ and $\sigma_2$ is a subpath of $\alpha_2$, we are done.
Finally, suppose that $y_1$ lies on $\omega^+$. Then Lemma \ref{moveQ} provides a point $y_2$ on $\nu^+$ at distance at most $k_0$ from $y_1$. As in the previous paragraph, there must be a point $y_3$ on $\xi_1\sigma_2$ at distance at most $\delta'$ from $y_2$. If $y_3$ lies on $\xi_1$, then we reach a contradiction exactly as in the previous paragraph. Thus $y_3$ must lie on $\sigma_2$, and since $d(y_0,y_3)\leq 2\delta' + k_0 $, we are done.
Given a point $y_0$ on $\sigma_1$, we have found a point on $\alpha_2$ at distance at most $2\delta'+k_0$ from $y_0$. Therefore any point $y_0'$ on $\alpha'_1$ is at distance at most $\delta=4\delta'+3k_0+2A$ from $\alpha'_2$. It follows that the bigon $\alpha'_1\alpha'_2$ is $\delta$--slim, and we conclude that $\Gamma(G,Q\cup Z_\rho)$ is hyperbolic.
\end{proof}
\begin{lem}[{cf. \cite[Proposition 4.6]{Amen}}] \label{focal}
If $Q$ is strictly confining, then the action $G \curvearrowright \Gamma(G, Q\cup Z_\rho)$ is quasi-parabolic. Otherwise the action is lineal.
\end{lem}
\begin{proof} By Remark \ref{rem:Hnoloxos}, the subgroup $H$ cannot contain any loxodromic elements. This implies that the action of $H$ on $\Gamma(G,Q\cup Z_\rho)$ is either elliptic or parabolic.
If $Q$ is not strictly confining, then for every $z\in \mathbb Z^n$ with $\rho(z) >0$, we have that $\gamma(z)(Q) = Q$. Using Definition \ref{def:confining}(a) and (b), we conclude that $Q = H$. Thus $H$ has bounded orbits in the action of $G$ on $\Gamma(G, Q\cup Z_\rho)$. Since the action of $\mathbb Z^n$ on $\Gamma(\mathbb Z^n, Z_\rho)$ is lineal, the action of $G$ on $\Gamma(G,Q\cup Z_\rho)$ is also lineal.
On the other hand, if $Q$ is strictly confining, then there exists a $z\in \mathbb Z^n$ such that $\gamma(z)(Q)$ is a proper subset of $ Q$. Remark \ref{rem:equivconditions} implies that we may choose such a $z$ satisfying $\rho(z) >0$. Since $\rho(z^n)$ grows linearly while the elements of $Q\cup Z_\rho$ have bounded image under the homomorphism $\rho$, the word lengths $\|z^n\|_{Q\cup Z_\rho}$ must grow linearly as well. Thus $z$ acts loxodromically on $\Gamma(G, Q \cup Z_\rho)$.
Consider the strictly ascending chain
$$
Q \subsetneq \gamma(z^{-1})(Q) \subsetneq \gamma(z^{-2})(Q)\subsetneq\cdots\subsetneq \gamma(z^{-k})(Q) \subsetneq\cdots.
$$ We will show that the word lengths of elements of $\gamma(z^{-i})(Q) \setminus \gamma(z^{-i+1})(Q)$ have linearly growing word length in $Q\cup Z_\rho$. This will then imply that $H$ has unbounded orbits in the action on $\Gamma(G,Q\cup Z_\rho)$.
Consider $h\in \gamma(z^{-i})(Q) \setminus \gamma(z^{-i+1})(Q)$ and suppose $\gamma(w)(h)\in Q$ for some $w\in \mathbb Z^n$. If $\rho(z^{i-1}w^{-1})\geq 0$, then \[\gamma(z^{i-1})(h)=\gamma(z^{i-1}w^{-1})\big(\gamma(w)(h)\big)\in Q.\] However, this contradicts our assumption on $h$, and so we must have $\rho(w)>\rho(z^{i-1})$.
By Lemma \ref{newpaths}, we may write $h$ as a geodesic word \[h=z_1\ldots z_r q_1\ldots q_s w_1\ldots w_t \] where $z_i\in Z_\rho$ satisfy $\rho(z_i)<0$, $q_i\in Q$, $w_i\in Z_\rho$ satisfy $\rho(w_i)\geq 0$, and $r+s+t=\|h\|_{Q\cup Z_\rho}$. Moreover, we have $s\leq k_0$. Writing $v=z_1\ldots z_r$, $h'=q_1\ldots q_s$, and $w=w_1\ldots w_t$, we have $h=vh'w$, and since $h'\in H$ we must have $w=v^{-1}$. Thus, $h=vh'v^{-1}$ and $\gamma(v^{-1})(h)=h' \in Q^s\subseteq Q^{k_0}$. Recall that there exists $z_0$ such that $\gamma(z_0)(Q\cdot Q)\subseteq Q$. We thus have $\gamma(z_0^{k_0})(Q^{k_0})\subseteq Q$, and therefore $\gamma(z_0^{k_0}v^{-1})(h)\in Q$. By the previous paragraph, this implies that \[k_0\rho(z_0) +\rho(v^{-1})=\rho(z_0^{k_0}v^{-1})>\rho(z^{i-1}).\]
Thus, $\rho(v^{-1})> (i-1)\rho(z)-k_0\rho(z_0)$. Since the image of any element of $Z_\rho$ under $\rho$ is bounded in absolute value by $C_\rho$, we have \[\|v\|_{Z_\rho} \geq \frac{(i-1)\rho(z)-k_0\rho(z_0)}{C_\rho} \ \ \ \text{ and } \ \ \ \|h\|_{Q\cup Z_\rho} \geq 2\left(\frac{(i-1)\rho(z)-k_0\rho(z_0)}{C_\rho}\right)+1.\]
Therefore $H$ has unbounded orbits in the action on $\Gamma(G,Q\cup Z_\rho)$, and so the action of $H$ is parabolic. Let $ \xi=\lim_{i\to\infty}z^{-i}$. We will show that $G$ fixes $\xi$. Since $\rho(z^{-i}) < 0$, we have for any $q\in Q$ and each $i\geq 1$ that $$d_{Q \cup Z_\rho}(qz^{-i}, z^{-i}) = d_{Q \cup Z_\rho}(z^{-i}q', z^{-i}) = d_{Q \cup Z_\rho}(q', 1) =1$$ for some $q'\in Q$. Thus $Q$ fixes $\xi$. As $\mathbb Z^n$ also fixes $\xi$ (since the action of $\mathbb Z^n$ is lineal) and $Q\cup \mathbb Z^n$ generates $G$, it follows that all of $G$ fixes $\xi$. Since $G$ has unbounded orbits and contains loxodromic elements, this shows that the action of $G$ on $\Gamma(G,Q\cup Z_\rho)$ is either lineal or quasi-parabolic. Since $H$ acts parabolically, the action must be quasi-parabolic.
\end{proof}
We now turn our attention to understanding the Busemann pseudocharacter associated to the action of $G$ on $ \Gamma(G, Q\cup Z_\rho)$. We begin with a general fact about homomorphisms from $\mathbb Z^n$ to $\mathbb R$.
\begin{lem} \label{lem:multiplekernel} For any homomorphisms $r, s\colon \mathbb Z^n \to \mathbb{R}$, the following are equivalent.
\begin{enumerate} [(1)]
\item $r$ and $s$ are scalar multiples of each other.
\item $r(z) \geq 0$ if and only if $s(z) \geq 0$ or $r(z) \geq 0$ if and only if $s(z) \leq 0$.
\end{enumerate}
Moreover, if $r(z) \geq 0$ if and only if $s(z) \geq 0$, then $r$ and $s$ are positive scalar multiples of each other, while if $r(z) \geq 0$ if and only if $s(z) \leq 0$, then $r$ and $s$ are negative scalar multiples of each other.
\end{lem}
\begin{proof}
Clearly (1) implies (2). The homomorphisms $r$ and $s$ are given by $r(z)=v\cdot z$ and $s(z)=w\cdot z$ for some vectors $v,w\in \mathbb R^n$. The homomorphisms are proportional if and only if $v$ and $w$ are proportional, which is the case if and only if the orthogonal complements $v^\perp$ and $w^\perp$ in $\mathbb R^n$ are equal. If $v^\perp$ and $w^\perp$ are not equal, then they partition $\mathbb R^n\setminus (v^\perp \cup w^\perp)$ into four convex cones corresponding to the four possible pairs of signs of $v\cdot u$ and $w\cdot u$. Each of these regions contains an integer vector and therefore (2) also implies (1).
\end{proof}
\begin{lem} \label{lem:Busemann} Let $p$ be the Busemann pseudocharacter associated to the action of $G$ on $\Gamma(G,Q\cup Z_\rho)$. For any $g=hz\in G$, where $h\in H$ and $z\in \mathbb Z^n$, we have that $p(g)=p(z)$. In other words, $p$ is the composition of the natural projection of $G$ to $\mathbb Z^n$ and the restriction of $p$ to $\mathbb Z^n$. Moreover, the restriction of $p$ to $\mathbb Z^n$ is proportional to the homomorphism $\rho$.
\end{lem}
\begin{proof}
By Remark \ref{rem:Hnoloxos}, $H$ cannot contain any loxodromic isometries. Thus $p(h)=0$ for all $h\in H$. Since $H$ is a normal subgroup of $G$, it follows from \cite[Lemma~4.3]{Amen} that $p$ induces a homogeneous quasi-character on $G/H\cong \mathbb Z^n$. In particular, for any $g=hz\in G$, we have $p(g)=p(z)$. To see this, let $D$ be the defect of $p$, and let $r$ be a positive integer. We have $(hz)^r=h'z^r$ for some $h'\in H$. Since $p(h')=0$ we obtain $|p((hz)^r)-p(z^r)|\leq D$. By using homogeneity, the left hand side is equal to $r|p(hz)-p(z)|$. Dividing both sides by $r$ and letting $r\to \infty$ we have $p(hz)=p(z)$. Additionally, since $\mathbb Z^n$ is abelian, all pseudocharacters are homomorphisms, and hence $p$ is a homomorphism (see \cite[Proposition 2.65]{scl}).
We now turn to the ``moreover" statement of the lemma. For any $z'\in \mathbb Z^n$, to understand the action of $ \langle z' \rangle $ on $\Gamma(G,Q\cup Z_\rho)$, we need only consider the action of $\mathbb Z^n$ on $\Gamma(\mathbb Z^n,Z_\rho)$.
Now $p(z') > 0$ if and only if $z'$ is a loxodromic element in the action on $\Gamma(G, Q\cup Z_\rho)$ with repelling fixed point $\xi$. This occurs if and only if $z'$ is loxodromic with respect to the action of $\mathbb Z^n$ on $\Gamma(\mathbb Z^n,Z_\rho)$ with repelling fixed point $\xi$. By \cite[Lemma 4.15]{ABO}, this is true if and only if $\rho(z') >0$.
Recall that $\Gamma(\mathbb Z^n,Z_\rho)$ is a quasi-line. In an action on a quasi-line, all elements are either elliptic or loxodromic. Thus if $p(z') =0$, then $z'$ is an elliptic element in the action of $\mathbb Z^n$ on $\Gamma(\mathbb Z^n,Z_\rho)$ and hence in the action of $G$ on $\Gamma(G, Q\cup Z_\rho)$. It again follows from \cite[Lemma 4.15]{ABO} that this happens if and only if $\rho(z') = 0$.
We have shown that $p(z') \geq 0$ if and only if $\rho(z') \geq 0$. By Lemma \ref{lem:multiplekernel}, we see that $\rho$ and $ p$ are positive scalar multiples of each other.
\end{proof}
Lemmas \ref{hyp}, \ref{focal}, and \ref{lem:Busemann} prove Theorem \ref{thm:main}(i), (ii), and (iii), respectively.
\subsection{Confining subsets from actions}
Throughout this section, we fix a group $G=H\rtimes_\gamma \mathbb Z^n$ and a cobounded action $G\curvearrowright X$ on a hyperbolic space with a global fixed point $\xi \in \partial X$. We additionally assume that the associated Busemann pseudocharacter $p$ satisfies $p(H)=0$. Thus $p$ restricts to a pseudocharacter $\mathbb Z^n\to \mathbb R$. As before, we see that $p$ is a homomorphism and, in fact, $p(hz)=p(z)$ for $h\in H,z\in \mathbb Z^n$.
We also fix the following data for the rest of the subsection. Let $\delta$ be a constant of hyperbolicity for $X$.
Since $p$ is non-zero and $p(H)=0$, there is an element $z_0\in \mathbb Z^n$ such that $p(z_0)\neq 0$. Thus $z_0$ is a loxodromic element, which must fix the point $\xi$. Let $\nu\neq \xi$ be the other fixed point of $z_0$ in $\partial X$. Let $c\colon (-\infty,\infty)\to X$ be a $(1,20\delta)$--quasi-geodesic from $\nu$ to $\xi$.
Such a $(1,20\delta)$--quasi-geodesic $c$ always exists between any two points of $\partial X$ (see \cite[Remark~2.16]{boundaries}, for instance). We fix a basepoint $x=c(0)$ of $X$.
Our first goal is to prove the following proposition.
This proposition has been used implicitly (in the $n=1$ case) in all three of the papers \cite{Bal, AR, Amen}, but to the best of the authors' knowledge it has never received a detailed proof. Because of its fundamental importance, we include a proof here.
\begin{prop}
\label{prop:smalltranslation}
Let $G=H\rtimes_\gamma \mathbb Z^n$ be a group acting on a hyperbolic space $X$ and fixing a point $\xi\in \partial X$, and let $p\colon G\to \mathbb R$ be the associated Busemann pseudocharacter. Assume $p(H)=0$, and fix a basepoint $x\in X$ as above. There exists a function $A\colon \mathbb R_{\geq 0}\to \mathbb R$ and a constant $B>0$ such that the following holds. For any $g\in G$ and $z\in \mathbb Z^n$ with $d(x,gx)\leq N$ and $p(z)\leq -A(N)$, we have $d(gz(x),z(x))\leq |p(g)|+B$.
\end{prop}
For simplicity of notation, we use $d$ to denote the metric on $X$ throughout the proof of the proposition. We may define the Busemann pseudocharacter $p$ associated to the action $G\curvearrowright X$ in the following way. First of all, we define $q\colon G\to \mathbb R$ by \[q(g)=\limsup_{t\to\infty} \Big(d(gx,c(t))-d(x,c(t))\Big)=\limsup_{t\to\infty} \Big(d(gc(0),c(t))-d(c(0),c(t))\Big).\] The Busemann pseudocharacter is then the homogenization $p$ defined by \[p(g)=\lim_{n\to\infty} \frac{q(g^n)}{n}.\]
Let $r_0$ be a constant such that any two $(1,20\delta)$--quasi-geodesic rays in $X$ with the same endpoint on $\partial X$ are eventually $r_0$--Hausdorff close and any two bi-infinite $(1,20\delta)$--quasi-geodesics with the same endpoints are $r_0$--Hausdorff close. For any $g\in G$, the ray $c|_{[0,\infty)}$ and its translate $gc|_{[0,\infty)}$ are both $(1,20\delta)$--quasi-geodesic rays that share the endpoint $\xi$ and thus are eventually $r_0$--Hausdorff close. Specifically, there are numbers $t_0=t_0(g)$ and $s_0=s_0(g)\geq 0$ depending on $g$ and $x=c(0)$ so that $c|_{[t_0,\infty)}$ and $gc|_{[s_0,\infty)}$ are $r_0$--Hausdorff close and $d(c(t_0),gc(s_0))\leq r_0$. In other words $s_0$ is roughly how long it takes for the ray $gc|_{[0,\infty)}$ to become close to the ray $c|_{[0,\infty)}$. This depends only on $d(x,gx)$, and $s_0(g)$ may be chosen smaller than a function of $d(x,gx)$. We consider the difference $l=t_0-s_0$ as the amount that $g$ ``shifts'' the quasi-geodesic $c$, which may be positive or negative.
We will prove the proposition in a series of lemmas. The first says that $g$ uniformly shifts the entire quasi-geodesic by the same amount $l$.
\begin{lem}
\label{lem:shift}
There exists a constant $D$ such that $d(c(s+l),gc(s))\leq D$ for any $g\in G$ and for all $s\geq s_0$. Additionally, for each $n\in \mathbb Z_{\geq 0}$ we have \[d\big(g^nc(s),c(s+nl)\big)\leq nD\] for all $s\geq \max\{s_0, s_0+ (n-1)l\}$.
\end{lem}
\begin{proof}
For each $s\geq s_0$ we have that $gc(s)$ is $r_0$--close to some point $c(t)$ with $t\geq t_0$. We have \[(t-t_0)-20\delta \leq d\big(c(t_0),c(t)\big)\leq d\big(gc(s_0),gc(s)\big)+2r_0 \leq (s-s_0)+20\delta+2r_0.\] Thus, $(t-t_0)\leq (s-s_0)+40\delta+2r_0$. By the same reasoning, we find $(s-s_0)\leq (t-t_0)+40\delta+2r_0$. In other words, \[|(s-s_0)-(t-t_0)|\leq 40\delta+2r_0.\]
We may rewrite this as \begin{equation}\label{eqn:stl}|(s-t)+l|\leq 40\delta+2r_0.\end{equation} We conclude that \[d\big(gc(s),c(s+l)\big)\leq d\big(gc(s),c(t)\big)+d\big(c(t),c(s+l)\big)\leq r_0 + |(s+l)-t|+20\delta\leq 60\delta+3r_0,\] where the first inequality follows from the triangle inequality, the second from our choice of $t$ and the fact that $c$ is a $(1,20\delta)$--quasi-geodesic, and the third from \eqref{eqn:stl}. Setting $D=60\delta+3r_0$ gives the first inequality in the statement of the lemma.
For the second inequality, note that $d(g^2c(s),gc(s+l))\leq D$ for $s\geq s_0$. By the first inequality, the point $gc(s+l)$ is in turn $D$--close to the point $c(s+2l)$ as long as $s+l$ is also at least $s_0$. In other words, as long as $s$ and $s+l$ are both at least $s_0$, the point $g^2c(s)$ is $2D$-close to $c(s+2l)$. Thus, $g^2$ shifts points of $c$ by $2l$, but the constant of closeness degrades from $D$ to $2D$ and $s_0$ degrades to $\max\{s_0,s_0+l\}$.
An induction argument using this reasoning gives the second inequality, completing the proof of the lemma.
\end{proof}
The next lemma shows that the shift constant $l$ and the closeness constant $D$ give bounds for $p(g)$.
\begin{lem}
\label{lem:quasimorphbounds}
We have
\[-l-D\leq p(g)\leq -l+D.\]
\end{lem}
\begin{proof}
By the triangle inequality, we have \[d\big(g^{-n}c(t),c(0)\big)-d\big(c(t),c(0)\big)\leq d\big(g^{-n}c(t),c(t-nl)\big)+d\big(c(t-nl),c(0)\big)-d\big(c(t),c(0)\big).\] If $t\geq \max\{s_0,s_0+(n-1)l\}+nl$, then Lemma \ref{lem:shift} and the fact that $c$ is a $(1,20\delta)$--quasi-geodesic imply that the above quantity is at most \[nD+(t-nl+20\delta)-(t-20\delta)=nD-nl+40\delta.\] Using the same reasoning we find that \[d\big(g^{-n}c(t),c(0)\big)-d\big(c(t),c(0)\big)\geq -nl-nD-40\delta\] whenever $t\geq \max\{s_0,s_0+(n-1)l\}+nl$. Thus, \[-nl-nD-40\delta \leq d\big(g^{-n}c(t),c(0)\big)-d\big(c(t),c(0)\big)\leq -nl+nD+40\delta\] for all $t$ sufficiently large. Taking the $\limsup$ on all sides we obtain
\[-nl-nD-40\delta \leq q(g^n)\leq -nl+nD+40\delta.\]
Dividing these inequalities by $n$ and letting $n$ go to infinity gives the bounds on $p$.
\end{proof}
Combining Lemma \ref{lem:shift} with Lemma \ref{lem:quasimorphbounds} we obtain the following corollary.
\begin{cor}
\label{cor:shiftfunction}
There is a constant $E>0$ so that for any $g\in G$, if $s\geq s_0(g)$ then $d\big(c(s-p(g)),gc(s)\big)\leq E$.
\end{cor}
\begin{proof}
By the triangle inequality, we have \[d\big(c(s-p(g)),gc(s)\big)\leq d\big(c(s-p(g)),c(s+l)\big)+d\big(c(s+l),gc(s)\big).\] By Lemma \ref{lem:quasimorphbounds}, $|l+p(g)|\leq D$. Thus, the first quantity on the right hand side is bounded by $D+20\delta$. As long as $s\geq s_0$, the second quantity on the right hand side is bounded by $D$. Taking $E=2D+20\delta$ completes the proof.
\end{proof}
To prove Proposition \ref{prop:smalltranslation} we need one more result.
\begin{lem}
\label{lem:abelianaxisdiam}
If $z\in \mathbb Z^n$ then $d\big(zx,c(-p(z))\big)\leq E$.
\end{lem}
\begin{proof}
Since $x=c(0)$, the orbit of $x$ under $\mathbb Z^n$ lies in the orbit of $c$ under $\mathbb Z^n$. Recall that $z_0\in \mathbb Z^n$ is a loxodromic isometry whose fixed points are the endpoints $\xi$ and $\nu$ of $c$. Since $\mathbb Z^n$ is abelian, every element of $\mathbb Z^n$ fixes these endpoints. Thus, for any $z\in \mathbb Z^n$, $c$ and $zc$ are $r_0$--Hausdorff close.
Corollary \ref{cor:shiftfunction} implies that $zc(s)$ is $E$--close to $c(s-p(z))$ for all $s$ sufficiently large. In fact, since $c$ and $zc$ are $r_0$--Hausdorff close, we have that $zc(s)$ is $E$--close to $c(s-p(z))$ for all $s\geq 0$, by chasing through the proofs of the above results. In particular, $zx=zc(0)$ is $E$--close to $c(-p(z))$.
\end{proof}
We are now ready to prove Proposition \ref{prop:smalltranslation}.
\begin{proof}[Proof of Proposition \ref{prop:smalltranslation}]
Fix $N\in \mathbb R_{\geq 0}$, and let $g\in G$ satisfy $d(x,gx)\leq N$. Let
$s_0=s_0(g)$ be the constant defined after the statement of Proposition \ref{prop:smalltranslation} for this element $g$. Recall that $s_0$ is bounded above in terms of $N$.
By Corollary \ref{cor:shiftfunction}, if $s\geq s_0$ then
\begin{equation}\label{eqn:s-pg}
d\big(c(s-p(g)),gc(s)\big)\leq E.
\end{equation}
By Lemma \ref{lem:abelianaxisdiam}, if $z\in\mathbb Z^n$ then
\begin{equation}\label{eqn:zx}
d\big(zx,c(-p(z))\big)\leq E.
\end{equation}
Now suppose that $z\in\mathbb Z^n$ satisfies $p(z)\leq -s_0+p(g)$. Applying the triangle inequality three times we find that $d(zx,gzx)$ is at most \begin{equation}\label{eqn:threetriangles}d\big(zx,c(-p(z))\big)+d\big(c(-p(z)),gc(-p(z)+p(g))\big)+d\big(gc(-p(z)+p(g)),gc(-p(z))\big)+d\big(gc(-p(z)),gzx\big).\end{equation} Equation \eqref{eqn:zx} bounds the first and last summands in \eqref{eqn:threetriangles} by $E$. Since $-p(z)+p(g)\geq s_0$, applying \eqref{eqn:s-pg} bounds the second summand in \eqref{eqn:threetriangles} by $E$. The third summand in \eqref{eqn:threetriangles} is bounded by $|p(g)|+20\delta$ since $c$ is a $(1,20\delta)$--quasi-geodesic.
We define \[
A(N) = \sup \{s_0(g)-p(g) \mid d(x,gx)\leq N\}
\]
and
\[
B=3E+20\delta.
\]
Since $s_0(g)$ depends only on $d(x,gx)$ and $|p(g)|\leq d(x,gx)$, the function $A(N)$ is well-defined. As $E$ is uniform, this completes the proof.
\end{proof}
We are now ready to prove the main result of this section, which will immediately imply Theorem \ref{prop:main}.
\begin{thm} \label{thm:actiontoconf}
Let $G = H \rtimes_\gamma \mathbb Z^n$, and let $G\curvearrowright X$ be a cobounded lineal or quasi-parabolic action on a hyperbolic space $X$. Let $p$ be the Busemann pseudocharacter associated to this action, and assume that $p(H) =0$, so that $p$ restricts to a homomorphism $\mathbb Z^n\to \mathbb R$. There exists a subset $Q\subseteq H$ which is confining under $\gamma$ with respect to $p$ such that $X$ is $G$--equivariantly quasi-isometric to $\Gamma(G,Q\cup Z_p)$, where $Z_p$ is as in \eqref{eqn:Zrho}. Moreover, if $G\curvearrowright X$ is lineal, then $Q$ is not strictly confining (and therefore $Q=H$), while if $G\curvearrowright X$ is quasi-parabolic, then $Q$ is strictly confining.
\end{thm}
\begin{proof}
By the Schwarz--Milnor Lemma (see Lemma \ref{lem:MS}), we may assume without loss of generality that $X$ is a Cayley graph $\Gamma(G,Y)$.
As described at the beginning of this section, we let $\xi$ be the fixed point of $G$ in $\partial \Gamma(G,Y)$ and $\nu$ be the other fixed point of $\mathbb Z^n$. Let $\delta$ be the constant of hyperbolicity of $\Gamma(G,Y)$. We choose $c$ to be a $(1,20\delta)$--quasi-geodesic with $c(\infty)=\xi$ and $c(-\infty)=\nu$. We let $x=c(0)$ and choose $r_0$ to be a constant such that any two $(1,20\delta)$--quasi-geodesics rays with the same endpoint are eventually $r_0$--Hausdorff close.
A slight difficulty presents itself since the quasi-geodesic $c$ may not pass through the identity 1 of $G$, which is the natural basepoint of $\Gamma(G,Y)$. To fix this, we note the following slight modification of Proposition \ref{prop:smalltranslation}.
\begin{claim}
\label{claim:smalltransimprovement}
There is a function $A_0\colon \mathbb R_{\geq 0}\to \mathbb R$ and a constant $B_0>0$ (depending on $x$) such that the following holds. For any $g\in G$ with $d_Y(1,g)\leq N$ and $z\in \mathbb Z^n$ with $p(z)\leq -A_0(N)$, we have $d_Y(gz,z)\leq |p(g)|+B_0$.
\end{claim}
\begin{proof}[Proof of Claim]
Let $B$ be the constant from Proposition \ref{prop:smalltranslation}, and let $z\in \mathbb Z^n$. Two applications of the triangle inequality yield
\[
d_Y(gz,z)\leq d_Y(gzx,zx)+2d_Y(1,x).
\]
Note that $d_Y(x,gx)\leq d_Y(1,g)+2d_Y(1,x)$. Thus if $d_Y(g,1)\leq N$ we have $d_Y(gx,x)\leq N+2d_Y(1,x)$. Additionally, if $z\in \mathbb Z^n$ with $p(z)\leq -A(N+2d_Y(1,x))$ we have \[d_Y(gz,z)\leq d_Y(gzx,zx)+2d_Y(1,x)\leq |p(g)|+B+2d_Y(1,x).\] Taking $A_0\colon \mathbb R_{\geq 0}\to \mathbb R$ to be the function $A_0(N)=A(N+2d_Y(1,x))$ and $B_0$ to be the constant $B_0=B+2d_Y(1,x)$ proves the claim.
\end{proof}
We first define a subset of $H$; we will show that it is confining momentarily. Consider the ball $B_Y(1,B_0)$ of radius $B_0$ centered at the identity in $\Gamma(G,Y)$, that is, the set of elements in $G$ of word length at most $ B_0$ in the generating set $Y$. We moreover consider the intersection $B_Y(1,B_0)\cap H$. Let $A_1=A_0(B_0)$, so that if $g\in B_Y(1,B_0)\cap H$ and $z\in\mathbb Z^n$ with $p(z)\leq -A_1$, then $d_Y(gz,z)\leq B_0$ (since $p(g) =0$). We define \[Q:=\bigcup_{\substack{z\in \mathbb Z^n \\ 0\leq p(z)\leq A_1}}\gamma(z)\big(B_Y(1,B_0)\cap H\big).\] That is, we take a ball in $\Gamma(G,Y)$ intersected with $H$ and close it under the set of elements of $\mathbb Z^n$ with small positive image under $p$ to obtain the set $Q$. If $A_1$ happens to be negative then we take simply $Q=B_Y(1,B_0)\cap H$, and the reader may check that the proof given below goes through with some simplifications.
Let us check that $Q$ is confining under $\gamma$ with respect to the homomorphism $p$.
\begin{itemize}
\item First we check that if $p(z)\geq 0$ then $\gamma(z)(Q)\subseteq Q$. Let $z$ be such an element of $\mathbb Z^n$. An element of $Q$ has the form $\gamma(w)(h)$ where $h\in B_Y(1,B_0)\cap H$ and $w\in \mathbb Z^n$ with $0\leq p(w)\leq A_1$. We have $p(zw)=p(z)+p(w)\geq p(w)$. If $p(zw)\leq A_1$, then we have $\gamma(z)(\gamma(w)(h))=\gamma(zw)(h)\in Q$ by definition. Otherwise we have $p(zw)\geq A_1$. Hence $p((zw)^{-1})\leq -A_1$, and our choice of $A_1$
ensures that \[B_0\geq d_Y\big(h(zw)^{-1},(zw)^{-1}\big)=d_Y\big((zw)h(zw)^{-1},1\big)=d_Y\big(\gamma(zw)(h),1\big).\] Thus, $\gamma(zw)(h)\in B_Y(1,B_0)\cap H\subseteq Q$.
\item Now let $h\in H$ be arbitrary. We want to show that $\gamma(z)(h)\in Q$ for some $z\in \mathbb Z^n$. Since $p$ is unbounded, there exists $z\in \mathbb Z^n$ satisfying $p(z)\geq A_0(d_Y(h,1))$, so that $p(z^{-1})\leq -A_0(d_Y(h,1))$.
Hence by Claim \ref{claim:smalltransimprovement} we have \[B_0\geq d_Y\big(hz^{-1},z^{-1}\big)=d_Y\big(zhz^{-1},1\big)=d_Y\big(\gamma(z)(h),1\big).\] Thus we have $\gamma(z)(h)\in B_Y(1,B_0)\cap H\subseteq Q$.
\item Finally, we need to show that $\gamma(z)(Q\cdot Q)\subseteq Q$ for some $z\in \mathbb Z^n$. To see this, we first find a bound on the word length of elements of $Q$. An element of $Q$ has the form $\gamma(z)(h)=zhz^{-1}$ for some $z\in \mathbb Z^n$ with $0\leq p(z)\leq A_1$. By construction, the element $h$ has word length in $Y$ bounded by $B_0$. The element $z$ also has bounded word length. To see this, we first apply Lemma \ref{lem:abelianaxisdiam}, which shows that $d_Y\big(zc(0),c(-p(z))\big)\leq E$. Then, by the triangle inequality, \[d_Y\big(zc(0),c(0)\big)\leq d_Y\big(zc(0),c(-p(z))\big)+d\big(c(-p(z)),c(0)\big)\leq E+p(z)+20\delta\leq E+A_1+20\delta.\] Another application of the triangle inequality yields \[d_Y(z,1)\leq E+A_1+20\delta+2d_Y(x,1).\] Finally, this gives us a bound on the word length of $\gamma(z)(h)=zhz^{-1}$: \[d_Y(zhz^{-1},1)\leq B_0+2(E+A_1+20\delta+2d_Y(x,1)).\] Call this upper bound $F$.
So far we have shown that $Q\subseteq B_Y(1,F)$, from which it immediately follows that $Q\cdot Q\subseteq B_Y(1,2F)$.
Since there exists $z\in \mathbb Z^n$ satisfying $p(z)\geq A_0(2F)$,
it follows from Claim \ref{claim:smalltransimprovement} that if
$h\in Q\cdot Q$, we have \[B_0 \geq d_Y(hz^{-1},z^{-1})=d_Y(zhz^{-1},1)=d_Y(\gamma(z)(h),1).\] That is, $\gamma(z)(Q\cdot Q)\subseteq B_Y(1,B_0) \cap H \subseteq Q$.
\end{itemize}
Now that we have constructed $Q$, we show that $\Gamma(G,Q\cup Z_p)$ is quasi-isometric to $\Gamma(G,Y)$, where the constant $C_p$ and the set $Z_p$ are chosen as in \eqref{eqn:Zrho}. This will complete the proof. To do this, we show that every element of $Q\cup Z_p$ has bounded word length with respect to the generating set $Y$ and vice versa.
First we show that every element of $Q\cup Z_p$ has bounded word length in $Y$. We have already shown that $Q\subseteq B_Y(1,F)$, so it remains to be shown that every element of $Z_p$ has bounded length in $Y$. For $z\in Z_p$ it follows exactly as in the third bullet point above that \[d_Y(z,1)\leq E+|p(z)|+20\delta+2d_Y(x,1)\leq E+C_p+20\delta+2d_Y(x,1).\]
Since this last quantity is independent of $z$, we have shown that every element of $Q\cup Z_p$ has bounded word length with respect to $Y$, as desired.
We now show that every element of $Y$ has bounded word length with respect to $Q\cup Z_p$. Consider an element $hz\in Y$ where $h\in H$ and $z\in \mathbb Z^n$. We will bound the word lengths of $h$ and $z$ with respect to $Q\cup Z_p$ separately.
First we bound the word length of $z$ with respect to $Q\cup Z_p$. Note that we have $p(z)=p(hz)$. Moreover, by the definition of $p$, we have \[|p(hz)|\leq d_Y(x,hzx)\leq 2d_Y(1,x)+d_Y(1,hz)\leq 2d_Y(1,x)+1.\] Call this upper bound $L$ so that $|p(z)|\leq L$.
This allows us to bound the word length of $z$. We have $p(t_i)\neq 0$ for some $i$. Without loss of generality assume $p(t_1)\neq 0$. Then we may choose $n$ with \[|p(t_1^n)-p(z)|=|np(t_1)-p(z)|\leq |p(t_1)|\leq C_p.\] Therefore $t_1^nz^{-1}\in Z_p$. Moreover, $|n|$ is bounded by $\frac{L}{|p(t_1)|}+1$ since $|p(z)|\leq L$, and this proves that $z$ has word length at most \[|n|+1\leq \frac{L}{|p(t_1)|}+2\] with respect to $Z_p$.
Now we bound the word length of $h$ with respect to $Q\cup Z_p$. We will first bound the word length of $h$ with respect to $Y$. Recall that we have already shown $|p(z)|\leq L$, and thus another calculation identical to that of the third bullet point above yields \[d_Y(1,z)\leq E+|p(z)|+20\delta+2d_Y(x,1)\leq E+L+20\delta+2d_Y(x,1).\]
From this and the fact that $hz\in Y$, it follows that \[d_Y(1,h)\leq d_Y(1,hz)+d_Y(hz,h)\leq 1+ 2d_Y(x,1)+E+L+20\delta.\]
Denote by $M$ this upper bound on $d_Y(1,h)$. By Claim \ref{claim:smalltransimprovement}, if $g \in B_Y(1, M)\cap H$ and $w\in \mathbb Z^n$ with $p(w)\leq -A_0(M)$, then $d_Y(gw,w)\leq B_0$. In particular, we have $p(t_1^n)=np(t_1)\leq -A_0(M)$ for some $n$ with $|n|\leq \frac{A_0(M)}{|p(t_1)|}+1$. For this value of $n$ we have $\gamma(t_1^n)(h)=t_1^nht_1^{-n}\in Q$. Therefore the word length of $h$ with respect to $Q\cup Z_p$ is at most \[2|n|+1\leq 2\frac{A_0(M)}{|p(t_1)|}+3.\] We have shown that every element of $Y$ has bounded word length with respect to $Q\cup Z_p$. We conclude that $\Gamma(G,Q\cup Z_p)$ is quasi-isometric to $\Gamma(G,Y)$ as desired.
It remains to show that $Q$ is \emph{strictly} confining exactly when $G\curvearrowright \Gamma(G,Y)$ is quasi-parabolic. Since $\Gamma(G,Y)$ is quasi-isometric to $\Gamma(G,Q\cup Z_p)$, it suffices to show that $Q$ is strictly confining exactly when $G\curvearrowright \Gamma(G,Q\cup Z_p)$ is quasi-parabolic.
If $Q$ is strictly confining, then it follows from Lemma \ref{focal} that $G \curvearrowright \Gamma(G, Q \cup Z_p)$ is quasi-parabolic. Conversely, suppose that $G \curvearrowright \Gamma(G,Y)$ is quasi-parabolic and, towards a contradiction, that $Q$ is confining but not strictly confining. That is, suppose that for every $z \in \mathbb Z^n$ with $\rho(z) \geq 0$, we have that $\gamma(z)(Q) = Q$. It then follows that $Q = \gamma(z^{-1})(Q)$ for any such $z$, as well. By Definition \ref{def:confining}(b), we see that it thus follows that $Q =H$. But since $\Gamma(\mathbb Z^n , Z_p)$ is a quasi-line, it follows that $\Gamma(G, Q \cup Z_p) = \Gamma(G, H \cup Z_p)$ is also a quasi-line, which contradicts the assumption that $G \curvearrowright \Gamma(G,Y)$ is quasi-parabolic. Hence $Q$ must be strictly confining.
\end{proof}
We now introduce an equivalence relation on homomorphisms from $\mathbb Z^n$ to $\mathbb R$.
\begin{defn}
We say two homomorphisms $\rho,\rho'\colon \mathbb Z^n\to \mathbb R$ are \emph{equivalent}, and write $\rho\sim\rho'$, if there exists a constant $j\in \mathbb R_{> 0}$ such that $\rho(z)=j\rho'(z)$ for all $z\in \mathbb Z^n$.
\end{defn}
As shown in Lemma \ref{lem:multiplekernel}, requiring that $j$ is positive ensures that $\rho$ and $\rho'$ have not only the same kernel, but also the same half space with positive image. The following lemma shows that a subset of $H$ is strictly confining with respect to at most one equivalence class of homomorphisms.
\begin{lem}\label{lem:notsim}
Suppose $Q\subsetneq H$ is strictly confining under $\gamma$ with respect to $\rho$. If $\rho'\sim\rho$, then $Q$ is strictly confining with respect to $\rho'$. Moreover, $Q$ is not confining under $\gamma$ with respect to $\rho''$ for any $\rho''\not\sim\rho$.
\end{lem}
\begin{proof}
By Lemma \ref{lem:multiplekernel}, $\rho$ is completely determined up to scaling by the kernel of its extension to $\mathbb R^n$, which we (by an abuse of notation) denote $\ker\rho$. We will show that $\ker\rho$ is completely determined by the strictly confining subset $Q$. This will prove both statements.
The kernel $\ker\rho$ is a linear codimension-one subspace of $\mathbb R^n$ that divides $\mathbb R^n\setminus \ker\rho$ into two half spaces, $H_1$ and $H_2$, in the following way: for any $z \in \mathbb Z^n$, $z\in H_1$ if and only if $\rho(z)>0$, and $z\in H_2$ if and only if $\rho(z)<0$.
We claim that for any $z\in\mathbb Z^n$, we have
$\gamma(z)(Q)\subsetneq Q$ if and only if $z\in H_1$, and $\gamma(z)(Q)\supsetneq Q$ if and only if $z\in H_2$.
We will show that the first statement holds; the proof of the second statement is similar.
Since $Q$ is strictly confining, there exists some $w\in \mathbb Z^n$ such that $\gamma(w)(Q)\subsetneq Q$. Suppose $z\in H_1$, so that $\rho(z)>0$. If $\rho(z)\geq \rho(w)$, then by writing $z=(zw^{-1})w$, we have
\[\gamma(z)(Q)=\gamma(w)\gamma(zw^{-1})(Q)\subseteq\gamma(w)(Q)\subsetneq Q.\]
On the other hand, if $0<\rho(z)<\rho(w)$, then $\rho(z^m)>\rho(w)$ for some $m$, and then by the argument above, we have
\[\gamma(z)^m(Q)=\gamma(z^m)(Q)\subsetneq Q.\]
But if $\gamma(z)(Q)=Q$, then $\gamma(z)^m(Q)= Q$, which is a contradiction. Therefore $\gamma(z)(Q)\subsetneq Q$.
Conversely, suppose $\gamma(z)(Q)\subsetneq Q$ for some $z\in \mathbb Z^n$. If $z\notin H_1$, then $\rho(z)\leq 0$, and so $\rho(z^{-1})\geq 0$. It follows that $\gamma(z^{-1})(Q)\subseteq Q$. Thus $Q=\gamma(zz^{-1})(Q)=\gamma(z)\gamma(z^{-1})(Q)\subseteq \gamma(z)(Q)\subsetneq Q$, which is a contradiction.
\end{proof}
\section{An example: $\mathbb Z[\frac1k]\rtimes \mathbb Z^n$}
Fix a natural number $k\geq 2$ which is not a power of a prime number. Let $k=p_1^{m_1}\cdots p_n^{m_n}$ be the prime factorization of $k$. Let $G_k=\mathbb Z[\frac1k]\rtimes_\gamma \mathbb Z^n$, where the homomorphism $\gamma:\mathbb Z^n \to \operatorname{Aut}(\mathbb Z[\frac{1}{k}])$ is defined as follows. Let $t_1,\ldots,t_n$ be a basis for $\mathbb Z^n$ as a free abelian group. For any $h\in\mathbb Z[\frac1k]$, we define $\gamma(t_i)(h)=t_iht_i^{-1}$ to be equal to $p_i^{m_i} h$ as an element of $\mathbb Z[\frac{1}{k}]$. Thus $G_k$ is the group with presentation \[G_k = \left\langle a, t_1,\ldots,t_n \mid [t_i,t_j]=1, \ t_iat_i^{-1}=a^{p_i^{m_i}} \text{ for all } i,j\right\rangle\] and is a higher-dimensional analog of a solvable Baumslag-Solitar group. Here $a$ corresponds to the normal generator 1 of $\mathbb Z[\frac1k]$. The relation $t_1at_1^{-1}=a^{p_1^{m_1}}$ implies that for any pseudocharacter $p\colon G_k\to \mathbb R$, \[p(a)=p(t_1at_1^{-1})=p_1^{m_1}p(a),\] and thus $p(a)=0$. Therefore any pseudocharacter vanishes on $\mathbb Z[\frac1k]$; this applies in particular to any Busemann pseudocharacter. Moreover, as before, $p$ turns out to be a homomorphism.
In addition to the standard representation of elements of $\mathbb Z[\frac1k]$ as Laurent polynomials in $k$, we also represent elements of $\mathbb Z[\frac1k]$ by their base $k$ expansions. For example, $\frac1k=0.1$ while $k+\frac1k+\frac{1}{k^4}=10.1001$. In general for $c\in \mathbb Z[\frac1k]$ we may write \[c=\pm c_r\ldots c_0.c_{-1}\ldots c_{-s}\] where each digit $c_i\in \{0,\ldots,k-1\}$. We will switch between these representations interchangeably. We note that in the base $k$ representation, multiplying and dividing by $k$ shifts the decimal point one place to the right and left, respectively.
The goal of this section is to prove Theorem \ref{thm:Z1k}, which we restate for the convenience of the reader.
\Gk*
Our strategy for classifying the quasi-parabolic structures reduces the problem to the classification of quasi-parabolic structures of the solvable Baumslag-Solitar group $BS(1,k)$, which was given by the first and third authors in \cite{AR}. The Baumslag-Solitar group $BS(1,k)$ is the group with presentation $BS(1,k) = \langle a,t \mid tat^{-1}=a^k\rangle$.
It is isomorphic to the semi-direct product $\mathbb Z[\frac{1}{k}]\rtimes_\alpha \mathbb Z$, where the automorphism $\alpha$ acts as multiplication by $k$. We will identify $BS(1,k)$ with this semi-direct product in all that follows.
The following theorem from \cite{AR} classifies the subsets of $\mathbb Z[\frac{1}{k}]$ which are confining under the action of $\alpha$. Let $s$ generate the factor $\mathbb Z$ so that $BS(1,k)\simeq \mathbb Z[\frac{1}{k}]\rtimes_\alpha \langle s\rangle$. We say a divisor $l$ of $k=p_1^{m_1}\ldots p_n^{m_n}$ is \emph{full} if $p_i^{m_i}$ divides $l$ whenever $p_i$ divides $l$. For example, the full divisors of 12 are 1, 4, 3, and 12.
\begin{prop}[{\cite[Theorem~1.1~\&~Proposition~3.12]{AR}}]\label{thm:BS1k}
If $C\subseteq\mathbb Z[\frac{1}{k}]$ is confining under the action of $\alpha$, then there is a full divisor $l$ of $k$ such that
\[
[C\cup \{s^{\pm 1}\}]= \left[\mathbb Z\left[\frac{1}{l}\right]\cup \{s^{\pm 1}\}\right]\]
as elements of $ \mathcal H_{qp}(BS(1,k))$.
If $C\subseteq\mathbb Z[\frac{1}{k}]$ is confining under the action of $\alpha^{-1}$, then either $[C\cup\{s^{\pm 1}\}]=[\mathbb Z[\frac{1}{k}]\cup\{s^{\pm 1}\}]$ or $[C\cup\{s^{\pm 1}\}]=[C_-\cup\{s^{\pm 1}\}]$ as elements of $ \mathcal H_{qp}(BS(1,k))$, where
\[
C_-=\left\{c\in \mathbb Z\left[\frac{1}{k}\right] \Big\vert \ c=\pm 0.c_{-1}c_{-2}\ldots c_{-m} \textrm{ for some $m\in \mathbb N$}\right\}.
\]
\end{prop}
\noindent Stated another way, $C_-$ is the unit ball of $\mathbb R$ intersected with $\mathbb Z[\frac1k]$.
\subsection{Quasi-parabolic structures}
In this subsection we describe the quasi-parabolic structures of $G_k$. In particular, we prove the following proposition.
\begin{prop}\label{prop:qp}
$\mathcal H_{qp}(G_k)$ consists of exactly $n+1$ incomparable structures.
\end{prop}
\subsubsection{Confining subsets of $\mathbb Z[\frac1k]$}
Fix a non-zero homomorphism $\rho\colon \mathbb Z^n\to \mathbb R$. We will describe \emph{all} of the subsets of $\mathbb Z[\frac1k]$ which are confining under $\gamma$ with respect to this particular $\rho$. We note that the subset $Q=\mathbb Z[\frac1k]$ is confining but not strictly confining under $\gamma$ with respect to all choices of $\rho$ and corresponds to a lineal structure by Lemma \ref{focal}.
To prove Proposition \ref{prop:qp}, we will show that there are exactly $n+1$ choices for $\rho$ with respect to which there are any subsets of $\mathbb Z[\frac1k]$ that are \emph{strictly} confining under $\gamma$. By Theorem \ref{thm:main}, each such subset corresponds to a quasi-parabolic structure. For each of these $n+1$ choices of $\rho$, we will show there is exactly one such structure.
We begin with a preliminary lemma, which is the analogue of \cite[Lemma~3.2]{AR} and \cite[Lemma 4.9]{Bal}. The proof follows the same lines with a few modifications. Note that this lemma holds for an arbitrary group $H\rtimes_\gamma\mathbb Z^n$.
\begin{lem}\label{lem:AddS}
Consider a group $H\rtimes_\gamma \mathbb Z^n$, and fix a homomorphism $\rho\colon \mathbb Z^n\to\mathbb R$. Suppose $Q$ is a symmetric subset of $H$ which is confining under $\gamma$ with respect to $\rho$. Let $S$ be a symmetric subset of $H$ such that there exists $z_0\in\mathbb Z^n$ with $\rho(z_0)\geq 0$ such that $\gamma(z_0)(g)\in Q$ for all $g\in S$. Then
\[
\overline Q=Q\cup\bigcup_{\rho(z)\geq 0}\gamma(z)(S)
\]
is confining under $\gamma$ with respect to $\rho$, and
\[
[Q\cup Z_\rho]=[\overline Q\cup Z_\rho].
\]
\end{lem}
\begin{proof}
Conditions (a) and (b) of Definition \ref{def:confining} are clear. To show that (c) holds,
note that for any $z\in\mathbb Z^n$ with $\rho(z)\geq 0$ and any $g\in S$,
\[
\gamma(z_0)(\gamma(z)(g))=\gamma(z)(\gamma(z_0)(g))\in \gamma(z)(Q)\subseteq Q.
\]
We also have $\gamma(z_0)(g)\in Q $ for any $g\in Q$. Hence, $\gamma(z_0)(\overline Q)\subseteq Q$. Let $g,h\in\overline Q$, and fix $z_1\in\mathbb Z^n$ such that $\gamma(z_1)(Q\cdot Q)\subseteq Q$. Then
\[
\gamma(z_0z_1)(gh)=\gamma(z_1)\big(\gamma(z_0)(g)\gamma(z_0)(h)\big)\in \gamma(z_1)(Q\cdot Q)\subseteq Q\subseteq \overline Q.
\]
Therefore (c) holds with the element $z_0z_1$.
To see that $[Q\cup Z_\rho]=[\overline Q\cup Z_\rho]$, note first that $[\overline Q\cup Z_\rho]\preceq [Q\cup Z_\rho]$ since $Q\subseteq \overline Q$. For the other direction, let $\rho(z_0)=K_0$. Then for $z\in\mathbb Z^n$ with $\rho(z)\geq K_0$, we have $\gamma(z)(S)\subseteq Q$, since $\gamma(z_0)(S)\subseteq Q$. Hence we may also write
\[
\overline Q=Q\cup \bigcup_{0\leq \rho(z)<K_0}\gamma(z)(S).
\]
Let $g \in \overline{Q}$. If $g \in Q$, then $\|g\|_{Q \cup Z_\rho} \leq 1$. As above, if $g = \gamma(z)(s)$ for some $s \in S$ and $0 \leq \rho(z) < K_0$, then $\gamma(z_0z)(s) \in Q$. Thus $g = \gamma(z)(s) \in \gamma(z_0^{-1})(Q)$. From this one can see that $\|g\|_{Q \cup Z_\rho} \leq 2||z_0||_{Z_\rho} +1$, which is a constant independent of $g$.
In other words, any element of $\overline Q\cup Z_\rho$ has uniformly bounded word length with respect to $Q\cup Z_\rho$, and so $[Q\cup Z_\rho]\preceq [\overline Q\cup Z_\rho]$.
\end{proof}
The following lemma is proven exactly as in the proof of \cite[Lemma~3.3]{AR}, with $p_i^{a_i}$ playing the role of $n$ and $t_i$ playing the role of $t$. We refer the reader to \cite{AR} for the proof. Here $Q\cup \mathbb Z$ denotes the union of subsets of $\mathbb Z[\frac{1}{k}]$.
\begin{lem}\label{lem:ZsubsetQ}
If $\rho(t_i)>0$ for some $i$, then $[Q\cup Z_\rho]=[(Q\cup\mathbb Z)\cup Z_\rho]$.
\end{lem}
\noindent In other words, the subring $\mathbb Z$ of $\mathbb Z[\frac1k]$ has bounded word length in $Q\cup Z_\rho$.
The next lemma describes $n$ distinct homomorphisms $ \mathbb Z^n\to \mathbb R$, and, for each homomorphism, identifies a subset of $\mathbb Z[\frac1k]$ which is strictly confining under $\gamma$ with respect to it. Define $k_i=\frac{k}{p_i^{m_i}}=p_1^{m_1} \cdots \widehat{p_i^{m_i}} \cdots p_n^{m_n}$, where $\widehat{\cdot}$ indicates that we omit that factor from the product.
\begin{lem}\label{lem:Q_i}
Let $\rho^+_i\colon\mathbb Z^n\to\mathbb R$ be projection to the $i$-th factor of $\mathbb Z^n$, and let $Q_i = \mathbb Z\left[\frac{1}{k_i}\right]$.
Then $Q_i$ is strictly confining under $\gamma$ with respect to $\rho_i^+$.
\end{lem}
\begin{proof}
Fix some $1\leq i\leq n$. We will first show that $Q_i$ is confining under $\gamma$ with respect to $\rho_i^+$. Fix $z\in\mathbb Z^n$ with $\rho_i^+(z)\geq 0$, so that $z=t_1^{b_1}\ldots t_n^{b_n}$, where $b_i\geq 0$. Note that $Q_i$ is closed under multiplication by integers. Since $p_1^{b_1m_1}\cdots \widehat{p_i^{b_im_i}}\cdots p_n^{b_nm_n}$ is an integer times a (possibly negative) power of $k_i$, it follows that for any $q\in Q_i=\mathbb Z[\frac{1}{k_i}]$ we have \[\gamma(z)(q) = p_i^{b_im_i} \left(p_1^{b_1m_1} \cdots \widehat{p_i^{b_im_i}} \cdots p_n^{b_nm_n} q\right) \in p_i^{b_im_i} \mathbb Z\left[\frac{1}{k_i}\right].\]
Since $b_i\geq 0$, we have $p_i^{b_im_i}\in \mathbb Z$, and so $\gamma(z)(q)\in Q_i=\mathbb Z[\frac{1}{k_i}]$, as desired.
Let $h=\pm h_m\dots h_0.h_{-1}h_{-2}\dots h_{-\ell}\in \mathbb Z[\frac1k]$. Since $\rho^+_i(t_1\ldots t_n)=1$, we have $\rho^+_i((t_1\ldots t_n)^\ell)=\ell>0$. Let $z=(t_1\ldots t_n)^\ell$. Then
\[
\gamma(z)(h)=\gamma((t_1\ldots t_n)^\ell)(h)=k^\ell h=\pm h_m\dots h_0h_{-1}h_{-2}\dots h_{-\ell}\in\mathbb Z\subseteq Q_i,
\]
and Definition \ref{def:confining}(b) is satisfied.
To see that Definition \ref{def:confining}(c) holds, notice that $Q_i$ is closed under addition, and so we can take $z_0$ to be the identity of $\mathbb Z^n$.
Finally, $Q_i$ is also \emph{strictly} confining with respect to $\rho_i^+$: $1\in Q_i$, but $1\notin \gamma(t_i)(Q_i)$ since $\gamma(t_i^{-1})(1)=\frac{1}{p_i^{m_i}}\notin Q_i$. Thus $\gamma(t_i)(Q_i)\subsetneq Q_i$.
\end{proof}
We now describe one additional homomorphism $ \mathbb Z^n\to\mathbb R$ and a subset which is strictly confining under $\gamma$ with respect to this homomorphism. We will show that this confining subset, along with the $n$ subsets constructed in Lemma \ref{lem:Q_i} give rise to the $n+1$ quasi-parabolic structures from Proposition \ref{prop:qp}.
\begin{lem}\label{lem:Q_-}
Let $\rho_-\colon\mathbb Z^n\to\mathbb R$ be given by $\rho_-(t_i)=-m_i\log p_i$ for each $i$, and let
\[
Q_-=\left\{x\in \mathbb Z\left[\frac1k\right]\Big\vert \ x=\pm 0.x_{-1}x_{-2}\dots x_{-m} \textrm{ for some }m\in \mathbb N\right\}\subsetneq \mathbb Z\left[\frac1k\right]
\]
(that is, $Q_-$ is the unit ball in $\mathbb R$ intersected with $\mathbb Z[\frac{1}{k}]$). Then $Q_-$ is strictly confining under $\gamma$ with respect to $\rho_-$.
\end{lem}
\begin{proof}
Suppose $z=t_1^{a_1}\ldots t_n^{a_n}\in\mathbb Z^n$ satisfies $\rho_-(z)\geq 0$. Then $-a_1m_1\log p_1-\cdots -a_nm_n\log p_n\geq0$, and so $p_1^{a_1m_1}\cdots p_n^{a_nm_n}\leq 1$. For $q=\pm0.x_{-1}x_{-2}\ldots x_{-m}\in Q_-$, we have
\[
\gamma(z)(q)=\pm (p_1^{a_1m_1}\cdots p_n^{a_nm_n})(0.x_{-1}x_{-2}\dots x_{-m}).
\]
In particular, we have a bound on absolute values $|\gamma(z)(q)|\leq |q|$, and thus $\gamma(z)(q)\in Q_-$. Therefore Definition \ref{def:confining}(a) holds. Next, let $h=\pm h_m\dots h_0.h_{-1}h_{-2}\dots h_{-\ell}$ be an arbitrary element of $ \mathbb Z[\frac1k]$.
Taking $z=(t_1^{-1}\ldots t_n^{-1})^m$, we see that
\[
\gamma(z)(h)=\gamma((t_1^{-1}\ldots t_n^{-1})^m)(h)=k^{-m} h=\pm 0.h_m\dots h_0h_{-1}h_{-2}\dots h_{-\ell}\in Q_- ,
\]
and Definition \ref{def:confining}(b) is satisfied. Finally, let $x,y\in Q_-$. Then we have
\[
x+y=\pm a_0.a_{-1}\ldots a_{-\ell}
\]
where each $a_i\in\{0,\dots, k-1\}$. Let $z_0=t_1^{-1}\ldots t_n^{-1}$. Then $\rho_-(z_0)>0$, and
\[
\gamma(z_0)(x+y)=\pm k^{-1}\left( a_0.a_{-1}\ldots a_{-\ell}\right)=\pm0.a_0a_{-1}\ldots a_{-\ell}\in Q_-,
\]
and so Definition \ref{def:confining}(c) holds with this choice of $z_0$.
It remains to show that $Q_-$ is \emph{strictly} confining.
Fix any $z=t_1^{a_1}\ldots t_n^{a_n} \in \mathbb Z^n$ with $p_1^{m_1a_1}\cdots p_n^{m_na_n}<\frac{1}{k}$. We have $\rho_-(z)=-\log(p_1^{m_1a_1}\cdots p_n^{m_na_n})>0$ and
\[
\gamma(z^{-1})(0.1)=(p_1^{m_1a_1}\cdots p_n^{m_na_n})^{-1}(0.1)>1.
\]
It follows that $\gamma(z^{-1})(0.1)\not\in Q_-$ and thus $0.1 \notin \gamma(z)(Q_-)$. Since $0.1\in Q_-$, we conclude that $Q_-$ is strictly confining under $\gamma$ with respect to $\rho_-$.
\end{proof}
In the following series of lemmas, we will show that given any homomorphism $\rho\colon\mathbb Z^n\to\mathbb R$, if there is a subset of $\mathbb Z[\frac{1}{k}]$ which is strictly confining under $\gamma$ with respect to $\rho$, then $\rho$ must be equivalent to $\rho_-$ or $\rho_i$ for some $i$, and the strictly confining subset must give rise to the same quasi-parabolic structure on $G_k$ as $Q_-$ or $Q_i$, respectively.
Fix a homomorphism $\rho\colon\mathbb Z^n\to \mathbb R$. We will consider three separate cases, depending on whether $\rho(t_1\ldots t_n)$ is positive, negative, or zero. Each case is dealt with in a separate lemma.
We first show that if $\rho(t_1\ldots t_n)=0$, there are \emph{no} subsets of $\mathbb Z[\frac{1}{k}]$ which are strictly confining under $\gamma$ with respect to $\rho$.
\begin{lem}\label{lem:rho=0}
Suppose $\rho(t_1\ldots t_n)=0$. If $Q\subseteq \mathbb Z[\frac1k]$ is confining under $\gamma$ with respect to $\rho$, then
\[
[Q\cup Z_\rho]=\left[\mathbb Z\left[\frac1k\right]\cup Z_\rho\right].
\]
\end{lem}
\begin{proof}
Suppose $Q\subseteq\mathbb Z[\frac1k]$ is confining under $\gamma$ with respect to $\rho$. Since $\rho$ is not identically equal to zero, it must be the case that $\rho(t_i)>0$ for some $i$. Thus, by Lemma \ref{lem:ZsubsetQ}, $[Q\cup Z_\rho]=[(Q\cup\mathbb Z) \cup Z_\rho]$, where $\mathbb Z$ denotes the subring of $\mathbb Z[\frac{1}{k}]$. This implies, in particular, that $\mathbb Z$ has bounded word length with respect to $Q\cup Z_\rho$.
Since $\rho(t_1 \ldots t_n)=0$, we have that $\rho(t_1^{-1}\ldots t_n^{-1})=0$, as well, and so $Q$ is closed under multiplication by $\frac{1}{k}$. Since $\mathbb Z$ has bounded word length with respect to $Q\cup Z_\rho$ and $Q$ is closed under multiplication by $\frac{1}{k}$, we see that all of $\mathbb Z[\frac{1}{k}]$ has bounded length with respect to $Q\cup Z_\rho$ as well.
This completes the proof.
\end{proof}
We next consider the case $\rho(t_1 \ldots t_n)>0$ and relate confining subsets of $\mathbb Z[\frac{1}{k}]$ in $G_k$ to confining subsets of $\mathbb Z[\frac{1}{k}]$ in the Baumslag-Solitar group $BS(1,k)$.
\begin{lem}\label{lem:QBS}
Let $Q\subseteq \mathbb Z[\frac1k]$ be confining under $\gamma$ with respect to $\rho$. View $Q\subseteq\mathbb Z[\frac1k]$ as a subset of the Baumslag-Solitar group $BS(1,k)=\mathbb Z[\frac1k]\rtimes_\alpha \mathbb Z$. If $\rho(t_1 \ldots t_n)> 0$, then $Q$ is confining under the action of $\alpha$.
\end{lem}
\begin{proof}
We will show that $Q$ satisfies the conditions of Definition \ref{genconfine}.
Recall that $BS(1,k)=\mathbb Z[\frac1k]\rtimes_\alpha\langle s\rangle$. Then $\alpha$ and $\gamma(t_1 \ldots t_n)$ both act on $\mathbb Z[\frac1k]$ as multiplication by $k$, and so $\alpha(Q)=\gamma(t_1\ldots t_n)(Q)$. Since $\rho(t_1\ldots t_n)> 0$, we have $\alpha(Q)\subseteq Q$, and Definition \ref{genconfine}(a) is satisfied. Moreover, for any $u\in \mathbb Z[\frac1k]$ and $z\in \mathbb Z^n$, we have $\gamma(z)(u)\in Q$ whenever $\rho(z)$ is sufficiently large. In particular $\alpha^a(u)=\gamma((t_1\ldots t_n)^a)(u)\in Q$ for $a\in \mathbb Z$ sufficiently large, and Definition \ref{genconfine}(b) is satisfied. Finally, since $\rho(t_1\ldots t_n)> 0$, there is some constant $b_0\in \mathbb Z$ such that $\rho((t_1\ldots t_n)^{b_0})>\rho(z_0)$, where $z_0$ is as in Definition \ref{def:confining}(c). Thus $\alpha^{b_0}(Q+Q)=\gamma\big((t_1\ldots t_n)^{b_0}\big)(Q+Q)\subseteq Q$, and Definition \ref{genconfine}(c) is satisfied. Therefore, $Q$ is confining under $\alpha$.
\end{proof}
\begin{lem}\label{lem:rho>0}
Suppose $\rho(t_1\ldots t_n)>0$ and $Q\subseteq \mathbb Z[\frac1k]$ is confining under $\gamma$ with respect to $\rho$.
If $Q$ is strictly confining, then for some $i$ we have
\[
[Q\cup Z_\rho]=[Q_i\cup Z_\rho]
\] and $\rho\sim\rho^+_i$. Otherwise, \[
[Q\cup Z_\rho]=\left [\mathbb Z\left[\frac1k\right ]\cup Z_\rho \right ].
\]
\end{lem}
\begin{proof}
Let $Q$ be confining under $\gamma$ with respect to $\rho$, where $\rho(t_1 \ldots t_n)>0$, as in the statement of the lemma.
Our assumption that $\rho(t_1 \ldots t_n)>0$ ensures that there exists $1\leq i\leq n$ with $\rho(t_i)>0$. We will show that when $Q$ is strictly confining (equivalently, when $[Q\cup Z_\rho]\neq \left[ \mathbb Z\left[\frac{1}{k}\right] \cup Z_\rho\right]$), there is a unique such index $i$, and $[Q\cup Z_\rho]=[Q_i\cup Z_\rho]$ for this $i$.
By Lemma \ref{lem:QBS}, we see that $Q$ is a confining subset of $\mathbb Z[\frac{1}{k}]$ under the automorphism $\alpha$ given by multiplication by $k$. Hence we may consider the Baumslag-Solitar group $BS(1,k)=\mathbb Z[\frac{1}{k}]\rtimes_\alpha \langle s \rangle$, and by Proposition \ref{thm:BS1k} we have that $[Q\cup \{s^{\pm 1}\}]=[\mathbb Z[\frac{1}{l}]\cup \{s^{\pm 1}\}]$, as generating sets of $BS(1,k)$, for some full divisor $l$ of $k$.
It follows that there exists a positive integer $N$ such that every element of $Q$ has word length at most $N$ in the generating set $\mathbb Z[\frac{1}{l}]\cup \{s^{\pm 1}\}$. We claim additionally that $\alpha^N(Q) = k^N Q \subseteq \mathbb Z[\frac{1}{l}]$. To see this, write an element $g\in Q$ as a word $g=g_1\ldots g_r$ in the generating set $\mathbb Z[\frac{1}{l}]\cup \{s^{\pm 1}\}$. Since $\alpha(\mathbb Z[\frac1l])=s\mathbb Z[\frac1l]s^{-1}\subseteq \mathbb Z[\frac1l]$, we may move any $g_i$ which is equal to $s$ to the right and any $g_i$ which is equal to $s^{-1}$ to the left, keeping the length of the word unchanged. The result is a geodesic word \[g=s^{-t} h_1 \ldots h_v s^u\] where $h_i \in \mathbb Z[\frac{1}{l}]$ for all $i$ and $t,u\geq 0$. Since $r\leq N$ we also have $t,u\leq r \leq N$. Moreover, since $\mathbb Z[\frac{1}{l}]$ is a subgroup of $\mathbb Z[\frac{1}{k}]$, we have $h_1\ldots h_v=h\in \mathbb Z[\frac{1}{l}]$. Finally, since $g$ is contained in $\mathbb Z[\frac{1}{k}]$ we have $t=u$. Thus \[g=s^{-t}hs^t=\alpha^{-t}(h),\] and this proves that $\alpha^t(g)=h\in \mathbb Z[\frac{1}{l}]$ with $t\leq N$.
We will next show that either $l=k$ or $l=k_i=p_1^{m_1} \ldots \widehat{p_i^{m_i}} \ldots p_n^{m_n}$, where $\widehat{\cdot}$ denotes omission of the corresponding factor. For any $j\neq i$, there exists $f>0$ sufficiently large that $\rho(t_i^f t_j^{-1})>0$. Consequently $Q$ is closed under $\gamma(t_i^ft_j^{-1})$, which is the automorphism given by multiplication by $p_i^{fm_i}/p_j^{m_j}$. For any $x\in Q\setminus \{0\}$ and any integer $r>0$, we have \[\frac{p_i^{rfm_i}}{p_j^{rm_j}}x\in Q,\] and thus
\[ k^N \frac{p_i^{rfm_i}}{p_j^{rm_j}} x = \alpha^N\left(\frac{p_i^{rfm_i}}{p_j^{rm_j}}x\right) \in \mathbb Z\left[\frac{1}{l}\right].\]
Writing this rational number as a reduced fraction we see that, as long as $r$ is sufficiently large, the denominator is divisible by $p_j$. Since any element of $\mathbb Z[\frac{1}{l}]$ has a divisor of a power of $l$ as its denominator when written as a reduced fraction, we must have that $p_j$ divides $l$. Finally, since $l$ is a \emph{full} divisor of $k$, this implies that $p_j^{m_j}$ divides $l$. Since this is true for \emph{any} $j\neq i$, it follows that $k_i$ divides $l$. Thus $l=k_i$ or $l=k$.
If there is some index $j\neq i$ such that $\rho(t_j)$ is also positive, then by running the above argument with $j$ in place of $i$, we see that $k_j$ must also divide $l$. This implies that $l=k$. In particular, the only way we can have $l=k_i$ is if $\rho(t_i)>0$ and $t_i$ is the \emph{unique} generator with positive image.
Regardless of whether $l=k_i$ or $l=k$, we have that $[Q\cup \{s^{\pm 1}\}]=[\mathbb Z[\frac{1}{l}]\cup \{s^{\pm 1}\}]$. This also proves $[Q\cup Z_\rho]=[\mathbb Z[\frac{1}{l}]\cup Z_\rho]$. To see this, note that every element of $\mathbb Z[\frac{1}{l}]$ has bounded word length in $Q\cup \{s^{\pm 1}\}$ and that $t_1\ldots t_n$, which acts by conjugation on $\mathbb Z[\frac{1}{l}]$ in the same way as $s$, has finite word length in $Z_\rho$. Thus $\mathbb Z[\frac{1}{l}]$ has bounded word length in $Q\cup Z_\rho$. Since elements of $Z_\rho$ trivially have bounded word length in $Q\cup Z_\rho$, all of $\mathbb Z[\frac{1}{l}]\cup Z_\rho$ has bounded word length in $Q\cup Z_\rho$. The fact that $Q\cup Z_\rho$ has bounded word length in $\mathbb Z[\frac{1}{l}]\cup Z_\rho$ is also trivial.
It remains to show that if $l=k_i$ then $\rho\sim \rho_i^+$. Recall that $i$ is the unique index with $\rho(t_i)>0$. Suppose towards a contradiction that $\rho(t_j)<0$ for some $j\neq i$. Since $Q$ is confining under $\gamma$ with respect to $\rho$, for any $h\in \mathbb Z[\frac{1}{k}]$, there is some $z\in \mathbb Z^n$ such that $\gamma(z)(h)\in Q$. In particular, for each positive integer $L$, there is such an element $z\in \mathbb Z^n$ so that $\gamma(z)\left(1/p_i^{Lm_i}\right)\in Q$. Since $\rho(t_j^{-1})>0$ we have $\rho(t_j^{-M})>\rho(z)$ for all sufficiently large $M$. Thus
\[
\gamma\left(t_j^{-M}\right)\left(\frac{1}{p_i^{Lm_i}}\right)=p_j^{-Mm_j}p_i^{-Lm_i}\in Q,
\]
and so the word length of $p_j^{-Mm_j}p_i^{-Lm_i}$ with respect to $\mathbb Z[\frac{1}{k_i}]\cup \{s^{\pm 1}\}$ is bounded independently of the choice of $L$, as long as $M$ is large enough. Taking $L$ arbitrarily large leads to a contradiction.
\end{proof}
Finally, we turn our attention to homomorphisms satisfying $\rho(t_1\ldots t_n)<0$ and again relate confining subsets of $\mathbb Z[\frac{1}{k}]$ in $G_k$ to confining subsets of $\mathbb Z[\frac{1}{k}]$ in $BS(1,k)$.
\begin{lem}\label{lem:QBS-}
Let $Q\subseteq \mathbb Z[\frac1k]$ be confining under $\gamma$ with respect to $\rho$. View $Q\subseteq\mathbb Z[\frac1k]$ as a subset of the Baumslag-Solitar group $BS(1,k)=\mathbb Z[\frac1k]\rtimes_\alpha \mathbb Z$. If $\rho(t_1 \ldots t_n)< 0$, then $Q$ is confining under $\alpha^{-1}$.\end{lem}
\begin{proof}
The proof follows the same lines as the proof of Lemma \ref{lem:QBS}. To show that Definition \ref{genconfine}(a) holds, we note that $\rho(t_1^{-1}\ldots t_n^{-1})>0$, and so $\alpha^{-1}(Q)=\gamma(t_1^{-1}\ldots t_n^{-1})(Q)\subseteq Q$. For Definition \ref{genconfine}(b), let $u\in \mathbb Z[\frac{1}{k}]$. By Definition \ref{def:confining}(b), $\gamma(z)(u)\in Q$ for all $z\in \mathbb Z^n$ with $\rho(z)$ sufficiently large. If $a\in \mathbb Z$ is chosen so that $\rho((t_1^{-1}\ldots t_n^{-1})^a)$ is sufficiently large, then $\alpha^{-a}(u)=\gamma((t_1^{-1}\ldots t_n^{-1})^a)(u)\in Q$. The proof that Definition \ref{genconfine}(c) holds is analogous.
\end{proof}
\begin{lem}\label{lem:rho<0}
Suppose $\rho(t_1\ldots t_n)<0$. If $Q\subseteq \mathbb Z[\frac1k]$ is strictly confining under $\gamma$ with respect to $\rho$, then
\[
[Q\cup Z_\rho]=[Q_-\cup Z_\rho]
\] and $\rho \sim \rho_-$.
\end{lem}
\begin{proof}
The proof follows the same lines as the proof of Lemma \ref{lem:rho>0}. Suppose $Q\subseteq\mathbb Z[\frac1k]$ is strictly confining under $\gamma$ with respect to $\rho$. By Lemma \ref{lem:QBS-}, $Q$ is a subset which is confining under $\alpha^{-1}$, when viewed as a subset of $BS(1,k)=\mathbb Z[\frac1k]\rtimes_\alpha \mathbb Z$. By Proposition \ref{thm:BS1k}, up to bounded word length, the subsets $A$ of $\mathbb Z[\frac1k]\subseteq BS(1,k)$ which are confining under $\alpha^{-1}$ are exactly $A=\mathbb Z[\frac1k]$ and $A=Q_-$, where here word length is measured in the generating set $A\cup \{s^{\pm1}\}$. As we assume that $Q$ is strictly confining under $\gamma$ with respect to $\rho$, the set $Q$ is not within bounded word length of $\mathbb Z[\frac1k]$. Therefore, $Q$ is within bounded distance of $Q_-$ when word length is measured in the generating set $Q_-\cup \{s^{\pm1}\}$.
As in the proof of Lemma \ref{lem:rho>0}, we see that $Q_-$ has bounded word length with respect to the generating set $Q\cup Z_\rho$ and vice versa. Finally, we show that $\rho\sim \rho_-$. The proof is analogous to the proof of the corresponding fact in Lemma \ref{lem:rho>0}. If $\rho\not\sim \rho_-$, then there exists $z\in \mathbb Z^n$ with $\rho(z)>0$ but $\rho_-(z)< 0$. Writing $z=t_1^{a_1}\ldots t_n^{a_n}$ and $y=p_1^{a_1m_1}\cdots p_n^{a_nm_n}\in \mathbb Z[\frac1k]$, we have that $\gamma(z)$ acts as multiplication by $y$ and that $y>1$ (since $\rho_-(z)<0$). Choosing any $x\in Q\setminus \{0\}$, we have that $\gamma(z^i)(x)=y^ix\in Q$ for any $i\geq 0$, and thus $y^ix$ has bounded word length in $Q_-\cup \{s^{\pm 1}\}$ for each $i\geq 0$. For very large $i$, the number $y^ix$ is very large in absolute value, and therefore the word length of $y^ix$ in $Q_-\cup \{s^{\pm 1}\}$ is also very large. This is a contradiction.
\end{proof}
We are now ready to prove Proposition~\ref{prop:qp}.
\begin{proof}[Proof of Proposition~\ref{prop:qp}] Fix $[Y]\in\mathcal H_{qp}(G_k)$, and let $p$ be the associated Busemann pseudocharacter. As explained at the beginning of Section 4, we have that $p(\mathbb Z[\frac1k])=0$ and $p$ is a homomorphism.
By Theorem \ref{prop:main}, there exists $Q\subseteq \mathbb Z[\frac1k]$ which is strictly confining under $\gamma$ with respect to $p$ and such that $[Q\cup Z_p]\sim [Y]$, where $Z_p$ is as in \eqref{eqn:Zrho}. Conversely, Theorem \ref{thm:main} shows that for each subset $Q\subseteq \mathbb Z[\frac1k]$ which is strictly confining under $\gamma$ with respect to some homomorphism $\rho\colon\mathbb Z^n\to\mathbb R$, we have $[Q\cup Z_\rho]\in\mathcal H_{qp}(G_k)$ and the Busemann pseudocharacter for this hyperbolic structure is equivalent to $\rho$.
Therefore Theorems \ref{thm:main} and \ref{prop:main} show that it suffices to classify the subsets of $\mathbb Z[\frac1k]$ which are strictly confining under $\gamma$ with respect to some homomorphism $\rho\colon \mathbb Z^n\to \mathbb R$. By Lemmas \ref{lem:rho=0}, \ref{lem:rho>0}, and \ref{lem:rho<0}, there are exactly $n+1$ such subsets: $Q_1,\dots, Q_n,$ and $Q_-$. It remains to be shown that the corresponding structures $[S_i]= [Q_i\cup Z_{\rho_i}]$ and $[S_-] =[Q_-\cup Z_{\rho_-}]$ are pairwise incomparable. By Theorem \ref{thm:main}, the Busemann pseudocharacters associated to the quasi-parabolic structures $[S_i]$ and $[S_-]$ are proportional to $\rho^+_i$ and $\rho_-$, respectively. If $i\neq j$, then $\rho_i(t_i)>0$ while $\rho_i(t_j)=0$, and $\rho_j(t_i)=0$ while $\rho_j(t_j)>0$. Therefore $t_i$ is a loxodromic isometry in the structure $[S_i]$ and elliptic in the structure $[S_j]$, while $t_j$ is elliptic in the structure $[S_i]$ and loxodromic in the structure $[S_j]$. Therefore $[S_i]$ and $[S_j]$ are incomparable for all $i \neq j$.
We now show that for each $i=1,\dots, n$, the structures $[S_i]$ and $[S_-]$ are incomparable. We consider the generator $t_i$ of $\mathbb Z^n$. By the definition of the Busemann pseudocharacter, the fixed point of $G_k$ on the Gromov boundary in the structure $[S_-]$ is the \emph{attracting} fixed point of $t_i$. In the structure $[S_i]$, the fixed point of $G_k$ on the Gromov boundary is the \emph{repelling} fixed point of $t_i$. If $[S_-]$ and $ [S_i]$ were comparable then $G_k$ would fix both fixed points of $t_i$ in the action corresponding to the smaller structure. This contradicts that the structures are quasi-parabolic. Thus the proof is complete.
\end{proof}
\subsubsection{Geometry of the actions: Bass-Serre trees} \label{section:actiongeometry}
In this subsection and the next, we give explicit geometric descriptions of the quasi-parabolic actions associated to the structures described in the previous subsection.
In this section, we consider the hyperbolic structure corresponding to \[Q_i=\mathbb Z\left[\frac{1}{p_1^{m_1} \cdots \widehat{p_i^{m_i}}\cdots p_n^{m_n}}\right]=\mathbb Z\left[\frac{1}{k_i}\right]\] and show that this is the equivalence class corresponding to an action of $\mathbb Z[\frac{1}{k}]\rtimes_\gamma \mathbb Z^n$ on a certain Bass-Serre tree.
The group $G_k$ has as a subgroup \[H_i=\mathbb Z\left[\frac{1}{k_i}\right]\rtimes_\gamma \langle t_1, \ldots, \widehat{t_i}, \ldots, t_n\rangle\] since each generator $t_j$ for $j\neq i$ restricts to an automorphism of $\mathbb Z\left[1/k_i\right]$. Moreover, the conjugation action of the generator $t_i$ on $\mathbb Z[\frac{1}{k}]$ restricts to an endomorphism from $\mathbb Z\left[1/k_i\right]$ onto the \emph{proper} additive subgroup $p_i^{m_i}\mathbb Z\left[1/k_i\right]$. Hence we may consider the ascending HNN extension of $H_i$ \[\langle H_i,s \mid shs^{-1}=t_i ht_i^{-1} \text{ for all } h\in H_i\rangle\] (note that here the conjugate $t_iht_i^{-1}$ lies in $H_i$ so this presentation makes sense). The fundamental group of this HNN extension is isomorphic to $\mathbb Z[\frac{1}{k}]\rtimes_\gamma \mathbb Z^n=G_k$ via the map which sends $s$ to $t_i$, and hence we have an action of $G_k$ on the corresponding Bass-Serre tree. Note in particular that $t_i$ acts loxodromically in this action whereas $H_i$ acts elliptically. By \cite[Proposition 3.14]{AR} the hyperbolic structure defined by this Bass-Serre tree is equal to $[Q_i \cup Z_{\rho^+_i}]$.
To give a more explicit description of the geometry of this action, we describe the Bass-Serre tree in another way. This construction should be compared to an analogous construction for $BS(1,k)$ in \cite[Section~3.1.3]{AR}. The vertices are identified with the set $\mathbb Q_{p_i^{m_i}}\times \mathbb Z$ modulo the equivalence relation $(x,h)\sim (y,h)$ if $\|x-y\|\leq (p_i^{m_i})^{-h}=p_i^{-m_ih}$, where $\|\cdot \|$ denotes the $p_i^{m_i}$--adic absolute value. For any $x\in \mathbb Q_{p_i^{m_i}}$, there is an edge joining (the equivalence classes of) $(x,h)$ and $(x,h+1)$.
The action of $\mathbb Z[\frac{1}{k}]\rtimes_\gamma \mathbb Z^n$ is defined via the following actions on vertices (here $a=1$ denotes a normal generator of $\mathbb Z[\frac{1}{k}]$):\[\begin{tabular}{l} $a: (x,h)\mapsto (x+1,h)$ \\
$t_i: (x,h)\mapsto (p_i^{m_i}x,h+1)$ \\
$t_j: (x,h)\mapsto (p_j^{m_j}x,h)$ for $j\neq i$. \end{tabular}\] To verify that this tree equipped with this action of $G_k$ is the same as the Bass-Serre tree we described, we need to study stabilizers of edges and vertices in the action. Before we do this, we give a particular example for concreteness.
\begin{ex}
We choose $k=6$ and the hyperbolic structure corresponding to $Q_2=\mathbb Z[\frac{1}{2}]$. Here the vertices of the Bass-Serre tree are identified with equivalence classes of pairs in $\mathbb Q_2\times \mathbb Z$. We denote our group by $G_6=\mathbb Z[\frac{1}{6}]\rtimes_\gamma \mathbb Z^2= \langle\hspace{-.7mm}\langle a \rangle\hspace{-.7mm}\rangle \rtimes_\gamma \langle s,t\rangle$. Here $a$ denotes the normal generator 1 of $\mathbb Z[\frac{1}{6}]$ and $\gamma(s)$ and $\gamma(t)$ act by multiplication by 2 and 3, respectively.
The generator $a$ is elliptic and acts as the 2--adic odometer $x\mapsto x+1$ on $\mathbb Q_2$; see the left hand side of Figure \ref{fig:bstrees}. The generator $s$ acts loxodromically and simply shifts vertices directly ``upward.'' The generator $t$ acts elliptically but has a more complicated action given by $x\mapsto 3x$ on $\mathbb Q_2$; see the right hand side of Figure~\ref{fig:bstrees}.
\end{ex}
\begin{center}
\begin{figure}[h!]
\begin{tabular}{ll}
\includegraphics[width=0.5\textwidth]{2adictreeodometer.pdf}
&
\includegraphics[width=0.5\textwidth]{2adictree.pdf}
\end{tabular}
\caption{Left: the action of the generator $a$ of $\mathbb Z[\frac{1}{6}]\rtimes \mathbb Z^2$. Right: the actions of the generators $s$ and $t$. In both figures heights are implicit, so that a single 2--adic number is given for the label of each vertex. The vertices at height zero are demarcated by a dotted line.}
\label{fig:bstrees}
\end{figure}
\end{center}
Finally we show that the tree described above is equivariantly isomorphic to the Bass-Serre tree of $G_k$ corresponding to the ascending HNN extension with vertex group $\mathbb Z\left[1/k_i\right]\rtimes_\gamma \langle t_1,\ldots, \widehat{t_i},\ldots,t_n\rangle$. For simplicity we assume that $i=n$. Since the tree described above has a single orbit of vertices and a single orbit of edges, it suffices to describe the stabilizers of an edge and its two incident vertices. We focus on the edge $E$ between the vertices $v_0=(0,0)$ and $v_1=(0,1)$. Consider an element $g=xt_1^{r_1}\ldots t_n^{r_n}$, where $x\in \mathbb Z[\frac{1}{k}]$, which changes heights in the tree by $r_n$. If $g$ fixes either vertex of $E$, then we must have $r_n=0$ and $g\in \mathbb Z[\frac{1}{k}] \rtimes \langle t_1,\ldots,t_{n-1}\rangle$. Thus \[g (0,0)=(x,0) \text{ and } g (0,1)=(x,1).\] Hence $g$ fixes $v_0$ if and only if the $p_n^{m_n}$--adic absolute value $\|x\|_{p_n^{m_n}}$ is at most one. This occurs exactly when $x$ is an element of \[\mathbb Z\left[\frac{1}{k_n}\right]=\mathbb Z\left[\frac{1}{p_1^{m_1}\cdots p_{n-1}^{m_{n-1}}}\right].\] Similarly, $g$ fixes $v_1$ if and only if $\|x\|_{p_n^{m_n}}\leq p_n^{-m_n}$, which occurs exactly when $x\in p_n^{m_n}\mathbb Z\left[1/k_n\right]$. Thus the quotient graph of groups has vertex group $\mathbb Z\left[1/k_n\right]\rtimes \mathbb Z^{n-1}$. The edge group is also $\mathbb Z\left[1/k_n\right]\rtimes \mathbb Z^{n-1}$, and it embeds isomorphically onto the vertex group on one end and as the subgroup $p_n^{m_n}\mathbb Z\left[1/k_n\right]\rtimes \mathbb Z^{n-1}$ on the other end. This completes the proof.
\subsubsection{Geometry of the actions: the hyperbolic plane}
The group $G_k$ also admits an action on the hyperbolic plane $\H^2$. We show that this action corresponds to the confining subset $Q_-$ associated to the homomorphism $\rho_-:\mathbb Z^n\to \mathbb R$ defined by $ t_j\mapsto -m_j \log(p_j)$.
To define the action $G_k\curvearrowright \H^2$, we consider the upper half plane model. We denote by $a$ the normal generator 1 of $\mathbb Z[\frac1k]$. For a point $w$ in the upper half plane we define \[a\colon w\mapsto w+1 \text{ and } t_j\colon w\mapsto p_j^{m_j}w.\] It is straightforward to verify that this induces an isometric action of $G_k$. (To avoid confusion, we use $\cdot$ to denote this action.) One may check that for $r \in \mathbb Z[\frac1k]$ we have $r\cdot w = w+r$ and for $z=t_1^{a_1}\ldots t_n^{a_n} \in \mathbb Z^n$ we have $z\cdot w = p_1^{m_1a_1}\cdots p_n^{m_na_n}w$.
We sketch the proof that the action $G_k\curvearrowright \H^2$ is equivalent to the action $G_k\curvearrowright \Gamma(G_k,Q_-\cup Z_{\rho_-})$ associated to the confining subset $Q_-$. This follows the proof of \cite[Proposition 3.16]{AR} closely, and we refer the interested reader there for more details.
The proof begins by invoking the Schwarz-Milnor Lemma (see Lemma~\ref{lem:MS}). We choose $i\in \H^2$ as a basepoint. The reader may check that the orbit of $i$ is dense in the horocycle $\Im(w)=1$. Applying powers of $t_1\ldots t_n\in \mathbb Z^n$ (corresponding to multiplication by $k$), we see that the orbit of $i$ is in fact dense in each horocycle $\Im(w)=k^j$, for $j\in \mathbb Z$. These horocycles are spaced a distance of $\log(k)$ apart, so any point of $\H^2$ is at distance at most $\log(k)$ from the orbit of $i$. In particular, the orbit of the ball of radius $\log(k)$ based at $i$ under $G_k$ covers $\H^2$. The Schwarz-Milnor Lemma now implies that the action $G_k\curvearrowright \H^2$ is equivalent to the action $G_k\curvearrowright \Gamma(G_k,S)$, where \[S=\{g\in G_k \mid d_{\H^2}(i,g\cdot i)\leq 2\log(k)+1\}.\] It remains to show that we have $[S] =[Q_-\cup Z_{\rho_-}]$ as generating sets of $G_k$.
First, we show that elements of $S$ have bounded word length with respect to $Q_-\cup Z_{\rho_-}$. We may write an element $g$ of $S$ as $g=rz$ with $r\in \mathbb Z[\frac1k]$ and $z=t_1^{a_1}\ldots t_n^{a_n} \in \mathbb Z^n$. We have $g\cdot i=li+r$ where $l=p_1^{m_1a_1}\cdots p_n^{m_na_n}$. Hence the distance $d_{\H^2}(i,g\cdot i)$ is at least $|\log(l)|=|\rho_-(z)|$. Since $d_{\H^2}(i,g \cdot i)$ is bounded by $2\log(k)+1$, this gives a bound on both $|\log(l)|$ and $|\rho_-(z)|$. The bound on $|\rho_-(z)|$ in turn implies a bound on the word length of $z$ with respect to $Z_{\rho_-}$. Similarly, using \[d_{\H^2}(i,g\cdot i)=2\operatorname{arcsinh}\left(\frac{1}{2}\sqrt{\frac{r^2+(l-1)^2}{l}}\right)\geq 2\operatorname{arcsinh}\left(\frac{1}{2}\frac{r}{\sqrt{l}}\right)\] and the bound on $l$ just obtained, we obtain a bound on $|r|$. Thus, choosing any $z'\in \mathbb Z^n$ with $\rho_-(z')$ larger than a constant depending only on $2\log(k)+1$, we have $|\gamma(z')(r)|<1$. In particular, $\gamma(z')(r)\in Q_-$. Since the word length of $z'$ with respect to $Z_{\rho_-}$ is bounded, this gives a bound on the word length of $r=(z')^{-1}\gamma(z')(r)(z')$ with respect to $Q_-\cup \mathbb Z_{\rho_-}$.
Finally, we show that elements of $Q_-\cup Z_{\rho_-}$ have bounded word length with respect to $S$. This follows by reversing the argument of the last paragraph. An element of $Q_-$ moves $i$ by distance at most $1$ and hence lies in $S$ by definition. On the other hand, if $z=t_1^{a_1}\ldots t_n^{a_n} \in Z_{\rho_-}$ and $l=p_1^{a_1m_1}\cdots p_n^{a_nm_n}$ then we have $ z\cdot i = li$ and the bound on $|\rho_-(z)|=|-\log(l)|$ implies a bound on $d_{\H^2}(i,z\cdot i)$. Using the $\log(k)$--density of the orbit of $i$ under $G_k$, we obtain a bound on the word length of $z$ with respect to $S$. This completes the proof.
\subsection{Proof of Theorem \ref{thm:Z1k}}
Proposition \ref{prop:qp} gives a complete description of the quasi-parabolic structures $\mc H_{qp}(G_k)$. We now consider the other structures in turn, beginning with lineal structures. We will show that the lineal structures are in bijection with equivalence classes of homomorphisms $\rho\colon \mathbb Z^n\to \mathbb R$.
Fix $\rho\colon \mathbb Z^n\to \mathbb R$. Then $\mathbb Z[\frac1k]$ is confining under $\gamma$ with respect to $\rho$, and by Theorem \ref{thm:main}, $[\mathbb Z[\frac1k]\cup Z_\rho]$ is a lineal structure. This defines a map $\phi$ from the set of equivalences classes of homomorphims $\mathbb Z^n\to \mathbb R$ to the set of lineal structures, where $\phi([\rho])= [\mathbb Z[\frac1k]\cup Z_\rho]$. We will show that $\phi$ is a bijection.
Let $\rho'\colon \mathbb Z^n\to\mathbb R$ be another homomorphism, and suppose first that $\rho\sim\rho'$. Then since $\rho$ and $\rho'$ are proportional, every element of $Z_\rho$ has bounded word length with respect to $Z_{\rho'}$, and vice versa. Therefore $[\mathbb Z[\frac{1}{k}]\cup Z_\rho]=[\mathbb Z[\frac{1}{k}]\cup Z_{\rho'}]$, which shows that $\phi$ is well-defined.
Suppose next that $\rho\not\sim \rho'$. Then the kernels of $\rho$ and $\rho'$ do not coincide, and there are elements of $\mathbb Z^n$ which are a bounded distance from the kernel of $\rho$ while being an unbounded distance from the kernel of $\rho'$. More precisely, there exists a constant $B$ and a sequence $\{z_i\}_{i=1}^\infty \subseteq \mathbb Z^n$ with $\rho(z_i)\geq i$ and $|\rho'(z_i)|\leq B$ for all $i$. Since $\rho$ and $\rho'$ are quasi-isometries from $\Gamma(G_k, \mathbb Z[\frac1k]\cup Z_\rho)$ to $\mathbb R$ and from $\Gamma(G_k, \mathbb Z[\frac1k]\cup Z_{\rho'})$ to $\mathbb R$, respectively, this proves that $[\mathbb Z[\frac1k]\cup Z_{\rho'}]\neq[\mathbb Z[\frac1k]\cup Z_\rho]$. This shows that $\phi$ is injective.
Moreover, by \cite[Theorem~4.22]{ABO}, we can also conclude that $[\mathbb Z[\frac1k]\cup Z_\rho]$ and $[\mathbb Z[\frac1k]\cup Z_{\rho'}]$ are incomparable.
Finally, we will show that $\phi$ is surjective. Given any lineal structure $[S]$ on $G_k$, Theorem \ref{thm:actiontoconf} implies that $[S]=[\mathbb Z[\frac{1}{k}]\cup Z_\rho]$ for some associated homomorphism $\rho\colon \mathbb Z^n\to\mathbb R$.
Therefore, $\phi$ is surjective and so a bijection.
Every quasi-parabolic structure dominates the lineal structure defined by its Busemann pseudocharacter. In particular, $[\mathbb Z[\frac1k]\cup Z_{\rho^+_i}]\preceq[Q_i\cup Z_{\rho^+_i}]$ and $[\mathbb Z[\frac1k]\cup Z_{\rho_-}]\preceq[Q_-\cup Z_{\rho_-}]$. Moreover by an analogous argument to the above proof that $\phi$ is injective, we see that if $\rho\not\sim\rho^+_i$ or $\rho\not\sim\rho_-$, then $[\mathbb Z[\frac1k]\cup Z_{\rho}]$ is not dominated by $[Q_i\cup Z_{\rho^+_i}]$ or $[Q_-\cup Z_{\rho_-}]$, respectively.
For our choice of $k \geq 2$, the group $G_k=\mathbb Z[\frac1k]\rtimes \mathbb Z^n$ is solvable, and so contains no free subgroups. By the ping-pong lemma, we must have $\mathcal H_{gt}(G_k)=\emptyset$.
Finally, for any group $G$, $\mathcal H_e(G)$ consists of a single element which is the smallest element of $\mathcal H(G)$. This completes the proof of the theorem.
\bibliographystyle{abbrv}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 8,137 |
require 'pantry/core_ext'
module Pantry
autoload :Base, 'pantry/base'
autoload :Item, 'pantry/item'
autoload :Record, 'pantry/record'
autoload :Observer, 'pantry/observer'
autoload :CellarItem, 'pantry/cellar_item'
end
require 'pantry/railtie' if defined?(Rails)
| {
"redpajama_set_name": "RedPajamaGithub"
} | 7,803 |
You Keep Me Hangin' On är en låt skriven av Brian Holland, Edward Holland Jr och Lamont Dozier och ursprungligen inspelad av The Supremes år 1966. Låten blev The Supremes åttonde listetta då den toppade Billboardlistan mellan den 13 och 27 november 1966.
Bakgrund
The Supremes släppte låten som singel den 12 oktober 1966 och på B-sidan fanns Remove This Doubt. You Keep Me Hangin' On skilde sig från deras vanliga, mjuka soulpop och var istället mer funkig rhythm and blues. Då låten spelades in hade The Supremes nämligen börjat tänka i nya musikaliska banor. Exempelvis hade deras föregående singel, You Can't Hurry Love, tydliga influenser av gospel.
Många delar av inspelningen - däribland gitarrerna, trummorna och Diana Ross sång - dubbelinspelades för att skapa en illusion av ett eko. Denna teknik användes flitigt under stora delar av 60-talet, bland annat av Phil Spector och George Martin.
Låten var den första singeln från deras album The Supremes Sing Holland-Dozier-Holland från 1967. När tidskriften Rolling Stone gjorde listan The 500 Greatest Songs of All Time, så hamnade You Keep Me Hangin' On med The Supremes på plats 339.
Coverversioner
Det har gjorts åtskilliga covers på låten, och många andra artister har haft en hit med den.
Vanilla Fudge spelade in en psykedelisk version av låten som blev en hit år 1967. Deras version tog sig upp till sjätte plats på Billboardlistan. Singelversionen var knappt tre minuter lång medan albumversionen 6:45 minuter lång. Låten spelades in under en enda tagning och var Vanilla Fudges första singel.
Kim Wilde fick en hit med låten år 1986. Hennes version är uppdaterad och upp-popad och finns med på hennes album Another Step. Kim Wilde spelade in en helt omarbetad version som var avsedd att föra The Supremes sound till 1980-talet. Hon och hennes bror, skivproducenten Ricki Wilde, hade inte hört låten på flera år då de bestämde sig för att spela in den. De kände inte till låten särskilt väl, så de behandlade den som en nyskriven låt. De ändrade till och med några textrader. Det blev den största hiten under Kim Wildes karriär, och den låg etta på listorna runt om världen.
Låten tolkades av countrysångerskan Reba McEntire på albumet Starting Over år 1996. Hennes version tog sig upp till andra plats på Hot Dance Club Play.
Låten tolkades i ett avsnitt av TV-serien Glee.
Även Rod Stewart har tolkat låten.
Madness spelade in låten till albumet The Dangermen Sessions Vol. 1.
Kim Wildes Version
"You Keep Me Hangin' On" var inspelad i en uppdaterad version av den brittiska sångerskan Kim Wilde år 1986. Den var släppt som den andra singeln från hennes album Another Step.
Wildes version var en helt omgjord jämfört med The Supremes originalversion. Kim och hennes bror Ricki Wilde hade inte hört låten på ett antal år och bestämde sig för att spela in den. Det var en bra idé för det blev nämligen hennes största hit i hennes hela karriär. Kims version blev listetta i flera länder världen över, bland annat i USA:s hot billboard top 100. I hennes hemland, Storbritannien, lyckades hennes version nå en andra plats på topplaceringarna.
Kims Listplaceringar
Externa länkar
The Supremes - You Keep Me Hangin' On på Youtube.
Vanilla Fudge - You Keep Me Hangin' On, från Ed Sullivan Show.
Kim Wilde - You Keep Me Hangin' On, officiell musikvideo.
Musiksinglar 1966
Musiksinglar 1967
Musiksinglar 1986
Musiksinglar 1996
Poplåtar
Rocklåtar
Psykedelisk musik
Engelskspråkiga sånger
Singelettor i USA
Sånger av Kim Wilde | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 6,209 |
[](https://secure.travis-ci.org/zendframework/zend-session)
[](https://coveralls.io/r/zendframework/zend-session?branch=master)
zend-session manages PHP sessions using an object oriented interface.
- File issues at https://github.com/zendframework/zend-session/issues
- Documentation is at https://zendframework.github.io/zend-session/
| {
"redpajama_set_name": "RedPajamaGithub"
} | 4,503 |
\section{Introduction} \label{sec:intro}
Ultrahot Jupiters ($T_{eq} \gtrsim 2000$\,K) are becoming increasingly targeted for studies of their atmospheres \citep[e.g.,][]{Haynes2015,Evans2016,Evans2017,Evans2018,Nugroho2017,Sheppard2017,Arcangeli2018,Hoeijmakers2018,Lothringer2018,Lothringer2019,Hoeijmakers2019,Fu2020,Gibson2020,Changeat2021}. In part this is due to their high temperatures leading to large atmospheric scale heights and relatively cloud-free atmospheres, as condensation is suppressed. This latter point makes hotter planets particularly favorable for atmospheric studies, as the majority of studied exoplanets show muted features due to clouds and hazes \citep[e.g.,][]{Sing2016,Wakeford2019}. However, the amplitudes of water features decrease as equilibrium temperatures rise above 2500\,K due to the thermal dissociation of water and impact of H$^-$ opacity \citep[e.g.,][]{Arcangeli2018,Lothringer2018,Parmentier2018,Gao2020}.
Recently, several ultrahot Jupiters have revealed a plethora of atomic absorption in high-resolution transmission spectra \citep[e.g.,][]{Hoeijmakers2018,Hoeijmakers2019,Hoeijmakers2020,Sing2019,Yan2019,Cabot2020,Ehrenreich2020,Gibson2020,Nugroho2020,Borsa2021,Yan2021}. These planets also show the strongest evidence for temperature inversions among exoplanet atmospheres, such as in WASP-121b \citep{Evans2017,Evans2020}, WASP-33b \citep{Haynes2015,Nugroho2017}, WASP-18b \citep{Sheppard2017,Arcangeli2018}, WASP-76b \citep{Fu2020}, and WASP-103b \citep{Kreidberg2018}. However, of these exoplanets only WASP-121b, WASP-33b, and WASP-76b show evidence for TiO or VO (albeit in some cases this evidence is disputed, \citealp[e.g.,][]{Merritt2020,Borsa2021}), which have long been predicted to be responsible for hot Jupiter temperature inversions \citep[e.g.,][]{Hubeny2003,Fortney2008,Spiegel2009}.
In this paper we present a new optical transmission spectrum of WASP-103b that reveals tentative evidence ($2.1\sigma$) for TiO in its atmosphere, which may be responsible for the planet's observed temperature inversion \citep{Kreidberg2018}.
\subsection{WASP-103b}
\object{WASP-103b}, discovered by \cite{Gillon2014}, is an ultrahot Jupiter ($\mathrm{M} = 1.51 \pm 0.11$\,{$\mathrm{M_{J}}$}, $\mathrm{R} = 1.623^{+0.051}_{-0.053}$\,{$\mathrm{R_{J}}$}, $\mathrm{T_{eq}} = 2484 \pm 67$\,K; \citealt{Delrez2018}). Its high equilibrium temperature owes to the fact that it orbits its F8V host star in 0.93 days \citep{Gillon2014,Delrez2018}. Because of its very high temperature, WASP-103b has a large scale height of 600\,km, which contributes 152\,ppm to the transit depth (assuming the parameters from \citealt{Delrez2018} and a mean molecular weight of 2.3\,amu).
WASP-103b has been the target of atmospheric studies on several previous occasions. \cite{Southworth2015} presented a transmission photometry study of the planet using transits acquired in seven different photometric bands, from $g'$ to $z'$. They found a steep slope (gradient, $\alpha(\lambda) = 19.0 \pm 1.5$) in their transmission spectrum rising towards their bluest wavelength bins and extending over ${\sim}10$ atmospheric scale heights. \cite{Southworth2015} concluded unocculted starspots were unlikely to cause the observed slope due to the lack of the host star's photometric variability \citep{Gillon2014} and the temperature of the host ($T_{\mathrm{eff}} = 6110$\,K), which they suggested was too hot for significant spot-induced activity.
\cite{Southworth2016} subsequently revisited the earlier transmission spectrum of \cite{Southworth2015} after new high-resolution photometry revealed the presence of a blended background star \citep{Wollert2015,Ngo2016}. While correcting for this third light source did reduce the gradient of the slope in their data to $\alpha(\lambda) = 11.2 \pm 0.9$, it remained significantly steeper than expected for Rayleigh scattering ($\alpha(\lambda) = 4$).
\cite{Turner2017} extended the observations of WASP-103b to the near-UV with ground-based observations of the planet in the U band. The transit depth they derived was consistent with the bluest bin of \cite{Southworth2016}, indicating that the optical slope may not continue to rise into the near-UV.
The presence of a slope in the optical transmission spectrum of WASP-103b was challenged by \cite{Lendl2017}, who presented results using the multi-object spectrograph GMOS on the Gemini-North telescope. They found no signs of the strong slope reported by \cite{Southworth2015} and instead found the atmosphere to be cloud-free with absorption from sodium and potassium.
Following these studies in transmission, \cite{Cartier2017} presented HST/WFC3 secondary eclipse observations of WASP-103b. Their near-IR emission spectrum was featureless to a precision of 175\,ppm, finding the planet's atmosphere to be approximately isothermal over the wavelength range probed (1.1--1.7\,$\mu$m). However, they also noted that a thermally inverted atmosphere and a monotonically decreasing atmosphere with C/O $>1$ were consistent with their data.
\cite{Delrez2018} presented 16 new ground-based secondary eclipses of WASP-103b in the $z'$ and $K_S$ bands, and combined these with the HST/WFC3 results of \cite{Cartier2017}. They found the $z'$ and HST/WFC3 observations to be best fitted with a vertically isothermal atmosphere. However, they detected an anomalously deep eclipse in the $K_S$ band, which suggested the presence of a thermal inversion, but they noted that the $K_S$ band is not expected to contain strong spectral features and so could not explain this feature. They additionally reanalyzed the transit data from \cite{Southworth2015}, finding consistent results, indicating that the slope seen by \cite{Southworth2016} is inherent to the data and not dependent on the data reduction method.
\cite{Kreidberg2018} presented phase curve measurements of WASP-103b observed with HST/WFC3 and Spitzer/IRAC. They found the phase curves to show large amplitudes and negligible hot spot offsets, indicating poor circulation of heat from the day side to the nightside of the planet. In the WFC3/IR/G141 bandpass (1.1--1.7\,$\mu$m), \cite{Kreidberg2018} found the phase-resolved spectra to be consistent with blackbodies with brightness temperatures ranging from 1880\,K on the nightside to 2930\,K on the day side. However, they observed a significantly higher brightness temperature in the Spitzer 4.5\,$\mu$m band that is likely due to CO in emission, indicating a thermal inversion in the planet's atmosphere. As a result, \cite{Kreidberg2018} speculated that either TiO, VO, or FeH may be present in the planet's upper atmosphere. By running atmospheric retrievals on their infrared data, they found WASP-103b to have a $23^{+29}_{-13} \times$ solar metallicity atmosphere but did not detect water, which they attributed to its dissociation.
Most recently, \cite{Wilson2020} presented new VLT/FORS2 data of WASP-103b covering the wavelength region of 4000--6000\,\AA. By running retrievals on the combined VLT, Gemini, and HST transmission spectrum, they found the optical transmission spectrum to be featureless, with evidence for Na at $2\sigma$, but they did detect H$_2$O at $4\sigma$ confidence.
Given the contrasting results regarding WASP-103b's optical transmission spectrum and the potential for a previously undetected species at optical wavelengths giving rise to the planet's temperature inversion, we present here a new optical transmission spectrum of WASP-103b. Our new transmission spectrum combines five transits from the ACCESS survey on Magellan/Baade \citep{Jordan2013,Rackham2017,Bixel2019,Espinoza2019,McGruder2020, Weaver2020,Weaver2021} and two transits from the LRG-BEASTS survey on the William Herschel Telescope \citep{Kirk2017,Kirk2018,Kirk2019,Louden2017,Alderson2020}. We combine these new transit observations with a re-analysis of the published Gemini/GMOS data \citep{Lendl2017} and VLT/FORS2 data \citep{Wilson2020}, and include these with the published HST/WFC3/IR/G141 and Spitzer/IRAC transmission spectrum of \cite{Kreidberg2018} for our retrieval analyses.
This paper is organized as follows.
We describe the observations in \autoref{sec:observations}, the data reduction in \autoref{sec:data_reduction}, our light curve fitting procedures in \autoref{sec:data_analysis}, and our corrections for third-light and night-side contamination in \autoref{sec:3rd_light_corr}.
We present the transmission spectrum of WASP-103b in \autoref{sec:results} and interpret it using the petitRADTRANS and POSEIDON retrieval frameworks in \autoref{sec:pRT} and \autoref{sec:POSEIDON}, respectively.
We discuss our results in \autoref{sec:discussion} and, finally, summarize our conclusions in \autoref{sec:conclusions}.
\section{Observations}
\label{sec:observations}
\subsection{ACCESS}
\label{sec:obs_ACCESS}
We observed five transits of WASP-103b in the 2015--2017 observing seasons with the Inamori-\textit{Magellan}{} Areal Camera and Spectrograph (IMACS) \citep{Dressler2011} on the 6.5-m \textit{Magellan}{} Baade Telescope at Las Campanas Observatory.
Our observation design largely mirrored that of previous ACCESS observations \citep{Jordan2013, Rackham2017, Bixel2019, Espinoza2019, McGruder2020, Weaver2020,Weaver2021}.
For each observation, we used the $f/2$ camera of IMACS in multi-object spectroscopy mode with 2$\times$2 binning (0.4\,\arcsec\,pixel$^{-1}$).
Conditions were clear for all observations except the first two nights (`ACCESS n1' and `ACCESS n2'), for which passing clouds impacted the data quality during the 2.6-hr transit for $\sim$1\,hr and ${\sim}$0.25\,hr, respectively.
Further details of these observations are provided in \autoref{tab:magellan_obs_log}.
We used a custom multislit mask with large slits ($10\,\arcsec$ wide by $21\,\arcsec$ long) for collecting spectra of \object{WASP-103} and six comparison stars simultaneously.
After the first three observations, we redesigned the mask so that each spectrum would only be dispersed across a single chip.
The second mask includes six comparison stars as well, four of which are repeated from the first mask (\autoref{tab:magellan_comps}).
We designed the two science masks for use with the 300 line/mm and 150 line/mm grisms, respectively, though the second is also compatible with the 300 line/mm grism over a narrower wavelength range.
For each science mask, we also made a mask with narrow (0.5\,\arcsec) slits for wavelength calibration.
After the first two unfiltered observations, we began using
the WB5600--9200 filter to block any potential contribution from second-order light.
For our final \textit{Magellan}{}/IMACS observation, we used the GG495 filter for increased sensitivity at bluer optical wavelengths.
We selected exposure times to provide a maximum count rate of $\sim$35,000 analog-to-digital units (ADU) in order to remain within the linear regime of the IMACS CCDs \citep[see Section~3.8 of][]{Bixel2019}.
We used the ``turbo'' readout mode for the first three transits and opted for the slightly slower and less noisy ``fast'' readout mode for latter transits.
For each observation, we collected a series of quartz lamp flats with the same mask, disperser, and binning as the science frames. Immediately before or after the science observations, we also collected a series of exposures of HeArNe lamps through the narrow-slit calibration mask to aid with wavelength calibration.
\begin{deluxetable*}{lrccccccccr}
\tabletypesize{\scriptsize}
\tablewidth{\linewidth}
\tablecaption{Log of Magellan/IMACS observations. \label{tab:magellan_obs_log}}
\tablehead{\colhead{Transit} &
\colhead{Date} &
\colhead{Time} &
\colhead{Airmass} &
\colhead{Seeing} &
\colhead{Grism} &
\colhead{Mask} &
\colhead{Filter} &
\colhead{Frames} &
\colhead{Exposure} &
\colhead{Readout +} \\
\colhead{} &
\colhead{(UTC)} &
\colhead{(UTC)} &
\colhead{} &
\colhead{} &
\colhead{} &
\colhead{} &
\colhead{} &
\colhead{} &
\colhead{Times (s)} &
\colhead{Overhead (s)} }
\startdata
ACCESS n1 & 5 Jun 2015 & 03:31--08:00 & $1.28 \rightarrow 1.24 \rightarrow 2.19$ & 0.7--1.2 & 300 line/mm (17.5\degree) & 3215 & Spectroscopic & 261 & 33 & 29 \\
ACCESS n2 & 6 Jun 2015 & 01:30--06:28 & $1.74 \rightarrow 1.24 \rightarrow 1.47$ & 0.7--1.4 & 300 line/mm (17.5\degree) & 3215 & Spectroscopic & 289 & 33 & 29 \\
ACCESS n3 & 2 Jul 2015 & 00:30--04:05 & $1.49 \rightarrow 1.24 \rightarrow 1.34$ & 0.7--1.0 & 300 line/mm (17.5\degree) & 3215 & WB5600--9200 & 210 & 33 & 29 \\
ACCESS n4 & 5 Apr 2017 & 05:45--10:13 & $1.65 \rightarrow 1.24 \rightarrow 1.40$ & 0.7--1.7 & 150 line/mm (18.8\degree) & 3397 & WB5600--9200 & 348 & 10--25 & 31 \\
ACCESS n5 & 1 May 2017 & 03:34--08:43 & $1.89 \rightarrow 1.24 \rightarrow 1.45$ & 1.0--1.8 & 300 line/mm (17.5\degree) & 3397 & GG495 & 262 & 40 & 31 \\
\enddata
\tablecomments{
Mask numbers may be used to query information about the masks via the IMACS Slit Mask Manager (\url{http://masks.lco.cl/search/}).
}
\end{deluxetable*}
\begin{deluxetable}{lllll}
\tabletypesize{\scriptsize}
\tablewidth{\linewidth}
\tablecaption{
Comparison stars for Magellan/IMACS observations.
$Gaia$ Data Release 2 \citep{GaiaDR2} identifier, R.\,A., Decl., $Gaia$ G-band magnitude, and relevant IMACS mask(s) are listed.
\label{tab:magellan_comps}
}
\tablehead{\colhead{$Gaia$ DR2 ID} &
\colhead{R.\,A. (J2000.0)} &
\colhead{Decl. (J2000.0)} &
\colhead{$G$} &
\colhead{Mask(s)}}
\startdata
4439093346050733440 & 16:36:41.654 & +07:13:52.99 & 11.93 & 3215, 3397 \\
4439098839311731968 & 16:37:13.193 & +07:16:16.58 & 12.28 & 3215, 3397 \\
4439102382661930496 & 16:36:39.917 & +07:16:53.63 & 12.20 & 3215, 3397 \\
4439089875717149696 & 16:36:34.512 & +07:07:02.69 & 12.70 & 3215, 3397 \\
4439092139162752128 & 16:36:48.826 & +07:11:18.59 & 12.82 & 3215 \\
4439076715937339648 & 16:36:47.243 & +07:01:06.98 & 12.98 & 3215 \\
4439092418337881088 & 16:36:32.904 & +07:09:20.49 & 12.53 & 3397 \\
4439078777521638144 & 16:37:17.850 & +07:05:51.90 & 13.28 & 3397 \\
\enddata
\end{deluxetable}
\subsection{LRG-BEASTS}
\label{sec:obs_LRG-BEASTS}
The LRG-BEASTS transits of WASP-103b were observed on the nights of 1 Jun 2016 (referred to as `LRG-BEASTS n1' hereafter) and 26 Jun 2016 (referred to `LRG-BEASTS n2'). Both transits were observed with the low-resolution ($R \approx 300$) grism spectrograph ACAM \citep{Benn2008} on the 4.2-m William Herschel Telescope (WHT) in La Palma. This is the same instrument as has been used in the previous five LRG-BEASTS studies \citep{Kirk2017,Kirk2018,Kirk2019,Louden2017,Alderson2020}.
Unlike IMACS, ACAM is a long-slit spectrograph. For both of the LRG-BEASTS nights, we used the wide 7.6\,\arcmin $\times$ 40\,\arcsec\ slit, allowing us to simultaneously observe the spectrum of WASP-103 and a comparison star through the same slit. While a wide slit is useful to avoid differential slit losses between the target and the comparison, it does mean that other stars can fall within the slit and whose light can contaminate both the target and comparison\footnote{We note that the blending of the background star detected by \cite{Wollert2015} and \cite{Ngo2016} is unavoidable at the spatial resolution of the spectrographs used here.}. We therefore had to balance our desire to have a comparison star with a similar magnitude and color to the target while avoiding both possible contaminating stars and the edges of the detector. For our LRG-BEASTS observations of WASP-103, we selected the bright HD\,149891 as our comparison star, which has a V magnitude of 8.7 and $B-V$ color of 1.1. By comparison, WASP-103 has a V magnitude of 12.1 and $B-V$ color of 0.6.
Given the brightness of the comparison, we had to use short, 9 second exposures to avoid saturation. In order to reduce the overhead, we used a fast readout mode and we windowed the CCD into two windows ([530:800, 1100:3100] for the target and [1302:1572, 1100:3100] for the comparison), which reduced the overhead to 5\,s.
On the first night, we acquired 1400 spectra of the target with an airmass varying between 1.40 $\rightarrow$ 1.08 $\rightarrow$ 1.43. The moon did not rise during our observations on this night. On the second night we took 1068 spectra of the target with an airmass varying between 1.09 $\rightarrow$ 1.08 $\rightarrow$ 1.70, with a moon illumination of 58\% at a distance of 108$^\circ$ from the target. Biases, tungsten lamp flats, sky flats, and CuAr plus CuNe arc spectra were taken at the start and end of both nights.
\subsection{Gemini/GMOS and VLT/FORS2 transits}
\label{sec:obs_GMOS}
Three transits of WASP-103b were observed with the Gemini North GMOS multi-object spectrograph on 27 Jun 2015 (`GMOS n1'), 10 Jul 2015 (`GMOS n2'), and 3 May 2016 (`GMOS n3'). A single transit of WASP-103b was observed using VLT/FORS2 on 1 May 2017. This was the same transit as observed by ACCESS (`n5'). For all GMOS and FORS2 transits, two comparison stars were observed in addition to WASP-103. We refer the reader to \cite{Lendl2017} and \cite{Wilson2020} for a description of these observations.
\section{Data Reduction}
\label{sec:data_reduction}
\subsection{ACCESS}
\label{sec:dr_ACCESS}
We reduced the \textit{Magellan}/IMACS data using our custom Python-based pipeline described previously \citep{Jordan2013, Rackham2017, Bixel2019, Espinoza2019, McGruder2020, Weaver2020, Weaver2021}.
The pipeline performs standard procedures for multi-object spectroscopy, including bias and flat calibration, bad-pixel and cosmic-ray correction, sky subtraction, spectral tracing and extraction, and wavelength calibration. It outputs for each observation sets of wavelength-calibrated 1D spectra for the target and comparison stars and arrays of state parameters useful for detrending systematics.
These include time, airmass, $x$ and $y$ detector positions of the spectra, sky background level, and the full-width half-maximum (FWHM) of the spectra.
As with previous ACCESS studies \citep{Rackham2017, Bixel2019, Espinoza2019, McGruder2020, Weaver2020,Weaver2021}, we found that flat fielding introduced additional noise into our high-SNR science images, and so we ultimately chose not to apply a flat-field correction. To extract the 1D spectra, the ACCESS pipeline uses standard aperture photometry. For all nights, we used a 15-pixel-wide aperture, corresponding to 6\,\arcsec, which we selected to limit the impact of seeing variations while also leaving adequate space in the spatial direction for estimating the sky background.
The extracted, wavelength-calibrated mean-averaged spectra for each ACCESS observation of WASP-103 are shown in \autoref{fig:stellar_spectra}.
\subsection{LRG-BEASTS}
\label{sec:dr_LRG-BEASTS}
To reduce the LRG-BEASTS long-slit data, we used the same custom-made Python scripts as used in \cite{Kirk2017,Kirk2018,Kirk2019} and \cite{Alderson2020}, and we refer the reader to those papers for a more in depth description of the process.
In brief, the pipeline performs bias removal, tracing of the target and comparison spectra, standard aperture photometry using a linear polynomial interpolated across the stellar spectra (in the spatial direction) to estimate the sky background, cosmic-ray removal, and wavelength calibration.
Master biases were created for each night and subtracted from the science data before extraction. For the first night 257 bias frames were median-combined to create a master bias, and 301 bias frames were combined for the second night. As with the ACCESS data, and our previous LRG-BEASTS studies, we chose not to apply a flat-field correction. In a test-run on LRG-BEASTS n1, we found that the use of a flat-field led to an identical transmission spectrum but with uncertainties $\sim10$\,\% larger than without the use of the flat-field.
We experimented with our choice of aperture width to extract the stellar spectra, finding an aperture width of 26 pixels to be optimal for night 1 and 40 pixels for night 2 (owing to the poorer seeing conditions). The optimal aperture width was determined as the aperture width that produced the minimum standard deviation following a fit of an analytic transit light curve with a cubic in time polynomial to the resulting white light curve. We note that the plate scale of ACAM is 0.25\,\arcsec \,pixel$^{-1}$.
The extracted, wavelength-calibrated LRG-BEASTS spectra of WASP-103 are shown in \autoref{fig:stellar_spectra}.
\subsection{Gemini/GMOS and VLT/FORS2 data}
\label{sec:dr_GMOS}
For the Gemini/GMOS and VLT/FORS2 transits, we used the stellar spectra as reduced by \cite{Lendl2017} and \cite{Wilson2020}. Importantly, we followed the approach of both \cite{Lendl2017} and \cite{Wilson2020} in using only one of the two comparison stars observed in those studies. This was due to the second comparison star leading to an increase in the noise in the data.
\subsection{Binning scheme and light curve creation}
\label{sec:binning_scheme}
Given the number of different transits used in our analysis, and the subsequently different wavelength coverage, we opted for a straightforward binning scheme comprised of 150\,\AA-wide wavelength bins from 3900--9450\,\AA. The bins and nightly mean-averaged spectra of WASP-103 from all 11 transits are shown in \autoref{fig:stellar_spectra}. We note that we excluded the four bins of the Gemini/GMOS data that included chip gaps.
\begin{figure}
\centering
\includegraphics[scale=0.47]{binning_scheme_all_spectra.pdf}
\caption{WASP-103's nightly mean-averaged spectra as observed on each of the 11 nights used in our analysis, grouped by instrument and with an offset applied for clarity. The different spectral shapes are a result of the different instrument throughputs. The dashed vertical lines indicate the edges of 37 150-\AA-wide bins we used to generate the spectroscopic transit light curves.}
\label{fig:stellar_spectra}
\end{figure}
Given \cite{Lendl2017}'s finding of strong sodium and potassium in the atmosphere of WASP-103b in 20\,\AA-wide bins, we additionally constructed separate 20\,\AA-wide bins centered on the sodium doublet and each of the two absorption lines in the potassium doublet.
Using our 150\,\AA\ and 20\,\AA-wide wavelengths bins, we then created the spectroscopic light curves by integrating the spectra of the target and comparison stars over these wavelength ranges. The white light curves were created by integrating over the full wavelength range used for each night.
For the LRG-BEASTS, GMOS, and FORS2 data, the target's light curves were divided by the comparisons' light curves at this point to correct for telluric absorption. However, the ACCESS light curves were treated differently due to the principal component analysis used in the ACCESS fitting routine (\autoref{sec:GPTransSpec}).
The white light curves for all 11 transits are shown in \autoref{fig:wlc_fits}.
\begin{figure*}
\centering
\includegraphics[scale=0.6]{white_light_fits_all_nights_v2.pdf}
\caption{The white light curves from each of the 11 transits we analyzed. Left-hand panel: The white light curves after dividing by the comparison star and with each offset by -0.015 in flux. The red line shows the best-fitting transit + systematics models. We note that the ACCESS light curves are shown as WASP-103's light curve divided by the `best' comparison's light curve. However, these differential light curves are not used in the ACCESS fits, as explained in \autoref{sec:GPTransSpec}, and so do not include a best fit model. Middle panel: the detrended light curves following the removal of the systematics model. The gray lines show the best-fitting transit models. Right-hand panel: The residuals for each of the fits, this time with smaller offsets applied (-0.003) to allow for a zoomed-in view. The right-hand axis lists the RMS in ppm for each transit's residuals, along with the RMS in 30 minute bins.}
\label{fig:wlc_fits}
\end{figure*}
\section{Light curve fitting}
\label{sec:data_analysis}
Here we describe the different procedures we used to fit the ACCESS, LRG-BEASTS, and archival light curves. For both ACCESS and LRG-BEASTS, these surveys have custom pipelines (\texttt{GPTransSpec} for ACCESS, \texttt{gppm\_fit}{} for LRG-BEASTS), written independently in Python, to perform the fitting. We refer the reader to the previous papers in the ACCESS and LRG-BEASTS series for more detail. In \autoref{sec:wb_comparing_GPTS_to_gppm_fit}, we compare the outputs of the two procedures on an identical data set and find excellent agreement between the two approaches.
We note that we treated the system parameters in two separate ways for all of our light curve fits with \texttt{GPTransSpec} and \texttt{gppm\_fit}{}. Firstly we fixed the planet's orbital period ($P = 0.9255456$), scaled semi-major axis ($a/R_* = 2.999$) and inclination ($i = 87.3$) to the values of \cite{Southworth2015}. These were the system parameters used by \cite{Kreidberg2018} for their IR transmission spectrum of WASP-103b and our choice of a consistent set of system parameters allows for more accurate stitching of multi-epoch transmission spectra for our later retrieval analysis. We refer to this set of fits as our `fixed system parameters' fits. However, we also ran fits to our light curves with these system parameters as free parameters, which allows us to report updated system parameters. We refer to this set of fits as our `free system parameters' fits.
\subsection{Fitting the ACCESS light curves}
\label{sec:GPTransSpec}
\subsubsection{Model setup}
We extracted transmission spectra from the \textit{Magellan}{}/IMACS datasets with the procedure introduced by \citet{Espinoza2019} and detailed further in subsequent ACCESS studies \citep{Weaver2020,McGruder2020}.
We refer here to this procedure and the code implementing it as ``\texttt{GPTransSpec}''.
In short, we model the target light curve in magnitude space as a linear combination of the transit signal
and `nuisance' signals introduced by instrumental systematics and observing conditions. We model the transit
signal using the analytic expressions of \cite{Mandel2002} as implemented in \texttt{batman} \citep{batman}. The systematics, on the other hand, are modelled as a sum of two components.
The first component is a set of basis signals obtained by performing principal
component analysis (PCA) on a set of comparison stars \citep[see][for details]{Jordan2013, Espinoza2019}, and thus the raw light curves are modelled directly, not the differential light curves. The second component comes from a Gaussian process (GP, \citealp[e.g.,][]{Gibson2012}), where we use external parameters as regressors. The motivation for this two-component systematic modelling is that the
PCA signals inform our modelling of common systematics to both the target and the comparison stars
(due to, e.g., atmospheric conditions), while the GP component allows us to incorporate
systematics which are particular to our target lightcurve (e.g., position-dependent systematics,
spectral profile fluctuations, etc.).
The number of basis signals $N$ obtained from our PCA analysis equals the number of
comparison stars by the very definition of PCA. However, typically only a subset $n<N$ of
those basis signals is actually informative for explaining/reconstructing the comparison (and target)
star lightcurves, with basis signals having larger eigenvalues being the most important for
this reconstruction. While in \cite{Jordan2013} the number of basis signals was decided via cross-validation, in \cite{Espinoza2019} Bayesian model averaging was used instead, where models
using the $n = 1,2,...,N$ most important basis signals were fitted to the data, with the
transit lightcurve parameters on each of these fits being later weighted by their log-evidences to
report the final, ``model-averaged'' parameters. We use this same technique here in order to
account for the uncertainty on the number $n$ of ``optimal'' basis signals.
We incorporate the GP in our modelling framework using
the \texttt{george} Python package \citep{Foreman-Mackey2017}.
In each of our fits, we use a multi-dimensional squared-exponential kernel, using as regressors
the airmass, $x$ position of the trace, $y$ position of the trace, full-width at half maximum (FWHM),
sky background and time as input variables. We assume a quadratic limb-darkening law for our
transit lightcurve. Rather than fitting directly for the linear and quadratic coefficients ($u1$ and $u2$), \texttt{GPTransSpec} uses the change of variables introduced in \cite{Kipping2013} ($u1 \rightarrow q1$, $u2 \rightarrow q2$). In this way \texttt{GPTransSpec} treats both limb darkening coefficients as free parameters with uniform priors to prevent unphysical values.
In total, for each ACCESS white light curve fit, \texttt{GPTranSpec} fits for $n$ coefficients,
which weigh the PCA-retrieved basis signals and 13 free parameters for both the transit lightcurve
and the GP component. The latter parameters are the limb-darkening coefficients ($q1$ and $q2$), the six inverse length scales of our squared exponential GP kernels ($\tau_1$,...,$\tau_6$), the amplitude of the GP ($a$), a white noise term which accounts for an underestimation of the photometric error bars in the light curves ($\sigma^2$), time of mid-transit ($T_C$), the scaled planetary radius ($R_P/R_*$) and a normalization factor ($f$) to account for imperfect normalization of the light curves.
We used a wide uniform prior in log space for $a$ between 10$^{-10}$ and 0.01, and used a gamma prior on the GP length scales with shape parameter unity, following the approach of, e.g., \cite{Gibson2012} and \cite{Evans2015}. Finally, we also placed a wide uniform prior on $\sigma^2$, bounded by 10$^{-10}$ and 0.01 in milli-magnitudes$^2$ (mmag$^2$), which corresponds to $0.01-100$\, mmag bounds on the uncertainty in the photometric error bars. We used wide uniform priors on the transit parameters to prevent unphysical values.
For the `free system parameters' white light curve fits (where we wanted to refine the system parameters but which are not used in our final transmission spectra), we additionally fitted for the scaled semi-major axis ($a/R_*$) and the inclination of the planet's orbit ($i$).
To explore the parameter space, \texttt{GPTransSpec} uses nested sampling via the \texttt{PyMultiNest} package \citep{Buchner2014} with 1000 live points.
\subsubsection{Application of the model}
Prior to fitting the ACCESS light curves, we inspected the differential (target/comparison) light curves for each comparison star for all ACCESS nights. This enabled us to remove significant outliers from our photometry and to check whether all the comparison stars had similar noise characteristics to the target star and thus would be useful for inclusion in our \texttt{GPTransSpec} fitting. For all ACCESS nights we ended up using 5 of the 6 available comparison stars, with the same comparison stars used for nights that had a common slit mask (\autoref{tab:magellan_obs_log}).
We removed any data points from the light curves that were taken at airmasses greater than 2 and those that corresponded to cloudy conditions. These were defined as frames where WASP-103's flux dropped below 80\,\% of its nightly maximum. For ACCESS n1, a significant portion (30\,\%) of the transit was contaminated by clouds and clipped before fitting (\autoref{fig:wlc_fits}). For ACCESS n2, 10\,\% of the transit was cloudy. For the remaining three ACCESS nights, no data points were clipped. We note that we compared the results of fitting the light curves with and without this data clipping step and find the resulting transmission spectra to be consistent, but the data clipping leads to greater precision.
Following the fits to the ACCESS white light curves, we used the best-fitting systematics model from each night to remove the common mode systematics in the spectroscopic light curves prior to fitting. This reduces sources of noise that are common among the spectroscopic light curves and provides greater precision in the resulting transmission spectra. We then fitted the spectroscopic light curves with \texttt{GPTransSpec} but this time holding the time of mid-transit ($T_C$) fixed to the nightly best-fitting value.
\subsection{The LRG-BEASTS procedure}
\label{sec:gppm_fit}
\subsubsection{Model setup}
Like ACCESS's \texttt{GPTransSpec}, LRG-BEASTS's \texttt{gppm\_fit}{} simultaneously fits quadratically limb-darkened transit light curves \citep{Mandel2002}, via the \texttt{batman} Python package \citep{batman}, together with a Gaussian process (also using the \texttt{george} Python package; \citealt{george}) to model correlated noise in the data.
Unlike \texttt{GPTransSpec}, \texttt{gppm\_fit}{} uses Markov chain Monte Carlo (MCMC) to perform the sampling of parameter space, via the \texttt{emcee} Python package \citep{emcee}. It also fits the differential light curves, unlike \texttt{GPTransSpec} which fits the raw stellar light curves in its PCA.
While \texttt{gppm\_fit}{} also uses quadratic limb darkening, we instead hold the quadratic limb darkening coefficient ($u2$) fixed to a theoretical value calculated by the Limb Darkening Toolkit (\texttt{LDTk}, \citealt{ldtk}). To calculate these values we used the stellar parameters of \cite{Delrez2018}. We then only fitted for the linear coefficient ($u1$), for which we used a uniform prior to prevent unphysical values.
To fit the systematics in the light curves, we used a combination of squared exponential GP kernels, taking various ancillary data (airmass, FWHM, etc.) as input variables. We specify which variables were used for each night in the following subsections. These kernels each had a separate length scale ($\tau$) but shared a common amplitude, $a$. We additionally included a white noise kernel, defined by the variance $\sigma^2$, to account for white noise not captured by the photometric error bars. We fitted for the natural logarithm of these values and fitted for the inverse length scale following previous studies \cite[e.g.,][]{Gibson2012,Gibson2017,Evans2017,Evans2018,Kirk2019,Alderson2020}.
Prior to fitting the data, the input variables were standardized by subtracting the mean and dividing by the standard deviation, following the procedure of, e.g., \cite{Evans2017,Evans2018,Kirk2019} and \cite{Alderson2020}. This gives each input variable a mean of zero and standard deviation of unity and helps the GP determine the inputs of importance for describing the noise characteristics.
Similar to \cite{Gibson2017} and \cite{Alderson2020}, we placed truncated uniform priors in log space on the GP hyperparameters. The amplitude, $a$, was bounded between 0.01 and $100 \times$ the out-of-transit variance and the length scales were bounded between the minimum spacing and twice the maximum spacing of data points of the standardized variables. For the white noise term, we placed wide uniform priors in log space bounded by 10$^{-8}$ and $2.5 \times 10^{-7}$, which corresponds to 100--5000\,ppm bounds on the uncertainty in the photometric error bars.
Prior to fitting the white and spectroscopic light curves with \texttt{gppm\_fit}{}, we fit a transit model multiplied by a cubic polynomial using a Nelder-Mead algorithm \citep{nelder1965} to remove $>4 \sigma$ outliers from our light curves. This typically clipped at most 1--2 points per light curve.
To find the starting values for the GP hyperparameters, we optimized the GP model to the out-of-transit data prior to fitting each light curve. The MCMC chains were subsequently started with a small scatter around these values. Following the \texttt{george} documentation\footnote{\url{https://george.readthedocs.io/en/latest/tutorials/model/}}, \texttt{gppm\_fit}{} runs two sets of chains for each light curve, with the second set of chains started with a smaller scatter around the best-fitting values from the first chain.
For all our light curve fits with \texttt{gppm\_fit}{}, the number of walkers equalled $6\times n_p$ (where $n_p$ is the number of free parameters) for 10000 steps each (split across the first and second runs as explained above).
\subsubsection{Application of the model}
Prior to fitting the LRG-BEASTS white and spectroscopic light curves, we binned the data from both nights to a time resolution of 60\,s. This reduced the number of data points to be fitted for all LRG-BEASTS light curves from 1400 to 337 for night 1 and from 1068 to 255 for night 2. We did this for computational reasons as GPs scale as $\mathcal{O}(n^3)$ for $n$ data points.
For LRG-BEASTS night 1 we used five GP kernels, each taking one of airmass, FWHM, $x$ position of the trace, $y$ position of the trace and sky background as input variables. Due to the additional noise in LRG-BEASTS night 2 (\autoref{fig:wlc_fits}), we additionally included time with a sixth GP kernel for the analysis of these light curves. In total for the LRG-BEASTS white light curve fits, there were 10 free parameters ($T_C$, $R_P/R_*$, $u1$, $a$, $\tau_1$,...$\tau_5$, $\sigma^2$) for night 1 and 11 for night 2 (with the addition of the time kernel).
Similar to the ACCESS procedure, we then removed the common noise models from the spectroscopic light curves prior to fitting. We also again fixed $T_C$ to the best-fitting values from the white light curve fits.
\subsection{Fitting the GMOS and FORS2 light curves}
To fit the Gemini/GMOS and VLT/FORS2 light curves, we used the same \texttt{gppm\_fit}{} code as we used to fit the LRG-BEASTS light curves.
For the GMOS data we again used 5 squared exponential GP kernels to fit the systematics in the data, with each taking one of airmass, FWHM, position angle, $y$ position of the trace, and sky background as input variables.
For the VLT data, we followed the approach of \cite{Wilson2020} in modelling the systematics with a single GP kernel, taking time as the input variable, combined with a linear in time polynomial.
The white light curve fits to the GMOS and FORS2 data are shown in \autoref{fig:wlc_fits}.
As with the ACCESS and LRG-BEASTS transits, we removed the common noise systematics model from the spectroscopic light curves prior to fitting.
As we show in \autoref{sec:r_transmission_spectra}, our resulting GMOS and FORS2 transmission spectra are in good agreement with the initial analyses of \cite{Lendl2017} and \cite{Wilson2020}, giving us confidence in the repeatibility of our results.
\subsection{Comparing \texttt{GPTransSpec} with \texttt{gppm\_fit}{}}
As an additional test of our light curve fitting routines, we generated a set of ACCESS differential light curves by dividing each night by the single `best' comparison star (as shown in \autoref{fig:wlc_fits}). The best comparison star was chosen as the comparison star that lead to the smallest median absolute deviation in the out-of-transit flux. We then ran these light curves through the same procedure as described in \autoref{sec:gppm_fit}. The results of this test are presented in \autoref{sec:wb_comparing_GPTS_to_gppm_fit} and show excellent agreement between \texttt{GPTransSpec} and \texttt{gppm\_fit}{}.
\section{Correcting for third-light and nightside contamination}
\label{sec:3rd_light_corr}
Due to the presence of the blended contaminant within the WASP-103 spectra, we had to correct our resulting transmission spectra for this. To perform this correction, we followed a similar process to that used in \citet{Southworth2016,Cartier2017,Lendl2017,Turner2017} and \cite{Delrez2018}. We used PHOENIX \citep{Husser2013} stellar models for the target ($T_{\mathrm{eff}} = 6110$\,K, $\log g = 4.22$\,cgs, [Fe/H] = 0.06\,dex, \citealt{Delrez2018}) and contaminant ($T_{\mathrm{eff}} = 4400 \pm 200$\,K, \citealt{Cartier2017}), and scaled these to have the correct $J$-band magnitudes \citep{Cartier2017}. We then calculated the ratio of the contaminant's flux to the target's flux for each of our wavelength bins as defined in \autoref{sec:binning_scheme}.
\autoref{fig:cont_ratios} shows the contamination ratios we calculate as compared with those measured by \cite{Wollert2015,Ngo2016,Southworth2016,Cartier2017,Lendl2017,Delrez2018} and \cite{Wilson2020}. This figure shows the good agreement between our calculated flux ratios and these previous studies. The third-light correction factors for our wavelength bins are given in \autoref{tab:transmission_spectrum}.
\begin{figure}
\centering
\includegraphics[scale=0.55]{flux_cont_ratios_psp_only_150A+20A.pdf}
\caption{The ratio of the blended contaminant's flux ($F_\mathrm{cont}$) to WASP-103's flux ($F_\mathrm{W103}$) as a function of wavelength. The contamination ratios calculated for our wavelength bins are shown by the black pentagons. The associated values from several previous studies are also shown.}
\label{fig:cont_ratios}
\end{figure}
To apply these flux corrections to our resulting transmission spectra, we used the following equation \cite[e.g.,][]{Kreidberg2018_review}
\begin{equation}
\label{eq:3rd}
d_\mathrm{corr} = d_\mathrm{obs}(1 + F_\mathrm{cont}(\lambda)/F_\mathrm{W103}(\lambda)),
\end{equation}
where $d_\mathrm{obs}$ are the observed transit depths, $F_\mathrm{cont}(\lambda)$ is the flux of the contaminant, $F_\mathrm{W103}$ is WASP-103's flux and $d_\mathrm{corr}$ are the corrected transit depths.
In addition to correcting for the contamination of the nearby star, we also considered dilution of the transit depth by the planet's nightside flux given the high equilibrium temperature of the planet \cite[e.g.,][]{Kipping2010}. While the effect is small in the optical, it can lead to a significant change in the infrared, as shown by \cite{Kreidberg2018} for WASP-103b.
\cite{Kreidberg2018} used their \textit{Spitzer} phase curve observations to measure the nightside temperature of WASP-103b, finding it to be 1700\,K. We then used a PHOENIX model for the star and a blackbody at the nightside temperature to calculate the flux dilution in each of our wavelength bins from the nightside of the planet.
The nightside flux corrections were applied to our resulting transmission spectra using the following equation \cite[e.g.,][]{Kipping2010,Kreidberg2018_review}
\begin{equation}
\label{eq:ns}
d_\mathrm{corr} = \frac{d_\mathrm{obs}}{1+F_{NS}(\lambda)/F_\mathrm{W103}(\lambda)},
\end{equation}
where $F_{NS}(\lambda)$ is the flux from the nightside of the planet. \autoref{fig:nightside_corr} shows our calculated correction factors (the denominator in \autoref{eq:ns}) along with those used by \cite{Kreidberg2018}. This figure demonstrates that the effect of the planet's nightside is significantly larger in the infrared as compared to the optical. In the wavelength range covered by our optical data, the maximum correction factor (corresponding to the reddest wavelength bin) leads to a 13\,ppm change in the transit depth. While we have applied this correction to our final transmission spectra, this correction is only 8\,\% of the typical error in the transit depths of our combined transmission spectrum and thus is negligible.
\begin{figure}
\centering
\includegraphics[scale=0.55]{nightside_correction_factors_150A+20A.pdf}
\caption{The correction factors due to the emission from WASP-103b's nightside (blue crosses). These were calculated using a 1700\,K blackbody for the planet's nightside. Also shown are the correction factors calculated by \protect\cite{Kreidberg2018} for their \textit{HST}/WFC3 and \textit{Spitzer}/IRAC wavelength bins (red circles).}
\label{fig:nightside_corr}
\end{figure}
\section{Results}
\label{sec:results}
\subsection{White light fits}
The results of our fits to the white light curves are shown in \autoref{fig:wlc_fits}. We note that we also include the differential ACCESS light curves in \autoref{fig:wlc_fits}, which correspond to the target's light curve divided by the best comparisons' light curve, for ease of comparison with the other 6 transit light curves. However, we did not actually fit the differential ACCESS light curves but instead fit the raw stellar light curves as described in \autoref{sec:GPTransSpec}.
As the number of transits and wavelength bins resulted in over 322 spectroscopic light curves, we only include example fits to our ACCESS and LRG-BEASTS data in the Appendix (Figs.\ \ref{fig:wbfit_ACCESS_n2} and \ref{fig:wbfit_LRG-BEASTS_n1}). The rest of our light curve fits can be found online\footnote{\url{https://github.com/JamesKirk11/WASP103_lc_fits}}.
\subsection{System parameters}
\label{sec:system_params}
\autoref{tab:r_system_parameters} lists the system parameters we derive from the `free system parameters' fits to our 11 white light curves. We note again that these results were not the ones used for our final transmission spectra, where we instead used the parameters of \cite{Southworth2015}, as used by \cite{Kreidberg2018}.
The $R_P/R_*$ values in \autoref{tab:r_system_parameters} are those after correcting for the third-light contamination and planetary nightside flux (\autoref{sec:3rd_light_corr}). This shows that while there is good overall agreement, there is scatter in each of these parameters. We plot the $R_P/R_*$ derived from each of our transits from both the `fixed' and `free' system parameters fits, along with the values of \cite{Southworth2016}, \cite{Lendl2017}, \cite{Delrez2018} and \cite{Wilson2020} in \autoref{fig:RpRs_variation}. This demonstrates that while there is some variation in $R_P/R_*$, each of our 11 transits are within 1--2$\sigma$ of the weighted mean. We note that ACCESS n5 and VLT/FORS2 are observations of the same transit epoch.
\begin{figure}
\centering
\includegraphics[scale=0.55]{RpRs_variation.pdf}
\caption{The reported white light $R_P/R_*$ values from literature studies (black triangles), along with our newly derived values when holding the remaining system parameters fixed to \protect\cite{Southworth2015} (orange points) and leaving these as free parameters (blue points). The plot symbols for our newly analyzed data are shared among transits that have a common wavelength range and comparison star. The dashed horizontal lines show the weighted means from our newly analyzed data, to which our transmission spectra (\autoref{fig:transmission_spectrum}) were normalized.}
\label{fig:RpRs_variation}
\end{figure}
\begin{table*}
\centering
\caption{The resulting system parameters from our white light curve fits with these as free parameters. In all cases we held the period fixed to 0.9255456\,d, as found by \protect\cite{Southworth2015} and used by \protect\cite{Kreidberg2018}. We note that these parameters were not used in the fitting of our spectroscopic light curves and hence our transmission spectrum. We also include the weighted mean of our results, labelled `Combined', and the results of \protect\cite{Southworth2015} and \protect\cite{Delrez2018} for comparison.}
\label{tab:r_system_parameters}
\begin{tabular}{lcccc} \hline
Data set & $T_C$ (BJD$_\mathrm{TDB}$) & $a/R_*$ & $i$ & $R_{P}/R_*$ \\ \hline\hline
ACCESS n1 & $2457178.747991^{+0.000215}_{-0.000248}$ & $2.97^{+0.06}_{-0.06}$ & $85.14^{+1.8}_{-1.44}$ & $0.11535^{+0.00258}_{-0.00306}$
\\
ACCESS n2 & $2457179.673866^{+0.000123}_{-0.000128}$ & $2.97^{+0.04}_{-0.05}$ & $86.2^{+1.89}_{-1.5}$ & $0.10947^{+0.00234}_{-0.00261}$
\\
ACCESS n3 & $2457205.588929^{+0.000119}_{-0.000108}$ & $3.03^{+0.01}_{-0.01}$ & $87.26^{+0.23}_{-0.23}$ & $0.11135^{+0.00114}_{-0.00116}$
\\
ACCESS n4 & $2457848.843293^{+0.000191}_{-0.000164}$ & $2.96^{+0.04}_{-0.05}$ & $85.4^{+2.44}_{-1.61}$ & $0.11754^{+0.00311}_{-0.00327}$
\\
ACCESS n5 & $2457874.758341^{+0.000087}_{-0.000089}$ & $3.00^{+0.01}_{-0.02}$ & $87.86^{+1.11}_{-1.32}$ & $0.11562^{+0.00099}_{-0.00101}$
\\
LRG-BEASTS n1 & $2457541.562056^{+0.000136}_{-0.000129}$ & $3.02^{+0.03}_{-0.05}$ & $87.08^{+1.87}_{-1.83}$ & $0.11155^{+0.00108}_{-0.00115}$
\\
LRG-BEASTS n2 & $2457566.551617^{+0.000117}_{-0.000106}$ & $3.01^{+0.02}_{-0.04}$ & $87.71^{+1.52}_{-1.82}$ & $0.11203^{+0.002}_{-0.00182}$
\\
FORS2 & $2457874.758372^{+0.000310}_{-0.000343}$ & $2.97^{+0.05}_{-0.07}$ & $86.25^{+2.43}_{-2.2}$ & $0.11567^{+0.00167}_{-0.00168}$
\\
GMOS n1 & $2457200.961020^{+0.000325}_{-0.000372}$ & $2.93^{+0.07}_{-0.07}$ & $84.15^{+1.82}_{-1.39}$ & $0.11095^{+0.00344}_{-0.00333}$
\\
GMOS n2 & $2457213.918548^{+0.000348}_{-0.000351}$ & $2.82^{+0.06}_{-0.06}$ & $82.13^{+1.22}_{-1.08}$ & $0.11194^{+0.00287}_{-0.00451}$
\\
GMOS n3 & $2457511.944288^{+0.000085}_{-0.000091}$ & $3.00^{+0.01}_{-0.03}$ & $88.08^{+1.31}_{-1.51}$ & $0.11456^{+0.00081}_{-0.00094}$
\\ \hline
\textbf{Combined} & $2456836.296374 \pm 0.000040$ & $3.01 \pm 0.01$ & $87.0 \pm 0.21$ & $0.1136 \pm 0.00045$
\\
\protect\cite{Southworth2015} & $2456836.296445 \pm 0.000055$ & $2.999 \pm 0.031$ & $87.3 \pm 1.2$ & $0.1127 \pm 0.0009$\\
\protect\cite{Delrez2018} & $2456836.296427 \pm 0.000063$ & $3.010^{+0.008}_{-0.013}$ & $88.8^{+0.8}_{-1.1}$ & $0.1150^{+0.0020}_{-0.0014}$
\\ \hline
\end{tabular}
\end{table*}
\subsection{Transmission spectrum}
\label{sec:r_transmission_spectra}
\begin{figure*}
\centering
\includegraphics[scale=0.45]{trans_spec_comparison_ACCESS_150A_20A.pdf}
\includegraphics[scale=0.45]{trans_spec_comparison_ACAM_150A_20A.pdf}
\includegraphics[scale=0.45]{trans_spec_comparison_GMOS_150A_20A_VLT_150A_20A.pdf}
\caption{The individual transmission spectra from all 11 transit observations are shown in the upper panels of all 3 figures. The lower panels show the weighted mean of the 5 ACCESS transits (upper left figure), 2 LRG-BEASTS transits (upper right figure), and the 1 FORS2 plus 3 GMOS transits (lower center figure). In the lower figure, we also include the Gemini/GMOS transmission spectrum as presented in \protect\cite{Lendl2017} and the VLT/FORS2 transmission spectrum as presented in \protect\cite{Wilson2020}.}
\label{fig:all_transmission_spectra}
\end{figure*}
In \autoref{fig:all_transmission_spectra}, we show the transmission spectra resulting from all 11 of our ground-based transits, following the correction for the third-light contamination and planetary nightside flux. The nightly transmission spectra in the top panels of \autoref{fig:all_transmission_spectra} have had offsets applied to ensure they have the same nightly mean $R_P/R_*$ as the weighted mean $R_P/R_*$ from all 11 nights, as discussed in \autoref{sec:system_params}. The nightly transmission spectra for all instruments are given in Tables \ref{tab:ts_ACCESS} and \ref{tab:ts_LRG-BEASTS} in the Appendix.
\autoref{fig:all_transmission_spectra} shows there is good overall agreement between each of the transits' transmission spectra. The most notable difference comes in the LRG-BEASTS transmission spectra, where the spectra diverge at blue wavelengths (although they are still consistent within $1\sigma$, other than in the bluest bin).
We also note that the Na signal is much deeper in the first LRG-BEASTS night. As an additional check, we performed light curve fits to five 30\,\AA-wide bins centered on Na to see whether this was caused by systematics related to the 20\,\AA\ bin being too narrow. In this case we found the central Na bin to remain deep but a neighbouring bin to be anomalously shallow, giving us reason to question the authenticity of the deep LRG-BEASTS n1 bin. This behaviour did not occur for any of the 11 other transits we analysed. We are unsure of the causes of this deep Na bin, however we tried different treatment of the stellar limb darkening (fixed vs.\ free coefficients), GP inputs and GP kernels (Mat\'{e}rn 3/2 vs.\ Squared Exponential), and the use of a flat field, and found these made no difference to the depth of the bin.
Notably, however, our final 11 transit-combined transmission spectrum changes by $\ll$1$\sigma$ regardless of whether the second LRG-BEASTS night or the LRG-BEASTS Na result is included. This is the advantage of combining 11 data sets. As a result, we do not exclude the LRG-BEASTS data from our final transmission spectrum.
In \autoref{fig:all_transmission_spectra}, we also plot the Gemini/GMOS and VLT/FORS2 transmission spectra as derived by \cite{Lendl2017} and \cite{Wilson2020}. This shows the good agreement between our re-analysis of these data sets and the previously published analyses. We believe that the small differences between our analysis of the Gemini/GMOS data as compared to the analysis of \cite{Lendl2017} could be due to the different system parameters used and different systematics modelling approaches used.
In \autoref{fig:transmission_spectrum}, we show the weighted-mean transmission spectra for each instrument and the 11-transit weighted-mean combination. In this figure, all the spectra have been corrected for the third-light contamination as described in \autoref{sec:3rd_light_corr}.
\autoref{fig:transmission_spectrum} shows an excellent agreement between all four instruments. This also highlights the precision we have achieved in our combined transmission spectrum with a median uncertainty on the transit depth of 148\,ppm. The transmission spectrum shows considerable structure, with an upwards slope from $\sim 4000$ to 5200\,\AA, before dropping towards 5600\,\AA\ and rising again towards 6200\,\AA. There is also a bump in the spectrum at around 7000\,\AA\ and a deeper transit centered on the Na doublet at 5893\,\AA, which we discuss in more detail in the following subsection.
\begin{figure*}
\centering
\includegraphics[scale=0.9]{trans_spec_comparison_all_combined_3rd_light_corr_NS_corr_talk_plot.pdf}
\caption{Top panel: the transmission spectra broken down into the component instruments. These are offset in wavelength by 20\,\AA\ for clarity. Bottom panel: the weighted mean of all 11 transmission spectra. The 20\,\AA-wide bins centered on Na and K are shown by the triangles.}
\label{fig:transmission_spectrum}
\end{figure*}
\begin{table*}
\centering
\caption{The weighted mean transmission spectrum of WASP-103b from all 11 ground-based transit light curves. These results have been corrected for the third-light contamination and the planet's nightside flux. We note that we also include the third-light correction factors ($F_\mathrm{cont}/F_\mathrm{W103}$) in this table.}
\label{tab:transmission_spectrum}
\begin{tabular}{ccccc|ccccc}
\toprule
Bin centre & Bin width & $R_P/R_*$ & $\sigma(R_P/R_*)$ & $F_\mathrm{cont}/F_\mathrm{W103}$ & Bin centre & Bin width & $R_P/R_*$ & $\sigma(R_P/R_*)$ & $F_\mathrm{cont}/F_\mathrm{W103}$ \\
($\AA$) & ($\AA$) & & & & ($\AA$) & ($\AA$) & & & \\ \hline
\midrule
3975 & 150 & 0.11415 & 0.00248 & 0.0086 & 6825 & 150 & 0.11512 & 0.00052 & 0.0573 \\
4125 & 150 & 0.11238 & 0.00145 & 0.0172 & 6975 & 150 & 0.11657 & 0.00059 & 0.0565 \\
4275 & 150 & 0.11291 & 0.00088 & 0.0118 & 7125 & 150 & 0.11660 & 0.00050 & 0.0585 \\
4425 & 150 & 0.11402 & 0.00089 & 0.0234 & 7275 & 150 & 0.11549 & 0.00058 & 0.0579 \\
4575 & 150 & 0.11330 & 0.00108 & 0.0205 & 7425 & 150 & 0.11419 & 0.00056 & 0.0653 \\
4725 & 150 & 0.11375 & 0.00066 & 0.0270 & 7575 & 150 & 0.11434 & 0.00069 & 0.0665 \\
4875 & 150 & 0.11415 & 0.00069 & 0.0283 & 7665 & 20 & 0.11440 & 0.00098 & 0.0664 \\
5025 & 150 & 0.11438 & 0.00068 & 0.0242 & 7699 & 20 & 0.11574 & 0.00085 & 0.0674 \\
5175 & 150 & 0.11458 & 0.00063 & 0.0229 & 7725 & 150 & 0.11442 & 0.00059 & 0.0680 \\
5325 & 150 & 0.11436 & 0.00060 & 0.0298 & 7875 & 150 & 0.11552 & 0.00057 & 0.0711 \\
5475 & 150 & 0.11356 & 0.00057 & 0.0336 & 8025 & 150 & 0.11532 & 0.00059 & 0.0720 \\
5625 & 150 & 0.11300 & 0.00056 & 0.0368 & 8175 & 150 & 0.11459 & 0.00060 & 0.0696 \\
5775 & 150 & 0.11372 & 0.00052 & 0.0432 & 8325 & 150 & 0.11411 & 0.00074 & 0.0733 \\
5893 & 20 & 0.11751 & 0.00107 & 0.0361 & 8475 & 150 & 0.11586 & 0.00069 & 0.0756 \\
5925 & 150 & 0.11439 & 0.00051 & 0.0450 & 8625 & 150 & 0.11555 & 0.00063 & 0.0761 \\
6075 & 150 & 0.11500 & 0.00050 & 0.0473 & 8775 & 150 & 0.11554 & 0.00070 & 0.0774 \\
6225 & 150 & 0.11519 & 0.00051 & 0.0467 & 8925 & 150 & 0.11579 & 0.00068 & 0.0795 \\
6375 & 150 & 0.11530 & 0.00053 & 0.0497 & 9075 & 150 & 0.11523 & 0.00084 & 0.0786 \\
6525 & 150 & 0.11527 & 0.00058 & 0.0524 & 9225 & 150 & 0.11641 & 0.00105 & 0.0778 \\
6675 & 150 & 0.11546 & 0.00072 & 0.0560 & 9375 & 150 & 0.11369 & 0.00142 & 0.0804 \\
\hline
\bottomrule
\end{tabular}
\end{table*}
\subsection{Significance of the Na bin}
\label{sec:Na}
In order to estimate the significance of the sodium detection in our combined transmission spectrum (\autoref{fig:transmission_spectrum}), we fitted a straight line across the neighbouring bins between 5625 and 6075\,\AA\ where the continuum is rising. This is the same process used to estimate the significance of sodium as used in, e.g., \cite{Nikolov2016,Carter2020} and \cite{Alderson2020}. Comparing the difference between our Na bin and the fitted continuum, we find the Na bin is higher at $3.1\sigma$ confidence.
At face value this appears significant. However, when we exclude the LRG-BEASTS Na bin from our combined transmission spectrum, which we believe could be affected by systematics (\autoref{fig:all_transmission_spectra}), the significance of Na by this method drops to $2.8\sigma$. While the inclusion of the LRG-BEASTS Na bin changes the transmission spectrum by $< 1\sigma$, owing to the fact we are combining 11 data sets, we favour our conservative $2.8\sigma$ evidence for Na, considering to the possible systematics affecting the LRG-BEASTS Na bin. \cite{Wilson2020} detect Na at $2.0\sigma$ confidence while \cite{Lendl2017} find signs of strong Na absorption. Based on our analysis, we cannot claim a significant detection of Na in WASP-103b's atmosphere.
\subsection{Comparing the ACCESS \& LRG-BEASTS fitting pipelines}
\label{sec:wb_comparing_GPTS_to_gppm_fit}
As an additional check of our results, we also fitted the ACCESS light curves with the LRG-BEASTS fitting code (\texttt{gppm\_fit}{}, \autoref{sec:gppm_fit}). \autoref{fig:GPTS_gppm_fit} shows the comparison between our final transmission spectra from both methods, prior to applying the third-light correction. This shows the excellent agreement between the two fitting routines despite the different approaches to the stellar limb darkening, systematics models, sampling algorithm, and the priors on the transit and systematic models' parameters. \autoref{fig:GPTS_gppm_fit} demonstrates our results and conclusions are not dependent on the different fitting methods used.
\begin{figure}
\centering
\includegraphics[scale=0.47]{trans_spec_comparison_all_combined_gppm_fit_GPTransSpec_comp.pdf}
\caption{A comparison of the transmission spectra resulting from the use of \texttt{gppm\_fit}{} only and \texttt{gppm\_fit}{} + \texttt{GPTransSpec}. In orange are the results from fitting all 11 transits with \texttt{gppm\_fit}{}. In blue are the results from fitting the 5 ACCESS transits with \texttt{GPTransSpec} and the remaining 6 transits with \texttt{gppm\_fit}{}, as was used for our final analysis.}
\label{fig:GPTS_gppm_fit}
\end{figure}
\subsection{Impact of third-light correction}
As described in \autoref{sec:3rd_light_corr}, we had to correct our transmission spectrum for the flux of the blended contaminant ($4400 \pm 200$\,K, \citealt{Cartier2017}). In \autoref{fig:3rd_light_corr} we plot the pre- and post-third-light-corrected transmission spectra. We additionally include (in dotted lines), the impact of the contamination assuming the effective temperature of the contaminant $\pm$ the 1 and 2$\sigma$ uncertainties reported by \cite{Cartier2017}, which shows that the uncertainty in the contaminant does not result in a significant change in the transmission spectrum. This was also found by \cite{Lendl2017}.
\autoref{fig:3rd_light_corr} demonstrates that while the third-light correction has a significant impact over a broad wavelength range, changing the transmission spectrum from gently sloping down towards red wavelengths to sloping upwards, it has a minor impact on the more localised features, such as the dip at ${\sim}5600$\,\AA, the Na bin, and the bump at ${\sim}7000$\,\AA. We explore the impact this correction has on our retrievals in \autoref{sec:POSEIDON}.
\begin{figure}
\centering
\includegraphics[scale=0.55]{combined_trans_spec_all_combined_3rd_light_corr_NS_corr.pdf}
\caption{The effect of applying the third-light correction to our transmission spectrum, assuming a K5 contaminant with an effective temperature of $4400 \pm 200$\,K \protect\citep{Cartier2017}. The blue points correspond to the pre-correction data and the orange points to the post-correction data. The grey dashed lines show the 1 and $2\sigma$ uncertainties on the corrected spectrum taking the reported uncertainty in the contaminant's effective temperature (200\,K, \protect\citealt{Cartier2017}).}
\label{fig:3rd_light_corr}
\end{figure}
\section{Forward models \& retrievals with petitRADTRANS}
\label{sec:pRT}
To interpret WASP-103b's transmission spectrum, we used both forward models and retrieval analyses using two seperate codes, firstly using petitRADTRANS \citep{Molliere2019}.
Given the significant structure seen in WASP-103b's transmission spectrum, its hot equilibrium temperature, and the evidence for a thermal inversion in its atmosphere, we generated forward models using petitRADTRANS that included only TiO, VO, and FeH as optical opacity sources. We assumed a cloud-free isothermal atmosphere at the equilibrium temperature of the planet (2489\,K), and took the planet's surface gravity and stellar radius from \cite{Delrez2018}. For these exploratory forward models, we assumed atmospheric mass fractions for TiO, VO, and FeH of 0.1\,\%. Importantly, as we discuss later, these initial TiO and VO forward models use the \cite{Plez1998,Plez1999} line lists as is the default for petitRADTRANS.
The forward models of TiO and VO are shown in \autoref{fig:pRT_models} along with a flat line. We do not include the FeH model, owing to the poor fit to the shape of the spectrum. These exploratory models show that, while none of these models provide an acceptable $\chi^2$, both TiO and VO can fit the downturn in the transmission spectrum we observe in the blue, while only VO is able to replicate the downturn seen at ${\sim}5600$\,\AA.
\begin{figure*}
\centering
\includegraphics[scale=0.8]{TiO_VO_pRT_forward_models_with_ExoMol_and_retrieved_v2.pdf}
\caption{The forward models generated using petitRADTRANS, along with the reduced $\chi^{2}$ for each with 39 degrees of freedom. We include two VO-only forward models, one using the \protect\cite{Plez1999} line list (orange) and one with the ExoMol line list \protect\citep{McKemmish2016} (green). The VO and TiO-only models have atmospheric mass fractions of 0.1\,\%. The retrieved model is shown in red and uses the \protect\cite{Plez1999} line list. This finds a VO abundance of $-5.65^{+0.46}_{-0.64}$\,dex ($\sim10^4 \times$ solar) and no evidence for TiO.}
\label{fig:pRT_models}
\end{figure*}
In order to test this hypothesis further, we also ran a retrieval using petitRADTRANS. We used an MCMC, through \texttt{emcee} \citep{emcee}, to sample the parameter space with 240 walkers, each with 4200 steps. We fitted for the abundances of CO, H$_2$O, CH$_4$, NH$_3$, CO$_2$, H$_2$S, Na, K, TiO, VO, and FeH. We also fitted for the surface gravity and reference pressure. Following the petitRADTRANS retrieval example\footnote{\url{https://petitradtrans.readthedocs.io}}, we also fitted for 6 parameters that defined the temperature-pressure profile, although we note that these were poorly constrained. The abundances of IR species were also poorly constrained. However, the retrievals did constrain the volume mixing ratio (VMR) of VO to be $-5.65^{+0.46}_{-0.64}$\,dex, which is about $10^{4} \times$ the solar abundance \citep{Woitke2018}. The TiO abundance was unconstrained, instead bumping up against the lower boundary of the uniform-in-log-space prior ($-10$ dex). This agreed with our forward model analysis that the transmission spectrum is better matched with VO than TiO, when using the Plez line lists. The retrieved model using the Plez line lists is also shown in \autoref{fig:pRT_models}.
Motivated by our retrievals run with POSEIDON (\autoref{sec:POSEIDON}), we also generated a VO forward model with petitRADTRANS but using the updated VO line list from the ExoMol group \citep{McKemmish2016}. This model is shown in green in \autoref{fig:pRT_models}. The difference between the orange and green models in \autoref{fig:pRT_models} is just the choice of VO line list, all other parameters were equal. This demonstrates how the choice of VO line list used makes a significant difference to the gradient of the slope in the blue and, to a lesser extent, the shallower transit depths seen around 5600\,\AA. However, we note that the goodness of fit is unaffected by the choice of line list.
\section{Retrievals with POSEIDON}
\label{sec:POSEIDON}
We additionally conducted a retrieval analysis of WASP-103b's transmission spectrum with the POSEIDON atmospheric retrieval code \citep{MacDonald2017}. While our petitRADTRANS retrieval (\autoref{sec:pRT}) focused on our optical transmission spectrum, our POSEIDON analysis further considers the addition of the near-infrared \textit{HST}/WFC3 and \textit{Spitzer}/IRAC observations from \citet{Kreidberg2018}. Our POSEIDON retrievals also include a prescription for unocculted stellar heterogeneity, which is a potential source of bias in exoplanet transmission spectra \citep[e.g.,][]{McCullough2014,Oshagh2014,Rackham2017,Rackham2018,Rackham2019}.
Our POSEIDON retrievals consider a wide range of atmospheric and stellar properties. We include the following chemical species with both prominent absorption features over our wavelength range and an expectation of occurrence in hot giant planet atmospheres \citep[e.g.][]{Sharp2007,Madhusudhan2016}: Na, K, H${-}$, TiO, VO, AlO, CrH, FeH, H$_2$O, CO, CO$_2$, and HCN. In our initial exploratory retrievals, we also included opacity from Li, Fe, Fe${+}$, Ti, Ti${+}$, H$_3{+}$, SiO, TiH, SiH, CH$_4$, NH$_3$, N$_2$O, NO$_2$, and NO but found these to be unconstrained and so did not include them in our final analysis.
Besides the line absorption from these species, POSEIDON also includes collision-induced absorption from H$_2$-H$_2$ and H$_2$-He pairs and Rayleigh scattering. We allow for inhomogenous clouds and hazes following the prescription in \citet{MacDonald2017}. We assume an isothermal temperature profile, given the quality of the present observations \citep{Rocchetto2016}. Our treatment of unocculted starspots or faculae is based on the parametrization of \citet{Pinhas2018}. In short, the heterogeneity `contamination factor' \citep{Rackham2017} is computed by interpolating stellar models from the Castelli-Kurucz 2004 atlas \citep{Castelli2003} using the pysynphot package \citep{pysynphot}.
In total, our POSEIDON retrievals have a maximum of 22 free parameters. The planetary atmosphere is defined by the volume mixing ratios ($X_i$) of the 12 chemical species listed above, the terminator temperature ($T$), a reference radius at 10\,bar ($R_{\rm{p, \, 10\,bar}}$), and the four-parameter cloud and hazes prescription from \cite{MacDonald2017}. The stellar heterogeneity contribution is described by the covering fraction of the active regions on the stellar disc ($f_{\rm{het}}$) and the temperatures of the active regions ($T_{*, \, \rm{het}}$) and stellar photosphere ($T_{*, \, \rm{phot}}$), respectively. For retrievals including the data from \citet{Kreidberg2018}, we opted to fit for a relative offset, $\delta_{\rm rel}$, between our optical transmission spectrum and the IR transmission spectrum (noting that instrumental offsets in the optical data were taken care of in \autoref{sec:system_params}). We ascribe uniform-in-the-logarithm priors on the mixing ratios ($10^{-16}$ to $10^{-1}$) and uniform priors on $T$ (400 to 3000\,K), $R_{\rm{p, \, 10 \, bar}}$ ($0.85 - 1.15\,R_p$), $f_{\rm{het}}$ (0 to 0.5), $T_{*, \, \rm{het}}$ (0.65 to 1.2 $T_{*, \, \rm{phot}, \rm{a priori}}$), and $\delta_{\rm rel}$ ($\pm$ 1000\,ppm). Since the stellar photosphere temperature is well-known \textit{a priori}, we place an informative Gaussian prior on $T_{*, \, \rm{phot}}$ (mean: 6110\,K; standard deviation: 160\,K - \citealp{Gillon2014}). The cloud and haze priors are as in \citet{MacDonald2017}.
We ran POSEIDON on four combinations of our new optical dataset and the IR transmission spectrum of \cite{Kreidberg2018}: the optical data alone following the application of the third-light correction (`Ground Corrected'); the optical data alone \textit{prior} to the application of the third-light correction (`Ground Uncorrected'); the HST and Spitzer data without the optical data; and the third-light-corrected optical data combined with the HST and Spitzer data. For each dataset, we conducted Bayesian parameter estimation and model comparisons via the nested sampling algorithm MultiNest \citep{Feroz2008,Feroz2009,Feroz2019,Buchner2014}, with 4,000 live points per retrieval. We report the results from our retrievals in \autoref{tab:POSEIDON_retrieval_results}. The main result is that the optical data reveals tentative evidence for TiO ($\sim 2\sigma$), while also showing strong evidence of contamination from unocculted stellar heterogeneities. We discuss these results in more detail in the following subsections.
\subsection{On the optical data alone}
Our retrieved spectra for both the third-light corrected and uncorrected optical data are shown in \autoref{fig:POSEIDON_retrieved_spectra} (top panels). Prior to the third-light correction (\autoref{sec:3rd_light_corr}), there is a gentle upwards slope towards blue wavelengths which is best fit by unocculted \textit{cool} active regions. Following the third-light correction, the spectral morphology changes into a steep downwards slope best explained by unocculted \textit{hot} active regions, which we interpret as faculae. Quantitatively, the evidence for stellar activity increases from 1.5 to $4.0\sigma$ following the third-light correction (see \autoref{tab:POSEIDON_retrieval_results}). Clearly the third-light correction makes a significant impact on the conclusions about stellar activity.
We additionally infer tentative evidence for atmospheric TiO absorption from our optical data. This TiO inference persists for both the uncorrected and third-light corrected data, changing from 2.3 to $1.7\sigma$ following the third-light correction. The TiO mixing ratio, however, is poorly constrained from the optical data alone. No other chemical species are favored by our Bayesian model comparisons with POSEIDON, with $2\,\sigma$ upper limits on their mixing ratios reported in \autoref{tab:POSEIDON_retrieval_results}. The non-detection of Na, despite the 20-\AA bin centered on the Na D-lines being ${\sim}3\sigma$ deeper than the surrounding continuum (\autoref{sec:Na}), is likely due to the lack of pressure-broadened Na wings in the surrounding data points \citep[e.g.,][]{Nikolov2018,Alam2021}.
The tentative evidence for TiO from POSEIDON is an interesting contrast with our earlier petitRADTRANS retrieval (\autoref{sec:pRT}), which instead inferred VO without the need for TiO. To better understand this discrepancy, we ran additional retrievals with both codes varying properties such as the prior ranges on the VMRs and the top of atmosphere pressure. Ultimately this made little difference. The most notable difference we identified is that POSEIDON uses updated ExoMol line lists for VO and TiO, resulting in considerably different optical band shapes compared to the petitRADTRANS VO and TiO cross sections (see \autoref{fig:pRT_models}). However, as we discuss in \autoref{sec:d_optical_trans_spec}, we cannot be certain that this is the cause the disagreement. Indeed, our $4\sigma$ preference for unocculted faculae with POSEIDON (for the corrected data) automatically considered VO as an alternative explanation via the Bayesian evidence computations. Therefore, we believe that the inclusion of stellar heterogeneity in our POSEIDON retrievals is the more likely cause of the disagreement.
\subsection{On the IR data alone}
Our IR-only retrievals on the HST/WFC3 and Spitzer/IRAC data from \citet{Kreidberg2018} weakly favor unocculted faculae and H$_2$O. We find a lower detection significance for faculae than that from the optical-only corrected spectrum ($2.4\sigma$ vs. $4.0\sigma$). This is expected, since the influence of unocculted stellar heterogeneities is largest at short wavelengths \citep[e.g.,][]{Rackham2018, Rackham2019}. The retrieved heterogeneity parameters from the IR data are consistent with those from our `Ground Corrected' retrieval (\autoref{tab:POSEIDON_retrieval_results}), giving us added confidence in this interpretation. Our inference of H$_2$O is marginal at best ($1.7\sigma$) and notably less significant than that found by \citet{Wilson2020} ($4.0\sigma$). We believe this discrepancy is due to our consideration of stellar heterogeneities, which were not included in the retrieval analyses of \citet{Wilson2020}. Finally, we note that TiO is not inferred from our IR-only retrievals, though the upper limit on its abundance is consistent with the `Ground Corrected' retrieval. In all, these consistent findings between each portion of the transmission spectrum strengthen the conclusions derived from the combined optical and IR data set.
\subsection{On the combined optical and IR data}
Our retrieval of the combined optical+IR data, shown in \autoref{fig:POSEIDON_retrieved_spectra} (bottom panel), identifies strong evidence of unocculted faculae ($4.3\sigma$) and tentative evidence for TiO ($2.1\sigma$), H$_2$O ($1.9\sigma$), and HCN ($1.7\sigma$). The inferred faculae are $\sim 350$\,K hotter than the stellar photosphere with a coverage fraction of $22^{+12}_{-9}$\,\%. The fitted offset between the optical and IR data is $210^{+83}_{-85}$\,ppm, consistent with the $1\sigma$ uncertainties in our optical transmission spectrum. Due to the weak evidence for individual molecules, we also derived the combined significance of TiO + H$_2$O + HCN from a Bayesian model comparison with all three species excluded. We find that the significance of \emph{at least one} of TiO, H$_2$O, or HCN, is $2.8\sigma$. Therefore, we conclude there is moderate evidence for molecular opacity from WASP-103b alongside the stellar faculae contamination.
We illustrate the contributions of each chemical species and the unocculted faculae to our best-fitting POSEIDON model in \autoref{fig:POSEIDON_best_fit_model}. This figure demonstrates that unocculted faculae still induce a slight downward slope between the red and blue ends of the HST/WFC3/IR/G141 bandpass, explaining why our IR-only retrievals also favor unocculted faculae. Unlike our retrievals with petitRADTRANS, we see that POSEIDON does not fit the dip in the transmission spectrum around $0.55\,\micron$, which may be due to the ExoMol line lists used (\autoref{fig:pRT_models}) or the inclusion of faculae -- we discuss this more in \autoref{sec:d_optical_trans_spec}. We note that the `minimal' model shown in this figure uses only those parameters required to fit the combined optical + IR data (i.e.\ without unconstrained chemical species or cloud parameters). This 9-parameter model achieves a minimum reduced chi-square of $\chi^2_{\nu} = 1.36$, which we consider an excellent fit to our transmission spectrum of WASP-103b. The full posterior corresponding to this best-fitting model is shown in \autoref{fig:POSEIDON_corner_plot}, with the parameter constraints also given in \autoref{tab:POSEIDON_retrieval_results}. We caution, however, that our recommended atmospheric and stellar properties are those from the `full' optical + IR retrieval (see \autoref{tab:POSEIDON_retrieval_results}), since the full retrieval accounts for marginalization over the entire parameter space.
Our inferred atmospheric properties for WASP-103b are summarized in \autoref{tab:POSEIDON_retrieval_results}. We find a TiO mixing ratio of $-7.31^{+2.14}_{-2.06}$\,dex, broadly consistent with expectations for a solar abundance atmosphere at WASP-103b's equilibrium temperature \citep{Woitke2018}. The retrieved H$_2$O mixing ratio, $-3.28^{+1.46}_{-4.08}$\,dex, spans a wide range from super-solar to sub-solar abundances. The latter is consistent with the suggestion by \citet{Kreidberg2018} of H$_2$O dissociation in WASP-103b's atmosphere. We suggest that \citet{Wilson2020}'s tighter constraint on the H$_2$O abundance of ${\sim}40\times$ solar, without sub-solar solutions, may arise from the absence of marginalization over unocculted faculae in their retrievals. A hint of HCN near $1.6\,\micron$ (see \autoref{fig:POSEIDON_best_fit_model}) emerges only from our combined optical + IR retrievals, though the abundance is poorly constrained with the present data. Future observations of WASP-103b can serve to confirm the presence of TiO, H$_2$O, and/or HCN, while strengthening their abundance determinations.
\begin{figure*}[ht!]
\centering
\includegraphics[width=0.492\textwidth]{WASP103b_retrieved_spectrum_corrected.pdf}
\includegraphics[width=0.492\textwidth, trim={0.0cm 0.0cm 0.0cm 0.0cm}]{WASP103b_retrieved_spectrum_uncorrected.pdf}
\includegraphics[width=\textwidth]{WASP103b_retrieved_spectrum_ground_space.pdf}
\caption{Retrieved transmission spectra of WASP-103b by POSEIDON. Each panel shows the median retrieved model (blue line) and associated $1\,\sigma$ and $2\,\sigma$ confidence regions (purple contours) from three separate retrievals of different datasets: our third-light and nightside corrected optical spectrum (top left); our uncorrected spectrum (top right); and the combination of our corrected optical spectrum with the WFC3 and Spitzer data from \citet{Kreidberg2018} (bottom). A 210\,ppm offset has been applied to the infrared data to represent the median retrieved offset between the ground and space-based observations. The corrected optical spectrum is best fit by unocculted stellar faculae with residual hints of atmospheric TiO. The uncorrected optical spectrum also contains hints of TiO, but with unocculted stellar spots rather than faculae. The full, corrected, optical + infrared spectrum of WASP-103b is best fit by unocculted faculae and hints of TiO, H$_2$O, and HCN.}
\label{fig:POSEIDON_retrieved_spectra}
\end{figure*}
\begin{figure*}[ht!]
\centering
\includegraphics[width=\textwidth]{WASP103b_spectral_contributions.pdf}
\caption{Spectral contributions to the best-fitting POSEIDON model of the transmission spectrum of WASP-103b. The maximum likelihood retrieved spectrum (green shading) is composed of contributions from unocculted faculae (grey), TiO (red), H$_2$O (blue), and HCN (orange). The equivalent model without faculae (purple) is shown for comparison. All models include background atmosphere H$_2$-H$_2$ collision-induced absorption (CIA) -- producing the broad continuum feature centered at 2.2\,$\micron$ visible in the faculae-only model. The instrument modes corresponding to each observed dataset are highlighted at the bottom. The best-fitting model, binned to the resolution of the data, is overlaid (gold diamonds). This `minimal' model achieves a reduced chi square of $\chi_{\nu}^2$ = 1.36 (for 43 degrees of freedom).}
\label{fig:POSEIDON_best_fit_model}
\end{figure*}
\begin{figure*}[ht!]
\centering
\includegraphics[width=\textwidth]{WASP103b_Posterior_POSEIDON.jpg}
\caption{Posterior distribution from the best-fitting POSEIDON retrieval of WASP-103b's transmission spectrum. This posterior corresponds to the fit in Figure~\ref{fig:POSEIDON_best_fit_model} and the final column in Table~\ref{tab:POSEIDON_retrieval_results}. The marginalized histograms for each parameter are overlaid with the median retrieved value and $\pm 1\sigma$ confidence levels (blue error bars). The retrieved parameters indicate strong evidence of unocculted faculae ($T_{*, \, \rm{het}} > T_{*, \, \rm{phot}}$), a bounded constraint on WASP-103b's TiO abundance, suggestive (but weak) constraints on the H$_2$O and HCN abundances, and a $\sim$200\,ppm relative offset between the optical and infrared datasets.}
\label{fig:POSEIDON_corner_plot}
\end{figure*}
\begin{deluxetable*}{lcccccc}[ht!]
\tabletypesize{\small}
\tablecaption{Atmospheric Retrieval Analysis Summary (POSEIDON) \label{tab:POSEIDON_retrieval_results}}
\tablehead{
\textbf{Dataset} & \phm{-} & Ground & Ground & WFC3 + & \multicolumn{2}{c}{\bfseries Ground Corrected +} \\
& \phm{-} & Corrected & Uncorrected & Spitzer & \multicolumn{2}{c}{\bfseries WFC3 + Spitzer} \\
\cmidrule{1-1} \cmidrule{3-7}
Retrieval & & Full & Full & Full & \textbf{Full} & Minimal
}
\startdata \\[-8pt]
\textbf{Planetary Atmosphere} \\
\hspace{0.5em} $T$ (K) & & $ \hspace{0.7em} 861^{+469}_{-303}$ & $ \hspace{0.7em} 968^{+519}_{-348}$ & $ \hspace{0.7em} 924^{+462}_{-321}$ & $ \hspace{0.7em} 782^{+283}_{-231}$ & $ \hspace{0.7em} 850^{+392}_{-245}$ \\
\hspace{0.5em} $R_{\rm{p, \, ref}}$ ($R_J$) & & $ \hspace{0.7em} 1.60^{+0.02}_{-0.03}$ & $ \hspace{0.7em} 1.48^{+0.02}_{-0.03}$ & $ \hspace{0.7em} 1.62^{+0.02}_{-0.02}$ & $ \hspace{0.7em} 1.62^{+0.01}_{-0.01}$ & $ \hspace{0.7em} 1.63^{+0.01}_{-0.01}$ \\
\hspace{0.5em} log($X_{\rm{Na}}$) & & $ \hspace{-3.2em} < -1.86$ & $ \hspace{-3.2em} < -2.07$ & $ \hspace{-3.2em} < -1.82$ & $ \hspace{-3.2em} < -2.36$ & --- \\
\hspace{0.5em} log($X_{\rm{K}}$) & & $ \hspace{-3.2em} < -2.44$ & $ \hspace{-3.2em} < -2.60$ & $ \hspace{-3.2em} < -1.90$ & $ \hspace{-3.2em} < -4.30$ & --- \\
\hspace{0.5em} log($X_{\rm{H^{-}}}$) & & $ \hspace{-3.2em} < -2.54$ & $ \hspace{-3.2em} < -4.40$ & $ \hspace{-3.2em} < -4.40$ & $ \hspace{-3.2em} < -8.30$ & --- \\
\hspace{0.5em} log($X_{\rm{TiO}}$) & & $ -6.36^{+2.24}_{-3.81}$ & $ -4.70^{+1.65}_{-1.88}$ & $ \hspace{-3.2em} < -2.26$ & $ -7.31^{+2.14}_{-2.06}$ & $ -9.56^{+1.53}_{-1.32}$ \\
\hspace{0.5em} log($X_{\rm{VO}}$) & & $ \hspace{-3.2em} < -1.84$ & $ \hspace{-3.2em} < -2.44$ & $ \hspace{-3.2em} < -2.09$ & $ \hspace{-3.2em} < -5.40$ & --- \\
\hspace{0.5em} log($X_{\rm{AlO}}$) & & $ \hspace{-3.2em} < -2.07$ & $ \hspace{-3.2em} < -2.70$ & $ \hspace{-3.2em} < -1.99$ & $ \hspace{-3.2em} < -3.50$ & --- \\
\hspace{0.5em} log($X_{\rm{CrH}}$) & & $ \hspace{-3.2em} < -2.12$ & $ \hspace{-3.2em} < -2.39$ & $ \hspace{-3.2em} < -2.29$ & $ \hspace{-3.2em} < -3.16$ & --- \\
\hspace{0.5em} log($X_{\rm{FeH}}$) & & $ \hspace{-3.2em} < -1.84$ & $ \hspace{-3.2em} < -2.25$ & $ \hspace{-3.2em} < -2.90$ & $ \hspace{-3.2em} < -4.30$ & --- \\
\hspace{0.5em} log($X_{\rm{H_2 O}}$) & & $ \hspace{-3.2em} < -1.72$ & $ \hspace{-3.2em} < -1.85$ & $ -4.15^{+2.28}_{-6.99}$ & $ -3.28^{+1.46}_{-4.08}$ & $ -4.68^{+1.68}_{-3.98}$ \\
\hspace{0.5em} log($X_{\rm{CO}}$) & & $ \hspace{-3.2em} < -1.84$ & $ \hspace{-3.2em} < -1.98$ & $ \hspace{-3.2em} < -1.70$ & $ \hspace{-3.2em} < -1.69$ & --- \\
\hspace{0.5em} log($X_{\rm{CO_2}}$) & & $ \hspace{-3.2em} < -1.96$ & $ \hspace{-3.2em} < -2.22$ & $ \hspace{-3.2em} < -1.85$ & $ \hspace{-3.2em} < -1.91$ & --- \\
\hspace{0.5em} log($X_{\rm{HCN}}$) & & $ \hspace{-3.2em} < -1.86$ & $ \hspace{-3.2em} < -1.90$ & $ \hspace{-3.2em} < -1.66$ & $ -4.07^{+2.08}_{-6.32}$ & $ -5.45^{+2.93}_{-7.00}$ \\[3pt]
\midrule
\textbf{Stellar Properties} \\
\hspace{0.5em} $f_{\rm{het}}$ & & $ \hspace{0.4em} 0.18^{+0.12}_{-0.08}$ & $ \hspace{0.4em} 0.09^{+0.03}_{-0.03}$ & $ \hspace{0.4em} 0.25^{+0.12}_{-0.10}$ & $ \hspace{0.4em} 0.22^{+0.12}_{-0.09}$ & $ \hspace{0.4em} 0.19^{+0.18}_{-0.11}$ \\[3pt]
\hspace{0.5em} $T_{*, \, \rm{het}}$ (K) & & $ 6501^{+243}_{-191}$ & $ \hspace{-3.0em} < 5972$ & $ 6728^{+282}_{-261}$ & $ 6499^{+218}_{-184}$ & $ 6570^{+399}_{-246}$ \\
\hspace{0.5em} $T_{*, \, \rm{phot}}$ (K) & & $ 6150^{+121}_{-117}$ & $ 6093^{+119}_{-126}$ & $ 6103^{+124}_{-121}$ & $ 6158^{+124}_{-125}$ & $ 6158^{+130}_{-140}$ \\
\midrule
\textbf{Optical - Infrared Offset} \\
\hspace{0.5em} $\delta_{\mathrm{rel}}$ (ppm) & & --- & --- & --- & $ \hspace{0.2em} 210^{+83}_{-85}$ & $ \hspace{0.2em} 273^{+88}_{-88}$ \\[3pt]
\midrule
\textbf{Detection Significances} \\
\hspace{0.5em} TiO & & $1.7\,\sigma$ & $2.3\,\sigma$ & --- & $2.1\,\sigma$ & $2.2\,\sigma$ \\
\hspace{0.5em} H$_2$O & & --- & --- & $1.7\,\sigma$ & $1.9\,\sigma$ & $2.1\,\sigma$ \\
\hspace{0.5em} HCN & & --- & --- & --- & $1.7\,\sigma$ & $1.6\,\sigma$ \\
\hspace{0.5em} TiO + H$_2$O + HCN & & $1.7\,\sigma$ & $2.3\,\sigma$ & $1.9\,\sigma$ & $2.8\,\sigma$ & $3.0\,\sigma$ \\
\hspace{0.5em} Stellar heterogeneity & & $4.0\,\sigma$ & $1.5\,\sigma$ & $2.4\,\sigma$ & $4.3\,\sigma$ & $4.1\,\sigma$ \\[3pt]
\midrule
\textbf{Model Statistics} \\
\hspace{0.5em} ln(Evidence) & & $276.6$ & $277.6$ & $84.7$ & $363.9$ & $365.7$ \\
\hspace{0.5em} $\chi^2_{\nu, \, \rm{min}}$ & & $2.62$ & $2.53$ & N/A & $1.96$ & $1.36$ \\
\hspace{0.5em} $N_{\rm param}$ & & $21$ & $21$ & $21$ & $22$ & $9$ \\
\hspace{0.5em} d.o.f. & & $19$ & $19$ & N/A & $30$ & $43$ \\[3pt]
\enddata
\tablecomments{Parameters without clear lower and upper bounds (e.g. abundances of undetected chemical species) are represented by 2$\sigma$ upper bounds. Cloud and/or haze parameters were completely unconstrained in all our retrievals. The detection significances were established by nested Bayesian model comparisons with respect to the model in each column. The combined significance `TiO + H$_2$O + HCN' represents the probability of \emph{at least one} of these molecules influencing WASP-103b's transmission spectrum. The reduced chi-square and degrees of freedom (d.o.f) are undefined for the WFC3 + Spitzer retrieval ($N_{\rm param} > N_{\rm data}$); we include this retrieval for comparison with the optical-only and optical + infrared retrievals. While the `minimal' model provides the best-fit (via the evidence or reduced chi-square), the `full' models include marginalization over a wider range of parameters---accounting for overlapping absorption features and other degeneracies---so our recommended atmospheric and stellar parameters are the `full' optical + infrared parameters (highlighted in bold / 5$^{\rm th}$ column).}
\end{deluxetable*}
\section{Discussion}
\label{sec:discussion}
\subsection{The optical transmission spectrum of WASP-103b}
\label{sec:d_optical_trans_spec}
As shown in \autoref{sec:pRT}, our petitRADTRANS retrievals that do not include stellar activity favor VO, albeit with an implausibly high volume mixing ratio (\autoref{fig:pRT_models}). However, retrievals that do include the impacts of stellar activity significantly favor stellar-activity contamination with tentative evidence for TiO (\autoref{sec:POSEIDON}). This may be due to the different opacity at bluer wavelengths; the \cite{Plez1999} VO line list used by petitRADTRANS leads to a steeper drop off than the ExoMol line list used by POSEIDON (\autoref{fig:pRT_models}). As a result, the POSEIDON retrievals with the ExoMol line list necessitate unocculted faculae to fit the downwards trend we observe at blue wavelengths (\autoref{fig:POSEIDON_best_fit_model}).
In order to place WASP-103b into context, we compare our transmission spectrum with that of another ultrahot Jupiter, WASP-121b \citep{Delrez2016}. WASP-121b's equilibrium temperature of $2358 \pm 52$\,K is 130\,K cooler than WASP-103b's, and it orbits an F6 dwarf, compared to WASP-103, which is an F8 dwarf.
WASP-121b's low-resolution HST/STIS transmission spectrum \citep{Evans2018} is shown in \autoref{fig:w121_comparison}. There is an excellent agreement between the transmission spectra of WASP-121b and WASP-103b, particularly between ${\sim}4000$ and $6500$\,\AA. \autoref{fig:w121_comparison} additionally demonstrates our ability to achieve HST-quality transmission spectra from the ground.
Figure \ref{fig:w121_comparison} also includes the near-UV photometric data point from \cite{Turner2017}. We did not analyze that data set in the current work nor include it in our retrieval analysis due to the different system parameters that \cite{Turner2017} used. However, at face value this point also seems to follow the subsequent rise in the transmission spectrum towards the UV, as seen in WASP-121b.
\subsubsection{On the potential for VO \& TiO}
\label{sec:d_VO}
In the case of WASP-121b, its low-resolution transmission spectral features are taken as strong evidence for VO \citep{Evans2016,Evans2018}. In secondary eclipse, WASP-121b shows water in emission, which is direct evidence for a temperature inversion in the planet's atmosphere \citep{Evans2017,Evans2019,Evans2020,Daylan2019,Bourrier2020}. It has been suggested that VO is responsible for this temperature inversion \citep{Evans2017,Evans2018,Evans2020,Daylan2019,Bourrier2020} although the presence of this molecule is debated at high-resolution \citep{Ben-Yami2020,Cabot2020,Hoeijmakers2020,Merritt2020,Borsa2021}, leading to suggestions that neutral Fe may instead explain WASP-121b's temperature inversion \citep{Gibson2020}.
Given the similarity between the low-resolution transmission spectra of WASP-103b and WASP-121b, VO seems a plausible explanation. If present, VO could also be responsible for WASP-103b's temperature inversion \citep{Kreidberg2018}.
The comparison to WASP-121b is strengthened when taking our transmission spectrum with the near-UV data point of \cite{Turner2017}, as this resembles the same rise in the transmission spectrum towards the UV as seen in WASP-121b (\autoref{fig:w121_comparison}). If this rise does indeed hold, then this would be evidence of a planetary atmospheric contribution and not unocculted faculae, which would continue trending downwards towards the UV. However, we caution that due to the small variations in $R_P/R_*$ seen in our own analysis (\autoref{fig:RpRs_variation}), any rise in WASP-103b's transmission spectrum towards the UV should be confirmed with future HST observations that cover a broad wavelength range.
In \autoref{sec:pRT} we suggested that the different line lists used by petitRADTRANS and POSEIDON could be responsible for the different interpretations of WASP-103b's transmission spectrum. However, in \cite{Evans2018}, the authors used the ATMO retrieval code which uses the ExoMol line list for VO \citep{Goyal2018}, like POSEIDON. Despite this, \cite{Evans2018} still find strong evidence for VO. This may be because of their greater spectral resolution (median wavelength bin size of 97\,\AA), their coverage of the UV, and the fact that ATMO does not fit for stellar activity. Taken together, it is unclear to what extent the choice of line list impacts our conclusions.
While the comparison between WASP-121b and WASP-103b is evidence for their similar atmospheric chemistry (in the absence of stellar contamination), we caution that the very high VO abundances derived from our petitRADTRANS retrievals are implausible (\autoref{sec:pRT}).
However, the retrievals run with POSEIDON (\autoref{sec:POSEIDON}) favor TiO, although with only marginal significance. Given the updated line lists that POSEIDON uses and the plausible $\sim$ solar TiO abundances it finds for both the optical and IR data, it is perhaps more likely that TiO is present in WASP-103b's atmosphere. If confirmed by follow-up studies, this would make WASP-103b more similar to WASP-33b and WASP-76b for which TiO and temperature inversions have been observed \citep{Haynes2015,Nugroho2017,Fu2020}.
Further high-resolution observations are needed of WASP-103b to search for TiO and VO via cross-correlation techniques. In any case, the tentative evidence for these species in our transmission spectrum is suggestive that they could be responsible for WASP-103b's temperature inversion as postulated by \cite{Kreidberg2018}.
\subsubsection{On stellar-activity contamination}
If instead stellar contamination is the cause of some structures in WASP-103b's transmission spectrum, then we can also compare with WASP-121b. WASP-103 is an F8 dwarf \citep{Gillon2014} while WASP-121 is an active F6 dwarf \citep{Delrez2016}.
In the case of WASP-121, it shows no photometric modulation above the 1~mmag threshold of the WASP photometry, no emission in the Ca\,{\footnotesize II} H and K line cores, and no spot-crossing events during transit \citep{Delrez2016}. However, it does show significant RV jitter. \cite{Delrez2016} conclude that this scenario for WASP-121 can be explained if the star is dominated by plage (the chromospheric counterpart to photospheric active regions), with a covering fraction of 8\,\%. This is significantly larger than the typical facular coverage of F6 dwarfs estimated from the variability of Kepler stars \citep{Rackham2019}. However, under this assumption, WASP-121b's transmission spectrum would likely also be contaminated. Ultimately though, the rise in WASP-121b's transmission spectrum at wavelengths shorter than 4000\,\AA\ cannot be caused by unocculted faculae, which would lead to a continued decrease in transit depth towards bluer wavelengths \citep[e.g.,][]{Rackham2017,Rackham2019}.
In the case of WASP-103, it shows a photometric modulation of $5 \pm 1$\,mmag in C14 automated imaging telescope data from Fairborn Observatory \citep{Kreidberg2018}. \cite{Gillon2014} do not report any activity in WASP-103's RV data but \cite{Staab2017} measure WASP-103's $\log R^{'}_{\mathrm{HK}}$ as $-4.57$, consistent with other active exoplanet host stars, such as WASP-19 \citep{Sing2016} and WASP-52 \citep{Hebrard2013}. Our retrievals that include activity suggest unocculted faculae $\sim350$\,K hotter than the surrounding photosphere with large covering fractions of $18^{+12}_{-8}$\,\% for the optical data and $22^{+12}_{-9}$\,\% for the combined optical and IR data (\autoref{tab:POSEIDON_retrieval_results}). Our retrieved faculae temperatures are consistent with solar faculae \citep{Topka1997}, while the relatively large uncertainties in the covering fractions would only make WASP-103 a $1.5\sigma$ outlier as compared to the Kepler sample \citep{Rackham2019}. However, as \cite{Delrez2016} and \cite{Rackham2019} discuss, estimates based from photometric modulation do not necessarily reveal the underlying activity coverage, particularly in the case of bright regions. Therefore we do not rule out the large covering fractions of faculae our retrievals with POSEIDON derive, particularly given WASP-103's high $\log R^{'}_{\mathrm{HK}}$ \citep{Staab2017}. UV spectra are needed to determine whether WASP-103b is indeed contaminated by unocculted faculae or instead follows the same trend as WASP-121b.
\begin{figure}
\centering
\includegraphics[scale=0.6]{w103_w121_comparison_with_T17.pdf}
\caption{Our transmission spectrum of WASP-103b (grey hexagons) compared to the HST/STIS transmission spectrum of WASP-121b from \protect\cite{Evans2018} (red circles). The transmission spectra have both been scaled to their respective scale heights: 152\,ppm for WASP-103b and 239\,ppm for WASP-121b (derived from \protect\citealt{Delrez2016}). We also include the near-UV photometric data point from \protect\cite{Turner2017} (green hexagon).}
\label{fig:w121_comparison}
\end{figure}
\subsection{Comparison with previous optical transmission spectra}
Figure \ref{fig:literature_comparison} shows the comparison between our newly derived transmission spectrum and the previously published results of \protect\cite{Southworth2016}, \protect\cite{Turner2017}, \protect\cite{Lendl2017}, and \protect\cite{Wilson2020}. In all cases the transmission spectra have been corrected for the third-light contamination. We note that in this figure we applied an offset in $R_P/R_*$ of 0.00065 and 0.0021 to the transmission spectra of \cite{Lendl2017} and \cite{Wilson2020}, respectively, so that their median $R_P/R_*$ is equal to the median of our newly derived transmission spectrum. We believe the larger offset for the \cite{Wilson2020} data is because those authors used a Gaussian prior on $R_P/R_*$ and took the mean and standard deviation from \cite{Southworth2015}, who did not account for the third light contamination (\autoref{sec:3rd_light_corr}). We have not applied an offset to the transmission spectrum of \cite{Southworth2016}, where a steep slope is found, nor to the single wavelength bin of \cite{Turner2017}.
This figure demonstrates the improved precision that we achieved by combining our 11 transits. It also shows the slight disagreement between our new transmission spectrum and some of the Gemini/GMOS and VLT/FORS2 bins of \cite{Lendl2017} and \cite{Wilson2020}, which highlights the benefits of combining many transits to form our transmission spectrum.
Additionally, we do not see the blueward rise as observed by \cite{Southworth2016}. However, other than \cite{Southworth2016}'s bluest photometric data point, our results are roughly consistent to $1\sigma$. Additionally, \cite{Turner2017}'s near-UV photometric band indicates a rise towards wavelengths bluer than our spectroscopic coverage. However, we caution against reading too much into this due to the different system parameters used and the offsets in $R_P/R_*$ needed to bring the spectroscopic data in agreement.
\begin{figure}
\centering
\includegraphics[scale=0.45]{trans_spec_comparison_all_combined_3rd_light_corr_NS_corr_literature_comparison.pdf}
\caption{A comparison between our new transmission spectrum (purple diamonds) and the previously published transmission spectra of \protect\cite{Southworth2016} (orange triangles), \protect\cite{Turner2017} (red pentagon), \protect\cite{Lendl2017} (blue circles), and \protect\cite{Wilson2020} (green squares).}
\label{fig:literature_comparison}
\end{figure}
\section{Conclusions}
\label{sec:conclusions}
We have presented a new ground-based optical transmission spectrum of the ultrahot Jupiter WASP-103b. We have combined 5 new transits from the ACCESS survey and 2 new transits from the LRG-BEASTS survey with a reanalysis of 3 published Gemini/GMOS transits and 1 VLT/FORS2 transit. Our 11-transit combined transmission spectrum has a median uncertainty in the transit depth of 148\,ppm ($<1 H$), which is of HST quality and is one of the most precise ground-based transmission spectra to date.
Our optical transmission spectrum shows evidence for sodium in a 20\,\AA-wide bin at $2.8\sigma$ and significant structure with a downwards slope towards blue wavelengths. Our transmission spectrum is in excellent agreement with WASP-121b, another ultrahot Jupiter of comparable temperature for which the presence of VO has been inferred. In our analysis of WASP-103b's optical transmission spectrum using the petitRADTRANS retrieval software, we find that VO can provide a good fit to the planet's spectral features but only if we ignore stellar activity and use implausibly high VO abundances.
In our separate optical-only retrievals with POSEIDON, which include unocculted stellar heterogeneity contamination and updated VO and TiO line lists, we find strong evidence for unocculted faculae ($4.0\sigma$), an absence of VO, and tentative evidence for TiO ($1.7\sigma$) at roughly solar abundances. Given WASP-103's high $\log R^{'}_{\mathrm{HK}}$, this is our favored conclusion.
When we combine our optical transmission spectrum with the previously published HST/WFC3/IR/G141 and Spitzer/IRAC transmission spectrum, we find a slightly higher evidence for unocculted faculae ($4.3\sigma$) and TiO ($2.1\sigma$), and weak evidence for H$_2$O ($1.9\sigma$) and HCN ($1.7\sigma$). If TiO is confirmed by future high-resolution observations in the optical and HST observations in the UV, this would make WASP-103b the fourth planet for which evidence of TiO and a temperature inversion have been observed in the same exoplanet.
Our result highlights the precision that ground-based transmission spectroscopy can reach, in addition to the need for a careful treatment of stellar activity contamination for exoplanets orbiting F-type stars.
\acknowledgments
The William Herschel Telescope is operated on the island of La Palma by the Isaac Newton Group in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrof\'{i}sica de Canarias. This paper includes data gathered with the 6.5 meter Magellan Telescopes located at Las Campanas Observatory, Chile. We thank the observing personnel for providing the facilities and guidance necessary for making the collection of the ACCESS datasets possible. B.V.R.\ thanks the Heising-Simons Foundation for support. A.J.\ acknowledges support from FONDECYT project 1210718, and ANID - Millennium Science Initiative - ICN12$\_$009. The results reported herein benefited from collaborations and/or information exchange within NASA's Nexus for Exoplanet System Science (NExSS) research coordination network sponsored by NASA's Science Mission Directorate, and funding through the NExSS Earths in Other Solar System (PI: Apai) and ACCESS (PI: L\'opez-Morales) teams. ICW and MLM thank the Brinson Foundation for their support. This paper includes data gathered with the 6.5 meter Magellan Telescopes located at Las Campanas Observatory (LCO), Chile. PJW acknowledges support from STFC under consolidated grants ST/P000495/1 and ST/T000406/1.
\vspace{5mm}
\facilities{Magellan/IMACS, WHT/ACAM, Gemini/GMOS, VLT/FORS2}
\software{Astropy \citep{astropy:2013,astropy:2018}, Batman \citep{batman}, emcee \citep{emcee}, George \citep{george,george2}, LDTk \citep{ldtk}, Matplotlib \citep{matplotlib}, MultiNest \citep{Feroz2008,Feroz2009,Feroz2019}, Numpy \citep{numpy}, petitRADTRANS \citep{Molliere2019}, PLATON \citep{Zhang2019,Zhang2020}, POSEIDON \citep{MacDonald2017}, PyMultiNest \citep{Buchner2014}, Scipy \citep{scipy}}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 8,035 |
Pence vows US will hold Khashoggi murderers to account
AFP, Saturday 17 Nov 2018
US Vice-president Mike Pence (REUTERS)
US sanctions 17 for role in killing of Saudi journalist Khashoggi
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Vice-president Mike Pence vowed Saturday the US would hold the murderers of Jamal Khashoggi to account, following media reports that the CIA had concluded the Saudi Crown Prince was behind the journalist's killing.
"The United States is determined to hold all of those accountable who are responsible for that murder," Pence said on the sidelines of an APEC summit in Papua New Guinea.
Pence described the Saudi journalist's killing as an "atrocity" and an "affront to a free and independent press" but declined to comment on classified information.
The vice-president's comments come after reports that the CIA believed the powerful Mohammed bin Salman was involved in the plot to murder the journalist.
If confirmed, the US assessment would directly contradict the conclusions of a Saudi prosecutor a day earlier, which exonerated the prince of involvement in the brutal murder.
And it would threaten to further fray relations between Washington and key ally Riyadh, which has sought to end discussion of the murder and rejected calls for an international investigation.
"We are going to follow the facts," said Pence.
But he also added the US wanted to find a way of preserving a "strong and historic partnership" with Saudi Arabia. | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 7,786 |
South Shore kan verwijzen naar de volgende plaatsen in de Verenigde Staten:
South Shore (Kentucky)
South Shore (South Dakota) | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 3,459 |
{"url":"https:\/\/socratic.org\/questions\/how-do-you-solve-2x-2-3x-7-0-using-the-quadratic-formula","text":"# How do you solve 2x^2 -3x - 7 = 0 using the quadratic formula?\n\nMar 25, 2016\n\n$x = - \\frac{1}{2} + \\sqrt{5}$ or $x = - \\frac{1}{2} - \\sqrt{5}$\n\n#### Explanation:\n\n$2 {x}^{2} - 3 x - 7 = 0$\n\nIdentify the a, b, and c terms\n\n$a {x}^{2} - b x - c = 0$\n$a = 2$\n$b = - 3$\n$c = - 7$\n\n$x = \\frac{- b \\left(\\frac{+}{-}\\right) \\sqrt{{b}^{2} - 4 a c}}{2 a}$\n\n$x = \\left(- 2 \\left(\\frac{+}{-}\\right) \\frac{\\sqrt{{2}^{2} - 4 \\left(- 3\\right) \\left(- 7\\right)}}{2 \\left(2\\right)}\\right)$\n\n$x = \\frac{- 2 \\left(\\frac{+}{-}\\right) \\sqrt{4 - 84}}{4}$\n\n$x = \\frac{- 2 \\left(\\frac{+}{-}\\right) \\sqrt{- 80}}{4}$ simplify the radical $i = \\sqrt{- 1}$\n\n$x = \\frac{- 2 \\left(\\frac{+}{-}\\right) 4 i \\sqrt{5}}{4}$ simplify the fractions\n\n$x = - \\frac{1}{2} + \\sqrt{5}$ or $x = - \\frac{1}{2} - \\sqrt{5}$","date":"2019-01-16 16:56:35","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 15, \"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\": 0.4873681664466858, \"perplexity\": 2032.7679848082646}, \"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-2019-04\/segments\/1547583657555.87\/warc\/CC-MAIN-20190116154927-20190116180927-00581.warc.gz\"}"} | null | null |
Designed to accommodate most lengths of short rod stabilizer, the Avalon Honeycomb Cover for Short Rods has an overall length of 50cm (approx 19.7in) and features a separating seam so two short rods can be carried in the same cover without risk of damage. The interior is lined with soft material giving additional protection. The exterior is finished in a black colour with a honeycomb pattern and an Avalon Archery logo on one size. The flap is fastened with velcro. | {
"redpajama_set_name": "RedPajamaC4"
} | 2,870 |
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Satan's Home Town: Washington, DC
Posted on March 14, 2013 by Arlen Grossman
By Paul Craig Roberts/ paulcraigroberts.org/ March 12, 2013
On March 5, 2013, Hugo Chavez, President of Venezuela and world leader against imperialism, died. Washington imperialists and their media and think tank whores expressed gleeful sighs of relief as did the brainwashed US population. An "enemy of America" was gone.
Chavez was not an enemy of America. He was an enemy of Washington's hegemony over other countries, an enemy of Washington's alliance with elite ruling cliques who steal from the people they grind down and deny sustenance. He was an enemy of Washington's injustice, of Washington's foreign policy based on lies and military aggression, bombs and invasions.
Washington is not America. Washington is Satan's home town.
Chavez was a friend of truth and justice, and this made him unpopular throughout the Western World where every political leader regards truth and justice as dire threats.
Chavez was a world leader. Unlike US politicians, Chavez was respected throughout the non-western world. He was awarded honorary doctorates from China, Russia, Brazil, and other countries, but not from Harvard, Yale, Cambridge, and Oxford.
Chavez was a miracle. He was a miracle, because he did not sell out to the United States and the Venezuelan elites. Had he sold out, Chavez would have become very rich from oil revenues, like the Saudi Royal Family, and he would have been honored by the United States in the way that Washington honors all its puppets: with visits to the White House. He could have become a dictator for life as long as he served Washington.
Each of Washington's puppets, from Asia to Europe and the Middle East, anxiously awaits the invitation that demonstrates Washington's appreciation of his or her servitude to the global imperialist power that still occupies Japan and Germany 68 years after World War II and South Korea 60 years after the end of the Korean War and has placed troops and military bases in a large number of other "sovereign" countries.
It would have been politically easy for Chavez to sell out. All he had to do was to continue populist rhetoric, promote his allies in the army, throw more benefits to the underclass than its members had ever previously experienced, and divide the rest of the oil revenues with the corrupt Venezuelan elites.
But Chavez was a real person, like Rafael Correa, the three-term elected president of Ecuador, who stood up to the United States and granted political asylum to the persecuted Julian Assange, and Evo Morales, the first indigenous president of Bolivia since the Spanish conquest. The majority of Venezuelans understood that Chavez was a real person. They elected him to four terms as president and would have continued electing him as long as he lived. What Washington hates most is a real person who cannot be bought.
The more the corrupt western politicians and media whores demonized Chavez, the more Venezuelans loved him. They understood completely that anyone damned by Washington was God's gift to the world.
It is costly to stand up to Washington. All who are bold enough to do so are demonized. They risk assassination and being overthrown in a CIA-organized coup, as Chavez was in 2002. When CIA-instructed Venezuelan elites sprung their coup and kidnapped Chavez, the coup was overthrown by the Venezuelan people who took to the streets and by elements of the military before Chavez could be murdered by the CIA-controlled Venezuelan elites, who escaped with their own venal lives only because, unlike them, Chavez was humanitarian. The Venezuelan people rose in instantaneous and massive public defense of Chavez and put the lie to the Bush White House claim that Chavez was a dictator.
Showing its sordid corruption, the New York Times took the side of the undemocratic coup by a handful of elitists against the democratically elected Chavez, and declared that Chavez's removal by a small group of rich elites and CIA operatives meant that "Venezuelan democracy is no longer threatened by a would-be dictator."
The lies and demonization continue with Chavez's death. He will never be forgiven for standing up for justice. Neither will Correa and Morales, both of whom are no doubt on assassination lists.
CounterPunch, Fairness & Accuracy in Reporting, and other commentators have collected examples of the venom-spewing obituaries that the western presstitutes have written for Chavez, essentially celebrations that death has silenced the bravest voice on earth. http://www.counterpunch.org/2013/03/08/obituaries-for-hugo-chavez/ [1]
http://fair.org/take-action/media-advisories/in-death-as-in-life-chavez-target-of-media-scorn/ [2]
Perhaps the most absurd of all was Associated Press business reporter Pamela Sampson's judgment that Chavez wasted Venezuela's oil wealth on "social programs including state-run food markets, cash benefits for poor families, free health clinics and education programs," a poor use of money that could have been used to build sky scrappers such as "the world's tallest building in Dubai and branches of the Louvre and Guggenheim museums in Abu Dhabi."
http://www.fair.org/blog/2013/03/06/ap-chavez-wasted-his-money-on-healthcare-when-he-could-have-built-gigantic-skyscrapers/ [3]
Among the tens of millions of Washington's victims in the world–the people of Afghanistan, Iraq, Libya, Sudan, Pakistan, Yemen, Somalia, Syria, Palestine, Lebanon, Mali, with Iran, Russia, China, and South America waiting in the wings for sanctions, destabilization, conquest or reconquest, Chavez's September 20, 2006 speech at the UN General Assembly during the George W. Bush regime will stand forever as the greatest speech of the early 21st century.
Chavez beards the lion, or rather Satan, in his own den:
"Yesterday, the devil himself stood right here, at this podium, speaking as if he owned the world. You can still smell the sulfur." (see The Big Picture Report, March 8)
"We should call a psychiatrist to analyze yesterday's statement made by the president of the United States. As the spokesman of imperialism, he came to share his nostrums, to try to preserve the current pattern of domination, exploitation and pillage of the peoples of the world. An Alfred Hitchcock movie could use it as a scenario. I would even propose a title: 'the Devil's Recipe.'"
The UN General Assembly had never heard such words, not even in the days when the militarily powerful Soviet Union was present. Faces broke out in smiles of approval, but no one dared to clap. Too much US money for the home country was at stake. [A reader pointed out that although Chavez's speech was not interrupted with clapping, he received a healthy round of applause at the end.]
The US and UK delegations fled the scene, like vampires confronted with garlic and the Cross or werewolves confronted with silver bullets.
(Continued/ Read Entire Article Here)
Boldface Added by BPR Editor
This entry was posted in foreign policy, media, politics and tagged Evo Morales, Hugo Chavez, Hugo Chavez U.N. speech, Paul Craig Roberts, Rafael Correa, Venezuela. Bookmark the permalink.
1 Response to Satan's Home Town: Washington, DC
Jeff Nguyen says:
Great analysis and separation of fact from fiction. I wish more Americans knew the truth about Chavez.
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Whiteout Press | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 7,306 |
Aghagallon är en ort i Storbritannien. Den ligger i distriktet Craigavon District och riksdelen Nordirland, i den västra delen av landet, km nordväst om huvudstaden London. Aghagallon ligger meter över havet och antalet invånare är .
Terrängen runt Aghagallon är platt. Den högsta punkten i närheten är meter över havet, km söder om Aghagallon. Runt Aghagallon är det ganska tätbefolkat, med invånare per kvadratkilometer. Närmaste större samhälle är Lisburn, km öster om Aghagallon. Trakten runt Aghagallon består i huvudsak av gräsmarker.
Kustklimat råder i trakten. Årsmedeltemperaturen i trakten är °C. Den varmaste månaden är augusti, då medeltemperaturen är °C, och den kallaste är december, med °C.
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Kontrollbehov inkommande wikilänkar | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 457 |
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